Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau [1st ed.] 978-981-13-7352-7;978-981-13-7353-4

Table of contents :
Front Matter ....Pages i-xv
Introduction (Shuang Yi)....Pages 1-25
Data (Shuang Yi)....Pages 27-35
GRACE Mass Inversion Method (Shuang Yi)....Pages 37-51
Global Sea Level Change (Shuang Yi)....Pages 53-63
Terrestrial Water Storage Changes in Asia (Shuang Yi)....Pages 65-95
Glacial and Tectonic Mass Transportation in High Mountain Asia (Shuang Yi)....Pages 97-139
Conclusion and Outlook (Shuang Yi)....Pages 141-143

Citation preview

Springer Theses Recognizing Outstanding Ph.D. Research

Shuang Yi

Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

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Shuang Yi

Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau Doctoral Thesis accepted by the Chinese Academy of Sciences, Beijing, P.R. China

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Author Dr. Shuang Yi Institute of Geodesy University of Stuttgart Stuttgart, Germany

Supervisor Prof. Wenke Sun Department of Earth Sciences Chinese Academy of Sciences Beijing, P.R. China

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-981-13-7352-7 ISBN 978-981-13-7353-4 (eBook) https://doi.org/10.1007/978-981-13-7353-4 Library of Congress Control Number: 2019935554 © Springer Nature Singapore Pte Ltd. 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Supervisor’s Foreword

I am honored to be invited to write a preface for Dr. Shuang Yi’s thesis. In 2010, when he graduated from Wuhan University, his university teacher (my friend) recommended him to apply for my postgraduate student, hoping to study for a degree under my guidance. At that time, I just returned home from University of Tokyo, hoping to have excellent students, which is what all teachers hope. Generally speaking, I believe that the students recommended by university teachers should be excellent, as evidenced by his entrance examination and five years of postgraduate life. At that time, the gravity satellite GRACE had been continuously observed for nearly ten years, providing good global time-varying gravity field data. Dr. Shuang Yi had a better understanding and mastery of GRACE knowledge and basic data processing skills during his university years. We chose the use of GRACE observation data to study surface mass transports as his research direction. On the basis of learning and mastering the achievements of predecessors, he quickly entered the fast lane of scientific research after questioning, exploring and thinking for a certain period of time. In the past five years, he has made important contributions to global sea level change, land water storage changes in Asia and China, glacier change in Asia and tectonic process in eastern Tibet, and has made great achievements in scientific research. The research results become the main content of this paper, including the new GRACE data processing method, the new discovery of the mass transfer problem at different spatial scales from global to local. Therefore, this book should be a good reference for those who want to use this method to recover and invert the mass changes of any spatial and temporal scales of the earth surface. Dr. Shuang Yi has two characteristics that make him outstanding in peers. The first one is his enthusiasm and keen insight into science. The second is his technical expertise. Based on his performance on different research topics, he can quickly learn new skills or cooperate with relevant scholars. He is good at mathematics and has a strong background in geophysics and geodesy. Especially, he thinks positively and is good at new discoveries. His doctoral dissertation and published journal papers show that he was a very excellent Ph.D. graduate. When he v

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graduated from the University of Chinese Academy of Sciences (2016), he won the title of outstanding postgraduate, the President Award of the Chinese Academy of Sciences, and the outstanding postgraduates in Beijing in 2016. His Ph.D. dissertation was one of 100 Excellent Ph.D. Dissertations of the Chinese Academy of Sciences in 2017. This is really a reward for his talent, his perseverance and unremitting efforts. I spent five years with Shuang Yi to study the application of time-varying gravity field. This is an important period for us to grow up. When I look back, it is like yesterday. I would like to thank him for his patience, diligence and creativity while working with me. Dr. Shuang Yi has become a very qualified young professional scientist. I believe he will make great achievements in scientific research. Thanks Springer for offering the opportunity to publish the book. I hope this is the new beginning of Dr. Shuang Yi’s academic career. I wish him a bright future. Beijing, P.R. China January 2019

Prof. Wenke Sun

Abstract

Human activities, climate change and environmental change are three tight coupling elements, whose relationship and evolution will impact the sustainability of human society. Since the three elements involve a global scope of diversified influences, it is impossible to be estimated by traditional techniques. The three elements are always accompanied by mass transports in the water circulation system, e.g., water exchange between the land and the ocean and glacier melting, so satellite gravimetry provides an effective approach to systematically evaluate them. The Tibetan Plateau is one of the most tectonically active regions of the world, and studies concerning its dynamics will benefit the understanding of continental collision and plateau building. Here, we also adopt satellite gravimetry to investigate the mass transports caused by melting glaciers and tectonic process in the Tibetan Plateau. The topics of the dissertation include four parts: 1. Global Sea Level Change The global mean sea level (GMSL) dropped 5 mm due to the 2010/11 La Niña and has been rising rapidly ever since. A reconciled sea level budget, based on observations by Argo project, altimeter and gravity satellites, reveals that the true GMSL rise has been obscured by ENSO-related fluctuations and its rate has increased since 2010. After extracting the large fluctuation brought by the land water storage, it is shown that the GMSL has been rising at a rate of 4.4 ± 0.5 mm/yr for more than three years, due to acceleration in the rate of both land ice loss and steric change. 2. Terrestrial Water Storage Changes in Asia and China A study of the Asian region shows that its TWS decreased 1500 km3 during the period of 2003–2009 but exhibited marked stability during 2010–2014, which was concurrent with an alternation between dry and wet years. This slowdown of water depletion can also be found in the water-depleting basins of Indus, Ganges, Tigris-Euphrates and Haihe. To correct for the climate-driven effect, we put forward a linear relationship between the variations of water storage and precipitation. We find that the anthropogenic water depletion in the Asia, Tigris-Euphrates and Ganges regions has been greatly over-estimated due to the

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perturbation of precipitation. Our study on the water storage in China shows that tremendous mass accumulation has occurred from the Tibetan Plateau (12.1 ± 0.6 Gt/yr) to the Yangtze River (7.7 ± 1.3 Gt/yr) and southeastern coastal areas, which is suggested to involve an increase in the groundwater storage, lake and reservoir water volume and the flow of materials from tectonic processes. Additionally, the mass loss has occurred in the Huang–Huai–Hai-Liao River Basin (−10.2 ± 0.9 Gt/yr), the Brahmaputra–Nujiang–Lancang River Basin (−15.0 ± 1.1 Gt/yr) and Tianshan Mountains (−4.1 ± 0.3 Gt/yr), a result of groundwater pumping and glacier melting. 3. Glacier Change in the Asian High Mountains A new spatial inversion method and 10 years of satellite gravimetry data are used to evaluate the glacier melting rate in high mountain Asia (HMA). We find that in HMA area there are three different kinds of signal sources that should be treated together. The two generally accepted sources, glacier melting and Indian underground water depletion, are estimated to change at the rate of −35.0 ± 5.8 Gt/yr (0.09 mm/yr sea level rising) and −30.6 ± 5.0 Gt/yr, respectively. The third source is the remarkable positive signal (+30 Gt/yr) in the inner Tibet Plateau, which is challenging to explain. Further, we have found that there is a five-year undulation in Pamir and Karakoram, which can be explained by the influence of Arctic Oscillation and El Niño-Southern Oscillation. We carefully examine glaciers in Tianshan, which have been steadily decreasing with a value of −4.0 ± 0.7 Gt/yr during 2003–2014 by space gravimetry and −3.4 ± 0.8 Gt/yr during 2003–2009 by laser altimetry. 4. Tectonic Process in Eastern Tibet Various geophysical observations, including seismological and magnetotelluric imaging, have implied that the deep crust beneath eastern Tibet may be partially melted and flowing faster than the brittle upper crust. However, it is still unclear how much faster the deep crust is flowing. We use modern geodetic observations, satellite gravimetry and GPS, to give a constraint in the flow rates of the middle and lower crust (MLC). Therefore, two plausible models for the surface uplift are discussed under the geodetic constraints. In the deep crustal flow model, the crustal thickening requires the horizontal flow rate of the MLC to be 330–670% of the rate of motion of the upper crust. In the hybrid model of deep crustal flow and convective removal, the Moho is uprising and there is a weak or moderate (130–250%) deep crustal flow, which comes with a weak or moderate crustal thickening beneath eastern Tibet.







Keywords Satellite gravimetry Mass transports Tibetan Plateau Sea level rise Terrestrial water storage Glacier melting










Published Work Parts of this book have been published in: 1. Yi, S.; Sun, W. Evaluation of glacier changes in high-mountain Asia based on 10 year grace rl05 models. Journal of Geophysical Research: Solid Earth 2014, 119, 2504–2517. 2. Yi, S.; Sun, W.; Heki, K.; Qian, A. An increase in the rate of global mean sea level rise since 2010. Geophys. Res. Lett. 2015, 42, 3998–4006. 3. Yi, S.; Wang, Q.; Sun, W. GRACE captures basin mass dynamic changes in China based on a multi-basin inversion method, Journal of Geophysical Research: Solid Earth 2016, 121, 3782–3803. 4. Yi, S.; Sun, W.; Feng, W.; Chen, J. Anthropogenic and climate-driven water depletion in Asia, Geophys. Res. Lett. 2016, 43, 9061–9069. 5. Yi, S.; Wang, Q.; Chang, L.; Sun, W. Changes in mountain glaciers, lake levels and snow coverage in Tianshan monitored by GRACE, ICESat, altimetry and MODIS, Remote Sensing 2016, 8, 798. 6. Yi, S.; Freymueller, J.; Sun, W. How fast is the middle-lower crust flowing in eastern Tibet? A constraint by geodetic observations, Journal of Geophysical Research: Solid Earth 2016, 121, 6903–6915.

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Acknowledgements

This dissertation was completed under the careful guidance of my supervisor Prof. Sun Wenke. In the course of my master’s and doctoral studies, Prof. Sun guided me to study hard by his profound professional knowledge, rich research and life experience, so that I could master the ideas and methods of scientific research. Not only did he give me enough room to study what I was interested in, he patiently urged and constantly guided me to move forward, and often encouraged me in my research work, which enhanced my research ability and achievements. In life, Prof. Sun also gave me a lot of care and teaching, and often encouraged us to touch new things. In my research study, recognizing and being instructed by Prof. Sun Wenke were my greatest fortune. I want to give the highest gratitude to Prof. Sun. If I had not met him, I would not have the achievements I have made today. I sincerely thank Prof. Sun for helping me grow into a qualified doctoral student in five years! Thanks to my bachelor supervisor, Prof. Shen Wenbin from Wuhan University, for helping me during my university studies and bachelor’s thesis, so that I could quickly find a direction in my graduate research. After my graduation, I met Prof. Shen occasionally in many meetings, and he often cared about my research and life. It is because of his recommendation that I can have the honor to meet Prof. Sun. I would like to thank other teachers who instructed and helped me, including Prof. Kosuke Heki from Hokkaido University (who is also the host professor of my first postdoc), Prof. Chen Jianli from the University of Texas and Prof. Jeff Freymuelley from the University of Alaska. The cooperation and communication with them inspired me to have a deeper understanding of my research. I am grateful to the University of Chinese Academy of Sciences for providing me with a comfortable research and living environment. I would also like to express my gratitude to my classmates for their frequent communications and discussions. Thanks to my high school classmate, Dr. Cao Tao, who graduated from the Shanghai Institute of Organic Chemistry and is currently working at Riken, Japan. Thank you for supporting me in my most difficult time. He made me not alone on the road of scientific research.

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Finally, I want to thank my family. Thanks to my parents, sister and brotherin-law for their understanding, support and encouragement in my research work. I would also like to thank my wife, Dr. Cai Yan. She and science complete my life.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Background of Previous Research and Problems . . . 1.2.1 Global Sea Level Change . . . . . . . . . . . . . . 1.2.2 Terrestrial Water Storage Change . . . . . . . . 1.2.3 Glacier Mass Balance . . . . . . . . . . . . . . . . . 1.2.4 Tectonics in the Tibet . . . . . . . . . . . . . . . . 1.3 Focus of This Book . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 GRACE Inversion Methods . . . . . . . . . . . . 1.3.2 Sea Level Budget . . . . . . . . . . . . . . . . . . . 1.3.3 Water Storage in Asia . . . . . . . . . . . . . . . . 1.3.4 Mass Transports in High Mountains of Asia 1.4 Structure of This Book . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Global Satellite Gravity Dataset GRACE 2.1.1 Data Filtering . . . . . . . . . . . . . . 2.2 Land Surface Model GLDAS . . . . . . . . 2.3 Altimetry . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Sea Level . . . . . . . . . . . . . . . . . 2.3.2 Lake Level . . . . . . . . . . . . . . . . 2.4 Post-Glacial Rebound Model . . . . . . . . . 2.5 Argo Data . . . . . . . . . . . . . . . . . . . . . . 2.6 Precipitation . . . . . . . . . . . . . . . . . . . . . 2.7 ICESat Data . . . . . . . . . . . . . . . . . . . . . 2.8 MODIS Data . . . . . . . . . . . . . . . . . . . . 2.9 Global Glacier Distribution . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 GRACE Mass Inversion Method . . . . . . . . . . . . . . . . . . . . 3.1 Math Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Spherical Harmonics and Gridded Observations . 3.1.2 Basin Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Uncertainties in a Study Region . . . . . . . . . . . . 3.1.4 Mascons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Necessity of the Inversion . . . . . . . . . . . . . . . . . . . . . . 3.3 Overview of Inversion Methods . . . . . . . . . . . . . . . . . . 3.4 Scaling Factor Method . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Spectral Domain Inversion (SEDI) . . . . . . . . . . . . . . . . 3.6 Spatial Domain Inversion (SADI) . . . . . . . . . . . . . . . . 3.6.1 Comparison Between SEDI and SADI Methods 3.7 Point-Mass Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Forward Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Multi-basin Inversion Method . . . . . . . . . . . . . . . . . . . 3.10 The Table for Data and Method . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Global Sea Level Change . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . 4.2 Data and Method . . . . . . . . . . . . . . 4.2.1 GRACE . . . . . . . . . . . . . . . 4.2.2 Altimetry . . . . . . . . . . . . . . . 4.2.3 Argo . . . . . . . . . . . . . . . . . . 4.3 Results . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Land Ice . . . . . . . . . . . . . . . 4.3.2 Land Water . . . . . . . . . . . . . 4.3.3 Discussions and Conclusions References . . . . . . . . . . . . . . . . . . . . . . . .

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5 Terrestrial Water Storage Changes in Asia . . . . . . . . . . . . 5.1 The Whole Asia Region . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Method and Data . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.4 Water Storage Change in the North China Plain 5.1.5 Isolating the Cause of the Recharge . . . . . . . . . 5.1.6 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Basin Mass Dynamic Changes in China . . . . . . . . . . . . 5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Basin Division . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Glacial and Tectonic Mass Transportation in High Mountain Asia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Glacier Mass Balance in HMA . . . . . . . . . . . . . . . . . . . . 6.2.1 Mascon Division . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Region A: Various Signals in the Inland of TP . . . . . . . . . 6.4 Region B: The Pamir Plateau . . . . . . . . . . . . . . . . . . . . . 6.4.1 Monsoons and Their Impact on the Mass Balance . 6.4.2 The 5-Year Undulating Signal . . . . . . . . . . . . . . . 6.5 Region C: The Tianshan . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Region D: The Eastern Tibet . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 7.1 Conclusion and Highlights . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Chapter 1

Introduction

1.1 Motivation Human activities, climate change and environmental change are three mutually influential elements. Factors such as the accumulation of greenhouse gases from human activities have led to global warming and more frequent extreme weather phenomena; intensive human activities and rising global temperatures have brought irreversible effects on the environment, of which the most significant and manifest is the mass transports in the water cycle system; the deterioration of the environment will further weaken the stability of the climate, which will ultimately threaten the sustainable development of human production and living environment. In recent years, people have become more and more aware of the significance of these three elements. The 2015 United Nations Climate Change Conference (http://unfccc.int/2860.php), held in Paris from November 30 to December 11, 2015, is a milestone in the world’s response to climate change. The aim is to enhance our response capacity to the threat of climate change, and to control the temperature increase in this century by 2 °C relative to the pre-industrial level. Behind the government’s decision-making, the importance of scientifical understanding of these three elements is self-evident. Studying the mass transport problem of the water circulation system plays an important role in understanding the changing rules and mechanisms of these three elements. The water cycle system has three main components: global ocean mass, global terrestrial water storage and glaciers distributed in the mountainous regions and polar regions. These large-scale mass transports vary the earth’s gravitational field and can therefore be monitored by satellite gravimetry. At the same time, satellite gravimetry is the most straightforward research tool at the global scale for mass transport. The changes in ocean water mass, terrestrial water storage and glacial mass are not isolated. They meet the conservation of total mass within the global water system; that is, the increase or decrease in global ocean mass comes from changes in global terrestrial water storages and land ices, so our research is centered around these three parts. The research content of this thesis includes: (1) global sea level change; © Springer Nature Singapore Pte Ltd. 2019 S. Yi, Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau, Springer Theses, https://doi.org/10.1007/978-981-13-7353-4_1

1

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1 Introduction

(2) changes in terrestrial water storage in Asia and China; (3) changes in glacier mass in high mountain areas of Asia. The high mountain of Asia mainly contains the third pole of the world, the Qinghai–Tibet Plateau, which is a research hotspot in many fields. The water system supplied by the widely distributed glaciers on the plateau may affect the water intake of billions of people, so it is also called the “Asian Water Tower.” The unique environment also gives other rich geophysical signals on the Tibetan Plateau, such as lakes, tectonic movements, weathering and erosion, which also attracts extensive attention in the fields of hydrology, geology, seismology and geodynamics. These geophysical phenomena can cause gravity changes, so we also use data such as satellite gravimetry to focus on: (4) mass transport of the Tibetan Plateau. According to the research objects, these four research contents can be divided into: sea level, water storage, glaciers and other comprehensive mass transports; according to the research spatial scale, they can be divided into: global ocean, Asia, China and the Tibetan Plateau, of which the last one is a key research area in this thesis. The GRACE (Gravity Recovery and Climate Experiment) gravity satellite program was jointly developed by the National Aeronautics and Space Administration (NASA) and the German Space Flight Center (Deutschen Zentrums für Luft- und Raumfahrt, DLR). Since the successful launch of GRACE dual satellite at the Plesetsk launch center in northern Russia on March 17, 2002, the GRACE team has continuously refined the gravity field model and released its observations globally (Tapley et al. 2004). The GRACE satellite uses a low–low satellite tracking technique that simultaneously launches two low-orbit satellites in the same orbit at a distance of approximately 220 km. The dual satellite is a near-polar orbit with an orbital inclination of 89° and an initial height of 500 km. The dual satellite surrounds the earth about 15 times a day. One-month data can be used to solve gravity field to the degree of 60–120. There is a trade-off between temporal resolution and spatial resolution. The GRACE gravity satellite is capable of detecting gravity changes caused by mass transports on or under the earth’s surface. Its main tasks include: (1) tracking groundwater movements; (2) tracking changes in glaciers and ocean waters; (3) studying surface and deep ocean currents; (4) studying solids earth structure changes (Fig. 1.1). The results of satellite gravity fields are especially important when field observations are scarce or costly. So far, it has been testified that GRACE can observe these changes: changes of surface water, soil moisture and groundwater in basins, ice mass balance in Greenland and Antarctic continents, post-glacial rebound signals, glacier melting in high mountain areas, coseismic and post-seismic earthquake deformation and so on (Cazenave and Chen 2010). We can get long-term gravity changes by fitting GRACE’s observation data for more than ten years. The long trend from 2003 to 2014 is shown in Fig. 1.2, and we can find that there are tremendous signal sources around the world. After deducting the effects of post-glacial rebound (see Sect. 2.4), the main observable geophysical activities include the following four categories: A. Changes in ice mass: (1) melting of the polar ice sheet in Greenland Velicogna and Wahr (2006a); (2) melting of the polar ice sheet in the Antarctic Peninsula

1.1 Motivation

3

Fig. 1.1 GRACE dual satellite and its major research targets, including ocean mass, ice melting, terrestrial water storage and solid earth such as giant earthquakes. Adapted from Cazenave and Cozannet (2014)

(Velicogna and Wahr 2006b; Chen et al. 2009); (3) mass accumulation in Queen Maude in the eastern Antarctic (Shepherd et al. 2012); (4) glacier melting in high mountains in Asia (Matsuo and Heki 2010; Yi and Sun 2014); (5) glacier melting in Alaska (Arendt et al. 2008; Luthcke et al. 2008, 2013); (6) glacier melting in the Batagria Mountains (Chen et al. 2007). B. Changes in terrestrial water storage: (1) groundwater depletion in northern India (Rodell et al. 2009; Tiwari et al. 2009); (2) groundwater loss in the North China Plain (Feng et al. 2013); (3) groundwater deficit in the middle east basins (Voss et al. 2013; Joodaki et al. 2014); (4) groundwater loss in California (Famiglietti et al. 2011); (5) watershed changes in Amazon (Chen et al. 2010; Syed et al. 2008); (6) water storage changes in the Congo Plain (Crowley et al. 2006; Syed et al. 2008). C. Coseismic and post-earthquake signals: (1) the 2004 MW 9.3 earthquake (Han et al. 2006; De Linage et al. 2009) and the 2012 MW 8.6 earthquake (Han et al. 2015, 2016) in Sumatra/Indian Ocean; (2) the 2011 MW 9.0 earthquake in northeastern Japan (Matsuo and Heki 2011; Wang et al. 2012b); (3) the 2010 MW 8.8 earthquake in Chile (Han et al. 2010; Heki and Matsuo 2010). D. Lake water level change: (1) the Caspian Sea (Swenson and Wahr 2007).

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1 Introduction

Fig. 1.2 Long-term gravity change between 2003 and 2014 by GRACE

There are also global ocean mass changes not marked. We are not concerned with local sea level changes. The mass-caused global mean sea level change is only ~2 mm/yr, so it is relatively weak. Global sea level change is closely linked to changes in water storages and in land ices that meet global conservation of mass (the long-term change in the atmosphere is ignored here). Except for seismic signals, other signals form a complete water cycle system that reflects climate change, environmental change and human activities, so they are the research targets of this thesis.

1.2 Background of Previous Research and Problems 1.2.1 Global Sea Level Change GMSL is an indicator of global climate and environment changes. It is a result of global warming, ice melting and water exchange between land and sea. The GMSL rise directly influences the coastal environment, such as erosion in coastal areas and higher flood risk (Cazenave and Cozannet 2014). In the last 100 years, GMSL has been rising in response to “global warming” caused by accumulation of

1.2 Background of Previous Research and Problems

5

Fig. 1.3 Global and regional sea level changes and the causes. Image credit (Church et al. 2013b)

anthropogenic greenhouse gases in the atmosphere (IPCC 2014). The understanding of past and present sea level changing states and mechanism is instructive for us to project the future sea level rise and to make proper adaption strategies. Sea level change can be presented in two ways: The first one is relative sea level change to solid earth surface, which plays a direct impact on human lives and can be measured by tide gauges.; the other is geocentric sea level change relative to terrestrial reference system and can be measured by satellite altimetry (Church et al. 2013a). The integration of relative sea level change gives sea water volume change. Global and regional sea level change is affected by various factors, including salinity and temperature changes, ocean currents, land ice melting, land–ocean water exchange and atmosphere–ocean water exchange (Fig. 1.3). The integration of absolute sea level change needs the correction of solid earth deformation (mainly comes from GIA) to get the ocean water volume change. The GIA correction is usually −0.3 mm/yr (Peltier 2001) [this value is updated to −0.32 mm/yr in the ICE-5G model (Peltier 2004)] with a large uncertainty stemming from the ice history model and earth viscoelastic structure model. This value may vary from −0.15 to −0.5 mm/yr (Tamisiea 2011). Global sea level used to fluctuate dramatically in history. The paleo-sea level records of the warm period of 3 million years show that when the global average temperature is 2 °C higher than before the industrial revolution, the global average sea level will be 5 m higher than it is now. During the last interglacial period (about 130,000 years ago to 120,000 years ago), the global sea level was at least 5 m higher than it is today and lasted for thousands of years, the main source of which was the melting of Greenland and Antarctic glaciers (Church et al. 2013a). Sea level has been on a rising period for nearly a hundred years. Historical tide station data show that the sea level rising rate from 1900 to 2009 is 1.7 ± 0.2 mm/yr, and the rate since 1961 is 1.9 ± 0.4 mm/yr (Church and White 2011). Since 1993, satellite altimetry has covered almost all of the world’s oceans, and its observations show that sea level rise has been 3.2 ± 0.4 mm/yr over the past 20 years. This rapid rate has also

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1 Introduction

been reached between 1920 and 1950. A recent study based on probabilistic methods shows that these values are overestimated to some extent, but the acceleration of sea level rise is underestimated: The rate of sea level rise is 1.2 ± 0.2 mm/yr from 1900 to 1990, and 3.0 ± 0.7 mm/yr from 1993 to 2010 (Hay et al. 2015). Despite this, it is widely believed that since the beginning of the twenty-first century, the rate of sea level rise has slowed, which is consistent with the slowdown of global warming during this period (Cazenave et al. 2014; England et al. 2014). The variation in GMSL is dominated by two factors: the steric change and mass contribution. The first concerns density change caused by thermal expansion and salinity change [the former is much stronger (Gregory and Lowe 2000)], which can be measured by the Argo project; the second includes water contribution from land water and land ice, covering polar ice sheets and glaciers and ice caps (GICs), which can be measured by Gravity Recovery and Climate Experiment (GRACE). Assuming that water interchange between land and oceans is subject to conservation of mass, the mass increase in oceans equals mass loss on land and vice versa. Theoretically, the GMSL change calculated from Argo and GRACE should approximate the altimetry observations, excluding the defect of Argo in the space coverage. Other factors that potentially influence sea level change, including earthquakes (Broerse et al. 2011), long-term tectonic processes [≤0.1 mm/yr (Moucha et al. 2008)] and deposit sediment [0.01 mm/yr (Syvitski and Kettner 2011)], are ignored. The relevant discussion is available in IPCC reports (Church et al. 2013a). After the sea level budget is reconciled, the causes of sea level change can be explained. Many researchers devoted to this goal, while early studies showed that altimetry had a much faster trend than the sum of mass and density rates (Table 1.1). Notably, an overestimated GIA rate due to improper treatment of the earth rotation [−1.8 mm/yr Peltier (2009)] can improve the agreement, and some studies mistakenly reconciled the sea level budget based on this incorrect GIA correction (Leuliette and Miller 2009; Cazenave et al. 2009; Peltier 2009). The relevant discussion can be found in other literature [e.g., (Tamisiea 2011; Chen et al. 2013)]. The results of the altimetry have high precision, so the difference mainly comes from the interception of the time period. The main difference in the calculation results is derived from the contribution of temperature–salinity and mass. The main difference in temperature–salinity is caused by the development of Argo buoys. Argo buoys have a dense global coverage since 2005. In earlier work than Leuliette and Willis (2011), the temperature data were in the waters above the depth of 900 m. Llovel et al. (2014) analyzed the contribution of temperature and salinity in deep seas from 2005 to 2013 and found that the contributions of 0–700, 700–2000 and below 2000 m were 0.53 ± 0.13, 0.38 ± 0.05 and −0.13 ± 0.72 mm/yr, respectively. Due to the lack of observation data, the result below 2000 m was based on other data comparisons, so the uncertainty was very large. Purkey and Johnson (2010) inferred that the contribution below 2000 m is 0.113 ± 0.100 mm/yr based on heat content. Therefore, the temperature–salinity data in different depth ranges have a great impact, which also leads to the generally small temperature–salinity results of early work. The negative result of Willis et al. (2008) was also due to the bias of early Argo data. The contribution of seawater quality can only be estimated by GRACE satellite

1.2 Background of Previous Research and Problems

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Table 1.1 The development of sea level budget. All errors are in a 95% confidence interval GIA model

Time span

Density change

Mass change

Sum of density and mass changes

Altimetry observation

Willis et al. (2008)

Paulson07

2003.5–2007.5

−0.5 ± 0.5

0.8 ± 0.8

0.3 ± 0.6

3.6 ± 0.8

Leuliette and Miller (2009)

Paulson07

2004.1–2007.12

0.8 ± 0.8

0.8 ± 0.5

1.5 ± 1.1

2.4 ± 1.1

Cazenave et al. (2009)

Paulson07

2003.1–2007.12

0.37 ± 0.1

0.9 ± 0.1

1.3 ± 0.1

2.5 ± 0.4

Cazenave and Llovel (2010)

Paulson07

2003.1–2007.12

0.25 ± 0.8

1.1 ± 0.1

1.4 ± 0.8

2.5 ± 0.4

Leuliette and Willis (2011)

Paulson07

2005.1–2010.9

0.5 ± 0.5

1.1 ± 0.6

1.6 ± 0.6

2.2 ± 0.8

Hanna et al. (2013)

Six models

1993–2011

1.10 ± 0.43

2.01

3.11 ± 0.56

3.22 ± 0.41

Chen et al. (2013)

Geruo13

2005.1–2011.12

0.6 ± 0.3

1.8 ± 0.5

2.4 ± 0.5

2.4 ± 0.4

Llovel et al. (2014)

Geruo13

2005.1–2013.12

0.90 ± 0.3

2.0 ± 0.2

2.9 ± 0.76

2.78 ± 0.64

Yi et al. (2015)

Geruo13

2005.1–2014.7

0.97 ± 0.36

2.03 ± 0.50

3.00 ± 0.62

3.13 ± 0.88

gravity data. Due to the low resolution (~300 km) of GRACE, there is a mixture of ocean and land signals near the coastline. It is generally considered that the land signal is relatively stronger, so mainly the land signal is leaked into the ocean. In order to solve this signal leakage problem, the general practice is to throw away all the oceanic signals within 300 km (or more) offshore. Chen et al. (2013) believed that this approach will lead to an underestimation of ocean water mass and therefore proposed a forward modeling approach. Their results had a larger contribution of ocean water mass than their predecessors, so they can finally fully explain the sea level change by altimetry. However, the degree-one terms were not included in their observations, and the degree-one terms in the inversion were also thrown away by mistake. Our research shows that the contribution of the degree-one terms cannot be ignored. Besides, only trends within a time span were given without time series changes, and there was no separation of the contribution of terrestrial water and terrestrial ice.

