Advances In Geosciences (A 4-volume Set) - Volume 29: Hydrological Science (Hs) : Hydrological Science (HS) 9789814405713, 9789814405706

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A d v a n c e s

i n

Geosciences Volume 29: Hydrological Science (HS)

8474hc.v29.9789814405706-tp.indd 1

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ADVANCES IN GEOSCIENCES Editor-in-Chief: Kenji Satake (University of Tokyo, Japan) A 5-Volume Set Volume 1: Solid Earth (SE) ISBN-10 981-256-985-5

A 6-Volume Set

Volume 2: Solar Terrestrial (ST) ISBN-10 981-256-984-7

Volume 17: Hydrological Science (HS) ISBN 978-981-283-811-7

Volume 3: Planetary Science (PS) ISBN-10 981-256-983-9

Volume 18: Ocean Science (OS) ISBN 978-981-283-813-1

Volume 4: Hydrological Science (HS) ISBN-10 981-256-982-0

Volume 19: Planetary Science (PS) ISBN 978-981-283-815-5

Volume 5: Oceans and Atmospheres (OA) ISBN-10 981-256-981-2

Volume 20: Solid Earth (SE) ISBN 978-981-283-817-9

A 4-Volume Set

Volume 21: Solar Terrestrial (ST) ISBN 978-981-283-819-3

Volume 6: Hydrological Science (HS) ISBN 978-981-270-985-1

Volume 16: Atmospheric Science (AS) ISBN 978-981-283-809-4

Volume 7: Planetary Science (PS) ISBN 978-981-270-986-8

A 6-Volume Set Volume 22: Atmospheric Science (AS) ISBN 978-981-4355-30-8

Volume 8: Solar Terrestrial (ST) ISBN 978-981-270-987-5

Volume 23: Hydrological Science (HS) ISBN 978-981-4355-32-2

Volume 9: Solid Earth (SE), Ocean Science (OS) Volume 24: & Atmospheric Science (AS) ISBN 978-981-270-988-2 Volume 25: A 6-Volume Set Volume 10: Atmospheric Science (AS) Volume 26: ISBN 978-981-283-611-3

Ocean Science (OS) ISBN 978-981-4355-34-6 Planetary Science (PS) ISBN 978-981-4355-36-0 Solid Earth (SE) ISBN 978-981-4355-38-4

Volume 11: Hydrological Science (HS) ISBN 978-981-283-613-7

Volume 27: Solar Terrestrial (ST) ISBN 978-981-4355-40-7

Volume 12: Ocean Science (OS) ISBN 978-981-283-615-1

A 4-Volume Set

Volume 13: Solid Earth (SE) ISBN 978-981-283-617-5

Volume 28: Atmospheric Science (AS) & Ocean Science (OS) ISBN 978-981-4405-67-6

Volume 14: Solar Terrestrial (ST) ISBN 978-981-283-619-9

Volume 29: Hydrological Science (HS) ISBN 978-981-4405-70-6

Volume 15: Planetary Science (PS) ISBN 978-981-283-621-2

Volume 30: Planetary Science (PS) and Solar & Terrestrial Science (ST) ISBN 978-981-4405-73-7 Volume 31: Solid Earth Science (SE) ISBN 978-981-4405-76-8

A d v a n c e s

i n

Geosciences Volume 29: Hydrological Science (HS)

Editor-in-Chief

Kenji Satake

University of Tokyo, Japan

Volume Editor-in-Chief

Gwo-Fong Lin

National Taiwan University, Taiwan

World Scientific NEW JERSEY

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LONDON

8474hc.v29.9789814405706-tp.indd 2

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SINGAPORE

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BEIJING

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SHANGHAI

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HONG KONG

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TA I P E I

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CHENNAI

23/7/12 5:02 PM

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

ADVANCES IN GEOSCIENCES A 4-Volume Set Volume 29: Hydrological Science (HS) Copyright © 2012 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 978-981-4405-66-9 ISBN 978-981-4405-70-6

(Set) (Vol. 29)

Typeset by Stallion Press Email: [email protected]

Printed in Singapore.

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EDITORS

Editor-in-Chief:

Kenji Satake

Volume 28: Atmospheric Science (AS) and Ocean Science (OS) Editor-in-Chief: (AS) Chun-Chieh Wu Editor-in-Chief: (OS) Jianping Gan Editors: (AS) Kevin K. W. Cheung Hyun Mee Kim Tieh-Yong Koh Mong-Ming Lu Seon-Ki Park Editor: (OS) Minhan Dai Volume 29: Hydrological Science (HS) Editor-in-Chief: Gwo-Fong Lin Editors: Kwan Tun Lee Sanjay Patil Srivatsan Vijayaraghavan Volume 30: Planetary Science (PS) and Solar & Terrestrial Science (ST) Editors-in-Chief: (PS) Anil Bhardwaj Vikram Sarabhai Editor-in-Chief: (ST) Andrew W. Yau Editors: (PS) Takashi Ito Paul Hartogh Editors: (ST) Yusuke Ebihara Susan Mckenna-Lawlor Gang Lu

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Editors

Volume 31: Solid Earth Science (SE) Editor-in-Chief: Ching-Hua Lo Editors: Yih-Min Wu J. Gregory Shellnutt

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REVIEWERS

The Editors of Volume 29 would like to acknowledge the following referees who have helped to review the manuscript publish in this volume: Shien-Tsung Chen Shen Chiang Lei Feng Sopan Ingle Sunil Kute Nepal Mondal

Pravin Nemade Ngoc Son Nguyen D T Shete Srivatsan Vijayaraghavan Minh Tue Vu Yu-Chi Wang

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PREFACE

The present volume set (volumes 28 to 31) of Advances in Geosciences (ADGEO ) is the sixth round of ADGEO series edited by the Asia Oceania Geosciences Society (AOGS), and contains papers presented at the eighth annual meeting held in Taipei in 2011. The AOGS is an international society legally registered in Singapore, aiming to cooperate and promote discussion on studies of the Earth and its environment, as well as the planetary and space sciences. To achieve this objective, the AOGS has held its annual meetings since 2004. The AOGS has six sections, Atmospheric Sciences (AS), Hydrological Sciences (HS), Ocean Sciences (OS), Planetary Sciences (PS), Solar and Terrestrial Sciences (ST), and Solid Earth Sciences (SE). In the current set, papers presented at AS and OS sections are included in volume 28, those at HS section are in volume 29, at PS and ST sections are in volume 30, and at SE section are in volume 31. ADGEO is not a scientific journal, but a monograph series or proceeding volumes of the AOGS meetings. Only papers presented at the AOGS meetings are invited to ADGEO series, and are published after peer reviews. The first (volumes 1 to 5), second (6 to 9), third (10 to 15) sets corresponded to the second, third and fourth AOGS annual meetings. The fourth volume set (16 to 21) included papers presented at the fourth and fifth annual meetings, and the fifth set (22 through 27) included those at the sixth and seventh meetings. As a young scientific society, AOGS needs to develop ways to promote information exchange and interaction among scientists in Asia and Oceania region, in the era of internet. Until we establish a journal or other means of publication, ADGEO is expected to serve as a publication tool among the AOGS members and society at large. Finally, I would like to thank authors, reviewers, volume editors and volume editors-in-chief for their timely efforts to publish the current

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volume set, Meeting Matters International (MeetMatt) for developing and maintaining a system for submission, review and editorial processes, and World Scientific Publishing Company (WSPC) for the editorial, publication and marketing processes.

Kenji Satake Editor-in-Chief

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PREFACE TO HS VOLUME

The Eighth annual meeting of the Asia Oceania Geosciences Society (AOGS) was held in Taipei in 2011. This special issue of Hydrological Science (HS) Section contains papers presented at the meeting. Papers published in this volume were selected from full manuscripts submitted by authors after the annual meeting. Through rigorous peer reviews, papers accepted are finally published in this special volume. This volume presents some of the highlights reported in the HS sessions during the meeting. The papers cover a wide range of topics in hydrological science. I would like to express my sincere appreciation to the volume editors and reviewers for their efforts to ensure the quality of the accepted papers. I also would like to acknowledge the assistance of Ms. Zaiyi Guo and the publisher.

Gwo-Fong Lin Editor-in-Chief, Hydrological Science Volume

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CONTENTS

Editors

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Reviewers

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Preface

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Preface to HS Volume

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Support Vector Machine-Based Model for Daily Evaporation Estimation Gwo-Fong Lin and Hsuan-Yu Lin Rainfall Forecast with Ensemble Performance of Translation Model and Numerical Weather Prediction Ngoc Son Nguyen, Shan He, Srivatsan V. Raghavan, Chi Dung Doan and Shie-Yui Liong

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Impact of Climate Variability and Change on Crop Water Consumption Chavalit Chaleeraktrakoon and Surasit Punyawansiri

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Climate Change and Socio-Hydrological Dynamics: Adaptations and Feedbacks Yali E. Woyessa and Worku A. Welderufael

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Towards River Rehabilitation as an Integrated Approach to Flood Management in Asian Cities David L. Higgitt

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Contents

Flow Structure and Erosion Supress by Vegetation in Overflow on Levees Motoyasu Sato, Takeshi Note, Akira Mano and Keiko Udo Auto-Calibration by Evolutionary Algorithm in Decision Support System for Flood Warning Jongkon Chongwilaikasem, Suwatana Chittaladakorn and Sompop Sucharit Decision Support for Periodical Optimum of Water Delivery from Reservoir by Decision Tree Eakawit Jornpradit and Suwatana Chittaladakorn Decision Support System for Coastal Protection Layout Design (DSS4CPD) Using Genetic Algorithm (GA) and Multicriteria Analysis (MCA) Phinai Jinchai and Suwatana Chittaladakorn Decision Support System for Water Supply Planning Chatree Ruangthanunrak and Suwatana Chittaladakorn Three-Source Dynamical Model for Estimating Parameters for Irregularly Spouting Geysers Induced by Gas Inflow Hiroyuki Kagami

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


SUPPORT VECTOR MACHINE-BASED MODEL FOR DAILY EVAPORATION ESTIMATION GWO-FONG LIN and HSUAN-YU LIN Department of Civil Engineering, National Taiwan University, Taipei, 10617, Taiwan

In this paper, a daily evaporation estimation model based on the support vector machine (SVM) is proposed. The SVM has better generalization ability over the back-propagation network (BPN). An application is conducted to clearly demonstrate the advantage. The result indicates that the proposed SVM-based model performs better than the existing BPN-based model. In conclusion, the proposed SVM-based model is recommended as an alternative to the existing models because of its accuracy. The proposed modeling technique is expected to be useful to improve the daily evaporation estimation.

1. Introduction Evaporation is a major factor in hydrological cycle, and the estimation of evaporation plays an essential role in the design of agricultural irrigation system, studies of water balance, and management of water resources. Improving the performance of the evaporation estimation model is always needed and desired. In practice, many engineers estimate the evaporation based on meteorological data. The highly non-linear and extremely complex process between meteorological factors and evaporation leads to a lot of difficulties in constructing a physically-based mathematical model. An attractive alternative to the physically-based models is the neural network approach. Generally speaking, neural networks (NNs) are information processing systems. Due to the great ability to model nonlinear systems without assumptions, NNs have found a growing number of applications in hydrology. In decades, NNs have been a well-known tool for hydrologists, water resources engineers and managers. ASCE Task Committee1,2 and Maier and Dandy5 have presented comprehensive reviews of the applications of NNs in hydrology. As to daily pan evaporation estimation, many NN-based models, that have 1

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better estimation ability than the empirical formula, have been proposed.3,6,8 More recently, a novel kind of NNs called support vector machine (SVM) have emerged as an alternative data-driven tool in many conventional NN dominated fields, especially for hydrologic time series forecasting.4,7,10,11 Based on statistical learning theory, the SVM has better generalization ability over the back-propagation network (BPN), which is the most frequently used NN. The attractive advantage of SVM prompted us to develop an SVM-based model to improve daily evaporation estimation. The objective of this paper is to develop a well-performed evaporation estimation model. For this purpose, first, the process of input determination is used to select the optimal combination of meteorological inputs. Then, SVM is adopted to construct the estimation model. An actual application to the Chianan Plain in Taiwan is conducted. Results are presented to demonstrate the superiority of the proposed model. The accuracy of the SVM-based model is compared with the BPN-based model and representative results are discussed in depth.

2. Support Vector Machines In the early 1990s, Vapnik developed the SVM for classification and then extended for regression.9 The SVM is originated from the statistical learning theory that uses computer learning. The SVM has been widely used in many areas because of its good generalization ability. Based on Nd training data [(x1 , y1 ), (x2 , y2 ), . . . , (xNd , yNd )], the objective of the support vector regression (SVR) is to find a non-linear regression function to yield the output yˆ, which is the best approximate of the desired output y with an error tolerance of ε. First, the input vector x is mapped onto a higher dimensional feature space by a non-linear function φ(x). Then the regression function that relates the input vector x to the output yˆ can be written as yˆ = f (x) = wT φ(x) + b,

(1)

where w and b are weights and bias of the regression function, respectively. Based on the structural risk minimization (SRM) induction principle, w and b are estimated by minimizing the following structural risk function: d
1 T Lε (ˆ yi ), w w+C 2 i=1

N

R=

(2)

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where the Vapnik’s ε-insensitive loss function Lε is defined as  0 for |y − yˆ| < ε Lε (ˆ y ) = |y − yˆ|ε = . |y − yˆ| − ε for |y − yˆ| ≥ ε

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(3)

The first and second terms on the right-hand side of Eq. (2) represent the model complexity and the empirical error, respectively. The trade-off between the model complexity and the empirical error is specified by a user-defined parameter C and C = 1 represents that the model complexity is as important as the empirical error. In addition, it is acceptable to set the error tolerance ε of 1% for evaporation estimation. Vapnik9 expressed the SVR problem in terms of the following optimization problem: Minimize R(w, b, ξ, ξ
) =

d
1 T w w+C (ξi + ξi
) 2 i=1

N

subject to yi − yˆi = yi − (wT φ(xi ) + b) ≤ ε + ξi

(4)

yˆi − yi = (wT φ(xi ) + b) − yi ≤ ε + ξi
ξi ≥ 0 ξi
≥ 0 i = 1, 2, . . . , Nd , where ξ and ξ
, which are slack variables, represent the upper and the lower training errors, respectively. The above optimization problem is usually solved in its dual form using Lagrange multipliers. Rewriting Eq. (4) in its dual form and differentiating with respect to the primal variables (w, b, ξ, ξ
) gives Maximize Nd


yi (αi − α
i ) − ε

i=1

Nd


(αi + α
i )

i=1

Nd
Nd 1
− (αi − α
i )(αj − α
j )φ(xi )T φ(xj ) 2 i=1 j=1

subject to Nd


(αi − α
i ) = 0

i=1

0 ≤ αi ≤ C

0 ≤ α
i ≤ C

i = 1, 2, . . . , Nd

(5)

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where α and α
are the dual Lagrange multipliers. Note that the solution to the optimal problem (Eq. (5)) is guaranteed to be unique and globally optimal because the objective function is a convex function. The optimal Lagrange multipliers α∗ are solved by the standard quadratic programming algorithm and then the regression function can be rewritten as f (x) =

Nd


α∗i K(xi , x) + b,

(6)

i=1

where the kernel function K(xi , x) is defined as K(xi , x) = φ(xi )T φ(x). The kernel function used in this paper is the radial basis function:   1 2 K(xi , x) = exp − |xi − x| , nx

(7)

(8)

where nx is the number of components in input vector x. Some of solved Lagrange multipliers (α − α
) are zero and should be eliminated from the regression function. Finally, the regression function involves the nonzero Lagrange multipliers and the corresponding input vectors of the training data, which are called the support vectors. The final regression function can be rewritten as f (x) =

Nsv


αk K(xk , x) + b,

(9)

k=1

where xk denotes the kth support vector and Nsv is the number of support vectors.

3. Application 3.1. The study area and data The study area is the Chianan Plain in southern Taiwan. The Chianan Plain with an area of 2,500 km2 is the largest plain and the largest agricultural area in Taiwan. The observed daily evaporation data and the meteorological data during June 2006 to February 2010 are collected. The observed daily evaporation data (E) were obtained from the US Weather Bureau Class A Pan measurement. The meteorological data include the mean daily temperature (Tmean), the maximum daily temperature (Tmax ), the minimum

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daily temperature (Tmin ), the dew-point temperature (Tdew ), the relative humidity (RH), the absolute humidity (AH), the mean daily wind speed (Wind), the solar radiation (Rad), the duration of sunshine (Sun), and the daily precipitation amounts (Pre). The data from June 2006 to February 2009 are chosen as training data and used to construct NN-based models. Then the performance of NN-based models is tested by the remaining data from March 2009 to February 2010. In addition to the observed daily evaporation data and the meteorological data, two variables defined herein are also used as input to the model. The first one is MD, where M is the number of the month in a year between 01 (January) and 12 (December) and D is the number of the day in a month between 01 and 31. The second one is SNday , the serial number of the day in a year between 001 (1 January) and 365 or 366 (31 December). MD and SNday can provide time characteristics in the evaporation model. According to our system of notation, for example, the date of 1 January is denoted as 0101 for MD and 001 for SNday , 1 February as 0201 for MD and 032 for SNday , and 31 December as 1231 for MD and 365 or 366 for SNday .

3.2. Model development and input determination The proposed model can be written in a general form as Et = f (P1,t , P2,t , . . . , Pm,t ),

(10)

where t is the current time, Pi (i = 1 ∼ m) are the inputs, and m is the number of inputs. In this paper, m is equal to 12. The process of input determination is schematized in Fig. 1. The criterion for selecting the inputs of meteorological data is the relative percentage error (RPE): RPE =

E(K) − E(K + 1) , E(K)

(11)

where E(K) and E(K + 1) are the RMSEs for models with K and K + 1 inputs, respectively. In general, the RMSE decreases with increasing number of inputs. When the RPE is less than 1%, the increase of input is stopped. Therefore, the optimal combination of inputs for the SVM- and BPN-based models is determined.

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Fig. 1.

Flowchart of the input determination.

3.3. Performance measures Three performance measures that are commonly used to evaluate the model performance are employed herein.

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1. Root Mean Square Error (RMSE):   N 1
RMSE =  (Eˆt − Et )2 , N t=1

(12)

ˆt denote the observed and estimated daily evaporation where Et and E at time t, respectively, and N is the number of data. 2. Mean Absolute Error (MAE): MAE =

N 1
ˆt |. |Et − E N t=1

(13)

3. Coefficient of Efficiency (CE): N ˆt )2 (Et − E , CE = 1 − t=1 N ¯ 2 t=1 (Et − E)

(14)

¯ is the average of the observed daily evaporation. If the where E estimation is perfect, the CE value is equal to one.

4. Results and Discussions As aforementioned, the process of input determination is used to improve the estimation performance. As shown in Table 1, the RMSE value of the SVM-based model decrease with increasing number of inputs. Rad is the first dominant input variable chosen by the input determination process. The RMSE value of the model with Rad is 1.37 mm/day. The second input is SNday with an RMSE of 1.31 mm/day. The RPE value of the model with the additional second input (SNday ) is 4.66%. The third, fourth, and fifth inputs are Wind, Tmean , and Pre, respectively. The RPE value of the model with

Table 1. model.

Performance measures for input determination of the SVM-based

Input Rad Rad + SNday Rad + SNday + Wind Rad + SNday + Wind + Tmean Rad + SNday + Wind + Tmean + Pre

RMSE (mm/day)

RPE (%)

1.37 1.31 1.24 1.21 1.20

4.66 4.71 2.69 0.62

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the additional fifth input (Pre) is 0.62%, which is less than 1%. Hence, Pre is not included in the optimal combination of inputs for the SVM-based model. That is, the key inputs to the model are Rad, SNday , Wind and Tmean . Figure 2 shows the scatter plots for the observed and estimated daily evaporation. The daily evaporation is also cumulated in monthly scale to present the model performance under different time scales. The time series of observed and estimated evaporation are presented in Fig. 3. As shown

Fig. 2. model.

Fig. 3.

Observed versus estimated daily evaporation resulting from the SVM-based

Comparison of the observed and the estimated evaporation in monthly scale.

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SVM-Based Model for Daily Evaporation Estimation Table 2.

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Performance measures for the SVM- and BPN-based models. RMSE (mm/day)

MAE (mm/day)

CE

Type of events

SVM

BPN

SVM

BPN

SVM

BPN

Training Testing

1.21 1.47

1.23 1.54

0.80 1.08

0.86 1.14

0.63 0.53

0.62 0.49

in Figs. 2 and 3, the estimated evaporation yielded by the SVM-based model is in good agreement with the observed. To compare the estimation performance of the SVM- and BPN-based models, values of the three performance measures are presented in Table 2. As shown in Table 2, the SVM-based model yields significantly higher CE and lower RMSE and MAE than the BPN-based model. The percentages of improvement in RMSE, MAE and CE are 4.40%, 5.35% and 9.12%, respectively.

5. Summary and Conclusions The objective of this paper is to develop a well-performed daily evaporation estimation model, which can supply useful information for agriculture and water resource management. A SVM-based model is proposed herein for this purpose. An input determination process, which is more convenient and time-saving than the trial and error procedure, is used to select the inputs. An application has been conducted to clearly demonstrate the superiority of the proposed model. The results show that the four key inputs to the model are Rad, SNday , Wind and Tmean for the study area. Next, the estimation performance of the SVM-based model is compared with the BPN-based model. It is found that the SVM-based model performs better than the BPN-based model. The proposed SVM-based mode is expected to be useful to improve the daily evaporation estimation.

References 1. ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, J. Hydrol. Eng. 5 (2000a) 115. 2. ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, J. Hydrol. Eng. 5 (2000b) 124. ¨ Terzi, J. Hydrol. Eng. 11 (2006) 65. 3. M. E. Keskin and O. 4. S. Y. Liong and C. Sivapragasam, J. Am. Water Resour. As. 38 (2002) 173. 5. H. R. Maier and G. C. Dandy, Environ. Model. Softw. 15 (2000) 101.

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6. A. Rahimikhoob, Theor. Appl. Climatol. 98 (2009) 101. 7. C. Sivapragasam and S. Y. Liong, Nord. Hydrol. 36 (2005) 37. 8. K. P. Sudheer, A. K. Gosain, D. Mohana Rangan and S. M. Saheb, Hydrol. Process. 16 (2002) 3189. 9. V. N. Vapnik, Springer (1995). 10. X. Y. Yu and S. Y. Liong, J. Hydrol. 332 (2007) 290. 11. X. Y. Yu, S. Y. Liong and V. Babovic, J. Hydroinform. 6 (2004) 209.

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


RAINFALL FORECAST WITH ENSEMBLE PERFORMANCE OF TRANSLATION MODEL AND NUMERICAL WEATHER PREDICTION NGOC SON NGUYEN∗,†,§ , SHAN HE∗,† , SRIVATSAN V. RAGHAVAN∗,† , CHI DUNG DOAN∗,† , and SHIE-YUI LIONG∗ Many urban catchments normally suffer from heavy flooding due to various reasons such as very large percentage of imperviousness or a short time of concentration. It is therefore of interest to provide an operationally useful forecast lead-time to allow mitigation measures to be undertaken. This paper presents the application of an ensemble model approach which combines rainfall nowcasting using translation model (TM) with rainfall forecasting using numerical weather prediction (NWP). The translation model is more precise in short-term forecast up to six hours while NWP has its advantage in long-term forecast up to several days. The performance of the ensemble model for some heavy rainfall events over Greater Singapore domain will be presented.

1. Introduction Many urban catchments normally suffer from heavy flooding due to various reasons such as very large percentage of imperviousness and a short time of concentration. It is therefore of interest to provide an operationally useful forecast lead-time to allow mitigation measures to be undertaken. One solution is to look into the quantitative precipitation forecasting.5 A number of approaches have been explored for short-term rainfall forecasting. In relation to the rain cell movement, Grecu and Krajewski5 investigated the use of Neural Network to simulate the evolvement of the rain cells (dynamic modeling). They concluded that there is no significant difference between the neural-network based procedure and the relatively simple advection schemes, and both approaches performed significantly ∗ Tropical

Marine Science Institute, National University of Singapore, Singapore. Water Alliance. (SDWA), National University of Singapore, Singapore. ‡ [email protected]. § Corresponding author. † Singapore-Delft

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better than the persistence scheme. They also suggested that the cloud model should be used to utilize the 3D information which contains in radar images. To produce the short-term rainfall forecasting in this paper, we apply the translation model (TM)10,11 with different types of translation vectors. The noise removal filter for radar images is also applied to improve the quality of the radar images which were used as input for the translation model. Weather forecasting using computer models is known as numerical weather prediction (NWP). NWP generally connotes the prediction of meteorological parameters by numerical solution of the hydrodynamic equations governing atmospheric motions. The Weather Research and Forecasting (WRF) model, developed at NCAR (National Center of Atmospheric Research), US was used for numerical weather prediction and this model was chosen because of its extensive capabilities with regard to using the model at higher spatial resolutions, nesting of domains and wide choices of physics options available (http://www.wrf-model.org).

