# Hydrodynamics and Water Quality: Modeling Rivers, Lakes, and Estuaries

ISBN: 978-0-470-13543-3
704 pages
January 2008

## Description

Mathematical modeling for environmental and water resources management

This hands-on reference illustrates the principles, basic processes, mathematical descriptions, and practical applications of modeling surface waters. It discusses hydrodynamics, sediment processes, toxic fate and transport, and water quality and eutrophication in rivers, lakes, estuaries, and coastal waters. There has been great progress in mathematical modeling that simulates surface waters numerically. Modeling is becoming a powerful tool, and this reference gets readers up to speed quickly. Practically organized to facilitate quick reference, Hydrodynamics and Water Quality: Modeling Rivers, Lakes, and Estuaries:
• Focuses on how to solve environmental problems in surface waters
• Uses a practical, application-oriented approach: chapters begin with an introduction of basic concepts, proceed to discussions of physical, chemical, and/or biological processes and their mathematical representations, and conclude with real-life case studies
• Has a companion CD that includes a modeling package and electronic files of numerical models, case studies, and model results, plus other materials to help readers use the models and tools
• Features case studies that show how to use models appropriate to environmental and water resources management
• Provides detailed information on how to use the three-dimensional Environmental Fluid Dynamics Code (EFDC) model supported by the EPA
This is a must-have reference for environmental scientists, engineers, geologists, chemists, and government regulators, as well as other water quality professionals. It is also an excellent text for graduate students in fields that encompass hydrodynamics and water quality.
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Forward.

Preface.

Acknowledgements.

1. Introduction.

1.1 Overview.

1.2 Understanding Surface Waters.

1.3 Modeling of Surface Waters.

2. Hydrodynamics.

2.1 Hydrodynamic Processes.

2.1.1 Water Density.

2.1.2 Conservation Laws.

2.1.2.1 Conservation of mass.

2.1.2.2 Conservation of momentum.

2.1.4 Mass Balance Equation.

2.1.5 Atmospheric Forcings.

2.1.6 Coriolis Force and Geostrophic Flow.

2.2 Governing Equations.

2.2.1 Basic Approximations.

2.2.1.1 Boussinesq approximation.

2.2.1.2 Hydrostatic approximation.

2.2.1.3 Quasi-3D approximation.

2.2.2 Equations in Cartesian Coordinates.

2.2.2.1 1D equations.

2.2.2.2 2D vertically averaged equations.

2.2.2.3 2D laterally averaged equations.

2.2.2.4 3D equations in sigma coordinate.

2.2.3 Vertical Mixing and Turbulence Models.

2.2.4 Equations in Curvilinear Coordinates.

2.2.4.1 Curvilinear coordinates and model grid.

2.2.4.2 3D equations in sigma and curvilinear coordinates.

