Modern Water Resources Engineering

Handbook of Environmental Engineering 15

Modern Water

Resources

Engineering

Lawrence K. Wang

Chih Ted Yang Editors

Modern Water Resources Engineering

For further volumes:

http://www.springer.com/series/7645

VOLUME 15

HANDBOOK OF ENVIRONMENTAL ENGINEERING

Modern Water

Resources Engineering

Edited by

Lawrence K. Wang, Ph.D., P.E., D.EE

Ex-Dean & Director

Zorex Corporation, Newtonville, New York, USA

Lenox Institute of Water Technology, Newtonville, NY, USA

Krofta Engineering Corporation, Lenox, Massachusetts, USA

Chih Ted Yang, Ph.D., P.E., D.WRE

Borland Professor of Water Resources

Department of Civil and Environmental Engineering

Colorado State University, Fort Collins, Colorado, USA

Editors

Lawrence K. Wang, Ph.D., P.E., D.EE

Ex-Dean & Director

Zorex Corporation, Newtonville, New York, USA

Lenox Institute of Water Technology, Newtonville, NY, USA

Krofta Engineering Corporation, Lenox, Massachusetts, USA

[email protected]

Chih Ted Yang, Ph.D., P.E., D.WRE

Borland Professor of Water Resources

Department of Civil and Environmental Engineering

Colorado State University, Fort Collins, Colorado, USA

[email protected]

[email protected]

ISBN 978-1-62703-594-1 ISBN 978-1-62703-595-8 (eBook)

DOI 10.1007/978-1-62703-595-8

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Preface

The past 35 years have seen the emergence of a growing desire worldwide that positive

actions be taken to restore and protect the environment from the degrading effects of all forms

of pollution—air, water, soil, thermal, radioactive, and noise. Since pollution is a direct or

indirect consequence of waste, the seemingly idealistic demand for “zero discharge” can be

construed as an unrealistic demand for zero waste. However, as long as waste continues to

exist, we can only attempt to abate the subsequent pollution by converting it to a less noxious

form. Three major questions usually arise when a particular type of pollution has been

identified: (1) How serious are the environmental pollution and water resources crisis?

(2) Is the technology to abate them available? and (3) Do the costs of abatement justify the

degree of abatement achieved for environmental protection and water conservation? This

book is one of the volumes of the Handbook of Environmental Engineering series. The

principal intention of this series is to help readers formulate answers to the above three

questions.

The traditional approach of applying tried-and-true solutions to specific environmental and

water resources problems has been a major contributing factor to the success of environmental

engineering, and has accounted in large measure for the establishment of a “methodology of

pollution control.” However, the realization of the ever-increasing complexity and interre￾lated nature of current environmental problems renders it imperative that intelligent planning

of pollution abatement systems be undertaken. Prerequisite to such planning is an under￾standing of the performance, potential, and limitations of the various methods of environ￾mental protection available for environmental scientists and engineers. In this series of

handbooks, we will review at a tutorial level a broad spectrum of engineering systems

(processes, operations, and methods) currently being utilized, or of potential utility, for

pollution abatement. We believe that the unified interdisciplinary approach presented in

these handbooks is a logical step in the evolution of environmental engineering.

Treatment of the various engineering systems presented will show how an engineering

formulation of the subject flows naturally from the fundamental principles and theories of

chemistry, microbiology, physics, and mathematics. This emphasis on fundamental science

recognizes that engineering practice has in recent years become more firmly based on

scientific principles rather than on its earlier dependency on empirical accumulation of

facts. It is not intended, though, to neglect empiricism where such data lead quickly to the

most economic design; certain engineering systems are not readily amenable to fundamental

scientific analysis, and in these instances we have resorted to less science in favor of more art

and empiricism.