2. Method 2.1. Translation model Translation model10,11 identifies the movement of the rain cells and extrapolates them to yield rainfall prediction. Since the movement of the rain cells is assumed to be constant, this type of model is in principle suitable only for short-term prediction. The model defines the horizontal rainfall intensity distribution, r(x,y,t), with spatial coordinate (x,y) at time t as shown in Eq. (1): w=

∂r ∂r ∂r +u +v , ∂t ∂x ∂y

(1)

with u=

dy dr dx ;v = ;w = , dt dt dt

where u and v are the translation vectors of rain cells along x and y directions, respectively and w is rainfall growth-decay rate along its movement.

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At each grid point (x,y), the model assumes: u(x, y) = c1 x + c2 y + c3 , v(x, y) = c4 x + c5 y + c6 ,

(2)

w(x, y) = c7 x + c8 y + c9 . With this assumption, the parameters c1 , c2 , . . . , c9 can be identified using observed rainfall data by the square root information filter. An example of radar observed rainfall over Greater Singapore region is shown in Fig. 1.

Fig. 1.

Radar image (radius 70 km).

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14

2.2. Numerical weather prediction The WRF model is a next-generation mesoscale NWP system to serve both operational forecasting and atmospheric research needs. The WRF model uses a three-dimensional grid to represent the atmosphere at scales ranging from meters to thousands of kilometers, topographical land information, and observational data to define initial conditions for a forecasting simulation. The system is useful for both the understanding and prediction of mesoscale weather and to accelerate the transfer of research advances into operations. The model is intended to improve forecast accuracy across scales ranging from cloud to synoptic, with priority emphasis on horizontal grid resolutions of 1–10 kilometers. The global forecast system (GFS) data were used as the driving large scale initial and lateral boundary conditions for the model. The GFS (sixhourly data at 1◦ resolution) is a global numerical weather prediction model run by NOAA (National Oceanic and Atmospheric Administration), in the USA. This mathematical model is run four times a day and produces forecasts up to 16 days in advance. After sensitivity tests were performed, we come up with a simulation system which is most suitable for rainfall forecasting of chosen region, Singapore domain. The single nested system with 5 km–30 km was employed for all simulations. The NWP model domain in shown in Fig. 2 consisting

Fig. 2.

Single nested WRF domain.

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of two domains: A mother domain with a spatial resolution of 30 km and a nested domain having a spatial resolution of 5 km. 2.3. Ensemble rainfall forecasting: coupling TM and NWP This section presents the approach to combine the results of TM and NWP, the ensemble rainfall forecasting, which offers both short- and medium-range rainfall forecasting. The ensemble rainfall forecasting approach is performed by combining two rainfall forecasting methods: TM (short-range forecast) and NWP (medium-range forecast). The combined/coupled TM and NWP model is to serve the operational rainfall forecasting. The results from the ensemble rainfall Forecasting were obtained with appropriate weights assigned to NWP and TM simulation results. TM, the radar based rainfall now-casting, gives rainfall estimates of the immediate next three hours. TM results are updated every hour. In the other hand, NWP requires spin-up period of the model; thus it could not generate an adequate accuracy for the first few hours. In addition, the availability of GFS data itself is often delayed by 2–3 hours to the actual time, if not longer. Considering the limitation of the computational facility used, the average time required to generate the first useful rainfall forecast is about 12 hours. Therefore, with the combination of TM and NWP for ensemble approach, a short-range rainfall now-casting (based on radar data) from TM comes very “handy” or “appropriately” to substitute the “missing” first 12 hour data of NWP forecast. Fig. 3 shows the combination of TM and NWP for ensemble approach. The results from NWP were updated every six-hours with the replacement of latest results to the previous one. In the other hand, TM results were updated every hour. The final product for ensemble approach was a weighted combine of TM result and NWP results, in which, the TM results which were more accurate in short-term forecast (due to radar information) contributed to a better accuracy of the final product.

3. Results The period of simulation, as an example, was chosen in between November 2008 to February 2009. For TM nowcasting, the radar domain covers a radius of about 140km × 140km.The radar data come in every 3–5 minutes. The quality of radar images in the past are improved with noise removal

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Ensemble rainfall forecasting: combination of TM results and WRF results.

filter and they were used to determine the translation vectors. The objective was to forecast rainfall up to three hours lead times. The TM was run with two different approaches for translation vector: Uniform and linearly nonuniform. The sample output from TM was compared with observed rainfall calculated from radar images. Fig. 4 shows the comparison results between TM forecast rainfall and radar observed rainfall for one hour lead time. The event is on 24th December 2008. The time 7:50:00 SGT (Singapore time) is assumed to be the “present time” of the forecast. And hence, 8:20:00 SGT and 8:50:00 SGT is the “future time” corresponding with 30 minutes and 1 hour lead time. Fig. 5 shows the results for a sample heavy rainfall event on 8th December 2008. The plots show the simulated rainfall from WRF and TM compared against the observed rainfall at Changi Station (Singapore). The examined time slices are assumed to be at 3:00 SGT, 4:00 SGT and 5:00 SGT on 8 December 2008. At each time, TM was performed to produce the forecast results in the next three hours. The forecast result information is provided in between the two purple dash-lines in each plot. Considering the forecast period at those time slices, the useful information from NWP will be collected from the WRF run at 14:00 SGT and 20.00 SGT on 7 December 2008, which are presented by red color bar

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Fig. 4. TM forecast with different translation vectors: (a) uniform; (b) linear nonuniform; (c) observed radar image.

in comparing with observed data presented by blue color bar (Please note that the first 12 hours results from WRF will not be used). The results from TM and NWP will be combined to get ensemble products. From the results of separated approach introduced in Figs. 5, 6 shows the comparison between observed rainfall and ensemble rainfall data on 8th December 2008 at Changi Station. The examined time slides are assumed to be at 3:00 SGT, 4:00 SGT and 5:00 SGT on 8 December 2008 which are corresponding with three plots in the figure. The ensemble results are presented by red color bars — match very well with observed rainfalls at Changi Station, which are presented by blue color bars. We can see that the ensemble products are more similar to TM results in the first three forecast hours from the examined time. This because TM result has 70% weighted in combining of TM and NWP result. In the other hand, the NWP result contributed less in the first three forecast hours of final product, but it will act as warning signal for big rainfall event in the fourth forecast hour onward.

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Fig. 5. Comparison between raingauge observed rainfall and simulated rainfall from WRF and TM on 8 December 2008 at Changi station.

Fig. 6. Comparison between raingauge observed rainfall and ensemble rainfall data on 8th December 2008 at Changi Station.

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The event that final product of ensemble approach is well matching with observed data provides a promising research direction on real-time rainfall forecast.

4. Conclusions In this paper, we presented the ensemble approach of combining TM and NWP. The TM is used for short-term rainfall forecast based on the radar images. The TM has shown moderately high accurate comparing with observed rainfalls. It is showed that TM is quite an effective tool for shortrainfall forecast. And it plays a more important role in the first few hours in the forecast result of ensemble approach. In the other hand, NWP, used WRF model with GFS data, can perform with a reasonable accuracy in long-term rainfall forecast. It may contribute an important role in providing the warning signal for some heavy rainfall event. The couple of TM and NWP enhances the strength and limits the weakness of each single method. The ensemble approach has showed good results in rainfall forecasting. Further improvement for ensemble TM and NWP is in progress to make it even better in term of ability for detection and accuracy.

References 1. L. Berthet, V. Andr’eassian, C. Perrin and P. Javelle, Hydrol. Earth Syst. Sci. 13 (2009) 819–831. 2. A. Brath, On the role of numerical weather prediction models in realtime flood forecasting. Proceedings of the International Workshop on River Basin Modeling: Management and Flood Mitigation, September 25–26, 1997, Monselice, Italy, 1999, pp. 249–259. 3. P. Burlando, A. Montanari and R. Ranzi, Atmos. Res. 42 (1996) 199–216. 4. K. W. Chau, C. L. Wu and Y. S. Li, J. Hydrologic Engrg. 10, 6 (2005) 485–491. 5. M. Grecu and W.F. Krajewski, J. Ocean. Atmos. Technol. 17, 2 (2000) 121–129. 6. S. Laroche and I. Zawadzki, . J. Atmos. Sci. 51, 18 (1994) 2664–2682. 7. S. Mecklenburg, A. Jurczyk, J. Szturc and K. Osrodka, COST Action 717: Use of radar observations in hydrological and NWP models. Topic WG1-8: Quantitative precipitation forecasts (QPF) based on radar data for hydrological models, 2002. 8. A. W. Seed, J. Appl. Meteorol. 42 (2003) 381–388.

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9. A. W. Seed, R. Strikanthan and M. Menabde, J. Geophys. Res. 104, D24 (1999) 31 623–31 630. 10. M. Shiiba, T. Takasao and E. Nakakita, Investigation of short-term rainfall prediction method by a translation model, Proceeding of 28th Japan Conference on Hydraulics, Japan, 1984, pp. 423–428. 11. T. Takasao, M. Shiiba and H. Nakakita, Stochastic and Statistical Methods in Hydrol. and Environm. Eng. 2 (1994) 339–351. 12. J. D. Tuttle and G. B. Foote, J. Atmos. Ocean. Tech. 7, 2 (1990) 218–232.

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


IMPACT OF CLIMATE VARIABILITY AND CHANGE ON CROP WATER CONSUMPTION CHAVALIT CHALEERAKTRAKOON Department of Civil Engineering, Faculty of Engineering, Thammasat University, Thailand 12121 SURASIT PUNYAWANSIRI Royal Irrigation Department, Thailand 11120

This paper presents a statistical downscaling approach that can be used to link the climate change predictions given by the GCMs to the water consumption of a crop at a single location. In particular, the proposed approach is composed of a combination of the accepted statistical downscaling models, SDSMs of minimum, average, and maximum daily temperatures and the well-known Hargreaves formula of reference water consumption with the crop coefficient of an interested crop. The downscaling approach has been developed using the 48-year (1961–2008) series of the observed daily temperatures data at Loei and Khon Kaen Provinces in the northeast of Thailand. The developed approaches have been applied to investigate the impact of climate variability and change on the water consumption for off-season rice. Results based on the HadCM3A2 scenario have shown that the water requirements of the next 10 years (2020s) grow, as compared with the demands during 1961−1990. The total increasing amounts are 33 and 30 mm for the starting November and December periods. However, the risk of water shortage during the last month of the December season is higher.

1. Introduction Information on crop water requirement is fundamental to the design of irrigation system and to the analysis of water deficit risk in a watershed area for water resource planning and management. The crop water consumption generally depends on several climate variables, such as temperature, relative humidity, wind velocity, and solar radiation. In particular, it varies proportionally with the temperature, wind velocity, and solar radiation variables while relating inversely to the humidity one. Climate variability and change will have important impacts on the water requirement at station level. General Circulation Models (GCMs) have been 21

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accepted in representing reasonably well the global distribution of basic climate parameters. However, the spatial resolutions of GCMs outputs are usually greater than 200 km that are too coarse for this impact studies. Most available dynamic downscaling approach and statistical downscaling scheme, (weather classification, stochastic weather generator, and regression technique) are considered for only temperature and precipitation.1−3 However, they are inapplicable for the downscaling of the crop water consumption because of the lack of this hydrologic variable at the global level. Therefore, the present study proposes a statistical downscaling approach that can be used to link the climate change predictions given by the GCMs to the crop water requirements at a single location. More specifically, the proposed approach is mainly based on a combination of the popular statistical downscaling models, SDSMs,4 of minimum, average, and maximum daily temperatures and the widely used Hargreaves formula of potential evapo-transpiration5 with a crop coefficient considered. Its illustrative applications at Loei and Khon Kaen Provinces in the northeast of Thailand have shown that the total water consumption for off-season rice based on the HadCM3A2 scenario for the next 10 years (2020s) tends to increase by 30–33 mm, as compared with that of the 1961–1990 base period.

2. A Statistical Downscaling Approach As mentioned above, the proposed downscaling approach consists of two basic steps: (1) A statistical downscaling method to link the largescale climate variables as provided by GCM simulations with each daily temperature at a local site using the SDSM and (2) a model to describe the relationship between the daily temperatures and crop water requirement using the Hargreaves formula.

2.1. A global climate parameters and station daily temperature linkage using SDSM The SDSM is an accepted statistical downscaling technique in practice for the construction of climate scenarios for various impact studies. The model is a hybrid of multiple regression-based model and stochastic weather generator. It could provide a linkage between station surface climate variable (i.e., temperature and precipitation) for daily time scale with grid-resolution daily GCM climate simulation outputs. Depending on the variation of an

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interested hydrological process, a suitable annual, seasonal, or monthly period is selected for the development of its linkage. For example, if the variability of the considered phenomenon (e.g., precipitation) is large, the monthly and seasonal relationships will be considered. Otherwise (e.g., temperature), the annual linkage will be adopted. Hence, the SDSM describes the temperature Tt (◦ C) at a single location during day t as Tt = a +

k


bj ujt ,

(1)

j=1

where a and bj are the parameters of multiple regression, and ujt is the j’th significant NCEP reanalysis variable of U t for GCMs. Note that the daily temperature in Eq. (1) can be its minimum T  , average T˜ , or maximum T ∗ . Moreover, in this study, a widely-used stepwise analysis6 which is the combination of forward and backward screenings is used for the selection of the significant climate predictors U t . The applied stepwise analysis is better than an enter screening adopted in the SDSM because it usually yields a definitive subset of the important explanatory variables U t . 2.2. A temperature and crop-water-consumption linkage using Hargreaves formula and crop coefficient In the following, the description of transforming the downscaled temperatures into the crop water consumption is briefly presented. In general, the daily temperatures (T  , T˜ and T ∗ ), and solar radiation Rs are usually the main explanatory climatic processes for reference crop water consumption. These referred phenomena often describe at least 80% of total variation of the potential evapo-transpiration.7 As irrigation practice is generally scheduled on a weekly basis. Hence, the daily temperatures are summarized as their averages over week τ for the computation of the reference water requirement ET τ (mm/d). The maximum evapo-transpiration is calculated via the four climatic processes8,9 as
ETτ = 0.0135Rsτ (T˜τ + 17.8) = 0.0135f Reτ (Tτ∗ − Tτ )0.5 (T˜τ + 17.8)

(2)

in which f is an empirical coefficient where it is suggested to be 0.162 and 0.19 for inland and coastal regions respectively,10 and Reτ is the extraterrestrial radiation in mm/d. The Hargreaves formula, Eq. (2),

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explains the relative humidity of air mass through the temperature difference. Its accuracy is comparable to several other empirical formulae, such as Thornthwaite, Makkink, Jensen-Haise, FAO Modified Penman, and Blaney-Criddle.5,11,12 Finally, the water consumption Wc of crop c is calculated as Wcτ = Kc ETτ ,

(3)

where Kc is crop coefficient.

3. Numerical Application To illustrate the application of the proposed statistical downscaling approach, a case study is carried out using the minimum, average, and maximum daily temperature data available at Loei (station code 353201, lat. 17◦ 27 00 , long. 101◦44 00 , the Khong catchment basin) and Khon Kaen (station code 381201, lat. 16◦ 27 48 , long. 102◦47 12 , the Chi watershed area) in the northeast of Thailand, crop coefficients for off-season rice13 and global GCM outputs. The provinces have been chosen because they are located in the region that produces the best quality jasmine rice in the world. The HadCM3A2 simulations for the 1961–1990 as well as for a future period of 2020s are selected as the global GCM predictors because HadCM3 has provided acceptable downscaling temperatures in the study area14 and the A2 scenario is the worst case among the other A1B and B2. The daily temperature data are available for the period of 1961–2008. Furthermore, the data for the 1961–1975 and 1976–1990 periods were considered for model calibration and validation respectively. The computational procedure for the proposed downscaling method can be summarized as follows: 1. Calibrate and validate the downscaling SDSM using the individual minimum, average, and maximum daily temperatures at a given site as predictand and global GCM atmospheric variables (NCEP data) as predictors. 2. Construct the HadCM3A2 scenario for each daily temperature series in the 1961–1990 and the 2020s intervals. 3. Apply the temperature and water consumption linkage for off-season rice to the constructed HadCM3A2 scenario. 4. Calculate the anomaly of the water consumptions between the 2020s and the 1961–1990 base periods.

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Table 1. Explained NCEP variables of HadCM3 for the daily temperatures of Loei and Khon Kaen. Station

Temperature

Loei

Minimum Average Maximum

X

Minimum

X

Khon Kaen

ncepp8 fas

Average Maximum

ncepr500

ncepr850as

ncepshumas

nceptempas

X

X X

X X X

X X X

X

X

X X

X X

X X

X

Note: ncepp8 fas.dat = 850 hPa airflow strength, ncepr500as.dat and ncepr850as.dat = relative humidity at 500 hPa and 850 hPa, ncepshumas.dat = surface specific humidity, and nceptempas.dat = mean temperature at 2 m.

Table 2. Coefficient of determination R2 , mean absolute error, and root mean square error of the calibrated multiple regression relationships between the significant NCEP predictors and the local temperatures of Loei and Khon Kaen. T
Station Loei Khon Kaen

T∗

T˜

R2

MAE

RMSE

R2

MAE

RMSE

R2

MAE

RMSE

0.866 0.861

1.148 1.058

1.576 1.387

0.812 0.819

1.049 1.017

1.311 1.289

0.718 0.737

1.294 1.257

1.719 1.660

For the purposes of illustration, Table 1 presents the explained NCEP variables of HadCM3 for the daily temperatures of Loei and Khon Kaen based on the stepwise analysis. The most common important predictors are surface specific humidity (ncepshumas.dat) and mean temperature at 2 m (nceptempas.dat). Table 2 shows the considered assessment statistics15 ; such as coefficient of determination R2 , mean absolute error (MAE), and root mean square error (RMSE); resulting from the calibration of the multiple regression relationship between the significant NCEP predictors and the local temperatures. The statistics indicate that the regression models are quite accurate in the calibration period. However, the results of the minimum and average temperatures are generally better than those of the maximum temperature as expected because their variations are usually smaller. Figure 1 displays the box plots15 of observed and downscaled annual means and variances of the minimum, average, and maximum temperatures at Loei (1961–1975). The figure demonstrates that the calibrated SDSMs

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(a) Mean of

(d) Variances of

(˚C)

(˚C)

(b) Mean of

(e) Variances of

(˚C)

(˚C)2

(c) Mean of

(f) Variances of

(˚C)

(˚C)

Fig. 1. Box plots of historical and downscaled annual means and variances for Loei (1961–1975).

(g) Mean of

(j) Variances of

(˚C)

(˚C)

(h) Mean of

(k) Variances of

(˚C)

(˚C)2

(i) Mean of

(l) Variances of

(˚C)

(˚C)

Fig. 2. Box plots of historical and downscaled annual means and variances for Khon Kaen (1976–1990).

adequately describe the historical basic properties because the modeled and historical temperature percentiles are close to each other. Figure 2 indicates that the models satisfactorily reproduce the referred statistics of the historical temperatures at Khon Kaen during the validation period of 1976–1990.

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Fig. 3. Loei and Khon Kaen anomalies and their sums between the 2020s and the 1961–1990 base periods of water consumption for off-season rice during the starting November and December seasons.

Figure 3 shows the Loei and Khon Kaen anomalies and their sums between the 2020s and the 1961–1990 base periods of total monthly waterconsumption for off-season rice during the starting November and December seasons. Note that the periods are widely used in practice for Thai farmers. It demonstrates that the water requirements throughout the cropping seasons in the next 10 years increase by 1.5–4 mm, as compared to the base period. However, the increasing trends of the two seasons are different. That is, the water consumption increases faster in November and December compared to January and February for the NDJF season. While, the water consumption of the other period is approximately constant throughout the season, except in March. Further, the total future consumption of the November case (≈ 33 mm) is larger than that of the December one (≈ 30 mm).

4. Conclusions The main objective of this study is to propose a statistical downscaling approach that can be used to link the climate change predictions given by the GCMs to the crop water requirements at a single location. The proposed approach consists of a combination of the SDSM with stepwise

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analysis for minimum, average, and maximum daily temperatures and the Hargreaves formula with the coefficient of the considered crop for its water consumption. The proposed downscaling method has been applied to the climate simulation outputs of the HadCM3 under the A2 scenario (HadCM3A2) and the available daily temperatures data at Loei and Khon Kaen for the 1961–2008 period. Results obtained are summarized as follows: •

•

•

•

The significant NCEP predictors are mean temperature at 2 m, surface specific humidity, relative humidity at 850 hPa and 500 hPa, and 850 hPa air flow strength. The calibrated SDSMs of the minimum, average, and maximum daily temperatures are shown to be accurate based on the R2 , MAE, and RMSE statistics. The SDSMs are able to sufficiently reproduce the annual mean and variance of the historical daily temperatures for the 1961–1975 calibration and 1976–1990 validation periods. The weekly water consumptions for off-season rice during the 2020s interval are greater than the 1961–1990 base period increase for both starting November and December seasons. The total increasing amounts for the November and December seasons are 33 and 30 mm respectively. However, the risk of water shortage during the last month of the December season is higher.

References 1. M. Rummukainen, J. Raisanen and B. Bringfelt, Clim. Dyn. 17 (2001) 339. 2. C. Harpham and R. L. Wilby, J. Hydrol. 312 (2005) 235. 3. G. Lenderink, A.V. Ulden, B. V. D. Hurk and F. Keller, Clim. Dyn. 29 (2007) 157. 4. R. L. Wilby, C. W. Dawson and E. M. Barrow, Env. Model. Soft. 17 (2002) 147. 5. Z. A. Samani and M. Pessarakli, Trans. ASAE 29 (1986) 522. 6. S. Shevade and S. Keerthi, Bioinformatics 19 (2003) 2246. 7. A. Gonzalez, M. F. Villazon and P. Willems, 1’st Int. Cong. Hydroclim. Cochabamba-Bolivia, August, 2009. 8. G. H. Hargreaves and Z. A. Samani, J. Irrig. Drain. Eng. ASCE 108 (1982) 223. 9. G. H. Hargreaves and Z. A. Samani Trans. ASAE 1 (1985) 96. 10. G. H. Hargreaves, Biology and Irrigation Engineering Department Paper, Utah State University, 1994.

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L. Salazar, Irrigation Scheduling Manual (Utah State University, 1988). M. N. Orang, M. E. Grismer and H. Ashktorab, CA Agri. (1995). Royal Irrigation Department, Report on Crop Coefficients, 2006. C. Chaleeraktrakoon and P. Punlum, Thammasat Int. J. Sc. Tech. 15 (2010) 64. D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers (2011) 768.

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


CLIMATE CHANGE AND SOCIO-HYDROLOGICAL DYNAMICS: ADAPTATIONS AND FEEDBACKS YALI E. WOYESSA School of Civil Engineering and Built Environment Central University of Technology, Free State Private Bag X20539 Bloemfontein 9300, South Africa WORKU A. WELDERUFAEL School of Civil Engineering and Built Environment Central University of Technology, Free State Private Bag X20539 Bloemfontein 9300, South Africa

A functioning ecological system results in ecosystem goods and services which are of direct value to human beings. Ecosystem services are the conditions and processes which sustain and fulfil human life, and maintain biodiversity and the production of ecosystem goods. However, human actions affect ecological systems and the services they provide through various activities, such as land use, water use, pollution and climate change. Climate change is perhaps one of the most important sustainable development challenges that threatens to undo many of the development efforts being made to reach the targets set for the Millennium Development Goals. Understanding the provision of ecosystem services and how they change under different scenarios of climate and biophysical conditions could assist in bringing the issue of ecosystem services into decision making process. Similarly, the impacts of land use change on ecosystems and biodiversity have received considerable attention from ecologists and hydrologists alike. Land use change in a catchment can impact on water supply by altering hydrological processes, such as infiltration, groundwater recharge, base flow and direct runoff. In the past a variety of models were used for predicting landuse changes. Recently, the focus has shifted away from using mathematically oriented models to agent-based modeling (ABM) approach to simulate land use scenarios. The agent-based perspective, with regard to land-use cover change, is centered on the general nature and rules of land-use decision making by individuals. A conceptual framework is developed to investigate the possibility of incorporating the human dimension of land use decision and climate change model into a hydrological model in order to assess the impact of future land use scenario and climate change on the ecological system in general and water resources in particular.

