United States
Environmental Protection
Agency
Environmental Research
Laboratory
At hens G A 30613
EPA 600 6-85 '002t>
September 1985
Revised
Research and Develooment
Water Quality
Assessment:
A Screening
Procedure for Toxic and
Conventional Pollutants in
Surface and Ground
Water—Part II
(Revised 1985)
Printed on Recycled Paper
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EPA/600/6-85/002b
September 1985
HATER QUALITY ASSESSMENT:
A Screening Procedure for Toxic
and Conventional Pollutants
(Revised 1985)
Part II
by
W.B. Mills, D.B. Porcella, M.J. Ungs, S.A. Gherini, K.V. Summers,
Lingfung Mok, G.L. Rupp, and G.L. Bowie
Tetra Tech, Incorporated
Lafayette, California 94549
and
O.A. Haith
Cornell University
Ithaca, New York 14853
Produced by:
JACA Corporation
Fort Washington, Pennsylvania 19034
Contract No. 68-03-3131
Prepared in Cooperation with U.S. EPA's
Center for Water Quality Modeling
Environmental Research Laboratory
Athens, Georgia
Monitoring and Data Support Division
Office of Water Regulations and Standards
Office of Water
Washington, D.C.
Technology Transfer
Center for Environmental Research Information
Cincinnati, Ohio
ENVIROWENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
-------
DISCLAIMER
tention of trade nones or commercial products does not constitute endorse-
ment or recommendation for use by the U.S. Environmental Protection Agency.
-11-
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ABSTRACT
New technical developments 1n the field of water quality assessment and
a reordering of water quality priorities prompted a revision of the first two
editions of this Manual. The utility of the revised manual 1s enhanced by
the Inclusion of Methods to predict the transport and fate of toxic chemicals
1n ground water, and by methods to predict the fate of metals In rivers. In
addition, major revisions were completed on Chapter 2 (organic toxicants),
Chapter 3 (waste loadings), and Chapter 5 (Impoundments) that reflect recent
advancements in these fields.
Applying the manual *s simple techniques, the user 1s now capable of
assessing the loading and fate of conventional pollutants (temperature,
biochemical oxygen demand-dissolved oxygen, nutrients, and sediments) and
toxic pollutants (from the U.S. EPA 11st of priority pollutants) 1n streams,
impoundments, estuaries, and ground waters. The techniques are readily
programmed on hand-held calculators or microcomputers. Most of the data
required for using these procedures are contained in the manual.
Because of Us size, the manual has been divided into two parts. Part
I contains the Introduction and chapters on the aquatic fate of toxic organic
substances, waste loading calculations, and the assessment of water quality
parameters in rivers and streams. Part II continues with chapters on the
assessment of Impoundments, estuaries, and ground water and appendices E, H,
I, and J. Appendices D, F, and G are provided on microfiche in the EPA-printed
manual. Appendices A, B. and C, which appeared in the first two editions,
are now out of date and have been deleted.
This report 1s submitted in fulfillment of Contract No. 68-03-3131 by
JACA Corp. and Tetra Tech, Inc. under the sponsorship of the U.S. Environ-
mental Protection Agency. Work was completed as of May 1985.
-iii-
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TABLE OF CONTENTS
PART II
DISCLAIMER 11
ABSTRACT 111
LIST OF FIGURES (Part II) ' 1x
LIST OF TABLES (Part II) xv
5 IMPOUNDMENTS 1
5.1 INTRODUCTION 1
5.2 IMPOUNDMENT STRATIFICATION 2
5.2.1 Discussion 2
5.2.2 Prediction of Thermal Stratification 6
5.3 SEDIMENT ACCUMULATION 19
5.3.1 Introduction 19
5.3.2 Annual Sediment Accumulation. 20
5.3.3 Short-Term Sedimentation Rates 23
5.3.4 Impoundment Hydraulic Residence Time 29
5.3.5 Estimation of Sediment Accumulation 43
5.4 EUTROPHICATION AND CONTROL 49
5.4.1 Introduction 49
5.4.2 tatHents, Eutrophy, and Algal Growth 50
5.4.3 Predicting Algal Concentrations 51
5.4.4 Mass Balance of Phosphorus 52
5.4.5 Predicting Algal Productivity, Secchl Depth,
and Blomass 60
5.4.6 Restoration Measures 64
5.4.7 Water Column Phosphorus Concentrations 64
5.5 IMPOUNDMENT DISSOLVED OXYGEN 71
5.5.1 Simulating Impoundment Dissolved Oxygen 73
5.5.2 A Simplified Impoundment Dissolved Oxygen Model 74
5.5.3 Temperature Corrections 85
5.6 TOXIC CHEMICAL SUBSTANCES 97
5.6.1 Overall Processes 99
5.6.2 Guidelines for Toxics Screening 104
5.7 APPLICATION OF METHODS AND EXAMPLE PROBLEM 109
5.7.1 The Occoquan Reservoir 110
5.7.2 Stratification Ill
5.7.3 Sedimentation 115
5.7.4 Eutrophl cation 123
5.7.5 HypoHmnetic 00 Depletion 128
5.7.6 Toxicants 133
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Chapter p.a.9g
REFERENCES 136
GLOSSARY OF TERMS 139
6 ESTUARIES 142
6.1 INTRODUCTION 142
6.1.1 General 142
6.1.2 EstuaMne Definition 143
6.1.3 Types of Estuaries 143
6.1.4 Pollutant Flow 1n an Estuary 145
6.1.5 EstuaMne Complexity and Major Forces 149
6.1.6 Methodology Summary 151
6.1.7 Present Water-Quality Assessment 153
6.2 ESTUARINE CLASSIFICATION* 155
6.2.1 General 155
6.2.2 Classification Methodology 155
6.2.3 Calculation Procedure 155
6.2.4 Stratification-Circulation Diagram Interpretation .... 157
6.2.5 Flow Ratio Calculation 163
6.3 FLUSHING TIME CALCULATIONS 165
6.3.1 General 165
6.3.2 Procedure 165
6.3.3 Fraction of Fresh Water Method 170
6.3.4 Calculation of Flushing Time by Fraction of Freshwater
Method 171
6.3.5 Branched Estuaries and the Fraction of Freshwater
Method 176
6.3.6 Modified Tidal Prism Method 176
6.4 FAR FIELD APPROACH TO POLLUTANT DISTRIBUTION IN
ESTUARIES 184
6.4.1 Introduction 184
6.4.2 Continuous Flow of Conservative Pollutants 185
6.4.3 Continuous Flow Non-Conservative Pollutants 197
6.4.4 Multiple Waste Load Parameter Analysis 204
6.4.5 D1spers1on-Advect1on Equations for Predicting
Pollutant Distributions 207
6.4.6 PMtchard's Two-Dimens1onal Box Model for Stratified
Estuaries 216
6.5 POLLUTANT DISTRIBUTION FOLLOWING DISCHARGE FROM A
MARINE OUTFALL 226
6.5.1 Introduction 226
6.5.2 Prediction of Initial Dilution 227
6,5.3 Pollutant Concentration Following Initial Dilution. ... 248
6.5.4 pH Following Initial Dilution 250
6.5.5 Dissolved Oxygen Concentration Following Initial
Dilution 255
6.5.6 Far Field Dilution and Pollutant Distribution 257
6.5.7 Farfield Dissolved Oxygen Depletion 263
6.6 THERMAL POLLUTION 266
6.6.1 General 266
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Chapter Page
6.6.2 Approach 267
6.6.3 Application 269
6.7 TURBIDITY 274
6.7.1 Introduction 274
6.7.2 Procedure to Assess Impacts of Wastewater Discharges
on Turbidity or Related Parameters 276
6.8 SEDIMENTATION 282
6.8.1 Introduction 282
6.8.2 Qualitative Description of Sedimentation 282
6.8.3 Estuarlne Sediment Forces and Movement 283
6.8.4 Settling Velocities 287
6.8.5 Null Zone Calculations 291
REFERENCES 295
7 GROUND WATER 300
7.1 OVERVIEW 300
7.1.1 Purpose of Screening Methods 300
7.1.2 Ground Water vs. Surface Water 301
7.1.3 Types of Ground' Water Systems Suitable for Screening
Method 302
7.1.4 Pathways for Contamination 303
7.1.5 Approach to Ground Water Contamination Problems 305
7.1.6 Organization of This Chapter 309
7.2 AQUIFER CHARACTERIZATION 310
7.2.1 Physical Properties of Water 310
7.2.2 Physical Properties of Porous Media 310
7.2.3 Flow Properties of Saturated Porous Media 319
7.2.4 Flow Properties of Unsaturated Porous Media 323
7.2.5 Data Acquisition or Estimation 329
7.3 GROUND WATER FLOW REGIME 345
7.3.1 Approach to Analysis of Ground Water Contamination
Sites 345
7.3.2 Water Levels and Flow Directions 346
7.3.3 Flow Velocities and Travel Times 353
7.4 POLLUTANT TRANSPORT PROCESSES 363
7.4.1 Dispersion and Diffusion 363
7.4.2 Chemical and Biological Processes Affecting Pollutant
Transport 374
7.5 METHODS FOR PREDICTING THE FATE AND TRANSPORT OF
CONVENTIONAL AND TOXIC POLLUTANTS 382
7.5.1 Introduction to Analytical Methods 382
7.5.2 Contaminant Transport to Deep Wells 390
7.5.3 Solute Injection Wells: Radial Flow 396
7.5.4 Contaminant Release on the Surface with 1-D Vertical
Downward Transport 403
7.5.5 Two-Dimensional Horizontal Flow with a Slug Source. . . . 410
7.5.6 Two-Dimensional Horizontal Flow with Continuous
Solute Line Sources 417
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Chapter
Page
7.6 INTERPRETATION OF RESULTS 423
7.6.1 Appropriate Reference Criteria 423
7.6.2 Quantifying Uncertainty 424
7.6.3 Guidelines for Proceeding to More Detailed Analysis ... 429
REFERENCES 435
References Sited 435
Additional References on Ground Water Sampling 444
APPENDIX A A-l
APPENDIX B B-l
APPENDIX C C-l
APPENDIX D IMPOUNDMENT THERMAL PROFILES D-l
APPENDIX E MODELING THERMAL STRATIFICATION IN IMPOUNDMENTS E-l
APPENDIX F RESERVOIR SEDIMENT DEPOSITION SURVEYS F-l
APPENDIX G INITIAL DILUTION TABLES G-l
APPENDIX H EQUIVALENTS BY COMMONLY USED UNITS OF MEASUREMENTS. ... H-l
APPENDIX I ADDITIONAL AQUIFER PARAMETERS 1-1
APPENDIX J MATHEMATICAL FUNCTIONS J-l
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LIST OF FIGURES
PART II
V-l Mater Density as a Function of Temperature and Dissolved
Solids Concentration ...................... 3
V-2 Water Flowing Into an Impoundment Tends to Migrate toward
a Region of Similar Density. .... .............. 3
V-3 Annual Cycle of Thermal Stratification and Overturn in
an Impoundment ......................... 5
V-4 Thermal Profile Plots Used 1n Example V-l ............ 15
V-5 Thermal Profile Plots Appropriate for Use In Example V-2 .... 18
V-6 Sediment Rating Curve Showing Suspended Sediment Discharge
as a Function of Flow ...................... 21
V-7 Relationship between the Percentage of Inflow-Transported
Sediment Retained within an Impoundment and Ratio of
Capacity to Inflow ....................... 22
V-8 Plot of C/R and CR2 Versus R .................. 25
V-9 Drag Coefficient (C) as Function of Reynold's Number (R)
and Particle Shape ....................... 26
V-10 Schematic Representation of Hindered Settling of Particles
in Fluid Column ......................... 27
V-ll Velocity Correction Factor for Hindered Settling ........ 27
V-12 Upper and Lower Lakes and Environs, Long Island, New York. ... 32
V-13 Impoundment Configurations Affecting Sedimentation ....... 34
V-14 Kellis Pond and Surrounding Region, Long Island, New York. ... 37
V-l 5 Hypothetical Depth Profiles for Kellis Pond ........... 38
V-16 Hypothetical Flow Pattern in Kellis Pond ........... 38
V-17 Hypothetical Depth Profiles for Kellis Pond Not Showing
Significant Shoaling ...................... 39
V-18 Lake Owyhee and Environs .................... 41
V-19 New Millpond and Environs .................... 42
V-20 Significance of Depth Measures D, D' and D" and the Assumed
Sedimentation Pattern ...................... 44
V-21 Settling Velocity for Spherical Particles ............ 45
V-22 Nomograph for Estimating Sediment Trap Efficiency ........ 46
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Figure Page
V-23 Formulations for Evaluating Management Options for Pollutants
V-24
V-25
V-26
V-27
V-28
V-29
V-30
V-31
V-32
V-33
V-34
V-35
V-36
V-37
V-38
V-39
VI-1
VI-2
VI-3
VI-4
VI-5
VI-6
VI-7
US OECD Date Applied to Vollenwelder (1976) Phosphorus Loading
and Mean Depth/ Hydraulic Residence Time Relationship
Relationship between Summer Chlorophyll and Spring Phosphorus. .
Maximal Primary Productivity as a Function of Phosphate
Conceptualization of Phosphorus Budget Modeling
Typical Patterns of Dissolved Oxygen (DO) 1n Hyrum Reservoir . .
Geometric Representation of a Stratified Impoundment
Quality and Ecologic Relationships
Rate of BOD Exertion at Different Temperatures Showing the
First and Second Deoxygenatlon Stages
Quiet Lake and Environs
Generalized Schematic of Lake Computations
The Occoquan River Basin .
Thermal Profile Plots for Occoquan Reservoir
Summary of Reservoir Sedimentation Surveys Made in the
United States through 1970
Dissolved Oxygen Depletion Versus Time in the Occoquan
Reservoir
Typical Main Channel Salinity and Velocity for Stratified
Estuaries
Typical Main Channel Salinity and Velocity Profiles for Well
Mixed Estuaries
Typical Main Channel Salinity and Velocity Profiles for
Partially Mixed Estuaries
Estuarine Dimensional Definition
Suggested Procedure to Predict Estuarine Hater Quality
Estuarine Circulation-Stratification Diagram
Examples of Estuarine Classification Plots
55
61
63
66
72
74
75
78
86
93
106
110
111
114
116
132
146
147
148
150
154
156
156
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Figure
VI-8 Circulation and Stratification Parameter Diagram 158
VI-9 The Stuart Estuary 160
VI-10 Stuart Estuary Data for Classification Calculations 161
VI-11 EstuaMne Circulation-Stratification Diagram 162
VI-12 Alsea Estuary Seasonal Salinity Variations 163
VI-13 Estuary Cross-Section for Tidal Prism Calculations 165
VI-14 Patuxent Estuary Salinity Profile and Segmentation Scheme
Used in Flushing Time Calculations 175
VI-15 Hypothetical Two-Branched Estuary 178
VI-16 Cumulative Upstream Water Volume, Fox Mill Run Estuary 182
VI-17 River Borne Pollutant Concentration for One Tidal Cycle 190
VI-18 Alsea Estuary Rlverborne Conservative Pollutant Concentration. . 192
VI-19 Pollutant Concentration from an Estuarine Outfall 193
VI-20 Hypothetical Concentration of Total Nitrogen 1n Patuxent
Estuary 196
VI-21 Relative Depletions of Three Pollutants Entering the
Fox Mill Run Estuary, Virginia 203
VI-22 Additive Effect of Multiple Waste Load Additions 204
VI-23 Dissolved Oxygen Saturation as a Function of Temperature
and Salinity 213
VI-24 Predicted Dissolved Oxygen Profile In James River 215
VI-25 Definition Sketch for PMtchard's Two-Dimensional Box Model. . . 218
VI-26 Patuxent Estuary Model Segmentation 225
VI-27 Waste Field Generated by Marine Outfall 228
VI-28 Example Output of MERGE - Case 1 240
VI-29 Example Output of MERGE - Case 2 241
VI-30 Schematic of Plume Behavior Predicted by MERGE 1n the Present
Usage 244
VI-31 Cross Diffuser Merging 247
VI-32 Plan View of Spreading Sewage Field 259
VI-33 Outfall Location, Shellfish Harvesting Area, and Environs. ... 262
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VI-34 Dissolved Oxygen Depletions Versus Travel Time 265
VI-35 Centerllne Dilution of Round Buoyant Jet In Stagnant
Uniform Environment 274
VI-36 Mean Suspended Solids in San Francisco Bay 276
VI-37 Water Quality Profile of Selected Parameters Near a Municipal
Outfall in Puget Sound, Washington 279
VI-38 Sediment Movement in San Francisco Bay System 287
VI-39 Idealized Estuarine Sedimentation 288
VI-40 Particle Diameter vs Settling Fall per Tidal Cycle Under
Quiescent Conditions 291
VI-41 Estuarine Null Zone Identification 293
VII-1 Major Aquifers of the United States 304
VI1-2 Geologic Section in Western Suffolk County, Long Island,
Showing Both Confined and Unconfined Aquifers 305
VII-3 Detailed Quaternary Geologic Map of Morris County 306
VI1-4 Generalized Cross-sections Showing Features Common in Arid
Western Regions of the United States 307
VI1-5 Number of Waste Impoundments by State 308
VII-6 Schematic Showing the Solid, Liquid and Gaseous Phases in a
Unit Volume of Soil 312
VI1-7 Soil Texture Trllinear Diagram Showing Basic Soil Textural
Classes 315
VI1-8 Typical Particle-Size Distribution Curves for Various Soil
Classifications 315
VI1-9 Schematic Cross-section Showing Both a Confined and an
Unconfined Aquifer 320
VII-10 Schematic of Matric and Osmotic Soil-Water Potential ...... 326
VII-11 Characteristic Curves of Moisture Content as a Function of
Matric Potential for Three Different Soils 328
VI1-12 Characteristic Curves of Moisture Content and Hydraulic
Conductivity as a Hysteretlc Function of Matric Potential
for a Naturally Occurring Sandy Soil 330
VI1-13 Hydraulic Conductivity as a Function of Moisture Content
for Three Different Soils 331
VI1-14 Cross-Sectional Diagram Showing the Water Level as Measured
by Piezometers Located at Various Depths 348
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Page
VI1-15 An Example of a Contour Plot of Water Level Data With
Inferred Flow Directions 351
VI1-16 Schematic Showing the Construction of Flow Direction Lines
from Equipotential Lines for Isotropic Aquifers and
Anisotropic Aquifers 352
VI1-17 Schematic Diagrams Showing Permeameters to Demonstrate
Darcy's Law 354
VI1-18 Schematic Showing How Travel Time Can Be Calculated for
Solute Transport When the Flow Velocity Varies: a) Original
Problem, t>) Discretized Representation of the Flow Line 360
VI1-19 Example Problem: Calculation of Travel Time for Sulfate
from Holding Basin to River 362
VI1-20 Schematic Showing the Effect of Scale on Hydrodynamic
Dispersion Processes 365
VI1-21 Field Measured Values of Longitudinal Dispersivity as a
Function of Scale Length for Saturated Porous Media 367
VII-22 A Plot of Longitudinal Dispersivity vs. Scale Length for
Saturated Porous Media 368
VII-23 A Plot of Longitudinal Oispersivity vs. Scale Length for
Unsaturated Porous Media 369
VI1-24 Schematic Showing the Solution of Equation VII-50 and the
Effect of Dispersion 371
VI1-25 Schematic Showing Hypothetical Vertical Variation in the
Ground Water Flow Velocity 375
VI1-26 Major Equilibrium and Rate Processes in Natural Waters 376
VI1-27 Hypothetical Adsorption Curves for Cations and Anions
Showing Effect of pH and Organic Matter 379
VI1-28 Dehydrochlorination Rate of Tetrachloroethylene and the
Production Rate of its Dechlorination Products 383
VI1-29 Summary of Model Describing Contaminant Transfer to Deep
Wells 385
VI1-30 Summary of Model Describing Radial Flow from an Injection
Well 386
VI1-31 Summary of Model Describing One-Dimensional, Vertically
Downward Transport of a Contaminant Released on the Surface. . . 387
VI1-32 Summary of Model Describing Two-Dimensional Horizontal Flow
With a Slug Source 388
VI1-33 Summary of Model Describing Two-Dimensional Horizontal Flow
With Continuous Solute Line Sources 389
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Figure Page
VII-34 Schematic of ROM to a Well Beneath a Contaminated Zone 392
VI1-35 Normalized Solute Concentration vs. Dlmenslonless Time 393
VI1-36 Schematic of Example Problem for Row to Well from a Shallow
Contaminated Zone 395
VI1-37 Schematic View of a Well Injection Solute Into a Confined
Aquifer 397
VI1-38 Schematic of the Example Problem Showing Radial Flow of
Plating Waste from an Injection Well 401
VI1-39 Schematic Showing Equation for 1-0 Vertical Transport from
a Surface Waste Source 404
VI1-40 Schematic of Example 1-0 Problem 407
VII-41 Schematic Showing a Slug Discharge of Waste Into a Reflonal
Flow Field 412
VI1-42 Schematic Showing a Continuous Discharge of Waste Into a
Regional Flow Field 419
VI1-43 General Sequence to Determine If a Modeling Effort 1s Needed . . 433
VI1-44 Steps Involved 1n Model Application 434
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LIST OF TABLES
PART II
Table
V-l
V-2
V-3
V-4
V-5
V-6
V-7
V-8
V-9
V-10
v-n
V-12
V-13
V-14
V-15
V-16
V-17
V-18
V-19
V-20
V-21
Parameter Values Used 1n Generation of Thermal Gradient Plots. .