Since an environmental engineer must understand science within the context of applications,

we first present the development of the scientific basis of a particular subject, followed by

exposition of the pertinent design concepts and operations, and detailed explanations of their

applications to environmental conservation or protection. Throughout the series, methods of

system analysis, practical design, and calculation are illustrated by numerical examples.

v

These examples clearly demonstrate how organized, analytical reasoning leads to the most

direct and clear solutions. Wherever possible, pertinent cost data have been provided.

Our treatment of environmental engineering is offered in the belief that the trained engineer

should more firmly understand fundamental principles, be more aware of the similarities

and/or differences among many of the engineering systems, and exhibit greater flexibility

and originality in the definition and innovative solution of environmental system problems.

In short, an environmental engineer should by conviction and practice be more readily

adaptable to change and progress.

Coverage of the unusually broad field of environmental engineering has demanded an

expertise that could be provided only through multiple authorships. Each author (or group of

authors) was permitted to employ, within reasonable limits, the customary personal style in

organizing and presenting a particular subject area; consequently, it has been difficult to treat

all subject materials in a homogeneous manner. Moreover, owing to limitations of space,

some of the authors’ favored topics could not be treated in great detail, and many less

important topics had to be merely mentioned or commented on briefly. All authors have

provided an excellent list of references at the end of each chapter for the benefit of the

interested readers. As each chapter is meant to be self-contained, some mild repetition among

the various texts was unavoidable. In each case, all omissions or repetitions are the respon￾sibility of the editors and not the individual authors. With the current trend toward metrica￾tion, the question of using a consistent system of units has been a problem. Wherever possible,

the authors have used the British system (fps) along with the metric equivalent (mks, cgs, or

SIU) or vice versa. The editors sincerely hope that this redundancy of units’ usage will prove

to be useful rather than being disruptive to the readers.

The goals of the Handbook of Environmental Engineering series are: (1) to cover entire

environmental fields, including air and noise pollution control, solid waste processing and

resource recovery, physicochemical treatment processes, biological treatment processes,

biotechnology, biosolids management, flotation technology, membrane technology, desalina￾tion technology, water resources, natural control processes, radioactive waste disposal,

hazardous waste management, and thermal pollution control; and (2) to employ a multimedia

approach to environmental conservation and protection since air, water, soil, and energy are

all interrelated.

This book is Vol. 15 of the Handbook of Environmental Engineering series, which has been

designed to serve as a water resources engineering reference book as well as a supplemental

textbook. We hope and expect it will prove of equal high value to advanced undergraduate

and graduate students, to designers of water resources systems, and to scientists and

researchers. The editors welcome comments from readers in all of these categories. It is our

hope that the book will not only provide information on water resources engineering, but will

also serve as a basis for advanced study or specialized investigation of the theory and analysis

of various water resources systems.

This book, Modern Water Resources Engineering, covers topics on principles and appli￾cations of hydrology, open channel hydraulics, river ecology, river restoration, sedimentation

and sustainable use of reservoirs, sediment transport, river morphology, hydraulic

vi Preface

engineering, GIS, remote sensing, decision-making process under uncertainty, upland erosion

modeling, machine learning method, climate change and its impact on water resources, land

application, crop management, watershed protection, wetland for waste disposal, water

conservation, living machines, bioremediation, wastewater treatment, aquaculture system

management, environmental protection models, and glossary for water resources engineers.

The editors are pleased to acknowledge the encouragement and support received from their

colleagues and the publisher during the conceptual stages of this endeavor. We wish to thank

the contributing authors for their time and effort, and for having patiently borne our reviews

and numerous queries and comments. We are very grateful to our respective families for their

patience and understanding during some rather trying times.

