Handbook of Drought and Water Scarcity: Principles of Drought and Water Scarcity [1 ed.] 9781498731027, 9781315404219, 9781315404202, 9781315404196, 9781315404226

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Handbook of Drought and Water Scarcity: Principles of Drought and Water Scarcity [1 ed.]
 9781498731027, 9781315404219, 9781315404202, 9781315404196, 9781315404226

Table of contents :

Editors


Contributors



1 Definition of Drought


Neil A. Coles and Saeid Eslamian



2 Desertification and Drought


Victor R. Squires



3 Meteorological Drought Indices: Definitions


Nicolas R. Dalezios, Zoltan Dunkel, and Saeid Eslamian



4 Hydrological Drought: Water Surface and Duration Curve Indices


Manish Kumar Goyal, Vivek Gupta, and Saeid Eslamian



5 Agricultural Drought Indices: Combining Crop, Climate, and Soil Factors


Nicolas R. Dalezios, Anne Gobin, Ana M. Tarquis Alfonso, and Saeid Eslamian



6 Agricultural Drought: Organizational Perspectives


Parvaneh TishehZan and Saeid Eslamian



7 Ocean Oscillation and Drought Indices: Principles


Olumide D. Onafeso



8 Ocean Oscillation and Drought Indices: Application


Mohammad Hadi Bazrkar and Saeid Eslamian



9 Cause and Occurrence of Drought


Rumia Basu, Chander Kumar Singh, and Saeid Eslamian



10 Drought Modeling Methods


João Filipe Santos, Inmaculada Pulido-Calvo, and Maria Manuela Portela



11 Drought Modeling Examples


Javad Bazrafshan, Somayeh Hejabi, and Saeid Eslamian



12 Observational Network and Drought Monitoring


Brij Bhushan



13 Real-Time Drought Management


Jonathan Peter Cox, Sara Shaeri Karimi, and Saeid Eslamian



14 Monitoring, Assessment, and Forecasting of Drought Using Remote Sensing and the Geographical Information System


Vaibhav Garg and Saeid Eslamian



15 Regionalization of Drought Prediction


Manish Kumar Goyal and Ashutosh Sharma



16 Drought Severity in a Changing Climate


Sergio M. Vicente-Serrano, Santiago Beguería, and Jesús Julio Camarero



17 Drought Early Warning and Information Systems


Richard R. Heim Jr., Michael J. Brewer, Roger S. Pulwarty, Donald A. Wilhite, Michael J. Hayes, and Mannava V.K. Sivakumar



18 Drought Assessment and Risk Analysis


Nicolas R. Dalezios, Ana M. Tarquis Alfonso, and Saeid Eslamian



19 New Approaches for Effective Drought Risk Assessment


Yildirim Kayam and Muslum Beyazgül



20 Drought and Acceptable Risks for Public Systems


Avanish K. Panikkar



21 Remote Sensing in Drought Quantification and Assessment


Nicolas R. Dalezios, Nicos V. Spyropoulos, and Saeid Eslamian



22 NASA Satellite–Based Global Precipitation Products and Services for Drought


Zhong Liu, Dana Ostrenga, William Teng, Steven J. Kempler, and Bruce Vollmer



23 Application of Data-Driven Models in Drought Forecasting


Shahab Araghinejad, Seyed-Mohammad Hosseini-Moghari, and Saeid Eslamian



24 Application of Intelligent Technology in Rainfall Analysis


Mehdi Vafakhah and Saeid Eslamian



25 Application of the Optimization Models and Decision Support Systems in Drought


Emery A. Coppola Jr., Manuel Sapiano, Michael Schembri, and Ferenc Szidarovszky



26 Copula Functions and Drought


Shahrbanou Madadgar and Hamid Moradkhani



27 Drought Frequency Characterization in Spain by Means of T Analysis


Javier Álvarez-Rodríguez and Luis Miguel Barranco



28 Rainfall Prediction Using Time Series Analysis


Mehdi Vafakhah, Hussein Akbari Majdar, and Saeid Eslamian



29 Meteorological Drought Indices: Rainfall Prediction in Argentina


Marcela H. González, Eugenia M. Garbarini, Alfredo L. Rolla, and Saeid Eslamian



30 Modeling Hydrological Process by ARIMA–GARCH Time Series


Reza Hadizadeh and Saeid Eslamian



31 Gradation of Drought-Prone Area


Never Mujere, Xiaohua Yang, and Saeid Eslamian



32 Social Aspects of Water Scarcity and Drought


Johanna Hohenthal and Paola Minoia



33 Drought Losses to Local Economy


Md Mahmudul Haque, Amir Ahmed, Ataur Rahman, and Saeid Eslamian



34 Analysis of Drought Factors Affecting the Economy


Bapon S.H.M. Fakhruddin and Saeid Eslamian



Index

Citation preview

Handbook of Drought and Water Scarcity Principles of Drought and Water Scarcity

Handbook of Drought and Water Scarcity Principles of Drought and Water Scarcity

Edited by

Saeid Eslamian and Faezeh Eslamian

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2017 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-498-73102-7 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright. com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Names: Eslamian, Saeid, editor. | Eslamian, Faezeh A., editor. Title: Handbook of drought and water scarcity : environmental impacts and analysis of drought and water / edited by Saeid Eslamian and Faezeh A. Eslamian. Description: New York : CRC Press, 2017Identifiers: LCCN 2016030589| ISBN 9781498731089 (v. 1 : hardback) | ISBN 9781315404226 (v. 1 : e-book) Subjects: LCSH: Droughts. | Drought forecasting. | Water-supply. | Environmental impact analysis. Classification: LCC QC929.24 .H36 2017 | DDC 551.57/73--dc23 LC record available at https://lccn.loc.gov/2016030589 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Contents Editors.. ...................................................................................................................... ix Contributors.............................................................................................................. xi

1

Definition of Drought.........................................................................................1

2

Desertification and Drought.. ...........................................................................13

3

Meteorological Drought Indices: Definitions................................................. 27

4

Hydrological Drought: Water Surface and Duration Curve Indices. . ............ 45

5

Agricultural Drought Indices: Combining Crop, Climate, and Soil Factors.............. 73

6

Agricultural Drought: Organizational Perspectives. . ......................................91

7

Ocean Oscillation and Drought Indices: Principles......................................109

8

Ocean Oscillation and Drought Indices: Application .................................. 127

9

Cause and Occurrence of Drought................................................................. 137

1 0

Drought Modeling Methods...........................................................................149

11

Drought Modeling Examples.......................................................................... 167

1 2

Observational Network and Drought Monitoring......................................... 189

13

Real-Time Drought Management.................................................................. 209

Neil A. Coles and Saeid Eslamian Victor R. Squires

Nicolas R. Dalezios, Zoltan Dunkel, and Saeid Eslamian

Manish Kumar Goyal, Vivek Gupta, and Saeid Eslamian

Nicolas R. Dalezios, Anne Gobin, Ana M. Tarquis Alfonso, and Saeid Eslamian Parvaneh TishehZan and Saeid Eslamian Olumide D. Onafeso

Mohammad Hadi Bazrkar and Saeid Eslamian

Rumia Basu, Chander Kumar Singh, and Saeid Eslamian

João Filipe Santos, Inmaculada Pulido-Calvo, and Maria Manuela Portela Javad Bazrafshan, Somayeh Hejabi, and Saeid Eslamian Brij Bhushan

Jonathan Peter Cox, Sara Shaeri Karimi, and Saeid Eslamian

v

vi

1 4

Contents

Monitoring, Assessment, and Forecasting of Drought Using Remote Sensing and the Geographical Information System. . ..................................... 217 Vaibhav Garg and Saeid Eslamian

15

Regionalization of Drought Prediction......................................................... 253

16

Drought Severity in a Changing Climate...................................................... 279

Manish Kumar Goyal and Ashutosh Sharma

Sergio M. Vicente-Serrano, Santiago Beguería, and Jesús Julio Camarero

1 7

Drought Early Warning and Information Systems....................................... 305

1 8

Drought Assessment and Risk Analysis........................................................ 323

1 9

New Approaches for Effective Drought Risk Assessment............................ 345

2 0

Drought and Acceptable Risks for Public Systems........................................ 361

2 1

Remote Sensing in Drought Quantification and Assessment.. ..................... 377

22

NASA Satellite–Based Global Precipitation Products and Services for Drought............................................................................... 397

Richard R. Heim Jr., Michael J. Brewer, Roger S. Pulwarty, Donald A. Wilhite, Michael J. Hayes, and Mannava V.K. Sivakumar Nicolas R. Dalezios, Ana M. Tarquis Alfonso, and Saeid Eslamian Yildirim Kayam and Muslum Beyazgül Avanish K. Panikkar

Nicolas R. Dalezios, Nicos V. Spyropoulos, and Saeid Eslamian

Zhong Liu, Dana Ostrenga, William Teng, Steven J. Kempler, and Bruce Vollmer

2 3

Application of Data-Driven Models in Drought Forecasting....................... 423

2 4

Application of Intelligent Technology in Rainfall Analysis..........................441

2 5

Application of the Optimization Models and Decision Support Systems in Drought.........................................................................................461

Shahab Araghinejad, Seyed-Mohammad Hosseini-Moghari, and Saeid Eslamian Mehdi Vafakhah and Saeid Eslamian

Emery A. Coppola Jr., Manuel Sapiano, Michael Schembri, and Ferenc Szidarovszky

2 6

Copula Functions and Drought......................................................................481

2 7

Drought Frequency Characterization in Spain by Means of T Analysis. . .... 505

28

Rainfall Prediction Using Time Series Analysis............................................ 517

Shahrbanou Madadgar and Hamid Moradkhani

Javier Álvarez-Rodríguez and Luis Miguel Barranco

Mehdi Vafakhah, Hussein Akbari Majdar, and Saeid Eslamian

2 9

Meteorological Drought Indices: Rainfall Prediction in Argentina.............541

3 0

Modeling Hydrological Process by ARIMA–GARCH Time Series............... 571

Marcela H. González, Eugenia M. Garbarini, Alfredo L. Rolla, and Saeid Eslamian Reza Hadizadeh and Saeid Eslamian

Contents

vii

31

Gradation of Drought-Prone Area. . ................................................................ 591

3 2

Social Aspects of Water Scarcity and Drought............................................. 607

3 3

Drought Losses to Local Economy................................................................ 627

3 4

Analysis of Drought Factors Affecting the Economy................................... 643

Never Mujere, Xiaohua Yang, and Saeid Eslamian Johanna Hohenthal and Paola Minoia

Md Mahmudul Haque, Amir Ahmed, Ataur Rahman, and Saeid Eslamian Bapon S.H.M. Fakhruddin and Saeid Eslamian

Index. . ..................................................................................................................... 657

Editors Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, where he has been since 1995. His research focuses mainly on statistical and environmental hydrology in a changing climate. In recent years, he has worked on modeling natural hazards, including floods, severe storms, wind, drought, pollution, water reuses, sustainable development and resiliency, etc. Formerly, he was a visiting professor at Princeton University, New Jersey, and the University of ETH Zurich, Switzerland. On the research side, he started a research partnership in 2014 with McGill University, Canada. He has contributed to more than 500 publications in journals, books, and technical reports. He is the founder and chief editor of both the International Journal of Hydrology Science and Technology (IJHST) and the Journal of Flood Engineering (JFE). Eslamian is now associate editor of three important publications: Journal of Hydrology (Elsevier), Eco-Hydrology and Hydrobiology (Elsevier), and Journal of Water Reuse and Desalination (IWA). Professor Eslamian is the author of approximately 150 book chapters and books. Dr. Eslamian’s professional experience includes membership on editorial boards, and he is a reviewer of approximately 50 Web of Science (ISI) journals, including the ASCE Journal of Hydrologic Engineering, ASCE Journal of Water Resources Planning and Management, ASCE Journal of Irrigation and Drainage Engineering, Advances in Water Resources, Groundwater, Hydrological Processes, Hydrological Sciences Journal, Global Planetary Changes, Water Resources Management, Water Science and Technology, Eco-Hydrology, Journal of American Water Resources Association, American Water Works Association Journal, etc. UNESCO has also nominated him for a special issue of the Eco-Hydrology and Hydrobiology Journal in 2015. Professor Eslamian was selected as an outstanding reviewer for the Journal of Hydrologic Engineering in 2009 and received the EWRI/ASCE Visiting International Fellowship in Rhode Island (2010). He was also awarded outstanding prizes from the Iranian Hydraulics Association in 2005 and Iranian Petroleum and Oil Industry in 2011. Professor Eslamian has been chosen as a distinguished researcher of Isfahan University of Technology (IUT) and Isfahan Province in 2012 and 2014, respectively. In 2016, he was a candidate for national distinguished researcher in Iran. He has also been the referee of many international organizations and universities. Some examples include the U.S. Civilian Research and Development Foundation (USCRDF), the Swiss Network for International Studies, the Majesty Research Trust Fund of Sultan Qaboos University of Oman, the Royal Jordanian Geography Center College, and the Research Department of Swinburne University of Technology of Australia. He is also a member of the following associations: American Society of Civil Engineers (ASCE), International Association of Hydrologic Science (IAHS), World Conservation Union ix

x

Editors

(IUCN), GC Network for Drylands Research and Development (NDRD), International Association for Urban Climate (IAUC), International Society for Agricultural Meteorology (ISAM), Association of Water and Environment Modeling (AWEM), International Hydrological Association (STAHS), and UK Drought National Center (UKDNC). Professor Eslamian finished Hakimsanaei High School in Isfahan in 1979. After the Islamic Revolution, he was admitted to IUT for a BS in water engineering and graduated in 1986. After graduation, he was offered a scholarship for a master’s degree program at Tarbiat Modares University, Tehran. He finished his studies in hydrology and water resources engineering in 1989. In 1991, he was awarded a scholarship for a PhD in civil engineering at the University of New South Wales, Australia. His supervisor was Professor David H. Pilgrim, who encouraged him to work on “Regional Flood Frequency Analysis Using a New Region of Influence Approach.” He earned a PhD in 1995 and returned to his home country and IUT. In 2001, he was promoted to associate professor and in 2014 to full professor. For the past 22 years, he has been nominated for different positions at IUT, including university president consultant, faculty deputy of education, and head of department. Professor Eslamian has made three scientific visits to the United States, Switzerland, and Canada in 2006, 2008, and 2015, respectively. In the first, he was offered the position of visiting professor by Princeton University and worked jointly with Professor Eric F. Wood at the School of Engineering and Applied Sciences for one year. The outcome was a contribution in hydrological and agricultural drought interaction knowledge by developing multivariate L-moments between soil moisture and low flows for northeastern U.S. streams. Recently, Professor Eslamian has completed the editorship of eight handbooks published by Taylor & Francis (CRC Press): the three-volume Handbook of Engineering Hydrology in 2014, Urban Water Reuse Handbook in 2015, Underground Aqueducts Handbook (2017), the three-volume Handbook of Drought and Water Scarcity (2017). Faezeh Eslamian is a PhD candidate of bioresource e­ngineering and research assistant at McGill University, Montreal, Quebec, Canada. She is currently working on the fate and transport of phosphorus through subsurface drained farmlands. Dr. Eslamian completed her bachelor’s and master’s degrees in civil and environmental engineering from Isfahan University of Technology, Iran, where she evaluated natural and low-cost absorbents for the removal of pollutants such as textile dyes and heavy metals. Furthermore, she has conducted research on the worldwide water quality standards, wastewater reuse, and drought guidelines.

Contributors Amir Ahmed EnviroWater Sydney Sydney, New South Wales, Australia Javier Álvarez-Rodríguez Center for Hydrographic Studies Ministry of Public Works Madrid, Spain Shahab Araghinejad Department of Irrigation and Reclamation Engineering University of Tehran Karaj, Iran Luis Miguel Barranco Center for Hydrographic Studies Ministry of Public Works Madrid, Spain Rumia Basu Department of Natural Resources TERI University New Delhi, Delhi, India Javad Bazrafshan Department of Irrigation and Reclamation Engineering University of Tehran Karaj, Iran Mohammad Hadi Bazrkar Department of Water Resources Engineering Bu-Ali Sina University Hamedan, Iran

Santiago Beguería Experimental Station of Aula Dei Higher Council for Scientific Research Zaragoza, Spain Muslum Beyazgül Ministry of Food, Agriculture and Livestock General Directorate of Agricultural Research and Policies Ankara, Turkey Brij Bhushan National Informatics Centre Ministry of Communications and Information Technology Government of India New Delhi, Delhi, India Michael J. Brewer NOAA National Centers for Environmental Information Asheville, North Carolina Jesús Julio Camarero Pyrenean Institute of Ecology Higher Council for Scientific Research Zaragoza, Spain Neil A. Coles School of Geography University of Leeds Leeds, United Kingdom and Institute of Agriculture University of Western Australia Perth, Western Australia, Australia xi

xii

Emery A. Coppola Jr. NOAH LLC Lawrenceville, New Jersey Jonathan Peter Cox Caribbean Institute for Meteorology and Hydrology Bridgetown, Barbados Nicolas R. Dalezios Department of Civil Engineering University of Thessaly Volos, Greece and Department of Natural Resources and Agricultural Engineering Agricultural University of Athens Athens, Greece Zoltan Dunkel Hungarian Meteorological Society Budapest, Hungary

Contributors

Marcela H. González Department of Atmospheric Sciences and Oceania and Research Center of the Sea and the Atmosphere University of Buenos Aires (CIMA) CONICET-UBA Buenos Aires, Argentina Manish Kumar Goyal Department of Civil Engineering Indian Institute of Technology Guwahati, Assam, India Vivek Gupta Department of Civil Engineering Indian Institute of Technology Guwahati, Assam, India Reza Hadizadeh Statistical Center of Iran Karaj, Iran

Saeid Eslamian Department of Water Engineering Isfahan University of Technology Isfahan, Iran

Md Mahmudul Haque Institute for Infrastructure Engineering Western Sydney University Penrith, New South Wales, Australia

Bapon S.H.M. Fakhruddin Department of Civil and Environmental Engineering Politecnico di Milano Milano, Italy

Michael J. Hayes National Drought Mitigation Center University of Nebraska-Lincoln Lincoln, Nebraska

Eugenia M. Garbarini Department of Atmospheric Sciences and Oceania University of Buenos Aires Buenos Aires, Argentina Vaibhav Garg Water Resources Department Indian Space Research Organisation Dehradun, Uttarakhand, India Anne Gobin Earth Observation Unit Vito, Belgium

Richard R. Heim Jr. NOAA National Centers for Environmental Information Asheville, North Carolina Somayeh Hejabi Department of Irrigation and Reclamation Engineering University of Tehran Karaj, Iran Johanna Hohenthal Department of Geosciences and Geography University of Helsinki Helsinki, Finland

xiii

Contributors

Seyed-Mohammad Hosseini-Moghari Department of Irrigation and Reclamation Engineering University of Tehran Karaj, Iran

Paola Minoia Department of Geosciences and Geography University of Helsinki Helsinki, Finland

Sara Shaeri Karimi Dezab Consulting Engineers Company Ahvaz, Iran

Hamid Moradkhani Department of Civil and Environmental Engineering Portland State University Portland, Oregon

Yildirim Kayam Institute for Environment and Sustainability Joint Research Center European Commission Ispra, Italy Steven J. Kempler NASA Goddard Earth Sciences Data and Information Services Center NASA Goddard Space Flight Center Greenbelt, Maryland Zhong Liu NASA Goddard Earth Sciences Data and Information Services Center Goddard Space Flight Center Greenbelt, Maryland and Center for Spatial Information Science and System George Mason University Fairfax, Virginia Shahrbanou Madadgar Department of Civil and Environmental Engineering Portland State University Portland, Oregon

Never Mujere Department of Geography and Environmental Science University of Zimbabwe Harare, Zimbabwe Olumide D. Onafeso Department of Geography Olabisi Onabanjo University Ago-Iwoye, Nigeria Dana Ostrenga NASA Goddard Earth Sciences Data and Information Services Center Goddard Space Flight Center Greenbelt, Maryland and ADNET Systems, Inc. Bethesda, Maryland Avanish K. Panikkar Griffith University Brisbane, Queensland, Australia

and

and

Department of Civil and Environmental Engineering University of California, Irvine Irvine, California

KMH Environmental Pvt. Ltd. Chatswood, New South Wales, Australia

Hussein Akbari Majdar Department of Watershed Management Tarbiat Modares University Tehran, Iran

Maria Manuela Portela Department of Civil Engineering and Architecture Technical University of Lisbon Lisbon, Portugal

xiv

Inmaculada Pulido-Calvo Department of Agroforestry Science High School of Engineering University of Huelva Huelva, Spain Roger S. Pulwarty National Integrated Drought Information System Boulder, Colorado Ataur Rahman Institute for Infrastructure Engineering and School of Computing, Engineering and Mathematics Western Sydney University Penrith, New South Wales, Australia Alfredo L. Rolla Research Center of the Sea and the Atmosphere University of Buenos Aires CONICET-UBA Buenos Aires, Argentina João Filipe Santos Department of Engineering Polytechnic Institute of Beja Beja, Portugal Manuel Sapiano Institute for Water Technology Water Services Corporation Luqa, Malta

Contributors

Chander Kumar Singh Department of Natural Resources TERI University New Delhi, Delhi, India Mannava V.K. Sivakumar World Meteorological Organization Geneva, Switzerland Nicos V. Spyropoulos Department of Natural Resources and Agricultural Engineering Agricultural University of Athens Athens, Greece Victor R. Squires University of Adelaide Adelaide, South Australia, Australia Ferenc Szidarovszky NOAH LLC Lawrenceville, New Jersey Ana M. Tarquis Alfonso Department of Applied Mathematics and CEIGRAM Technical University of Madrid Madrid, Spain William Teng NASA Goddard Earth Sciences Data and Information Services Center Goddard Space Flight Center Greenbelt, Maryland and ADNET Systems, Inc. Bethesda, Maryland

Michael Schembri Institute for Water Technology Water Services Corporation Luqa, Malta

Parvaneh TishehZan Water Science and Engineering Faculty Shahid Chamran University of Ahwaz Ahwaz, Iran

Ashutosh Sharma Department of Civil Engineering Indian Institute of Technology Guwahati Guwahati, Assam, India

Mehdi Vafakhah Department of Watershed Management Tarbiat Modares University Tehran, Iran

xv

Contributors

Sergio M. Vicente-Serrano Department of Geoenvironmental Processes Pyrenean Institute of Ecology Higher Council for Scientific Research Zaragoza, Spain

Donald A. Wilhite School of Natural Resources University of Nebraska-Lincoln Lincoln, Nebraska

Bruce Vollmer NASA Goddard Earth Sciences Data and Information Services Center NASA Goddard Space Flight Center Greenbelt, Maryland

Xiaohua Yang School of Environment Beijing Normal University Haidian, Beijing, People’s Republic of China

1 Definition of Drought Neil A. Coles University of Leeds and University of Western Australia

Saeid Eslamian Isfahan University of Technology

1.1 Introduction .......................................................................................... 1 1.2 Defining Drought ................................................................................. 1 1.3 Drought and Rainfall Classification ..................................................4 1.4 Drought by Design ...............................................................................5 1.5 Summary and Conclusions .................................................................8 Authors ..............................................................................................................8 References ..........................................................................................................9

Abstract  The word drought in its definitive sense is derived from the archaic English and Scottish form of the word “drouth” that is an archaic or dialectal word for thirst. In more recent times, it has been used as a collective term to refer to an acute water shortage rather than thirst specifically. However, the term “drought” can be applied to the lack or scarcity of anything or a prolonged absence of something specified, but historically it has been used to signify a prolonged period of dryness or low rainfall. This chapter only discusses the use of the term drought as it relates to water shortages and how it is applied in various instances from forecasting to design.

1.1  Introduction Drought is a natural hazard and is one of the least understood and manageable phenomena impacting the world today [30]. Vulnerability to drought is increasing as the global climate varies, human population expands, water resources come under increasing pressure for alternate uses, and people use water in so many different ways and apply alternate demands relative to human consumption (including drinking water and sanitation), industrial uses, agricultural production systems, and environmental requirements such that there is no universal definition of drought [2,11,30].

1.2  Defining Drought Droughts are a normal part of climate variability and are generally recognized around the world as a lack of rainfall; however, this is not the only description that can be applied in defining what a drought is and the effect it has either locally or regionally. The following definitions of drought were first introduced in Britain in 1887: • Absolute droughts—Periods of more than 14 consecutive days absolutely without rain • Partial droughts—Periods of more than 28 consecutive days, the aggregate rainfall of which does not exceed 0.01 in. per diem • Engineers’ droughts—Periods of three or more consecutive months, the aggregate rainfall of which does not exceed half the average [21] The term “dry spell” in reference to drought was also first used in British rainfall records in 1919 [1]. 1

2

Handbook of Drought and Water Scarcity

The following dictionary or conceptual definitions have been used to define a “drought”: Continuous dry weather [24] Extreme dryness due to lack of rain [26] A prolonged period of scanty rainfall [25] Therefore, in the most general sense, a drought is defined as a deficiency of precipitation over an extended period of time—(for agricultural production—usually a season or more), resulting in a water shortage for some activity, industry group, community, or environmental sector [15]. This period of time can be prolonged and may be an abnormally dry period when the water availability is insufficient to satisfy expected (or normal) demand and could also be described as an extended period—a season, a year, or several years—of deficient rainfall relative to the statistical multiyear mean for a region [11]. Droughts, as such, are not purely a physical phenomenon that is defined strictly in terms of climate variability. A drought, therefore, is not simply classified as low rainfall; if it was, most of the arid and semiarid regions of the world (e.g., inland Australia, southwestern [SW] United States, Sahel, and Gobi), for instance, would be in almost perpetual drought [2]. In essence, drought can thus be determined by the balance between water supply and demand. The effect of a drought is governed by the interplay between a natural event (less precipitation or water inputs than expected) and the demand placed on the water supply, with human activities normally exacerbating the impact of a drought [15]. Beyond the conceptual definition of drought, the extent and severity of drought can be monitored in several ways and is normally dependent on the impact a drought has on a specific activity or phenomenon. This is often referred to as the operational definition of a drought and is monitored for example in terms of • • • •

Rainfall deficiencies The impact on primary industries, such as agricultural production Groundwater recharge and streamflow Social expectations, economics, and perceptions of water availability

As a result, drought has come to be defined in both conceptual and operational terms such that six general classes of drought have been previously recognized [21,28,30] as follows: • Meteorological drought—Defined only in terms of precipitation deficiencies, in absolute amounts, for a given period • Climatological drought—Defined in terms of precipitation deficiencies, in percentages of normal values • Atmospheric drought—Defined not only in terms of precipitation deficiencies but possibly in terms of temperature, humidity, or wind speed • Agricultural drought—Defined principally in terms of soil moisture and plant behavior* • Hydrological drought—Defined in terms of reduction in streamflow, reduction in lake or reservoir storage, and the lowering of groundwater levels [21] • Water management drought—Defined in terms of water supply shortages caused by the failure of water management practices or facilities, such as an integrated water supply system and surface or subsurface storage, to bridge normal or abnormal dry periods and equalize the water supply throughout the year [14] As can be deduced from the descriptions earlier, a drought can only be described fully by the depiction of its numerous climatic, hydrologic, and operational elements [31]. Following an extensive research and

* Includes green drought—defined as a period of limited rainfall resulting in new but insubstantial plant growth [23].

3

Definition of Drought

review [29], the six classifications suggested earlier were further revised into four basic approaches to measuring drought: • Meteorological drought—A period of abnormally dry weather sufficiently prolonged for the lack of water to cause serious hydrologic imbalance in the affected area [13] • Agricultural drought—A climatic excursion involving a shortage of precipitation sufficient to adversely affect crop production* or range production [20] • Hydrological drought—A period of below average water content in streams, reservoirs, groundwater aquifers, lakes, and soils [32] • Socioeconomic and environmental drought—A period when the declining water supply relative to demand affects human activities and ecosystem function to the point of failure and may be associated with elements of meteorological, hydrological, and agricultural drought [29]. See Figure 1.1. The first three definitions earlier deal with ways to measure drought and the fourth deals with drought in terms of the impact on supply and demand [12] with the fourth term being a variation on a water

Natural climate variability

Meteorological drought Agricultural drought Hydrological drought Increased impact over time

Environmental impact

Economic impact

Social impacts

Water management drought

FIGURE 1.1  Types of drought and impacts. Simplified flow diagram illustrating the progression of drought as a result of natural climate variability, and the relationship between economic, social and environmental impacts. An  additional component associated with water management drought has been linked to impacts and may be considered both as one of the causes and one of the options for mitigation. Development and extent of the impacts of drought are normally independent of the time scale as these may occur at variable times within a drought cycle. (Adapted from flow diagram developed by the Drought basics—What is drought? Webpage, NDCM, Lincoln, NE, http://drought.unl.edu/DroughtBasics/WhatisDrought.aspx, accessed October 12, 2014; http://www.drought.unl. edu/whatis/concept.html.)

* This would also include a green drought in which rainfall received results in germination but insufficient crop growth or causing crop failure in the longer term due to reduced rainfall.

4

Handbook of Drought and Water Scarcity

management drought [14] and the engineers’ drought [22]. In such cases, socioeconomic definitions of drought have evolved to provide a link between the supply and demand of an economic good with elements of meteorological, hydrological, and agricultural drought. This proposition differs from the other types of drought in that it is dependent on the supply chain, while this supply chain is also climate or weather dependent. Therefore, many of the economic goods, such as water, forage, food grains, fish, and hydroelectric power, are affected. Thus, owing to the natural variability of climate, the availability of water will determine the relative supply and demand of goods [19,29,30]. All droughts begin as a natural variation in climate that results in a decline in the delivery of rainfall over a particular time frame relevant to the climatology* of the area (or region) affected. The initial declines or deficiencies are classed as a meteorological drought. As the length of the deficiency period increases, often in association with above-average temperatures, high winds, and low relative humidity, significant impacts are felt in the agricultural and hydrological systems (Figure 1.1). Extended periods of rainfall deficiency lead to agricultural droughts, particularly if the soil moisture deficits are already high prior to the growing season or rainfall expected during the growing season is diminished, such that crop growth and development is suppressed [16]. These extended droughts may also be punctuated by periods when stored water or river flows used for irrigation are restricted or unavailable for allocation, defined as hydrological droughts. Socioeconomic droughts occur when the demand for an economic good exceeds the supply as a result of a weatherrelated shortfall in water supply. The drought may result in significantly reduced hydroelectric power production because power plants are dependent on streamflow rather than storage for power generation and are by default linked to hydrological droughts. The demand for economic goods is increasing as a result of population growth and economic development creating increasing pressure on water resources to deliver goods, energy, food, and water for human consumption, with additional negative impacts extended to the environment and ecosystem function as water availability declines. When both supply and demand increase, the critical factor is their relative rate of change [19]. Droughts therefore are naturally occurring phenomena, with the intensity and severity often ­influenced by local topographic, water demand, and climatological characteristics, and can end almost as quickly as they begin if moisture or water deficits are small [16]. Regional droughts may be driven by global phenomena such as droughts in eastern Australia, which are influenced by the Southern Oscillation Index, which is driven by variations in the surface temperature of the Pacific Ocean [3]. This level of influence provides opportunities for prediction or indicative tools and some limited preparations but to date are not considered as absolute measures of the length and severity of drought that may develop with each climate zone influenced by very different large-scale, predominant weather and climate patterns [2]. Due to this diversity of definition, impact assessment, and management, clarity has been sought by developing various indices in which the duration and intensity of drought could be categorized. Once again this approach has spawned an increasing number of indices to enable the context and diversity of impacts to be assessed or described. These diverse drought types impact different sectors, and in many instances the impacts associated with each overlap both temporally and spatially [12].

1.3  Drought and Rainfall Classification In the preceding section, drought has been described as representing a decline in precipitation over a set time period relative to normal or average expectations or demands. This relationship has been used by various meteorological bureaus and government agencies to classify drought and their severity and extent, on the basis of existing rainfall records, and how much the decline in rainfall represents a deficiency based on the known climatological records. To do this, drought indices were developed as a * This is relevant as a 14-day period of no rain may present as an absolute drought in the United Kingdom, whereas the same dry period in semiarid regions such as Australia would be considered normal.

5

Definition of Drought TABLE 1.1  Rainfall Deficiency Definitions Used by the Australian Bureau of Meteorology Lowest on record Severe deficiency Serious deficiency Very much below average Below average Average Above average Very much above average

Lowest since at least 1900 when the data analyzed begin Rainfalls in the lowest 5% of historical totals Rainfalls in the lowest 10% of historical totals, but not the lowest 5% Rainfalls in the lowest 10% of historical totals Rainfalls in the lowest 30% of historical totals, but not the lowest 10% Rainfalls in the middle 40% of historical totals Rainfalls in the highest 30% of historical totals, but not the highest 10% Rainfalls in the highest 10% of historical totals

Source: Bureau of Meteorology, Australia (BoM), 2015. Drought. http://www.bom.gov.au/climate/ drought/#tabs=About-drought, accessed July 1, 2015.

way of expressing drought information in a manner that also gives the user more information than just how the current situation compares to a historical average and to identify the degree of water shortage associated with the dry event (i.e., duration and intensity) [12]. An indicator is a measure of a variable, be it meteorological, hydrological, agricultural, or socioeconomic in origin, that provides an indication of potential drought-related stress or deficiency, whereas an index is a method of deriving “value-added” information related to drought through the comparison of existing conditions to historical data. Thus, indices attempt to quantify drought and its magnitude or severity [12]. The Bureau of Meteorology (BoM) in Australia employs a deficiency classification index, as a series of definitions shown in Table 1.1. This system employs a relatively simple process of drought determination by comparing actual precipitation to the long-term average or mean (in Australia’s case since 1900 when records began). The severity is classified on the basis of recorded rainfall against expected averages for a particular region over a selected time frame, with categories ranging from the lowest on record to one very much above average. These data are provided by the BoM as both a forecasting and an assessment tool providing farmers, pastoralists, and governments with data on which to make seasonal, operational, and policy decisions. A map providing current drought and severity conditions in Australia for 29 months between October 2012 and June 2015 is given in Figure 1.2. The U.S. National Weather Service (operated by the National Oceanic and Atmospheric Administration) [18] also employs a similar definition system for rating the severity of drought with an example for the SW United States given in Figure 1.3. The U.S. Drought Monitor (USDM) provides a general summary of current drought conditions, with the USDM map color-coded for four levels of drought intensity. An additional category, “abnormally dry,” is used to show areas that might be moving toward a drought, as well as those areas that may have recently experienced drought. The dominant type of drought is also indicated. Both systems employ definitions of drought based on the severity and extent of the drought within a given region. These are just two examples of drought definitions and indices that have been used to relay information concerning drought that can be used for alternate purposes to assist in managing the effects of drought and the impacts on the activities undertaken in these regions. While drought indices are important for contextualizing drought, they will not be described further within this chapter, as they are dealt with elsewhere in this volume.

1.4  Drought by Design While drought is a natural phenomenon, it represents a hazard to be managed due to the impact on human activities, particularly the availability of water for human consumption, food, and energy ­production. While the natural variability in rainfall delivery or the increased variance due to climate change, is difficult to manage, many water supplies for these activities can be designed to “fail gracefully,” that is, within a certain period of time of relative rainfall or water availability such that the

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Rainfall percentile ranking 10

Australian Government Bureau of Meteorology

5

Serious deficiency Severe deficiency Lowest on record

Rainfall deficiencies: 29 months 1 October 2012 to 28 February 2015 Distribution based on gridded data Product of the National Climate Centre

FIGURE 1.2  Map showing rainfall deficiencies based on severity classification system used by the Australian Bureau of Meteorology [3]. (From Bureau of Meteorology, Australian Government, Australia (BoM), 2015, http:// www.bom.gov.au/climate/drought/, accessed July 01, 2015.)

U.S. Drought Monitor West

July 14, 2015 (Released Thursday, July 16, 2015) Valid 8 a.m. EDT Drought Conditions (Percent Area) None D0–D4D1–D4D2–D4D3–D4 D4 Current

25.49 74.51 61.37 43.76 18.87 7.17

Last Week 7/72015

22.40 77.60 61.14 43.04 18.87 7.26

3 Months Ago 4/14/2015 Start of Calendar Year 12/30/2014 Start of Water Year 9/30/2014 One Year Ago 7/15/2014

26.55 73.45 61.00 37.91 17.04 7.63 34.76 65.24 54.48 33.50 18.68 5.40 31.48 68.52 55.57 35.65 19.95 8.90 31.51 68.49 60.35 46.65 23.56

6.02

Intensity: D0 Abnormally Dry D1 Moderate Drought D2 Severe Drought

D3 Extreme Drought D4 Exceptional Drought

The Drought Monitor focuses on broad-scale conditions. Local conditions may vary. See accompanying text summary for forecast statements. Author: David Simeral Western Regional Climate Center

http://droughtmonitor.unl.edu/

FIGURE 1.3  Map showing rainfall deficiencies in south western United States based on a severity classification system used by U.S. Drought Monitor [17]. (From U.S. Drought Monitor Website, 2015, http://www.drought.unl. edu/dm/index.html, accessed July 18, 2015.)

Definition of Drought

7

potential reliability of a supply is known, and the relative risk of failure due to drought is factored into the design, creating what was first termed an “engineer’s drought” in 1887 [22]. This is particularly important for agricultural (livestock) and small community (or domestic) water supplies. For example, in the dryland agricultural areas of Western Australia, seasonal fluctuations in rainfall necessitate the design of reliable on-farm water supplies so that the farming enterprises can continue to function in years with low rainfall or drought. This region has often been severely impacted by water shortages in times of extended dry periods [9], and these have been exacerbated in recent years due to changes in climate, an associated decline in annual rainfall, and/or a variation in rainfall delivery ­patterns [5]. Suitably designed storages such as dams, raintanks, and soaks or adequately defined and equipped bores are required to ensure water supply availability to satisfy demand created from operational activities (e.g., livestock watering, crop spraying) and domestic use during periods of low rainfall. To ensure reliability, two measures are required: What is the expected demand? What is the capacity of the storages? The links between these two measures are (1) capacity to control demand and (2) cost of maintaining reliability of supply [8]. The cost of designing and maintaining a reliable supply is dependent on the acceptable level of risk a landholder is willing to take, based upon the losses incurred if the supplies fail versus the cost of meeting long-term demand under low rainfall conditions [8]. To understand the threat posed by droughts to a water supply, appropriate design criteria are required. Artificial catchments and storage combinations impact both the efficiency and cost of these systems; so these combinations are generally determined to satisfy a targeted demand reliability relative to the known rainfall patterns and expected periods of low rainfall or drought [6]. Managing droughts (and periods of low rainfall) requires defining the reliability of the water supply relative to the climatic conditions and expected demand. Reliability is a term used to express how often you are prepared to accept the failure of a system, in this case a water supply. This term, reliability or rate of failure, is determined by balancing the costs associated with the development to a certain capacity against the negative costs of the system failure. This includes both the rate (i.e., number of times) and the length of time that a system remains inactive owing to drought [7]. Available water supply can be calculated by a water balance simulation based on catchment size, dam volume, rainfall, water demand, and evaporation losses, with the resultant water balance simulation applied to estimate the reliability. The water balance simulation relies on the relationship between the modeling time interval (i.e., daily, weekly, or monthly calculation intervals), the available water supply amount (volume-based estimation), and the time period of water supply failure (period-based estimation) as shown in Figure 1.4 [6,10]. The level of reliability is also determined by the relative cost and impact that supply failure (or drought) will have on the operation or activity for which the water is being used. Obviously if the supply is a community drinking water supply, the cost of investment and reliability will be higher than that for a livestock water supply [9]. Reliability is usually expressed in terms of a percentage or as a failure rate in a given number of years (i.e., 1 in 10 yr or 90%). This system would be expected to fail once in 10 years in the long term; however it is possible for such a system to fail more than 1 year in succession, where two or three one-year in ten (or greater) events occur together [7]. The level of designed reliability required is determined by how often those affected are prepared to pay for the cost of failure. Some landholders may be prepared to accept a water supply failure rate of one in 5 years, while others may design for one in 20 years. The more reliable the system is required to be, the more care must be taken with the size, design, and construction. Consequently, the cost of the system also increases. For systems that have high dependence, like drinking water supplies, the level of success rate and costs will be high. Based on the previous example, the level of failure or rate of deficiency relative to low rainfall or drought has been engineered such that the risk associated with failure has been assessed and appropriate designs have been implemented. This type of drought is defined as engineered or managed in that it can be relatively climate independent and is related to design, demand, and knowledge of regional rainfall

8

Hi

gh

Weekly

Lo

Hi

gh

w

Ca lcu C lat ost ed Ri reli sk ab ili ty

Hi

Lo

Lo

w

Daily

Modeling time interval

Monthly

Handbook of Drought and Water Scarcity

VE

PEw PEm PEd Definition of reliability

w

gh

PEa

FIGURE 1.4  Relationship between time interval and defined reliability, costs and risks associated with designing reliable water supplies to manage extended dry periods (or droughts). VE, volume-based estimation; PE, period-based estimation (days, weeks, months, annual). (Adapted from Coles, N.A. and Baek, C.W., Impact of climate change on the design criteria for rainwater harvesting systems in Western Australia, Proceedings of the 18th Congress of the Asia and Pacific Division of the International Association for Hydro-Environment Engineering and Research, Jeju, Korea, August 2012.)

occurrence and climate variability. This is not to suggest that the water supply will not be impacted by drought but that the effects of moderate meteorological and hydrological droughts can be ameliorated and the operational risk managed.

1.5  Summary and Conclusions Water is the giver of life, and as such its shortage and availability caused by drought affects all life on this planet, which is attuned in some way to its presence or absence. As can be observed from this discussion, drought is often poorly understood and classified; it is not driven by any particular factor but can be influenced by local and regional phenomena, and its impacts vary both spatially and temporally and can impact significantly on human endeavors, agricultural productivity, and environmental functionality. The impacts of drought are often complex and may persist for considerable time beyond its immediate cessation and thus make it difficult to prepare for and manage. Continuing research into the weather phenomena and atmospheric drivers of drought is providing an improved predictive capability, but drought preparedness and risk management remain challenging aspects in coping with droughts. Improvements in collecting data, monitoring, and climate modeling have provided opportunities to deliver better water resources design and river management scenarios to assist with the development of engineering options to manage droughts, but long-term, regionally extensive droughts remain a high risk, and are inherently difficult event to manage. While this chapter has provided an introduction to drought, in terms of its definition and complexity, subsequent chapters in this text explore the impacts, assessment, monitoring, and management of droughts.

Authors Neil Coles is a senior Cheney fellow at the University of Leeds, Leeds, United Kingdom, and research consulting professor at the Institute of Agriculture, University of Western Australia (UWA), Perth, Australia. He has 30 years of research and practical experience in water resources, mining, and agricultural

Definition of Drought

9

industries. Prior to his appointment at UWA, Professor Coles was employed by the WA Department of Agriculture as a senior research scientist, conducting, directing, and extending research on land and water resource management in the dryland agricultural areas in southwestern Australia. He continued in this post until 2009 when he was appointed as the director for the Centre for Ecohydrology, UWA, as an internationally recognized leader in ecohydrology research with industry applications. As a dedicated research analyst and administrator, he has continued to foster the interdisciplinary approach to improving water resources, agricultural production and protecting and understanding ecosystems. He  is committed to achieving better outcomes for the myriad of environments on this unique and singular planet. Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, Iran, where he has been since 1995. He received his PhD from the University of New South Wales, Australia, under the supervision of Professor David Pilgrim. His research focuses mainly on water resources planning and management and statistical and environmental hydrology in a changing climate. Formerly, he was a visiting professor at Princeton University, New Jersey, and the University of ETH Zurich, Switzerland. On the research side, he has started a research partnership from 2014 with McGill University, Canada. He has contributed to more than 500 publications in journals and books or as technical reports. He is the founder and chief editor of both International Journal of Hydrology Science and Technology (Scopus, Inderscience) and Journal of Flood Engineering. Currently, he has been the author of more than 100 book chapters and books. Recently, Professor Eslamian has started the editorship of several handbooks published by Taylor & Francis Group (CRC Press). A three-volume Handbook of Engineering Hydrology (2014), Urban Water Reuse Handbook (2015), a three-volume Handbook of Drought and Water Scarcity (2017), and Underground Aqueducts Handbook (2017) are published ones.

References 1. Air Ministry. 1944. Meteorological Glossary, 3rd edn., British Government, London, U.K., p. 68. 2. Bureau of Meteorology, Australia (BoM). 2014. Drought statement-rainfall deficiencies, Available at: http://www.bom.gov.au/climate/drought/drought.shtml, Accessed November 1, 2014. 3. Bureau of Meteorology, Australia (BoM). 2014. Southern oscillation index, Climate Glossary, Available at: http://www.bom.gov.au/climate/glossary/soi.shtml, Accessed November 2, 2014. 4. Bureau of Meteorology, Australia (BoM). 2015. Available at: http://www.bom.gov.au/climate/ drought/, Accessed July 1, 2015. 5. Bureau of Meteorology, Australia (BoM). 2011. Australian climate change and variability, Available at: http://www.bom.gov.au/climate/change/aus_cvac.shtml, Accessed June 10, 2011. 6. Baek, C. W. and Coles, N. A. 2011. Defining reliability for rainwater harvesting systems, International Congress on Modelling and Simulation (MODSIM 2011), December 12–16, Perth, Western Australia, Australia. 7. Baek, C. W. and Coles, N. A. 2013. An artificial catchment rainfall-runoff collecting system: Design efficiency and potential considering climate change in Western Australia, Agricultural Water Management, 121: 124–134. 8. Coles, N. A. 2004. Designing for Reliable Water Supplies, Department of Agriculture, Farmnote No. 72/2004, Perth, Western Australia, Australia. 9. Coles, N. A. and Baek, C. W. 2012. Impact of climate change on the design criteria for rainwater harvesting systems in Western Australia, Proceedings of the 18th Congress of the Asia and Pacific Division of the International Association for Hydro-Environment Engineering and Research, Seoul, South Korea.

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10. Coles, N. A., Hauck, E. J., Simons, J. A., and Laing, I. A. F. 2000. Farm water planning strategies for dryland agricultural areas: Local and regional perspectives, Xth World Water Congress, March 11–17, IWRA, Melbourne, Victoria, Australia. 11. Druyan, L. M. 1996. Arid climates, in: Schneider, S. H., ed., Encyclopedia of Climate and Weather, Vol. 1, Oxford University Press, New York, pp. 48–50. 12. Fuchs, B. A., Svoboda, M. D., Wilhite, D. A., and Hayes, M. J. 2014. Drought indices for drought risk assessment in a changing climate, in: Eslamian, S., ed., Handbook of Engineering Hydrology, Vol. 2, Modeling Climate Changes and Variability, Taylor & Francis/CRC Press, Boca Raton, FL (Chapter 12). 13. Huschke, R. E., ed. 1959. Glossary of Meteorology, American Meteorological Society, Boston, MA, 638pp. 14. Matthai, H. F. 1979. Hydrologic and human aspects of the 1976–1977 drought, U.S. Geological Survey Professional Paper 1130, Washington DC, 84pp. 15. National Drought Mitigation Center (NDCM). 2014. Drought basics—What is drought? Webpage, NDCM, Lincoln, NE, Available at: http://drought.unl.edu/DroughtBasics/WhatisDrought.aspx, Accessed October 12, 2014. 16. National Drought Mitigation Center (NDCM). 2014. Drought basics—Types of drought, Webpage, NDCM, Lincoln, NE, Available at: http://drought.unl.edu/DroughtBasics/TypesofDrought.aspx, Accessed November 1, 2014. 17. National Drought Mitigation Center (NDCM). 2015. United States drought monitor, United States of America Government, Lincoln, NE, Available at: http://droughtmonitor.unl.edu/, Accessed July 1, 2015. 18. NOAA National Weather Service. 2008. Drought public fact sheet, Available at: www.nws.noaa. gov/os/brochures/climate/DroughtPublic2.pdf, Accessed July 1, 2015. 19. Ojos Negros Research Group (ONRG). 2006. Drought facts, Available at: http://ponce.sdsu.edu/ three_issues_droughtfacts01.html, Accessed January 5, 2016. 20. Rosenberg, N. J., ed. 1979. Drought in the great plains—Research on impacts and strategies, Proceedings of the Workshop on Research in Great Plains Drought Management Strategies, March 26–28, University of Nebraska, Lincoln, NE, Water Resources Publications, Littleton, CO, 225pp. 21. Subrahmanyam, V. P. 1967. Incidence and spread of continental drought: World Meteorological Organization, International Hydrological Decade, Reports on WMO/IHD Projects, No. 2, Geneva, Switzerland. 22. Symons’ British Rainfall (SBR). 1887. G. Shield, Printer, Sloane Square, Chelsea, SW London, 1888. 23. The English Oxford Dictionary (EOD). 2015. Oxford University Press, University of Oxford, Oxford, U.K. Available at: http://www.oxforddictionaries.com/definition/english/green-drought, Accessed January 5, 2016. 24. Ostler, G. 1969. The Little Oxford Dictionary (LOD), Clarendon Press, Oxford, U.K. 25. McLeod, W. T. and Hanks, P., eds. 1988. The New Collins Concise Dictionary of the English Language (NCCD), Guild Publishing, London, U.K. 26. Moore, W. G. 1982. The Penguin Dictionary of Geography (PDG), Penguin Books, Ringwood, Victoria, Australia. 27. US Drought Monitor Website. 2015. Available at: http://www.drought.unl.edu/dm/index.html, Accessed July 14, 2015. 28. United States Geological Survey (USGS). 2014. What is drought? North Dakota Water Science Center, USGS Webpage, http://nd.water.usgs.gov/drought/faqs/faq1.html, Accessed November 10, 2014. 29. Wilhite, D. A. and Glantz, M. H. 1985. Understanding the drought phenomenon: The role of ­definitions, Water International, 10(3): 111–120.

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30. Wilhite, D. A. 2012. Drought Assessment Management and Planning: Theory and Case Studies, Business and Economics, Springer Science and Business Media, Dordrecht, the Netherlands, 293pp. 31. Williams-Sether, T., Macek-Rowland, K. M., and Emerson, D. G. 1994. Climatic and hydrologic aspects of the 1988-92 drought and the effect on people and resources of North Dakota, North Dakota State Water Commission, Water Resources Investigation 29, Bismarck, ND, 55pp. 32. Vujica, Y., Hall, W. A., and Salas, J. D., eds. 1977. Drought research needs, Proceedings of the Conference on Drought Research Needs, December 12–15, Colorado State University, Fort Collins, CO, 276pp.

2

Desertification and Drought 2.1 Introduction ..........................................................................................13 2.2 Desertification ..................................................................................... 14 2.3 Drought: What Is It? How to Quantify and Assess Its Effects and Consequences ............................................................................... 16 Aridity and Drought • Causes of Drought • Classification of Droughts • Drought Intensity Indicators 2.4 Drought Impact and the Desertification Process ............................ 19 2.5

Victor R. Squires University of Adelaide

Drought Sequences: A Key to Assessing Its Long-Term Impacts

Causes of Land Degradation and the Links to Widespread Desertification .....................................................................................22 2.6 Processes of Land Degradation Leading to Desertification ...........23 2.7 Summary and Conclusions ................................................................24 Author...............................................................................................................24 Further Readings ............................................................................................24

Abstract Both desertification and drought are ill-defined concepts, as will be explained here. A significant problem militating against clearer understanding of desertification as a tangible process relates to its confused relationship with the terms “drought,” “climatic variation,” “climate change,” and “climatic fluctuation,” which are all used interchangeably in the literature. Some clarification of these terms is necessary as climate is inherently variable at all scales. Confusion also arises in the literature relating to the corresponding adaptive vegetation changes that the cyclicity of rainfall imposes on the plant community vis-à-vis negative conditions imposed on vegetation as a result of sustained anthropogenic activity. Both cyclical (climatic) and anthropogenic changes are evident in most drylands worldwide. However, the difficulty of differentiating between the effects of normal cyclical changes and anthropogenic changes has led to unreasonable attempts to exclude vegetative indicators from studies of desertification.

2.1 Introduction It is significant that the United Nations Convention to Desertification (UNCCD) is in reality an international convention on desertification and drought. So, to be sure of what it is that this chapter is about, we need to define both terms. This is not a simple task though as both desertification and drought are ill-defined, as will be explained in the following.

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2.2 Desertification The earliest UN definition arises from the 1977 Conference in Nairobi. Desertification is defined as “the diminution of or destruction of the biological potential of the land and can lead ultimately to desert-like conditions.” In the 1992 UN Conference on Environment and Development (UNCED) held in Rio de Janeiro, desertification was formally defined as “land degradation in arid, semi-arid and dry sub-humid areas* resulting from various factors, including climatic variations and human activities.” Land, in this context, includes soil and local water resources, land surface, and vegetation or crops. Degradation implies reduction of resources potential by one or a combination of processes acting on land. These processes include water erosion, wind erosion, and sedimentation by these agents, long-term reduction in the amount or diversity of natural vegetation, where relevant, and salinization and sodification [20]. Another 1992 UN Report concluded its definition of desertification with the phrase “resulting mainly from adverse human impact” [21]. This UN definition explicitly focuses desertification on the linkages between humans and their environments that affect human welfare in arid and semiarid regions. However, this definition does not lend itself to easy quantification and requires elaboration. (Is it a process or a state? Are processes like deforestation and salinization causes or symptoms? What exactly is the role of drought?) It is fair to say that not everyone agrees with this UNCCD definition and some authors have devised variations. In fact, more than 100 definitions of desertification have been proposed, each emphasizing unique issues and (often) particular spatial and temporal scales of interest [12]. Initially, desertification processes were believed to be hinged on the reduction of biological productivity. Early definitions of desertification refer to “the diminution or destruction of the biological potential of land, leading ultimately to desert-like conditions” [20]. The early biological-based definitions have, however, tended to confuse the processes of desertification with natural cyclical fluctuations of vegetation growth, especially along desert fringes. The processes of desertification are now more broadly defined as land degradation as set out earlier. While these kinds of definitional problems have in the past led to global overestimations of the extent of desertification by as much as 66% [18], severe dangers can arise if obvious environmental problems are downplayed. In addition, a significant problem militating against clearer understanding of desertification as a tangible process relates to its confused relationship with the terms “climatic variation,” “climate change,” and “climatic fluctuation,” which are all used interchangeably in the literature. Some clarification of these terms is necessary as climate is inherently variable at all scales. Confusion also arises in the literature relating to the corresponding adaptive vegetation changes that the cyclicity of rainfall imposes on a plant community vis-à-vis negative conditions imposed on vegetation as a result of sustained anthropogenic activity. Both cyclical (climatic) and anthropogenic changes are evident in most drylands worldwide. However, the difficulty of differentiating between the effects of normal cyclical changes and anthropogenic changes [15] has led to unreasonable attempts to exclude vegetative indicators from studies of desertification. Stafford Smith and Reynolds [15] have done much to clarify the situation, and their ideas are encapsulated in a diagram reproduced here as shown in Figure 2.1. Desertification is, first and foremost, the outcome of resource management failure. Resource management in drylands, in particular, has been influenced not only by potentials of the ecosystem and skills of the peoples but also by the cultural and institutional frameworks within which the resource management has taken place. These frameworks have posed problems for resource managers. In practice, desertification occurs as a result of a long-term failure to balance the human demand for ecosystem services and the amount the ecosystem can supply [10]. We can further subdivide these ecosystem services (the benefits people obtain from ecosystems) into categories. These include provisioning services such as food and water; regulating services such as flood and disease control; cultural services * These affected lands have come to be known collectively as “drylands” and the distinctions between them rely on climatic factors, mainly the ratio between potential evapotranspiration and precipitation.

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Meteorological dimensions

Ecological dimensions Range and crop production

Animal production

Climate

Resource use pattern and intensity

Plant species composition and soil limits Human dimensions

Crops and natural resources

Rural livelihoods

Rural institutions

Trade

Services Education Health Shelter Food, etc.

Resource access (tenure and equity)

Rural population

Herd size and quality

Cash income

(across scale)

Wage labor, pensions, etc.

Policy

FIGURE 2.1  Example of a preliminary mechanistic model that emphasizes the links between, rather than the internal function of the human and environment subsystems, for rangelands/human interactions in subsistence pastoral systems of Africa. Note that this model can be applied at various scales. Solid lines indicate driving processes, dashed lines controlling feedbacks, and the heavier arrows (and their feedbacks) indicate where there is a close integration of social and biophysical factors. (After Reynolds, J.F. and Stafford Smith, D.M., eds., Global Desertification: Do Humans Cause Deserts? Dahlem University Press, 2002.)

such as spiritual, recreational, and cultural benefits; and supporting services such as nutrient cycling that maintain the conditions for life on Earth. Provisioning services are the products obtained from ecosystems, including genetic resources, food and fiber, and freshwater. Regulating services are the benefits obtained from the regulation of ecosystem processes, including the regulation of climate, water, and some human diseases. Cultural services are the nonmaterial benefits people obtain from ecosystems through spiritual enrichment, cognitive development, reflection, recreation, and aesthetic experience, including knowledge systems, social relations, and aesthetic values. Supporting services are ecosystem services that are necessary for the production of all other ecosystem services. Some examples include biomass production, production of atmospheric oxygen, soil formation and retention, nutrient cycling, water cycling, and provisioning of habitat. The pressure is increasing on dryland ecosystems for providing services such as food, forage, fuel, building materials, and water that is needed for humans, livestock, irrigation, and sanitation. This increase is attributed to a combination of human factors (such as population pressure and land use patterns) and climatic factors (such as droughts). While the global and regional interplay of these factors is complex, it is possible to understand it at the local scale. There is a widespread consensus that the pressing issues of desertification, land degradation, and drought (DLDD) are inadequately addressed in today’s political agenda at the global, regional, and national levels. It is therefore of vital importance to raise awareness of the issues, not only on the negative impacts of DLDD

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in terms of socioeconomic development but also on the opportunities that they may create to help to guide current and future land management practices to be more sustainable and resilient. Understanding and evaluating the economic and social costs and benefits associated with DLDD are essential to developing cost-effective policies and strategies for addressing DLDD and in raising this awareness [19]. Many scientists studying desertification think that the UN definition is too broad [8]. The definition encompasses things like drought, overgrazing, and inadvisable cropping. Scientists are beginning to say that desertification is a reduction in the productivity of the land that is not reversible or at least not within a human life span [14,15,17]. In other words, land is desertified when it can no longer support the same plant growth it had in the past, and the change is permanent on a human time scale. Many things can cause desertification: drought, overgrazing, fire, and deforestation can thin out vegetation, leaving exposed soil. If the nutrient-rich top soil blows or washes away, plants may not be able to return. Overfarming or drought can change the soil so that rain no longer penetrates, and the plants lose the water they need to grow. If the changing force is lifted—drought ends or livestock are removed, for example—but the land cannot recover, it is desertified. The loss of productive land for a season or even a few years is one thing, but to lose it effectively forever is clearly far more serious. Much has been written about both desertification and drought and there is no real agreement about the definition of either term. There is much more agreement about how to ascribe the consequences of both desertification and drought. An enumeration of these symptoms can help define the terms in ways that are less academic and more relevant to land managers and policy makers. The causes or drivers of land degradation and desertification have been identified as being of two types: proximate and underlying [7]. Proximate causes include biophysical factors (topography, climate conditions and change, natural hazards) and unsustainable land management practices. Underlying causes indirectly affect proximate causes, for example, unsustainable land management practices are driven by land shortage, poverty, migration, and economic pressures, which, in turn, have their own drivers. Many studies (reviewed by [3]) suggest that although desertification is the result of a complex interaction of a number of factors, the direct causes are human actions—which themselves are a function of population density, cultural traditions, land tenure, and other socioeconomic and political factors. Although climate and soil types are important in determining the severity and rate of desertification, it is ignorance or the force of circumstance in failing to match the use and management of the land to the soil and prevailing climate that leads to the removal of soil. Overstocking, deforestation, wood collection, and overcultivation usually are cited as the principal direct causes of the problem; estimates of the percentage of desertified land attributed to each of these factors are available [3]. However, a somewhat different view of the causes of desertification also exists. For some Asian environments and particularly for African environments, there is a growing body of literature that emphasizes the impact of extended droughts over the last several decades in the desertification process or suggests that desertification has been overstated due to a lack of adequate information. Prince [14] and others [2,20], studying the phenomenon of desertification, have narrowed the key elements of any satisfactory definition down to two things: A clear definition of what actually qualifies as desertification and access to long-term records of vegetation so that one of the major criteria (irreversibility) can be tested. These matters are discussed in the following.

2.3 Drought: What Is It? How to Quantify and Assess Its Effects and Consequences There is much confusion about two related but separate aspects. These two are aridity and drought.

2.3.1 Aridity and Drought Aridity results from a combination of factors affecting the capacity of the meteorological conditions to supply moisture to an area. These factors include the basic physics of air movement, the global pattern of

Desertification and Drought

17

insolation, and the geometry of the land and sea relative to atmospheric movements. Coastal deserts are common off the coast of Africa and of South America, and their location is ascribed to the cold ocean currents. Other common situations where aridity is the norm are in “rain shadow” areas, where the cool moist air rises on one side of the mountain emptying the clouds as they rise and the descending air on the other side is dry. These situations prevail in southern Patagonia, parts of the Great Plains in North America, and in Central Asia, including Xinjiang in far-west China. In addition to this “vertical geometry” of the land and its interaction with the atmospheric circulation, the pattern of land and sea also contributes to global aridity. The greater the distance from the ocean traveled by rain-bearing winds, the lesser the total moisture carried. The interior of the large continents (Africa, Asia, and Australia) therefore has less potential moisture available than most coasts. Finally, the basic seasonal global climates fueled by the solar oscillation between the tropics means that these areas receive the highest amounts of solar energy input. Much of the massive solar energy load is used in the evaporation of any moisture on land or in the atmosphere, but much remains to maintain a high-temperature regime that is so typical of many arid regions.

2.3.2 Causes of Drought While the pattern of global aridity seems to be dictated by the basic global energy flux and the resultant patterns of atmospheric circulation, drought occurs as the result of specific shortfalls in moisture availability in the face of specific demands for moisture. Drought can therefore occur in any climatic zone. While definitions of drought vary, a general definition is as follows: “an unexpected shortage of available moisture sufficient to cause severe hardship to human resource use in the area affected.” An expected shortage, say from the effects of the seasonal “dry” period, would not therefore be classified as a drought, but if the shortage occurred in the normal “wet” season or the size of the shortage was significantly greater than in a normal “dry” season (and had serious effects on the resource use), then a drought would be said to occur. Given the spectrum of precipitation in arid lands (from the extreme arid areas with no rain in some years to the semiarid lands with possibly a definite wet season) and the characteristic variability of precipitation over time and space, it is not surprising that droughts are recognized even in arid areas. The occurrence of drought in many ways reflects the overoptimistic human appraisal of the moisture availability of an area as a component of resource potential. Such appraisals have fluctuated over time with subsequent significance for the success of resource use.

2.3.3 Classification of Droughts As indicated earlier, there is no clear definition of drought and opinion is divided on the terminology surrounding drought [20]. Despite this, several main types of drought are recognized: (1) meteorological drought (see earlier) characterized by an amount of precipitation lower than a definite percentage of the long-term average for an area, (2) agricultural (agroclimatic) drought associated with nonuniformity of distribution of precipitation in the critical phases of the vegetation period, (3) soil drought caused by insufficient moisture in the soil to support plant growth, and (4) hydrological drought associated with a deficiency of surface runoff and drying up of ponds, reservoirs, lakes, and cessation of flow in rivers. With respect to their intensity and duration, droughts are divided into moderate, strong, and very strong (Table 2.1). In India, where monsoonal rains play such an important role in agriculture and commerce and the population is huge, the incidence of drought has serious consequences and India gives an official recognition to additional categories of drought: Socioeconomic drought: It reflects the reduction of availability of food and loss of income on account of crop failures, endangering food and social security of the people in the affected areas. Famine: A famine occurs when a large-scale collapse of access to food occurs that, without intervention, can lead to mass starvation.

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Handbook of Drought and Water Scarcity

TABLE 2.1  Drought Is Generally Classified according to Two Broad Criteria: (A) Water and Its Availability and (B) Duration but Type and Severity Are Further Classified A.1. Meteorological Drought indicates a greater or lesser deficit in precipitation a. Slight drought: When rainfall is 11%–25% lower than the normal rainfall b. Moderate drought: When rainfall is 26%–50% lower than the normal rainfall c. Severe drought: When rainfall is more than 50% lower than the normal rainfall 2. Hydrological drought: Is defined as the situation of rainfall deficit when the hydrological sources like streams, rivers, lakes, wells dry up and groundwater level depletes. This affects the rural community (in particular); industry and power generation 3. Agricultural drought: This is the situation resulting from inadequate rainfall, when soil moisture fails to meet the water demands of the crop during growth. Thus, crop may wilt due to soil moisture stress, resulting in a marked reduction of yield

B. Drought onset and duration differ and allow classification 1. Permanent drought: This is the area generally of permanent dry, arid desert regions. Crop production is not possible without irrigation. In these areas, vegetation like cactus, thorny shrubs, xerophytes, etc., are generally observed. 2. Seasonal drought occurs in the regions with clearly defined rainy (wet) and dry climates. Seasonal drought may occur due to large-scale seasonal circulation, e.g., in monsoon areas. 3. Contingent drought results from irregular and variable rainfall, especially in humid and subhumid regions. The occurrence of such droughts may coincide with growth periods of the crops when the water needs are greatest. Severe reductions in crop yields may follow.

Ecological drought: Ecological drought takes place when the productivity of a natural ecosystem fails significantly as a consequence of distress-induced environmental damage, often leading to outward migration as “ecological refugees.” Further class classification of drought may be helpful, for instance, to distinguish between atmospheric and soil drought. Soil drought is the condition when the soil moisture depletes and falls short to meet potential evapotranspiration of the crop. Atmospheric drought: It results from low humidity, dry and hot winds and leads to desiccation of plants. This may occur even when the rainfall and moisture supply is adequate. Drought is a serious matter in the Mediterranean basin and much work has been done to develop classification systems and indices that are relevant [1].

2.3.4 Drought Intensity Indicators A drought indicator is typically a single number far more useful than raw data for decision-making. Therefore, drought indices are used to determine thresholds, the severity, the duration, the probability of occurrence, and the spatial extent of drought episodes. Drought intensity categories are based on five key indicators, numerous supplementary indicators including drought impacts, and local reports from expert observers. The accompanying drought severity classification (Table 2.2) developed in the United States shows the ranges for each indicator for each dryness level. Because the ranges of the various indicators often do not coincide, the final drought category tends to be based on what the majority of the indicators show and on local observations. The analysts producing the map also weigh the indices according to how well they perform in various parts of the country and at different times of the year. Additional indicators are often needed in the West, where winter snowfall in the mountains has a strong bearing on water supplies. It is this combination of the best available data, local observations, and experts’ best judgment that makes the U.S. Drought Monitor more versatile than other drought indicators. Different types of drought require different types of drought indicators. Some indicators are better to assess agricultural drought, other hydrological drought, and so on. The assessment of socioeconomic drought requires socioeconomic and nutritional indicators.

19

Desertification and Drought TABLE 2.2  Drought Sequences in Central Australia (23°42′0″S/133°53′0″E) in the Period 1886–1985 according to Their Classification into Good, Average, and Bad Years on the Basis of Summer and Winter Rainfall Year

Sequence of Years

1886–1905

OOOOOdddOO

1906–1915

OOgOggdOdd

1916–1925

OgOOOgOOd

1926–1935

OOddddgOOd

1936–1945

OdgOOddgdd

1946–1955

OOOdgOgOdO

1956–1965

OOdOdOddOO

1966–1975

OddgOOOdgg

1976–1985

OddgOgOdOO

Remarks

The period 1928–1935 was widely seen as an 8-year drought despite being interspersed by “g” years.

The period 1967–1974 was widely seen as a 9-year drought despite being interspersed by “g” years

Source: Foran, B. and Stafford Smith, M., J. Environ. Manage., 33(1), 17, 1991. Note: “d = drought,” “O = average, ” “g = good,” overall there were 29 drought years, 51 average years, and 20 good years in this 90-year sequence.

Integrated systems like the drought indicator developed in the United States (Table 2.3) allow us to reunite indicators developed from different types of drought to be displayed in a graphical form as a unique map showing the areas suffering most from drought severity.

2.4 Drought Impact and the Desertification Process The impact of drought on natural ecosystems is measured by plant cover and biomass production and by the disruption of food production systems. Drought reduces the number, phytomass, and ground cover of plants and hence reduces the protection of the soil against erosion. Desertification has much more profound and lasting effects. Desertified soils are subject to extensive water and wind erosion and therefore lose much of their depth and ability to store water and nutrients. In the worst cases, all perennials are removed, and the soil surface is subjected to large-scale wind and water erosion. Without permanent vegetation protection, the soil surface is eroded by running water, sealed and crusted by raindrop splash, and made increasingly impervious and hence prone to more erosion. Soil surface sealing and encrustation reduce water intake, resulting in a drier environment. Thus, a whole spiral of self-perpetuating edaphic aridity is triggered. Eventually, all of the soft soil layers are removed, and the situation becomes irreversible. Schlesinger et al. [18] propose that not only does drought and the loss of vegetation cover lead to desertification, but a mere shift in plant growth form dominance, as a consequence of overgrazing, may drastically reduce productivity. Overgrazing results in the redistribution of organic matter and nutrients may be the primary agent responsible for the current conversion of previously productive grasslands to unproductive shrublands. Where resources within semiarid grasslands previously were homogeneously distributed, overgrazing results in their concentration beneath shrub islands. Not only is the productivity of the land reduced, but positive feedback processes render the changes irreversible [18]. Drought is an inherent characteristic of climatic variation and occurs in all regions of the world. It is a consequence of a natural reduction in the amount of precipitation received over a period of time in relation to the normal. The economic, social, and ecological effects of drought depend not only on the length, severity, and spatial extent but also on the vulnerability of society to the event. See the earlier comments apropos India in this context. Rangelands are likely to be prone to desertification because of their inherent fragility. For example, the effect of climate change on plant and animal production in the Great Plains of North America was

Abnormally dry

Moderate drought

Severe drought

Extreme drought

Exceptional drought

D1

D2

D3

D4

Description

D0

Category

• Widespread water shortages or restrictions • Exceptional and widespread crop/pasture losses • Shortages of water in reservoirs, streams, and wells creating water emergencies

• Major crop/pasture losses

• Water restrictions imposed

• Water shortages common

• Crop or pasture losses likely

• Streams, reservoirs, or wells low, some water shortages developing or imminent • Voluntary water use restrictions requested

• Some damage to crops, pastures

• Pastures or crops not fully recovered

• Some lingering water deficits

Coming out of drought:

• Short-term dryness slowing planting, growth of crops or pastures

Going into drought:

Possible Impacts

TABLE 2.3  Drought Severity Classification in United States

3–5

0–2

−5.0 or less

6–10

11–20

21–30

CPC Soil Moisture Model (Percentiles)

−4.0 to −4.9

−3.0 to −3.9

−2.0 to −2.9

−1.0 to −1.9

Palmer Drought Severity Index (PDSI)

0–2

3–5

6–10

11–20

21–30

USGS Weekly Streamflow (Percentiles)

−2.0 or less

−1.6 to −1.9

−1.3 to −1.5

−0.8 to −1.2

−0.5 to −0.7

Standardized Precipitation Index (SPI)

0–2

3–5

6–10

11–20

21–30

Objective Drought Indicator Blends (Percentiles)

20 Handbook of Drought and Water Scarcity

Desertification and Drought

21

modeled and results showed a reduction in plant nitrogen content during summer grazing and decreased animal production because of an increased ambient temperature and decreased forage quality. Carrying capacities would need to drop to maintain 90% confidence of not overstocking. Desertification causes the soil to lose its ability to support rainfed crops. It inevitably results in emigration as the land cannot sustain the original inhabitants. There are indications that as much as 3% of the African population has been ­permanently displaced, largely as a result of environmental degradation [22]. Desertification is often confused with drought or desiccation. Desiccation refers to longer-term (decadal order) deficits in rainfall that seriously disrupt ecological and social patterns and require national and global responses. Recovery after desiccation is much slower, for trees may have died and vegetation may then take years to recover. Responses include management of population movements and the development of alternative livelihood systems. However, it does not necessarily follow that drought or desiccation per se will give rise to or cause desertification in dryland areas. Much depends on the resource management in these areas. When human misuse or mismanagement of land weakens the natural system, drought and desiccation often lead to desertification. While the latter should not be confused with drought and desiccation, the definition provided by UNCED in 1992* cites climate variation as a direct causal factor and implicitly links desertification with climatic variation or climate change. Climatic variation or climate change refers to short-term climate variability and longer-term climatic trends or shifts caused by natural mechanisms or by human a­ ctivity. Climate change does cause global warming often through greenhouse gas (GHG) emissions. Natural ­climate change, which typically operates at a slow pace, is not a problem. Climate has been changing constantly for hundreds of millennia. As a result of the slow advance of natural processes, the planet has warmed and cooled, passing from ice ages to warm, interglacial periods. These gradual transitions, often spanning thousands of years, have allowed life on earth to adjust relatively smoothly to each new climatic equilibrium. Nonetheless, during these transitions, the boundaries of ecological communities have shifted and the associated human cultures have flourished and, occasionally, disappeared. However, something important has changed recently. During the last few decades, the natural greenhouse effect has become the “greenhouse problem.” In the foreseeable future, rising concentrations of GHGs threaten to induce rapid shifts in global and regional climate regimes, disrupting economic systems and inflicting significant economic damage on the affected societies.

