Water-Quality Engineering in Natural Systems: Fate and Transport Processes in the Water Environment Book

PREFACE xvii

1 INTRODUCTION 1

1.1 The Problem 1

1.2 Sources of Water Pollution 2

1.2.1 Point Sources 2

1.2.1.1 Domestic Wastewater Discharges 3

1.2.1.2 Combined Sewer Overfl ows 3

1.2.1.3 Stormwater Discharges 3

1.2.1.4 Industrial Discharges 3

1.2.1.5 Spills 4

1.2.2 Nonpoint Sources 4

1.2.2.1 Agricultural Runoff 4

1.2.2.2 Livestock 4

1.2.2.3 Urban Runoff 5

1.2.2.4 Landfi lls 5

1.2.2.5 Recreational Activities 5

1.3 Control of Water Pollution 5

2 WATER QUALITY 7

2.1 Introduction 7

2.2 Physical Measures 7

2.2.1 Flow Conditions 7

2.2.2 Substrate 8

2.2.3 In-Stream Habitat 9

2.2.4 Riparian Habitat 9

2.2.5 Thermal Pollution 10

2.3 Chemical Measures 10

2.3.1 Dissolved Oxygen 10

2.3.2 Biochemical Oxygen Demand 12

2.3.3 Suspended Solids 14

2.3.4 Nutrients 15

2.3.4.1 Nitrogen 15

2.3.4.2 Phosphorus 16

2.3.5 Metals 17

2.3.6 Synthetic Organic Chemicals 18

2.3.6.1 Pesticides 18

2.3.6.2 Volatile Organic Compounds 18

2.3.7 Radionuclides 18

2.3.8 pH 19

2.4 Biological Measures 19

2.4.1 Human Pathogenic Microorganisms 20

2.4.2 Indicator Organisms 23

2.4.3 Biological Integrity 24

Problems 25

3 FUNDAMENTALS OF FATE AND TRANSPORT 27

3.1 Introduction 27

3.2 The Advection–Diffusion Equation 27

3.2.1 Nondimensional Form 29

3.2.2 Transformation to the Diffusion Equation 31

3.2.2.1 Conservative Tracers 31

3.2.2.2 Nonconservative Tracers with First-Order Decay 32

3.2.3 Moment Property of the Diffusion Equation 32

3.3 Fundamental Solutions of the Advection–Diffusion Equation 33

3.3.1 Diffusion in One Dimension 34

3.3.1.1 Spatially and Temporally Distributed Sources 36

3.3.1.2 Impermeable Boundaries 39

3.3.1.3 Continuous Plane Source 42

3.3.2 Diffusion in Two Dimensions 46

3.3.2.1 Spatially and Temporally Distributed Sources 47

3.3.2.2 Continuous Line Source 48

3.3.2.3 Continuous Plane Sources 49

3.3.3 Diffusion in Three Dimensions 52

3.3.3.1 Spatially and Temporally Distributed Sources 53

3.3.3.2 Instantaneous Point Source in Shear Flow 53

3.3.3.3 Continuous Point Source with Constant Diffusion Coefficient 54

3.3.3.4 Continuous Point Source with Variable Diffusion Coefficient 58

3.3.3.5 Instantaneous Line Source 59

3.3.3.6 Instantaneous Volume Source 60

3.4 Transport of Suspended Particles 60

3.5 Turbulent Diffusion 62

3.5.1 Relationship of Turbulent Diffusion Coefficient to Velocity Field 63

3.5.2 Eulerian Approximation 65

3.6 Dispersion 68

Problems 72

4 RIVERS AND STREAMS 78

4.1 Introduction 78

4.2 Transport Processes 79

4.2.1 Initial Mixing 79

4.2.2 Longitudinal Dispersion 85

4.2.2.1 Field Measurement of KL 85

4.2.2.2 Empirical Estimates of KL 88

4.3 Models of Spills 90

4.3.1 Substances with First-Order Decay 90

4.3.1.1 Instantaneous Release 90

4.3.1.2 Continuous Release 91

4.3.2 Spills of Volatile Organic Compounds 93

4.4 Models of Dissolved Oxygen 95

4.4.1 Oxygen Demand of Wastewater 95

4.4.2 Reaeration 96

4.4.3 Streeter–Phelps Model 98

4.4.4 Other Considerations 102

4.4.4.1 Nitrification 102

4.4.4.2 Photosynthesis, Respiration, and Benthic Oxygen Demand 107

4.4.4.3 Distributed Sources of BOD 111

4.4.5 Chapra–Di Toro Model 113

4.4.6 Empirical Models 116

4.4.7 Numerical Models 116