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1 Introduction

1.2.2 Terrestrial Water Storage Change The scope of the global water cycle includes oceans, land and atmosphere. This global cycle dominates many natural phenomena on various scales on the earth and is closely related to human production and life. El Niño, La Niña (an anti-El Niño phenomenon), drought, floods and other relevant phenomena have a very important impact on human economic life, accompanied by a very significant change in water redistribution. In addition to well observations and satellite gravity measurements, land surface models can also provide estimates of groundwater changes. Scientists often use time-varying surface atmospheric observations as boundary conditions, substituting water balance and energy balance equations to solve temporal global water storage changes. Atmospheric data include atmospheric conditions (temperature, humidity, wind) and water in the atmosphere, energy fluctuations (precipitation, radiation). One well-known hydrological model is GLDAS (Global Land Data Assimilating System) (Rodell et al. 2004), which is often used as a comparison model for GRACE inversion results. Land surface models can provide estimates of global groundwater fluxes, but their results can vary considerably based on the different approaches adopted (Wada et al. 2010; Church and White 2011; Konikow 2011). For example, in the entire Asia region, our estimated value of −100 ± 47 Gt/yr for 2003–2014 based on GRACE data is similar to the modeled values of −111 ± 30 Gt/yr for 2001–2008 (Konikow 2011), but is only 2/3 of the modeled value of −150 ± 25 Gt/yr for 2000 (Wada et al. 2012a). The anthropogenic and climate-driven contributions isolated by direct observations in this work could provide constraints for future land surface models, which poorly estimate long-term trends. Land surface models have limitations; for example, Church and White (2011) noted that withdrawal and recharge processes are inadequately accounted for in the study of Wada et al. (2010), and Taylor et al. (2013a) stated that focused recharge caused by a water surplus has not been incorporated into the current models. Groundwater can be recharged by strong precipitation via leakage. This type of process has been proven to play a role in maintaining the groundwater resources in East Africa over the last 55 years (Taylor et al. 2013b). Global sea level changes are also affected by changes in terrestrial water storage caused by human activities. The changes in water storage caused by human activities are mainly due to water surplus caused by dam storage (Chao et al. 2008) and water loss caused by groundwater exploitation (Wada et al. 2010), bringing the sea level to drop and rise, respectively. The constraints of land surface models mainly come from climatic conditions (Wada et al. 2010; Gleeson et al. 2012) or extrapolation of water loss from well-studied areas (Konikow 2011). It is estimated that between 1970 and 1990, the construction of dams has caused a sea level drop of −0.15 ± 0.09 mm/yr (Wada et al. 2012b). However, the rise of groundwater exploitation and the gradual reduction of dam construction caused the contribution of land water to sea level to be reversed to 0.38 ± 0.12 mm/yr between 1993 and 2010 (IPCC 2014), which will be further expanded in 2050. To +0.87 ± 0.14 mm/yr (Wada et al. 2012b). Despite these model-based rates, the latest satellite gravity observations show that land water

1.2 Background of Previous Research and Problems

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has contributed little to the long-term sea level changes between 2003 and 2014. It can be found that there is still a large difference between the model prediction and the actual observation results in the long-term change of land water.

1.2.3 Glacier Mass Balance Global sea level rise has a huge impact on human life and the environment. This realistic and serious scientific problem may be caused by many factors, one of which is the melting of glaciers. Modern geodesy makes it possible to make an accurate global or local sea level change and measurement of glacier mass changes (Table 1.2). The average rate of sea level rise from 1993 to 2010 was 3.18 mm/yr, to which an important contributor was the melting of glaciers (Cazenave and Remy 2011; Church et al. 2013b). Glacier mass balance can be estimated by different observation methods, which are mainly divided into three categories: 1. Model estimation. The existing models use two principles: surface mass balance (SMB) and changes in the amount of outflows of the glacier. The existing models are generally based on one of these two methods, and a small amount combines both methods. The surface material balance method is to evaluate the glacier state by calculating the mass difference between the mass loss and the mass increase brought by snowfall. The net mass increase can be obtained by ice core measurement. Under the premise of known thickness of the ice sheet, the amount of outflow can be estimated by the ice movement speed observed by photogrammetry, GPS and InSAR. This method is suitable for regional ice matter balance estimation, but its error is very large for the overall estimate. The existing research results show that surface mass balance is the main way to change the mass of Greenland ice sheets (Enderlin et al. 2014). 2. Volume change. After correction of the surface displacement caused by isostasy and tectonic movement, the volume change of the ice sheet can be then estimated. Since 1978, radar altimetry satellites (Seasat, Geosta, ERS-1, ERS-2) have been used to measure the rate of elevation change in Greenland and the Antarctic continent. The radar altimeter satellites have large footprints, which give reliable measurement only when the surface slope is small. Therefore, the scope of application is limited to the Greenland and Antarctic inland areas. Aviation altimeters have been widely used in Greenland measurements since the 1990s. With the launch of NASA’s ICESat and Europe’s Cryosat, the measurement accuracy has been greatly improved, especially in the outer edge area, where the ice melts the fastest. But it is necessary to assume the density of ice and snow to get a mass change. 3. Gravity change. The GRACE gravity satellite provides monthly observations since 2002, with a spatial resolution of greater than 300 km, so satellite gravity is only suitable for large-scale estimation. The observed gravity signal is a comprehensive signal, which needs to be deducted from GIA and other interferences.

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1 Introduction

Table 1.2 Current states of global glaciers [Steffen et al. 2010] GICs

Greenland

Antarctic

Area(106 km2 )

0.57–0.79

1.7

12.3

Volume(106 km3 )a

0.25

2.9

24.7

Total potential contribution of sea level (m)

0.6

7.3

56.6

Annual change (Gt/yr)b

720

500

1850

Annual change in sea level equivalent(mm/yr)

2

1.4

5.1

Contribution to sea level in 2006 (mm/yr) Meier et al. (2007)

1.1 ± 0.24

0.5 ± 0.1

West: 0.32 ± 0.04 East: −0.15 ± 0.07

Current states

It has been thinning since at least 1960, and the rate has been at least doubled since 1990. After 2000, the loss is about 300 Gt/yr

After about 1990, the area above 2000 m above sea level is thickened, showing an accelerating trend; the low-altitude area is thinning, which is also accelerating, and the total mass is also accelerated losing. After 2005, the loss rate is >200 Gt/yr

After the early 1990s, the central southern parts of the Antarctic continent slowly thickened; the Antarctic Peninsula and the Amundsen Sea region were locally accelerated thinning. The mass was likely balanced by 2000, and loses at the rate of >100 Gt/yr after 2005

a1

km3 of ice has the mass of 0.92 Gt ice shelf Note All melt contribution to sea level includes corrections for low-altitude areas filled with seawater

b Excluding

Because the Antarctic lacks data on current uplift rates and geomorphologically determined ice load history (Chen et al. 2009), the uncertainty of the GIA model is large and is the main source of error in its ice mass estimation (Velicogna and Wahr 2006b; Peltier 2009). The satellite altimetry data provide a low-degree gravitational field from 1990, and the results show that Greenland glacier has almost no mass loss from 1990 to 2002 (Matsuo et al. 2013). There are two other observation methods for the length of glaciers: 1. Field observations. This method is inefficient and difficult, and the number of observations is limited to large glaciers. There is nothing to do with loosely distributed debris that may account for more than 30% of the total. 2. Remote sensing satellites. Glacier length, area and digital elevation (DEM) changes can be estimated by comparing remote sensing images taken by remote

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sensing satellites from different periods. Remote sensing satellites are not continuous observations with limited number of shots, but have a good spatial resolution. Before discussing the results of the glacier mass change study, we will introduce some terminologies: • Glacier: There are two meanings: One is the glaciers of all sizes on the surface of the earth in general, so the small glaciers in the polar regions are called peripheral glacier, and the glaciers in the high mountains of the nonpolar region are called mountain glacier. The second type refers to the glaciers of small areas, the ones with medium areas are called the ice caps, and the largest ones are the ice sheets distributed in the Antarctic continent and Greenland. • Ice cap: Located on an island or mountain and is dome-shaped. • Ice sheet: A large area of ice covered in the Antarctic continent and Greenland. • GICs (Glaciers and ice caps): Glaciers distributed near the large ice sheet (also known as peripheral glacier) or high mountains in low latitudes. The individual areas are much smaller than the ice sheet. • Peripheral glaciers: Glaciers on the Antarctica continent and Greenland that are not connected to the ice sheets. Their variability may not be consistent with the ice sheet, so they are generally studied separately. For example, Bolch et al. (2013) used the ICESat laser altimeter satellite from 2003 to 2008 to study the peripheral glaciers around Greenland and found that their melting rate is 40.9 ± 16.5 Gt/yr, which accounts for 14–20% of the melting of the whole Greenland glaciers. However, in satellite gravity, because their spatial locations are very close, they are often not studied separately (Jacob et al. 2012). The GRACE satellite gravity field data greatly enhance geoscience research capabilities, especially for glacial change observations in uninhabited areas such as Antarctica and Greenland (Ramillien et al. 2006; Chen et al. 2009; Velicogna 2009; Rignot et al. 2011). Some representative work is listed in Tables 1.3 and 1.4. Recently, scholars have turned their attention to the glacier changes in the high mountains of Asia. A variety of approaches have been adopted, including GRACE satellite gravity, ICESat laser altimetry, satellite remote sensing images and ground-based field observations (Matsuo and Heki 2010; Jacob et al. 2012; Gardner et al. 2013; Gardelle et al. 2012; Yao et al. 2012). After deducting the post-ice rebound model, the small glacial model and the contribution of soil moisture, it is believed that all the remaining signals in the GRACE observations are generated by glaciers. In this study, we found that this assumption may be reasonable in the polar regions, but it should be more cautious in the high mountains of Asia because the glaciers here are not continuously distributed and the tectonic activity here is strong. Recent estimates of glacier mass balance in the high mountain areas of Asia are listed in Table 1.5. Matsuo and Heki (2010) used GRACE data to estimate snow and ice changes in high mountains of Asia. They believe that the melting rate of glaciers is −47 Gt/yr without considering GIA. However, because they underestimated the contribution of groundwater in northern India, their results of glacier melting were overestimated.

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Table 1.3 Advances in Antarctica ice sheet mass balance Authors

Time period

GIA model

Result

Chen et al. (2009)

2002.4–2009.1

IJ05

Total: 190 ± 77 Gt/yr; west: 132 ± 26 Gt/yr; east: −57 ± 52 Gt/yr

Velicogna and Wahr (2006b)

2002.4–2005.8

ICE-5G and IJ05

Total: 152 ± 80 km3 /yr, west: 148 ± 21 km3 /yr; east: 0 ± 56 km3 /yr

Ramillien et al. (2006)

2002.7–2005.3

IJ05

West: −107 ± 23 km3 /yr; east: + 67 ± 28 km3 /yr

Velicogna (2009)

2002.4–2009.2

ICE-5G and IJ05

2002–2006: −104 Gt/yr 2006–2009: −246 Gt/yr Acceleration: −26 ± 14 Gt/yr2

Shepherd et al. (2012)

2000–2011

ICE-5G, W12a, IJ05_R2

−87 ± 43 Gt/yr

Jacob et al. (2012)

2003–2010

ICE-5G

−165 ± 72 Gt/yr

Table 1.4 Advances in Greenland ice sheet mass balance Authors

Time period

GIA model

Result

Velicogna and Wahr (2006a)

2002.4–2006.4

ICE-5G

−248 ± 36 km3 /yr

Ramillien et al. (2006)

2002.7–2005.3

ICE-4G

−129 ± 15 km3 /yr

Velicogna (2009)

2002.4–2009.2

ICE-5G

2002–2003: −137 Gt/yr 2007–2009: −286 Gt/yr Acceleration: −30 ± 11 Gt/yr2

Chen et al. (2006)

2002.4–2005.11

ICE-5G

−239 ± 23 km3 /yr

Luthcke et al. (2006)

2003.7–2005.7

ICE-5G

−101 ± 16 Gt/yr; above 2000 m: 54 Gt/yr; below 2000 m: −155 Gt/yr

Wouters et al. (2008)

2003.2–2008.1

ICE-5G

−179 ± 25 Gt/yr

Shepherd et al. (2012)

2000–2011

Simpson, ICE-5G, ANU

−211 ± 37 Gt/yr

Jacob et al. (2012)

2003–2010

ICE-5G

−222 ± 9 Gt/yr

Jacob et al. (2012) gave a new trend of −4 ± 20 Gt/yr. This result underestimated the rate of glacier melting because they believed that the positive signals inside the Tibetan Plateau come from glacial growth, which is unrealistic. These two results vary from −4 to −47 Gt/yr (Table 1.5), which means that there are still significant uncertainties in glacial changes in the high mountains of Asia. Regional glacier research is also controversial. Here are two examples in the Pamir and Karakorum Mountains (referred to as the P–K Glaciers) and the Tianshan Glacier. The P–K Glaciers present very complex fluctuations. Because the glaciers here are very large and inaccessible, there has been no site measurement yet (Cogley 2012). Different studies give different results, including both positive and negative trends. Globally, the glaciers as a whole show a negative trend. The results observed by GRACE since 2002 in this region show a negative trend, such as those of Jacob et al. (2012), Gardner et al. (2013). However, some scholars believe that the P–K Glaciers are inconsistent with the globally negative trend. On the contrary, they show

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Table 1.5 Advances in glacier and snow mass balance in high mountains of Asia Authors

Time period

Data

Remark

Matsuo and Heki (2010)

2003–2009

Result −47 ± 12

GRACE

Groundwater in India was pre-assigned a trend of −10 Gt/yr

Jacob et al. (2012)

2003–2010

−4 ± 20

GRACE

Positive signals in the inner Tibet were interpreted as glacier advance. Regularization is needed for dense mascons divided in the study

Kääb et al. (2012)

2003–2008

−12.8 ± 3.5

ICESat

Including only Pamir–Hindu Kush-Himalayan region

Gardner et al. (2013)

2003–2009

−26 ± 12

GRACE + ICESat

Joint inversion

Neckel et al. (2014)

2003–2009

−15.6 ± 10.1

ICESat

Excluding the Tianshan and Pamir

Yi and Sun (2014)

2003–2012

−35.0 ± 5.8

GRACE

Three signal sources are separated and discussed

an increasing trend (Gardelle et al. 2012; Yao et al. 2012; Bolch et al. 2012). For example, Gardelle et al. (2012) used remote sensing to measure glacial change in the Karakorum Mountains. By comparing the height difference between December 2008 and February 2000, they found that the height change of this place is spatially heterogeneous. The overall mass of the area of 5600 km2 (about one quarter of the entire Karakorum Glaciers) showed a slight increase of +0.11 ± 0.22 m/yr. A recent work published in the journal Nature Geoscience (Farinotti et al. 2015) used satellite gravity, laser altimetry and glacier models to study the snow and ice states in the Tianshan Mountains. However, in their work, the time series of the glaciers in the Tianshan Mountains showed great interannual changes (Fig. 2a in their article), and glacier mass changes even showed an increasing trend in 2010 (Fig. 6 in their article). This creates an impression that the Tianshan glaciers have great interannual variations.

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1.2.4 Tectonics in the Tibet The Tibetan Plateau, developing from the collision of India with Eurasia since the early Cenozoic and still one of the most tectonically active regions in the world, has attracted enormous focus on its origin, growth and inner structure (e.g., Royden et al. 2008). One of the most popularly studied areas is the eastern margin of the plateau, which features motion of several distinct crustal blocks, and includes an extraordinary “north–south seismic belt” filled with many large and damaging earthquakes (Wang et al. 2003). The eastern Tibetan Plateau is mainly composed of two blocks: the Songpan and Chuandian blocks, both of which have a crustal thickness of about 60 km and intense internal deformation in the form of shortening or rotation. The South China block east of the plateau has a 40-km-thick crust and is rather rigid and stable with minimal late Cenozoic deformation (Zhang 2013). A great deal of work has been focused on this region, trying to reveal the structure, evolution and active tectonic background, especially after the devastating 2008 Mw 7.9 Wenchuan earthquake (Shen et al. 2009; Wang et al. 2011b). Studies in several disciplines have achieved progress in this topic: Geology provides the evidence for mountain building and the uplift history back to tens of millions of years ago (Wang et al. 2012a); geodesy shows that the present-day crustal movement in eastern Tibet shows a clockwise rotation around the eastern Himalayan syntaxis as a whole, strike-slip/shortening along faults, and an overall uplift (Wang et al. 2001; Zhang et al. 2004; Liang et al. 2013); seismology shows that the crust in eastern Tibet has low P-wave, S-wave and surface wave velocities, a low Q value and a high Poisson’s ratio (Wang et al. 2007, 2008b; Xu et al. 2007; Liu et al. 2014), all of which favor a partly melted middle/lower crust; magnetotellurics agrees there is a weak crust with a high electoral conductivity and further sheds light on its flow patterns (Bai et al. 2010); the static gravity field constrains the depth and structure of the Moho interface (Braitenberg et al. 2000; Shin et al. 2009, 2015; Fu et al. 2014), the important density discontinuity between the crust and the mantle. However, we do not yet understand the present-day rates of crustal thickening nor other subsurface processes that affect the dynamic uplift of the plateau. Abutting the stable Sichuan Basin to the east, the steep Longmenshan mountain range is formed along that edge, but the topography gradually decreases outward to the north and south. Geological and geodetic observations show that there is little young crustal shortening along most parts of the eastern margin of the plateau (Royden et al. 1997), which implies that the uplift within eastern Tibet is likely caused by interior material, rather than crustal shortening. Two popular models could explain this feature: the crustal flow model and the convective lithospheric detachment model. In the deep crustal flow model, the lower crust is weak and flowing eastward rapidly to contribute the thick crust of eastern Tibet (Royden et al. 1997, 2008; Clark and Royden 2000), which is favored by the extreme topographic relief coupled and contrasting structure of eastern Tibet and Sichuan Basin. More recent studies, including the latest results from seismic and magnetotelluric imaging (Wang et al. 2007; Royden et al. 2008; Bai et al. 2010; Zhang 2013; Liu et al. 2014], give support to the

1.2 Background of Previous Research and Problems

15

crustal flow model. In the convective lithospheric detachment model, the lithosphere in the early Miocene (~20 Myr ago) would have been much thicker than today. The model proposes that since that time, high-density lower lithosphere beneath Tibet has been removed by convective instability, which causes a mass decrease in the lithosphere so that the whole crust rises due to isostasy (Molnar et al. 1993; Fielding 1996; Marotta et al. 1998, 1999). The largest difference between these two models is whether the surface uplift is caused by a thickening of the crust or an overall uplift of the crust. Modern geodesy is particularly sensitive to the present-day geodynamic change of the plateau. By virtue of GPS and absolute gravimeter measurements over 10 years at three stations, Sun et al. (2009) first attempted to estimate the dynamic change of the Moho interface beneath southern Tibet. The depth change of the Moho interface is well constrained by gravity observations because the Moho has the largest density contrast within the lithosphere. However, precise measurements of gravity change are available only in three spots: Lhasa, Kunming and Dali. Whether their conclusions are applicable to the vast interior plateau areas needs further validation.

1.3 Focus of This Book 1.3.1 GRACE Inversion Methods Because the gravity is attenuated with the square of the distance, the spatial resolution of the gravity field observed in the satellite orbit is limited, and the spherical harmonic coefficients of the gravity field are truncated to a certain degree. GRACE’s surface spatial resolution is about 300 km, corresponding to spherical harmonic coefficients of 60°. In addition, due to the noise of the GRACE observations, we need to smooth the data. While the smoothing method suppresses the noise, some of the signals are also removed. When GRACE data are used to study the mass change of a particular signal source, the observed gravity signals are distorted, i.e., attenuation and leakage due to the truncation and smoothing. Signal attenuation means that the observed signal strength is weakened relative to the realistic signal; signal leakage means that the range of the observed signal is expanded relative to the realistic one. In fact, these two effects are related; that is, a sharp local signal will become a wider range of smooth signals under the action of truncation and smoothing. Due to these two effects, we cannot directly sum the signals in the study area, because the signal in the study area leaks out of the area, so the direct summation will usually be weaker than the true value; at the same time, signals outside the study area may leak into and pollute the estimate. The purpose of the inversion method is to restore the true strength of the signal while reducing leakage, i.e., separating signals inside and outside the study area. Several common inversion methods are introduced here, including scale factors, spectral domain inversion, spatial domain inversion, forward modeling and multi-basin inversion methods. The forward modeling method is an improved method

16

1 Introduction

on the original one, and the spatial domain method and multi-basin inversion are the newly proposed here. This book will compare the similarities and differences, and advantages and disadvantages of these methods in detail, and classify the types of problems applicable to different methods.

1.3.2 Sea Level Budget According to the models by the IPCC, in the worst case, the sea level may rise by 1 m in 2100. This prediction is based on the existing observations. Clear understanding of the reason and the law of current sea level change is important for the prediction of future sea level change. By studying the changes in sea level in recent decades, this book attempts to get an updated knowledge on this topic. Altimetry results show that during the observation period from 1993 to 2014, sea level increased rapidly between 1993 and 2002, but slowed from 2003 to 2010. The La Niña phenomenon that occurred between 2010 and 2011 was the strongest El Niño-Southern Oscillation event in 80 years, and the global mean sea level thus dropped rapidly by 5 mm. Then, the sea level quickly recovered to the normal growth level, and the growth rate was further increased from the slow growth period from 2003 to 2010. Because sea level changes are seriously affected by long-term interannual fluctuations, it is impossible to clearly obtain the trend of sea level changes in the short term simply by relying on altimetry data. However, an alternative approach is to scrutinize the mechanism of sea level change, i.e., to investigate the main contributors to sea level change–density and mass changes. This paper uses the latest GRACE and Argo data to study the mass change and density change of seawater, separately, and to isolate the contribution of terrestrial water and land ice. We found that changes in the land ice and seawater density are relatively stable, and the fluctuations in sea level mainly come from the terrestrial water. Changes in terrestrial ice and seawater density are major contributors to sea level increases, so their trend changes can reflect realistic changes in sea level.

1.3.3 Water Storage in Asia Water resources play a critical role in the security of human living environments and ecosystems (United Nations World Water Assessment Programme 2015). Groundwater resources and local glaciers, which account for approximately 99% of the global land water storage and may take hundreds of thousands of years to renew (AeschbachHertig and Gleeson 2012), have attracted widespread public concern (Gleeson et al. 2012; Jacob et al. 2012). It is well known that long-term water exploitation that exceeds the recharge rate will cause water depletion (mainly of groundwater). Many scholars have tried to estimate this human-induced effect [e.g., Wada et al. (2014)]. However, because precipitation change caused by climate variability can greatly impact the evaluation of the water balance over limited numbers of years, current

1.3 Focus of This Book

17

estimates of depletion rates are actually a mixture of anthropogenic and climatedriven effects and differ over different observation periods. The water storage in Asia, a region that contains 60% of the global population and that is responsible for 75% of the loss in global groundwater (Taylor et al. 2013b), is comprehensively analyzed here. Four river basins in Asia with reports of significant water resources deficits are specifically examined: the Tigris–Euphrates, Indus, Ganges and Haihe basins. All four basins have a long history of human disturbance and are famous for giving rise to the Mesopotamian, Indian and Chinese civilizations due to their exceptional environmental advantages, especially with regard to water resources. To date, these basins are still among the most densely populated areas and are heavily dependent on water resources to maintain sustainable economic and social development. Last, we made a review on the mass transports in the whole of China. China is located in a complex geographical environment with roughly three topographies, which gradually transform from plains in the east to plateaus in the west. The climate is also diverse, and water resources are unevenly distributed across this area. Copious geophysical phenomena pervade the country because of this diversity in landforms, climates and recent anthropogenic activities. Glaciers on and around the Tibetan Plateau (TP) have recently been reported to be melting rapidly because of global warming (Kang et al. 2010; Yao et al. 2012; Yi and Sun 2014). The water levels of hundreds of lakes inside the plateau were generally observed to be rising because of greater precipitation and lower evaporation (Ma et al. 2010; Zhang et al. 2013). The water level in the Three Gorges Reservoir has periodically increased since its construction in 2002 (Wang et al. 2011a; Xinhua Net 2015). The North China Plain (NCP) has experienced groundwater loss because of its stressful water demand (Changming et al. 2001; Kendy et al. 2003; Feng et al. 2013). The plentiful geophysical phenomena in this region have attracted substantial interest. Nonetheless, investigating these concerns with field studies is costly and impractical. By virtue of the Gravity Recovery and Climate Experiment (GRACE) gravity satellites, these surveys can be performed more easily because most of the events are strong enough to be detected from space. This system also permits a comprehensive examination of the entire region, which has yet to be conducted.