2.4.1 Drought Sequences: A Key to Assessing Its Long-Term Impacts More still needs to be known about the biological responses of the land to stocking pressure, especially in and after drought periods. Droughts, and what to do about them, have bedeviled farmers, politicians, bureaucrats, and scientists alike. A number of strategies for drought mitigation have been tried, but drought has tended to be regarded as an aberration. Today, however, drought is increasingly accepted as a normal part of the farming system and not as a “crisis.” Many farmer groups no longer wish to be beholden to a drought declaration and subsequent drought subsidies and are asking for more technical information and for the financial freedom to deal with drought as individual enterprises. At the same time, many so-called droughts are being recognized as carrying capacity crises brought on by inappropriate stocking policies. Uncertainties of climate, markets, and financial returns pose complex problems and stresses for the management, managers, and resource base of arid pastoral systems. Pastoral lands have a highly variable climate. For example, each year of the historical sequence 1886–1985 for Alice Springs, Australia (23°42′0″S/133°53′0″E), was classified by Foran and Stafford Smith [7] as good, average, or dry on the basis of effective summer and previous winter rainfall (Table 2.2). Good, average, and dry years (defined in terms of production rates below average) occur randomly with an approximate probability of 0.25, 0.50, and 0.25, respectively, in central Australia. When these were separated into individual 10-year sequences, they provided 10 decades of “real” rainfall sequences * The UNCED, also known as the Earth Summit, took place in Rio de Janeiro, Brazil, from June 2 to 14, 1992.

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Handbook of Drought and Water Scarcity

for a third appreciation of the different management strategies (assessed on the basis of financial returns). Within a management time frame of 10 years, there are 59,049 (310) possible combinations of these three year types. First, the three strategies were run through all 59,049 (310) possible 10-year sequences to assess the overall expected mean and variance of financial return. Second, the ability of each strategy to cope with drought was examined in more detail by running the strategy through drought sequences of 1–5 years, followed by a recovery sequence of average years up to year 20. The first year of a dry sequence resulted in “poor” biological rates, and subsequent years in that sequence obtained “bad” rates. Three management strategies commonly found in central Australia were evaluated. The average enterprise ignores drought in the hope that the rains will soon come. The high-stock enterprise accepts the risk of drought, running 33% more stock on the same land resource than the “average” strategy, but responds aggressively to the first indications of drought by selling all male stock and the older cows from the herd. The low-stock enterprise avoids drought as much as possible, by carrying only two-thirds of the stock numbers on the average property and maintaining high biological rates for the herd by superior animal husbandry, plant introduction, and water harvesting techniques.

2.5 Causes of Land Degradation and the Links to Widespread Desertification Land degradation is a continuous phenomenon; it implies a decline in crops, a deterioration in vegetation cover, an exacerbation of external dynamics of the land surface, a qualitative and quantitative regression of water resources, and a degradation of soils and pollution of the air. Degradation is a point of evolution that leads to a reduction of resource potential. The word desertification can be used when degradation reaches an irreversible degree on a human time scale (see earlier). The degree can be considered irreversible when the soil is degraded to such a point that the seeds in soil cannot germinate because the soil has lost its ability to conserve humidity. Drought can exacerbate the effects of land degradation and this effect has been dubbed “the crucible of drought.” It is the added stress imposed by drought that can create a tipping point when ecosystems are put under increased strain. It is this stress that can shift land degradation to desertification. Understanding, assessing, and combating desertification can be facilitated by differentiating causes, processes (or manifestations), and consequences or status, which means degrees of severity of reduction of resource potential. The causes of land degradation can be classified as

1. Natural, which means climatic—deficient rainfalls with droughts but may also include excessive rainfall with destructive floods and landslides 2. Anthropogenic, which includes socioeconomic aspects with negative feedback—desertified land with a reduction of potential leading to a greater pressure on land users who increase the destruction of the land; a vicious circle or downward spiral Four major anthropogenic causes of land degradation have been described:



1. Overstocking, overgrazing, and all types of vegetation clearing that leave the soil bare of cover and induce physical processes of degradation. Worldwide water erosion is a cause of loss of soil through water erosion on 25,000 million ha. 2. Soils repeatedly worked over with heavy equipment that causes physical damage of the soil’s water holding capacity. 3. Intensive cropping regimes without rotation or nutrient inputs. This deprives the soil of carbon and its essential mineral elements. 4. Poor irrigation practices and badly drained soils resulting in salinization because water pumped over the fields evaporates and the dissolved salts collect on or near the soil surface.

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Desertification and Drought

2.6 Processes of Land Degradation Leading to Desertification Adaptation to drought and desertification has challenged pastoralists, ranchers, and farmers for centuries. Pastoralists and ranchers have drought-evading strategies and farmers have drought-enduring strategies. Drought-enduring strategies include the adoption of a light stocking rate that preserves the dynamics of the ecosystems and their ability to recover after drought and the utilization of agroforestry techniques, whereby fodder shrubs and trees that can store large amounts of feed over long periods of time are planted in strategic locations in order to provide an extra source of feed when drought occurs. These provide and thus encourage a more permanent rather than nomadic existence even when the rangeland is dry and parched. In dryland environments, formidable challenges exist for implementing sustainable development. Among these are unpredictable and severe drought, desiccation due to persistent drought, and dryland degradation or desertification. Because these problems overlap in their effects on the ground, often those who seek sustainable development for the drylands tend to view the problems as one and the same. Yet to facilitate the development of appropriate and effective mitigating measures, it is important that the differences and interrelationships be clearly understood. In arid and semiarid lands, human activities like overgrazing, coupled with the degradation of the natural vegetation can lead to changes in particular climatic parameters. Initially, surface albedo could rise by roughly 5% increasing by 10% ± 15% under conditions of desertification. Reduced vegetation cover and increased surface albedo may, however, result from naturally occurring periods of drought. Reduced vegetation cover also increases dust emission in arid and semiarid lands due to intensified degradation and thus contributes to the anthropogenic particle emission, one-third of which is due to land use degradation. However, because arid and semiarid lands are climatically determined, any changes in climate that result in an expansion or contraction will alter the extent of the area in which desertification can be expected to occur, but deciding its precise contribution is problematic. Hulme and Kelly [9] and Williams and Balling [30] have provided an extensive discussion on the interactions of desertification and climate, with a fairly comprehensive review of the existing literature on climate and human impact on dryland environments. That climate change does occur is now an established fact (Figure 2.2). Determining the precise contribution of climate change to the problem of desertification is not an easy matter. One can generalize in the light of recent research findings that there is a causal link between the two. A key question is at what point though should long-duration drought be reclassified as climate change and its land-degrading consequences be included within the umbrella of desertification. While the relative contribution of climate change (often manifest as more frequent and severe droughts) is difficult to determine, there is little doubt that it can aggravate the problem, especially where resource management failure

Local factors

Natural change

Feedback Management failure

External change

Desertification

Desiccation Greenhouse gases

Key

The oceans Anthropogenic change

Causal relationships about which we are confident Causal relationships about which there is uncertainty

FIGURE 2.2  Desertification and its linkages. Some relationships and feedback loops in the interaction between desertification and dessication induced by drought. (Redrawn from Hulme, M. and Kelly, M., Environment, 35(6), 4, 1993.)

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Handbook of Drought and Water Scarcity

has occurred or where, as a result of natural or anthropogenic disturbances, prevailing management systems of land use in arid and semiarid lands reach their resilience thresholds. The so-called crucible of drought can apply intense pressure on plants, livestock, and land users.

2.7 Summary and Conclusions Local foci of desertification processes appear in innumerable new places every year, and it is most efficient to deal with them and the causes of their development as they arise. Left unattended because of lack of commitment, concern, political will, technology, or financial resources, these spots of desertification expand, sometimes at an accelerating rate. The task of dealing with the multifaceted aspects of desertification and drought (and their interactions) is not easy. Some aspects often appear as a by-product of some usually important life-sustaining human activity, especially in the drylands in developing countries. Yet desertification and drought (especially when they are concurrent) in the long run destroy the ­all-important resource base on which an ever-increasing population must increasingly depend. There are few other environmental issues that deserve a global focus of attention as urgently as does the impact of drought and desertification, now adding to the life-threatening pressures on inhabitants of drought-prone regions in particular.

Author Victor Squires is an Australian who, as a young man, studied animal husbandry and rangeland ecology. He has a PhD in rangeland science from Utah State University, United States. He is former dean of the Faculty of Natural Resource Management at the University of Adelaide, where he worked for 15 years after a 22-year career in Australia’s CSIRO. He is the author/editor of 13 books, including Combating Desertification in Asia, Africa and the Middle East: Proven Practices (Springer, 2014) and Rangeland Ecology, Management and Conservation Benefits (2015) and numerous research papers on aspects of rangeland ecology/livestock relations. Dr. Squires was a visiting fellow in the East–West Center, Hawaii. Since retirement from the University of Adelaide, he works as an adjunct professor at the University of Arizona, Tucson, and at the Gansu Agricultural University, Lanzhou, China. He has been a consultant to the World Bank, Asian Development Bank, and various UN agencies in Africa, China, Central Asia, and the Middle East. He was awarded the 2008 International Award and Gold Medal for International Science and Technology Cooperation and, in 2011, the Friendship Award by the government of China. The gold medal is the highest award for foreigners. In 2015, Dr. Squires was honored by the Society for Range Management (United States) with an Outstanding Achievement Award.

Further Readings

1. Aghrab, A., Boubabid, R., and Elalouli, A. C. 2008. Drought characterization using drought indices in two areas of the Mediterranean basin: Meknes, Morocco and Cordoba, Spain, Options Mediterraneeness Series A, 80: 191–198. 2. Anyamba, A. and Tucker, C. 2005. Analysis of Sahelian vegetation dynamics using NOAA-AVHRR NDVI data from 1981–2003, Journal of Arid Environments, 63: 596–614. 3. Bullock, P. and Le Houerou, H. 1996. Land degradation and desertification, in: Working Group II Contribution to the Second Assessment Report of the IPCC, Available at: https://www.ipcc-wg2.gov/ publications/SAR/SAR_Chapter%204.pdf, Chapter 4, Accessed on July 28, 2016. 4. CIHEAM/ICARDA/FAO. 2008. Drought management: Scientific and technological innovations, Proceedings of the First International Conférence “Drought Management” MEDROPLAN Project and MEDA Water Programme, CIHEAM/ICARDA/FAO, Zaragoza, Spain, 429pp.

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5. Eslamian, S. S., Khatoonabadi, S. A., Shahidi Hamadani, A., and Nazari, R. 2003. Water resources mismanagement and desertification of a semiarid region, Gahavand Plain, Seventh International Conference on Dry Land Development: Sustainable Development of Dry Lands in the 21st Century, The International Dry Lands Development Commission (IDDC), Tehran, Iran. 6. Eslamian, S. S., Khajedin, S. J., and Amiri-Maleki, A. 2002. Role of dam construction in developing desert regions of arid zone climates, Eighth International Conference on Understanding Future Dryland Environmental Changes from Past Dynamics, Yazd University, Yazd, Iran. 7. Foran, B. and Stafford Smith, M. 1991. Risk, biology and drought management strategies for cattle stations in central Australia, Journal of Environmental Management, 33(1): 17–33. 8. Geist, H. J. and Lambin, E. F. 2004. Dynamic causal patterns of desertification, Bioscience, 54: 817–829. 9. Herrmann, S. and Hutchinson, C. 2005. The changing contexts of the desertification debate, Journal of Arid Environments, 63: 538–555. 10. Heshmati, G. A. and Squires, V. R. 2013. Combating Desertification in Asia, Africa and Middle East: Proven Practices, Springer, Dordrecht, the Netherlands, 476pp. 11. Hulme, M. and Kelly, M. 1993. Exploring the links between desertification and climate change, Environment, 35(6): 4–45. 12. Millennium Ecosystem Assessment. 2005. Ecosystems and Human Well-Being: Synthesis, Island Press, Washington, DC. 13. Nicholson, S. E. 2000. Land surface processes and Sahel climate, Reviews of Geophysics, 38: 117–139. 14. Prince, S. 2004. Mapping desertification in southern Africa, in: Gutman, G., Janetos, A., Justice, C. O., Moran, E. F., Mustard, J. F., Rindfuss, R. R., Skole, D., and Turner, II, B. L., eds., Land Change Science: Observing, Monitoring, and Understanding Trajectories of Change on the Earth’s Surface, Kluwer, Dordrecht, the Netherlands, pp. 163–184. 15. Prince, S. D., Wessels, K. J., Tucker, C. J., and Nicholson, S. E. 2007. Desertification in the Sahel: A reinterpretation of a reinterpretation, Global Change Biology, 13: 1308–1313. 16. Reynolds, J. F. 2001. Desertification, in: Levin, S., Reynolds, J. F., and Stafford Smith, D. M., eds., Encyclopedia of Biodiversity, Vol. 2, Academic, San Diego, CA, pp. 61–78. 17. Reynolds, J. F. and Stafford Smith, D. M., eds. 2002. Global Desertification: Do Humans Cause Deserts?, Dahlem University Press, Berlin, Germany. 18. Schlesinger, W. H., Reynolds, J. F., Cunningham, G.L., Huenneke, L.F., Jarrell, W.M., Virginia, R. A., and Whitford, W.A. 1990. Biological feedbacks in global desertification, Science, 247: 1043–1048. 19. Squires, V. R. 1995. Drought in Australia with special reference to pastoralism: Lessons learned or experience wasted, Secheresse, 6(1): 127–134 (in French). 20. Squires, V. R. 2007. Detecting and monitoring impacts of ecological importance in semiarid rangelands, in: El-Beltagy, A., Mohan, C., Saxena, C., and Wang, T., eds., Human and Nature—Working Together for Sustainable Development of Drylands (Proceedings of the Eighth International Conference on Development of Drylands, February 25–28, 2006, Beijing, China), ICARDA, Alleppo, Syria, pp. 718–723. 21. Stafford Smith, D. M. and Reynolds, J. F. 2002. Desertification: A new paradigm for an old problem, in: Reynolds, J. F. and Stafford Smith, D. M., eds., Global Desertification: Do Humans Cause Deserts? Dahlem Workshop Report 88, Dahlem University Press, Berlin, Germany, pp. 403–424. 22. Stiles, D. 1997. Linkages between dryland degradation and migration: A methodology, Desertification Control Bull. No. 30, UNEP, Nairobi, Kenya, pp. 9–18. 23. Thomas, D. S. G. 1993. Sandstorm in a teacup? Understanding desertification, The Geographical Journal, 159: 318–331. 24. Thomas, D. S. G. and Middelton, N. J. 1994. Desertification: Exploding the Myth, John Wiley, Chichester, U.K., 194pp. 25. Tucker, C. 2005. Analysis of Sahelian vegetation dynamics using NOAA-AVHRR NDVI data from 1981–2003, Journal of Arid Environments, 63: 596–614.

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26. UNCCD. 2013. White Paper 1 economic and social impacts of desertification, land degradation and drought, Second UNCCD Science Conference, April 9–12, 2013, Bonn, Germany, 79pp. 27. Middleton, N. J. and Thomas, D. S. G., eds. 1992. World Atlas of Desertification (United Nations Environment Programme), Edward Arnold, London, U.K., 69pp. 28. UNEP/UNCOD. 1977. United Nations Conference on desertification round-up, plan of action and resolutions, Available at: http://www.ciesin.org/docs/002-478/002-478.html, Accessed July 14, 2016. 29. UNSO. 1992. Assessment of desertification and drought in the Sudano-Sahel Region 1985±1991, United Nations Sudano-Sahelian Office, New York. 30. Williams, A. J. and Balling, Jr., R. C. 1996. Interactions of Desertification and Climate, WMO and UNEP, Nairobi, Kenya.

3 Meteorological Drought Indices: Definitions Nicolas R. Dalezios University of Thessaly and Agricultural University of Athens

Zoltan Dunkel Hungarian Meteorological Society

Saeid Eslamian Isfahan University of Technology

3.1 Introduction ���������������������������������������������������������������������������������������27 3.2 Drought Concepts ..............................................................................29 3.3

Drought Definitions and Types   •  Drought Quantification and Monitoring   •  Drought Features and Characteristics

Meteorological Drought and Indices ............................................... 33 Meteorological Drought   •  Classification of Meteorological Drought Indices   •  Description of Selected Meteorological Drought Indices

3.4 Discussions ..........................................................................................39 3.5 Summary and Conclusions ...............................................................40 Authors ............................................................................................................40 References ........................................................................................................ 41

Abstract  Drought is part of nature’s climate variability recurring diachronically at a regional scale. Drought is considered as one of the major natural hazards having significant impact on several sectors of the economy, society, and environment. Drought is basically caused by the lack of precipitation events in a region over a period of time and can be regarded as an extreme climatic event. The early stages of accumulated precipitation deficiencies are referred to as meteorological drought being a region-specific natural event, since the atmospheric conditions that result in deficiencies of precipitation are highly variable from region to region. This chapter covers meteorological drought and its quantification through several drought indices. An attempt is undertaken to understand meteorological drought and explore several features through drought indices. There are many drought indicators and indices being used around the world. Indeed, the most commonly used drought indices are presented. Moreover, monitoring and assessment of meteorological droughts is also considered, along with significant drought impacts. The Standardized Precipitation Index is recommended by the World Meteorological Organization to be used universally, but it may not be accepted as the only and absolute index. Based on specific regional and climatic conditions, the use of other indices should also be taken into consideration.

3.1  Introduction Drought is part of nature’s climate variability. Indeed, drought is considered as a natural regional phenomenon with a temporal periodicity. Essentially, droughts originate from a deficiency or lack of precipitation in a region over an extended period of time. This is why droughts are also referred to as “nonevents” and can be considered as extreme climatic events associated with water resources deficit. Moreover, drought is considered as one of the major natural hazards having significant impact on several sectors of the economy, society, and environment [35,37]. There are several unique characteristics, 27

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which differentiate droughts from other environmental hazards, namely, its slow onset often characterized as a creeping phenomenon; its nonstructural impacts, which can be regional or local lasting for a long time or a very short time; and the absence of a universal definition leading to inaction [52]. Moreover, the impacts of droughts may be severe and are neither immediate nor easily measured. All these may accumulate difficulties in drought assessment and response, which consequently may result in slow progress on drought preparedness plans and mitigation actions. There is a need to establish the context in which the drought phenomenon and its associated impacts are being described leading to a better definition. More than 150 published definitions of drought have been identified [46]. If drought is considered as a phenomenon, it is certainly an atmospheric phenomenon. However, when considering drought as a hazard, there is a tendency to define and classify droughts into different types. Definitions of drought help in identifying the duration and severity of drought and are useful in recognizing and planning for it. Four operational definitions are commonly used, namely, meteorological or climatological, agricultural or agrometeorological, hydrological, and socioeconomic drought [24]. With the exception of meteorological drought, the other types of drought, such as agricultural and hydrological, emphasize on the human or social aspects of drought in terms of the interaction between the natural characteristics of meteorological drought and human activities that depend on precipitation. As their names imply, these diverse drought types impact different sectors, but in most instances, the impacts related to each sector overlap both temporally and spatially. As already mentioned, all droughts begin with a deficiency of precipitation in a region over a period of time. These early stages of accumulated departure of precipitation from normal or expected are usually considered as meteorological drought [36]. A continuation of these dry conditions over a longer period of time, sometimes in association with above-normal temperatures, high winds, and low relative humidity, quickly results in impacts on agricultural and hydrological sectors (Figure 3.1). Meteorological droughts are characterized by a change in the local meteorological conditions, such as the prevalence of a highpressure ridge. The geomorphological and climatological characteristics of a region play an important role in meteorological drought, since they may imply different ­precipitation regimes. Meteorological droughts can develop quickly, but they can also end just as quickly, if the precipitation deficits are

Time (duration)

Reduced infiltration, runoff, deep percolation, and groundwater recharge

High temp., high winds, low relative humidity, greater sunshine, less cloud cover Increased evaporation and transpiration

Soil water deficiency Plant water stress, reduced biomass and yield Reduced streamflow, inflow to reservoirs, lakes, and ponds; reduced wetlands, wildlife habitat Economic impacts

Social impacts

Hydrological Agricultural drought drought

Precipitation deficiency (amount, intensity, timing)

Meteorological drought

Natural climate variability

Environmental impacts

FIGURE 3.1  Drought types and temporal sequential procedure. (From Dalezios, N.R. et al., Nat. Hazards Earth Syst. Sci., 14, 2435, 2014.)

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relatively small. However, these types of drought may also develop into a multiseasonal event leading to one of the other types of drought. This chapter covers the subject of meteorological drought indices. A comprehensive presentation of drought concepts, definitions, and types is attempted. This is followed by a description of meteorological drought, along with its features and characteristics. Then, quantification of meteorological drought is presented through the use of indices. Drought monitoring and assessment is also considered. Moreover, the improvement of drought prediction and early warning methods, as well as dissemination of warnings, requires a continuous effort. Indeed, the impacts of drought are often slow to appear. A  description of indicative meteorological drought indices is presented. The adoption of the Standardized Precipitation Index (SPI) and recommendation to be applied universally and the need for the development of a global drought risk model are also discussed.

3.2  Drought Concepts Drought differs from other environmental hazards in several ways. Among the extreme meteorological events, drought is possibly the most slowly developing and long-lasting event and probably the least predictable among atmospheric hazards. As already mentioned, drought is a slow-onset environmental hazard, also known as a creeping phenomenon. The driving factor is the cumulative precipitation deficiency, which may happen quickly or may take months before the impacts become apparent. Similarly, due to its creeping nature, drought effects are also slow to appear, lagging precipitation deficits by weeks or months. Moreover, the assessment of the onset and the end of a drought period is a complicated task. It is recognized that because of these mainly temporal characteristics, drought cannot be compared with other environmental hazards, such as flood, hailstorm, or frost, which can also contribute significantly to a regional annual loss due to unfavorable natural circumstances. Due to its peculiar character, drought deserves the greatest scientific and operational investigation. The current trend consists of analyzing several well-accepted and widely used drought indices and assessing and comparing their theoretical and practical advantages, limitations, interrelations, potential joint implementation, and numerical effectiveness.

3.2.1  Drought Definitions and Types Drought constitutes a compound concept. As a first guess, it seems that drought may be addressed and considered in a homogeneous way. However, after a detailed and thorough consideration, it has become evident that there is no precise and universally accepted definition of drought [16]. Indeed, there are hundreds of definitions, which simply contribute to the confusion about the existence of a drought and its degree of severity [45]. Needless to say, definitions of drought should be region and application or impact specific. In fact, droughts are regional in extent and each region maintains specific climatic characteristics. As an example, the amount, seasonality, and form of precipitation may differ significantly between regions. Moreover, besides precipitation consideration, temperature, wind, and relative humidity may also be important factors to identify the regional character of drought. In addition, definitions also need to be application specific, since drought impacts vary between sectors. Even within sectors, there are many different assessments and considerations of drought, because impacts may differ significantly. Starting with the International Meteorological Vocabulary [50], which is one of the most authentic sources, two very simple definitions of drought are provided: (1) prolonged absence or marked deficiency of precipitation and (2) period of abnormally dry weather sufficiently prolonged for the lack of precipitation to cause a serious hydrological imbalance. From the same source, the definition of “dry season” is included: period of the year characterized by the (almost) complete absence of rainfall, where the term is mainly used for low latitude regions. Moreover, the definition of “dry spell” is also presented: period of abnormally dry weather, where the use of this term should be confined to conditions less severe than those of a drought. From the definitions mentioned earlier, it is evident that dealing with

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drought is not a simple task and a drought may be identified from a number of different points of view. Indeed, drought has different meanings to various groups of the society, depending on either their specific interest or their historical and economic perspective. Therefore, it is difficult to find a completely adequate definition of drought, which could be acceptable throughout the world. For a better understanding, drought is classified into several types; however, the relationship between the different types of drought is complex. Specifically, the American Meteorological Society groups drought definitions and types into four categories, which have already been mentioned before, namely, meteorological or climatological, agricultural, hydrological, and socioeconomic drought [24]. Two more drought types are added, namely, atmospheric and physiological drought. Keeping in mind that the subject of this chapter is meteorological drought, a brief description of the drought types mentioned earlier follows. Atmospheric drought occurs if too high a saturation deficit has been measured for a durable time. This drought type more or less refers to the dry spell category. It can be stated that, in general, droughts are shown to be associated with the persistence of ridges or centers of high-pressure systems at the middle level in the atmosphere. Moreover, the corresponding reduced cloud cover results in positive temperature anomalies in the lower atmosphere, which produces the middle-level pressure anomaly and favors subsidence in the high level, keeping the atmosphere significantly drier and more stable than normal [7,34]. Studies in several areas around the world have shown that drought periods are often characterized by a substantial decrease in the amount of rainfall per day, by an increase in the continentality of the clouds, and by a lack of rain-producing clouds. Meteorological drought means a longer period of time with considerably less than average precipitation amounts, which corresponds to the general definition of drought. Agricultural drought receives two explanations: the first one is that the available soil moisture is inadequate and the second one is that yield is considerably less than the average because of water shortage. Agricultural drought occurs when plant water availability—from precipitation and water stored in the soil—falls below that required by a plant community during a critical growth stage. This leads to belowaverage yields in both pastoral and grain-producing regions. Hydrological drought is generally defined as a period of below normal conditions for one or a combination of factors, such as streamflow, reservoir storage, and groundwater. Hydrological drought normally occurs on a rather large area, such as a watershed. Physiological drought can occur when the plant is unable to take up water in spite of sufficiently available soil moisture. This situation refers to the circumstances when plant shows drought symptoms, but there is no drought assessment based on the prevailing atmospheric conditions. This situation could be caused by abnormally cold weather or in the case when the plant is infected. Socioeconomic drought is defined in terms of loss from an average or expected return. It can be measured by both social and economic indicators, of which profit is only one [27]. Socioeconomic drought can be considered as the integration of several drought categories. It may imply any disadvantageous impact of consecutively repeating dry spells. It may also mean the lack of some economic goods due to meteorological, hydrological, and/or agricultural drought. Under specific conditions, its definition can be close to the definition of famine.

3.2.2 Drought Quantification and Monitoring Drought quantification and assessment can be implemented through the use of indicators and/or indices. Drought indicators are measures of climate variables, which describe features of drought, and provide an indication of potential drought-related stress or deficiency. Data analysis, interpretation, and aggregation lead to drought indicators, where several of them can be synthesized into the development of a drought index. Indeed, an index is a method of deriving “value-added” information related to drought and constitutes an attempt to quantify a drought and its magnitude. It is also important to note

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31

that indices are indicators as well. Clarifications are always required about the scientific and operational validity of an index, that is, how each indicator is combined and weighted in the index and how an index value is related to geophysical and statistical characteristics of drought [38]. Drought indices can be easily implemented and are extensively used in drought quantification, assessment, and monitoring. There are several review studies on the use of drought indices [3,10–13,17,22,28,31] based on both conventional and satellite data [8,9,27]. It should be noted that the progression of drought indices development emphasizes on the derivation of a number or value that can constitute an expression of drought severity. As other drought indices have also been developed, it has been assessed that not all indices can be applied in all locations, since many have been developed to address a particular problem in a certain climatic zone. In evaluating and selecting various drought indices, it is best to look at the various applications in which they are likely to be used. Many drought indices have the potential to be used in multiple applications or can be applied to various sectors. In judging the overall utility of drought indices, a set of weighted decision criteria and assigned values is constructed into each index. These criteria are based on desirable properties that an index should ideally possess, namely, robustness, tractability, transparency, sophistication, expandability, and dimensionality. The list of criteria may be expanded or condensed, but the criteria mentioned earlier provide a reasonable framework for the evaluation of drought indices without excessive complication. The criteria weights, which basically reflect the relative importance of the evaluation criteria, are difficult to be precisely justified, as their determination is ultimately affected by professional experience and personal judgment [24]. Nevertheless, the weights can be adjusted to comply with local or regional climatic or geographic conditions. Drought monitoring is an equally important issue. Given the complexity of drought phenomenon, it is necessary to know how droughts develop and what indicators are available to quantify drought identification and monitoring. Gathering information about the primary weather and climate characteristics of a region is an important first step needed to understand both the climate and drought climatology of the region in order to monitor droughts. Drought early warning systems (DEWS) focalize on monitoring drought conditions and constitute an important part for adequate drought preparation [47,48,51]. Nevertheless, DEWS for the monitoring of drought evolution and development is of critical importance in economically and environmentally sensitive regions and prove to offer very significant inputs in any drought preparedness and mitigation plan [7]. Needless to say, without adequate planning and preparedness, drought impacts may lead to even more severe consequences for many sectors. Indeed, drought forecasting and prediction, or the use of DEWS, can be considered in several ways. Indeed, prediction of the drought index value into the future could be based on either weather forecasting or climate prediction through global circulation models. Alternatively, time series analysis of drought index values could be used for drought forecasting, such as autoregressive integrated moving average (ARIMA) models, although this is a black-box modeling approach. With the basic characteristics of drought involving a lack or deficit of precipitation, it is critical to have reliable and long-term records of precipitation. Traditional methods of drought assessment and monitoring rely on rainfall data, which are usually limited in a region, often inaccurate and, most importantly, difficult to obtain in near real time [40]. If the precipitation distribution for a region is typically seasonal, then a shortage of precipitation during this time is not necessarily an indication of the beginning of a drought. Thus, it is important to determine the “crucial” period(s) of precipitation for any region. Even though precipitation is the basis of many drought indicators, many other indicators are also significant in the assessment and monitoring of drought severity. What is usually problematic is that some indicators may not have a sufficient record length, and this is usually the case with remotely sensed data. Nevertheless, it is recognized that remote sensing has gradually become an important tool for the detection of the spatial and temporal distribution and characteristics of drought at different scales. In summary, it is best to consider multiple indicators to verify the existence and severity of drought.

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3.2.3  Drought Features and Characteristics In order to assess and monitor drought hazards and to alleviate their impact, it is necessary to detect several drought features, such as severity, duration, periodicity, areal extent, onset, and end time. Indeed, conventional and/or remote sensing data and methods can be used to delineate the spatial and temporal variability of several drought features in quantitative terms [8,9,24]. A brief description of some key features follows. Severity or intensity of drought refers to the degree of the precipitation shortfall and/or the severity of impact associated with the shortfall. The severity of drought is defined as escalation of the phenomenon into classes, such as mild, moderate, severe, and extreme. The severity is usually determined through drought indicators and indices, which include the classes mentioned earlier. Indeed, the severity is measured by the departure of some climatic parameter, such as precipitation; indicator, such as reservoir level; or index, such as Palmer Drought Severity Index (PDSI), from normal and is closely linked to duration in the determination of impact. The regions affected by severe drought evolve gradually, and there is a seasonal and annual shift of the so-called epicenter, which is the area of maximum severity. There is not a single unifying technique to quantify drought severity. Even within an individual category, the supremacy of a specific index is not immediately clear. Periodicity is considered the recurrence interval of drought. Indeed, the frequency of an extreme event, such as drought, is usually expressed by its return period or recurrence interval, which may be defined as the average interval of time within which the magnitude of the event is reached or exceeded once. The magnitude of an extreme event is given by the total depth occurring in a particular duration, and data for extreme events, such as droughts, can be usually presented by severity–duration–frequency curves for several sites throughout a region [6]. Duration of a drought episode is defined as the time interval from the start to the end time expressed usually in months. Droughts usually require a minimum of 2–3 months to become established and can continue for months or years. Since drought is a complex phenomenon, the assessment of start and end time is a complicated technical subject. Moreover, the magnitude of drought impacts is closely related to the timing of the onset of precipitation deficiency, its severity, and the duration of the event. Onset or the beginning of a drought is determined by the occurrence of a drought episode. The beginning of a drought is assessed through indicators or indices reaching certain threshold value. On the other hand, end time of a drought episode signifies the termination of drought based again on threshold values of indicators or indices. It is usually difficult to determine the onset and the end time of a drought and on what criteria these determinations should be made. Moreover, it should be considered whether an end to drought is signaled by a return to normal precipitation and what is the required time period of normal precipitation to be sustained for the drought to be terminated. Similarly, one should also consider whether reservoirs and groundwater levels are required to return to average or normal conditions. Areal extent of drought is considered the spatial coverage of the phenomenon, as is quantified in severity classes by indicators or indices. Remote sensing has contributed significantly in the delineation of this parameter by counting the number of pixels in each class. It is recognized that droughts also differ by their spatial characteristics. It should be mentioned that the areal extent of severe droughts evolves gradually and varies with time, shifting from season to season and from year to year. Moreover, the climatic diversity and size of large regions, such as the United States, justify the occurrence of drought every year; however, it is not expected to affect the entire region. Nevertheless, the spatial characteristics of drought may have serious implications for several sectors of the economy, such as agriculture, energy, transportation, health, recreation and tourism, and affect land use planning.

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3.3 Meteorological Drought and Indices It is well known that a drought index is one type of climate index and ocean index is another. Nevertheless, this chapter covers the subject of meteorological drought indices. As already mentioned, meteorological drought must be considered as a region-specific natural event, since the atmospheric conditions, which prevail and develop through multiple causes resulting in precipitation deficiencies, are highly variable from region to region. Moreover, drought indices constitute an attempt to quantify and assess the severity of drought over a region by assimilating data on rainfall and other parameters, such as soil moisture, vegetation, snowpack, streamflow, or other environmental indicators into a comprehensive numerical value. This section presents a brief review of meteorological drought and drought indices, as well as a list of available meteorological drought indices, along with a description of a few indicative and widely used indices, namely, rainfall deciles, PDSI, SPI, and Standardized Precipitation Evapotranspiration Index (SPEI).

3.3.1 Meteorological Drought Meteorological drought is usually defined as the degree of dryness specified by precipitation deficiency as compared to some “normal” or average amount and by the duration of the dry period [44]. For the identification of meteorological drought, a threshold of precipitation deficiency over some predetermined period of time is usually considered. The selected thresholds of deficiency and the corresponding duration, for example, 80% of normal and 6 months, respectively, are expected to vary locally according to the existing climatic conditions. Nevertheless, the beginning of any other type of drought, such as agricultural or hydrological drought, starts with the onset of meteorological drought, which then prevails long enough to impact the agricultural and/or the hydrological sectors. As expected, there are different characteristics of meteorological drought for different regional climatic zones. Specifically, for regions characterized by year-round precipitation regimes, such as tropical or humid subtropical climates, meteorological drought may consider and identify periods of drought based on the number of days with precipitation lower than some specified threshold. On the other hand, for regions characterized by seasonal rainfall patterns, the consideration mentioned earlier seems unrealistic. Moreover, for monsoon regions, for example, actual precipitation deviations from normal may be related to average amounts on a monthly, seasonal, or annual basis.

3.3.2 Classification of Meteorological Drought Indices Meteorological drought indices can be used in the context of DEWS in order to provide timely information on drought for decision-making [13]. It should be stated that a meteorological drought index value is essentially considered far more useful than raw data, especially in the case of drought monitoring for near-real-time decision-making [36]. Moreover, several other uses of a meteorological drought index involve the assessment of thresholds for a number of drought features, such as onset, severity, magnitude, duration, and end time. Furthermore, a meteorological drought index can also be used as groundtruthing information for modeling efforts or remotely sensed detection of several drought features. A classification and grouping of drought indices is considered based on recently conducted studies and using similarity characteristics [12], namely, atmospheric drought indices, indices of precipitation anomaly, aridity indices, soil moisture indices, combined or recursive indices, and indices based on remotely sensed information. Although this classification refers to indices from all types of drought, the current presentation is restricted to meteorological drought indices. Table 3.1 presents an indicative list of available and commonly used meteorological drought indices in different classes with the corresponding reference. A brief description of the classes of meteorological drought indices follows.

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Handbook of Drought and Water Scarcity TABLE 3.1  Indicative List of Classes and Indices of Meteorological Drought Classification of Drought Indices 1. Atmospheric drought indices 1.1 Saturation deficit 2. Precipitation anomaly indices 2.1 Precipitation index

References [50] [33] [49]

2.2 Relative precipitation sum 2.3 Relative anomaly 2.4 Standardized anomaly index (SAI) 2.5 Average standard anomaly 3. Aridity indices 3.1 Lang’s rainfall index

[5]

3.2 De Martone aridity index 3.3 Ped’s drought index (PDI1) 3.4 Selyaninov’s hydrothermal coefficient 3.5 Thornthwaite index 3.6 Potential water deficit

[30] [33] [41]

3.7 Potential evaporation ratio 3.8 Aridity index: moisture available index 3.9 Relative evaporation 3.10 Surface energy balance 3.11 Bowen ratio 4. Recursive indices 4.1 Fooley anomaly index (FAI) 4.2 Bhalme–Mooley drought index (BMDI) 4.3 Palmer drought severity index (PDSI) family 4.4 Standardized precipitation index 4.5 Surface water supply index (SWSI)

[37] [14] [2] [29] [26]

4.6 Reclamation drought index (RDI) 4.7 Palmer drought index (PDI) 4.8 Palmer crop moisture index (CMI) 4.9 Keetch–Byram drought index (KBDI) 4.10 Effective drought index 4.11 Reconnaissance drought index (RDI) 5. Remotely sensed information 5.1 Crop water stress index (CWSI) 5.2 Vegetation index 5.3 Normalized difference vegetation index (NDVI) 5.4 Stress degree days

[43] [45] [19,20] [43] [18,31]

3.3.2.1 Indices of Atmospheric Drought The standard signal for a dry spell is low humidity. The water vapor saturation deficit is commonly used for the characterization of atmospheric drought, although the temporal scale for this type of analysis is usually much shorter than a month, sometimes only a few days, but the consequence of these days could be catastrophic in the case of certain species. These indices are not commonly accepted indices [33], but sometimes it is worth introducing them mainly in effective water use for irrigation. The corresponding meteorological drought index takes the simple form of a typical meteorological element, namely, the saturation deficit [50].

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35

3.3.2.2 Indices of Precipitation Anomaly Any forms of drought indices are related to some antecedent precipitation amounts. This past period of time could last from 3 or 4 weeks to years. Nevertheless, it is understood that drought usually occurs after an abnormal rainy season or period. Therefore, the simplest drought index is the deviation from a normal or average precipitation value. There are certainly some combinations, or normalization, or generalization of deviation for possibly better performance. Indeed, there have to be long-term comparisons between drought index and yield data before the establishment of any threshold value. There are several existing precipitation anomaly indices (Table 3.1). 3.3.2.3 A ridity Indices Aridity is a characteristic of climate, which is related to precipitation inadequacy to maintain vegetation. The theoretical base for the aridity index is the evapotranspiration/precipitation ratio [5]. The simplest approach is to use empirical models to estimate evapotranspiration based only on temperature or degree-days, since the difference in the aridity indices is in the approximation of the evapotranspiration. There are several types of aridity indices (Table 3.1). 3.3.2.4 Recursive Drought Indices These indices attempt to describe and express the cumulative effect of prolonged moisture deficits on a monthly basis. These indices have proven to be of high utility in the delineation of meteorologically determined droughts or dry spell, which possess a kind of memory, where actual values depend on previous values of the corresponding meteorological variables. These indices are called recursive indices due to their method of computation. There are several recursive indices including the family of PDSI (Table 3.1). 3.3.2.5 Indices Based on Remotely Sensed Parameters Most of the existing and widely used remotely sensed drought indices are based on spectral reflectance of vegetation and, thus, are mainly used as indices of agricultural drought, known as vegetation indices. Nevertheless, agricultural drought indices are outside the scope of this chapter. It is worth mentioning that in recent years, there has been significant progress and development in the field of remote sensing due to scientific and technological advances with increasing reliability on data and methods. As a general rule, it can be stated that any meteorological drought index can be converted to a remotely sensed index provided that precipitation and/or temperature are used in the index and are computed by remotely sensed algorithms or methods. Moreover, the utility of remotely sensed drought indices is expected to increase drastically in the forthcoming years due to the availability of precipitation and temperature data platforms at a global scale.

3.3.3 Description of Selected Meteorological Drought Indices From Table 3.1, and for illustrative purposes, a few commonly and widely used meteorological drought indices are presented, namely, rainfall deciles, PDSI, SPI, and SPEI. 3.3.3.1 Rainfall Deciles A rainfall decile–based system for monitoring meteorological drought has been suggested [15], where monthly precipitation totals from a long-term record are first ranked from highest to lowest to construct a cumulative frequency distribution. The median is used instead of the mean to assess the central tendency of the record. Climatological observations above and below this marker may be divided into 10  quantiles, or deciles. The distribution is then split into 10 parts (tenths of distribution or deciles). The first decile is the precipitation value not exceeded by the lowest 10% of all precipitation values in a record; the second is between the lowest 10% and 20% and the fifth decile would be the median.

36

Handbook of Drought and Water Scarcity TABLE 3.2  The Rainfall Deciles Classification Table Decile Level

Moisture Level

Deciles 1–2: Lowest 20% of data Deciles 3–4: Next lowest 20% of data Deciles 5–6: Middle 20% of data Deciles 7–8: Next highest 20% of data Deciles 9–10: Highest 20% of data

Much below normal Below normal Near normal Above normal Much above normal

Source: Gibbs, W.J. and Maher, J.V., Rainfall deciles as drought indicators, Bulletin No. 48, Bureau of Meteorology, Melbourne, Victoria, Australia, 1967.

Any precipitation value (e.g., from the current or past month) can be compared with and interpreted in terms of these deciles. A reasonably long precipitation record (30–50 years) is required for this approach. Decile indices (DIs) are grouped into five classes, two deciles per class, which are shown in Table 3.2. DI is relatively simple to calculate and requires only precipitation data and fewer assumptions than more comprehensive indices, such as PDSI. However, this simplicity can lead to conceptual difficulties. For example, it is reasonable for a drought to terminate when observed rainfall is close to or above normal conditions. But minor amounts of precipitation during periods in which little or no precipitation is routine, such as dry summer months, can activate the first stopping rule, even though the absolute quantity of precipitation is trivial and does not terminate the water deficit. Therefore, climates with highly seasonal precipitation may not be well suited to rainfall deciles when relying upon the two stopping criteria. A supplemental, third rule, which is used by the Drought Watch Service of the Australian Bureau of Meteorology, considers total precipitation, since the beginning of a drought. If this total exceeds the first decile for all such months, then the meteorological drought may be considered to have ended [24]. This method is simple but needs a long-term period of record to have the most utility. The straightforward nature automatically determines the status of the dryness for a location or region, allowing researchers to know exactly where the current precipitation regime compares historically. For the implementation of this method, certain deciles must be used as thresholds, which trigger some type of response. Having the rainfall deciles method as part of a DEWS establishes when a drought begins and ends, according to the data and characteristics of drought in the region, by defining the thresholds being used. With the flexibility of establishing thresholds based on the climate of the region, the deciles method can be used to monitor all types of drought, as it has been applied to monitor both agricultural and hydrological droughts. 3.3.3.2 SPI The SPI [26] quantifies the precipitation deficit for multiple time scales, such as for 3-, 6-, 9-, and 12-month periods, relative to the same months historically [25,38]. Ideally, at least 20–30 years of serially complete monthly values are needed with 50–60 years (or more) being more optimal and preferred [16]. The historical rainfall data of the station are fitted to a gamma distribution. This is conducted through a process of maximum likelihood estimation of the gamma distribution parameters, β and γ (Equation 3.1):



P (x)

x g -1 exp ( - x / b ) bg G ( g )

where P(x) is the probability density frequency (p.d.f.) equation x is the variable

g >0



(3.1)

37

Meteorological Drought Indices TABLE 3.3  Standardized Precipitation Index Classification Scale Standardized Precipitation Index Value

Moisture Level

+2.0 and greater +1.5 to 1.99 +1.0 to 1.49 −0.99 to 0.99 −1.0 to −1.49 −1.5 to −1.99 −2.0 and less

Extremely wet Very wet Moderately wet Near normal Moderately dry Severely dry Extremely dry

Source: Guttman, N.B., J. Am. Water Resour. Assoc., 35(2), 311, 1999.

McKee [26] used a classification system to define drought severities (intensities) resulting from the SPI (Table 3.3). The SPI is computed by dividing the difference between the normalized seasonal precipitation and its long-term seasonal mean by the standard deviation (Equation 3.2). Thus,

SPI =

Xij - Xim s

(3.2)

where Xij is the seasonal precipitation at the ith rain gauge station and jth observation Xim is the long-term seasonal mean σ is its standard deviation A drought event occurs anytime the SPI is continuously negative and reaches an intensity of −1.0 or less. The event ends when the SPI becomes positive. This is where the SPI has a great amount of utility. Each drought event, therefore, has a duration defined by its beginning and end and intensity for each month that the event continues. The positive sum of the SPI for all the months within a drought event can be termed the drought’s “magnitude.” Similar to the PDSI, SPI may be used for monitoring both dry and wet conditions. Another reason for the SPI’s appeal is that the index can be calculated with missing data. Nevertheless, the SPI is flexible and can be calculated for both short- and long-term periods by selecting different time steps. Initially, the SPI has been calculated for periods from 1 to 72 months, but it is mostly used for periods of 24 months or less. This flexibility has allowed the SPI to be very useful in monitoring not only meteorological but also agricultural and hydrological droughts, where time scales and impacts are variable. Seven classes of SPI are shown in Table 3.3. 3.3.3.3 SPEI Drought indices that also account for temperatures can help put into proper perspective how temperatures are impacting the water balance of a region. Typical examples of such indices are, respectively, the SPEI [43], which uses the difference between precipitation and potential evapotranspiration (PET), and an equivalent index, namely, the Reconnaissance Drought Index [8,9,42], which is based on the ratio between precipitation and PET. The SPEI is essentially based on the SPI and adds a temperature component for the computation of a simplified water balance. The SPEI, like the PDSI, uses a simple water balance computation, which is based on the model for calculating PET [40]. Alternatively, the Blaney–Criddle [4] method could be used for PET, which is valid mainly for dry and warm summers. Several studies have shown that good estimates of PET can be obtained using several meteorological parameters, but for drought indices this is not a requirement, since only a general estimation of the water balance is required. This also keeps the calculations simple and usable, given the additional data requirements for determining actual evapotranspiration values. Having the same flexibility that the SPI has in being able to be updated weekly

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using a moving window for each time step, the SPEI uses the difference between the basic calculations for PET and precipitation to determine a wet or dry period. Given the flexible nature of the SPEI, it has the capacity to be utilized in monitoring the different types of droughts, since the methodology includes water balance calculations. As such, it has the potential to better track agricultural drought. 3.3.3.4 PDSI One of the most widely used indices, especially in the United States, has been the PDSI [29]. The PDSI is considered an attempt to put the full water balance into a regional perspective, with the additional potential to identify meteorological and agricultural drought episodes [6,21]. Although PDSI is referred to as an index of meteorological drought, however, the procedure considers precipitation and soil moisture conditions, which are determinants of agricultural and hydrological drought, as it measures the availability of moisture in the region being monitored using a water balance equation. The PDSI incorporates antecedent precipitation, temperature, and soil moisture supply and demand based on evapotranspiration estimation [32,40], as well as a previous PDSI value. In addition, the PDSI is standardized for different regions and time periods to facilitate direct comparisons of the PDSI between different regions. Like the SPI, the PDSI has both a wet and dry categorization scheme, with most values falling into the range of +4 to −4 (Table 3.4). A brief conceptual description of the five steps for the computation of PDSI follows [17]. Step 1: Hydrological accounting. PDSI uses a two-layered model for soil moisture computations with certain assumptions concerning field capacity and transfer of moisture to and from the layers. A monthly hydrologic accounting is carried out for a long series of years using five parameters: precipitation, evapotranspiration, soil moisture loss and recharge, and runoff. Step 2: Climatic coefficients. The results of step 1 are summarized to compute four monthly coefficients, namely, evapotranspiration, recharge, runoff, and loss, which are dependent on the analyzed local climate. Step 3: CAFEC values. The series are reanalyzed using the derived coefficients to determine the amount of moisture required for “normal” weather during each month. These normal, or climatically appropriate for existing conditions (CAFEC), quantities are computed for each of the parameters listed in step 1, in order to assess the dimensionless index across space and time. Step 4: Moisture anomaly index. The precipitation departure (precipitation minus CAFEC precipitation) for each month is computed and denoted as D and then converts the departures to indices of moisture anomaly (Equation 3.3). This moisture anomaly index has come to be known as the Palmer Z index and reflects the departure of the weather of a particular month from the average

TABLE 3.4  The Palmer Drought Severity Index Classification Scale 4.0 or more 3.0 to 3.99 2.0 to 2.99 1.0 to 1.99 0.5 to 0.99 0.49 to −0.49 −0.5 to −0.99 −1.0 to −1.99 −2.0 to −2.99 −3.0 to −3.99 −4.0 or less Source: Mirabbasi, R. et al., J. Hydrol., 492, 35, 2013.

Extremely wet Very wet Moderately wet Slightly wet Incipient wet spell Near normal Incipient dry spell Mild drought Moderate drought Severe drought Extreme drought

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moisture climate for that month, regardless of what has occurred in prior or subsequent months. The equation of Z index is Z = K j × D



(3.3)

where Kj is the weight coefficient of month j D is the precipitation departure Step 5: Drought severity. In this final step, the Z-index series is analyzed to determine the beginning, ending, and severity of the drought periods. The methodology involves computing, for each month, three intermediate indices (X 1, X 2, and X 3), and a probability factor. These intermediate indices are computed by X j = 0.897 × X j -1 +



Zj 3

(3.4)

where Zj represents accumulated values of the moisture anomaly index for the driest intervals Xj is the value of PDSI for the jth month Palmer’s procedure has been initially characterized as a very satisfactory solution by jointly using precipitation and temperature as predictor variables [1,21]. The PDSI has become widely used in the United States, as well as internationally, and has been applied in countless research studies, as well as on an operational basis [23,49]. Despite several assumptions made in the water balance calculations, its other limitations and deficiencies, and the empirical nature of some of the standardized coefficients, the PDSI can be a useful tool for both research and operational drought assessment, if used appropriately and its limitations stated earlier acknowledged [1,6,23].

3.4  Discussions As already mentioned, all droughts begin with a deficiency of precipitation in a region over a period of time. These early stages of accumulated departure of precipitation from normal or expected are usually considered as meteorological drought. Indeed, meteorological drought is characterized as a regional natural event, due to the regional, and highly variable, character of the prevailing atmospheric conditions, which originate from multiple causes and result in precipitation deficiencies. A continuation of these dry conditions over a longer period of time, sometimes in association with above-normal temperatures, high winds, and low relative humidity, quickly results in impacts on agricultural and hydrological sectors (Figure 3.1). As work toward developing drought indices continues, knowing which indices work best for a region and how to apply them, it becomes critical in establishing a functional DEWS, which focalize on monitoring drought conditions through the use of drought indicators and indices [13]. The United States Drought Monitor (USDM) system uses a composite of multiple indicators covering various short- and long-term time frames, to develop a ranking methodology for drought analysis leading to a single product [39]. The USDM system has also the flexibility to integrate new tools and data and additional information, if available, in order to enhance the level of accuracy [48]. Depending on the data availability and quality for any particular area, it may be possible to utilize many drought indices that are available and determine the most suitable for any particular area or season for drought monitoring and DEWS. Using an approach that considers all the available indicators would also allow for the flexibility to implement more temperature-based indicators for drought monitoring and early warning systems. Similarly, the Drought Management Center for South East Europe, located in Ljubljana, Slovenia, conducts drought monitoring based on SPI and issues regular bulletins for the whole region [3].

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With some indices requiring large volumes of data and, thus, becoming more complex, the World Meteorological Organization (WMO) wanted to put forward a recommendation for a single meteorological drought index to be the minimum standard and starting point for every country to calculate and assess drought in order to provide more comparability between regions. An international expert workshop at the University of Nebraska (November 8–11, 2009) announced via the “Lincoln Declaration on Drought Indices” that the SPI is adopted by WMO and recommended as the drought index to be computed and used globally by National Meteorological and Hydrological Services as the common meteorological drought index [51]. The SPI computation for any region and location is based on long-term precipitation records for a desired period or window, ranging typically from 1 to 24 months. The SPI is flexible, since it is designed to quantify the precipitation deficit for multiple time scales, which reflect the impact of drought on the availability of the different water resources. Specifically, soil moisture conditions respond to precipitation anomalies on a relatively short scale. Streamflow, reservoir storage, and groundwater reflect the long-term precipitation anomalies. Indeed, a 1- or 2-month SPI can be applicable to meteorological drought, from 1 to 6 months for agricultural drought, and from 6 up to 24 months or more for hydrological drought analyses and applications. In fact, shorter time scale SPIs, that is, up to a 3-month SPI, can provide DEWS and can contribute to the assessment of drought severity. Moreover, the SPI is considered as spatially consistent, which means that there is comparability between different locations in different climates for any given SPI value. Besides the previously described advantages for using SPI globally, there are also some drawbacks that have to be considered. At first, the computation of SPI is based only on precipitation data. Moreover, there is no soil water balance component. In addition, the SPI is not applicable to climate change analysis due to lack of temperature as an input parameter, which leads to the inability even for empirical calculation of evapotranspiration.

3.5 Summary and Conclusions In this chapter, the subject of meteorological drought indices has been addressed. At first, a comprehensive presentation of drought concepts, definitions, and types has been considered. Then, a description of meteorological drought, along with its features and characteristics, has been presented, followed by the quantification of meteorological drought through the use of indices. Drought monitoring and assessment is also considered. A description of indicative and widely used meteorological drought indices is presented. The adoption of the SPI by the WMO and its recommendation to be applied universally is also discussed. There is an international need to continue working toward newer and potentially better drought indices that can also account for a changing climate in which there may be a shift in both temperature and precipitation regimes. However, drought impacts are not yet systematically recorded internationally and there are data constraints, as well as lack of sufficient and suitable data, for modeling drought hazard. Despite these current limitations and difficulties, the international interest continues for addressing drought risk and developing global drought risk models. At the present time, international efforts to develop and implement standards for drought quantification and monitoring, as well as systematically account for drought losses and impacts, constitute an important starting step toward drought risk assessment. Moreover, DEWS and disaster insurance measures are certainly critical elements of drought risk management and risk reduction. All these eventually contribute to building credible drought risk models at all scales, from local to global.

Authors Nicolas R. Dalezios is professor of agrometeorology and remote sensing, University of Thessaly, Volos, Greece, and Agricultural University of Athens, Greece (2011–today). He was professor and founding director of the Laboratory of Agrometeorology, University of Thessaly, Greece (1991–2011). He received

Meteorological Drought Indices

41

his postgraduate degrees in meteorology (Athens, 1972) and hydrological engineering (University of Delft, the Netherlands, 1974) and received his PhD in civil engineering (University of Waterloo, Ontario, Canada, 1982). He has a long-standing record in research in agrometeorology, agrohydrology, remote sensing, modeling, environmental hazards, risk assessment, and climate variability/change. He is the author or coauthor of more than 280 refereed publications and technical reports, editor and reviewer in International Scientific Journal, author of two books, editor or coeditor of 15 edited books and coauthor of 25 book chapters, and author or coauthor of numerous research articles and projects on drought analysis, monitoring, and assessment. Zoltan Dunkel is a retired meteorologist with the Hungarian Meteorological Service (OMSZ; 1977–2013). After retirement, he worked as invited lecturer of Kaposvar University (Hungary). He was president of the Hungarian Met Service (2005–2007 and 2011–2013) and scientific secretary of European commission cooperation in science and technology (EC COST) Meteorology (1998–2001). His research interests include agrometeorological modeling, use of remote sensing in agricultural meteorology, and climate change impacts to agriculture. He has been involved in international organizations, such as WMO, European Geoscience Union (EGU), and cooperation in science and technology (COST). He has participated in several international research projects, including studies on drought assessment with numerous refereed publications. He is honorary professor as well as editor and reviewer in international scientific journals. He has organized several international scientific events. He has been awarded with the Knight’s Cross of Hungarian honors and the For National Defence 1st Class Medal. Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, Iran, where he has been since 1995. He received his PhD from the University of New South Wales, Australia, under the supervision of Professor David Pilgrim. His research focuses mainly on water resources planning and management and statistical and environmental hydrology in a changing climate. Formerly, he was a visiting professor at Princeton University, New Jersey, and the University of ETH Zurich, Switzerland. On the research side, he has started a research partnership from 2014 with McGill University, Montreal, Quebec, Canada. He has contributed to more than 500 publications in journals and books or as technical reports. He is the founder and chief editor of both International Journal of Hydrology Science and Technology (Scopus, Inderscience) and Journal of Flood Engineering. He has authored more than 100 book chapters and books. Recently, Professor Eslamian has started the editorship of several handbooks published by Taylor & Francis Group (CRC Press). A three-volume Handbook of Engineering Hydrology in 2014, Urban Water Reuse Handbook in 2015, a three-volume Handbook of Drought and Water Scarcity (2017), and Underground Aqueducts Handbook (2017) are published ones.

References

1. Alley W. M. 1984. The palmer drought severity index: Limitations and assumptions, Journal of Applied Meteorology, 23: 1100–1109. 2. Bhalme, H. N. and Mooley, D. A. 1980. Large-scale drought/floods monsoon circulation, Monthly Weather Review, 108: 1197–1211. 3. Bihari, Z., Kovács, T., Lakatos, M., Móring, A., Nagy, A., Németh, Á., Szentimrey, T., and Vincze, E. 2012. Droughts in Hungary, DMCSEE Procekt, summaries, Hungarian Meteorological Service (HMS), pp. 37–41. 4. Blaney, H. F. and Criddle, W. D. 1950. Determining water requirements in irrigated areas from cli­ matological and irrigation data, USDA Soil Conservation Service, Technical Paper No. 96, USDA, Washington, DC, 48pp. 5. Budyko, M. I. 1952. Climate change and national plan of environment modification of Arid USSR Areas (in Russian), Gidrometeoizdat, Leningrad, Soviet Union.

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6. Dalezios, N. R., Loukas, A., Vasiliades, L., and Liakopoulos, H. 2000. Severity-durationfrequency analysis of droughts and wet periods in Greece, Hydrological Sciences Journal, 45(5): 751–770. 7. Dalezios, N. R., Bampzelis, D., and Domenikiotis, C. 2009. An integrated methodological procedure for alternative drought mitigation in Greece, European Water, 27(28): 53–73. 8. Dalezios, N. R., Blanta, A., and Spyropoulos, N. V. 2012. Assessment of remotely sensed drought features in vulnerable agriculture, Natural Hazards and Earth System Sciences, 12: 3139–3150. 9. Dalezios, N. R., Blanta, A., Spyropoulos, N. V., and Tarquis, A. M. 2014. Risk identification of agricultural drought for sustainable agroecosystems, Natural Hazards and Earth System Sciences, 14: 2435–2448. 10. Dunkel, Z. 2009. Brief surveying and discussing of drought indices used agricultural meteorology, Időjárás, 113: 23–37. 11. Eitzinger, J. et al. 2008. Agroclimatic indices and simulation models, in: Nejedlik, P. and Orlandini, S., eds., Survey of Agrometeorological Practices and Applications in Europe Regarding Climate Change Impacts, COST-ESF, European Commission (EC), Luxembourg City, Luxembourg, pp. 15–92. 12. Farago, T., Kozma, E., and Nemes, C.S. 1989. Drought indices in meteorology, Időjárás, 93: 45–59. 13. Farrell, D., Trotman, A., and Cox, C. 2010. Drought early warning and risk reduction: A case study of the Caribbean drought of 2009–2010, Global Assessment Report: GAR 2011 on Disaster Risk Reduction, UNISDR, Geneva, Switzerland, 22pp. 14. Fensham, R. J. and Holman, J. E. 1999. Temporal and spatial patterns in drought related tree dieback in Australian savanna, Journal of Applied Ecology, 36: 1035–1050. 15. Gibbs, W. J. and Maher, J. V. 1967. Rainfall deciles as drought indicators, Bulletin No. 48, Bureau of Meteorology, Melbourne, Victoria, Australia. 16. Guttman, N. B. 1999. Accepting the standardized precipitation index: A calculation algorithm, Journal of the American Water Resources Association, 35(2): 311–322. 17. Heim, R.R. Jr. 2002. A review of twentieth-century drought indices used in the United States, Bulletin of the American Meteorological Society, 83(8): 1149–1165. 18. Idso, S. B., Jackson, R. D., Pinter, P. J. Jr., Reginato, R. J., and Hatfield, J. L. 1981. Normalizing the stress-degree-day concept for environmental variability, Agricultural and Forest Meteorology, 32: 249–256. 19. Jackson, R. D., Idso, S. B., Reginato, R. J., and Pinter, P. J. Jr. 1981. Canopy temperature as a crop water stress indicator, Water Resources Research, 17: 1133–1138. 20. Jackson, R. D., Reginato, R. J., and Idso, S. B. 1984. Wheat canopy temperatures: A practical tool for evaluating water requirements, Water Resources Research, 13: 651–656. 21. Jankó Szép, I., Mika, J., and Dunkel, Z. 2005. Palmer drought index as soil moisture indicator: Physical interpretation, statistical behaviour and relation to global climate, Physics and Chemistry of the Earth, 30: 231–243. 22. Kanellou, E. C., Domenikiotis, C., and Dalezios, N. R. 2009. Description of conventional and satellite drought indices, in: Tsakiris, G., ed., PRODIM final report, EC, European Commission (EC), Luxembourg City, Luxembourg, pp. 23–59, 448pp. 23. Karl, T. R. 1986. The sensitivity of the Palmer Drought Severity Index and Palmer’s Z-index to their calibration coefficients including potential evapotranspiration, Journal of Applied Meteorology, 25(1): 77–86. 24. Keyantash, J. and Dracup, J. A. 2002. The quantification of drought: An evaluation of drought indices, Bulletin of the American Meteorological Society, 83(8): 1167–1180. 25. Lakatos, M., Szentimrey, T., and Bihari, Z. 2010. Analysis of long time Standard Precipitation Index series to detect the drought frequency changes in Hungary, European Conference on Applied Climatology (ECAC), September 13–17, Zürich, Switzerland.

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26. McKee, T. B., Doesken, N. J., and Kleist, J. 1993. The relationship of drought frequency and duration to timescales, Preprints, Eighth Conference on Applied Climatology, American Meteorological Society, Anaheim, CA, pp. 179–184. 27. McVicar, T. R. and Jupp, D. L. B. 1998. The current and potential operational uses of remote sensing to aid decisions on drought exceptional circumstances in Australia: A review, Agricultural Systems, 57(3): 399–468. 28. Mirabbasi, R., Anagnostou, E. N., Fakheri-Fard, A. Dinpashoh, Y., and Eslamian, S. 2013. Analysis of meteorological drought in northwest Iran using the Joint Deficit Index, Journal of Hydrology, 492: 35–48. 29. Palmer, W. C. 1965. Meteorological drought, U.S. Weather Bureau Research Paper 45, Silver Springs, MD, 58pp. 30. Ped, L. A. 1975. On the new drought and over-moistening index (in Russian), Transactions of the USSR Hydrometeorological Center, Vol. 156, Moscow, Soviet Union, pp. 19–39. 31. Rostamian, R., Eslamian, S., and Farzaneh, M. R. 2013. Application of standardised precipitation index for predicting meteorological drought intensity in Beheshtabad watershed, central Iran, International Journal of Hydrology Science and Technology, 3(1): 63–77. 32. Seguin, B., Courault, D., and Guérif, M. 1994. Surface temperature and evapotranspiration: Application of local scale methods to regional scales using satellite data, Remote Sensing of Environment, 48: 1–25. 33. Selyaninov, G. T. 1958. The nature and dynamics of the droughts, Droughts in the USSR, their nature, recurrences and impact on crops yields (in Russian), Gidrometeoizdat, Leningrad, Soviet Union. 34. Silverman, B. A. December 1986. Static mode seeding of summer cumuli: A review, in: Braham, R.R. Jr., ed., Precipitation Enhancement: A Scientific Challenge, Meteorological Monographs, Vol. 21(43), AMS (American Meteorological Society), Boston, MA, pp. 7–24. 35. Sivakumar, M. V. K., Motha, R. P., and Das, H. P., eds. 2005. Natural Disaster and Extreme Events in Agriculture, Springer, Berlin/Heidelberg/New York, 367pp. 36. Sivakumar, M. V. K., Wilhite, D. A., Svoboda, M. D., Hayes, M., and Motha, R. 2010. Drought and meteorological droughts, in: Global Assessment Report: GAR 2011 on Disaster Risk Reduction, UNISDR, Geneva, Switzerland, 26pp. 37. Skvortsov, A. A. 1950. On the question of heat and water exchange in the surface air (in Russian), Transactions of Middle Asian State University, Vol. 22, Moscow Soviet Union, No. 6. 38. Steinemann, A., Hayes, M. A., and Cavalcanti, L. 2005. Drought indicators and triggers, in: Wilhite, D. A., ed., Drought and Water Crises: Science Technology and Management Issues, Marcel Dekker Inc., New York, pp. 71–90. 39. Svoboda, M. et al. 2002. The drought monitor, Bulletin of the American Meteorological Society, 83(8): 1181–1190. 40. Thenkabail, P. S., Gamage, M. S. D. N., and Smakhtin, V. U. 2004. The use of remote sensing data for drought assessment and monitoring in Southwest Asia, Research report, International Water Management Institute, No. 85, IWMI (International Water Management Institute), Colombo, Sri Lanka, pp. 1–25. 41. Thornthwaite, C. W. 1948. An approach toward a rational classification of climate, Geographical Review, 38: 55–94. 42. Tsakiris, G. and Vangelis, H. 2005. Establishing a drought index incorporating evapotraspiration, European Water, 9(10): 3–11. 43. Tsiros, E., Domenikitios, C., and Dalezios, N. R. 2006. Aridity mapping with the use of NDVI and satellite derived degree days, in: Dalezios, N. R. and Tzortzios, S., eds., Third HAICTA International Conference on Information System in Sustainable Agriculture, COST-University of Thessaly, Volos, Greece, pp. 853–865.

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44. Vicente-Serrano, S. M., Begueria, S., and Lopez-Moreno, J. I. 2010. A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index, Journal of Climate, 23: 1696–1718. 45. Wagner, W., Borgeaud, M., and Noll, J. 1996. Soil moisture mapping with the ERS scatterometer, Earth Observation Quarterly, 54: 4–7. 46. Wilhite, D. A. and Glantz, M. H. 1985. Understanding the drought phenomenon: The role of definitions, Water International, 10: 111–120. 47. Wilhite, D. A. 2005. The role of disaster preparedness in national planning with specific reference to droughts, in: Sivakumar, M. V. K., Motha, R. P., and Das, H. P., Natural Disasters and Extreme Events in Agriculture, Springer, New York, pp. 23–37. 48. Wilhite, D. A. 2009. The role of monitoring as a component of preparedness planning: Delivery of information and decision support tools, in: Iglesias, A., Cancelliere, A., Cubillo, F., Garrote, L., and Wilhite, D., eds., Coping with Drought Risk in Agriculture and Water Supply Systems: Drought Management and Policy Development in the Mediterranean, Springer Publishers, Dordrecht, the Netherlands. 49. WMO. 1975. Drought and agriculture, WMO Technical Note 138, Geneva, Switzerland. 50. WMO. 1992. International meteorological vocabulary, WMO No. 182, Geneva, Switzerland. 51. WMO. 2011. Lincoln declaration on Drought Indices, Proceedings of Expert Meeting, June 2–4, 2010, Murcia, Spain. 52. Wu, H. and Wilhite, D. A. 2004. An operational agricultural drought risk assessment model for Nebraska, USA, Natural Hazards, 33: 1–21.

4 Hydrological Drought: Water Surface and Duration Curve Indices Manish Kumar Goyal Indian Institute of Technology Guwahati

Vivek Gupta Indian Institute of Technology Guwahati

Saeid Eslamian Isfahan University of Technology

4.1 Introduction ........................................................................................45 Drought  • Climate Change and Drought  • Drought Hazard  • Drought Classification 4.2 Hydrological Drought Characteristics and Estimation ...............49 Indices Based on Low-Flow Characteristics  • Deficit Characteristics  • Multivariate Index  • Frequency Analysis 4.3 Case Study ............................................................................................58 Study Area and Data  • Parameter Selection  • Drought Duration and Severity Calculation • Identification of the Probability Distribution Function  • Other Case Studies across the World 4.4 Summary and Conclusions ...............................................................67 Authors.............................................................................................................67 References ........................................................................................................68

Abstract  Hydrological drought is defined as significant reduction in all forms of water availability within the land phase of the hydrological cycle (e.g., surface water, snowmelt, spring flow, and groundwater). Hydrological drought occurs due to a lack of precipitation over a prolonged period resulting in lakes, reservoirs, and rivers drying up and groundwater being depleted. In this chapter, the authors discuss the basic concepts of drought, the classification of drought, and the various types of water loss due to drought. The main focus is on hydrological drought, that is, the drought related to surface water storage, whose various characteristics and indices will be explained. The chapter also includes a case study of an analysis of hydrological drought using the L-moments method on the Satluj River in Himachal Pradesh, India.

4.1  Introduction Drought is considered to be the costliest among all natural disasters. Almost 70% of the world’s population lives in drought-prone areas, which represent almost 38% of the total land area on earth. Drought in a region starts with a shortage of precipitation, which leads to a later scarcity of surface storage and soil moisture, which in turn affect the agricultural productivity of an area. For optimal management of the water resources of a country, it is necessary to understand the nature of droughts and predict their occurrence in different regions.