4.5 Models of Nutrients 116

4.6 Models of Pathogens 118

4.7 Contaminant Loads 119

4.7.1 Total Maximum Daily Loads 119

4.7.1.1 Derivation of the Load Duration Curve 119

4.7.1.2 Applications of the Load Duration Curve 122

4.7.2 Long-Term Contaminant Loads 128

4.8 Management and Restoration 131

4.8.1 Nonstructural Techniques 131

4.8.2 Structural Techniques 132

Problems 134

5 GROUNDWATER 142

5.1 Introduction 142

5.2 Contaminant Sources 142

5.2.1 Septic Tanks 142

5.2.2 Leaking Underground Storage Tanks 143

5.2.3 Land Application of Wastewater 144

5.2.4 Irrigation Return Flow 145

5.2.5 Solid Waste Disposal Sites 146

5.2.6 Waste Disposal Injection Wells 146

5.2.7 Agricultural Operations 147

5.3 Fate and Transport Models 147

5.3.1 Instantaneous Point Source 149

5.3.2 Continuous Point Source 150

5.3.3 Continuous Plane Source 152

5.4 Transport Processes 154

5.5 Fate Processes 160

5.5.1 Sorption 160

5.5.2 First-Order Decay 165

5.5.3 Combined Sorption and Decay 167

5.5.4 Biocolloids 169

5.5.4.1 Conventional Colloid Filtration Theory 169

5.5.4.2 Modifi ed Colloid Filtration Theory 169

5.5.4.3 Accounting for Dieoff 169

5.6 Nonaqueous Phase Liquids 170

5.6.1 Residual Saturation 171

5.6.2 Raoult’s Law 172

5.6.2.1 Effects on Saturation Vapor Pressure 173

5.6.2.2 Effects on Saturation Concentration 173

5.6.2.3 Soil and Aquifer Samples 174

5.7 Monitoring Wells 175

5.8 Remediation of Subsurface Contamination 179

5.8.1 Remediation Goals 180

5.8.1.1 Vadose Zone 180

5.8.1.2 Saturated Zone 180

5.8.2 Remediation Strategies 181

5.8.2.1 Free Product Recovery 181

5.8.2.2 Excavation and Disposal 183

5.8.2.3 Soil Vapor Extraction 184

5.8.2.4 Bioventing 188

5.8.2.5 Air Sparging 188

5.8.2.6 Pump-and-Treat Systems 188

5.8.2.7 Bioremediation 194

5.8.2.8 In Situ Reaction Walls 195

5.8.2.9 In Situ Containment 195

5.8.2.10 Natural Attenuation 196

Problems 196

6 WATERSHEDS 203

6.1 Introduction 203

6.2 Urban Watersheds 203

6.2.1 Sources of Pollution 205

6.2.2 Fate and Transport Processes 208

6.2.2.1 Event Mean Concentration Model 208

6.2.2.2 Buildup–Wash-Off Models 213

6.2.3 Stormwater Control Measures 215

6.2.3.1 Source Control Measures 216

6.2.3.2 Hydrologic Modifi cations 216

6.2.3.3 Attenuation of Pollutants 219

6.2.3.4 Collection System Pollution Control 221

6.2.3.5 Detention–Retention Facilities 222

6.3 Agricultural Watersheds 224

6.3.1 Sources of Pollution 224

6.3.2 Fate and Transport Processes 226

6.3.2.1 Erosion 226

6.3.2.2 Soil Pollution 232

6.3.3 Best Management Practices 236

6.3.3.1 Cropping Practices 237

6.3.3.2 Integrated Pest Management 237

6.3.3.3 Nutrient Management 238

6.3.3.4 Terraces and Diversions 238

6.3.3.5 Critical Area Treatment 238

6.3.3.6 Sediment Basins and Detention–Retention Ponds 239

6.3.3.7 Animal Waste Storage and Treatment 239

6.3.3.8 Livestock Exclusion Fences 239

6.3.3.9 Filter Strips and Field Borders 239

6.3.3.10 Wetland Rehabilitation 239

6.3.3.11 Riparian Buffer Zones 240

6.3.3.12 Irrigation Water Management 240

6.3.3.13 Stream Bank Stabilization 240

6.3.3.14 Range and Pasture Management 240

6.4 Airsheds 240

Problems 241

7 LAKES AND RESERVOIRS 243

7.1 Introduction 243

7.2 Physical Processes 245

7.2.1 Circulation 245

7.2.2 Sedimentation 247

7.2.3 Light Penetration 248

