**Part I: COMPLETELY MIXED SYSTEMS**

**1. Introduction**

Engineers and Water Quality / Fundamental Quantities / Mathematical Models / Historical Development of Water-Quality Models / Overview of This Book

**2. Reaction Kinetics**

Reaction Fundamentals / Analysis of Rate Data / Stoichiometry / Temperature Effects

**3. Mass Balance, Steady-State Solution, and Response Time**

Mass Balance for a Well-Mixed Lake / Steady-State Solutions / Temporal Aspects of Pollutant Reduction

**4. Particular Solutions**

Impulse Loading (Spill) / Step Loading (New Continuous Source) / Linear ("Ramp") Loading / Exponential Loading / Sinusoidal Loading / The Total Solution: Linearity and Time Shifts / Fourier Series (Advanced Topic)

**5. Feedforward Systems of Reactors**

Mass Balance and Steady-State / Time Variable / Feedforward Reactions

**6. Feedback Systems of Reactors**

Steady-State for Two Reactors / Solving Large Systems of Reactors / Steady-State System Response Matrix / Time-Variable Response for Two Reactors / Reactions with Feedback

**7. Computer Methods: Well-Mixed Reactors**

Euler's Method / Heun's Method / Runge-Kutta Methods / Systems of Equations

**Part II: INCOMPLETELY MIXED SYSTEMS**

**8. Diffusion**

Advection and Diffusion / Experiment / Fick's First Law / Embayment Model / Additional Transport Mechanisms

**9. Distributed Systems (Steady-State)**

Ideal Reactors / Application of the PFR Model to Streams / Application of the PFR Model to Estuaries

**10. Distributed Systems (Time-Variable)**

Plug Flow / Random (or "Drunkard's") Walk / Spill Models / Tracer Studies / Estuary Number

**11. Control-Volume Approach: Steady-State Solutions**

Control-Volume Approach / Boundary Conditions / Steady-State Solution / System Response Matrix / Centered-Difference Approach / Numerical Dispersion, Positivity, and Segment Size / Segmentation Around Point Sources / Two- and Three-Dimensional Systems

**12. Simple Time-Variable Solutions**

An Explicit Algorithm / Stability / The Control-Volume Approach / Numerical Dispersion

**13. Advanced Time-Variable Solutions**

Implicit Approaches / The MacCormack Method / Summary

**Part III: WATER-QUALITY ENVIRONMENTS**

**14. Rivers and Streams**

River Types / Stream Hydrogeometry / Low-Flow Analysis / Dispersion and Mixing / Flow, Depth, and Velocity / Routing and Water Quality (Advanced Topic)

**15. Estuaries**

Estuary Transport / Net Estuarine Flow / Estuary Dispersion Coefficient / Vertical Stratification

**16. Lakes and Impoundments**

Standing Waters / Lake Morphometry / Water Balance / Near-Shore Models (Advanced Topic)

**17. Sediments**

Sediment Transport Overview / Suspended Solids / The Bottom Sediments / Simple Solids Budgets / Bottom Sediments as a Distributed System / Resuspension (Advanced Topic)

**18. The "Modeling" Environment**

The Water-Quality-Modeling Process / Model Sensitivity / Assessing Model Performance / Segmentation and Model Resolution

**Part IV: DISSOLVED OXYGEN AND PATHOGENS**

**19. BOD and Oxygen Saturation**

The Organic Production/Decomposition Cycle / The Dissolved Oxygen Sag / Experiment / Biochemical Oxygen Demand / BOD Model for a Stream / BOD Loadings, Concentrations, and Rates / Henry's Law and the Ideal Gas Law / Dissolved Oxygen Saturation

**20. Gas Transfer and Oxygen Reaeration**

Gas Transfer Theories / Oxygen Reaeration / Reaeration Formulas / Measurement of Reaeration with Tracers

**21. Streeter-Phelps: Point Sources**

Experiment / Point-Source Streeter-Phelps Equation / Deficit Balance at the Discharge Point / Multiple Point Sources / Analysis of the Streeter-Phelps Model / Calibration / Anaerobic Condition / Estuary Streeter-Phelps

**22. Streeter-Phelps: Distributed Sources**

Parameterization of Distributed Sources / No-Flow Sources / Diffuse Sources with Flow