Lawrence K. Wang

Newtonville, New York, USA

Chih Ted Yang

Fort Collins, Colorado, USA

Preface vii

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

1. Introduction to Hydrology

Jose D. Salas, Rao S. Govindaraju, Michael Anderson,

Mazdak Arabi, Fe´lix France´s, Wilson Suarez,

Waldo S. Lavado-Casimiro, and Timothy R. Green ..................... 1

1. Introduction . . . .......................................................... 2

2. Hydroclimatology ......................................................... 3

2.1. The Hydroclimatic System . . ............................................... 4

2.2. Hydroclimatic System Patterns: Atmospheric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3. Hydroclimatic System Patterns: Coupled Atmosphere-Ocean Patterns ..................... 5

2.4. Hydroclimatic System Patterns: Ocean System Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.5. Interactions Across Scales and Extreme Events . .................................. 7

2.6. Climate Change . . . . . . . . . . . . . . . . . ...................................... 8

2.7. Remarks . . . ......................................................... 8

3. Surface Water Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1. Precipitation . ......................................................... 9

3.2. Interception and Depression Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3. Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.4. Evaporation and Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.5. Runoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4. Soil Moisture Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1. Basic Concepts and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2. Soil Moisture Recycling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3. Variability of Soil Moisture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.4. Scaling of Soil Moisture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5. Hydrology of Glaciers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1. Basic Concepts and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2. Glacial and Snow Fusion Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3. Glacier Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6. Watershed and River Basin Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.1. Basic Concepts and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2. Brief Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.3. Model Calibration and Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.4. Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.5. Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

7. Risk and Uncertainty Analyses in Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

7.2. Frequency Analysis of Hydrologic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.3. Stochastic Methods in Hydrology and Water Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.4. Nonstationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

8. Advances in Hydrologic Data Acquisition and Information Systems . . . . . . . . . . . . . . . . . . . . . . . . . 94

8.1. Satellite Precipitation Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

8.2. Spaceborne Methods for Estimating Surface Waters: Rivers, Wetlands, and Lakes . . . . . . . . . . . . . 96

8.3. Spaceborne Methods for Estimating Soil Moisture, Evaporation, Vegetation,

Snow, Glaciers, and Groundwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

ix

8.4. Advances in Measuring Large River Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8.5. Using Dendrohydrology for Extending Hydrologic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

8.6. Developments in Hydrologic Information Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

2. Open-Channel Hydraulics: From Then to Now and Beyond

Xiaofeng Liu ................................................... 127

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

1.1. Specific Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

1.2. Specific Momentum (Specific Force) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

1.3. Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

1.4. Rise of the Computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

2. Numerical Modeling of Open-Channel Hydraulics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

2.1. Review of Numerical Modeling of Open-Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

2.2. One-Dimensional Modeling of Open-Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

2.3. Two-Dimensional Modeling of Open-Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

2.4. Three-Dimensional CFD Modeling of Open-Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

3. Modern and Future Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

3.1. Revisiting Past Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

3.2. Effects of Climate Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

3.3. Challenges of Natural Open Channels in the Arid Environment . . . . . . . . . . . . . . . . . . . . . . . . . 156

3.4. Discovering and Implementing New Synergies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

3. River Ecology

Zhao-Yin Wang and Bao-Zhu Pan .................................. 159

1. River Ecosystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

1.1. Background Information of Rivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

1.2. Spatial Elements of River Ecosystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

1.3. Ecological Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

1.4. Biological Assemblages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

1.5. Ecological Functions of Rivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

2. Ecological Stresses to Rivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

2.1. Natural Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

2.2. Human-Induced Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

2.3. Introduction of Exotic Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

3. Assessment of River Ecosystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

3.1. Indicator Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

3.2. Metrics of Biodiversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

3.3. Bioassessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

3.4. Habitat Evaluation and Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

4. River Restoration

Hyoseop Woo ................................................... 237

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

1.1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

1.2. Backgrounds and Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

2. Overview of River and Disturbances Affecting River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

2.1. Overview of River in Terms of Restoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

2.2. Overview of Disturbances Affecting Rivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

3. River Restoration Planning and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

3.1. River Restoration Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

3.2. River Restoration Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

x Contents

4. Restoration Implementation, Monitoring, and Adaptive Management . . . . . . . . . . . . . . . . . . . . . . . . . 269

4.1. Restoration Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

4.2. Monitoring Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

4.3. Adaptive Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Appendix: Guidelines and Handbooks of River Restoration (Written in English)