7.3 Eutrophication 249

7.3.1 Biomass–Nutrient Relationships 250

7.3.2 Measures of Trophic State 252

7.3.3 Depth of Anoxia 255

7.4 Thermal Stratifi cation 255

7.4.1 Layer Characteristics 257

7.4.2 Gravity Circulation 257

7.4.3 Water-Quality Impacts 258

7.4.4 Measures of Mixing Potential 259

7.4.4.1 Richardson Number 259

7.4.4.2 Densimetric Froude Number 260

7.4.5 Artificial Destratification 260

7.5 Water-Quality Models 261

7.5.1 Zero-Dimensional (Completely Mixed) Model 261

7.5.1.1 Conservation of Mass Model 262

7.5.1.2 Conservation of Energy Model 265

7.5.2 One-Dimensional (Vertical) Models 266

7.5.2.1 Conservation of Mass Model 266

7.5.2.2 Conservation of Energy Model 268

7.5.2.3 Estimation of the Vertical Diffusion Coefficient 269

7.5.3 Two-Dimensional Models 272

7.5.3.1 Nearshore Mixing Models 272

7.6 Management and Restoration 275

7.6.1 Control of Eutrophication 275

7.6.1.1 Control of Point Sources 275

7.6.1.2 Control of Nonpoint Sources 275

7.6.1.3 Chemical Treatments for Phosphorus 275

7.6.1.4 Limitation of Internal Loading 276

7.6.1.5 Limitation of Algal Development 276

7.6.2 Control of DO Levels 277

7.6.2.1 Artificial Circulation 277

7.6.2.2 Water Fountains 278

7.6.2.3 Hypolimnetic Aeration 278

7.6.2.4 Oxygen Injection 278

7.6.2.5 Pump-and-Baffl e Aeration System 278

7.6.2.6 Snow Removal to Increase Light Penetration 278

7.6.3 Control of Acidity 279

7.6.4 Control of Aquatic Plants 280

Problems 282

8 WETLANDS 286

8.1 Introduction 286

8.2 Natural Wetlands 286

8.2.1 Classifi cation 287

8.2.1.1 Marshes 287

8.2.1.2 Swamps 287

8.2.1.3 Bogs 288

8.2.1.4 Fens 289

8.2.2 Delineation of Wetlands 289

8.2.2.1 Vegetation 289

8.2.2.2 Soils 290

8.2.2.3 Hydrology 291

8.2.3 Water Budget 291

8.2.3.1 Net Surface Water Inflow 292

8.2.3.2 Net Groundwater Inflow 292

8.2.3.3 Evapotranspiration 292

8.3 Constructed Treatment Wetlands 292

8.3.1 Classification 293

8.3.1.1 Free Water Surface Wetlands 294

8.3.1.2 Horizontal Subsurface Flow Wetlands 294

8.3.1.3 Vertical Flow Wetlands 295

8.3.2 Design of FWS Wetlands 295

8.3.2.1 Hydrology and Hydraulics 295

8.3.2.2 Performance-Based Sizing 300

8.3.2.3 Other Considerations 303

Problems 305

9 OCEANS AND ESTUARIES 307

9.1 Introduction 307

9.2 Ocean Outfall Discharges 307

9.2.1 Near-Field Mixing 311

9.2.1.1 Single Plumes 311

9.2.1.2 Line Plumes 316

9.2.1.3 Design Considerations 320

9.2.2 Far-Field Mixing 323

9.3 Estuaries 328

9.3.1 Classification of Estuaries 329

9.3.2 Water-Quality Issues 329

9.3.3 Salinity Distribution 330

9.3.4 Dissolved Oxygen: The Estuary Streeter–Phelps Model 331

9.3.5 Flow and Circulation 334

9.3.5.1 Flushing Time 335

9.3.5.2 Net Flow 336

Problems 337

10 ANALYSIS OF WATER-QUALITY MEASUREMENTS 340

10.1 Introduction 340

10.2 Probability Distributions 340

10.2.1 Properties of Probability Distributions 340

10.2.2 Mathematical Expectation and Moments 341

10.3 Fundamental Probability Distributions 342

10.3.1 Normal Distribution 342

10.3.2 Log-Normal Distribution 344

10.3.3 Uniform Distribution 345

10.4 Derived Probability Distributions 346

10.4.1 Chi-Square Distribution 346

10.4.2 Student’s t Distribution 347

10.4.3 F Distribution 348

10.5 Estimation of Population Distribution from Sample Data 348