2.2.5 Initial Conditions and Boundary Conditions.

2.2.5.1 Initial conditions.

2.2.5.2 Solid boundary conditions.

2.3 Temperature.

2.3.1 Heatflux Components.

2.3.1.3 Evaporation and latent heat.

2.3.1.4 Sensible heat.

2.3.2 Temperature Formulations.

2.3.2.1 Basic equations.

2.3.2.2 Surface boundary condition.

2.3.2.3 Bed heat exchange.

2.4 Hydrodynamic Modeling.

2.4.1 Hydrodynamic Parameters and Data Requirements.

2.4.1.1 Hydrodynamic parameters.

2.4.1.2 Data requirements.

2.4.2 Case Study I: Lake Okeechobee.

2.4.2.1 Background.

2.4.2.2 Data sources.

2.4.2.3 Model setup.

2.4.2.4 Model calibration.

2.4.2.5 Hydrodynamic processes in the lake.

2.4.2.6 Discussions and conclusions.

2.4.3 Case Study II: St. Lucie Estuary and Indian River Lagoon.

2.4.3.1 Background.

2.4.3.2 Model setup.

2.4.3.3 Tidal elevation and current in SLE/IRL.

2.4.3.4 Temperature and salinity.

2.4.3.5 Discussions on hydrodynamic processes.

2.4.3.6 Conclusions.

3. Sediment Transport.

3.1 Overview.

3.1.1 Properties of Sediment.

3.1.2 Problems Associated with Sediment.

3.2 Sediment Processes.

3.2.1 Particle Settling.

3.2.2 Horizontal Transport of Sediment.

3.2.3 Resuspension and Deposition.

3.2.4 Equations for Sediment Transport.

3.2.5 Turbidity and Secchi Depth.

3.3 Cohesive Sediment.

3.3.1 Vertical Profiles of Cohesive Sediment Concentrations.

3.3.2 Flocculation.

3.3.3 Settling of Cohesive Sediment.

3.3.4 Deposition of Cohesive Sediment.

3.3.5 Resuspension of Cohesive Sediment.

3.4 Noncohesive Sediment.

3.4.1 Shields Diagram.

3.4.2 Settling and Equilibrium Concentration.

3.5 Sediment Bed.

3.5.1 Characteristics of Sediment Bed.

3.5.2 A Model for Sediment Bed.

3.6 Wind Waves.

3.6.1 Wave Processes.

3.6.2 Wind Wave Characteristics.

3.6.3 Wind Wave Models.

3.6.4 Combined Flows of Wind Waves and Currents.

3.6.5 Case Study: Wind Wave Modeling in Lake Okeechobee.

3.6.5.1 Background.

3.6.5.2 Measured data and model setup.

3.6.5.3 Model calibration and verification.

3.6.5.4 Discussions.

3.7 Sediment Transport Modeling.

3.7.1 Sediment Parameters and Data Requirements.

3.7.2 Case Study I: Lake Okeechobee.

3.7.2.1 Background.

3.7.2.2 Model configuration.

3.7.2.3 Model calibration and verification.

3.7.2.4 Discussions and conclusions.

3.7.3 Case Study II: Blackstone River.

3.7.3.1 Background.

3.7.3.2 Data sources and model setup.

3.7.3.3 Hydrodynamic and sediment simulation.

4. Pathogens and Toxics.

4.1 Overview.

4.2 Pathogens.

4.2.1 Bacteria, Viruses, and Protozoa.

4.2.2 Pathogen Indicators.

4.2.3 Processes Affecting Pathogens.

4.3 Toxic Substances.

4.3.1 Toxic Organic Chemicals.

4.3.2 Metals.

4.3.3 Sorption and Desorption.

4.4 Fate and Transport Processes.

4.4.1 Mathematical Formulations.

4.4.2 Processes Affecting Fate and Decay.

4.4.2.1 Mineralization and decomposition.

4.4.2.2 Hydrolysis.

4.4.2.3 Photolysis.

4.4.2.5 Volatilization.

4.4.2.6 pH.