Temperature, Cloud Cover, and Dew Point Data for the Ten
Geographic Locales Used to Develop Thermal Stratification
Plots
Limpid Lake Characteristics
Physical Characteristics of Lake Smith
Comparison of Monthly Cl imatologic Data for Shreveport,
Louisiana and Atlanta, Georgia .
Hypothetical Physical Characteristics and Computations
for Upper Lake, Brookhaven, Suffolk County, New York
Hypothetical Physical Characteristics and Computations
for Lower Lake, Brookhaven, Suffolk County, New York
Hypothetical Physical Characteristics and Computations
Preliminary Classification of Trophic State Based on
Classification of Lake Restoration Techniques
Oxygen Demand of Bottom Deposits
Solubility of Oxygen in Water
Characteristics of Quiet Lake
Water Quality and Flow Data for Tributaries to Quiet Lake. . . .
Precipitation and Runoff Data for Quiet Lake Watershed
DO Sag Curve for Quiet Lake Hypolimnion
Significant Processes Affecting Toxic Substances in Aquatic
Ecosystems
Comparison of Modeled Thermal Profiles to Observed Temperatures
1n Occoquan Reservoir
Annual Sediment and Pollutant Loads in Occoquan Watershed in
Metric Tons per Year
Sediment Loaded into Lake Jackson
Calculation Format for Determining Sediment Accumulation in
Reservoirs
8
9
14
16
17
31
33
36
56
65
79
81
87
87
90
97
98
115
118
118
119
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Table
V-22 Particle Sizes in Penn Silt Loan ................ 120
V-23 Calculation Format for Determining Sediment Accumulation in
Reservoirs ........................... 121
V-24 Sewage Treatment Plant Pollutant Loads in Bull Run Sub-Basin
in Metric Tons per Year ..................... 125
V-25 Calculated Annual Pollutant Loads to Occoquan Reservoir ..... 125
V-26 Observed Annual Pollutant Loads to Occoquan Reservoir ...... 126
V-27 Calculated and Observed Mean Annual Pollutant Concentrations
in Occoquan Reservoir ...................... 127
VI -1 Summary of Methodology for Estuarine Mater Quality Assessment. . 152
VI -2 Tidal Prisms for Some U.S. Estuaries .............. 166
VI-3 Sample Calculation Table for Calculation of Flushing Time by
Segmented Fraction of Freshwater Method ............. 173
VI -4 Patuxent Estuary Segment Characteristics for Flushing Time
Calculations .......................... 175
VI-5 Flushing Time for Patuxent Estuary ............... 177
VI-6 Sample Calculation Table for Estuarine Flushing Time by the
Modified Tidal Prism Method ................... 180
VI-7 Data and Flushing Time Calculations for Fox Mill Run Estuary . . 184
VI-8 Pollutant Distribution in the Patuxent River .......... 188
VI-9 Incremental Total Nitrogen in Patuxent River, Expressed as
Kilograms ............................ 188
VI-10 Sample Calculation Table for Distribution of a Locally
Discharged Conservative Pollutant by the Fraction of
Freshwater Method ........................ 194
VI-11 Nitrogen Concentration in Patuxent Estuary Based on Local
Discharge ............................ 195
VI-12 Typical Values for Decay Reaction Rates 'k1 ........... 198
VI-13 Sample Calculation Table for Distribution of a Locally
Discharged Non-conservative Pollutant by the Modified
Tidal Prism Method ....................... 20C
VI-14 Salinity and CBOD Calculations for Fox Mill Run Estuary ..... 202
Vl-15 Distribution of Total Nitrogen in the Patuxent Estuary Due
to Two Sources of Nitrogen ................... 207
VI-16 Tidally Averaged Dispersion Coefficients for Selected Estuaries. 209
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Table
VI-17 Tidally Averaged Dispersion Coefficients 210
VI-18 Salinity and Pollutant Distribution in Patuxent Estuary Under
Low How Conditions 224
VI-19a Water Densities (Expressed as Sigma-T) Calculated Using the
Density Subroutine Found 1n Merge 231
VI-19b Water Densities (Expressed as S1gma-T) Calculated Using the
Density Subroutine Found in Merge 233
VI-19c Water Densities (Expressed as Sigma-T) Calculated Using the
Density Subroutine Found in Merge 235
VI-20 Plume Variables, Units, and Similarity Conditions 238
VI-21 Values of Equilibrium Constants and Ion Product of Water as
a Function of Temperature for Freshwater and Salt Water 251
VI-22 Estimated pH Values After Initial Dilution 253
VI-23 Dissolved Oxygen Profile in Commencement Bay, Washington .... 256
VI-24 Subsequent Dilutions for Various Initial Field Widths and
Travel Times 260
VI-25 Data Needed for Estuary Thermal Screening 268
VI-26 Allowable Channel Velocity to Avoid Bed Scour 284
VI-27 Sediment Particle Size Ranges 289
VI-28 Rate of Fall 1n Water of Spheres of Varying Radii and
Constant Density of 2 as Calculated by Stokes1 Law 290
VII-1 Aquifer Parameters and Their Relative Importance as Screening
Parameters 311
VI1-2 Range and Mean Values of Dry Bulk Density 314
VI1-3 Effective Grain Size and the Range of Soil Particle Sizes for
Various Materials 316
VI1-4 Range and Mean Values of Porosity 318
VI1-5 Typical Values of Saturated Hydraulic Conductivity and Intrinsic
Permeability 321
VI1-6 Summary of Methods for Measuring Soil Moisture 333
VI1-7 Techniques for Measuring Saturated Hydraulic Conductivity. ... 336
VII-8 Sample Size for Various Confidence Levels Using the Student's
t-Distribution 342
VI1-9 Standard Normal Distribution Function 343
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Table Page
VII-10 Percentage Points of the Student's t-Distribution 343
VII-11 Methods for Measuring Ground Water How Velocity 358
VI1-12 Summary of Solution Methods 384
VI1-13 Primary Drinking Water Standards 425
VII-14 Interim Secondary Drinking Water Standards 426
VI1-15 Data Needs for Numerical Models 432
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CHAPTER 5
IMPOUKOMENTS
5.1 INTRODUCTION
This chapter contains several methods for assessing water quality and physical
conditions 1n Impoundments. The general topics covered are sediment accumulation.
thermal stratification, DO-BOD, eutroph1cat1on, and toxicant concentrations. These
topics cover the major water problems likely to occur 1n impoundments. The methods
developed are easy to use and require readily obtainable data. Because the methods
depend upon a number of simplifying assumptions, estimates should be taken only as a
guide pending further analysis. Also, since pollutant inputs are dependent on
previous calculations, familiarity with the methods in previous chapters will be very
helpful and expand understanding of the various processes.
Some of the techniques are more mechanistic and reliable than others. For
example, the thermal stratification technique is based upon output of a calibrated
and validated hydrothermal model. The model has been shown to be a good one, and to
the extent that physical conditions in the studied impoundments resemble those of the
model, results should be very reliable. On the other hand, the methods for predict-
ing eutrophication are empirical and based upon correlations between historical water
quality conditions and algal productivity In a number of lakes and reservoirs.
Because algal blooms are sensitive to environmental factors and the presence of
toxicants and factors other than those involved in the estimation methods, the
methods for predicting eutrophication will occasionally be inapplicable. Additional
approaches have been developed to broaden the applicability of these empirical
models.
In using the techniques to be presented, it 1s important to apply good "engi-
neering judgment" particularly where sequential application of methods is likely to
result in cumulative errors. Such would be the case, for example, in evaluating
Impoundment hypolimnlon DO problems resulting from algal blooms. If methods presented
below are used to evaluate hypolimnlon DO, the planner should determine when strati-
fication occurs, the magnitude of point and nonpoint source BOD loads, and algal
productivity and settling rates. From all of this, he may then predict BOD and DO
levels in the hypolimnlon. Since each of these techniques has an error associated
with It, the-end result of the computation will have a significant error envelope and
results must be interpreted accordingly. The best way to use any of the techniques
1s to assume a range of values for important coefficients 1n order to obtain a range
of results within which the studied impoundment is likely to fall.
Although scientists and engineers are familiar with the metric system of units,
planners, local interest groups, and the general public are more accustomed to the
English system. Most morphometric data on lakes and impoundments are in English
-1-
-------
units. The conversion tables in Appendix H should be thoroughly familiar before
using these techniques and users should be able to perform calculations in either
system even though metric units are simpler to use. Also, dimensional analysis
techniques using unit conversions are very helpful in performing the calculations.
The methods presented below are arranged in an order such that the planner
should be able to use each if he has read preceding materials. The order of presen-
tation is:
• Impoundment stratification (5.2)
• Sediment accumulation (5.3)
• Eutrophication (5.4)
• Impoundment dissolved oxygen (5.5)
• Fate of Priority Pollutants (Toxics) (5.6).
It is strongly recommended that all materials presented be read and examples
worked prior to applying any of the methods. In this way a better perspective can be
obtained on the kinds of problems covered and what can be done using hand calculations.
A glossary of terms has been placed after the reference section so that equation
terms can easily be checked.
The final section (5.7) is an example application to a selected site. This
example allows the user to have an integrated view of an actual problem and applica-
tion. Also "the goodness of fit" to measured results can be evaluated.
5.2 IMPOUNDMENT STRATIFICATION
5.2.1 Discussion
The density of water 1s strongly influenced by temperature and by the concentra-
tion of dissolved and suspended matter. Figure V-l shows densities for water as a
function of temperature and dissolved solids concentration (from Chen and Orlob,
1973).
Regardless of the reason for density differences, water of lowest density
tends to move upward and reside on the surface of an impoundment while water of
greatest density tends to sink. Inflowing water seeks an impoundment level contain-
ing water of the same density. Figure V-2 shows this effect schematically.
Where density gradients are very steep, mixing 1s Inhibited. Thus, where the
bottom water of an Impoundment is significantly more dense than surface water,
vertical mixing is likely to be unimportant. The fact that low density water tends
to reside atop higher density water and that mixing 1s inhibited by steep gradients
often results in impoundment stratification. Stratification, which is the establish-
ment of distinct layers of different densities, tends to be enhanced by quiescent
conditions. Conversely, any phenomenon encouraging mixing, such as wind stress,
turbulence due to large inflows, or destabilizing changes in water temperature will
tend to reduce or eliminate strata.
-2-
-------
.0090
1.0070
1.0050
1.0030
*•«
0
1.00(0
0.9990
0.9970
Dissolved solids, ppm
35 40 45 50 55 60 65
Temperature, °F
70
75
80
85
FIGURE V-l
WATER DENSITY AS A FUNCTION OF TEMPERATURE AND DISSOLVED SOLIDS
CONCENTRATION (FROM CHEN AND ORLOB, 1973)
STRATIFIED
IMPOUNDMENT
PROFILE
Dentity *f
W«rm I* fluent
FIGURE V-2 WATER PLOWING INTO AN IMPOUNDMENT TENDS TO MIGRATE TOWARD
A REGION OP SIMILAR DENSITY
-3-
-------
5.2.1.1 Annual Cycle 1n a Thermally Stratified Impoundment
Figure V-3 shows schematically the processes of thermal stratification and
overturn which occur in many Impoundments. Beginning at "a" 1n the figure (winter),
cold water (at about 4°C) flows Into the Impoundment which may at this point be
considered as fully mixed. There Is no thermal gradient over depth and the Impound-
ment temperature 1s about 6°C. During spring ("b*), Inflowing water 1s slightly
warmer than that of the Impoundment because of the exposure of the tributary stream
to warmer air and increasingly intense sunlight. This trend continues during the
summer ("c"), with tributary water being much warmer and less dense than the deep
waters of the impoundment. At the same time, the surface water of the Impoundment 1s
directly heated by insolation. Since the warm water tends to stay on top of the
Impoundment, thermal strata form.
As fall approaches ("d"), day length decreases, air temperatures drop, and solar
intensity decreases. The result is cooler inflows and a cooling trend in the surface
of the impoundment. The bottom waters lag behind the surface in the rate of tempera-
ture change, and ultimately the surface may cool to the temperature of the bottom.
Since continued increases in surface water density result In Instability, the Impound-
ment water mixes (overturns).
5.2.1.2 Konomictlc and Dimictic Impoundments
The stratification and overturn processes described in Figure V-3 represent what
occurs in $ monocnictic or single-overturn water body. Some Impoundments, especially
those north of 40°N latitude and those at high elevation, may undergo two periods of
stratification and two overturns. Such impoundments are termed "d1m1ct1c." In
addition to the summer stratification and resulting fall overturn, such impoundments
stratify in late winter. This occurs because water is most dense near 4*C, and
bottom waters may be close to this temperature, while inflowing water is colder and
less dense. As the surface goes below 4°C, strata are established. With spring
wanning of the surface to 4°C, wind induced mixing occurs.
5.2.1.3 Importance of Stratification
Stratification is likely to be the single most important phenomenon affecting
water quality in many impoundments. Where stratification is absent, water mixes
vertically, and net horizontal flow is significant to considerable depths. Since the
water is mixed vertically, DO replenishment usually occurs even to the bottom and
anoxic (literally "no oxygen") conditions are unlikely. Generally speaking, fully
mixed impoundments do not have DO deficiency problems.
When stratification occurs, the situation is vastly different. Flow within the
impoundment is especially limited to the epllimnlon (surface layer). Thus surface
velocities are somewhat higher in an impoundment when stratified than when unstrati-
-4-
-------
L»TI FALL-WMTEK
FALL
I* tO M
TI'CI
$e«INC
OuMlO*-;
• UMMCft
D i c rt to n
ITI-CI
FIGURE V-3 ANNUAL CYCLE OF THERMAL STRATIFICATION AND OVERTURN IN AN IMPOUNDMENT
-5-
-------
fied. Since vertical mixing is inhibited by stratification, reaeration of the
hypo limn ion (bottom layer) is virtually nonexistent. The thenwcline (layer of steep
thermal gradient between epilimnion and hypolimnion) is often at considerable depth.
Accordingly, the euphotic (literally "good light") zone Is likely to be limited to
the ep111 inn ion. Thus photosynthetlc activity does not serve to reoxygenate the
hypolimnion. The water that becomes the hypolimnion has some oxygen demand prior to
the establishment of strata. Because bottom (benthic) matter exerts a further
demand, and because some settling of paniculate matter into the hypolimnion may
occur, the 00 level in the hypolimnion will gradually decrease over the period of
stratification.
Anoxic conditions in the hypolimnion result in serious chemical and biological
changes. Hicrobial activity leads to hydrogen sulflde (HgS) evolution as well as
to formation of other highly toxic substances, and these may be harmful to Indigenous
biota.
It should be noted that the winter and spring strata and overturn are relatively
unimportant here since the major concern 1s anoxlc conditions in the hypolimnion In
summer. Thus all Impoundments will be considered as monomlctic.
Strong stratification is also important in prediction of sedimentation rates and
trap efficiency estimates. These topics are to be covered later.
5.2.2 Prediction of Thermal Stratification
Computation of impoundment heat influx is relatively straightforward, but
prediction «f thermal gradients is complicated by prevailing physical conditions,
physical mixing phenomena, and impoundment geometry. Such factors as depth and
shape of impoundment bottom, magnitude and configuration of inflows, and degree of
shielding from the wind are much more difficult to quantify than insolation, back
radiation, and still air evaporation rates. Since the parameters which are difficult
to quantify are critical to predicting stratification characteristics, no attempt has
been made to develop a simple calculation procedure. Instead, a tested model (Chen
and Orlob, 1973; Lorenzen and Fast, 1976) has been subjected to a sensitivity analysis
and the results plotted to show thermal profiles over depth and over time for some
representative geometries and climatolovjical conditions. The plots are presented 1n
Appendix D.
The plots show the variation in temperature (*C) with depth (meters). Temper-
ature is used as an index of density. Engineering judgment about defining layers
Is based on the pattern of temperature with depth. If stratification takes place,
the plot will show an upper layer of uniform or slightly declining temperature
(epllimnion), an intermediate layer of sharply declining temperature (thermocHne),
and a bottom layer (hypolimnion). A rule of thumb requires a temperature change of
at least 1'C/meter to define the thermocline. However, this can be tempered by the
observation of a well defined mixed layer.
-6-
-------
To assess thermal stratification 1n an Impoundment, 1t is necessary only to
determine which of the sets of plots most closely approximates climatic and hydro-
logic conditions in the impoundment studied. Parameters which were varied to gener-
ate the plots and values used are shown In Table V-l.
Table V-2 shows the cUmatological conditions used to represent the geographic
locales listed 1n Table V-l. For details of the simulation technique, see Appendix E,
5.2.2.1 Using the Thermal Plots
Application of the plots to assess stratification characteristics begins with
determining reasonable values for the various parameters listed in Table V-l. For
geographic locale, the user should determine whether the impoundment of interest is
near one of the ten areas for which thermal plots have been generated. If so, then
the set of plots for that area should be used. If the Impoundment 1s not near one of
the ten areas, then the user may obtain data for the parameters listed in Table V-2
(climatologlc data) and then select the modeled locale which best matches the region
of interest.
Next, the user must obtain geometric data for the impoundment. Again, if
the Impoundment of Interest 1s like one for which plots have been generated, then
that set should be used. If not, the user should bracket the studied Impoundment.
As an example, 1f the studied Impoundment Is 55 feet deep (maximum), with a surface
area of about 4xl07 feet2, then the 40 and 75 foot deep impoundment plots should
be used.
Mearr hydraulic residence time (TW, years) may be estimated using the mean
total inflow rate (Q, m3/year) and the impoundment volume (V, m3):
T
W
V/Q (V-l)
Again, the sets of plots bracketing the value of TW ,should be examined, khere
residence times are greater than 200 days, the residence time has little influence on
stratification (as may be verified in Appendix 0) and either the 200 day or infinite
time plots may be used.
Finally, the wind mixing coefficient was used to generate plots for windy areas
(high wind) and for very well protected areas (low wind). The user must judge where
his studied impoundment falls and interpolate in the plots accordingly (See Appendix
D).
-7-
-------
TABLE Y-l
PARAMETER VALUES USED IN GENERATION OF
THERMAL GRADIENT PLOTS (APPENDIX D)
Parameter
Value
Geographic Locale
Geometry
Atlanta, Georgia
6111 ings, Montana
Burlington, Vermont
Flagstaff, Arizona
Fresno, California
M1nneapol1s, M1nnesota
Salt Lake City, Utah
San Antonio, Texas
Washington, D.C.
Wichita, Kansas
Depth
(maximum,
feet)
20
40
75
100
200
Surface 9
Area (feet*)
8.28 x 106
3.31 x 107
1.16 x 108
2.07 x 108
8.28 x 108
Volume (feet3)
7.66 x 107
6.13 x 108
4.04 x 109
9.58 x 109
7.66 x 1010
Mean Hydraulic Residence Time
Wind Mixing'
•See Appendix E.