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1. Introduction The land use and landscape changes that are being observed today could signal the possibility that extreme events (such as floods, droughts, heat waves, etc.) could occur with higher frequency in any given year. These changes also imply that changes in natural ecosystems and socioeconomic activities are bound to occur. For example, change in climatic conditions could shift the sustainability of natural resources, such as water, air, land, forests, fish and wildlife. This is because these systems cannot adapt as quickly as the climate (Flannery, 2006 and McBean, 2006; cited in Prodanovi’c and Simonovi, 2007). The implications of climate change on the socioeconomic systems are also great. The threats of adequate supply of drinking water, energy and other necessary services in light of changing hydro-climatic conditions are real, and need to be addressed. Land-use/land-cover change occurs through complex interactions between land users (agents) on one hand and biophysical and socioeconomic factors on the other hand. The complex interaction between environment and social factors could bring emergent changes in land uses. As a consequence of land use change, the water balance of a specific catchment could significantly be affected. The altered hydrological cycle resulting from the land use change may significantly affect a local climate such as the precipitation and temperature of a particular ecology. This may impact the sustainable usage of water resources and ecological balance of an environment. For a given environment land use change can be predicted by an agent based model (ABM), based on the possible interactions between agents (land users), socio economic and the biophysical factors. An ABM consists of autonomous decision making entities (agents), an environment through which agents interact, rules that define the relationships between agents and their environment, and rules that determine sequence of actions in the model. Agents in ABMs are considered as components that can learn from their environments and change their behaviors accordingly. Purnomo and Guizol17 described agents as entities with defined goals, actions and domain knowledge which operate and exist in an environment. Adhering to the emerging paradigm shift, decision to change land use would only be obtained after a complex interactions of the socioeconomics and environmental factors which influences the behavior of the farm manager. ABMs can be useful tools for studying the effects of land-use/ cover change processes on the water resources at multiple scales and organizational levels. Bousquet et al.4 recognized ABMs as useful tools

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in involving stakeholders in a collective design of management plans. Brown (2006) defined ABMs as computer representations of systems that are comprised of multiple, interacting actors (i.e., agents). These models have components for the socioeconomic factors as well as for the biophysical inputs.2,6 ABMs are also considered useful in capturing emergent phenomena as a result of complex interactions happening in an environment. They are also praised in providing a natural environment for the study of systems composed of real-world entities, and by their flexibility particularly in relation to the development of geospatial models.7,15 Generally, ABM is a method by which one investigates and describes complex systems and their emergent properties.3,5,14,18,19 ABMs are also used to simulate different scenarios for use in future policy and management preferences. For instance, Polhill et al.16 used an ABM model known as FEARLUS to investigate the effect of different events such as market globalization and global change of climate on land use change. Their long-term goal also encompasses providing advice to policy makers on possible land-use outcomes. For instance, Becu et al.2 integrated a hydrological model in an ABM known as CATCHSCAPE to manage the conflicts arising between upstream and downstream water users and to investigate impacts of upstream irrigation management on downstream agricultural viability in northern Thailand. This ABM is equipped with biophysical modules, which simulate the hydrological system with its distributed water balance, irrigation scheme management and crop and vegetation dynamics.

2. Procedure An integrated conceptual socio-hydrological model for the prediction of the impact of land use and climate change on water resources was developed for the central region of South Africa in the Upper Modder River basin (Fig. 1). The focus of this exercise was on C52A, a quaternary catchment in the Upper Modder River basin of the central region of South Africa. The catchment is characterized by semi-arid climate and dominated by soil type which is susceptible to surface crust formation. The annual mean rainfall is about 588 mm. The maximum mean daily temperature is 29o C while the minimum mean daily temperature is −0.1◦C. The catchment is dominated by the slope range of 0–3% which comprises 57% of the catchment area followed by the slope range of 3–8% which covers 34% of the catchment area.

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Fig. 1.

The study area.

The interactions which was assumed to take place in the catchment was conceptualized rationally through an interactive process with different stakeholders, namely hydrologist, soil scientist, socio-economist and information technologist. Similarly, a climate change scenario was built in using appropriate climate change model that will link up with the climate database.

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3. Conceptual Socio-Hydrological Model Figures 2 and 3 present the integrated conceptual model for the quaternary catchment C52A. In Fig. 2, it can be seen that the environment comprises all resources, agents and socioeconomic interactions that are taking place. The environment is assumed to include both external as well as internal agents. Agents represented by farmers or farm managers, after a complex interaction with similar agents and/or other agents and with the environment, will be assumed to undergo a behavioral change. These agents who may acquire an immense knowledge from the interaction and the environment can react individually or as a group. A reaction may lead to a decision towards change of land use. Land use changes could occur spatially as well as temporally within the environment. The environment may contain spatially different soil types and physiographic features which can be considered static for a considerable period. This, in combination with climatic changes, could contribute to the generation of surface runoffs depending on the land-use, soil type and topography of the explicitly situated land/agricultural land.

Fig. 2.

Socio-hydrological conceptual framework.

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Fig. 3.

Integration of land use and climate change model.

Figure 3 shows the conceptual model illustrating the database types and its linkage to the different nodes in the process of the model. The socioeconomic factors and the interaction that lead to decision in land use change would be captured by the ABM module while changes in the stream flow would be dealt by the hydrologic module integrated in the system (SWAT). In this way, all land use changes resulted by the interactions will be simulated by the ABM while climate change scenario is captured and linked to the climate database within the GIS system. The cyclic effect of climate and land use change will be continuously updated in the GIS database module. The GIS database supplies data to both the ABM and hydrological models, creating a means of investigating the impact of one on the other in addition to their combined impact on the water resources.

4. Hydrological Simulation The impact of different land use scenarios on the water balance of C52A (see Fig. 1) was demonstrated using Soil and Water Assessment Tool (SWAT), which was developed by the United States Department of Agriculture (USDA) to simulate the impacts of land-use changes and

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land management practices on water balance of catchments, especially for ungauged catchments.1 SWAT has also proven to be an effective tool for understanding pollutions from fertilizer applications and point sources1,11 and for wider environmental studies.12 The model is also used as a decision support tool in land use planning by simulating the impact of different land use scenarios on water resources.10 The following figures (Figs. 4 and 5)

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present hydrological simulation results of three different land use scenarios, namely pasture (PAST), agriculture using conventional tillage (Agri-CON), agriculture using rainwater harvesting technique (Agri-IRWH). The model was able to illustrate the potential impact of different land use types on the water resources of quaternary catchment C52A. The results of the scenario analysis revealed that conventional agricultural land use type generated the highest direct flow compared to the ones dominated by pasture or IRWH land use types. The use of the ABM in the prediction of land use scenario (see Fig. 2) is still in the process of development. Once this is in place, it will make it

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possible to have a realistic simulation of land use decision which will serve as input to the SWAT hydrological model for impact analysis.

5. Conclusions Global climatic changes threaten the livelihoods of the farming community in the developing countries and in most of the Sub-Saharan African countries. The cyclic effects of climate and land use change may cause a double fold negative impact on the water resources of the aforementioned countries. As most of the populations of these countries income and food depend on agricultural production, water is the most critical natural resource. To minimize the future crises in water resources resulting from land use and global climatic change and in order to take proactive measures for sustainable water resources utilization, development of an integrated socio-hydrological model could be a step in the right direction for decision support system.

References 1. J. G. Arnold, R. Srinivasan, R. S. Muttiah and J. R. Williams, J. Amer. Water Res. Assoc. 34, 1 (1998) 73–89. 2. N. Becu, P. Perez, A. Walker, O. Barreteau and C. Le Page, Ecological Modelling 170 (2003) 319–331. 3. E. Bonabeau, Agent-based modelling: Methods and techniques for simulating human systems, Proceedings of the National Academy of Sciences of the United States of America, Vol. 99, Suppl. 3, 2002, pp. 7280–7287. 4. F. Bousquet, O. Bareteau, P. D’aquino, M. Etienne, S. Boissau, S. Aubert, C. Le Page, D. Babin and J. C. Castela, in Complexity and Ecosystem Management: The theory and Practice of Multi-Agent Approaches, ed. M. Janssen (Elgar Publishers, Northampton, England, 2002), 248–285. 5. R. Bradbury, in Complexity and Ecosystem Management, ed. M. A. Janssen (Cheltenham, Edward Elgar, 2002) pp. 48–62. 6. D. G. Brown, in The Earth’s Changing Land: An Encyclopaedia of LandUse and Land-Cover Change, ed. H. Geist (Greenwood Publishing Group, Westport CT, 2006), pp. 7–13. 7. C. J. E. Castle and A. T. Crooks, Principles and concepts of agent-based modelling for developing geospatial analysis, Working Paper Series 110 (2006), p. 60. 8. H. Couclelis, Why I no longer work with agents: A challenge for ABMs of human environment interactions, Proceedings of an International Workshop, eds. D. C. Parker, T. Berger and S. M. Manson, Irvine, California, USA, 2001. 9. P. Droogers and G. Kite, Irrigation and Drainage Systems 13 (1999) 275–290.

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10. N. Fohrer, K. Eckhardt, S. Haverkamp and H.-G. Frede, Applying the SWAT model as a decision support tool for land use concepts in peripheral regions in Germany, In Sustaining the Global Farm, 10th International Soil Conservation Organization Meeting, D.E. Stott, R.H. Mohtar and G.C. Steinhardt, Purdue University and the USDA-ARS National Soil Erosion Laboratory, USA, 2001. 11. Fohrer, S. Haverkamp and H.-G. Frede, Hydrol. Process 19, 3 (2005) 659–672. 12. P. W. Gassman, M. R. Reyes, C. H. Green and J. G. Arnold, Trans. ASABE 50, 4 (2007) 1211–1250. 13. E. F. Lambin, H. J. Geist and E. L. Lepers, Annu. Rev. Environ. Resour. 28 (2003) 205–241. 14. S. Moss, Policy analysis from first principles, Proceedings of the National Academy of Sciences of the United States of America, Vol. 99, Suppl. 3 (2002), 7267–7274. 15. A. Patt and B. Siebenh¨ uner, Vierteljahrshefte zur Wirtschaftsforschung 74, 2 (2005) 310–320. 16. J. G. Polhill, N. M. Gotts and A. N. R. Law, Cybernetics Systems 32, 1–2 (2001) 285–307. 17. H. Purnomo and P. Guizol, Math. Comput. Model. 44 (2006) 535–552. 18. R. K. Sawyer, Sociol. Method. Res. 31, 3 (2003) 325–363. 19. L. Tesfatsion, J. Econ. Dyn. Control 25 (2001) 281–293.

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


TOWARDS RIVER REHABILITATION AS AN INTEGRATED APPROACH TO FLOOD MANAGEMENT IN ASIAN CITIES DAVID L. HIGGITT∗ Department of Geography, National University of Singapore, 1 Arts Link, Singapore 117570

Flood management in Asian cities has conventionally been approached through structural intervention where floods are regarded as a threat requiring control through engineering infrastructure. Such a command and control paradigm represents a marked transition from the way that monsoon flood regimes have been traditionally perceived across Asia. Rapid urbanization and climate change has imposed increasingly difficult flood management challenges as an extension of impermeable surfaces generates rapid runoff and flash flooding, while cities expand into flood-prone areas. Property and communities are placed at enhanced risk. Urbanization reallocates risk as channel and floodplain modification influences flood regimes, while demands for flood protection at certain locations can redistribute risk to other areas. An increasing concern about flood hazard across Asian cities questions whether conventional solutions reliant on structural intervention are sustainable. Such questioning is mirrored by an alternative paradigm of rehabilitation in integrated river basin management — a recognition that restoring and sustaining functional river ecosystems with high biodiversity is one of the greatest challenges facing society. Rehabilitation initiatives demand a new approach to river basin management which encourage interdisciplinary activity, particularly between engineers, hydrologists, geomorphologists and ecologists. The paper sets out some preliminary ideas from a research project investigating the potential for river rehabilitation as a central tenet of flood management, with a particular focus on Asian cities.

1. The Challenge of Sustainable Flood Management 1.1. Introduction The evidence that flood disasters have an increasingly significant impact across Asia is a matter of concern. Data recently compiled for a United Nations World Water Assessment Programme indicate a trebling of designated flood disasters each year in the period 1980 to 2006.1 Asia 41

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also dominates the statistics for flood disaster fatalities (64% of global total) and displacements (96% of global total) over the same period. The vulnerability of Asian populations to flood hazard is partly explained through the historical development of cities in fertile river basins which are subject to monsoon rainfall regimes. Traditional settlement patterns, resource management and cultural processes evolved to provide partial accommodation to an annual flood cycle but engineering intervention to harness water resources and seek protection from flood events has a long history. Therefore, approaches to flood management in Asian cities have conventionally been approached as a technical challenge requiring strong institutions to implement control through infrastructure. There are two broad areas of concern questioning the ability of a conventional command and control approach to flood management to continue deliver effective flood mitigation. The first relates to an emerging paradigm of river rehabilitation as a central pillar of integrated river basin management. The second questions the ability of conventional solutions to flood hazard to keep pace with the challenges imposed by rapid urbanization and climate change. Both of these issues are introduced briefly below before the paper considers some emerging themes in integrated management which may have particular relevance to Asia. 1.2. Rehabilitation: A reframing for integrated river basin management In juxtaposition to the “command and control” strategies frequently adopted by water resource institutions, there is a growing international movement concerned with the desire to restore and maintain functional river systems with high biodiversity. The emerging paradigm has been characterized as the dawn of an “era of river repair”.2 The roots of this movement can be traced back about three decades as aquatic scientists considered how to apply some of the developments in ecological restoration of terrestrial ecosystems to streams and rivers.3 Developing in North America and Europe, and more recently in Australia, the river restoration movement focused initially on recovering systems form past engineering (e.g., channelization, disconnection from floodplains) extending into the idea that recovered aquatic ecosystems could complement biodiversity objectives. Such thinking is evident in the European Union’s Water Framework Directive (WFD) which was established to improve ecological status and water quality in rivers in member states. To some extent, the impetus for protecting aquatic ecosystems and recognizing the

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ecosystems services provided by rivers has been motivated by societal demands for healthy rivers. Specific schemes have often been driven by local communities. When experience from western countries is applied to Asia, however, the perceptions and interests of communities may be rather different. The potential for reframing ideas about river basin management therefore requires due consideration of the “visions” for managing rivers among various stakeholders.4 The Asian Development Bank has developed flood management policies which stress stakeholder engagement, public education and capacity building. A balance needs to be achieved between protecting infrastructure and associated water resource needs while promoting ecosystem services and enhancing environmental value. A move towards rehabilitation as a framework for river basin management also demands greater interdisciplinarity including, inter alia, engineers, hydrologists, geomorphologists, ecologists, landscape architects, planners and policy makers. 1.3. Are conventional solutions sustainable? Conventional solutions to flood problems tackled through engineering intervention have been successful in reducing the incidence of flooding in many Asian cities. An assessment of flood disaster impact5 indicates widespread improvements in preparedness across many parts of South and East Asia, compromised by an apparent increase in the severity of floods and reduced capacity to deal with extreme events. The problem is not the integrity of engineering solutions per se, but rather the moving target of delivering flood protection constrained by rapid urbanization, changing climate and the expectations of society. Rapid urbanization increases the extent of impermeable surfaces reducing infiltration and groundwater recharge and increasing the flashiness of runoff response. Floodwater can result from overflow of watercourses (such as rivers and major canals), backing up from feeder drains or from surface flow which does not enter the engineered drainage network. Conventional structural intervention has a tendency to focus on the capacity and performance of the drainage system. The response to damaging floods often focuses on the need to upgrade the drainage pathways. However, the cause of the problem — the increased runoff from urban surfaces — might be addressed by considering how to reduce flow into the drainage system. Localized retrofitting of bioretention basins, storage areas and wetlands are examples of alternative strategies to increasing drainage capacity. Indeed decoupling of urban runoff from stormwater drainage pipes was identified as an important step in an

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ecological restoration program in urban streams in Melbourne, Australia6 as even small events disrupted ecological recovery. However, the urbanization process in Asian cities is not just changing the infiltration and runoff characteristics of surfaces but also expanding settlement into flood prone areas. Ironically it is often the “protection” offered by infrastructure that encourages settlement to move into vulnerable locations. Newell and Wasson7 refer to the problem of a levee-only policy of flood management which is encountered in many parts of Asia. Using a system dynamics framework, a causal loop is described where the response to flood loss is pressure to take action which leads to levee construction or extension. This intervention results in a system where the frequency of small to medium flood events is reduced but the probability of extensive damage increases if the augmented levees were to be overtopped. Reduced frequency of moderate floods can also equate to limiting experience of preparedness and to perception that the hazard has been minimized. This perception of reduced community vulnerability, in turn increases pressure for floodplain development. Hence the unintended consequence of a visible action to reduce flood loss results in expansion of development into floodplain environments. Within Asian cities there is an added dimension to this sequence which is the expansion of slum development in flood-prone areas as a result of rural to urban migration. Chronic examples of informal settlement in flood-risk areas include Dhaka, Yangon and Jakarta.8,9 Flood management in Asian cities is therefore subject to increasingly difficult challenges as land use zoning has been ineffective in preventing communities moving into vulnerable locations while previous structural interventions have created a perception and/or expectation that flood hazard can be controlled. Demands for protection at one location transfer risk downstream but the implications have received limited attention. Added to these challenges is the uncertainty of climate change. While the dynamical downscaling of future regional climate projections remains problematic, there is some consensus that intensification of heavy precipitation events is occurring and will become more pronounced.10 Within the urban fabric, more intense precipitation extremes will more likely contribute to ponding of surface flow before it reaches drainage channels such that strategies to deal with reducing the speed of runoff entering the engineered drainage system from source are likely to be more significant. For many urban environments in Asia where topographic information may be limited, the question of the source of flood water and the sites where it accumulates will become more critical. The challenge imposed by urbanization, expansion into flood prone

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locations and the future impact of climate change make conventional ways of dealing with flood management unsustainable. Innovative approaches are required. 2. River Rehabilitation as an Alternative Paradigm 2.1. Restoration networks The river restoration movement in North America and Europe achieved momentum in the 1990s. Following the Fourth World Water Forum, the Asian River Restoration Network (ARRN) was formally established in 2006. ARRN is a non-governmental organization based in Japan which aims to promote and exchange knowledge, experience and technology for restoration projects. It has associated national organizations in Japan, Korea, and China. The development of the network is predated by transitions in the focus of water resource management over recent decades which have some parallels to experience in western countries. In Korea, for example, the focus on hydropower and stable water supply was augmented by a “close to nature” program in the 1990s which sought to promote eco-friendly and sustainable water resources development. This represents a shift in focus from predominance of flood control to both flood management and habitat conservation.11 The celebrated restoration of the Chunggye Stream in Seoul which had been entombed beneath an elevated highway was completed in 2005. As the flow in the original stream was limited a minimum ecological flow is achieved by transferring water from the nearby Han River such that this example is more about creating a community-friendly riverine landscape in the city center than restoring the pre-development feature. In Japan, a similar sequence of transition in river basin management is apparent with the introduction of “nature-orientated” river work from the 1990s, an emphasis on citizen participation and “whole of system” focus. As a tectonically active location with steep, short rivers debauching onto densely populated alluvial plains a high degree of engineering intervention has been necessary to reduce flood hazard. Sabo dams (check dams) are built on headwater locations to reduce the downstream transmission of sediment from unstable headwater reaches, while channel works are necessary to prevent channel migration on alluvial fan surfaces. Consequently Japanese rivers are heavily impacted by canalization, separation of channel and floodplain and by intensive urbanization. Restoration initiatives are mostly focusing towards simultaneous improvement of flood protection and ecosystem integrity.12 Singapore provides an example of an interpretation

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of restoration which focuses on turning riparian corridors into clean and aesthetically pleasing attractions. This is encapsulated under the Active Beautiful Clean (ABC) Waters Program launched in 2006. Like Korea and Japan this initiative can be seen as augmenting a conventional strategy to discharge monsoon rainfall quickly in hydraulically smooth canals with measures to promote community and recreational use of water bodies.

2.2. Reframing rehabilitation The suitability of the term “restoration” has often been debated. It is perhaps ironic that the development of a restoration network in Asia should coincide with a repositioning of key ideas among protagonists of the rehabilitation movement. Restoration implies returning a degraded system to its pre-disturbance state and, as such, requires some assumption of a pristine reference state. Reappraisal of the concept of dynamic equilibrium in geomorphological systems has questioned the notion of whether a stable historical reference can be identified and maintained, or, for that matter, whether any historical reference can be attributed as the equilibrium condition. In any case, the boundary conditions for the new designed state are likely to be different from the historical conditions. For this reason Wohl et al.13 advocate that projects focus on the restoration of process rather than a fixed end-point. Similarly Dufour and Pi´egay14 argue for an objective-based strategy where the project is designed to deliver an ecologically improved system but is not an attempt to return the site to its pre-disturbance state. If geomorphic systems are characterized by transient behavior, the reference is a product of a set of historical contingencies. It is more logical to consider the task in hand to be characterized as rehabilitation — the attempt to achieve healthy and sustainable rivers under prevailing conditions.2 This more pragmatic approach to rehabilitating rivers is likely to gain more favor in Asia, not least because river systems have been modified by humans for millennia. Indeed the riparian environment is a cultural landscape where human activity is strongly linked with traditional ecosystem functions. For this reason the ARRN recognizes the need for develop strategies suitable for the Asian Monsoon region where floodplain areas are dominated by paddy fields, rather than to mimic approaches from western countries. Thus rehabilitation strategies could be seen as a softening of conventional approaches to seek the best attainable ecological conditions which are compatible with flood control and other water resource functions.

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2.3. Reflection, experience and learning The brief description of trends in river basin management in selected Asian countries indicates that there has been some progress towards promoting an ecosystems-based approach, or at least acknowledging the importance of working with nature, which has supplanted earlier visions which were very much focused on engineering interventions for specific purposes such as flood control and hydropower generation. This growing awareness mirrors the rise of environmental management in general and its diffusion into a wide range of community and government activities. Yet, water resource management in Asia has remained to a large extent in the domain of command and control strategies. The question posed at the outset of the paper is to consider the potential for rehabilitation to become a central tenet of flood management. In this section, brief attention is given to considering how institutions might reflect and learn from experience of applying novel techniques. It is useful to begin this discussion by caricaturing the main contrasts between the command and control and the rehabilitation approaches, represented as conventional and alternative strategies. Whereas a conventional approach seeks to reduce uncertainties by devising technical solutions to narrowly defined problems, the alternative sees river basin management as a co-evolving complex adaptive system which embraces uncertainty as a key feature. It follows that management strategies should be focused on enhancing ability to adapt to uncertainty rather than focusing on controlling change to reduce a specific risk. A rehabilitation approach to sustainable river management is influenced by four features: An ecosystembased approach, whole-of-system (i.e., catchment-based) planning, adaptive management and participation.15 Adaptive management recognizes that inherent complexity necessitates a willingness to realign content and process according to context which is quite different from the linear and sequential planning processes envisaged conventionally. In other words there is a need to learn from pilot studies and experimentation. Within urban flood management, some evidence of a willingness to experiment with new approaches is apparent. Conventional approaches to increase the capacity of drains have been rebalanced by experimentation to reduce the amount of runoff reaching the drainage system. This concentration on the source of floodwater, which is most appropriate for dealing with flash flood generation from impervious surfaces can involve small scale retrofit of water retention features or design of new building development which incorporate areas to dispose of excess runoff as well as the possibility of road surfaces acting as flood conveyance channels during

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extreme events. However, the general message from the literature is that there have been limited shifts in the governance frameworks for managing water resources and that local scale experiments using novel designs have been relatively few in number. A recent analysis from Australia, where the concepts of river rehabilitation have received relatively high levels of empathy, has shown that organizational cultures, regulatory frameworks and centralized management systems militate against experimentation.16 Risk aversion and the fear of failure are prevalent. Drawing on ideas from sustainability science and organizational management, strategies to overcome the inertia of institutions can be explored. Central to the debate is the role of social learning. Social learning encapsulates the need for management to support collective action and reflection. It recognizes the need to develop the capacity of relevant authorities and other stakeholders to negotiate goals of environmental policy and translate these into action. Social learning can be characterized as a hub for collaborative and adaptive management which facilitates multistakeholder engagement in reflecting on activities — in this case pertaining to sustainable flood risk management which optimizes river health. Power relations between multiple interest groups will result in conflicts which need to be negotiated. As far as new approaches to flood management in Asia are concerned, the negotiation of a shared vision for sustainable development of river basins is critical. Social learning has also been presented as “third order” learning which provides opportunities for transformation. The first order is technical learning where outcomes can be used to refine techniques or policy instruments (within the status quo). The second order is conceptual learning where the fundamental aim and objectives of policy may be reconsidered and the perception of the “problem” re-evaluated.16 The sustainability science literature identifies numerous roles for social learning to contribute to capacity building and adaptiveness. Critical analysis of the effectiveness of learning processes applied to water governance in Asia remains modest.17

3. Summary River rehabilitation provides a framework for advancing a “whole-ofsystem” approach to sustainable river basin management which identifies the needs of water users and seeks to enhance ecological objectives. As such, flood mitigation is just one of several issues to be addressed within an integrated approach to improving river health. The “command and control”

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approach is characteristic in most Asian countries where institutions responsible for river management have traditionally been concerned with providing structural solutions to defined problems. There are signs from the diffusion of interest in river restoration into Asia and recent examples of alternative schemes to enhance aesthetic and/or ecological aspects of river systems to suggest that conventional approaches to flood hazard management based on structural intervention may be subject to negotiation. There are indications that ideas about adaptive management, governance structures and social learning are being debated and transformed in Asian contexts. Building community involvement and stakeholder interest remains a key challenge. In the face of the widespread damage caused by floods in several Asian cities in the summer monsoons of 2010 and 2011, there will be some pressure to enhance conventional flood mitigation strategies which may overwhelm debate about longer-term improvements for sustainable management of river basins. How visions for river management are negotiated requires further attention.