1.3.4 Mass Transports in High Mountains of Asia Global climate change has had a profound and lasting impact on the environment, which is in turn an indicator of global climate change. The melting of glaciers caused by global warming has inspired a large number of scholars to study the glaciers in the third pole, the high mountains of Asia (HMA). Within the area of HMA, there are about 120,000 km2 of glaciers, spanning several different countries. Most of the glaciers are located in or around the Tibetan Plateau (TP). Starting from forty-five million years ago, an intercontinental collision made the TBP a vast flat highland with an average altitude of about 4500 m. The TBP still has some of the most active tectonic

18

1 Introduction

movements in the world. As a result, the multitude of geological phenomena will complicate the separation of different gravity signals detectable by GRACE: glaciers, plate motion [the uplift or subsidence of the ground surface and the Mohoroviˇci´c Discontinuity (Moho)], permafrost, weather denudation, terrestrial water storage and controversial GIA on the TBP since the Last Glacial Maximum (LGM). To properly discuss these gravity signals, interdisciplinary research, including the field of meteorology, hydrology, geology and geodynamics, is essential. Some parts, such as glaciers and total water storage (TWS), are the leading factors of gravity signals and show strong seasonal variation; some (TWS, GIA, denudation) can be deducted by models or in situ observation, and some (glaciers, GIA, plate motion) still have a great deal of uncertainty and become the subjects of the current research. In addition to a comprehensive study of the mass balance of the entire glacier, we have selected three local areas for more detailed research: the Pamirs, the Tianshan Mountains and the eastern margin of the Tibetan Plateau. The glaciers of the Pamirs and Karakorum Mountains (referred to as the P–K Glaciers) present very complex fluctuations. Results of previous studies indicate that it is still controversial on whether the P–K Glaciers are increasing or decreasing. The advantage of GRACE different from other observation methods is that it gives overall continuous observations. Therefore, we use GRACE satellite gravity data to analyze the time variation of this region in more detail. Some unique features of the Tianshan Mountains make it worthwhile to study separately. First of all, the Tianshan Mountains are the farthest from the ocean in the Eurasia, so the humid ocean air is not easy to reach here. The local area relies more on the melting of snow and ice. Secondly, the Tianshan Mountains are mainly affected by the mid-latitude westerly winds, which are completely different from the Himalayan glaciers affected by the low-latitude Indian Ocean monsoon. The Tianshan Mountains have a diverse geophysical environment and are affected by the combined effects of climate change and human activities. Here locate glaciers, snow, lakes and emerging residential and agricultural bases. These factors are closely related to each other, so a comprehensive study will help to better understand the impact and evolution mechanisms here. This work is characterized by a systematic and comprehensive study of precipitation, snow, lakes, glaciers and human activities in the Tianshan area. The eastern margin of the Tibetan Plateau is basically unaffected by signals such as glaciers and lakes, but it shows a relatively obvious gravity increase and ground uplift. We use two models to constrain/interpret gravity and GPS observations. The two models are a middle–lower crust flow model and a mixing model of convective removal and middle–low crust flow. We believe that the tectonic signal of this place is relatively strong, and modern geodesy can be used to quantitatively constrain the internal dynamic processes, that is, the changing state of the Moho surface and the flowing velocity of the middle and lower crust relative to the upper crust. These dynamic changes are difficult to achieve by other means of observation.

1.4 Structure of This Book

19

1.4 Structure of This Book Chapter 2 of this book introduces all the data used, focusing on the GRACE satellite gravity data that are mainly used. Chapter 3 elaborates six commonly used GRACE inversion methods, including the new methods proposed in this paper, and finally compares their respective advantages and applicable conditions. Chapter 4 focuses on the global sea level, mass and density state changes measured by satellites, gravity satellites and ocean buoys in the last decade. Based on a reconciled sea level budget, the current trends and causes of sea level rise are analyzed. Chapter 5 investigates the changes of water storages in Asia, China and four watersheds with serious groundwater loss, and discusses the interference caused by the fluctuation of precipitation on the long trend of water storages and proposes a method to deduct this interference. Chapter 6 discusses the changes of glacier mass in the high mountainous areas of Asia, focusing on the glacial changing law in the Pamirs and Tianshan areas. Finally, the internal tectonic movement state of the eastern margin of the Tibetan Plateau is studied by using satellite gravity and GPS data, by which the movement of the Moho surface and the speed of the middle and lower crust are quantitatively determined.

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Chapter 2

Data

2.1 Global Satellite Gravity Dataset GRACE To determine how mass migrates on the earth surface, GRACE Release 05 datasets (and also Release 04 in some cases) are here used to compute ice melting and land water storage changes. The datasets come from three organizations: the Center for Space Research at the University of Texas, GeoForschungsZentrum, Potsdam and Jet Propulsion Laboratory (http://icgem.gfz-potsdam.de/ICGEM/). We process the GRACE data by replacing all the degree two coefficients with satellite laser ranging ones (Cheng et al. 2011) and adding back the degree one (geocenter) coefficients (Swenson et al. 2008).

2.1.1 Data Filtering Strong north–south stripe noises exist in GRACE datasets, and data filtering is essential in the GRACE data processing to improve the signal-to-noise ratio. These filtering strategies are implemented in the follow studies: • Gaussian filter with a smooth radius of 300–500 km (Wahr et al. 1998), hereinafter referred to as G300, G500 and so on. • Decorrelation filter (Swenson and Wahr 2006), such as P4M6. • DDKx filters (Kusche et al. 2009), x represents numbers starting from 1, the larger the number the weaker the smoothing.

© Springer Nature Singapore Pte Ltd. 2019 S. Yi, Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau, Springer Theses, https://doi.org/10.1007/978-981-13-7353-4_2

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2 Data

2.2 Land Surface Model GLDAS GLDAS is a set of surface water and energy fields that were measured by the Goddard Space Flight Center (GSFC) in the National Aeronautics and Space Administration (NASA) and the National Centers for Environmental Prediction (NCEP) in the National Oceanic and Atmospheric Administration (NOAA) (Rodell et al. 2004). This system features a global surface modeling system with constraints from both ground and satellites observations and with high resolutions both in space (from 1–0.25°) and time (from 1 month to 3 h). The system improves its reliability with the assimilation of various forcing fields, which include precipitation, radiation, temperature, wind, etc. Dozens of climatic outputs exist, ranging from the surface to several meters in depth; only those that concern water contents are adopted here. These products have proven to be quite effective in estimating the SWS thanks to many validation experiments (Zaitchik et al. 2010; Spennemann et al. 2015). In this study, monthly outputs that cover 2003–2014 from four land surface models (Noah, Mosaic, Community Land Model and Variable Infiltration Capacity) that are driven by GLDAS are averaged to reduce the model bias.

2.3 Altimetry 2.3.1 Sea Level The altimetry data are produced by five processing groups: 1. University of Colorado (CU; http://sealevel.colorado.edu/); 2. Archiving, Validation and Interpretation of Satellite Oceanographic Data (AVISO; http://www.aviso.altimetry.fr/en/data/products/ocean-indicatorsproducts/mean-sea-level.html); 3. Commonwealth Scientific and Industrial Research Organization (CSIRO; http:// www.cmar.csiro.au/sealevel/sl_hist_last_decades.html); 4. National Aeronautics and Space Administration (NASA; http://podaac-ftp.jpl. nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_GMSL_ASCII_V2); 5. National Oceanographic and Atmospheric Administration (NOAA; http://www. star.nesdis.noaa.gov/sod/lsa/SeaLevelRise/). These data are based on Topex/Poseidon, Jason-1/2 missions. Their time series are compared in Fig. 2.1, and their rates are given in Table 2.1.

2.3 Altimetry

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Fig. 2.1 Time series of altimetry from five groups from 1993 to 2014 (up) and the mean value and variation range (down). The upper and lower boundaries of the variance range are from the maximum and minimum values in the five groups. For all series, the periods have been removed. A one-year moving windows technique is also applied in the lower plot Table 2.1 Trends of sea level rise from different datasets (mm/yr). σmean is the standard deviation among these five products in the 95% confidence interval

2003–2009

2010–2013

2003–2013

CU

2.62

4.67

2.82

AVISO

2.93

4.61

3.11

CSRIO

2.8

4.83

3.15

NASA

2.55

4.86

2.79

NOAA

2.29

4.1

2.57

mean

2.64

4.61

2.89

σmean

0.48

0.60

0.47

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2 Data

2.3.2 Lake Level Processed lake level changes by altimetry can be downloaded from USDA (http:// www.pecad.fas.usda.gov/cropexplorer/global_reservoir/Default.aspx) and LEGOS (Crétaux et al. 2011).

2.4 Post-Glacial Rebound Model A 3-D Geruo13 PGR model (Geruo et al. 2013) is used to correct the PGR signal in GRACE. We find this model is closed to the traditional 1-D Paulson07 model (Paulson et al. 2007). The Paulson07 model for the land mass correction is 1.27 mm/yr. The Geruo13 model for the land mass correction is 1.39 mm/yr. Their difference is only 10%. Their difference in spatial distribution is demonstrated in Fig. 2.2. There are differences of 10% in Hudson Bay, Greenland, Scandinavia and Antarctica. The PGR models mainly influence the results in Antarctic (±72 Gt/yr) and Greenland (±21 Gt/yr), and this uncertainty is also included in the total estimation. The GIA uncertainty for Greenland and Antarctica is estimated as 21 and 72 Gt/yr, respectively (Velicogna and Wahr 2013). These observation uncertainties are included in the uncertainties of the secular trend.

2.5 Argo Data The temperature and salinity of the upper layer of the ocean measured by the Argo profiling floats are used to estimate the steric contribution. The Argo project started in 2000, but only after 2005 was the spatial coverage globally dense enough to guarantee a reasonable evaluation (Chen et al. 2013). The Argo data used here are from the International Pacific Research Center (IPRC), the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) and the Scripps Institution of Oceanography (SIO) (http://www.argo.ucsd.edu/Gridded_fields.html). Their mean value is adopted as our steric estimation. These data have a spatial resolution of 1° between about 65° S and 65° N and range from surface to about 2000 m in depth. The details about the Argo data processing and data error discussion can be found in Chen et al. (2013). The time series with and without periodic terms are shown in Fig. 2.3.

2.6 Precipitation Precipitation is a key factor that directly influences the SWS and both directly and indirectly influences the GWS. Thus, changes in TWS are highly correlated to fluctuations in precipitation. Here, the Global Precipitation Climatology Project

2.6 Precipitation

31

Fig. 2.2 Equal water height from different PGR models. The units are cm/yr. a Geruo13; b Paulson07; c Geruo13-Paulson07. Noted the color range in plot (c) is shorter

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2 Data

Fig. 2.3 Global steric sea level change derived from Argo measurements. The left and right column is the result with and without periodic terms, respectively. The first row shows the result from three products, and their average is given in the second row

(GPCP) model (Adler et al. 2003) is implemented to investigate this feature (available from http://www.esrl.noaa.gov/psd/data/gridded/tables/precipitation.html). The GPCP precipitation dataset incorporates observations from ground and satellite observations and has been issued monthly from 1979 to present, covering the entire planet with a resolution of 2.5° × 2.5°. In this study, we adopt the GPCP data in the same period and interpolate the grid values to a resolution of 1° × 1°.

2.7 ICESat Data The Global Land Surface Altimetry Data Version 34 (GLA14) of ICESat production from the U.S. National Snow and Ice Data Center (NSIDC) is used in this study. The product contains date, footprint geospatial location, ellipsoid elevation, geoid, saturation correction and others. The location of glaciers is based on the Global Land Ice Measurements from Space (GLIMS). Due to a large cross-track gap in the midlatitude region, a reference digital elevation model is needed to correct for topographic differences in the ICESat sampling footprints (Kääb et al. 2012). The changing rate of elevation of the glacier surface is calculated based on the elevation difference between the ICESat and the Shuttle Radar Topography Mission (SRTM).

2.7 ICESat Data

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SRTM is a near-global dataset containing the surface topography in 2000 (Farr et al. 2007). The density of glacier ice (850 ± 60 kg/m3 ) is used to convert volume change to mass change (Huss 2013).

2.8 MODIS Data The Moderate Resolution Imaging Spectroradiometer (MODIS) is an important detector loaded on the satellites Terra and Aqua. The multi-band data of MODIS can be used to study the land surface condition and various characteristics concerning cloud, seawater and atmosphere. The spatial resolution of MODIS data can be as fine as 250 m, and global coverage is obtained every one or two days. There are numerous MODIS-derived products, and in this study, we use the snow coverage product (with the identifier MOD10) (Hall et al. 2006). Although the temporal resolution can be as fine as 1 or 8 days, a resolution of 1 month (with the identifier MOD10CM) is chosen to reduce the influence of cloud shielding, which is very common in this area. The MOD10CM data are provided globally with a resolution of 0.05°. Here, MODIS data from January 2000 to December 2015 are used. The data are obtained from the National Snow and Ice Data Center (http://nsidc.org/data/ MOD10CM).

2.9 Global Glacier Distribution The glacier distribution information is based on World Glacier Inventory (WGI). WGI is mainly derived from aerial photographs, and the dataset can be viewed as a snapshot of the distribution of glaciers in the second half of the 20th (WGMS and NSIDC 1999). The dataset is available at http://nsidc.org/data/docs/noaa/g01130_ glacier_inventory/. Another glacier inventory dataset is GLIMS Glacier Database (http://nsidc.org/glims/). These two inventories are presented in Fig. 2.4.

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Fig. 2.4 Global glacier inventories (http://www.grid.unep.ch/glaciers/graphics.php)

2 Data

References

35

References Adler, R. F., et al. (2003). The version-2 global precipitation climatology project (GPCP) monthly precipitation analysis (1979–present). Journal of Hydrometeorology, 4(6), 1147–1167. https:// doi.org/10.1175/1525-7541(2003)004%3c1147:tvgpcp%3e2.0.co;2. Chen, Y., Yang, K., Qin, J., Zhao, L., Tang, W., & Han, M. (2013). Evaluation of AMSR-E retrievals and GLDAS simulations against observations of a soil moisture network on the central Tibetan Plateau. Journal of Geophysical Research: Atmospheres, 118(10), 4466–4475. https://doi.org/ 10.1002/jgrd.50301. Cheng, M., Ries, J. C., & Tapley, B. D. (2011). Variations of the Earth’s figure axis from satellite laser ranging and GRACE. Journal of Geophysical Research: Solid Earth (1978–2012), 116(B1). Crétaux, J.-F., Jelinski, W., Calmant, S., Kouraev, A., Vuglinski, V., Bergé-Nguyen, M., et al. (2011). SOLS: A lake database to monitor in the Near Real Time water level and storage variations from remote sensing data. Advances in Space Research, 47(9), 1497–1507. Farr, T. G., Rosen, P. A., Caro, E., Crippen, R., Duren, R., Hensley, S., et al. (2007). The shuttle radar topography mission. Reviews of geophysics, 45. Geruo, A., Wahr, J., & Zhong, S. (2013). Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: An application to Glacial Isostatic Adjustment in Antarctica and Canada. Geophysical Journal International, 192(2), 557–572. Hall, D., Salomonson, V., & Riggs, G. (2006). Modis/terra snow cover daily l3 global 500 m grid. Version 5. Boulder, CO, USA: National Snow and Ice Data Center. Huss, M. (2013). Density assumptions for converting geodetic glacier volume change to mass change. The Cryosphere, 7, 877–887. Kääb, A., Berthier, E., Nuth, C., Gardelle, J., & Arnaud, Y. (2012). Contrasting patterns of early twenty-first-century glacier mass change in the Himalayas. Nature, 488(7412), 495–498. Kusche, J., Schmidt, R., Petrovic, S., & Rietbroek, R. (2009). Decorrelated grace time-variable gravity solutions by gfz, and their validation using a hydrological model. Journal of Geodesy, 83, 903–913. Paulson, A., Zhong, S. J., & Wahr, J. (2007). Inference of mantle viscosity from GRACE and relative sea level data. Geophysical Journal International, 171, 497–508. Rodell, M., et al. (2004). The global land data assimilation system. Bulletin of the American Meteorological Society, 85(3), 381–. https://doi.org/10.1175/bams-85-3-381. Spennemann, P. C., Rivera, J. A., Saulo, A. C., & Penalba, O. C. (2015). A comparison of GLDAS soil moisture anomalies against standardized precipitation index and multisatellite estimations over South America. Journal of Hydrometeorology, 16(1), 158–171. Swenson, S., Chambers, D., & Wahr, J. (2008). Estimating geocenter variations from a combination of GRACE and ocean model output. Journal of Geophysical Research: Solid Earth (1978–2012), 113(B8). Swenson, S., & Wahr, J. (2006). Post-processing removal of correlated errors in GRACE data. Geophysical Research Letters, 33(8), https://doi.org/10.1029/2005gl025285. Velicogna, I., & Wahr, J. (2013). Time-variable gravity observations of ice sheet mass balance: Precision and limitations of the GRACE satellite data. Geophysical Research Letters, 40(12), 3055–3063. Wahr, J., Molenaar, M., & Bryan, F. (1998). Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. Journal of Geophysical ResearchSolid Earth, 103(B12), 30205–30229. https://doi.org/10.1029/98jb02844. WGMS and NSIDC. (1999). updated 2012. World Glacier Inventory. Compiled and made available by the World Glacier Monitoring Service, Zurich, Switzerland, and the National Snow and Ice Data Center, Boulder CO, USA. https://doi.org/10.7265/n5/nsidc-wgi-2012-02. Zaitchik, B. F., Rodell, M., & Olivera, F. (2010). Evaluation of the Global Land Data Assimilation System using global river discharge data and a source-to-sink routing scheme. Water Resources Research, 46(6).

Chapter 3

GRACE Mass Inversion Method

3.1 Math Prerequisites 3.1.1 Spherical Harmonics and Gridded Observations A set of spherical observations can be expanded into a sum of spherical harmonics (SHs) (Wahr et al. 1998): fi = f (θi , φi ) = =

 lm

l ∞   l=0 m=0

i Ylm Alm

=



Yki Ak = Yi,. · A

(3.1a)

k

  cos mφi ˜ = = Plm (cos θi ) sin mφi      1 cos mφ Clm = = d f (θ, φ)P˜ lm (cos θ) Slm sin mφ 4π Yki

Ak = Alm

  P˜ lm (cos θi ) Cˆ lm cos mφi + Sˆ lm sin mφi

i Ylm

(3.1b) (3.1c)

where f i is the observation in the grid (θi , φi ), the variable pair of (l, m) is combined as a single variable k, Yki is the associated Legendre function and Ak is a SH coefficient. All the observations in different grids compose a column vector: T  F = f1 , . . . fp = YA.

(3.2)

The equal water height (EWH) anomaly observation vector  equals f EWH = (σ1 , . . . , σi , . . .)T = YAEWH .

© Springer Nature Singapore Pte Ltd. 2019 S. Yi, Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau, Springer Theses, https://doi.org/10.1007/978-981-13-7353-4_3

(3.3a)

37

38

3 GRACE Mass Inversion Method

GR GR The coefficient array AEWH comprises the Clm and Slm from the GRACE solutions [Eq. 13 in Wahr et al. (1998)]:

EWH

A

=

WlEWH AGR

  GR Re ρe 2l + 1 Clm = GR 3ρw 1 + kl Slm

(3.3b)

WlEWH is a function of only degree l that transforms the physical dimension (here, in the form of EWH). Apart from EWH, this transformation matrix can also be geoid δg WlN and gravity disturbance Wl : WlN = Re δg

Wl =

GMe (l − 1) 4π Gρe Re = (l − 1) 2 Re 3

(3.3c) (3.3d)

where ρe , Re and Me are the average density, radius and mass, respectively, of the earth. ρw is the density of water (1 g/cm3 ), G is the universal gravitational constant, kl is the loading love number, the first 200 terms of which can be obtained from Wahr et al. (1998). For truncation at a degree of n, the size of vector A is (n + 1)2 .

3.1.2 Basin Mask Suppose we have N basins to be studied and a mask function h that outlines the area of the pth basin (p = 1, 2, . . . , N ):  p

hi = hp (θi , φi ) =

1 ith grid is inside the pth basin . 0 ith grid is outside the pth basin

(3.4a)

The ith grid has an area of si : si = sin θi d θi d φi

(3.4b)

This grid can also be expanded into SHs in the form of Eq. (3.2): p

hi = Yi,. · Abs p

(3.4c)

 p T p Hp = h1 , . . . , hi , . . . = YAbs p

(3.4d)

where Abs P is the SH of the pth basin as defined in Eq. (3.4a). Equations (3.4a) and (3.4d) are the same as Eqs. (3.15) and (3.18) in Swenson and Wahr (2002), but we attempt to extend them to a group of basins. Thus, the total mass in the pth basin is

3.1 Math Prerequisites

39

 Mp = =

hp (θ, φ)σ (θ, φ)d  

p

hi σi si

i

= HpT · diag(S) · 

T Y T · diag(S) · YAEWH = Abs p

(3.5)

where the ith element of the column vector S is si . The superscript T means the transposition of a matrix. The symbol diag means a diagonal matrix. Five items are present in the final expression; the middle three Y T · diag(S) · Y comprise a symmetric matrix. Let Z ij be its element in the position of (i, j): Zij =





 j

Yki Yk sk = R2e

k

Y i Y j d =

sphere

4π R2e i = j 0 i = j

(3.6)

where Re is the radius of the Earth. The last step is based on the orthogonality of the associated Legendre function (Chao and Gross 1987). Thus, the total mass anomaly in the pth basin is simplified as

T mp = 4π R2e Abs AEWH p

(3.7a)

The masses in all the basins are T  T  M = m1 , . . . , mp , . . . , mN = 4π R2e Abs AEWH

(3.7b)

Equation (3.7a) can be separated into two parts:

T mp = 4π R2e Abs AEWH p 2 = 4π R2e (n+1) AEWH Abs j p,j (n → ∞) j 2 (n+1)2 EWH bs 2 = 4π R2e (60+1) AEWH Abs Ap,j (n → ∞) j p,j + 4π Re j=1 j=3722 Aj

(3.8)

Because all the AEWH values in the second part are zero (the GRACE solution j is truncated at 60°), only the first part remains. This result implies that the final mass is limited by the variable with the lower resolution, while variable with the higher resolution is a non-issue. The omission of the second part is inevitable and creates truncation error, similar to how a smoothing factor creates a smoothed error). One plausible method to recover this information is to assume a uniform EWH in the basin (detailed information is missing, so the simplest uniform model is assumed). By comparing how much of the signal remains after expansion and truncation (possibly

40

3 GRACE Mass Inversion Method

with further smoothing), we can determine how much of the signal was lost and then add it back by scaled factors (Velicogna and Wahr 2006). This method only concerns the total amount regardless of the spatial distribution within the basin, which can increase the signal-to-noise ratio because finer spatial resolution comes with a higher noise level.

3.1.3 Uncertainties in a Study Region Assuming that the correlations between the GRACE coefficients are zero, the error in the basin δmp can be propagated from the GRACE error δjEWH :

δmp =

4π R2e

2 

EWH Abs p,j · δAj j

(3.9)

Note no truncation is applied here, so no truncation error is included. In a practical application, we suppose the truncation error can be largely removed by inversion methods described below.

3.1.4 Mascons The assumption of a uniform EWH is very rigorous, and the result may be biased if the assumption does not agree with reality. As a result, the basin area must not be too large and its signal pattern should be quite homogeneous. On the other hand, the subbasin range must not be too small. One reason is that a strong regularization factor is required when the sub-basin is too small; a point-mass method can be used in extreme cases (Baur and Sneeuw 2011). The point mass cannot elucidate extra details because the input data do not contain high-frequency signals; the result is spatially smoothed. Moreover, the estimation is more vulnerable to data noise, which is also common in small spatial ranges (corresponding to high-frequency signals). The second reason is that if the basin size is too small, the error cannot be estimated by propagating from the calibrated errors (in the form of Eq. 3.8), which are truncated at 60° and do not contain any information regarding exceedingly small basins. The previous scaled factor method is only suitable for single basins. Here, we derive a compromised method that is applicable to a group of basins. A large basin is divided into several sub-basins, each one of which is assumed to share a uniform water anomaly.

3.2 Necessity of the Inversion

41

3.2 Necessity of the Inversion A simulation is given here to show the impact of truncation and smoothing on signals. Suppose a water of 1 cm is uniformly distributed in the region of 8°E–12°E, 8°N–12°N, totally 5° × 5° (Fig. 3.1a). The gravity signal of this water layer is expanded into SH and truncated at the degree of 60 (Fig. 3.1b). The truncated signals with G300 and G500 are shown in Fig. 3.1c, d, respectively. The section profiles of these signals are given in Fig. 3.1f. It is shown that the signal has a weaker strength (named attenuation) but a wider spatial coverage (named leakage) after truncation and smoothing. If we intend to get the mass of the original model, we need an inversion method to recover the signal strength and reduce the leakage effect. In the second step, we try a mass model with non-uniform distribution (Fig. 3.2a), which shares the same total mass as the model in Fig. 3.1. Despite the contrary mass patterns in models, the truncated and smoothed signals are nearly identical, which means that the details of mass distribution are lost, and we cannot retrieve the original mass pattern from the observation. Therefore, we disregard the mass distribution, but focus on the total mass amount, and the uniform mass distribution—the simplest one, is adopted for inversion. One mascon in one specific region shares the same mass change and has only one unknown. The mascon can be any shape or size and is composed by a group of point masses, so the number of unknowns is much smaller than point masses in the same region.

Fig. 3.1 A uniform model (a) and its SH expansion in different degrees and filters (b–d). The section profiles are given in f

42

3 GRACE Mass Inversion Method

Fig. 3.2 The same as Fig. 3.1, except for a non-uniform model

3.3 Overview of Inversion Methods All methods assume that the mass changes take place on the earth surface due to the fact that gravity-based inversion has no discrimination in the vertical direction without other auxiliary information (Chao 2005). Therefore, all mass changes implicate surface mass changes. Six inversion methods are introduced here. Inversion methods can be separated into spectral and spatial domains in the view of fitting objects, or into mascons and point masses in the view of mass shapes. Their details are summarized in Table 3.1.

3.4 Scaling Factor Method The implementation of a smoothing technique will attenuate the signal strength and exaggerate the leakage effect, so a recovery method is required to restore the real signals. One method involves a scaling factor (Velicogna and Wahr 2006), which assumes a uniform mass change and checks how much of the signal has been attenuated after being smoothed. The uniform mass change is apparently not applicable when many local disparities exist. In fact, the scaling factor changes with the spatial pattern of the signal (Fig. 3.3). Therefore, instead of a simple uniform factor, an inhomogeneous scaling factor that takes advantage of signal distribution patterns from land surface models (LSM) is presented (Landerer and Swenson 2012). Generally, a wider range of positive/negative signals comes with a larger scaling factor because more signals are leaked out of the studied region, but a mixture of both negative

3.4 Scaling Factor Method

43

Table 3.1 Summary of inversion methods Methods

Spatial

Scaling factor

+

SEDI

Spectral

Mascons

Point source

+

+

Remark Only single basin, and assumption of uniform mass distribution

+

+

Globally applicable, no regularization factor, not applicable in locally dense mascons

+

+

Applicable in various problems. Regularization factors are essential when unknowns are too much

SADI

+

point-mass

+

+

Fitting at the orbit height with most information lost

Forward modeling

+

+

Applicable in sea level budget and locally dominant signals

Multi-basin

+

+

Data errors are considered in the fitting, but complicated basin division is a prerequisite

and positive signals complicates this situation. However, the result will be somehow biased if some key processes (e.g., deep groundwater change, anthropogenic activities) are not adequately simulated in the models because the scaling factor greatly depends on the signal pattern (i.e., the reliability of the LSMs). Thus, a recent study that considers human activities was conducted to derive a better set of scaling factors (Long et al. 2015). However, the scaling factor method is subject to pattern information in models and lacks further constraints on the GRACE observations, which may be quite divergent from the signals that are restored by this method (Long et al. 2015). For instance, LSMs generally perform poorly and lack mountain glacier components on the TP, so this uncertainty will greatly deteriorate the application of scaled GRACE observations in this region, which are instead relatively reliable. Here, we present a multi-basin method that can recover the real signal after the observations are smoothed. The multi-basin method sacrifices its resolution for subbasins (approximately 200,000 km2 ) but has the virtue of taking full advantage of

44

3 GRACE Mass Inversion Method

Fig. 3.3 Scaling factors in the Yangtze River Basin from different signal ranges. In each column, the modeled mass is the red areas in the top panel, with smoothed signals in the middle and bottom panels. G300 and G500 indicate Gaussian smoothing with a radius of 300 and 500 km, respectively. The spatial scope of the Yangtze River Basin is outlined in black curves

GRACE observations and being independent of additional LSMs. This sacrifice in resolution is acceptable when only the status in the entire basin is considered.