Days
10
30
75
250
High
Low
-8-
-------
TABLE V-2
TEMPERATURE, CLOUD COVER, AND DEW POINT DATA
FOR THE TEN GEOGRAPHIC LOCALES USED TO DEVELOP THERMAL
STRATIFICATION PLOTS (APPENDIX 0). SEE FOOT OF TABLE FOR NOTES.
Temoerature ( F)
Max. Mean
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
May
June
July
August
September
October
November
December
Atlanta
54
57
63
72
81
87
88
88
83
74
62
53
killings
27
32
38
51
60
68
79
7S
67
55
38
32
(Lat:
45
47
52
61
70
77
79
78
73
63
51
44
(Lat:
18
22
27
38
47
54
63
61
52
42
29
22
Mln,
33.8°N,
36
37
41
50
57
66
69
68
63
52
40
35
45.8°N,
9
12
16
26
34
40
46
45
37
30
20
14
Dew C
. Point (°F) F
Long:84.4°W)
34
34
39
48
57
65
68
67
62
51
40
34
Long:108.5°W)
11
16
20
28
38
46
48
46
38
31
22
15
loud Cover Wind
faction (MPH)
.63
.62
.61
.55
.55
.58
.63
.57
.53
.45
.51
.62
.68
.63
.71
.70
.64
.60
.40
.42
.54
.56
.66
.66
11
12
12
11
9
8
8
8
8
9
10
10
13
12
12
12
11
11
10
10
10
11
13
13
-9-
-------
TABLE y-2 • COHT,
Temoerature I F)
Max.
Mean
Burlington (Lit:
January
February
March
April
May
June
July
August
September
October
November
December
27
29
38
53
67
54
82
80
71
59
44
31
18
19
29
43
56
66
71
68
60
49
38
23
Flagstaff (Lat:
January
February
March
April
May
June
July
August
September
October
November
December
40
43
50
59
68
77
81
79
75
63
51
44
27
30
36
43
51
60
66
64
59
47
36
30
Mill.
44.5°K.
9
1Q
20
33
44
77
59
57
49
39
29
15
35.2°H,
14
17
22
28
34
*2
50
49
42
31
21
17
Dew Cloud Cover Wind
Point (°F) Fraction (HPH)
Lat:73.2°W)
12
12
20
32
43
54
59
58
51
40
30
17
Long:111.3°H)
14
16
17
20
22
25
43
43
35
25
20
15
.72
.69
.66
.67
.67
.61
.58
.57
.60
.65
.79
.78
.59
.49
.50
.49
.41
.24
.54
.53
.29
.31
.34
.44
10
10
10
10
9
9
8
8
8
9
10
10
8
9
11
12
11
11
9
9
8
8
8
7
-10-
-------
TABLE V-2 CONT.
Temperature (°F)
Max.
Mean
Min.
Dew .
Point (°F)
Cloud Cover Wind
Fraction (MPH)
Fresno (L*t:36.7°N, Long:119.8°W)
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
May
June
July
August
September
October
November
December
55
61
68
76
85
92
100
98
92
81
68
57
Mlnneapol
22
26
37
56
70
79
85
82
72
60
40
27
46
51
55
61
68
75
81
79
74
65
54
47
1s (Lat:
12
16
28
45
58
67
76
71
61
48
31
18
37
40
42
46
52
57
63
61
56
49
40
38
45.0°N,
3
5
18
33
46
56
61
59
49
37
21
9
38
41
41
44
45
48
51
52
51
46
42
40
Long : 93. 3° W)
6
10
20
32
43
55
60
59
50
40
25
13
.67
.61
.53
.44
.34
.19
.11
.11
.15
.28
.44
.70
.65
.62
.67
.65
.64
.60
.49
.51
.51
.54
.69
.69
6
6
7
7
8
8
7
6
6
5
5
5
11
11
12
13
12
11
9
9
10
11
12
11
-11-
-------
TABLE V-2 CONT.
Temoerature (°F)
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
May
June
July
August
September
October
November
December
Max
Salt
37
42
51
62
72
82
92
90
80
66
49
40
San
62
66
72
79
85
92
94
94
89
82
70
65
Mean
Lake City (Lat:
27
33
40
50
58
67
76
75
65
53
38
23
Min.
40.8°K
18
23
30
37
45
52
61
59
50
39
28
32
Antonio (Lat:29.4°N.
52
55
61
68
75
82
84
84
79
71
59
42
42
45
50
58
65
72
74
73
69
60
49
54
Dew Cloud Cover
Point (°F) Fraction .
. Long: 111
20
23
26
31
36
40
44
45
38
34
28
24
Long: 98. 5°
39
42
45
55
64
68
68
67
65
56
46
41
.9°W)
.69
.70
.65
.61
.54
.42
'.35
.34
.34
.43
.56
.69
w)
.64
.65
.63
.64
.62
.54
.50
.46
.49
.46
.54
.57
Wind
(MPH)
7
8
9
9
10
9
9
10
9
9
8
7
9
10
10
11
10
10
10
8
8
8
9
9
-12-
-------
TABLE V-2 COKT.
Temperature 1
Max. Mean
January
February
March
April
May
June
July
August
September
October
November
December
Washington
44
46
54
60
76
83
87
85
79
68
57
46
. D.C.
37
38
45
56
66
74
78
77
70
59
48
43
Wichita (Lat:37.
January
February
March
April
May
June
July
August
September
October
November
December
42
47
56
68
77
88
92
93
84
72
34
45
32
36
45
57
66
77
81
81
71
60
55
36
(°F) 1
Wn. Po
(Lat:38.9°N.
30
29
36
46
56
65
69
68
61
50
39
31
7°N, Long:97.
22
26
33
45
55
65
69
69
59
48
44
27
Dew „
Int (°
Long:
25
25
29
40
52
61
65
64
59
48
36
26
3°W)
21
25
30
41
53
62
65
53
55
43
33
25
Cloud Cover Wind
F) Fraction (MPH)
77.0°W)
.61
.56
.56
.54
.54
.51
.51
.51
.48
.47
.54
.58
.50
.51
.52
.53
.53
.46
.39
.38
.39
.40
.44
.50
11
11
12
11
10
10
9
8
9
9
10
10
12
13
15
15
13
13
12
11
12
12
13
12
-13-
-------
TABLE V-2 CONT.
Notes: Mean: Normal dally average temperature, °F.
Max.: Normal dally maximum temperature, °F.
Min.: Normal dally minimum temperature, °F.
Wind: Mean wind speed, MPH
Dew Point: Mean dew point temperature, °F.
*Complete data were not available for Billings. Tabulated
data are actually a synthesis of available data for
Billings, Montana and Yellowstone, Wyoming.
All data taken from Climatic Atlas of the U.S., 1974.
EXAMPLE V-l
Thermal Stratification
Suppose one wants to know the likelihood that hypothetical Limpid Lake 1s
stratified during June. The first step 1s to compile the physical conditions for
the lake in terms of the variables listed in Table V-l. Table V-3 shows how this j
might lie done. Next, refer to the indexes provided in Appendix D to locate the
plot set for conditions most similar to those of the studied impoundment. In this
case, the Wichita plots for a 200-foot deep impoundment with no inflow and high J
mixing rate would be chosen (see Table V-3). Figure V-4 is a reproduction of the I
appropriate page from Appendix D. |
i
I
i
TABLE V-3 I
LIMPID LAKE CHARACTERISTICS •
1 tern
location
Depth, ft (maximum)
Volume, ft3
Mean residence time (T )
Mi x i no
Limpid Lake
Manhattan, Kansas
180
6 x 1010
500 days
high (windy)
Available Plot
Wichita, Kansas
200
7.66 x 1010
oo (no inflow)
high coefficient
-14-
-------
•Ml
JtK
1
j
i
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a.
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i
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^^
^^
10 70 3
TEMP. C
;
/
10 fO 1
TEMP, c
0
IO
^
o 60c
0
20-
£
O.
UJ
0 C
10 20 3
Tenr. c
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TEMP. C
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10 70 3
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TEMP. C
20-
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°.o.
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TEMP. C
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WICMITR. KRNSR5 1
200' [NiriPL MOXJMUM OEfTH 1
INFINITE MYO«. RES- TlnE j
nRxinun n]x[NG j
I
I
i
10 70 30
TEMP. C |
1 PIRURE V-4 THERMAL PROFILE PLOTS "SED IN EXAMPLE V-] I
i I
i !
i i
i i
-15-
-------
I According to the plots, Limpid Lake 1s likely to be strongly strati-
i
| fled in June. Distinct strata fora 1n Hay and overturn probably occurs 1n
j December. During June, the epillnnlon should extend down to a depth of about
j eight or ten feet, and the thenwcllne should extend down to about 30 feet. The
; gradient in the thennocHne should be about 1° C per meter.
END OF EXAMPLE V-l '
EXAMPLE V-2
I I
I Thermal Stratification I
i • '—••- ™ •• ™^^^—^^.^^.^^^ ,
I I
| What are the stratification characteristics of Lake Smith? |
j The hypothetical lake 1s located east of Carthage, Texas, and Table V-4 shows j
j its characteristics along with appropriate values for the thermal plots. j
i i
I I
1 TABLE V-4 j
PHYSICAL CHARACTERISTICS OF LAKE SMITH
- - — - — — — — — — _ . _ - i
Mem Lake Smith Plot Values I
" '^^«^^-^^—^H_^—^MM (
Location 15 miles east of \
Carthage Texas |
Depth, ft (maximum) 23 20 j
Volume, ft3 3 x 108 1.66 x 10® j
Mean residence time 250 days co J
Mixing low (low wind) low mixing coefficient
From the available data for Lake Smith, it appears that plots for a 20-foot
deep impoundment with no inflow and low mixing coefficient should give a good
indication of the degree of summertime stratification. The one remaining problem
is climate. Data for nearby Shreveport, Louisiana compare well with those of
Atlanta (Table V-5), for which plots are provided in Appendix D, and latitudes are
similar. Shreveport 1s somewhat warmer and Insolation 1s higher, but this Is a
relatively uniform difference over the year. The net effect should be to shift
the thermal plots to a slightly higher temperature but to Influence the shape of
the plots and the timing of stratification little. As a result, the plots for
-16-
-------
TABLE V-5
COMPARISON OF MONTHLY CLIMATOLOGIC DATA
FOR SHREVEPORT, LOUISIANA AND ATLANTA, GEORGIA
DATA ARE PRESENTED AS SHREVEPORT/ATLANTA
(CLIMATIC ATLAS OF THE U.S., 1974)
Temperature. °F
January
February
March
April
May
June
July
August
September
October
November
December
Shreveport
Atlanta Lat
Max.
57/54
60/57
67/63
75/72
83/81
91/87
92/88
94/88
88/83
79/74
66/62
59/53
Lat: 32. 5°
:33.8°N,
Mean
48/45
50/47
57/52
65/61
73/70
81/77
82/79
83/78
78/73
67/63
55/51
50/44
N, Long:94°W
Long:84.4°W,
Mln.
38/36
41/37
47/41
55/50
63/57
71/66
72/69
73/68
67/63
55/52
45/40
40/35
Dew
Point, °F
38/34
40/34
44/39
54/48
62/57
69/65
71/68
70/67
65/62
55/51
45/40
39/34
Cloud
Cover,
Fraction
.60/.63
.S8/.62
.54/.61
.50/.55
.48/.S5
.44/.5S
.46/.63
.40/.57
.40/.53
.38/.4S
.46/.51
.S8/.62
Wind,
MPH
9/11
9/12
10/12
9/11
9/9
8/8
7/8
7/8
7/8
7/9
8/10
9/10
Atlanta may be used, bearing 1n mind that the temperatures are likely to be biased
uniformly low. Figure V-5 (reproduced from Appendix D) shows thermal plots for a
20-foot deep Atlanta area impoundment having no significant inflow and low wind
stress. From the figure, 1t 1s clear that the lake is likely to stratify from
April or May through September, the epilimnion will be very shallow, and the
thermocHne will extend down to a depth of about 7 feet. The thermal gradient is
in the range of about 7°C per meter, as an upper limit, during June. Bottom water
warms slowly during the summer until the Impoundment becomes fully mixed 1n
October.
-17-
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10 20 3
TEMP. C
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10 20 3
TEMP. C
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tic
10 tl it 0 10 t'a 3
TEMP. C TEMP. C
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RTLRNTR. GEORGIR j
20' INITIBL MHXIMUM DEPTH |
INFINITE MYOR. RES- TIME j
MINIMUM MIXING
1
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• FIGURE V-5 IHERMAL PROFILE PLOTS APPROPRIATE FOR USE IN F.XAMPLE V-2 :
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run (V PYiuoi c u_o _._ J
-18-
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5.3 SEDIMENT ACCUMULATION
5.3.1 Introduction
Reservoirs, lakes, and other Impoundments are usually more quiescent than
tributary streams, and thus act as large settling basins for suspended participate
matter. Sediment deposition 1n Impoundments gradually diminishes water storage
capacity to the point where lakes fill 1n and reservoirs become useless. In some
cases, sediment accumulation may reduce the useful life of a reservoir to as little
as ten to twenty years (Marsh, et^ al_., 1975).
Just how much suspended matter settles out as water passes through an impound-
ment, as well as the grain size distribution of matter which remains suspended, is of
interest to the planner for several reasons. Suspended sediment within an impound-
ment may significantly reduce light penetration thus limiting algal and bottom-rooted
plant (macrophyte) growth. This, 1n turn, can adversely affect food availability for
indigenous fauna, or may slow plant succession, as part of the natural aging process
of lakes.
Settling of suspended matter may eliminate harborage on impoundment bottoms
thus reducing populations of desirable animal species. More directly, suspended
particulates impinging on the gills of fish may cause disease or death.
Some minerals, particularly clays, are excellent adsorbents. As a result,
farm chemicals and pesticides applied to the land find their way to an impoundment
bottom and into its food chain. The sediment which settles is likely to have a
substantial component of organic matter which can exert an oxygen demand, and under
conditions of thermal stratification, anoxic conditions on the impoundment bottom (in
the hypolimnion) can result in generation of toxic gases. Indigenous biota may be
harmed or even killed as a result.
Knowing the rate of sediment transport and the deposition within an impoundment
allows for effective planning to be Initiated. If sedimentation rates are unaccept-
able, then the planner can begin to determine where sediments originate, and how to
alleviate the problem. For example, densely planted belts may be established between
highly credible fields and transporting waterways, farming and crop management prac-
tices may be changed, or zoning may be modified to prevent a worsening of conditions.
These considerations, along with others relating to sediment carriage and
deposition in downstream waterways, make estimates of sedimentation rates of interest
here. Impoundment -sediment computation methods discussed in this section will permit
the planner to estimate annual impoundment sediment accumulation as well as short
term accumulation (assuming constant hydraulic conditions). Application of the
methods will permit the planner to estimate the amount of sediment removed from
transport in a river system due to water passage through any number of impoundments.
-19-
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5.3.2 Annual Sediment Accumulation
Three different techniques are used to estimate annual sediment accumulation:
available data, sediment rating curves, and a three step procedure to determine
short-term sedimentation rates. As discussed under each technique, caution should be
used 1n selecting one method or another. If data are not available, 1t may not be
feasible to use one or more techniques. When drawing conclusions, the uncertainty 1n
the results should be considered 1n drawing conclusions based on whichever analysis
that 1s selected. In addition, each technique has Its own degree of uncertainty,
which should be considered when drawing conclusions.
5.3.2.1 Use of Available Data
Data provided In Appendix F permit estimation of annual sediment accumulation 1n
acre-feet for a large number of Impoundments 1n the U.S. The data and other materials
presented provide some basic Impoundment statistics useful to the planner In addition
to annual sediment accumulation rates.
To use Appendix F, first determine which Impoundments within the study area are
of Interest 1n terms of annual sediment accumulation. Refer to the U.S. map Included
1n the appendix and find the Index numbers of the region within which the Impoundment
1s located. The data tabulation in the appendix, total annual sediment accumulation
1n acre feet, 1s given by multiplying average annual sediment accumulation 1n acre
feet per square mile of net drainage area ("Annual Sediment Accum.") by the net
drainage area ("Area") 1n square miles:
Total Accumulation • Annual Sediment Accum. x Area (V-2)
To convert to average annual loss of capacity expressed as a percent, divide total
annual accumulation by storage capacity (from Appendix F), and multiply by 100. Mote
that this approach and those presented later do not account for packing of the
sediment under its own weight. This results in an overestimate In loss of capacity.
Note also that other data 1n Appendix F may be of interest in terms of drainage area
estimates for determining river sediment loading and assessment of storm water
sediment transport on an annual basis.
5.3.2.2 Trap Efficiency and the Ratio of Capacity to Inflow
Where data are not available 1n Appendix F for a specific Impoundment, the
following method will permit estimation of annual or short-term sediment accumulation
rates. The method 1s only useful, however, for normal ponded reservoirs.
To use this approach, a suspended sediment rating curve should be obtained
for tributaries to the impoundment. An example of a sediment rating curve 1s
provided 1n Figure V-6.
-20-
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IQOOO
1,000
SUSPENDED SEDIMENT DISCHARGE, S; (tons/day)
100,000
FIGURE V-6 SEDIMENT RATING CURVE SHOWING SUSPENDED
SEDIMENT DISCHARGE AS A FUNCTION OF FLOW
(AFTER LINSLEY, KOHLER, AND PAULHUS, 1958)
On the basis of such a curve, one can estimate the mean sediment mass transport
rate (S^ In mass per unit time for tributaries. If neither rating curve nor data
are available, one may estimate sediment transport rates on a basis of data from
nearby channels, compensating for differences by using mean velocities. To a first
approximation, 1t would be expected that:
S, « 3A7T-
where
(V-3)
Si - sediment transport rate to be determined in tributary "1" in mass
per unit time
Sj « known transport rate for comparable tributary (j) in same units
as Si
Vi • mean velocity for tributary 1 over the time period
Vj • mean velocity In tributary j over the same time period as V}.
Once average transport rates over the time period of interest have been deter-
mined, the proportion, and accordingly the weight of sediment settling out in the
impoundment may be estimated. Figure V-7 is a graph showing the relationship between
percent of sediment trapped in an Impoundment versus the ratio of capacity to inflow
rate. The implicit relationship Is:
where
(V-4)
percent of Inflowing sediment trapped
capacity of the Impoundment 1n acre-feet
-21-
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0001
0003 OOO7
003 0.07 O.I 0.3 O.S
Ratio of Capacity to Inflow
5 T 10
FIGURE V-7 PELATIONSHIP BETWEEN THE PERCENTAGE OF INFLOW-TRANSPORTED SEDIMENT
RETAINED WITHIN AN IMPOUNDMENT AND PATIO OF CAPACITY TO INFLOW
(LlNSLEY, KOHLER, AND PAULHUS, 195R)
Q-j • water inflow rate in acre-feet per year.
Data used for development of the curves in Figure V-7 Included 41 Impound-
ments of various sizes throughout.the U.S. (Linsley, Kohler, and Paulhus, 1958).
To estimate the amount of suspended sediment trapped within an Impoundment
using this method, the capacity of the impoundment in acre-feet must first be
determined. Next, average annual inflow, or better, average flow for the time
period of interest is estimated.
Then:
H - sip (V-5)
where
St « weight of sediment trapped per time period t
P « trap efficiency (expressed as a decimal) from Figure V-7.
A word of caution is in order here. The above described techniques for evalua-
ting sediment deposition in impoundments are capable of providing reasonable esti-
mates, but only where substantial periods of time are involved - perhaps six months
or longer. The methods may be used for shorter study periods, but results must then
be taken only as very rough estimates, perhaps order-of-magnitude.
-22-
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5.3.3 Short-Term Sedimentation Rates
The three-step procedure presented below provides a means to make short-term
sediment accumulation rate estimates for storm-event analysis and to estimate amounts
of different grain-size fractions passing through an Impoundment. The steps are:
• Determine terminal fall velocities for the grain size distribution
• Estimate hydraulic residence time
• Compute trap (sedimentation) rate.