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4.1.1  Drought A drought is a climatic state of insufficient precipitation over a prolonged period, which brings a significant amount of social and economic loss. In addition to affecting human activities, drought may interrupt the agricultural and natural ecosystems [29]. It may extend from weeks to months and years. The implications of a drought may be physically seen in the partial or full drying out of streams and in decreases in the water levels of lakes, reservoirs, and wells [25]. As one cannot define the starting point of the hydrological cycle, so the origin of a drought cannot be stated absolutely. Conventionally, a decrease in precipitation from the average is considered as the beginning of a drought, which results in a reduction in storage volume (surface and subsurface) and fluxes involved in the hydrological cycle [27]. In general, there is no exact definition available for droughts as they vary from region to region and definition of drought depends on the perspective of the analysis. McGuire and Palmer [24] defined drought as “monthly or annual precipitation less than some particular percentage of normal.” Takeuchi [38] defined drought as the condition where the available water is less than the amount expected to satisfy human demand. McMahon and Arenas [21] defined drought as “a period of abnormally dry weather sufficiently prolonged for the lack of precipitation to came a serious hydrological imbalance and carries connotations of a moisture deficiency with respect to man’s usage of water.” According to the American Meteorological Society [1], “drought is a natural temporary feature of the climate cycle that quickly wreaks havoc on the most regions of the globe.” The National Drought Mitigation Center refers to this definition as a “conceptual definition,” which helps people to understand the term; however, it also refers to an “operational definition,” which helps to define the onset, severity, and end of droughts. Numerous operational definitions have been proposed on the basis of certain mathematical indices. The discussion so far has shown there is no exact definition of drought. For example, meteorologists identify drought as a deficit in precipitation, hydrologists as a deficit in water storage, agriculturists as a deficit in water for crops, and sociologists as socioeconomic loss. So the definition of drought depends on the focus of the analysis.

4.1.2  Climate Change and Drought According to the Intergovernmental Panel on Climate Change, climate change can be defined as “a change in state of climate that can be identified (e.g. using statistical tests) by changes in the mean and/or variability in its properties, and that persist for an extended period, typically decades as larger” [30]. A short-period phenomenon such as El Niño cannot be considered as climate change because it relates to a periodic warming of ocean water, generally occurring at an interval of 2–3 years. Recently, the emission of greenhouse gasses has increased historically. The amount of CO2 in the atmosphere has increased to 36% more than in preindustrial times and is at its highest level for the past 420,000 years [50]. Due to this huge increase in greenhouse gasses, the average temperature of the atmosphere has increased by 0.6°C around the world [50]. Such an increase in the global temperature raises the capacity of the atmosphere to store water vapor, resulting in less frequent but heavier rainfall, which increases the number of dry spells. Because of climate change, wet places are becoming wetter, while dry places are becoming drier [6]. Also, as there is more concentration of greenhouse gasses over land masses, so evapotranspiration is increasing in the atmosphere over these regions. This increased amount of water vapor in the atmosphere prohibits the ingression of vapor from the ocean, which creates drier conditions over land masses [6].

4.1.3  Drought Hazard A hazard can be defined as a physical event that creates loss to life, property, biodiversity, or economy. A hazard can be natural or may be man-made. Other natural hazards such as earthquakes, volcanic eruptions, and floods are very short-term phenomena, but droughts can prolong for years [44]. Thus, proper

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estimation of drought severity and duration is required for the planning of the water resources of a country [49]. Nagarajan [25] suggests that the perception of the extent of a drought varies according to the degree of aridity that has been seen in the past, as well as the personality, age, educational level, and type of occupation of the individual. Historically, drought has caused plenty of devastation in the form of economic, environmental, and social loss. 4.1.3.1  Economic Losses Long-term and severe drought may harm a country’s economy in the form of losses to agricultural production, livestock production, timber production, and fishery production: • Losses to agricultural production. Reduced amount of precipitation causes harm to annual or perennial crops and reduces yield, which leads to an income loss to farmers. Because of low streamflows, farmers have to bear higher irrigation costs. Insect infection and plant diseases are also potential threats of drought. • Losses to livestock production. Because of lack of water, productivity of rangeland decreases, leading to closure or the limitation of public land to grazing, resulting in high cost/unavailability of feed for livestock and in increased feed transportation costs. Sometimes, livestock producers also have to bear the cost of new or supplementary water resources (wells, pipelines, dams, etc.). Reduced milk production, high livestock mortality rate, and disruption of reproduction cycles are also side effects of drought [23]. • Losses from timber production. Drought reduces the humidity in the air, which enables the spreading of forest fires. Reduced soil moisture lowers the productivity of forest land, which results in the mortality of young trees. • Losses of fishery production. Low streamflows damage fish habitats, which results in the loss of fish and other aquatic animals. • Losses in power generation. Because of low streamflow, water in dams falls below the threshold for electricity generation, necessitating the country to produce electricity by some other means (e.g., thermal, nuclear), which may have some limitations. 4.1.3.2  Environmental Losses Drought carries a high risk of causing environmental and ecological imbalances. It may endanger animal species, plant communities, and the hydrology of the area. Drought also creates a potential threat of famine and desertification: • Damage to animal species. During a drought period, because of food scarcity and lack of drinking water, wild animals start moving into nearby villages and cities, which results in greater mortality rates. Animal diseases and increased stress to endangered species cause great harm to biodiversity. • Hydrological effects. The primary impact of drought on the hydrology of catchment areas is decreased water levels in river streams and reservoirs, resulting in an increase in the concentration of salts, which affects water quality. Loss of wetlands is also one of the after-effects of drought. • Damage to plant communities. Reduced soil moisture availability leads to forest dieback in urban landscapes and shelterbelts. During a drought period, the number of forest fires also increases, which results in a loss of biodiversity. • Desertification. “Desertification means land degradation in arid, semiarid and dry sub humid areas resulting from various factors including climate variation and human activities” (UNCED, Agenda 21, 1992) [43]. It is the process of the conversion of a productive fertile land to a nonproductive infertile deserted land owing to overgrazing, deforestation, and extreme climatic events [14]. During a drought period, the area of grazing land decreases, resulting in overgrazing. Fires reduce the area of forest. As vegetation decreases, the soil holding capacity of roots decreases, and hence the soil becomes more prone to weathering by air, which causes desertification.

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4.1.3.3 Social Losses Social losses due to drought are generally considered losses on the health, quality of life, and safety of the people: • Health. Drought decreases crop yield, which affects the financial health of farmers, which is also affected by increased interest rates, decreased goods prices, and unfavorable exchange rates. Environmental degradation also increases mental stress [36], so the number of suicides increases during periods of drought. Degraded quality of water, low nutrition content, and dying animals in cities increase diseases, resulting in higher mortality rates. • Increased conflicts. Reduced availability of water increases user conflicts, political conflicts, and managerial conflicts. • Famine. Famine is the condition of low food production over a prolonged period caused either by natural hazards or by wars or by both [22]. During drought periods, reduced crop yield creates a condition of low food availability, which, if it continues for a long period, causes high morbidity and mortality rates, which in turn result in famine.

4.1.4 Drought Classification A number of classification systems for drought are available in the literature. Drought can be classified according to the perspective of the study, the period of occurrence. 4.1.4.1  Based on the Study Perspective Wilhite and Glantz [48] classified drought into four categories, namely, meteorological, hydrological, agricultural, and socioeconomic. The first three approaches basically deal with physical phenomena such as rainfall, evapotranspiration, and streamflow, and the last deals with the shortage of goods that depends on water. Meteorological Drought 4.1.4.1.1  Meteorological drought mainly deals with deficits in precipitation (compared with average precipitation) and generally occurs at the regional scale, being measured with respect to time. Although the definition changes from region to region, it can be measured at the level of season, year, and decade [25,35]. Some definitions suggest that drought occurs if some specific threshold days pass without rainfall. This definition is only valid in places of year-round precipitation, such as England and Brazil, but in places such as the central United States or West Africa, where the rainfall pattern is seasonal, or in dry places such as Egypt or Chile, the same definition of “some specific threshold days” is not valid. However, numerous meteorologists accept the meteorological drought as a shortfall in rainfall over the time frame of the month, season, or year. 4.1.4.1.2  Hydrological Drought Hydrological drought is defined as a period of deficit in water in hydrological sources such as rivers, streams, lakes, and wells. The term “hydrological drought” should not be confused with “low-flow period,” which is the annual cycle of streamflow; that is, this low-flow period comes once or twice every year depending on the climatic conditions. For example, an equatorial climate has two rainy and two dry seasons, which results in two high-flow periods and two low-flow periods [21]. However, a monsoon climate has a single wet season and so has one low-flow period and one high-flow period, while a hydrological drought is an extended period of infrequent low streamflow and groundwater flow. Hydrological drought can be further subdivided into groundwater drought and streamflow drought. Meteorological drought is the starting point of any type of drought. A deficit in precipitation causes a deficit in soil moisture, streamflow, and reservoir levels, which is immediately reflected as agricultural drought and hydrological drought. However, a reduced amount of precipitation alone cannot be responsible for other droughts because this is only an input factor; other output factors in the form of water loss

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also play a great role in the occurrence of drought. For example, if in any year the precipitation in any region is normal but, in that year only, the government builds a dam upstream of the river and there is no or less supply downstream, then that would cause a hydrological drought, which is generally measured in the catchment area or at river basin level. 4.1.4.1.3  Agricultural Drought Agricultural drought represents an inadequate amount of soil moisture to fulfill the needs of crops during the growing season [8]. It is basically a link between various categories of drought, such as meteorological drought and hydrological drought, and their impact on agriculture [28]. Agricultural drought is generally interpreted as physiological drought, which represents a deficiency of water in the soil and air. 4.1.4.1.4  Socioeconomic Drought Socioeconomic drought mainly relates to the supply and demand of the commodities that are dependent on water [16]. The situation is said to be a drought if either the supply of a particular commodity has decreased or the demand has increased. The supply of many commodities such as food grains, water, fish, and hydroelectric power depends on the weather. In some cases, socioeconomic drought may lag some time behind the occurrence of meteorological drought. For example, in the case of hydroelectric power generation, water shortage might not happen suddenly following meteorological drought or hydrological drought because there may be sufficient storage in the reservoir for power production [10]. 4.1.4.2 Based on Period of Occurrence On the basis of the period of occurrence, drought can be classified into three types [2]: 1. Areas of permanent drought. Areas of permanent drought include permanently dry, arid, and desert regions. Because of insufficient rainfall and a lack of irrigation facilities, only vegetation such as cactus, xerophytes, and thorny shrubs generally grows in these regions. 2. Seasonal drought. This occurs in regions with clearly defined rainy (wet) and dry climates (monsoon regions) and may be the result of large-scale seasonal circulation. 3. Contingent drought. This is the result of irregular and variable rainfall, especially in humid and subhumid regions. The occurrence of such droughts may coincide with large growth periods of crops when water requirements are critical and impacts are the greatest, that is, in the form of yield reduction.

4.2  Hydrological Drought Characteristics and Estimation Before looking in depth at drought indices, we will first consider the concept of “index” in general. An index is just an indicator that can be used to interpret and spot some phenomenon. It is basically a quantitative measurement given as a single numeric value, which is generally computed from a large amount of data arrays. Indices are generally oversimplified quantitative measurements of a physical phenomenon. According to Friedman [13], an index can be said to be a good drought index if its time scale is appropriate for describing the problem, if it can quantify a large-scale long-term drought, and if a historical record is either available or can be computed. Hisdal et al. [18] suggested studying hydrological drought in two ways: as low-flow characteristics and as deficit characteristics.

4.2.1  Indices Based on Low-Flow Characteristics 4.2.1.1  Flow Duration Curve and Percentiles A flow duration curve (FDC) is a graphical representation of the relationship between the streamflow magnitude and its daily, weekly, and monthly frequency for a particular river basin. An FDC provides a simple graphical overview of the historical variability of streamflow in a river basin [45].

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An FDC displays what percentage of time within the whole period the value of discharge was greater than the observed value. This can be represented as a plot of discharge above its exceedance frequency (the percentage of time a value is equaled or exceeded). If a discharge is exceeded p% of the time, then this value can be said to be a p-percentile of FDC, Qp. For using FDC as a hydrological drought index, one needs to define a certain threshold that can work as an index and can represent the low-flow regime. Generally, a high frequency of exceedance, such as a 95-, 90-, or 70-percentile of FDC (Q95, Q90, or Q70), is used as a threshold for representing a drought event. For calculating the FDC, the data are first arranged in decreasing order; the rank, i, is assigned to each value in descending order; that is, the highest value will have rank 1 and the lowest will have N in the dataset of N. If x is the percentage of data that exceeds a value, then

x=

i N

(4.1)

The percentile Qp will be

(

Q p = Q min ( x ³ p )

)

(4.2)

4.2.1.2 Mean Annual Minimum n-Day Discharge Method The annual minimum (AM) n-day discharge is considered to be the smallest average discharge of consecutive n-day time series (n-day filter). It can be easily calculated by moving an n-day filter over a daily time series of discharge and selecting its minimum. So in this manner, one can obtain a time series that can be used for low-flow analysis. Generally, 1, 7, 10, and 30 days are used as the length of the n-day filter; however, Hisdal et al. [18] recommended using a moving average (MA) interval of 10 days. The mean AM n-day discharge (MAM [n-day]) is the average of the AM (n-day) time series and is one of the most frequently used hydrological indices. Generally, MAM is recommended over FDCs because it implies the duration aspect also.

4.2.2 Deficit Characteristics 4.2.2.1 Threshold Level Method According to Yevjevich [52], drought is the period during which the water supply is less than the water demand. A time series of deficit, Y(t), can be prepared using Equation 4.3, where S(t) and D(t) refer to storage and demand at time t, respectively:

Y ( t ) = S ( t ) - D ( t )

(4.3)

The threshold level method is based on the theory of runs. A drought event can be considered as the uninterrupted sequence of the negative difference of supply and demand. However, the statistical analysis of Y(t) is difficult because the supply is either a stochastic process or a periodic stochastic process, and also because the demand is a trend stochastic process, which results in Y(t) containing both periodicity and stochasticity. It is difficult to apply the theory of runs to a trend– periodic stochastic process [53]. In order to resolve this statistical problem, Yevjevich considered the demand as constant, Q0, and defined the drought as the event when the supply was less than this constant threshold demand (Figure 4.1). The threshold can be selected in a number of ways, but mainly, the selection depends on the type of water deficit to be studied [8]. In cases such as reservoir-specific yield, the threshold can be considered as a well-defined flow value; sometimes, it can also be considered as some percentage mean flow or a percentile of the FDC.

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Hydrological Drought

Flow

1500

Fixed threshold Daily demand Stream flow

1000

500 Water shortage

Drought total deficit Time (days)

FIGURE 4.1  Definition of low-flow and drought characteristics.

The threshold can be fixed or variable; it is interpreted as fixed if a constant value, Q 0, is used as the threshold over the whole time series. For seasonal drought, two different thresholds for summer and winter drought may be defined; however, while considering only a winter or summer time series, threshold can be regarded as fixed. Generally, monthly flow can be considered as a variable threshold. Originally, Yevjevich [52] suggested the temporal resolution of the time series as 1 month or longer; however, a later number of studies used daily discharge time series [4,39,40,54] and suggested a daily time scale as more powerful in analyzing a stochastic seasonal drought event (within a year). However, the use of a daily time series introduces problems of interdependency of consecutive drought events and of the arrival number of minor droughts. Sometimes, if a short-period high flow comes between two prolonged drought events, then these two droughts can be said to be dependent droughts (Figure 4.2). Moreover, sometimes, the introduction of short periods of high flow in between a prolonged drought period may generate a series of minor drought events, which may lead to a false drought frequency analysis. For avoiding these problems such as dependency of drought and minor drought, pooling between mutually dependent droughts is required to identify one independent drought. Tallaksen et al. [39] suggested three pooling procedures: the MA procedure, the sequent peak algorithm (SPA), and the interevent time and volume criterion (IC). 4.2.2.2 Interevent Time and Volume Criterion The interevent criterion is based on the concept that two drought events can be considered as mutually dependent if the interevent time and excess volume between them are less than the specific predefined critical duration and excess volume. And if two consecutive drought events, ei and ei+1, are mutually dependent, then these should be pooled as a single large drought event.

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Handbook of Drought and Water Scarcity

Threshold

Dependent drought

Minor droughts Time (days)

FIGURE 4.2  Dependent and independent drought definition.

Zelenhasic and Salvai [54] used only interevent criteria and suggested that two drought events can be mutually dependent if ti £ t c



(4.4)

where τ i is the interevent time period tc is the critical duration Zelenhasic and Salvai [54] used a critical duration of 6 days. The interevent volume criterion can be selected in a number of ways. It can be taken as an absolute value in m 3 or it can be taken as a fraction, p c , of the preceding drought’s deficit volume. Tallaksen et al. [39] analyzed streamflow drought events in two perennial streams in Denmark and found tc to be 5 days and pc to be 0.01. They used the following definition of pooled total drought duration, dpool, and pooled total deficit volume, vpool: dpool is the duration between the time when the first drought event started and the time when the last drought event ended:

d pool = di + di +1 + ti

(4.5)

where di is the duration of drought event ei di+1 is the duration of the drought event ei+1 τ i is the time between two drought events ei and ei+1 Pooled total deficit volume, vpool, is the difference between the sum of the single deficit volumes and the interevent excess volume:

v pool = vi + vi +1 - si

(4.6)

where vi and vi+1 are the deficit volumes of drought events ei and ei+1, respectively. Si is the interevent excess volume.

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However, Zelenhasic and Salvai [54] did not consider interevent duration and interevent excess volume in defining dpool and vpool. They defined the drought characteristics as follows:

d pool = di + di +1

(4.7)



v pool = vi + vi +1

(4.8)

Since vi and di are much greater than si and τ i, respectively, the results of both methods differ only slightly. However, they can neither be equated nor compared: only results from the same method can be used for comparison. 4.2.2.3 Moving Average The MA process is a tool to smoothen the time series over an n-day period. An MA filter is passed through the whole time series that simply smoothes it since discharge on a particular day is replaced by the average of n-days before and after that day. So, in this way, a short excess flow period between two drought events and a minor drought between two excess flow periods can be removed. The main advantage of the MA method is that, on the one hand, it reduces the problem of minor droughts and, on the other hand, it does the pooling between two mutually dependent events. However, the choice of the value of the n-days is critical. Too large a value of n-day may lead to a danger of generating dependency between two independent drought events, and too small a value may lead to the inability to remove the minor drought events. Tallaksen et al. [39] and Hisdal et al. [16] suggested the MA period to be 10 days. 4.2.2.4 Sequent Peak Algorithm The SPA, which is equivalent to the mass curve, is the most commonly used procedure for designing a storage reservoir based on the daily discharge series. It can be derived from a time series of maximum deficit. A cumulative deficit water volume is calculated for a given time period, which represents the total water requirement in the reservoir to maintain the minimum discharge at the level of threshold q0 at that time. Let qt denote the daily inflow in the reservoir and q0 the threshold of the desired yield, then the storage, wt (in units of discharge), at the beginning of time period t, can be given as



ìïwt -1 + qt - q0 wt = í îï0

if positive otherwise

(4.9)

When the value of qt is below q0, the value of deficit volume, wt, increases with time and the storage in the reservoir decreases; when the inflow increases beyond q0, the storage in the reservoir starts increasing and the value of the deficit volume, wt, starts decreasing. If high input continues up to a time when the reservoir reaches its original level or the value of wt reaches 0, then a drought can be said to have finished. The value of maximum wt (in units of discharge) can also be converted to max vt (in units of volume). For using the SPA as the pooling procedure, a period of deficit between two consecutive days when wt = 0 can be considered as a single drought. The total required storage during the period of drought is max{wt}, which can restore the reservoir storage to the original level, so max{wt} can be defined as the drought deficit volume, si, and the period between time τ 0 (corresponding to the first positive value of wt) and τ max (the time corresponding to the maximum deficit value, w max) can be defined as a drought of duration (τ max − τ 0 + 1 = di). The main advantage of the SPA is that the method does not have any initial parameter to be calculated, as in the case of the MA or IC method. However, in this method, there arises the problem of too many minor droughts. Kjeldsen et al. [19] suggested up to 40% more small drought events, which may create complications in the drought frequency analysis. However, the choice of a value of 40% is arbitrary and can be considered as the parameter of the method.

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4.2.3  Multivariate Index A number of multivariate indices have been proposed for quantifying hydrological drought. Some important ones are discussed in this section. 4.2.3.1  Surface Water Supply Index The surface water supply index (SWSI) [34] is one of several multivariable hydrological drought indices. It was developed as a complementary index to the Palmer drought severity index (PDSI). The PDSI, when developed, performed very well in most parts of the United States, but, in the western part, where the hydrology is highly dependent on the snowpack accumulation and runoff, which the PDSI did not account for, results were unsatisfactory. The SWSI was mainly designed to accommodate mountain water–dependent areas that mainly depend on snowmelt runoff. Thus, the SWSI and PDSI, when used together, reflect overall moisture conditions completely and accurately. The SWSI helps water resource engineers to compare the water supply in the different catchment areas and also to assess drought severity in different parts of the United States. Basic data requirements for calculating the SWSI are historical time series of precipitation, streamflow and reservoir water levels, and monthly time series of snowpack and frequency distribution for all type of data series and also for all selected basins. The formula for calculating the SWSI can be given as



é( a ´ PN SP ) + (b ´ PN PCP ) + ( c ´ PN RS ) - 50 ù û SWSI = ë 12

(4.10)

PN represents the nonexceedance probability (%) SP, PCP, and RS represent the snowpack, precipitation, and reservoir storage, respectively a, b, and c are the weights for the snowpack, precipitation, and reservoir storage, respectively The value of each weight changes from month to month and represents the approximate contribution of different sources to the surface water supplies of the basin (a + b + c = 1). For centering the sum of weighted nonexceedance probabilities about zero, a value of 50% is deducted from the numerator. Division by 12 compresses the range of the index to between −4.2 and +4.2, which makes the range equivalent to the PDSI. As frequency analysis of very extreme values is not very reliable, exceedance probabilities greater than 99% and less than 1% are generally not considered in the analysis; so, although theoretically the SWSI ranges between −4.2 and +4.2, operationally it lies between −4.1 and +4.1. Drought classification scales based on SWSI values are given in Table 4.1. 4.2.3.2 Streamflow Drought Index Most of the indices available for analyzing hydrological droughts, such as the Palmer hydrological drought index (PHDI) and the SWSI, either need a long data series with a very fine resolution on the TABLE 4.1  Drought Classification according to Values of SWSI SWSI

Drought Type

+4.0 +2.0 −1.0 −2.0 −3.0 −4.0

Abundant supply Near normal Water availability task force activated Moderate drought Severe drought Extreme drought

Source: Shafer, B.A. and Dezman, L.E., Development of a Surface Water Supply Index (SWSI) to assess the severity of drought conditions in snowpack runoff areas, Proceedings of the Western Snow Conference, Colorado State University, Fort Collins, CO, 1982, pp. 164–175.

55

Hydrological Drought TABLE 4.2  Drought Classification according to Values of SDI SDI

Drought Type

SDI ≥ 0 −1 ≤ SDI –0.84 and 18,000

≤30 30–100 100–200 200–500 500–1000 1000–2000 2000–4000 >4000

(c)

(d)

FIGURE 11.8  Regionalization of critical drought return period over Iran for the following periods: (a) 1981–2010, (b) 2011–2040, (c) 2041–2070, and (d) 2071–2100.

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11.5  Summary and Conclusions In this chapter, several studies on drought monitoring and modeling in different parts of and all of Iran have been reviewed and discussed. Over the last two decades, Iranian researchers have published a large number of articles regarding drought, suggesting the importance of this natural disaster in the decline of water resources of the country. The main points from this chapter can be summarized as follows: • An important point of these researches is that the majority of them have not been financially supported or ordered by a university, an institute, or an organization in the country, and the subjects have been only interesting to the researcher(s). It means that most of the researches on drought are not proportional to the needs of the country or do not resolve the country’s problems in coping with drought impacts. • Our knowledge about droughts that occurred in the distant past (the period before meteorological factors began to be measured) in Iran is poor. It is necessary to reconstruct historical droughts using proxy data such as tree rings data collected from trees sensitive to climatic elements. Although limited researches have been conducted on precipitation and temperature data reconstructing through tree rings in a few parts of the country, we could not find, up to this time, more than one work [62] done on reconstructing drought indices for the last two centuries in the west of Iran. • Many researches have been conducted on monitoring and modeling droughts but are less connected to the impacts of drought. Drying lakes, rivers, wells, and qanats in many parts of the country in the last decades confirm that despite the rapidly growing number of drought studies, we could not succeed in coping with drought impacts. For the ongoing and suitable management of water resources of the country, it is valuable to find ways for linking drought severity to its effects on different land sources.

Authors Javad Bazrafshan is an associate professor of agrometeorology in the Department of Irrigation and Reclamation Engineering at the University of Tehran, Karaj, Iran. He completed his PhD from the University of Tehran, supervised by Professor Dr. Ali Khalili, in 2009. His research interests have focused on drought monitoring and modeling for 15 years from 2001 to the present. He has authored or coauthored many journal articles at national and international levels and has supervised MSc and PhD theses in the field of drought monitoring and modeling in Iran. Recently, Dr. Bazrafshan conducted the project “Design of the National Drought Monitoring Portal” with the contribution of I.R. in collaboration with the I.R. Meteorological Organization. Somayeh Hejabi is a PhD student of agrometeorology at the University of Tehran, Iran. She is the top student in the PhD course, as she was in the MSc course. She worked on the “issue of drought forecasting in diverse climates of Iran” as the subject of her MSc thesis. Now, she is working on her PhD thesis, titled “Development of a Water-Energy Balance Model in the Framework of the Palmer Drought Severity Index.” She has authored or coauthored several journal articles at national and international levels. Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, Iran, where he has been since 1995. He received his PhD from the University of New South Wales, Australia, under the supervision of Professor David Pilgrim. His research focuses mainly on water resources planning and management and statistical hydrology in a changing climate. In recent years, he has been working on modeling water reuses, climate change and variability, IWRM, sustainable agriculture, resilience and vulnerability research, and natural resources governance and management. Formerly, he was a visiting professor at Princeton University, USA, and the University of ETH Zurich, Switzerland. On the research side, he has started research partnership from 2014 with McGill University, Canada. He has contributed to more than 500

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publications in journals and books or as technical reports. He is the founder and chief editor of both International Journal of Hydrology Science and Technology (Scopus, Inderscience) and Journal of Flood Engineering. His professional experience includes being on the editorial boards and a reviewer of about 40 Web of Science (ISI) journals. He has authored more than 100 book chapters and books. Recently, he has started the editorship of several handbooks published by Taylor & Francis Group (CRC Press). A  three-volume Handbook of Engineering Hydrology (2014), Urban Water Reuse Handbook (2015), a three-volume Handbook of Drought and Water Scarcity (2017), and Underground Aqueducts Handbook (2017) are published ones.

References

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15. Brittlebank, W. 1873. Persia during the Famine: A Narrative of the Tour in the East and of the Journey Out and Home, Scholar’s Choice, London, U.K. 16. Byun, H. R. and Wilhite, D. A. 1999. Objective quantification of drought severity and duration, Journal of Climate, 12: 2747–2756. 17. Byzedi, M., Saghafian, B., Mohammadi, K., and Siosemarde, M. 2014. Regional analysis of streamflow drought: A case study in southwestern Iran, Environmental Earth Sciences, 71: 2955–2972. 18. Cohen, W. and Fiorella, M. 1998. Comparison of methods for detecting conifer forest change with thematic mapper imagery, in: Lunetta, R. S. and Elvidge, C. D., eds., Remote Sensing Change Detection: Environmental Monitoring Methods and Applications, Ann Arbor Press, London, U.K., pp. 89–102. 19. Dai, A. 2011. Drought under global warming: A review, Wiley Interdisciplinary Reviews Climatic Change, 2(1): 45–65. 20. Damberg, L. and AghaKouchak, A. 2014. Global trends and patterns of droughts from space, Theoretical and Applied Climatology, 117(3): 441–448. 21. Dastorani, M. L. and Afkhami, H. 2011. Application of artificial neural networks on drought prediction in Yazd (Central Iran), Desert, 16: 39–48. 22. De Planhol, X. 2012. Famines, in: Yarshater, E., ed., Encyclopedia Iranica, IX/2, Encyclopaedia Iranica Foundation, New York, pp. 203–206. 23. Dezfuli, A. K., Karamouz, M., and Araghinejad, S. 2010. On the relationship of regional meteorological drought with SOI and NAO over southwest Iran, Theoretical and Applied Climatology, 100: 57–66. 24. Dinpashoh, Y. 2002. Study of meteorological droughts in Iran using pattern analysis. PhD thesis in Water Engineering, University of Tabriz, Tabriz, Iran. 25. Ebrahimpour, M., Rahimi, J., Nikkhah, A., and Bazrafshan, J. 2015. Monitoring agricultural drought using the Standardized Effective Precipitation Index, Journal of Irrigation and Drainage Engineering, 141(1): 04014044. 26. Ebrahimzadeh, S., Bazrafshan, S. J., and Ghorbani, Kh. 2013. Study of the identification of the variations in plant vegetation using remote sensing and ground-based drought indices (case study: Kermanshah province), Iranian Journal of Agricultural Meteorology, 1(1): 37–48. 27. Eslamian, S., Hassanzadeh, H., Abedi-Koupai, J., and Gheysari, M. 2012. Application of L-moments for regional frequency analysis of monthly drought indices, Journal of Hydrologic Engineering, 17(1): 32–42. 28. Eslamian, S., Ghasemizadeh, M., Biabanaki, M., and Talebizadeh, M. 2010. A principal component regression method for estimating low flow index, Water Resources Management, 24: 2553–2566. 29. Farokhnia, A., Morid S., and Byun H. R. 2011. Application of global SST and SLP data for drought forecasting on Tehran plain using data mining and ANFIS techniques, Theoretical and Applied Climatology, 104(1–2): 71–81. 30. Fatehi Marj, A. and Meijerink, A. M. J. 2011. Agricultural drought forecasting using satellite images, climate indices and artificial neural network, International Journal of Remote Sensing, 32(24): 9707–9719. 31. Ghorbani-Aghdam, M., Dinpashoh, Y., and Mostafaeipour, A. 2013. Application of factor analysis in defining drought prone areas in Lake Urmia Basin, Natural Hazards, 69: 267–277. 32. Golian, S., Mazdiyasni, O., and AghaKouchak, A. 2015. Trends in meteorological and agricultural droughts in Iran, Theoretical and Applied Climatology, 119(3–4): 679–688. 33. Heidari, N. 2014. Meteorological drought risk analysis under climate change using copulas in the region of Iran. MSc thesis, University of Tehran, University College of Agriculture and Natural Resources, Karaj, Iran.

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34. Heim, R. R. 2002. A review of twentieth-century drought indices used in the United States, Bulletin of the American Meteorological Society, 84: 1149–1165. 35. Hosseini-Moghari, S. M. and Araghinejad, Sh. 2015. Monthly and seasonal drought forecasting using statistical neural networks, Environmental Earth Sciences, 74: 397–412. 36. Jalali, L., Bazrafshan, J., and Tavakoli, A. 2013. The assessment of a Crop-Specific Drought Index (CSDI) for rainfed wheat crop (case study: Maragheh), The International Conference on Plant, Water, Soil and Weather Modeling, Kerman, Iran, May 8–9. 37. Jalalkamali, A., Moradi, M., and Moradi, N. 2015. Application of several artificial intelligence models and ARIMAX model for forecasting drought using the Standardized Precipitation Index, International Journal of Environmental Science and Technology, 12: 1201–1210. 38. Jamshidi, H., Rezaeian Zadeh, M., Abghari, H., Khalili, D., and Singh, V. P. 2009. Multilayer perceptron networks for streamflow forecasting, ICWR Conference on Water Research, August 16–18, Vol. 1, University of Shah Rood, Shah Rood, Iran, pp. 665–670. 39. Kao, S. C. and Govindaraju, R. S. 2010. A copula-based joint deficit index for droughts, Journal of Hydrology, 380: 121–134. 40. Karamouz, M., Torabi, S., and Araghinejad, S. 2004. Analysis of hydrologic and agricultural droughts in central part of Iran, Journal of Hydrologic Engineering, 9(5): 402–414. 41. Katiraie-Boroujerdy, P. S., Nasrollahi, N., Hsu, K., and Sorooshian, S. 2015. Quantifying the reliability of four global datasets for drought monitoring over a semiarid region, Theoretical and Applied Climatology, 123(1): 387–398, doi:10.1007/s00704-014-1360-3. 42. Kazemzadeh, M. and Malekian, A. 2015. Spatial characteristics and temporal trends of meteorological and hydrological droughts in northwestern Iran, Natural Hazards, 80(1): 191–210, doi:10.1007/ s11069-015-1964-7. 43. Khalili, A. 2004. The climatology of Iran, in: Banaei, M. H., Bybordi, M., Moameni, A., and Malakouti, M. J., eds., The Soils of Iran, Soil and Water Research Institute, Tehran, Iran, pp. 24–71. 44. Kousari, M. R., Dastorani, M. T., Niazi, Y., Soheili, E., Hayatzadeh, M., and Chezgi, J. 2014. Trend detection of drought in arid and semi-arid regions of Iran based on implementation of reconnaissance drought index (RDI) and application of non-parametrical statistical method, Water Resources Management, 28(7): 1857–1872. 45. Mansouri Daneshvar, M. R., Bagherzadeh, A., and Khosravi, M. 2013. Assessment of drought hazard impact on wheat cultivation using standardized precipitation index in Iran, Arabian Journal of Geosciences, 6: 4463–4473. 46. Massah Bavani, A. R., Poormohammadi, S. M., Dastorani, T. M., and Rahimian, H. 2011. Assessment of potential climate change impacts on drought indicators (case study: Yazd station, Central Iran), Desert, 16(2): 157–166. 47. McKee, T. B., Doesken, N. J., and Kleist, J. 1993. The relationship of drought frequency and duration to time scales, Proceeding of Eighth Conference of Applied Climatology, American Meteorological Society, Boston, MA, pp. 179–184. 48. Melville, C. 1984. Meteorological hazards and disasters in Iran: A preliminary survey to 1950, Iran, 22, 113–150. 49. Memarian, H., Pourreza Bilondi, M., and Rezaei, M. 2015. Drought prediction using co-active neuro-fuzzy inference system, validation, and uncertainty analysis (case study: Birjand, Iran), Theoretical and Applied Climatology, 125(3): 541–554, doi:10.1007/s00704-015-1532-9. 50. Meyer, S. J., Hubbard, K. G., and Wilhite, D. A. 1993. A crop specific drought index for corn, I. Model development and validation, Agronomy Journal, 85(2): 388–395. 51. Mirabbasi, R., Anagnostou, E. N., Fakheri-Fard, A., Dinpashoh, Y., and Eslamian, S. 2013. Analysis of meteorological drought in northwest Iran using the Joint Deficit Index, Journal of Hydrology, 492: 35–48.

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52. Mirabbasi, R., Fakheri-Fard, A., and Dinpashoh, Y. 2012. Bivariate drought frequency analysis using the copula method, Theoretical and Applied Climatology, 108: 191–206. 53. Mirakbari, M., Ganji, A., and Fallah, S. R. 2010. Regional bivariate frequency analysis of meteorological droughts, Journal of Hydrologic Engineering, 15(12): 985–1000. 54. Mishra, A. K. and Desai, V. R. 2006. Drought forecasting using feed-forward recursive neural network, Ecological Modeling, 198: 127–138. 55. Mishra, A. K. and Singh, V. P. 2011. Drought modeling—A review, Journal of Hydrology, 403(1–2): 157–175. 56. Modarres, R. 2007. Streamflow drought time series forecasting, Stochastic Environmental Research and Risk Assessment, 21: 223–233. 57. Mohammadian, A., Koohi, M., and Adinehbeighi, A. 2010. Comparison of drought monitoring using the SPI, DI, PNI and their regionalization (case study: North Khorasan Province, Iran), Journal of Soil and Water Conservation, 17(1): 177–184 (in Farsi). 58. Mokhtari, A. H., Adnan, R., and Busu, I. 2013. A new approach for developing comprehensive agricultural drought index using satellite-derived biophysical parameters and factor analysis method, Natural Hazards, 65: 1249–1274. 59. Moradi Dashtpagerdi, M., Kousari, M. R., Vagharfard, V., Ghonchepour, D., Esmaeilzadeh Hosseini, M., and Ahani, H. 2015. An investigation of drought magnitude trend during 1975–2005 in arid and semi-arid regions of Iran, Environmental Earth Sciences, 73: 1231–1244. 60. Morid, S., Smakhtin, V., and Moghaddasi, M. 2006. Comparison of seven meteorological indices for drought monitoring in Iran, International Journal of Climatology, 26: 971–985. 61. Morid, S., Smakhtin, V., and Bagherzadeh, K. 2007. Drought forecasting using artificial neural networks and time series of drought indices, International Journal of Climatology, 27: 2103–2111. 62. Nadi, M. 2015. Dendroclimatological reconstruction of dry periods during last two centuries in some forestry sites of Iran. PhD thesis, University of Tehran, University College of Agriculture and Natural Resources, Karaj, Iran. 63. Nalbantis, I. 2008. Evaluation of a hydrological drought index, European Water, 23(24): 67–77. 64. Nazemosadat, M. J. and Cordery, I. 2000. On the relationship between ENSO and autumn rainfall in Iran, International Journal of Climatology, 20: 47–61. 65. Nazemosadat, M. J. and Ghasemi, A. R. 2004. Quantifying the ENSO-related shifts in the intensity and probability of drought and wet periods in Iran, Journal of Climate, 17: 4005–4018. 66. Nelsen, R. B. 2006. An Introduction to Copulas, Springer, New York. 67. Nikbakht Shahbazi, A. R., Zahraie, B., Sedghi, H., Manshouri, M., and Nasseri, M. 2011. Seasonal meteorological drought prediction using support vector machine, World Applied Sciences Journal, 13(6): 1387–1397. 68. Nikbakht, J., Tabari, H., and Hosseinzadeh Talaee, P. 2012. Streamflow drought severity analysis by Percent of Normal Index (PNI) in Northwest Iran, Theoretical and Applied Climatology, 112(3): 565–573, doi: 10.1007/s00704-012-0750-7. 69. Noghankar, H., Bazrafshan, J., and Hejabi, S. 2011. Risk analysis of agricultural drought characteristics under current climate and changing climate conditions in various climates of Iran, Iranian Water Resources Journal, 6(11): 175–183. 70. OFDA/CRED International Disaster Database. 2015. Université catholique de Louvain-BrusselsBelgium. http://www.emdat.be. 71. Palmer, W. C. 1965. Meteorological drought. Research Paper No. 45, U.S. Department of Commerce Weather Bureau, Washington, DC. August 21, 2014 from the URL: https://www.ncdc.noaa.gov/ temp-and-precip/drought/docs/palmer.pdf. 72. Pourasghar, F., Tozuka, T., Jahanbakhsh, S., Sari Sarraf, B., Ghaemi, H., and Yamagata, T. 2012. The interannual precipitation variability in the southern part of Iran as linked to large-scale climate modes, Climate Dynamics, 39: 2329–2341.

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73. Rahimzadeh Bajgiran, P., Darvishsefat, A. A., Khalili, A., and Makhdoum, M. F. 2008. Using AVHRR-based vegetation indices for drought monitoring in the Northwest of Iran, Journal of Arid Environment, 72(6): 1086–1096. 74. Raziei, T., Daneshkar Arasteh, P., and Saghafian, B. 2007. Investigation of spatial and temporal meteorological droughts in SiatanvaBalochistan province, Science Agriculture Journal, 30(1): 85–99 (in Farsi). 75. Raziei, T., Bordi, I., and Pereira, L. S. 2011. An application of GPCC and NCEP/NCAR datasets for drought variability analysis in Iran, Water Resources Management, 25: 1075–1086. 76. Raziei, T., Bordi, I., and Pereira, L.S. 2013. Regional drought modes in Iran using the SPI: The effect of time scale and spatial resolution, Water Resources Management, 27: 1661–1674. 77. Raziei, T., Daryabari, J., Bordi, I., Modarres, R., and Pereira, L. S. 2014. Spatial patterns and temporal trends of daily precipitation indices in Iran, Climatic Change, 124(1): 239–253. 78. Raziei, T., Saghafian, B., Paulo, A. A., Pereira, L. S., and Bordi, I. 2009. Spatial patterns and temporal variability of drought in western Iran, Water Resources Management, 23: 439–455. 79. Rezaeian-Zadeh, M. and Tabari, H. 2012. MLP-based drought forecasting in different climatic regions, Theoretical and Applied Climatology, 109(1): 407–414. 80. Rostamian, R., Eslamian, S., and Farzaneh, M. R. 2013. Application of standardised precipitation index for predicting meteorological drought intensity in Beheshtabad watershed, central Iran, International Journal of Hydrology Science and Technology, 3(1): 63–77. 81. Saghafian, B. and Mehdikhani, H. 2014. Drought characterization using a new copula-based trivariate approach, Natural Hazards, 72: 1391–1407. 82. Sayari, N., Bannayan, M., Alizadeh, A., and Farid, A. 2013. Using drought indices to assess climate change impacts on drought conditions in the northeast of Iran (case study: Kashafrood basin). Meteorological Applications, 20: 115–127. 83. Shahabfar, A., Ghulam, A., and Eitzinger, J. 2012. Drought monitoring in Iran using the perpendicular drought indices, International Journal of Applied Earth Observation and Geoinformation, 18: 119–127. 84. Shiau, J. T. and Modarres, R. 2009. Copula-based drought severity-duration frequency analysis in Iran, Journal of Applied Meteorology, 16(4): 481–489. 85. Shiau, J. T., Modarres, R., and Nadarajah, S. 2012. Assessing multi-site drought connections in Iran using empirical copula, Environmental Modeling and Assessment, 17: 469–482. 86. Shirmohammadi, B., Moradi, H. R., and Moosavi, V. 2013. Forecasting of meteorological drought using wavelet-ANFIS hybrid model for different time steps (case study: Southeastern part of east Azerbaijan province, Iran), Natural Hazards, 69(1): 389–402. 87. Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8: 229–231. 88. Smith, E. 1876. The Perso-Afghan mission, 1871–72, in: Goldsmid, F. J., ed., Eastern Persia, Adamant Media Corporation, London, U.K., pp. 225–391. 89. Sonali, P. and Nagesh Kumar, D. 2013. Review of trend detection methods and their application to detect temperature changes in India, Journal of Hydrology, 476: 212–227. 90. Tabari, H., Abghari, H., and Hosseinzadeh Talaee, P. 2012. Temporal trends and spatial characteristics of drought and rainfall in arid and semiarid regions of Iran, Hydrological Processes, 26(22): 3351–3361. 91. Tabari, H., Nikbakht, J., and Hosseinzadeh Talaee, P. 2013. Hydrological drought assessment in Northwestern Iran based on Streamflow Drought Index (SDI), Water Resources Management, 27: 137–151. 92. Tabrizi, A. A., Khalili, D., Kamgar-Haghighi, A. A., and Zand-Parsa, Sh. 2010. Utilization of timebased meteorological droughts to investigate occurrence of streamflow droughts, Water Resources Management, 24: 4287–4306. 93. Tsakiris, G. and Vangelis, H. 2005. Establishing a drought index incorporating evapotranspiration, European Water, 9–10: 1–9.

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94. Vafakhah, M., Eslamian, S., and Khosrobeigi Bozchaloei, S. 2014. Low-flow hydrology, in: Eslamian, S., ed., Handbook of Engineering Hydrology, Vol. 1: Fundamentals and Applications, Taylor & Francis, CRC Group, Chapter 20, pp. 433–453. 95. Vicente-Serrano, S. M., Beguería, S., and López-Moreno, J. I. 2010. A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index, Journal of Climate, 23: 1696–1718. 96. Yevjevich, V. 1967. An objective approach to definitions and investigations of continental hydrologic droughts. Hydrology Papers 23. Colorado State University Pubs, Colorado State University, Fort Collins, CO. 97. Zarei, R., Sarajian, M., and Bazgeer, S. 2013. Monitoring meteorological drought in Iran using remote sensing and drought indices, Desert, 18: 89–97. 98. Zoljoodi, M. and Didevarasl, A. 2013. Evaluation of spatial–temporal variability of drought events in Iran using palmer drought severity index and its principal factors (through 1951–2005), Atmospheric and Climate Sciences, 2013(3): 193–207.

12 Observational Network and Drought Monitoring 12.1 Introduction ...................................................................................... 190 12.2 Observational Networks ...................................................................191 12.3 Network of Meteorological Observatories .....................................191 Meteorological Observations

12.4 Hydrological Network ...................................................................... 192 Hydrological Measurements • Rivers • Lakes and Reservoirs • Groundwater Observations • Infiltration • Soil Moisture • Evaporation • Water Quality

12.5 Agricultural Networks ..................................................................... 195 Global Agricultural Monitoring System  •  The FAO Global Information and Early Warning System  •  USDA Foreign Agricultural Service  •  Monitoring of Agriculture with Remote Sensing: FOODSEC  •  USAID Famine Early Warning Systems Network  •  European Space Agency Global Monitoring for Food Security Programme  •  FAO Food Insecurity and Vulnerability Information and Mapping Systems  •  Southern African Development Community Regional RS Unit Drought Monitoring Centre  •  Consortium for Spatial Information of the Consultative Group on International Agricultural Research  •  Agricultural Monitoring in the United States  •  Agricultural Monitoring in Europe • Agricultural Monitoring in Australia • Agricultural Monitoring in Russia  •  Agricultural Monitoring in China  •  Agricultural Monitoring in India  •  Agriculture in the Middle East and North Africa

12.6 Socioeconomic Observing Systems ...............................................200 Socioeconomic Observations

12.7 Information and Knowledge Networks ........................................ 201 U.S. Drought Monitor  •  Integrated Drought Management Programme  •  Global Drought Information System (www.drought.gov)

12.8 Remote Sensing for Drought Monitoring .....................................202 12.9 Drought Monitoring ....................................................................... 203 Drought Observations  •  Drought Monitoring in the United States  •  Drought Monitoring in Australia  •  Experimental African Flood and Drought Monitor

Brij Bhushan National Informatics Centre

12.10 Summary and Conclusions .............................................................206 Author ............................................................................................................207 References ..................................................................................................... 207

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Abstract  Observational networks for drought monitoring are maintained by national meteorological services, hydrological services, departments of agriculture, departments for welfare and economic upliftment, NGOs, etc. They have a large number of objectives to provide service to a variety of users. These networks keep on recording observations on weather, hydrology, agriculture, and socioeconomic conditions of the population irrespective of a drought. The number of parameters, quality of observations, instrumentation, and observing techniques are nonuniform in countries and within countries. Thus, the historical records are not of uniform quality and length. Satellites are being used to remotely sense Earth. From 1960 onward, the tremendous improvement in remote sensing technology has resulted in more parameters becoming available at improved resolution. In 1960s, the resolution of the satellite images was limited to identifying the objects of size 10 × 10 km, while WorldView-4, launched on November 11, 2016, will identify the objects of size 31 × 31 cm, thus facilitating improved drought monitoring. This chapter is written to describe observing networks as sources of information generation and how these information are collected. Drought monitoring requires a portion of data observed by these networks. Drought monitoring at global scale and some important drought monitoring systems are described.

12.1  Introduction Drought may be defined as the deficiency of precipitation from the expected or “normal” level that extends over a season or a longer period of time, and water supply is insufficient to meet the demands of human activities and the environment. The droughts are categorized into four types, that is, meteorological, agricultural, hydrological, and socioeconomic, described briefly as follows: • • • •

Meteorological drought: Significant departure of precipitation is below normal values. Agricultural drought: Soil moisture is not adequate for vegetation (crops) or livestock. Hydrological drought: Surface/subsurface water levels are significantly below normal. Socioeconomic drought: Water shortage begins to have an effect on daily life.

An integrated drought monitoring system needs to be comprehensive in scope (coupling climate, soil, and water data), incorporate local and regional scale data, use the best available indices and triggering tools, link index values or thresholds to impacts, be flexible, and incorporate the needs of users [12–14]. Monitoring drought requires computation of indices or deciles. These values are required to be observed on multiple locations simultaneously and to be watched for a sufficiently long period. The key indicators for drought monitoring are given in Table 12.1. Some authors call all the drought indices as indicators [8]. However, drought indices have a certain value indicating the severity of the drought. Water quality in the region, greenness observed through remote sensing (RS), increased rates of evaporation, and increased fire danger are other important indicators of drought. TABLE 12.1  Key Indicators of Drought Meteorological Precipitation Temperaturea Windsa Humiditya Evaporationa Forecasts

Agricultural

Hydrological

Socioeconomic

Soil moisture Crop condition Low average Fodder scarcity Grazing land Vegetation

Water availability Streamflow Groundwater Reservoirs level Snow pack Wet lands

Food security Reduced employment Economic impacts Social impacts Migration Starvation

a High temperature, strong winds, low humidity, and high evaporation are ­associated features of drought.

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Drought index is a value associated with drought computed by comparing current conditions to historical information. Drought index attempts to quantify drought and its severity. Some well-known drought indices are • • • • • • • •

Standardized Precipitation Index (SPI) Standardized Precipitation Evapotranspiration Index Palmer Drought Severity Index Crop Moisture Index Self-Calibrated Palmer Drought Severity Index Deciles/percentiles Surface Water Supply Index Multivariate Standardized Reliability and Resilience Index

SPI and modified SPI are found to be sensitive to the timescale and lead to inconsistent results; the Joint Deficit Index (JDI) produced improved results while studying long-term drought monitoring of Urmia [5]. A comprehensive list of drought indices is given by Wanders et al. [25]. None of the indices are inherently superior to the rest in all circumstances; some indices are better suited than others for certain uses, namely, the Palmer Drought Index [6] is most commonly used although it has limitations [1]. We have attempted a comprehensive way to monitor drought’s availability of past data, and computing indices is a major issue in most of the countries.

12.2  Observational Networks The following networks operate to observe basic data used to monitor drought: • • • • •

Networks of meteorological observatories Network of hydrological stations—streamflow, reservoirs, and groundwater Network of agricultural institutes and departments of agriculture Government departments/NGO for socioeconomic aspects, relief, and mitigation Information and knowledge networks on drought

12.3  Network of Meteorological Observatories Every country has a network of meteorological observatories. The observatories have a barometer, thermometers, raingauge, wind measuring instruments, and some autographic instruments. All these observatories are not similar as the meteorological networks have evolved over a period of time. To supplement this network, there are networks of automatic weather stations (AWS), raingauge stations. The number of observatories, AWS, and raingauge stations is planned according to national, regional, and global requirements. For example, India has about 600 manned observatories, some 5,000 AWS, and 30,000 raingauges. The expansion of AWS network and raingauges has taken place in the last 5–10 years; thus, the length of historical records is nonuniform. Meteorological services have networks of upper-air observatories; networks of storm detection radars, Doppler radars, wind profilers, Lidars, and lightning position and tracking systems; and a number of satellites for RS of weather. The WMO has provided guidelines on standardization of instruments, their upkeep, exposure of sensors, and maintenance and procedures for observations [17].

12.3.1  Meteorological Observations Meteorological observations are made with carefully calibrated and harmonized instruments such as barometer, thermometers, wind vane, anemometer, and raingauge at predetermined timings. Some observations like visibility, cloud amount, and cloud type are estimated by the observer. The number

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and type of instruments/sensors may vary from observatory to observatory. Human-operated observatory takes observations daily every 3 h starting from 00 GMT. These data are kept locally and communicated to a central location—the weather office, where these data are analyzed to issue weather forecast and warnings. Past data and current data are used to compute anomalies and the number of derived parameters. Agrometeorological observatories take observations on parameters like wind, temperature, humidity, evaporation, sunshine, soil temperature, and soil moisture. Observatories located at airports may take observations even at a shorter duration. Observatories at sea and the coast take observations on sea surface conditions also. There could be automatic instruments recording the observations and communicating to a computer and a computer network to send the entire data set to a designated location as soon as it is recorded. Some of these data flow across the globe. AWS record weather data at small intervals of time varying from a minute to an hour and transmit through a communication network. There are raingauge stations where data are recorded manually and reported through a range of communication systems. Automatic raingauge stations in remote locations communicate rainfall data through satellite links. Reporting frequency from manned observatories is two to eight times in 24 h, as frequent as recoded from AWS, and one to two times a day from manned raingauge stations. There are raingauge stations that record rains every day but report only at month’s end. The national meteorological services maintain records of observed data for varying periods ranging up to more than 100 years for rainfall and snow for a large number of locations. These data are used to assess droughts. Observations are made on air quality, ozone layer, sea surface conditions, and upper-air conditions through a variety of instruments and observing systems.

12.4  Hydrological Network Agenda 21 of the United Nations Environment Programme (UNEP) [10] recognized that monitoring and assessment of water resources, in terms of quantity and quality, require adequate meteorological, hydrological, and related data. The 2005 World Summit called for assistance to developing countries’ efforts to prepare integrated water resources management and water efficiency plans as part of their development strategies. Unfortunately, the capability to collect and manage water resources-related information within countries remains inadequate in many parts of the world. This situation often arises from a lack of financial support from governments in view of demands from other sectors. As a result, data collection networks are deteriorating, and the ability of the national Hydrological Services to provide information on the status and trends of water resources is declining [26]; however, Eslamian et.al. [3] used 32 parameters including monthly discharge, severity, duration, timing of occurrence of extreme events, and the rate of change in river flow in the impact study of dams. A large number of countries, including India, observe groundwater after a gap of many years through surveys, and the results are published a few years later; thus, groundwater observations do not become part of drought monitoring in these counties. The data are helpful only to support research, long-term planning, and policy making on the use of groundwater.

12.4.1 Hydrological Measurements The water circulates throughout Earth in different pathways and at varying rates of volume and speed. The water evaporates from the ocean and water bodies, which forms clouds. These clouds drift over the land and produce rain/snow. The rainwater flows into lakes, rivers, or aquifers. It then either evaporates back to the atmosphere or flows back to the ocean completing a cycle. Water changes its state of being several times throughout this cycle. Some portion of this water is consumed for drinking, cleaning, irrigation, absorption by soil, vegetation, intake by humans and animals, industry, etc. This water joins the cycle somewhere in some form. The water diverted by human activities through dams, canals, etc., also joins the water cycle somewhere.

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Observational Network and Drought Monitoring TABLE 12.2  List of Hydrological Parameters for Drought Monitoring Surface Flow Volume Runoff Erosion

Reservoirs

Ground water

Rivers vs Aquifers

Met/Soil Moisture

Water Quality

Volume Surface Evaporation

Quantity Flow direction Pressure Depth Hydraulic conductivity Storativity Transmissivity Recharge Infiltration

Volume released from aquifer Recharge of aquifer Infiltration

Rain/snow Rain rate Rain area Temp Evaporation Soil-moisture RS data

Solutes Sediment Dissolved oxygen Chemical changes Micro-biological analysis

Rainfall becomes runoff when all loss processes are satisfied as the rain occurs. Runoff results from rainfall not lost to infiltration, interception, depression storage, and evaporation. Infiltration is the process of water penetrating the ground surface into the soil. Interception loss occurs when water is retained on vegetation and other surfaces. Intercepted water may evaporate or infiltrate. Loss due to depression storage occurs when water accumulates in depressions of all sizes that are not connected to a flow path. Evapotranspiration is the process of evaporating water from vegetation into air. Different methods have been developed to model rainfall losses. These include runoff coefficients, constant loss parameters, the Horton method, exponential loss calculations, and Green–Ampt losses. The Modified Rational Method uses runoff coefficients. Thus, after rain occurs, a number of parameters are observed in the hydrologic cycle [16]. For monitoring drought, the main parameters are streamflow and level in reservoirs and of groundwater. As the volume of water reduces in these water resources, the concentration of dissolved impurities goes up; thus, measuring the quality of water also becomes important. Table 12.2 depicts the list of parameters for hydrological observations needed for drought monitoring. Water levels under natural conditions are measured at gauging stations [18], where limnographs and marigraphs are utilized for recording them. The head and pressure of a liquid are measured by piezometers and pressure gauges. Under natural conditions, water depth is measured by poles, depth gauges, and plumb lines. Depths are recorded by water-measuring profilographs, which may be mechanical, hydrostatic, or acoustic. The flow velocity of water currents is measured at certain points in the flow by current meters, tubes, thermal measurement devices, vanes, floats, and electronic and mechanical instruments. In studying flow turbulence, the readings of many instruments are recorded on an oscillograph. The average vertical velocities of a headless flow are measured by integrator floats, water-measuring rods, and current meters by moving them vertically in the flow. The discharge of water is determined by various means, which depends mainly on the type of movement of the liquid, with or without head, and on the amount of the discharge. The most precise methods are by weight and volume, but they are suitable for determining only small-scale discharges. Diaphragms, venturis, and flow meters are used to measure the discharge of pressured flows. For river flows, the method used most frequently is based on the measurement of the local velocities and depths, from which the discharge may be calculated. In water currents with a high degree of turbulence, the use of the mixture method, which consists in the introduction of an indicator solution into the flow and the measurement of its concentration on a range with a complete mix, is appropriate. Water-measuring installations such as spillways, water-measuring chutes, man-made control cuts, and measuring nozzles are set up in small water currents. The quantity of alluvium transported by the flow is measured by bathometers. The concentration of pulp is measured by a gamma-ray density meter. The runoff of water, the volume of water that flows during a day, month, or year, is recorded by water meters in a water supply system and by runoff recorders in river hydrology. To determine the runoff of a river, the levels are measured each day, and, according to the correlation established between discharge and level, the runoff is calculated for any given time.

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12.4.2 R ivers The flow rate or discharge of a river is the volume of water flowing through a cross section in a unit of time and is usually expressed as cubic meter per second (m3/s). It is calculated as the product of average velocity and cross-sectional area but is affected by water depth, alignment of the channel, gradient, and roughness of the riverbed. Discharge may be estimated by the slope-area method, using these factors in one of the variations of the Chezy equation [9]. More accurate values for discharge are obtained when a permanent gauging station is established on a stretch of a river where there is a stable relationship between stage (water level) and discharge, and this has been measured and recorded. Once this relationship is established, readings need only be taken off the stage, because the discharge may then be read from a stage–discharge curve. Water quality samples may be taken a short distance upstream or downstream, provided that no significant inflow or outflow occurs between the sampling and gauging stations.

12.4.3 Lakes and Reservoirs In lakes and reservoirs, hydrological information, particularly volume and water residence time, is needed for the interpretation of data and the management of water quality. The size of the water body and surface area are also monitored. If the water surface is calm and a water-level gauge has been installed, a single reading may be sufficient. If there is no official gauge, the water level should be recorded in relation to a conveniently located landmark that is reasonably permanent. If there is any reason to suspect that this water-level marker might move, reference should be made to a second landmark. If there are waves, average of highest and lowest position is to be taken as level. Currents may cause water quality to vary appreciably within short distances or time periods. The flow velocities that normally occur in lakes are measured with sensitive recording current meters anchored at given depths. In reservoirs, the operation of valves or sluices can create localized currents that can affect the water quality in their vicinity.

12.4.4 Groundwater Observations Drought monitoring requires monitoring of depleting groundwater level. The detailed procedures to monitor groundwater are given in Todd [10] and groundwater technical procedures of the U.S. Geological Survey [11]. Groundwater recharges streams and rivers in some areas, while it is recharged by surface water. As the rate of flow of groundwater is much lower than that of surface water, there is a significant risk that contaminants can build up in aquifers to the point where the water becomes unusable. This could force the abandonment of boreholes and result in a permanent reduction in the quantity of usable groundwater. Groundwater flow is three dimensional and, therefore, more difficult to observe than surface water. In addition, whereas surface water flow direction can be easily determined by topographical survey, groundwater flow direction depends on aquifer type and hydraulic conditions in the aquifer and is difficult to assess without carrying out pump tests and tracer studies. Information on the direction of groundwater flow can be obtained by mapping out water levels in boreholes within the same aquifer. This gives an indication of the hydraulic gradient and, thus, an idea of groundwater movement. Groundwater flow information will assist in the prediction of contaminant movement in groundwater, in particular the spread and speed of movement of contaminants. Groundwater hydrology (hydrogeology) considers quantifying groundwater flow and solute transport. Problems in describing the saturated zone include the characterization of aquifers in terms of flow direction, groundwater pressure, and, by inference, groundwater depth. Measurements here can be made using a piezometer. Aquifers are also described in terms of hydraulic conductivity, storativity, and transmissivity.

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12.4.5 Infiltration Infiltration is the process of water entering the soil. Some of the water is absorbed, and the rest percolates down to the water table. The infiltration capacity, the maximum rate at which the soil can absorb water, depends on several factors. An already-saturated layer provides a resistance that is proportional to its thickness, while that plus the depth of water above the soil provides the driving force. Dry soil can allow rapid infiltration by capillary action. This force diminishes as the soil becomes wet. Surface cover increases the capacity by retarding runoff, reducing compaction, and other processes. Higher temperatures reduce viscosity, increasing infiltration.

12.4.6 Soil Moisture Soil moisture influences hydrological and agricultural processes, runoff generation, drought development, and many other processes. Soil moisture is a source of water for evapotranspiration. Soil moisture was recognized as an essential climate variable in 2010 [20]. Soil moisture can be measured in various ways, by capacitance probe, time domain reflectometer, or tensiometer. Other methods include solute sampling, geophysical methods, and RS.

12.4.7 Evaporation Evaporation is partly affected by humidity, which can be measured by a sling psychrometer, dry–wetbulb thermometers. It is also affected by the presence of snow, hail, and ice and can relate to dew, mist, and fog. Hydrology considers evaporation of various forms: from water surfaces and as transpiration from plant surfaces in natural and agronomic ecosystems. A direct measurement of evaporation can be obtained using Symon’s evaporation pan.

12.4.8 Water Quality In hydrology, studies of water quality concern organic and inorganic compounds and both dissolved and sediment material. In addition, water quality is affected by the interaction of dissolved oxygen with organic material and various chemical transformations that may take place. Measurements of water quality may involve either in situ methods, in which analyses take place on-site, often automatically, or laboratory-based analyses that may include microbiological analysis. The special characteristics of reservoirs and their operation, in relation to water quality monitoring, are described in Water Quality Assessments [15].

12.5  Agricultural Networks Almost every country has departments of agriculture and agricultural research institutes conducting research and working toward improving the quality and quantity of agriculture produce. These departments and institutes monitor crop growth and crop yield and impact thereon of various inputs and prevailing weather. The farmers, who have not gotten any formal education, have in-depth knowledge on what should be sown at what time during the year and when the crop will be harvested. The farmers grow crops in a well-organized manner that almost all of them sow the crops during a period of sowing. If someone deviates from this practice, there are losses, due to inappropriate weather, attacks of pests and birds/­animals, etc. In the case of pest attacks, crop disease, animal disease, and waiting and watching rains for agricultural operations, the farmers interact with each other in villages. Some operations like harvesting are done by groups of farmers together. At a number of places, cooperative farming is practiced. Thus, farmers are somehow networked for agricultural activities. The agricultural institutes keep on giving inputs to the government and advisories to the farmers. There are networks at local, regional, national, and global levels to provide information on agriculture inputs, market information, and agriculture produce.

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12.5.1  Global Agricultural Monitoring System The Group on Earth Observations (GEO)/Integrated Global Observing Strategy was established in July of 2007. This community of practice represents 25 national and international organizations concerned with agricultural monitoring. Its purpose is to develop and implement a strategy for global agricultural monitoring in the framework of GEO. The GEO acknowledges sustainable agriculture as one of the societal benefit areas (SBA) for international cooperation and collaboration [21]. The agriculture SBA call for a system for monitoring global agriculture that includes the following three functional components: • Global mapping of changes in distribution of cropland area and cropping systems • Global monitoring of agricultural production for timely reporting of agricultural statistics and forecasting of shortfalls in crop production and food supply and facilitating reduction of risk and increased productivity at a range of scales • Early warning of famine, for timely mobilization of an international response

12.5.2  The FAO Global Information and Early Warning System The Global Information and Early Warning System (GIEWS) monitors food supply and demand at the global scale and provides early warning of serious regional food shortages. GIEWS is used to identify impending food security crises so that the UN World Food Programme and other international/national agencies can develop country-specific needs assessments. GIEWS integrates satellite-derived information on land cover and land use with in situ data on agricultural statistics, livestock, agricultural markets, and weather. GIEWS monitoring is designed to enable direction of ground-based sampling to validate crop production estimates and the development of quick, early, partial indemnity for immediate action.

12.5.3  USDA Foreign Agricultural Service The Foreign Agricultural Service (FAS) monitors world agricultural production, supply, and demand for agricultural products to provide baseline market information and information for U.S. domestic early warning. FAS analyses rely on meteorological data, field reports, and satellite observations at moderate and high spatial resolutions to help crop and growth-stage identification and yield analysis. These data are used to confirm or deny unsubstantiated information about forecast crop yields and to identify unreported events likely to impact crop yields. To bring these disparate sources of data together, FAS has developed the Crop Explorer, a GIS-based decision support system.

12.5.4  Monitoring of Agriculture with Remote Sensing: FOODSEC The Food Security (FOODSEC) monitors food security for at-risk regions worldwide. The information produced contributes to the EU external aid and development policies, in particular food aid and food security policy. The desired outcome is to avoid food shortages and market disruptions and to better calibrate and direct European food aid. Satellite observations and meteorological data are integrated with baseline data on regional agronomic practices into crop growth models to develop FOODSEC monthly bulletins with yield forecasts of crop. In addition to qualitative and quantitative crop yield assessments, indicators, like rainfall, radiation, temperature, and water satisfaction indices, are published in the bulletins. They parameters are compared with long-term historical average and to last year’s indicators to help food security administrators.

12.5.5 USAID Famine Early Warning Systems Network The USAID Famine Early Warning Systems Network (FEWSNET) is an information system designed to identify problems in the food supply system that potentially lead to famine or other food-insecure

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conditions in sub-Saharan Africa, Afghanistan, Central America, and Haiti. FEWSNET is a multidisciplinary project that collects, analyzes, and distributes regional, national, and subnational information to decision-makers about potential or current famine or other climate hazard, or socioeconomic situations, allowing them to take timely measures to prevent food-insecure conditions in these nations. Regions and countries with FEWSNET representatives include Angola, Burkina Faso, Chad, Djibouti, Ethiopia, Kenya, Malawi, Mali, Mauritania, Mozambique, Niger, Nigeria, Rwanda, Somalia, Sudan, Tanzania, Uganda, Zambia, Zimbabwe, Guatemala, Honduras, Nicaragua, Afghanistan, and Haiti.

12.5.6  European Space Agency Global Monitoring for Food Security Programme The objective of the Global Monitoring for Food Security (GMFS) project developed by the European Space Agency is to improve operational and sustainable information services, derived partly from the Earth’s observation data, to assist food aid and food security decision-makers. The GMFS aims to consolidate, support, and complement existing regional information and early warning systems on food and agriculture. The long-term goal of the GMFS is to develop a network of geographically distributed service providers on satellite observations related to agricultural production monitoring. It provides vegetation data to Africa through EUMETCast, for promoting data utilization and capacity building of regional participants.

12.5.7  FAO Food Insecurity and Vulnerability Information and Mapping Systems The Food Insecurity and Vulnerability Information and Mapping Systems (FIVIMS) try to find foodinsecure and vulnerable people, their location, number, reason of vulnerability, measures, risk factors, and ability to cope with these risks. The FIVIMS undertakes analyses that integrate information from different sectors to assess supply and demand for food. An important FIVIMS product is the FIVIMS Global GIS Database, which illustrates the spatial and environmental contexts for agricultural productivity and accessibility and poverty maps derived using socioeconomic data and satellite imagery.

12.5.8  Southern African Development Community Regional RS Unit Drought Monitoring Centre The Regional RS Unit (RRSU) is a program coordinated by the Southern African Development Community that is designed to support early warning for food security of its 14 member nations. The goal of the program is to promote sustainable natural resource use and to enhance information for disaster risk management.

12.5.9  Consortium for Spatial Information of the Consultative Group on International Agricultural Research The Consultative Group on International Agricultural Research (CGIAR) applies geospatial science to sustainable agricultural development, natural resource management, biodiversity conservation, and poverty alleviation in developing countries. The CGIAR system of research centers has been monitoring global agriculture since the early 1970s. CGIAR activities include analyses of agricultural biodiversity and genetic resources, food security and food policy, water and soil resource conservation, and agricultural and natural resources management. The 15 centers are modeling the spatial dimensions of crop growth, irrigation, pests and pathogens, and forests and fisheries.

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12.5.10  Agricultural Monitoring in the United States The National Agricultural Statistics Service (NASS) provides timely and useful statistics in service to U.S. agriculture. These statistics cover virtually every facet of U.S. agriculture, from production and supply of food and fiber to prices paid and received by farmers and ranchers. Every 5 years, NASS conducts Census of Agriculture, which provides a comprehensive statistical summary of many aspects of U.S. agriculture. RS data are used to improve the accuracy of NASS statistics. The NASS uses RS data to construct and sample area frames for statistical surveys, estimate crop area, and create crop-specific land-cover data layers for GIS. The NASS uses Landsat imagery, digital orthophoto quadrangles, and other remotely sensed inputs for all 48 states and Puerto Rico to select the yearly area-based samples and supplemental samples. The RS acreage estimation project analyzes RS data over the major corn- and soybean-producing states to give independent crop acreage estimates at the state and county levels and a crop-specific categorization called the Cropland Data Layer. The NASS is also in a continuing partnership with the USDA/Agricultural Research Service using NASA RS data as inputs for setting early season small-area yield estimates in several Midwestern states. The NASS also produces vegetation condition products based on the normalized difference vegetation index (NDVI) during the growing.

12.5.11  Agricultural Monitoring in Europe The mission of the crop production forecast activities of the European Commission at the Joint Research Centre (MARS-Stat) is to provide independent and timely crop yield forecasts and crop production biomass including biofuel crops for the union territory and other strategic areas of the world. MARS-Stat has been developing and operationally running a Crop Yield Forecasting System since 1992 in order to provide crop production forecasts for Europe. This system is able to monitor crop vegetation growth and include the short-term effects of weather on crop productions to provide yearly European crop predictions. The MARS-Stat system is made by RS and weather data, ECMWF data, agrometeorological modeling, and statistical analysis tools. MARS-Stat is also a depositary of techniques developed using RS and area frame sampling in Europe to estimate crop areas. MARS-Stat will continue the development of new improvements for the Crop Yield Forecasting and Crop Area Estimation Systems.

12.5.12  Agricultural Monitoring in Australia Earth observation for agricultural monitoring in Australia ranges from broad-scale monitoring of vegetation for greenhouse gas accounting through to sub-paddock precision agriculture across numerous industries such as cropping, livestock grazing, viticulture, and rice and sugar industries. In addition, there are a number of static national data sets, for example, land tenure, remnant vegetation, land use, soil climate information, and census data, that are integrated with Earth observations. Earth observation applications are developed for particular agroclimatic zones and tailored for specific market segments. Products are qualitative indices, for example, the NDVI, pasture biomass, and growth rate, and in many instances are integrated with models. Near-real-time applications include fire monitoring, biosecurity surveillance, extreme events, and precision agriculture. Temporal resolution remains varied, namely, strategic application of fertilizers utilizes a few key images per year, whereas livestock grazing applications for stock movement decisions utilize weekly imagery.

12.5.13  Agricultural Monitoring in Russia The national agricultural monitoring system, in Russia, relies on the combined use of information from regional agricultural committees, RS data, and ground agrometeorological observations. The main foci of the agricultural monitoring system are arable land area, crop land use mapping, crop rotation, and seasonal crop development. The system contributes to crop production forecasts, greenhouse gas flux monitoring, and soil erosion risk assessment.