3.5 Spectral Domain Inversion (SEDI) Our spatial inverse method is based on the work by Jacob et al. (2012). In this session, we first introduce the mascon inverse method used by Jacob et al. (2012) in a concise form, which we have named the SEDI method. Then, we further develop the SEDI method into the relevant spatial domain inverse (SADI) computing scheme. In practical computation, it is important to properly build the mascons in the area of interest. Suppose there are N mascons, and we can determine the Stokes for each mascon j with unit mass based on Eq. (3.1c). We coefficient vector Amas j , and let the mass of each mascon be mj . Then, the Stokes coefficient define B.,j = Amas j vector generated by all mascons is Amas = Bm. We can also determine the vector AGR for 1 month of GRACE model data. The GRACE observed vector AGR and the

3.5 Spectral Domain Inversion (SEDI)

45

mascon-generated vector Amas should be the closest, i.e., the SEDI method from Jacob et al. (2012) can be concisely expressed as:  2 minAGR − Bm2

(3.10)

m = G † AGR

(3.11)

 −1 G † = BT B BT

(3.12)

The solution is:

3.6 Spatial Domain Inversion (SADI) Inversion in the spatial domain is more straightforward and widely used than the SEDI method. However, it was often limited to be solved by iterative fitting (Wouters et al. 2008; Matsuo and Heki 2010; Chen et al. 2013). In others words, the solution is adjusted in each step until it has a good fitting to the observation. Here, we put forward a SADI method based on least-square criterion. To convert this expression into spatial domain, we need first rewrite the linear summation of spherical harmonics into the matrix form (3.3a). We  based on Eq. can get observations from GRACE Stokes coefficients f GR = YSAGR and masconsimulated ones (f mas = YSAmas = YSBm). Then, the spatial domain inverse (SADI) gives the least discrepancy between these two equations: min||f GR − f mas ||22 = min||YSAGR − YSBm||22

(3.13a)

 −1 G † = (YSB)T YSB (YSB)T YS

(3.14)

where S is a diagonal matrix independent of observation and consists of the dimensional coefficient (EWH is taken here) and the smoothing factor: Sl,l = ωl WlEWH

(3.15)

Singularity is always a problem in reverse problems and regularization is usually applied. Since the points inside a mascon share the same mass, the mass distribution will be oversmoothed if the mascons are assigned with areas which are too large. On the other hand, if the mascons are tiny and dense, there will be a singularity problem, i.e., positive and negative mascons are cross-arranged, making a coarse mass distribution. To keep the mascons small and guarantee the solution stability, a regulation must be applied. In this paper, we introduce the Tikhonov regularization method. The zero-order Tikhonov regularization is simple and widely applicable. In case of the SADI method, we have:

46

3 GRACE Mass Inversion Method

min||YSAGR − YSBm||22 + α 2 ||Lm||22

(3.13b)

where α is the smoothing factor; L is a unit matrix for zero-order Tikhonov regularization.

3.6.1 Comparison Between SEDI and SADI Methods Comparing Eqs. (3.13a) and (3.10) indicates that the form of SADI looks similar to SEDI, but there really is a difference between them. Multiplying the matrices Y in Eq. (3.13a) makes the inversion process in the spatial domain, in which the global signals are resampled. Generally speaking, more observations will increase the complexity and instability of the inversion. The SEDI method has a fixed number of observations, i.e., (n + 1)2 − 1 = 3720 for n = 60; while SADI has unknowns flexible with the number of the mascons. In addition, the SADI method filters out the signals outside the region, while the SEDI method contains all signals over the whole sphere. In conclusion, the SADI method is suitable for local gravity inverse. For a global case, it is better to choose the SEDI method. Because global information is retained in the SEDI, the standard error of the fitting residual is always large in a local study, so it is difficult to use a regularization factor to distinguish the under-fitting and over-fitting.

3.7 Point-Mass Method Point-mass method was introduced by Baur and Sneeuw (2011). It is an inversion method in spatial domain with least-square criterion. The point-mass method is different from SADI only in two aspects. First, this method fits data at the 500 km orbit height, rather than on the earth surface. This is equivalent that an exponentially filter ωexp (n) = (Ra /(Ra + h))n is applied to each degree of the SH. Here, Ra is the earth radius, h is the orbit height and n is the degree. In the SADI, the data are fitted on the surface with a Gaussian filter ωGauss (n). These two filters are compared in Fig. 3.4, which shows that most of the information is lost in the exponential filter. Second, the SADI uses mascons as unknowns, rather than point masses, so the number of unknowns is largely reduced. Therefore, irregularity can be avoided when the number of mascons is not too much and the regularization is not necessary in this case. However, regularization is always essential in the point mass, due to the large amount of point masses.

3.8 Forward Modeling

47

Fig. 3.4 Smoothing factors of Gaussian method and exponential attenuation

3.8 Forward Modeling A global forward modeling method introduced by Chen et al. (2013) is adopted to alleviate the signal leakage problem in GRACE. In brief, in each step of the iterative fitting, the difference between the observation and the model is added back in the next step. As a result, the modeled mass change becomes closer and closer to the GRACE observations. This process is repeated for all monthly solutions from the three groups. We only take one modification that the degree one coefficients are included in the iteration. The results with and without degree one are compared and the former gave a slightly better sea level budget. The forward modeling method contains such steps: 1. The smoothed equivalent water height (EWH) observation f 0 in the study area is taken as a hypothesized mass m0 (in the unit of EWH) with a spatial resolution of 1° by 1°. 2. The mass m0 is then expanded into spherical harmonics, and the same smoothing techniques as those applied to the GRACE data are applied. In this way, the recovered signal f 1 is obtained. 3. The difference between the GRACE observation and the recovered signal (f 0 − f 1 ) is added to the mass m0 . 4. The third step iterates after a fixed number of steps or until the observed signal is mostly recovered. To speed up the convergence, an amplifier of 1.5 is often used in step three, i.e., m0 = m0 + 1.5 × (f 0 − f 1 ).

48

3 GRACE Mass Inversion Method

Fig. 3.5 Demonstrations of the forward modeling method. a GRACE observation in September 2003 smoothed by a 500-km Gaussian filter; b same as a but with a tighter color scale and signals on land are masked; c mass recovered by the forward modeling method, note that the ocean is filled by a uniformly inverse mass; d same as b, but after subtracting smoothed signals generated by the mass in c

The GRACE observation in September 2003 is chosen to illustrate how the forward modeling method can reduce the leakage of land signals into the ocean. The leakage effect is mainly in southeastern Asia because of the local intense precipitation. With a 500-km Gaussian filter, the land signals (Fig. 3.5a) seriously leak into the ocean (Fig. 3.5b). If we directly sum the TWAA on the land, the total mass in Asia is 1191.7 Gt. Using the forward modeling method to recover the water mass on the land (Fig. 3.2c) and after subtracting the signals caused by this recovered mass, we obtain a residual signal for the ocean, which is much weaker (Fig. 3.5d). It is shown that the leaked signals around the India peninsula, the Indo-China peninsula, the Korean peninsula and the Japan islands are largely reduced. The mass recovered in Asia is 1603.3 Gt, which is 35% larger than the direct method.

3.9 Multi-basin Inversion Method Smoothed mass anomalies in basins are modified from Eq. (3.7b):  ˜ = 4π R2e Abs T W AEWH M

(3.16)

3.9 Multi-basin Inversion Method

49

Let the pth basin be distributed with a uniform unit EWH and expand it into SHs. We can obtain a column vector Aunit p if its EWH value is set with a model value mp ; unit then the SHs change into Ap ·mp , and the combined SHs from all the basins become

Aunit

Amodel = Aunit M 0

 unit = Aunit , . . . , A , . . . 1 p

 T M 0 = m1 , . . . , mp , . . .

(3.17a) (3.17b) (3.17c)

The smoothed mass anomalies from model signals are  ˜ model = 4π R2e Abs T W Amodel M

(3.18)

We can fit the signals from the modeled basin mass anomalies very closely to those from GRACE. However, the error, which cannot be completely depressed by smoothing techniques, will also be inevitably fitted. Because we already had a priori error, assimilating this information would also be helpful. Thus, we introduce a weighted matrix P:   1 1 (3.19) ,..., P = diag δm ˜1 δm ˜N δm ˜ i is the smoothed basin mass error that is estimated from Eq. (3.9). Finally, we construct an objective function that is a combination of the basin mass error and model complexity:     T   (3.20) F(m, λ) = P · Abs W AEWH − Aunit m  + λm ˜ model in Eq. (3.18). For simplicity, the constant Here, m has the same meaning as M 2 4π Re is included in the matrix P. We attempt to minimize the object function: minF(m, λ)

(3.21)

Thus, m is solved by m=

 −1 T Aunit QAunit + λI Aunit QAEWH  T Q = W T Abs P T P Abs W

(3.22a) (3.22b)

The regularization factor λ can be determined based on the signal-to-noise ratio of the input solution.

50

3 GRACE Mass Inversion Method

Table 3.2 Data and methods used in Chaps. 4–6 Research content

Chapter

Date

Inversion method

Global sea level rise

4

GRACE, altimetry, Argo

Forward modeling

Water storage change in Asia

5.1

GRACE, Precipitation, GLDAS, Well measurements, Altimetry

Forward modeling

Water storage change in China

5.2

GRACE, precipitation, GLDAS, ICESat, altimetry on lakes

Multi-basin

Glacier mass balance in the Tibetan and Pamir Plateaus

6.2, 6.3 and 6.4

GRACE, ICESat, precipitation, GLDAS

SADI

Glacier mass balance in the Tianshan

6.5

GRACE, ICESat, MODIS, precipitation, altimetry on lakes

SADI

Tectonics in the eastern Tibet

6.6

GRACE, GLDAS, GPS

SADI

3.10 The Table for Data and Method Various data and methods are used in the following chapters. They are summarized in Table 3.2 for reference.

References Baur, O., & Sneeuw, N. (2011). Assessing Greenland ice mass loss by means of point-mass modeling: A viable methodology. Journal of Geodesy, 85(9), 607–615. Chao, B. F. (2005). On inversion for mass distribution from global (time-variable) gravity field. Journal of Geodynamics, 39, 223–230. https://doi.org/10.1016/j.jog.2004.11.001. Chao, B. F., & Gross, R. S. (1987). Changes in the Earth’s rotation and low-degree gravitational field induced by earthquakes. Geophysical Journal International, 91(3), 569–596. Chen, J., Wilson, C., & Tapley, B. (2013). Contribution of ice sheet and mountain glacier melt to recent sea level rise. Nature Geoscience, 6(7), 549–552. Jacob, T., Wahr, J., Pfeffer, W. T., & Swenson, S. (2012). Recent contributions of glaciers and ice caps to sea level rise. Nature, 482(7386), 514–518. https://doi.org/10.1038/nature10847. Landerer, F., & Swenson, S. (2012). Accuracy of scaled GRACE terrestrial water storage estimates. Water Resources Research, 48(4). Long, D., Yang, Y., Wada, Y., Hong, Y., Liang, W., Chen, Y., et al. (2015). Deriving scaling factors using a global hydrological model to restore GRACE total water storage changes for China’s Yangtze River Basin. Remote Sensing of Environment, 168, 177–193. Matsuo, K., & Heki, K. (2010). Time-variable ice loss in Asian high mountains from satellite gravimetry. Earth and Planetary Science Letters, 290(1–2), 30–36. https://doi.org/10.1016/j. epsl.2009.11.053.

References

51

Swenson, S., & Wahr, J. (2002). Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment (GRACE) measurements of time-variable gravity. Journal of Geophysical Research: Solid Earth (1978–2012), 107(B9), ETG 3-1–ETG 3-13. Velicogna, I., & Wahr, J. (2006). Acceleration of Greenland ice mass loss in spring 2004. Nature, 443(7109), 329–331. Wahr, J., Molenaar, M., & Bryan, F. (1998). Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. Journal of Geophysical ResearchSolid Earth, 103(B12), 30205–30229. https://doi.org/10.1029/98jb02844. Wouters, B., Chambers, D., & Schrama, E. J. O. (2008). GRACE observes small-scale mass loss in Greenland. Geophysical Research Letters, 35(20). https://doi.org/10.1029/2008gl034816.

Chapter 4

Global Sea Level Change

4.1 Introduction We compute the GMSL rate from altimetry data over five-year-long moving windows to show the interannual variance in the period 1993–2014 and depict the results in Fig. 4.1. The average trend from 1993 to 2014 is 3.2 ± 0.4 mm/yr. Rates faster/slower than the whole-period average are expressed in red/blue. Figure 4.1 shows that the GMSL rate was fast in 1996–2004 and slow in 2005–2010. Since then, the five-year trend appears to be accelerating again, indicating that the GMSL is rising faster since 2010. The 2010/11 La Niña, the strongest ENSO cold event in the past 8 decades, caused a drop of 5 mm in GMSL (Boening et al. 2012). The drop is a result of excesses of terrestrial water storage in Australia, Northern South America and Southeast Asia, within which Australia had a dominant contribution (Fasullo et al. 2013). Their studies showed that this event seemed to end and the GMSL rate recovered from the drop in late 2011. In this work, we extend the time period to mid-2014. It shows that the GMSL went further up rather than just recovering from the drop and the fluctuation brought by this La Niña episode lasted longer to late 2013. We adopt a line with annual–semiannual periods to fit the GMSL records in the recent ten years, and after removing the background rate (3.0 mm/yr, 2005–2014) and periods, we find the GMSL has experienced large fluctuation since 2010. The GMSL dropped 7.9 mm from start of 2010 to start of 2011 and rose 11.6 mm afterward to the end of 2012, and then dropped 4.4 mm in half a year. To understand the mechanism responsible for the GMSL rise, a reconciled sea level budget is achieved. The contributions from land water, land ice and steric change are discussed.

© Springer Nature Singapore Pte Ltd. 2019 S. Yi, Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau, Springer Theses, https://doi.org/10.1007/978-981-13-7353-4_4

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Fig. 4.1 Temporal evolution of the GMSL rate computed over five-year-long moving windows. The horizontal line represents the average rate 3.2 mm/yr from 1994 to 2014. The red and blue areas indicate the fast and slow rates w.r.t. the average rate, respectively. The GMSL rate was fast from 1996 to 2004, slow from 2005 to 2010 and then fast again

4.2 Data and Method Theoretically, the GMSL change calculated from Argo and GRACE should approximate the altimetry observations, excluding the defect of Argo in the space coverage. In this study, the GMSL rise rate is computed using the latest GRACE, altimetry and Argo data, to investigate the current status of GMSL change and discuss the mechanism for its fluctuation.

4.2.1 GRACE To determine how mass migrates on the earth surface, GRACE Release 05 datasets covering from January 2003 to July 2014 are here used to compute ice melting and land water storage changes. The datasets come from CSR, GFZ and JPL. Their mean values are taken as our final estimation. The low degree terms are specially treated. We process the GRACE data by applying a 500-km Gauss smoothing filter (Wahr et al. 1998) and reduce the leakage effect by a forward modeling method. The post-glacial rebound effect is corrected by a 3-D Geruo13 PGR model (Geruo et al. 2013).

4.2 Data and Method

55

Fig. 4.2 Land ice distribution. Each group of colored dots represents a set of glaciers or ice sheets

We adopted the forward modeling method to reduce the land-to-ocean leakage, so we can get a set of recovered land mass change. The land water and land ice are separated based on their spatial locations (Fig. 4.2). The glaciers in the inner Tibet plateau are not included because the glacier signal there is weaker than the lake water and others.

4.2.2 Altimetry The mean values of the five organizations (referred to the data chapter) from January 2003 to July 2014 are adopted. The trend error of the altimetry result in 20 years is 0.4 mm/yr (1-standard deviation) in all five groups. The discussion on this problem can be found in Church and White (2011). The error of trend in a dedicated time period is estimated from the variance of trends among the five groups. It turns out that a shorter time period results in a larger error range. In a period of five years, the uncertainty is about 0.5–0.8 mm/yr. In Fig. 4.3, the variance range is taken from the minimum and maximum values of observations from five groups in each epoch.

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Fig. 4.3 GMSL from altimetry (in black, variance range in gray shading), steric (in magenta) and mass contribution estimated from GRACE (green for terrestrial water storage contribution and blue for land ice contribution). The red line is the combined effect of GRACE and Argo. Trend of land ice from 2003 to 2009 is in blue dash line. Trend of land water from 2003 to 2014 is in green dash line. The error bar of each plot is shown. The annual and semiannual periods are removed, and a half-year sliding window smoothing is applied. Four arrows indicate the four specific times in Fig. 4.4. The time series of Southern Oscillation Index (SOI) is shown in the bottom figure. The red curve is a smoothed result from five-month-long moving windows

4.2 Data and Method

57

4.2.3 Argo The mean value from three different Argo products is adopted as our steric estimation. The uncertainty of data is based on the fitting residue of the periodicity and is estimated as 3.6 mm. The contribution from “ocean water” below the observation depth of Argo is 0.11 mm/yr (Purkey and Johnson 2010), which is included in our trend error.

4.3 Results With a reconciled GMSL budget, it is necessary to understand the mechanisms underlying the changes in GMSL. Some previous studies (Cazenave et al. 2009; Chen et al. 2013; Leuliette and Miller 2009; Leuliette and Willis 2011) investigated this budget, but only Chen et al.’s (2013) result agreed well, with the help of a more realistic GIA model and a global forward modeling method, which is also adopted in this paper. The time series of GMSL from altimetry, the steric change from Argo and mass change from GRACE are depicted in Fig. 4.3 and their trends listed in Table 4.1. The annual and semiannual periods are removed using the method described above, and a half-year sliding window smoothing is applied. The error bars have been reduced by sqrt(6) to account for the half-year smoothing. Variations in GMSL shown by Argo and GRACE are closely consistent with altimetry observations (the red and black curves in Fig. 4.3). The sea level budget is better established ever since 2008, while the result between 2005 and 2008 is not so good. Considering that during the studied period the altimeter and GRACE satellites were under stable condition, while the Argo project was in a development stage, we speculate this mismatch is due to the flaw in the Argo early observation.

Table 4.1 Trends of GMSL from altimetry, Argo and GRACE with GIA corrected (mm/yr) January 2005–December 2009

January 2010–July 2014

January 2005–July 2014

Altimetry

2.49 ± 0.85

4.49 ± 0.62

3.13 ± 0.44

Argo + GRACE

2.39 ± 0.56

4.33 ± 0.60

3.00 ± 0.31

Argo

0.98 ± 0.44

1.77 ± 0.23

0.97 ± 0.18

GRACE

1.41 ± 0.35

2.56 ± 0.55

2.03 ± 0.25

−0.27 ± 0.25

0.38 ± 0.48

0.07 ± 0.13

Land ice

1.69 ± 0.25

2.18 ± 0.28

1.96 ± 0.22

Greenland

0.57 ± 0.09

0.89 ± 0.09

0.77 ± 0.06

Antarctica

0.45 ± 0.23

0.71 ± 0.25

0.60 ± 0.21

GICs

0.67 ± 0.05

0.58 ± 0.08

0.58 ± 0.04

Land water

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Table 4.1 indicates that from January 2005 to July 2014, the steric change contributes 25–35%, land water contributes less than 7%, and land ice contributes 55–70%. The ocean mass contribution of Greenland, Antarctica and the glaciers and ice caps to GMSL rise is 23–27, 13–26 and 17–20%, respectively. The huge ice volume of Greenland (equals 7-m sea level) and West Antarctica [the instable part of the continent, equals 3–5 m (Cazenave and Cozannet 2014), has higher potential of contributing to the GMSL than to the GICs, whose share of contribution is declining now as a result. Table 4.1 and Fig. 4.3 show that the GMSL rising rate increases 80% from 2.5 to 4.5 mm/yr after 2010. The abnormal terrestrial water storage, accelerated melting in land ice and steric changes are all the contributors. The blue curve in Fig. 4.3 represents the contribution of global ice melting, and it shows an increase since 2010. To compare our results with previous studies, we also computed the trends during 2003–2009. The total contribution of Greenland and Antarctica ice in our study is 0.89 ± 0.25 mm/yr, and this agrees with 0.82 ± 0.16 mm/yr from Hanna et al. (2013); our total land ice estimation (1.47 ± 0.23 mm/yr) agrees well with 1.51 ± 0.16 mm/yr from Gardner et al. (2013). The contribution of ocean warming during 1993–2010 is 1.1 ± 0.3 mm/yr (IPCC 2014), which is almost constant in recent decades, except the speedup in the last few years. It, however, needs more observations to tell it a long-term interannual variance.

4.3.1 Land Ice The melting rate of land ice shows an increase since 2010. After extending the 2003–2009 trend, we find the land ice trend since 2010 shows an apparent deviation from it, as represented by the light blue shading in Fig. 4.3. To find the acceleration in melting of land ice, we extract the three components: Antarctica, Greenland and GICs. The results are shown in Fig. 4.4. In the last decade, the ice melt in Greenland is regarded to be accelerated (Velicogna 2009; Velicogna et al. 2014; Wouters et al. 2013). This work put a check on the acceleration of the mass change of Greenland. Because the giant mass lost in Greenland has largely stopped since 2013, here we only recheck its changing characteristic from 2003 to 2012. Traditionally, its mass change is fitted by a quadratic polynomial with annual and semiannual periods (hereinafter P2O2). However, with a closer inspection, we find the P2O2 does not fit well from 2009 to mid-2010, during which a sharp change in trend is discernible. Therefore, we tried a different fitting strategy, a two-piecewise linear fitting with a break in 2010 January and with annual and semiannual periods (hereinafter P2W2). For a better comparison with the linear trend after 2010, the trend from 2003 to 2009 is extrapolated. Compared with the residue of P2O2, the result of P2W2 has a 15% lower standard variance and shows a closer pattern to Gaussian distribution (red lines), the statistical behavior of a set of random data. Based on these two reasons, we conclude that P2W2 is a better choice. The change pattern of Greenland ice mass from 2003 to 2012 is closer to piecewise linear, i.e., the time series is relatively

4.3 Results

59

Fig. 4.4 a Time series of mass in Antarctic, GICs and Greenland. The variances among the three GRACE models are shown in gray lines. The time series of Greenland mass is fitted by two strategies: P2O2 (polynomial of order 2 with 2 periods) and P2W2 (2-piecewise line with 2 periods) in blue and red dash lines, respectively. Their fitting residues are shown in b and c; in each of them the red line represents the theoretical Gaussian distribution of the residuals. Mu and sigma are the expectation and standard deviation of the Gaussian distribution

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linear before 2010 and an increase of 100% afterward (1.1 ± 0.1 mm/yr in 2010–2012 compared to 0.54 ± 0.1 mm/yr in 2003–2009). This acceleration is due mainly to the loss of ice from the southwest coast of Greenland. Greenland did not show mass loss from 1990 to 2002 (Matsuo et al. 2013), but from 2010 to 2012 it was melting more than twice faster than Antarctica (1.1 ± 0.1 mm/yr compared to 0.4 ± 0.3 mm/yr). This tremendous mass losing rate has stopped abruptly since 2013. But the whole land ice is still losing mass quickly because this alleviation in Greenland is counteracted by a simultaneously accelerated ablation in the Antarctic ice. The mass balance status in Antarctica is less well determined because of the large fluctuation in only eleven years. However, the Antarctic ice was melting slower before 2006 (Chen et al. 2009) and an acceleration seems to have started recently.

4.3.2 Land Water Previous studies showed that interannual variance of GMSL is related to ENSO (Nerem et al. 2010; Cazenave et al. 2014) and land water storage (Llovel et al. 2011). Here, the relationship between ENSO and the land water storage is checked. The SOI data are taken from http://www.bom.gov.au/climate/current/soi2.shtml. The land water storage is positively correlated with SOI, i.e., a positive SOI (La Niña event) corresponds to a mass increase on land, so a drop in GMSL and vice versa. The large and long-sustaining La Niña event from mid-2010 to the start of 2012 together with abnormal Indian Ocean Dipole and Southern Annular Mode (Fasullo et al. 2013) caused the largest excess in land water storage ever since 2003, contribution to the GMSL a drop of 3.8 mm, compared with the linear trend in the whole range. This value is 5.1 mm when compared with January 2010, the same as in (Boening et al. 2012). However, straight after this mass accumulation and starting in mid-2012, the land water storage shows a giant mass loss, contributing to GMSL a rise of 3.0 mm. This mass loss lasted for more than one year and ended in the end of 2013. One noteworthy phenomenon is that this mass loss on land is unrelated to ENSO, which is too moderate during this period to cause such an extreme condition. The mass loss may be explained by a subsequent undulation that resulted from the tremendous mass loss around 2011 or other climatic factors, some of which were observed to have a key role in the drop of GMSL in 2010/11 (Fasullo et al. 2013). The water storage in land had little net mass change from 2003 to 2014. Even the strongest ENSO cold event in eighty years could only cause a temporary water surplus. IPCC (2014) gave the contribution of land water to GMSL at a longer term: The trend is −0.11 ± 0.5 mm/yr for 1901–1990, but 0.38 ± 0.12 mm/yr for 1993–2010. The current balance may be a result of counteraction of the progress of anthropogenic processes, like groundwater withdrawal and impoundment in reservoirs (Chao et al. 2008; Konikow 2011). This fluctuation in land water should be excluded when evaluating the secular GMSL trend. To show the change of land water storage in the SOI extreme episodes, the mass anomalies in four specified times are demonstrated in Fig. 4.5. Here, “anomaly”

4.3 Results

61

Fig. 4.5 Global mass anomalies in four specific epochs. They are also annotated with arrows in Fig. 4.3. The equal water depth on land is a recovered result from GRACE observations, while the ocean is assigned with a uniform mass layer to guarantee the mass conservation

means the deviation from the secular trend, after the annual and semiannual periods are removed. The four epochs are 2005AMJ (mean of the April, May and June and so on), 2010JFM, 2011MAM and 2012NDJ, which are marked out with arrows in Fig. 4.3. 2005AMJ, 2010JFM and 2012NDJ show a land water storage loss, contributing to a rise in GMSL. 2011MAM shows a land water storage increase. The anomalies concentrate mainly in equatorial areas (between 30° north and south) and North America, where relatively heavy precipitation occurs. As it has been mentioned above, the 2012NDJ is not related to ENSO, but is a result from anomalies in 2011MAM. The other three related to ENSO have a consistent mass status in the equatorial area, although local contrast can be found in South America and Africa. The abnormal GMSL rise in 2012 was caused by the water storage loss in Siberia, North America and South America. It is interesting that Australia, who played a dominant role in the fall of the ocean in the 2010/11 La Niña, is absent in the mass loss area in 2012NDJ, probably due to its unique surface hydrology (Fasullo et al. 2013).