5.3.3.1 Pall Velocity Computation
When a particle 1s released 1n standing water, It will remain roughly stationary
if its density equals that of the water. If the two densities differ, however, the
particle will begin to rise or fall relative to the water. It will then tend to
accelerate until the drag force Imposed by the water exactly counterbalances the
force accelerating the particle. Beyond this point, velocity 1s essentially constant,
and the particle has reached terminal velocity. For spheres of specific gravity
greater than 1, Stokes' law expresses the relationship between fall velocity (terminal
velocity) and several other physical parameters of water and the particles:
Vmax " Ttf VVd * TK
-------
criterion 1s met. For large particles, how far conditions deviate from this may be
observed using the following approach (Camp, 1968). According to Newton's law for
drag, drag force on a particle 1s given by:
tt • ttojfll (V-8)
where
F
max " v/Tf p
w
All variables 1n the expression for V (Equation V-9) may be easily
estimated except C, since C Is dependent upon Reynold's number. According to Equa-
tion V-7, Reynolds number is a function of v. Thus a "trial and error" or iterative
procedure *ould ordinarily be necessary to estimate C. However, a somewhat simple"*
approach is available to evaluate the drag coefficient and Reynolds number. First,
estimate CR2 using the expression (Camp. 1968):
CR2 • AD.. (o_ - pj gd3/3u2 (V-10)
W j) W
Then, using the plot in Figure V-8, estimate R and then C. For R>0.1 use of Equation
V-9 will give better estimates of V than will Equation V-6.
generally, one of the two approaches for spherical particles will give good
estimates of particle fall velocity in an effectively laminar flow field (1n Im-
poundments). Occasionally, however, it may prove desirable to compensate for
nonsphericity of particles. Figure V-9, which shows the effect of particle shape on
the drag coefficient C, may be used to do this. Note that for R < 1, shape of
particle does not materially affect C, and no correction is necessary.
A second problem in application of the Newton/Stokes approach described above is
that it does not account for what is called hindrance. Hindrance occurs when the
region of fluid surrounding a falling particle Is disrupted (by the particle motion)
and the velocity of other nearby particles is thereby decreased. Figure V-10 shows
this effect schematically.
A very limited amount of research has been done to determine the effect of
particle concentration on fall velocity (Camp, 1968). Some data have been collected
-24-
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10 »
10
^'p' Jf
./I
10'
\
10
10'
-2
IO'3 10-2
10'
10
102 103
Valuts of R*
vd
FIGURE V-8 PLOT OF C./R AND rP2 vERSus " (CAMP, 1968)
-25-
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10 3
u
C to2
o
U
o
w
O
10
10'
\
LEGEND'
A - StokM' tt«
B - Spheres
C - Cylinders, L *
0 - Discs
K
2
I 10 K>2 IO3 tO4 K)9 IO*
Reynolds Numbtr, R
FIGURE V-9 ORAG INEFFICIENT (C) AS FUNCTION OF REYNOLD'S NUMBER (R)
AND PARTICLE SHAPE (CAMP, 1968)
however, and Figure V-ll 1s a plot of a velocity correction factor, v /v, as a
function of volumetric concentration. Volumetric concentration 1s given by:
where
,
'vol
volumetric concentration
(v-n)
» weight concentration.
As an approximation, the curve for sand may be used to correct v as a function
of Cvol•
-26-
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Particles which
velocity is offtcttd
by vertical velocity
fitld
Region of disruption,
upward fluid motion
Settling sphere
Water column
containing settling
particles
FIGURE V-10 SCHEMATIC REPRESENTATION OF HINDERED SETTLING
OF PARTICLES IN FLUID TOLUMN
I.U
0.9
0.8
>|> 0 7
£ 06
(J
0
u.
0.5
C
o
0 04
•
5 °>
0.2
0 1
n
X
X
V^v
v^
\
«
v^
s^
\
^
"^
^
X
vA
4-
>
^
>s
LEGEND:
A - Red Blood Ctll*
B - Lucite Spheres, d<0.0l8lcm., P, « 1.194
C - Round Sand Graint, d «O.OI67 cm., f, * 2.66
^
X
^^.
^<
X
^*-
^0>
>
^
^
^
k.
•^^.
^s^
^^>
^>-
'^-^
^
(Ci
^^^ <
0.05
010
015
0.20
0.25
O.SO
0.35
Volumetric Concentration, C f
FIGURE V-ll VELOCITY CORRECTION FACTOR FOR HINDERED SETTLINS (FROM CAMP, 1968)
-27-
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j EXAMPLE V-3 1
i i
j Settling Velocity j
i i
Assume that a swiftly moving tributary to a large reservoir receives a heavy •
! loading of sediment which 1s mostly clay particles. The particles tend to clump
{ somewhat, and average diameters are on the order of 2 microns. The clumps have a \
I specific gravity of 2.2. Applying Stokes1 law for 20"C water: I
n . % • &.
V
'max T8u x"p *V
• — c-x [(2.2 x 62.4/32.2) - (62.4/32.2)] x (6.56 x 10'6)2
(18 x 2.1 x 10-b)
• 8.53 x 10-6 ft sec-l . .03 ft hr-1
Thus the particles of clay might be expected to fall about nine Inches per
day in the reservoir. It should be noted that for such a low settling rate,
turbulence in the water can cause very significant errors. In fact, the estimate
1s useful only in still waters having a very uniform flow lacking substantial
vertical components.
'. END OF EXAMPLE V-3
EXAMPLE V-4
I !
I Settling Velocity for a Sand and Clay '
i j
j Suppose a river 1s transporting a substantial sediment load which 1s mainly |
j sand and clay. The clay tends to clump to form particles of 10 micron diameter j
• while the sand is of 0.2 mm diameter. The sand particles are very Irregular 1n j
• shape tending toward a somewhat flattened plate form. The specific gravity of the j
' clay is about 1.8 while that of the sand is near 2.8. Given that the water
j temperature is about 5eC, the terminal velocity of the clay may be estimated as 1n !
I Example V-3: I
i 2 i
I Vmax ' TaV (pp ' Pw} d I
' (16 x fll x 10-5) * '°-8 * «•* / ".2) x (3.28 x 10-5,2 j
i
• 9.4 x lO'5 ft sec"1 !
• 8 ft day-1 I
-28-
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I For the sand, apply Equation V-10:
j CR2 - 4ow (Cp - 0J gd3/3u2
j , 62.4 1.8 x 62.4 32.2 x (6.56 x IP"4)3
* x -jj-j j^3 x (3.17 x 10-5)2
| CR2 . 82
I Referring to Figure V-8, a value of CR2 equal to 82 represents RS2.8 and
| CaiO.3. From Figure V-9, the corrected drag coefficient for discs Is close
j to 10.3 (no correction really necessary). Then, using Equation V-9 as an approxi-
nation:
/49 (p - p J d
v « ' °
max \
I 4
J 3
V . / " « 32.2 x (1.8 x 62.4 / 32.2) x 6.56 x IP"4
max J 3 x 10.3 x 62.4 / 32.2
.„„ 0.07 ft sec'1 • 252 ft hr'1
max
Thus the clay will settle about 8 feet per day while the sand will settle about
6,048 feet per day (252 feet per hour).
END OF EXAMPLE V-4
5.3.4 Impoundment Hydraulic Residence Time
Once settling velocities have been estimated for selected grain sizes, the final
preparatory step 1n estimating sediment deposition rates 1s to compute hydraulic
residence time.
Hydraulic residence time represents the mean time a particle of water resides
within an impoundment. It is not, as is sometimes thought, the time required to
displace all water 1n the impoundment with new. In some impoundments, inflowing
water may be conceptualized as moving In a vertical plane from Inflow to discharge.
This is called plug flow. In long, narrow, shallow impoundments with high inflow
velocities, this 1s often a good assumption. As discussed later, however, adoption
of this model leads to another problem, namely, is water within the plug uniform or
does sediment concentration vary over depth within the plug?
A second model assumes that water flowing into an Impoundment Instantaneously
mixes laterally with the entire receiving layer. The layer may or may not represent
the entire impoundment depth. This simplification is often a good one in large
surfaced, exposed impoundments having many small Inflows.
Regardless of the model assumed for the process by which water traverses
an impoundment from Inflow to discharge, hydraulic residence time 1s computed
-29-
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as 1n Equation V-l. That is:
% • V/Q
The only important qualification is that to be meaningful, V must be computed
taking account of stagnant areas, whether these are regions of the impoundment
isolated from the main flow by a sand spit of promontory, or whether they are
isolated by a density gradient, as in the themocline and hypolimnion. Ignoring
stagnant areas may result in a very substantial overestimate of TM, and in sediment
trap computations, an overestimate in trap efficiency. Actually TH computed in
this way is an adjusted hydraulic residence time. All references to hydraulic
residence time in the remainder of Section 5.3 refer to adjusted TM.
Hydraulic residence time is directly influenced by such physical variables as
impoundment depth, shape, side slope, and shoaling, as well as hydraulic character-
istics such as degree of mixing, stratification, and flow velocity distributions.
The concepts Involved in evaluating many of these factors are elementary. The
evaluation itself is complicated, however, by irregularities in Impoundment shape and
data inadequacies. Commonly, an impoundment cannot be represented well by a simple
3-dimensional figure, and shoaling and other factors may restrict flow to a laterally
narrow swath through the water body.
In most cases, hydraulic residence time may be estimated, although it is clear
that certain circumstances tend to make the computation error-prone. The first step
in the estimation process is to obtain impoundment inflow, discharge, and thermal
regime data as well as topographic/bathymetric maps of the system. Since a number of
configuration types are possible, the methods are perhaps best explained using
examples.
EXAMPLE V-5
Hydraulic Residence Time in Unstratificd Impoundments
The first step in estimating hydraulic residence time for purposes of
sedimentation analysis is to determine whether there are significant stagnant
areas. These would include not only regions cut off from the main flow through
the body, but also layers isolated by dense strata. Consequently, it must be
determined whether or not the impoundment stratifies. Consider Upper Lake located
on the Carmans River, Long Island, New York. The lake and surrounding region are
shown in Figure V-12, and hypothetical geometry data are presented in Table V-6.
Based upon Upper Lake's shallowness, its long, narrow geometry, and high tributary
inflows, it is safe to assume that Upper Lake is normally unstratified. Also,
because of turbulence likely at the high flows, one can assume that the small sac
northeast of the discharge is not stagnant and that Upper Lake represents a slow
-30-
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TABLE V-6
HYPOTHETICAL PHYSICAL CHARACTERISTICS AND
COMPUTATIONS FOR UPPER LAKE, BROOKHAVEN, SUFFOLK COUNTY, NEW YORK
Distance Downstream
from Inflow
Miles (feet)
0.05 (264)
0.10 (528)
0.15 (792)
0.20 (1,056)
0.25 (1,320)
0.30 (1,534)
0.35 (1,848)
0.40 (2,112)
0.45 (2,376)
0.50 (2,640)
D
Average
Depth
ft.
3
4
6
7
7
8
7
8
7
10
W
Average
Width
ft.
63
no
236
315
340
315
550
550
354
350
CSA
Cross-sectional
Area.,D x W
ft2
189
440
1,416
2.205
2,380
2,520
3,850
4,400
2.478
3,500
mean 2,338
Total length • 0.5 mi. (2,640 ft.)
Inflow from upstream » 380 cfs )
Outflow to downstream » 380 cfs I
steady-state}
Computation
Volume (Vol) * Total length x mean cross-sectional area
« 2,640 ft. x 2,338 ft2 « 6.17 x 106 ft3
Residence time (T ) « Vol/flow
- 6.17 x 106 ft3/(380 ft3/sec) • 1.62 x 104 sec (4.5 hr)
Velocity (Vel) «
» 2,640 ft/1.62 x 10 sec = .163 ft/sec
moving river reach. With these assumptions, the computation of hydraulic residence
time is as shown in Table V-6.
Also shown in Figure V-12 is Lower Lake. According to the hypothetical data
presented in Table V-7, Lower Lake is much deeper than Upper Lake. Its volume is
significantly greater also, but the inflow rate is similar. In this case, par-
ticularly during the summer, it should be determined if the lake stratifies. For
this example, however, we will assume that the time of the year makes stratifica-
-31-
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FIGURE V-12 UPPER AND LOWER LAKES AND ENVIRONS,,
LONG ISLAND, NEW YORK
tion very unlikely, and that Lower Lake 1s a slow moving river reach. We then
compute hydraulic residence time as shown 1n Table V-7. Figure V-13, 1n particular
diagram 1, shows what these assumptions mean 1n terms of a flow pattern for both
lakes.
-32-
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TABLE V-7
HYPOTHETICAL PHYSICAL CHARACTERISTICS AND
COMPUTATIONS FOR LOWER LAKE, BROOKHAVEN, SUFFOLK COUNTY, NEW YORK
Distance Downstream
from Inflow
Miles (feet)
0.075 { 396)
0.150 { 792)
0.225 (1.188)
0.300 (1,584)
0.375 (1.980)
0.450 (2,376)
0.525 (2,772)
0.600 (3.168)
0.675 (3.564)
0.750 (3.960)
0.825 (4,356)
0.900 (4,752)
0.975 (5,148)
1.050 (5.544)
1.125 (5.940)
Total length « 1.125 mi (5
0
Average
Depth
ft.
15
20
20
25
35
30
35
35
40
42
41
51
42
40
37
,940 ft.)
Inflow from upstre«m 400 cfs |
> (surface
Outflow to downstream 390 cfs )
Average flow « 395 cfs
Comoutation
W
Average
Width
ft.
157
165
173
197
197
228
232
197
220
315
433
591
551
433
323
rising)
CSA
Cross-sectional
Area,,D x W
ft2
2.355
3,300
3,460
4,925
6.895
6,840
8,120
6,895
8,800
13,230
17,753
30,141
23,142
17,320
11,951
mean 11 ,008
Volume (Vol) * Total lenath x mean cross-sectional area
- 5,940 ft. x 11,008 ft2 • 6.54 x 107 ft3
Residence Time (t ) « Vol/flow
« 6.54 x 107/(395 ft3/sec) » 1.65 x 105 sec (46 hr)
Velocity (Vel) • length/fw
• 5,940 ft/1.65 x 105 sec • .036 ft/sec
-33-
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I
MMMACtO. HOMMniT (MALLOW J
OMIKT, VfKT LO* VfLOClTlK I
//
•UUft*. WOC Hl«(0 (TU«*UCC«T)
(41
%xx'x*x*> *•*••••' L«?*» •.-;:"-:-:-:-::;^-x
Ktr.
1iM*uiC*T
T —
FIGURE V-13 IMPOUNDMENT CONFIGURATIONS AFFECTING SEDIMENTATION
END OF EXAMPLE V-5
-J4-
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r EXAMPLE V-6 '
i i
j Assume for this example that Lower Lake 1s stratified during the period of |
j interest. This significantly changes the computation of residence time. To a j
• first approximation, one can merely revise the effective depth of the impoundment j
! to be from the surface to the upper limit of the thermocline rather than to the
j bottom. Figure V-13 shows schematically what this simple model suggests for Lower .
Lake as a stratified impoundment (diagram 2 or possibly 3). The figure also shows '
wind-driven shallow, and deep impoundments. To the right of each diagram is a I
plot of the temperature profile over depth. Actually, the profile could represent |
a salinity gradient as well as a thermal gradient. j
Table V-8 shows the procedure to estimate travel time for stratified Lower
Lake. The upper boundary of the thermocline 1s assumed to be at a depth of
10 feet. For all later computations of sediment accumulation, this same 10
foot depth would be adopted. Such an assumption is valid presuming that the {
thermocline and hypolimn ion are relatively quiescent. Thus once a particle enters I
the thermocline it can only settle, and cannot leave the impoundment.
END OF EXAMPLE V-6 '
EXAMPLE V-7
I
i
Large, Irregular Surface Impoundment I
j
Figure V-14 shows Kellis Pond and surrounding topography. This small (
pond is located near Bridgehampton, New York and has a surface area of about j
36 acres. From the surface shape of the pond, 1t is clear that it cannot j
be considered as a stream reach.
Figure V-15 shows a set of hypothetical depth profiles for the pond.
From the profiles, 1t is evident that considerable shoaling has resulted in j
the formation of a relatively well defined flow channel thorugh the pond. I
Peripheral stagnant areas have also formed. Hypothetical velocity vectors |
for the pond are presented in Figure V-16. Based upon them, it is reasonable j
to consider the pond as being essentially the hatched area in Figure V-15. j
To estimate-travel times, the hatched area may be handled in the same way as
for the Upper Lake exampl« presented above. It should be noted, however, that !
this approach will almost certainly result 1n underestimation of sediment depo- J
sition in later computations. This is true for two reasons. First, estimated I
travel time will be smaller than the true value since impoundment volume is
underestimated. Second, since the approach Ignores the low flow velocities to
-35-
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TABLE V-8
HYPOTHETICAL PHYSICAL CHARACTERISTICS AND
COMPUTATIONS FOR LOWER LAKE, BROOKHAVEN, SUFFOLK COUNTY, NEW YORK
(ASSUMING AN EPILIMNION DEPTH OF 10 FEET)
Distance Downstream
from Inflow
Miles (feet)
0.075
0.150
0.225
0.300
0.375
0.450
0.525
0.600
0.675
0.750
0.825
0.900
0.975
1.050
1.125
D
Average
Depth
ft.
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
w
Average
Width
ft.
160
170
175
200
198
230
233
200
222
316
435
590
552
435
325
CSA
Cross-sectional
Area,JJ x W
ftr
1,600
1.700
1.750
2,000
1.980
2,300
2,330
2.000
2.220
3,160
4,350
5.900
5,520
4,350
3,250
Total length • 1.125 mi (5,940 ft.) mean CSA « 2,961 ft*
Inflow from upstream 397 cfs ) (steady-state surface, difference
Outflow to downstream 393 cfs )
Average flow » 395 cfs
due to loss to water table)
Computation
Volume (Vol) » Total length x mean cross-sectional area
- 5,940 ft. x 2,961 ft2 • 1.76 x 107
Residence Time (~w) • Vol/flow
- 1.76 x 107/(395 ft3/sec) • 4.46 x 104 sec (12.3 hr) j
I Velocity (Vel) - length/T
5,940 ft/4.46 x 10 sec - 0.133 ft/sec
-36-
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SOUTHAMPTON
BRIDGE HAMPTON
1/2
MILES
FIGURE V-14 KELLIS POND AND SURROUNDING REGION, LONG ISLAND,
NEW YORK
-37-
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INFLOW.
PLAN VIEW
FIGURE V-15 HYPOTHETICAL DEPTH PROFILES
FOR KELLIS POND
STAGNANT
STAGNANT-
FIGURE V-16 HYPOTHETICAL FLOW PATTERN IN KELLIS POND
-38-
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V
TRANSECTS
^^•H
A
-FIGURE V-17
HYPOTHETICAL DEPTH PROFILES FOR KELLIS POND
NOT SHOWING SIGNIFICANT SHOALING
either side of the central channel and nonunlform velocities within it, heavier
sedimentation than computed is likely.
Still more difficult to evaluate 1s the situation where shoaling and scour
have not resulted 1n formation of a distinct central channel. Figure V-17 shows
hypothetical depth profiles for Kellis Pond for such a case.
Here, velocity distribution data should be obtained, particularly if the
impoundment 1s of much Importance. If such data are not available but it is
deemed worthwhile to do field studies, methods available for evaluating 'low
patterns -include dye-tracing and drogue floats. A simple but adequate method (at
least to evaluate the surface velocity distribution) is to pour a large number of
citrus fruits (oranges, grapefruit) which float just below the surface, into the
impoundment, and to monitor both their paths and velocities. Although it is true
that surface velocities may be greater than the velocity averaged over depth, this
-39-
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I will permit estimation of hydraulic residence time directly or generation of data |
j to use in the prescribed method. In the latter case, the data might be used to j
' define the major flow path through an Impoundment of a form like Kellls Pond. j
* '
! END OF EXAMPLE V-7
. EXAMPLE V-8 1
t . i
Complex Geometries
I I
I The final hydraulic residence time example shows the degree of complex-
I 1ty that sediment deposition problems may entail. Although U 1s possible
| to make rough estimates of sediment accumulation, 1t 1s recommended that for
j such impoundments more rigorous methods be used - mathematical modeling and/or j
j detailed field investigations. j
Figure V-18 shows Lake Owyhee in eastern Oregon. This impoundment is well
outside the range of complexity of water bodies which can be evaluated using these !
| calculation methods. Because of geometry, the number of tributaries, and size, 1t j
I is not feasible to conceptually reduce the Impoundment 1n such a way as to estimate I
| travel times. Flow patterns are likely to be very complex, and sediment deposition |
j is difficult to predict both in terms of quantity and location. j
In contrast, Figure V-19 shows New Mlllpond near Islip, New York and surround- j
ing features. Although this water body does not have a simple surface geometry,
! it can be reduced to three relatively simple components as shown in the figure.