4.5 Contaminant Modeling.

4.5.1 Case Study I: St. Lucie Estuary and Indian River Lagoon.

4.5.1.1 Analysis of measured copper data.

4.5.1.2 Sediment and copper modeling results.

4.5.1.3 Summary and discussions.

4.5.2 Case Study II: Rockford Lake.

4.5.2.1 Background.

4.5.2.2 Data sources and model setup.

4.5.2.3 Model results.

5. Water Quality and Eutrophication.

5.1 Overview.

5.1.1 Eutrophication.

5.1.2 Algae.

5.1.3 Nutrients.

5.1.3.1 Nitrogen cycle.

5.1.3.2 Phosphorus cycle.

5.1.3.3 Limiting nutrients.

5.1.4 Dissolved Oxygen.

5.1.5 Governing Equations for Water Quality Processes.

5.1.5.1 Hydrodynamic effects.

5.1.5.2 Temperature effects.

5.1.5.3 Michaelis-Menton formulation.

5.1.5.4 State variables in water quality models.

5.2 Algae.

5.2.1 Algal Biomass and Chlorophyll.

5.2.2 Equations for Algal Processes.

5.2.3 Algal Growth.

5.2.3.1 Nutrients for algal growth.

5.2.3.2 Sunlight for algal growth and photosynthesis.

5.2.4 Algal Reduction.

5.2.4.1 Basal metabolism.

5.2.4.2 Algal predation.

5.2.4.3 Algal settling.

5.2.5 Silica and Diatom.

5.2.6 Periphyton.

5.3 Organic Carbon.

5.3.1 Decomposition of Organic Carbon.

5.3.2 Equations for Organic Carbon.

5.3.3 Heterotrophic Respiration and Dissolution.

5.4 Phosphorus.

5.4.1 Equations for Phosphorus State Variables.

5.4.1.1 Particulate organic phosphorus.

5.4.1.2 Dissolved organic phosphorus.

5.4.1.3 Total phosphate.

5.4.2 Phosphorus Processes.

5.4.2.1 Sorption and desorption of phosphate.

5.4.2.2 Effects of algae on phosphorus.

5.4.2.3 Mineralization and hydrolysis.

5.5 Nitrogen.

5.5.1 Forms of Nitrogen.

5.5.2 Equations for Nitrogen State Variables.

5.5.2.1 Particulate organic nitrogen.

5.5.2.2 Dissolved organic nitrogen.

5.5.2.3 Ammonium nitrogen.

5.5.2.4 Nitrate nitrogen.

5.5.3 Nitrogen Processes.

5.3.1.1 Effects of algae.

5.3.1.2 Mineralization and hydrolysis.

5.3.1.3 Nitrification.

5.3.1.4 Denitrification.

5.3.1.5 Nitrogen fixation.

5.6 Dissolved Oxygen.

5.6.1 Biochemical Oxygen Demand.

5.6.2 Processes and Equations of Dissolved Oxygen.

5.6.3 Effects of Photosynthesis and Respiration.

5.6.4 Reaeration.

5.6.5 Chemical Oxygen Demand.

5.7 Sediment Fluxes.

5.7.1 Sediment Diagenesis Model.

5.7.1.1 Three fluxes of the sediment diagenesis model.

5.7.1.2 Two-layer structure of benthic sediment.

5.7.1.3 Three G classes of sediment organic matter.

5.7.1.4 State variables of the sediment diagenesis model.

5.7.2 Depositional Fluxes.

5.7.3 Diagenesis Fluxes.

5.7.4 Sediment Fluxes.

5.7.4.1 Basic equations.

5.7.4.2 Parameters for sediment fluxes.

5.7.4.3 Ammonium nitrogen flux.

5.7.4.4 Nitrate nitrogen flux.

5.7.4.5 Phosphate phosphorus flux.

5.7.4.6 Chemical oxygen demand and sediment oxygen demand.

5.7.5 Silica.

5.7.6 Coupling with Sediment Resuspension.

5.8 Submerged Aquatic Vegetation.

5.8.1 Introduction.

5.8.2 Equations for a SAV Model.

5.8.2.1 Shoots production and respiration.

5.8.2.2 Carbon transport and roots respiration.

5.8.2.3 Epiphytes production and respiration.

5.8.3 Coupling with the Water Quality Model.

5.8.3.1 Organic carbon coupling.

5.8.3.2 Dissolved oxygen coupling.

5.8.3.3 Phosphorus coupling.

5.8.3.4 Nitrogen coupling.

5.8.3.5 Total suspended solid coupling.

5.9 Water Quality Modeling.

5.9.1 Model Parameters and Data Requirements.

5.9.1.1 Water quality parameters.

5.9.1.2 Data requirements.

5.9.2 Case Study I: Lake Okeechobee.

5.9.2.1 Background.

5.9.2.2 Model setup and data sources.

5.9.2.3 Water quality modeling results.

5.9.2.4 SAV modeling results.

5.9.2.5 Discussions and Summary.

5.9.3 Case Study II: St. Lucie Estuary and Indian River Lagoon.

5.9.3.1 Model setup.

5.9.3.2 Water quality model calibration and verification.

5.9.3.3 Hydrodynamic and water quality processes in the SLE.

5.9.3.4 Summary and conclusions.

6. External Sources and TMDL.

6.1 Point Sources and Nonpoint Sources.

6.2 Atmospheric Deposition.

6.3 Wetlands and Ground Water.

6.3.1 Wetlands.

6.3.2 Ground Water.

6.4 Watershed Processes and TMDL Development.

6.4.1 Watershed Processes.

6.4.2 Total Maximum Daily Load (TMDL).

7. Mathematical Modeling and Statistical Analyses.

7.1 Mathematical Models.

7.1.1 Numerical Models.

7.1.2 Model Selection.

7.1.3 Spatial Resolution and Temporal Resolution.

7.2 Statistical Analyses.

7.2.1 Statistics for Model Performance Evaluation.

7.2.2 Correlation and Regression.

7.2.3 Spectral Analysis.

7.2.4 Empirical Orthogonal Function (EOF).

7.2.5 EOF Case Study.

7.3 Model Calibration and Verification.

7.3.1 Model Calibration.

7.3.2 Model Verification and Validation.

7.3.3 Sensitivity Analysis.

8. Rivers.

8.1 Characteristics of Rivers.

8.2 Hydrodynamic Processes in Rivers.

8.2.1 River Flow and the Manning Equation.

8.2.2 Advection and Dispersion in Rivers.

8.2.3 Flow over Dams.

8.3 Sediment and Water Quality Processes in Rivers.

8.3.1 Sediment and Contaminants in Rivers.

8.3.2 Impacts of River Flow on Water Quality.

8.3.3 Eutrophication and Periphyton in Rivers.

8.3.4 Dissolved Oxygen in Rivers.

8.4 River Modeling.

8.4.1 Case Study I: Blackstone River.

8.4.1.1 Modeling metals in the Blackstone River.

8.4.1.2 Impacts of sediment and metals sources.

8.4.1.3 Discussion and conclusions.

8.4.2 Case Study II: Susquehanna River.

8.4.2.1 Background.

8.4.2.2 Model application.

8.4.2.3 Discussions.

9. Lakes and Reservoirs.

9 1 Characteristics of Lakes and Reservoirs.