Acknowledgments The paper reports preliminary ideas from a research project funded by the Global Asia Institute, National University of Singapore. Ideas expressed here have benefitted from discussion with the following collaborators based at NUS: Alan Ziegler, Lim Han She, Robert Wasson, May Chui, Daryl Lam and Zach Smith and especially from conversations with Gary Brierley (University of Auckland, New Zealand).

References 1. Y. Adikari and J. Yoshitani, Global Trends in Water-Related Disatsers: An insight for policy makers, United Nations World Water Development Report 3, 2009. 2. G. Brierley and K. Fryirs eds., River Futures (Island Press, Washington DC, 2008). 3. S. Ormerod, Aquatic Conserv: Mar. Fresh. Ecosyst. 14 (2004) 543. 4. D. Higgitt and G. Brierley, Innovation 10 (2011) 36. 5. R. Osti, S. Hishinuma, K. Miyake and H. Inomota, J. Flood Risk Management 4 (2011) 203. 6. C. Walsh, T. Fletcher and A. Ladson, J. N. Am. Benthol. Soc, 24 (2005) 690. 7. B. Newell and R. Wasson, Conflict and Cooperation Related to International Water Resources: Historical Perspectives, UNESCO SC.2002/WS/53 (UNESCO, Grenoble, 2002).

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8. Y. Adikari, R. Osti and T. Noro, J. Flood Risk Management 3 (2010) 185. 9. World Bank, Climate Change, Disaster Risk, and the Urban Poor (World Bank, Washington DC, 2011). 10. S.-K. Min, X. Zhang, F. Zwiers and G. Hegerl, Nature 470 (2011) 378. 11. H. Woo, J. Hydro-Environment Res. 4 (2010) 269. 12. C. Yoshimura, T. Omura, H. Furamai and K. Tockner, River Res. Appl. 21, 93 (2005). 13. E. Wohl, P. Angermeier, B. Bledsoe, G. M. Kondolf, L. MacDonnell, D. M. Merritt, M. A. Palmer, N. L. Poff and D. Tarboton, Water Resour. Res. 41, W10301 (2005). 14. S. Dufour and H. Pi´egay, River Res. Appl. 25, 568 (2009). 15. C. Gregory, G. Brierley and R. LeHeron, Geography Compass 5, 182 (2011). 16. M. Farrelly and R. Brown, Global Environ. Change doi 10.1016/j.gloenvcha. 2011.01.07, (2011). 17. L. Lebel, T. Grothman and B. Siebenh¨ uner, Int Environ. Agreements 10, 333, (2010).

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


FLOW STRUCTURE AND EROSION SUPRESS BY VEGETATION IN OVERFLOW ON LEVEES∗ MOTOYASU SATO† Engineering graduate course, Tohoku University, Sendai, Miyagi, Japan TAKESHI NOTE Engineering graduate course, Tohoku University, Sendai, Miyagi, Japan AKIRA MANO Engineering graduate course, Tohoku University, Sendai, Miyagi, Japan KEIKO UDO Engineering graduate course, Tohoku University, Sendai, Miyagi, Japan

Prototype experiments on levee breach by overflow show significant effect of vegetation on erosion suppress. This is favorite finding for the levee protection. However, the detailed mechanism is not studied yet. The purpose of this study is to find the fundamental characteristics of flow among the vegetation and to make the mathematical model. Hydraulic experiments were conducted for supercritical flow through inflexible vegetation model. The flow field was measured by laser doppler anemometer. K-
model was developed to reproduce the velocity profile.

1. Introduction By recent frequent heavy rains and local heavy rains, the risk of the estimated high-water level excess flood increases. In addition, in the limitation of the cost side such as a headwind or the public-works spending reduction for the dam construction, efficient reinforcement technique and ∗ This

study is supported by the GRANDE project, in the framework of JST/JICA SATREPS. † Corresponding author. 51

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rating method of the preexisting levee, the demand of the method of analysis corresponding to the overflow damage rise. In accordance, Ministry of Land, Infrastructure and Transport performs the overflow experiment of the real scale using the old levee, and the case on shortcutted vegetation briefly gets a result that the erosion of the levee main body is significantly suppressed. This is useful knowledge to be able to keep levee for an overflow at long time.1 However, the mechanism is not examined why vegetation delays erosion. About a study of the overflow dyke break, Faeh2 almost predicts time to suffer dyke break and overflow discharge based on past theoretical empirical knowledge. However, this study remains in a prediction, the inspection on the scale that is macro, and the study that paid its attention to physical property and vegetation of the levee surface on the scale that is a micro is not performed. On the other hand, from the viewpoint of river improvement and irrigation, hydrophilic function, the study that is going to clarify the influence that vegetation gives to stream flow is performed flourishingly. The eddy flow model that can explain the turbulent structure in a simulated vegetation layer in a mild slope flow is suggested.3,4 However, anyone applies these to a heavy slope flow such as the bank overtopping and does not examine a flow change in structuretextural change by the influence of the vegetation and relations of the erosion rate restraint through experiments actually. In this study, we confirm a flowing change in structuretextural change by the existence of the vegetation and relations of the erosion rate restraint through an open channel experiment having mock vegetation in a heavy slope flow such as the bank overtopping. This study is intended that we examine a model to clarify the underlying mechanism of the levee back slope side sheet erosion with the simple and easy mathematical model which assumed the basic dynamics expressing this basis.

2. Experiment 2.1. Experimental setup We used a channel of length 5.0 m, 0.2 m width and heavy slope open channel which we assumed to be of gradient 1/10. This slope gradient can get water stream like flood stream and no experiments did in this range because of difficulty of experimental setup. The real levee shape varies, but the overflow of the levee generally switches over from a subclinical flow to a supercritical

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flow through critical depth in a crown, and it is thought that it is with uniform flow depth in the vicinity of top of slope. When vegetation does not exist at all when the flow of the back slope side is very fast and examines it using the number of Rouse from the viewpoint of earth and sand hydraulics, as for the earth and sand of the slope, cases to satisfy a condition rolled up as floating sand are often found. In consideration of these things and spatial limit, it is the channel which it set. The model of the vegetation used bamboo of rigid non-flexible 3 mm in diameter. By the experiment of Ministry of Land, Infrastructure and Transport, it is confirmed that justifiable erosion becomes late the case that harvested vegetation briefly, and there is little down-flow clearly in comparison with in front of that the vegetation of this case cuts, and this vegetation contributes to restraint of the erosion rate. Therefore, by this experiment, we adopted a non-flexible vegetation model including a meaning of the simplification of the problem as the model which was in this state. In addition, the vegetation bends for fast flow velocity when vegetation is long. The study of the case is conducted by Rhee et al.5 We fitted a Styrofoam board between the most base and the channel wall of the channel and inserted bamboo Higo every 2 cm in the shape of a rightness diamond there. The vegetation density (the cover area per unit capacity of the flow) of this time is 0.075. The height of the vegetation assumed to be 3 cm in all experiment cases. The test section reached in the 50 cm upper reaches from downstream edge. We show the experiment plant layout drawing which we used in Fig. 1. We experimented on the flow quantity under conditions of 5 L/s, 8 L/s, three kinds of 11 L/s. We tested the immobilized bed because that was in a state that attached the paint which the particle size chose 0.1 mm, 0.2 mm, the earth and sand of 0.3 mm and mixed this with to 120 cm section floor thinly towards the upper reaches from the downstream edge. In addition, we set the opening of the valve to keep a fixed flow quantity beforehand.6 Q = Ch5/2


2 
h 0.2 0.004 + 0.14 + 1/2 − 0.09 , C = 1.350 + h B W where Q: Discharge (m3 /s), h: Overflow depth (m),

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Fig. 1.

Experiment setup.

C: Capacity-coefficient (m0.5 /s), B: Channel width (m), W : Height of the gate (m).

2.2. Experimental cases The measurement of the flow velocity used laser anemometer at a spot of 30 cm towards the upper reaches from the down stream edge. We assumed the measuring point which was the nearest to the bottom 0.5 mm from a base and subsequently measured it with 1 mm, 2 mm. After that we pushed forward the measurement for a vertical upswing every 2 mm after it for a base. The test frequency of the laser anemometer was set to 100 Hz and we

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Table 1.

Experiment cases.

Cases

Discharge (L/s)

Particle size (mm)

Vegetation

Measure point

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8 8 8 5 8 11 5 8 11 8 8 8 8 8 8

0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.3 0.1 0.2 0.3

with with with with with with without without without with with with without without without

1 2 3 1 1 1 1 1 1 1 1 1 1 1 1

measured and performed 1,000 times in total of the mean with flow velocity in each measuring point for 10 seconds. We performed the experiment by flow quantity, floor particle size, existence or nonexistence of the mock vegetation, measuring point distinction. We show the experiment case as shown in Table 1. In addition, we performed this measuring point with three points of the blue (First Point) red (Second Point) green (Third Point) to show it in Fig. 2. This is because some changes were seen in flow velocity profile by measuring point in an experiment using mock Habu where Huai et al. went to.7

2.3. Results 2.3.1. A measuring point comparison We show each point flow velocity profile in Fig. 3. The flow velocity difference at each point had a gap between around 10 cm/s in around 3 cm/s, First Point and Third Point in First Point and Second Point. This is because flow velocity was confused by flow separation under the influence that we are most recent, and mock vegetation is placed for Third Point of upper reaches. However, the flow velocity vertical distribution becomes similar structure both if we look qualitatively.

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Fig. 2.

Fig. 3.

Measure points.

Velocity structures at three measures points.

2.3.2. A flow velocity suppressant effect due to the vegetation We show a result of Case4∼Case9 in Fig 4. Case7∼9 is flow velocity profile when there is not vegetation. The flow velocity profile obeyed logarithmic

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Velocity structure with/without vegetation.

law, and the difference of the flow quantity of each case appears by increase of the flow velocity conspicuously, and the increase of the one depth of the water is uncommon. This is equal with a result predicted in flow velocity formulas of Manning. Case 3∼5 is flow velocity profile when there is vegetation. Distribution form of the flow velocity out of the vegetation (we call it a vegetation outer layer) is different from vegetation (we call it a vegetation inner layer). Flow velocity is largely in comparison with case when there is not vegetation reduced. In addition, it was with about the same flow velocity in the vegetation inner layer in spite of flow quantity changing in each case in three Cases. Because the depth of the water increases with increase of the flow quantity, the flow for the increase of the flow quantity understands that we go along the vegetation outer layer. Therefore, the vegetation understood that it became hard to be affected by the flow quantity. In addition, characteristic flow velocity profile is provided at the neighborhood of base and the upper part when we watch flow velocity profile in the vegetation of Case 3∼5. In a vegetation inner layer, a layer (bottom vegetation) that is extremely near to a base, two characteristic distribution such as the upper part (a middle class in the vegetation) exist, and put it together with a vegetation outer layer, and three layers exist. We show the result that Fig. 5 changes particle size, and measured flow velocity profile. Case 13∼15 is flow velocity profile when there is not vegetation and shows a theoretical value of the scabrous turbulence logarithmic law with a curve for experimental conditions of Case 14. The experimental value of Case 14 accords to a theoretical value and understands that normal open channel eddy flow is reproduced. Case 10∼12

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Fig. 5.

Fig. 6.

Velocity structure with/without vegetation.

Velocity structure at bottom layer with vegetation.

is experimental value when there is vegetation. The flow velocity profile changes by particle size with a vegetation inner layer and the vegetation outer layer to some extent, but the influence is small. 2.3.3. A characteristic of the layer in the vegetation Flow velocity profile of the few stories in the vegetation of Case 4∼6 is Fig. 6 and understands that it becomes the logarithmic profile. Furthermore, the flow velocity becomes small in case where particle size is big when we read Fig. 7 which showed flow velocity profile of Case 10∼12 every base particle size and understands that we are affected by the base particle size. In other

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Velocity structure at bottom layer with vegetation.

words, the bottom layer in the vegetation is the scabrous turbulence domain where wall law decided from botom layer is established.

3. Mathematical Model 3.1. A calculation method According to the study of the past, turbulence ground is formed in the vegetation inner layer by the flow of the vegetation outer layer. Therefore, analysis to consider the turbulent structure including these two layers is necessary because momentum exchange is performed with an outer layer in the vegetation. The Shimizu and others (1992) announced the model that included resistance of the vegetation and referred to the model of this fielder this time and reproduced the phenomenon.4 We show the model that we used this time in the Fig. 8. The difference scheme took the centered difference about forward difference, the space about time. In addition, we gave the uniform flow depth which we got from an experiment for known amount (Fig. 13), and quantity of change of unknown variable U , K, e demanded a convergent solution on a condition to fit into less than 0.1% for a time step before one. The calculating area located a calculation lattice point every in these intervals. Here, it was said that it was sand granules rough surface of the particle size. The base boundary condition, the surface of the water boundary condition set it in reference to a fielder together. The conditional expression is derived from logarithmic law prescribed to friction velocity. In addition, we almost supposed the turbulent structure to be isotropy in the vicinity of the surface of the water, and K, the condition of e supposed that

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U

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 ∂U ∂V   ∂U ∂ P 1 ∂  ∂U  ∂  ∂U   + +V = g sinθ −   − Cdx λU U 2 + V 2 +  2(ν t + ν )  +  (ν t + ν ) ∂x ∂y ∂x  ρ  2 ∂x  ∂x  ∂y   ∂y ∂x  

 ∂U ∂V   ∂  ∂V  ∂V ∂V ∂ P 1 ∂     +  2(ν t + ν ) +V + = − g cosθ −   − Cdy λU U 2 + V 2 +  (ν t + ν ) ∂y  ∂x ∂y ∂y  ρ  2 ∂x   ∂y ∂x   ∂y  2 2 2     ∂K  ∂   ν t  ∂K       ∂K ∂K ∂   ν t  + ν t 2  ∂U  +  ∂V   +  ∂U + ∂V   − ε + C fk   1 Cdx λU U 2 + V 2  U +  1 Cdy λU U 2 + V 2  V   +   U +V = + ν  + ν      ∂x   ∂y    ∂y ∂x   ∂x ∂y ∂x   σ k  2    2  ∂x  ∂y   σ k  ∂y       U

U

 ∂ε  ∂   ν  ∂ε  ε ∂ε ∂ε ∂  ν +V =   t + ν   +   t + ν   + ∂y ∂x   σ k ∂x  ∂x  ∂y   σ k  ∂y  K

ν T = Cµ

2 2  2        C1 ν t 2  ∂U  +  ∂V   +  ∂U + ∂V    + C fε   1 Cdx λU U 2 + V 2  U +  1 Cdy λU U 2 + V 2  V  − C2ε   2        ∂x   ∂y    ∂y ∂x     2          

K2

ε

y : Distance from the base

Cµ = 0.09, C1 = 1.44, C2 = 1.92, σ K = 1.0, σ ε = 1.3

ν T : Eddy viscosity coefficient ν : Kinematic - viscosity coefficient

The certified and established value C fK = 0.07C fε = 0.16

U : Average flow velocity

The value by Shimizu

K : Turbulence energy

ε : Turbulence dissipation energy λ : Confluence degree of the vegetation C D : Drag coefficient

Fig. 8.

Fig. 9.

Mathematical model.

Velocity structure Q = 5.

only the change flow velocity of the depth of the water direction disappeared on the surface of the water like Nezu, Nakagawa. In addition, the depth of the water used the thing which an experiment provided.

3.2. Calculation result We show flow quantity 5 L/s, a calculated value at particle size 0.2 mm in 8 L/s 11 L/s and the experimental value comparison to Figs. 9, 10, and 11. We show an experimental value and good agreement with three cases, and it may be said that we are good and reproduce few stories in the vegetation,

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Fig. 10.

Velocity structure Q = 8.

Fig. 11.

Velocity structure Q = 11.

a middle class in the vegetation, three levels of characteristic flow velocity profile structure of the vegetation outer layer. This was similar with particle size 0.1 mm, the case of 0.3 mm. In addition, the relations of base layer thickness and the particle size by the particle size in the few stories in the vegetation were approximately around 15 times. We show flow quantity 5 L/s, a calculated value of the intensity of turbulence at particle size 0.2 mm in 8 L/s 11 L/s and the experimental value comparison to Fig. 12 of Fig. 13 of Fig. 14. Both become the overestimate in the vicinity of Habu High School, but show an experimental value and safe agreement in the vegetation in an estimate of the bottom face shear force from the neighborhood of important base. The thing which compared the base shearing stress that demanded it than a calculated value with the base shearing stress that supposed few

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Fig. 12.

Intensity structure Q = 5.

Fig. 13.

Intensity structure Q = 8.

Fig. 14.

Intensity structure Q = 11.

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Table 2.

Experiment Calculated

Bottom shear stress.

Vegetation

Bottom shear stress (N/m2)

with without with

2.54 19.4 2.77

stories to be distribution of the logarithmic law according to wall law by an experiment is shown in Table 2.

4. Conclusion We showed influence on flow field due to the vegetation by we tested a turbulence lower open channel having mock vegetation in this study, and having examined flow velocity vertical distribution, disorder intensity distribution. In addition, we did it with knowledge for the elucidation of the erosion suppressant effect under flowing field structure, the vegetation that had the vegetation which there was few of the past study till now by showing the model that could reproduce this distribution. We compile below concrete content. (1) When there was not vegetation, we compared it, and flow velocity was largely reduced by existence of the vegetation, and the difference of the flow quantity of each case understood what we produced with a vegetation outer layer mainly. Therefore, we do not receive influence of the flow quantity in the vegetation inner layer very much, and the flow velocity is almost kept to a constant value. (2) The vegetation inner layer was divided into a bottom layer in the vegetation and a middle class in the vegetation, and influence of the vegetation drag was dominant, and the thing, the latter that wall law affected by the bed roughness consisted as for the former understood that we showed the approximately same distribution to vertical direction. (3) We understood that we could reproduce a vegetation outer layer, the flow velocity profile of the vegetation inner layer by using the model of two dimensions of plumbs. (4) The base shearing stress understood that it was damped under the influence of vegetation to about 1/8. In addition, we showed agreement

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with an experimental value and a calculated value when there was vegetation.

References 1. R. Faeh, J. Hydr. Engrg. 133, 9 (2007) 1000–1009. 2. Ministry of Land, Infrastructure and Transport t Tohoku district maintenance station Yamagata river national highway office: Sugawa levee experiment analysis examination business report, 2006. 3. Y. Shimizu, T. Tsujimoto, H. Nakagawa and T. Kitamura, Period: Experimental study about the flow field structure with the upright habit vegetation layer, Japan Society of Civil Engineers collected papers, No. 438, II–17, 1991, pp. 31–40. 4. Y. Shimizu, T. Tsujimoto and H. Nakagawa, Study on numerical calculation of the flow field with the upright habit vegetation layer, Japan Society of Civil Engineers collected papers, No. 447, II–19, 1992, pp. 35–44. 5. D. Rhee, H. Woo, B. Kwon and H. Ahn, River Res. Appl. 24 (2008) 673–687. 6. Japan Society of Civil Engineers: Hydrology formulary, 1999 version, p.243. 7. W. X. Huai, Y. H. Zeng, Z. G. Xu and Z. H. Yang, Adv. Water Resour. 32, (2009) 487–492. 8. Takeshi Note, Study on erosion properties of the levee back slope side outer layer by the overflow, Tohoku University graduate school master’s thesis, 2009. 9. I. Nezu and H. Nakagawa, Numerical calculation of the open channel eddy flow by the modified eddy flow model, Japan Society of Civil Engineers collected papers No. 387, 1987, pp. 125–134.

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


AUTO-CALIBRATION BY EVOLUTIONARY ALGORITHM IN DECISION SUPPORT SYSTEM FOR FLOOD WARNING JONGKON CHONGWILAIKASEM Department of Water Resources Engineering, Kasetsart University, Bangkok, Thailand funcy [email protected] SUWATANA CHITTALADAKORN∗ Associate Professor, Ph.D., Department of Water Resources Engineering, Kasetsart University, Bangkok, Thailand [email protected] SOMPOP SUCHARIT Royal Irrigation Department, Bangkok, Thailand [email protected]

The development of decision support system is very important for flood warning. One of the major parts in developed system is the distributed rainfallrunoff model with the near real time information. The result of this model is used as the important information for the decision makers in decision support system. However, this model has a huge number of model parameters varying widely in space and time, which is required in calibration. Therefore, automatic calibration routine, developed to calibrate spatial variation of flow characteristics within the basin, needs to be emphasized. In this study, the Huai Mae Nai basin and Huai Mae Rim basin which are the sub-basins in the Upper Ping River Basin of Northern Thailand was used as the case study. The auto-calibration procedure using Genetic Algorithm (GA) for multiobjective function is presented in the model. base of this decision support system. This algorithm was used for auto-calibration in solving and calibrating the distributed rainfall-runoff model.

1. Introduction Floods are the most occurring natural hazards which are the causes of loss of life and widespread damage to properties. The effects of flooding ∗ Corresponding

author. 65

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can be decreased by warning system protection. The decision support system for flood warning has become popular in making decision related to complex problem in water resources systems. Generally, the decision support system consists of three major components — data base, model base, and dialogues base. The decision support system for flood warning is for people preparation and evacuation. The system needs to have a sufficient of meteorological and hydrological data both in space and time inputting to the distributed rainfall-runoff (RR) models. The distributed RR model aims to predict the runoff from the precipitation over the catchment area. Moreover, each model involves huge number of calibration parameters, values varying widely in space and time, which are required for calibration. Manual calibration in every input data was a time consuming task.3 Therefore, more attention is given to automatic calibration procedures, by which parameters are adjusted automatically according to a specified search scheme and numerical measures. Although, in general, the automatic calibration routines are based on a single objective formulation, multi-objective formulation has been more applied for calibration in RR models because of their multi-objective nature processes.2,4,7,8,12 Most multi-objective techniques attempt to identify a set of optimal solutions for complex problems. In model calibration, no single-objective function is adequate to measure property for the simulation of all the important characteristics of the system that are reflected to the existing condition. Therefore, the multi objective for model calibration is needed to be considered.12 The most optimization algorithm for multi-objective problem is evolutionary algorithms (EAs), which are one of the population based optimization algorithms. These algorithms have become increasingly popular in the last few years in many study fields because of their effectiveness in finding optimal solutions. Therefore, the objective of this research is to develop an auto-calibration procedure for distributed RR model by EA. In this research, the hydrological information observed in the sub-basin of Upper Ping River Basin, Thailand was used as a case study.

2. Methodology The developed RR model in this study used the updated data in Upper Ping River Basin, Thailand. The spatial data, which are used in this study consists of digital elevation model (DEM), soil type, and land use. The

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methodology to evaluate the distributed runoff in RR model is developed in Visual Basic. This model is based on raster or grid-based structure that can describe the characteristic in area as grid cell. The grid cell size of all input data is prepared in the same resolution size. The modeling approach was developed to enable the prediction of spatial runoff distribution throughout a catchment and runoff hydrograph at a selected grid cell in the catchment area. The optimal parameters set, searching by EA, have the potential to predict the spatial runoff and runoff hydrograph.

2.1. Distributed rainfall-runoff model Currently, the development of distributed RR model is increasing rapidly. The distributed RR can provide the specific characteristic of the basin. This study used distributed parameters to simplify the hydrological processes. The developed model structure is able to incorporate distributed rainfall and can provide runoff information in different points of the catchment. The catchment is split into hydrological grid cells (50 × 50 m), which is treated as a small catchment. The distributed rainfall is derived from the point rainfall data with the same resolution as the hydrological grid cells by using the Inverse Distance Weight (IDW) method.5 The runoff simulation consists of two processes (see Fig. 1); the first process is runoff calculation in each grid cell that the Rational Method and the SCS-CN method is used for generating runoff.11 The equations used in this process are as follows; CN total = CNR + CNS + CNV + CNSU , CN Adj = CN total + RainCoefficient , Qp = aRb CN cAdj Ad ,

(1) (2) (3)

where CN total = total Curve Number, CNR = the Curve Numbers defining from characteristic of relief, CNS = the Curve Numbers defining from characteristic of soil infiltration, CNV = the Curve Numbers defining from characteristic of vegetative cover, CNSU = the Curve Numbers defining from characteristic of vegetative cover, Qp = the peak runoff rate (cfs), CN Adj = adjusted curve number, A = catchment area (km2 ), and a, b, c, d = coefficient parameters. The second process is the routing process. The generated runoff is routed from the first grid to the next grid cell by water balance incorporating

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Fig. 1.