I Bearing in mind the limitations imposed by wind mixing, stratification, and the j
I presence of stagnant regions described In earlier examples, deposition might I
| nevertheless be estimated in arms A, B, and C. Because of the difficulty of |
i predicting velocities and turbulence in section D, estimates of sedimentation |
: cannot be reliably made there. However, it is likely that much of inflowing j
sediments will have settled out by the time water flows through the arms and Into
section D.
I I
-40-
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FIGURE V-18 LAKE OWYHEE AND ENVIRONS
-41-
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SMITHTOWN
0
I
1/2
_J
MILES
FIGURE V-19 NEW MILLPOND AND ENVIRONS, NEW MILLPOND is
SUBDIVIDED FOR PURPOSES OF FSTIMATING SFPI-
MENTATION IN REGIONS A, B, AND (*.,
END OF EXAMPLE V-8
I
-42-
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5.3.5 Estimation of Sediment Accumulation
Estimation of quantities of sediment retained in an impoundment follows directly
from the computations of settling velocity and travel time, although the computation
depends upon whether the adopted model is plug flow, or a fully mixed layer or
impoundment.
In the case of plug flow, one of two subordinate assumptions is made: that the
plug 1s fully mixed as 1n turbulent flow, or that 1t moves in a "laminar" flow
through the impoundment. In terms of sediment accumulation estimates, the fully
mixed plug assumption is handled in the same way as the fully mixed Impoundment
model. Thus we have two kinds of computations:
Case A • Plug flow with the plug not mixed vertically.
• Plug flow assuming a vertically mixed plug
Case B
• A fully mixed impoundment or stratum.
Equation V-12 is pertinent to both cases A and B. It defines the mass of
sediment trapped as a function of trap efficiency and inflowing sediment mass.
Equation V-13 should be used for case A, and Equation V-14 for case B:
St - S,P (V
p . ((T^V) * 0" -0 J/D"
D'
where
P « mean proportion of S\ trapped (1 _>_ P _>. 0)
S^ « mass of sediment trapped per unit time
S-j « mass of sediment in inflows per unit time
v - particle settling velocity
D • discharge channel depth
D' » flowing layer depth
D" « inflow channel depth.
Figure V-20 shows the significance of the various depth measures D, D', D'',
and the assumed sedimentation pattern. In case B, in the absence of substantial
erratic turbulence and unpredicted vertical velocity components, and within the
constraints of «vailable data, it is clear that this approach can give reasonable
estimates of trap efficiencies. In case A, however, small changes in D or D*' can
strongly affect trap efficiencies. It is important to remember in applying case A
that Pisa mean, preferably used over a period of time. It is also important to
recognize that conditions within an impoundment leading to selection of case A or B
are subject to change, thus affecting estimates.
For convenience. Figure V-21 1s included to provide estimates of v
max
-43-
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-5L
PLUG FLOW, PLUG NOT MIXED VERTICALLY
T
^N
>
/
|
1
j
£•
/[:•:
"*-
•"«*•"•**
;.;-;•;
"•"•X
::::"•'•(
.:••:,-':• 0
• • . • 4
•"•*•*•***.*•*.*.*.***
Hypolimmon
5«aiment Loytr ;.;.;.v.v.;.;.v.y
•IMPOUNDMENT
CASE A
Flow
no-
PLUG FLOW, VERTICALLY MIXED PLUG
1 '
I
t
IMPOUNDMENT
FULLY MIXED IMPOUNDMENT OR STRATUM
Lay«f vX'.'-vX1'--
IMPOUNDMENT
CASE B
FIGURE V-20 SIGNIFICANCE OF DEPTH MEASURES D, D', AND
D". AND THE ASSUMED SEDIMENTATION PATTERN
-44-
-------
35
V-21
-45-
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10
10
10
S«tt11ng velocity In feet/
second
Hydraulic residence tine
in seconds
D': Flowing layer depth
Mass of sediment trapped
Mass of sediment entering
impoundment
10°
FIGURE V-22 NOMOGRAPH FOR ESTIMATING SEDIMENT TRAP EFFICIENCY
for spherical particles of 2.7 specific gravity. The data are presented as a
function of particle diameter and temperature. Figure V-22 1s a nomograph relating
trap efficiency, P (in percent) to depth D', V • and TW. The nomograph is
useful only for case B assumptions.
-46-
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EXAMPLE V-9
Sedimentation in Upper and Lower Lakes
I
of Example V-4, for case A:
! Using the data from Table V-6 and settling velocities for the clay an-J sand
4
T • 1.6x10 sec
fop day « 8 ft day"1
l
Vmax for sand * 252 ft hour I
*
Although it is not specified in Table V-6, the Inflow channel depth at j
the entrance to Upper Lake is 3 feet. The discharge channel depth is 10 feet. I
Assuming "laminar" flow with minimal vertical components (Case A), for clay: |
'
[{T x v) t D" - D] !
p . - 2 - i
D" !
p . [(1.6 x 104 x 9.3 x 10-5) + 3 - IQ] '
3 I
- -5.5 j
The negative value implies that the proportion settling out is virtually zero. |
Thus the clay will to a large extent pass through Upper Lake. However, TW for j
this example is very small (4.5 hours). Many impoundments will have substantially
larger values.
For the sand:
p m [(1.6 x 10* x 7 x 10-2) +3-10]
3
- 371
All of the sand will clearly be retained. Note that a clay or very fine silt of
V » 5xlO~4 ft sec'l would be only partially trapped:
p « [(1.6 x 104 x S x 10-*) * 3 - 10]
3
• 0.33
Thus about one-third of this sediment loading would be retained. Note that
if D is large, trap efficiency drops using this algorithm. For the silt, a
discharge channel depth (at the outflow from Upper Lake) of 11 feet rather
than 10 would give:
p . [(1.6 x 104 x 5 x 10-*) ^ 3 - 11]
-47-
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1 Thus with 0 • 11, all silt exits the Impoundment. If D 1s only 9 feet, then: I
1 p [(1.6 x 10* x 5 x 10-*) * 3 - 9] j
i ' 3 i
• .66 j
! Two-thirds of the silt 1s retained. Remember that P represents a mean value.
{ Clearly during some periods none of the silt will be retained (due to turbulence, ;
I higher velocities) while during other periods, all of the silt will be trapped. j
| The key here 1s the word "mean.' I
| If the Impoundment 1s assumed to be vertically nixed (case B), compute j
j the mean depth 0: j
n
I D - I D./n I
i i
where
n • the number of cross-sections
I QI » depth at the 1th cross-section. j
I For Upper Lake: I
i i
I 0 - 6.7 - D' I
I Then: j
I v T 1
For the ciay:
P . 9.3 x 1(TS x 1.6 x 104
6.7
- 0.22
About one-fourth of the clay 1s retained:
For the sand:
P . 7 x 10-2 x 1.6 x 10*
6.7
• 167
All of the sand will be trapped within about 1/167 times the length of the
lake. If the dally Influent loading of sand Is one ton, while the loading
of clay Is fifteen tons, then the dally accumulation will be one ton of sand
and 0.22 x-15 «.-3.3 tons of clay.
Finally, as an example of use of Figures V-21 and V-22, assume that the
sediment loading consists primarily of silt particles in the sl2e range of
.002mm diameter, and that the water temperature is 5*C. Further, assume Tw has
been estimated as 2.77 days (104 seconds), and that 0* « 50 feet. From
Figure V-21, the settling velocity is about 1 x 10"4 feet per second.
-48-
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I In Figure V-22, draw a line from 10~4 on the V axis to 104 on the
j Tw axis. The point of Intersection with axis I 1s L*. Next, compute
j 1°91050 " 1-699. Draw a line from this point or the D' axis to L*.
• Where this line crosses the St/Si (I) axis gives the log of the percent
• of the sediment trapped. This 1s 1QO-3 » 1.99321.
I
I END OF EXAMPLE V-9
5.4 EUTROPHICATION AND CONTROL
5.4.1 Introduction
Eutroph1cat1on 1s the process of Increasing nutrients 1n surface waters.
The presence of nutrients in an impoundment generally favors plant growth. Depending
upon antecedent conditions, the relative abundance of nitrogen, phosphorus, light,
and heat, and the status of a number of other physical and chemical variables, the
predominant forms may be diatoms, other microscopic or macroscopic algae, or bottom-
rooted or free-floating macrophytes. The quantity of plant matter present In an
Impoundment 1s Important for several reasons. First, plant cells produce oxygen
during photosynthesis, thereby providing an Important source of dissolved oxygen to
the water column during daylight hours. Plant cells also consume oxygen through the
process of respiration. Respiration occurs along with photosynthesis during the day,
but occurs at night when photosynthesis does not. Oxygen consumed at night may be
considerable, not only because it serves to sustain the plant cells, but because the
cells actively perform various vital metabolic functions in the dark. Also, cells
that fall below the photic zone will consume additional oxygen irrespective of the
time of day.
Plant growth within an impoundment is also important because plant biomass is a
major source of nutrition for Indigenous fauna, and the growth of plants constitutes
what is called "primary production." The stored energy and nutrients provide food
for various grazers higher in the food chain, either through direct consumption of
living plant tissue by fishes and zooplankton or through consumption of detritus by
fishes, microorganisms, and zooplankton. The grazers, 1n turn, provide food for
predatory fishes, mammals. Insects, and other higher forms. The kinds and amounts of
primary producers effect the other members of the food chain resulting In a good
sport fishery or "trash fish," depending on nutrient conditions.
Finally, plant development in Impoundments 1s important because It tends to
accelerate Impoundment aging. As plants grow, organic matter and sediment accumulate.
As the Impoundment fills with rock fragments, soil, and plant detritus, an excellent
substrate forms upon which more suspended matter may be trapped and which may ulti-
mately support the growth of higher plants and trees. The gradual filling in of an
-49-
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Impoundment In this way reduces Us usefulness, and may finally eliminate the Impound-
ment completely.
5.4.2 Nutrients, Eutrophy, and Algal Growth
Eutrophy means literally a state of good nutrition. Plants require a number of
nutrients, but to vastly different degrees. Some nutrients, such as carbon, nitrogen,
potassium, and phosphorus, are needed 1n large quantity. These are termed macronutrl-
ents. The micronutMerits, e.g. Iron, cobalt, manganese, zinc, and copper, are needed
in very small amounts. In nature, the nricronutrlents, carbon, and potassium are
usually in adequate supply (although not always), while nitrogen and phosphorus are
commonly growth limiting.
Nitrogen, particularly as nitrate and ammonium Ions, 1s available to water-borne
plant cells to be used in synthesis of proteins, chlorophyll a_, and plant hormones.
Each of these substances 1s vital for plant survival.
Phosphorus, an element found in a number of metabolic cofactors, 1s also neces-
sary for plant nutrition. The biosynthesis and functioning of various biochemical
cofactors rely on the availability of phosphorus, and these cofactors lie at the very
foundation of plant cell metabolism. Without adequate phosphorus, plant cells cannot
grow.
Since nitrogen and phosphorus are commonly in limited supply, many impoundments
tend inherently to be clear and essentially free of clogging algae and vascular
plants. Over long periods of time and depending on geological conditions, natural
sources of nutrients may lead to eutrophication in lakes. Because of society's
ever-increasing size and need for food, chemical sources of nitrogen and phosphorus
are synthesized and spread over vast tracts of farmland. Stormwater washes off these
nutrients, which then flow through streams and into natural and artificial impound-
ments. Also, excessive nutrients occur in wastewaters from municipalities and
industry. Due to the fact that many impoundments have very low flow velocities,
impoundments represent excellent biological cultunng vessels, and often become
choked with plant life when nutrients Increase.
Since a plant cell has at any point in time a specific need for nitrogen and for
phosphorus, one or the other or both may limit cell growth or replication. Where
nitrogen is the nutrient that restricts the rate of plant growth, that is, where all
other nutrients aod /actors -are present in excess.-we *ay that nitrogen 1s growth
limiting. In general, N:P mass ratios in the range of 5 to 10 are usually associ-
ated with plant growth being both nitrogen and phosphorus limited. Where the ratio
is greater than 10, phosphorus tends to be limiting, and for ratios below 5, nitrogen
tends to be limiting (Chiaudani, et_ al^, 1974). In most lakes, phosphorus 1s the
limiting nutrient. In many nitrogen-limited lakes, phosphorus 1s still controlling
because of the process of nitrogen fixation. Thus, the focus In this manual is on
phosphorus.
-50-
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In addition to nitrogen and phosphorus, any necessary nutrient or physical
condition may limit plant growth. For example, 1n high nutrient (eutrophic) waters,
algal biomass may increase until light cannot penetrate, and light Is then limiting.
At such a point, a dynamic equilibrium exists in which algal cells are consumed,
settle or lyse (break) at the same rate as new cells are produced. In other cases,
light may be limiting due to non-algal partlculate material.
To summarize, the process of eutrophlcation (or fertilization) is enrichment of
a lake with nutrients, particularly nitrogen and phosphorus. However, the problems of
eutrophication are caused by increased plant biomass as a result of enrichment.
Therefore, the objective 1s to predict plant biomass as related to nutrient concen-
trations. The method for predicting plant biomass is based on the rate of phosphorus
supply (loading), the concentration of phosphorus 1n the lake, and the amount of
plant biomass that is predicted based on the phosphorus concentration. The plant
biomass is exemplified by the phytoplankton (algae) concentration but macrophytes
(aquatic weeds) are also of concern. The plant biomass and related variables define
the scalar relationships of eutrophlcation.
5.4.3 Predicting Algal Concentrations
Predicting algal blooms or predominance of macrophytes using a mechanistic
approach can be a very complex problem, and most methods are not suited to a simple
hand calculation technique. However, relationships regarding algal productivity
have been derived that permit an evaluation of the eutrophic state of an impoundment.
Because the methods permit algal biomass to be estimated with relatively little.
easily obtained data, and because algae are very important in assessing impoundment
water quality, these techniques are useful here. The methods presented below are
based upon the fact that in most cases (perhaps 60 percent) phosphorus is the biomass
limiting nutrient (EPA, 1975). One such approach has been developed by Vollenweider
(Vollenweider, 1976; Vollenweider and Kerekes. 1981; Lorenzen, 1976). It may be
used to predict the degree of impoundment eutrophication as a function of phosphorus
loading.
5.4.3.1 Nutrient Limitation
Before considering application of any of the methods to assess eutrophlcation,
it is important to examine the nitrogen to phosphorus ratio. This Indicates whether
any of the methods presented below is likely to give realistic results. Gener-
ally, an average algal cell has an elemental composition for the macronutrients of
^106 N16 ^1* H^tn ^ atoms of nitrogen for each atom of phosphorus, the average
composition by weight 1s 6.3 percent nitrogen and 0.87 percent phosphorus or an N/P
ratio of 7.2/1. Although all nutrient requirements must be met, the relative rate
of supply is significant and must be determined to know which is limiting. For N/P
-51-
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ratios greater than 7.2, phosphorus would be less available for growth ("limiting")
and when less than 7.2, nitrogen would be limiting. In paractice, values of less
than 5 are considered nitrogen Uniting, greater than 10 are phosphorus limiting, and
between 5 and 10. both are limiting.
In many cases of eutrophlc lakes, nitrogen 1s not limiting because of the
process of nitrogen fixation. Some blue-green algae, a particularly noxious type of
algae, have enzymatic processes for the biochemical conversion of dissolved elemental
nitrogen into reduced nitrogen (amlne groups) suitable for growth and metabolism.
Special cells called heterocysts perform this process and only appear when nitrogen
is limiting. It can be argued that In general nitrogen is not limiting (Schindler,
1977) and a "worst case" analysis can be made for a screening approach using phos-
phorus. This is the basis for the eutrophlcation screening method. However, it
should be remembered that the chlorophyll produced Is affected by the N/P ratio as
are the algal species (Smith, 1979).
5.4.3.2 Nutrient Avail ability
Availability of nutrients is also important. Partlculate nitrogen and phosphorus
in the inflowing tributaries generally settle and can therefore be considered unavail-
able. Few estimates of bioavailable nutrients have been made. The estimates have
been made primarily for phosphorus using algal assay techniques. Cowen and Lee
(1976) indicated that 30 percent or less of urban runoff phosphorus was available to
algae whil* Dorich et_ aj_. (1980) found a value of 20 to 30 percent for sediment bound
phosphorus (as would occur in rural runoff). It appears that a fraction of 0.3 would
provide a conservative estimate of bioavailable phosphorus in the absence of actual
measurements.
5.4.4 Mass Balance of Phosphorus
A material entering a lake or impoundment will partition between the aqueous and
solid phases. The solid phase can settle and become bottom sediment or outflow can
remove suspended and aqueous phase material. A diagrams tic presentation of the
concept of Inflow, partitioning and settling, and outflow is shown in Figure V-23.
The concentration of the material can be calculated very simply after making several
assumptions: the lake is completely mixed, the lake is at steady state and inflowing
water equals outflow, and the annual average rates are constant. Although these
assumptions are not met entirely for phosphorus, they are satisfied well enough to
meet requirements for a screening analysis of eutrophlcation. Based on Its histor-
ical development the eutrophication screening method is termed the "Vollenweider
Relationship".
As shown 1n Figure V-23, any of three different forms of the steady state
equation can be used to predict phosphorus concentrations 1n lakes. Each form may be
-52-
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A • AREA
QI - INFLOW
XI « CONCENTRATION
OF POLLUTANT
WATER
V
/ / / / j / / / / v / /
OUTFLOW » Q
SEDIMENTS
V - VOLUME
X « CONCENTRATION IN LAKE
For Example - Phosphorus, P • X
LOADING
Lp " QI • PI / A, mg/ral year
MASS BALANCE
Assumptions: completely mixed, steady state. Q a QI, annual average
rates are constant
Definitions: Mean depth, Z • V/A; hydraulic flushing or dilution
rate, D • Q/Y; hydraulic loading, q » Q/A; M •
QI • PI; K « net rate of solid phase removal and
release (proportional to P), typically negative when
averaged over the annual cycle.
- KP • 0
(Mass Balance Form) U)
(Mass Inflow Form) (2)
(Loading Form) (3)
Solving for P,
„ _ D • PI
•HhlTT
P •
zi
D * K)
FIGURE V-23 FORMULATIONS FOR EVALUATING MANAGEMENT OPTIONS
FOR POLLUTANTS IN LAKES AND RESERVOIRS
-53-
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more or less suitable for a specific data set. The Important variables are the
hydraulic flushing or dilution rate (Q/V, Inverse of residence time), lake volume to
area ratio (V/A, equals mean depth), phosphorus 1n the Influent (PI), and the net
rate of removal (K).
The variables Q, V, A must be determined from other data. The influent phosphorus
can be based on measurements or estimated from calculations performed as in Chapter 3
and including any municipal and industrial effluents. Generally, effluents are
considered totally available for growth. Nonpoint sources should be assessed as 100
percent available and as 30 percent available to provide limits for screening purposes.
Estimation of the net rate of removal (K) 1s not as clear. Vollenweider (1976)
and Larsen and Hercier (1976) Independently estimated the net rate of removal as
a function of dilution rate:
K « Vb~~~
This is the most accepted approach for screening. Jones & Bachmann (1976) estimated
that K - 0.65 by least squares fitting of data for 143 lakes.
Equivalently, Vollenweider and Kerekes (1981) provide a derivation of the mass
balance equation (Equation 1, Figure V-23) in terms of phosphorus residence time and
based on regression analysis:
P - l- (PI) - P1
1 + "/D
Regression of predicted phosphorus and actual phosphorus for 87 lakes showed a
reasonable correlation (r • 0.93) but indicated that there was a predicted slight
underestimate at low concentrations (<8 ^g/1 ) and a slight overestimate at higher
concentrations (<20ng/l) (Vollenweider and Kerekes, 1981).