(in Chronological Order) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

5. Sediment Management and Sustainable Use of Reservoirs

Gregory L. Morris............................................... 279

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

2. Reservoir Construction and Sedimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

3. Reservoirs and Sustainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

3.1. Economic Analysis and Sustainable Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

3.2. Sustainability Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

4. Sedimentation Processes and Impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

4.1. Longitudinal Sedimentation Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

4.2. Reservoir Deltas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

4.3. Turbid Density Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

4.4. Reservoir Volume Loss and Reservoir Half-Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

4.5. Sedimentation Impacts Above Pool Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

4.6. Sedimentation Impacts Below the Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

4.7. Sedimentation Impact Thresholds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

5. Predicting Future Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

5.1. Reservoir Surveys to Measure Sedimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

5.2. Future Sedimentation Rate and Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

5.3. Sediment Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

5.4. Climate Change and Sediment Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

5.5. Reservoir Trap Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

5.6. Sediment Bulk Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

5.7. Preliminary Sedimentation Assessment for a Single Reservoir . . . . . . . . . . . . . . . . . . . . . . . . . 301

5.8. Regional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

6. Classification of Sediment Management Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

7. Reduce Sediment Inflow from Upstream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

7.1. Reduce Sediment Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

7.2. Sediment Trapping Above the Reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

8. Route Sediments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

8.1. Timewise Variation in Sediment Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

8.2. Sediment Rating Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

8.3. Sediment Bypass by Offstream Reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

8.4. Sediment Bypass at Onstream Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

8.5. Turbid Density Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

8.6. Sediment Routing by Reservoir Drawdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

9. Recover, Increase, or Reallocate Storage Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

9.1. Pressure Flushing for Localized Sediment Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

9.2. Empty Flushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

9.3. Downstream Impacts of Flushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

9.4. Flushing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

9.5. Dredging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

9.6. Dry Excavation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

9.7. Raise the Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

9.8. Structural Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

9.9. Reuse of Reservoir Sediments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

Contents xi

10. Toward Achieving Sustainable Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

10.1. Modeling of Sediment Management Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

10.2. Implementation Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

10.3. Additional Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

6. Sediment Transport, River Morphology, and River Engineering

Chih Ted Yang ................................................. 339

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

2. Sediment Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

2.1. Basic Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

2.2. Unit Stream Power Formulas for Rivers and Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

2.3. Unit Stream Power Formula for Surface Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

3. Minimum Energy Dissipation Rate Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

4. Generalized Sediment Transport Model for Alluvial River Simulation (GSTARS) . . . . . . . . . . . . . . . . 353

5. River Morphology and Hydraulic Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

6. Hydraulic Engineering Case Studies Using GSTARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

6.1. Mississippi River Lock and Dam No. 26 Replacement Project . . . . . . . . . . . . . . . . . . . . . . . . . . 359

6.2. Lake Mescalero Unlined Emergency Spillway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

6.3. Tarbela Reservoir Sedimentation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

6.4. Channel Degradation Downstream of the Mosul Dam in Iraq and Sediment Deposition

in the Upper Rhone River in Switzerland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