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4.3.3 Discussions and Conclusions It is no surprise that the rate of GMSL rise accelerated after the ~5 mm drop in the 2010/11 La Niña event, as it did after the 1998 El Niño. Thus, the apparent accelerating in the following several years is matter of course. However, whether it is under-recovering or over-recovering is hard to discriminate based solely on altimetry data. With the help of GRACE data, we can extract individual components and learn their mechanisms. In conclusion, the increase in GMSL rate can be explained by three factors: From start of 2011 to end of 2012, the land water storage went from a minimum to a peak, contributing 6.8 mm in 2 years; the land ices, especially those in Greenland, have been melting 30% faster ever since 2010 (2.2 ± 0.3 mm/yr compared to 1.7 ± 0.3 mm/yr); and a speedup in rise from steric change also makes a contribution. Our work goes further ahead of Boening et al. (2012). Not only we have a longer study period, but also we give a more self-consistent sea level budget. The GRACE+Argo in their Fig. 4.2 failed to catch up with the rise of altimeter observations since mid-2011. We adopt a different method to process GRACE models to circumvent the signal leakage problem, and the Argo data we used have a better spatial resolution and cover larger depth (to about 2000 m). With longer observations, we find there is a large land water storage deficit irrelevant to ENSO that lasted from 2012 to 2013. Our results of sea level steric change, mass change and altimetry observation are very similar with the curves shown in Llovel et al. (2014), except that we smooth the data and also separate the components of land water and land ice. Their steric and mass contribution is 0.9 ± 0.15 and 2.0 ± 0.1 mm/yr between 2005 and 2013, very closed to ours 0.97 ± 0.18 and 2.0 ± 0.2 mm/yr during January 2005–July 2014. From Fig. 4.3, we can find that ever since 2011, the contributions from land ice and steric change have been in a fast and steady increase. Since 2011, the steric change, at a value of 2.2 ± 0.4 mm/yr, with the 2.2 ± 0.3 mm/yr from the land ice melt, has made the GMSL rise rate as high as 4.4 ± 0.5 mm/yr. More records are needed to tell whether this high rate will continue or not. The drop of GMSL in mid-2013, a transient result of the recharge of the land water, has blinded us to an upcoming faster GMSL rise rate, which has actually been on its way for more than 3 years.

References Boening, C., Willis, J. K., Landerer, F. W., Nerem, R. S., & Fasullo, J. (2012). The 2011 La Niña: So strong, the oceans fell. Geophysical Research Letters, 39(19). Cazenave, A., & Cozannet, G. L. (2014). Sea level rise and its coastal impacts. Earth’s Future, 2(2), 15–34. Cazenave, A., Dieng, H.-B., Meyssignac, B., von Schuckmann, K., Decharme, B., & Berthier, E. (2014). The rate of sea-level rise. Nature Climate Change, 4(5), 358–361.

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Cazenave, A., Dominh, K., Guinehut, S., Berthier, E., Llovel, W., Ramillien, G., et al. (2009). Sea level budget over 2003–2008: A reevaluation from GRACE space gravimetry, satellite altimetry and Argo. Global and Planetary Change, 65(1), 83–88. Chao, B. F., Wu, Y., & Li, Y. (2008). Impact of artificial reservoir water impoundment on global sea level. Science, 320(5873), 212–214. Chen, J., Wilson, C., Blankenship, D., & Tapley, B. (2009). Accelerated Antarctic ice loss from satellite gravity measurements. Nature Geoscience, 2(12), 859–862. Chen, J., Wilson, C., & Tapley, B. (2013). Contribution of ice sheet and mountain glacier melt to recent sea level rise. Nature Geoscience, 6(7), 549–552. Church, J. A., & White, N. J. (2011). Sea-level rise from the late 19th to the early 21st century. Surveys in Geophysics, 32(4–5), 585–602. Fasullo, J. T., Boening, C., Landerer, F. W., & Nerem, R. S. (2013). Australia’s unique influence on global sea level in 2010–2011. Geophysical Research Letters, 40(16), 4368–4373. Gardner, A. S., et al. (2013). A reconciled estimate of glacier contributions to sea level rise: 2003 to 2009. Science, 340(6134), 852–857. Geruo, A., Wahr, J., & Zhong, S. (2013). Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to Glacial Isostatic Adjustment in Antarctica and Canada. Geophysical Journal International, 192(2), 557–572. Hanna, E., Navarro, F. J., Pattyn, F., Domingues, C. M., Fettweis, X., Ivins, E. R., et al. (2013). Ice-sheet mass balance and climate change. Nature, 498(7452), 51–59. Intergovernmental Panel on Climate Change (IPCC). (2014). Climate change 2013: The physical science basis. Cambridge, UK, and New York: Cambridge University Press. Konikow, L. F. (2011). Contribution of global groundwater depletion since 1900 to sea-level rise. Geophysical Research Letters, 38(17). Leuliette, E. W., & Miller, L. (2009). Closing the sea level rise budget with altimetry, Argo, and GRACE. Geophysical Research Letters, 36(4). Leuliette, E. W., & Willis, J. K. (2011). Balancing the sea level budget. Oceanography, 24. Llovel, W., Becker, M., Cazenave, A., Jevrejeva, S., Alkama, R., Decharme, B., et al. (2011). Terrestrial waters and sea level variations on interannual time scale. Global and Planetary Change, 75(1), 76–82. Llovel, W., Willis, J. K., Landerer, F. W., & Fukumori, I. (2014). Deep-ocean contribution to sea level and energy budget not detectable over the past decade. Nature Climate Change, 4(11), 1031–1035. Matsuo, K., Chao, B. F., Otsubo, T., & Heki, K. (2013). Accelerated ice mass depletion revealed by low-degree gravity field from satellite laser ranging: Greenland, 1991–2011. Geophysical Research Letters, 40(17), 4662–4667. Nerem, R. S., Chambers, D. P., Choe, C., & Mitchum, G. T. (2010). Estimating mean sea level change from the TOPEX and Jason altimeter missions. Marine Geodesy, 33(S1), 435–446. Purkey, S. G., & Johnson, G. C. (2010). Warming of global abyssal and deep Southern Ocean waters between the 1990s and 2000s: Contributions to global heat and sea level rise budgets. Journal of Climate, 23(23), 6336–6351. Velicogna, I. (2009). Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE. Geophysical Research Letters, 36. https://doi.org/10.1029/2009gl040222. Velicogna, I., Sutterley, T., & Broeke, M. (2014). Regional acceleration in ice mass loss from Greenland and Antarctica using GRACE time-variable gravity data. Geophysical Research Letters. Wahr, J., Molenaar, M., & Bryan, F. (1998). Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. Journal of Geophysical ResearchSolid Earth, 103(B12), 30205–30229. https://doi.org/10.1029/98jb02844. Wouters, B., Bamber, J., van den Broeke, M., Lenaerts, J., & Sasgen, I. (2013). Limits in detecting acceleration of ice sheet mass loss due to climate variability. Nature Geoscience, 6(8), 613–616.

Chapter 5

Terrestrial Water Storage Changes in Asia

5.1 The Whole Asia Region 5.1.1 Introduction Heavily dependent on the water resources, the development of human society and the associated increasing food demand have caused widespread water crises around the world. This issue is especially serious in populated cities and food production bases, such as northern India (Rodell et al. 2009), the Tigris–Euphrates region (Voss et al. 2013) and the North China Plain (Feng et al. 2013) in Asia and California (Famiglietti et al. 2011) in North America. All these studies cite the Gravity Recovery and Climate Experiment (GRACE) satellite mission. GRACE has proved to be useful in detecting water storage changes from space (Tapley et al. 2004), especially for glacier storage and groundwater storage (GWS) (Rodell et al. 2009; Matsuo and Heki 2010; Jacob et al. 2012), which are very difficult to measure by traditional methods. The precipitation in Asia from 1979 to 2015 is investigated in Fig. 5.1. Water storage in Asia was lost rapidly during 2000–2009; however, the water storage was nearly balanced during 2010–2013, when the climate conditions were predominantly moist. Therefore, Asian water storage is susceptible to changes in climate. Moreover, climate-driven effects can greatly offset anthropogenic changes on a global scale. These phenomena indicate that the climate variability should be carefully corrected for to estimate the anthropogenic contribution.

5.1.2 Method and Data Herein, we only focus on the variation aspects of water storage. By subtracting the mean value for the whole period, we can obtain the anomalies. The terrestrial water storage anomaly (TWSA) includes the surface water storage anomaly (SWSA, © Springer Nature Singapore Pte Ltd. 2019 S. Yi, Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau, Springer Theses, https://doi.org/10.1007/978-981-13-7353-4_5

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Fig. 5.1 Precipitation during 1979–2015 and water storage during 2003–2014 in Asia. The study region is the gray area on the world map. The precipitation anomalies (gray bars) are deviations from the average over the whole period (616.7 mm for 1979–2015). The red curve in the upper plot is smoothed by a three-year window, and blue line denotes the average over the wet years of 2010–2013, during which the water storage components (bottom right) decrease rather slowly. Total water storage and its two components estimated by space gravimetry and land surface models are presented here

which mainly includes changes in lakes), soil moisture anomaly (SMA), groundwater storage anomaly (GWSA) and changes in glaciers (GLA). These components satisfy the equation: TWSA = SWSA + SMSA + GWSA

(5.1)

The TWSA can be estimated from a global gravity dataset derived from the GRACE satellites. The SMA is evaluated from a global land surface model, i.e., the Global Land Data Assimilation System (GLDAS) (Rodell et al. 2004). The change in lake levels can be monitored by altimetry satellites and is generally well quantified, especially for large lakes with abundant coverage of altimetry satellites. The glacier component is largely absent in most areas except in the high mountain areas of Asia and the Caucasus Mountains. Therefore, in most areas we can obtain the GWSA by subtracting the SWSA from the TWSA observations. There are over one thousand lakes on the Tibet Plateau, and their lake levels are mostly reported to have been rising rapidly over the last decade. Their contribution is 8.0 Gt/yr (Zhang et al. 2013; Yi et al. 2016), which is deducted from the final GWS estimation.

5.1 The Whole Asia Region

5.1.2.1

67

Mass Contribution from Lakes

The largest contribution comes from the Caspian Sea, the largest saltwater lake in the world with an area of 4.36 × 105 km2 . It rose by approximately 0.4 m during 2002–2005 but has been falling steadily ever since, and the amount of drop has recently reached 1 m. Most of this rise/drop in lake level is the result of mass increase/decrease, as shown in Fig. 5.2. The rate of mass change was 43 ± 13 Gt/yr from 2003 to 2005 and −35 ± 3 Gt/yr from 2006 to 2014. There are other two large lakes, the Aral Sea and Balkhash Lake. The Aral Sea shrank rather rapidly (−0.40 ± 0.02 m/yr) at the end of last century. The shrinkage then gradually slowed, and the lake level has been nearly stable (−0.06 ± 0.01 m/yr) since 2009, which is consistent with the slowdown in the Asian water depletion. Balkhash Lake was nearly balanced during our study period; thus, its contribution is not considered. The other large water bodies near our study area, including the Black Sea and the Red Sea, are neglected because they do not show apparent mass trends during our study period (Feng et al. 2014; Wahr et al. 2014). Other smaller inland lakes may cancel each other to some extent. In total, because we ignore the influence of peripheral seas and lakes, we add an error of 10 Gt to each monthly uncertainty.

5.1.2.2

Lake Correction in the Tigris–Euphrates Basin

The lake contribution in the Tigris–Euphrates Basin is so large that it cannot be ignored (Longuevergne et al. 2013). We specifically check contributions from three large lakes (Van, Tharthar and Razazah) in this basin and another large lake named Urmia near this region (Fig. 5.3). Only observations in Tharthar and Urmia are available during the entire period, and both of them decreased over 2003–2009 and were stable over 2010–2014. Their balanced trends after 2010 are also used to fill empty observations for the other two lakes. This extrapolation does not bias the lake contribution because (1) it is reasonable to suppose all the lakes have been balanced since 2010 and (2) over 80% of the lake contribution comes from Lake Tharthar, which changes much faster than the other lakes.

5.1.2.3

Linear Relationship Between Variation in Precipitation and Water Storage

To investigate how changes in precipitation influence the variation in TWS, the following linear relationship is proposed: m = a( p − p0 ) + b

(5.2)

where m is the annual TWS change (the difference between two successive years, in Gt); p is the annual precipitation (in mm); p0 is the average precipitation over a

68

5 Terrestrial Water Storage Changes in Asia

Fig. 5.2 Lake level change in the Caspian Sea (a), the Aral Sea (b) and Balkhash Lake (c). In a, the GRACE series has been corrected for steric change by the World Ocean Atlas (Boyer et al. 2013)

long-term period (in mm); a is the ratio of change between TWS and precipitation (in Gt/mm), i.e., the sensitivity factor of TWS to precipitation; and b is the average annual depletion mass without the influence of precipitation (in Gt).

5.1 The Whole Asia Region

69

Fig. 5.3 Lake level changes in the Tigris–Euphrates Basin. The unavailable observations in the Van Lake and Razazah Lake since 2011 (red dashed curves) are assumed to be balanced based on the observations from the surrounding Tharthar and Urmia lakes

5.1.3 Result Four river basins in Asia with reports of significant water resources deficits are specifically examined: the Tigris–Euphrates, Indus, Ganges and Haihe Basins (Fig. 5.4). All four basins have a long history of human disturbance and are famous for giving rise to the Mesopotamian, Indian and Chinese civilizations due to their exceptional environmental advantages, especially with regard to water resources. To date, these basins are still among the most densely populated areas and are heavily dependent on water resources to maintain sustainable economic and social development. The TWS/GWS in all four regions decreased markedly during 2003–2014, as has been well documented in previous studies (Rodell et al. 2009; Feng et al. 2013; Voss et al. 2013). However, their decreasing trends exhibit large fluctuations, which appear to be connected to the alternation of wet and dry years (Fig. 5.4). For example, all four basins experienced increased rainfall from 2010 to 2013, which made the previously decreasing trends mostly cease or even rebound during this period. The linear relationship between variations in precipitation and TWS change is shown in Fig. 5.5, with annual TWS change (defined as the difference in TWS between two successive years) and precipitation amount (defined as the accumulation of region-averaged precipitation for one whole year) in the left panels and their

Fig. 5.4 Time series of water storage in the four study basins: Tigris–Euphrates, Indus, Ganges and Haihe. The insets depict the time-dependent mass variations in total terrestrial water storage (blue), groundwater storage (red), glacier change (yellow) and precipitation anomalies (gray bars). Several prominent wet and dry years are also marked

70 5 Terrestrial Water Storage Changes in Asia

5.1 The Whole Asia Region

71

linear relation in the right panels. Considering the time lag in the response of TWS, the starting month of annual precipitation is shifted by three or four months (e.g., a shift of three months means a period from October to September) to obtain the maximum correlation between precipitation and TWS changes. The average precipitation during 1979–2015 is taken as the reference value (black dashed lines), for which we assume the climate-driven effect is zero. We use this reference to obtain the anthropogenic contribution (the variable b in the equation). The fitted parameters of Eq. (3.2) are shown in the titles of Fig. 5.5, and all the uncertainties are one standard deviation (at the 68.3% confidence level). All Asia For the entire Asian region (colored areas in Fig. 5.4), the temporal evolution of TWS exhibits two stages. First, the TWS decreased steadily between 2003 and 2009, during which approximately 1500 Gt of water was lost. In contrast, the TWS and its components show quasi-balanced fluctuations during 2010–2014 (Fig. 5.5). The total amount of TWS depletion from 2003 to 2009 was caused by two separate components: Approximately 25% of the loss came from soil water during 2003–2006 and 75% of the loss came from glaciers and GWS during 2007–2009. This is reasonable because only when surface water fails to meet water demand will the costlier groundwater be utilized. After considering the precipitation perturbation, we calculate that an increase of 1 mm in rainfall will increase the TWS by 4.8 ± 2.8 Gt. Under average precipitation conditions, the TWS is estimated to be exhausted at a rate of 187 ± 38 Gt/yr and the GWS is estimated to be lost at a rate of 100 ± 47 Gt/yr. Haihe The Haihe Basin is located in the North China Plain. This area represents the major agricultural area for wheat and corn in China; therefore, a large amount of groundwater is needed for irrigation (Sun et al. 2006). With the rapid development of industry and agriculture since the 1970s, there has been an accompanying surge in demand for water resources in this area. The groundwater in the Haihe River Basin has been excessively exploited, causing a funnel-shaped depression in the groundwater table as well as significant ground subsidence and fissures in some areas (Liu et al. 2001). Precipitation was abundant in 2004, 2012 and 2013, during which we observe peak values in TWS. The precipitation variation is highly correlated with the TWS year-to-year variations (0.95); thus, the parameter uncertainties are small (Fig. 5.5). The anthropogenic component in TWS and GWS is estimated to be −8.4 ± 0.9 and −6.9 ± 1.1 Gt/yr, respectively. The annual TWS variations are the least sensitive to precipitation changes, with a rate of only 0.17 ± 0.02 Gt/mm, which is less than half of the rates found in the other three basins. Tigris and Euphrates The scarcity of water resources and critical water stress arising from socioeconomic development in the Middle East has caused conflicts for a significant period of time (Waslekar et al. 2011). The current intensive multinational water infrastructure, including dams and reservoirs, has complicated the water management and usage. The Tigris–Euphrates region experienced severe TWS depletion (−23.0 ± 1.7 Gt/yr) over a short time period (2006–2009). Stored water was lost dramatically during these years. The observations from GRACE indicate that the TWS returned to a mostly stable state, when the precipitation increased slightly (to a level still below the long-term average as shown in Fig. 5.4). This change in trend is

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Fig. 5.5 Year-to-year TWS changes and annual precipitation variations in Asia and the four study basins. The linear relation between TWS and precipitation is shown in the right panels. The red lines are obtained by least square fitting, and the parameters are shown in the associated chart title. The error bars are at 68.3% confidence intervals. The precipitation is shifted by three or four months to account for the time lag in the response of TWS

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also consistent with lake level measurements from satellite altimetry (Fig. 5.3). We conclude that the human-induced rate of change in the water levels in this region is quite moderate (8.0 ± 5.7 Gt/yr for TWS, 3.4 ± 3.9 Gt/yr for GWS). We maintain that the previously reported large GWS loss [e.g., −25 ± 3 Gt/yr in Joodaki et al. (2014)] is primarily climate-driven. This basin is the most sensitive to precipitation changes among the study basins, i.e., a 1-mm decrease in precipitation causes the annual TWS to decrease by 0.51 ± 0.11 Gt. This effect is 140–300% larger than that in the other three basins. This explains why the severe drought that started in 2007 greatly reduced the water storage in this region despite the low anthropogenic contribution (Joodaki et al. 2014). Ganges The Ganges is a densely populated basin located on the southern side of the Himalayas, and this region has one of the highest levels of precipitation in the world. Despite its abundant rain supply, the increase in the number of inhabitants and the intensity of water exploitation (groundwater pumping from wells) have caused the groundwater to decline (Shamsudduha et al. 2012). This basin also includes the Brahmaputra River, which flows for half its length along snowy mountains and therefore contains a more considerable component of glacier meltwater (Immerzeel et al. 2010). The Ganges area experienced the most serious losses in water storage (−43.6 ± 2.6 Gt/yr) during 2003–2009 and suffered from a massive loss of both groundwater and mountain glaciers (Yi and Sun 2014). However, the trend reversed, becoming slightly positive (5.2 ± 2.7 Gt/yr), during the 2010–2014 period. The anthropogenic TWS change is −29 ± 8 Gt/yr. However, a large part of this signal is located in the glacier zone, and the GWS change in the non-glacier zone is −11 ± 7 Gt/yr. Indus Although adjacent to the Ganges Basin, the Indus Basin receives much less precipitation, as it extends further northward along the Himalayas. The large demand for water resources makes the Indus area heavily dependent on glacier meltwater and groundwater (Immerzeel and Bierkens 2012), and the groundwater in the area has consequently experienced the most severe water loss in Asia (Rodell et al. 2009). The TWS in the Indus Basin has a much larger interannual variation than the other three basins. A 1-mm decrease in precipitation causes the TWS to decrease by 0.38 ± 0.15 Gt, similar to the value of 0.38 ± 0.10 Gt in the neighboring Ganges Basin. In addition to the climate-driven effect, the TWS change caused by anthropogenic activity is −25 ± 7 Gt/yr (−15 ± 5 Gt/yr for GWS).

5.1.4 Water Storage Change in the North China Plain Given the sparse spatial and temporal coverages of well station measurements, it is nearly impossible to use in situ observations to estimate the groundwater status at a scale comparable to the GRACE spatial resolution (~100,000 km2 ). A benchmark study in Bangladesh has been conducted (Shamsudduha et al. 2012), but this only partially covered the Ganges River Basin and did not quantify the glacier contribution. The Haihe Basin (~300,000 km2 ) is an ideal place to validate the reliability

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of the GRACE estimation of groundwater due to its dense distribution of monitoring stations (~140,000 km2 , absent in mountain areas) by the Ministry of Water Resources of China (MWRC), and it is free from the influence of glaciers. Monthly groundwater well observations of shallow aquifers were obtained from the Web site of the MWRC (available at: http://dxs.hydroinfo.gov.cn/shuiziyuan/). To convert the water level variations into volume changes, we assume a specific yield of 0.07 based on the study of Feng et al. (2013). Due to the poor understanding of groundwater states in mountainous areas and deep aquifers (Feng et al. 2013) (whose pattern of change is potentially similar to that of the shallow plain observations), we compare the basin-averaged equivalent water height of the GWS from GRACE (rather than the total mass) with the shallow-aquifer well observations. The groundwater status estimates for the Haihe Basin based on both GRACEGLDAS and well stations are shown in Fig. 5.6. There is a correlation of 0.91 between these two datasets. During 2003–2009, both the satellite and ground observations show a declining rate of −1.7 cm/yr. However, the trend during 2010–2014 exhibits a decrease of −0.6 ± 0.3 cm/yr based on GRACE-GLDAS and −0.2 ± 0.3 cm/yr based on well observations. This deceleration is in line with several emerging intense precipitation trends. However, in 2014, a sharp decrease in precipitation seemed to indicate a return to the accelerated decline in the groundwater table. The large interannual variation also highlights the importance of the precipitation correction introduced here. In conclusion, we demonstrate that the trend transformation in the Haihe Basin is real via in situ observations.

5.1.5 Isolating the Cause of the Recharge The recharge of TWS/GWS could also be the result of decreased water exploitation. However, we believe this is unlikely to be the main cause. The water depletion in Asia, especially in these four populated basins, is mainly caused by agricultural irrigation and domestic use (Rodell et al. 2009; Wada et al. 2012; Feng et al. 2013; Joodaki et al. 2014), which represent inelastic demands. A check in cereal grain production shows that the crop yield in these regions steadily grew or remained stable during 2003–2014 (Fig. 5.7). Instead, the dry and wet years in all four basins are generally accompanied by a decline and increase in TWS/GWS (Fig. 5.4). On the one hand, changes in precipitation alter the recharge rate of the surface water and groundwater. On the other hand, an abundant or deficient water supply due to variable precipitation will lead to a lessened or increased dependence on the groundwater. We also find that the Indus and Haihe regions have experienced an extraordinary period of wet years since 2010, which is likely related to the strong La Nina event in approximately 2011 (Boening et al. 2012; Yi et al. 2015).

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Fig. 5.6 a Interannual groundwater fluctuation and b monthly precipitation in the Haihe Basin. The GRACE-GLDAS results and well station observations are offset arbitrarily for better identification. The groundwater change is estimated using two methods: indirect measurement based on water storage compositions and direct in situ well observations. The observations are smoothed by a oneyear running average filter (red and blue curves). The datasets were split into two groups before and after 2010 for linear fitting (red and blue lines with shading) with each trend and 1-sigma error annotated in the figure (unit is cm/yr). Both groundwater measurement methods indicated reduced depletion rates since 2010 with a simultaneous increase in precipitation

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Fig. 5.7 Cereal production in China, India and the Middle East. The data are from the Web site of Food and Agriculture Organization of The United Nations (http://faostat3.fao.org/download/Q/ QC/E)

5.1.6 Brief Summary The TWS in Asia is volatile due to the large climate variability in this region. Asia lost water rather rapidly (−261 ± 25 Gt/yr) over the short time period from 2003 to 2009. The Asian water resource system as a whole seems to be more robust when the precipitation is abundant than has been previously conjectured. Therefore, the status of water storage in Asia should be studied in more detail with consideration of climatic factors. Here, we find that there is generally a good consistency between the variation in water storage and the variation in precipitation; therefore, we propose a linear regression method to separate the anthropogenic and climate-driven effects. After correcting for the influence of climate variability using this method, the anthropogenic depletion of terrestrial water and groundwater in Asia is −187 ± 38 and −100 ± 47 Gt/yr, respectively. We also find that the previously reported water depletion in the Tigris–Euphrates region is almost entirely caused by inadequate precipitation. The GWS change observed via space gravimetry is also validated by dense

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well station measurements in the Haihe Basin. Our method will certainly aid future estimations of water storage, especially for observations spanning relatively short periods of time.