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12.5.14  Agricultural Monitoring in China Since the late 1990s, rapid development of RS technology and departments and research agencies have focused their research on agriculture, and a number of these set up their own RS-based crop or agriculture monitoring systems. Current operational systems include the China Agriculture RS Monitoring System (CHARMS), the China CropWatch System (CCWS), and the China Meteorological Administration’s crop growth monitoring and yield prediction system. The CHARMS developed by the RS Application Centre of the Ministry of Agriculture has been operational since 1999. It monitors crop acreage change, yield, production, crop growth, drought, and other agriculture-related information for five main crops in China. The CCWS was developed by the Institute of RS Applications in 1998. The CCWS covers China as well as 46 main grain-growing countries around the world. The CCWS monitors crop growing conditions, production, drought, crop plantation structure, and cropping index. The CCWS publishes 7 monthly bulletins and 20 newsletters every year. In 2004, the National Bureau of Statistics began to use RS technology to improve agriculture statistics.

12.5.15 Agricultural Monitoring in India The National Crop Forecasting Centre of the Department of Agriculture and Cooperation (DAC) was established in 1998, to develop a framework for providing crop production forecasts at district, state, and national levels. It is responsible for providing information on crop sowing progress, crop condition throughout the growing period, and effect of floods, drought, hail, pests, disease, etc., on crop production. The Space Applications Centre (SAC) has led the project in developing (1) a RS-based procedure for crop acreage estimation at district level, (2) spectral and weather models for yield forecasting, (3) semiautomatic software CAPEWORKS for the analysis of RS data, and (4) technology transfer to teams across the country that use these procedures and make crop production forecasts. LISS-III data from the Indian RS satellites are being regularly used to make crop production forecasts. Forecasting Agricultural output using Space, Agrometeorology and Land-based observations (FASAL) has been developed by the SAC. FASAL envisage providing information on crop prospects at the beginning of the crop season with econometric models, followed by weather-based models to forecast crop acreage early in the season, and later on yield. RS data from wide-field sensor (WiFS)/ advanced WiFS (AWiFS) are used to provide area estimates under crops about 6–8 weeks after sowing. Cropping system analysis of the Indo-Gangetic Plain has been done. First, a gross crop rotation mapping was done using the Satellite Pour l’Observation de la Terre (SPOT)-Vegetation data. Subsequently, seasonal cropping patterns for Kharif, winter, and summer seasons have been mapped using AWiFS and Radarsat ScanSAR Narrow Beam-2 data at a larger scale. Crop rotation maps have been generated using the cropping pattern data. Field survey has been carried out to identify and characterize the cropping systems of the region. Cropping system performance indicators like area diversity index, cultivated land utilization index, and multiple cropping index have been developed. Village-wise field-level enumeration is done by DAC with 20% villages covered every year. Crop cutting experiments by randomly selected fields are carried out for the estimation of crop yield. The DAC, Indian Council of Agricultural Research (ICAR), Indian Agriculture Statistics Research Institute (IASRI), and India Meteorological Department (IMD) have very large current and historical databases.

12.5.16  Agriculture in the Middle East and North Africa The Middle East and North Africa (MENA), the most water-scarce and dry region in the world, has many countries in the region, especially around the Mediterranean Sea, and is highly dependent on agriculture. The contribution of the agricultural sector to the overall economy varies from about 3.2% in Saudi Arabia to 13.4% in Egypt. Large-scale irrigation coupled with mechanization has enabled intensive production of high-value cash crops, including fruits, vegetables, cereals, and sugar in the Middle East.

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Crop residues such as bagasse, straw, stem, stalk, leaves, husk, shell, peel, pulp, and stubble cause a major disposal problem. Wheat and barley are the major staple crops grown in the Middle East. In addition, significant quantities of rice, maize, lentils, chickpeas, vegetables, and fruits are produced throughout the region, mainly in Egypt, Tunisia, Saudi Arabia, Morocco, and Jordan. Egypt is one of the world’s largest producers of rice and cotton. Crop residues are considered to be the most important and traditional source of domestic fuel in rural Egypt. The total amount of crop wastes in Egypt is estimated at about 16 million tons of dry matter per year. In Tunisia, major crops are cereals and olive. Tunisia is one of the world’s largest producers of olive oil, and it exports dates and citrus fruits that are grown mostly in the northern parts of the country. Very large quantities of crop residues are produced annually in the region and are vastly underutilized. Current farming practice is usually to plow these residues back into the soil, or they are burned, left to decompose, or grazed by cattle.

12.6  Socioeconomic Observing Systems Most of the drought-related socioeconomic information, in developing countries, go unnoticed, unless some mitigation measures are initiated. In the developing world, the information network is media and political links, which takes the decision-makers to extend financial subsidies and measures to help the affected population. Socioeconomic data are collected through a number of census and surveys and are used for assessing the vulnerability of a community. Governments keep on launching welfare schemes on agriculture, animal husbandry, and small- and medium-scale industries irrespective of a drought episode. Thus, observing the impact of relief is a complex process and needs critical examination for studying the effect of drought relief measures. The impact of drought is proportional to vulnerability. The impacts of drought are a result of the interactions of social, political, and economic systems. However, such a focus does not examine how human water use exacerbates deficits in water supply and quality. As a result, there is a worldwide insufficiency of disaster preparedness and mitigation methods that adequately address the socioeconomic effects of drought.

12.6.1  Socioeconomic Observations The International Panel for Climate Change (IPCC) has published a set of baseline statistics of the early to mid-1990s for 195 countries. The data were collated from a variety of sources, such as the World Bank, UNEP, and FAO, and they comprise a range of factors organized into seven categories [22]: • Population and human development: Total population, current and projected (2025) population density, total urban population, and urban population in coastal cities • Economic conditions: GDP per capita, GDP from agriculture, from industry and from services, and GDP annual growth rate • Land cover/land use: Total land area, arable and permanent cropland, permanent pasture, forest and woodland, and other land use • Water: Water resources per capita and annual withdrawals for domestic, industrial, and agricultural use • Agriculture/food: Irrigated land, agricultural labor force, total labor force, stocks of cattle, sheep, goats, pigs, equines, buffalo, and camels • Energy: Consumption of total energy, traditional fuel, and hydroelectricity • Biodiversity: Known and endemic mammal, bird, and plant species These tabulated data are available from the Data Distribution Centre. These are only selected; summary data and individual impact studies are likely to require information on other factors or at a higher

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spatial resolution. The original sources of the IPCC data set, collected through census and surveys, may be able to provide additional country-level information. Otherwise, national or regional sources of data will need to be accessed.

12.7  Information and Knowledge Networks There are many information and knowledge networks sharing information and knowledge on drought around the globe. Information is scattered over a large number of websites and databases. Quality, timeliness, and length of the data availability are a big issue in many countries. The National Drought Mitigation Center (NDMC) has compiled an extensive set of resources related to drought indicators, RS, forecasts and advisories, and water resources. The international drought community produces globalscale and country-specific drought monitoring tools and information. There are information gaps as the data are not shared properly among organizations within a country and also among countries. A few programs and networks keeping watch on drought are as follows.

12.7.1  U.S. Drought Monitor The U.S. Drought Monitor (USDM) is the largest information and knowledge network for drought having the following partners [23]: 1 Joint Agricultural Weather Facility (USDA, Department of Commerce/NOAA) 2. Climate Prediction Center 3. National Climatic Data Center (DOC/NOAA) 4. National Drought Mitigation Center (University of Nebraska–Lincoln) 5. U.S. Geological Survey 6. National Water and Climate Center 7. Climate Diagnostics Center (DOC/NOAA) 8. Regional Climate Centers 9. National Weather Service Advanced Hydrologic Prediction Service (DOC/NOAA) 10. State climatologists 11. Local, state, and federal experts

12.7.2  Integrated Drought Management Programme The IPCC, 2007, stated that the world has been more drought prone during the past 25 years. In order to address the drought issues, the World Meteorological Organization (WMO) has initiated (1) Integrated Drought Management Program (IDMP) in 2011 and (2) High-Level Meeting on National Drought Policy in March 2013. Both of the drought initiatives will contribute to the Global Framework for Climate Services by engaging users of drought information in order to highlight areas where drought information needs to be improved. The IDMP works with a wide range of partners to support stakeholders at all levels by providing them with policy and management guidance through a globally coordinated generation of scientific information and sharing best practices and knowledge for integrated drought management.

12.7.3  Global Drought Information System (www.drought.gov) The Global Drought Information System is an effort to pull together the best nonprescriptive drought information from local providers and provide comparison of drought conditions around the world. The North American Drought Monitor is a cooperative effort between drought experts in Canada, Mexico, and the United States to monitor drought across the continent based on the highly successful USDM.

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12.8  Remote Sensing for Drought Monitoring Earth scientists use RS to monitor or measure phenomena found in the Earth’s lithosphere, biosphere, hydrosphere, and atmosphere. The sensors are either passive or active. Passive sensors detect energy when the naturally occurring energy is available. Active sensors provide their own energy source as radar and record its reflection by the target. RS imagery has applications in mapping land use, agriculture, soils, and forestry, city planning, archaeological investigations, military observation, and geomorphologic surveying. Foresters use aerial photographs to prepare forest cover maps, locate possible access roads, and measure forest cover. Specialized photography using color infrared film has also been used to detect disease and insect damage in forests. Drought indicators can be derived from RS data. The characteristic spatial resolution of 10 km at which well-calibrated long-term historical data are freely available is coarse for effective drought monitoring. A successor to the AVHRR is the moderate-resolution imaging spectrometer (MODIS), from which composite reflectance data were made available at no cost every 8 days by NASA and USGS, through the Earth Resources Observation Systems data center. The time series of MODIS imagery provided near-real-time, continuous, and relatively high-resolution data. The IRS-1C/D WiFS could provide spatial resolution of 188 m and weekly repeat coverage. Other new sensors that could contribute toward drought monitoring are the vegetation WiFS on SPOT and the MERIS sensor on Envisat. Traditional methods of drought assessment and monitoring rely on rainfall data, which are limited in the region. It is often difficult to obtain this data in near real time. In contrast, the satellite-sensor data are consistently available and can be used to detect the onset of drought and its duration and magnitude. For drought observation, the satellite images are used to monitor soil moisture, vegetation cover, forest cover, forest fire, the NDVI, and crop conditions and estimate water in resources such as lakes, reservoirs and rivers, and snow line. Thus, RS has become a powerful tool to observe drought intensity and extent. Radars are used to monitor rains and its intensity and coverage. The radar images are useful for estimating drought break. Regular and timely images are helpful in identifying regions of drought break, situation that returns to normal, and post-drought effects like forest fire and desertification. The NDVI is a quantitative indicator of the relative abundance and activity of green vegetation. It is well correlated with several biophysical characteristics of vegetation, namely, leaf area index, green cover, green biomass, and chlorophyll. The vegetation health index estimates vegetation health based on greenness (the NDVI) and temperature. Large-area NDVI data sets are also available from other satellite-based RS instruments (MODIS, SPOT-Vegetation, and MERIS), but they lack a long historical record of information. Rainfall estimate (RFE) uses a combination of satellite-based observations (cloud temperature and cold cloud duration) and ground-based raingauge data. NASA’s Goddard Space Flight Center generates groundwater and soil moisture drought indicators each week. They are based on terrestrial water storage observations derived from satellite data and integrated with other observations, using a sophisticated numerical model of land surface water and energy processes. The MODIS and AVHRR, carried on board Terra–Aqua and NOAA satellites, respectively, are cost-effective sensors. The AVHRR sensor collects radiance data in five spectral bands including red visible (0.58–0.6 μm), near-infrared (0.725–1.1 μm), mid-infrared (3.55–3.93 μm), and two thermal infrared bands (10.3–11.3 and 11.5–12.5 μm). These radiance data were pre-processed by NASA’s Goddard Space Flight Center and made available for free downloading. Pre-processing includes the derivation of maximum-value composite (MVC) monthly images from original daily radiance data. The procedure of deriving monthly MVCs includes the examination of daily radiance values for each wave band, together with the NDVI values, for each month for each pixel. The first meteorological satellite, TIROS-1, was launched by the United States on April 1, 1960. This weather satellite used vidicon cameras to scan wide areas of the Earth’s surface. Early satellite remote sensors used the digitally captured images and transmitted these to receiving stations on the Earth’s surface. The Geostationary Operational Environmental Satellite system (GOES) provided most of the remotely sensed weather information on the United States. Advanced sensors aboard the GOES

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produced a continuous data stream so that images could be viewed at any instance in the visible and infrared ranges. Infrared images can capture weather conditions during the night. Another sensor aboard the satellite can determine vertical temperature profiles, vertical moisture profiles, total perceptible water, and atmospheric stability. Since 1972, several generations of Landsat satellites with multispectral scanners have been providing continuous coverage of Earth for almost 44 years. Currently, Landsat satellites orbit the Earth’s surface at an altitude of approximately 700 km. Spatial resolution of objects on the ground surface is 79 × 56 m. Band 4 at 0.5–0.6 μm and band 5 at 0.6–0.7 μm receive the green and red wavelengths in the visible range. Band 6 at 0.7–0.8 μm and band 7 at 0.8–1.1 μm are near-infrared wavelengths. A second sensing system, the Thematic Mapper, was added to Landsat satellites launched after 1982, which records seven wavelength bands from the visible to far-infrared ranges. In addition, the ground resolution of this sensor was enhanced to 30 × 20 m. Launched on February 11, 2013, Landsat-8 collects high-resolution multispectral data of the Earth’s surface. SPOT has launched five satellites since 1986. SPOT satellites use two different systems. One system produces black-and-white panchromatic images from the visible band (0.51–0.73 μm) with a ground resolution of 10 × 10 m. The other sensing device is multispectral, capturing green, red, and reflected infrared bands at 20 × 20 m. SPOT-5 was launched in 2002 and is much improved from the first four versions of SPOT satellites. SPOT-5 has a ground resolution of 2.5 × 2.5 m in both panchromatic mode and multispectral operation. SPOT-6 was launched on September 9, 2012, while SPOT-7 was launched on June 30, 2014. They form a constellation of Earth-imaging satellites designed to provide continuity of high-resolution, wide-swath data up to 2024. SPOT-7 image product panchromatic/color has 1.5 m and multispectral has 6 m resolution. Radarsat-1 was launched by the Canadian Space Agency in November 1995. Radarsat is an active RS system that used microwave radiation. Radarsat’s microwave energy penetrates clouds, rain, dust, or haze and produces images regardless of the sun’s illumination allowing it to image in darkness. Radarsat images have a resolution between 8 and 100 m. This sensor has found important applications in crop monitoring, defense surveillance, disaster monitoring, geologic resource mapping, sea-ice mapping and monitoring, oil slick detection, and digital elevation modeling. Radarsat-2 was launched on December 14, 2007, having a resolution of 1–3 m. GeoEye-1, launched in September 2008, is capable of producing imagery with 46 cm resolution. As of February 2013, following the merger of GeoEye and DigitalGlobe, GeoEye-2 satellite sensor will be held in storage until needed. DigitalGlobe’s next satellite is with 34 cm resolution in the panchromatic or black-and-white mode. It will collect multispectral or color imagery at 1.36 m resolution. On July 31, 2014, DigitalGlobe announced that the GeoEye-2 satellite sensor will be renamed WorldView-4 and launched in 2016 with a panchromatic resolution of 30 cm and multispectral resolution of 1.20 m.

12.9  Drought Monitoring Monitoring of drought requires computation of some drought indices and observes it for some duration or season or sometimes for a few years till the conditions restore to normal. In the United States, the drought indices are computed every week. India monitors agricultural situation; area sown; availability of inputs like seed, fertilizers, and pesticides; and status of water resources and reservoirs once a week through the DAC, but a quantitative drought monitoring is not in place. Drought prediction is a difficult task. Analyses of model-simulated soil moisture drought indices and precipitation-minus-evaporation suggest increased risk of drought in the near future. There are large differences in the observed and model-simulated drying patterns. Previous studies show that changes in sea surface temperatures have large influences on land precipitation. The inability of the coupled models to reproduce many observed regional precipitation changes is linked to the lack of the observed natural change patterns in sea surface temperatures. Some models reproduce not only the influence of El Niño– Southern Oscillation (ENSO) on drought over land but also the observed global mean aridity trends [2].

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Thus, ENSO and climate models are the initial indicators of drought early warning systems. The longrange forecasts issued by the meteorological services and forecasts generated by crop models are also indicators of future droughts. Historical records of precipitation, streamflow, reservoirs, data on the crops, and long-range forecast are an integral part of pre-drought observations. There may not be any drought, but the observing agencies keep regular watch on the weather, climate, environment, and water resources. Governments also keep on observing socioeconomic information, that is, the population, their income and economic conditions, job patterns, and job potentials. Data on supply of water, electricity, and fuel to agriculture and to rural sector form a part of pre-drought observations. Some of these observations are not made with the intention of monitoring drought. If drought occurs, these are critical information for decision-makers on drought relief and mitigation.

12.9.1  Drought Observations Observing drought is observing deficit of rainfall/snowfall and its impact over a region for a duration in which its impact is felt. Drought observations involve analysis of precipitation data, water availability, vegetation, state of agriculture, and impact on a community. The first attention goes on water resources, if there is sufficient water available to meet the crisis, for example, water for cities, agriculture, and hydroelectricity. The data on water supply/availability, streamflow, and the surface inland water resources are used to assess the hydrological drought. RS is used to assess hydrologic conditions on large regions. Once the drought is set, humidity and soil moisture are reduced, the temperatures go up and winds also become strong, and then the water requirements of crops go up. Thus, monitoring these parameters and soil moisture and soil temperature becomes important. Agricultural drought monitoring requires observations on crop conditions from sowing to harvest, crop production, fodder, soil moisture, soil temperature, evaporation and evapotranspiration, etc. Socioeconomic drought requires monitoring of stocks of food grains, price of food items, availability of water in reservoirs, and electricity production. The impact of drought depends on the vulnerability of the community. For relief measures, watch is kept on economic conditions, purchasing power, supply of water and essential goods, employment scenario, job potential, and migration of people and animals and wild life. Monitoring starvation, deaths of people and animals in different parts of drought-affected area, and epidemics are also important in extreme drought situations. After drought is set, it is necessary to watch till the drought breaks. While observing a drought severity, temporal and spatial extent, onset, break, and long-term aftereffects should be monitored. Occurrence of rainfall and its quantity and number of rainy days need be monitored over a time and region on which drought has occurred. Gibbs method [4] provides a statistical approach to declare onset and break of drought. The color patterns and indices on the USDM give indication to restoration. The post-drought effects, particularly on sowing of crops, availability of grazing land, and deaths of animals due to drought-breaking rains, are important post-drought observations. There could be bad law and order situation when relief material is supplied. The economic, environmental, and social losses should also be estimated and monitored over the drought-affected regions. Economic losses are due to production losses in agriculture and related sectors, including forestry and fisheries. It causes a loss of income and purchasing power, particularly among the rural population. All the industries that are dependent upon these primary sectors for their raw materials would suffer losses due to reduced supply and increased prices. Drought thus has a multiplier effect on the economy. Environmental losses are due to lower water levels in reservoirs, lakes, and ponds and reduced flows from springs and streams would reduce the availability of feed and drinking water and adversely affect fish and wildlife habitat. It may also cause loss of forest cover, migration of wildlife, and their greater mortality due to increased contact with agricultural producers. A prolonged drought may bring stress for the endangered species and loss of biodiversity. Reduced streamflow and loss of wetlands may bring changes in the levels of salinity. Increased groundwater depletion, land subsidence, and reduced

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recharge may damage aquifers and adversely affect the quality of water. The degradation of landscape quality, including increased soil erosion, may lead to a more permanent loss of biological productivity of the landscape and thus cause land degradation and desertification. Droughts cause an enormous amount of social losses and deprivations, which arise from lack of income, conflicts among the water users, and migration of the population out of the drought-affected areas. People seek to cope with drought in several ways that affect their sense of well-being: they withdraw their children from schools, postpone daughters’ marriages, and sell their assets such as land or cattle. Inadequate food intake may lead to malnutrition and, in some extreme cases, cause starvation. Access and use of scarce water resources generate a situation of conflict, which could be socially very disruptive.

12.9.2  Drought Monitoring in the United States The USDM, established in 1999, generates weekly maps of drought conditions that are produced jointly by the NOAA, the USDA, and the NDMC at the University of Nebraska, Lincoln. The map summarizes and synthesizes information from the local and state levels to the national scale, making it the most widely used gauge of drought conditions in the country. The USDM maps provide a summary of drought conditions across the United States and Puerto Rico. Often described as a blend of art and science, the map is updated weekly by combining a variety of data-based drought indices and indicators and local expert input into a single composite drought indicator. The map depicts four levels of drought intensity (D1–D4) and one level of “abnormal dryness” (D0). Also depicted are the areas experiencing agricultural (A) or hydrological (H) drought impacts. These impact indicators help communicate whether short- (S) or long-term (L) precipitation deficits are occurring.

12.9.3  Drought Monitoring in Australia One of the most successful approaches, and one of the simplest in concept, uses the first decile of accumulated rainfall for a given period as an indicator of drought [4]. The first decile is the amount of rainfall that exceeded on 90% of occasions for the period of the year specified, for example, winter, spring, or indeed any period of consecutive months. An area is categorized as having a rainfall deficiency when the rainfall for a period of at least 3 months falls within the lowest 10% (below the first decile) of the historically recorded rainfalls for the same period of that year. Table 12.3 provides the meaning of rainfall deficiencies. “Serious rainfall deficiency” exists for a specific period of 3 (or more) months when the rainfall is above the lowest 5% of recorded rainfalls but is less than the 10% value. “Severe rainfall deficiency” exists for a specific period of 3 (or more) months when the rainfall is among the lowest 5% of recorded rainfalls. TABLE 12.3  Types of Rainfall Deficiency Type of Deficiency Lowest on record Severe deficiency Serious deficiency Very much below average Below average Average Above average Very much above average

Rainfalls in the Range Lowest since 1900 when data analyses began Lowest 5% of historical totals lowest 5% Lowest 10% of historical totals Lowest 30% of historical totals, but >10% Middle 40% of historical totals Highest 70% of historical totals, but = 0.85 Missing Cloud Snow

Vegetation condition index (VCI) Dekad 2 September 2015 METOP-AVHRR WGS84, Geographic Lat/Lon

FIGURE 14.17  Global VCI of dekadal of September 2, 2015. (From FAO, Italy, http://www.fao.org/giews/ earthobservation/asis/index_2.jsp?lang=en, accessed on September 25, 2015.)

A value of −0.35 was suggested by Kogan [43] as a threshold for identifying extreme drought conditions. The value close to 0 reflects an extreme dry month (NDVI value close to its long-term minimum value). The global VCI developed using Metop AVHRR is given in Figure 14.17 for decadal of September 2, 2015. The VCI provides accurate information limited not only to well-defined, prolonged, widespread, and intensive drought but also to very localized, short-term, and not well-defined droughts [43]. 14.3.2.5 Temperature Condition Index In order to determine temperature-related vegetation stress, Kogan [43] introduced another index termed as temperature condition index (TCI). The algorithm of TCI calculation is almost similar to VCI, the only formula that was modified to reflect different responses of vegetation to temperature. The conditions were estimated based on minimum/maximum temperature envelope using the following equation: TCIijk =

BTi ,max - BTijk BTi ,max - BTi ,min

(14.5) where BTijk is the brightness temperature at channel 4 of NOAA AVHRR for pixel i in month j for year k BTi,min and BTi,max are the multiyear minimum and maximum brightness temperature, respectively, for pixel i

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The channel 4 of NOAA AVHRR is selected because it is less responsive to water vapor in the atmosphere [43]. TCI improved the accuracy of drought monitoring by explaining the temperature contribution to the analysis. It also provided useful information for monitoring vegetation stress due to soil saturation. 14.3.2.6 Vegetation Health Index In order to express their (VCI and TCI) additive approximation of vegetation stress, Kogan [43] combined the two with some weights assigned to each as follows:

VHI = 0.70 * VCI + 0.30 * TCI

(14.6)

As the NDVI reflects both temperature and precipitation conditions and used to develop VCI, the higher weights were assigned to VCI. It was also suggested that these weights should be reexamined based on the correlation analysis. The vegetation indicators NDVI anomaly, VCI, and vegetation health index (VHI) that have been considered as a proxy to detect potential drought based on water-stressed vegetation condition are provided at the global scale by the Food and Agriculture Organization at http://www.fao.org/giews/earthobservation/ asis/index_2.jsp?lang=en. These vegetation indicators are based on a 10-day (dekadal) vegetation data from the Metop-AVHRR sensor at 1 km resolution (2007 and after). Data at 1 km resolution for the period 1984–2006 were derived from the NOAA-AVHRR dataset at 16 km resolution. These indicators can be visualized at any country for any decadal. Many studies have shown the NDVI to be related to the leaf area index (LAI), green biomass, percent green cover, and fraction of absorbed photosynthetically active radiation (fAPAR). Relationships between fAPAR and NDVI have been shown to be near linear in contrast to the nonlinearity experienced in LAI–NDVI relationships with saturation problems at LAI values over 2. Other studies have shown the NDVI to be related to carbon fixation, canopy resistance, and potential ET allowing its use as an effective tool for drought monitoring.

14.3.3 Based on Land Surface Temperature The LST has been considered as a valuable diagnostic parameter of biospheric stress caused by soil moisture deficiencies [5]. During the past decade, significant advancement has been made to estimate land surface emissivity and temperature through remote sensing using a thermal IR band (8–14 μm). Kahle et al. [37] estimated the surface temperature assuming constant emissivity in one channel and using previously determined atmospheric parameters. According to Hook et al. [31], the thermal log residuals and alpha residuals have also been used to extract emissivity from multispectral thermal IR data. Based on these techniques, a temperature–emissivity separation method has been recently developed for the Advanced Spaceborne Thermal Emission and Reflection Radiometer products [10]. In addition, three more methods have been developed to estimate LST from space: the single IR channel method, the split window method that is used in various multichannel sea surface temperature (SST) algorithms, and a new day/night MODIS LST method that is designed to take advantage of the unique capability of the MODIS instrument. The first method of LST estimation requires surface emissivity, a radiative transfer model, and atmospheric profiles that can again be taken by satellite soundings data. In the second method, the corrections for the atmospheric and surface emissivity effects are made by using surface emissivity as an input based on the differential absorption in a split window [73]. The third method is the improved version of Li and Backer [47] that uses day/night pairs of TIR data in seven MODIS bands instead of AVHRR bands for simultaneously retrieving surface temperatures and band-averaged emissivities without knowing the atmospheric temperature and water vapor profiles to high accuracy. An extensive review on status and perspective of satellite-derived LST has been done by Li et al. [48]. The development of an accurate algorithm for LST is a difficult task due to the difficulties associated with the correction of both atmospheric and surface emissivity effects. The accuracy of atmospheric corrections is limited to radiative transfer methods, uncertainties in atmospheric absorption coefficients,

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aerosol absorption/scattering coefficients, and atmospheric profiles. The following atmospheric transmittance/radiance codes in the development of SST and LST algorithms have widely been used: LOWTRAN6 [42], LOWTRAN7 [41], MODTRAN [15], and MOSART [20]. In the year 2013 onward, Landsat 8 data also provided two TIR bands that were extensively exploited to develop high-resolution LST data using the split window approach [33]. Figure 14.18 shows an 8-day composite LST as observed by MODIS in clear-sky conditions for the time period July 28–August 5, 2015. Surface temperature could be quite complementary to vegetation indices derived from the combination of optical bands. LST has a strong negative correlation with NDVI, due to enhanced evaporation and the consequent decrease in soil moisture caused by an increase in temperature, which results in the declination of the vegetation cover considering water as the main limiting factor for its growth [13]. McVicar and Bierwirth [56] suggested the ratio of LST and NDVI (LST/NDVI) as a rapid means to assess drought conditions in cloudy environments. Bayarjargal et al. [14] proposed a new index, DSI, which is calculated as a subtraction of standardized LST and NDVI for a certain month (see Equations 14.7 through 14.9), based on the normalization approach to bring NDVI and LST at the same comparable scale in terms of their ranges:





DSIijk = DLSTijk - DNDVIijk DLSTijk =

DNDVIijk =

(14.7)

( LST - LST ) ij

ijk

sLSTij

( NDVI

ij

- NDVIijk

sNDVIij

(14.8)



)

(14.9)



where LSTijk is the LST for pixel i in month (or decadal) j for year k LSTij is the multiyear average LST for pixel i in month (or decadal) j σLSTij is the standard deviation of LST for pixel i in month (or decadal) j

°C –25

10

45

FIGURE 14.18  LST (day 8—Terra/MODIS) for a period from July 28 to August 5, 2015. (From NASA Earth Observation, Washington, DC, http://neo.sci.gsfc.nasa.gov/view.php?datasetId=MOD11C1_E_LSTDA&date=2015-08-01, accessed on August 16, 2015.)

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14.3.4 Based on Evapotranspiration The estimation of water stress in vegetation or low ET from crops is another indicator of drought. As water stress increases, the canopy resistance for vapor transport results in canopy temperature rise in order to dissipate the additional sensible heat. Sensible heat transport (ET) between the canopy (Ts) and the air (Ta) is proportional to the temperature difference (Ts − Ta). In other words, ET represents the exchange of mass and energy between the soil–water–vegetation system and the atmosphere [68]. The long prevailing weather conditions affect reference ET (ETo) through numerous variables such as radiation, temperature, wind, and relative humidity. Moreover, actual ET (ETa) is also affected by land cover class and soil moisture at that particular duration. As the accurate ET measurement at large spatial extent is a difficult task, large hydrological models have been adopted to estimate ETa using satellite remote sensing inputs. These models are usually grouped into two: water balance [3] and energy balance mode [12]. The water balance group of models concentrates on tracking the pathways and magnitude of rainfall in the soil–vegetation system. However, energy balance models use LST as a primary constraint in the partitioning of available surface radiant energy between heat and water flux [68,69]. Both of these models use the same concept of an ETo to estimate maximum possible ET under unlimited water conditions, considering ideal reference crop with standardized bulk and aerodynamic resistance factors for vapor transport. The only difference between the two groups of models is the calculation of a correction factor for evaluating soil moisture impact on evaporation, that is, estimating ETa as a fraction of ETo. The NDVI is the main remote sensing input for water balance models; however, NDVIs along with LST are inputs for energy balance models. Further details on these types of models can be found at Senay et al. [68]. From a drought monitoring point of view, ETa and their anomalies are generally calculated for an accumulation period (monthly to seasonal) that is appropriate for the growing season. The global spatial distribution of monthly ETa anomaly (%) as a fraction of the average (2003–2013) for June 2015 is provided in Figure 14.19.

180°

135°W

90°W

45°W



45°E

90°E

135°E

180°

60°N 30°N 0° 30°S 60°S

ETa anomaly (%) 150

90–110 130–150

FIGURE 14.19  Global spatial ETa anomaly (%) map produced by the energy balance model for August 2015. (From USGS FEWS NET/EROS, http://earlywarning.usgs.gov/fews/search/Global, accessed on September 15, 2015.)

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It can be seen that the Maharashtra region of India that is known for drought hazard is under a prominent drought condition. In this way, the severity and extent of drought can be identified in any part of the globe using ET information.

14.3.5 Based on Soil Moisture From an early warning of agricultural drought point of view, soil moisture in the root zone is a key parameter. It has a significant role in the partitioning of the energy at the ground surface into sensible and latent (ET) heat exchange with the atmosphere. It also helps in the partitioning of precipitation into infiltration and runoff. Estimation of soil moisture through a remote sensing technique overcomes most of all limitations of conventional techniques owing to its capability to capture any spatial variation over a large extent at a frequent time interval. However, the extraction of soil moisture requires subsurface information; therefore, appropriate spectral bands that are capable of penetrating the soil surface are essential. The remote sensing–based estimation of soil moisture is mostly being carried out using thermal and microwave bands of the EMR spectrum. In thermal remote sensing, soil moisture is interpreted based on the thermal inertia of the land surface. The coarser spatial resolution and poor capability to penetrate through vegetation are drawbacks of use of thermal bands. Nghiem et al. [62] considered soil moisture as key variable for drought monitoring. It was suggested that both passive and active microwave remote sensing sensors can fill the information void with regard to soil moisture measurement over a large spatial extent with few or no missing gap. The presence of water in soil changes its dielectric constant, and in turn the brightness temperature, both of which have been used to map soil moisture using remote sensing [22]. Wagner et al. [77] mentioned that the microwave L band (wavelength 15–30 cm), C band (wavelength 3.8–7.5 cm), and X band (wavelength 2.5–3.8) are the most effective bands for soil moisture estimation. Passive microwave radiometers have shown the greatest potential among other remote sensing methods for the soil moisture measurement. The advantages of microwave measurements at 1–3 GHz (1) are directly sensitive to changes in surface soil moisture, (2) are the least affected by clouds, and (3) can penetrate moderate amounts of vegetation. Depending on the wavelength and soil wetness, these sensors can measure surface moisture up to depths of 2–5 cm. The effect of soil moisture on the measured passive microwave radiometer signal dominates over that of surface roughness; however, the converse is true for active microwave radars. Higher-frequency Earth-imaging passive microwave radiometers, namely, the scanning multichannel microwave radiometer launched on the Seasat (1978) and Nimbus-7 (1978–1987) satellites, the SSM/I launched on the DMSP satellite series, TMI, Advanced Microwave Scanning Radiometer for the Earth Observation System (AMSR-E), and Soil Moisture and Ocean Salinity (SMOS), have been utilized in soil moisture studies. The capabilities of these higher-frequency instruments are limited to soil moisture measurements over predominantly bare soil and in a very shallow surface layer (2 1.5 to 1.99 1.0 to 1.49 −0.99 to 0.99 −1.0 to −1.49 −1.5 to −1.99 0 ba G ( a )

(15.2)

where α(>0) is a shape factor β(>0) is a scale factor x > 0 is the precipitation value Γ(α) is the gamma function, which is defined as ¥

ò

G ( a ) = y a -1e - y dy

0

(15.3)

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Shape factor (α) and scale factor (β) required for fitting the distribution to the data are obtained using the following equations: a =

1 æ 4A ç1 + 1 + 4 A çè 3 b =

where A = ln ( x ) -

x a

ö ÷÷ ø

(15.4)

(15.5)

å ln ( x ) /n for n observations.

Then, the cumulative probability distribution of precipitation for any timescale is calculated using the following equation: x

ò

G ( x ) = g ( x ) dx = 0

x

1

òx b G ( aˆ ) a



a -1

e - x /b dx

(15.6)

0





Substitution t for x / b in Equation 15.6 reduces the equation to incomplete gamma function: G(x) =

x

1 a t -1e -1 dt G ( aˆ )

ò 0

(15.7)

Gamma function is defined for x > 0 but the precipitation records may contain zero values, so the cumulative precipitation function becomes

H ( x ) = u + (1 - u ) G ( x )

(15.8)

where u is the probability of the zero value of precipitation. The cumulative probability function H(x) is then transformed to the standard normal random variable Z with mean as zero and variance as one using normal inverse cumulative distribution function. The normal inverse function is defined in terms of the normal cumulative distribution function as

{

}

(15.9)

2 - t -m /2 s2 e ( ) dt

(15.10)

x = F -1 ( p |m,s ) = x : F ( x |m,s ) = p

where



p = F ( x |m,s ) =

1 s 2p

x

ò





x is the solution of Equation 15.10 for a desired value of probability p. x here is SPI values (Z) and probability p is H(x) obtained from Equation 15.8. Figure 15.3 shows SPI calculated at Ajmer station (Station 1) for 1-, 3-, 6-, and 12-month timescales.

261

SPI 6

SPI 3

SPI 1

Regionalization of Drought Prediction

SPI—1-month scale 4 3 2 1 0 –1 –2 –3 –4 1901 1906 1911 1916 1921 1926 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 Year SPI—3-month scale 3 2 1 0 –1 –2 –3 –4 1902 1907 1912 1917 1922 1927 1932 1937 1942 1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 19972002 Year SPI—6-month scale 4 3 2 1 0 –1 –2 –3 –4 1902 1907 1912 1917 1922 1927 1932 1937 1942 1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002

SPI 12

Year SPI—12-month scale 4 3 2 1 0 –1 –2 –3 –4 1902 1907 1912 1917 1922 1927 1932 1937 1942 1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 Year

FIGURE 15.3  Different timescale SPI for Ajmer Station (Station 1).

Advantages of SPI as discussed by Hayes et al. [26] and Mishra and Desai [38] are as follows:

1. It requires only rainfall as input. So it can be easily used for catchments where other hydrometeorological parameters are not known. 2. It can be computed for different timescales. This property can be used to study different kinds of drought like meteorological, hydrological, and agricultural. 3. SPI is not adversely affected by topography. 4. The fourth advantage of SPI is due to its normal distribution, which ensures that the frequencies of extremes at any location and on any timescale are consistent.

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Limitations of SPI as discussed by Mishra and Singh [39] are as follows:



1. SPI values are significantly affected by the length of precipitation record. Similar and consistent results were obtained when the SPI values, computed from different record lengths, have similar gamma distribution over different time periods. However, the SPI values are significantly discrepant when the distributions are different. 2. As discussed earlier, SPI is based on fitting of a precipitation distribution. Commonly used distributions are gamma distribution [37,38], Pearson Type III distribution [23], and lognormal, extreme value, and exponential distributions [34,35,56]. The use of different distributions affects the SPI values.

15.5.4 Fuzzy c-Means (FCM) Clustering Fuzzy c-means (FCM) algorithm was proposed by Dunn [10] and was further extended by Bezdek [5]. The algorithm iteratively optimizes a fuzzy objective function. Consider a cluster c having M objects in which Yk is the data vector for kth object, k = 1, 2, …, M. The fuzzy objective function is J (U ,C ) =



M

c

ååu

a ik

Yk - Ci

k =1 i =1

2

(15.11)

where uik is the degree of membership of kth data point in ith cluster Ci is the center of ith cluster ‖Yk − Ci‖2 is squared Euclidean distance of data vector k from the center of ith cluster α is called fuzzifier Fuzzifier can have any value greater than 1, but generally its value is set between 1 and 2.5. Fuzzy c-means algorithm steps:

1. Number of clusters and cluster centers are assumed randomly. 2. Membership matrix is calculated using the following equation: é uit 3B42) dominate in both JJA and DJF, especially in rain regimes of high rain rate. Over ocean, negative MD values (3B42RT < 3B42) prevail. In general, relative (to their means) MD values increase as rain rate in the rain regimes increases. Variation of the individual differences between the two products is small (large) over regions of heavy (light) rain. There is no significant interannual variation in the seasonal mean statistics. The differences between the two products are likely due to the differences in the algorithms [36].

22.6 Application Examples 22.6.1 The 2013–2014 Brazil Drought A severe drought has hit the coffee-growing region in southeast Brazil, ruining local coffee crops and pushing prices up around the world, according to news reports. Climatologically, austral summer (DJF) is the raining season in Brazil. However, rainfall during the past rainy season fell short of the normal. With Giovanni TOVAS, an animation of rainfall anomaly for this event can be generated from the TMPA monthly rainfall product, 3B43. Figure 22.8 shows the evolution of the drought event during the past rainy season. It is seen that the rainfall fell below the normal since the beginning of the austral summer in December in southeast Brazil. During the 3-month period in the rainy season, the region is dominated by the below-normal anomaly (Figure 22.8), and the worst month occurred in January 2014, which is climatologically the peak month for rainfall in the region (Figure 22.9a). ASCII data from time series in TOVAS can be easily imported to Microsoft Excel for further analysis. Figure 22.9 contains three time series for the drought-affected region, and they are the monthly total rainfall and its climatology (Figure 22.9a), the anomaly or departure from its climatology (Figure 22.9b), and the normalized rainfall anomaly (divided by its climatology) in percentage (Figure 22.9c). Figure 22.9a and b shows that the monthly rainfall the region received is less than the climatology since the rainy season begins. In January 2014, more than 60% of the normal monthly rainfall total had not been received in the region. In fact, compared to normal, very little rain had been received since August 2013.

22.6.2 The 2013–2014 California Drought The recent droughts in California have been described as the most severe droughts on record, causing severe damage to agriculture production, properties due to wild fires, etc. As described earlier, the TMPA near-real-time product, 3B42RT, can be used to monitor rainfall conditions in drought-affected regions. Figure 22.10 shows two accumulated precipitation maps for 2014 (Figure 22.10a) and 2010 (Figure 22.10b), respectively. By comparing these two maps, it is seen that, as of June 26, 2014, still less precipitation was received in the state, especially in the southern part of California, indicating that the drought situation has not improved there. In California, the seasonal variation of precipitation can be basically described as dry in summer and wet in winter. Unfortunately, people there will have to wait for the next wet season for the improvement if a normal rainfall is received. In Figure 22.10, dots of spurious heavy precipitation estimates over lakes, such as Lake Tahoe and Pyramid Lake in Nevada, which is a known issue of the data product as mentioned earlier.

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22.7 Summary and Conclusions In this chapter, two important NASA satellite missions for measuring global precipitation have been presented, including their global data products, data services, product differences, and examples for drought monitoring activities around the world. For precipitation algorithm development, brightness temperature data were introduced: (1) the merged IR product from merged geostationary satellites and (2) microwave products from TRMM TMI, GPM GMI, and other microwave instruments from their partner satellites. For global precipitation products, the TMPA and IMERG products with spatial resolutions ranging from 0.25° to 0.1° and temporal resolutions from 3 hourly to half hourly were presented as well. A wide variety of data services are available at the GES DISC, providing different ways for accessing and exploring these global precipitation data products. Basic capabilities, such as subsetting and format conversion, are among the most basic services that users are after. Giovanni TOVAS provides quick data visualization and analysis without downloading data and software, greatly simplifying data access for novices. The data comparison tools in TOVAS allow online comparison of different precipitation products including different versions in a user-defined region of interest and time span. These tools provide a means to understand differences in several popular precipitation products, such as systematic difference and biases. The concept of data rods was described along with a prototype in a very popular desktop tool, CUAHSI-HIS, in the hydrologic community. Two online map services were mentioned. The website for current conditions at the GES DISC allows a quick view of drought conditions in different regions around the world. The 10-day TMPA precipitation and its normalized anomaly maps can be displayed in the USDA Crop Explorer, along with other similar products and more. The Crop Explorer provides an integrated online environment for drought monitoring activities. Other data accessing methods mentioned are OPeNDAP, WMS, etc., which are frequently used in drought monitoring applications. The large-scale difference between two popular TMPA global precipitation products, the near-realtime product (3B42RT) and the research product (3B42), was briefly described in five different rain regimes and over two different surface types. The results show that systematic differences exist in these two products. Over land, 3B42RT estimations are higher than 3B42 and, over ocean, vice versa. Two examples were presented to describe the use of the TMPA near-real-time and research products. The former (usually available in few hours) is suitable for monitoring ongoing drought development, and the latter (available 2 months after observation) more suitable for historical drought studies. More data services are being developed for the new and improved global precipitation product suite, the IMERG, which can be used to address drought issues in a very fine scale. The effort to add the standard verification methods [9,10] from the International Precipitation Working Group to Giovanni is being implemented. Major drought indices [16] are being considered for future value-added products and data services. GIS shapefile–based product subsetting capabilities are being developed to allow data subsetting for irregular regions, such as watersheds, water districts, states, and countries. Integration and fusion of other remote sensing and ground-based products can overcome issues and weaknesses solely based on precipitation products and help develop a holistic understanding about drought events, which warrants further research and development.

Authors Zhong Liu is a research professor at the Center for Spatial Information Science and Systems of George Mason University. He is also a member of the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) Data Support Team, providing user support for Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Mission precipitation products. He was the lead developer for the NOAA/NESDIS Interactive Multisensor Snow and Ice Mapping System project. He initiated the TRMM Online Visualization and Analysis System (TOVAS), the very first instance of the NASA Goddard Giovanni family. He has been the lead developer of the Hurricane Data Analysis Tool at the GES DISC.

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He was the principal investigator for “Integrate IPWG Validation Algorithms into TRMM Online Visualization and Analysis System (TOVAS)” and the coinvestigator of “Integrating NASA Earth Science Enterprise Data into Global Agricultural Decision Support Systems” in which he served as the lead developer of the global agriculture information system. Dana Ostrenga has more than 17 years of experience working with a wide variety of NASA data product research with 15 years focused on product data management services. Her recent work includes the management of data archival and dissemination and the technical development of the services for the satellite and modeling missions supported by the NASA Goddard Earth Science and Data Information Services Center (GES DISC). Her primary focus has been on the Precipitation DISC with the dissemination of the Global Precipitation Mission and Tropical Rainfall Measuring Mission data and the Modeling Assimilation DISC with the dissemination of MERRA/MERRA-2 data. Her science focus and background has been in climatology and meteorology. As a principal support scientist for ADNET Systems based at the NASA GSFC GES DISC, she possesses a familiarity with multiple data formats, management and organization of data, and various computer languages. William Teng is a principal scientist of ADNET Systems at the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC). His work at the GES DISC includes end-to-end, value-added, and user-focused science support for NASA hydrology-related data and services. He has led projects to integrate NASA precipitation, soil moisture, and other hydrological data into operational decision support environments of the USDA, NOAA, and UN World Food Program and into the Hydrologic Information System of the Consortium of Universities for the Advancement of Hydrologic Science, Inc. His research experience includes active and passive microwave remote sensing of soil moisture, vegetation, and other terrain characteristics. He received his PhD from Cornell University in civil and environmental engineering. Steven J. Kempler is currently the manager of the Goddard Earth Sciences Data and Information Services Center (GES DISC). He has more than 20 years of experience overseeing development, implementation, and operations of NASA Earth science data systems, as well as facilitating the evolution of Earth science data systems, emphasizing the develop and operation of innovative solutions to meet new challenges. For the 10 years at NASA/GSFC, prior to serving the GES DISC, among his many past projects, he is particularly proud to have worked on the science-shattering missions, Voyager and COBE. Bruce Vollmer serves as the mission support lead for the NASA Goddard Earth Sciences Data and Information Services Center. The mission and science teams he supported include the Aqua and Aura missions, NASA’s Making Earth System Data Records for Use in Research Environments Program, and more recently Global Precipitation Measurement and Orbiting Carbon Observatory missions. Other work activities include metadata modeling, near-real-time data availability, and the utility of digital object identifiers for datasets available from NASA. Vollmer spent his first 6 years at the NASA GSFC in the Climate and Radiation Branch participating in atmospheric moisture studies utilizing microwave radiometry including observations from Nimbus-7 SMMR and DMSP SSMI.

Acknowledgments This project is supported by the NASA GES DISC and partially supported by the NASA Research Opportunities in Space and Earth Science-2010, NNH10ZDA001N-ESDRERR, Appendix A.32: “Earth System Data Records Uncertainty Analysis,” and the NASA Earth Science Research, Education, and Applications Solutions Network (CAN-02-OES-01). Special thanks are given to the GES DISC Giovanni development team. The TMPA and IMERG data were provided by the NASA GSFC Mesoscale Atmospheric Processes Laboratory and Precipitation Processing System, which develop and compute the TMPA and IMERG as a contribution to TRMM and GPM.

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53. Rozante, J. R., Moreira, D. S., de Goncalves, L. G. G., and Vila, D. A. June 2010. Combining TRMM and surface observations of precipitation: Technique and validation over South America, Weather and Forecasting, 25(3): 885–894. 54. Rui, H., Teng, B., Strub, R., and Vollmer, B. 2012. Data reorganization for optimal time series data access, analysis, and visualization, AGU Fall Meeting, December 3–7, 2012, San Francisco, CA. 55. Rui, H., Strub, R., Teng, W. L., Vollmer, B., Mocko, D. M., Maidment, D. R., and Whiteaker, T. L. 2013. Enhancing access to and use of NASA earth sciences data via CUAHSI-HIS (Hydrologic Information System) and other hydrologic community tools, AGU Fall Meeting, December 9–13, 2013, San Francisco, CA. 56. Schneider, U., Becker, A., Finger, P., Meyer-Christoffer, A., Ziese, M., and Rudolf, B. 2013. GPCC’s new land surface precipitation climatology based on quality-controlled in situ data and its role in quantifying the global water cycle, Global Precipitation Climatology Centre, Deutscher Wetterdienst, Offenbach, Germany; Theoretical and Applied Climatology, Volume 115, Issue 1, pp. 15–40. doi:http://dx.doi.org/10.1007/s00704-013-0860-x. 57. Schneider, U., Ziese, M., Becker, A., Meyer-Christoffer, A., and Finger, P. 2015. Global precipitation analysis products of GPCC. ftp://ftp-anon.dwd.de/pub/data/gpcc/PDF/GPCC_intro_ products_2008.pdf. Last accessed: December 26, 2016. 58. Sorooshian, S., Hsu, K.-L., Gao, X., Gupta, H. V., Imam, B., and Braithwaite, D. 2000. Evaluation of PERSIANN system satellite-based estimates of tropical rainfall, Bulletin of the American Meteorological Society, 81: 2035–2046. doi:10.1175/1520-0477(2000)0812.3.CO;2. 59. Su, F., Gao, H., Huffman, G. J., and Lettenmaier, D. P. 2011. Potential utility of the real-time TMPA-RT precipitation estimates in streamflow prediction, Journal of Hydrometeorology, 12: 444–455. 60. Teng, B., Maidment, D. R., Vollmer, B., Peters-Lidard, C., Rui, H., Strub, R., Whiteaker, T., Mocko, D., and Kirschbaum, D. 2012. Bridging the digital divide between discrete and continuous space–time array data to enhance accessibility to and usability of NASA Earth Sciences data for the hydrological community, AGU Fall Meeting, December 3–7, San Francisco, CA. 61. Tian, Y., Peters-Lidard, C., and John, B. 2010. Real-time bias reduction for satellite-based precipitation estimates, Journal of Hydrometeorology, 11: 1275–1285. 62. Tian, Y. and Peters-Lidard, C. 2010. A global map of uncertainties in satellite-based precipitation measurements, Geophysical Research Letters, 37(L24407): 1–6. 63. Tripoli, G. J., Medaglia, C. M., Dietrich, S., Mugnai, A., Panegrossi, G., Pinori, S., and Smith, E. A. 2005. The 9–10 November 2001 Algerian flood: A numerical study, Bulletin of the American Meteorological Society, 86: 1229–1235. 64. Unidata. 2016. Software for manipulating or displaying NetCDF data, Unidata, http://www. unidata.ucar.edu/software/netcdf/software.html. Last accessed: December 26, 2016. 65. USDA FAS. 2016. The Crop Explorer, USDA-FAS, Washington, DC, http://www.pecad.fas.usda. gov/cropexplorer/mpa_maps.aspx. Last accessed: December 26, 2016. 66. Wang, J.-J., Adler, R. F., Huffman, G. J., and Bolvin, D. 2014. An updated TRMM composite climatology of tropical rainfall and its validation, Journal of Climate, 27: 273–284. 67. Wikipedia. 2016. Drought, https://en.wikipedia.org/wiki/Drought. Last accessed: December 26, 2016. 68. Wu, H., Adler, R. F., Hong, Y., Tian, Y., and Policelli, F. 2012. Evaluation of global flood detection using satellite-based rainfall and a hydrologic model, Journal of Hydrometeorology, 13: 1268–1284. 69. Yilmaz, K., Adler, R., Tian, Y., Hong, Y., and Pierce, H. 2010. Evaluation of a satellite-based global flood monitoring system, International Journal of Remote Sensing, 31: 3763–3782.

23 Application of Data-Driven Models in Drought Forecasting 23.1 Introduction ......................................................................................423 23.2 Preprocessing of Data: First Step before Forecasting ................. 426 Principal Component Analysis  •  Standardizing

23.3 Artificial Neural Networks .............................................................427

Shahab Araghinejad University of Tehran

Seyed-Mohammad Hosseini-Moghari University of Tehran

Saeid Eslamian Isfahan University of Technology

Multilayer Perceptron  •  Radial Basis Function  •  The Generalized Regression Neural Network  •  Probabilistic Neural Network

23.4 Adaptive Neuro-Fuzzy Inference System .....................................430 23.5 Support Vector Machine .................................................................. 431 Support Vector Classification  •  Support Vector Regression

23.6 Case Study ..........................................................................................436 Application of Models

23.7 Summary and Conclusions .............................................................439 Authors ..........................................................................................................439 References ..................................................................................................... 440

Abstract  Modeling a drought forecasting system is one of the most significant challenges in the field of water resources and environmental engineering that arise as a result of the physical complexity of a natural phenomenon or the time-consuming process needed for analyzing different components of a system. Data-driven models have been found to be very powerful tools that can help overcome such challenges by presenting opportunities to build basic models from the observed patterns as well as accelerating the response of decision-makers in facing with the real-world problems. Since they are able to map causal factors and consequent outcomes of an event without the need for a deep understanding of the physical process surrounding the occurrence of an event, these models have become popular among water resources and environmental engineers. Also, as recent progresses in soft computing have enriched the collection of data-driven techniques by presenting new models as well as enhancing the classic ones, the continuity of such popularity is expected.

23.1  Introduction Drought is known as the deficiency of water in one or several components of the hydrological cycle. It occurs when the available water of a system is not sufficient to supply at least one of the b ­ iological, ­economic, and social water needs during a considerable time period [11]. A drought plan depends on indicators and triggers to characterize drought conditions and guide drought responses. Drought indices 423

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would be suitable if they provide reliable information to forecast the onset and termination of a drought. Despite their importance, drought forecasting based on the combination of different indicators and triggers is usually the weak part of drought plans, often lacking operational relevancy and scientific justification. A drought forecasting process could be viewed by different points of view, methods, and models. In a very rough classification, drought forecasting methods are divided into two methods: direct and indirect. Also the viewpoints are divided into quantity and quality viewpoints. Furthermore, the models are divided into direct methods and multistep recursive methods (Figure 23.1). It is safe to say, nowadays, that most forecasts of drought are based on data-driven models. Datadriven models have different types that might cover different views to drought forecasting. Modeling a drought forecasting system is one of the most significant challenges in the field of water resources and environmental engineering that arise as a result of the physical complexity of a natural phenomenon or the time-consuming process needed for analyzing different components of a system. Data-driven models have been found as very powerful tools to help overcoming those challenges by presenting opportunities to build basic models from the observed patterns as well as accelerating the response of decision-makers in dealing with the real-world problems. Since they are able to map causal factors and consequent outcomes of an event without the need for a deep understanding of the physical process surrounding the occurrence of an event, these models have become popular among water resources and environmental engineers. Also, as recent progresses in soft computing have enriched the collection of data-driven techniques by presenting new models as well as enhancing the classic ones, the continuity of such popularity is expected. Data-driven models, as their name suggests, refer to a wide range of models that simulate a system by the data experienced in the real life of that system. They include different categories generally divided into statistical and soft computing (also known as artificial intelligence) models. Data-driven models are often inexpensive, accurate, precise, and, more importantly, flexible, which make them able to handle a wide range of real-world systems with different degrees of complexity based on our level of knowledge and understanding about a system. As far as the statistical type is concerned, these models could be considered among the very primary models in the life of modern engineering. However, they could be  categorized as brand new models with regard to the soft computing type. Data-driven modeling could be defined as a solution defined by the paradigm of “engineering thinking and judgment” to the world of modeling to deal with the problems, which are considered too complex by our knowledge of mathematical equations. Data-driven models have been brought up to their present form by the ideas and applications from different fields of engineering. In case the drought index is forecasted directly, the forecasting method is called a direct method. On the other hand, if the basic variables of calculating the drought index are forecasted instead, the method is called an indirect method.

Drought forecasting

FIGURE 23.1  Methods, point of view, and models in drought forecasting.

Direct models

Models

Recursive models

Qualitative forecast

Quantitative forecast

Point of view

Indirect methods

Direct methods

Methods

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Application of Data-Driven Models in Drought Forecasting

Some researchers believe that the importance of an accrued forecasting of a drought index is not more important than the prediction of the category of drought (for instance, mild or severe), so some methods deal with the category of a drought instead of forecasting a quantitative value. Models that are used in long-lead drought forecasting could be considered as two major categories. In the first category, the model is used in a direct way from the predictors (inputs) through the outputs (Figure 23.2). Instead, several models could be used in a hybrid model to predict drought in a long-leadtime manner (Figure 23.3). This hybrid model might be called a recursive model where the output of Input 1

Output 1

Input 2

Output 2 Model

Input 3

Output 3

Input n

Output m

FIGURE 23.2  A view from a direct model. Input 1 Input 2 Model

Output 1

Model

Output 2

Input 3

Input n

Output 1 Input 2 Input 3

Input n

FIGURE 23.3  A view from a recursive model.

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a model is actually the input of another model (Figure 23.3). While selecting the type of methods and models and viewpoints is a basic need for a drought plan, it is important to select a model among different data-driven models to support the objective of a drought plan.

23.2 Preprocessing of Data: First Step before Forecasting Preprocessing data before entering the forecasting models, although not required, can sometimes have an important role in improving the performance of models. Three common preprocessing methods can be used in principal component analysis (PCA) and standardizing the data. These methods are presented in this section.

23.2.1 Principal Component Analysis PCA is a method that can be used for two aims. The first aim is to reduce the dimension of data and the second aim is to remove the linear correlation between variables. PCA replaces groups of correlated variables with new uncorrelated variables called the principal components (PCs). PCA replaced the cartesian coordinate system by a new orthogonal coordinate system, where the first axis passes through the long axis of the data scatter and the new origin. This new coordinate system has the advantage over the initial coordinate system where the first axis can be used to describe most of the variance, while the second axis contributes only a little. Therefore, it is possible to reduce the data dimension by dropping the second axis without losing much information in case of significant correlation. Considering the n vector of correlated vectors, Xi and PCs are linear combinations of those n vectors. The number of PCs is equal to n where all PCs together contain the full variance of the data set. The variance is concentrated in the first few PCs, which explains most of the information content of the data set; it is possible that we ignore some PCs where a little of the variance is described. n PCs are calculated as PC1 = a11 X1 + a12 X2 +  + a1n Xn PC2 = a21 X1 + a22 X2 +  + a2n Xn  PCn = an1 X1 + an2 X2 +  + ann Xn



(23.1)

Figure 23.4 shows an example of PC analysis for a 2D data set. X2

PC2

PC1

X1

FIGURE 23.4  An example of PCA for a 2D data set.

Application of Data-Driven Models in Drought Forecasting

427

23.2.2 Standardizing Data standardization is very simple, but usually it can improve the performance of the model. In standardizing, all variables are transmitted to a specified range (usually between zero and one). Standardizing causes input variables with different ranges and does not affect the performance of the model. There are many equations for standardizing, and the most common is the following equation: xnormal =



x - x min x max - x min

(23.2)

where xnormal is the normalized x value x max and x min are the maximum and minimum values of x, respectively Based on the statement mentioned earlier that is applied on each of the input and output vectors, separately, all variables will be transferred to range zero to one.

23.3 Artificial Neural Networks There are different types of artificial neural networks (ANNs). This chapter introduces the popular models of these networks including multilayer perceptron (MLP), radial basis function (RBF), generalized regression neural network (GRNN), and probabilistic neural network (PNN). Before further discussion, it is necessary to be familiar with some of the following definitions: Neuron: This is the basic unit of an ANN, which by using a transfer function and based on specific input variable determines a suitable response. Architecture: A network architecture includes a number of hidden layers, a number of neurons in each hidden layers, the specific transfer functions, the flow of data (straight or recurrent), and the way neurons are connected. Train network: Training is defined as the process of calibrating the network using pairs of input/ output.

23.3.1 Multilayer Perceptron The MLP is the most famous ANN that consists of an input layer, one or more hidden layers, and an output layer [4,5]. MLP uses a supervised training procedure that consists of providing inputs and outputs to the network; the training process goes on in such a way that the following function would be minimized: E= where K is the number of data yk is the kth observation output y k is the kth forecasted output

1 K

K

å( y k =1

k

- y k

)

2



(23.3)

428

Handbook of Drought and Water Scarcity TABLE 23.1  Examples of Transfer Functions Name

Function

Linear

f(x) = x

Log sigmoid

f (x) =

Tangent sigmoid

æ 2 f (x) = ç - ax è 1+ e

Radial basis

f ( x ) = e-x

1 1 + e -ax

2

a>0 ö ÷ -1 a > 0 ø

/s2

In a three-layer MLP with m neurons in the hidden layer and n input variables, y is calculated as



é y = f ê ê ë

æ wj × g ç ç j =1 è m

å

ù ö w ji xi + w j 0 ÷ + wo ú ÷ ú i =1 ø û n

å

(23.4)

where wb is the weight that connects the jth neuron of the hidden layer and a neuron of the output layer wji is the weight connecting the ith input variable and jth neuron of hidden layer xi is the ith input variable wj0 is the bias of the jth neuron of hidden layer wo is the bias related to the output neuron g is the transfer functions for the hidden layer f is the transfer functions for the output layer Some of the transfer functions that are usually used within the artificial neurons are presented in Table 23.1. Determining the MLP architecture plays an important role in its efficiency [1,6,7]. In the architecture of an MLP, the number of hidden layers and number of neurons in each layer should be determined. Hornick et al. [5] showed that three-layer perceptrons with a sigmoid transfer function are universal approximators, which means that they can be trained to approximate any mapping between the inputs and outputs. Therefore, what is important in determining the architecture of an MLP is the number of neurons in the hidden layer. Some scholars have suggested the appropriate number of neurons (m) based on the number of input (n) or number of data (K). For example, Tang and Fishwick [10] offered “n,” Wong [15] “2n,” and Wanas et al. [13] “log (K)” as the appropriate number of neurons. Finally, by using trial-and-error method, the optimal number of neurons in the hidden layer should be determined; however, the reported offers can be used as a starting point. The low number of neurons makes the simplicity of the network, and the large number of neurons makes the complexity of the network. Therefore, it should be noted that a too simple network results in underfitting, and conversely, becoming too complex causes overfitting.

23.3.2 Radial Basis Function RBF is a three-layer network including an input layer, a hidden layer, and an output layer. This network is the basis for radial basis networks, which constitutes a group of neural networks, namely, statistical neural networks. Statistical neural networks are referred to as the networks that, in contrast to the conventional neural networks, use regression-based methods and are not inspired by the biological neural

429

Application of Data-Driven Models in Drought Forecasting

system [8]. In an RBF network, the input of transfer function for each neuron is the Euclidean distance between the input and the center of that neuron. The popular transfer function in RBF is the Gaussian function, and the Gaussian function uses the following relation [2]:

f ( X r , Xb ) = e

- éë||Xr - Xb ||*0.8326/h ùû

2



(23.5)

where Xr is the input with unknown output Xb is the observed inputs in time b h is the spread The output of the function is close to 0 when ||X r − X b|| approaches a large value and close to 1 when ||X r − X b|| approaches 0. Eventually, the dependent variable (Yr) by predictor X r is calculated as follows: m



Yr =

åw * f ( X , X ) + w b

r

b

0

(23.6)

b =1

where wb is the weight of connections from the bth hidden layer to the output layer w 0 is the bias

23.3.3 The Generalized Regression Neural Network GRNN is another type of statistical network that was introduced by Specht [9]. GRNN in the training process is very fast. In GRNN, the number of neurons in its hidden layer is equal to the number of observed data. This network including four layers consists of the input layer, pattern layer, summation layer, and output layer. The input layer is fully connected to the pattern layer. The output of each neuron in the pattern layer is connected to two neurons in the summation layer, which are called S-summation and D-summation neurons. S-summation neuron calculates the sum of the weighted outputs of the pattern layer, and D-summation neuron sums the unweighted outputs of the pattern neurons. The connecting weight between a neuron of the pattern layer and S-summation neuron is equal to the target output value corresponding to each given input pattern, while for D-summation, the connecting weight is unity. The output layer acquires the unknown output value corresponding to an input vector only by dividing the output of each S-summation neuron by the output of each D-summation neuron. GRNN uses the following equation to calculate an output:

å T × f (X , X ) Y = å f (X , X ) m

r



b =1 m

b

b =1

where Yr is the output value Tb is the target associated with the bth observation

r

r

b

b

(23.7)

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Handbook of Drought and Water Scarcity

23.3.4 Probabilistic Neural Network PNN is a network for the classification problems. This network has an architecture similar to that of the RBF network. When an input is presented, the first layer computes distances from the input vector to the calibration input vectors and produces a vector of probabilities as f(Xr, Xb). In the last layer, a compete transfer function on the output picks the maximum of these probabilities. PNN can be used as a tool for qualitative forecasting because it is not a regression model, and thus, it cannot be predicted as continuous variables.

23.4 Adaptive Neuro-Fuzzy Inference System The adaptive neuro-fuzzy inference system (ANFIS) is the result of the combination of ANN and fuzzy logic. ANFIS can describe the behavior of a complex system based on the fuzzy if–then rules that are based on the Sugeno fuzzy inference system. Assume the fuzzy inference system with two inputs, x and y, and one output, z. For the first-order Sugeno fuzzy model, a typical rule set with four fuzzy if–then rules can be expressed as follows: Rule 1: if Rule 2: if Rule 3: if Rule 4: if



x is A1 x is A1 x is A2 x is A2

and and and and

y is B1 then z1 = p1x + q1 y + r1 y is B2 then z 2 = p2 x + q2 y + r2 y is B1 then z 3 = p3 x + q3 y + r3 y is B2 then z 4 = p4 x + q4 y + r4

(23.8)

where Ai and Bi (i = 1, 2, 3, 4) are the fuzzy sets pi, qi, and ri (i = 1, 2, 3, 4) are the design parameters that are determined during the training process The architecture of ANFIS consists of five layers: input nodes layer, rule nodes layer, average nodes layer, consequent nodes layer, and output nodes layer (Figure 23.5). A brief introduction of these layers is as follows: Layer 1: Input nodes layer. All the nodes in this layer are adaptive nodes. The outputs of layer 1 are the fuzzy membership grade of the inputs, which are given by Oi1 = m Ai ( x ) , i = 1, 2

(23.9)

Oi1 = m Bi-2 ( x ) , i = 3, 4

Layer 1

Layer 2

Layer 3 w

w

A1

Π

N

A2

Π

N

x

Layer 4 x, y

Layer 5 wz

S B1

Π

N

B2

Π

N

y

FIGURE 23.5  ANFIS model for a two-input Sugeno model with four rules.

Output

431

Application of Data-Driven Models in Drought Forecasting

where μ is the membership function Oi1 is the output from node i Layer 2: Rule nodes layer. In the second layer, the nodes are fixed nodes labeled ∏, and the AND operator is applied to obtain one output that represents the result of the antecedent for that rule. The kth output of this layer (wk) is represented as

Ok2 = wk = m Ai ( x ) m B j ( x ) i = 1, 2; j = 1, 2; k = 1, 2, 3, 4

(23.10)

that represents the firing strength of each rule. The firing strength means the degree to which the antecedent part of the rule is satisfied, and it shapes the output function for the rule. Layer 3: Average nodes layer. In this layer, the nodes are fixed nodes labeled N. The task of this layer is the normalization of firing strengths from the previous layer. The outputs of this layer (wi ), which are the so-called normalized firing strengths, can be represented as Oi3 = wi =

wi

å

4

l =1

wk

, i = 1, 2, 3, 4

(23.11)

Layer 4: Consequent nodes layer. The fourth layer computes the contribution of each ith rule toward the total output. The output of each node in this layer is simply the product of the normalized firing strength and the first-order Sugeno model. Thus, the outputs of this layer can be represented as

Oi4 = wi zi = wi ( pi x + qi y + ri ) , i = 1, 2, 3, 4

(23.12)

Layer 5: Output nodes layer. In this layer, there is only one single fixed node labeled S. The task of the fifth layer is the summation of all incoming signals. Hence, the final output of the ANFIS model is given by 4



Oi5 =

åw z i i

(23.13)

i =1

It can be observed that there are two sets of parameters that must be adjusted. The first set is related to the input membership functions, which are the so-called premise parameters. The second set is the three parameters related to the first-order Sugeno model {p, q, r}. These parameters are the so-called consequent parameters. The method of least squares is used to optimize the consequent parameters, and backpropagation algorithm is applied to adjust premise parameters not separately but rather in combination. It has been proven that a hybrid algorithm has high efficiency in training the ANFIS.

23.5 Support Vector Machine Support vector machines (SVMs) are a kind of data-driven models with supervised learning that analyze data and recognize patterns used for clustering, classification, and regression analysis. SVM was developed by Vapnik in 1995 [12]. The following two types of SVM, which can be used to forecast drought, were introduced.

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23.5.1  Support Vector Classification Support vector classification (SVC) is a classification tool; therefore, it can only be used for qualitative forecasting. The difference between SVC and other classifiers is to divide the decision space in a way that the risk of classification is minimized. It means that two classes have maximum distance from both lines. This means that from the different separator, the separator is chosen to be the maximum distance of all classes. Figure 23.6 shows the difference between the ANN classification and SVC classification approach. Lines a and b are separators with error = 0, but if a new input is added, these lines may lose their accuracy, while line c has the least risk of losing its accuracy. The equation of line c is written as wT x + b = 0



(23.14)

where x is the variable in the decision space w and b are the parameters of the classifier As shown in Figure 23.6, SVC considers a margin for a classification that the equations of the marginal lines are as follows: wT x + b = 1



(23.15)

T

w x + b = -1



(23.16)

The distance of a line from the origin is obtained by |b|/||w||. Therefore, the distance between the upper marginal line and the classifier line is obtained as d=

b -1 w

-

b w

=

1 w

(23.17)

So the width of the margin is D=

X2

(23.18)

X2

b

(a)

2 w

c

a

X1

(b)

FIGURE 23.6  Schematic view of classification with the ANN (a) and the SVM approach (b).

X1

433

Application of Data-Driven Models in Drought Forecasting

The objective function of SVC is maximizing D value or 1 Min L = wT w 2



(23.19)

Also with variables in the decision space belonging to the first class (y = 1), wTx + b should be greater than or equal to 1, and with variables in the decision space belonging to the second class (y = −1), wTx + b should be smaller than or equal to −1; hence, the optimization problem is written as follows: 1 Min L = wT w 2 subject to

(

(23.20)

)

T

y w x +b ³1



The optimization problem mentioned earlier is used for the approach of “hard margin” where a solid border is considered for the support vectors (SVs), but we need an SVC with more flexibility for practical purposes. This SVC will be obtained with accepting an error of ξ for each of the borderlines. So the optimization becomes 1 Min L = wT w + C 2 subject to

(



n

åx

i

i = 1,¼, n

i =1

(23.21)

)

T

yi W X + b ³ 1 - xi

i = 1,¼, n

xi ³ 0

i = 1,¼, n

where ξi is a slack variable giving a soft classification boundary C is a penalty parameter In order to simplify the optimization process, we can solve the dual problem. The dual solution to this problem can be expressed as n

Max LD =

å

ai -

i =1

subject to 0 £ ai £ C

1 2

n

n

ååy × y a × a x i

j

i

T j i

× xj

i =1 j =1

(23.22) i = 1,¼, n

n



åa y = 0 i i

i =1

i = 1,¼, n



where αi ∈  ℜn are Lagrange multipliers; there is an αi for each vector in the training set. SVs define the decision surface and correspond to the subset of nonzero αi; these vectors can be seen as the most informative. SVs show the location of the marginal line; Figure 23.6 points where the SVs are located in marginal lines.