9.1.1 Key Factors Controlling a Lake.

9.1.2 Vertical Stratification.

9.1.3 Biological Zones in Lakes.

9.1.4 Characteristics of Reservoirs.

9.1.5 Lake Pollution and Eutrophication.

9.2 Hydrodynamic Processes.

9.2.1 Inflow, Outflow, and Water Budget.

9.2.2 Wind Forcing and Vertical Circulations.

9.2.3 Seasonal Variations of Stratification.

9.2.4 Gyres.

9.2.5 Seiches.

9.3 Sediment and Water Quality Processes in Lakes.

9.3.1 Sediment Deposition in Reservoirs and Lakes.

9.3.2 Algae and Nutrient Stratifications.

9.3.3 Dissolved Oxygen Stratifications.

9.3.4 Internal Cycling and Limiting Functions in Shallow Lakes.

9.4 Lake Modeling.

9.4.1 Case Study I: Lake Tenkiller.

9.4.1.1 Introduction.

9.4.1.2 Data sources and model setup.

9.4.1.3 Hydrodynamic simulation.

9.4.1.4 Water quality simulation.

9.4.1.5 Discussion and conclusions.

9.4.2 Case Study II: Lake Okeechobee.

9.4.2.1 Sediment and nutrient fluxes into the Fisheating Bay.

9.4.2.2 Impact of Hurricane Irene.

9.4.2.3 Impacts of SAV on nutrient concentrations.

10. Estuaries and Coastal Waters.

10.1 Introduction.

10.2 Tidal Processes.

10.2.1 Tides.

10.2.2 Tidal Currents.

10.2.3 Harmonic Analysis.

10.3 Hydrodynamic Processes in Estuaries.

10.3.1 Salinity.

10.3.2 Estuarine Circulation.

10.3.3 Stratifications of Estuaries.

10.3.3.1 Highly stratified estuaries.

10.3.3.2 Moderately stratified estuaries.

10.3.3.3 Vertically mixed estuaries.

10.3.3.4 An example of estuarine stratifications.

10.3.4 Flushing Time.

10.4 Sediment and Water Quality Processes in Estuaries.

10.4.1 Sediment Transport under Tidal Forcing.

10.4.2 Flocculation of Cohesive Sediment and Sediment Trapping.

10.4.3 Eutrophication in Estuaries.

10.5 Estuarine and Coastal Modeling.

10.5.1 Open Boundary Conditions.

10.5.2 Case Study I: Morro Bay.

10.5.2.1 Introduction.

10.5.2.2 Field data measurements.

10.5.2.3 Model setup.

10.5.2.4 Wetting and drying approaches.

10.5.2.5 Wet cell mapping.

10.5.2.6 Hydrodynamic processes in Morro Bay.

10.5.2.7 Summary and conclusions.

10.5.3 Case Study II: St. Lucie Estuary and Indian River Lagoon.

10.5.3.1 Ten-year simulations.

10.5.3.2 Influence of sea level rise on water quality.

Appendix A: Environmental Fluid Dynamics Code.

A1 Overview.

A2 Hydrodynamics.

A3 Sediment Transport.

A4 Toxic Chemical Transport and Fate.

A5 Water Quality and Eutrophication.

A6 Numerical Schemes.

A7 Documentation and Application Aids.

Appendix B: Conversion Factors.

Appendix C: Contents of Electronic Files.

C1 Channel Model.

C2 St. Lucie Estuary and Indian River Lagoon Model.

C3 Lake Okeechobee Environmental Model.

C4 Documentation and Utility Programs.

References.

Index.

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## Author Information

Zhen-Gang (Jeff) Ji, PHD, DES, PE, has more than twenty years of professional experience in surface water modeling and model development. His expertise includes hydrodynamics, wave simulation, eutrophication, toxic process, and sediment transport. He has developed and applied state-of-the-art hydrodynamic models and water quality models to the simulation of rivers, lakes, estuaries, and coastal waters. Currently, Dr. Ji is an oceanographer and numerical modeler with the Minerals Management Service.

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## Reviews

"On the whole, the topics are well organized, the prose is easy to read and understand, the style is lucid, and there is a wealth of information reflecting the knowledge and experience of the author. The book will also be useful to practicing water and environmental engineers.." (Journal of Hydrologic Engineering, August 2009)“

As a water quality professional, I found the book to be helpful and a very informative reference. It provides much needed information for solving practical environmental water resources problems through modeling. It would also be a great addition to any university library.” (Journal of the American Water Resources Association, July 2009)

“This hands-on reference illustrates the principles, basic processes, mathematical descriptions, and practical applications of modeling surface waters.” (APADE, 2009)

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