5.2 Basin Mass Dynamic Changes in China 5.2.1 Introduction China is located in a complex geographic environment with roughly three topographies, which gradually transform from plains in the east to plateaus in the west. The climate is also diverse, and water resources are unevenly distributed across this area, which spans dozens of degrees in both longitude and latitude. Copious geophysical phenomena pervade the country because of this diversity in landforms, climates and recent anthropogenic activities. Glaciers on and around the Tibetan Plateau (TP) have recently been reported to be melting rapidly because of global warming (Kang et al. 2010; Yao et al. 2012; Yi and Sun 2014) (number 1 in Fig. 5.8). The water levels of hundreds of lakes inside the plateau were generally observed to be rising because of greater precipitation and lower evaporation (Ma et al. 2010; Zhang et al. 2013) (number 2). The water level in the Three Gorges Reservoir has periodically increased since its construction in 2002 (Wang et al. 2011; Xinhua Net 2015) (number 4). The North China Plain (NCP) has experienced groundwater loss because of its stressful water demand (Changming et al. 2001; Kendy et al. 2003; Feng et al. 2013) (number 3), similar to what is occurring in northern India (Rodell et al. 2009) (number 5). The plentiful geophysical phenomena in this region have attracted substantial interest. Nonetheless, investigating these concerns with field studies is costly and impractical. By virtue of the Gravity Recovery and Climate Experiment (GRACE) gravity satellites, these surveys can be performed more easily because most of the events are strong enough to be detected from space. This system also permits a comprehensive examination of the entire region, which has yet to be conducted. The three landform types progress from vast plateaus in the west to plains in the east. The TP, which is located in western China, is still one of the world’s most active geological and climatic regions. The plateau is also known as the ‘world’s third pole’ and contains large amounts of glaciers, lakes and permafrost, which act as the source of five major river systems (Immerzeel et al. 2010). The Yangtze River and Yellow River—the world’s third and fifth longest rivers—originate from the TP and meander downwardly through extensive mainland to the eastern part of China, where the other five major river systems are located (Fig. 5.8). These seven major river systems nourish vast plains and hilly lands, which contain the main food production bases of the nation and the majority of people in the country. The climate, which is partly influenced by miscellaneous landforms, is also diverse across the country. Precipitation is concentrated in the humid eastern and southern China, with decadal-scale interannual variance that is affected by multiple climatic

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Fig. 5.8 Relief map of China. Five popularly discussed topics of mass balance in China are marked out in red or blue lumps (schematically representing mass increase or decrease, respectively) with their scope in black dashed lines. 1, glacier melting in High Mountain Asia; 2, mass accumulation in inner Tibet; 3, groundwater depletion in the North China Plain; 4, water impounding in the Three Gorges Reservoir; 5, groundwater depletion in North India. Red solid lines denote the seven major river systems of China. Other large rivers, including three in India, are also marked in black solid lines

factors, such as the East Asian and Indian monsoons (Becker et al. 2008). The average annual temperature and precipitation decrease rapidly to the north, which becomes a semi-humid–semiarid temperate monsoon climate. A plateau climate with cold and dry weather and scarce afforestation is present to the west, with coexisting glaciers and the Gobi Desert. Regardless of its unbalanced nationwide water resources, China has been vulnerable to calamitous climate extremes (floods, droughts, snowstorms and heatwaves) in most of the country during the past several decades (Yan et al. 2002; Piao et al. 2010). Most of these environmental problems are anthropogenic in nature. China has approximately 5–7% of the world’s freshwater resources but must nourish 20% of the world’s population (Qiu 2010). The development of urbanization and increasing food demands put heavy tension on water resources. Groundwater has been widely exploited for such needs. As a result, many regions in China are facing overexploited groundwater and water shortage issues. An additional obvious consequence is the ground subsidence that has occurred across the country (Hu et al. 2004). This developmental and environmental dilemma is also occurring in other populated areas such as northern India (Rodell et al. 2009), the Middle East (Voss et al. 2013) and western America (Famiglietti et al. 2011). Another anthropogenic problem is global warming, which has accelerated the melting rate of glaciers in High Mountain Asia and

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permafrost in the TP (Kang et al. 2010) and may also change the behavior of precipitation in these regions (Intergovernmental Panel on Climate Change (IPCC) 2014). The temperature in China has increased by 1.2 °C since 1960 and will continue to increase, which may threaten China’s future agriculture security (Piao et al. 2010). The Chinese government has issued multiple relevant policies and projects to relieve the droughts in the north and floods in the south (Piao et al. 2010). A costly and complex one is the South-to-North Water Diversion (SNWD) project, which has been conducted under the leadership of the Ministry of Water Resources and Electric Power (http://www.nsbd.gov.cn/zx/english/). This project has been employed through three lines: an eastern route, a middle route and a western route. The eastern route project, which starts in the downstream reaches of the Yangtze River, travels northward, supplies water to the areas alongside and ends in Tianjin and Shandong Peninsula, carrying 14.8 km3 of water per year. The middle line, which starts in the Danjiangkou reservoir, is located in a large tributary that flows into the middle reach of the Yangtze River, travels northward to Beijing and delivers 13 km3 of water per year. The western line intends to connect the upper reaches of the Yangtze River and Yellow River and will divert 17 km3 of water per year. The diversion amount will gradually increase and the maximum capacity will be reached by 2030. The eastern and middle routes began operation in 2013 and 2014, respectively, while the western line is still in the blueprint stage (Zhu and Chao 2012; Kaiman 2014). For simplicity, we declare that the glacier/groundwater storage is obtained by subtracting the soil moisture from the terrestrial water storage. However, many other geophysical factors may cause gravity changes, and we must be careful to explain the results, especially for regions with complex geographic environments such as China. In eastern China, the observed signals are mainly groundwater and soil moisture; in western China, the widely distributed lakes and large areas of permafrost on the plateau, glaciers on mountains and active tectonic processes complicate any explanation (Yi and Sun 2014; Yi et al. 2016). One solution is using models or auxiliary observations to extract the known factors. In this study, we examine the contributions from lakes and the Three Gorges Reservoir and discuss possible contributions from other sources. For this purpose, dividing the studied region based on the river basin scope is reasonable for water applications. This study also includes some peripheral basins and oceans around China mainland, totaling 26 parts, to reduce the boundary effect during inversion. GRACE data that span from 2003 to 2014 are used to estimate the water storage. Land surface models are used to estimate the soil moisture component. ICESat observations from Tibetan lakes and altimetry observations on two large lakes in the Yangtze Basin are examined to determine the lake level contribution.

5.2.2 Basin Division According to the river distribution in China and the peripheral areas, the study area is divided into 26 regions, including 3 on the seas (Fig. 5.9). In fact, only the results of

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16 basins in the inner study area are shown. The peripheral mascons are only used to decrease the boundary effect. The boundary effect means that the mascons will absorb signals from regions outside the study area if no peripheral mascon is present to fit it. Thus, the results in the peripheral mascons are expected to be biased by the boundary effect (from signals even outside the peripheral mascons), so their results are ignored. The boundary is based on the basin map from the National Administration of Surveying, Mapping and Geoinformation (http://www.sbsm.gov.cn/article/zxbs/ dtfw/zgbt/200709/20070900000741.shtml) and datasets from HydroSHEDS at the U.S. Geological Survey (http://hydrosheds.cr.usgs.gov/datadownload.php?reqdata= 30bass). Areas with exceeding large sizes are further subdivided into smaller regions (named sub-basins). The sub-basins are divided manually based on landforms, major rivers or branches, or mountain glacier into appropriate sizes that are not too large or too small. For instance, the Yangtze basin is divided by the Yangtze River to the north and south and further by large branches, totaling seven sub-basins; the Songhua River Basin is divided based on the Northeast China Plain; and the Tarim and Brahmaputra Basins have a mascon for mountain glaciers. These 26 regions are listed in Table 5.1.

Fig. 5.9 Map for the mascon division strategy that was used in this paper. A total of 26 mascons, which are divided according to the river systems, are shown in different color lumps. Larger mascons were further divided into smaller segments, which are separated by dashed curves. The transparent regions represent peripheral mascons, which were included to reduce the boundary effect; their results were discarded

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5.2.3 Results The trends of the mass changes in the 16 basins are shown in Fig. 5.10, along with the annual mass variations and basin areas. We can observe several characteristics. First, more basins have been dissipating mass (11) than accumulating mass (5). Second, larger basin generally exhibited larger trends, along with larger annual variance. The Yangtze River had the largest area (1.8 × 106 km2 ) in this study and exhibited the largest annual variation (73 Gt) in China. Exceptions did exist; for example, the Tarim Basin, which is mostly covered by desert, is vast in area but was balanced in mass, and the TP, which has been gaining mass the fastest, showed tiny annual variations.

Table 5.1 Basin division information No.

Name

Subregions

Area (×105 km2 )

1

Yangtze River

7

17.7

2

Yellow River (also named Huanghe River)

5

8.4

3

Songhua River

3

9.3

4

Zhujiang River

2

5.4

5

Huaihe River

2

3.3

6

Haihe River

2

2.7

7

Liao–Luan Rivers

2

3.7

8

Inner Mongolia

1

3.1

9

Hexi

1

4.4

10

Jungar Basin

2

4.8

11

Tarim Basin

4

11.1

12

Inner Tibet (including Qadam Basin)

4

10.5

13

Brahmaputra River

3

6.5

14

Lancang–Nu Rivers

2

3.8

15

Southeastern coast

1

2.5

16

Southeast Asia

3

13.8

17

Ganges River

4

9.9

18

Indian Peninsula

3

10.0

19

Indus River

5

11.9

20

Large western areas

6

19.3

21

Mongolia

3

12.9

22

Outside Amur

3

9.8

23

Korean Peninsula

1

2.2

24

Japan Sea

3

10.1

25

East China Sea

3

12.4

26

South China Sea

2

12.0

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Third, the masses in southern China, the TP and northeastern China exhibited obvious increases, while other parts were nearly balanced or decreasing. The TP region (12.1 ± 0.6 Gt/yr) and the Yangtze River Basin (7.7 ± 1.3 Gt/yr) have been the two fastest growing systems in China because of their vast size and steady growth. Explaining the mass increase in the TP is challenging because the region convolved many factors, most of which remain undetermined (Yi and Sun 2014). We will discuss this topic in the following discussion section. The NCP, Tienshan, Ganges, Brahmaputra and Nujiang–Lancang Rivers have experienced serious mass loss, a combined effect of groundwater depletion and glacier melting (when applicable) (Rodell et al. 2009; Feng et al. 2013; Yi and Sun 2014). The Huang–Huai–Hai River (downstream of the Huanghe River, Huaihe River and Haihe River, shortened to HHH hereafter) Basins exhibited a total mass loss of −10.2 ± 0.9 Gt/yr, which is larger than the results from a previous study (Feng et al. 2013) in both value and spatial scope. However, the upstream region of the Yellow River in the TP exhibited a mass increase, making the status in the Yellow River region less negative. The interannual variances of the TWS, SWS, GWS and precipitation of eight representative basins are shown in Fig. 5.11. Several features can be described. First, both the TWS and SWS varied with precipitation, with a lag of several months. This pattern is especially clear in the (a) Yangtze River, (c) Songhua River and (g) Liao–Luan River. The interannual variance of the water storage in the Yangtze River Basin was significantly related to El Niño–Southern Oscillation (ENSO) events through its influence on the precipitation (Zhang et al. 2015). Second, the groundwater appeared to be more stable. A tremendous rainfall shortage in the Yangtze River in 2011 decreased both the TWS and SWS, while the GWS was less influenced. The TWS in the Songhua River experienced drastic interannual fluctuations because of unstable precipitation, though the GWS varied relatively smoothly. Third, the reliability of the trends over 12 years in many of the basins was still subject to interannual variance. The Yellow River and Hai River Basins experienced groundwater depletion, but recently these declining trends seemed to have decelerated. Since 2010, the Songhua River and Liao–Luan River have experienced several intense precipitation events, which overwhelmed their changing trends and muddled their statuses. The change in 2010 may be associated with the 2010–2011 La Nina, which was the strongest in the last eighty years (Boening et al. 2012) and caused large fluctuations in the land water storage over the following several years (Yi et al. 2015). The trends of the TWS, SWS and GWS are also shown in map form in Fig. 5.12. Overall, tremendous mass accumulation spread from the TP to the Yangtze River and further to the southeastern coastal areas, while the HHH, the adjacent Liao–Luan River Basins, the Brahmaputra–Nujiang–Lancang (shortened to BNL hereafter) River Basin and northwestern Tienshan experienced mass loss. The mass throughout the entirety of China (regions 1–15, but only the northern parts of region 13) has grown slightly (4.2 ± 3.6 Gt/yr).

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Fig. 5.10 Mass balance (blue histograms, red error bars are one standard deviation), amplitude of the annual period (yellow squares) and areas (violet circles) of 16 river basins. Following the name in the bracket is the corresponding mascon number

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Fig. 5.11 Time series of precipitation and different mass balances in eight specified regions. A one-year sliding window smoothing was applied. The SWS was derived from GLDAS, the TWS was derived from GRACE, and the GWS was obtained by the difference between the TWS and SWS. The error bars represent one standard deviation. The precipitation anomaly was amplified by a factor of three

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85

Fig. 5.12 Trends of the GWS, TWS and SWS in the basins. Cities with reported land subsidence are also marked as open and solid (higher severity) circles in a. The circles are generally located in regions with mass loss, except for the Yangtze Delta

5.2.4 Discussion 5.2.4.1

Groundwater Depletion and Ground Subsidence

Groundwater extraction can be divided into domestic water, industrial water and agricultural water. The first two cover small ranges around cities, while agricultural water that is used in croplands involves a wider range (>100,000 km2 ) of groundwater exploitation, which is more feasibly observed by gravity satellites. Although space observations have only limited resolutions, localized ground subsidence, which is usually caused by extreme groundwater exploitation for domestic use on a scale of hundreds of meters, can provide a supplementary reference. Here, we compared maps of groundwater depletion and ground subsidence and found that they shared some similarities. Persistent groundwater depletion can produce ground subsidence, whose geographic regions in China can be categorized into three types: (1) the coastal plain and river delta regions in East China; (2) plain regions next to major mountains such as the NCP and Northeast China Plain; and (3) valley and basin regions among mountains, such as the Loess Plateau in the midstream reach of the Yellow River (Hu et al. 2004). Cities with reported ground subsidence are marked in Fig. 5.12, in which solid circles indicate more severe conditions. Regions with GWS depletion are more likely to experience ground subsidence events, while regions with abundant water are less likely. The NCP and middle reaches of the Yellow River are more in line with this law. However, the Songhua River and Yangtze River Delta do not match this trend.

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The Yangtze River Delta belongs to the first category but exhibits a positive trend. The GRACE signals in the coastal areas may have been polluted by ocean signals. Nonetheless, the recently strict control of groundwater pumping in this region may have played a role. Shanghai and Tianjin were the first cities to report ground subsidence, as early as the 1920s, and their situations deteriorated with time. However, scientific exploitation and groundwater recharge policies were established after 1966. Thus, the amount of exploitation reduced by nearly 70% since 1966, and the amount of recharge has surpassed exploitation ever since 2010 (Yang et al. 2014). Cities in the Northeast China Plain fall within the second category but also exhibit increasing water storage trend in terms of both the GWS and TWS. As mentioned above, the water status in the Songhua River was overwhelmed by intense rainfall events in 2010 and 2013, the latter of which caused the most severe flood in a century (CCTV 2013). Other than the above two exceptions, good consistency exists between GWS depletion and ground subsidence in the NCP, which implies that the groundwater situation is worsening in both large and small spatial scales, which may complement each other. The NCP contains one of China’s main grain production bases, including a double cropping system of growing wheat in winter and maize in summer. However, the precipitation fails to meet this water demand, especially in winter when little rain drops, so the groundwater supplies have been strongly exploited (Qiu 2010). Furthermore, the problem becomes aggravated in city regions, where the demand for domestic and industrial water is extremely large. Many other cities are located inside our high-potential-risk region, but no such problems have emerged yet, possibly because these cities are still under affordable levels or because techniques have delayed these issues. This GWS depletion is more widespread than ever before, and these cities have higher risk for such issues. Ground subsidence may threaten civil infrastructure and citizen safety, but its assessment remains challenging (Hu et al. 2004). The GRACE system can help to evaluate the potential risk of a city to humaninduced ground subsidence, although finer spatial resolution is required to improve the reliability in local regions.

5.2.4.2

Lake Levels in the Middle Reaches of the Yangtze and on the TP

Many geophysical factors may cause gravity changes. Gravity observations alone cannot distinguish every component and must be carefully studied to explain the results. Figure 5.12a shows a large range of mass increase that continuously stretches from the high plateau in the west to the Yangtze Basin in the east. As shown above, the water storage is highly correlated with changes in precipitation (evaporation and runoff also play essential roles but are assumed to also change with precipitation), which is believed to directly affect the lake water storage. From this viewpoint, we studied the lake level observations in the middle reaches of the Yangtze River with altimetry and on the TP by ICESat to understand these positive signals. Dongting and Poyang are two large lakes in the middle reaches of the Yangtze River that have been monitored by altimetry from 2003 to 2011 (Crétaux et al. 2011),

5.2 Basin Mass Dynamic Changes in China

87

as shown in Fig. 5.13. The time series is available from http://www.legos.obs-mip.fr/ en/soa/hydrologie/hydroweb/Page_2.html. The lake levels have risen slightly (0.02 ± 0.07 and 0.02 ± 0.08 m/yr, respectively), with a total mass contribution of 0.12 ± 0.33 Gt/yr. Therefore, neither the lake levels nor the SWS in the two largest lakes increased much (Fig. 5.11a). We further considered the contributions from the Three Gorges Dam, which has been obstructing 23.3 km3 of water during 2002–2008 (Wang et al. 2011) and a maximum capacity of 40 km3 by the end of 2015 in the midstream area of the Yangtze River (Xinhua Net 2015). The mass increase in the Yangtze Basin (at a rate of 7.7 ± 1.3 Gt/yr) was approximately two times the storage increase in the Three Gorges Dam (less than 4 Gt/yr), suggesting an important contribution from the groundwater, which is believed to have been caused by intensive anthropogenic irrigation (Huang et al. 2015). ICESat data from 2003 to 2009 were adopted to study the lake level changes on the TP. A total of 403 one-by-one-degree grids were used, of which only 96 could be measured directly by the satellite (approximately 4.6 Gt/yr). For lakes without observations, we applied the following steps to interpolate their trends. First, the height change of the unit lake area was calculated; then, the lakes without observations were interpolated; finally, the observed volume changes of the lakes were divided by the area of the grid in which they resided to obtain the trend of each grid. Interpolation produced 262 grids with values, adding up to 8.0 Gt/yr. This value is very close to 8.06 Gt/yr given by Zhang et al. (2013). Figure 5.14 shows that the signals from lake water uplift were much more restricted in the spatial range, although they were comparable with the GRACE observations in magnitude (also truncated in the same period). The peak lake water value was located at Siling Lake in the center of the TP. Around this site were many other large lakes that have also been rising very quickly, although the GRACE results showed a uniform increase (Fig. 5.14c). The peak location from ICESat was mostly buried by the strong negative signals from glacier melt in the eastern Himalayas (the large area of negative signals from glacier melt and groundwater depletion were masked off here; see (Yi and Sun 2014) for more discussion on this topic). This result implies that the retreating trends of glacier at this location may be underestimated when using only GRACE data because of its mixture with lake contributions. This rise in lake level may explain the mass increase in the TP (Zhang et al. 2013). Nonetheless, we argue that the mass increase in the TP has been greatly underestimated. The inner TP, shown as the number 12 in Fig. 5.9 (with an area of 1.06 × 106 km2 ), is the main distribution area of the lakes, and the mass trend that was estimated by GRACE with an SWS correction during 2003–2009 was 16.2 ± 2.4 Gt/yr. Therefore, the lake contribution only explains half of the observed mass accumulation. Moreover, this area does not include the upper streams of the Yellow River and Yangtze River, which also represent a positive trend. Examining a wider range of the TP (an area of nearly 3 × 106 km2 ) indicates a tremendous mass accumulation rate of 26.8 ± 2 Gt/yr (1-sigma) during 2003–2012 (Yi and Sun 2014). The shape of the positive signal resembles the outline of the TP and is quite uniformly distributed (Fig. 5.14c) regardless of the uneven distribution of lakes, especially on

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Fig. 5.13 Lake level changes from altimetry in the middle and lower reaches of the Yangtze River. Both lakes slightly increased but exhibited large uncertainty. The errors are one standard deviation

5.2 Basin Mass Dynamic Changes in China

89

Fig. 5.14 Lake level uplift that was observed by ICESat (a) and its smoothed EWH signal (b) compared to GRACE observations (c). Topography contours of 2000 m and 4000 m were annotated to reference the scope of the TP. The negative areas in GRACE were masked off. G300 means a Gaussian filter with a radius of 300 km; P4M6 means a decorrelation filter that started from an order of 6 and was fitted by a polynomial of order 4 (Chen et al. 2007)

the eastern side where almost no lakes exist, which implies that this large positive signal is likely related to groundwater, permafrost and tectonic processes.

5.2.4.3

Implications for Water Resource Planning

A strong La Nina event occurred in 2010–2011 and changed the water storage statuses in many continents, such as Australia, northern South America and Southeast Asia (Boening et al. 2012). As shown in Fig. 5.11, the anomalous precipitation around this time greatly affected the mass status in several basins, especially the Yangtze River and Songhua River. In this section, we demonstrate how much the basin water

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storage was affected by transient climate factors, which will be instructive for large water resource planning projects such as the SNWD. We adopted the concept of interannual variance to determine whether the interannual changes were stable or fluctuant according to the following steps. First, the water storage was averaged by years to obtain the total annual variation. Then, the long trend was fitted and deducted from the annual mean variation to obtain the interannual anomalies, the standard deviations of which served as our interannual variance. The results are presented in Fig. 5.15a. An initial glance shows that the basins in the northeast, southern coast and Himalayas experienced large interannual variations. The SNWD was designed to alleviate water problems in southern and northern China through three lines. The eastern and middle routes (completed at the end of 2013) are illustrated as black curves in Fig. 5.15a, and 1.7 km3 (or 1.7 Gt) of water has been delivered from central China to North China in 2015 (http://www.nsbd. gov.cn/zx/mtgz/201602/t20160223_435973.html). By 2050, the transferred amount from the Yangtze to the Haihe Basin is projected to be 7–13 Gt/yr (Berkoff 2003) and the northern part roughly gets a half (4–7 Gt/yr). The starting/ending areas of the project are outlined and annotated as S/N. As in our study period, the project has only operated for one year and is still not fully operational, so we cannot yet estimate the effect of the SNWD project. Here, we present the variations in the S/N area and discuss how this project will be theoretically affected, assuming that it is fully operational during the entire studied period. Area-S and area-N have an interannual variance of approximately 2.3 and 2.5 cm, respectively (in water height), equaling 7.6 and 3.6 Gt in mass, respectively. These values are comparable with the 1.7 or 4–7 Gt that the project plans to deliver in 2015 or 2050, which implies that the effectivity of SNWD will be possibly reduced by the interannual variances in the source and target areas (i.e., central China and northern NCP). The variation series are shown in Fig. 5.15b. After extracting the background of the declining trend, seven years (out of twelve) of the area-N exhibit an extra mass deficiency of over 1.5 Gt, which will greatly offset the effect of the delivered 1.7 Gt of water in 2015. Another three years exhibit a mass excess of approximately 5 Gt, which is even several times larger. Thus, the water shortage in the northern Haihe Basin has dynamically changed with climate factors; a water surplus was sometimes present. In 2013, the source area had a water deficiency of 9.2 Gt, while the target area had a water excess of 6.7 Gt. The water transfer was outperformed by natural forces in the form of precipitation, so it would be economically efficient and not put too stress on the sustainability of the source area if the delivering amount is reduced correspondingly. Figure 5.11 clearly shows that reduced precipitation decreased the water storage, but no simple quantitative relationship exists between these changes. We evaluated the impact of climate change through gravity satellite data. The SNWD is expected to perform more efficiently if the formulation of its delivered amount is dynamically regulated by the annual water status at both the source and the destination. Geodetic methods can serve as a valuable reference for this demand. However, a three-month delay usually exists in the release of GRACE solutions, which greatly hinders their

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91

Fig. 5.15 a Eastern and middle lines of the NSWD (black curves with arrows) with the interannual variation in the background. b Annual anomalies in the beginning and ending areas of the NSWD. The interannual variation, which is an indicator of the stability of the change, is the standard deviation of the annually accumulated water storage in each basin, with its long trend deducted. The ending area (N) and starting area (S) of the project are outlined in a, and their annual mass anomalies are presented in b

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implementation. However, strong dry/wet events could persist for half a year or more (shorter events are not as serious). Therefore, reducing this delay to one month or weeks in the future or establishing a forecasting model could be promising.

5.2.5 Brief Summary A multi-basin inversion method was used to derive the mass variance in 16 drainage basins in mainland China and peripheral areas. A comprehensive estimation of the entire region was conducted. The results were compared with land surface models and precipitation, altimetry and remote sensing data. The following conclusions can be drawn: 1. One belt of positive trends and three clusters of negative trends are the key characteristics of the mass changes. The belt of positive trends spreads from the TP, crosses the Yangtze River and covers all of South China, with three clusters in the HHH Basins, Tienshan and the BNL Basins. However, the mass over the entirety of mainland China has been slightly increasing. 2. The NCP exhibits good consistency between the TWS deficiency scope from gravity satellites and the locations of cities with reported subsidence, which implies that the availability of water resources in this area has been severe at both micro- and macroscales. 3. Positive trends exist in both the TP and Yangtze River Basin, but these trends were created by different mechanisms. The mass increase in the TP was driven by the climate: Approximately half originated from lake water, while the other half may have originated from groundwater, tectonic processes and permafrost. The mass increase in the Yangtze River Basin was anthropogenic: Approximately half originated from the Three Gorges Reservoir, while the other half originated from GWS because of intense irrigation. 4. We have shown that the water status in the northern and southern regions of China is subject to interannual fluctuations that are comparable with the delivered amount of water from the SNWD project. Gravity data from satellites can adequately monitor changes in the TWS, which is informative for policies and projects in water resource management.

References Becker, S., Hartmann, H., Zhang, Q., Wu, Y., & Jiang, T. (2008). Cyclicity analysis of precipitation regimes in the Yangtze River basin, China. International Journal of Climatology, 28(5), 579–588. https://doi.org/10.1002/joc.1572. Berkoff, J. (2003). China: The south–north water transfer project—is it justified? Water Policy, 5(1), 1–28.

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Ma, R., Duan, H., Hu, C., Feng, X., Li, A., Ju, W., et al. (2010). A half-century of changes in China’s lakes: Global warming or human influence? Geophysical Research Letters, 37(24). Matsuo, K., & Heki, K. (2010). Time-variable ice loss in Asian high mountains from satellite gravimetry. Earth and Planetary Science Letters, 290(1–2), 30–36. https://doi.org/10.1016/j. epsl.2009.11.053. Piao, S., et al. (2010). The impacts of climate change on water resources and agriculture in China. Nature, 467(7311), 43–51. https://doi.org/10.1038/nature09364. Qiu, J. (2010). China faces up to groundwater crisis. Nature, 466(7304), 308–308. Rodell, M., et al. (2004). The global land data assimilation system. Bulletin of the American Meteorological Society, 85(3), 381–394. http://doi.org/10.1175/bams-85-3-381. Rodell, M., Velicogna, I., & Famiglietti, J. S. (2009). Satellite-based estimates of groundwater depletion in India. Nature, 460(7258), 999-U980, https://doi.org/10.1038/nature08238. Shamsudduha, M., Taylor, R., & Longuevergne, L. (2012). Monitoring groundwater storage changes in the highly seasonal humid tropics: Validation of GRACE measurements in the Bengal Basin. Water Resources Research, 48(2). Sun, H.-Y., Liu, C.-M., Zhang, X.-Y., Shen, Y.-J., & Zhang, Y.-Q. (2006). Effects of irrigation on water balance, yield and WUE of winter wheat in the North China Plain. Agricultural Water Management, 85(1), 211–218. Tapley, B. D., Bettadpur, S., Ries, J. C., Thompson, P. F., & Watkins, M. M. (2004). GRACE measurements of mass variability in the Earth system. Science, 305(5683), 503–505. Voss, K. A., Famiglietti, J. S., Lo, M., Linage, C., Rodell, M., & Swenson, S. C. (2013). Groundwater depletion in the Middle East from GRACE with implications for transboundary water management in the Tigris-Euphrates-Western Iran region. Water Resources Research, 49(2), 904–914. Wada, Y., Beek, L. P. H., & Bierkens, M. F. P. (2012). Nonsustainable groundwater sustaining irrigation: A global assessment. Water Resources Research, 48(6), 335–344. Wahr, J., Smeed, D. A., Leuliette, E., & Swenson, S. (2014). Seasonal variability of the Red Sea, from satellite gravity, radar altimetry, and in situ observations. Journal of Geophysical Research: Oceans, 119(8), 5091–5104. Wang, X., de Linage, C., Famiglietti, J., & Zender, C. S. (2011). Gravity Recovery and Climate Experiment (GRACE) detection of water storage changes in the Three Gorges Reservoir of China and comparison with in situ measurements. Water Resources Research, 47(12). Waslekar, S., Vishwanath, A., Bakshi, G., & Motwani, P. R. (2011). The blue peace: Rethinking Middle East water. Strategic Foresight Group. Xinhua Net. (2015). The three Gorge is in a new round of experimentally increasing its water level to 175 m (in Chinese). L. Zheng (Ed.). http://www.china.com.cn/newphoto/news/2015-10/08/ content_36763591.htm. Yan, Z., Jones, P., Davies, T., Moberg, A., Bergström, H., Camuffo, D., et al. (2002). Trends of extreme temperatures in Europe and China based on daily observations. In Improved understanding of past climatic variability from early daily European instrumental sources (pp. 355–392). Springer. Yang, T., Wang, H., & Jiao, X. (2014). Land subsidence zoning control in Shanghai. Shanghai Land & Resources, (4), 105–109. https://doi.org/10.3969/j.issn.2095-1329.2014.04.025. Yao, T., et al. (2012). Different glacier status with atmospheric circulations in Tibetan Plateau and surroundings. Nature Climate Change, 2(9), 663–667. https://doi.org/10.1038/nclimate1580. Yi, S., & Sun, W. (2014). Evaluation of glacier changes in high-mountain Asia based on 10 year GRACE RL05 models. Journal of Geophysical Research: Solid Earth, 119(3), 2504–2517. Yi, S., Sun, W., Heki, K., & Qian, A. (2015). An increase in the rate of global mean sea level rise since 2010. Geophysical Research Letters. Yi, S., Wang, Q., & Sun, W. (2016). Is it possible that a gravity increase of 20 µGal yr−1 in southern Tibet comes from a wide-range density increase? Geophysical Research Letters. https://doi.org/ 10.1002/2015gl067509.