Distributed rainfall-runoff model.

with Topographic Index.1 The equations used in this process are as follows;
 A
T I = ln , (4) L tan β Qout = T I × Qin ,

(5)

where T I = topographic index of each grid cell, A
= small watershed area (m2 ), L = distance of flow (m), L tan β = grid slope, Qout = the outflow of each grid cell (cfs), and Qin = the inflow of each grid cell (cfs). At the basin outlet, the total runoff will be the runoff accumulation from the upstream grid cells. 2.2. Evolutionary optimization algorithms EAs are family of population based optimization algorithms, which have become increasingly popular in the last few years in water resources studies. The well-known EAs are for example; Genetic Algorithm (GA), Evolution Strategy (ES), Genetic Programming (GP), Evolutionary Programming (EP), and Differential Evolution (DE), etc. Each algorithm maintains a population of solutions to the optimization problem, (also called

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individuals or chromosomes), which evolve over a number of generations.12 The goodness of each individual, i.e., its fitness, is given by a function defined for the specific optimization problem. Evolution is performed using genetic operators that depend on the specific problem and encoding, e.g., (i) mutation operator, which modifies one solution from the population, to obtain a new one and (ii) crossover operator, which uses several parents to create a number of offspring, etc. For each generation, a new set of solutions is produced from the previous population, either by replacing some parent individuals by children, or by performing fitness-based selection on all parents and children, (see Fig. 2). From the various EAs, the most popular algorithm is GA, because of its better performance compared to other search algorithm. The GA belong to the larger class of EA, which generate solutions for optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. One seeks the solution of a problem

Start Population (Decision Variable)

Genetic Algorithm

Evaluation Strategy Evaluation (Fitness)

Genetic Programing Differential Evolution(DE)

Reproduction (Crossover, Mutation)

Evaluation

New generation

Selection

NO

Fig. 2.

Meet termination criterion?

YES

Typical flowchart of EA iteration.

End

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in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved), by applying operators such as recombination and mutation (sometimes one, sometimes both).3 This type of EA is often used in optimization problems. In this research, the GA was applied for searching the appropriate parameters in distributed RR model. 2.3. Auto-calibration procedure Many real-world optimization problems, especially numerical calibration situations, required the process of determining a set of values of decision variables that satisfy the constraints and provide the optimal response to the objective function. Figure 3 shows the flow chart of an auto-calibration procedure. The auto-calibration procedure is based on a multi-objective calibration and the GA. The process is start from setting up the initial decision variable,

Start GA

Set up initial decision variable (a,b,c, and d) Rainfall-Runoff Model

Initial population

Selection

a,b,c, and d

New a, b, c, and d Reproduction (Crossover, Mutation)

Q=aRbCNcAd -

Runoff calculation New Population

Observed Runoff

Objective function

Meet termination criterion ? YES

End Fig. 3.

The flow chart of an auto-calibration procedure.

NO

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coefficient parameter. Then the model will simulate the runoff and examine the result for the multi-objective function. The result would change when the decision variables change. Therefore, to in each computation loop, the GA will be searching the new sets of decision variables and the process will repeat until a specified stopping criterion is satisfied. For the multi-objective optimization, the main components are as follows: • The decision variables. • The objective function. • The Constrains and termination criterion. 2.3.1. Decision variable The Decision Variables sets used in this study composed of four parameters (a,b,c, and d) are as in Eq. (3). 2.3.2. The objective function There are many formulations of performance measure for hydrological model that can consider as objective function. Basically, they are based on a comparison between the observed and simulated flow at the outlet or at any flow gauge station in the watershed. However, the suitable objective function is one of the key for a successful calibration scheme. In this research, two objective functions are formulated as follows: • Objective function 1; Percentage of water balance error: V (θ) =

Vsim (θ) − Vobs × 100%. Vobs

• Objective function 2; Root Mean Square Error (RMSE):  T 2 t=1 (Qobs,t − Qsim,t (θ)) , RMSE (θ) = T

(6)

(7)

where θ = model parameter set, T = number of the time steps in the calibration period, Vobs = observed total discharge volume, Vsim = simulated total discharge volume, Qobs,t = observed discharge at time step t, Qsim,t (θ) = simulated discharge at time step t, and Qobs = mean value of the observed discharge. The multi-objective calibration problem can be stated as follows: M inimize{V (θ), RMSE (θ)},

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where Objective function 1 : Min Z2 = ∆V,

and

Objective function 2 : Min Z1 = RMSE(Q). The objective function 1 is the hard constrain where the objective is to minimize the difference in volume error for each simulation. The optimal value is 0.0. While the objective function 2 is the soft constrain where the objective is to minimize the difference in flow rate error for each simulation. The RMSE value represented the quality of the calibration of both mass balance and the routing. The optimal value is 0.0. 2.3.3. The constrains and termination criterion Constrains in this problem are divided into three types as follows: 1. Equality Constrains The equality constrains in this study consist of: 1.1 The runoff evaluation equation in each grid cell: c Ad . Qmodel = aRb CNAdj

(8)

1.2 Runoff volume at the outlet or at any flow gauge station in the watershed:  t2 f (Qmodel )dt. (9) Vmodel = t1

2. Inequality Constrains The inequality constrains in this study consist of: • The decision variable values (a,b,c, and d) in range between zero and one. • The positive values of simulated total discharge volume. 3. Non-Negativity Constrains The non-negativity constrains in this study consist of: Qmodel , Vmodel , R, C, N, A, N, a, b, c, d ≥ 0.

(10)

The auto-calibration will search the parameter set to meet the objective function 1 before concerning the objective function 2 and search the new parameters set that meet both objective function. Generally, the automatic calibration procedure has three termination criteria in each generation.10 The processes will stop when one of the criteria is arrived first. In this study, three stopping criteria used to terminate the

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algorithm are as follows: • • •

Function convergence: The calibration process will stop when the objective functions values within the 50 loop was less than 0.001. Parameter convergence: The calibration process will stop when the population of points converged into 0.0001 of the original parameter space. Maximum number of iterations: The calibration process will stop when the number of model evaluations was greater than 5,000.

3. Case Study The described methodology was tested at the Huai Mae Rim (515 km2 ) and Huai Mae Nai (18 km2 ), which are sub-basins located in the Upper Ping River Basin of Northern Thailand (see Fig. 4). The characteristics of soil

Fig. 4.

Huai Mae Rim catchment and Huai Mae Nai catchment.

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type of the catchments are of silt clay and the underlying layer consists of Gneisses and Schists. The soil layer is shallow to moderate depth. The land use characteristics are mixture of mixed forests, sparsely wooded grasses and bush. Landuse, soil and topographic data were aggregated to the 50 m resolution. The average rainfall in Huai Mae Nai is 0.56 mm/year and in Huai Mae Rim is 7.95 mm/year. Two flow gauging stations, P.21 and P.27A, as shown in Fig. 4, are located in the study area recording daily water level and daily water discharge. Furthermore, daily precipitation from seven raingauge stations was used. For the calibration, five storm events, which consist of event no. 1 (May 31, 1979 to June 26, 1979), event no. 2 (June 15, 1985 to July 15, 1985), event no. 3 (September 5–29, 1996), event no. 4 (July 25, 2001 to August 16, 2001), and event no. 5 (September 14, 2006 to October 12, 2006) as shown in Fig. 5 were used. 4. Result and discussion Five storm events, as shown in Fig. 5 were used for model verification. The limited values and initial values of calibration parameters are shown in Table 1. When used in auto-calibration processes, it was found that optimum parameter sets, which are obtained from each storm event, are different and varies with time. The results from using the auto-calibration tool are as in Table 2 and the comparison between observed and simulated values for the discharges are shown in Fig. 6. The results show reasonable agreement between observed and simulated values for all variables. The

Precipitation (mm)

0 10 20 30 40 50 60 70 80 90

26/6/1979

24/6/1979

22/6/1979

20/6/1979

18/6/1979

16/6/1979

14/6/1979

12/6/1979

10/6/1979

8/6/1979

6/6/1979

4/6/1979

2/6/1979

31/5/1979

Date

Event No.1

Fig. 5. Five storm events of study case. The x axis is date and the y axis is precipitation in mm.

Precipitation (mm)

0 10 20 30 40 50 60 70 80 90

Fig. 5.

Event No.5

(Continued ) 16/8/2001

14/8/2001

12/8/2001

10/8/2001

29/9/1996

27/9/1996

25/9/1996

23/9/1996

21/9/1996

19/9/1996

17/9/1996

15/9/1996

13/9/1996

11/9/1996

9/9/1996

15/7/1985

13/7/1985

11/7/1985

9/7/1985

7/7/1985

5/7/1985

3/7/1985

1/7/1985

29/6/1985

27/6/1985

25/6/1985

23/6/1985

21/6/1985

19/6/1985

17/6/1985

15/6/1985

9in x 6in

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2/10/2005

30/9/2005

28/9/2005

26/9/2005

24/9/2005

22/9/2005

8/8/2001

6/8/2001

4/8/2001

2/8/2001

31/7/2001

29/7/2001

7/9/1996

5/9/1996

Precipitation (mm)

ADGEO

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18/9/2005

16/9/2005

14/9/2005

12/9/2005

10/9/2005

8/9/2005

6/9/2005

4/9/2005

200 27/7/2001

0 20 40 60 80 100 120 140

2/9/2005

25/7/2001

Precipitation (mm) 25

31/8/2005

29/8/2005

Precipitation (mm)

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0

10 5

15

20

30

Event No.2 Date

Event No.3 Date

50 0

100

150

Event No.4

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performance evaluation of model using percentage of water balance and RMSE are in Table 2, it can see that the model’s accuracy is acceptable. For the accuracy of decision variables, the values are satisfied when compared with the suggestion values in Jongkon’s report6 and Pongsak’s report7 (see Table 3). The number of iteration depends on the objective Table 1.

The feasible decision variable space used in auto-calibration.

Calibration Parameters

Initial Values

Lower Limit

Upper Limit

a

0.0005

0.00

1.00

b

0.05

0.00

1.00

c

0.50

0.00

1.00

d

0.05

0.00

1.00

Table 2.

Optimum decision variable set and auto-calibration results. Storm Event no.

Calibration Parameters Decision Variable a b c d No. of iteration Auto-calibration result Performance Measures Water Balance (%) RMSE (m3 /s)

1

2

3

4

5

0.0743 0.7840 0.1680 0.0650

0.0011 0.7940 0.8800 0.0440

0.0179 0.7780 0.6300 0.0330

0.0096 0.7910 0.6900 0.1030

0.1091 0.7500 0.0880 0.0970

1342

1483

121

795

276

0.00700

0.00110

0.00900

0.00025

0.06086

0.00069 0.05690

0.0004 0.0650

0.0001 0.0210

0.0006 0.0012

0.0003 0.0840

25 Observed Simulated

Discharge(m^3/s)

20 15 10 5 0 31/5/1979

5/6/1979

10/6/1979

15/6/1979

20/6/1979

25/6/1979

30/6/1979

Date

Fig. 6. Observed and simulated hydrographs obtained by GA multi-objective methodology.

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Observed Simulated

Discharge(m^3/s)

7 6 5 4 3 2 1 0 15/6/1985

22/6/1985

29/6/1985 Date

6/7/1985

13/7/1985

40

Observed Simulated

Discharge(m^3/s)

35 30 25 20 15 10 5 0 4/9/1996

11/9/1996

18/9/1996 Date

25/9/1996

45

Observed Simulated

40 Discharge(m^3/s)

2/10/1996

35 30 25 20 15 10 5 0 25/7/2001

4/8/2001

14/8/2001 Date

24/8/2001

3/9/2001

60 Observed Simulated

Discharge(m^3/s)

50 40 30 20 10 0 29/8/2005

8/9/2005

Fig. 6.

18/9/2005 Date

(Continued )

28/9/2005

8/10/2005

77

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Table 3. The suggestion decision variable Jongkon’s report and Pongsak’s report. Decision variable a b c d

from

Jongkon’s report

Pongsak’ report

0.0009 0.795 0.807 0.652

0.0008–0.67 0.02–1.18 0.80–1.00 0.38–1.00

function convergence criteria. The multi-objective in the last column is less than 0.01 that means the model can satisfy the objective function.

5. Conclusion This research provided the developed auto-calibration procedure for distributed RR model. The optimization technique by GA was applied by searching coefficient parameters of this model. The methodologies have been demonstrated for multi-objective problems by using data from case study. The results of this process are the parameters, which varies in space and time. When applied in Huai Nae Nai and Huai Mae Rim sub-basin for verification, the parameters are in the recommended range values.6,7 This process is very useful for runoff forecasting in general area and more accuracy of runoff forecasting in flood warning can be obtained by this method. This model can provide runoff information in different grid cell of the catchment area. The suggestion for the future work is to use the information provided by meteorological forecasting to predict the runoff. Moreover, the additional events and the more robust calibration strategy can be added for model development in other basins.

References 1. C. Colosimo and G. Mendicino, in Geographical Information System in Hydrology, eds. V. P. Singh and M. Fiorentino (Kluwer Academic Publishers, Netherlands, 1996), pp. 195–229. 2. H. Madsen, J. Hydrol. 235, 3–4 (2000) 276–288. 3. H. Madsen and G. Wilson et al., J. Hydrol. 261, 3–4 (2002) 48–59. 4. H. Madsen, Adv. Water Resour. 26, 2 (2003) 205–216. 5. J. Chongwilaikasem, S. Chittaladakorn and S. Sucharit, Determination of spatial distributed data for rainfall-runoff model by excel and GIS technique,

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6. 7. 8. 9. 10. 11. 12.

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The Proceeding of the 1st International Conference on Water Resources Engineering, Petchaburi, Thailand, 2011, pp. 198–202. J. Chongwilaikasam, GIS based rainfall-runoff model, M. E. Thesis, King Mongkut’s University of Technology Thonburi, Thailand, 2004. K. Eckhardt and J. G. Arnold, J. Hydrol. 251 (2001) 103–109. N. Kannan and C. Santhi et al., J. Hydrol. 369 (2008) 1–15. P. Witthawatchutikul, Modelling for evaluation of critical condition of watershed in Thailand, PhD Thesis, Kasetsart University, 1997. S. Sorooshian and V. K. Gupta, in Computer Models of Watershed Hydrology, ed. V. P. Singh (Water Resources Publications, Colorado, 1995), pp. 23–68. V. T. Chow, D. R. Maidment and L. W. May, Applied Hydrology (McGrawHill, New York, 1988). Y. Liu, Expert Systems with Applications, 36, 5 (2009) 9533–9538.

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


DECISION SUPPORT FOR PERIODICAL OPTIMUM OF WATER DELIVERY FROM RESERVOIR BY DECISION TREE EAKAWIT JORNPRADIT Ph.D. Candidate, Department of Water Resources Engineering, Kasetsart University, Bangkok, Thailand [email protected] SUWATANA CHITTALADAKORN∗ Associate Professor, Ph.D., Department of Water Resources Engineering, Kasetsart University, Bangkok, Thailand [email protected]

The Decision Tree Model on the basis of Bayes’ Theorem coupled with an optimization technique by Evolutionary Algorithm was developed to analyze the short term (daily/weekly) of the reservoir operation. This new purpose methodology analyzed and accounted for three stages of water amount; first, the amount of water affected by rainfall in the past interval; second, the amount of water affected by the probability of supposed rainfall in the future changed from the current storage; and third, the amount of water affected by probability in the policy on the storage gap for controlling between the current storage and the optimal storage. Based on the Most Likely Line (MLL), the optimal rule of the storage is used for controlling the long term of the reservoir operation, the shortterm operation try to follow this guideline by controlling the water released to meet the downstream demand and reduce the gap between the current storage and the guided storage from the MLL line. This methodology facilitated for the operator in decision making instead of using only the conventional method by the upper and lower rule curves.

1. Introduction The reservoir operation in practice is a decision making in a short term, which means the daily or the weekly operation. The operation decision depends on three stages of the water amount; first, the amount of the water affected by rainfall in the past interval that differs from average rainfall, ∗ Corresponding

author. 81

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second, the amount of water affected by the change of the past to current demands, and third, the amount of water affected by the operational rule or the policy and the capability on the storage gap between the current storage and the optimal storage. This inventive research presents the new method of decision making for the reservoir operator in practice which is able to appropriately evaluate related water amount at a short term released interval from the reservoir through the developed model. The Decision Tree Model on the basis of Bayes’ Theorem coupled with an optimization technique by Evolutionary Algorithm (EA) was developed to analyze the short term of the reservoir operation. The input phase needs three categories of the data; the dynamic data of the supply side, the dynamic data of the demand side, and the dynamic data of the operational rule, analyzed for optimal storage which is called the Most Likely Line (MLL).9 1.1. The dynamic data of the supply side The dynamic data of the supply side for operating the reservoir involved daily inflow into the reservoir which deviates from the expected average. Therefore, the rainfall compensation is a necessary concept which aims to correct the error of inflow runoff estimation in the past interval. For the supply side estimation, the rainfall quantity in the past interval is assumed on the average level. But in the actual condition, since the assumed interval has passed, there was an error between the assumed and the actual rainfall that has occurred. Therefore, for the next interval of water release, it should be considered to compensate those differences. 1.2. The dynamic data of the demand side The dynamic data of the demand side involved the downstream actual water use which differs from its plan. The changing in demand data should be examined for water delivery in each time operation. The dynamic demand need to be up-to-date data by field observation such as the progression of planting in the irrigation area, and other up-to-date required water demand, etc. 1.3. The dynamic data of the operational rule The operational rule using MLL needs to be changed according to the new up-to-date information. The change of this guideline would be adjusted by current situation depended on the latest information both of the supply and demand sides. To follow up this guideline, it is the monitoring of the

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Fig. 1. The Box–Whisker plot of the monthly operational rule is used for analysis by interpolating as guide for the short-term operation.

different storage between at the past stage and at the current stage in order for adjusting the water release to converge the actual operating line approaching to the MLL line. To appraise the short-term operation, it must be analyzed by interpolation from the most likely operational rule shown in the graph of Fig. 1. by Box–Whisker plot. 2. Methodologies The developed model comprises five theoretical bases. The first basis is the decision tree setting for analyzing alternatives of expected values. The second basis is the Bayes’ theorem to use for setting the logical relationship between the priori-probability and posterior-probability of all uncertainties of the input and output data. The third basis is the mass conservation law of the water balance. The fourth basis is the short-term operation system setting for three stages — past, current, and next stages. The last basis is the model simulation applying the optimization algorithm. 2.1. Decision trees The decision tree is a graphical representation of a problem describing chance events and decisions in chronological order. Events represented by branch from their successors, making the final model look like a tree. Traditionally, decision trees begin with a decision node. Haimes6 has given the components of decision tree that composed of many “Alternatives”, represented by the type of node signs in a decision tree include:
(The rectangular sign), A decision node has a branch extending from it for every available option.

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(The circular sign), A chance node has a branch for each possible outcome.  (The triangular sign), An end node has no branches succeeding it and returns the payoff (pmn ) and probability (Pmn ) for the associated path. At a point of the decision node extending with the branch lines lead as “state of nature”, represented by the “chance node” and it is also extending with the branch lines lead as “consequences” showing in Fig. 2. Therefore, the likely to occur as a result would be affiliated with an opportunity to decide which is the earlier. The relationship to this possibility occurs by the chance of “reason” to the chance of “result2 ” in terms of expected values by the Bayes’ theory. The decision tree always describes the logical relationship in a graphical picture. But another form of the same meaning can be described by a matrix notation. µmn represented in the form of the alternatives matrix (m, n) showing in Fig. 3 as a function of the alternative variables to am and sn .

Fig. 2. The typical components of the decision tree shows consequences of the alternatives.




µ11 (a1 , s1 ) µ12 (a1 , s2 )



µ21 (a2 , s1 ) µ22 (a2 , s2 )



µ (a , s ) µ (a , s )
31 3 1 32 3 2 Fig. 3.

The alternatives matrix (m, n) rewrite from the typical decision tree.

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2.2. Bayes’ theorem Bayes’ theorem was named after the Reverend Thomas Bayes (1702– 1761), who studied how to compute a distribution for the probability parameter of a binomial distribution. Bayes presented his work as the solution to a problem: Given the number of times in which an unknown event has happened and failed [. . . Find] the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named.1 Bayesian Theory or Bay’s Theorem is a theory that represents the relative value of conditional probability. The structure of the network tree represents two events that occurred before and after. Their probability can also be calculated forward and backward called the influence diagram.8 For example, there are rain gauge station at the point A and point B with the connected boundary. If there is the probability of the event at point A, and at the same time, there is the rain that will fall at the point B in a certain probability event. Or vice versa, it can be implied that if there is the probability of the falling rain event at point B, then it will also have a probability in the falling rain event at point A relatively as shown in the Fig. 4. 2.2.1. Definition of terms This is the notation used to define the terms involved in conditional probability which is a major basis in Bayes’ Theorem. P(A) the probability that an event A will occur. P(AB) the probability that events A and B will both occur (A and B) is equal to P(BA). P(A|B) the probability that events A will occur if B occur (A given B), but does not equal P(B|A). ˜ the probability that events A will not occur (not A), equals P(A) 1−P(A).

Fig. 4. The influence diagram or logical relationship of the probability of returning forth-back to the same conditions.

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Bayes’ Theorem can be derived by start with two basic rules: The first rule P (A|B) =

P (AB) . P (B)

(1)

The second rule ˜ P (A) = P (AB) + P (AB).

(2)

Using the second rule ˜ P (B) = P (BA) + P (B A).

(3)

Substitute P(B) in (1) P (A|B) =

P (AB) . ˜ P (BA) + P (B A)

(4)

Using the first rule ˜ = P (B|A)P ˜ (A), ˜ P (B A)

(5)

P (BA) = P (B|A)P (A).

(6)

˜ in Eq. (5) Substitute P(BA) and P(BA) P (A|B) =

P (B|A)P (A) . ˜ (A) ˜ P (B|A)P (A) + P (B|A)P

(7)

The Eq. (7) is a Bayes’ Theorem that describes the probability of event A given the occurrence of event. 2.2.2. The example of Bayes’ Theorem in a simple application Figure 5 shows a simple example of rainfall event. It perceptibly applies Bayes’ Theorem7 with the decision tree. For example of the priori probability in the first tree has been related to the posterior probability in the last tree. It means that; if (priori probability) given the 30% probability of it-rain at point A, and the 50% probability of it-rain at point B occur in the same time, then (posterior probability) the 51.72% probability of it-rain at point B would be inferred to the 29% probability of it-rain at point A.

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Fig. 5. A simple of the conditional probability in an example applied the Bayes’ Theorem with the decision tree showing the logical relationship between the priori and posterior probability.

This inference calculation basis was adopted in the developed decision tree model. 2.3. Mass conservation law of the water balance The operational line indicates the storage at any time achieved by mass conservation law so called the water balance. Whenever, the operation rule is used as a guideline in practice, it means that the short-term operation

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involves the water balance is applied for estimation of the change in current storage volume. The equation covers time steps in the previous and next interval as follows: For the previous period, St = St−1 +



It+1 −



Rt−1 .

(8)

The compensate volume, Sˆt − St = ±ε.

(9)

When Sˆt is the current observed storage volume, St is the planned storage volume by calculation in current, St−1 is the previous observed  storage volume which lastly used in the past estimation. It−1 is the summation of the inflow volume sources (if may be more than inflow runoff)  in the past period. Rt−1 is the summation of the release volume sources including losses, evaporation, in the past period, and ±ε is the error between the last planned and actual storage volume needed to compensate in the next period operation plan. All variables unit are in million cubic meters. It is notifying that all parameters are already known its value by observation. For the next period,   It − Rt . (10) St+1 = Sˆt + The compilation with hedging policy, Sˆt+1 − St+1 = ±ϕ.

(11)

When Sˆt+1 is the target of the next period to forced storage volume by hedging policy to fit for the nearest the optimal operation rule, St+1 is  the planned storage volume by calculation for the next period. It is the summation of the inflow volume sources (if may be more than inflow runoff)  in the current period. Rt is the summation of the release volume sources including losses, evaporation, in the current period, and ±ϕ is the hedging policy between reduce and increase storage volume needed to control storage in the guideline of the operation rule. All variables unit are in million cubic meters. It is notifying that all parameters are unknown which needed to analyze in optimization process in order to fit for the nearest to the MLL line. In compilation, the previous, current, and next time intervals are merged in unity equation of the Eq. (12). Sˆt+1 = St−1 + [ΣIt − ΣRt ] + [ΣIt−1 − ΣRt−1 ] ± ε ± ϕ.

(12)

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Diagram shows the calculation mechanism for following up the MLL line.

2.4. Short term operation system The relationship in each stage of time and time interval of the shortterm operation, shown in Table 1, is classified in terms of systematically processing of input phase, process phase, and output phase.

2.5. Decision tree model formulation for alternatives creation Figure 7 shows the formulation of tree diagram that starts with two branches of it-rain and no-rain events. In each divided node, it is classified into two nodes of over and under estimate in the differences of actual and average rainfall. For the next level, each node also classifies into two nodes of hedge up and hedge down for approaching to the MLL line. 2.5.1. Probability values The probability values P (n) = R% when P (n): Probability value of node n and R denoted is Real number. 2.5.2. Expected values The expected values E(n) = R when E(n): The part of the release volume value of node n and R denoted is Real number.