Also the value of K can be estimated from the ratio (R) of the measured mass
phosphorus retained (in minus out) and the mass inflow:
R m QI-PI - Q-P .. PI-P
QI • PI * PI
P-7
To assess the placement of a specific lake relative to a set of lakes, phosphorus
loading (Lp) is graphed as a function of hydraulic loading (q ) (Figure V-24).
The data for 49 measurements of U.S. lakes are shown. (Some lakes occur more than
once because of multi-year studies.)
Hore recently, Vollenweider and Kerekes (1981) have presented the OECD Eutrophl-
cation Program results showing that lakes can be classified Into discrete groups
according to their eutrophication characteristics (Table V-9). However, as they
note, there is overlap between the different categories showing that these charac-
teristics are not complete descriptors of trophic state but are relative Indicators.
-54-
-------
10
"^
>*
^
E
X
Q.
Z 1
O
z
o
PHOSPHORUS L0>
o
OOl
o
; 1 i i -i i i ii| i i 1 i i i ii| 1 1 — r— r-r-TTTj r i i i i i i
1 "• *» l« 121 X
; EUTROPHIC • * /EXCESSIVE
." 1 .« / '
* • »50 / 'PERMISSIBLE
•« **« ' /
-«T 22 •* 30 «» ' X
n • •* • • / x
r • .j **• «, « / /
: „- "»$•»•'','
: • , v ••$''&/
•^— -<^ ^.X INVESTIC»TO*-l*OlCATrD
— '" ^-^ TROPHIC STATC •
j3.493 2J-i -*•-" •-EOTRO^MIC
o ?SA^O.^ A -*«t SOT^O^HIC
O~*"" O?4-l O -OLICOTWOPMIC
2*-*
: o«z
0«
'*C02I
g 4i OLIGOTROPHIC
1 1 1 1 1 1 III 1 1 t 1 1 1 1 ll 1 t 1 1 1 1 1 it 1 1 1 1 1 1 1
I 1 10 100 10
-
-
oc
MEAN DEPTH 2/HYDRAULIC RESIDENCE TIME. Tw
( m/yr )
FIGURE V-24 US OECD DATA APPLIED TO VOLLENWEIDER (1976)
PHOSPHORUS LOADING AND MEAN DEPTH/HYDRAULIC
RESIDENCE TIME RELATIONSHIP (TAKEN FROM RAST
AND LEE, 1973)
-55-
-------
TABLE V-9
PRELIMINARY CLASSIFICATION OF TROPHIC STATE BASED OH INVESTIGATOR OPINION
(ADAPTED FROM VOLLENUEIDER AND KEREKES. 1981)
Variable* OHqotropMc Hesotrophlc EutrooMc
Total Phosphorus
wan 8 27 84
range (n) 3-18(21) 11-96(19) 16-390(71)
Total Nitrogen
•can 660 750 1900
range (n) 310-1600(11) 360-1400(8) 390-6100(37)
Chlorophyll a
•can ~ 1.7 4.7 14
range (n) 0.3-4.5(22) 3-11(16) 2.7-78(70)
Peak Chlorophyll a
•can ~ 4.2 16 43
range (n) 1.3-11(16) 5-50(12) 10-280(46)
Secchl Depth, •
•can 9.9 4.2 2.4
range (n) 5.4-28(13) 1.5-8.1(20) 0.8-7.0(70)
*g/l(or ng/m ) except Secchl depth; Means are geometric annual »eans
{Iog10), except peak chlorophyll i.
•• EXAMPLE V-10
Big Reservoir and
The Vollenweider Relationship
To use the Vollenweider relationship for phosphorus loading, data on long-
term phosphorus loading rates must be available. It is also important that the
rates represent average loading conditions over time because transient phosphorus
loading pulses will give misleading results. Big Reservoir is a squarish reservoir
and has the following characteristics:
Big Reservoir
Available Data (all values are means):
Length 2.0 mi • 3.22 k«
Width 5. ml « .805 km
Depth (Z) 200 ft - 20 m
Inflow (Q) 50 cfs - 1.42 cms
-56-
-------
Total phosphorus concentration 1n water column 0.482 ppm
Total nitrogen concentration in water column 2.2 ppm
Total phosphorus concentration In the inflow 1.0 ppm
In order to apply the plot In Figure V-24, the first step is to make as
certain as possible that algal growth is phosphorus limited. In this case,
the weight to weight N:P ratio is 2.2/.4S « 4.6. Presumably, algal growth
in Big Reservoir is not phosphorus limited, and the Vollenweider relationship for
phosphorus is not a good one to use. In this case a rigorous model should be
used. If nitrogen fixation is observed to occur (heterocystous blue-green algae),
an estimate of the potential problem can be obtained by assuming phosphorus to be
limiting:
V - length • depth • width
» 322Chi • 805m • 20m • 51.8 million m3
1.42 m3 86400 sec 365 day 0.865
' '
Plotting Lp and q on Figure V-24 shows that the reservoir could be extremely
Q/A - 7rw » 20/1.16 - 17.2 m/yr
>
eutrophic.
END OF EXAMPLE V-10
EXAMPLE V-ll
Bigger Reservoir and
The Vollenweider Relationship
The physical characteristics of Bigger Reservoir are:
Bigger Reservoir
Available Data (all values are means):
Length 20 mi « 32.2 km
Width 10 mi « 16.1 km
Depth (D 200 ft • 61 m
Inflow (Q) 500 cfs
Total phosphorus concentration in inflow 0.8 ppm
Total nitrogen concentration In inflow 10.6 ppm
As in the preceding example, first determine whether phosphorus is likely to
be growth limiting. Since data are available only for influent water, and since
-57-
sec 51. 8 da> *' yr I
T » 1.16 years |
K • VB . 0.93/yr j
p ' Trrr " °-482 m*/] \
Lp • Q • PI/A « 17.3 g/m2 yr j
-------
I no additional data are available on Impoundment water quality, N:P for Influent
j water will be used.
j N:P « 10.6/0.8 » 13.25
j Thus algal growth 1n Bigger Reservoir 1s probably phosphorus United.
• Compute the approximate surface area, volume and the hydraulic residence time.
j Volume (V) * 20 n1 x 10 ml x 200 ft x 52&02-
j 1.12 x 1012ft3 • 3.16 x 1010«3
j Hydraulic residence time (TW) • V/Q «
; 1.12 x 1012ft3/500 ft^ec"1 » 2.24 x 109sec • 71 yr
Surface area (A) • 20 mi x 10 ml x 52802 •
j 5.57 x 109ft2 • 5.18 x 108m2
j Next, compute q$
i <' • T/T-
q • 61 m/71 yr « 0.86 m yr
! Compute annual Inflow, Q
Q• Q x 3.15 x 107 sec yr"1
' Qy - 1.58 x 1010ft3yr"1
! Phosphorus concentration In the Inflow 1s 0.8 ppm or 0.8 mg/1. Loading (Lp)
I in grams per square meter per year 1s computed from the phosphorus concentration,
1 1n mg/1:
j ft3 lOOOmg * 5.18xl08m2 ' yr
-2 -1
I Lp • 0.70 gm yr
| Now, referring to the plot In Figure V-24, we would expect that Bigger Reservoir
j is eutrophlc, possibly with severe summer algal blooms.
- END Of EXAMPLE V-ll
•-EXAMPLE V-12
The Vollenweldcr Relationship
Using Monthly Inflow Quality Data
Is Frog Lake eutrophlc? Frog Lake's physical characteristics are as shown
below:
-58-
-------
1
i
i
•
i
i
i
i
i
•
i
i
i
i
i
i
i
i
,
i
!
i
q
Month
October
November
December
January
February
March
April
May
June
July
August
September
Frog Lake
Available Data:
Mean length 2 mi
Mean width 1/2 mi
Mean depth 25 ft
Available Inflow Hater Quality Data:
(monthly mean, cfs) Total P (mg/1) Inorganic N (mg/1)
1972 1974 1972 1974 1972 1974
50 65 0.1 0.08 7.2 6.0
80 90 0.02 0.02 6.3 2.4
40 40 0.03 0.04 3.1 1.5
_ _ - — _ -
- -
60 58 0.01 0.02 2.0 1.9
80 BO 0.01 0.01 2.3 0.50
75 76 0.04 0.05 0.55 0.52
40 70 0.03 0.08 1.20 1.35
25 - 0.11 - 2.01
38 20 0.09 0.04 3.50 1.29
38 25 0.06 0.05 2.80 1.00
j First, estimate the mean annual flow and the hydraulic residence time. To compute
i
i
i
i
i
i
i
j
i
i
i
.
i
mean annual flow,
y
Q • ( L
1-1
where
Qi.j "
y
n.
Q
Now estimate the
V » 2
1.
A * 2
n.
1 y
r QJ i\/ z n.
j»l i*l
the individual flow measurements
the number of years of data
the number of observations per year
1050/19 - 55.3 cfs • 1.75 x 109ft3/yr
volume, surface area, hydraulic residence time, and q$
ml n 1/2 mi x 25 ft x (^280 ft) - 5 07 x in^ft3 -
mi
98 x 107m3 2
mi it 1/2 mi x (5280 ft) , £ 79 x io7ft2 - 2 59 x lO^m2
1
i
i
i
i
i
*
i
i
*
i
i
•
i
i
i
i
i
i
*
i
i
i
i
*
i
4
1
i
i
i
*
'
i
i
i
i
i
i
i
i
*
i
i
i
-59-
-------
I T . V/Q « 6.97 x 108ft3/55.3 cfs « 1.26 x 107 sec - 0.4 yr ,
j «s ' I/Tw I
j q . 25 ft. °'3048 "V0.4 yr « 19.05 m/yr j
! s ft
J Next, calculate the weighted mean Inflow phosphorus and nitrogen concentrations [
I 7 and TT as follows: I
I j
i y ni y ni i
! 7 (or if) - ( z z tL , x c, J/(r r Q< J
| i-l j-l 1§J >J 1-1 J-l 'J |
j 7 » 43.86/1050 • 0.042 mg/1 j
j TJ - 2671.902/1050 • 2.54 mg/1 j
The N:P ratio in the inflows is 60. Therefore if one of the two is growth limiting,-
it is probably phosphorus. Compute the phosphorus loading, Lp.
1 g x 0.042 mg K 1 x 1.75xl09ft3 j
lOOOmg / 2.59xl06mZ yr I
( Lp » 0.80 g/m2 yr !
| Now, referring to the plot in Figure V-24 with Lp « 0.80 g/m yr and q$ • 19 m/yr, |
I the impoundment is well into the mesotrophic region. I
i i
! END OF EXAMPLE V-12 :
5.4.5 Predicting Algal Productivity, Secchi Depth, and Biomass
The prediction of eutrophication effects is based primarily on prediction of
chlorophyll a_ concentrations from phosphorus concentrations rather than on general
impoundment trophic status. The method r>as been advanced by several researchers
including Sakamoto (1966), Lund (1971), Dillon (1974), and Dillon and Rigler (1975).
Originally, the method related mean summer chlorophyll a_ concentrations to spring
mean total phosphorus. As shown in Figure V-25, the relationship is highly correlated,
and a regression of the log of summer mean chlorophyll a_ on the log of spring mean
phosphorus is linear (units are i^g/1). Using a least squares method gives the equation
of the line as (Lorenzen, 1978):
log (chl £) - 1.5 log (P)-l.l
or
chl a_ • O.O^P)1'5 for P<250 mg/m3 - 0.25 ppm
More recently (Vollenweider and Kerekes, 1981), additional data have been
compiled and equations have been derived for predicting annual average chlorophyll j»
from annual average total phosphorus (r « 0.88, n»78):
chl a - 0.27(P)°'99 (V-15)
-60-
-------
1000
m
2
x
(9
100-
a.
g "OH
o
-------
• •* *SD
where
I » Initial light Intensity, light units
o
I_D • Intensity at Secchl depth, light units
SD * Secchl depth, m
k • extinction coefficient, 1/m.
Algal blooms reduce transparency. Algal blooms are measured using the average
summertime (July-August) chlorophyll ^ concentration (CA. ng/1) 1n the mixed layer
epilimnion) since non-plant materials do not contain chlorophyll. Lorenzen (1973,
1980) showed that the extinction coefficient (k) could be considered 1n two parts;
that is, light attenuation would be the result of absorption and scattering by algal
cells and by the water and non-algal materials in the water column:
k « a + b • CA
Hutchinson (1957) and others have shown that the Secchl depth occurs over a relatively
narrow range of light intensity ratios (I/I ). If 1t 1s assumed that this ratio
is a constant (ln(I/I ) » R), we can substitute (A - a/R; B • b/R). and solve for
Secchi depth as a function of chlorophyll aj
1/SD - A + B * CA
In the equation, A represents non-algal attenuation while B*CA represents
attenuation by chlorophyll a_. Larsen and Kalueg (1981) used data from several lakes
to compute this relationship. Similarly, data from 226 lakes were used to obtain the
foil owing- equation:
1/SD « 0.02 CA * 0.6
However, B is considered a constant (B • 0.02, Megard et_ i]_., 1980), while A will vary
with the background light attenuation in the water due to dissolved and particulate
matter (Lorenzen, 1980). It should be noted that as the particulate matter increases,
the relationship will be less likely to hold.
Figure V-26 shows a plot of maximal primary production In terms of milligrams
carbon incorporated in algae per square meter per day as a function of phosphate
phosphorus levels. As was the case with predicting chlorophyll ^ concentrations, the
relationship appears to be reasonably robust and therefore useful.
Because dried algae contain very roughly 3 percent chlorophyll £ (J.A. Elder,
pers. comm., 1977), dry algal biomass may be estimated from chlorophyll ^ concentra-
tion by multiplying by thirty-three. Similarly, carbon productivity, as In the plot
in Figure V-26, may be converted to total algal biomass. Since approximate analysis
of dried algae has been determined as (Stumm and Morgan, 1970):
C106H263°110N16P1
-62-
-------
2500-
o
•o
tvi
0 2000-
c
o
1500-
o
h_
0.
>>
^
§
V_
CL
1000-
500-
0.05 0.10
P04S (os P, mg/l)
0.15
FIGURE V-26 MAXIMAL PRIMARY PRODUCTIVITY AS A FUNCTION OF PHOSPHATE
CONCENTRATION (AFTER CHIAUDANI, EI AL,, 1974)
the gravimetric factor 1s -ywyr^.S. Thus, maximal carbon productivity may
be multiplied by 2.8 to give a rough estimate of maximal algal biomass productivity.
The user should bear in mind that applying this technique can only lead to rough
estimates. If it is desired to predict biomass or productivity with accuracy, more
sophisticated approaches may be necessary.
EXAMPLE V-13
j Phosphorus and Summer Chlorophyll a
i
j Lake Sara mean annual total phosphorus concentration, P - .03 mg/l - 30 mg/m"
0.99
chl a. - 0.27(PT
chl £ » 7.8 mg/m'
algal dry biomass » 7.8 x 33 - 258 mg/m
3
Peak chlorophyll a^ would be 22 mg/rrr. If calculated from loading rates, the
-63-
-------
numbers would differ. Secchi depth would be approximately 1.3 meters assuming
that the average background light extinction was 0.6.
END OF EXAMPLE V-13
In the absence of measured data, the in-lake concentration (P) can be computed
based on the various point and nonpoint loadings (n):
Then chlorophyll j> can be estimated as shown in the previous paragraphs.
5.4.6 Restoration Measures
Control of eutrophication in lakes can be evaluated by a variety of approaches
(Table V-10). Some methods are directed at external sources (PI) and others at
recycling from in-lake sources (K). Changes in volume (V) and inflow (Q) obviously
will affect predicted results. For example, on a long term basis dredging will
decrease the return of phosphorus for the sediments (i.e. increase K) and increase
the volume land therefore decrease the dilution rate, 0). If the input concentration
(PI) is the critical variable, then source controls should be investigated. If
internal sources are involved, then in-lake controls should be evaluated. In many
lakes, both source and in-lake controls will be needed.
Problem treatment is directed at the productivity directly. These controls are
often the only alternative for many lake situations. These methods are evaluated
only in a qualitative way. Indexes for evaluating lake restoration have been devel-
oped (Carlson, 1977; Poreel la et^al_., 1980). These are useful for prioritizing lake
restoration projects and for evaluating progress.
5.4.7 Mater Column Phosphorus Concentrations
The relationships described in 5.4.5 for predicting algal biomass are predicated
on phosphorus levels within the impoundment. A more precise mechanism for estimating
phosphorus lake concentrations based on Interactions between bottom sediments and
overlying water has been developed.
lorenzen, et^ al_. (1976) developed a phosphorus budget model (Figure V-27) which
may be used to estimate water column and sediment bound phosphorus in a fully mixed
system. A mass balance on both sediment and water column phosphorus concentrations
-64-
-------
TABLE V-10
CLASSIFICATION OF LAKE RESTORATION TECHNIQUES
I. Source Controls
A. Treatment of inflows
B. Diversion of inflows
C. Watershed management (land uses, practices, nonpoint source
control, regulations and/or treatments).
0. Lake riparian regulation or modification
E. Product modification or regulation
II. In-Lake Controls
A. Dredging
B. Volume changes other than by dredging or compaction of
sediments
C. Nutrient inactivation
D. Dilution/Flushing
E. Flow adjustment
F. Sediment exposure and dessication
G. Lake bottom sealing
H. In-lake sediment leaching
I. Shoreline modification
J. Riparian treatment of lake water
K. Selective discharge
III. Problem Treatment (directed at biological consequences of lake
condition)
A. Physical techniques (harvesting, water level fluctutations,
habitat manipulations)
B. Chemical (algicides, herbicides, pesticides)
C. Biological (predator-prey manipulations, pathological
reactions).
D. Mixing (aeration, mechanical pumps, lake bottom modification)
E. Aeration (add DO; e.g. hypolimnetic aeration)
-65-
-------
Water Column
Sediment
:(*)Q(o)
FIGURE V-27 CONCEPTUALIZATION OF PHOSPHORUS BUDGET
MODELING (LORENZEN ET AL,, 1976)
yields the coupled differential equations:
dt
(V-17)
(V-18)
~ar
M
V
vs
A
Q
• average annual total phosphorus concentration 1n water column (g/m )
* total exchangeable phosphorus concentration 1n the sediments (g/m )
• total annual phosphorus loading (g/yr)
• lake volume (m )
• sediment volume (m )
• lake surface area (m ) - sediment area (• )
• annual outflow (m /yr)
• specific rate of phosphorus transfer to the sediments (n/yr)
• specific rate of phosphorus transfer from the sediments (m/yr)
* fraction of total phosphorus Input to sediment that 1s unavailable
for the exchange process
-66-
-------
When the differential equations relating water column phosphorus to the
various controlling phenomena are solved analytically, the following
equation results for steady-state water column phosphorus concentration:
or
(V-20)
where
C • steady-state water column phosphorus concentration 1n ppm
C. • steady-state Influent phosphorus concentration In ppm
The steady-state sediment phosphorus concentration 1s then given by:
S K2(l
It 1s Important to observe that these relationships are valid only for steady-
state conditions. Where phosphorus loading 1s changing with time, where sediment
deposition or physical characteristics are changing, or where there are long-term
changes 1n physical conditions, the steady-state solutions are not applicable.
Lorenzen applied the model to Lake Washington data and obtained very good
results. With their data set, the most satisfactory coefficients had the following
values:
K: - 43 m/yr
K2 • 0.0014 »/yr
*3 " °-5
It should be recognized, however, that this model 1s relatively untested and that
coefficient values for other impoundments will vary from those cited here.
| ------------------- EXAMPLE V-14 ------------------------ 1
I
A Comprehensive Example
Impoundment Water Column Phosphorus
What will be the steady-state concentration of phosphorus 1n the water
column of Lake Jones following diversion of flow? How will this affect algal
abundance?
-67-
-------
Lake Jones: i
Area, A. 20 miles2 • 5.6 x 10Bft2 -5.2 x 107m2 |
Volume, V. 3.08 x 10Uft3 • 8.73 x 10V j
Available Data (prior to diversion): |
Inflows: j
Mean Annual j
Flow, cfs Mean P, mg/1
1. Janes River 75 .15 !
2. Jennies River 22 .07 |
3. Johns Creek 5 .21 I
4. Direct stormwater Influx (nominal, may be disregarded) |
The diversion, which is for Irrigation purposes, has decreased the mean j
annual inflow from Jennies River to 1 cfs with an average annual phosphorus j
concentration of 0.01 mg/1. Additionally, there 1s a reduction of flow in Janes
River to 55 cfs. but the mean P concentration stays the same.