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Chapter 6

Glacial and Tectonic Mass Transportation in High Mountain Asia

6.1 Introduction Nearly each part of the HMA glaciers develops in its own individual features. For instance, glaciers on the TP are generally of three different types and are controlled by diverse factors. The southern TP glaciers are influenced by high precipitation brought by the Indian monsoon in the summer, while the Pamir glaciers are affected by the westerlies in the winter (Fig. 6.1). The interior of the TP is less influenced by these two circulation systems and is dominated more by continental climatic conditions (Yao et al. 2012). As a result, their mass peak values occur at different seasons, and more importantly, they show different melting patterns. Glaciers on the southeastern TP and Karakoram are retreating most rapidly, while the interior parts are retreating less rapidly (Yao et al. 2012). The Pamir glaciers take on a more complex change, even change at an increasing rate over some periods (Gardelle et al. 2012). In this study, 10-year data from the University of Texas at Austin, Center for Space Research (UT-CSR) Release 05 models from January of 2003 to December of 2012, were used to evaluate the glacier changes in HMA. A new spatial domain inverse method is used to separate signals from three sources: a negative one from glacial regions, another negative one from northern Indian groundwater depletion areas and a positive one from the inner TP. Four glacial regions were investigated: Tianshan, Pamir and Karakoram, Western and Central Himalaya and Eastern Himalaya. Extra attention was paid to the 10-year variance of the Pamir and Karakoram (P&K) glacial region.

© Springer Nature Singapore Pte Ltd. 2019 S. Yi, Application of Satellite Gravimetry to Mass Transports on a Global Scale and the Tibetan Plateau, Springer Theses, https://doi.org/10.1007/978-981-13-7353-4_6

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Fig. 6.1 The Tibetan Plateau glaciers (white dots) and monsoons (blue represents westerlies and red represents Indian monsoon). The Indian monsoon blows northwardly along the Himalayas, facing the Pamir, thus influencing the precipitation and glaciers there

6.2 Glacier Mass Balance in HMA 6.2.1 Mascon Division In this study, we divide the study area (HMA) into several mascons based on the distribution of glaciers from the World Glacier Inventory, as shown in Fig. 6.2. Each color represents a mascon with the same density, and the dotted curves mark different groups. The groups are: Tianshan (A); Pamir and Karakoram (B); western and central Himalaya (C); Eastern Himalaya (D); northern India (E); northeastern India (F) and inland TP (G).

6.2.2 Results In this study, we have used the CSR05 data, combination of the SADI and SEDI methods, and the three periods (annual, semiannual and 5-yr) curve fitting to obtain the final mass change estimate. We have taken the average of these two methods to be the final result. The half of their difference is taken as error of the inverse method and included in the final error estimate. The observations and the inversed rates are

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99

Fig. 6.2 Mascon partitions and groups on the background of the equal water height secular trend obtained from CSR-RL05. The groups are: (A) Tianshan; (B) Pamir and Karakoram; (C) western and central Himalaya; (D) eastern Himalaya; (E) northern India; (F) northeastern India and (G) inland TP

shown in Fig. 6.3. After the negative rates of groundwater and glacier are deducted from the observations, the positive signals are noticeable. We have also deducted the mean GLDAS model trend from the results. The mass change time series inverted from CSR04, CSR05 and the mean GLDAS models are shown in Fig. 6.4, and the final glacier estimate is shown in Table 6.1.

Fig. 6.3 a Observed trend from CSR RL05 models; b Inversed change rate of Indian undergroundwater and glaciers; c Residue calculated by deducting b from a

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Fig. 6.4 Time series of mascon groups, where year is presented on the x-axis, ‘Gt’ is presented on the y-axis, and the numbers indicate the long-term trend with the error (Gt/yr). Colors are defined in the legend. Each color has two curves, the time series and the long-term trend. The long trend of CSR05 also includes a 5-year period. Plots a–g are the results of group a–g, respectively. Plot h demonstrates how average time series (black curve) are calculated from four GLDAS models’ observations (different red symbols) in group b

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Table 6.1 Secular trend estimates of each group of mascons Group

CSR04

CSR05 σT

T

TWS avg σT

T

CSR05—TWS σT

T

σT

T

A

−8.01

2.76

−5.92

2.29

2.49

0.78

−8.41

2.41

B

−13.07

2.62

−8.11

2.35

−2.01

0.78

−6.10

2.48

C

−6.12

2.58

−6.48

1.97

0.15

1.44

−6.64

2.44

D

−12.98

1.93

−13.79

1.43

0.03

0.93

−13.82

1.71

E

−22.05

3.69

−19.55

3.23

0.62

1.14

−20.17

3.42

F

−5.93

2.88

−7.66

2.64

2.76

1.08

−10.43

2.85

23.30

4.88

26.79

4.00

−3.25

1.72

30.04

6.88

All Ice

−40.17

6.38

−34.31

5.37

0.66

2.04

−34.97

5.75

All UGW

−27.97

5.38

−27.21

4.74

3.38

1.57

−30.59

4.99

G

‘All Ice’ is the sum from A to D. ‘All UGW’ is the sum of E and F

The 10-year data are very helpful in confirming the negative trend. Both mass estimates in group A and group E show a steady rebound in 2010. If the GRACE data are shorter (say, truncated in 2011), the negative trend may be questionable, and the final assessment will be biased. This increasing trend stopped in 2012, so these negative trends are assuring. In group B, the “M” shape is easy to identify. Group D has an accelerated decrease in mass in recent years. Group G is the sum of mass changes in all interior areas. The steady increase implies that an accumulation of mass exists in the TP inland. We find that there are three different kinds of signal sources in the HMA area. The first one is the strong negative source from northern India groundwater depletion (group E plus group F) (Rodell et al. 2009; Tiwari et al. 2009). The second one comes from the glacier mass balance (from group A to group D) (Matsuo and Heki 2010; Jacob et al. 2012). The third one is the positive trend in the inner TP (group G) (Zhang et al. 2013). The mechanism of the third source has not been well discussed, so it was ignored or improperly treated as ice accretion, as was done by Matsuo and Heki (2010) and Jacob et al. (2012). We will discuss this problem below in detail. The trend errors from the CSR05 model are ~20% lower, implying a more stable variance. From RL04 to RL05, the trend of ice melting changes from −40.2 to −34.3 Gt/yr, while the trend of the inner TP changes from +23.3 to +26.8 Gt/yr, suggesting that RL04 tends to overestimate the glacier melting rate while underestimate the mass accumulation rate in the inland TP. We then check the influence of the 5-yr period on the final trend. Only trends of group A and group B are ~10% larger, while the sum of the final trend is slightly changed. This result is reasonable because 10-year data are long enough. Also, we have compared the different results between SADI and SEDI. The total final estimates are very similar, but in groups, the difference can be as large as 20%.

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6.3 Region A: Various Signals in the Inland of TP The total ice melting rate is −35.0 ± 5.8 Gt/yr, without GIA correction. We directly take the GIA and LIA corrections from Jacob et al. (2012) for reference. After considering these effects (−6 ± 3 Gt/yr), this ice melting rate is −41 ± 6.5 Gt/yr. It should be noted that the correction is plausible but very extreme; in fact, the true value may be very small. Ignoring the vast inland of the TP can reduce the interference of GIA. This is only a rough reference, and we state that this GIA correction should be discussed in more detail. The corrections for denudation and plate motion happen to cancel each other out in the Himalaya. Sun et al. (2009) declared that the denudation rate on TP is 2.3 mm/yr. The value is calculated by attributing all the sediment fluxes to the margin (southern–eastern) area where denudation is concentrated (Sun et al. 2009). A more recent study suggests that the Himalayan range is still rising at a rate of ~2 mm/yr (Liang et al. 2013). It implies that in the periphery of TP, the uplift is canceled mostly by denudation. We have found a larger positive signal (+30 Gt/yr) in the inner TP than the rate of 7 Gt/yr reported by Jacob et al. (2012). First, we should determine whether it can be attributed to glacier advance. This possibility can be excluded because field-based observations for the inner TP show that in recent years glaciers have been retreating, but slower than the margin areas (Bolch et al. 2010; Yao 2010; Yao et al. 2012). Zhang et al. (2013) concluded that this mass increase can be mainly explained by the water level rise of the lakes in the TP. They studied 53% of the total lake area in the TP and found a mass increase rate of +4.28 Gt/yr. If this rate holds true for all lakes, the total mass variance rate is +8.06 Gt/yr according to the area ratio. The reason for lake level rise might be due to the significant increase in precipitation in the TP over the past several decades, especially in the central TP (Zhang et al. 2013). It seems that it almost explains the total 7 Gt/yr signal given by Jacob et al. (2012), but it is not enough for our larger value (30.0 Gt/yr, group G). As mentioned above, the composited signals in TP cover various sources, i.e., glaciers, terrestrial water storage, groundwater storage, tectonic process, permafrost, weather denudation and GIA. The first two have been determined by site observations and models, while the uncertainty of others can be considered to explain the remaining positive signal. We consider the correction of denudation, GIA to be zero. Denudation can be neglected because the orographic precipitation and efficient river networks concentrate erosion on the edges, while the interior is protected from significant erosion (Fielding 1996; Sun et al. 2009). We also do not consider the GIA correction because we prefer the assumption that there was no huge ice cap over the TP in the Last Glacial Maximum (LGM) for lack of geological evidence (Shi et al. 1992). The statuses of permafrost and groundwater are unclear now. Permafrost is very complex and not yet well understood. During 1960–2007, the annual mean surface temperature averaged over 90 stations in the TP shows that the rate is 0.036 °C/yr (Wang et al. 2008), and there was a simulation model which describes the melting pattern of permafrost in the TP (Nan et al. 2005). The melting may introduce a

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mass loss; however, it also can result in a mass increase. Because permaforst has little capacity to hold water, after it melts, the capacity increases. There has been no groundwater storage data covered the whole TP available until now, but it is easy to understand that a higher lake level requires larger groundwater storage. Almost all the lakes in the inner TP have no surface outflows, and water seepage plays an important role (Zhou et al. 2013). For the tectonic effect, we use a simple Bouguer layer correction. The Indian plate is still moving toward the Asian plate at a rate of 5 mm/yr and bringing extra mass into the TP. As a result, the thickness of the TP crust expands. Sun et al. (2009) had made the pioneering attempt to estimate the Moho interface changes, but their observations are in the peripheral, and the Moho varying status in the inner TP is still unclear. Here, we just assume the Moho interface will change only as a response of the isostasy. The extent of isostasy may range from 100% (totally isostasy) to 0% (non-isostasy). In the former condition, the Bouguer correction is 0 Gt/yr; in the latter condition, the Moho interface will stay still, and the thickening rate of crust can be determined from surface vertical velocity, e.g., ~2 mm/yr from Liang et al. (2013). We take the density of crust as 2.6 × 103 kg/m3 and the area of TP as 2.5 × 106 km2 . Then the Bouguer correction is 13 Gt/yr. The above discussion is summarized in Table 6.2. It is not easy but still possible to explain the large mass accumulation (26.8 Gt/yr). Because some sources still remain unclear, it is challenging to determine the status of all the categories. However, the overall status is restricted by GRACE. The inversion is taken to get the surface mass change, on the assumption that mass transports only on the surface. For most factors, this assumption is very convenient; for some phenomena, this assumption does not hold true, e.g., GIA and tectonic process. In these cases, it should be treated in gravity anomaly and then converted to this equivalent surface mass, as a correction for GRACE observations. The gravity anomaly and surface mass change are easy to mutually convert.

6.4 Region B: The Pamir Plateau 6.4.1 Monsoons and Their Impact on the Mass Balance Glaciers in the P&K bear very complex variance and different studies have presented conflicting mass changing values, containing both positive and negative trends. To better understand this complexity in the P&K, we must take into consideration the major climatic factor, i.e., the monsoons. It is generally accepted that the Pamir is dominated by the monsoons (Matsuo and Heki 2012; Yao et al. 2012). Referring to the amplitude of annual precipitation (Fig. 6.5a), we find that the India monsoon is obstructed by the Himalayas, damply moving northwardly along the plateau, until encountering the Pamir plateau and bringing rainfall on the southern side. The westerlies monsoon brings heavy precipitation on the west side and blows further east

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Table 6.2 Various signals in inner TP Category

Status

Remark

The sum

26.8 Gt/yr

Detected by GRACE, without GIA correction

Terrestrial water storage

−3.3 Gt/yr

The average of four GLDAS models

Glaciers

Slightly negative

From field observation (Bolch et al. 2010; Yao 2010; Yao et al. 2012)

Lake water storage

8.1 Gt/yr

Given by Liang et al. (2013)

Groundwater storage

Unclear, likely to be positive

It is likely to be positive as a response of lake water level rise

Tectonic process correction

0–13 Gt/yr

Bouguer layer assumption, ranging from totally isostatic (0 Gt/yr) and non-isostatic (13 Gt/yr)

Permafrost

Unclear

The status can be either positive or negative

Weather denudation

~0 Gt/yr

The interior is protected from significant erosion (Fielding 1996; Sun et al. 2009)

GIA correction

Unclear, close to 0 Gt/yr

The lack of geological evidence for huge ice cap (Shi et al. 1992) means even it there exists GIA, it will be very small

along Tianshan (Fig. 6.1). From Fig. 6.6b, we can find that the precipitation in the Pamir is also influenced by El Niño-Southern Oscillation (ENSO) in June, for it slightly increases. The scale and phase of Arctic Oscillation (AO) is represented by the AO index (AOI) derived as the first leading mode of the empirical orthogonal function (EOF) of monthly mean SLP anomaly field north of 20 N (Matsuo and Heki 2012). ENSO warm phases are associated with warmer sea surface temperature in the equatorial Pacific as well as in the Indian Ocean, which is scaled by the Southern Oscillation Index (SOI) (Shrestha et al. 2000). Both the AOI and SOI used in this paper are from CPC/NOAA (http://www.cpc.ncep.noaa.gov/products/ precip/CWlink/daily_ao_index/ao_index.html, http://www.cpc.ncep.noaa.gov/data/ indices/soi). The precipitation data are from the Global Precipitation Climatology Project (GPCP) (Adler et al. 2003). Below, we demonstrate in detail how different factors affect the interannual variance of the P&K glaciers. The annual variance of mass, precipitation, and monsoon index in group B and group F is presented in Fig. 6.6. A 3-month delay in the response of both groundwater and glaciers to rainfall is found. When we analyze the interannual variance, and we take the average value of these extreme months as the strength of that year. That is, for group B, the SOI, AOI and precipitation are used from January to March, and

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Fig. 6.5 a Annual amplitude of precipitation from GPCP; b 5-year undulating amplitude of CSR05

the mass is used from April to June. For group F, the SOI and precipitation are taken from May to July, and the mass is taken from August to October. The interannual correlation of mass, precipitation, AOI and SOI in group B and group F is shown in Fig. 6.6a. In group B, the correlation of mass with AOI is −0.59 and with SOI is −0.67. The precipitation is clearly controlled by ENSO (−0.62) rather than AO (−0.20). The mass estimate presents a steadier annual and interannual variance than that of AOI, SOI or precipitation. For longer periods, several studies on monsoon precipitation in India indicated a strong relationship between the monsoon and the ENSO (Shrestha et al. 2000). However, during these 10 years, the correlation between precipitation and SOI is very low. In general, both glaciers and groundwater have a strong correlation with precipitation (0.59 and 0.89, respectively).

6.4.2 The 5-Year Undulating Signal This study has paid particular attention to the variation of glaciers in group B and group F. Glaciers in group B are influenced by the westerlies monsoon in winter. Groundwater in Group F is affected by the Indian monsoon in summer. In the group B time series (Fig. 6.4b) derived by the GRACE gravity inverse method, a visual “M pattern” of variance is seen. A Fourier transform (FT) was applied to perform periodic analysis, and it was found that there is a very strong 5-year frequency (Fig. 6.7). There is also a quasi-5-year frequency existing in group F, where the heaviest precipitation is located (Fig. 6.5a). Because the long-term trend will contaminate the low frequencies, before the FT is applied, a linear fit is performed and subtracted from the data. The spectrum power of the 5-year undulating signal is comparable to that of a half-year period (Fig. 6.7a). A spectral analysis of the monthly SOI record of nearly 30 years

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Fig. 6.6 Yearly and monthly time series of different signals in group B and group F: a correlation of different factors in group B (P&K) and group F (eastern India). The inserted table represents the detailed correlations in group B; b inner-year variance of the CSR mascon result, precipitation and AOI in the P&K. Mass peak is delayed by three months; c inner-year variance of CSR mascon result, precipitation and AOI in eastern India. Mass peak is delayed by three months

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Fig. 6.7 Change features of different groups: a the frequency of group B and group F showing a strong 5-year undulating signal; b amplitude of three different periods in each group

shows the presence of significant peak at 4.7 years (Shrestha et al. 2000); therefore, it is clear that the signal of the 5-year undulating signal of glacial change in the P&K is controlled by both the ENSO and AO, the former playing a greater role. In group F, the monsoon affected by the ENSO brings tremendous rainfall. When a 5-year period curve fit is performed on the whole HMA, strong signals are found in three places: P&K, eastern India and western India (Fig. 6.5b). We conclude

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that glaciers in the P&K have a strong 5-year variance and a powerful annual change, which are two times greater than other glacial areas in the HMA (Fig. 6.7b). This finding is very interesting because the precipitation in P&K is almost one-sixth of that in eastern India, which is supplied by heavy Indian monsoon rainfall. One plausible explanation is that in the northern hemisphere, the consolidation of precipitation and moist air into ice occurs in winter, just overlapping the period when the westerlies monsoon brings strong rainfall in the P&K. The Landsat data also confer with this conclusion, in which Bolch et al. (2012) indicate that the glacial horizontal speed of Karakoram (max 350 m/yr, calculated based on the deduction of the Sept. 2000 number by that of Sept. 2001) is much larger than that of Bhutan (max. 100 m/yr, calculated by Jan. 2001 deducting Oct. 2002). Considering the great annual and interannual variance in the P&K, to explain the large mass balance difference in these areas, it is applicable to assess the glacier changes by adopting continuous observations such as GRACE and ICESat, rather than the snapshot method, as described in Gardelle et al. (2012). The trend estimated from limited observations is easily biased. We must state that 10 years is not long enough to ensure the duration of this 5-year undulating signal. However, this undulation is clear under present observations and helps us better understand the interannual variance. In addition, since the ENSO and AO are changing irregularly (with a cycle, generally 2–7 years for ENSO and dozens of years for AO) and their impacts on glaciers is not so clear, longer observations by GRACE may reveal more detailed, complex interannual variance.

6.5 Region C: The Tianshan 6.5.1 Introduction The spatial scope of Asian high mountains mainly includes the Tibetan Plateau and the Tianshan. The Tianshan has some distinct features and is worth studying specifically. Recently, there has been a study in the Tianshan using three methods: satellite gravimetry, laser altimetry and glaciological modeling (Farinotti et al. 2015). However, the mass change time series show great interannual variance, and the annual trend of glacier change even becomes positive around 2010 [refer to Figures in Farinotti et al. (2015)]. This suggests that there is a large interannual variation in the glacier changes in the Tianshan. However, we have shown that there is a 5year fluctuation in the Pamirs in an earlier work (Yi and Sun 2014), and the large interannual variation in the Tianshan might be leakage from the signal in the Pamirs. One of the purposes of this work is to determine the spatial range of the large interannual fluctuation and check whether it affects estimates for glaciers in the Tianshan. The Tianshan is mainly located in Xinjiang Province in western China. In the past decades, western China has been greatly developed as a result of its national poli-

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Fig. 6.8 The negative gravity trend in the Tianshan. The white areas represent the location of glaciers and the red dots represent the footprint of ICESat. The violet patches represent the location of lakes, and their names are annotated. The gray dashed curve marks the scope of lake area

cies. The geographical conditions in the Tianshan are diversified and are impacted jointly by climate change and anthropogenic activities. There are glaciers, snow, lakes and burgeoning residential and agricultural districts in the area. These factors are intricately associated, and a synthetic study will aid in the understanding of the influencing and evolving mechanisms. This work features a systematic and comprehensive study of precipitation, snow, lakes, glaciers and human activities in the Tianshan. Bosten Lake, a large lake located just at the foot of Tianshan and disturbed by intense anthropogenic activities, is specifically discussed (Fig. 6.8).

6.5.2 Method To correct for the leakage effect and recover the glacier signal, we adopt a spatial domain inversion (SADI) method. In the SADI method, we first need to define mass concentrations (also termed mascons) that represent the location and shape of signals. We optimize the mass changes in the mascons to best fit the GRACE observations, providing an estimate of the mass change in each mascon. A regularization factor α is needed in the application of the SADI method to reduce singularities in the inversion. The factor α is determined by the L-curve approach, which chooses an optimal trade-off between model complexity and data fit (Hansen and O’Leary 1993). Mascons that represent the location and shape of signals need to be defined to apply the method. There is an apparent negative gravity trend in the Tianshan region.

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We assume that this is mainly caused by melting glaciers. We define nine mascons according to the glacier distribution (Fig. 6.9a). The factor α is determined by the L-curve approach (Fig. 6.9b), and the blue star in the corner (1E-3.0) is chosen as the optimal factor based on this criterion. The observed signal by GRACE from CSR with 300-km Gaussian smoothing for the optimal is shown in Fig. 6.9c. The estimated mass change is shown in Fig. 6.9e, and its inferred GRACE signal is shown in Fig. 6.9d. The difference between observation and inversion is shown in Fig. 6.9f, which indicates that the negative signal is well fit, but the surrounding signal is nearly unaffected. The negative signal is concentrated in the nine mascons, so the strength significantly increases (the extreme value is amplified by about ten times).

Fig. 6.9 Presentation of results of from the inversion method used in this study: a There are nine mascons defined according to the glacier distributions (gray dots), and they are labeled with different colors; b the L-curve, which represents the relation between the model complexity and the fit to the data, with the variation in the regularization factor. The values annotated are the exponential item of each factor; c the gravity trend in the form of equivalent water height (EWH) observed by the GRACE project, with a Gaussian filter of 300 km; d the gravity trend from the inversion model; e the recovered mass change by the inversion method. Note the larger color scale; f post-fit residuals between the observation and inversion

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111

6.5.3 Results The solutions from CSR and the G300 smoothing method are chosen here, and the result is shown in Fig. 6.10. By the SADI method, we can obtain the time series of the nine mascons. After summing up the time series of all the mascons, we obtain the total mass change (Fig. 6.10a). It is evident that the interannual variations are large in this region, e.g., there is a rapid jump from 2009 to 2010 as marked by the dashed ellipses. A similar jump could also be found in a recent work by Farinotti et al. (2015). The secular trend based on our result is −6.34 ± 0.65 Gt/yr. However, the large variations mean that the trend estimate is sensitive to the time window chosen, and even an increasing trend is possible if a different time period is chosen. The trend from 2003 to 2014 could possibly be biased by variations over a long period ranging from several years (as we can see in the existing observations) to decades (likely to exist but has not confirmed by data). The time series of each mascon is checked to investigate whether this fluctuation is widespread or limited in spatial range (Fig. 6.10b). The jump only exists in three mascons (5, 6 and 9). Mascon 9 has the largest interannual variation and is much different from the others. It is influenced by the glacier change in the Pamirs, which displayed a strong 5-year fluctuation during 2003–2012. The three mascons are located in the western or northern edge of the Tianshan region (Fig. 6.9a). Therefore, the central part of Tianshan is less influenced by the interannual fluctuations. The majority of the glacier retreat is located there. The interannual variation might be caused by the change in the other signal sources (such as soil moisture and lakes) rather than the glaciers, and we will try to confirm this conjecture later. If we sum up the other mascons that have no jump in 2010 (marked with stars in Fig. 6.10c), it is found that the linearity of the time series is much improved, and the trend is −5.43 ± 0.36 Gt/yr. Therefore, in the central Tianshan region, the mass is decreasing more steadily than previously recognized, and the large fluctuations only come from the peripheral regions.

6.5.3.1

Result by GRACE

The time series in Fig. 6.10c is the combined effect of all signal sources including glaciers, soil moisture and the Bosten Lake (the other lakes are out of this region). The soil moisture is estimated by four GLDAS land water models, and the change in the Bosten Lake level is derived from altimetry observations. To avoid a potential bias in a specific GRACE dataset or the smoothing method, we adopted solutions from three organizations and three smoothing methods, providing a total of nine combinations. After the contributions from soil moisture and the Bosten Lake are corrected, the change in glaciers based on the mean of the nine datasets is shown in Fig. 6.11a (excluding mascons 5, 6 and 9). The change in glaciers is steady without the jump in 2010. The trends of the glaciers from all combinations are shown in Fig. 6.11b, and their mean value is adopted as the final estimation, which is −4.0 ± 0.7 Gt/yr. The

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Fig. 6.10 a Time series of the total mass of all mascons. The dashed ellipse indicates a large jump from 2009 to 2010; b time series of the mass of each mascon with their numbers on the left side. The jumps from 2009 to 2010 are also marked by dashed ellipses. The other series without such jumps are marked by a star on the right side, and their sum is presented in c. The linearity of the time series is greatly improved in c

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Fig. 6.11 a Time series of the glacier mass with influences from soil moisture and lake water corrected. The values and uncertainties are based on the nine datasets shown in the bottom plot; b trends of glacier mass from nine datasets (blue) and their mean (red). “CSR_G300+P4M6” means the solution comes from CSR and the smoothing method is a combination of the Gaussian smoothing in 300 km and the decorrelation filter of P4M6

error bars are estimated based on the post-fit residuals, under the assumption that there is no systematic error in the GRACE solutions. This trend is smaller in absolute value than the previous estimate of −6.6 ± 2.0 Gt/yr (one standard deviation) (Farinotti et al. 2015). The main reason is the uncorrected contributions (e.g., from the soil moisture or the snow coverage) that cause the large fluctuations. The end of Farinotti and coworkers’ study period is a trough year, so all the components are varying more intensely than their normal trends. As a result, the uncertainty in each data will be amplified. A large improvement in our estimation is that the large interannual fluctuation is effectively eliminated, so the mass reduction trend of glaciers is better determined. Another reason is that our study region is a little smaller than used by Farinotti, but that will only cause a small difference because the negative gravity trend is mostly located in our study area, and the contribution from the regions we exclude is minute.