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Table 1. The system of the sequence in data preparation and calculation by the number of equation shows in time stages. System

Previous time stage

Input Phase Eq. (1) 1) St−1 : Observed storage volume Eq. (2) 2) ΣIt−1 : Sum of observed Inflows Eq. (3) 3) ΣRt−1 : Sum of actual Release Volume 4) Sˆt : Observed/actual storage volume 5) St : Calculated storage volume 6) ΣIt : Sum of assumed average Inflows 7) ΣRt : Sum of assumed Release Volumes 8) SRULE : Storage volume indicated by the optimal operation rule (Interpolate & Read out) Process Phase 9) ±ε = Sˆt − St : Error checking for compensate 10) Sˆt+1 : Planned storage volume to approach target 11) St+1 : Calculated storage volume 12) ±ϕ = Sˆt+1 − St+1 : Error checking for hedging policy 13) µn (ε, ϕ)t : Alternatives evaluate by Decision Tree 14) ∆S = SRULE − Sˆt+1 , all of alternatives [∆Sµn (ε,ϕ)t ] And checking all of constraints Output Phase 15) Minimal ∆Sµn (ε,ϕ)t /Nearest Sˆt+1 to SRULE /optimal ε, ϕ/and Recommend Optimal Release in Decision Making: Rt

Current time stage

Next time stage

Eq. (4) Eq. (5) Eq. (6) Eq. (7) Eq. (8)

Eq. (9) Eq. (10) Eq. (11) Eq. (12) Eq. (13) Eq. (14)

Eq. (15)

2.5.3. Effective rainfall volume in the field The effective rainfall volume in the field is a reduce volume from the water requirement. It depends on the probability of its rain appearance and of rainfall quantity occurrence. In case of rainfall as considering situation, the probability would indicate the quantity that is able to convert to the daily effective rainfall by following criteria.

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Fig. 7. The decision tree for release decision in the short term expressed the alternative logic classified by the uncertainty events.

if 0 ≤ P(Precipitation) ≤ 20 then P(effective) = 2 if 20 < P(Precipitation) ≤ 70 then P(effective) = 2 + ((32 − 2)/(70 − 20)) × (P − 70) if 70 < P(Precipitation) ≤ 250 then P(effective) = 32 + ((175 − 32)/(250 − 70)) × (P − 250) (This Estimation Used-Type 3 relies on FAO-Method./Source: http://www.fao.org/docrep/s2022e/s2022e03.html)4 Therefore, It−1 = Iaverage

P(effective) . P(Precipitation)

(13)

When P(Precipitation) is the daily rainfall at current time stage t, P(effective) is the effective rainfall in the field that is estimated calculating by the given criteria.

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2.5.4. Effect of hedge policy The effect of the hedge policy is the rectification policy to follow up the optimal operational line determined by the difference between the optimal storage volume and the planned storage which denoted by ∆S. if V(Allowance) ≤ ∆S
0 then ϕ = −c × ∆S if ∆S = 0 then ϕ = 0 if 0
∆S ≤ V(Allowance) then ϕ = +c × ∆S When V(Allowance) = The constraint volume of the daily keeping or releasing by the physical limit, such as spillway’s channel capacity, tail water channel capacity and river outlet constraints. ∆S = The difference between the storage volume guided by the operational rule: (SRULE ), and the planned storage: (Sˆt+1 ) ϕ = The rectify volume to control the storage in the optimal guideline c = The scale coefficient use for enlarging or reducing ∆S stipulated by subjective consideration of the operator 2.5.5. Calculation method The calculation method in decision tree consists of two couple parts: The Probability values P (n) = R% and the Expected values E(n) = R. For the Probability values, the calculation method is presented by Bayes’ Theorem in Sec. 2.2. But the expected values, the calculation method can be considered in three parts as follows: Part 1: The water volume for compensation to the past stage. Part 2: The water volume releasing for demand in the current stage. Part 3: The water volume for rectifying by hedge policy in the next stage. The calculation is as follows: Part 1: ±ε = Sˆt − St   ±ε = Sˆt − St−1 + ΣIt−1 − ΣRt−1     P(effective) ˆ ±ε = St − St−1 + Σ Iaverage − ΣRt−1 P(Precipitation)

(14) (15) (16)

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Part 2: −ΣRt = −Sˆt − ΣIt + St+1

(17)

−ΣRt = −Sˆt + (St+1 − ΣIt )

(18)

Part 3: ±ϕ = Sˆt+1 − St+1

(19)

Part 1 + Part 2 + Part 3 := ±ε − ΣRt ± ϕ

(20)

±ε − ΣRt ± ϕ = Sˆt+1 − St−1 + ΣIt   P (effective) − Σ Iaverage + ΣRt−1 P (Precipitation)

(21)

2.5.6. Alternatives (µn ) The eight alternatives depend on three chances of two “states of nature” of the probability. It consists of the chance of it-rain or no-rain, the chance of rainfall occurrence in the past stage after more than or less than estimate, and the chance of the current storage which is upper or lower side of the optimal operational line. The number of eight alternatives as the tree for decision can be expressed as follows: Alternative µ1 occur when if it is in condition of; it-rain stage, ε is negative (−ε), and ϕ is negative (−ϕ), Alternative µ2 occur when if it is in condition of; no-rain stage, ε is negative (−ε), and ϕ is negative (−ϕ), Alternative µ3 occur when if it is in condition of; it-rain stage, ε is positive (+ε), and ϕ is negative (−ϕ), alternative µ4 occur when if it is in condition of; no-rain stage, ε is positive (+ε), and ϕ is negative (−ϕ), Alternative µ5 occur when if it is in condition of; it-rain stage, ε is negative (−ε), and ϕ is positive (+ϕ), Alternative µ6 occur when if it is in condition of; it-rain stage, ε is positive (+ε), and ϕ is positive (+ϕ), Alternative µ7 occur when if it is in condition of; no-rain stage, ε is negative (−ε), and ϕ is negative (−ϕ), Alternative µ8 occur when if it is in condition of; no-rain stage, ε is positive (+ε), and ϕ is negative (−ϕ).

in the past in the past in the past in the past in the past in the past in the past in the past

.

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Two probabilities are involved in the decision tree system; first, the probability of rainfall event will occur in the next time stage; second, the probability of the estimated volume of the next stage. The EA was used as a searching tool. In this study, it would compromise for the need of compensation in the past stage of error due to uncertainty rainfall condition, determination in the current stage of average assumption in the uncertainty rainfall, and assuming in the next time stage of the storage movement that should be adjusted according to the convergence to the MLL. The decision tree model play the important roles to carry out the expected values of the release rate volume (E(n)) = ±ε − ΣRt ± ϕ which is related to the probability of the uncertainty rainfall condition (P (n) = Rf ± ∆Rf ). When E(n) and P (n) are the expected values and probability of the uncertainty rainfall condition at node of decision tree. 2.6. Model simulation and optimization algorithm Model simulation in this study comprises two main algorithms which inherently process to optimize two quantities at each node of the decision tree model at the same time. Those quantities are the expected value of release volume, and the probability value of rainfall condition and storage allocation condition. The alternatives are originated by the uncertainty conditions which would be in the optimal justifying procedure. It is driven by the EA.4 The conceptual relationship of the decision tree with the optimization algorithm is shown in Fig. 8. 2.6.1. The optimization model formulation The optimization model formulation in the mathematical can be described as follow: Decision variables

The decision variables sets for the short term operation composed of three parameters; those are ±ε, the compensate volume; R, the current water duty to delivery in average amount; and ±ϕ, the hedging policy to converging force the actual storage line to MLL. In the optimization process, only two parameters are selected for convergence driven searching of the storage line in the optimization evaluation. Those parameters are ±ε and ±ϕ.

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Diagram of decision tree model in the process of short-term operation using EA.

Objective Function



M in.Z =
∆S µn (ε, ϕ)t
,

(22)

where [∆S] is the matrix set of the difference between the storage volume guided by the operational rule: (SMLL ), and the planned storage: (Sˆt+1 ) or, and predicted storage by calculation, ∆S = SMLL − Sˆt+1 .

∆S µ

(23)


)t
is absolute of the matrix set of eight alternatives (µn ) contained with the compensate volume: ±ε, and the hedging policy: ±ϕ of decision variables in the time stage t of the matrix set of [∆S]. The minimizing of those matrix members must be in form of absolute values. n (ε,ϕ

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Subject to Constraints

The constraints are divided into four categories: the equality constraints, the inequality constraints, the conditional constraints, and the non-negativity constraints as following: 1. Equality Constraints 1.1. Mass balance constraint : This equation is the same equation and same meaning as equation (21) described in Sec. 2.5.5. ±ε − ΣRt ± ϕ = Sˆt+1 − St−1 + ΣIt   P (effective) − Σ Iaverage + ΣRt−1 . (24) P (Precipitation ) 1.2. Minimum constraint of water release rate: This rate is the water requirement for environmental support estimated by Papayom Irrigation Project. Rmin = 6,287 cu.m./day, (0.073 cms)

(25)

1.3. Maximum constraint of water release rate: This rate is the highest river outlet capability appraised by Papayom Irrigation Project. Rmax = 70,040 cu.m./day, (0.822 cms)

(26)

1.4. Minimum constraint of storage volume: This volume is the physical constraint of designed reservoir informed by Papayom Irrigation Project. Smin = 0.8 Million cu.m.

(27)

1.5. Maximum constraint of storage volume: This volume is the physical constraint of designed reservoir informed by Papayom Irrigation Project. Smax = 20.5 Million cu.m.

(28)

2. Inequality Constraints There are two inequality constraints in this study those are the water release gap and the storage volume gap. Rmin ≤ R(t) ≤ Rmax

∀t = 1, 2, . . . , T

(29)

Smin ≤ (t) ≤ Smax

∀t = 1, 2, . . . , T

(30)

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3. Non-negativity Constraints Apart from decision variables (±ε and ±ϕ), the non-negativity constraints is set for all involved constraints; monthly inflow: I(t), water demand or water release: R(t), storage volume, and discrete value of time step: t and number of alternatives: n must be non-negativity constraints. I(t), R(t), S(t), t and n ≥ 0

(31)

3. Results and Discussion 3.1. PAPAYOM reservoir irrigation project, the case study Papayom Reservoir has the capacity of 20.5 million cubic meters. It locates on Songkhla Lake basin. Its catchment area is 24 square kilometers. The storage aims to serve the irrigation area while in deficit of rain. It can be illustrated in Fig. 9 and schematic in Fig. 10. Reservoir was fixed at the dead storage at the capacity of 0.8 million cubic meters. 3.1.1. Stochastic operational rule The reservoir operation plan includes the long term and the short term as the guideline. Figure 11 shows a sample of interpolation results of the monthly data into daily data of the MLL line. The MLL10 obtained by the optimization process analyzed by the use of synthetic data as input3 shown in Fig. 1. The synthetic process of the daily

Fig. 9. Location map of case study site the Papayom reservoir irrigation project, Phatthalung, Thailand.

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Fig. 10. Schematic diagram of Papayom reservoir showing irrigable area and the catchment area of reservoir and side flow.

Fig. 11. The daily MLL, the long term of the operational guideline, expressed in the Box–Whisker plot uses as guide for the stochastic operational rule.

data is inferred from the historical data. The daily MLL is a representative for the stochastic operational rule upon which it can indicate the risk range for water deficit or surplus. The risk can be implied in quartile ranges by the following statistical means of the Box–Whisker ranges9 shown in Table 2.

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Table 2. The risk range for water deficit or surplus classified by the quartile range. Order

Quartile range

1 2 3 4 5 6

0%–10% 10%–25% 25%–50%(MLL) 50%(MLL)–75% 75%–90% 90%–100%

Risk level High risk for water deficit Risk for water deficit Normal risk for water deficit Normal risk for water surplus Risk for water surplus High risk for water surplus

Fig. 12. The daily average inflow (shown in line) and a sample year round set of the transformed data of daily inflow runoff by using a sample set of daily rainfall data (shown in shed).

3.1.2. Average inflow series Three related quantity series involved in the operation decision either the short or long term is the storage, supply, and demand series. The storage series is presented by the MLL in Fig. 11, as described in Sec. 3.1.1. The supply series used in this study is presented by the daily average inflow runoff for current estimated release by the set of daily inflow runoff, as required field data, to be used for simulation, a sample shown in Fig. 12. 3.1.3. Average demand series The demand series used in this study is obtained by the monthly demand volume shown in Fig. 13. For the daily demand estimation, it is the interpolation results of the monthly data into daily data of the demand volume shown in Fig. 14.

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Fig. 13. The monthly series of the water demand volume estimated by Papayom irrigation project.

Fig. 14.

The interpolation results to the daily series of the water demand volume.

3.2. Required field data The required field data for updating the storage volume data is one of the input data to be used in this model. This is for checking the convergent movement of how difference between the current actual and the current optimal storage. In this study, the required storage data from the field

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was assumed to be the same amount as from estimation for the next period.

3.3. Result of decision tree and optimization driven The result of the decision is the performance of the operational mechanism. The decision tree model will perform its functions in searching for minimal ∆S of eight alternatives. The optimal alternative is obtained from the optimization driven. The overall result can be shown in Fig. 15 in order to satisfy an appropriate release rate for operator in the decision making. In combination of all year round decision, the different scenario simulation result can be shown the converged lines to the MLL line in Fig. 16. Those initial are at 10, 15, and 20 million cubic meters. Likewise, in combination of all year round decision, Fig. 17 shows the scenario results as converged lines to the MLL line in various initial conditions of the 15 million cubic meters storage, but at the several time stages. Those start at the day of 0, 50, 100, 150, 200, 250, and 300. The results show all scenarios nicely converging to the MLL line.

Fig. 15. The minimum alternative obtained from concurrence performance by the decision tree and the optimization procedure.

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Fig. 16.

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The convergence lines to the MLL line in several cases different initial volumes.

Fig. 17. The convergence line to the MLL line by setting initial volumes of 15 million cubic meters at different time stages in simulation results.

3.4. Decision making for short term operation The finalized results of the decision making for short-term operation are the determination of the optimal release rate of the water volume of the reservoir. The following up of the actual storage line to MLL line, produced by optimization simulation, is a recommendation for short-term decision for the optimal operation guideline. The optimal release rate of the recommended water volume of the reservoir is the differential volume between the next estimation and the current determination at that time interval. This volume should be a preference of the decision making to the operator who controls the reservoir in practice.

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4. Conclusions The method for supporting decision in this study is the new way to control water releasing from the reservoir in short-term operation. It is created by the integrated model through the decision tree algorithm on the basis of Bayes’ theorem coupled with an optimization technique by EA. This method is reasonable for controlling the water storage depending on inflow at supply side and outflow or demand side accounting for related time intervals at the past, present, and future with the uncertainty conditions. The decision making technique for following up the MLL line is for adjusting the water budget situation according to uncertainty climate condition. By this method, the operator easily controls the periodic optimum of water release instead of using only the conventional method by upper and lower rule curves.

References 1. T. Bayes and R. Price, Philos. T. Roy. Soc. 53 (1763) 370–418. 2. J. R. B. Cockett and J. A. Herrera, J. Assoc. Comput. Mach. 37 (1990) 815–842. 3. E. Jornpradit and S. Chittaladakorn, Optimal identification and parameter estimation of probability density function for daily rainfall by evolutionary algorithm, The 1st EIT International Conference on Water Resources Engineering, Thailand, 01 (2011), 203–213. 4. FAO, (2011), Corporate Document Repository. Available at: http://www.fao. org/docrep/S2022E/s2022e03.htm. 5. D. E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning (Addison Wesley, 1989), p. 41. 6. Y. Y. Haimes, K. A. Loparo, S. C. Olenik and S. K. Nanda, Water Resources Research 16, 3 (1980), 467–475. 7. A. H. Ronald and E. M. James, in The Principles and Applications of Decision Analysis, Vols. I and II, ed. Matheson (Strategic Decisions Group, Menlo Park, 1989). 8. R. M. Oliver and Q. S. James, Influence Diagrams, Belief Nets and Decision Analysis (John Wiley and Sons, New York, 1990). 9. M. Robert, W. T. John and A. L. Wayne, The American Statistician 32, 1 (1978) 12–16. 10. S. Chittaladakorn and E. Jornpradit, The most likely line: MLL, the tool for optimal reservoir operation, Department of Water Resources Engineering (Kasetsart University, Thailand, 2011).

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


DECISION SUPPORT SYSTEM FOR COASTAL PROTECTION LAYOUT DESIGN (DSS4CPD) USING GENETIC ALGORITHM (GA) AND MULTICRITERIA ANALYSIS (MCA) PHINAI JINCHAI Department of Water Resources Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10903, Thailand [email protected] SUWATANA CHITTALADAKORN∗ Associate Professor, Ph.D., Department of Water Resources Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10903, Thailand [email protected]

This research has its objective to develop the decision support system on GIS to be used in the coastal erosion protection management. The developed model in this research is called Decision Support System for Coastal Protection Layout Design (DSS4CPD). It has created both for systematic protection and solution measures to the problem by using Genetic Algorithm (GA) and Multicriteria Analysis (MCA) for finding the coastal structure layout optimal solution. In this research, three types of coastal structures were used as structure alternatives for the layout, which are seawall, breakwater, and groin. The coastal area in Nakornsrithammaraj, Thailand was used as the case study. The studied result has found the appropriate position of coastal structures considering the suitable rock size relied on the wave energy, and the appropriate coastal structure position based on the wave breaking line. Using GA and MCA in DSS4CPD, it found the best layout in this project. This DSS4CPD will be used by the authorized decision makers to find the most suitable erosion problem solution.

1. Introduction For coastal protection solution, one alternative is to use coastal structures. However, there are variety of coastal structure designs and complexities. In addition, it is involved with many data patterns and many mathematical ∗ Corresponding

author. 105

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models working together. For such reasons, the study to make the coastal protection design and to solve coastal erosion problems is difficult and takes much time. Furthermore, as it is known that to solve the coastal erosion problems by using the coastal structure design might cause the environmental impact in adjacent areas as well. Such environmental impact must be evaluated and might lead to another more coastal protection design. As a result, because of time consuming, coastal engineers have to select what it is the best solution in their points of view. For all reasons above, this research has its objectives to develop the decision support system for coastal protection design by develop GIS working together with mathematical models for coastal protection design. Moreover, the optimization using genetic algorithm (GA) is applied to make an appropriate coastal structure layout and evaluate the environmental impact for any single layout design. In addition multicriteria (MCA), the criteria for selection of coastal erosion solutions which will be suitable to the project area shall be thoroughly considered. Finally, its system will lead to the best coastal protection solution. The decision support system for coastal protection design is a set of mathematical model base, coastal data base, and dialog base.

2. Objectives The primary objectives of this paper are to integrate a coastal designing data and coastal mathematical models by develop a GIS plug-in and used that plug-in as a decision support system for coastal protection design. The specific objectives are to develop the decision support system for coastal protection design data base, to integrate coastal models, and to develop the decision support system for coastal protection design.

3. Methodology For the coastal structure layout design, there are many information data needed for the decision making. In order to develop the decision support system, the information must contain area physical data which are beach profiles and water depth data, sediment, and wind and wave data. To make the appropriate DSS for the decision maker, there are three major parts: 1. Data Base 2. Model Base 3. Dialogue Base

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Model Base

Data Base Geometric data -Topographic Data -Bathymetric Data -Shoreline Data -Beach Profile Data Wave Database -Buoy data -WAM Database

WAVE Hind-casting Model

Wave Height Wave Direction Wave Design

WAVE Transformation Model

Beach Protection Layout

Dialog Base

Wave Height Wave Direction Wave Breaking Zone

GIS software -Mapwindow GIS Plug-in -DSS4CPD

Shoreline Change Model

DSS for layout design report

Decision maker Fig. 1.

Methodology of DSS4CPD.

All three parts are integrated by Geographic Information System(GIS) to have DSS4CPD presented in the pattern of pictures. The flow diagram is as shown in Fig. 1. 4. Data Base The data base of DSS4CPD consists of two main parts which are meteorological data base such as wave data base and Coastal Structure Alternative Data Base. For the meteorological data base, it has come from the simulation using WAM of Hydrographic Department, Royal Thai Navy, which has 12 year data record covering the areas of both in the Gulf of Thailand and Andaman Sea. In fact, there are 12 data as follows: 1. Wind Speed 2. Wind Direction

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3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

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Mean Wave Direction Wave Peak Frequency Wave Peak Period Mean Wave Period Normalized Wave Stress Drag Coefficient Mean Frequency Friction Velocity Significant Wave Height Maximum Wave Height

For the Structural Methods for Shore Protection of Coastal Structure Alternative Data Base, it is to be mentioned in Sec. 6. 5. Model Base The mathematic model for coastal structure design consists of four main mathematic models, which are: — — — —

Wave Hide-Casting Model Wave Transformations Model Shoreline change model Coastal structure layout design

5.1. Wave hind-casting model In this research, the Wave Hide-Casting Model to be used in the project is WAM. WAM-model solves the wave transport equation explicitly without any presumptions on the shape of the wave spectrum.1 The model runs for any given regional or global grid with a prescribed topographic dataset. The model outputs the significant wave height, mean wave direction and frequency, the swell wave height and mean direction, wind stress fields corrected by including the wave induced stress and the drag coefficient at each grid point at chosen output times, and also the 2D wave spectrum at chosen grid points and output times.2 The model result will be stored as the database. Model description The WAM model describes the evolution of a two-dimensional ocean wave spectrum. It computes the 2D wave variance spectrum through integration

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of the transport equation3 : ∂(φF ) ∂(λF ) ∂(θF ) dF + + + = S, dt ∂φ ∂λ ∂θ

(1)

where F f θ φ λ

= = = = =

the spectral density with respect to (φ, θ, φ, λ) denotes frequencies directions latitudes longitudes

θ, φ, λ are the rate of change of the position and propagation direction of a wave packet traveling along a great circle path. The source function S is represented as a superposition of the wind input Sin , white capping dissipation Sdis , and nonlinear transfer Snl S = Sin + Sdis + Snl .

(2)

5.2. Wave transformations model The Steady-state spectral Wave model is a steady-state finite difference model based on the wave-action balance equation.4 When the waves approach the shoreline, they are affected by the seabed through processes such as refraction, shoaling, bottom friction and wave-breaking. The wave transformation model are take care term of wave affection that occurs from deep water to shoreline. In this research, the important results for a coastal structure design including are: Wave direction and wave height map, map of wave breaking line. Model description Interaction of waves with currents is considered in a reference frame moving with the current. The wave dispersion relationship is given in the moving reference frame as5 : ωr2 = gk tanh(kd), where ω g k d

= = = =

angular frequency gravitational acceleration wave number water depth

(3)

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5.3. Shoreline change model The mathematical model called Generalized Model for Simulating Shoreline Change (GENESIS) developed by the Coastal Engineering Research Center, US Army Corps of Engineers, Department of the Army is to be used in this research. GENESIS is designed for coastal change analysis in the long term occurring due to the coastal sediment movement. The model is also able to analyze the change due to the construction of coastal structures and beach nourishment. The input data of the model are offshore wave characteristic, beach characteristic, detail of structures, sand nourishment, etc. The following equation is used to calculate the coastal-parallel sediment movement rate in GENESIS6 :
 ∂Hb 2 Q = (Hb Cgb ) K1 sin 2αb − K2 cos αb , (4) ∂y where Hb Cgb αb Q y K1 , K2

= = = = = =

wave amplitude where it breaks, wave-group amplitude where it breaks, diffraction angle where the wave breaks, coastal-parallel sediment movement rate, distance measured along the shoreline, coefficients of sediment flow.

6. Structural Methods for Shore Protection In this research, three types of coastal structures were used as the structure alternatives for the layout, which are seawall, breakwater, and groin. 6.1. Seawalls As in Fig. 2, seawalls are massive, vertical structures used to protect backshore areas from heavy wave action. They can be constructed using a range of materials, the most common being poured concrete, steel sheet pile, concrete blocks, gabions, and timber cribs. 6.2. Breakwaters As in Fig. 3, breakwaters are shore-parallel structures that reduce the wave energy reaching the protected area. The reduction in wave energy slows

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Fig. 2.

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Seawall picture and seawall in GENESIS.

the littoral drift, produces sediment deposition and a shoreline bulge in the sheltered area behind the breakwater. 6.3. Groins As in Fig. 4, groins are the shore-connected, beach stabilization structure. They are structures that extend, fingerlike, perpendicularly or nearly right angles from the shore. Usually constructed in groups called groin fields, their primary purpose is to trap and retain sand, nourishing the beach compartments between them. Groins initially interrupt the longshore transport of littoral drift.

7. Rock Size Calculation Coastal structure rock size consists of interior graded layers of stone and another armor layer of stone.

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Fig. 3.

Breakwater picture and breakwaters in GENESIS.

