Kinematic Wave Modeling in Water Resources

Kinematic wave (KW) modeling methods are gaining wide acceptance as fast and accurate methods for handling a wide range of water modeling problems. This book provides a through reference to the application of KW methods to such problems as the spatial representation of watersheds, overland flow routing, and channel flow routing.

Vijay P. Singh and are the authors of Kinematic Wave Modeling in Water Resources, Environmental Hydrology, published by Wiley.

PREFACE

xiii

(4)

ACKNOWLEDGMENTS

xvii

PART I: PRELIMINARIES

1

(105)

1. INTRODUCTION

1

(10)

1.1 Environmental Continuum

2

(1)

1.2 Water Continuum

2

(2)

1.3 Definition of Environmental Hydrology

4

(1)

1.4 Scope of Environmental Hydrology

4

(3)

1.5 Approach to Environmental Problems

7

(2)

Exercises

9

(1)

References

10

(1)

2. HYDRAULIC EQUATIONS FOR SUBSURFACE FLOW

11

(18)

2.1 Subsurface Saturated Flow Equations

11

(13)

2.2 Subsurface Unsaturated Flow Equations

24

(3)

Exercises

27

(1)

References

27

(2)

3. HYDRAULIC PROPERTIES OF SOIL

29

(77)

3.1 Hydraulic Properties

30

(5)

3.2 Methods of Estimation

35

(1)

3.3 Estimation of Water-Retention Curve

36

(16)

3.4 Estimation of Hydraulic Conductivity

52

(12)

3.5 Comparison of Hydraulic Conductivity Models

64

(1)

3.6 Estimation of Soil-Water Diffusivity

65

(14)

3.7 Estimation of Sorptivity

79

(3)

3.8 Spatial Variability of Hydraulic Properties

82

(2)

Exercises

84

(4)

References

88

(18)

PART II: SUBSURFACE FLOW

106

(120)

4. UNSATURATED FLOW

106

(80)

4.1 Kinematic Wave Formulation without Plant-Root Extraction

107

(3)

4.2 Kinematic Wave Model with q(0) = k(0)

110

(22)

4.3 Kinematic Wave Model with Complex Surface Wetting

132

(9)

4.4 Kinematic Wave Model Formulation with Plant-Root Extraction

141

(24)

4.5 Macropore Flow

165

(16)

Exercises

181

(2)

References

183

(3)

5. SUBSURFACE STORMFLOW

186

(40)

5.1 Saturated Gravity Flow

187

(4)

5.2 Dimensional Kinematic Wave Solutions

191

(4)

5.3 Dimensionless Kinematic Wave Solutions

195

(2)

5.4 Steady-State Water-Table Profiles

197

(14)

5.5 Unsteady-State Case: The Rising Hydrograph

211

(3)

5.6 Unsteady-State Case: The Recession Hydrograph

214

(3)

5.7 Error in Kinematic Wave Approximation

217

(3)

Exercises

220

(3)

References

223

(3)

PART III: SURFACE IRRIGATION

226

(140)

6. FLOW ADVANCE OVER POROUS BEDS: APPLICATION TO SURFACE IRRIGATION

226

(109)

6.1 Irrigation Flow Process

226

(1)

6.2 Mathematical Models of Border Irrigation

227

(3)

6.3 Mathematical Preliminaries

230

(2)

6.4 Kinematic Wave Modeling

232

(3)

6.5 Analytical Solution for Case A: T XXX (n - 1)g/f

235

(25)

6.6 Analytical Solution for Case B: T XXX (n - 1)g/f

260

(17)

6.7 Kinematic Wave Model with Linear Cumulative Infiltration

277

(12)

6.8 Kinematic Wave Model of Border-Dyke Irrigation

289

(6)

6.9 Cumulative Volumes: Constant Infiltration

295

(4)

6.10 Cumulative Volumes: Variable Infiltration

299

(4)

6.11 Numerical Solution Based on Integral Formulation

303

(5)

6.12 Sequential Solution

308

(1)

6.13 Lax-Wendroff Method

308

(4)

6.14 Method of Characteristics

312

(9)

Exercises

321

(8)

References

329

(6)

7. FLOW IN INFILTRATING CHANNELS: FURROW IRRIGATION

335

(31)

7.1 Furrow Geometry

336

(8)

7.2 Furrow Infiltration

344

(2)

7.3 Governing Equations

346

(2)

7.4 Initial and Boundary Conditions

348

(1)

7.5 Methods of Solution

348

(13)

Exercises

361

(2)

References

363

(3)

PART IV: SNOW HYDROLOGY

366

(87)

8. MOVEMENT OF WATER THROUGH SNOW

366

(45)

8.1 Water Flow in Homogeneous Snow

368

(33)

8.2 Flow through Layered Snowpacks

401

(3)

8.3 Similarity Solution

404

(2)

8.4 Solution Using Moving Coordinates

406

(1)

Exercises

407

(1)

References

408

(3)

9. GLACIER FLOW

411

(42)