To apply the Vollenwelder relationship, first to the prediversion status of ;
Lake Jones, compute q : I
2 . 6.73xlQ9m3 n
S.2xloV
Based upon the conceptualization (see Figure V-27), it 1s reasonable that the
coefficients interact. For example, Kj, the rate of phosphorus uptake by the
sediment must be related to the rate of phosphorus release by the sediment. The
model requires however, that the product K^K-j be constant. The value used by
Lorenzen, et_ al_. was 21.6. As they point out, the coefficients must satisfy
certain conditions, specifically those established by the derived equations. The
equations are:
C ' (V-22)
w
and
7- " (V-23)
s K-K
From (V-22)
M-QCW
(V-24)
I
-68-
-------
Computation of K., therefore, requires a value for K-. This coefficient,
(K3) unfortunately, 1s usually unavailable. It represents the fraction of
phosphorus entering the sediment which 1s not returned to the water column.
Processes contributing to this phenomenon are burial caused by steady-state
sediment accumulation, and steady-state chemical precipitation of phosphorus,
such as with iron to form Fe3(P04)« 8H20 (vivianlte). Lorenzen's value for
Lake Washington was SO percent. Because the fraction is likely to vary signifi-
cantly from system to system and because the coefficient is difficult to evaluate.
the planner is advised to use 30 percent as the lower limit, 50 percent as a
probable value, and 70 percent as an upper limit for estimating sediment
phosphorus content. The water column concentration is independent of changes in
K» because the product of K, and IU is a constant.
Using Equation (V-24), K7 uniquely defines K, . Then, from Equation
(V-23):
is therefore also defined by fixing K,, providing C and C are known
, 2B.3U 11 g , 3.16xl07sec j
ft 1000 mg * y7I
M • 1.24x10^ gP/yr J
j Q . (75+22-5)ft3 3.16xlQ7sec . 3.22x10^ 9.13xlQ7m3 1
j sec yr yr yr j
I TW • B^SxloV/g.lSxloVyr-1 - 95.6 yr I
j j
i qs " 168/95.6 » 1.76 m yr'1 j
j i
| Compute phosphorus loading: I
I I
! Lp" "5" j
; . , . 1.24xl07 q yr"1 ... -2 -1
Lp « —*-i 0.24 gm V I
5.2xl07m2
.69-
-------
I Referring to Figure V-24 with q$ • 1.76 and Lp • 0.24. one can see that this
| lake may have eutrophlcatlon problems under pre-dlverslon conditions.
j After the diversion,
8.73 x lo
T . - --. - « 125 yr
I * 6.98 x lOV/yr
Assuming the lake depth Is not materially changed over the short term, j
q$ - 168/125 - 1.34 5L- !
t
For the new conditions,
H • 8.33 x 106 gP yr"1 j
Lp . 8.33 « 106 g yr-1 . ^2 -
C 7 „ inlL '
3.i X 10 m i
Now, according to the Vollenwelder plot (Figure V-24), this is in the region \
between "dangerous" and "permissible" - the mesotrophic region. Under the j
new circumstances, algal blooms are less likely than before the flow diversions I
were established, but blooms are by no means to be ruled out. |
Turning now to an estimate of algal biomass under pre-diversion,conditions, we j
must calculate the inlake concentration (P). j
First, D - I/TW - 1/125 « 0.008; K - VT - 0.09 j
Since our data are already In the loading form: j
P. ft 1
0.24 1 ,. . 3
» - - -15 mg/m
168 0.008*0.09
Based on annual average chlorophyll a^,
°'79
chl a - 0.37(P)
chl a_ « 3.1 mg/m
Under post -divers ion conditions,
168 0.008*0.09
10
chl a_ « 2.3 mg/m"
Note that these low levels of chlorophyll ^ almost certainly mean that the
j lake 1s oligotrophic to mesotrophic, and that the Vollenwelder method suggests
• worse conditions than may actually exist in this case (Table V-9).
Consequently, one might choose to use the Lorenzen model to evaluate K.
I and K3 and determine whether the impoundment is at steady state with respect
I to phosphorus levels in the water column and sediment. Generally, this Is
| the case where K^ lies in the range of 20 to 40. If K.K, 1s outside of
-70-
-------
I this range, field data should be obtained for current water column phosphorus.
I Sediment volume, V Irrelevant for steady-state solution
I Phosphorus (water column) .15 mg/1
i
I
0.5
M-Q(
*JJ
M-QCW
0.15 «g/l • .015 g/»3
. /1.24xlD7gP _ g.nxicfm3 x ^^3\ /
\ yr yr m //
yr yr
x 5.2 x lo - 28.3
m
• 44 x 0.5 - 14
j This result, therefore, gives reason to suspect non steady-state conditions
I for water column phosphorus. If more definitive answers are needed, additional
| field data should be collected.
i
END OF EXAMPLE V-14
5.5 IMPOUNDMENT DISSOLVED OXYGEN
Organic substances Introduced into an impoundment with inflowing water, falling
onto its surface, or generated in the water column Itself through photosynthesis, may
be oxidized by indigenous biota. The process consumes oxygen which may, in turn, be
replenished through surface reaeration, photosynthetic activity, or dissolved oxygen
in inflowing water. The dynamic balance between DO consumption and replenishment
determines the net DO concentration at any point in time and at any location within
the water column.
These processes result in characteristic dissolved oxygen (DO) concentrations in
the water columns of stratified lakes and reservoirs (Figure V-28). During strati-
fication, typically during summer months, the DO is highest on the surface due to
photosynthesis and reaeration. It decreases through the thermocHne and then, in the
hypolimnion, the DO decreases to zero in those lakes that have high organic matter
concentrations.
During spring, after turnover, when lakes are not stratified, the DO is essen-
tially uniform. However, in highly organic lakes benthic processes can already begin
to deplete oxygen from lower depths, as shown 1n Figure V-28.
-71-
-------
April 17. 1973
Dissolved Oxygen, mg/1
FIGURE V-28 TYPICAL PATTERNS OF DISSOLVED OXYGEN (DO) IN
HYRUM RESERVOIR (DRURY, EI AL,, 1975)
Essentially, the patterns result from processes that are restricted due to
incomplete mixing. The overall effects of such patterns as shown 1n Figure V-28, are
to restrict fishery habitat and create water quality problems for downstream users,
especially for deep water discharge.
BOD exertion 1s not the only sink for DO. Some important sources and sinks of
impoundment dissolved oxygen are listed below:
Sources
Photosynthesis
Atmospheric reaeration
Inflowing water
Rainwater
Sinks
Water Column BOD
Benthic BOD
Chemical oxidation
Deoxygenatlon at surface
Plant and animal respiration
Many of the processes listed above have a complex nature. For example, the
atmospheric reaeration rate Is dependent In part upon the near-surface velocity
gradient over depth. The gradient, 1n turn, 1s Influenced by the magnitude, dlrec-
-72-
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tlon, and duration of wind, as well as the depth and geometry of the impoundment.
Photosynthetic rates are affected by climatological conditions, types of cells
photosynthesizing, temperature, and a number of biochemical and biological factors.
Exertion of BOD is dependent upon the kind of substrate, temperature, dissolved
oxygen concentration, presence of toxicants, and dosing rate.
Despite this degree of complexity, a number of excellent models of varying
degrees of sophistication have been developed which include simulation of impoundment
dissolved oxygen.
5.5.1 Simulating Impoundment Dissolved Oxygen
Because an unstratified impoundment generally may be considered as a slow-moving
stream reach, only stratified impoundments are of interest here. For estimating DO
in unstratified impoundments, one should refer to the methods described in Chapter 4.
To understand the phenomena affecting dissolved oxygen in a stratified impound-
ment and to gain an appreciation of both the utility and limitations of the approach
presented later, 1t is useful to briefly examine a typical dissolved oxygen model.
Figure V-29 shows a geometric representation of a stratified impoundment. As indi-
cated in the diagram, the model segments the impoundment into horizontal layers.
Each horizontal layer is considered fully mixed at any point in time, and the model
advects and diffuses mass vertically into and out of each layer. The constituents
and interrelationships modeled are shown schematically in Figure V-30.
The phenomena usually taken into account in an impoundment DO model include:
~i Vertical advection
• Vertical diffusion
• Correction for element volume change
• Surface replenishment (reaeration)
• BOD exertion utilizing oxygen
• Oxidation of ammonia
• Oxidation of nitrite
• Oxidation of detritus
• Zoopl ante ton respiration
• Algal growth (photosynthesis) and respiration
• DO contribution from inflowing water
• DO removal due to withdrawals.
Hany of the processes are complex and calculations in detailed models involve
simultaneous solution of many cumbersome equations. Among the processes simulated
are zooplankton-phytoplankton interactions, the nitrogen cycle, and advection-
diffuslon. Thus 1t is clear that a model which is comprehensive and potentially
capable of simulating DO in impoundments with good accuracy is not appropriate for
hand calculations. A large amount of data (coefficients, concentrations) are needed
-73-
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tributary
inflow,
evaporation
tributary
inflow
Vertical
edvection
outflow
FIGURE V-29 GEOMETRIC REPRESENTATION OF A STRATIFIED
IMPOUNDMENT (FROM HEC, 1974)
to apply such a model, and solution is most easily done by computer. Furthermore,
some of the terms in the model equation of state do not improve prediction under some
circumstances. This is true, for example, where there are no withdrawals or in an
oligotrophic impoundment where chlorophyll a_ concentrations are very low.
Hand calculations must be based upon a greatly simplified model to be practical.
Since some DC-determining phenomena are more important than others, it 1s feasible to
develop such a model 1f some assumptions are made about the impoundment Itself.
5.5.2 A Simplified Impoundment Dissolved Oxygen Model
For purposes of developing a model for hand calculations, the following assump-
-74-
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<
6ENTHIC
ANIMALS
ORGAUIC
SEOIMEHT
SUSFEMtfD V.
DETPITLIS >P-
TOTAL
INORGANIC
CARBON
1
1 M^
|
< '
t f7\ '
'•Ml
M^>
| HARVEST
B .
A Aeration
B Bocttnal De:ov
C Chemical Eerier
E Eicrero
G Growrn
M f.'ortality
P Pnotosynthetis
R Respiration
S Settling
H Harvest
FIGURE V-30 QUALITY AND ECOLOGIC RELATIONSHIPS
(FROM NEC, 1974)
tions are made:
• The only condition where DO levels may become dangerously low is
in an impoundment hypolimnion and during wanm weather.
• Prior to stratification, the impoundment is mixed. After strata
form, the epllimnion and hypolimnion are each fully mixed.
• Dissolved oxygen in the hypolimnion is depleted essentially through BOD
exertion. Significant BOD sources and sinks to the water column prior
to stratification are algal mortality, BOD settling, and outflows. A
-75-
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minor source 1s Influent BOD. Following formation of strata, sources
and sinks of BOD are BOD settling out onto the bottom, water column BOD
at the time of stratification, and benthlc BOD.
• Photosynthesis 1s unimportant 1n the hypolimnlon as a source of DO.
• Once stratification occurs (a theraocline gradient of 1°C or greater per
meter of depth) no mixing of thermocllne and hypolimnlon waters occurs.
• BOD loading to the unstratlfled Impoundment and to the hypolimnlon
are 1n steady-state for the computation period.
5.5.2.1 Estimating a Steady-State BOD Load to the Impoundment
Equation V-25 1s an expression to describe the rate of change of BOD concentra-
tion as a function of time:
$ • ". - V • k>c ' ^ (v-25)
where
C « the concentration of BOD in the water column in mgl-1
ka « the mean rate of BOO loading from all sources in mgl-l day!
ks « the mean rate of BOD settling out onto the impoundment bottom in
day"1
k^ « the mean rate of decay of water colunm BOD in day1
0 • mean export flow rate in liters day -1
V • impoundment volume in liters.
Integrating Equation V-25 gives:
-------
5.5.2.2 Rates of Carbonaceous and Nitrogenous Demands
The rate of exertion of BOD and therefore the value of kj 1s dependent
upon a number of physical, chemical, and biological factors. Among these are
temperature, numbers and kinds of microorganisms, dissolved oxygen concentration,
and the kind of organic substance Involved. Nearly all of the biochemical oxygen
demand 1n impoundments 1s related to decaying plant and animal matter. All such
material consists essentially of carbohydrates, fats, and proteins along with a vast
number of minor constituents. Some of these are rapidly utilized by bacteria, for
example, the simple sugars, while some, such as the celluloses, are metabolized
slowly.
Much of the decaying matter in impoundments is carbonaceous. Carbohydrates
(celluloses, sugars, starches) and fats are essentially devoid of nitrogen. Proteins,
on the other hand, are high in nitrogen (weight of carbon/ weight of nitrogen ?• 6)
and proteins therefore represent both carbonaceous and nitrogenous demands.
The rate of exertion of carbonaceous and nitrogenous demands differ. Figure
V-31, which shows the difference graphically and as a function of time and tempera-
ture, may be considered to represent the system response to a slug dose of mixed
carbonaceous and nitrogenous demands. In each two-section curve, especially where
concentrated carbonaceous wastes are present, the carbonaceous demand is exerted
first, and this represents the first stage of deoxygenation. Then nitMfiers increase
in numbers and ammonia is oxidized through nitrite and ultimately to nitrate. This
later phase is called the second phase of deoxygenation.
BOD decay (either nitrogenous or carbonaceous alone) may be represented by first
order kinetics. That is, the rate of oxidation is directly proportional to the
amount of material remaining at time t:
g| • -kC (V-28)
The rate constant, k, is a function of temperature, bacterial types and numbers,
composition and structure of the substrate, presence of nutrients and toxicants, and
a number of other factors. The value of the first stage constant kj was first
determined by Phelps in 1909 for sewage filter samples. The value was 0.1 (Camp,
1968). More recent data show that at 20°C, the value can range from 0.01 for slowly
metabolized industrial waste organics to 0.3 for relatively fresh sewage (Camp,
1968).
The typical effect of temperature on organic reactions is to double reaction
rates for each temperature rise of 15°C. The relationship for correcting kj for
temperature is:
-77-
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"0 4 8 12 16 20
Period of Incubation, Days
FIGURE V-31 RATE OF BOD EXERTION AT DIFFERENT TEMPERATURES
SHOWING THE FIRST AND SECOND DEOXYGENATION
STAGES
ki.(20'0 e(T'2n)
(V-29)
where
I « the temperature of reaction
6 « correction constant • 1.047.
However, Thereault has used a value foreof 1.02, while Moore calculated values
of 1.045 and 1.065 for two sewages and 1.025 for river water (Camp, 1968).
Streeter has determined the rate of the nitrification or second deoxygenation
stage in polluted streams. At 20°C, kj for nitrification is about 0.03 (Camp,
1968). Mobre found the value to be .06 at 20°C and .035 at 10°C (Camp, 1968). For
purposes of this analysis, BOO exertion will be characterized as simple first order
decay using a single rate constant.
Bentnic demand, which is important in later computations, may vary over a
wide range because in addition to the variability due to the chemical nature of
the benthic matter, rates of oxidation are limited by upward diffusion rates of
oxidizable substances through pores in the benthos. Since the nature of the sediment
is highly variable, benthic oxygen demand rates vary more than values for kj 1n the
water column. In a study using sludges through which oxygenated water was passed,
initial rates of demand ranged from 1.02 g/m2 day (see Table V-I1) for a sludge
depth of 1.42 cm up to 4.6g g/m2 day for a sludge depth of 10.2 cm (Camp, 1968).
-78-
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TABLE V-ll
OXYGEN DEMAND OF BOTTOM DEPOSITS
(AFTER CAMP, 1968}
Initial Area Osr.snd
Benthic
Depth
(mean) cm
10.2
4.75
2.55
1.42
1.42
Initial
Vol ume of _2
Sol Ids, koirf
3.77
1.38
0.513
0.188
0.188
L (gnf2)
739
426
227
142
134
initial
Demand
om" dav"
4.65
3.09
1.70
1.08
1.02
day"1
k4(20°C)
.0027
.0031
.0032
.0033
.0033
In that study, the values found were for Initial demand since the sludge was not
replenished. The rate per centimeter of sludge depth, then, can vary from a low of
0.46 g/m2 day for 10.2 centimeter depth sludge up to 0.76 g/m2 day for 1.42
centimeter depth sludge.
The constant loading rate (ka) used 1n Equation V-25 1s best estimated
from historical data. Alternatively, Inflow loading (see Chapter IV) and algal
productivity estimates (this chapter) may be used. In the latter case, a value
must be adopted for the proportion of algal biomass ultimately exerted as BOD.
To a first approximation, ka may be estimated using this value and adopting
some percentage of maximal primary productivity {see Figure V-25). Thus:
where
ka(algae) - SMP x 10-3/D
algal contribution to BOD loading rate
stoichlometric conversion from algal biomass as carbon to
BOD « 2.67
proportion of algal biomass expressed as an oxygen demand
(unltless)
Primary production 1n m
(V-30)
ka(algae)
S
M
P
The difference between algal biomass and the parameter M representing the
proportion of algal biomass exerted as BOD may be conceptualized as accounting for
such phenomena as incorporation of algal biomass Into fish tissue which either leaves
the Impoundment or Is harvested, loss of carbon to the atmosphere as CH4, and loss
-79-
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due to outflows.
The settling rate coefficient, k$ 1n Equation V-25 must be estimated for
the Individual case. It represents the rate at which dead plant and animal matter
(detritus) settles out of the Mater column prior to oxidation. Clearly, this co-
efficient Is sensitive to the composition and physical characteristics of suspended
matter and the turbulence of the system. Quiescence and large particle sizes in the
organic fraction will tend to give high values for ks while turbulence and small
organic fraction particle sizes will give small values for ks.
5.5.2.3 Estimating a Pre-Strat1f1cation Steady-State Dissolved Oxygen Level
Prior to stratification, the impoundment Is assumed to be fully mixed. One of
the important factors leading to this condition Is wind stress, which also serves to
reaerate the water. As a rule, unless an Impoundment acts as a receiving body for
large amounts of nutrients and/or organic loading, dissolved oxygen levels are likely
to be near saturation during this period (O.J. Smith, pers. comm., November, 1976).
Table V-12 shows saturation dissolved oxygen levels for fresh and saline waters as a
function of temperature and chloride concentrations, and 00 levels may be estimated
accordingly.
The hypolimnetic saturation dissolved oxygen concentration Is determined
by using the average (or median) temperature for the hypo11ranion as determined
during the period of interest throughout the depth of the hypol1mn1on. Informa-
tion on the hypolimnion is obtained using the procedures described 1n Section
S.2. For example, hypolimnetic water at the onset of stratification might be
4-5°C and during the critical summer months be 10°C. The value 10°C should be
used having a saturation DO of 11.3 mg/1.
Most lakes are near sea level (<2000 ft elevation) and are relatively fresh
(<2000 mg TDS/1). For lakes that do not meet these criteria, corrections for atmos-
pheric pressure differences and salting out due to salinity might be needed. Pressure
effects can be approximated by using a ratio of barometric pressure (B) for the
elevation of interest and sea level (BSTP) as follows:
e.g. B at 4600 ft elevation,
_JL . 6*2 , in m Hg,
BSTP 760 *
- 0.84
DOsat at 10°C « 0.84 x 11.3
« 9.5 mg/1.
Chloride is an estimator of dilutions of sea water 1n fresh water where 20000
mg Chloride/1 is equivalent to 35000 mg salt (TOS/1), that 1s, typical ocean water.