434

Handbook of Drought and Water Scarcity TABLE 23.2  Some Common Kernel Functions Name

Function

Polynomial

( ) k (x , x ) = (x

RBF

k(xi, xj) =  exp (−γ‖xi − xj‖2)  γ > 0

k xi , x j = xiT × x j

Linear

i

j

T i

)

× xj +1

(

d

k ( xi ,x j ) = tanh gxiT x j + r

Sigmoid kernel

)

Decision space variables (x) could be mapped to a higher-dimensional space using the function ϕ(x). Applying this transformation, the dual problem becomes n

1 Max LD = ai 2 i =1

å

n

n

ååy × y i

j× j

a i × a j × k ( x i ,x j )

i =1 j =1

subject to 0 £ ai £ C

(23.23) i = 1,¼, n

n

åa y = 0 i i



i = 1,¼, n

i =1



where k(xi, xj) = ϕ(xi) ⋅ ϕ(xj) is called the kernel function. Based on the SVs, the SVC can be carried out as follows: æ f ( x ) = sign ç ç è



ö y i a i k ( x ,x i ) + b ÷ ÷ i =1 ø n

å

(23.24)

This distinguishing function is the so-called SVC. The kernel functions generally used in SVM’s formulations are presented in Table 23.2. The SVC presented in this chapter can be classified into two classes. When one deals with more than two classes, an appropriate multiclass method is needed. A number of possible methods for this purpose are as follows [3]:

1. Modifying the design of the SVC to incorporate the multiclass learning directly in the quadratic solving algorithm 2. Combining several binary classifiers with two methods: a. “One against one,” which applies pair comparisons between classes b. “One against the others,” which compares a given class with all the other classes According to a comparison study [14], the accuracy of these methods is almost the same.

23.5.2 Support Vector Regression The basic difference between the application of SVM for support vector regression (SVR) and the application of SVM for classification is that in SVR, y is considered as a real number instead of a binary n ­ umber.

{

}

n

Considering ( xi ,t i ) as a data set, x, ti, and n represent the ith input vector, ith output vector, and total i number of observations, respectively. The following is the function used for the SVR estimation:

y = wf ( x ) + b

(23.25)

435

Application of Data-Driven Models in Drought Forecasting Lz(ti, yi) ξ*i

t y

ε ti – yi

0

ξi ε

y = wφ(x) + b

ξ*i x

FIGURE 23.7  Schematic view of SVR.

where w and b are regressive factors ϕ(x) is the high-dimensional feature space that is nonlinearly mapped from the input space x SVR seeks to minimize the risk, the same as SVC, but in SVR, the goal is that all the estimated variables are placed between the upper and lower marginal lines. The upper and lower marginal lines in SVR are y = wϕ(x) + b + ε and y = wϕ(x) + b − ε, respectively. So if a point is outside the desired range, it should be fined. Figure 23.7 shows a schematic view of SVR. An optimization process was used to find out w and b coefficients as follows: Min L = C



1 n

n

1

åL (t ,y ) + 2 w × w e

i

i

T

(23.26)

i =1

ïì t - y - e Le (t i ,yi ) = í îï 0

t-y >e otherwise

(23.27)

where ε, L ε, and C represent the acceptable error (tube size), insensitive loss function, and penalty parameter, respectively. Both ε and C are user-prescribed parameters. The dual function of the problem with application of Lagrange multipliers is as follows: n

Max LD =

å( i =1

-

1 2

n

) å( a + a* )

t i ai - a*i - e n

n

i =1

j =1

i

i

i =1

åå ( a - a* )( a - a* ) k ( x , x ) i

i

j

j

i

j

(23.28)

subject to n

å ( a - a* ) = 0 i

i

i =1

0 £ ai £ C i = 1, 2,¼, n

0 £ a*i £ C i = 1, 2,¼, n



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Handbook of Drought and Water Scarcity

After solving the optimization problem, w and b are determined. The Lagrange multipliers with nonzero values were assumed as the supporting vector. Then, the SVR can be carried out as follows: n

y=

å ( a - a* ) k ( x,x ) + b i

i

(23.29)

i

i =1

Among the various kernel functions in SVR, RBF is the most popular kernel function. Therefore, a SVR with RBF kernel function could be presented with its three parameters as SVR(γ, C, ε).

23.6  Case Study This section deals with a real case study of applying data-driven models in a real-world case study. This illustrative example adopted from Araghinejad [2] described a data-driven solution with the aim of hydrological drought prediction in a basin. The Zayandeh-rud River is the main surface resource for irrigation and domestic demands in the central part of Iran, especially in the Isfahan metropolitan area. As water demands increase in Isfahan, water withdrawals from the river increase, and it is critical that climate variability is incorporated into water resources–related decision-making. The Zayandeh-rud reservoir (Figure 23.8) with 1470 million cubic meters of volume controls streamflow upstream of Isfahan city. This example aims to set up an appropriate model based on ANNs to forecast winter inflow (inflow from January to March) to the Zayandeh-rud reservoir with emphasis on drought condition. Data of the 30-year period from 1971 to 2002 were used in this study. The predictors of the winter inflow include “October to December streamflow,” “averaged southern oscillation index from October to December,” and “rainfall from October to December” (Table 23.3).

51°,00΄

52°,00΄

53°,00΄

N

33°,00΄

33°,00΄

Isfahan city Falavarjan city Zarin shahr city Zayandeh-rud reservoir Zayandeh-rud river

32°,00΄

50 km

51°,00΄

FIGURE 23.8  Map of the Zayandeh-rud basin.

52°,00΄

53°,00΄

31°,00΄

437

Application of Data-Driven Models in Drought Forecasting TABLE 23.3  Predictors and Streamflow Data of the Study Predictor 1

Predictor 2

Predictor 3

Dependent Variable

Year

October to December Streamflow

Averaged SOI from October to December

October to December Rainfall

January to March Streamflow

1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

181.37 112.91 136.15 146.79 241.02 368.61 210.26 150.44 210.85 189.13 208.71 156.69 130.35 121.48 193.93 230.64 200.10 191.19 127.92 159.57 184.65 290.65 397.95 123.48 130.89 104.09 111.51 118.04 81.66 119.30 137.06 —

13.60 −9.77 18.27 6.47 18.00 −0.07 −12.30 −2.47 −1.93 −3.50 1.70 −24.23 4.47 0.30 −2.27 −4.33 −6.07 18.57 3.67 −3.70 −12.27 −7.90 −6.83 −12.87 1.07 3.67 −15.93 11.50 7.27 14.00 2.23 —

472.50 281.70 184.50 394.00 356.00 231.00 637.00 163.00 245.10 128.70 237.00 445.00 227.00 337.00 416.00 613.00 414.00 553.00 630.00 70.00 554.00 451.00 361.00 1041.00 99.50 116.00 315.00 98.00 385.00 380.00 350.00 —

— 187.43 346.06 201.75 223.89 376.61 293.98 449.25 302.30 228.88 359.68 207.64 207.03 193.94 188.46 168.35 412.90 489.07 278.49 346.09 198.91 220.49 478.63 330.08 323.51 197.57 133.38 296.57 180.56 139.65 151.39 324.80

23.6.1  Application of Models This study uses a combination of ANN-based models instead of relying on an individual network. The main idea of the approach of this case is to apply different networks, each trained to perform better in specific conditions. Actually, a network is trained to simulate dry conditions (below average streamflow) and another is trained for wet seasons (below average streamflow). To switch between these two networks in real-time forecasting, a classifying network (say, PNN) could be applied to decide if a condition is likely to be either a dry or a wet season. This approach is summarized in Figure 23.9. The following program is provided to train an MLP for dry or wet seasons. The difference between this MLP and a conventional MLP is actually in the “performance function.” Where a conven-

(

)

2

tional MLP uses the well-known performance function ånp =1 y p - y p , the following modified MLP

438

Handbook of Drought and Water Scarcity Seasonal streamflow predictors Use PNN for classifying wet or dry seasons Dry season

Wet season

ANN for dry season modeling

ANN for wet season modeling

Seasonal streamflow forecasting

FIGURE 23.9  The algorithm of the proposed method.

400.00 350.00 300.00 250.00 200.00 150.00 Actual streamflow

100.00

Forecast by weighted error

50.00 0.00

Forecast by normal error 1

2

3

4

FIGURE 23.10  Comparison of the simulation obtained by the dry season model by what is obtained by a conventional MLP model. ­

(

)

2

uses ånp =1 y p - y p ´ 1.2( ). To stress on dry seasons, the pairs of input/target are sorted in an a­ scending order of targets and vice versa. A comparison of the simulation obtained by the dry season model by what is obtained by a conventional MLP model is shown in Figure 23.10. Also, a comparison between the simulation obtained by the wet season model and by what is obtained by a conventional MLP model is shown in Figure 23.11. A PNN program similar to what is presented in Section 23.6 could be employed to classify dry and wet conditions. 31- p

Application of Data-Driven Models in Drought Forecasting

439

800 700 600 500 400 300 Actual streamflow

200

Forecast by weighted error

100 0

Forecast by normal error 1

2

3

4

FIGURE 23.11  Comparison of the simulation obtained by the wet season model by what is obtained by a conventional MLP model.

23.7  Summary and Conclusions As the complexity of a system increases, the efficiency of drought forecasting models offered by datadriven methods in modeling the system rises. For systems with little complexity, analytical models based on mathematical equations provide precise descriptions, but for the ones with significant complexity, data-driven models are more useful to define the patterns within the behavior of the system. The inexpensive process of developing data-driven models makes them a good choice either as the main tool for modeling a system or as an alternative to the baseline model to be compared with the results obtained by analytical and physical models in order to validate or to provide useful data and information to enhance these models. There has been an increasing interest on data-driven modeling in the field of drought forecasting during the recent decade. The need for increased accuracy and precision in drought forecasting has motivated the researchers to apply innovative data-driven models. In addition to the applicable fields of a model, they all have specific characteristics called their strengths and weaknesses. The ability or inability of modeling nonlinear systems, multivariate systems, uncertainty of processes, and descriptive data are examples to determine the strengths and weaknesses of data-driven models. Furthermore, the simplicity and easiness of calibration of models and also their complexity of formulation are other important characteristics that increase or decrease the strengths of a model.

Authors Shahab Araghinejad is an associate professor at the University of Tehran. He has more than 15 years of experience in the field of water resources planning and management. His research area is focused on the climate-based water resources management and decision support systems in the context of water resources. Seyed-Mohammad Hosseini-Moghari is a PhD candidate of water resources engineering at the University of Tehran and has more than four years of experiences in the drought and hydroinformatics field. His research is focused on drought monitoring and forecasting. Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, Iran, where he has been since 1995. He received his PhD from the University of New South Wales, Australia, under the supervision of Professor David

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Pilgrim. His research focuses mainly on water resources planning and management and s­tatistical hydrology in a changing climate. In recent years, he has been working on modeling water reuses, ­climate change and variability, IWRM, sustainable agriculture, resilience and vulnerability research, and natural resources governance and management. Formerly, he was a visiting professor at Princeton University, New Jersey, and the University of ETH Zurich, Switzerland. On the research side, he has started a research partnership from 2014 with McGill University, Montreal, Quebec, Canada. He has contributed to more than 500 publications in journals and books or as technical reports. He is the founder and chief editor of both the International Journal of Hydrology Science and Technology (Scopus, Inderscience) and Journal of Flood Engineering. His professional experience includes being on the editorial boards and being a reviewer of about 40 Web of Science (ISI) journals. He has authored more than 100 book chapters and books. Recently, he has started the editorship of several handbooks published by Taylor & Francis Group (CRC Press). A three-volume Handbook of Engineering Hydrology (2014), Urban Water Reuse Handbook (2015), a three-volume Handbook of Drought and Water Scarcity (2017), and Underground Aqueducts Handbook (2017) are published ones.

References

1. Abedi-Koupai, J., Amiri, M. J., and Eslamian, S. S. 2009. Comparison of artificial neural ­network and physically based models for estimating of reference evapotranspiration in greenhouse, Australian Journal of Basic and Applied Sciences, 3(3): 2528–2535. 2. Araghinejad, S. 2014. Data-Driven Modeling: Using MATLAB in Water Resources and Environmental Engineering, Springer, Netherlands. 3. Chapelle, O., Haffner, P., and Vapnik, V. N. 1999. Support vector machines for histogram-based classification, IEEE Transactions on Neural Networks, 10(5): 1055–1064. 4. Eslamian, S. S., Abedi-Koupai, J., Amiri, M. J., and Gohari, S. A. 2009. Estimation of daily reference evapotranspiration using support vector machines and artificial neural networks in greenhouse, Research Journal of Environmental Sciences, 3(4): 439–447. 5. Hornick, K., Stinchcombe, M., and White, H. 1989. Multilayer feedforward networks are universal approximators, Neural Networks, 2(5): 359–366. 6. Khorsandi, Z., Mahdavi, M., Salajeghe, A., and Eslamian, S. S. 2011. Neural network application for monthly precipitation data reconstruction, Journal of Environmental Hydrology, 19(5): 1–12. 7. Matouq, M., El-Hasan, T., Al-Bilbisi, H., Abdelhadi, M., Hindiyeh, M., Eslamian, S. S., and Duheisat, S. 2013. The climate change implication on Jordan: A case study using GIS and Artificial Neural Networks for weather forecasting, Journal of Taibah University for Science, 7(2): 44–55. 8. Picton, P. 2000. Neural Networks, 2nd edn., Palgrave, New York. 9. Specht, D. F. 1991. A general regression neural network, IEEE Transactions on Neural Networks, 2(6): 568–576. 10. Tang, Z. and Fishwick, P. A. 1993. Feedforward neural nets as models for time series forecasting, ORSA Journal of Computing, 5(4): 374–385. 11. Tsakiris, G., Pangalou, D., and Vangelis, H. 2007. Regional drought assessment based on the reconnaissance drought index (RDI), Water Resources Management, 21: 821–833. 12. Vapnik, V. N. 1995. The Nature of Statistical Learning Theory, Springer, New York. 13. Wanas, N., Auda, G., Kamel, M. S., and Karray, F. 1998. On the optimal number of hidden nodes in a neural network, Proceedings of the IEEE Canadian Conference on Electrical and Computer Engineering, Vol. 2, Waterloo, Canada, pp. 918–921. 14. Weston, J. and Watkins, C. 1998. Multiclass support vector machines, Technical report, CSD-TR-98-04, Department of Computer Science, Royal Holloway, University of London, Egham, U.K. 15. Wong, F. S. 1991. Time series forecasting using backpropagation neural networks, Neurocomputing, 2: 147–159.

24 Application of Intelligent Technology in Rainfall Analysis 24.1 Introduction ..................................................................................... 442 24.2 Preprocessing Analysis ................................................................... 442 Homogeneity Test • Input Data Selection • Standardizing

Mehdi Vafakhah Tarbiat Modares University

Saeid Eslamian Isfahan University of Technology

24.3 ANNs ................................................................................................. 443 24.4 Development of a Particular ANN Model ................................... 444 Selecting a Network Architecture  •  Network Training  •  Determining the Number of Hidden Nodes 24.5 ANFIS ................................................................................................ 445 24.6 SVM ................................................................................................... 448 24.7 Case Studies on Rainfall Forecasting ............................................ 451 ANNs Case Study  •  ANFIS Case Study  •  SVM Case Study 24.8 Summary and Conclusions .............................................................456 Authors...........................................................................................................457 References ......................................................................................................457

Abstract  Hydrological forecasting is the estimation of hydrological and meteorological phenomena for a special future time span. Hydrological forecasting can be categorized into two classes including short-term and long-term hydrological forecasts. Short-term hydrological forecasts often refer to a period of up to 2 days and apply flood warning systems and real-time operation of water resources systems. On the other hand, long-term hydrological forecasts refer to a period exceeding 1 week up to 1 year and apply water resources management. A hydrological forecasting service combines real-time and historical data inputs with hydrological models and modeling. Many forecasting techniques for carrying out relationships among the independent and dependent variables have been developed. Conceptual models also the same as statistical models establish relationships among the independent and dependent variables. The main difference of these models compared with statistical models is in their calibration process. The calibration process of these models is usually also performed based on experimental methods or innovation methods such as artificial intelligence (AI). The efficient techniques in AI are the artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS), and support vector machine (SVM). During the recent decades, the ANNs, ANFIS, and SVM have been applied and regarded as three of the most successful tools in the various areas of hydrology. The AI methods provide better estimations than the conventional physical methods. The AI models are suitable in various applications such as flood and drought forecasting, rainfall–runoff modeling, water quality, groundwater forecasting, and regionalization of flood and low flow. 441

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24.1  Introduction Rainfall is one of the most complicated effective hydrologic processes in runoff prediction and water management. Time series analysis has already taken place in rainfall forecasting. Time series analysis, for example, ARMA and AR models, is devoted to preserving statistical properties from the stochastic process underlying a given sample to generate long undistinguishable synthetic samples to provide for better analysis or derived processes. These models are characterized by the use of information from the analyzed series. For instance, provided the situation and information at a given time, the model can forecast what is likely to occur within a few time intervals, its expected value, and its possible variability. However, if an exogenous phenomenon is either linked to or is the cause of the process, it seems logical to introduce the information available on the phenomenon into the forecast. Artificial intelligence (AI)–based methods are usually considered as a black box tool, which is able to provide a correct matching in the form of output data for a set of previously unseen input data. AI-based methods are among the mathematical models that use experimental data to analyze real-world phenomena. In this chapter, AI-based methods will be briefly described and a case study will be added.

24.2 Preprocessing Analysis 24.2.1  Homogeneity Test An important step in data analysis is the preprocessing part. There are different methods to assess the homogeneity of the collected data. These methods are classified into two groups as absolute method and relative method. In the first method, the test is applied for each station separately. In the second method, the neighboring (reference) stations are also used in the testing [9]. Due to difficulty in finding reference stations with a high correlation and a homogeneous structure in wide regions, the absolute method is used very commonly for homogeneity test. One of the absolute methods is called run test. In order to check the homogeneity of the data, the basis of this method is annual frequency; data were collectively converted to annual and then this method can be applied on the data. A comprehensive discussion of quality control and homogeneity test algorithms is described by Guijarro [10].

24.2.2 Input Data Selection The partial autocorrelation function (PACF) of rainfall data may be used to identify an appropriate set of input combinations. The PACF is often used to identify significant correlation between current-day rainfall (Rt) and one-day-lag rainfall (Rt-1), two-day-lag rainfall (Rt-2), three-day-lag rainfall (Rt-3), etc. The PACF and corresponding 95% confidence limits can be used to identify an appropriate set of input combinations. Another method is to use the AI-based methods to help identify input combinations through trial and error and a sensitivity analysis. The AI-based methods can be used to generate sensitivity ratios that quantify how the training and validation errors change with and without the inclusion of each of the candidate input variables.

24.2.3 Standardizing Data standardization, as one of the frequently standardized data preprocesses in progress of the AI-based methods, was used due to issues caused by large attribute values. There are two main advantages in standardizing its features before applying the AI-based methods. One advantage is to avoid attributes in greater numeric ranges from dominating those in smaller numeric ranges, and the other advantage is

443

Application of Intelligent Technology in Rainfall Analysis

to avoid numerical difficulties during the calculation. It is optional to linearly scale each attribute to the range [0.1, 0.9], [–1, +1], or [0, 1]. The following equation standardizes the inputs to fall in the range [0, 1]: Ni =



xi - x min x max - x min

(24.1)

where Ni is the standardized value xi is the original data x min and x max are, respectively, the minimum and maximum of data

24.3 A NNs The first serious discussions and analyses of neural networks were made by McCulloch and Pitts [21]. In the structure of neural networks, there are three kinds of neurons: input, output, and hidden. The structure of a three-layer perceptron is shown in Figure 24.1, where m is the number of inputs, n is the number of outputs, and p is the number of nodes in the hidden layer [4]. Each node in a layer receives and processes weighted input from a previous layer and transmits its output to the nodes in the following layer through links. The connection between ith and jth neuron is characterized by the weight coefficient Wij and the ith neuron by the threshold coefficient ϑi. The weight coefficients reflect the degree of importance of the given connection in the network. The output value of the ith neuron Xi is computed as follows: Xi = f ( xi )



(24.2)

with xi = Ji +

åW X ij

jÎGi-1



(24.3)

j



where ξi is the potential of the ith neuron function f(ξi) is the activation function

y1

y2

h1

x1

yn–1

h2

x2

yn

hp

xm–1

xm

B

FIGURE 24.1  Three-layer perceptron structure. (From Coppola, Jr. E.A. et al., Artificial neural network–based modeling of hydrologic processes, in: Eslamian, S., ed., Handbook of Engineering Hydrology, Modeling, Climate Change, and Variability, Taylor & Francis Group, LLC, 2014, pp. 19–34.)

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The threshold coefficient can be understood as a weight coefficient of the connection with formally added neuron j, where Xi = 1. For computational purposes, f is selected either sigmoid (Equation 24.4), hyperbolic tangent (Equation 24.5), or linear (Equation 24.6) activation functions:

f (x) =

1 1 + e -x

(24.4)

f (x) =

e x - e -x e x + e -x

(24.5)

f ( x) = x

(24.6)

The sigmoid and hyperbolic tangent transfer functions allow nonlinearity to be introduced in the neural network processing and are broadly used in artificial neural network (ANN) modeling [23]. The weights and biases are parameters of a network that should be fixed before using an ANN. Weight and bias matrices of an ANN could be obtained by either supervised or unsupervised approaches. Training is an expression, which is usually termed the supervised approach for determining weights and biases of a network. The supervised training of an ANN could be obtained by the well-known delta rule. To apply the delta rule into the training process of an ANN, backpropagation (BP) algorithm is widely used. The BP algorithm changes the mathematical expression of the delta rule to the computational relations, which could be applied through an iterative procedure. The BP algorithm, also called the generalized delta rule, provides a way to calculate the gradient of the error function efficiently using the chain rule of differentiation. In this algorithm, network weights are moved along the negative of the gradient of the performance function through each iteration (which is usually called epoch) in the steepest descent direction [2].

24.4 Development of a Particular ANN Model 24.4.1 Selecting a Network Architecture A network architecture includes a number of hidden layers, a number of hidden neurons, specific transfer functions, the flow of data (straight or recurrent), and the way neurons are connected (say, fully connected). There are well-known networks with specific architecture that are widely used in the field of water resources and environmental engineering. Multilayer perceptron, recurrent neural networks (RNNs), time-delay neural networks (TDNNs), radial basis function (RBF) networks, generalized regression ­neural networks, and probabilistic neural networks are examples of the well-known architectures [2].

24.4.2 Network Training Before training networks, the data are usually divided into three subsets. The first subset is the training set, which is used for computing the gradient and updating the network weights and biases. The second subset is the validation set. The error on the validation set is monitored during the training process. The validation error normally decreases during the initial phase of training, as does the training set error. However, when the network begins to overfit the data, the error on the validation set typically begins to rise. The network weights and biases are saved at the minimum of the validation set error. The third subset is the test set. The test set error is used neither in training nor in validation. It is used to compare different models. It is also useful to plot the test set error during the training process. If the error on the test set reaches a minimum at a significantly different iteration number than the validation set error, this might indicate a poor division of the data set. As far as the function mapping is concerned, training is defined as the process of calibrating the network using pairs of input/output. ANNs may suffer from underfitting and overfitting during the

445

Estimation error

Application of Intelligent Technology in Rainfall Analysis

Validation data Training data Epochs Training stops here

FIGURE 24.2  Selection of optimum epoch based on the network performance in data training and testing.

training procedure [5]. These two factors tend to decrease the ability of the network in the generalization performance. Increasing the number of epochs in the training procedure results in decreasing the underfitting of the network, but if the number of epochs is greater than a specific number, overfitting may occur. The number of epochs is optimally determined by comparing the error in the training and testing procedure of the model. The optimal number of epochs is the number that causes the minimum validation error (Figure 24.2).

24.4.3 Determining the Number of Hidden Nodes Identifying the optimal number of hidden nodes is problem dependent, and a certain amount of trial and error is necessary. From Kolmogorov’s theorem, Hecht-Nielsen [13] derived that the upper bound of the required number of hidden nodes is one greater than twice the number of input nodes. The number of hidden nodes must be capable of achieving the two objectives simultaneously: providing sufficient representation of the task but sufficiently low to achieve generalization in order to avoid overfitting. If the data do not contain much information or contain a high degree of noise, a fewer number of hidden nodes than the theoretical limit are advisable in order to prevent overfitting. In some cases, a fan-in approach may be desirable, where a fewer number of hidden nodes are used related to the number of input nodes. This fan-in structure reduces the dimensionality of the data set, promoting generalization. Therefore, in many cases, the optimum number of hidden nodes may be significantly less than the theoretical limit.

24.5 A NFIS The adaptive neuro-fuzzy inference system (ANFIS) is a fuzzy inference model of Sugeno type and is a composition of ANNs and fuzzy logic approaches [15]. The model identifies a set of parameters through a hybrid learning rule combining the BP gradient descent and a least-squares method. It can be used as a basis for constructing a set of fuzzy if–then rules with appropriate membership functions (MFs) in order to generate the previously stipulated input–output pairs [26]. The Sugeno fuzzy inference system is computationally efficient and works well with linear techniques, optimization, and adaptive techniques. As a simple example, we assume a fuzzy inference system with two inputs x and y and one output z. The first-order Sugeno fuzzy model, a typical rule set with two fuzzy if-then rules, can be expressed as follows:

Rule 1 : If x is A1 and y is B1 , then f1 = p1x + q1 y + r1

(24.7)



Rule 2 : If x is A2 and y is B2 , then f 2 = p2 x + q2 y + r2

(24.8)

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Handbook of Drought and Water Scarcity A1

B1

A2

X

W1 f = p x + q y + r 1 1 1 1 Y

B2

f= W2 f2 = p2 x + q2 y + r2

x

X

y

Layer 4

Layer 3

Layer 2

x A2

w1 + w2

= w1 f1 + w2 f2

Y

Layer 1

A1

w1 f1 + w2 f2

TT

w1

x

y

Layer 5

n

N

w1

w1nf1 ∑

B1 y

TT

w2

N

f

w2nf2 w2n x

B2

y

FIGURE 24.3  Two inputs first-order Sugeno fuzzy model with two rules and architecture of ANFIS.

The resulting Sugeno fuzzy reasoning system is shown in Figure 24.3. It illustrates the fuzzy reasoning mechanism for this Sugeno model to derive an output function (f ) from a given input vector [x, y]. The corresponding equivalent ANFIS architecture is a five-layer feedforward network that uses neural network learning algorithms coupled with fuzzy reasoning to map an input space to an output space, and nodes are associated with MFs. It is shown in Figure 24.3, and an introduction of the model is as follows. Layer 1: Input nodes. Each node of this layer generates membership grades based on the appropriate fuzzy set they belong to using MFs. The node output OPi1 is defined by

OPi1 = m Ai ( x ) for i = 1, 2

(24.9)



OPi1 = m Bi-2 ( y ) for i = 3, 4

(24.10)

where x (or y) is the input to the node and Ai (or Bi−2) is a fuzzy set associated with this node, characterized by the shape of the MFs in this node, and can be any appropriate functions that are continuous and piecewise differentiable such as Gaussian, generalized bell-shaped, trapezoidal-shaped, and triangularshaped functions. The triangular and trapezoidal MFs, due to their simplicity and computational efficiency, are used extensively in the formulation of MF consist. The Gaussian, the generalized bell, and the sigmoidal MFs are smooth and nonlinear functions and are increasingly popular for specifying fuzzy sets. The generalized bell function has one parameter more than the Gaussian MFs, resulting in

447

Application of Intelligent Technology in Rainfall Analysis

an extra degree of freedom to adjust the steepness at the crossover points. The generated bell-shaped MF is given as follows: OPi1 = m Ai ( x ) =

(

1

1 + ( x - ci ) / ai

)

2bi

1

OPi1 = m Bi-2 ( y ) =

1+

(( y - c ) / a )

(24.11)

2bi

i

i



where {ai, bi, ci} is the parameter set of the MFs in the premise part of fuzzy if–then rules that changes the shapes of the MF with the maximum equal to 1 and the minimum equal to 0. Layer 2: Rule nodes. Nodes in this layer are labeled ∏, whose output represents a firing strength of a rule. The node generates the output (firing strength) by cross multiplying all the incoming signals:

OPi2 = wi = m Ai ( x ) m Bi ( y ) i = 1, 2

(24.12)

Layer 3: Average nodes. Every node in this layer is labeled as N and computes the normalized firing strength as



OPi3 = wi =

wi w1 + w2

i = 1, 2

(24.13)

where wi is the output of layer 3 and {pi, qi, ri} is the consequent parameter set. Layer 4: Consequent nodes. Node i in this layer computes the contribution of the ith rule toward the model output, with the following node function:

OPi 4 = wi fi = wi ( pi x + qi y + ri )

(24.14)

Layer 5: Output nodes. The single node in this layer computes the overall output of the ANFIS as

OPi5 = overall output =

å

wi f i =

i

åwf åw i i

i

i

(24.15)

i

A particular form of neuro-fuzzy systems is ANFIS, which has shown significant results in modeling nonlinear functions [17]. The ANFIS is a universal estimator and is able to approximate any real continuous function on a compact set to any degree of accuracy [17]. The basic structure of the type of fuzzy inference system can be seen as a model that maps input characteristics to input MFs [22]. Then it relates input MF to rules and the rules to a set of output characteristics. Finally, it maps output characteristics to output MFs and the output MF to a single output or a decision associated with the output [17]. Each fuzzy system contains three main parts: fuzzifier, fuzzy database, and defuzzifier. Fuzzy database includes two main parts: fuzzy rule base and inference engine. Figure 24.3 represents a typical ANFIS architecture. In layer 1, every node is an adaptive node with a node function such as a generalized bell MF or a Gaussian MF. In layer 2, every node is a fixed node representing the firing strength of each rule and is calculated by the fuzzy and connective of the product of the incoming signals. In layer 3, every node is a fixed node representing the normalized firing strength of each rule. The ith node calculates the ratio of the ith rule’s firing strength to the summation of two rules’ firing strengths. In layer 4, every node is an adaptive node with a node function indicating the contribution of ith rule toward the overall output. In layer 5, the single node is a fixed node indicating the overall output as the summation of all incoming signals [16].

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There is not any basic rule to determine the number of MFs of ANFIS models, and they usually are determined by trial and error [24,27]. To select the number of MFs, a modeler should avoid using a large number of MFs or parameters to save time and calculation effort [18].

24.6  SVM In recent years, modern tools regarding AI called a support vector machine (SVM) have had many applications in learning method machines [3]. This method successfully has been used in information categorization and lately in regression problems. Mathematically, SVM is placed in classification and regression algorithms range, which is formulated using the principles of statistical learning theory by Vapnik [28]. This model was first used for water resources management by Sivapragasam et  al. [25], Dibike et al. [7], and Han and Yang [11], and its new model is called reference vector machines used by Han et al. [12]. A short explanation is given for these models in the succeeding texts. The main relationship for statistical learning process is as follows:



y = f (X) =

M

åw f ( X ) = W f( X ) i i

(24.16)

i =1

where the output of the model is the part of linear M and the converter is shown by the nonlinear model by ϕ(X). This equation is converted as follows for SVM model:



ìï M üï y = f ( X ) = í w i k ( X i ,X ) ý - b îï i =1 þï

å

(24.17)

where k is the kernel function wi and b are parameters of the model N is the total number of learning patterns Xi is the data vector for network learning X is an independent vector The parameters of the model are determined with maximizing the objective of function. The general structure of these models is shown in Figure 24.4. SVM uses some of the specific kernel functions, which convert the input vector as the input data from the nonlinear function in this model. Selection of an appropriate kernel function is a complex stage often using the standard kernel function. y

α1

K(x1, x)

x1

FIGURE 24.4  Structure of SVM model.

x2

α2

αN

K(x2, x)

x3

K(xN, x)

xn

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The aim of this linear regression model is to find the linear function, which is the best interpolation for training point, shown in the following equation: y = f ( X ) = áw × x ñ + b



(24.18)

According to the method, by minimizing the sum of squares of obtained data 〈w ⋅ x〉, parameters are determined [6]. å ( y i áw × x ñ + b ) 2



(24.19)

In order to consider the error between actual values and modeling values, value e is entering the limitations of the model mentioned earlier:

yi - w × x - b < e

(24.20)



yi - w × x + b £ e

(24.21)

It can be assumed that a band is placed around the function f(x) that causes training error for a point out of this band and unless the covariate variable is called ξ. This covariate variable is for the point in zero band and increases exponentially for outside points. This regression method is called ε − SV, which is the most common modeling method. In this model, the cost function, which is shown in Figure 24.5, is formulated as the following: ì0 if y - f ( x ) £ e ï x = y - f (x) = í ïî y - f ( x ) - e



(24.22)

Two layers around the layer of function f(x) should be determined in a way to maximize the boundary area, which has an inverse relation with smooth Euclidean smooth vector ||w||2. Therefore, smooth Euclidean smooth vector should be minimized considering the cost function Min

æ 1 2 w + Cç ç 2 è

l

ö

l

å åx ÷÷ø i

x*i +

(24.23)

i

i



ε

y

ξ

0 –ε

–( y1 – yˆ1) x

FIGURE 24.5  Cost function of SVM model.

–ε

0



y1 – yˆ1

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subject to

yi - áw × x ñ - b £ e + xi

(24.24)



áw × x ñ + b - yi £ e + xi*

(24.25)



xi , xi* ³ 0

where C is the cost factor. This equation can be solved using Lagrange multipliers. The obtained Lagrangian equation is as follows: Min L =

æ 1 2 w + Cç ç 2 è

l

ö xi ÷ + ÷ ø

l

å å x*i +

i

i

å ( h x + h*x* ) l

i i

i

l



i

i

åa* ( e + x* + y - áw × xñ - b ) l

å

a(e + xi + yi + áw × x ñ + b) -

i

i

i

i

(24.26)

i

where hi , hi* , ai , a*i ³ 0 are the factors of Lagrange multipliers. The partial derivative of this equation compared with initial variables w,b,xi ,x*i is the following:

(

)

¶L æ =ç ¶b ç è



¶L =w ¶w



åa* - a ÷÷ø = 0 i

(24.27)

i

i =1



å ( a* - a ) x = 0 l

i

i

(24.28)

i

i =1

¶L =C¶x*i



ö

l

l

å ( a * - h * ) = 0 ( ) i

( ) i

(24.29)

i =1

where h(i *) , e(i *) , a(i *) correspond with h*i , ei* , ai* and ηi , εi , αi. By replacing Equations 24.27 through 24.29, therefore, we have Min

1 2

å( l

ij =1

)(

)

ai - a*i a j - a*j á xi ,x j ñ -

å( l

) åy (a - a* ) = 0

ai + a*i +

i =1

l

i

i

i

(24.30)

i =1

subject to (24.31)



å ( a - a* ) = 0



ai , a*i Î éë0,C ùû

(24.32)

l

i

i

i =1

After rewriting Equation 24.28, it can be replaced in the following equation:

å ( a - a* ) x l

w=

i

i =1

i

i

(24.33)

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Application of Intelligent Technology in Rainfall Analysis



f (x) =

å ( a - a* ) áx ,xñ + b l

i

i

(24.34)

i

i =1

This developed equation of support vectors is for a linear model, which is used for nonlinear relationships. It is not appropriate for many hydrological analyses to use linear regression for modeling, and therefore, it is appropriate to convert kernel by putting data in a space with more dimensions and then use the linear regression. Kernel function k〈x, z〉 is 〈ϕ(x), ϕ(z)〉. Appropriate selection of kernel function provides the possibility of using a nonlinear function in input space for changing to linear function in characteristics space. There are four standard conversions of kernel function mostly used in regression and modeling [20] including the following: 1. Linear kernel: The simplest kernel function is as follows [11]:

k á x ,z ñ = á x ,z ñ

(24.35)

2. Polynomial kernel: Polynomial mapping is a common method for nonlinear modeling:

k á x ,z ñ = á gx ,z ñ d

(24.36)



k á x ,z ñ = ( á gx ,z ñ + r ) , g > 0

(24.37)

d

Usually, the second kernel is preferred because it solves the problems of Hessian so as to close to zero. 3. RBF: A function based on RBF that is more similar to Gaussian (bell shape) is given as follows [11]:

(

)

k á x ,z ñ = exp - g|x - z|2 , g > 0



(24.38)

In traditional methods, RBF is used in order to determine the subgroup at the center, in general, a cluster method for selecting the center’s subgroup. One of the features of SVM is that it is an unconditional selector, that is, any participated support vector in Gaussian function can achieve the center of the points. Considering that this feature can bring about a possibility to select the diagonal band function -S-, they use SRM rule [28]. 4. Sigmoid kernel: The sigmoid kernel function is as follows:

k á x ,z ñ = tanh ( - g á x ,z ñ + r )

(24.39)

where γ, r, and d are kernel parameters [8].

24.7  Case Studies on Rainfall Forecasting 24.7.1  A NNs Case Study Luk et al. [19] applied the three alternative types of ANNs, namely, multilayer feedforward neural networks (MLFNs), partial recurrent neural networks (PRNNs), and TDNNs in Upper Parramatta River Catchment located in the western suburbs of Sydney, with a catchment size of about 112 km2. Within the catchment, the dominant land use is typical to that of urban environments with a mix of residential, commercial, industrial, and open space (parkland) areas.

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The development of an ANN for rainfall forecasting involves the following important considerations: • Select an appropriate ANN to represent the Markovian process. • Estimate the lag for the ANN, that is, to determine the number of past rainfall values to be included as inputs. • Determine the optimal complexity of the ANN appropriate to the problem, that is, to determine the number of hidden layers and number of nodes in a hidden layer. Presented in Figure 24.6 is a generic structure of an MLFN designed for rainfall forecasting. The output nodes of the network are the rainfall during the next time step, which contain N elements, representing the spatial locations of rainfall. For example, if forecasting rainfall at 16 points in space is needed, N is equal to 16. The number of hidden nodes, H, which defines the complexity of the network, is a key variable to be estimated. Note that the number of hidden layers can be more than one. The input layer contains k sets of input nodes. The k is referred to as the lag of the network and is another key variable to be determined. The most popular PRNN, called the Elman network, was adopted in this study. Shown in Figure 24.7 is the structure of an Elman network designed for rainfall forecasting. The key variable for an Elman network is the number of hidden nodes, H. A rainfall time series usually contains local features, such as bursts of heavy rain between periods of prolonged low-intensity rainfall. These local features do not have a fixed position in time, rendering the prediction of their occurrence extremely difficult. A TDNN was adopted to handle this problem. As an illustration, the TDNN shown in Figure 24.8 contains four time frames as input and three time frames in the hidden layer. Two time frames are combined to form a window to represent a duration in time. There is a total of three windows in the input, with corresponding time delays of 1, 2, and 3 (shown in dotted lines). Each node in the hidden layer is connected to a window of two time frames of input nodes. The output is obtained by integrating (summing) the information over three time frame windows in the hidden layer. The main variables of a TDNN that need to be defined are the numbers of time frames in the input and hidden layers, window size (time delay), and number of hidden nodes. Rainfall amounts during 15 min intervals at the 16 rain gauges were obtained from January 1991 to September 1996. During this period, 34 storms occurred with a daily rainfall total greater than 20 mm,

1

2 Input nodes (time t – k + 1)

N

1

2

N

1

2

H

1

2

N

Input nodes (time t – 1)

FIGURE 24.6  Structure of an MLFN designed for rainfall forecasting.

Output nodes (time t + 1)

Hidden nodes

1

2 Input nodes (time t)

N

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Application of Intelligent Technology in Rainfall Analysis

Recurrent link

1

2

1

2

N

1

2

N

1

H

Context units (time t – 1)

Output nodes (time t + 1)

Hidden nodes

2

N

Input nodes (time t)

FIGURE 24.7  Structure of an Elman network designed for rainfall forecasting.

1 2

Output layer (time t + 1) (1 time frame)

N

Time window

1

1

1

2

2

2

H

H

H

1

2

3

1

1

1

1

2

2

2

2

N

N

N

N

t–3 t–2 t–1

Hidden layer (3 time frames)

t

Input layer (4 time frames)

Time

FIGURE 24.8  Structure of a TDNN with three moving windows at inputs.

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Handbook of Drought and Water Scarcity

with 1749 rainfall amounts at each site. According to the early stopping method, the data were split into three sets, namely, a training set (16 storms with a total of 748 rainfall periods), a monitoring set (8 storms with a total of 376 rainfall periods), and a validation set (10 storms with a total of 625 rainfall periods). The maximum epoch for training was set at 1000. Where appropriate, a sigmoid activation function was adopted for the hidden nodes, whereas a linear activation function was used for the output nodes. To achieve better performance and faster convergence in training, the data were transformed with the log function. During the development of the alternative ANNs, various network connections were attempted in order to determine the effect of two key variables, which are the lag of network and number of hidden nodes. For the MLFN, networks with lags 1, 2, 3, and 4 were attempted. In addition, the numbers of hidden nodes tried were 2, 4, 8, 16, 24, 32, 64, and 128. Networks with two layers of hidden nodes were also attempted. For the Ehnan network, the order of lag was fixed at 1 because the network would learn the temporal structure implicitly. The numbers of context units tried were 2, 4, 8, 16, 24, 32, and 64. Finally, for the TDNN, networks with 2, 3, and 4 input windows were attempted. In general, all three types of networks showed comparable performance. The normalized mean squared error (NMSE) of the validation samples for all networks was in the range of 0.63–0.67, with only small differences between the networks. The reduction in the number of hidden nodes with an increase in lag, and vice versa, might indicate the existence of an optimal complexity of network for the problem being considered, given the data available. Another interesting aspect of the results was that the networks with a lower lag had a slightly better performance than those of a higher lag. This might suggest that the rainfall series did not have long-term dependence structures. The short-term memory characteristics of the rainfall time series helped to explain why the simple MLFN had comparable performance with the more sophisticated TDNN and Elman networks.

24.7.2  A NFIS Case Study Akrami et al. [1] compared the conventional and modified ANFIS (MANFIS) models for rainfall forecasting in Klang River, which flows through Kuala Lumpur and Selangor in Malaysia. Basically, a fuzzy inference system is composed of five functional blocks:

1. Input characteristics to input MFs 2. Input MF to rules 3. Rules to a set of output characteristics 4. Output characteristics to output MFs 5. The output MF to a single-valued output or a decision associated with the output

The available data for catchment (144 patterns) are divided into three groups: training set (calibration), testing set (validation), and checking set (checking). The data for training and testing patterns are randomly selected to 100 and 44 and 30 input patterns, respectively. The generalized bell function has been used in this study. One of the limitations of using the ANFIS is that the complexity of its topology increases exponentially as the rules are generated with all possible combinations of premises, which is a function of the number of variables. The number of generated rules N for a system with n inputs and p premises is Pn; therefore, it might become unaffordable to use an ANFIS for problems with several variables. Of course, although utilizing human expertise in determining an ANFIS structure is preferable, this solution is not always available. The number of fitting parameters per MF is m. The number of premise fitting parameters per input is p ∙ m, so the total number of premise fitting parameters is n ∙ p ∙ m. The number of consequent fitting parameters per rule is n + 1 (layer 4), and the number of rules is Pn, so the total number of consequent fitting parameters is Pn(n + 1). The total number of fitting

455

Application of Intelligent Technology in Rainfall Analysis Input

Inputmf

Rule

Outputmf

Output

Logical operations and or not

FIGURE 24.9  Structure of the ANFIS model.

parameters (premise + consequent) is F(n, p, m) = n · p · m + Pn(n + 1)Pn(n + 1). On the other hand, to achieve good generalization capability, the number of training data points should be larger than the number of parameters to be estimated. The structure of ANFIS model with four inputs and two MFs is shown in Figure 24.9. To improve the performance of the ANFIS system, three matters must be handled: finding the optimal number of the rules, discovering the appropriate MFs, and learning algorithm. The second scenario used the MANFIS to improve the rainfall forecasting efficiency. The second scenario proposed that the number of rules in FIS can be represented by the number of input fuzzy sets. In this study, two scenarios were introduced; in the first scenario, monthly rainfall was used solely as an input in different time delays from the time (t) to the time (t − 4) to conventional ANFIS; the second scenario used the MANFIS to improve the rainfall forecasting efficiency. The result showed that the model based on MANFIS performed a higher rainfall forecasting accuracy, low errors, and a lower computational complexity (total number of fitting parameters and convergence epochs) compared with the conventional ANFIS model.

24.7.3  SVM Case Study Hong and Pai [14] employed support vector regression (SVR) in forecasting volumes of rainfall during typhoon seasons. In addition, simulated annealing (SA) algorithms are employed to choose parameters of the SVR model. Subsequently, rainfall values during typhoon periods in Taiwan’s Wu-Tu watershed are used to demonstrate the forecasting performance of the proposed model. The procedure of SA algorithm is described as follows: Step 1: Initialization. Set upper bounds of the three SVR positive parameters, σ, C, and ε. Then, generate and feed the initial values of the three parameters into the SVR model. The forecasting error is defined as the system state (E). Here, the initial state (E0) is obtained. Step 2: Provisional state. Make a random move to change the existing system state to a provisional state. Another set of three positive parameters is generated in this stage. Step 3: Acceptance tests. The following equation is employed to determine the acceptance or rejection of the provisional state:

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Handbook of Drought and Water Scarcity

ìAccept the provisional state, if E ( snew ) > E ( sold ) , and p < P ( accept snew ) , 0 £ p £ 1. ïï (24.40) íAccept the provisional state, if E ( snew ) £ E ( sold ) . ï ïîReject the provisional state, otherwise. In Equation 24.40, the p is a random number for determining the acceptance of the provisional state. If the provisional state is accepted, then set the provisional state as the current state. Step 4: Incumbent solutions. If the provisional state is not accepted, then return to Step 2. Furthermore, if the current state is not superior to the system state, then repeat Steps 2 and 3 until the current state is superior to the system state, and set the current state as the new system state. Step 5: Temperature reduction. After the new system state is obtained, reduce the temperature. The new temperature reduction is obtained by using the following equation:



New temperature = ( Current temperature ) ´ r, where 0 < r < 1

(24.41)

Here, ρ is set to be 0.9 in this study. If the predetermined temperature is reached, then stop the algorithm, and the latest state is an approximate optimal solution. Otherwise, go to Step 2. In this investigation, three models including the Holt–Winters (HW) method, the seasonal Holt and Winters (SHW) linear exponential smoothing approach, and the RNN model are employed for comparing the forecasting accuracy with the proposed SVRSA model. Hourly volumes of rainfall (from August 1985 to August 1997) of the three rain gauges served as experimental data in this study. During this period, nine typhoon events occurred. In this investigation, the hourly volumes of rainfall brought by typhoons Nelson, Abby, and Sarah were employed as training data set. The validation data set included the hourly volumes of rainfall brought by typhoons Ruth, Polly, and Seth. The hourly volumes of rainfall brought by the other three typhoons served as the testing data set. In this investigation, a rolling-based forecasting procedure was conducted and a one-hour ahead forecasting policy was adopted. Based on the forecasting policy, several types of data rolling are considered as a time series to feed into the SVRSA model in forecasting rainfall depth in the next hour. In the training stage, the rainfall data contain three typhoon events; the number of rainfall data fed into SVRSA model is designed by considering the following two issues: the capture of rainfall data pattern from each typhoon event and prevention of the overfitting problem. Hence, the number of rainfall data fed into SVRSA model equals to the total rainfall hours of the previous two typhoons (129 rainfall data) or one typhoon (41 rainfall data). For NMSE accuracy index, the proposed SVRSA model with satisfactory forecasting performance is capable to be employed to forecast rainfall depth during typhoon period. Similarly, for the coefficient of efficiency index, the proposed SVRSA model also deserved to be confident. For coefficient of correlation (CC) index, the forecasting rainfall depth values from SVRSA model have a higher correlation relationship with actual rainfall depth values than both HW and SHW models. However, the RNN model has a higher CC than the SVRSA model. In addition, it is observed that SVRSA model can capture the data pattern of rainfall during the peak periods. However, the other three models cannot follow the data pattern successfully. Therefore, the nonlinear mapping ability and the proper selection of SVR parameters make the SVRSA successful in rainfall forecasting.

24.8 Summary and Conclusions Due to the complexity of natural phenomena and the difficulty of physical models parameter estimation, AI models as black box models are powerful tools for modeling the hydrologic parameters including rainfall, evaporation, temperature, runoff, water level, flood, drought, and groundwater.

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They  have accurately predicted future system states. AI models use experimental data to analyze ­real-world phenomena and nonstationary and nonlinear problems. They do not need to estimate physical model parameter values because they employ the black box approach. This black box approach causes that modelers apply easily measurable variables to account the physics of the system via the data. As water resources are increasingly stressed and depleted, the need for a more accurate modeling will only increase. That AI models can be continuously updated by real-time data streams, can be combined with other modeling techniques for increasing the domain of predictions and achieving superior real-time prediction capability, and can serve as segments in optimization models, all of which will ensure that they will continue to be used to address some of the most pressing water problems confronting the humans in the twenty-first century.

Authors Mehdi Vafakhah received BSc in natural resources engineering from Gorgan University of Agricultural Sciences and Natural Resources, Iran, in 1996, and MSc and PhD in watershed management engineering from Tarbiat Modares University and the University of Tehran in 1999 and 2008, respectively. He was with the faculty of natural resources of Tarbiat Modares University as a lecturer from 1998 to 2009, as assistant professor from 2009 to 2013, and as associate professor from 2013. His research interests include surface hydrology, snow hydrology, geostatistics and parameter estimation with artificial neural networks, adaptive neuro-fuzzy inference system, and data-driven techniques. He has published 87 journal articles, 2 book chapters, and more than 67 papers presented in international and national conferences and is also involved in many national watershed management projects. Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, Iran, where he has been since 1995. He received his PhD from the University of New South Wales, Australia, under the supervision of Professor David Pilgrim. His research focuses mainly on water resources planning and management and statistical hydrology in a changing climate. In recent years, he has been working on modeling water reuses, climate change and variability, IWRM, sustainable agriculture, resilience and vulnerability research, and natural resources governance and management. Formerly, he was a visiting professor at Princeton University, New Jersey, and the University of ETH Zurich, Switzerland. On the research side, he has started a research partnership from 2014 with McGill University, Canada. He has contributed to more than 500 publications in journals and books or as technical reports. He is the founder and chief editor of both International Journal of Hydrology Science and Technology (Scopus, Inderscience) and Journal of Flood Engineering. His professional experience includes being on the editorial boards and a reviewer of about 40 Web of Science (ISI) journals. He has authored more than 100 book chapters and books. Recently, he has started the editorship of several handbooks published by Taylor & Francis Group (CRC Press). A three-volume Handbook of Engineering Hydrology (2014), Urban Water Reuse Handbook (2015), a three-volume Handbook of Drought and Water Scarcity (2017), and Underground Aqueducts Handbook (2017) are published ones.

References

1. Akrami, S.A., El-Shafie, A., and Jaafar, O. 2013. Improving rainfall forecasting efficiency using modified adaptive neuro-fuzzy inference system (MANFIS), Water Resources Management, 27, 3507–3523. 2. Araghinejad, S. 2014. Data-Driven Modeling: Using MATLAB in Water Resources and Environmental Engineering, Water Science and Technology Library, Vol. 67, Springer Science+Business Media, Dordrecht, the Netherlands.

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3. Campbell, C., Cristianini, N., and Shawe-Taylor, J. 1999. Dynamically adapting kernels in support vector machines. Advances in Neural Information Processing Systems, 11, 204–210. 4. Coppola, Jr. E.A., Szidarovszky, A., and Szidarovszky, F. 2014. Artificial neural network-based modeling of hydrologic processes, in: Eslamian, S. (Ed.), Handbook of Engineering Hydrology, Modeling, Climate Change, and Variability, Taylor & Francis Group, LLC, pp. 19–34. 5. Coulibaly, P., Anctil, F., and Bobée, B. 1999. Prévision hydrologique par réseaux de neurones artificiels: État de l'art. Canadian Journal of Civil Engineering, 26(3), 293–304. 6. Cristianini, N. and Shawe-Taylor, J. 2000. An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods, Cambridge University Press, New York. 7. Dibike, Y.B., Velickov, S., Solomatine, D., and Abbott, M.B. 2001. Model induction with support vector machines: Introduction and applications. Journal of Computing in Civil Engineering, 15, 208–216. 8. Eslamian, S.S., Abedi-Koupai, J., Amiri, M.J., and Gohari, A.R. 2009. Estimation of daily reference evapotranspiration using support vector machines and artificial neural networks in Greenhouse. Research Journal of Environmental Sciences, 3(4), 439–447. 9. Firat, M., Turan, M.E., and Yurdusev, M.A. 2009. Comparative analysis of fuzzy inference systems for water consumption time series prediction. Journal of Hydrology, 374, 235–241. 10. Guijarro, J.A. 2014. Quality control and homogenization of climatological series, in: Eslamian, S. (Ed.), Handbook of Engineering Hydrology, Fundamental and Application, Taylor & Francis Group, LLC, Abingdon, U.K., pp. 501–513. 11. Han, D. and Yang, Z. 2001. River flow modeling using support vector machines, in: 29th IAHR Congress, Beijing, China, September 17–21. 12. Han, D., Chan, L., and Zhu, N. 2007. Flood forecasting using support vector machines. Journal of Hydroinformatics, 9, 267–276. 13. Hecht-Nielsen, R. 1990. Neurocomputing, Addison-Wesley, Reading, MA. 14. Hong, W.-C. and Pai, P.-F. 2006. Potential assessment of the support vector regression technique in rainfall forecasting. Water Resources Management, 21(2), 495–513. 15. Jang, J.S.R. 1993. ANFIS: Adaptive-network-based fuzzy inference system. IEEE Transactions on System Management in Cybernetics, 23(3), 665–685. 16. Jang, J.S.R. and Sun, C.T. 1995. Neuro-fuzzy modeling and control. Proceedings of IEEE, 83, 378–406. 17. Jang, J.S.R., Sun, C.T., and Mizutani, E. 1997. Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice-Hall, Eaglewood Cliffs, NJ, pp. 665–685. 18. Keskin, M.E. and Taylan, D. 2009. Artificial models for interbasin flow prediction in southern Turkey. Journal of Hydrologic Engineering, 14, 752–758. 19. Luk, K.C., Ball, J.E., and Sharma, A. 2001. An application of artificial neural networks for rainfall forecasting. Mathematical and Computer Modelling, 33, 683–693. 20. Matouq, M., El-Hasan, T., Al-Bilbisi, H., Abdelhadi, M., Hindiyeh, M., Eslamian, S., and Duheisat, S. 2013. The climate change implication on Jordan: A case study using GIS and Artificial Neural Networks for weather forecasting. Journal of Taibah University for Science, 7(2), 44–55. 21. McCulloch, W.S. and Pitts, W. 1943. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115–133. 22. Moosavi, V., Vafakhah, M., Shirmohammadi, B., and Behnia, N. 2013. A wavelet-ANFIS hybrid model for groundwater level forecasting for different prediction periods. Water Resources Management, 27(5), 1301–1321. 23. Shamseldin, A.Y. 1997. Application of a neural network technique to rainfall-runoff modelling. Journal of Hydrology, 199, 272–294. 24. Shirmohammadi, B., Vafakhah, M., Moosavi, V., and Moghaddam Nia, A. 2013. Application of several data-driven techniques for predicting groundwater level. Water Resources Management, 27(2), 419–432. doi: 10.1007/s11269-012-0194-y, Published online: November 14, 2012.

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25. Sivapragasam, C., Liong, S., and Pasha, M. 2001. Rainfall and runoff forecasting with SSA-SVM approach. Journal of Hydroinformatics, 3, 141–152. 26. Vafakhah, M. 2012. Application of artificial neural networks and adaptive neuro-fuzzy inference system models to short-term streamflow forecasting. Canadian Journal of Civil Engineering, 39, 402–414. 27. Vafakhah, M., Janizadeh, S., and Khosrobeigi Bozchaloei, S. 2014. Application of several datadriven techniques for rainfall-runoff modeling. ECOPERSIA, 2(1), 455–469. 28. Vapnik, V. 1999. The Nature of Statistical Learning Theory, Springer, Berlin, Germany.

25 Application of the Optimization Models and Decision Support Systems in Drought Emery A. Coppola Jr. NOAH LLC

Manuel Sapiano Institute for Water Technology, Water Services Corporation

Michael Schembri Institute for Water Technology, Water Services Corporation

Ferenc Szidarovszky NOAH LLC

25.1 Introduction ......................................................................................462 25.2 Defining Drought .............................................................................463 25.3 Growing Prevalence and Uncertainty of Drought ......................463 25.4 Common Drought Indicators ........................................................ 464 25.5 Advanced Decision Support Systems for Drought Management ................................................................................. 465 25.6 Real-Time Decision Support System for Drought Forecasting and Management ....................................................... 466 Introduction and Overview • Real-Time Data Streams • Introduction to ANN Modeling 25.7 Malta Case Study ..............................................................................470 Background • Water Resources • Optimization Management Description • Mathematical Optimization Formulation 25.8 Summary and Conclusions .............................................................477 Authors.......................................................................................................... 478 References ..................................................................................................... 478

Abstract  Drought is becoming a far more common phenomenon worldwide due to climate change. More prevalent and prolonged droughts combined with growing water demand are putting critical human activities like food production and economic development at severe risk. Vulnerable and valuable ecosystems are also threatened. Despite these risks, most water decision-makers rely on a reactive system for identifying and managing drought, which can seriously undermine efforts to mitigate negative impacts. An alternative approach is a proactive real-time drought forecasting system combined with formal optimization to provide decision-makers with an early warning system that also provides strategies for mitigating risk to the extent possible. This chapter presents some of the issues related to real-time decision support systems for drought mitigation, including a more formal definition of this phenomenon, its inherent uncertainty and growing prevalence worldwide, motivating the need for a proactive decision support system. A short survey of decision support systems with optimization published in the literature will be followed by illustrative example components for a real-time decision support system. This will include real-time prediction capabilities for drought indicators and operational variables, including groundwater levels, salinity concentrations, and water demand, with an example management optimization formulation for the country of Malta. 461

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25.1  Introduction The term “drought” conjures some of our worst fears; withering crops and dying livestock with a displaced population wandering aimlessly for water amidst a sun-parched landscape. While tragically this does occasionally occur and marks the awful extreme, drought is a nebulous concept with various degrees of severity and a range of impacts. Even among decision-makers in a given area, there often is no consensus of what constitutes a drought. Unfortunately, by the very nature of its slow encroachment and ambiguity, there is often a loss of precious time in implementing desperately needed adaptive and mitigative measures. Even when there is agreement on drought status among those affected, there are natural conflicts between different stakeholders like agricultural and municipal users that complicate the decision-making process of how best to respond. And worse, there are times when there simply is not enough water to go around, due to extreme drought combined by a shortage of water resources. The famous San Joaquin Valley of California, known as “the breadbasket of the world,” cultivates more than 250 crop varieties and has an annual gross value of agricultural production of more than $25 billion. The U.S. Environmental Protection Agency [17] describes its complex water system as follows: The Valley owes much of its agricultural success to a remarkable water storage and distribution system that has the federal Central Valley Project at its heart. The Central Valley Project annually distributes roughly four million acre feet of water from the Bay-Delta and San Joaquin River throughout the Valley. Most of this diverted river water is utilized for agriculture, while Valley communities rely mostly on ground water to drink. Yet for all this investment and technical ingenuity, the effects of extreme drought are turning agricultural success into failure. California has been in the midst of one of its worst droughts on record, with much of the effect felt by the San Joaquin Valley, and approximately 20,000 farm jobs in California, the vast majority within the San Joaquin valley, will be lost. While these seasonal job losses and associated economic impacts like higher food prices may be viewed as short-term impacts (although certainly serious to those who experience them), longer-term impacts include degradation of critical ecosystems like wetlands, where natural water flows are diverted for agricultural use, and further over-use of groundwater resources, which may ultimately force some farmers, businesses, and residents to move. Given the projected increase in frequency and intensity of drought in the southwestern United States, these extreme consequences will become less rare, which will impose additional long-term strains on the environment, the economy, and society as a whole. A more detailed description of anticipated climate change impacts on hydrology and water resources worldwide may be found in Mujere and Eslamian [10]. Although drought impacts cannot be avoided, a proactive early warning alert and management system that integrates real-time data streams with prediction and optimization models could reduce the effects. Despite the recognized superiority of a “proactive” approach over a “reactive” one, there is practically a complete lack of real-time decision support systems for drought forecasting and management. Rossi et al. [13] provide an excellent overview of some of the “scientific, institutional, and social factors” behind the general lack of proactive systems, including “an inadequate understanding of the natural drought phenomenon and an inadequate development of appropriate tools.” This chapter presents some of the issues related to real-time decision support systems for drought mitigation, including a more formal definition of this phenomenon, its inherent uncertainty and growing prevalence worldwide, and the need for a proactive decision support system. A short survey of decision support systems with optimization published in the literature will be followed by illustrative example components for a real-time decision support system. This will include real-time prediction capabilities for drought indicators and operational variables, including groundwater levels, salinity concentrations, and water demand, with an example management optimization formulation for the country of Malta.

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Malta is an ideal case study. A densely populated island country in Europe with relatively little freshwater resources, the vast majority of which is contained in over-exploited groundwater aquifers [14]. Located in a semiarid Mediterranean environment, Malta is among the most water stressed countries in the world and the most stressed in Europe. Although desalination of seawater is extensively used by the country, comprising slightly more than 50% of its water used for potable purposes, it still imposes significant production costs due to energy consumption. Worse, this source is highly vulnerable to disruption by the persistent risk of a large oil spill from one of the many off-shore tankers transporting crude in the Mediterranean Sea. With Malta’s vibrant economy, population growth, and foreseen climate change impacts, increasing stress on the already vulnerable natural water resources and delivery system will continue to occur. As discussed by Sapiano [14]: “As an EU Member State, Malta is obliged to take a more sustainable and integrated approach to groundwater management.” This strategic approach will be presented in this chapter, through the conceptual presentation of a real-time decision support system with real-time forecasting and optimization for water management under drought conditions.

25.2  Defining Drought In short, drought is when expected water demand exceeds the available supply [8]. To be precise, experts recognize four different types of drought: meteorological, indicated by low rainfall and high net evapotranspiration; agricultural, where there are low soil moisture contents, thereby decreasing food production; hydrological, where surface and groundwater resources decrease; and socioeconomic, “whereby there are adverse effects on the ‘supply and demand of goods’ and ‘human wellbeing’” [6]. While defining drought is a critical starting point to understanding and eventually managing it, the definitions do not clearly delineate when a drought begins or ends, nor do they quantify the severity of a drought. They do, however, convey the multidimensional impacts of drought, not only in time and space, but how its insidious effects extend to all sectors of society and the environment as a whole. This demonstrates just how complex the phenomenon of drought is, the importance of forecasting its onset while mitigating its negative impacts, and removing as much uncertainty as humanly possible.

25.3  Growing Prevalence and Uncertainty of Drought Droughts are becoming more frequent and persistent, challenging water managers worldwide to meet the demand of increasingly thirsty populations, and forcing a rethinking of developing and implementing more effective techniques and strategies for forecasting and managing drought. The Intergovernmental Panel on Climate Change warns that because of climate change, “droughts will especially increase in subtropical areas, such as the U.S. Southwest, Australia and parts of Africa and Europe, as Earth’s warming causes more evaporation and shifts weather patterns, pushing the paths of storms that bring thirst-quenching rains farther north” [18]. Drought can have devastating impacts that may alter if not destroy the environmental, political, cultural, economic, and social landscapes of the affected region. This is exemplified by the “Dust Bowl” of the 1930s, which devastated vast tracts of farmland through much of the United States, displacing millions of Americans, the human tragedy of which is famously captured by John Steinbeck’s Pulitzer Prize winning novel The Grapes of Wrath. The uncertainty of drought and its impacts increases the risk to all these sectors. Within the context of mathematical modeling, uncertainty consists of natural uncertainty, model uncertainty, and data uncertainty. Unknown future conditions like weather often force decision-makers to make a “best guess” on model inputs. Our inability to perfectly predict highly complex systems even under the unattainable condition of complete and accurate information introduces additional uncertainty in model outputs. Because risk increases in proportion to uncertainty, it is important that any real-time support system explicitly accounts for uncertainty. Accordingly, uncertainty for the real-time decision support system should be included in the forecasting/prediction models and the management

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optimization models. A variety of statistical methods and modeling approaches can help provide decision-makers with a more informed appreciation of the level of uncertainty associated with their modeling results. In this chapter, one such method for reducing risk is presented.

25.4  Common Drought Indicators Drought status is commonly determined by drought indicators, which are general measures of the hydrological, meteorological, and/or agricultural state of the system. Typical drought indicators include groundwater levels, surface water flows, deviation of precipitation from its historical mean precipitation, soil moisture deficits, and available supplies in surface water reservoirs. As implied by the indicators, there is a wide range of drought conditions, which necessitate different status designations and correspondingly different mitigative response measures. In addition, the drought status as measured by various indicators can obviously vary over space within a decision-making boundary. Even with a range of quantitative indicators, decision-makers often exercise subjective judgment when determining drought status based upon a number of factors. For example, the State of New Jersey within the United States has a system of drought indicators to help it designate drought conditions for six distinct “drought regions,” with four drought status levels, normal, watch, warning, and emergency. The drought indicators used by the state include groundwater levels, surface water reservoir levels, streamflow, and precipitation with monitoring locations distributed throughout each of the six regions. Still, determining the drought status is not based upon some numerically weighted value of the various indicators or some other quantitative calculation. The New Jersey Geological Survey Informational Circular entitled “New Jersey Water-Supply Drought Indicators” [7] concludes with a number of points recurrent to drought management:New Jersey drought indicators are not triggers that are automatically designated when a drought begins or ends. There are several reasons for this. Different water sources vary in importance. Second, anticipating water demand. Third, apply professional experience in determining drought status. This statement highlights several important factors that water managers must consider when designing and implementing a real-time decision support system. First, even for relatively small areas like the State of New Jersey, there can be significant spatial variations in drought, and how it affects different water sources. Thus, sufficient spatial resolution and accurate system characterization is essential for properly defining and responding to drought. Second, drought indicators alone are not necessarily a direct indication of the severity of a drought; decision-makers must also consider the expected water demand. Related to this, the more accurate both demand and drought conditions as measured by indicators can be forecasted, the more effectively the future status of water scarcity can be anticipated and appropriate measures identified. Third, while quantitative measures are obviously necessary for helping to determine a drought status, there will always be some degree of human judgment. This is similar to the approach implemented by the United States National Drought Mitigation Center (NDMC) at the University of Nebraska-Lincoln, which each week produces a drought status map for the entire United States based on measurements of climatic, hydrologic, and soil conditions as well as reported impacts and observations from more than 350 contributors around the country. The five indicators are the Standardized Precipitation Index, the Palmer Drought Severity Index, the Crop Moisture Index, the Surface Water Supply Index, and the Reclamation Drought Index. Even then, numerous experts are used to assess the measures each week and, based upon their professional judgment, determine the drought status for each region. As pointed out by Andreu et al. [1], overly pessimistic predictions can result in excessively cautious management responses that can negatively affect the community. Conversely, overly optimistic predictions can result in a valuable loss of time in implementing effective responses to mitigate drought, resulting in excessive loss of resources, while further degrading the resiliency of the system.

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In order to reduce to the extent possible human errors in judgment of water professionals and/or political pressure from stakeholders, an effective drought system will use as much relevant information and data as possible, including real-time data, from which drought conditions can be defined and forecasted. Some drought indicators like groundwater levels may also serve as decision variables and/or constraints for optimizing water resources management during normal and extreme conditions. For maximum capability, real-time data streams are coupled with prediction and optimization models to identify the optimal management strategies that minimize the risk of water shortages while ensuring an adequate supply of water for the forecasted drought period and beyond.

25.5  Advanced Decision Support Systems for Drought Management Drought produces an increased stress on the affected water resources and ecosystems, which often necessitates adaptive measures, ranging from water use restrictions to alternative use of water supplies. Droughts can obviously engender numerous negative effects, which are additive in time. A proactive decision support system that can serve as both an early alert warning system for drought and a realtime optimization management tool for water resources provides managers and decision-makers with numerous benefits during drought and other conditions. All too frequently, “drought only receives the attention of decision makers when it is at peak levels of intensity and spatial extent and when water management options are quite limited. This approach is sometimes referred to as the ‘hydro-illogical cycle’ where concern and panic lead to a reactive response to associated economic, social and environmental impacts, followed by apathy when precipitation restarts and water resources return to normal. This approach has been characterized as ineffective, poorly coordinated and untimely” [9]. During its inception and duration, drought management strategies must carefully balance near term with longer-term goals and concerns. Drought in the short term, particularly before restrictions are put in place, often increases water consumption as major users like agriculture compensate for reductions in precipitation. In a coastal area, for example, this can have the effect of further reducing groundwater levels in the coastal aquifer from over-pumping, which by potentially increasing saltwater intrusion may further degrade water quality, further reducing potable supply. One potential consequence of inappropriate responses are increases in water costs due to a combination of higher energy, source, and treatment costs, which have obvious economic impacts on businesses and consumers as well as the environment. Due to an inability to accurately forecast and manage it, drought often stimulates short-term responses by water users and managers that ignore or fail to adequately address longer-term consequences. More accurate forecasts are a necessary condition for identifying appropriate management decisions that more effectively balance short-term with longer-term objectives. Management decisions can be further enhanced through formal optimization models, which can further reduce costs and risk. By providing a more accurate and complete understanding of the possible future conditions and consequences of actions (or lack thereof), a more informed and rationale decision-making process is possible. To date, real-time decision support systems for managing drought are rare. Most systems are reactive, which compromises both shorter- and longer-term water management decisions. As noted by Andreau et al. [1], “The reactive approach consists in measures adopted both during and after the drought period, once its consequences are perceived. While this approach is still today the most common response to drought emergencies, obviously, the actions undertaken are, as a rule, of brief duration and nonstructural in nature, entail high economic and environmental costs for the community and often do not reduce the system’s vulnerability to similar future events.” In addition, there are few examples where simulation models are combined with optimization for identifying optimal management solutions. Andreu et al. [1] present a drought management decision support system by means of risk analysis. The system is based upon a Simrisk module that allows

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simulations of the water system under different management options with a probabilistic risk of failure for each given different possible future water inflow and storage in surface water reservoirs and aquifers. Various drought indicators, including meteorological, agricultural, hydrological, and operative are combined into the analysis, with their probabilistic frequencies computed and accounted for in the analysis via time series analysis. Sechi and Sulis [15] present a mixed simulation-optimization technique for managing water resources under drought. The system, named WARGI (Water Resources system optimization aided by Graphical Interface), is a simulation model for a multi-reservoir system combined with formal mathematical optimization. WARGI is used to identify the optimal short- and medium-term actions to “minimize the vulnerability of higher priority demands in the water resource system during drought periods.” Using 54 years of hydrological time series measured at 19 stations at monthly intervals, different hydrological scenarios with respect to reservoir inflows and water demand were considered in the optimization module. The authors extended their approach to water quality modeling of a surface water reservoir system to minimize the occurrence of algal blooms during drought-induced lower flow periods, a recurring problem worldwide.