10.5.1 Sample Probability Distribution 349

10.5.2 Comparisons of Probability Distributions 350

10.5.2.1 The Chi-Square Test 350

10.5.2.2 Kolmogorov–Smirnov Test 351

10.6 Estimation of Parameters of Population Distribution 352

10.6.1 Method of Moments 352

10.6.2 Maximum Likelihood Method 354

10.6.3 Method of L-Moments 355

10.7 Probability Distributions of Sample Statistics 356

10.7.1 Mean 356

10.7.2 Variance 356

10.7.3 Coeffi cient of Skewness 357

10.7.4 Median 357

10.7.5 Coeffi cient of Variation 357

10.7.6 Useful Theorems 358

10.8 Confi dence Intervals 359

10.8.1 Mean 359

10.8.2 Variance 359

10.8.3 Variance Ratios 360

10.9 Hypothesis Testing 361

10.9.1 Mean 361

10.9.2 Variance 362

10.9.3 Population Differences 362

10.9.3.1 t-Test 362

10.9.3.2 Kruskal–Wallis Test 363

10.9.4 Normality 364

10.9.4.1 Shapiro–Wilk Test 364

10.9.4.2 Shapiro–Francia Test 365

10.9.4.3 Data Transformations to Achieve Normality 366

10.9.5 Trends 366

10.9.5.1 Mann–Kendall Test 366

10.9.5.2 Sen’s Slope Estimator 367

10.10 Relationships between Variables 368

10.10.1 Correlation 368

10.10.2 Regression Analysis 369

10.10.2.1 Confi dence Limits of Predictions 371

10.10.2.2 Coeffi cient of Determination 372

10.11 Functions of Random Variables 372

10.11.1 Addition and Subtraction 372

10.11.2 Multiplication 373

10.11.3 Division 374

10.11.4 Other Functions 375

10.12 Kriging 375

10.12.1 The Stationary Case 376

10.12.2 The Intrinsic Case 379

Problems 382

11 MODELING OF WATER QUALITY 387

11.1 Introduction 387

11.2 Code Selection 388

11.3 Calibration 388

11.3.1 Sensitivity Analysis 390

11.3.2 Performance Analysis 391

11.3.2.1 Error Statistics 392

11.3.2.2 Modified Error Statistics 394

11.3.2.3 Coefficient of Determination 395

11.3.2.4 Model Efficiency 395

11.3.2.5 Index of Agreement 397

11.3.2.6 Hydrologic Measures 397

11.3.2.7 Selection of Performance Measures 397

11.3.3 Parameter Estimation 398

11.3.3.1 Multiobjective Optimization 399

11.3.3.2 Bayesian Approaches 399

11.3.3.3 Generalized Likelihood Uncertainty Estimation 400

11.3.3.4 Other Methods 401

11.4 Validation 401

11.5 Simulation 402

11.6 Uncertainty Analysis 402

11.6.1 Bayesian and GLUE Analyses 402

11.6.2 Monte Carlo Analysis 403

11.6.3 Analytical Probability Models 403

11.6.4 First-Order Uncertainty Analysis 404

A UNITS AND CONVERSION FACTORS 406

A.1 Units 406

A.2 Conversion Factors 408

B FLUID PROPERTIES 409

B.1 Water 409

B.2 Organic Compounds Found in Water 409

C STATISTICAL TABLES 411

C.1 Areas under the Standard Normal Curve 411

C.2 Critical Values of the t Distribution 413

C.3 Critical Values of the Chi-Square Distribution 413

C.4 Critical Values of the F Distribution (α = 0.05) 414

C.5 Critical Values for the Kolmogorov–Smirnov Test Statistic 416

D SPECIAL FUNCTIONS 417

D.1 Error Function 417

D.2 Bessel Functions 417

D.2.1 Defi nition 417

D.2.2 Evaluation of Bessel Functions 418

D.2.2.1 Bessel Function of the First Kind of Order n 418

D.2.2.2 Bessel Function of the Second Kind of Order n 418

D.2.2.3 Modified Bessel Function of the First Kind of Order n 418

D.2.2.4 Modified Bessel Function of the Second Kind of Order n 418

D.2.2.5 Tabulated Values of Useful Bessel Functions 419

D.3 Gamma Function 420

D.4 Exponential Integral 421

BIBLIOGRAPHY 422

INDEX 442