9.1 Types of Wave Phenomena

416

(2)

9.2 Mechanisms for Motion of Glacier Ice

418

(5)

9.3 Assumptions in Glacier Theories

423

(1)

9.4 Glacier Response to Seasonal and Climatic Changes: Surface Waves

423

(20)

9.5 Glacier Surging

443

(5)

Exercises

448

(1)

References

449

(4)

PART V: EROSION AND SEDIMENT YIELD

453

(111)

10. EROSION AND SEDIMENT TRANSPORT PROCESSES

453

(37)

10.1 Erosion and Transport Processes

455

(2)

10.2 Differences between Overland Erosion and Streambed Erosion

457

(1)

10.3 Interrill Erosion

458

(2)

10.4 Rill Erosion

460

(7)

10.5 Rill Width

467

(1)

10.6 Total Sediment Load of a Plane

468

(1)

10.7 Sediment Transport Capacity

468

(11)

10.8 Evaluation of Transport Capacity Equations

479

(1)

10.9 Mathematical Models of Soil Erosion

480

(1)

Exercises

481

(1)

References

481

(9)

11. EROSION ON A PLANE

490

(74)

11.1 Conservation of Sediment Mass

490

(2)

11.2 Kinematic Wave Formulation

492

(1)

11.3 Solutions for the Case with f = 0 and Rainfall of Indefinite Duration

493

(17)

11.4 Solutions for the Case with f = 0 and Rainfall of Finite Duration

510

(29)

11.5 Solutions for the Case with f greater than 0

539

(15)

11.6 Sediment Yield Equations

554

(4)

Exercises

558

(2)

References

560

(4)

PART VI: WATER QUALITY

564

(193)

12. SOLUTE TRANSPORT

564

(32)

12.1 Transport Process

565

(9)

12.2 Solute Transport by Surface Runoff

574

(11)

12.3 Solute Transport in Soil

585

(1)

12.4 Governing Equation

586

(2)

12.5 Initial and Boundary Conditions

588

(1)

12.6 Transport Models

589

(1)

Exercises

590

(1)

References

590

(6)

13. SOLUTE TRANSPORT BY SURFACE RUNOFF

596

(67)

13.1 Pollutant Transport by Runoff over an Impervious Plane: Instantaneous Mixing

597

(20)

13.2 Pollutant Transport by Runoff over an Impervious Plane: Finite-Period Mixing

617

(14)

13.3 Pollutant Transport by Runoff over an Infiltrating Plane: Finite-Period Mixing

631

(21)

13.4 Pollutant Transport by Overland Flow and Infiltration: Mixing Zone

652

(5)

Exercises

657

(5)

References

662

(1)

14. SOLUTE TRANSPORT IN POROUS MEDIA

663

(33)

14.1 Kinematic Wave Model without Chemical Reactions

663

(7)

14.2 Multiphase Solute Transport in the Vadoze Zone

670

(5)

14.3 Transport by Dissolved Constituents

675

(9)

14.4 Solute Transport in Macropores

684

(8)

Exercises

692

(1)

References

693

(3)

15. SEDIMENTATION

696

(37)

15.1 Sedimentation Process

696

(11)

15.2 Kinematic Wave Theory

707

(21)

15.3 Fluidization

728

(1)

Exercises

729

(1)

References

730

(3)

16. CHROMATOGRAPHIC TRANSPORT IN SOILS

733

(24)

16.1 Theory of Chromatography

734

(1)

16.2 Governing Equations

735

(4)

16.3 Transport Model with General Isotherm

739

(6)

16.4 Characteristic Solution with Linear Adsorption Isotherm

745

(3)

16.5 Transport Model with Langmuir Adsorption Isotherm

748

(2)

16.6 Characteristic Solution with a General Isotherm

748

(2)

Exercises

750

(4)

References

754

(3)

PART VII: STREAMFLOW

757

(64)

17. STREAMFLOW GENERATION

757

(31)

17.1 Approaches to Storm-Runoff Generation

757

(6)

17.2 Flow Paths

763

(1)

17.3 Effect of Spatial Variability

764

(2)

17.4 Mathematical Models of Hillslope Hydrology

766

(1)

17.5 Smith-Hibbert Model for Hillslope Hydrology

767

(16)

Exercises

783

(1)

References

784

(4)

18. EFFECT OF SPATIAL AND TEMPORAL VARIABILITY ON STREAMFLOW HYDROGRAPH

788

(33)

18.1 Controlling Factors

788

(1)

18.2 Influence of Storm Dynamics

789

(17)

18.3 Influence of Watershed Segmentation

806

(3)

18.4 Influence of Watershed Characteristics

809

(4)

18.5 Similarity and Length Scale for Overland Flow

813

(1)

18.6 Concluding Remarks

814

(1)

Exercises

814

(1)

References

815

(6)

APPENDIX: PROPERTIES OF THE FUNCTION F(n)(x)

821

(4)

INDEX

825

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Kinematic Wave Modeling in Water Resources Environmental Hydrology

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