25.6  Real-Time Decision Support System for Drought Forecasting and Management 25.6.1  I ntroduction and Overview What makes drought even more problematic beyond its obvious adverse impacts is that it is often difficult to forecast, it usually proceeds slowly and consequently is often referred to as a “creeping phenomenon.” The importance of an early warning system for effective drought management cannot be overstated. As observed by McNutt et al. [8]: “Having an early indication that drought will develop or intensity is critical to employing timely strategies that can mitigate and reduce its impacts.” Accurate forecasting models can provide decision-makers with an early warning alert system that provides a window into likely future conditions. As presented in the preceding text, different indicators are commonly used to help determine the drought status of an area. While some early warning systems use weather forecast information in conjunction with drought indices to help determine the status of the region, generally speaking, real-time explicit forecasting of indices is not the norm. Although weather forecasts are obviously necessary for helping project future system conditions, a valuable extension would be to explicitly forecast drought indices based upon forecasted weather and other relevant conditions like expected water use. In this manner, instead of relying on subjective professional judgment to extrapolate from weather and water use to future indices values, real-time models would directly forecast indices values, providing decision-makers with a more objective and accurate projection and assessment of future conditions. Future water demand is a critical variable for assessing the potential status of a drought. During periods of expected lower water demand, the necessity of declaring a more severe drought status is less warranted than during periods of expected higher demand. While demand often shows distinct seasonality, real-time water demand in many regions typically varies both temporally and spatially as a function of other factors, like weather conditions. As noted previously, drought often increases demand above what it would normally be. To help account for inherent uncertainty, statistical analysis can be used to correct these predictions by using one-sided confidence intervals [12]. Water managers often have multiple sources and means for meeting water demand. The challenge is how best to allocate the various resources to most effectively meet present demand while minimizing both impacts and system vulnerability to future drought conditions. There are a variety of optimization formulations that can be used as part of a real-time decision support system. For example, achieving the forecasted water demand without violating any imposed constraints, or alternatively, achieving the required demand while simultaneously minimizing the total impact on indices, such as minimizing

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total declines in groundwater levels, surface water reservoir levels, and/or some combination of indices and even other constraints. There are both single and multi-objective optimization management approaches that can be used, which may also include uncertainty and dynamic conditions. In this section, we present the conceptual framework for a real-time decision support drought management system that combines real-time data streams with artificial neural networks and formal mathematical optimization. The system can also be used to manage water resources under normal conditions, which further increases its value as a general water management decision support system. However, given that operational decisions and resources are more constrained and exposed to higher risk during drought, the value of such a system is greater during this extreme. The components of this system include data collection and control systems for measuring and transmitting important state and control variable values to the decision support system, artificial neural networks, a form of artificial intelligence for generating real-time predictions and system simulations, and formal mathematical optimization for identifying the optimal management solutions, which can then be implemented in real or near real time via the control system. Last, it is worth repeating that an incorrect forecast that misses or minimizes the occurrence of a drought is not the only case that produces negative consequences; similarly, there can be serious costs when the abatement or diminishment of drought is also incorrectly forecasted or managed.

25.6.2 Real-Time Data Streams Maximizing real-time decision-making effectiveness requires good data and information, including real-time data streams. While during most time periods there may be time lags for significant changes in system state conditions to occur, like groundwater levels, forecasting subtle but potentially important system changes would provide decision-makers with valuable lead time to anticipate a new drought status. Accurate modeling forecasts of critical indices require real-time at least near-real-time data for maximum forecasting accuracy. For example, human control variables like pumping rates of a major wellfield can quickly modify the state of a groundwater system. As discussed briefly by Coppola et al. [5], Supervisory Control and Data Acquisition (SCADA) Systems consist of remote sensors that collect important meteorological, hydrological state, and human control variables, like precipitation and temperature, groundwater levels and salinity concentrations, and pumping rates of production wells, respectively, the values of which are automatically transmitted and stored in a central database at any frequency of interest (e.g., every minute and hour). These data are ideal for the development and implementation of real-time prediction models using technology like artificial neural networks. The historical data can be used to develop and refine the models, which can be retrained at the frequency desired as new data become available. Once the prediction models are validated to achieve satisfactory performance, they are directly integrated with the data streams to provide real-time prediction capability. To enhance real-time decision-making, the ANN models are combined with formal mathematical optimization to identify optimal management ­strategies in real time. An example formulation of this approach is provided in the following text.

25.6.3 Introduction to ANN Modeling Artificial neural networks (ANNs), a form of artificial intelligence, are used extensively in a wide variety of fields, including such disparate areas as medical research, chemical processing, investment strategies, military applications, and energy load forecasting. In addition to being recognized as extremely robust models capable of accurately modeling highly complex nonlinear systems, ANNs have the advantage of being “data-driven,” and hence excel with large and continuous data streams. Because continuous data streams collected in real time are becoming increasingly available with the proliferation of SCADA systems, the possibilities offered by ANNs are seemingly endless for improving decision-making strategies and optimizing operations.

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ANNs are becoming a common modeling methodology for hydrologic processes [5]. A “learning” modeling paradigm modeled after the human brain, ANNs do not require explicit conformance with physical or mathematical assumptions. Instead, using historical data sets, the ANN obtains a complex mathematical relationship that predicts outputs, constituting the system behavior of interest, in response to predictor input variables. The ANN consists of layers of individual nodes interconnected via transfer functions, analogous to brain neurons interconnected via synapses. During learning, data patterns are processed through the ANN structure, and the strengths of the connections between nodes are systematically changed by adjusting the values of coefficients within the transfer functions. This functional mapping is done in a manner analogous to human learning, where observation data are processed through an interconnected network of nodes in an effort to learn relationships between cause and effect variables. The learning proceeds to minimize the difference between the ANN estimated output values and the actual values. A more detailed description of this technology may be found in Coppola et al. [5] and Poulton [11]. In the next section, three real-world applications of ANN models developed for predicting variables of interest for a real-time decision support system for drought are presented. The first variable is water demand, which is important for both assessing the potential deficits as a result of water use and optimizing decisions. The next two variables, groundwater levels and salinity concentrations in coastal aquifers like those in Malta, can be used as “drought indicators” for assessing the state of the system. In addition, these variables can also be used in the optimization formulation, particularly if they are affected by human water management controls either directly or indirectly. 25.6.3.1  Water Demand Forecasting Expounding on the importance for accurately forecasting demand in real time, McNutt et al. [8] observe: “In its most basic form, drought can be thought of as insufficient water to meet demand. Demand can be based on ecosystem processes or on institutional and economic systems linked to human health and welfare. Because understanding demand is critical, systems designed to provide early warning of drought should ideally be able to evaluate changes in both the demand for, and supply of, water, and successfully communicate the information to groups or institutions that can apply drought risk reduction strategies.” In this case example, ANN models were developed to predict wastewater volume generation (­surrogate to water demand) for a large southeastern section of the State of New Jersey. The data utilized consisted of daily wastewater volume data, spanning June 2001–2005, in conjunction with daily weather data collected at the Atlantic City Airport. Several ANN models were developed to forecast wastewater volumes for “Total Atlantic City,” containing Atlantic City and several other smaller municipalities for three different forecasting periods: 1-day ahead, 7-days ahead, and 30-days ahead. For the 1-day-ahead forecasting period, three different models were developed, ranging from a relatively simplistic model, consisting of relatively few predictor variables (5), to a relatively complex model, consisting of a relatively high number of predictor variables (35). For the 7- and 30-day-ahead forecasting periods, one model was developed for each case. The types of input variables consisted of recent historical weather conditions preceding the prediction period, “future” weather conditions, which in this case was known a priori, and recent historical wastewater volume data. Recent historical wastewater volume data were used to account for the fact that there typically is a “memory” or correlation between recent wastewater volumes and future volumes. The weather variables, consisting of precipitation and temperature, are used to account for the fact that wastewater volumes (i.e., water use) are generally influenced by weather patterns. For example, during a hot dry spell, residents may water lawns more frequently, and a larger number of vacationers and day trippers may go to the shore, increasing water consumption. Because water consumption determines wastewater volume, this type of consumer demand relationship between wastewater volume and weather was deemed appropriate. High correlation coefficients and low absolute mean errors demonstrated that the ANNs were able to extract relationships between recent historical wastewater volume patterns and weather conditions with future wastewater volume. The ANN models performed better for longer prediction periods,

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where short-term water use variations are more random, particularly for situations that are not well represented by the data (e.g., a large convention event). However, even for the 1-day-ahead prediction period, the ANN was able to reproduce lower and higher water volumes. While the mean absolute change between consecutive days in wastewater volume over the study period is approximately 0.62 million gal, for the 1-day-ahead prediction period, the mean absolute error for the Complex ANN model was 0.46 million gal during validation. Consequently, the ANN model was not “keying” off the previous day’s wastewater volume but was extracting some relationships between the input predictor variables and the next day’s water consumption (i.e., demand). The 7- and 30-day-ahead forecasting models achieved much higher accuracy, with correlation coefficients over 0.90 for the validation data sets. 25.6.3.2  Forecasting Groundwater Levels in a Complex Multilayered Aquifer System As groundwater constitutes a significant portion of the total water consumed worldwide today, its enormous value as a water source cannot be overstated. For example, approximately 44% of the U.S. population derives its drinking water from this source, and groundwater is often a source of replenishment to surface water systems. Hence, its usefulness as a general indicator of drought status is high. Furthermore, because of its value as both a source of water and its relationship to the general health of ecosystems, optimization management decisions centered around this variable would be an important component of any decision-support management system where groundwater resources are used. Development of models for accurately predicting and simulating groundwater levels in real time in response to variable pumping and weather conditions would be an invaluable component of both an early warning alert system and a real-time management decision support system. In this case study, ANN models were developed for the coastal community Tampa Bay, a relatively large city located along the southwestern Florida coast, which has undergone tremendous population growth over the past several decades. Because of high demand, the groundwater system used to meet much of the area’s water demand has suffered excessive water level declines. The area resides above a complex hydrogeologic system, with a sedimentary unconfined aquifer overlying a low permeability clay layer, below which lies a semi-confined and more complex limestone aquifer that is characterized by complex karst features in places. An ANN model was developed to predict groundwater levels at monitoring wells over forecast periods (i.e., stress period) ranging from 3 to 24 days in response to variable pumping and weather conditions. ANN predictive capability was compared both against measured groundwater levels and reforecasts (i.e., back-prediction using information pertaining to that period) of groundwater levels by a coupled numerical surface water/groundwater flow model developed and operated by the water utility that manages the wellfield. A validation data set consisting of 10 consecutive weeks of weekly data that was not included in the model training set was used to test how effectively the ANN model learned to simulate groundwater-level responses to variable weather and pumping conditions. For the 120 validation predictions (i.e., 12 monitoring wells over 10 stress periods), the ANN model not only achieved a significantly lower validation error than the numerical model, 0.16 versus 0.85 m, respectively, but also accurately reproduced the general behavior, accurately capturing increasing and decreasing water-level periods in response to variable weather and pumping conditions in both the unconfined sedimentary aquifer and deeper semi-confined limestone aquifer. The interested reader is referred to Coppola et al. [2] for a more in-depth presentation of this work. 25.6.3.3 Forecasting Salinity Concentrations in a Coastal Aquifer According to the United Nations Atlas of the Oceans [16], approximately 44% of the world population lives within 150 km of the coast. In coastal areas where groundwater constitutes a major water source, its vulnerability to saltwater intrusion, particularly during drought conditions when demand is highest, is acute and serious. Salinity concentrations in these vulnerable coastal areas can also increase due to reductions in natural groundwater recharge from decreased precipitation. Consequently, a real-time model that can accurately predict and simulate salinity concentrations in a coastal aquifer in response to

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variable pumping and/or weather conditions is extremely valuable as both an early warning alert system and a water management system under drought conditions. Provincetown, Massachusetts, situated on a peninsula between the Cape Cod Bay and the Atlantic Ocean, is a popular resort that experiences significantly higher water use during summer. A production well was installed in the middle of the peninsula in 1987 to help meet water demand for the community. Over time, increases in salinity concentrations in the aquifer were measured in a monitoring well located near the production well. The salinity concentrations in the aquifer, as measured in the monitoring well, generally decrease during lower demand periods, but increase during higher pumping periods. In order to predict variable salinity concentrations (i.e., electrical conductivity) in the monitoring well in response to variable pumping and weather conditions, ANN models were developed to predict conductivity levels 30-, 60-, and 90-days ahead. The ANN model inputs consisted of initial conductivity value, measured at the beginning of the prediction period in the monitoring well, total pumping extraction over the prediction period, total precipitation over the prediction period, and average air temperature. The ANN models in general achieved excellent predictive accuracy, accurately reproducing variable conductivity levels in the monitoring well over time. A final ANN model was used to perform an extended 46-month simulation period using monthly time-steps. The model accurately simulated variable conductivity levels in the monitoring well over the extended period, reproducing the higher and low conductivity periods. This performance demonstrates that ANN models can be used for providing extended simulations over multiple time steps that span years into the future. A more detailed overview of this research may be found in Coppola et al. [3]. 25.6.3.4 Formal Optimization Methodology Formal optimization can be performed to identify the optimal values for human control or decision variables that minimize a negative objective (e.g., operating costs) and/or maximize a positive objective (e.g., water supply) while satisfying both management objectives (e.g., minimum required water levels) and the physics of the problem (e.g., conservation of mass). Optimization has been used extensively in water resources planning and management, ranging from groundwater extraction policies that minimize environmental impacts while maximizing water supply to surface water extractions that maximize storage while minimizing flooding. Traditionally, physical-based models (e.g., numerical) have been used as the basis for performing the optimization. As presented by Coppola et al. [5] because of their mathematical structure and inherent configurability with real-time data streams, ANN models developed for the physical system of interest can serve as a more efficient and accurate surrogate for traditional physical-based models in performing optimization, including conflicting multi-objective optimization. In a study performed for a real-world public supply wellfield, total volumetric groundwater pumping was traded off with vulnerability to contamination from a nearby contaminant plume [4].

25.7  Malta Case Study 25.7.1  Background The climate of the island of Malta is typically semiarid Mediterranean, with long, dry summers and mild, wet winters. The mean annual rainfall is around 564 mm* and is mainly characterized by storm events of high intensity but of a relatively short duration. The prevailing climatic conditions present a high intraannual variability with rainfall being mainly concentrated between the months of September and March, and also a high inter-annual variability where annual minima of 339 mm and maxima of 900 mm have been registered by the National Meteorological Office. Furthermore, regional climate change impact statistics indicate that in the long term, reductions in the mean annual rainfall depth ranging between −4% and −27% are projected, where the rainfall is also expected to become concentrated in a lower number of higher * Rainfall data for Luqa Meteorological Office Gauge, 1975–2013.

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intensity storm events, further exacerbating the situation from a water availability point of view. The further application of the “Reconnaissance Drought Index,” which takes into consideration both the rainfall depth and the evapotranspiration losses when classifying drought conditions, to Malta’s climate data has shown an increase in the number of dry years and therefore a shift toward less water availability. From a natural water resources perspective, the hydrogeological structure of the Maltese islands does not permit the development of surface water bodies of sufficient capacity to enable their economic exploitation. In fact, the dry valley systems of the island only sustain flows of water in the immediate period following high-intensity rainfall events. A system of dams has been developed to retain this storm discharge; however, its storage capacity is severely constrained by the relatively small dimensions of the valley systems. In fact, the design storage capacity of these dams is estimated at just around 250,000 m3. These natural conditions leading to a low availability of water resources also have to be considered from a water demand perspective. The Maltese islands at 1292 inhabitants/km2 ranks among the highest national population densities in the world. This leads to very high demand for water consumption, resulting in an extremely low water availability per capita, which is estimated to range between 80 and 120 m3/annum, far below the 500 m3 limit that the United Nations considers as the limit which defines chronic water scarcity. In fact, the islands’ national water demand of around 64 million m3/year is estimated to stand at two times the sustainable yield of their natural freshwater resources. Figure 25.1 depicts water availability per capita for a number of European countries, which highlights Malta’s challenging situation with regard to water scarcity.

25.7.2  Water Resources The islands’ natural freshwater resources consist primarily of a series of unconfined bodies of groundwater with a total annual sustainable yield of around 25 million m3. The major groundwater bodies are in direct lateral and vertical contact with seawater and are thus highly vulnerable to the intrusion of seawater in response to over-abstraction. The lack of surface water bodies of economic exploitation importance limits surface water resources to the harvesting of rainwater runoff. Utilization of this surface water is severely constrained by reservoir carrying-over capacity, which limits its current resource potential to an annual volume of 2 million m3. Consequently, Malta relies on a combination of groundwater and desalinated seawater for the purpose of potable supply, with current contributions from each source at 43% and 57%, respectively. The chronic lack of water availability effectively mandated the development of unconventional water resources, particularly since the early 1980s where the application of membrane desalination technology has seen a steady increase in freshwater production capacity, with production levels today standing at around 16 million m3/year. Water produced from the islands’ reverse osmosis (RO) plants has a stable quality all year round, and an optimization exercise could envisage the varied production of desalinated water in response to the optimized variation in quality of the groundwater blend in order to produce the best possible water supply blend for eventual distribution to consumers. Municipal water supply through dedicated distribution facilities is operated and managed by the Water Services Corporation (WSC), the main water utility in Malta. Municipal water is essentially a blend of groundwater and desalinated water, with varying blending levels aimed at managing the saline content of the water supply. Municipal water demand currently shows a negative trend, mainly as a result of an aggressive leakage management and repair program being undertaken by the WSC. Groundwater is sourced from 134 boreholes and 13 pumping stations* primarily tapping the Malta and Gozo mean sea-level aquifer systems and 3 desalination plants located at the Western, Eastern, and Northern coast of the island of Malta. Desalinated water has significantly lower salinity concentrations compared to groundwater, and therefore water from these two sources is blended (mixed) at distribution * Pumping Stations are high-yield groundwater abstraction stations that have groundwater collection galleries sustaining a central abstraction point.

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Malta Cyprus Denmark Poland Belgium Germany United Kingdom Spain Italy France Netherlands Lithuania Portugal Luxembourg Estonia Slovakia Austria Hungary Ireland Latvia Slovenia Sweden Finland 0

5,000

10,000

15,000

Water availability (m3/cap/year)

20,000

25,000

FIGURE 25.1  Water availability per capita for a number of European countries.

reservoirs to achieve an optimum quality level in the water supplied to consumers. Figure 25.2 conceptually illustrates the municipal water supply system in Malta. The sea-level groundwater bodies that are utilized for public supply have a heterogeneous hydrogeology with a prevalence of secondary (fracture) permeability. Abstraction from these aquifer systems is highly susceptible to upconing in the underlying saline water body, with the level of upconing being dependent on both the rate of abstraction and the permeability of the aquifer matrix at the abstraction point. The quality of abstracted groundwater therefore presents a varied response at different abstraction points in relation to the prevailing hydrogeological conditions. Seasonal effects, mainly arising from the increased abstraction by the private sector during the dry season, introduce further variability in the quality of the abstracted water. The two major water use categories also present significantly different seasonal variability. Municipal water demand is generally stable but shows a slight peak during the summer months, mainly in response

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473

Distribution reservoir Reverse osmosis plant

Seawater

Groundwater abstraction wells

Control unit

Freshwater

FIGURE 25.2  Schematic illustration of the municipal water supply in Malta.

to a higher demand by the tourism sector. In contrast, water demand by the agricultural sector peaks significantly during the dry summer months, as compared to the winter period where the demand for irrigation water is extremely low.

25.7.3  Optimization Management Description For this real-time decision support system example, drinking water for the municipal and industrial sectors is the focus of the optimization component. However, portions of the real-time drought management system can be used to advise the agricultural sector of possible drought conditions, helping them to predict and thereby plan more effectively (e.g., plant less water-intensive crops). As described earlier, the demand of the municipal and industrial sectors is sustained by groundwater extracted by 134 production wells of different production capacity and Mediterranean seawater desalinated by three RO plants. These two water sources are discharged into 24 distribution reservoirs. The reservoirs serve as “buffers” to permit the blending of significantly less saline RO water with groundwater to produce acceptable chloride concentrations. The final mixed reservoir water is distributed to consumers. The existing water storage within the reservoirs is all that is available for consumers at any given time, which have a combined maximum storage capacity of approximately 4–5 days of the daily average drinking water demand. As in most real-world optimization management problems, the utility has multiple objectives that it wants to simultaneously address, namely, maximizing water quality distributed to consumers while minimizing the total energy consumption required for providing this water. In accordance with these objectives and associated constraints, the decision management problem will identify the optimal extraction rates of individual municipal supply wells, the total volume of desalinated water, and the blending rates. Maximizing water quality has obvious benefits to both the utility and the consumer. This includes higher water quality for human consumption and promotion of high-tech manufacturing production capabilities, which increase overall consumer satisfaction for the utility. Minimizing energy consumption reduces financial costs assumed by both the consumers and the utility; in addition, it also helps minimize carbon emissions that contribute to global warming.

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For the two objectives, there are unit coefficients associated with each. For groundwater, the current s­ pecific energy consumption unit is 0.8 kWh/m3, while for RO it is 3.6 kWh/m3. Water quality ranges between 130 and 150 mg/L for the RO plants, while for groundwater it ranges between 130 and 3100 mg/L, depending on the particular production well. Note that the two objectives are measured by non-­commensurable units: chloride concentrations for water quality and kilowatt hours for energy consumption. Because these units are non-commensurable, both units must be normalized to range between 0 and 1 in accordance with their minimum and maximum possible respective values. And because this is a multi-objective optimization problem, the Pareto frontier or trade-off curve must be generated from which the optimal trade-off point is identified in accordance with the priorities of the decision-makers. There are a variety of management and operational constraints. In addition to meeting the forecasted monthly water demand, there are a number of other management constraints. Except under extraordinary conditions (e.g., prolonged drought conditions), the chloride concentrations extracted from any single municipal production well must not exceed 1000 mg/L. This constraint is imposed to reduce both blending requirements and localized saltwater intrusion due to over-pumping. The total blended water quality of the two combined sources (i.e., groundwater and reverse osmosis) must not exceed 350 mg/L to ensure conformance with aesthetic, health, and manufacturing requirements as set forth by the utility. The operational constraints include the maximum sustainable pumping rates of the individual production wells, and the production capacity of the RO plants. The decision variables for production well pumping rates and RO water generation are generally not continuous variables. Most of the wells lack variable control pumps, and thus the decision is whether or not to pump (i.e., turn on) an individual well, rather than the pumping rate of the well. The average daily baseline production rates of the Pembroke, Lapsi, and Cirkewwa RO plants during the winter months are 24,918, 10,284, and 4,143 m3/day, respectively, when there is less demand. Obviously, production increases with the onset of the summer months, which are warmer and drier. However, any increases above the RO production baseline must be increased stepwise. For the Cirkewwa and Pembroke plants, stepwise increases of 4200 m3/day are achieved for each additional RO unit that is brought on line, while for the Lapsi plant, stepwise increases of 3800 m3/day occur for each additional unit. For this management problem, the only real-time forecasting is projected water demand over the next week using weather and consumer water use patterns. Because forecasted demand will always have some inherent uncertainty, a robust analysis would explicitly account for this uncertainty. In this case, the optimization model explicitly accounts for inherent uncertainty by optimizing expectation and minimizing the variance of the objective function. Because the management period selected is over a 1-week period, average daily values will be used. In reality, a number of variables are not constant, but measurably vary over different time scales. For example, chloride concentrations in production wells change in response to pumping patterns. Within a 1-week period, chloride concentration changes within the aquifers are generally not measureable. For longer-term management periods, however, real-time models like ANN that can reasonably predict such changes would have long-term value for resources protection and cost savings. An optimization component that is far more dynamic is energy coefficient costs, which could vary by time of day. A more advanced decision support system would include real-time predictions of changing chloride concentrations over select time periods, as well as temporally variable cost coefficients for energy. In short, although the optimization model presented here can significantly reduce operational costs while improving water quality for the utility, it can be further improved by including both uncertainty and dynamic changes for all variables and cost coefficients.

25.7.4  Mathematical Optimization Formulation There are three water resources that must be managed conjunctively. They are as follows:

1. Water wells with variable pumping rates (variable speed pumps). 2. Water wells with fixed pumping rates (non-variable speed pumps). 3. RO plants that can produce water amounts on given discrete levels.

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They can be characterized by the following parameters: 1. NW1 = number of water wells of type 1 1 PRi( ) = pumping rate as decision variable for well i of type 1 1 ci( ) = chloride amount per unit water supply from well i of type 1 2. NW2 = number of water wells of type 2 if well j is on if well j is off , as decision variables

ïì1 xj = í îï0





(2)

c j = chloride amount per unit volume of water supply of well j of type 2 NRo = number of RO plants k k k k L(o ) , L(1 ) ,…, L(l ( k) ) = production levels with L(o ) = 0 for RO plant k k if RO plant k operates on level L(l ) otherwise, as decision variables

ìï0 k xl( ) = í îï1





As the RO plant can operate on only one level: l(k )

åx ( ) = 1 l



k

(25.1)

l =0

ck( ) = chloride amount per unit water supply by RO plant k The produced water volumes are collected in reservoirs.   NRC = number of reservoirs   Capr = capacity of reservoir r R

The produced water is transported to the reservoirs, so let   zir = water amount transported from well i of type 1 to reservoir r   zjr = water amount transported from well j of type 2 to reservoir r   zkr = water amount transported from RO plant k to reservoir r Water balance equations of the wells and of the RO plants: NRC

åz



ir

(i = 1,2,¼, NW )

= PRi( ) 1

1

r =1

NRC

åz



jr

( j = 1,2,¼, NW )

2 = x j PR(j )

2

r =1

l(k )

NRC

å åL( )x ( ) z kr =



r =1

l

k

l

(25.2)



k

(25.3)



( k = 1,2,¼, NR )

l =0

o

(25.4)



Total water amount to reservoir r is limited: NW1



NRo

NW2

å å åz zir +

i =1

z jr +

j =1

k =1

kr

 Capr

( r = 1,2,¼, NRC )

(25.5)

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The chloride amount per unit water amount is limited:

å

NW1 i =1

zir ci( ) + 1

å



NW1 i =1

zir

å +å

NW2

å +å

2 z jr c (j ) +

j =1 NW2 j =1

z jr

NRo

k =1 NRo

k =1

R z kr ck( )

z kr

 Er

(25.6)

The total water supply should satisfy demand: NW2 æ NW1 ç zir + z jr + ç r =1 è i =1 j =1

NRC

ö z kr ÷  D ÷ k =1 ø

NRo

åå å å



(25.7)

The decision variables are as follows:

PRi( ) ( i = 1,2,¼, NW1 ) continuous variables 1

x j ( j = 1,2,¼, NW2 ) binary variables

xl( ) (k = 1, 2,  … , NRo; l = 0, 1,  … , l(k)) binary variables zir (i = 1 , 2 ,  …  , NW1; r = 1, 2, …, NRC) continuous variables zjr (j = 1 , 2 ,  …  , NW2; r = 1, 2, …, NRC) continuous variables zkr (k = 1 , 2 ,  …  , NRo; r = 1, 2, …, NRC) continuous variables k

Possible objective functions: 1. Maximizing total cost tir = production and transportation cost of unit water amount from well i of type 1 to reservoir r tjr = same for well j of type 2 tkr = same for RO plant k Tr = transportation cost of unit water amount to consumers from reservoir r NW2 æ NW1 ç zir (t ir + Tr ) + z jr ( t jr + Tr ) + ç r =1 è i =1 j =1

NRC



åå

å

ö

NRo

åz k =1

kr

(t kr + Tr ) ÷÷ ® min ø

(25.8)

2. Satisfy demand as well as possible NW2 æ NW1 ç zir + z jr + ç r =1 è i =1 j =1

NRC

NRo

å å å åz



k =1

kr

ö ÷ ® max ÷ ø

(25.9)

if the demand cannot be met. In this case, constraint (25.7) must be omitted. 3. Optimizing water quality



ì maximum ï í 1  r  NRC ï î

å

NW1 i =1

å +å

NW2

zir ci( ) +

å

1

NW1 i =1

zir

j =1 NW2 j =1

å z c( ) üïý ® min ï +å z z þ

2 z jr c (j ) +

z jr

NRo

k =1 zir +

k =1

R kr k

(25.10)

kr

Regardless of which objective function is selected, this is a mixed (continuous-binary) optimization problem. Notice that constraints (25.1) through (25.5) and (25.7) are linear and (25.6) can also be rewritten into linear form by multiplying both sides by the denominator: NW1



å ( i =1

1

NW2

NRo

) åz (c( ) - E ) + åz (c( ) - E )  0

zir ci( ) - Er +

jr

j =1

j

2

r

kr

R k

r

k =1

Objective functions (25.8) and (25.9) are also linear, however (25.10) is nonlinear.

(25.11)

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477

The model in this form is static and deterministic; however, it can easily be extended into a dynamic model and also include uncertainty.





1. In the dynamic extension, all decision variables are time dependent, and the objective function is the present value of the sum of all future objective values. If the total water amount in reservoirs exceeds D(t), then the excess amount has to be added to the amount transported into each 1 2 R reservoir. The demand (D), quality parameters (ci( ) , c (j ) , ck( )), quality requirements (Er ), and costs (tir, tjr, tkr, Tr) might depend on time. Any recharge into the reservoirs must also be added to the total water volume in storage. 2. If any parameter is uncertain, then it has to be considered as a random variable. If it is in a constraint, then its deterministic counterpart is obtained by “chance constraints,” meaning that we require that the constraint has to be satisfied at least with a given probability level. If it is an objective function, then we can compute its expectation E and variance V. In the economic literature, the random outcome is replaced by its certainty equivalents: E + aV or E - aV

(25.12)

depending on the nature of the objective function. If it is minimized, then the first version is minimized, and if it is maximized, then the second version is maximized. The coefficient alpha reflects the risk-taking attitude of the decision-maker. For α = 0 only expectation is optimized and as α increases, the risk is given more weight. 3. If more than one objective has to be considered, then a multi-objective optimization problem has to be solved by combining the different objectives into a “composite objective.” Many different techniques are known from the literature of multi-objective optimization.

25.8  Summary and Conclusions Drought is becoming a more serious and prevalent problem worldwide. Practive decision support systems that help forecast and mitigate drought are rarely implemented, the absence of which compromises rational decision making to the detriment of society as a whole. Consequently, there is typically an inability to respond in a timely and effective manner, thereby magnifying the consequences of extreme and increasingly prolonged dry conditions and increasing system vulnerability to future drought. As presented in this chapter, real-time data collection and control systems like Supervisory Control and Data Acquisition (SCADA) interfaced with ANN can provide accurate models that provide valuable lead time while reducing inherent human error and bias that often hinder effective drought management decisions. By deploying a robust and accurate real-time forecasting system, decision-makers can anticipate changes in the current status, providing them with valuable lead time for adapting management policies that mitigate adverse effects. A variety of real-time prediction models that include water demand and common drought indices and water management variables like groundwater levels and surface water flows can be combined within a formal optimization management model. The optimization model can quickly and accurately identify optimal management decisions that can simultaneously maximize benefits and minimize costs, even for cases where two or more objectives in conflict exist. While not explicitly represented by the optimization model presented here, both uncertainty and dynamic changes can also be included. For the Malta case study presented in this chapter, the real-time drought management system has the further advantage of also managing the complex water resources of the country during “normal” conditions. Increasing water demand worldwide, diminishing water resources from over-use and contamination, and additional uncertainty in the face of climate change ensure that the “new normal” will require

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advanced decision support systems that utilize real-time data streams in combination with advanced prediction and optimization models.

Authors Emery A. Coppola Jr. is president and co-founder of NOAH LLC, which specializes in the application of ANN, optimization, and other advanced techniques to water resources management. Dr. Coppola received a BS in geology and oceanography from the University of Miami (Florida), an MS in geological engineering from Drexel University, and a PhD in hydrology from the University of Arizona. One of the most experienced hydrologists in the United States for applying artificial neural networks (ANNs) to water resources management problems, Dr. Coppola has served as project manager on ANN modeling projects that include groundwater resources, water distribution systems, and surface water systems. Manuel Sapiano is the Water Director for Malta and heads the Water Policy Unit at the Sustainable Energy and Water Conservation Unit within the Ministry for Energy and Health. He obtained a masters in hydrology at the University of Malta and furthered his studies in island hydrogeology and isotope hydrology. His role at the ministry involves the coordination of the national implementation process of the EU’s Water Framework Directive and the development of a National Water Management Plan for the Maltese Islands. Furthermore, he also manages sustainable energy and water conservation units (SEWCU’s) participation in a number of EU-funded projects in the field of water resources management. He has also collaborated as an expert with various regional and international institutions such as the Plan Bleu and the Food and Agriculture Organisation of the United Nations. Michael Schembri works as a policy officer as part of the Water Policy Unit within the Ministry for Energy and Health. Within the unit, his main responsibilities include the coordination of water resources management initiatives as well as supporting the implementation process of the Water Framework Directive, leading to the establishment of the National Water Management Plan. Michael is also responsible for the management of groundwater qualitative and quantitative monitoring network program required under the Water Framework Directive. He graduated in geography from the University of Malta, followed his postgraduate studies with a masters in geographic information science from the University of London, and is currently reading for a doctoral degree at University College London. Ferenc Szidarovszky, vice-president, cofounder, and director of operations research for NOAH LLC, received his PhD in mathematics from Eotvos University of Sciences of Budapest, Hungary, and a ­second PhD in economics from the Budapest University of Economic Sciences. Dr. Szidarovszky was a full professor with the Systems and Industrial Engineering Department at the University of Arizona, with a joint appointment in the Department of Hydrology and Water Resources. Dr. Szidarovszky is the author of nine textbooks and monographs in the United States, including a recent one on water resources systems analysis and of over 300 research publications in leading journals. He was recognized with the prestigious award (1998) “Dr. Habil in Engineering” by Budapest Technical University.

References

1. Andreu, J., Perez, M. A., Ferrer, J., Villalobos, A., and Paredes, J. 2007. Drought management decision support system by means of risk analysis models, in: Rossi, G., Vega, T., and Bonaccorso, B., eds., Methods and Tools for Drought Analysis and Management, Springer, Dordrecht, the Netherlands, pp. 195–216. 2. Coppola, E., Szidarovszky, F., Poulton, M., and Charles, E. 2003. Artificial neural network approach for predicting transient water levels in a multilayered groundwater system under variable state, pumping, and climate conditions, Journal of Hydrologic Engineering, 8(6): 348–359.

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3. Coppola, E., McLane, C., Poulton, M., Szidarovszky, F., and Magelky, R. 2005. Predicting conductance due to upconing using neural networks, Journal of Ground Water, 43(6): 827–836. 4. Coppola, E., Szidarovszky, F., Davis, D., Spayd, S., Poulton, M., and Roman, E. 2007. Multiobjective analysis of a public wellfield using artificial neural networks, Journal of Ground Water, 45(1): 53–61. 5. Coppola, E., Szidarovszky, A., and Szidarovszky, F. 2014. Artificial neural network-based modeling of hydrologic processes, in: Eslamian, S., ed., Handbook of Engineering Hydrology. Modeling Climate Change and Variability, CRC Press, Boca Raton, FL, pp. 19–34. 6. Hennesy, K. et al. 2008. An assessment of the impact of climate change on the nature and frequency of exceptional climatic events, Bureau of Meteorology and CSIRO, Canberra, Australian Capital Territory, Australia. 7. Hoffman, J. and Domber, S. 2003. New Jersey water-supply drought indicators, http://www.state. nj.us/dep/njgs/enviroed/infocirc/droughtind.pdf, last accessed on June 2014. 8. McNutt, C. A., Hayes, M. J., Darby, L. S., Verdin, J. P., and Pulwarty, R. S. 2013. Developing early warning and drought risk reductions, in: Botterill, L. C. and Cockfield, G., eds., Drought, Risk, and Policy Decision Making under Uncertainty, CRC Press, Boca Raton, FL. 9. Mediterranean Water Scarcity and Drought Working Group. 2007. Mediterranean Water Scarcity and Drought Report, Technical Report-009-2007, Joint EU Water Initiative/Water Framework Directive Joint Process, Mediterranean Water Scarcity and Drought Working Group, http://www. emwis.net/topics/WaterScarcity/PDF/MedWSD_FINAL_Edition, Accessed on May 2014. 10. Mujere, N. and Eslamian, S. 2014. Climate change impacts on hydrology and water resources, in: Eslamian, S., ed., Handbook of Engineering Hydrology. Modeling Climate Change and Variability, CRC Press, Boca Raton, FL, pp. 113–126. 11. Poulton, M. M. 2001. Computational Neural Networks for Geophysical Data Processing, Pergamon, Amsterdam, the Netherlands. 12. Ross, S. M. 1987. Introduction to Probability and Scientist, John Wiley & Sons, New York. 13. Rossi, G., Cancelliere, A., and Giuliano, G. 2006. Role of decision support system and multicriteria methods for the assessment of drought mitigation measures, in: Andreau, A., Rossi, G., Vagliasindi, F., and Vela, A., eds., Drought Management and Planning for Water Resources, CRC Press, Boca Raton, FL, pp. 203–240. 14. Sapiano, M. 2008. Measures for facing water scarcity and drought in Malta, European Water, 23(24): 79–86. 15. Sechi, G. M. and Sulis, A. 2007. Mixed simulation-optimization technique for complex water resource analysis under drought conditions, in: Rossi, G., Vega, T., and Bonaccorso, B., eds., Methods and Tools for Drought Analysis and Management, Springer, Dordrecht, the Netherlands. 16. United Nations. 2010. United Nations Atlas of the Oceans, http://coastalchallenges.com/2010/01/31/ un-atlas-60-of-us-live-in-the-coastal-areas/, accessed on May 2014. 17. United States Environmental Protection Agency Region 9 Strategic Plan. 2011–14. Geographic Area of Focus: San Joaquin Valley, http://www.epa.gov/region9/strategicplan/sanjoaquin.html, last accessed on May 2014. 18. Wolchover, N. 2014. What is a drought? Definition of droughts live science, http://www.livescience. com/21469-drought-definition.html, last accessed on November 2014.

26 Copula Functions and Drought 26.1 Introduction ....................................................................................... 481 What Is Drought? • Characterizing Drought Events  • Drought Monitoring and Forecasting

Shahrbanou Madadgar Portland State University

Hamid Moradkhani Portland State University

26.2 Copula Functions ............................................................................. 484 Mathematical Definition  • Different Classes of Copulas  • Identifying the Best Copula 26.3 Drought Identification by Copulas .................................................488 Univariate Return Period  • Multivariate Return Period 26.4 Probabilistic Drought Forecasting by Copulas .............................. 491 Bayesian Network of Drought Sequences  • Hydrologic Drought Forecasting in Temporal Extent  • Drought Forecasting in Spatiotemporal Extent

26.5 Summary and Conclusions ..............................................................497 Authors............................................................................................................................... 498 References ........................................................................................................................ 498

Abstract  Copula functions are a group of multivariate distribution functions that join the marginal distribution of multiple variables. They have been used in different fields of science and engineering during the past decades. The main advantage of copulas over other multivariate distribution functions is their flexible structure in choosing marginal distributions. They are also strongly capable of characterizing the joint behavior of dependent random variables. The focus of this chapter is on the application of copula functions in hydrology, specifically in predicting drought events. The first application explains how copulas can help to identify the multivariate return period (i.e., conditional and joint return ­periods) of drought events with particular duration, severity, and intensity under climate change impacts. The second application involves drought forecasting at seasonal and multiseasonal lead times. The copula-based drought-forecasting model is a conditional model given the past observation of drought status. This model can provide decision-makers with probability maps of drought severity and useful information on drought recovery in forecast season. Copulas have demonstrated appealing performance in hydrological applications and it is expected to witness more applications in the future.

26.1 Introduction 26.1.1 What Is Drought? Droughts and water scarcity are among the costliest hydroclimatic extreme events on Earth. Unlike other natural disasters, such as flood, hurricanes, and tornadoes, droughts are creeping disasters without a clear beginning and end. They slowly expand over a region and gradually fade out. In the past few decades, 481

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droughts with different severities have extended across the world [71]. Large areas in South, Central, and North America, Europe, Asia, Africa, and Australia have been affected by recent droughts. In 2012, more than 70% of the United States experienced different levels of water scarcity in a broad range of abnormally dry to exceptional droughts [104]. Several studies have been conducted during the past few years to enhance forecast accuracy, mitigation policies, and damage estimates of drought events throughout the world [8,10,16,19,23,35,83,116]. The North America Drought Monitor, produced by the National Oceanic and Atmospheric Administration’s (NOAA) National Climate Data Center (NCDC), reported that droughts have been among the costliest natural disasters in the United States since 1980, with an estimated damage of over $100 billion theretofore [56]. Lott and Ross [57] estimated a huge damage of $174 billion to the U.S. economy due to drought and heat wave–induced phenomena between 1980 and 2005. In 2002, the economic cost of droughts across the western United States was estimated at over $10 billion, as reported by NCDC [77]. Droughts as natural hazards have various impacts on different aspects of the natural environment and human lives, including water quality and quantity, society and public health, crop production and agriculture, hydropower generation, living environments, and wildfires. Droughts root in a lack of precipitation over an extended period of time. A lack of precipitation over a region can cause deficits in soil moisture, surface runoff, and subsurface and groundwater resources. According to the drought-affected zone, four different types of drought with different disciplinary perspectives can be identified in the most general sense: meteorological, agricultural, hydrological, and socioeconomic [78]. Nevertheless, the four types of drought are closely related to each other and a particular drought may extend from one type to another [18]. As the precipitation received over a particular location for a certain period of time drops below the average precipitation over a historical period, a meteorological drought begins. Then, lack of precipitation may expand further into soil moisture, and surface and subsurface water resources and cause agricultural and hydrological droughts. Finally, hydrological droughts can decrease the inflow to hydropower plants and may affect the production of hydroelectric energy, leading to socioeconomic drought.

26.1.2 Characterizing Drought Events Each of the four drought categories (meteorological, agricultural, hydrological, and socioeconomic) ­utilizes certain indices to identify drought events. Some drought properties like duration, severity, intensity, and inter-arrival time can be characterized by drought indices. While various drought indices have been introduced over the past several years, deficient precipitation remains the primary component in the identification of any drought category. A brief list of drought indices includes the Palmer Drought Severity Index (PDSI; [85]), the Rainfall Anomaly Index (RAI; [112]), the Crop Moisture Index (CMI; [86]), the Soil Moisture Drought Index (SMDI; [38]), the Crop-Specific Drought Index (CSDI; [66]), the Surface Water Supply Index (SWSI; [99]), the National Rainfall Index (NRI; [36]), the Standardized Precipitation Index (SPI; [64,65]), the Reclamation Drought Index (RDI; [117]), the Aggregated Drought Index (ADI; [47]), the Vegetation Drought Response Index (VegDRI; [7]), and the Regional Drought Area Index (RDSI; [25]). The CSDI is further divided into the following indices: the Corn Drought Index (CDI; [68]), the Soybean Drought Index (SDI; [67]), and the Vegetation Condition Index (VCI; [49]). After introducing the SPI to identify meteorological droughts, it has been applied to variables other than precipitation, and several standardized indices have been developed accordingly. Replacing precipitation by streamflow, Nalbantis [79] introduced the Streamflow Drought Index (SDI) to evaluate hydrological droughts. Sklar [105] developed the Standardized Runoff Index (SRI) using the runoff simulated by a hydrological model. Wan et al. [113] combined the merits of PDSI and SPI and proposed another alternative drought index named the Standardized Precipitation Evapotranspiration Index (SPEI). To capture the correlation of hydrological variables, Kao and Govindaraju [45] developed the Joint Deficit Index (JDI) addressing the marginal distributions of precipitation and streamflow. They applied copulas to account for the joint behavior of precipitation and streamflow. Technological advances and availability of satellite data initiated the development of another category of indices based on remote sensing. The VCI [49] was a primary

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483

application of satellite observations in developing drought indices. Some other indices utilizing satellite data include the Temperature Condition Index (TCI; [50]), the Vegetation Health Index (VHI; [51,52]), the Normalized Difference Vegetation Index Anomaly (NDVIA; [2]), the Standardized Vegetation Index (SVI; [89]), the Vegetation Temperature Condition Index (VTCI; [114]), and the Normalized Multi-Band Drought Index (NMDI; [115]).

26.1.3 Drought Monitoring and Forecasting Reliable forecasting of hydrologic extreme events is a primary requirement for efficient planning and management of water resources. In spite of recent advances in hydrologic forecasts, the impacts of climate variability, global warming, and climate change highlight the significance of more reliable methods in predicting extreme events such as floods and droughts [27,37,59,71,73–76,92,111]. Given the limited sources of manageable water and the population growth rate, the quality and quantity of supplied water are strongly affected by ongoing droughts across different regions of the world. The NOAA-NCDC reported that 2012 was the warmest year on record for the United States, during which the average temperature of the contiguous United States was 3.2°F above that of the twentieth century. According to the U.S. Drought Monitor, the drought of 2012 covered more than 70% of the contiguous United States. In contrast with the major droughts of 2012, most of which were noticeably recovered, some areas in 2013 remained under dry conditions. Since global warming and climate change are likely to be the main reasons of regional droughts over the past few years [90,110], future droughts are expected to occur more frequently throughout the world [13,100]. Although drought phenomena are likely to intensify in the future, it is possible to mitigate drought impacts with accurate forecasts with sufficient lead time  [14]. Reliable drought forecasting strongly affects efficient planning and management of available water resources and aids water suppliers to survive under enduring drought conditions. Since reliable drought forecasting is prone to different sources of uncertainty in a dynamic system of interacting components, a number of recent studies have focused on developing advanced forecast methodologies to accurately identify future droughts and approximate their occurrence likelihood (e.g., [14,15]). In 1987, Karl et al. estimated the unconditional probability of receiving sufficient precipitation to recover from drought conditions. The limitation of their method was in applying an unconditional distribution to obtain probabilities, where the dependency and autocorrelation of precipitation were ignored. Since then, several alternative methods have been developed for drought forecasting. Stochastic renewal models [46,54], the Markov Chain model [55,107], stochastic autoregressive models [69], and artificial neural networks (ANN) [5,70] are among the initial applications of statistical methods in drought forecasting. However, Hwang and Carbone [40] argued the limitation of autoregressive and neural network models in deterministic estimation of mean drought status. In another study [84], a wavelet and fuzzy logic combination model was applied to the long-lead drought forecasting across Texas, United States. Although the combined model has merits over fuzzy logic, ANN, or coupled wavelet and ANN models, it requires significant work prior to application. Aside from statistical methods, some studies have utilized the products of climate forecast models to estimate future droughts. References 9 and 40 incorporated the seasonal forecast products of NOAA Climate Prediction Center (CPC), with historical climate records to address the uncertainties of future droughts. During the past few years, different versions of climate forecast products have become available, and they have been extensively applied in operational drought forecasting across the United States [22,58,72,120]. While a number of studies have focused on accurate characterization of future droughts, work is still required on the forecast methods to identify the probabilistic features of future droughts. Most of the currently available methods are unable to estimate the full probability distribution of droughts. Developing the conditional probability of a drought status in the future, given the observed status in the past, requires advanced methodologies to address the connections and dependencies between drought events. For this purpose, a group of powerful statistical functions, called copula functions, has been recently utilized to establish drought forecasting models with substantial probabilistic features [60,62,87]. Copulas are

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multivariate distribution functions that join the random variables with some level of correlation and dependency. Since there are a lot of correlated variables in hydrologic applications, copula functions have been extensively used in the modeling of various hydrologic phenomena, including flood analyses (e.g., [24,96,121]), rainfall and runoff analyses [28,44,95,122], spatial analysis of groundwater quality parameters [3,4], and synthesizing and downscaling of monthly river flow [53]. In another recent study, copulas contributed to the postprocessing of hydrologic forecasts [61] and were found to be a robust alternative for reducing the uncertainty and increasing the reliability of hydrologic forecasts. In low-flow and drought analyses, copulas have been employed to characterize drought events according to the dependent structure between droughts’ severity, intensity, and duration [21,45,59,103,119]. Recently, Madadgar and Moradkhani [60,62] introduced a new application of copula functions, where they defined a copula-based forecast model and studied the probabilistic features of seasonal droughts.

26.2 Copula Functions 26.2.1 Mathematical Definition Supported by Sklar’s theorem [106], for n continuous random variables {X1,  …, Xn} with uniform marginal cumulative distribution functions (CDFs) ui = FXi (xi ), i = 1, …, n, there is a unique n-dimensional copula such that C ( u1 ,¼, un ) = F ( x1 ,¼, xn )

(26.1)

where

ui = FXi ( xi ) , i = 1,¼, n





where C refers to the CDF of copula FXi (xi ) is the marginal distribution of the ith variable Thus, copulas are multivariate distributions on the unit hypercube that joins marginal distributions, C : [0, 1]n → [0, 1] [43,81]. According to Equation 26.1, copulas return the multivariate joint probability of random variables: C ( u1 ,¼, un ) = P éëU1 £ u1 ,¼, U n £ un ùû





A copula should satisfy the “boundary” and “increasing” conditions defined as follows: • Boundary conditions C(u) = 0 if {ui = 0, i ∉ ϕ}; that is, there is an i such that ui = 0, ϕ is the null set. 1. 2. C(u) = u if {ui = u, uj = 1 ∀ j ≠ i}; that is, all components of u are equal to 1 except ui. • Increasing condition The probability of any n-dimensional hypercube in the unit hypercube is nonnegative: 2

2

å å ¼



k1 =1

n

k ( -1)åi=1 i C ( u1k1 ,¼,uiki ,¼,unkn ) ³ 0 for all 0 £ ui1 £ ui2 £ 1 kn =1

In a 2D copula, the boundary and increasing conditions are simply defined as • Boundary conditions 1. C ( u1 ,0 ) = C ( 0,u2 ) = 0 2. C ( u1 ,1) = u1 , C (1, u2 ) = u2

(26.2)

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Copula Functions and Drought

• Increasing condition

C ( u12 ,u22 ) + C ( u11 ,u21 ) ³ C ( u12 ,u21 ) + C ( u11 ,u22 ) for u11 £ u12 and u21 £ u22

In applying copula functions, the joint distribution of independent variables is expressed as C(u1, u2) = u1u2, and in the case of fully dependent variables, their joint distribution function is expressed as C(u1, u2) =  min (u1,u2). For an absolutely continuous CDF from a copula (C), the copula density c(u1,  … , un) is written as follows:



c ( u1 ,¼, un ) =

¶ nC ( u1 ,¼, un ) ¶u1 ¼¶un

(26.3)



The joint probability density function (PDF) of a set of random variables (X1,  … , Xn) can be defined as the product of copula density and the marginal density function of each variable:



f ( x1 ,¼, xn ) = c ( u1 ,¼, un )

n

Õf i =1

Xi

( xi )

(26.4)



Using Equation 26.4, the joint PDF, f(x1,  … , xn), is simply obtained from the marginal distributions and copula density function without identifying the unknown relations and complications among the random variables. The main advantage of applying copula functions is to utilize distinct marginal distributions while at the same time reflecting their inherent correlations. Beyond correlations, no information is required to develop the joint distribution function of Equation 26.4.

26.2.2 Different Classes of Copulas There are a large number of copulas in the literature, which are classified into three major categories: (1) elliptical, (2) Archimedean, and (3) extreme value. The Gaussian (normal) and t-copulas are classified as elliptical copulas. The class of one-parameter Archimedean copulas includes Ali–Mikhail–Haq, Clayton, Frank, [29,80], and Gumbel–Hougaard copulas and their extension [31], and Joe copulas [42]. The two-parameter family of Archimedean copulas includes Joe’s BB1, BB2, BB3, BB6, and BB7 copulas [43]. Extreme-value copulas include Gumbel–Hougaard (also classified as an Archimedean copula), Joe’s BB5 [43], Galambos [26], Hüsler [39], and Tawn [108] copulas. There are also other miscellaneous copulas such as Farlie–Gumbel–Morgenstern and Plackett copulas [91]. Among all available copulas, the elliptical and Archimedean families are the most frequently used copulas in hydrological applications. More details about these two classes of copulas are defined in the following sections. 26.2.2.1 Elliptical Copulas Elliptical copulas are simply the copulas of elliptical distributions. The key advantage of elliptical copulas is that they can capture different levels of correlation among a set of random variables. However, the variables are required to have a positive–definite correlation matrix. In statistics, a covariance matrix is a positive–definite matrix unless one variable is an exact linear combination of the others. The key disadvantage of elliptical copulas is that they do not have a closed-form expression. The most commonly used elliptical copulas are the Gaussian (normal) and t copulas. Table 26.1 presents the definition of each copula function for n = 2.

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Handbook of Drought and Water Scarcity TABLE 26.1  Summary of Elliptical Copulas with n = 2 Copula Gaussian

Function C ( u1 ,u2 ) =

F -1( u2 ) F -1( u1 )

ò ò





1

(

2 p 1 - r2

u1 = F ( x1 ) , u2 = F ( x2 )

)

1/2

Support

ì 2 ü ï x + x22 - 2rx1x2 ï exp í- 1 ý dx1 dx2 2 2 1- r ïî ïþ

(

)

x1 , x2 ∈ R

ρ: Linear correlation coefficient Φ: Standard normal cumulative distribution function

t

C ( u1 ,u2 ) =

tn-1( u2 )tn-1( u1 )

1

ò ò 2p (1 - r )



1/2

2



u1 = tn ( x1 ) , u2 = tn ( x2 )

ì ü ï x 2 + x22 - 2rx1x2 ï exp í1 + 1 ý 2 n 1- r ïî ïþ

(

)

-(n +2 )/2

dx1 dx2

x1 , x2 ∈ R

tν: Cumulative distribution function of t distribution with ν degree of freedom.

TABLE 26.2  Summary of Commonly Used Archimedean Copulas with n = 2 Copula

Function

Support

Gumbel

C(u1, u2) =  exp {−[(− ln u1)θ + (− ln u2)θ]1/θ} θ: Measure of dependency between u1 and u2. Either Pearson’s correlation coefficient or Kendal’s tau correlation are usually used to estimate θ.

θ ∈ [1 ,  ∞ )

Clayton

C ( u1 ,u2 ) = u1- q + u2- q - 1

Frank

C ( u1 ,u2 ) = -

Ali–Mikhail–Haq

C ( u1 ,u2 ) =

Joe

C(u1, u2) = 1 − [(1 − u1)θ + (1 − u2)θ − (1 − u1)θ(1 − u2)θ]1/θ

(

)

-1/q

(

θ ∈ (0, θ)

)(

) ùú

é e - qu1 - 1 e - qu2 - 1 1 ê ln 1 + q ê e -q - 1 ë

ú û

u1u2 1 - q (1 - u1 ) (1 - u2 )

θ ∈ R θ ∈ [ − 1 , 1) θ ∈ [1 ,  ∞ )

26.2.2.2 Archimedean Copulas The key advantage of Archimedean copulas is that they are easily constructed and are capable of capturing different dependence structures. Unlike elliptical copulas, these copulas have closed-form expressions, but do not preserve all pair-wise correlations if there are more than two random variables. While there are a large number of Archimedean copulas [82], Table 26.2 summarizes a list of those functions that are frequently used in the literature. However, Gumbel copulas with an asymmetric function are capable of properly modeling different hydrological phenomena [21,61,98,119,122].

26.2.3 Identifying the Best Copula A copula application starts with finding marginal distributions that properly fit the random variables and then exploring an appropriate copula function to join the marginal distributions. This section explains the procedure of fitting a copula function to a dataset and discusses the statistics of goodness-of-fit (GOF) tests utilized for copula selection. 26.2.3.1 Fit a Marginal Distribution A group of probability distributions is examined to find the best fit for each random variable. The choices may be Gaussian, Famma, lognormal, beta, Weibull, Gumbel, exponential, generalized extreme value,

487

Copula Functions and Drought

and other parametric distributions. The method of maximum likelihood estimation (MLE) is used to estimate the parameters of each distribution. The best choice is selected upon some test statistics including the Kolmogorov–Smirnov test (K-S; [48,63]) and the Akaike information criterion test (AIC; [1]). The K-S test statistic (D) measures the maximum distance of the empirical CDF to the CDF of the reference distribution:

{

D = max F ( x ) - G ( x )

}

(26.5)

where F(x) and G(x) are the empirical and reference CDFs, respectively. The null hypothesis (H0) of the K-S test states that the dataset belongs to the reference distribution. The AIC test statistic measures the relative quality of parametric distributions and is defined as follows:

AIC = 2K - 2 ln ( L )

(26.6)

where K is the number of parameters of marginal distribution L is the maximized value of the likelihood function of the reference distribution While the K-S test evaluates the appropriateness of a particular distribution fitting a given dataset, the AIC test can find the best alternative in a group of distributions. Indeed, by considering the number of parameters of the reference distribution (Equation 26.6), the AIC test accounts for the complexity of distribution. None of these tests is conclusive by itself to find the best choice in a group of distributions. The appropriateness of a distribution should be first accepted by the K-S test. The K-S test returns the p-value, which should be greater than a predefined significance level (α) to accept the null hypothesis. Under the null hypothesis, the dataset is assumed to appropriately follow the reference distribution. If the GOF of a particular distribution is approved by the K-S test, then its superiority to other alternative distributions is evaluated by the AIC test, where the distribution with the smallest AIC value is assumed to be the best choice among others. 26.2.3.2 Fit a Copula Function After picking the best margin for each random variable, several copula functions are then tested for joining the marginal distributions, among which the best may be found by a GOF test. There are some methods to estimate the parameters of copula functions, including exact maximum likelihood (EML) [21], inference functions for margins (IFM) [21,43,119], and canonical maximum likelihood (CML) [12,13,30,98]. The best copula among several candidates is found with a GOF test. The simplest method is a visual inspection of scatterplots of the parametric and empirical copulas. The copula function with the closest scatterplot to the line 1:1 would be the best choice among others. However, the statistical GOF tests are more objective than visual inspection. Genest and Rémillard [33] introduced a bootstrapping process to measure the distance between the empirical copula and the parametric copula under the null hypothesis (H0). The bootstrapping process is used to obtain the Cramér–von Mises statistic for copula selection:

ò

Sn = DCn ( u ) dCn ( u )

2

u

(26.7)

where Sn is Cramér–von Mises statistic and ∆Cn is expressed as

DCn = n (Cn - Cqn )

where Cn is the empirical copula with n data points Cqn is the parametric copula fit to the dataset

(26.8)

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Handbook of Drought and Water Scarcity

The p-value of the test might be obtained via a Monte Carlo sampling [34]. Since the null hypothesis is that the data come from the parametric copula (H 0: Cn Î Cqn ), the p-values greater than a predefined significance level (α) imply the acceptance of the null hypothesis. Otherwise, the null hypothesis is rejected (Cn Ï Cqn ). Therefore, among a group of copulas, the one with the greatest p-value (and the smallest Sn) is preferred. While there are some other test statistics in copula selection based on Kendall’s transform [32,97], Rosenblatt’s transform [93], and the extended version of the Kullback–Leibler information criterion [17], the GOF test statistics based on the distance between the empirical and parametric copulas are confirmed to be more reliable than others [6,34,118]. Therefore, the Cramér–von Mises statistic (Equation 26.7) is suggested for copula selection.

26.3 Drought Identification by Copulas Unlike other natural hazards, such as flood, tornadoes, or hurricanes, it is difficult to specify a clear beginning and end time for drought events. Primary characteristics of drought events are identified by a number of classified drought indices. Since there is no universal definition of drought, each class of indices reflects a particular disciplinary perspective. Four basic classes of droughts are recognized in different regions: meteorological, hydrological, agricultural, and socioeconomic. If precipitation is below the normal or average amount, meteorological drought starts, which may further extend to hydrological, agricultural, and socioeconomic droughts. Regardless of the drought category, four primary characteristics can be specified for any drought event: onset, duration, severity, and intensity. The onset of a drought is the time that the drought index drops a truncation level; duration is the length of time period that the index value remains below that truncation level; severity is the cumulative index value during the drought; and intensity is defined as severity divided by duration [18,20]. The duration between the beginning of two successive droughts is called inter-arrival time [103]. Figure 26.1 illustrates the definition of duration, severity, and intensity using a truncation level applied to the SPI [64,65]. In Figure 26.1, the truncation level to recognize dry periods from wet periods is set as SPI =  − 1.

26.3.1 Univariate Return Period Similar to flood frequency analysis, the return period for drought events is defined as the inverse of exceedance probability. For a particular return period, the probability should exceed a certain amount. Since a drought event is identified by its duration, severity, and intensity, the return period is defined 2 Intensity =

1.5

Severity S = Duration D

1

SPI

0.5 0 –0.5

D

–1 –1.5

S

–2

FIGURE 26.1  Identification of drought events using truncation level of a certain index (e.g., SPI).

489

Copula Functions and Drought

for each characteristic separately. The univariate return periods of the severity, duration, and intensity of droughts, being equal or greater than certain values s, d, and i, respectively, are defined as follows [11,59,101,103]: E (L)

TS =

P (S ³ s )

TD =

E (L)

P (D ³ d )

TI =

E (L)

P (I ³ i)

=

=

=

E (L)

1 - FS ( s )

(26.9)

E (L)

1 - FD ( d )

(26.10)

E (L)

1 - FI (i )

(26.11)

where TS,  TD, and TI are the return periods with severity, duration, and intensity greater than or equal to specified values for s, d, and i, respectively P(·) denotes probability of drought characteristic exceeding a certain value FS(·), FD(·), and FI(·) are the non-exceedance probability or the CDF associated with severity, duration, and intensity, respectively E(L) is the expected inter-arrival time

26.3.2 Multivariate Return Period Drought characteristics are dependent variables, with the magnitude of one variable affecting the magnitude of other variables. To develop effective water-supply strategies and drought mitigation plans, sufficient information is required on the probability of exceeding a certain magnitude for each drought characteristic. Therefore, an analysis of multivariate probability and corresponding return period is essential to capture the joint behavior of different drought characteristics. Multivariate return periods may refer to conditional and joint return periods. 26.3.2.1 Conditional Return Period Conditional return periods are essential for effective drought mitigation planning and management. A conditional return period can be expressed as a drought characteristic exceeding a particular amount (e.g., S > s), given the magnitude of another characteristic, such as duration, exceeding a certain threshold (i.e., D > d). According to Shiau [103], the conditional return period of Xi ≥ xi given Xj ≥ xj is expressed as follows: TXi |X j =

TX j

P ( Xi ³ xi | X j ³ x j )

=

E (L) 1 ´ 1 - FX j ( x j ) 1 - FXi ( xi ) - FX j ( x j ) + FXi X j ( xi , x j )

(26.12)

where FXi X j (xi , x j ) is the joint non-exceedance probability of (xi , xj), which can be replaced by a copula (Equation 26.1): TXi |X j =

E (L)

(

)

é1 - FX j ( x j ) ù é1 - FXi ( xi ) - FX j ( x j ) + C FXi ( xi ) ,FX j ( x j ) ù ë ûë û

(26.13)

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Handbook of Drought and Water Scarcity

Using copula functions, the conditional probability is expressed as follows for Xi ≤ xi given Xj ≥ xj: P ( Xi £ xi | X j ³ x j ) = Þ P ( Xi £ xi | X j ³ x j ) =



P ( Xi £ xi , X j ³ x j ) P(Xj ³ xj )

=

FXi ( xi ) - FXi X j ( xi ,x j ) 1 - FX j ( x j )

(

FXi ( xi ) - C FXi ( xi ) , FX j ( x j ) 1 - FX j ( x j )

)

(26.14)



26.3.2.2 Joint Return Period Using copula functions, the joint return period for drought characteristic was initiated for drought duration (D ≥ d) and severity (S ≥ s) by Shiau [102,103]. Two different cases were examined: (1) return period for Ç È (D ≥ d and S ≥ s) denoted as TDS and (2) return period for (D ≥ d or S ≥ s) denoted as TDS : Ç TDS =



E (L)

P (D ³ d Ç S ³ s)

=

È TDS =



E (L)

=

1 - FD ( d ) - FS ( s ) + FDS ( d ,s ) E (L)

P (D ³ d È S ³ s)

=

E (L)

E (L)

(

1 - FD ( d ) - FS ( s ) + C FD ( d ) ,FS ( s )

1 - FDS ( d ,s )

=

(

E (L)

1 - C FD ( d ) ,FS ( s )

)

(26.15)

(26.16)

)

Figure 26.2 illustrates an example of the bivariate return periods of drought duration and severity for “and” (Figure 26.2a) and “or” (Figure 26.2b) cases. Each contour line is associated with a particular return period. Figure 26.2a and b represents situations where each variable (drought duration and severity, here) is specified with only one time series, for example, historical observations, as opposed to situations where a variety of time series exist for each variable (Figure 26.2c and d), for example, climate projections obtained from global climate models (GCMs, IPCC [41]). The contour plots in Figure 26.2c and d may refer to the joint return period of drought duration and severity in a climate change impact study, where a particular return period, given the uncertainties of GCM products, may specify a range of drought duration and drought severity (rather than a single value). Hence, there is an upper and lower margin for the contour plots in such situations. In contrast, a bivariate drought analysis during a historical time period leads to a single contour plot for each return period, as shown in Figure 26.2a and b. The bivariate return period for either “and” or “or” case may be extended to a trivariate return period using the following expressions [59]: Ç TDSI =

Ç TDSI =

E (L)

P (D ³ d Ç S ³ s Ç I ³ i) E (L)

1 - FD ( d ) - FS ( s ) - FI (i ) + FDS ( d ,s ) + FDI ( d ,i ) + FIS (i,s ) - FDSI ( d ,s,i )

(26.17)

Ç TDSI = E ( L ) éë1 - FD ( d ) - FS ( s ) - FI (i )

( ) ( - C ( F ( d ) ,F ( s ) ,F ( i ) ) ù û

) (

+ C FD ( d ) ,FS ( s ) + C FD ( d ) ,FI (i ) + C FI (i ) ,FS ( s ) D



È TDSI =

S

E (L)

)

I

P (D ³ d È S ³ s È I ³ i)

=

E (L)

1 - FDSI ( d ,s,i )

=

(

E (L)

1 - C FD ( d ) ,FS ( s ) ,FI (i )



)

(26.18)

491

Copula Functions and Drought 90

0 10 yr

50

yr 20 0 10

yr

yr

50

Duration

yr

yr

Duration

10

yr yr

2

yr

(b)

10

Severity

20

Increasing return period

yr

Increasing return period

2

(a)

90

Severity

50 yr 2 yr

Duration

Duration

100 yr

100 yr

50 yr 2 yr (c)

Severity

(d)

Severity

FIGURE 26.2  Contour plots of bivariate joint return periods for “AND” (a and c) and “OR” (b and d) cases for historical droughts (a and b) versus future droughts under climate change impacts (c and d).

26.4 Probabilistic Drought Forecasting by Copulas While there are a number of studies focusing on reliable drought forecasting, there are a few methods that support the full probabilistic distribution of future droughts. In developing the distribution of future droughts, particular attention should be given to maintaining the dependencies among drought statuses of consecutive times. Since drought is an evolving extreme event that expands over both spatial and temporal scales, the drought status of a region at a given time is dependent on its previous status. Developing the conditional probabilities of future droughts, given the past status, requires application of powerful statistical methods that can support the analysis of interactions and correlations among dependent variables. For this purpose, copula functions are potential tools in establishing the forecast models with conditional probabilistic features. Such forecast models are capable of relating historical availability of water to future droughts.

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26.4.1 Bayesian Network of Drought Sequences Since drought is a persistent event over time, drought-related variables (e.g., runoff, streamflow, drought indices) are statistically dependent on their past status. Given this fact, the conditional dependencies of drought variables can be expressed within Bayesian networks [88] via directed acyclic graphs (DAGs). A DAG is established for a set of random variables in a direct ordering without any direct circuits. A detailed description of a DAG is given by Thulasiraman and Swamy [109]. If a set of random variables x = {x1,  …, xn} is considered as a DAG, their conditional dependencies can be described within Bayesian networks [94]: f ( x ) = f ( x1 ,¼, xn ) =

Õf (x |x ( ) ) i

pa xi

(26.19)



xi Îx

where x pa( xi ) is the subset of x representing the parent variables of xi. According to Equation 26.19, the joint probability density function of the random variables in x is the product of the conditional density function of each variable (xi), given its parent variables (x pa( xi ) ). For the random variables evolving over time {xt1 , …, xti , …, xtn } (e.g., streamflow or drought states), a Bayesian network can express the probabilistic queries of the chain of variables. If the dependency ordering of random variables exactly follows the temporal sequence and the parent variables of xti are considered as the set of all prior variables (xti-1 , …, xt1 ), then Equation 26.19 turns into the following form: f ( xt1 ,¼, xtn ) =

Õf (x

ti

| xti-1 ,¼, xt1 )

(26.20)

ti ÎT

Another approach for modeling the probability distribution of dependent variables is to apply directed Markov networks. Similar to Bayesian networks, a directed Markov network represents the sequence of variables in a directed acyclic order. Although the two networks have similar structures, their primary difference is that a Markov network is generally undirected and can be cyclic. Thus, Bayesian networks are a more general representation of directed acyclic networks. Expanding the right-hand side of Equation 26.20, the conditional distribution of xtn given xtn-1 , …, xt1 is calculated as follows:

f ( xt1 ,¼, xtn ) =

Õf (x

ti

| xti-1 ,¼, xt1 )

ti ÎT

f ( xt1 ,¼, xtn ) = f ( xtn |xtn-11 ,¼, xt1 )

Õ

ti Î{t1¼tn-1}

f ( xti |xti-1 ,¼, xt1 ) (26.21)

f ( xt1 ,¼, xtn ) = f ( xtn |xtn-1 ,¼, xt1 ) × f ( xt1 ,¼, xtn-1 )



Þ f ( xtn |xtn-1 ,¼, xt1 ) =

f ( xt1 ,¼, xtn )

f ( xt1 ,¼, xtn-1 )



Direct calculation of the conditional pdf f (xtn |xtn-1 ,…, xt1), from the joint pdfs on the right-hand side of Equation 26.21, requires sufficient knowledge of the relationships and interactions among the random

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variables and is therefore analytically intensive. However, by using Equation 26.4, copula functions can help to decompose the joint pdfs and reformulate the conditional pdf as follows [60,62]: f ( xt1 ,¼, xtn ) = c ( u1 ,¼,un ) f ( xtn | xtn-1 ,¼, xt1 ) =

Õ )Õ

c ( u1 ,¼, un ) c ( u1 ,¼, un-1

Õf

Xi

( xt ) i

(26.22)

ti ÎT

n

i =1 n -1 i =1

f Xi ( x t i ) f Xi-1 ( xti -1 )

=

c ( u1 ,¼, un ) f Xn ( xtn ) c ( u1 ,¼, un-1 )



An advantage of Equation 26.22 over Equation 26.21 is the application of copula functions, which avoids an excessive effort of estimating the joint distribution of random variables. It might be analytically difficult to directly model the joint behavior of hydrologic variables, whereas fitting a copula function to the marginal distribution of random variables is simpler.

26.4.2 Hydrologic Drought Forecasting in Temporal Extent The drought status of a location, at a particular time, is dependent on the previous drought status over a relatively short or long period of time. Since the volumetric flow at a particular section of a river contributes to the hydrological drought throughout the upstream basin, a reliable forecast of streamflow is required for accurate prediction of future droughts and effective development of drought mitigation policies. Owing to the autocorrelation of streamflow over a limited period of time, a Bayesian framework as discussed in the previous section can be utilized to acquire the conditional probabilities of streamflow, and hence the corresponding drought status. Although drought events expand over both spatial and temporal scales, this section involves only the temporal extension of hydrological droughts from one time step to another. In this section, hydrological droughts are defined based on the total flow that reaches the basin outlet. 26.4.2.1 First-Order Conditional Forecast In developing the conditional forecast via Equation 26.22, the autocorrelation of the forecast variable is used to determine the extent of lag time for which the correlation between the values is significant. In the firstorder conditional forecast, the autocorrelation of the forecast variable (e.g., streamflow) is insignificant for lag times greater than 1. In other words, the forecast variable at any time is assumed to be only dependent on its magnitude at the previous time step. This is equivalent with n = 2 in Equation 26.22, which would return the conditional distribution of the forecast variable at time tn given the streamflow at time tn − 1:



f ( xt2 | xt1 ) =

c ( u1 , u2 ) × f X2 ( xt2 ) × f X1 ( xt1 ) f X1 ( xt1 )

= c ( u1 ,u2 ) × f X2 ( xt2 )

(26.23)

If streamflow dependency is insignificant for lag times greater than 1, Equation 26.23 can generate the conditional distribution of streamflow at a given time. Figure 26.3 shows the conditional pdf of a drought-related variable (e.g., streamflow) for a forecast season (e.g., spring), given the drought status of the past season (e.g., winter). The PDFs are illustrated in a shaded scheme and scaled between 0 and 1, where 1 (the dark shade) represents the most probable spring flow (mode of each PDF) and 0 is associated with the tail of each PDF (the bright shade). Since the dark-shaded zone closely surrounds the mode of PDFs, the corresponding range of spring flow is more likely to occur if the given winter flow is observed. Hence, such shaded representation indicates the likelihood of different drought statuses in the forecast season given the past observed drought status. As an example, given D4 drought in winter, the spring drought status is expected to be D4, D3, or D2, depending on the exact magnitude of winter flow.