**23. Nitrogen**

Nitrogen and Water Quality / Nitrification / Nitrogenous BOD Model / Modeling Nitrification / Nitrification and Organic Decomposition / Nitrate and Ammonia Toxicity

**24. Photosynthesis/Respiration**

Fundamentals / Measurement Methods

**25. Sediment Oxygen Demand**

Observations / A "Naive" Streeter-Phelps SOD Model / Aerobic and Anaerobic Sediment Diagenesis / SOD Modeling (Analytical) / Numerical SOD Model / Other SOD Modeling Issues (Advanced Topic)

**26. Computer Methods**

Steady-State System Response Matrix / The QUAL2E Model

**27. Pathogens**

Pathogens / Indicator Organisms / Bacterial Loss Rate / Sediment-Water Interactions / Protozoans: Giardia and Cryptosporidium

**Part V: EUTROPHICATION AND TEMPERATURE**

**28. The Eutrophication Problem and Nutrients**

The Eutrophication Problem / Nutrients / Plant Stoichiometry / Nitrogen and Phosphorus

**29. Phosphorus Loading Concept**

Vollenweider Loading Plots / Budget Models / Trophic-State Correlations / Sediment-Water Interactions / Simplest Seasonal Approach

**30. Heat Budgets**

Heat and Temperature / Simple Heat Balance / Surface Heat Exchange / Temperature Modeling

**31. Thermal Stratification**

Thermal Regimes in Temperate Lakes / Estimation of Vertical Transport / Multilayer Heat Balances (Advanced Topic)

**32. Microbe/Substrate Modeling**

Bacterial Growth / Substrate Limitation of Growth / Microbial Kinetics in a Batch Reactor / Microbial Kinetics in a CSTR / Algal Growth on a Limiting Nutrient

**33. Plant Growth and Nonpredatory Losses**

Limits to Phytoplankton Growth / Temperature / Nutrients / Light / The Growth-Rate Model / Nonpredatory Losses / Variable Chlorophyll Models (Advanced Topic)

**34. Predator-Prey and Nutrient/Food-Chain Interactions**

Lotka-Volterra Equations / Phytoplankton-Zooplankton Interactions / Zooplankton Parameters / Nutrient/Food-Chain Interactions

**35. Nutrient/Food-Chain Modeling**

Spatial Segmentation and Physics / Kinetic Segmentation / Simulation of the Seasonal Cycle / Future Directions

**36. Eutrophication in Flowing Waters**

Stream Phytoplankton/Nutrient Interactions / Modeling Eutrophication with QUAL2E / Fixed Plants in Streams

**Part VI: CHEMISTRY**

**37. Equilibrium Chemistry**

Chemical Units and Conversions / Chemical Equilibria and the Law of Mass Action / Ionic Strength, Conductivity, and Activity / pH and the Ionization of Water / Equilibrium Calculations

**38. Coupling Equilibrium Chemistry and Mass Balance**

Local Equilibrium / Local Equilibria and Chemical Reactions

**39. pH Modeling**

Fast Reactions: Inorganic Carbon Chemistry / Slow Reactions: Gas Transfer and Plants / Modeling pH in Natural Waters

**Part VII: TOXICS**

**40. Introduction to Toxic-Substance Modeling**

The Toxics Problem / Solid-Liquid Partitioning / Toxics Model for a CSTR / Toxics Model for a CSTR with Sediments / Summary

**41. Mass-Transfer Mechanisms: Sorption and Volatilization**

Sorption / Volatilization / Toxicant-Loading Concept

**42. Reaction Mechanisms: Photolysis, Hydrolysis, and Biodegradation**

Photolysis / Second-Order Relationships / Biotransformation / Hydrolysis / Other Processes

**43. Radionuclides and Metals**

Inorganic Toxicants / Radionuclides / Metals

**44. Toxicant Modeling in Flowing Waters**

Analytical Solutions / Numerical Solutions / Nonpoint Sources

**45. Toxicant/Food-Chain Interactions**

Direct Uptake (Bioconcentration) / Food-Chain Model (Bioaccumulation) / Parameter Estimation / Integration with Mass Balance / Sediments and Food Webs (Advanced Topic)

Appendix A: Conversion Factors

Appendix B: Oxygen Solubility

Appendix C: Water Properties

Appendix D: Chemical Elements

Appendix E: Numerical Methods Primer

Appendix F: Bessel Functions

Appendix G: Error Function and Complement