6.5. Bed Sorting and Armoring Downstream from a Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

6.6. Reservoir Delta Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

7. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

7. GIS and Remote Sensing Applications in Modern Water

Resources Engineering

Lynn E. Johnson ................................................ 373

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

2. Overview of Geographic Information Systems and Remote Sensing . . . . . . . . . . . . . . . . . . . . . . . . . 378

2.1. GIS Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

2.2. GIS Data Development and Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

2.3. Remote Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

2.4. GIS Data Models and Geodatabases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

2.5. GIS Analysis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

2.6. User Interfaces and Interaction Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

2.7. GIS System Planning and Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

2.8. GIS Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

3. GIS for Surface Water Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

3.1. GIS Data for Surface Water Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

3.2. GIS for Surface Water Hydrology Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

4. GIS for Floodplain Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

4.1. Floodplain Mapping Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

4.2. Floodplain Geodatabase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

4.3. Floodplain Hydraulic Modeling with GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

5. GIS for Water Supply Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

5.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

5.2. GIS-Based Water Supply Demand Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

5.3. Pipe Network Design with GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

xii Contents

6. GIS for Groundwater Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

6.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

6.2. GIS for Groundwater Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

6.3. Case Example: MODFLOW for Rio Grande Valley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408

8. Decision Making Under Uncertainty: A New Paradigm

for Water Resources Planning and Management

Patricia Gober.................................................. 411

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

2. Climate Uncertainty and Vulnerability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

2.1. Sources of Climate Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

2.2. Stationarity Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

2.3. Extremes Matter! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416

2.4. Vulnerability to Extreme Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

3. Decision Making Under Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

3.1. Problems of Deep Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

3.2. Scenario Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

3.3. Simulation/Exploratory Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

3.4. Elements of Robust Decision Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

3.5. Anticipatory Governance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

3.6. WaterSim: An Example of DMUU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

4. Human Factors in the Water Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

4.1. Water Planning as a Social Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

4.2. Boundary Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

4.3. Decision Theater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

5. Sustainable Water Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

9. Upland Erosion Modeling

Pierre Y. Julien, Mark L. Velleux, Un Ji, and Jaehoon Kim .............. 437

1. Upland Erosion Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

1.1. Surface Runoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

1.2. Upland Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

1.3. Soil Erosion Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

1.4. Overland Sediment Transport Capacity Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

1.5. Channel Transport Capacity Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

1.6. Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

2. Watershed Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

2.1. CASC2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

2.2. TREX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

3. Watershed Model Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

3.1. Naesung Stream Site Description and Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

3.2. Naesung Stream Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

3.3. Model Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

3.4. Design Storm Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

Contents xiii

10. Advances in Water Resources Systems Engineering: Applications

of Machine Learning

John W. Labadie ................................................ 467

1. Introduction and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468

2. Stochastic Optimization of Multireservoir Systems via Reinforcement Learning . . . . . . . . . . . . . . . . . . 470

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

2.2. Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

2.3. Bellman Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

2.4. Q-Learning Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

2.5. ε-Greedy Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

2.6. Temporal-Difference Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

2.7. Discounting Scheme for Optimal Average Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

2.8. Case Study: Geum River Basin, South Korea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

3. Machine Learning Approach to Real-Time Control of Combined Sewer Overflows . . . . . . . . . . . . . . . . 485

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

3.2. Optimal Control Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

3.3. Neural Network Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

3.4. Case Study: West Point Combined Sewer System, Seattle, Washington, USA . . . . . . . . . . . . . . . . 496

4. Stormwater Management for Coastal Ecosystem Restoration: Learning Optimal

Fuzzy Rules by Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502

4.2. Integrated Reservoir Sizing and Operating Rule Optimization: OPTI6 . . . . . . . . . . . . . . . . . . . . . 504

4.3. Application of OPTI6 for Optimal Restoration Plan Development in St. Lucie Estuary . . . . . . . . . . 512

5. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

11. Climate Change and Its Impact on Water Resources

Vijay P. Singh, Ashok K. Mishra, H. Chowdhary,

and C. Prakash Khedun .......................................... 525

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

2. Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

2.1. What Is Climate Change? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

2.2. Causes of Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

2.3. Debate on Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

3. Evidence of Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530

3.1. Increases in Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530

3.2. Changes in Precipitation Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

4. Impacts of Climate Change on Water Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

4.1. Runoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

4.2. Floods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

4.3. Drought . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

4.4. Snowmelt and Glacier Melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

4.5. Water Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

4.6. Groundwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

4.7. Transboundary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

4.8. Agriculture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

4.9. Ecosystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

5. Continental-Scale Impact of Projected Climate Changes on Water Resources . . . . . . . . . . . . . . . . . . . 545

5.1. Africa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

5.2. Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

5.3. Asia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548

5.4. North America . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

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