494

Handbook of Drought and Water Scarcity 1.0 Wet 0.8

Spring flow

D0 D1

0.6

D2

0.4

D3 0.2 D4

D3

D2

D1 D0

Wet 0.0

Winter flow

FIGURE 26.3  Conditional PDF of spring flow given the winter flow in a shaded scheme. The dark and bright shaded pixels specify the high-probability and low-probability zones of spring flow respectively. Two sample PDF curves are also shown for a clear understanding of the shaded pixels. Dash lines identify the range of different drought categories in each season.

The conditional forecast model can also provide information about the probability of different drought statuses that may possibly occur in the forecast season. The probability of streamflow in the forecast season (i.e., spring, here) exceeding a flow threshold x D i, corresponding to a particular drought status Di, is defined as follows:



P ( Xt2 ³ x Di | xt1 ) = 1 - P ( Xt2 £ x Di | xt1 ) = 1 - FXt2 |Xt1 ( x Di | xt1 )

(26.24)



where FXt2 |Xt1 is the conditional CDF of spring flow given the streamflow of the past winter. An important product of Equation 26.24 is the chance of recovery from an ongoing drought in the forecast season; that is, the probability of D0/wet condition in the forecast season. It is essential for water managers to identify the probability of drought termination and return to normal conditions within a specific time period. 26.4.2.2 Second-Order Conditional Forecast As discussed earlier, an autocorrelation analysis is required to identify the seasons with strong correlation in their streamflow volumes. Assuming that streamflow in the forecast season has significant correlation with its previous two values, Equation 26.22 is simplified to the following form:



f ( xt3 | xt2 , xt1 ) =

c ( u1 ,u2 ,u3 ) × f X3 ( xt3 ) × f X2 ( xt2 ) × f X1 ( xt1 ) c ( u1 , u2 ) × f X2 ( xt2 ) × f X1 ( xt1 )

=

c ( u1 , u2 ,u3 ) × f X3 ( xt3 ) c ( u1 , u2 )

(26.25)

where xt3 , xt2 and xt1 are the random variables of t3, t2, and t1, respectively, with the corresponding probabilities of u. Given that xt3 , xt2 , and xt1 denote the seasonal flow of spring, winter, and fall, respectively, Equation 26.25 would return the second-order conditional pdf of spring flow, given streamflow observations in the past winter and fall seasons. Figure 26.4 illustrates an example of the conditional PDFs of spring flow,

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Copula Functions and Drought

5

×10–3 Fall = D4, win = D4 Fall = D4, win = D0 Fall = D0, win = D4 Fall = D0, win = D0

4.5

Probability density

4 3.5 3 2.5 2 1.5 1 D4 D3

0.5 0

0

50

100

D2 150

D1

D0 200

Normal/wet 250

300

350

400

450

500

Apr–May–Jun (KAF)

FIGURE 26.4  Distribution of spring flow given the drought status of D0 to D4 in the past winter and/or fall. (Adapted from Madadgar, S. et al., Hydrol. Process., 28, 104, 2014. Copyright American Meteorological Society. Used with permission.)

given D0 and D4 drought statuses in the past winter and/or fall. The PDFs associated with other drought conditions (D1, D2, D3) are located somewhere in between these curves. As seen, if the winter drought is fixed at D0 or D4, and the fall drought is set free to change from D0 to D4, the distribution of spring flow change would be insignificant. However, if the opposite situation occurs, that is, the fall drought is fixed at D0 or D4 and the winter drought changes from D0 to D4, the PDF of spring flow would change significantly. This is evidence of high correlation in the (winter, spring) pair, compared with (fall, spring) pair.

26.4.3 Drought Forecasting in Spatiotemporal Extent While Section 26.4.2 described drought prediction based on streamflow forecasts at a particular section of the river, this section considers the extension of drought events across the entire area of the river basin, and evaluates the variation of droughts both in space and in time. In this section, hydrological droughts are defined at distinct spatial units across the basin. Depending on the application, any spatially distributed variable such as runoff, soil moisture, and snowpack might be selected for this purpose. The forecast model is then established for each spatial unit using Equation 26.22. Owing to the persistence of selected variables over time, the lag time for drought forecasting might vary in Equation 26.22. For variables with low persistence, say runoff, the lag time (n in Equation 26.22) might not be longer than 2 or 3 time steps. Alternatively, for persistent variables, such as soil moisture, n might be much longer depending on the hydrological processes. The forecast model requires the fitting of an appropriate copula to the marginal distributions at each spatial unit. The only knowledge required to estimate the drought status of the forecast period is the magnitude of the forecast variable in relation to the historical record. Therefore, there is no need to use hydrological models to estimate the forecast variable, which is an advantage of the copula-based forecast model. Although copulas appear to be purely statistical models, they are established on the joint behavior of predictors and predictand during a historical time period, creating a model that accounts for interactions between different hydrological processes and preserves the inherent dependencies among the predictors and predictand.

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Probabilistic estimation of future droughts is the primary focus of the copula-based forecast model, as expressed by Equation 26.22. As the conditional PDF of the forecast variable is developed, two queries may be studied: (1) the probability of a particular future drought condition, given the drought status in the past, and (2) the status of future drought corresponding to a particular probability. In other words, the first query seeks the probability of a specific drought condition in the future, given the past status, and the second query tries to identify the future drought condition with a specific probability of occurrence. Assuming X1 and X2 as the drought-related variables at times t1 and t2, respectively, Figure 26.5 illustrates the first query, where the probability of a particular drought in

p(X2|X1)

P(X2|X1)

(a)

>0.95 P=?

Q0 ) = 1 T T

(27.1)

This expression is commonly used in flood characterization based on annual maxima of rainfall and river flows, though it needs to be adapted when dealing with droughts, as remarked by Fernández and Salas [10,11], Chung and Salas [7], Salas et al. [24], and Shiau and Shen [25]. First, the independence of annual data when studying droughts is not directly assumed. Second, droughts are defined at the least by their intensity and duration in a certain region, and this bivariate dependence causes difficulties in frequency distribution parameterization. Regarding drought definition, Mishra and Singh [19] cited the return period concept formulated by Haan, that is, the average time between the occurrence of events with a certain magnitude or less. Loaiciga and Mariño [13] and Shiau and Shen [25] referred to a similar definition as the averaged elapsed time between occurrences of critical events. So, the return period concept has been adapted in relation to the inter-arrival time: from the onset of the drought until the onset of the following one [7,10,11,13,19,20,24,25]. Hence, a return period is defined as the product of the expected number of

Drought Frequency Characterization in Spain by Means of T Analysis

507

droughts during a period and the inter-arrival time for a drought E characterized by its duration D0 and its deficit S0. According to Shiau and Shen [25] and Salas et al. [24], the return period may be expressed as T=

p01 + p10 1 p +p 1 × = 01 10 × p01 × p10 P ( E ) p01 × p10 P ( S > S0 , D = D0 )



(27.2)

with p01 being the probability of passing from a drought state (0) to a nondrought one (1) and p10 the opposite, from a nondrought to a drought state. Under the assumption of independence between events, p01 and p10 are then p0 and p1, that is, probabilities of a nondrought and drought states, simplifying the previous expression as summing one: 1 1 × T= (27.3) p1 × p0 P ( S > S0 , D = D0 ) Given this expression, the objective of this study is to identify and characterize droughts that occurred in Spain based on the return period law depending on drought duration and deficit. By means of a hydrological model, other variables apart from rainfall are considered and their differences in drought frequency may also be assessed. Rainfall is the prime input to the hydrological cycle and may recharge aquifers or runoff depending on other variables such as PET as well as the hydrodynamic effect of soils and aquifers. A description of drought propagation from rainfall to runoff is valuable for the implementation of DMSs in the river basins of Spain. The present research also gives the basis not only to c­ haracterize the actual droughts but also to study the impact of climate change on droughts in Spain [1,5].

27.2  Data and Hydrological Simulation Rainfall and runoff are periodically assessed in Spain for water resources planning as well as recharging aquifers [6,17]. For this purpose, a water-budget model was developed in SIMPA to simulate an unaltered (i.e., natural) hydrologic regime. SIMPA is a Spanish acronym meaning “Integrated System for Rainfall-Runoff Modeling.” It comprises several tools to analyze spatial and temporal hydrological variables and to simulate several hydrological processes. It was implemented in the Center for Hydrographic Studies of CEDEX [3]. Its spatial database is the Geographic Information System GRASS-GIS (GRASS Development Team, 2015 [12]). The hydrological cycle is conceptualized by means of soil and aquifer storages as well as different laws to estimate water transfers between them [8,21,23,26]. Hydrological variables simulated are rainfall, PET and actual evapotranspiration (AET), soil water content, recharge, direct runoff, and groundwater runoff. The water resources model is implemented in monthly steps for the whole Spanish territory using a 500 m cell resolution from October 1930 to September 2011. Monthly maps of rainfall and PET are derived by interpolation of the historical rainfall and temperature series of the Spanish Meteorological Agency (AEMET by its Spanish acronym) database. More than 10,000 historical stations were used, and temporal availability was homogenized by means of filling temporal gaps using a multiple correlation equation. Interpolation procedures take into account the orographic effect [2]. PET assessment considers the Hargreaves formula and corrections with respect to Penman–Monteith [17]. Once AEMET recorded rainfall and temperature are interpolated across the whole Spanish territory and PET is estimated, monthly maps are used as a forcing input to assess water resources. Figure 27.2 shows a compilation of the main results over a mean yearly step. A national hydrological monitoring system was developed by the Center for Hydrographic Studies of CEDEX. This work was coordinated by the Spanish Directorate of Waters. The DMS comprises quantity hydroclimatic variables and its first goal was to use monthly variables related to water quantity—those related to rainfall, river flows, water stored in reservoirs, and piezometric levels—to facilitate an overview of dryness occurring in Spain. Other sources of data are the snow volumes (Assessment of snowfall water resourcesERHIN) and flooded area in wetlands which were provided by the Spanish the General Directorate for Waters. The time step selected is the monthly one and the water state is evaluated by means of percentiles regarding the time series of monthly data, cumulated values from the onset of the hydrological year, cumulated

(d)

1000

(b)

1100

(e)

1000

(c)

800

FIGURE 27.2  Hydrological components considered in the water resources model: (a) rainfall (mm/year), (b) PET (mm/year), (c) AET (mm/year), (d) recharge (mm/year), and (e) runoff (mm/year).

(a)

1000

508 Handbook of Drought and Water Scarcity

509

Drought Frequency Characterization in Spain by Means of T Analysis

C. I. PAIS VASCO

Tera Órbigo Esla Valderabuey

Miño-Sil

PORTUGAL

Douro RB Atlantic Sea

Tagus RB

FRANCE

Cantábrico

C.I. GALICIA COSTA

Tormes Agueda

Cantábrico Batas Zadorra Inglares Irati Arga Ega Tirn Najerilla Aragn Iregua Margen Arbas Gállego Dcha Cinca Leza-Huecha Alto Duero Riaza Jaln

Cabecera Carrin Pisuerga Arlanza

Adaja Cega Bajo Duero

Henares Tajuña

Jarama Guadarrama Bajo Tajo Margen Dcha

Alberche

Jabaln Bullaque

Cabecera Alto Turia

Cuenca Alta

Júcar Medio

Guadiana RB

Guadalquivir RB

Gvir Medio Margen Dcha

Cabecera Margen Dcha

Cabecera

Júcar RB

Bajo Júcar

Margen Izqda

Margen Dcha Guadiana Gvir Medio Litoral Menor Margen Bajo Gvir Izqda Alto Sistema V Margen Almonte Genil Izqda Marismas Sistema IV Sistema II C.I. Sistema III Guadalete ANDALUCIA Sistema I Barbate Sur Tinto Piedras Odiel

Ebro RB

Norte Bajo Turia

Centro

Bajo Gvir Margen Dcha

C.I. CATALUÑA

Segre

Huerva Aguas Vivas Martin Guadalope Matarraña

Alto Júcar

Tajo Medio Margen Izqda

Bajo Tajo Margen Izqda

Jiloca

Ésera Noguera Ribagorzana

ISLAS BALEARES

Sur

Mediterranean Sea

Segura RB

Main Spanish River Basins (RB)

CEUTA MELILLA ISLAS CANARIAS

FIGURE 27.3  Spanish regions used in the drought monitoring system.

values of the last 12 months, and cumulated values of the last 3 months. Deviations from normal values are also considered. Some drought indices are used to identify meteorological droughts. Models based on the theory of runs are used and incorporate a critical parameter to pool minor identified events. A major problem in DMS development is a consequence of the lack of a real-time system capable of recording and transmitting hydrological homogenized data across all Spanish territory. Efforts were made by people responsible for data recording to adapt the possibilities of their existing networks to these requirements, especially when renewal data on time are considered. Stations were selected were selected considering mot only the quality of data and length of historical records, but also because of being capable of transmitting data on time to upgrade the information about the hydrological status. The implementation of a DMS at a national scale encompassed the identification of 62 regions over a 505,000 km2 area [4]. These regions were delimited by river basin authorities according to hydrological characteristics and the relationships between water consumption and resources (Figure 27.3). These regions are the study area units where drought hazard has been assessed in this chapter.

27.3  Methodology Regional droughts are defined by their deficit and duration. Their dependence and the scarce number of droughts that may be identified in a rainfall and runoff historical period of 81 years would make insufficient a sample of droughts for a frequency characterization, given that a time series synthetic generation scheme has also been handled. Then, 50,000 yearly series of rainfall and runoff were obtained, which increment the number of droughts identified and which are accessible for frequency characterization. Then, a two-parameter gamma distribution is used to represent drought deficit, and geometric distribution is used to represent drought duration. Under the hypothesis of independence, the bivariate random variable is expressed as the product of these two distributions. This assumption facilitates the management of the

510

Handbook of Drought and Water Scarcity

Rainfall (mm/year)

theoretical distribution of drought frequency and the composition of regional frequency–duration–deficit curves. The detailed procedure is described in the following paragraphs. First, annual time series of rainfall and runoff (mm) were obtained for each one of the defined regions by summing monthly values from October 1930 to September 2011. Taking into account the persistence of the deficit needed to define a drought and the rejection of seasonal droughts, a yearly time step was chosen to perform the return period characterization of droughts. The time step matches with the Spanish hydrological year starting in October. Averaged time series comprised the 81 years between 1930–1931 and 2010–2011. Finally, two sets of 62 annual series of rainfall and runoff (62 × 2) were obtained, one per region and variable. A second step was constituted by the synthetic generation of rainfall and runoff time series. Regional droughts are defined by their rainfall or runoff deficit and duration. A time series synthetic generation scheme was also handled and 50,000 yearly series of rainfall and runoff were obtained. R stats and MASS library were the software used for synthetic generation and statistical analysis [22]. Synthetic series were derived from each of those 62 × 2 previous series by means of the auto regressive moving average (ARMA) scheme. Although this work was focused on an annual basis, ARMA models can be easily applied to monthly time series by means of integrated ARMA or autoregressive integrated moving average (ARIMA) models. Parameterization and model selection of the 62 × 2 ARMA is done by means of Akaike criteria and the correspondence of the autocorrelation and partial autocorrelation functions. Results show that moving averaged terms are predominant in regional rainfall, although autoregressive and moving averaged terms are also predominant in regional runoff series parameterization. Once the ARMA model was defined, the mentioned series of 50,000 years were obtained. The time series synthetic generation scheme is based on the hypothesis of stationarity. Figure 27.4 shows rainfall (a) and runoff (b) series averaged in the Iberian Peninsula. The main yearly evolution is illustrated as well as their general trends. The first and third quartiles and the median value are also added in order to highlight the larger frequency and more intense droughts given at the last third part of the series, particularly

(a)

950 900 850 800 750 700 650 600 550 500 450 450

Runoff (mm/year)

400 350 300 250 200 150 100 (b)

1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Hydrological year

FIGURE 27.4  Trends in rainfall (a) and runoff (b) averaged in the Iberian Peninsula.

511

Drought Frequency Characterization in Spain by Means of T Analysis

from 1985 until the end of the series. Diminishing general trends were then obtained and some of them are of significance by the Mann–Kendall test (level of significance 5%). Considering the scarcity of data for a drought definition and the occurrence of intense drought runs during the last periods of the time series, no correction has been applied to trends found prior to the ARMA implementation. Droughts are identified in this work as periods of deficit with respect to the median value. The onset and the recovery thresholds are considered equal to the median value. No pooling method has been applied in order to aggregate minor droughts into longer ones. Under the hypothesis of independence of yearly values of rainfall and runoff, the probabilities of a humid or dry year are 50%. A two-parameter gamma distribution was adjusted to the total cumulated drought deficit (S). The occurrence of a drought with a certain duration (D, discrete variable) was considered using a geometrical distribution. Under the hypothesis of independence between duration and deficit, the composition of both distributions to represent the probability of exceedance of a deficit for a certain drought duration was represented by means of the product of both frequency distributions. This facilitates the management of the theoretical distribution of drought frequency and the composition of regional frequency–duration–deficit curves. Historical droughts are then characterized by means of the theoretical frequency. According to Salas et al. [24], the probability of a drought exceeding a certain deficit, S0, with a certain duration, D0, is given by ¥

P éëS > S0 , D = D0 ùû =

ò

S0



æzö 1 ×ç ÷ b × G ( D0 × r ) è b ø

D0 ×r -1

P éëS £ S0 , D = D0 ùû = G ( S0 ) × p01 × (1 - p01 )

D0 -1

× e - z /b × p01 × (1 - p01 )

D0 -1

dz

(27.4)

where r is the shape parameter of gamma distribution (G(S0)) β is its scale parameter p01 is the transition probability of having a record greater than the median after one lower than the median Under the hypothesis of independence, p01 can be managed as the probability of a nondrought year. Frequencies are estimated by means of a return period (T) defined as the inter-arrival time between two consecutive events (Equation 27.3). This gives a T for a drought when S and D are known. On the other hand, duration-mean annual deficit and frequency curves (DmaDF) can be drawn to illustrate the relationships between S and D for each T.

27.4  Case Study Figure 27.5 represents the drought characterization considering the Iberian Peninsula as a region where rainfall has been averaged as well as runoff. The x-axis is for D and the y-axis is for the mean annual deficit, that is, the total deficit S divided by the number of years of a drought. Each graph shows two different collations of DmaDF curves. The first collation is the frequency curves of rainfall (DmaDF-PRE), which are drawn with a dashed line for different T. The second collation is the frequency of runoff (DmaDFESC). In this case, lines are continuous for different T. Finally, identified droughts that happened during the 1930/1931–2010/2011 period are represented as squared dots (rainfall droughts) and circular dots (runoff droughts). Their graphical position reveals the values of S, D, and T. Some results may be highlighted when analyzing regional DmaDF-PRE and DmaDF-ESC. Deficit on rainfall gives higher T than in runoff when a certain drought is considered. For example, T for the 1990–1994 rainfall drought almost reaches 300 years, but the runoff drought only reaches 200 years. Differences are also reflected in the 2004–2005 drought. Estimated T for rainfall nearly reaches 100 years, while the estimated drought for runoff only reaches 50 years. Furthermore, different droughts are identified considering rainfall and runoff independently. Some differences are explained by taking into account the pooling effect given from shorter and discontinuous

512

Handbook of Drought and Water Scarcity DurDefT. Region: Spanish Iberian Peninsula 400 350

Mean annual deficit (mm/year)

PRECIPITATION

PRECIPITATION T = 20 PRECIPITATION T = 50 PRECIPITATION T = 100 PRECIPITATION T = 200 PRECIPITATION T = 500 PRECIPITATION T = 1000

300 250

RUNOFF T = 20 RUNOFF T = 50 RUNOFF T = 100 RUNOFF T = 200 RUNOFF T = 500 RUNOFF T = 1000

200 150 100 50

Droughts/1930–2010 PRECIPITATION RUNOFF

0 1

2

3

4

5 6 Duration (years)

7

8

9

Hydrological year 1930–1930 1933–1934 1941–1941 1943–1944 1947–1949 1952–1954 1956–1957 1964–1964 1966–1966 1972–1975 1979–1982 1984–1986 1988–1988 1990–1994 1998–1999 2001–2001 2007–2008

Duration (years) 1 2 1 2 3 3 2 1 1 4 4 3 1 5 2 1 2

RUNOFF

Hydrological year 1931–1931 1934–1934 1937–1937 1941–1944 1947–1949 1952–1954 1956–1957 1964–1964 1966–1966 1972–1975 1979–1982 1985–1986 1988–1988 1990–1994 1998–1999 2001–2011 2007–2008

Duration (years) 1 1 1 4 3 3 2 1 1 4 4 2 1 5 2 1 2

10

FIGURE 27.5  DmaDF-PRE and DmaDF-ESC curves in the Iberian Peninsula.

rainfall droughts to longer runoff events based on the parameterization of natural reservoirs and aquifers, which are simulated in SIMPA with a tank submodel. The 4-year duration drought in runoff occurring in the Iberian Peninsula from 1941/1942 to 1944/1945 can be related with two different rainfall droughts whose durations are 1 (1941/1942–1941/1942) and 2 years (1943/1944–1944/1945). The DmaDF-PRE and DmaDF-ESC curves shown in Figure 27.5 allow handling this question of which was the worst drought event due to the combined deficit and duration. For the whole Iberian Peninsula, the 5 years duration drought of 1990-1994 is the worst drought reaching a T of almost 200 years (runoff) and 300 years (rainfall). Regional analysis of droughts and their propagation can be done. In Northern Spanish basins, droughts occurring in the 40’s reaches a T of 200 and 300 years. Regional analysis of droughts and their propagation can also be done. In northern Spanish basins, droughts occurring in the 1940s reach a mentioned T of 200 and 300 years. The Upper Tagus basin in the central Iberian Peninsula constitutes an important basin for Spanish water management because of its being the source of water for ATS (Spanish acronym meaning Tagus to Segura Aqueduct) water transfer. The worst runoff drought identified occurred from 1988/1989 to 1994/1995. Then, its duration was 7 years, and its T reaches 500 years. This drought is related to minor rainfall droughts, as those which happened from 1991/1992 to 1994/1995 and from 1988/1989 to 1989/1990. Another different runoff drought happened in the Upper Tagus from 1979/1980 to 1983/1984 and was caused by a rainfall drought occurring from 1979/1980 to 1982/1983. These two droughts, the rainfall and runoff droughts, almost reached a T of 100 years. Drought behavior in the south-eastern Iberian Peninsula differs from the one in the northern and central basins. DmaDF-PRE and DmaDF-ESC curves show important increments of T for relatively reduced increments of duration and deficit. The worst rainfall droughts occurred during 1980/1981– 1984/1985 and 1992/1993–1994/1995. These 5 and 3-year duration droughts corresponds to T between 200 and 500 year and between 100 and 200 year, respectively but depends on the region. If runoff droughts are studied, the worst occurred from 1990/1991 to 1994/1995. This drought may be related to a sequence of rainfall droughts that happened in 1990/1991 and from 1992/1993 to 1994/1995.

0

100

200

300

400

500

600

1

2

3

4

6

Duration (years)

5

7

8

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PRECIPITATION RUNOFF

Droughts/1930–2010

RUNOFF T = 20 RUNOFF T = 50 RUNOFF T = 100 RUNOFF T = 200 RUNOFF T = 500 RUNOFF T = 1000

PRECIPITATION T = 20 PRECIPITATION T = 50 PRECIPITATION T = 100 PRECIPITATION T = 200 PRECIPITATION T = 500 PRECIPITATION T = 1000

FIGURE 27.6  Drought characterization in four regions of Spain.

Mean annual deficit (mm/year)

DurDefT. Region: Tera-Órbigo-Esla-Valderaduey

Mean annual deficit (mm/year) 0

50

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RUNOFF T = 20 RUNOFF T = 50 RUNOFF T = 100 RUNOFF T = 200 RUNOFF T = 500 RUNOFF T = 1000

PRECIPITATION T = 20 PRECIPITATION T = 50 PRECIPITATION T = 100 PRECIPITATION T = 200 PRECIPITATION T = 500 PRECIPITATION T = 1000

4

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DurDefT. Region: Cataluna

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RUNOFF T = 20 RUNOFF T = 50 RUNOFF T = 100 RUNOFF T = 200 RUNOFF T = 500 RUNOFF T = 1000

PRECIPITATION T = 20 PRECIPITATION T = 50 PRECIPITATION T = 100 PRECIPITATION T = 200 PRECIPITATION T = 500 PRECIPITATION T = 1000

Drought Frequency Characterization in Spain by Means of T Analysis 513

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Figure 27.6 represents a collation of DmaDF curves that characterize drought in four different regions in Spain. Each region has been characterized by its own collation of DmaDF curves, which facilitates their use in a DMS comprising information about the regional evolution of deficit, duration, and frequency.

27.5  Summary and Conclusions This chapter has presented the application of a law that establishes a relationship between deficit, duration, and frequency of droughts occurring in Spain. It assumes the hypothesis of independence between drought deficit and duration to compose and parameterize a bivariate distribution function as stated in the referred literature. The described methodology has been applied by considering two different purposes. A regional drought characterization was obtained by means of the relationship existing between its frequency, duration, and deficit. Once regional laws have been obtained, the next step is focused on using them as a basis for a DMS once different levels of hazard, that is, return periods, have been obtained for rainfall and runoff droughts. Return periods dependent on the main regional drought characteristics can be selected to identify prealert, alert, or emergency levels in a mitigation strategy. Furthermore, differences between rainfall and natural runoff droughts have been highlighted. This fact constitutes a valuable feature to design mitigation actions if water resources are considered. Moreover, the characterization of droughts provides a basis for analyzing changes in them once hydrological or climate factors change. This strategy was adopted to study the impact of climate change on droughts in Spain. For this study, changes were assessed by forcing the hydrological model with a set of downscaled general circulation model outputs corresponding to two different emissions scenarios. Climate scenarios are the basis of hydrologic scenarios in which droughts were characterized by DmaDF curves. The impact of climate change on droughts was then assessed by analyzing differences in DmaDF curves.

Authors Javier Álvarez-Rodríguez joined the CEH in 1996. Currently, he works in the Water Resources Department of the CEH as a technical scientific coordinator. His areas of expertise include water resources modeling, droughts, and climate change impact. He is a director and lecturer on the International Course of General and Applied Hydrology of CEDEX. Luis Miguel Barranco has been working in the Water Resources Department of the CEH since 2007. He has been involved in water resources modeling, droughts, and climate change. He previously dealt with natural risks in the Geological Survey of Spain and in the General Directorate of Civil Protection. His PhD was on the impact of climate change on water resources in Spain.

References

1. Álvarez-Rodríguez, J., Barranco Sanz, L. M., and Potenciano de las Heras, Á. 2014. Evaluación del impacto del cambio climático en los recursos hídricos de España. Monografías CEDEX M-116, Spanish Ministry of Public Works, Madrid, Spain. 2. Álvarez-Rodríguez, J. 2011. Estimación de la distribución espacial de la precipitación en zonas montañosas mediante métodos geoestadísticos. PhD thesis. E.T.S.I. Caminos, Canales y Puertos (UPM), Madrid, Spain. 3. Álvarez-Rodríguez, J., Sánchez, A., and Quintas, L. 2005. SIMPA, a GRASS based tool for hydrological studies, International Journal of Geoinformatics, 1(1): 13–20; Proceedings of the FOSS/GRASS Users Conference, September 12–14, 2004, Association for Geoinformation Technology, Bangkok, Thailand.

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4. Álvarez-Rodríguez, J., Villaverde Valero, J. J., and Incio-Caballero, L. 2005. A national drought monitoring system in Spain, Proceedings of the American Geophysical Union, Fall Meeting 2005, San Francisco, CA, H32B-04. 5. Barranco, L. M., Álvarez-Rodríguez, J., Olivera, F., Potenciano, Á., Quintas, L., and Estrada, F. 2014. Assessment of the expected runoff change in Spain using climate simulations, Journal of Hydrologic Engineering, 19(7): 1481–1490. 6. Cabezas, F., Estrada, F., and Estrela, T. 1999. Algunas contribuciones técnicas del Libro Blanco del Agua en España, Ingeniería Civil, 115, 79–96 (Centro de Experimentación de Obras Públicas, CEDEX, Secretaría General Técnica, Centro de Publicaciones, Ministerio de Fomento). 7. Chung, C. H. and Salas, J. D. 2000. Drought occurrence probabilities and risks of dependent hydrologic processes, Journal of Hydrologic Engineering, 5(3): 259–268. 8. Estrela, T. and Quintas, L. 1996. A distributed hydrological model for water resources assessment in large basins, First International Conference on New/Emerging Concepts for Rivers, RIVERTECH 96, September 22–26, 1996, IWRA, Chicago, IL. 9. Estrela, T. and Vargas, E. April 2012. Drought management plans in the European Union. The case of Spain, Water Resources Management, 26(6): 1537–1553. 10. Fernandez, B. and Salas, J. D. 1999. Return period and risk of hydrologic events. I: Mathematical formulation, Journal of Hydrologic Engineering, 4(4): 297–307. 11. Fernández, B. and Salas, J. D. 1999. Return period and risk of hydrologic events. II: Applications, Journal of Hydrologic Engineering, 4(4): 308–316. 12. GRASS Development Team, 2015. Geographic Resources Analysis Support System (GRASS) Software, Version 6.4. Open Source Geospatial Foundation. http://grass.osgeo.org, accessed on June 2014. 13. Loaiciga, H. A. and Mariño, M. A. 1991. Recurrence interval of geophysical events, Journal of Water Resources Planning and Management-ASCE, 117(3): 367–382. 14. MARM. 2008. Gestión de la sequía de los años 2004 a 2007, in: Estrela, T. and Rodríguez Fontal, A., eds., Spanish Ministry of the Environment and Rural and Marine Affairs, MARM, General Technical Secretary of the Ministry, Madrid, Spain. 15. McKee, T. B., Doesken, N. J., and Kleist, J. 1993. The relationship of drought frequency and duration to time scales, Preprints, Eighth Conference on Applied Climatology, January 17–22, Anaheim, CA, pp. 179–184. 16. McKee, T., Doesken, N. J., and Kleist, J. 1995. Drought monitoring with multiple time scales, 9th Conference on Applied Climatology, January 15–20, American Meteorological Society, Dallas, TX, pp. 233–236. 17. MIMAM. 2004. Water in Spain, Spanish Ministry for the Environment, MIMAM, General Technical Secretary of the Ministry, Madrid, Spain. 18. MIMAM. 2007. Planes Especiales de Sequía, Spanish Ministry for the Environment, MIMAM, General Technical Secretary of the Ministry, Madrid, Spain. http://www.magrama.gob.es/es/ agua/temas/observatorio-nacional-de-la-sequia/planificacion-gestion-sequias/observatorio_ nacional_sequia_3_1_planes_especiales_sequia.aspx, accessed on June 2014. 19. Mishra, A. K. and Singh, V. P. 2010. A review of drought concepts, Journal of Hydrology, 391(1–2): 204–216. 20. Mishra, A. K. and Singh, V. P. 2011. Drought modeling—A review, Journal of Hydrology, 403(1–2): 157–175. 21. Potenciano, Á. and Villaverde, J. J. 2009. Implementación del modelo hidrológico de Témez para la evaluación de recursos hídricos con GRASS: fase superficial y subterránea. III Jornadas de SIG Libre, Universidad de Gerona, Spain, http://dugi-doc.udg.edu/bitstream/handle/10256/1387/C18. pdf?sequence=1, accessed on June 2014. 22. R Development Core Team. 2013. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http:// www.R-­project.org.

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23. Ruiz-García, J. M. 1998. Desarrollo de un Modelo Hidrológico Distribuido de Simulación Continua Integrado con un Sistema de Información Geográfica, Centro de Experimentación de Obras Públicas, CEDEX. Secretaría General Técnica. Centro de Publicaciones. Ministerio de Fomento, Madrid, Spain, May 1998. 24. Salas, J. D., Fu, C. J., Cancilliere, A., Dustin, D., Bode, D., Pineda, A., and Vincent, E. 2005. Characterizing the severity and risk of drought in the Poudre River, Colorado, Journal of Water Resources Planning and Management—ASCE, 131(5): 383–393. 25. Shiau, J. T. and Shen, H. W. 2001. Recurrence analysis of hydrologic droughts of differing severity, Journal of Water Resources Planning and Management—ASCE, 127(1): 30–40. 26. Témez, J. R. 1977. Modelo matemático de transformación “precipitación-aportación”, ASINEL, Madrid, Spain.

28 Rainfall Prediction Using Time Series Analysis

Mehdi Vafakhah Tarbiat Modares University

Hussein Akbari Majdar Tarbiat Modares University

Saeid Eslamian Isfahan University of Technology

28.1 Introduction ...................................................................................... 517 28.2 Historical Development ................................................................... 518 28.3 Autoregressive Models .....................................................................520 28.4 Moving Average Models ...................................................................521 28.5 Autoregressive–Moving Average Models ......................................521 28.6 Autoregressive Integrated Moving Averages Models ..................522 28.7 Seasonal ARIMA ..............................................................................522 28.8 Time Series Modeling ...................................................................... 523 Tests of Normality  • Test for Stationary • Trend • Seasonal Variations  • Cyclical Variations  • Jump  • Handling Missing Values  • Building ARIMA Models  • Forecasting Accuracy Measures  • Example Application 28.9 Summary and Conclusions ............................................................. 537 Authors........................................................................................................... 537 References ......................................................................................................538

Abstract  Due to the obscure and lack of sufficient knowledge about physical processes in hydrological cycle, stochastic modeling is an important activity in the field of hydrology and water resources management. Drought has the stochastic behavior and the important role in water resources planning and management. Rainfall is one of the most important elements in water cycle and drought analysis. Therefore, rainfall forecasting is an important activity in water resources planning and management. This chapter is concerned with forecasting methods based on the use of time series analysis. The concepts of random variable have been used in the field of hydrology since the beginning of the twentieth century. The formal development of stochastic modeling began with the introduction and application of autoregressive models to seasonal and annual hydrologic time series. The process of time series modeling and forecasting can be divided as follows: selection of the model among the range of AR(p), ARMA(p, q), ARIMA(p, d, q), and SARIMA(p, d, q)(P, D, Q) s models, selection of the order of models by using the autocorrelation and partial autocorrelation functions, determination of the parameters of the models, and simulation and validation for data generation and forecasting. This chapter is divided into time series analysis and time series modeling. An example is finally given on rainfall data in Iran.

28.1  Introduction Similarly, the manager of a watershed is interested in estimating the available water in the coming year so that proper planning can be carried out with regard to water allocations. However, the first step in making estimates for the future consists of gathering information from the past. In this connection, one usually 517

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Rainfall (mm)

80 60 40 20 0

1

6

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Time (month)

FIGURE 28.1  A time series of rainfall measured in monthly time steps in Samian station, Iran.

deals with statistical data that are collected, observed, or recorded at successive intervals of time. Such data are generally referred to as “time series.” Thus, when the numerical data are observed at different points of time, the set of observations is known as time series. A rainfall time series is a sequence of rainfall data, measured typically at successive points in time spaced at uniform time intervals (Figure 28.1). Forecasting is an important and unavoidable task in water resource and drought management. Though time series analysis is a broad area of research, it is mostly used to optimize planning and consists of two primary goals: identifying the nature of the phenomenon represented by the sequence of observations and forecasting (predicting future values of the time series variables). Both of these goals require that the pattern of observed time series data is identified and more or less formally described. Once that pattern is established, it can be interpreted and integrated into other data. Regardless of the depth of our understanding and the validity of our interpretation of the phenomenon, one can extrapolate the identified pattern to predict future events. The major objectives for studying time series are the understanding and description of the generating mechanism, the forecasting of future values, and optimal control of a system. The inherent nature of a weather data time series is that its observations are correlated with the observation in the past. The stochastic models, which are often known as time series models, have been used in scientific, economic, and engineering applications for the analysis of time series. Time series modeling techniques have been shown to provide a systematic empirical method for simulating and forecasting the behavior of uncertain hydrologic systems and for quantifying the expected accuracy of the forecasts [19]. Application of time series modeling in the field of hydrology and hydroclimatology has been extensively reported, including trend analysis of data [4,25], short-term streamflow forecasting [24], forecasting of monthly discharge [5,6,20], long-memory properties in streamflow time series [12], determination of rainfall climates [22], and drought forecasting [11].

28.2 Historical Development Babylonian astronomy used the time series of the relative positions of stars and planets to predict astronomical events. Observations of the planets’ movements formed the basis of the laws Johannes Kepler discovered. In the middle of the nineteenth century, the methodological approach used for astronomy was taken up by the economists Charles Babbage and William Stanley Jevons. The decomposition into unobserved components that depend on different causal factors, as it is usually employed in the classical time series analysis, was developed by Warren M. Persons in 1919 [13]. The classical time series analysis assumes that the systematic components, that is, trend, business cycle, and seasonal cycle, are not influenced by stochastic disturbances and can thus be represented by deterministic functions of time. Stochastic impact is restricted to the residuals.

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However, since the 1970s, totally different approaches have increasingly been applied to the statistical analysis of time series. The purely descriptive procedures of classical time series analysis were abandoned, and, instead, the results and the methods of probability theory and mathematical statistics have been employed. This has led to different assessments of the role of stochastic movements with respect to time series. Whereas the classical approach regards these movements as residuals without any significance for the structure of time series, the modern approach assumes that there are stochastic impacts on all components of a time series. Thus, the “law of movement” of the whole time series is regarded as a stochastic process, and the time series to be analyzed is only one realization of the data-generating process. Now the focus is on stochastic terms with partly rather complex dependence structures. The first steps in this direction were taken by the Russian statistician Evgeny Evgenievich Slutzky and the British statistician George Udny Yule at the beginning of the last century. Both of them showed that time series with cyclical properties similar to economic (and other) time series can be generated by constructing weighted or unweighted sums or differences of pure random processes. E.E. Slutzky and G.U. Yule developed moving average (MA) and autoregressive (AR) processes as models to represent time series. Herman Wold in 1938 systematized and generalized these approaches in his doctoral thesis. Their widespread practical usage is due to George E.P. Box and Gwilym M. Jenkins in 1970, who developed the methods to implement these models empirically [7]. They had abandoned the idea of different components and assumed that there was a common stochastic model for the whole generation process of time series. First, this method identifies a specific model on the basis of certain statistical figures. Second, the parameters of this model are estimated. Third, the specification of the model is checked by statistical tests. If specification errors become obvious, the specification has to be changed and the parameters have to be reestimated. This procedure is reiterated until it generates a model that satisfies the given criteria. This model can finally be used for forecasts. Recently, the idea of decomposing a time series has been taken up again, particularly for the modeling of seasonal variations. However, contrary to the classical approach, it is now assumed that all components of a time series can be represented by simple stochastic models. The procedure for the seasonal adjustment of time series used by Eurostat is, for example, based on such an approach. Moreover, since the 1980s, the possible nonstationarity of time series has increasingly been taken into consideration. Nonstationarity might not only be caused by deterministic but also by stochastic trends, and, furthermore, the nonstationarity of time series is no longer simply eliminated through the application of filters in order to continue within the framework of stationary models [16]. An intrinsic feature of the time domain approach is that, typically, adjacent points in time are correlated and that future values are related to past and present values. Autoregressive integrated moving average (ARIMA) modeling is one of the most widely implemented methods for analyzing univariate time series data [7,23]. In time series modeling, the ARIMA models, having forecasting capability and richer information on time-related changes, have the advantages over other methods like exponential smoothing and neural network. In weather data series, there is a serial correlation among observed data. This characteristic is considered by the ARIMA model. This model also provides systematic searching stage including identification, estimation, and diagnostic check for an appropriate model. AR models are coupled with MA models to form the autoregressive–moving average (ARMA) models. In ARMA model, the current value of the time series is expressed as a linear aggregate of previous values and a weighted sum of previous deviations (original value minus fitted value of previous data) plus a random parameter. However, they can be used if the data are stationary. By allowing differencing of data series, this kind of models can be extended to nonstationary series, which are called the ARIMA models [7]. The model of the ARIMA family is classified by three parameters (p, d, q) that can have zero or positive integral values. The ARIMA model is AR to order p and MA to order q and operates order d for difference of the time series. Hydrologic time series many times contain seasonal component, and these features are of an annual cycle, and these series are periodically nonstationary. Box et al. (1994) have

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generalized the ARIMA model to deal with seasonality and define a general multiplicative seasonal ARIMA (SARIMA) model, which are commonly known as SARIMA models. In short notation, the SARIMA model described as ARIMA(p, d, q)(P, D, Q)S, where (p, d, q) is the nonseasonal part of the model and (P, D, Q) is the seasonal part of the model [19].

28.3  Autoregressive Models In time series modeling, the dependent and independent variables come from a similar data, and both of them refer to an original time series. Here, the difference between the time of occurrence of each data causes the difference between independent and dependent variables. In AR models, the current value of the series is estimated as a function of the past values. The basic idea for an AR model comes from the idea of a linear regression model as Y = β1x + β0 + ε, where Y is the dependent variable, x is the independent variable, and ε is a random number. An AR model of order p can be written as follows:

x t = F1x t -1 + F 2 x t -2 +  + F p x t - p + w t

(28.1)

where xt is stationary series Φ1, Φ 2, …, Φp are the parameters of the AR(Φp ≠ 0) w t is assumed as a Gaussian white noise series with mean zero and variance s2w The highest-order p in the model is referred to as the order of the model. The model in lag operators takes the form as the following [23]:

(1 - F B - F B 1

2

2

)

-  - F pBp x t = w t



(28.2)

where the lag operator B is defined as B p x t = x t - p , p = 0,1, 2,¼

(28.3)

F (B) x t = w t

(28.4)

F ( B ) = 1 - F1B - F 2B2 -  - F pBp

(28.5)

And the model can be expressed as The AR operator Φ(B) is defined as

The values of Φ that make the process stationary are such that the roots of Φ(B) = 0 lie outside the unit circle in the complex plane [9]. If all roots of Φ(B) are larger than one in absolute value, then the process is a stationary process satisfying the AR equation and can be represented as [23] ¥

xt =

åY w

The coefficients of Ψj converge to zero, such that no stationary solution exists.

j

j =0

(28.6)

t-j



¥

åY j =0

j

< ¥. If some roots are exactly one in ­modulus,

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A plot of the autocorrelation function (ACF) of a stationary AR(p) model shows a mixture of damping sine and cosine patterns and exponential decays depending on the nature of its characteristic roots. The other characteristic feature of AR(p) models is that the partial autocorrelation function (PACF) defined as PACF(j) = corr. (xt, xt−j|xt−1, xt−2, …, xt−j+1) becomes exactly zero for values larger than p.

28.4  Moving Average Models MA of a period m in a time series is a series of successive arithmetic means of m terms at a time starting with first, second, third, and so on. The MA model is covariance stationary and ergodic for all moments. As an alternative to the AR model in which the x t on the left side of the equation are assumed to be combined linearly, the MA model of order q assumes that the white noise (w t) on the right side of the equation is combined linearly to form the observed data. A MA process of order q is characterized by

x t = w t + q1w t -1 + q2 w t -2 +  + qq w t - q ,

(28.7)

where θ1, θ2, …, θq are the MA parameters. MA(q) models immediately define stationary; every MA process of finite order is stationary [10]. In order to have a unique representation, generally, the requirement is imposed that all roots of θ(B) = 1 + θ1B + θ2B2 + ⋯ + θqB q = 0 in absolute value are greater than one. If all roots of θ(B) = 0 tend  outside the unit circle, the MA process has an AR representation of generally infinite order å ¥j=0 Ψjxt−j = wt with å ¥j=0 |Ψj| < ∞. MA process as with an infinite order AR representation is said to be invertible. A characteristic feature of MA(q) is that their ACF, ρj, becomes statistically insignificant after j = q. The characteristics of the ACF should be reflected in the correlogram, which should cut off after q. The PACF lies to zero geometrically.

28.5  Autoregressive–Moving Average Models In most case, for building a stochastic model, which represents a stationary time series, it is best to develop a mixed ARMA model. The order of an ARMA model is defined by the terms of p and q. These parameters relate to what happens in period t to both the past values and the random errors that occurred in the past periods. An ARMA model can be written as follows [23]:

x t = F1x t -1 + F 2 x t -2 +  + F p x t - p + w t + q1w t -1 + q2 w t -2 +  + qq w t - q

(28.8)

Equation 28.8 will be simplified by a backward shift operator B to obtain

F ( B ) x t = q ( B ) w t

(28.9)

The ARMA model is stationary if all roots of Φ(B) = 0 are larger than one in absolute value. The representation is unique if all roots of Φ(B) = 0 tend outside the unit circle and Φ(B) and θ(B) 𝑑𝑜 not have common roots. The stationary state of the ARMA models always has an infinite order MA representation. If the absolute value of all roots of Φ(B) is larger than one, it has an infinite order AR representation. The model is invertible only when the roots of θ(B) tend outside the unit circle [23]. In order to have an ARMA(p, q) model, both ACF and PACF should be decaying to zero. The autocorrelation of an ARMA(p, q) model is determined at greater lags by the AR(p) part of the model as the effect of the MA part dies out. So finally, the ACF consists of mixed damped exponentials and sine terms. Correspondingly, the partial autocorrelation of an ARMA(p, q) model is determined at greater lags by the MA(q) part of the model. Therefore, eventually the PACF will also consist of a mixture of damped exponentials and sine waves [23].

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28.6 Autoregressive Integrated Moving Averages Models The ARIMA class of time series models is an influential forecasting tool and is the base of many fundamental concepts in time series analysis. The ARIMA phrase stands for “autoregressive integrated moving average.” The ARIMA models are specific subset of univariate modeling, in which a time series is described in terms of past values of itself (the AR component) plus current and lagged values of a “white noise” error term (the MA component). The ARIMA models are univariate models that consist of an AR polynomial, an order of integration (d), and a MA polynomial. An ARIMA process (p, d, q) can be written as [23] F ( B ) Ñd x t = q ( B ) w t



(28.10)

where ∇d = (1 − B)d with ∇d xt and dth is the consecutive differencing. If E(∇d xt) = μ, the model can be written as F ( B ) Ñd x t = a + q ( B ) w t



(28.11)

where α is a parameter related to the mean of the process {x t}, by a = m (1 - F1 -  - F p )



(28.12)

This process is called a white noise process that is defined as a sequence of uncorrelated random variables from a fixed distribution, constant variance, and constant mean, which are usually assumed to be zero. If d = 0, the model is called ARMA(p, q), when d = 0 and q = 0, the model is referred to as AR of order p, and when p = 0 and d = 0, it refers to the MA of order q model [23].

28.7  Seasonal ARIMA SARIMA can be used when the time series exhibits a seasonal variation. Natural phenomena such as river flow, temperature, and rainfall have strong components corresponding to seasons. Then, the natural variability of many physical and environmental processes tends to match with seasonal oscillation. Therefore, it is appropriate to introduce AR and MA polynomials that recognize with seasonal lags. The resulting seasonal ARMA model (ARMA(P, Q)S) then takes the following form [21]:

( )

( )

F P Bs x t = F Q Bs w t



(28.13)



in which the operators is defined as

( )

F P Bs = 1 - F1s Bs - F 2s B2s -  - F Ps BPs



(28.14)

and

( )

qQ Bs = 1 - q1s Bs - q2s B2s -  - qQs BQs



(28.15)

where ΦP and θQ are the seasonal AR operator and the seasonal MA operator of orders P and Q, respectively, with seasonal period S. Similar to the properties of nonseasonal ARMA models, the pure seasonal ARMA(P, Q)S is causal only when the roots of ΦP(Zs) lie outside the unit circle, and also, it is invertible only when the roots of θQ(Zs) lie outside the unit circle.

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In general, the seasonal and nonseasonal operators can be combined into a multiplicative seasonal ARMA model and can be written as the following:

( )

( )

F P Bs j ( B ) x t = qQ Bs q ( B ) w t



(28.16)



The combination of a seasonal AR and a seasonal MA will form the ARIMA(p, d, q) × (P, D, Q)S, which is given by

( )

( )

F P Bs j ( B ) ÑSD x t = a + QQ Bs q ( B ) w t



(28.17)

in which w t is the usual Gaussian white noise process. The polynomials Φ(B) and θ(B) are the ordinary AR and MA components, which are represented by orders p and q, respectively, while Φ P(BS) and θ Q(BS) are the seasonal AR and MA components, which are represented by orders P and Q .The ordinary and seasonal difference components can be written as [23]

Ñ d = (1 - B )

d

(

and ÑSD = 1 - BS

) D

(28.18)

28.8  Time Series Modeling The time series model development consists of three stages: identification, estimation, and diagnostic check. In the identification stage, data transformation is often needed to make the time series stationary. Stationarity is a necessary condition in building an ARIMA model that is useful for forecasting. The estimation stage of model development consists of the estimation of model parameters. The last stage of model building is the diagnostic checking of model adequacy. This stage checks if the model assumptions about the errors are satisfied. Several diagnostic statistics and plots of the residuals can be used to examine the goodness of fit of the tentative model to the observed data. If the model is inadequate, a new tentative model should be identified, which is subsequently followed, again, by the stages of estimation and diagnostic checking [2]. The following steps give an overview of a general approach to time series modeling [9]: • Plot the series and examine the main features of the graph, checking in particular whether there is trend, seasonal component, any apparent sharp changes in behavior, and any outlying observations. • Remove the trend, seasonal, and cyclical components to get stationary. To achieve this goal, it may sometimes be necessary to apply a preliminary transformation to the data. • Choose a model to fit the residuals, making use of various sample statistics including the sample ACF. • Forecasting will be achieved by forecasting the residuals and then inverting the transformations described earlier to arrive at forecasts of the original series.

28.8.1 Tests of Normality In many time series techniques, the normality is a common assumption. In practice, time series are not normally distributed. In this case, they should be transformed to some normal time series, if possible, and then be analyzed. A visual inspection of the histogram of the rescaled residuals is a rough check for normality. A Gaussian Q–Q plot of the residuals can also be a useful tool. But the Kolmogorov–Smirnov test is used more extensively.

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If the constant variance and normality assumptions are not true, they are often reasonably well satisfied when the observations are transformed by a Box–Cox transformation [21]: ì x lt - 1 , ï x =í l ï ln x t , î

l¹0

l t



(28.19)

l = 0

Choose the value of λ that maximizes n é1 L ( l ) = - ln ê 2 ên ë



n

ù

n

û

j =1

å ( x( ) - x ( ) ) úú + ( l - 1) å ln x j

l

l

j =1

2

(28.20)

j



28.8.2 Test for Stationary Most of the theories in time series literature are only applicable to stationary processes. In forecasting a time series, the presence of nonstationarity in the data series causes more complexity and more calculations. A time series is stationary if there is no systematic trend, no systematic change in variance, and no periodic variations or seasonality. Applying a difference operator to the data series is a method to make a nonstationary time series stationary. A number of movements or fluctuations in a time series may affect its values. These elements are called components of time series and are of four types: trend, seasonal variations, cyclical variations, and irregular variations. Application of time plot and a visual inspection of the time series are the first step in the analysis of time series. If any patterns of nonstationary components (trend, seasonality, and cyclical variation) are present, they must be omitted using transformations in the data series.

28.8.3 Trend A general tendency of data to grow or decline over a long period of time is called trend. This component shows basic tendency of the series. In many cases, there is a linear trend in time. The series can be detrended by fitting a linear regression and then doing a time series analysis on the residuals. The linear trend is presented by the following equation, where Tx is the linear trend, t is time, and a and b are the parameters of the model [3]:

Tx = at + b

(28.21)

An alternative to fitting a linear regression is to use differencing. Differencing is performed, as the name implies, as YtD = Yt - Yt -1, that is, subtract the previous value from the current value. You will lose one data point in the process as the difference for the first observation cannot be computed. Second differences, that is, differences of the differences, can be used to remove a quadratic trend. Rarely is more than second differencing performed in practice (Figure 28.2). Several methods are used for the measurement of trend. Some of them are listed here:

1. Freehand curve method or eye inspection method 2. Semiaverage method 3. Method of MA 4. Method of least squares 5. Turning point method 6. Mann–Kendall test

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Rainfall Prediction Using Time Series Analysis

Rainfall (mm)

80 60 40 20 0

1

6

11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 Time (month)

FIGURE 28.2  The trend component in a rainfall time series.

The first method is subjective and its results may not be reliable. In the second method, the whole data are divided into two equal parts with respect to time, and an average of each part is obtained. Then, these two points are plotted and joined by a straight line, which represents the trend line of the data series. Turning point method and Mann–Kendall test are two useful and extensively used methods that are available in literatures [3,23]. 28.8.3.1 T urning Point Test A turning point means when the series changes from increasing to decreasing or vice versa. That is, xt−1 < xt > xt+1 or xt−1 > xt < xt+1. Let T be the number of turning points in an n period series. In order to carry out the test of white noise with this test, we must determine the distribution of the number of turning points in a series. It is known that with increasing n, the distribution of T is approximately normally distributed [14]. Then, the test statistic (NT) defined and approximated in Equation 28.22 should be compared with the z-table critical value. The hypothesis of randomness should be rejected at α significance level if the absolute value of NT > NT(1−α/2), where NT(1−α/2) is the (1 − α/2) quartile of standard normal distribution [23]: NT = where

T - mT

Var ( T )

» N ( 0,1)

(28.22)

æ2ö mT = ç ÷ ( n - 2 ) è3ø



Var ( T ) =



(28.23)

(16n - 29 ) 90

(28.24)



28.8.3.2 Mann–Kendall Test Mann–Kendall test has been presented by Mann [18] and extended by Kendall [15]. This test is used to check the presence of a trend in a time series. If a time series contains a trend, this component should be considered in the time series modeling. For a Mann–Kendall test of trend, the hypotheses take the following form [3]: The null hypothesis, H0, means time series has no trend. The alternative hypothesis, H1, means time series has either an increasing or a decreasing trend. The test statistic, Z, is obtained as follows. First, for a time series, xi, S is calculated as n -1

S=

n

åå sgn ( x - x ) j

k =1 j = k +1

(28.25)

k



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Handbook of Drought and Water Scarcity

where ì+1 ïï sgn ( x ) = í 0 ï ïî-1



if ( x j - x k ) > 0 if ( x j - x k ) = 0 if ( x j - x k ) < 0

(28.26)

In the case that the data are independent and uniformly distributed, the average of S is E(S) = 0 and its variance will be Var ( s ) =



n ( n - 1) ( 2n + 5 ) -

å 18

m

(

t i ( t i - 1) 2t i + 5

i =1

)

(28.27)

In this equation, n is the number of data and m is the number of ties. Each tie is a set of similar consequent data in a time series where the number of data in each of them is t. Finally, the statistic of this test, Z, is computed as ì S -1 ï ï Var ( S ) ï 0 Z=í ï S +1 ï ï Var ( S ) î



if S > 0 if S = 0

(28.28)

if S < 0

Critical values: Mann–Kendall is a two-tailed test, which means that the test statistic should be compared by a critical value from the table of normal standard distribution, Z α/2. In the case that Z α/2 ≤ Z ≤ Z1−α/2, the null hypothesis is accepted by α percent of error. In the case that the null hypothesis is rejected, the time series of xi is considered to have either an increasing trend if S is positive or a decreasing trend if S is negative [3].

28.8.4 Seasonal Variations This regular and periodic type of variation is generally annual in period and has a similar pattern of behavior at a particular time of the year (Figure 28.3).

Rainfall (mm)

80 60 40 20 0

1

6

11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 Time (month)

FIGURE 28.3  The seasonality in a rainfall time series.

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Rainfall Prediction Using Time Series Analysis

In order to represent such a seasonal effect, allowing for noise but assuming no trend, we can use the simple model x t = St +Yt, where St is a periodic function with period (St−d = St). A convenient choice for St is a sum of harmonics (or sine waves) given by k

St = a 0 +

å (a cos ( l t ) + b sin ( l,t )) j

j

(28.29)

j

j =1



where a0, a1, ..., a k and b1, ..., bk are the unknown parameters λ1, ..., λ k are the fixed frequencies, each being some integer multiple of 2π/d [8] The method of simple averages, ratio-to-trend method, ratio-to-MA method, and link relative method are different devices to measure the seasonal variations.

28.8.5 Cyclical Variations This type of variation occurs for a period of more than 1 year. The regular movement in a time series with a period more than 1 year is called a cyclical variation (Figure 28.4). Some of the methods used for measuring cyclical variations are residual method, reference cycle analysis method, direct method, and harmonic analysis method. The differencing method is a common mechanism used to transform a nonstationary time series into stationary. The function of log is another method for this purpose.

28.8.6 Jump A sudden significant change observed in the long-term average of a time series. A time series with jump is not stationary type I since its average is not constant in the entire length of the time series.

28.8.7 Handling Missing Values In order to replace missing values of the observations, several options are available. Each one of the following methods can be used to estimate the missing data: • • • •

Replace with the mean of the data series. Use the current time value for the next time. Average the adjacent values. Use the regression equation of the form, x t = α + βt, of the data series.

Rainfall (mm)

80 60 40 20 0

1

6

11

16

21

26

31

36

41

46 51 56 61 Time (month)

FIGURE 28.4  A cyclical variations in a rainfall time series.

66

71

76

81

86

91

96 101 106

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Handbook of Drought and Water Scarcity

28.8.8 Building ARIMA Models Identification of an ARIMA model can be carried out based on a methodology that consists of four phases as follows: 1. Model identification 2. Estimation of model parameters 3. Diagnostic checking for the identified model 4. Forecasting 28.8.8.1 Model Identification The purpose of the identification stage is to determine the differencing required to achieve stationarity and also the order of both the seasonal and the nonseasonal AR and MA operators for the residual series. There are a number of identification methods proposed in the literature. The ACF and the PACF are the two most useful tools in any attempt at time series model identification. 28.8.8.1.1  Autocorrelation Function The sample ACF (rk) measures the amount of linear dependence between observations in a time series that are separated by a lag k. To use the ACF in model identification, estimate rk and then plot rk series against lag k up to a maximum lag of about five times the seasonality interval, and this should be less than one-fourth of the series under study. A theoretical pattern for parameters identification is presented in Tables 28.1 and 28.2. The values at nonseasonal lags h ≠ Ks, for K = 1, 2,…, are zero. When the process is SARIMA(0, d, q) × (0, D, Q)S model, rk truncates and is not significantly different from zero after lag q + sQ. If rk spikes out at lags that are multiples of s, this implies the presence of a seasonal AR component. The failure of the ACF to truncate at other lags may imply that a nonseasonal AR term is required. The autocorrelation of order k is simply the correlation between x t and xt−k, that is, rk =

{

}

E ( x t - m ) (x t - k - m



{

E ( xt - m)

2

}

(28.30)

TABLE 28.1  Behavior of the Autocorrelation Function and Partial Autocorrelation Function for Autoregressive Moving Average Models

ACF PACF

AR(P)

MA(Q)

ARMA(P, Q)

Tails off Cuts off after lags P

Cuts off after lags Q Tail off

Tail off Tail off

Source: Janacek, G. and Swift, L., Time Series: Forecasting, Simulation, Applications, Ellis Horwood, Chichester, England, 1993, p. 333.

TABLE 28.2  Behavior of the Autocorrelation Function and Partial Autocorrelation Function for Pure SARMA Models ACF PACF

AR(P)s

MA(Q)s

ARMA(P, Q)s

Tails off at lags Ks, K = 1, 2, … Cuts off after lags Ps

Cuts off after lags Qs Tails off at lags Ks

Tails off at lags Ks Tails off at lags Ps

Source: Janacek, G. and Swift, L., Time Series: Forecasting, Simulation, Applications, Ellis Horwood, Chichester, England, 1993, p. 333.

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Rainfall Prediction Using Time Series Analysis

In practice, one never knows the true autocorrelations and partial autocorrelations, and at the identification stage, one has to rely on the sample ACF and PACF imitating the behavior of the corresponding parent quantities. True autocorrelations (ρ k) can be estimated by

å r =

n-k

k

t =1



( x t - x ) ( x t+k - x )

å t=1( x t - x ) n

(28.31)

2



where x is the sample mean of xt. 28.8.8.1.2  Partial Autocorrelation Function PACF can also be used for determining the possible order seasonal AR, nonseasonal AR and MA, and seasonal MA that should be incorporated in the model with the help of Tables 28.1 and 28.2. When the process is a pure SARIMA(p, d, 0) × (P, D, 0) 12 model, rkk cuts off and is not significantly different from zero after lag p + SP. If rkk damps out at lags that are multiples of s, this suggests the incorporation of a seasonal MA component into the model. The failure of the PACF to truncate at other lags may imply that a nonseasonal MA term is required. To obtain an estimate for partial autocorrelations (φj(k)) at lag k, we can employ successive autoregressive estimation procedure. The first step is to model the x t series by finite AR models of order K given by Box and Jenkins [7]:



rk =

å

k j =1

j j (k )rk - j



(28.32)

where φj(k) is the kth autoregressive coefficient and k = 1, 2,..., p. Estimate of these coefficients by ordinary least squares or maximum likelihood estimation method gives the kth sample partial autocorrelation. 28.8.8.2 Parameter Estimation After choosing the most appropriate model (step (i) given earlier), the model parameters are estimated by using several estimation procedures. The estimation stage results will be used to check (1) parameter estimates and (2) the appropriateness of coefficient estimates, which includes the statistical significance of estimated coefficient and standard error and correlation matrix. In maximum likelihood methods, the likelihood function is maximized in order to obtain the parameter estimates. The likelihood of a set of data is the probability of obtaining that particular set of data, given its distribution. The philosophy behind maximum likelihood estimates is to find a set of parameters, which maximize the likelihood of observing the data to which the model is being fitted. The linear optimization algorithm is used to maximize the likelihood function with respect to the parameter space [21]. In time series analysis, there may be several adequate models that can be used to represent a given data set, and hence, numerous criteria for model comparison have been introduced in the literature. One of them is based on the so-called information criteria. The idea is to balance the risks of underfitting (selecting an order smaller than the true order) and overfitting (selecting an order larger than the true order). To choose the appropriate ARMA(p, q) model, the Akaike information criterion (AIC) is used to select the value of p and q by the following equation [1]:

AIC = N lnse + 2 ( p + q )

where N is the number of time series data σε is the variance of the error of the model p and q are the orders of the model

(28.33)

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Handbook of Drought and Water Scarcity

The optimal order of the model is chosen by the value of k, which is a function of p and q, P, and Q, so that the value of k yielding the minimum AIC specifies the best model. 28.8.8.3 Diagnostic Checking After fitting a provisional time series model, we can assess its adequacy in various ways. The usual approach is to extract from the data a sequence of residuals to correspond to the underlying, last unobservable, white noise sequence and to check that the statistical properties of these residuals are indeed consistent with white noise. Most diagnostic tests deal with the residual assumptions in order to determine whether the residuals from the fitted model are independent, have a constant variance, and are normally distributed. Several diagnostic statistics and plots of the residuals can be used to examine the goodness of fit of the tentative model to the historical data. The first approach that can be used to evaluate the adequacy of a model is the plot of the errors over time, which can be written [21] as wt =



(x

t

- x tt -1

)

t -1 t

P

(28.34)

where x t - x tt -1 is the one-step-ahead prediction of (xt) based on the fitted model Ptt -1 is the estimated one-step-ahead error variance If visual inspections of the errors reveal that they are randomly distributed over time, then we have a good model. The ACF of the series can also be used to examine whether the residual of the fitted model is white noise or not. If the ACF is significantly different from zero, this implies that there is dependence between observations [13]. There are different applications related to the residual ACF for the independence of residuals. The first one is the correlogram drawn by plotting rk(w) against lag k:

å ww = å w n

rak

t = k +1 n

t =1

t

2 t

t -k

(28.35)

Under the assumption that the residual follows a white noise process, the standard errors of these (rak) are approximately equal to 1/ T. Thus, under the null hypothesis that the residual follows a white noise process, roughly 95% of the autocorrection coefficient (rak) should fall within the range of ±1.96/ T. If more than 5% of the coefficient fall outside of this range, then most likely, residual does not follow a white noise process [17]. There are many statistical tests used for diagnostic checking of randomness. The Ljung–Box Q-statistic, turning point, and runs tests can be used for the diagnostic checking of residuals for independence. 28.8.8.4 Forecasting The last step in time series modeling is forecasting. There are two kinds of forecasts: sample period forecasts and postsample period forecasts. The former are used to develop confidence in the model and the latter to generate genuine desired forecasts. In forecasting, the goal is to predict future values of a time series, xt+m, m =1, 2, … based on the data collected to the present, x = {x t, xt−1, …, x 1}. Throughout this section, we will assume xt is stationary and the model parameters are known. Minimum mean square error forecasts ARIMA(p, d, q) process can be written as

F ( B ) Ñd x t = q ( B ) w t

(28.36)

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Rainfall Prediction Using Time Series Analysis

Forecasting a value x tt +m , m = 1, 2, 3 …, when we are currently standing at time t is said to be made m-step ahead forecast. Then, three explicit forms of the model for the observation (x tt +m ) generated by the ARIMA process may be expressed as follows [7]: Directly in terms of the difference equation

x t +m = F1x tt +m -1 +  + F p+d x t +m -p-d - q1w t +m -1 -  - qq w t +m -q

(28.37)

Infinite weighted sum of current and previous shocks (w t) m -1

x t +m ==

åY w j

(28.38)

t +m- j



j=0

where m0 = 1 and mj’s may be obtained by equating the coefficients in

(

)

f ( B ) 1 + m1B + m2B2 +  = q(B)

(28.39)

Infinite weighted sum of previous observations, plus a random shock m -1

x t +m ==

åp x

(28.40)

j t +m- j



j=0

where å ¥j=1 p j = 1 and πj’s may be obtained by equating the coefficients in

f ( B ) = (1 - p1B - p2B2 - )q(B)

(28.41)

Standing at origin t, we can take a minimum mean square error predictor, x t + m of xt+m, which is a linear function of current and previous observations of xt, xt−1, …, and then it will also be a linear function of current and previous shocks. The minimum mean square error predictor (x t + m) for lead time m is the conditional expectation of xt+m at the origin t. From Equation 28.38, we can obtain x t +m = E ( x t +m |x t ,¼, x t ) =

m -1

åY E ( w j

t +m- j

)

(28.42)

j=0

Then, the mean square prediction error can be written as [21] Ptt+ m = E ( x t + m - x t + m ) = s2w 2



m -1

åY j=0

2 j

(28.43)

To assess the precision of the forecasts, prediction interval can be calculated as

x tt + m + C a/2 Ptt+ m

where C α/2 is chosen to get the desired degree of confidence.

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Handbook of Drought and Water Scarcity

28.8.9 Forecasting Accuracy Measures Once forecasts are made, they can be evaluated if the actual values of the series to be forecasted are observed. There are several measurements of the accuracy of forecasts. Four of them are introduced here. These are root mean square error (RMSE), coefficient of determination (R 2), percent error in mean (PEM), and Theil’s inequality coefficient (Theil-U). These efficiency criteria are calculated using the following equations:

( )

Coefficient of determination R 2





1 n

Root Mean Squared Error ( RMSE ) =

æ ç =ç ç ç è

å å

n

i =1

n

( Oi - Pi ) i =1

i =1

2

(28.44)

2

(O - O)( P - P ) i

i

(O - O)

2

i

Percent error in mean =

Theil’s inequality coefficient (Theil-U) =

n

å

å

n

(P - P)

2

i =1

i

ö ÷ ÷ ÷ ÷ ø

P-O O

(28.46)

(1/n ) å t =1 ( Ot - Pt ) æ ç (1/n ) è

å

n

2

ö æ Pt2 ÷ v ç (1/n ) t =1 ø è

å

n

(28.45)

ö O2t ÷ v t =1 ø

n

(28.47)

where Oi is the observed data Pi is the simulated data O is the average of the observed data P is the average of the simulated data n is the number of observation The scaling of U is such that it will always lie between 0 and 1. If U = 0, it is the best estimation, and if U = 1, the predictive performance is as bad as it possibly could be. RMSE depends on the scale of the dependent variable. These should be used as relative measures to compare forecasts for the same series across different models; the smaller the error, the better the forecasting ability of that model according to that criterion. However, R 2, PEM, and Theil’s inequality coefficient are scale invariant. If the selected model is inadequate, the three-step model building process is typically repeated several times until a satisfactory model is finally obtained. The final selected model can then be used for prediction purposes.

28.8.10 Example Application In the mentioned example of rainfall data series of Lazurah station, Iran, the data of the last 48 months are estimated using the data of early 60 months using SARIMA model, and the following results were obtained. Considering the monthly rainfall data of Table 28.3, the statistical parameters and normal curve and normality test are given in Figures 28.5 and 28.6.

R

9.5 13 21 31 42 52 43 66 53 31 10 22.5

No.

1 2 3 4 5 6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24

No.

0 31 23 31 41 44 42 77.5 31 44 11 21

R 25 26 27 28 29 30 31 32 33 34 35 36

No. 15 27.5 39 31 45 51 41 51 19 3.00 3.00 13.00

R 37 38 39 40 41 42 43 44 45 46 47 48

No. 23.5 51 40 35 41 31 29.5 33.5 44 23 4 4

R 49 50 51 52 53 54 55 56 57 58 59 60

No. 41 18.6 22 26 31 32.4 37 20.8 13.9 1 3.8 0.2

R 61 62 63 64 65 66 67 68 69 70 71 72

No. 8.0 14.0 30.0 25.0 19.0 30.0 35.0 35.0 22.0 8.8 3.0 15.6

R 73 74 75 76 77 78 79 80 81 82 83 84

No.

TABLE 28.3  Monthly Rainfall Data (mm) of Lazurah Station in Golestan Province, Iran

23.0 29.0 21.0 24.5 22.0 25.0 41.0 42.0 20.7 5.0 3.0 6.6

R 85 86 87 88 89 90 91 92 93 94 95 96

No. 13.2 18.6 14.4 13.2 13.2 18.6 22.0 24.6 9.8 6.6 3.6 4.7

R 97 98 99 100 101 102 103 104 105 106 107 108

No.

11.0 25.0 28.0 27.0 21.0 25.0 31.0 44.0 17.0 11.0 9.0 6.0

R

Rainfall Prediction Using Time Series Analysis 533

534

Handbook of Drought and Water Scarcity Summary for the data

Anderson–Darling normality test 2

A P-Value Mean StDev Variance Skewness Kurtosis N

0

15

30

45

60

Minimum 1st quartile Median 3rd quartile Maximum

75

0.69 0.070 24.647 15.240 232.264 0.580299 0.385965 108 0.000 13.050 23.000 34.625 77.500

95% confidence interval for mean 21.740 27.554

95% Confidence intervals

95% confidence interval for median

Mean

21.000 27.321 95% confidence interval for StDev 13.443 17.596

Median 21

22

23

24

25

26

27

FIGURE 28.5  The statistical parameters and normal curve of monthly rainfall data of Lazurah station.

Normal

99.9 99

Percent

95 90 80 70 60 50 40 30 20 10 5

Mean StDev N KS P-Value

1 0.1

–20

0

20

40

60

80

Rainfall

FIGURE 28.6  The normal probability paper plot of monthly rainfall data of Lazurah station.