Armor units must be of sufficient size to resist wave attack. In this research, Hudson formula is to be used for calculating the coastal structure rock size which relies on the wave height. In fact, the wave transformation data result is to be used by DSS4CPD in the calculation of the structure as shown in Fig. 5. To illustrate, the rock size in layer A which is the biggest rock size layer, is to be able to absorb the wave energy directly. For the next layer, the rock size is varied under the standard ratio. The governing equation is as followed: Hudson’s formula10 w=

γa H 3 , kd (sa − 1)3 cot(α)

where: w γa kd Sa α

= = = = =

Weight of individual stone (N), Specific weight of stone (N/m3 ), Stone shape coefficient, Specific gravity of stone (N/m3 ), Slope angle of breakwater (degree).

(5)

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Fig. 4.

Fig. 5.

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Groin picture and groins in GENESIS.

Typical rubble mound breakwater cross-section.

8. Basis of Genetic Algorithms (GA) A GA is a random search algorithm that provides a robust method for searching for the optimum solution to complex problems.7 In a GA, the problem is represented by a population of string (or chromosome, in biological terminology). Each string comprises a number of blocks, which represent individual decision variables of the problem (genes, in biological

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terminology). The variables represented in the string can be processed in an evaluation function or fitness function, which is in effect the objective function. In early GAs, decision variables were represented in binary coding in which each block, or gene, is further broken down into a series of binary digits.7 It has been demonstrated (for example, Wardlaw and Sharif 8 ) that real-value representation, in which genes represent a single variable as a real number, offer a significant advantage over binary coding for some problems. Strings are processed and combined according to their fitness (objective function value) in order to generate new strings that contain the best features of two parent strings. Strings with the highest fitness have the greatest chance of contributing to future generations, as in the process of natural selection. Excellent introductions to GAs are given by Goldberg and Michalewicz.9 Three fundamental operators are involved in manipulating strings and moving to a new generation: Selection, crossover, and mutation. For GA, the approach taken to operators of selection, crossover and mutation, and the objective function of the project is: Min Z = cost (e),

(6)

where cost (e) = φ (number, spacing, distance, size) e = {Engineering, Environment, Economics). In this research, GA has been applied to define the optimal layout of coastal structures, calculated the coastal alteration using GENESIS, and reviewed the computational result using the land evaluation, damage value of the land due to the erosion, and the cost of the structure that depends on the water depth. And finally, the cost optimization in engineering cost, environmental cost, and economics cost of the project must be performed.

9. The Coastal Structure Layout Design Using GA The location of coastal protection structure will directly affect the coastal alteration condition. Such alteration is caused by deposition and erosion processes due to the coastal structures. For example, when the coastal structures as breakwaters are to be built, they might block some of high power waves originating the blind zone behind the breakwaters where moving sediment deposits. The outline of equilibrium shoreline happening

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behind the breakwaters can be calculated using mathematical model which will determine where the erosion and deposition zones shall be. However, to select the coastal structure location, the criteria that must be taken into consideration are the erosion area and the price. If the breakwater is to be in very deep water the cost would be high. On the other hand, if the breakwater is to be put at very close to the shore the sand would be filled up and it will act as the groin, subsequently, the problem of downstream erosion will take place. To put the breakwater into the appropriate location therefore must take into account these significant factors. In the design system using GA, it started from each coastal structure layout that performed one shoreline change. In fact, the parameters of coastal structure alternatives are number of coastal structures in any layout, spacing between each coastal structure in the layout, distance from shore of coastal structures, size of coastal structures. When any parameter has been adjusted, GA helped to do it all operators to rank, to evaluate together with GENESIS in order to have the best layout in the last generation. The procedure is as shown in Fig. 6.

2

1

GA

No

3

Breakwaters

GENESIS

Groins

Next Generation

Seawall

The Best Layout from last generation

The most Appropriate Layout

Mutation Process

structure Layout No.1

yes

6

structure Layout No.1

No.3 No.2

Stop

Fig. 6.

4

Final Shoreline No.1

5

Evaluation And Ranking Process

The design system using GA.

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Fig. 7.

System integration using Visual Basic.

9.1. Model development In this study, as shown in Fig. 7, Visual Basic Version 2008 is the principle tool used in this developing of the design system. To illustrate, GA defines the layout location of coastal structures, and then, GENESIS is used in order to calculate coastal alteration, and review the computational result using the land evaluation, damage value of the land due to the erosion and the cost of the structure that depends on the water depth. And Visual Basic Version 2008 integrates what mentioned above in the system. For Visual Basic Version 2008, the program has been designed consisting of four segments as follows: a. Elementary data segment composing of: — — — —

Starting beach line Beach profile Land use and land cost Construction cost at different water depths

b. Coastal Structure layout location segment In this section the GA will select the breakwater location. Users may define the controlling data for layout design such as a number of breakwaters, maximum and minimum length, maximum and minimum interval between coastal structures, etc.

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c. Beach alteration calculation segment In this section, the specified data from GA will be used to create input data for the model GENESIS to calculate the beach characteristic which will be used for the project cost evaluation. d. Evaluation segment In this section, the calculation result of the beach lines together with the cost of the eroded land, the land that the erosion can be prevented, the construction cost of coastal structures as from the layout, will be considered. When the evaluation process is complete the next process will be repeated; the model will select the suitable layout as a prototype to be used in accordance with GA principle. The process will repeat until the layout with lowest cost is afforded as per the number of Generations. The calculation result will then be reported.

10. Multicriteria Analysis (MCA) As shown in Fig. 8, in evaluation process of the coastal structure layout, MCA helps in weighting by concerning all eight requirements and working together with GA, to get what should be the most appropriate layout for the project. In fact, MCA is the criteria for selection of coastal erosion solutions which will be suitable to the project area shall be thoroughly considered. The considerations shall take into account the engineering aspects, economic and environmental impacts, including the local requirements in the project area. As such, the eight requirements to be used in selecting the appropriate resolutions for coastal erosion are defined, which are:

10.1. Wind wave protection factor The wind-wave protection factor is crucial for selection of coastal erosion resolution. The resolution shall be high in wind-wave protection potentiality which results in minor influences on coastal alteration.

10.2. Impact on safety of navigation In the area where native people are fishermen the resolution shall not cause danger to navigation. However, the project area is low density of fishery this element will be rated with low points.

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Fig. 8.

The design system using GA and MCA.

10.3. Utilization area along the beach The resolution shall not cause the discontinuity of the beach, e.g., the protection structure blocks the beach range so that limited by the length of beach blocks. This element is crucial to the tourist-attractive beaches because, apart from scenic beauty, activities are suitable on the continuous beaches. 10.4. Construction cost Cost of construction affects directly the governmental budget due to its limitation. If the resolution is low cost and high effective it means the economy of governmental budget. 10.5. Scenery harmonization and tourism This factor is very important for the tourism area. To illustrate, the coastal structure should not impact or interfere the nature scenery. Furthermore, the coastal structure layout should not decrease the tourist activity area: For example, swimming area, beach area.

Utilization area along the beach (C3)

Impact on safety of navigation (C4)

Scenery harmonization and tourism (C5)

Environmental impact (C6)

Long term maintenance (C7)

Local participation (C8)

Total

Weight

Wind Wave Protection Factor (R1)

0

3

3

3

2

2

3

1

17

0.152

Impact on Safety of Navigation (R2)

1

0

1

2

1

1

2

1

9

0.080

Utilization Area along the Beach (R3)

1

3

0

3

2

1

3

1

14

0.125

Cost of Construction (R4)

1

2

1

0

2

1

2

1

10

0.089

Scenery Harmonization and Tourism (R5)

2

3

2

2

0

2

2

1

14

0.125

Environmental Impact (R6)

2

3

3

3

2

0

3

1

17

0.152

Element

Long Term Maintenance (R7)

1

2

1

2

2

1

0

1

10

0.089

Local Participation (R8)

3

3

3

3

3

3

3

0

21

0.188

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Total

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Table 1.

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10.6. Environmental impact Coastal erosion prevention structure built in the sea, which will affect the water quality, aqua ecology, especially the area of rock disposal will affect plankton and sea-bed organisms by reducing their nutrition. This causes them to be deceased, and impacts the environment as a whole system. As a result, the solution without any construction in sea has the better environmental impact score than the solution with construction in sea.

10.7. Maintenance cost The long-term maintenance cost is the factor that continuously impact the annually government budget. In addition, the maintenance for coastal structure cause more works for government organization. As a result, the more works, the more money has to be spent for any coastal structures.

10.8. Local participation The considerations shall take not only into account the engineering aspects, economic and environmental impacts, but also the local requirements in the project area. In fact, the coastal structures to be built in the projected area will be with people who live there as long as the structures last. Therefore, local participation is very important and has a high weighting score. From Comparison of the eight elements for the coastal erosion solution consideration using MCA, the weighting calculation is: Total score = 40%(Engineering) + 30%(Economic) + 30%(Environment) Thus, Total score = 40(0.152R1 + 0.08R2 + 0.12R3 ) + 30(0.089R4 + 0.089R7) + 30(0.125R5 + 0.152R6 + 0.188R8)

(7)

For this research, the result from the coastal structure alternatives using MCA is shown in Table 2.

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Decision Support System for Coastal Protection Layout Design (DSS4CPD) Table 2.

Concerning Engineering Economics Environment Total Ranking

121

MCA result in the project area. Alternative 1

Alternative 2

Alternative 3

Score

Breakwaters

Groins

Seawall

40 30 30 100

34.97 18.53 20.28 73.78 1

27.12 15.74 18 60.68 3

31.37 21.49 13.48 66.31 2

11. Dialog Base Graphic user interface (GUI) or dialogue base is the important part of DSS because it is a transition between the system and users. In the dialogue base for DSS4CPD, GIS is to be used in order to integrate all three main models together. The DSS4CPD described herein is a MapWindow (Ames 2010) plugin for the design of coastal protection design. The plug-in was developed in VB .NET 2008 and compiled as a dynamic link library (DLL file). MapWindow can connect to the DLL, or plug-in, with interfacing functions, and data and event commands. MapWindow GIS is an open-source GIS application and set of programmable mapping components. It has been adopted by the United States Environmental Protection Agency as the primary GIS platform for its better assessment science integrating point and nonpoint sources (BASINS) watershed analysis and modeling software. MapWindow is distributed as an open source application under the Mozilla Public License, and it can be reprogrammed to perform different or more specialized tasks. Other plug-ins is also available to expand compatibility and functionality. The application is built upon Microsoft .NET 2008 technology. For the advantage of the MapWindow, it is to be used as the developed DSS. For more details, those will be mentioned later.

11.1. Geographical information systems (GIS) The GIS is a computer system capable of holding and using data describing places on the earth’s surface, while the more complex defines it as an organized collection of computer hardware, software, geographic data and personal designed to efficient capture, store, update, manipulate, analyze and display all forms of geographically referenced information.

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A GIS can map any information stored in spreadsheets or databases that has a geographic component to allow you to see patterns, relationships, and trends that could not otherwise have been seen in a table or list format. It gives an entirely new, dynamic perspective on information and helps make better decisions. A GIS is characterized by a unique ability of a user to overlay spatial layers information and perform spatial queries to create new information, the results of which are automatically tabulated and mapped. Graphical elements describing the location and shape of layer features are dynamically connected to databases, which describe the properties of the features. 11.2. DSS4CPD The DSS4CPD model described herein is a MapWindow (Ames 2010) plugin for the design of coastal structure layouts. The plug-in was developed in VB .NET and compiled as a dynamic link library (DLL file). MapWindow can connect to the DLL, or plug-in, with interfacing functions, and data and event commands. Although it is a single plug-in to MapWindow, it involves the components given above which perform various sophisticated functions and include several thousand lines of code. 12. Application For DSS4CPD, DSS operation is to be presented starting from wave hindcasting: fetch map, dominant wave display, wave analysis table, and wave transformation: wave height map, wave direction map, and wave breaking map. In fact, they are all important data to be used in the decision making for coastal protection design. To illustrate, the deep water wave is the representative of the wave boundary in the project area. For the wave transformation, wave height and wave direction are the indication for coastal structure layout position and sizes. In addition, wave height in the near shore area determines the coastal structure size since the wave height is directly related to wave force or wave energy going to the beach. To use DSS4CPD, it has been started from loading the design data base which is stored in the shape file pattern into Legend of MapWindow and then, selecting the point of position the deep water wave to be calculated to be used in this project area as shown in Fig. 9.

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Fig. 9.

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A wave hind-casting point.

DSS4CPD will investigate the wind direction line and make it to be fetch length map. In order to have designer understand the wind and wave behaviors in the study area because the wave height and wave direction relies on the chosen positions which are impacted by the distance of the wind coming on the water surface, wind speed and wind frequency as shown in Fig. 10. After setting the information of wave, the system will be linked to database in the part of wave climate database and the hind cast result will be presented in the pictures of wave rose and wave analysis table. For all data, they will be stored and be continuously evaluated in the wave transformation as shown in Fig. 11. For the calculation of wave transformation, the users must select the base line which is very important since that baseline is going to be used for analysis, design and evaluation of the coastal structure design in the project by always referring to that baseline. The way to select the baseline is that the users must select for the system, this should be perpendicular to the dominant wave direction. In fact, the baseline must draw clockwise only as shown in Fig. 12.

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Fig. 10.

Fetch length of wave hind-casting point.

Fig. 11.

Wave-rose overlay on GIS map.

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Fig. 12.

125

Baseline reference for wave transformation model.

After the baseline has been made, the next step is to determine the right offshore distance to start running the wave from deep water to the shoreline. By using the water depth from the Geometry Database, the wave transformation is to be presented as shown in Fig. 13. After that the system will simulate the wave in the study area and will make the map and report to use as the fundamental information for the engineering designer in order to make the coastal structure layout for the decision maker to make any decision on the project design. The figures are as shown in Figs. 14 to 16. After the dominant wave direction have been presented, then the calculation of how waves transform to the shoreline. At this point, the wave transformation model will present the results of wave heights, direction toward the shoreline, wave periods, wave numbers, and the wave breaking line. All data will be presented in the terms of Grid Table in direction X, (along shoreline), and Y (perpendicular to the shoreline). For the developed

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Fig. 13.

Simulation area of the wave transformation model.

Fig. 14.

Table of wave analysis results.

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Fig. 15.

127

Near shore wave map (wave direction and height).

system, the interface is presented by gathering all data and demonstrating as the maps on GIS. For example, wave height and wave direction map and wave breaking line map. As the data mentioned, all data are in information for decision making in order to help the designer of coastal structure system. After that, DSS4CPD has done the rest of the process to make the optimal layout for the project. To illustrate, it started from each coastal structure layout that performed one shoreline change. In fact, the parameters of the coastal structure alternatives are number of coastal structures in any layout, spacing between each coastal structure in the layout, distance from shore of coastal structures, size of coastal structures. When any parameter has been adjusted, GA helped to do it all operators to rank, to evaluate together with GENESIS in order to have best layout in the last generation. Working together between GA and MCA, DSS4CPD designed the coastal structure layout in this project as shown in Fig. 17.

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Fig. 16.

Wave breaking map.

13. Conclusion In this study, the development result is DSS4CPD that is the integration of wave hindcasting model, wave transformation model, shoreline change model, and coastal structure layout design model. In the system, the MapWindow Plug-in was used for helping in calculating deep water wave, wave transformation, and wave breaking line. In DSS4CPD, the users can select any position in the deep water along the coastline. After that, the system will calculate the selected position data and will show the result of wave height, wave direction and wave period in term of wave rose and also its data in the table. Especially, the system can demonstrate the wave rose picture on GIS Map. As a result, the coastal structure designer can view and understand the wave behavior and the wave transformation from the deep water to the beach precisely. Then, DSS4CPD had done the rest of the process to make the optimal layout for the project. To illustrate, it started from each coastal structure layout that performed one shoreline

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Fig. 17.

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The breakwater layout design in the project.

change. The parameters of the coastal structure alternatives are: number of coastal structures in any layout, spacing between each coastal structure in the layout, distance from shore of coastal structures, and size of coastal structures. When any parameter has been adjusted, GA helped to do it all operators to rank, to evaluate together with GENESIS in order to have best layout in the last generation. Working together between GA and MCA, DSS4CPD designed and recommended the most suitable coastal structure. Therefore, the authorized decision makers are able to use DSS4CPD as a tool for solving the erosion problem appropriately.

References 1. G. J. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann and P. A. E. M. Janssen, Dynamics and Modeling of Ocean Waves (Cambridge University Press, 1994). 2. H. Gunther, S. Hasselmann and P. A. E. M. Janssen, Wave model cycle 4. Revised version, Technical Report No. 4, Hamburg, Germany, 1992. 3. The WAMDI Group, J. Phys. Oceanogr. 18, 12 (1988) 1775–1880.

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4. J. M. Smith, A. R. Sherlock and D. T. Resio, STWAVE: Steady-State Spectral Wave Model, Users Manual for STWAVE Version 3.0, US Army Corps of Engineers, Engineering Research and Development Center; 2001, pp. 6–8. 5. I. G. Jonsson, in The Sea, eds. B. LeMehaute and D. M. Hanes, Vol. 9, Part A (John Wiley & Sons, Inc., New York, 1990). 6. R. A. Allard, J. Kaihatu, Y. L. Hsu and J. D. Dykes, Oceanography 15, 1 (2002) 67–76. 7. D. E. Goldberg, Genetic Algorithms in Search Optimization Machine learning (Addision-Wesley, Reading, Mass. USA, 1989). 8. R. B. Wardlaw and M. Sharif, J. Water Resour. Planning Mgmt. 125 (1999) 25–33. 9. Z. Michalewicz, Genetic Algorithms + Data Structure = Evolution Programs (Springer-Verlag, New York, Inc., New York, 1992). 10. US Army Corps of Engineers, Department of the Army, Shore Protection Manual (1984). 11. J. Hirschfeld, D. Hadley, R. Mongruel and J. D’Hernoncourt, Multi-criteria analysis — Specification sheet and supporting material, Spicosa Project Report, IOeW, Berlin, (2011).

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


DECISION SUPPORT SYSTEM FOR WATER SUPPLY PLANNING CHATREE RUANGTHANUNRAK Department of Water Resources Engineering, Kasetsart University, Bangkok, Thailand [email protected] SUWATANA CHITTALADAKORN∗ Associate Professor, Ph.D., Department of Water Resources Engineering, Kasetsart University, Bangkok, Thailand [email protected]

The project for water supply planning in the case of the water treatment expansion generally is to link the new expanding plant to the previous system to save the investment budget. The linkage between the new and the old system might cause the complexity of hydraulic conditions. If planers do not have enough experiences, it might cause the new improved system to have the problems in water supply operation in term of bottle neck problem. Therefore, in this research, the decision support system namely DSS4WSP was developed to support the decision for expanding the water supply system. This model uses GIS base by MapWindow plug-in for facilitating to line up all elements of the water treatment plant units and to link related components connected with linkage pipelines. Then, the model simulation was tested those facilities and searching for appropriate alternative using optimization technique and hydraulic simulation to solve the problem.

1. Introduction Presently, Thailand has a population of about 66 million, or about 13.2 million households. But there still be many people who do not have clean water for consumption which is many up to 8.6 million people or about 2.2 million households. As shown in Fig. 1, the demand for water consumption is increasing 6–7% per year since 2003 to 2010.1 Therefore, there is a need for many projects to extend the water supply systems all over the country every year. ∗ Corresponding

author. 131

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Fig. 1.

Growth rate of water demand in Thailand.

The water supply planning project for improving and extending the water supply system mostly relies upon the expertise and experiences of engineers, in order to make the decision for extending the water supply distribution related to the required water quantity for people usage which substantially increasing. Generally, the project planning for improving and expanding the water supply system is always initiated the new water supply system linked to the previous system to save the investment budget. The old or previous water supply system was able to be repeatedly improved. The linkage between the new and the old system might cause the complexity of hydraulic conditions. If planers do not have enough experiences, it might cause the new improved system to have the problems in water supply operation in term of bottle neck problem. For the high budget projects, they cannot risk with this kind of problem. 2. Water Treatment Process A water treatment process is to improve the quality of raw water from a natural water source to meet water quality standard for consumption. Normally, the water treatment process has seven main steps. Those are (1) raw water transmission to the plant, (2) rapid mixing & slow mixing, (3) sedimentation, (4) filtration, (5) disinfection, (6) water quality control, and (7) water distribution. These processes must be continuously run through all operation units for water treatment plant.

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2.1. Operation unit The operation units are water structures that facilitate for water treatment by chemical and physical processes. Normally operation units consist of 10 elements as follows2 : 1. Intake: The unit transmits raw water into the plant. 2. Split box: The unit divides flow rate into each module. 3. Rapid mixing: The unit mixes raw water with chemical agents such as chlorine, lime, and alum. 4. Flocculation tank: The unit brings the particle into contact and to form into bigger particle for sedimentation. 5. Sedimentation tank: The unit is used for separating water from sludge. 6. Filtration tank: The unit is used for filtering out the remaining particles from the tank bottom. 7. Clear Water tank: The unit stores clean water for distribution. 8. Pump station: The unit is used for the installation of pumps for distribution. 9. Elevated tank: The water tank is used for distribution. 10. Water demand: The pattern of changes in the water demand within one day. In general, the connections between the operating units are often used by pipe systems. The simple model can be shown in Fig. 3. 2.2. Hydraulic grade line Hydraulic grade line (HGL) is a line which plotted ordinate position representing the sum of pressure head plus elevation head for the various positions along a given fluid flow path, such as along a pipeline or a ground water streamline. Figure 2 demonstrates the connection between the operating units of treatment plant with pipelines. It can see that both

Fig. 2.

Sample of hydraulic grade line for operating units of water treatment plant.

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the differences in elevations of connected units and in the sizes of connected pipes may cause the differences in flow gradient. 2.3. Simple model and complex model The meaning of simple model is the operation units that place their units in sequence of series functions to complete the conventional treatment process. Each unit usually connects to nearby units with the connecting appropriate sized pipes. The connection of this simple model can be shown as a single line model in Fig. 3. However, when demand has increased, more water is needed to supply to the water users. The expansion of the existing treatment plant is therefore necessary. In general practice, the improvement by construction of the additional treatment plant which is parallel and connected to the original plant would be implemented. Therefore, the function of the treatment plant will be more complicate and it will become more and more complex when the expansion needs to be repeated several times as shown the sample in Fig. 4.

Fig. 3.

Simple model of water treatment plant.

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Fig. 4.

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Complex model of water treatment plant.

Fig. 5.

Bottleneck problem.

2.4. Bottleneck and unsuitable hydraulic profile problem A bottleneck problem as shown in Fig. 5 is a stage in a process that causes the entire process to slow down the flow in other word causing the problem of flow constriction in the system. In this context, bottleneck is the point where flow rates passing through any connected pipe is decreased or less than the

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Fig. 6.

Unsuitable hydraulic profile problem.

designed capacity of the system. This problem can happen at any point in the water treatment plant, since some units of the existing plant may be designed to work in cooperation with the new expanded units. Moreover, in some case of operation practice, both new and existing facilities may need to switch operation between each other single line unit, such as the need for specific maintenance of other units in different lines. The unsuitable hydraulic profile problem may be caused by improper setting of structures level of some operating units. This can be occurred by several reasons, such as the steep of terrain which cannot place the structures or the problem of different condition due to difference in design criteria and period, etc. These problems usually reduce the efficiency of those facilities units, for example the problem of dead zone in the tank shown in Fig. 6. 3. Methodology The decision support system for water supply planning (DSS4WSP) consists of three major parts: (1) Data base, (2) Model base, and (3) Dialog base shown in Fig. 7. All parts are integrated by GIS base using MapWindow plug-in. 3.1. Data base The data base of this research consists of four main parts as follows: 1. 2. 3. 4.

Operation unit and configurations. Pipe data (Type, Diameter, Length, friction factor) Water demand pattern GIS Map

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Fig. 7.

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Three bases of the decision support system for water supply planning.

Fig. 8.

Model base of water treatment.

3.2. Model base The model base consists of two parts: (1) Hydraulic model and (2) Optimization model shown in Fig. 8.

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Hydraulic model : The Darcy Weisbach’s equation and Bernoulli’s equation are used to determine flow rate and head loss through HGL of the system.3 hf = f ·

L V2 · , D 2g

(1)

where hf L D V g f

= = = = = =

the the the the the the

head loss due to friction (m), length of the pipe (m), hydraulic diameter of the pipe (m), average velocity of the fluid flow (m/s), local acceleration due to gravity (m/s2 ), Darcy friction factor. Z1 +

αV 21 αV 22 P1 P2 + = Z2 + + + hf , ρg 2g ρg 2g

(2)

where Z1 , Z2 = the elevation of the point (m), V1 , V2 = the velocity of the fluid flow (m/s), P1 , P2 = the pressure at the chosen point (N/m2 ), g = the acceleration due to gravity (m/s2 ), ρ = the density of the fluid (kg/m3 ), hf = the head loss due to friction (m). Optimization model : This research used the optimization process by Genetic Algorithm (GA). The GA is a random base optimization for searching solution of the complex problem.4 In GA, the problem is represented by a population of string (or chromosome) each string comprises a number of fitness, which represents the individual decision variables of the problem. The variables represented in the string can be processed in an evaluating function or fitness function, which is in effect to the objective function. In early GA, decision variables were represented in binary coding in which each block, or gene, is broken down into a series of binary digits. Strings are processed and combined according to their fitness (objective function value) in order to generate new strings that contain the best features of two parent strings. Strings with the highest fitness have the greatest chance of contributing to future generations, as in the

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process of natural selection. Excellent introductions to GAs are given by Goldberg4 and Michalewicz.5 Three fundamental operators are involved in manipulating strings and moving to a new generation: selection, crossover, and mutation. The objective function in this study is: Min · Z = |∆Q|.