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Result by ICESat

The estimation based on ICESat is shown in Fig. 6.12. Since we have excluded the western part of the Tianshan region (Mascon 9), we treat it here separately from the eastern part. Footprints in the northern part (Mascons 5 and 6) are too sparse to give a reliable estimation, so they are omitted as well. There are no more than three observation periods (winter, summer and fall) in each year, so the influence of the annual variation is hard to correct. For this reason, the trends are fitted separately in winter and fall (the summer observations are ignored as there are only three samples). The glacier elevation in the western part has larger fluctuations and a smaller trend than in the eastern part, which is consistent with the GRACE results in the previous section. This confirms that it is reasonable for us to exclude the western part. The changing trend of elevation in the western part is −0.02 ± 0.14 m/yr in fall or −0.12 ± 0.11 m/yr in winter, which corresponds to a mass change of –0.04 ± 0.28 or −0.24 ± 0.22 Gt/yr. The changing trend of elevation in the eastern part is −0.44 m/yr in both fall and winter (the uncertainties are 0.08 and 0.06 m/year, respectively), which corresponds to a mass change of −3.4 ± 0.8 Gt/yr (hereafter we conservatively take the larger one). The counts for each footprint are displayed in the bottom plots in Fig. 6.12. Our trend of −3.4 ± 0.8 Gt/year is quite different from the previous estimation of −5.4 ± 1.5 Gt/yr (one standard deviation) by Farinotti et al. (2015). The large difference partly comes from the total area of glaciers: the eastern part has an area of ~8500 km2 and the western part has an area of ~2500 km2 , making ~11,000 km2 in total, while Farinotti et al. (2015) studied an area of about 13,700 km2 , 20% larger. Even if our trend is amplified by 20% (−4.1 Gt/yr), it still would be only three-fourths of that of Farinotti et al. (2015) (−5.4 Gt/yr). It is worth noting that our footprint count is roughly twice as large as that used by Farinotti et al. (e.g., in winter of 2003, our count is about 3000, while theirs is about 1500). This might be caused by a more restrictive filtering strategy on the original data in their method. To sum up, with a narrower study area, albeit twofold more samples, we obtain a smaller glacier trend of −3.4 ± 0.8 Gt/yr compared with −5.4 ± 2.9 Gt/yr by Farinotti et al. (2015).

6.5.3.3

Snow Coverage

The annual and seasonal mean of snow coverage from 2000 to 2015 by MODIS is shown in Fig. 6.13. There is a clear annual variation that varies from the highest coverage ratio in winter to the lowest in summer over the entire region. The snow coverage has several features. First, the higher the latitude, the greater the amount of snow preserved in the warmer time period, and in summer, only a small quantity is retained on the mountaintops. Secondly, the snow coverage is obviously greater in the western and northern sides of the mountains, which is the windward side against the westerlies. Thirdly, it is clear that the snow coverage ratio is much higher on the northern side than on the southern side of Tianshan, i.e., there is hardly any snow covering over the entire Tarim basin throughout the year, while vast areas on the

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Fig. 6.12 Time series of glacier elevation change by ICESat in a the western Tianshan and b the eastern Tianshan. The trends are fitted in different seasons to reduce the influence from annual variation. The series on land provide references that are not expected to change with time. The footprint count in each sample is shown in the bottom plots

northern side of Tianshan have plentiful snowfall in winter. This clearly outlines the influence zone of the westerlies. The monthly variations in the mountain region and the lake area are specially presented in Fig. 6. The mountain region has a more moderate annual variation compared with the lake area. Moreover, the peak month in the mountain region is one month later (i.e., February, compared with January in the lake area). The time series of snow coverage in the Tianshan (only the mountain region is included) is shown in Fig. 6.14. The pattern is dominated by strong annual and interannual variation with an inconspicuous secular trend. There are peak months in 2002 and 2011 and trough months in 2007 and 2013. It is worth noting that MODIS only provides the area change; without the change in thickness, we cannot estimate the mass contribution. Assuming the snow has a density of 0.1 g/cm3 and the height change is 10 cm, then a variation of 1 × 105 km2 will cause a mass change of 1 Gt.

6.5.4 Discussion 6.5.4.1

A Rapid Transition from a Dry Year (2009) to a Wet Year (2010)

Changes in lake level, precipitation, snow coverage and the total mass of the lake area are shown in Fig. 6.15. Two sets of dry and wet years are identified. Since different physical phenomena have different response speeds, the dry and wet years are

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Fig. 6.13 Annual and seasonal mean of snow coverage in percentage by MODIS in the Tianshan area and the lake areas (the dashed curves). Spring is from November to January and so forth

shifted/shrunk in different observations. It seems that the AOI is inversely correlated with other phenomena, i.e., a negative AOI corresponds to a mass surplus. Therefore, in wet years, the AOI is negative and vice versa. The AOI, which indicates the variation in the westerlies (Thompson and Wallace 1998), is the earliest to show the start of the dry and wet years. The changes in precipitation and snowfall follow this trend and bring the change to the total mass half a year later. The alternation of dry and wet years is also captured by the change in the lakes. There is a synchronous lake level increase in the start of 2010 in all lakes, but some lakes rise 1 year earlier (e.g., Issykkul and Kapchagayskoye, both of which are located in the western position), implying a faster response to the change in the westerlies.

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Fig. 6.14 Annual and monthly anomalies in snow coverage in the Tianshan. The average snow coverage over the whole period is deducted

After checking the AOI records back to 1950, it turns out that its value at the start of 2010 is the strongest in the last 65 years. The evolution of dry and wet years in these five datasets indicates that the westerlies are the cause and they affect the precipitation and snowfall; thus, the lake level and the total mass are subsequently influenced. The difference in total mass between 2009 and 2010 was calculated to investigate the spatial range of the jump in 2010 (Fig. 6.16). The results from the nine datasets are shown, and they share a high resemblance. Figure 6.16 also shows that the result is more influenced by the smoothing method than by the solution source. The method of G300+P4M6 is weaker than G300 because of the implementation of the extra decorrelation P4M6. DDK4 has the largest strength, which is likely due to the fact that the non-isostropic filter is more effective in preserving signals in the lower degrees than the Gaussian filter. The spatial range of the anomaly in 2010 coincides with the influence zone of the westerlies: It starts from the Pamir Plateau, spans northward along the Tianshan ridge and exactly covers the lake areas outlined in this study. From Figs. 6.15e and 6.16, it is shown that the average jump in the whole lake area is about 7 cm and that the peak value is over 10 cm. It is interesting that the zone only covers the northern side of Tianshan, and the central region of Tianshan is less influenced. It is likely that the high mountain edges block the intrusion of the westerlies and constrain their impact mainly to the northern lower altitudes. If so, the central region of Tianshan is actually protected from the influence of the westerlies. However, the Pamir Plateau, the area in the forward position that blocks the westerlies, is overwhelmed by the westerlies despite its high altitude. The annual differences in precipitation and snowfall are also examined. Rainfall and snowpack are the main water supplies in our study region and are expected to be

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Fig. 6.15 a Time series of lake levels; b arctic oscillation index (AOI); c precipitation; d snow coverage; and e total mass in the lake area. The yellow patches represent dry seasons and the green represent wet seasons. In a, the lake levels are amplified to a comparable scale, and each scaling is shown in the bracket after its name. One-year smoothing means using a 1-year running window to smooth the monthly data. The 1-year smoothed series in b are amplified three times for a better presentation

quite sensitive to the AOI. The precipitation increased in two steps from 2008 to 2010 (Fig. 6.15c), so the difference between 2008 and 2010 is shown here (Fig. 6.17a). An advance of 1 year is reasonable because it will take time for the change in precipitation to affect the mass change. We have separately checked the difference between 2009 and 2010 as well as between 2008 and 2009, and the results show that the anomaly zone was first located in the Pamir Plateau during 2008–2009 and is then shifted subsequently to the lake area during 2009–2010 (not shown here). This dynamic change is consistent with the blowing direction of the westerlies. The precipitation anomaly zone is identical to the anomaly zone in the total mass (Fig. 6.16). The annual precipitation in this region is about 1000 mm, and the annual anomalies are generally less than 50 mm (Fig. 6.15c). However, the jump from 2008 to 2010 can reach 400 mm, so this is a major event in the climatic change in this region.

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Fig. 6.16 Difference in total mass between 2009 and 2010 by nine GRACE datasets. The scope of lake area is indicated by the dashed curve

Fig. 6.17 a The difference in precipitation amount between 2008 and 2010; and b the difference in snow coverage between 2009 and 2010. The scope of the lake area is indicated by the dashed curve

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The annual difference in snow coverage between 2009 and 2010 is shown in Fig. 6.17b. The anomaly zone is also located in the lake area. The high altitudes of the Tianshan as well as the Pamir Plateau are less impacted by this snow anomaly. One possible reason is that the snow coverage ratio is already very high in the high altitudes, so further increases are limited. Compared with the anomaly zone of the total mass, the precipitation anomaly has a higher similarity than the snow in the spatial pattern, which implies that precipitation is a primary impact factor.

6.5.4.2

Water Level Change in Bosten Lake Over 60 Years

Bosten Lake, the largest freshwater lake in Xinjiang, is located at the foot of Tianshan. Bosten Lake is the end of the Kaidu River and is also the source of the Konqi River. Recharge from the Kaidu River accounts for 84.7% of the influx to the Bosten Lake (Sun et al. 2006b). Unlike the other lakes in the lake area, Bosten Lake involves intensive human activities, so it is a good example to show the combined influence of climate change and anthropogenic activities. Water level records of the Bosten Lake from three data sources are shown in Fig. 6.18. The change in Bosten Lake level since 1955 can be separated into four stages: an accelerated drop of a total of 3.5 m from 1955 to 1985, a steady uplift of 4.5 m from 1986 to 2001, a rapid drop of 4.5 m from 2002 to 2010 and a fluctuation of 0.5 m around the mean level of 1045.5 m. The first stage is a result of decreasing runoff in Kaidu River along with increasing water consumption, and the condition was greatly exacerbated during 1976–1985 (Li et al. 2003). In the second stage, the exploitation of water resources was strictly curbed, and the contributions from precipitation and meltwater increased over time. At the end of the second stage, the runoff in Kaidu River was about 50% larger than its long-term average, and the water level in the Bosten Lake reached the highest on record with an area of 1646 km2 . The third stage coincides with the period of the GRACE mission, which has produced a declining trend of −0.48 ± 0.02 Gt/yr during 2003–2010, which cannot be neglected in the estimated glacier trend of −4.0 Gt/yr. The lake level reached the low water level of 1045 m in 1986 and has shown fluctuation ranging from 1045 to 1046 m ever since. Qiu et al. (2013) checked the relationship between the change in runoff at the Dashankou station in the upper reach of the Kaidu River (protected from anthropogenic activities) and records of precipitation and temperature. Their work shows that the change in runoff has a closer relationship with change in temperature (0.55) than with precipitation (0.34). A warmer and wetter period during 1990–2002 was obviously responsible for the increased runoff in the Kaidu River. Afterward, the precipitation went back to normal, but the temperature continued to rise. A consequent seriously retreating snowline has been observed, and it has been declared to be the main reason for the fast reducing runoff in the Kaidu River, which has been further decreased by the emerging hydropower stations upstream, according to a local report (http://news.ts.cn/content/2014-04/14/content_9549017_all.htm). The report also pointed out that another problem is the over-exploitation of water resources, including mining, industry development, the expansion of farm land and well dig-

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Fig. 6.18 Change of the lake level in Bosten Lake over the last 60 years. The time series reference three data sources, Shi et al. (2006), LEGOS and USDA. The declining trend from 2003 to 2010 is fitted in the black dashed line, whose trend is also annotated. The explanations (light red background) and information (light green background) of the change in series are annotated. The environment of the Bosten Lake and three large rivers is shown in the inset

ging. From 1949 to 2012, the population in the basin has increased threefold, and the cultivated land has increased fivefold (Wang et al. 2012). Bosten Lake is a good example that shows how glacier melting will impact the local environment and economy. There is a benefit in the short run because of the extra water supply from melting snow and glaciers. This may create a false impression that the environment is improving and its supportive capacity is increasing. As a result, the relevant policies may be implemented more flexibly and the water consumption will rise. There is always a time lag in the response to adaptation. Once the extra supplement passes the peak and begins decreasing again, the increased water usage will seriously harm the local water resource. In the example of Bosten Lake, it only took 8 years for the lake level to go from the best on record to the worst on record.

6.6 Region D: The Eastern Tibet 6.6.1 Introduction Modern geodesy is particularly sensitive to the present-day geodynamic change of the plateau. By virtue of GPS and absolute gravimeter measurements over 10 years at three stations, Sun et al. (2009) first attempted to estimate the dynamic change of the Moho interface beneath southern Tibet. The depth change of the Moho interface is well constrained by gravity observations because the Moho has the largest density contrast within the lithosphere. However, precise measurements of gravity change are

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available only in three spots, Lhasa, Kunming and Dali (green squares in Fig. 6.19). Whether their conclusions are applicable to the vast interior plateau areas needs further validation. As a follow-up work, this study adopts the same principle as Sun et al. (2009) using the secular trend from 11-years of GRACE gravity observations along with GPS data to estimate the rate of crustal thickening or thinning over the eastern Tibetan Plateau. Abutting the stable Sichuan Basin to the east, the steep Longmenshan mountain range is formed along that edge, but the topography gradually decreases outward to the north and south. Geological and geodetic observations show that there is little young crustal shortening along most parts of the eastern margin of the plateau (Royden et al. 1997), which implies that the uplift within eastern Tibet is likely caused by interior material, rather than crustal shortening. There are two popular models could explain this feature: the crustal flow model and the convective lithospheric detachment model. We choose a region of 5° by 5° (98°E–103°E, 30°N–35°N) in eastern Tibet as our study area (blue dashed box in Fig. 6.19) and extend it downward

Fig. 6.19 Secular trend of gravity change (colored background) by GRACE and GPS velocities both in the vertical and horizontal directions (red and blue arrows) in the Tibetan Plateau. Glaciers on the Himalaya are marked as white dots and lakes on the Tibetan Plateau are marked as light blue patches. Three green squares are the stations with long-term gravimeter in Sun et al. (2009). Main faults are annotated as dashed curves. Abbreviations: ATF (Altyn Tagh Fault), KF (Kunlun Fault), JRS (Jisha River Suture), BNS (Bangong-Nujiang Suture), YZS (Yarlung-Zangbo Suture), MBT (Main Himalaya Thrust), XSHF (Xianshuihe Fault), LMSF (Longmenshan Fault), RRF (Red River Fault), XJF (Xiaojiang Fault) and NTM (Nyenchen Tonglha Mountains). Blue dashed box is the mainly studied region in this work and black dotted box annotates the range in Fig. 6.22. The ellipse/bar along with the horizontal/vertical GPS velocity represents the 1 standard deviation

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through the whole crust (the depth is set to 60 km), so the research region is a rectangular solid fixed in space [a Lagrangian specification (Batchelor 2000)]. We build a three-layer crustal model, in which the middle and lower crust (MLC) is weak and able to move faster than the upper crust.

6.6.2 Method 6.6.2.1

Hypothesis of Volume Conservation

A model using the analogy of a sink is presented to show how we can estimate the interior dynamics based on surface movement and gravity change. For a sink with a fixed bottom and an inlet tube (Fig. 6.20a), it is easy to tell how fast water is flowing in through the tube according to the rate of increase in height of water in the sink. A hypothesis made here is that density does not change, so that mass conservation and volume conservation are equivalent. Within the crust, temporal changes in the density are mainly influenced by two factors: pressure and temperature. After millions of years of development, the whole crust is assumed to be in a quasi-equilibrium condition: current tectonic adjustment is in the order of millimeters per year and the heat flow flux is moderate. Therefore, the variation of pressure or temperature is not strong enough to cause significant density changes over short times. We use a more complex model to describe the eastern boundary of the Tibetan Plateau (Fig. 6.20b). This model has four inlets or outlets, representing the influx of

Fig. 6.20 Cartoons to show how the deep flowing rate can be estimated from the surface observation. Left, the volume of the sink is fixed so the height of the material rises proportionally to the flux of material flowing in, so only GPS uplift rate data would be enough to solve the problem. Right, the model is a bit more complex that the bottom of the sink to the Moho interface)  (corresponding   is movable and two sources (V0 and V1 ) and two sinks ( V0 and V1 ) are connected. In this case the secular gravity trend δg is introduced to determine this extra variable, so still we can estimate the influx rate with the combination of GPS and gravity data

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  material in the upper crust (V0 ), the outflux of material in the upper crust V0 , the  influx of material in the MLC (V1 ), and the outflux of material in the MLC V1 . The “sink” itself represents the eastern part of the plateau. We separate the crust into two parts: The deformation of the upper crust involves block extrusion and collision, although here we approximate it as continuous deformation (Zhang et al. 2004), while the lower crust is weak and flowing faster than the  (Royden et al. 1997).  upper crust We can constrain the fluxes for the upper crust V0 and V0 using the surface GPS horizontal observations, assuming that deformation uniform with depth within the  is   upper crust. The fluxes within the MLC V1 and V1 are the focus of this study, and there  is a trade-off between them, i.e., a larger V1 could be counteracted by a larger V1 . For simplicity, we assume   that the outflow rate in the MLC is not faster than in the upper crust (speeds of V0 and V1 are identical), which amounts to an assumption that the crust is not thickening beneath the Sichuan Basin except perhaps by overall compression. Second, the bottom of the sink, which represents the Moho interface, is not fixed (Fig. 6.20b). With the accumulation of mass in the crust, both the surface and the Moho may change in response. The variation of Moho is caused by two effects: volume change caused by crust compression and isostatic adjustment caused by extra mass influx. As the Moho has a large density difference across it, its dynamics will cause a gravity change. Sun et al. (2009) combined surface vertical movement measured by GPS and gravity change measured by absolute gravimeters to determine the change of the Moho. Their result showed that the Moho is descending at a rate of about 2 cm/yr. The similar principle is adopted here, but in this study, we use the satellite gravity observations across the whole region (rather than three spots), and the free air correction is not needed as it would be for surface measurements. However, we must account for and remove gravity changes due to changes in surface hydrologic loads. To sum up, the Moho status is constrained by the gravity observation, and the MLC velocity in the north, east and south side is also inherited from the surface observation, so the western side flow-in velocity V1 is the only unknown. We express the horizontal velocity in the MLC in terms of its ratio with the surface horizontal velocity V 0 (which has an average value of 18 mm/yr), so it is expressed as multiples of V 0 .

6.6.2.2

GRACE Gravity Observation

We adopt the monthly Release 05 solutions over 2003–2014 from three groups: Center for Space Research (CSR) in University of Texas, GeoForschungsZentrum (GFZ) in Potsdam and Jet Propulsion Laboratory (JPL). In the middle of Tibet, there are thousands of lakes (light blue patches in Fig. 6.19), and the general rising lake levels have an effect on the gravity observation (Zhang et al. 2013; Yi et al. 2016). In the western and southern margins of the plateau, glaciers are melting rapidly (white dots) which causes a loss of mass and gravity reduction (Matsuo and Heki 2010; Yi and Sun 2014). Although our study area does not include these signal sources,

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the GRACE estimates can be affected by signal leakage from the nearby drastic glacier melting signal in the Nyenchen Tonglha Mountains. We adopt the spatial domain inversion method to separate these signals, which reduces the leakage error and recovers the original strength of signal from the smoothed GRACE estimate. Two mascons are defined here to separate the signals of tectonic processes, which are homogeneous over the whole region, from the glacier melt, which is concentrated in the glacier location. Therefore, there are only two unknowns and the solution is simple. Four GLDAS land water models (NOAH, CLM, MOS, VIC) are considered here to account for the soil moisture contribution to uplift and gravity change in our study area.

6.6.2.3

GPS Three-Dimensional Movements

The GPS velocities in the horizontal and vertical directions are taken from the recent solution of Liang et al. (2013). The measurements are from 745 GPS stations (with 158 continuous stations and 587 campaign-mode stations) on/around the Tibet since 1999. The observations generally over 10 years provide a set of reliable velocities in both the horizontal and vertical directions (Liang et al. 2013). Because the GPS stations are irregularly distributed, the Kriging interpolation method is used to derive regular gridded values in our study area (outlined in Fig. 6.19). Kriging is especially good for clustered or unevenly distributed data (Bohling 2005). Unlike the poor GPS station coverage in western Tibet, eastern Tibet has a dense distribution of GPS stations, and both their horizontal and vertical observations show good consistency, which guarantees a reliable interpolation. We use the Monte Carlo method (Fishman 2013) to propagate the uncertainty of the GPS observations into our interpolation values. The same techniques are also used and well presented in another research in the Tibet by Zhu and Shi (2011).

6.6.2.4

Crust Density Structure Model

To derive the gravity change caused by crustal movements, a crustal density model is essential. The thickness of the whole crust in the eastern Tibet is assumed to be 60 km, which is divided into the upper (20 km, 2.67 g/cm3 ), middle (15 km, 2.75 g/cm3 ) and lower (25 km, 2.9 g/cm3 ) crust (Fig. 6.21). The mantle is set with a density of 3.3 g/cm3 . The Sichuan Basin is located east of the eastern Tibetan Plateau and has a thinner crust of 40 km. These two structures are separated by the Longmenshan Fault (LMSF). This model is based on previous seismology and gravity studies (Wang et al. 2007; Jiménez-Munt et al. 2008), and we only consider a three-layered structure. Transverse inhomogeneity or local disparity is neglected. The gravity change caused by the thickness variation of a group of Bouguer layers is (Heiskanen and Moritz 1967):

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Fig. 6.21 Schematic diagram of the crustal density model. The crust is assumed to be divided into three layers with differing thickness in the Tibetan Plateau and the Sichuan Basin. LMSF: Longmenshan Fault

δg = 2π



ρi h i

i

in which G is the gravitation constant; ρi is the density of a layer, which would be one of three crustal layers or one mantle layer here; and h i is the thickness change of a layer.

6.6.3 Results By the spatial domain inversion method, we try to restore the unsmoothed signals from the smoothed GRACE solutions (Fig. 6.22a). We define two mascons to separate the two different kinds of signals in Fig. 6.22a, in which the group of black boxes represents the tectonic process and the group of red boxes represents the glaciers. The prediction of the best fit model is shown in Fig. 6.22b based on the method introduced in Yi and Sun (2014). The post-fit residuals are shown in Fig. 6.22c, and the largest errors are mainly due to boundary effects (i.e., signals outside our study area). The inversion result is shown in Fig. 6.22d and the predicted gravity changes for each source are separated into the signals of tectonic process (Fig. 6.22e) and glacier melting (Fig. 6.22f). Due to the leakage effect, these two signals overlap each other somewhat so the peak positions are shifted away and their strengths are weakened. After extracting the influence of glacier melting, there is an obvious mass accumulation in the eastern Tibet.

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Fig. 6.22 Demonstrations for the inversion of GRACE secular trend. a Two mascons are defined here: the group of black boxes represents the tectonic process and the group of red boxes represents the glaciers. The inversion result is shown in d and its smoothed signal is shown in b. The fitting residuals (observations minus model predictions) are shown in c. The smoothed signal from tectonic process/glacier is shown in e/f. The whole range is outlined as black dotted box in Fig. 1, and the blue dashed box is the mainly studied area

To reduce potential bias coming from any one particular GRACE solution, we calculate the solutions from three different analysis centers: CSR, GFZ and JPL. We also add/replace the low degree terms to check their influence on the solution (it is quite small). Totally, there are six results shown in Fig. 6.23, in which ‘+n1_n2’ means the low degree terms are specially treated; details can be found in the figure annotation. All results are very consistent, and their mean value is 0.34 μGal/yr, presented as the dashed line in Fig. 6.23, with a standard deviation of only 0.02 μGal/yr, much smaller than the smallest uncertainty for any solution. Because these are not independent solutions, we adopt the smallest uncertainty as the uncertainty for the mean (0.05 μGal/yr). For the soil moisture contribution, we find the long term trend is insignificant but with a large uncertainty (0.00 ± 0.06 μGal/yr). We also consider the mass change in Qinghai Lake, the largest lake in this region. The level of Qinghai Lake rose by 0.11 m/yr over 2003–2009 by ICESat measurements (Zhang et al. 2013), equivalent to

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Fig. 6.23 Averaged gravity trends for tectonic processes in the study area inversed from different data sources. Solutions from CSR, GFZ and JPL are adopted. CSR + n1_n2 means in the CSR solution degree-1 coefficients (geocenter) are added back and all degree-2 coefficients are replaced by SLR observations. This process of degree-1 and degree-2 will generally make the trend estimation 0.01–0.02 μGal/yr smaller. Their mean value is taken as the final estimation (in red). The error ranges are 1 standard deviation and span from 0.05 to 0.11 μGal/yr. The final uncertainty is set to 0.05, based on the smallest standard deviation of the input solutions

0.02 μGal/yr if this contribution is averaged on the whole region. The other potential contributors, like groundwater, permafrost and others, are considered to be small and ignored. Therefore, the final estimation of gravity change from tectonic process is 0.32 ± 0.08 μGal/yr, which will put a constraint on how the crust is thickening and the Moho is deepening. We interpolate GPS velocities to a set of regular grid points, as shown in Fig. 6.24. We used a 6 × 6 grid of nodes with a spacing of 1° (blue box) and interpolate the velocities to these grid nodes. The interpolation uncertainty is also estimated by the Monte Carlo method and is presented together with the interpolated values. For the horizontal movement (Fig. 6.24a), there is a continuous variation in both the direction and rate of displacement, and the interpolation values appear to be consistent with their surrounding background velocities. Of the four borders of the grid, only the west side has material flowing into the volume; the other three sides all have material flowing out, mainly to the east. The vertical velocities (Fig. 6.24b) have some local variations with a general uplift signal, which may be due to noise and smaller-scale tectonic movements. The volume change (material flux) within the box due to horizontal movement  is i Si Vi ei , where S i is the area of each grid boundary, equal to the product of the length and depth for side faces; V i is the interpolated horizontal velocity; and ei is the normal direction of each grid section. For vertical movements, we use a single average surface uplift rate and Moho depth change rate, and multiply this by the entire grid area. The precision of the vertical velocity is much worse than the precision of the horizontal components. The error in vertical direction could be

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Fig. 6.24 Observation (black arrows) and interpolation (red arrows) results of horizontal velocity (left panel) and vertical velocity (right panel). Blue box is the mainly studied area

2–3 mm/yr for each station, at the same level of current vertical movement. However, because we only focus on the average uplift rate and there are dozens of stations in this region sharing the similar trend, the error in the average vertical rate will be greatly reduced except for any correlated error among the GPS stations. The final estimation of average uplift rate is 2.7 ± 0.3 mm/yr. A cross-section plot of our study area is shown in Fig. 6.25. As discussed above, the crust is divided into a brittle upper crust and a ductile middle–lower crust (MLC). The net volume change by horizontal movement in the upper crust is 0.005 ± 0.006 km3 /yr, determined by summation of the volume contribution in the four side faces. The surface uplift causes a volume increase of 0.70 ± 0.08 km3 /yr (with an average uplift rate 2.7 ± 0.3 mm/yr), which is two orders of magnitude larger than predicted by the horizontal shortening. This implies that the upper crustal shortening makes no contribution to the surface uplift. Instead, the uplift may be attributed to an excess of material from either the MLC or mantle (i.e., movement of the Moho). The mean gravity change is 0.32 ± 0.08 μGal/yr. Based on this gravity variation range and the uncertainty in ground GPS velocities, we use the Monte Carlo method to evaluate the uncertainty range of the Moho and MLC movement (Table 6.3). Using no constraints other than the gravity and GPS observations, the Moho change and MLC motion are 0.0 ± 4.7 mm/yr (all the uncertainty ranges are for 68.3% confidence, positive means uplift) and (2.7 ± 3.1) × V 0 (>V 0 means the MLC is moving faster than the upper crust,