24.65 15.24 108 0.055 >0.150

535

Rainfall Prediction Using Time Series Analysis Trend analysis plot for the data Linear trend model Yt = 34.8102 – 0.186476 × t 80 70 60 Rainfall

50 40 30

Variable Actual Fits

20

Accuracy measures MAPE 222.134 MAD 11.163 MSD 196.317

10 0 1

11

22

33

44

55

66

77

88

99

Index

FIGURE 28.7  Original and linear trend time series.

The kernel density estimate and the normal probability paper plot indicate that the monthly rainfalls are near normally distributed. As Figure 28.7 shows, there is a clear trend decreasing in the monthly rainfall data of Lazurah station. A regression-based method is used to remove the trend component of the data series (Figure 28.7). The process of this method, which is based on Equation 28.48, is presented in Table 28.4. In this method, the trend component of the data is removed considering the slope of its regression equation (−0.186476): x¢ = x - ( -0.186476 ) t



(28.48)

where x′ is the detrended data x is the original data t is the time ACF and PACF graphs are presented in Figures 28.8 and 28.9. As it is obvious by the plot, ACF is almost zero from lag 3 later on. It is concluded that the best model for the data is MA(2). TABLE 28.4  Processes of the Detrending in the Data Series Using the Regression-Based Method No. 1 2 3

x

Equation

x′

9.5 13 21

9.5 − (−0.186476) × 1 13 − (−0.186476) × 2 21 − (−0.186476) × 3

9.7 13.4 21.6

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Handbook of Drought and Water Scarcity Autocorrelation function for the data (with 5% significance limits for the autocorrelations) 1.0 0.8 Autocorrelation

0.6 0.4 0.2 0.0 –0.2 –0.4 –0.6 –0.8 –1.0 2

4

6

8

10

12

14

16

18

20

22

24

26

Lag

FIGURE 28.8  ACF plot for monthly rainfall time series. Partial autocorrelation function for the data (with 5% significance limits for the partial autocorrelations) 1.0

Partial autocorrelation

0.8 0.6 0.4 0.2 0.0 –0.2 –0.4 –0.6 –0.8 –1.0 2

4

6

8

10

12

14

16

18

20

22

24

Lag

FIGURE 28.9  PACF plot for monthly rainfall time series. TABLE 28.5  Accuracy Measures of Models Model(p, d, q)(P, D, Q)S

AIC

RMSE

R2

PEM (%)

Theil-U

SARMA(1 1)(1 1)12 SARMA(2 1)(2 1)12 SARIMA(1 1 1)(1 1 1)12 SARIMA(2 1 1)(2 1 1)12 SARIMA(2 1 2)(2 1 2)12 SARIMA(3 1 1)(3 1 1)12

61 51 38 35 34 31

32.4 21.2 15 11 8.3 5.6

0.25 0.33 0.44 0.51 0.68 0.73

45 34 31 25 21 18

0.51 0.41 0.38 0.3 0.25 0.2

26

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Rainfall Prediction Using Time Series Analysis

Rainfall (mm)

60

Observed

50

Estimated

40 30 20 10 0

1

6

11

16

21

26

31

36

41

46

Month

FIGURE 28.10  Observed versus estimated values of the example rainfall, estimated by the model SARIMA(3 1 1) (3 1 1)12.

As it is obvious by the plot, PACF is almost zero from lag 4 to lag 6. Please note that the significant values of PACF in lag 10 might be a random phenomenon and does not mean any real correlation between data. As a result, the optimum lag for an AR model to be fitted on the data is 1 or 3. According to the results given earlier, the seasonal autoregressive moving average (SARMA) and SARIMA models were fitted to data, and accuracy measures of these models are presented in Table 28.5. As can be seen in Table 28.5, SARIMA(3 1 1)(3 1 1)12 has the smallest AIC, RMSE, PEM, and Theil-U and has the highest R 2. Figure 28.10 shows the observed and estimated value of this model.

28.9  Summary and Conclusions Time series modeling is widely used for the generation of synthetic data, prediction, forecasting, estimation of missing and censored data, and extending records. Usually, forecasted data are used for the operation of water resources and environmental systems, where synthetic generated data are used for the simulation of such systems for the designing purposes. A time series (xt) in general is affected by four main components. These components are a deterministic periodic term (Pt), a deterministic linear or nonlinear trend (Tt), a jump term (Jt), and a stochastic term (Zt), which can be separated from the observed time series. A time series should be stationary type I by removing Jt and Pt and Tt before being processed through the component of Zt. Two nonparametric tests (e.g., turning point method and Mann–Kendall test) for the determination of trend and spectral analysis test for the determination of periodic term were presented. Time series models have been used generally for the generation of synthetic data and forecasting in hydrology and particularly in rainfall analysis. Time series modeling processes include selection of model, selection of the order of models, determination of the parameters of the models, and simulation and validation.

Authors Mehdi Vafakhah received BSc in natural resources engineering from Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran, in 1996, and MSc and PhD in watershed management engineering from Tarbiat Modares University and the University of Tehran in 1999 and 2008, respectively. He was with the Faculty of Natural Resources of Tarbiat Modares University as a lecturer from 1998 to 2009, as assistant professor from 2009 to 2013, and as associate professor from 2013. His research interests include surface hydrology, snow hydrology, geostatistics, and parameter estimation with artificial neural networks, adaptive neuro-fuzzy inference system, and data-driven techniques. He has published 87 journal articles, 2 book chapters, and more than 67 papers presented in international and national conferences and is also involved in many national watershed management projects.

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Hussein Akbari Majdar graduated in the field of range and watershed management from Gonbad-e Kavus University in Iran in 2008. In the same year, he pursued a course on watershed management and received his MSc from Gorgan University of Agricultural Science and Natural Resource. His MSc thesis was in the field of rainfall–runoff simulation using SWAT model. His scientific researches and articles are mainly related to hydrological modeling. He is as a PhD candidate in the field of watershed management at Tarbiat Modares University. Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, Iran, where he has been since 1995. He received his PhD from the University of New South Wales, Australia, under the supervision of Professor David Pilgrim. His research focuses mainly on water resources planning and management and statistical hydrology in a changing climate. In recent years, he has been working on modeling water reuses, climate change and variability, IWRM, sustainable agriculture, resilience and vulnerability research, and natural resources governance and management. Formerly, he was a visiting professor at Princeton University, United States, and the University of ETH Zurich, Switzerland. On the research side, he has started a research partnership from 2014 with McGill University, Canada. He has contributed to more than 500 publications in journals, books, or technical reports. He is the founder and chief editor of both International Journal of Hydrology Science and Technology (Scopus, Inderscience) and Journal of Flood Engineering. His professional experience includes being on the editorial boards and reviewer of about 40 Web of Science (ISI) journals. He has authored more than 100 book chapters and books. Recently, he has started the editorship of several handbooks published by Taylor & Francis Group (CRC Press). A three-volume Handbook of Engineering Hydrology in 2014, Urban Water Reuse Handbook in 2015, a three-volume Handbook of Drought and Water Scarcity in 2016, and Underground Aqueducts Handbook in 2016 are published/contracted ones.

References

1. Akaike, H. 1978. A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19(6): 716–723. 2. Anteneh, B. 2012. Short-term and Long-term SPI drought forecasts using wavelet neural networks and wavelet support vector regression in the Awash River Basin of Ethiopia, MSc thesis, McGill University, Montreal, Quebec, Canada, p. 147. 3. Araghinejad, S. 2014. Data-Driven Modeling: Using MATLAB in Water Resources and Environmental Engineering, Water Science and Technology Library 67, Springer Science+Business Media, Dordrecht, the Netherlands, doi: 10.1007/978-94-007-7506-0_4. 4. Bahmani, R., Radmanesh, F., Eslamian, S., and Parham, G. 2013. Reservoir evaporation trend analysis and its prediction using time series, JISE—Irrigation Science and Technology, 3(36): 67–80. 5. Bashari, M. and Vafakhah, M. 2010. Comparison of different time series analysis methods for forecasting monthly discharge in Karkheh watershed, Iran—Irrigation and Water Engineering, 1(2): 75–86. 6. Biabanaki, M. and Eslamian, S. S. 2005. Monthly flow forecasting by time series models in Ghezelozen river, Iran-Korea Climate Modeling Workshop, Mashhad, Iran. 7. Box, G. E. and Jenkins, G. M. 1976. Time Series Analysis: Forecasting and Control, revised edn., Holden-Day, A John Wiley & Sons, Inc. Publication, New York. 8. Brockwell, P. J. and Davis, R. A. 2002. Introduction to Time Series and Forecasting, 2nd edn., Springer-Verlag, New York, p. 421. 9. Chatfield, C. 2004. Time-Series Forecasting, Chapman and Hall/CRC, Boca Raton, FL, p. 265. 10. Diebold, F. 2006. Elements of Forecasting, Cengage Learning, South-Western College Pub, Cincinnati, OH. 11. Eslamian, S. S., Bazrkar, M. H., and Mousavi, S. F. 2012. Drought forecasting in Isfahan Province using time series analysis of rainfall monthly data, Watershed Management and Engineering, 4(1): 21–30.

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12. Hadizadeh, R., Eslamian, S., and Chinipardaz, R. 2013. Investigation of long-memory properties in streamflow time series in Gamasiab River, Iran, International Journal of Hydrology Science and Technology, 3(4): 319–350. 13. Janacek, G. and Swift, L. 1993. Time Series: Forecasting, Simulation, Applications, Ellis Horwood, Chichester, England, p. 333. 14. Kendall, M. G. and Ord, J. K. 1990. Time-Series, Vol. 296, Edward Arnold, London, U.K.. 15. Kendall, M. G. 1976. Rank Correlation Methods, 4th edn., Griffin, Oxford University Press, Oxford, U.K. 16. Kirchgassner, G., Wolters, J., and Hassler, U. 2012. Introduction to Modern Time Series Analysis, Springer, Berlin, Germany. 17. Lehmann, A. and Rode, M. 2001. Long-term behaviour and cross-correlation water quality analysis of the river Elbe, Germany, Journal of Water Resources, 35: 2153–2160. 18. Mann, H. B. 1945. Nonparametric tests against trend, Econometrica: Journal of the Econometric Society, 13: 245–259. 19. Mishra, A. K. and Desai, V. R. 2005. Drought forecasting using stochastic models, Stochastic Environmental Research and Risk Assessment, 19(5): 326–339. 20. Modarres, R. and Eslamian, S. S. 2006. Streamflow time series modeling of Zayandehrud river, Iranian Journal of Science and Technology, Transaction B, Engineering, 30(B4): 567–570. 21. Shumway, R. H. and Stoffer, D. S. 2010. Time Series Analysis and Its Applications with R Examples, 3rd edn., Springer, Berlin, Germany, p. 607. 22. Soltani, S., Modarres, R., and Eslamian, S. S. 2007. The use of time series modeling for the determination of rainfall climates of Iran, International Journal of Climatology, 27(6): 819–829. 23. Takele, R. 2012. Statistical analysis of rainfall pattern in Dire Dawa, Eastern Ethiopia, MSc thesis, Addis Ababa University, Addis Ababa, Ethiopia, p. 111. 24. Vafakhah, M. 2012. Application of artificial neural networks and adaptive neuro-fuzzy inference system models to short-term streamflow forecasting, Canadian Journal of Civil Engineering, 39(4): 402–414. 25. Vafakhah, M., Bakhshi Tiragani, M., and Khazaei, M. 2012. Analysis of rainfall and discharge trends in Kashafrood watershed, Geography and Development Iranian Journal, 10(29): 77–90.

29 Meteorological Drought Indices: Rainfall Prediction in Argentina Marcela H. González University of Buenos Aires and Research Center of the Sea and the Atmosphere (CIMA) CONICET-UBA

Eugenia M. Garbarini University of Buenos Aires

Alfredo L. Rolla Research Center of the Sea and the Atmosphere CONICET-UBA

Saeid Eslamian Isfahan University of Technology

29.1 Introduction ......................................................................................542 29.2 Meteorological Indices as Climate Forcing Indicators ...............543 Indices Derived from Sea Surface Temperatures  •  Indices Derived from Atmospheric Circulation Patterns

29.3 Meteorological Indices and Rainfall Long-Term Variability .......547 29.4 Relation between Meteorological Indices and Seasonal Rainfall in Argentina .......................................................................549 Low-Frequency Climate Forcing  •  Interannual Variability Climate Forcing

29.5 Summary and Conclusions .............................................................565 Authors ..........................................................................................................565 Acknowledgments ........................................................................................566 References ......................................................................................................566

Abstract  There are many meteorological indices being used to detect the climate atmospheric and oceanic forcing. Some of them are hemispheric and represent climate forcing associated with changes in atmospheric circulation, which drive rainfall anomalies in different parts of the earth. They are known as “teleconnections” and the most relevant is the El Niño–Southern Oscillation. Other indices are defined near the area to detect the possible causes of rainfall anomalies; they are closely related to the regional circulation patterns, like mountains or local winds. The challenges of a changing climate increase the need to continue working toward the development of better indicators and methods to monitor rainfall in different parts of the world. Rainfall behavior becomes important for regional economies, especially in agricultural resources and hydrological energy generation, among other activities. The aim of this chapter is to identify some of the meteorological indices that are actually being used and their development and uses in Argentina.

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29.1 Introduction Argentina is located in southeastern South America and occupies a total area of 2,791,810 km2. Because of the extensive territory, areas with different climate features can be found. It is important to distinguish the difference between circulation at low levels, east of the Andes, and north and south of 38°S. In the northern region, the Andes chain prevents the access of humidity from the Pacific Ocean; the flow is governed by the South Atlantic High, and as a consequence, winds prevail from the northeast. An intermittent low-pressure system, whose origin could be a combination of thermal and dynamical effects, is located between 20°S and 30°S in a dry and relatively high area east of the Andes in northwestern Argentina. This system is observed all year long, but it is deeper in summer than in winter. When this low is present, northerly flow is favored at low levels over the subtropical region. Therefore, the water vapor entering at low levels comes either from the tropical continent or from the Atlantic Ocean. In the first case, the easterly low-level flow at low latitudes is channeled toward the south between the Bolivian Plateau and the Brazilian Planalto, advecting warm and humid air to southern Brazil, Paraguay, Uruguay, and subtropical Argentina and depicting a typical feature that many authors have studied [7,36,52,67,68]. Often, in this flow there is an intense low-level jet that enhances humid and warm air advection [13,49,58,60] and causes significant storms. Intermittent eruptions of polar fronts from the south modify this picture, causing a west or a southwest flow in low levels after the frontal passage. This happens with more frequency and greater displacement to the north in winter than in summer. These factors determine that the precipitation regime in subtropical Argentina is characterized by maximum summer precipitation. González and Barros [16] analyzed the mean annual rainfall cycle in subtropical Argentina using a principal component analysis and showed a minimum in winter, which is more pronounced in the west, with dry conditions prevailing from May to September. They also identified a region in central Argentina where rainfall had two peaks, both in transition seasons, probably derived from both humid northern flow and fronts from the south. South of 38°S, humid air arrives from the Pacific Ocean and air mass eruptions from the polar region have trajectories over Patagonia, the southern continental portion of Argentina. The mean flow is from the west during all months in this region and an intense contrast between the dense vegetation over the western part of the Andes Mountain and the dry plain that extends toward the Atlantic Ocean is one of the most enhanced features. The storm frequency is great and erosion caused by intense winds is significant. In central Andes, south 36°S, the annual rainfall cycle reverts and maximum precipitation takes place in winter. Meanwhile, rainfall mainly decreases toward the Atlantic coast. In the dry region, the availability of drinking water is scarce and generally rivers provide the most important water supply. The river runoff mostly depends on the actual rainfall and snow accumulated in the high mountains of the Andes. Thus, it is necessary to increase the knowledge of climate variability of this region with the aim to improve the seasonal statistical forecast performance. Many authors have pointed out the difficulties still detected when forecasting seasonal climate ([6,35,51,54], to name only a few). It is argued that because of the atmosphere’s internal variability, the seasonal predictability is inherently limited and there are some papers that deal with different methodologies to detect if seasonal prediction is more accurate than the simple climatology [5,11,33] and especially in South America, an evaluation of seasonal climate forecast has been done [15,47]. The predictability of seasonal rainfall variability in subtropical South America seems to result ­primarily from the influence of remote forcing like the El Niño–Southern Oscillation (ENSO) [31,55]. The ENSO signal varies along both phases (cold and warm), and it differs between subregions [25]. Vera et al. [66] found that the difference in El Niño response over the southern hemisphere might be mainly driven by atmospheric changes, which induce extratropical sea surface temperature (SST) anomalies. Compagnucci and Vargas [12] show that winter that precedes a mature phase of El Niño (La Niña) is characterized by especially great (little) snow over the Andes. Aceituno [1] and Ruttlant and Fuenzalida [56] also noted winter precipitation greater than normal in central Chile during a negative phase of the Southern Oscillation, and Aceituno and Garreaud [2] related the volume of river water in Chile with the

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ENSO signal. Therefore, Montecinos and Aceituno [43] have detected a close relation between equatorial Pacific Ocean conditions and rainfall in central Chile depicting that a greater number of blocked systems develops during El Niño. Although the ENSO is the most important remote forcing, without a doubt, the variability originated by other regional or remote sources cannot be disregarded. The Indian Ocean is another source of oceanic forcing like the Pacific Ocean. The Atlantic Ocean SST also influences South American rainfall, and although it seems to be more limited than the Pacific and Indian signals [47], it deserves to be investigated. Moreover, the relative intensity and position of subtropical highs and subpolar lows in the surrounding oceans in South America determines different conditions that can increase or decrease normal precipitation. The major economic income in Argentina comes mainly from agricultural activities. Besides, an important part of the energy production comes from hydroelectric dams, some of them located near the Andes Mountains. Both sectors, agriculture and energy, are greatly influenced by interannual climate variability, especially by rainfall variability. Therefore, the study of climate forcings of rainfall anomalies using indices especially designed is very important for decision support. In this chapter, some climate indices in Argentina, which act as indicators of relevant signals, will be investigated.

29.2 Meteorological Indices as Climate Forcing Indicators The main factors that influence precipitation in Argentina will be described here. First, some oceanic factors related to SST anomalies in tropical oceans, like the ENSO, Indian Dipole, and some Atlantic Indices, were detailed. Second, other circulation forcings have been investigated, for example, the Southern Annular Mode (SAM) and the South American Monsoon. A brief summary of all indices used is shown in Table 29.1.

29.2.1 Indices Derived from Sea Surface Temperatures SST anomalies in tropical oceans act as remote forcing generating teleconnections. Although the ENSO is the main one, the Indian Ocean anomalies are also relevant. The SST anomalies in tropical Pacific and Indian Oceans generate Rossby wave trends, which propagate meridionally toward middle latitudes from the tropical source [30,42,50]. Mo [42] studied the southern hemispheric climate patterns and defined these waves in the Pacific as “Pacific South American Pattern.” In the Indian Ocean, the “Indian Ocean Dipole” (IOD) [57] is defined: a positive IOD phase is characterized by cooler than normal water in the tropical eastern Indian Ocean and warmer than normal water in the tropical western Indian Ocean. Saji et al. [57] also detect that this phase is associated with a rainfall decrease in central and southern Australia. In South America, the IOD influences precipitation distribution too. Chan et al. [10] showed that the IOD is also associated with a Rossby wave trend extending from the tropical Indian Ocean to the South Pacific and causes a dipolar pattern in rainfall anomalies between subtropical La Plata basin and central Brazil where rainfall is reduced (enhanced) over the latter (former) during austral spring. Liu et al. [38] explain this teleconnection using the theory of planetary waves [27]: the energy propagation path of planetary waves is approximately along the path of the Rossby wave train. The intensity of the IOD is represented by an anomalous SST gradient between the northwestern (NW) equatorial Indian Ocean (50°E–70°E; 10°S–10°N) and the southeastern (SE) equatorial Indian Ocean (90°E–110°E; 10°S–0°N). This index is positive (negative) during the positive (negative) phase of the IOD (in °C):

IOD = SSTNW - SSTSE

(29.1)

Data were obtained from Japan Agency for Marine-Earth Science and Technology (JAMSTEC) [76].

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TABLE 29.1  Definition of the Indices Used in the Study Index Name Indian Ocean Dipole (IOD)

El Niño Modoki Index (EMI)

Atlantic Multidecadal Oscillation (AMO)

Tropical Atlantic Ocean Dipole Index (TAODI)

South Atlantic Ocean Dipole Index (SAODI)

Antarctic Oscillation (AAO)

El Niño–Southern Oscillation (ENSO3.4)

Pacific Decadal Oscillation (PDO) Outgoing Longwave Radiation Index (OLRI)

Atlantic Niño (ATL)

Definition Anomalous SST gradient between the northwestern (NW) equatorial Indian Ocean (50°E–70°E; 10°S–10°N) and the southeastern (SE) equatorial Indian Ocean (90°E–110°E; 10°S–0°N): IOD = SSTNW – SSTSE Derived from the area-averaged SST anomaly over each of the regions: A (165°E–140°W, 10°S–10°N), B (110°W–70°W, 15°S–5°N), and C (125°E–145°E, 10°S–20°N): SSTA – 0.5SSTB – 0.5SSTC Defined as the difference between SST in two different regions. Region a: 0°–60°N, 0°–80°W and Region b: 60°S–60°N: SSTa − SSTb Defined as the difference between the north and south basins of the tropical Atlantic SST anomaly (SSTA) from the mean in 1960–1990. Where the north basin (NB) is the area (5°N–30°N; 60°W–15°E); the south basin (SB) is (5°N–20°S; 60°W–15°E) TAODI = (SSTANB − SSTASB)/SE Defined by differencing the domainaveraged normalized SST anomaly from the mean 1950–2008 (SSTA) of the two centers. NEP: 10°E–20°W, 0°–15°; SWP: 10°–40°W, 25°–40°S. SAODI = SSTANEP − SSTASWP Defined as the difference of sea-level pressure anomaly from the mean 1979–2000 (SLPA) in two different latitudes 70°S and 40°S: AAO = SLPA (70°S) – SLPA (40°S) SSTA [C] from Hadley Centre SST dataset HadISST1, cutting out region Lon= {−170.000; −120.000}, Let = {−5.000; 5.000}, SSTA normalized to 1971–2000 [C]. Defined as the leading PC of monthly SST anomalies in the North Pacific Ocean, poleward of 20N Defined as the OLR anomaly (OLRA) over the area of maximum variability of the mean annual OLR cycle second eigenvector (Lat: 0–15°S; Lon: 45°–75°W): OLRI = OLRA (0–15°S; 45°–75°W) Defined as the mean SST anomaly in the area (3°N–3°S; 0°O–20°O)

Period (Years)

Linear Trend (Index/Year)

Periodicities (Years)

(1958–2012)

0.00563/year

{3}

(1870–2012)

−0.0005/year

{(10–30)}

(1902–2012)

−0.00042/year

{44; 22}

(1850–2012)

−0.00385/year

{64; 32; (10–15)}

(1854–2012)

0.0058/year

{62; 31; 15}

(1979–2012)

0.00852/year

{—}

(1870–2012)

0.0145/year

{(4–6)}

(1948–2012)

−0.0017/year

{46; 23; 6}

(1979–2012)

0.0174/year

{—}

(1850–2012)

0.0095/year

{64; 32}

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The mean SST anomaly (SSTA) in the region (5°N–5°S; 170°W–120°W) from Hadley Center dataset (Had1sst1) was considered to evaluate the impact of the ENSO in this work (ENSO3.4, in °C) (Royal Netherlands Meteorological Institute, KNMI) [77]. Among the SST forcings, a special El Niño called “Modoki” [3,4] is considered. Its warm phase is characterized by positive SST anomalies in the central tropical Pacific Ocean but accompanied by cold anomalies in the eastern and western tropical Pacific. The Modoki Niño has been studied in the last years and their impacts are not the same as those generated by normal ENSO [70,71]. To quantify the Modoki Niño, [3] defined and index named the “El Niño Modoki Index” (EMI) (in °C) which is defined as

EMI = SSTA - 0.5SSTB - 0.5SSTC

(29.2)

The three terms on the right-hand side of the equation are derived from the area-averaged SSTA over each of the regions: A (165°E–140°W, 10°S–10°N), B (110°W–70°W, 15°S–5°N), and C (125°E–145°E, 10°S–20°N), respectively. The EMI index used in this study was obtained from JAMSTEC [76]. An interannual phenomenon similar although weaker than the Pacific El Niño occurs in the Atlantic Ocean. During the Atlantic Niño, the largest near-equatorial SST anomalies are in the equatorial eastern Atlantic [9,34,73]. Some authors have related this phenomenon with the ENSO and have studied some impacts in different places [26,28,48,69]. The index, which describes this climate pattern, was named ATL (in °C), defined as the mean SSTA in the area (3°N–3°S; 0°O–20°O). ATL index was calculated using SST from the Hadley Center’s dataset (HadSST2) [78]. The Pacific Decadal Oscillation (PDO) is a long-lived El Niño–like pattern of Pacific Ocean ­variability. The PDO Index (in °C) is defined as the leading principal component of monthly SST anomalies in the North Pacific Ocean, poleward of 20°N. The monthly mean global average SST anomalies are removed to separate this pattern of variability from any “global warming” signal that may be present in the data. The periodicity of the PDO is about 15–25 years and 50–70 years, and the major signals are found in North Pacific and American sectors. However, there is evidence that the PDO positive (negative) phase is related to a stronger ENSO warm (cold) phase [40,41,74]. A cold phase of PDO was observed in 1947–1976; a warm phase prevailed in 1925–1946 and 1977–1995. The cause of these anomalies is not fully understood yet and the potential predictability of the PDO is studied and monitored all over the world. PDO data used in this study were obtained from the University of Washington [79]. The interannual variability of Atlantic Ocean’s SST is an important feature to be considered. The Atlantic Multidecadal Oscillation (AMO, in °C) is a mode of variability of the SST in the North Atlantic Ocean that Schlesinger [62] first defined. The periodicity of this oscillation is 60–80 years [65]. The AMO index [64] is defined as the difference between SST in two different regions:

AMO = SSTa - SSTb

(29.3)

where Region a: 0°–60°N, 0°–80°W Region b: 60°S–60°N They proposed to subtract the global rise of SST 60°S–60°N to obtain a measure of the internal variability, arguing that the effect of external forcing on the North Atlantic should be similar to the effect on the other oceans. The variability of this oscillation has been related to precipitation in different parts of the world ([14], among others). AMO data to perform this work were obtained from KNMI [77].

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Servain [59] defined the Tropical Atlantic Ocean Dipole Index (TAODI, in °C). It is the difference between the north and south basins of tropical Atlantic SSTA from the mean in 1960–1990, considering a thermal equator in 5°N: TAODI =



SSTANB - SSTASB SE

(29.4)

where the north basin (NB) is the area (5°N–30°N; 60°W–15°E), the south basin (SB) is (5°N–20°S; 60°W–15°E), and SE is the standard deviation of the series (SSTNB − SSTSB). This oscillation has a periodicity of 10–15 years when the period 1960–1990 is used. SST data used to compute TAODI were obtained from the HadSST2 dataset [78]. The South Atlantic Ocean Dipole Index (SAODI, in °C) is defined by differencing the domain-averaged normalized SSTA from the mean 1950–2008 of the two centers [45]: SAODI = SSTANEP - SSTASWP



(29.5)

where the two regions, over which the SSTA averages are computed are located in the South Atlantic Ocean and they are defined as NEP: 10°E–20°W, 0°–15° SWP: 10°–40°W, 25°–40°S This dipole has a periodicity of about 8 months and so it can influence interannual rainfall variability. Data used in this study were obtained from the Institute of Atmospheric Physics of China [80].

29.2.2 Indices Derived from Atmospheric Circulation Patterns Hemispheric and regional circulations partly determine the intensity and location of vertical velocity and indeed rainfall areas. That is the reason why some geopotential height patterns were analyzed. The Antarctic Oscillation is a hemispheric annular-like pattern called “Southern Annular Mode” [63] and its positive phase is defined by negative pressure anomalies at high latitudes combined with a wavelike pattern at middle latitudes. SAM-positive phase increases zonal winds at high latitudes, decreases heat exchange between poles and midlatitudes, and so prevents fronts from displacing meridionally along the South Pacific toward northeastern Argentina. Meanwhile, during SAM-negative phase, zonal winds decrease, the heat exchange between latitudes is greater, and fronts can displace freer toward the north. There is an index that quantifies this mode: the Antarctic Oscillation Index (AAO, in HPa); it is constructed using the westerly wind belt that circles Antarctica, dominating the middle to higher latitudes of the southern hemisphere. The changing position of the westerly wind belt influences the strength and position of cold fronts and midlatitude storm systems, and it is an important driver of rainfall variability in South America. Nan and Li [44] defined this index as the difference of sea-level pressure anomaly from the mean 1979–2000 (SLPA) in two different latitudes, 70°S and 40°S:

AAO = SLPA ( 70°S ) - SLPA ( 40°S )

(29.6)

Data used in this work were obtained from the Climate Prediction Center [81]. This pattern is associated with rainfall in the southern hemisphere, for example, Zheng and Frederiksen [75] showed that this signal affects summer rainfall variability in the New Zealand sector, and Reason and Rouault [53] showed that wetter (drier) winters in western South Africa occur during the negative (positive) SAM phase. Some regional patterns that affect circulation are taken into account. The annual displacement of the Intertropical Convergence Zone over South America generates a poleward extension of the summer convection in the tropical Americas, large land–sea temperature contrast, a thermally direct circulation with a

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continental rising branch and an oceanic sinking branch, surface low pressure, an upper-level anticyclone, intense low-level inflow of moisture to the continent, and associated seasonal changes in precipitation. This phenomenon is called the “South American Monsoon System” [7,67]. This displacement generates a rainy season in central Brazil in austral summer and causes the entrance of humid air from the north toward subtropical Argentina. The great interannual variability of such displacement influences precipitation anomalies, especially in transition seasons. To detect this convection area, outgoing longwave radiation (OLR) was used [32]. When OLR is less than 240 W/m2, a very thick layer of cloud is present and convection is relevant. To quantify this effect, the index OLRI (in W/cm2 min) is defined as the OLR anomaly (OLRA) over the area of maximum variability of the mean annual OLR cycle second eigenvector [16]:

OLRI = OLRA ( 0 - 15°S;45° - 75°W )

(29.7)

OLRI was calculated using OLR data from the National Center of Environmental Prediction reanalysis [29].

29.3 Meteorological Indices and Rainfall Long-Term Variability Monthly rainfall data from 67 stations from the National Meteorological Service and the Sub Secretariat of Water Resource of Argentina measurement networks during the period 1961–2012 were used in this study (Figure 29.1). Missing data are completed by monthly mean and all the series have less than 10% missing data. Lund’s [39] methodology was applied to monthly rainfall data to determine homogeneous regions. Nine regions were derived using a threshold of 0.6 for the correlation coefficient. Each one of the regions was characterized by a monthly rainfall series calculated as the average of all stations included in each one of the regions. Linear trend approximation was used to evaluate the observed change in annual and seasonal rainfall time series over each region previously defined, using a linear trend method of minimum squares, and tested using a normal test of statistical significance. Figure 29.1 shows the results; only Comahue (region 5) and southern Patagonia (region 6) show negative annual rainfall trends. This fact implies that most of the territory has experienced a rainfall increase since 1961. This result agrees with Barros et al. [8] who calculated linear trends using a shorter period, ending in 1996, and with Liebmann et al. [37] who detected an increase in summer rainfall in most of southeastern South America. However, results are different in different southern hemisphere seasons (DJF, December to February, austral summer; MAM, March to May, austral autumn; JJA, June to August, austral winter; and SON, September to November, austral spring). Only in a few cases, trends were significant with 90% of confidence: in northwestern Argentina in winter (region 1) and in northeastern Argentina in spring (region 9). In eastern Argentina positive trends were observed in summer and autumn and negative trends in winter (regions 2, 3, 7, and 8). Nevertheless, in northwestern Argentina and southern Patagonia (regions 1 and 6) positive trends are detected in summer and negative trends in autumn, winter, and spring. In Mendoza province (region 4), positive trends were found in summer, autumn, and winter; meanwhile, in spring they were negative. The mean rainfall series in each region was considered to evaluate the possible cycles included in the data. A spectral analysis for annual values for the whole period detailed in the third column of Table 29.1 was ­performed using the Blackman–Tukey methodology with a Hann window and a maximum lag of 30% of the total number of years [72]. In Figure 29.2, peaks corresponding to those significant at 90% confidence level were detailed for each region. Some significant annual rainfall frequencies were detected: a 30-year peak in northwestern and central Argentina and northern Patagonia (regions 1, 2, 4, and 7), a 15-year peak in northern Patagonia and Buenos Aires (regions 7 and 8), an 8-year peak in central Argentina (region 8), a 10-year peak in Buenos Aires (region 8), and a 3–4-year peak in northern Mesopotamia (region 9). Annual linear trends in the register period for each one of the indices defined in the previous paragraph are detailed in Figure 29.3 (gray line) and in the fourth column of Table 29.1. The results indicate that trends are not significant for any one of the indices considered, except for the IOD whose linear

548

Handbook of Drought and Water Scarcity

Region 9 Annual = 5.3 DJF = 0.15 MAM = 1.14 JJA = 0.12 SON = 2.5(*)

Region 1 Annual = 0.63 DJF = 0.69 MAM = –0.18 JJA = –0.16(*) SON = –0.16

–30

Region 2 Annual = 0.29 DJF = 0.32 MAM = 0.23 JJA = –0.42 SON = 0.24

–35 Latitude

Region 4 Annual = 0.82 DJF = 0.19 MAM = 0.4 JJA = 0.2 SON = –0.02

Region 3 Annual = 1.66 DJF = 0.67 MAM = 0.45 JJA = –0.42 SON = 0.81

–40 Region 8 Annual = 1.33 DJF = 0.69 MAM = 0.32 JJA = –0.23 SON = 0.44

Region 5 Annual = –0.44 DJF = –0.05 MAM = – 0.24 JJA = –0.07 SON = –0.15

Region 6: Annual = –0.20 DJF = 0.05 MAM = – 0.07 JJA = –0.06 SON = –0.13

–70

–65 Longitude

Region 7 Annual = 0.19 DJF = 0.09 MAM = 0.05 JJA = –0.05 SON = 0.10

FIGURE 29.1  Stations used (cross marks) and regions (bounded by black lines) classified by their rainfall regime. Light grey regions have an annual positive trend while dark grey regions have an annual negative trend, in mm/ year. Trends that are depicted with (*) are significant with 90% of confidence.

trend is slightly significant (r = 0.37) with 95% confidence level. It is interesting to note that this trend value is dependent on the register length because the values of the head of the series are highly negative; meanwhile, the values in the tail are highly positive, increasing substantially the slope. Considering the available record length of data indices (in third column of Table 29.1), the significant cycles contained in them were computed (fifth column of Table 29.1). Also, a spectral analysis was applied to the series of annual indices (Figure 29.4) using the Blackman–Tuckey method [72] and a 90% confidence level (Table 29.1). Peaks of 46, 23, and 6 years were detected in the PDO series and peaks of 22 and 44 years in AMO series. TAODI annual data have significant frequencies in 64, 32, and around 10–15 years. Peaks of 64 and 32 years were detected in the ATL series. EMI has peaks around 10–30 years, ENSO3.4 around 4–6 years, and SAODI in 62, 31, and around 15 years. A peak of 3 years was detected in IOD data although slightly significant, and no significant peaks were detected in the AAO and OLRI series.

549

Meteorological Drought Indices

Spectral density: Region 1

Spectral density: Region 9

Frequency: 30 years

Frequency: 4 and 3 years

Spectral density: Region 4 Frequency: 30 years

–25

Spectral density: Region 5

–30

Spectral density: Region 3 Frequency: NSF

Frequency: NSF

Spectral density: Region 2

–35

Latitude

Frequency: 30 and 8 years

–40

Spectral density: Region 8

Spectral density: Region 6 Frequency: NSF

Frequency: 15 and 10 years

–45

Spectral density: Region 7

–50

Frequency: 30 and 15 years –55 –70

–65

–60

–55

Longitude

FIGURE 29.2  Annual rainfall spectral analysis and significant frequencies found for the mean series in each defined region, period 1961–2012 (NSF, none significant frequencies).

Some small differences in the main periodicities were encountered between these results and those described in Sections 29.2.1 and 29.2.2. The possible causes could be the different record lengths and the definitions used to identify the indices and the methodology used to elaborate the spectrum.

29.4 Relation between Meteorological Indices and Seasonal Rainfall in Argentina To study the relation between different climate forcing and seasonal rainfall, the correlation method was applied to detrended data series. Correlations between the indices that represent the forcings and accumulated rainfall for each season, DJF, MAM, JJA, and SON for the common period 1961–2012, were calculated. For this record, a correlation coefficient greater than 0.27 resulted significant with a 95% confidence level. Figures in the next paragraphs show in black (dark gray) negative (positive) areas significant with 95% confidence level. Light gray areas are not significant with 95% confidence level.

29.4.1 Low-Frequency Climate Forcing Some climate forcings have long periodicities, for example, PDO (46 and 23 years), AMO (44 and 22 years), and TAODI (64, 32, and 10–15 years). These three indices represent the variability of the North Pacific, North Atlantic, and equatorial Atlantic Oceans. In order to consider the total variability of

550 2 1 0 –1 –2 0.5

AAO

TAODI

–0.5 3 2 1 0 –1 –2 –3 1

IOD ENSO3.4

EMI

–0.5 1

SAODI

(Y = 7.804 – 0.00385*X)

(Y = –16.989 + 0.00852*X)

0 –1 0.5

OLRI

(Y = 3.345 – 0.0017*X)

(Y = 0.843 – 0.00042*X)

AMO

PDO

Handbook of Drought and Water Scarcity

(Y = –11.18 + 0.00563*X)

(Y = 0.97–5e – 04*X)

0 –1 2 1 0 –1 –2 2 1 0 –1 –2 1.5 0.5

(Y = –2.867 + 0.00145*X)

(Y = –1.127 + 0.00058*X)

(Y = –34.721 + 0.0174*X)

–0.5 (Y = –18.25 + 0.00945*X)

1850 1852 1854 1856 1858 1860 1862 1864 1866 1868 1870 1872 1874 1876 1878 1880 1882 1884 1886 1888 1890 1892 1894 1896 1898 1900 1902 1904 1906 1908 1910 1912 1914 1916 1918 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

ATL

–1.5 2 1 0 –1 –2

FIGURE 29.3  Annual linear trend calculated for indices for the maximum record available detailed in Table 29.1. Gray lines are the linear trend adjustment.

them, a new index was defined to evaluate the total contribution. The partial contribution of normalized PDO (PDON), AMO (AMON), and TAODI (TAODIN) is shown in Figure 29.5. The total contribution of all of them is represented by the sum of the three normalized indices, called LF, which is shown in Figure 29.5. LF (in °C) is indeed defined as

LF = PDON + AMON + TAODIN

(29.8)

551

Meteorological Drought Indices

Spectral density (PDO)

0.2 0.3 Frequency

0.4

Log (S)

3

0

0.1

0.2 0.3 Frequency

0.4

Spectral density (ENSO3.4)

8

6 5

6 2 0

0

0.1

0.2

0.3

0.4

0

0.1

4

0

0.1

6 4

Log (S)

Log (S)

2 0.2 0.3 Frequency

0.5

Spectral density (SAODI)

2 0

0.1

0.2

0.3

0.4

0.5

0.4

0.5

6

0.4

0.5

Spectral density (ATL) 64

8

4

0.1

0.2 0.3 Frequency

32

Spectral density (OLRI)

0

0.4

2

Frequency

6

0

0.5

Spectral density (EMI)

Frequency 8

0.2 0.3 Frequency

6

0

0.5

0.4

2

8

4

0.5

4

0

0.5

0.4

Spectral density (AAO)

8

2

0.2 0.3 Frequency

6

0

0.5

Spectral density (IOD)

4

0.1

2

Log (S) 0.1

Log (S)

Log (S)

64 32 16 13 11

0

0

8

6

0

0

0.5

2

8 Log (S)

0.4

4 0

Log (S)

0.2 0.3 Frequency

Spectral density (TAODI)

8 6

0.1

28 19 14 11 9 8

0

2

62 31 21 16 12 10

0

4

44

Log (S)

6

4 2

6 22

46 23

6

Spectral density (AMO)

8

4 4

Log (S)

8

4 2 0

0

0.1

0.2 0.3 Frequency

FIGURE 29.4  Indices spectral analysis for the maximum record available detailed in Table 29.1. Significant peaks (90% confidence level) are labeled. Dark gray lines indicate a 90% confidence level.

552

amoN

3 2 1 0 –1 –2 –3

taodiN

3 2 1 0 –1 –2 –3 5 4 3 2 1 0 –1 –2 –3 –4 –5

(Y = 3.206 – 0.00164*X)

(Y = 5.006 – 0.00256*X)

(Y = 6.902 – 0.00358*X)

(Y = 15.18 – 0.00781*X)

1900 1902 1904 1906 1908 1910 1912 1914 1916 1918 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

pdoN

3 2 1 0 –1 –2 –3

LF

Handbook of Drought and Water Scarcity

FIGURE 29.5  Evolution of the partial contribution of standardized PDO, AMO, and TAODI and the total contribution of them all (LF) for the period 1900–2012. Gray lines are the linear trend adjustment.

The spectral analysis of the annual values of LF (Figure 29.6) shows three frequency peaks: 44, 22, and 15 years. They were significant with 90% confidence level. Seasonal correlation between PDO and rainfall (Figure 29.7) shows that precipitation in spring (SON) increases in the central part of Argentina when PDO negative phase is present and in the north and south when the positive phase develops. PDO has largely remained negative from mid-2007 collaborating to increase rainfall in central Argentina. This pattern is hinted in winter, decreases in summer, and reverses in autumn when correlations are mainly positive, showing areas with significant correlations (95% confidence level) in northern Patagonia and central Mesopotamia. Figure 29.8 is the correlation field between AMO and precipitation. Results indicate that rainfall decreases in all seasons with AMO positive phase, as it has been noticed from 2011. Areas with significant correlations are greater in winter and spring than in summer and autumn. When TAODI was considered, significant correlations were localized only in small areas, for example, in central Atlantic coast in autumn and in central-eastern Argentina in winter (Figure 29.9). The long periodicities associated with these indices imply that rainfall interannual variability is little affected by these forcings. However, it is important to point out that when other forcings of interannual variability are absent or have a small signal, the way that low-frequency forcings affect rainfall becomes more relevant. For example, the result is different if a positive rainfall anomaly is produced in a period when all low-frequency forcings contribute to increase rainfall or if it develops in other periods when all of them contribute to decreased precipitation. Therefore, the monitoring of these low-frequency forcings becomes relevant when other higher-frequency forcings have no signal. To summarize the influence of low-frequency variability on precipitation, the correlation between LF and seasonal rainfall was calculated (Figure 29.10). Figure 29.10 shows that rainfall is favored by the negative phase of LF in spring especially in central-west Argentina; meanwhile the signal is localized in small

553

Meteorological Drought Indices Spectral density (LF)

22

44

8

Log (S)

15

7

6

5

4 0

0.1

0.2

0.3

0.4

0.5

Frequency

FIGURE 29.6  LF annual values spectral analysis for the period 1900–2012. Significant peaks (90% confidence level) are labeled. Dark gray line indicates 90% confidence level.

regions in other seasons. For example, the positive LF phase favored summer rainfall in the Comahue region and winter rainfall in the central and southern Andes and autumn rainfall in northeastern Patagonia.

29.4.2 Interannual Variability Climate Forcing Climate’s higher-frequency forcing influences the interannual rainfall variability. This shorter variability forcing acts in combination with the low-frequency periodicities detailed in the previous paragraph. Hereinafter, the most important high-frequency climate forcings will be detailed. Figure 29.11 shows the correlation between ENSO3.4 and seasonal rainfall. It shows a tendency to increase rainfall in central and eastern (northwestern) Argentina when the ENSO warm (cold) phase is present almost the whole the year. However, the areas with significant correlation are localized in northeastern Argentina and the southern Andes, especially in spring and with less signal in autumn; meanwhile, the signal is present in southeastern Argentina in winter. When Modoki Niños were considered, the correlation between EMI and seasonal precipitation (Figure 29.12) shows a relevant relation only in spring in northeastern Argentina and the southern Andes. Therefore, Vera et al. [66] have detected differences in El Niño response in the southern hemisphere. Figure 29.13 shows the correlation field between IOD and seasonal rainfall. The results indicated that there is a significant signal only in spring. Rainfall increases in a northeastern–central–s­outhwesternly direction, when the positive phase of IOD is present. González and Vera [18], González et al. [19], and González and Dominguez [20] detected the same important signal studying seasonal rainfall predictors over the Comahue region for winter rainfall and also González et al. [21,22] and González and Murgida [23] analyzing summer rainfall in the eastern Chaco region. SAODI does not seem to influence precipitation significantly (Figure 29.14) except in spring when a negative phase of SAODI induces a rainfall increase in central-eastern Argentina. In fact, this dipole determines regional circulation that influences humidity advection and determines air ascent, which modify rainfall. The negative phase of SAODI implies a warm SST in the southwestern part of the dipole, increasing the warm humid air that enters South America from the Atlantic Ocean through the South Atlantic High. Nnamchi et al. [45] have detected the influence on western Africa summer rainfall, and González and Rolla [24] have studied this relation in Buenos Aires province (Argentina) especially

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Handbook of Drought and Water Scarcity

PDO

DJF

–25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.7  Correlation between PDO and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

555

Meteorological Drought Indices

DJF –25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

AMO

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.8  Correlation between AMO and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

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Handbook of Drought and Water Scarcity

TAODI

DJF –25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

–25

–25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

JJA

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.9  Correlation between TAODI and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

557

Meteorological Drought Indices

DJF

LF

MAM

–25

–25

Latitude

–35 –40 –45 –50 –55

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.10  Correlation between LF and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

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Handbook of Drought and Water Scarcity

DJF

ENSO3.4 –25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.11  Correlation between ENSO3.4 and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

559

Meteorological Drought Indices

DJF

EMI

–25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.12  Correlation between EMI and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

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Handbook of Drought and Water Scarcity

DJF

IOD

–25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–35 –40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.13  Correlation between IOD and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

561

Meteorological Drought Indices

DJF

SAODI

–25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.14  Correlation between SAODI and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

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Handbook of Drought and Water Scarcity DJF

ATL

–25

–25

Latitude

–35 –40 –45 –50

–70

–65

–60

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

JJA

–55

–25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–60

SON

–25

–55

–65

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.15  Correlation between ATL and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

in winter and spring rainfall. The influence of SST over rainfall has been detected in other parts of the world like the Persian Gulf [46]. The correlation field between seasonal rainfall and ATL (Figure 29.15) shows that negative ATL values (SST in the Atlantic Ocean colder than normal) are associated with rainfall greater than normal in almost the whole of Argentina in autumn, winter, and spring. Significant correlations (95%) were

563

Meteorological Drought Indices DJF

AAO –25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

JJA –25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–55

SON

–25

–55

–65 –60 Longitude

–40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.16  Correlation between AAO and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

detected in a northwestern–central–eastern fringe, which is visualized in summer and autumn and enhances in winter and spring. The relation between SAM and rainfall can be explained when the correlation between AAO and ­seasonal precipitation is considered (Figure 29.16). There is a tendency for a rainfall increase during the negative (positive) phase of AAO in northeastern Argentina and southern Andes (central Argentina)

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in transition seasons. When the negative phase of AAO is present, zonal winds get weak, the exchange between latitudes increases, and fronts can freely displace toward the continent. Areas with significant correlation reduce substantially in summer and winter. Previous papers have shown SAM influence on rainfall variability in some regions of South America. For example, Silvestri and Vera [61] found a significant relation between them in southeastern South America particularly during November and DJF

OLRI

–25

–25

Latitude

–35 –40 –45 –50

–70

–65 –60 Longitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30 –35 Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

–55

MAM

–40 –45 –50 –55

–55

–70

–55

–25

–25

–35 –40 –45 –50

–70

–65 –60 Longitude

–55

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9

–30

Latitude

–60

SON

JJA

–55

–65

Longitude

–35 –40 –45 –50 –55

–70

–65 –60 Longitude

–55

FIGURE 29.17  Correlation between OLRI and seasonal rainfall anomalies. Shaded (not shaded) areas are negative (positive). Values greater than 0,3 are significant with 95% confidence level.

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December; Reboita et al. [52] detected a decrease of frontal activity when the positive phase of SAM is present. In other regions of the southern hemisphere, some authors have detected some relations between rainfall and SAM too. González and Vera [18] and González et al. [19] detected a close relation between SAM and winter rainfall in the Comahue region and González et al. [22] encountered a relevant influence of SAM from October to April rainfall in the Chaco plains in subtropical Argentina. To evaluate the influence of the South American Monsoon over precipitation, the correlation field between OLRI and seasonal rainfall was calculated (Figure 29.17). When OLRI is negative (positive), it implies that convection is greater (lower) than normal. Figure 29.17 shows that spring and winter rainfall is greater than normal in central Argentina when convection is reinforced in central Brazil (OLRI negative) and autumn rainfall is greater than normal in the eastern coast of Argentina when convection is lower than normal. González and Barros [16,17] have explored the relation between the interannual variability of the austral South American Monsoon onset date and the interannual variability of spring rainfall in subtropical South America. They found that rainfall in transition seasons is affected by convection in central Brazil. They also detailed that an early (delayed) onset is associated with decreased (enhanced) rainfall only in southern Brazil, while in Argentina and Uruguay the signal is opposite.

29.5 Summary and Conclusions The relation of some indices, which represent the climate atmospheric and oceanic forcings, with the seasonal rainfall was investigated. The analysis of rainfall trend during 1961–2012 indicated that changes have not been significant in Argentina and only in the area of Comahue and southern Patagonia rainfall was decreasing. There were significant rainfall cycles detected, in particular, a 30-year peak in northwestern and central Argentina and northern Patagonia, a 15-year peak in northern Patagonia and Buenos Aires, an 8-year peak in central Argentina, a 10-year peak in Buenos Aires, and a 3–4-year peak in northern Mesopotamia. The PDO, AMO, and TAODI (and LF as the total contribution of the three forcings) are low-­frequency forcings, which become relevant whenever other forcings of interannual variability (like ENSO or IOD) are absent or have a small signal. The evolution of LF shows that this compound index has three main periodicities: 44, 22, and 15 years. Some of other forcings are related to interannual rainfall variability. Although the relationships depend on the season and the area, the most relevant signal was found for spring rainfall. Spring rainfall in northeastern Argentina and western Patagonia is especially favored by the warm phase of the ENSO, the positive phase of IOD, the negative phase of SAODI, the negative phase of AAO, and increased convection in Brazilian forest.

Authors Marcela H. González joined the University of Buenos Aires in 1988 and the National Scientific and Technical Research Council in 2003. She worked as a regional climatologist in research and education. She is a professor in the Department of Atmospheric Science and Oceans at the University of Buenos Aires. She is an independent researcher at the Center of Investigations of Sea and Atmosphere (CIMA-CONICET/UBA). Her main investigations deal with statistical forecast of seasonal rainfall in Argentina. Marcela participates with other researchers in the production of the seasonal rainfall and temperature predictions for Argentina. Eugenia M. Garbarini studies atmospheric sciences at the University of Buenos Aires since 2010. She has been working with Marcela H. Gonzalez since 2013 and is currently investigating how climate forcing could influence seasonal precipitation in different regions of Argentina as her thesis in order to obtain the atmospheric sciences degree.

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Alfredo L. Rolla is a member of the National Scientific and Technical Research Council (CONICET) at the Center of Investigations of Sea and Atmosphere and UMI-IFAECI/CNRS. He is an expert in computer sciences. His current research areas of interest are the statistical forecast of seasonal precipitation, application of statistical methods to quantifying and dealing with uncertainty in meteorological and climate data and forecasts, crop models, and development of decision support systems. Saeid Eslamian is a full professor of hydrology and water resources engineering in the Department of Water Engineering at Isfahan University of Technology, Iran, where he has been since 1995. He received his PhD from the University of New South Wales, Australia, under the supervision of Professor David Pilgrim. His research focuses mainly on water resources planning and management and statistical hydrology in a changing climate. In recent years, he has been working on modeling water reuse, climate change and variability, IWRM, sustainable agriculture, resilience and vulnerability research, and natural resources governance and management. Formerly, he was a visiting professor at Princeton University, New Jersey, and the University of ETH Zurich, Switzerland. On the research side, he has started a research partnership from 2014 with McGill University, Canada. He has contributed to many publications, including technical reports, in journals and books. He is the founder and chief editor of both the International Journal of Hydrology Science and Technology (Scopus, Inderscience) and the Journal of Flood Engineering. His professional experience includes being on the editorial boards and reviewer of about 40 Web of Science (ISI) journals. He has authored more than 100 book chapters and books. Recently, he has started the editorship of several handbooks published by Taylor & Francis Group (CRC Press). A three-volume Handbook of Engineering Hydrology in 2014, Urban Water Reuse Handbook in 2015, a three-volume Handbook of Drought and Water Scarcity (2017), and Underground Aqueducts Handbook (2017) are published ones.

Acknowledgments To the National Meteorological Service of Argentina for the provision of rainfall data and the financial support provided by UBACyT 2013–2016 20620120100003BA, UBACyT 2014–2017 20020130100133BA.

References

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10. Chan, S., Behera, S. K., and Yamagata, T. 2008. Indian Ocean dipole influence on South American rainfall, Geophysical Research Letters, 35: L14S12. 11. Coelho, C., Stephenson, D., Balmaseda, M., Doblas Reyes, F., and Oldenborge, G. 2005. Towards an integrated seasonal forecasting system for South America, Journal of Climate, 19: 3704–3721. 12. Compagnucci, R. and Vargas, W. 1998. Inter-annual variability of the Cuyo river streamflow in the Argentinean Andean Mountains and ENSO events, International Journal of Climatology, 18: 1593–1609. 13. Douglas, M., Nicolini, M., and Saulo, C. 1998. Observational evidences of a low level jet east of the Andes during January–March 1998, Meteorologica, 23: 63–72. 14. Enfield, D. B., Mestas-Nunez, A. M., and Trimble, P. J. 2001. The Atlantic Multidecadal Oscillation and its relationship to rainfall and river flows in the continental U.S., Geophysical Research Letters, 28: 2077–2080. 15. Goddard, L., Barnston, A., and Mason, S. 2003. Evaluation of the IRI’s “net assessment” seasonal climate forecasts 1997–2001, Bulletin of the American Meteorological Society, 84(12): 1761–1781. 16. González, M. H. and Barros, V. 1998. The relation between tropical convection in South America and the end of the dry period in subtropical Argentina, International Journal of Climatology, 18(15): 1669–1685. 17. González, M. H. and Barros, V. 2002. On the forecast of the onset and end of convective season in the Amazon, Theoretical and Applied Climatology, 73(3–4): 169–188. 18. González, M. H. and Vera, C. S. 2010. On the interannual winter rainfall variability in Southern Andes, International Journal of Climatology, 30: 643–657 19. González, M. H., Skansi, M. M., and Losano, F. 2010. A statistical study of seasonal winter rainfall prediction in the Comahue region (Argentine), Atmosfera, 23(3): 277–294. 20. González, M. H. and Dominguez, D. 2012. Statistical prediction of wet and dry periods in the Comahue Region (Argentina), Atmospheric and Climate Sciences, 2(1): 23–31. 21. Gonzalez, M. H., Cariaga, M. L., and Skansy, M. M. 2012. Some factors that influence precipitation in Argentinean Chaco, Advances in Meteorology, 2012: Article ID 359164, Tang, Y., An, S.-I., and Duan, W., eds., Hindawi Publishing Corporation. 22. González, M. H., Dominguez, D., and Nuñez, M. 2012. Long term and interannual rainfall variability in Argentinean Chaco plain region, in: Martín, O. E. and Roberts, T. M., eds., Rainfall: Behavior, Forecasting and Distribution, Nova Science Publishers Inc., New York, pp. 68–89 (Chapter 4). 23. González, M. H. and Murgida, A. M. 2012. Seasonal summer rainfall prediction in Bermejo River Basin in Argentina, in: Hannachi, A., ed., Climate Variability—Some Aspects, Challenges and Prospects, INTech, Rijeka, Croatia, pp. 141–160 (Chapter 7). 24. González, M. H. and Rolla, A. L. 2014. Ocean and atmospheric forcing for interannual rainfall variability in Argentinean Buenos Aires Region, WCRP-Conference for Latin America and the Caribbean, Developing, Linking, and Applying Climate Knowledge, Montevideo, Uruguay. 25. Grimm, A., Barros, V., and Doyle, M. 2000. Climate variability in Southern South America associated with El Niño and La Niña events, Journal of Climate, 13: 35–58. 26. Gu, G. 2010. Summer time rainfall variability in tropical Atlantic, in: Simard, S. and Austin, M., eds., Climate Change and Variability, SCIYO, Rijeka, Croatia (Chapter 3). 27. Hoskins, B. J. and Karoly, D. J. 1981. The steady linear response of a spherical atmosphere to thermal and orographic forcing, Journal of the Atmospheric Sciences, 38: 1179–1196. 28. Hu, Z. and Huang, B. 2007. Physical processes associated with the tropical Atlantic SST gradient during the anomalous evolution in the southeastern Ocean, Journal of Climate, 20: 3366–3378. 29. Kalnay, E. et al. 1996. The NCEP/NCAR reanalysis 40 years-project, Bulletin of the American Meteorological Society, 77: 437–471. 30. Kidson, J. 1999. Principal modes of southern hemisphere low frequency variability obtained from NCEP-NCAR reanalyses, Journal of Climate, 1: 1177–1198.

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31. Kiladis, G. and Diaz, H. 1989. Global Climatic Anomalies associated with extremes in the Southern Oscillation, Journal of Climate, 2: 1069–1090. 32. Kousky, V. E. 1988. Pentad outgoing longwave radiation climatology for the South America sector, Revista Brasilera de Meteorología, 3: 217–231. 33. Kumar, A. 2006. On the interpretation and utility of skill information for seasonal climate predictions, Monthly Weather Review, 135: 1974–1984. 34. Latif, M. and Grotzner, A. 2000. The equatorial Atlantic oscillation and its response to ENSO, Climate Dynamics, 16: 213–218. 35. Leetmaa, A. 2003. Seasonal forecasting, innovation in practice and institutions, Bulletin of the American Meteorological Society, 84: 1686–1691. 36. Lenters, J. D. and Cook, K. H. 1997. On the origin of Bolivian High and related circulation feature of the South American Climate, Journal of the Atmospheric Sciences, 54: 656–677. 37. Liebmann, B., Vera C. S., Carvalho, L., Camilloni, I., Hoerling, M., Allured, D., Barros, V., Báez, J., and Bidegain, M. 2004. An observed trend in Central South American precipitation, Journal of Climate, 17(22): 4357–4367. 38. Liu, N., Chen, H., and Lu, L. 2007. Teleconnection of IOD signal in the upper troposphere over southern high latitudes, Journal of Oceanography, 63: 155–157. 39. Lund, I. A. 1963. Map pattern classification by statistical methods, Journal of Applied Meteorology, 2: 56–65. 40. Mantua, N. J., Hare, S. R., Zhang, Y., Wallace, J. M., and Francis, R. C. 1997. A Pacific interdecadal climate oscillation with impacts on salmon production, Bulletin of the American Meteorological Society, 78: 1069–1079. 41. Minobe, S. 1997. A 50–70 year climatic oscillation over North Pacific and North America, Geophysical Research Letters, 24: 683–686. 42. Mo, K. C. 2000. Relationships between low frequency variability in the Southern Hemisphere and sea surface temperature anomalies, Journal of Climate, 13: 3599–3610. 43. Montecinos, A. and Aceituno, P. 2003. Seasonality of the ENSO related rainfall variability in Central Chile and associated circulation anomalies, Journal of Climate, 16: 281–296. 44. Nan, S. and Li, J. 2003. The relationship between summer precipitation in the Yangtse River Valley and the previous Southern hemisphere Annular Mode, Geophysical Research Letters, 30(24): 2266. 45. Nnamchi, H. C., Li, J., and Anyadike, R. 2011. Does a dipole mode really exist in the South Atlantic Ocean? Journal of Geophysical Research: Atmospheres, 116 (D15). doi: 10.1029/2010JD015579. 46. Nazemosadat, M. J., Cordery, I., and Eslamian, S. S. 1995. The impact of Persian Gulf Sea surface temperatures on Iranian rainfall, Regional Conference on Water Resources Managements, Isfahan University of Technology, Isfahan, Iran, pp. 809–918. 47. Nobre, C., Marengo, J., Cavalcanti, I., Obregon, G., Barros, V., Camilloni, I., Campos, N., and Ferreira, A. 2005. Seasonal to decadal predictability and prediction of South America Climate, Journal of Climate, 19(23): 5988–6004. 48. Okumura, Y. and Xie, S. P. 2006. Some overlooked features of tropical Atlantic climate leading to a new Niño like phenomenon, Journal of Climate, 19: 5859–5874. 49. Paegle, J. 2000. American low level jets in observation and theory: The All project, Preprint Sixth International Conference on Southern Hemisphere Meteorology and Oceanography, Santiago, Chile, pp. 161–162. 50. Paegle, J. and Mo, K. C. 2002. Linkages between summer rainfall variability over South America and sea surface temperature anomalies, Journal of Climate, 15: 1389–1407. 51. Quan, X., Hoerling, M., Whitaker, J., Bates, G., and Xu, T. 2006. Diagnosing source of US Seasonal forecast skill, Journal of Climate, 19: 3279–3293.

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75. Zheng, X. and Frederiksen, C. 2006. A study of predictable patterns for seasonal forecasting of New Zealand rainfall, Journal of Climate, 19: 3320–3333. 76. http://www.jamstec.go.jp/frcgc/research/d1/iod/e/iod/dipole_mode_index.html. 77. http://climexp.knmi.nl/data/ihadisst1_nino3.4a.dat. 78. http://www.metoffice.gov.uk/hadobs/hadsst2/. 79. http://jisao.washington.edu/pdo/. 80. http://ljp.lasg.ac.cn/dct/page/65592. 81. http://www.cpc.ncep.noaa.gov/products/precip/CWlink/.

30 Modeling Hydrological Process by ARIMA– GARCH Time Series 30.1 Introduction ......................................................................................572 30.2 Time Series Models ..........................................................................572 ARMA-Type Models • ARIMA Models • ARFIMA Model  •  GARCH Model  •  ARIMA Models in Presence of ARCH/ GARCH Effect (ARIMA–GARCH Model)

30.3 Model Identification, Parameter Estimation, Model Adequacy, Forecasting, and Model Selection ............................... 575

Reza Hadizadeh Statistical Center of Iran

Saeid Eslamian Isfahan University of Technology

Model Identification  •  Estimation of Model Parameters  •  Model Adequacy  •  Forecasting and Model Selection

30.4 Case Study ..........................................................................................577 Data Preparation  •  Results and Modeling

30.5 Summary and Conclusions .............................................................584 Authors ..........................................................................................................587 References ......................................................................................................587

Abstract  Nowadays, time series analysis is widely used in many branches of engineering, physical science, and economics, and it can be said that most branches of science lead to the study of data that are in the form of time series. A time series is a collection of statistical data collected regularly at certain time intervals. Time series analysis is a process through which the collected data is statistically analyzed. Time series analysis usually follows two purposes: first, understanding or modeling the random mechanism that leads to the observed series and second, forecasting future values of series takes place on the basis of its past. Important characteristic of stochasticity of the hydrological phenomena has led the hydrologists to utilize the concepts of random variables and time series for modeling and forecasting hydrological variables. Application of time series in modeling of hydrological processes started four decades ago and reached its peak with Box and Jenkins models (ARMA- and ARIMA-type models). These models had been known as the linear time series models and not suitable for modeling nonlinear mechanisms. The ARCH and GARCH models are nonlinear time series models. Box and Jenkins models are used to combine different models to obtain new models with better performance. The ARIMA–GARCH models are a combinational model, which consist of two parts. The part of ARIMA models forecasts the mean of process and the part of GARCH models forecasts the variance of process in the time series. 571

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30.1 Introduction Various methods of time series analysis are commonly used for forecasting hydrological factors. Time series modeling is one of the data-driven methods that can be displayed in the form of a mathematical model. Modeling the hydrological processes is usually difficult as there are too many factors involved. The important point here is that the obtained results of the modeling to be consistent with all factors. So for planning and especially exploitation of water sources, it is needed to forecast the hydrological factors with due attention to the previous collated data in the form of time and local series. Time series modeling with the intention of data production and hydrological variable forecasting is an important step in planning and analysis of water sources sensitiveness [28]. In the past, specific models were being applied for time series modeling; these models had been known as the standard model of autoregressive–­moving average (ARMA) time series [44]. However, these linear models are not always suitable for hydrological processes as these processes are inherently dynamic and nonlinear. If the purpose of time series analysis is ­forecasting, determining the linearity or nonlinearity will not be sufficient, but if the process is ­nonlinear, an appropriate model is required [17]. The ARMA-type models, either stationary such as autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and seasonal ARMA (SARMA) models or nonstationary such as autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA), are linear models and short-memory time series which have already been used in many research studies to forecast the hydrological variables [3,10,11,13,15,16,18,19,21,29,33,35,36,38,41]. Another kind of time series models are long-memory models that are similar to linear short-memory model and shown by AutoRegressive Fractional Integrated Moving Average (ARFIMA) (p, d, q). Burlando et al. [7], Montanari et al. [25], Pelletier and Turcotte [31], Rao and Bhattacharya [32], Ooms and Franses [30], Mudelsee [26], Yusof et al. [43], Hadizadeh et al. [12], and Yang and Bowling [40] have used this model for modeling. In addition to linear models, since streamflow processes in short time scales have been accepted as nonlinear processes, some of the nonlinear models such as threshold AR have been used to forecast [2,37]. Another kind of nonlinear time series, which is originated from econometric, is autoregressive conditional heteroscedasticity model (ARCH-type model) that in contrary to linear model does not have equality of variance assumption (homoscedasticity). Primarily, Engle [9] presented the ARCH-type time series model. This model had some limitations that are removed by promoting generalized ARCH (GARCH) by Bollerslev [4]. These models, used for variance forecasting, have been broadly employed in recent years along with ARMA* linear models to forecast the hydrological variables. The ARMA part is used to forecast the average and the ARCH part to forecast the variance of hydrological process. These models are shown as ARMA–GARCH that many researchers such as Wang et al. [38], Elek and Markus [8], Yusof and Kane [42], and Modarres and Ouarda [22–24] have used it for forecasting.

30.2 Time Series Models 30.2.1 A RMA-Type Models The ARMA-type models include stationary models such as AR, MA, ARMA, and SARMA. The general form of ARMA (p, q) time series model is given by

f p ( B ) xt = qq ( B ) et

where B is the backward operator (βxt = xt − 1) ϕ(B) and θ(B) are the AR component with p order and MA with q order, respectively * AutoRegressive Moving Average.

(30.1)

Modeling Hydrological Process by ARIMA–GARCH Time Series

573

If p = 0, then ARMA (0, q) model reduces to MA(q) model, and if q = 0, then it reduces to AR(p) model. The εt is a white noise with zero mean and σ 2 variance. If time series process has a seasonal structure represented by SARMA(p, q) × (P, Q), the general form of seasonal time series is given by

( )

( )

f p ( B ) F P B s xt = qq ( B ) QQ B s et



(30.2)



where ϕ(B) and θ(B) are the same as AR and MA deseasonal components mentioned earlier. The Φ(Bs) and Θ(Bs) are seasonal AR with P order and seasonal MA with Q order, respectively.

30.2.2 ARIMA* Models The ARIMA models are a nonstationary kind of the ARMA-type models that are converted with differencing to a stationary model. The general form of the ARIMA models is similar to the ARMA model with differencing parameter that is denoted by ARIMA (p, d, q) and the following equation: f p ( B ) Ñd xt = qq ( B ) et



(30.3)

where ϕ(B) and θ(B) are the same as mentioned earlier. The parameter (d) is a differencing parameter that if d = 0, then the ARIMA model reduces to the ARMA model. If the ARIMA processes have a seasonal structure, then they are modeled by SARIMA(p, d, q)  ×​ (P, D, Q) model that has the following general form:

( )

( )

f p ( B ) F P B s Ñd Ñ Ds xt = qq ( B ) QQ B s et



(30.4)

And also the parameters of SARIMA model, namely, ϕ(B) , θ(B) , d , Φ(Bs), and Θ(Bs), are the same as mentioned earlier. The parameter D is a seasonal differencing parameter.

30.2.3 ARFIMA† Model The ARMA-type models are known as short-memory models. But there is another kind of time series models that are known as long-memory models. Long-memory, or long-range dependence, refers to a non-negligible dependence between distance observations in a time series. There are methods for identifying the existence of long memory and estimating the fractional differencing parameter d. These techniques include graphical methods (e.g., autocorrelation function [ACF] analysis, classic rescaled adjusted range analysis [R/S analysis], aggregated variance method, and detrended fluctuation analysis), semiparametric methods (e.g., Lo’s modified R/S test and Geweke and Porter-Hudak (GPH) test), and parametric methods (maximum likelihood estimation of the fractional differencing parameter d and Whittle’s estimator [W-MLE]). The ARFIMA (p, d, q) time series model is given by

f p (b ) Ñd xt = qq (b ) et , d < 0.5

* AutoRegressive Integrated Moving Average. † AutoRegressive Fractional Integrated Moving Average.

(30.5)

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where ϕp(β) = (1 − ϕ1 B −  ⋯  − ϕpBp)(n ! /r ! (n − r)!) and θq(β) = (1 − θ1 B −  ⋯  − θqBq) are the AR and MA ­components, respectively. ∇ = 1 − B is a difference operator and ∇d = (1 − B)d can be presented in terms of a binomial expansion, Ñd = (1 - B ) = d

pj =

å

¥

j =0

G( j - d)

p j B j , where

G ( j + 1) G ( -d )

=

k -1- d , j = 0,1, 2,¼ k 0£k £ j

Õ

30.2.4 GARCH* Model GARCH models are the statistical methods that are used especially in economic time series. Let {εt} be a real-valued discrete-time stochastic process and ψt the set of all information available at time t. The GARCH (p, q) process is given by et | yt -1 ~ N ( 0,st ) p

åf s + åq e

; c0 > 0, fi ³ 0, q j ³ 0, i = 1, 2,¼, p, j = 1, 2,¼, q

= c0 + A ( L ) et2 + B ( L ) st2



st2 = c0 +

i

i =1



q

2 t -1

2 i t -1

i =1

(30.6)

where q is the degree of the ARCH process and p is the degree of the GARCH process, while the degrees p and q are often identified by means of the ACF and a partial autocorrelation function (PACF) of the square of residuals. If p = 0, the process reduces to ARCH (q) and for p = q = 0 is simply the white noise. An ordinary ARCH model is a special case of a GARCH specification in which there are no lagged forecast variances in the conditional variance equation. In the ARCH (q) process, the conditional variance is specified as a linear function of the past squared observations only, whereas the GARCH (p, q) process allows lagged conditional variance to enter as well. The most widespread model is GARCH (1, 1). It is the simplest and most robust of the family of volatility models. Bollerslev [4] argued that a simple GARCH model provides a marginally better fit and a more possible learning mechanism than the ARCH model. The GARCH (1, 1) process is given by et | yt -1 ~ N ( 0,st )

st2 = var ( et |yt -1 ) = st2 = c0 + f1st2-1 + q1et2-1

(30.7)

As the variance is expected to be positive, we expect that α0 > 0 , ϕ1 ≥ 0 , θ1 ≥ 0, while the stationary of the variance is conserved, if ϕ1 + θ1