(3)

D and ∆H.

(4)

∆Q = Qdemand − Qdesign .
gπ 2 D5 ∆Qdesign = ∆H · . 8fL

(5)

Decision Variables:

Subject to

Qdesign ≥ Qdemand. ∆H = Elev1 − Elev2 ,

(6) (7) (8)

where ∆H L D Q V g f

= = = = = = =

the the the the the the the

head loss due to friction (m), length of the pipe (m), hydraulic diameter of the pipe (m), flow rate (m3 /s), average velocity of the fluid flow (m/s), local acceleration due to gravity (m/s2 ), Darcy friction factor.

In this research, the GA has applied to define the optimal diameter pipe and head loss complex model. The objective function of this research is to minimize the difference between the rate of flow from demand and flow from design. If the difference between the flow rate is negative, indicating that the bottleneck in the system is occurred. On the other hand, if the difference between the flow rate is positive, it will require high investment. The result of the system is the most suitable pipe size which will not cause bottlenecks in the system. In addition, by trial different structure levels, the head loss of the system can also be further optimized.

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3.3. Dialog base Dialogue base is the important part of DSS because it will communicate between the model and the users. In the dialogue base for this research, the GIS is to be used in order to integrate all three main models together. The DSS described herein is a MapWindow (Ames 2010) plug-in for the planning of water supply. The plug-in was developed in VB.NET and compiled as a dynamic link library (DLL file). MapWindow can connect to the DLL, or plug-in, with interfacing functions, and data as well as for treatment plant facility lay out. MapWindow GIS6 is an open-source GIS application and set of programmable mapping components. To use DSS for water supply planning [DSS4WSP], it is started from input the GIS map which is stored in the shape file pattern into Legend of Map Window and then, selecting the water treatment area site as shown in Fig. 9. After setting up the location, the operation units are arranged by functionality and all the units are connected by pipes. The operating unit and the pipe will be configured and store the value in the database as shown in Fig. 10. After the installations of the operating units have been made, the next step is to run hydraulic model. It is necessary to retrieve data from the

Fig. 9.

Location layer configuration.

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Fig. 10.

Fig. 11.

141

The placement of the operating units by functions.

The hydraulic model runs with the pattern of water demand.

pattern of water demand in each period used, and the entire system would be simulated at that pattern of water demand shown in Fig. 11. It is noted that this example is from the Burirum waterworks which is the case of the fifth expansion of this treatment plant.

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Fig. 12.

Results of hydraulic model.

Fig. 13. The hydraulic model shown the point of bottleneck problem and the optimization model determined the optimal size of pipe.

The results of hydraulic model have demonstrated the changes in water balance between water entering and leaving each unit. Thus, when considering the inflow & outflow of each unit, the bottleneck problem if occurred can be identified in the table results as shown in Figs. 12 and 13. After the point of bottleneck has been identified, the optimization

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model will simulate to find the appropriate diameter size of the connecting pipe recommended for this layout planning, and finally will repeatedly be simulated to confirm no bottleneck problem in the case of that structural setting level profile.

4. Conclusions This research developed the decision support system namely DSS4WSP to support the decision for expanding the water supply system. This model uses GIS base by MapWindow plug-in for facilitating to line up all elements of the water treatment plant units and to link related components connected with linkage pipelines. The optimization technique and hydraulic simulation are used to solve the bottleneck problem while expanding the treatment plant capacity. This model is also facilitated for checking the appropriate hydraulic grade line due to the change in structural setting level profile of the treatment plant. The example from Burirum waterworks in Burirum province of Thailand was presented as the case study for the fifth expansion of this treatment plant. As the results of model simulation by DSS4WSP, the bottleneck problems of different proposed alternative layouts can be nicely identified, therefore it is very useful for designer to support decision in this complex case.

References 1. Provincial Waterworks Authority (PWA), Annual Report 2010, Thailand, 2011. 2. Kawamura, Integrated Design and Operation of Water Treatment Facilities, 2nd edn. (John Wiley & Sons, Inc. New York, 2000). 3. R. E. Featherstone and C. Nalluri, Civil Engineering Hydraulics (Baran, Blackwell Science, USA, 1995). 4. D. E. Goldberg, Genetic Algorithms in Search Optimization & Machine Learning (Addision- Wesley, Reading, Mass. USA, 1989). 5. Z. Michalewicz, Genetic Algorithms, Data Structure, Evolution Programs (Springer-Verlag, New York, Inc., New York, 1992).

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Advances in Geosciences Vol. 29: Hydrological Science (2011) Ed. Gwo-Fong Lin c World Scientific Publishing Company


THREE-SOURCE DYNAMICAL MODEL FOR ESTIMATING PARAMETERS FOR IRREGULARLY SPOUTING GEYSERS INDUCED BY GAS INFLOW HIROYUKI KAGAMI∗ Department of Preschool Education, Nagoya College, 48 Takeji, Sakae-cho, Toyoake, Aichi, 470-1193 Japan

The author has previously proposed a static mathematical model, a dynamical model and a modified dynamical model of geysers induced by gas inflow (periodic bubbling springs) based on observations and model experiments on geysers, and has also proposed a model combining the above two dynamical models, with certain improvements. As a result, the spouting mechanism of regularly spouting geysers induced by gas inflow has been clarified. The author has also formulated an extended dynamical model that assumes two underground gas sources in order to clarify the spouting mechanism of irregularly spouting geysers induced by gas inflow. In the present study, this model is extended further by assuming three underground gas sources, and then the effects of three underground gas sources are discussed through numerical simulations based on the three-source dynamical model. Finally, the threesource dynamical model is applied to an actual irregularly spouting geyser induced by gas inflow in order to estimate the relevant parameters.

1. Introduction Geysers are classified into two types depending on the inducer. One type involves geysers induced by boiling, and the other type involves geysers induced by gas inflow (periodic bubbling springs). The latter type is the target of a series of studies conducted by the authors. Geysers induced by boiling are rather common, and several theories about their spouting mechanism have been proposed.1 On the other hand, there are few geysers induced by gas inflow, and correspondingly few theories describing their spouting mechanism have been proposed.2 Iwasaki (1962)2 conducted model experiments on geysers induced by gas inflow and showed that the injection of gas under high pressure induces intermittent spouting of water. Using ∗ Corresponding

author. 145

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the gas supply rate as a parameter, Iwasaki also formulated a mathematical model of gas balance to calculate the spouting time and pause time. However, Iwasaki’s model does not cover spouting dynamics. In this regard, the author has proposed a static mathematical model,3,4 a dynamical model4,5 and a modified dynamical model of geysers induced by gas inflow4,6,7 based on observations8 and model experiments on such geysers,9 as well as a combined model combining the static model and the dynamical model.4 Numerical simulations based on the modified dynamical model or the combined model reproduced the dynamics of spouting of geysers induced by gas inflow and allowed for the parameters (volume of the underground space, depth of the spouting hole and so forth) for such geysers to be estimated through comparison between the simulation results and observation data.4,7 Moreover, the author has verified the above models through geological exploration, analysis of hot spring water and radioactive prospecting,10 modifying the models as necessary.11−13 As a result, the spouting mechanism of regularly spouting geysers induced by gas inflow has been clarified. However, in addition to regularly spouting geysers, there are also irregularly spouting geysers induced by gas inflow, an example of which is the Hirogawara Geyser (Yamagata, Japan). The spouting mechanism of such geysers cannot be explained with the above-mentioned dynamical model, which assumes a single underground gas source. Accordingly, a natural conclusion is that there are multiple underground gas sources, whose interaction produces an irregular spouting period. To account for such cases, the author has proposed a dynamical model that assumes two underground gas sources by extending the abovementioned dynamical models.14,15 Through numerical simulations based on this extended dynamical model, the author has shown that a complex spouting period arises as a result of the interaction between two underground gas sources. In the present study, the extended dynamical model is extended further by assuming three underground gas sources in order to account for more complex spouting periods. Subsequently, the author applied the threesource dynamical model to an actual irregularly spouting geyser induced by gas inflow. Specifically, the results of numerical simulations based on this model were compared with data obtained from observations of an actual irregularly spouting geyser induced by gas inflow in order to estimate the relevant parameters. The results demonstrate that the parameters of the underground configuration for such irregularly spouting geysers can be estimated from their spouting dynamics.

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2. Model In this section, first the main points of the former dynamical model, the static mathematical model and the combined model of geysers induced by gas inflow (periodic bubbling springs) are introduced. Then, the derivation of an extended dynamical model which assumes two underground gas sources by extension of the original dynamical model is described. Subsequently, the extended dynamical model is further extended by assuming three underground gas sources. Finally, the results of numerical simulations based on the three-source dynamical model are reported and the effects of three underground gas sources are discussed. 2.1. The former model Detailed derivations of the original dynamical model, the static mathematical model and the combined model of geysers induced by gas inflow (periodic bubbling springs) can be found in the relevant references.4,7,13 Therefore, only the main results are shown here. First, if friction between the walls of the spouting pipe and water contained in it is not taken into account, an evolution equation of temporal variations in height of the surface of the water column in the spouting pipe of a periodic bubbling spring can be written as (n0 + βt)(V0 + Sx)ρH

d3 x dx = (V0 + Sx)pβ, + (n0 + βt)pS 3 dt dt

(1)

where n0 represents the molar number of gas in the underground space immediately before the water column begins to move up toward the upper entrance of the spouting pipe, β is a constant concerning the gas supply rate, V0 represents the volume of gas contained in the underground cave, S represents the area of the cross section of the spouting pipe, H represents the length (height) of the water column in the pipe, p represents the pressure of the gas contained in the underground cave, x is taken as the position of the lower interface between the water and the gas, and the upward direction is regarded as the positive direction of the x axis. Furthermore, if friction between the walls of a spouting pipe and water contained in it is taken into account, Eq. (1) becomes (n0 + βt)(V0 + Sx)ρH + (n0 + βt)pS

d3 x 8πηH d2 x (n0 + βt)(V0 + Sx) 2 + 3 dt S dt

dx = (V0 + Sx)pβ, dt

(2)

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300

8/17/2003 13:30 8/18/2003 11:30 Simulation

200 100 0 0

10

20

Fig. 1. A graph of numerical simulation of Eq. (2) comparison with graphs of observation of a geyser induced by inflow of gas (Hirogawara geyser (Yamagata, Japan)).14

where η represents a viscosity coefficient. In other words, the second term, which represents the effects of viscosity, is added in Eq. (2). An example of the results of a numerical simulation based on Eq. (2) is shown in Fig. 1, which shows a graph corresponding to the numerical simulation in comparison with graphs plotting observational data. Through this comparison, the parameters of the underground configuration can be easily determined, which cannot be measured easily owing to geological peculiarities. Specifically, the results of the numerical simulation can be fit to the observation data by changing the values of the parameters introduced above. The best fit to the two sets of data indicates the most likely values of the parameters for the actual underground configuration. Using the static mathematical model, variables such as the spouting period τ are represented as functions of various parameters. For example, the spouting period τ can be written as 
fk S V0 + (3) (fk + P0 + ρgH) τ= αβ ρgαβ where α = RT and R represents the gas constant, T represents the temperature, fk represents the pressure due to surface tension at the interface between the water column in the spouting pipe and the gas in the underground cave, P0 represents the atmospheric pressure, and g represents gravitational acceleration. For example, when determining the spouting period of a geyser induced by gas inflow, the parameters of the underground configuration (volume of the underground space (V0 ), depth of spouting hole (H) and so forth) can be evaluated from Eq. (3). The combined model encompasses the original dynamical model and the static mathematical model and allows for more reliable estimation of the parameters of the underground configuration for geysers induced by gas inflow. Specifically, although either of the dynamical model or the static mathematical model can be used independently to determine the parameters

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of geysers induced by gas inflow, as shown above, several sets of parameters reproduce the spouting dynamics or period in each model. In other words, we cannot determine the most appropriate parameter set by using a single model. However, an essential quality of the combined model is that it allows for determining the most appropriate parameter set by using the dynamical model together with the static mathematical model. 2.2. Extended two-source dynamical model In this section, the derivation of an extended two-source dynamical model by extension of the original dynamical model is briefly introduced.14,15 To start, let us assume a simple underground system with two underground gas sources, as shown in Fig. 2. There is a water column for each gas source. The upper surface of the water is common to both water columns. The central dotted line in Fig. 2 shows that two water columns are separated under the water surface. Each water column moves independently, except for interaction at the upper surface of the water. Next, we define the x, y and z axes in the vertical direction and set their respective origins at the lower surface of the right water column, the lower water surface of the left water column and the upper surface of the water, respectively. The watercourses on the right and on the left are denoted as A and B, respectively. With this setup, the basic dynamical equation for each watercourse (A and B) based on the original model is written as (n0A + βA t)(V0A + SA x)ρ(z − x)

dx d3 x + (n0A + βA t)pA SA dt3 dt

= (V0A + SA x)pA βA ,

(4) z=0

HB y=0

HA SA pA

Gas supply source B

SA pA

x=0

Gas supply source A

Fig. 2. Assumed system of an extended dynamical model which assumes two underground gas supply sources.

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(n0B + βB t)(V0B + SB y)ρ(z − y)

dy d3 y + (n0B + βB t)pB SB 3 dt dt

= (V0B + SB y)pB βB ,

(5)

where n0A and n0B represent the molar numbers of gas in the underground spaces immediately before the corresponding water column begins to move upward, βA and βB are constants concerning the gas supply rates, V0A and V0B represent the volumes of gas contained in the underground caves, SA and SB represent the areas of the cross sections of the spouting pipes, and pA and pB represent the pressures of gas in the underground caves in watercourses A and B, respectively. The equation governing the conservation of water volume can be written as SA (z − x) + SB (z − y) = SA HA + SB HB ,

(6)

where HA and HB represent the initial heights of the water columns in watercourses A and B, respectively. 2.3. Three-source dynamical model By the same procedure as above, a three-source dynamical model is derived. At the beginning, let us assume a simple underground system with three underground gas sources as shown in Fig. 3. The meanings of the symbols in the figure are the same as those in Fig. 2. In this case, we define the x, y, z and w axes in the vertical direction and set their origins at the lower surface of the right water column, at that of the left water column, at that of the z=0 HC

HB y=0

SB

SC

pB

pC

HA

w=0 SA

x=0

pA

Gas supply source A Gas supplysource B Gas supply source C Fig. 3. Assumed system of an extended dynamical model which assumes three underground gas supply sources.

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central water column and at the upper surface of the water, respectively. The watercourses on the right, on the left and in the middle are denoted as A, B and C, respectively. The basic dynamical equation for each watercourse (A, B and C) based on the original model is written as (n0A + βA t)(V0A + SA x)ρ(z − x)

dx d3 x + (n0A + βA t)pA SA 3 dt dt

= (V0A + SA x)pA βA , (n0B + βB t)(V0B + SB y)ρ(z − y)

(7) dy d3 y + (n0B + βB t)pB SB dt3 dt

= (V0B + SB y)pB βB , (n0C + βC t)(V0C + SC w)ρ(z − w)

(8) 3

dw d w + (n0C + βC t)pC SC 3 dt dt

= (V0C + SC w)pC βC ,

(9)

where n0A , n0B and n0C represent the molar numbers of gas in the underground spaces immediately before the corresponding water column begins to move upward; βA , βB and βC are constants concerning the gas supply rates; V0A , V0B and V0C represent the volumes of gas in the underground caves; SA , SB and SC represent the areas of the cross sections of the spouting pipes; and pA , pB and pC represent the pressures of gas contained in the underground caves in watercourses A, B and C, respectively. The equation governing the conservation of water volume is written as SA (z − x) + SB (z − y) + SC (z − w) = SA HA + SB HB + SC HC ,

(10)

where HA , HB and HC represent the initial height of the water column of watercourses A, B and C, respectively. 2.4. Results of numerical simulation based on the above model and discussion In this section, the results of a numerical simulation are presented based on the three-source dynamical model, followed by a discussion. Figure 4 shows an example of the dependence of the variation in water pole height depending on the number of underground gas sources, with respect to the cross sections of watercourses. In this example, the cross sections of the watercourses are as follows: SA = 2.5 × 10−2 [m2 ], SB = 1.1 × 10−2 [m2 ], SC = 5.0 × 10−1 [m2 ] (Sc is taken into account in

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14 12 10 8 6 4 2 0

2 underground gas sources 3 underground gas sources

0

10

20 30 Time [min]

40

50

Fig. 4. A sample of dependence of variation of height of a water pole on the number of underground gas supply sources concerning cross section of watercourse.

only the case of three underground gas sources). It can be seen that the complexity of irregular spouting in the case of the model with three underground gas sources is somewhat higher as compared with that of the model with two underground gas sources. Next, the dependence of the variation in water pole height on one parameter in the three-source dynamical model is shown. In the case of three underground gas sources, the results of numerical simulation based on the model, which are obtained as the result of interaction between various parameters, are extremely complex and chaotic. Therefore, it is difficult to provide an argument regarding a general solution (the results of the numerical simulation) of the model. Since the dependence of the variation in water pole height on the type of parameter (S, V , and H) and the general effects of each type of parameter on the variation in water pole height are discussed extensively in previous papers,14,15 due to limited space, only the dependence of the variation in water pole height on the cross section of a single watercourse (SA ) are presented, where the cross sections of the other watercourses are SB = 1.1 × 10−2 [m2 ] and SC = 5.0 × 10−1 [m2 ]. The plotted results are shown in Fig. 5, where it is clear that a larger difference between the cross section of one watercourse (SA ) and those of the other watercourses (SB , SC ) entails a smaller amplitude of the temporal variation in the water pole height and a shorter irregular period. These characteristics are similar to the case of two underground gas sources. Next, Fig. 6 shows an example of the dependence of the variation in height of a water pole on the number of underground gas sources with respect to the volume of the underground caves. In this example, the volumes of the underground caves of the watercourses are as follows: VA = 6.0×102[m3 ], VB = 4.0×102[m3 ], and VC = 2.0×102[m3 ] (VC is taken

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14 12 10

Sa=2.5E-02[m*m] Sa=5.0E-02[m*m] Sa=1.0E-01[m*m]

8 6 4 2 0 0

10

20 30 Time [min]

40

50

Height of water pole [m]

Fig. 5. Dependence of variation of height of a water pole on cross section of one side’s watercourse (SA ) in case of values of cross sections of the other side’s watercourses are SB = 1.1 × 10−2 [m2 ] and SC = 5.0 × 10−1 [m2 ].

25 20 15 10 5 0

2 underground gas sources 3 underground gas sources

0

50 Time [min]

100

Fig. 6. A sample of dependence of variation of height of a water pole on the number of underground gas supply sources concerning volume of underground cave of watercourse.

into account only in the case of three underground gas sources). We can see that the complexity of irregular spouting in the case of three underground gas sources is somewhat higher as compared with that of two underground gas sources. The dependence of the variation in water column height on the volume of one underground cave (V0A ) is next examined when the volumes of the other underground caves are fixed. It is clear that a larger difference between the volume of one underground cave (V0A ) and those of the other underground caves (V0B , V0C ) entails a smaller degree of irregularity of temporal variation in the water column height because the cave with the largest volume exerts the strongest influence on the overall temporal variation of the height. Also, a larger volume of one underground cave (V0A ) produces a larger amplitude of the temporal variation in water column height and a longer irregular period. The reason for this is the same as in the case of one or two underground gas sources.14

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3. Comparison of Results of a Numerical Simulation Based on the Three-Source Dynamical Model with Observation Data on an Irregularly Spouting Geyser Induced by Gas Inflow

Height [m]

In this section, the results of a numerical simulation based on the three-source dynamical model are compared with observation data for an irregularly spouting geyser induced by gas inflow. Specifically, each parameter of the model is chosen by considering the spouting dynamics based on a numerical simulation where the model agrees with that based on observation data for an irregularly spouting geyser induced by gas inflow as closely as possible. The method of estimating the parameters is as follows. First, a numerical simulation is conducted under any set of parameters, after which the degree of fitness of the set of parameters is estimated by comparing the results of numerical simulation with the observation data. Therefore, multiple numerical simulations are conducted by gradually changing the values of the parameters. Finally, the set of parameters for which the result of the numerical simulation produces the closest fit to the observation data is evaluated as the most appropriate set of parameters. Observation data for the Hirogawara Geyser are used as data for an irregularly spouting geyser induced by gas inflow. Through this process, we can estimate the actual parameters of the underground configuration of an irregularly spouting geyser induced by gas inflow. A comparison of the results of numerical simulations based on the threesource dynamical model with observation data for an irregularly spouting geyser induced by gas inflow is shown in Fig. 7. The parameters for the underground configuration as estimated through this comparison are listed

5 4 3 2 1 0 −1 20 −2 −3 −4

30

40

50

60

70

Observation (Hirogawara geyser (Yamagata, Japan)) (observed on 22 May 1999) Simulation (The model which assumes three underground gas supply sources)

Time [min] Fig. 7. A sample of comparison of results of numerical simulation of the further extended dynamical model with observation of irregularly spouting geyser induced by inflow of gas.

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Table 1. Estimated underground parameters through comparison of results of numerical simulation of the further extended dynamical model with observation of irregularly spouting geyser induced by inflow of gas. HA HB HC SA SB SC VA VB

80 [m] 100 [m] 110 [m] 0.0012 [m2 ] 0.0020 [m2 ] 0.0051 [m2 ] 240 [m3 ] 200 [m3 ]

VC fkA fkB fkC βA βB βC T

100 [m3 ] 42 [N/m2 ] 32 [N/m2 ] 22 [N/m2 ] 0.00019 [mol/s] 0.00019 [mol/s] 0.00019 [mol/s] 320 [K]

in Table 1. Here, fkA , fkB and fkC represent pressure due to surface tension at the interface between water in the spouting pipe and gas in the underground cave for watercourses A, B and C, respectively. Through the above procedure, we can estimate the parameters of the underground configuration of an irregularly spouting geyser induced by gas inflow. 4. Conclusions and Future Work By using the extended dynamical model with two underground gas sources, a further extended dynamical model was derived for a geyser induced by gas inflow in the case of three underground gas sources. It can be seen that the complexity of irregular spouting in the case of the three-source model is somewhat higher as compared with that of the twosource model, owing to effects of each parameter of the third underground gas source are added to the results obtained for two gas sources through numerical simulation based on the further extended dynamical model. The parameters of the underground configuration for an irregularly spouting geyser induced by inflow of gas can be estimated in the particular case of the Hirogawara Geyser through comparison of the results of numerical simulation based on the three-source dynamical model with observation data for Hirogawara Geyser. The parameters of an irregularly spouting geyser induced by gas inflow are considered, in general, to be estimable by this method. References 1. K. Honda and T. Terada, Publ. Earthq. Inv. Com. 22B (1906). 2. I. Iwasaki, Bull. Tokyo Institute of Technology, No. 46, 1962.

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3. H. Kagami, Abstracts of The 53th Annual Meeting of the Balneological Society of Japan, 27, 2000. 4. H. Kagami, Advances in Geosciences Vol. 4: Hydrological Science (HS) 191, 2006. 5. H. Kagami, Abstracts of The 55th Annual Meeting of the Balneological Society of Japan, 33, 2002. 6. H. Kagami, The 2003 IUGG General Assembly, HW04/09P/C31-004, 2003. 7. H. Kagami, Proceedings of The 38th Conference of Sciete Internationale des Techniques Hydrothermales and The 56th Annual Meeting of the Balneological Society of Japan, 2003, pp. 55–60. 8. E. Ishii et al., Abstracts of The 52th Annual Meeting of the Balneological Society of Japan, 1999, p. 28. 9. M. Katase et al., Abstracts of a meeting for presenting research papers of Kanto Gakuin University College of Engineering, 1999, pp. 99–100. 10. H. Kagami, Advances in Geosciences Vol. 6: Hydrological Science (HS), 203, 2007. 11. H. Kagami, Advances in Geosciences Vol. 11: Hydrological Sciences, 37, 2009. 12. H. Kagami, Advances in Geosciences Vol. 17: Hydrological Sciences, 103, 2010. 13. H. Kagami, Data Sci. J. 9, (2010) IGY110. 14. H. Kagami, Advances in Geosciences Vol. 17: Hydrological Sciences, 113, 2010. 15. H. Kagami, Mathematical Modelling in Civil Engineering 7, 2 (2011) 29.