-80-
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TABLE V-12
SOLUBILITY OF OXYGEN IN WATER (STANDARD METHODS, 1971)
Chloride Concentration in Water - mg/1
Temp.
in
°C
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
IB
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
0
14.6
14.2
13.8
13.5
13.1
12.8
12.5
12.2
11.9
11.6
11.3
11.1
10.8
10.6
10.4
10.2
10.0
9.7
9.5
9.4
9.2
9.0
8.8
8.7
8.5
8.4
8.2
8.i
7.9
7.8
7.6
7.5
7.4
7.3
7.2
7.1
5,000
13.8
13.4
13.1
12.7
12.4
12.1
11.8
11.5
11.2
11.0
10.7
10.5
10.3
10.1
9.9
9.7
9.5
9.3
9.1
8.9
B.7
8.6
8.4
8.3
8.1
8.0
7.8
7.7
7.5
7.4
7.3
10,000
Dissolved
13.0
12.6
12.3
12.0
11.7
11.4
11.1
10.9
10.6
10.4
10.1
9.9
9.7
9.5
9.3
9.1
9.0
8.8
8.6
8.5
8.3
8.1
8.0
7.9
7.7
7.6
7.4
7.3
7.1
7.0
6.9
15,000
Oxygen - mg/1
12.1
11.8
11.5
11.2
11.0
10.7
10.5
10.2
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.5
8.3
8.2
8.0
7.9
7.7
7.6
7.4
7.3
7.2
7.0
6.9
6.8
6.6
6.5
Sea
Water
11.3
11.0
10.8
10.5
10.3
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.5
8.3
8.1
8.0
7.8
7.7
7.6
7.4
7.3
7.1
7.0
6.9
6.7
6.6
6.5
6.4
6.3
6.1
Difference
- per 100 mg
Chloride
0.017
0.016
0.015
0.015
0.014
O.OH
0.014
0.013
0.013
0.012
0.012
0.011
0.011
0.011
0.010
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.008
0.008
0.008
0.008
0.008
0.008
0.008
0.008
0.008
-81-
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5.5.2.4 Estimating Hypo11mn1on DO Levels
The final step in use of this model 1s preparation of a DO-versus-time plot for
the hypo 11 ran ion (or at least estimation of 00 at Incipient overturn) and estimation
of BOO and phosphorus loadings which result in acceptable hypo limn ion DO levels. An
equation to compute 00 at any point in time during the period of stratification
is:
— •
dt
where
0 » dissolved oxygen 1n ppm
*4 « benthic decay rate In day'1
L « a real BOO load in gnr2
0 « depth in m.
The second term in the equation requires that an estimate be made of the magni-
tude of BOD loading in benthic deposits. To do this within the present framework, it
is assumed that BOO settles out throughout the period of stratification. Although
many different assumptions have been made concerning benthic BOO decay. 1t was
assumed that benthic demand was a function of BOD settling and the rate of benthic
BOD decay. This BOD includes that generated In the system by algal growth and that
which enters in tributaries and waste discharges. Based upon the rate of settling
used earlfer in estimating a steady-state BOD concentration (Equation V-25) and rate
of decay for conditions prior to stratification, the rate of benthic matter accumula-
tion is:
•T » kSCSsl>-k4l.
dt
where
Css • concentration of BOD in the water column in gm-3 at steady-state.
The assumption of steady-state BOD concentration reduces Equation V-32 to the
same form as Equation V-25 and integration gives:
ksDCss (Y-33)
For steady-state deposition (dL/dt » 0, OksCss » constant):
(V-34)
-82-
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where
Lss • steady-state benthic BOD load in gnr2.
Application of Equation V-34 with ks and k4 appropriately chosen for the
month or two preceding stratification will give an estimate of the benthic BOD load
upon stratification. Application of Equation V-33 gives the response of L to different
water column BOD (steady-state) loading rates and changes in rate coefficients.
After strata form, benthic matter decays while hypolimnion water column BOD
decays and settles. The change in L over the period of stratification Is:
— - -k4L + DksC (V-35)
dt
Since
•- -ksC -kiC • -(k!+ks)C (V-36)
and
- C0 e-(*l * k$)t (v-37)
— » -k4L + DksC0e-(kl * ks)t (V-38)
dt
then
Water column BOD in the hypolimnion is given by Equation V-36 and the integrated
form is Equation V-37.
Note that ks, the settling coefficient is equal to vs/D where vs is the
settling velocity of the BOD, and D is the depth of the hypolimnion (or when the
impoundment is unstratified, D is the depth of the entire impoundment). Also note
that we usually assume that the DO 1s at saturation at the onset of stratification.
Thus we can ignore the assumptions and calculations (Equation V-32 to V-34) done for
periods prior to onset.
The equation presented earlier (Equation V-31) for hypolimnion DO was:
dt
-83-
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Equation V-31 1s not Integrable 1n Its present form, but since L and C are defined as
functions of t (Equations V-39 and V-37 respectively), 1t 1s possible to determine
dissolved oxygen 1n the water column. The equation for oxygen at time t 1s:
Ot " 0Q - AOL - AOC (V-40)
where
O^ • dissolved oxygen at time t
00 • dissolved oxygen at time t • 0
&OL • dissolved oxygen decrease due to benthlc demand
ADC • dissolved oxygen decrease due to hypol1mn1on BOO.
From Equation V-39, and using 155 as L0 and Css as Co:
and from Equation V-37:
(V-42)
c - £4» f l-e-<
c kj+fcj y
Solution of Equation V-40 gives an estimated 00 concentration 1n the hypol1mn1on
as a function of time.
To compute equation V-40, a simpler form of equation V-41 can be derived by
substituting as follows:
since Lss » s* ss ,
"4
To simplify computations, the following stepwlse solutions can be made:
A -
-84-
-------
then
A
(•-I)
£0C • E • F
5.5.3 Temperature Corrections
All reactions are computed on the basis of the optimum temperature, but the
environment 1s often at different temperatures. Some rate coefficients for chemical
and biological reactions vary with temperature. A simple correction for such rate
coefficients to 20°C 1s as follows:
„ „ x , 047 (T - 20'C)
l\ * JvT^n *
For example. 1f a rate at 20°C - 0.01 and the lake is at 10°C, then:
KT - 0.01 x 1.047 (1° " 20)
Hy - 0.00632.
Generally the following optima are used:
k. - first order decay rate for water column BOD,
use 20eC
k. - benthie BOD decay, use 20°C
P - productivity rate, use 30QC.
In the screening methods we do not have to correct for temperature except in the
oxygen calculation for the rate coefficients, K., K4, P and 1n the toxics
section (5.6) for the biodegradatlon rate coefficients.
EXAMPLE V-15
Quiet Lake
(Comprehensive Example)
Quiet Lake is located a few miles south of CoIton, New York. The lake
is roughly circular In plan view (Figure V-32) and receives inflows from three
tributaries. There 1s one natural outlet from the lake and one withdrawal used
for quarrying purposes.
The first step in evaluation of lake hypolimnion DO levels is physical
and water quality data collection. Table V-13 shows characteristics of Quiet
Lake, Table V-14 shows tributary discharge data along with withdrawal and outflow
levels, and Table V-15 provides precipitation and runoff information.
In order to evaluate hypolimnion DO as a function of time, the very first
question to be answered is, does the impoundment stratify? If so, what are the
beginning and ending dates of the stratified period, how deep Is the upper surface
-85-
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D
PUMP HOUSE
STftEAM QUALITY
AND FLOW STATION
RUNOFF QUALITY
SAMPLING STATION
SAMPLES TAKEN MOM SMALL
EROSION CHANNELS NEAft LAKf
FIGURE V-32 OUIET LAKE AND ENVIRONS
-86-
-------
TABLE V-13
CHARACTERISTICS OF QUIET LAKE
Length (in direction of flow)
Width
Mean Depth
Maximum Depth
Water Column P
3.5 miles • 18,480 ft.
4.0 miles « 21,120 ft.
22 ft.
27 ft.
0.014
-------
TABLE V-14 (Continued)
First Creek (Station 5)
Month
October
November
December
January
February
March
April
May
June
July
August
September
Month
October
November
December
January
February
March
April
May
June
July
August
September
Mean Flow, cfs
5
3
2
2
3
4
6
8
10
8
6
4
Second Creek
Mean Flow, cfs
14.0
i:.o
12.5
5.0
1.2
2.0
2.5
4.0
8.0
12.0
8.0
5.5
Total K
1.0
2.0
0.5
1.2
1.3
2.3
2.0
1.8
1.6
1.4
1.5
0.8
{Sution 4)
Total N
15
16
10
9
12
13
8
6
5
7
6
8
Total P
ppn
.01
.01
.02
.01
.02
.01
.01
.02
.01
.01
.00
.00
Total P
ppm
.15
.08
.20
.15
.12
.10
.11
.07
.08
.20
.22
.25
BOO
0.5
1.0
1.5
1.0
0.8
0.6
0.5
0.6
0.8
0.8
1.0
1.2
BOO
7
8
10
7
7
6
7
9
12
3
4
8
-88-
-------
TABLE V-14 (Continued)
Swift
Month
October
November
December
January
February
March
April
May
June
July
August
September
River (Stations 2 and 3}
Pumped
Withdrawal, cfs
22.6
22.0
3.5
1.2
0.8
0.4
12.0
24.0
30.7
89.5
29.8
43.9
and Pumoed Withdrawal
Mean Monthly
Station ?
69.5
50.0
20.0
7.5
1.2
9.1
44.5
63.2
100.0
168.5
80.6
91.3
Flow, cfs
Station 3
?7.0
55.0
22.0
9.0
1.4
10.1
48.75
69.5
110.0
184.8
88.5
100.25
Notes: All three tributaries have their headwaters within the shed.
Trie net inflow-outflow to the groundwater is known to be close to
zero in the two creeks. Swift River is usually about 105 effluent over
its entire length (105 of flow comes into the river from the
groundwater table).
| of the hypolimnion, and what 1s its volume, and what is the distribution of
I hypolimnion mean temperatures during the period? To answer these questions.
| either use field observation data, or apply some computation technique such as
j that presented earlier in this section. Assuming that methods presented earlier
j are used, the selection of appropriate thermal profile curves hinges around three
factors. These are:
• Climate and location
j • Hydraulic residence time
j • Impoundment geometry.
I
-89-
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TABLE V-15
PRECIPITATION AND RUNOFF DATA FOR QUIET LAKE WATERSHED.
VALUES ARE MEANS OF DATA COLLECTED FROM BOTH STATIONS
(SEE FIGURE V-31). THE WATERSHED HAS AN AREA OF 55
SQUARE MILES INCLUDING THAT OF THE LAKE
Mean Total
Monthly Prccipi
tation. inches
October
November
December
January
February
March
April
May
June
July
August
September
Total
3.0
2.4
1.0
0.5
0.3
0.6
2.0
2.8
4.2
7.6
3.5
4.2
32.1
Runoff Quality
Total N
6.0
6.5
4.0
3.0
1.0
1.5
2.5
3.2
3.6
7.0
7.8
9.2
Total P
ppm
0.1
0.2
0.1
0.008
0.07
0.1
0.15
0.25
0.20
0.40
0.60
0.80
BOO
27
37
46
34
33
30
40
50
40
37
45
50
Note: Infiltration to the water table on a monthly basis accounts for roughly 301 |
of precipitation volume. I
In terms of climate and location, the Quiet Lake area is similar to Burlington,
Vermont. Examination of the Burlington plots from Appendix D reveals that a
20-foot maximum depth impoundment can stratify in an area shielded from the wind.
The area surrounding Quiet Lake does provide good shielding, so the next task 1s
to estimate the hydraulic residence time to select a specific set of plots.
Inspection of all Burlington plots indicates that stratification is likely to
occur at most from May to August. Accordingly, for purposes of plot selection, we
are most Interested 1n a twan hydraulic residence time based on flows in the
period from about March to August. Since hydraulic residence time (T ) 1s
given by-r^ - v/Q, we compute mean Q (Q~). "§ represents the
-90-
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average of tributary Inflows during this period, computed as follows:
w 6 + 40 * 55 + 85 + 150 + 70 . 4+6+8+10+8+6 .
U 5 * 5
(Swift River) (First Creek)
2+2.5+4+8+12+8
6
(Second Creek)
• 68 + 7 + 6.08 • 81.1 cfs
However, 1n order to fully account for mass transport as well as properly estimate
hydraulic residence time, one more factor should be considered. This 1s non-point
inflow. At this point, we have enough Information to estimate the stormwater
contribution directly to Quiet Lake. In view of the available data, the computa-
tion is as follows:
-L)-( :
Q » APK(1-
S \i«l
where I
i
QS « stormwater or non-point inflow in cfs (excluding rivers and I
creeks) j
A » area of shed In square miles j
n - number of tributaries
Q.J » monthly mean pickup (in cfs) in the 1th tributary
P « monthly total precipitation, in inches per month !
1^ « percent (expressed as a decimal) of flow contributed j
by exfiltration (from the water table into the channel) I
L • the proportion of precipitation lost by infiltration into the |
soil (expressed as a decimal) j
K « unit correction « 0.895 ft3mo mi"2in"1sec"1. j
i
As an example, the computation for October 1s:
? in ft3 I
Q • 55 mi x 3.0 — x 0.896 I1 mo x (1-0.3) - .'
00 miSn sec J
(54(1-0.1) + 5(1-0.0) + 14(1-0.0) + (77-69.5)(1-0.1)) - 29.1 cfs J
Now, since we know the pumped withdrawal rates as well as the difference between I
flows at stations 2 and the sum of 1, 4, and 5, and that the Impoundment surface j
is at steady-state over the mouth, we also can estimate the net infiltration rate j
from the lake Into the groundwater. The infiltration rate Is (again, for October): J
Net efflux - Q($t- j + 4 + 5) - Q^-Q, j
- 73.0 - 69.5 + 29.1 - 22.6 - 10.0 cfs
Note that the pickup in each channel above Quiet Lake is equal to the flow
at the pertinent sampling station. This is the case because the three channels '
-91-
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have their headwaters within the watershed. If one were concerned about a subshed
with tributary headwaters above the subshed boundary, the difference in Q between
each of stations 1, 4, and 5 and the respective flows at the upstream subshed
boundary would be used.
To estimate hydraulic residence time add the mean stormwater contribution
over the months of interest to that of the tributaries, as computed earlier.
The individual stormwater computations are not shown. The method is as just
described.
6.6 t- 20.7 + 29.4 * 41.4 + 92.5 + 36.6
. 81.1 * ~, - 119 cfs
Then the hydraulic residence time Is given by:
V/Q . irr*0/Q
x 5280
where
L • length of the lake 1n ml
H • width of the lake In ml
D » mean depth 1n ft
r • radius in ft.
3.14 x
x 5280 x 22/119
« 5.69 x 10 sec - 658 days
Accordingly, the infinite hydraulic residence time plots for a 20-foot deep,
wind-protected, Burlington, Vermont, impoundment should suffice. Note that
the entire impoundment volume was used in the above computation. Strictly,
one should use the epilimnion volume during stratification. In this case,
such a change would not alter selection of the plots because T^ would still be
greater than 200 days. A reproduction of the appropriate plot from Appendix D is
presented in Figure V-33. As indicated. Quiet Lake is likely to be weakly strati-
fied from May to August inclusive, with a thermocline temperature gradient of
about l°ft~ . The hypolimnion should extend downward to the bottom from a
depth of about 3-1/2 meters, giving a mean hypolimnion depth of:
22 ft
3.29 ft m
7J~" - 3.5 m • 3.2 meters
-92-
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1
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10 70 M 0 10 70 30 0 10 70 30 '
TCHP.
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c TEMP, c Tcnr. c :
If . tCl '
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TEMP. C TEMP. C TEMP. C 1
10
TEMP
j FIGURE V-33
i
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t
i
tt
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\
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t
£
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BURLINGTON. VERMONT j
20' IN1TIHL MPXtMUH DEPTH j
IMF1NHE MXOR. RES. TIME
niNinun nixiNC !
|
i
i
„
i
THERMAL PROFILE PLOTS FOR USE IN QUIET LAKE EXAMPLE I
i
*
i
*
i
-93-
-------
The approximate hypo11*n1on volune, then, 1s:
I V • |4£x 1.9X1011!- 9.2xl010l
' H o./ffi
. Over the period of Interest, the hypol1mn1on mean temperature distribution
Mean
Temperature, *C
j narcn 2.0
j April 5.5
9.5
12.5 :
14.0 !
15.5 I
The next step in use of the DO model Is to determine a steady-state or I
i
mean water column BOD loading (k^) and DO level prior to stratification. |
This is a multi-step process because of the several 600 sources. The sources are i
tributaries, runoff, and primary productivity. First, we estimate algal produc- j
tivity using methods of this chapter (or better, field data),
Using the curve in Figure V-26 and phosphorus data from Table V-14, the
-2 -1 I
maxima"! primary productivity should be 1n the range 1,400 mg CM day ;
to 1,900 mgCm day . To convert to loading in mgl day" . divide by I
(1000 1m"3 x 6.7m). This gives the loading as 0.21 to 0.28 mgl~lday~ . j
Now assuming that maximal productivity occurs at about 30°C and that produc- I
tivity rates obey the same temperature rule as BOO decay, temperature-adjusted |
estimates of productivity rates can be made. Using the maximal rate range of 0.21 j
to O.ZSmgl'^ay"1, the adjusted rates are: j
Productivity - (0.21, 0.28) x 1.047{3'75"30> j
• (.06,.08) mgl"1 day"1
Then, according to Equation V-30 and assuming M • 1, k due to algae is
estimated by:
ka(algae) " 2'67 x ('06' '08) " ('16' '21) "tf'W"1 j
The next contributor to water column BOD is BOD loading of Inflowing waters.
The value to be computed 1s the loading in milligrams per liter of impoundment j
water per day: I
-94-
-------
Da fly BOO loading rate
(n L4 \ / .
« A«u'tJ /«•
i«l j«l ' ' k»l
I where
| n • the number of time periods of measurement
| V • volume of Impoundment 1n liters
j d • the number of days per time period
j L • the number of Inflows.
. For all Inflows, the value is therefore approximately:
I
j * ' (2185 + 48.3 + 643.9 + 14240) x 2.45 x 106 x
a(Tr1b) . . . - — -
(Swift (First (Second (Storm (Units (Impound-
River) Creek) Creek) water Conversion) ment
Runoff) Volume)
0.22
I Now, summing the two contributions:
! ka ' ka (algae) * ka(Tr1b) . .
I ka - (.16, .21) + .22 • (.38, .43) ragTNlay'1
| The value of k^ will be assumed as 0.1 at 20°C with 6 1n Equation
j (V-29) equal to 1.047. Then at 3.75°C:
l' kl(3.75'C) -kl(20-C)x 1.047<3-75-ZO>
• .1 x 1.047("16'25) - 0.047
Now ^(discharge) ^mean for ^^^ arxl April) and V are known, with:
Qf,Hcrh,«,^ • 26-8 (Swift River, Station 2)
(discharge) ?R S? » i
+ 6.2 (pumped withdrawal) x **•*'* . 9351 sec 1
ft i
I 11 I
! V « 1.9 x 1011!
! then !
I 38 43 !
j °ss ' {0.3*. 047 M935/1.9 x 1011)) ' 4>94> 5'58 |
| For further computations, C • 5.25 will be assumed. J
| Since k has been defined as .03, a steady-state areal concentration I
j of benthlc BOO prior to stratification can be estimated. If ^4(20*0 * I
j .003 and C$s - 5.25, using Equation (V-34): j
k4(3.75«C) ' -003x1.
• .0014
-95-
-------
, .03 x 5.25 x 6.7
ss " .0014
• 754 gm'2
The next step 1n evaluating hypol1inn1on DO depression Is to estimate pre-
stratification DO levels. If we assume saturation at the mean temperature
1n April (S.5°C), the dissolved oxygen concentration at onset of strata should be
about 12.7 (from Table V-12).
Now we have all values needed to plot hypol1mn1on DO versus time using
Equations V-40 through V-42.
Using
Lo ' Lss
co - css
k, - O.lxl.047(9'5~20) • .062, (T - 9.50C for May)
ks • 0.03
k4 - .003x1.047(9'5'20) • .002
t • 5 days
and applying Equation V-42:
0-062x5.25 , -(0.062+0.03)5
then, according to Equation V-41:
A.. k.C \ /
AO, -
. /7S4 0.03x5.25 \ /, .-0.002x5 \ / 0.03x5.25 \
L ^3.2 0.03-K).062-0.002 I I '"* I" I 0.03*0.062-0.002 )
/ 0.002 \ /. .-(0.062*0.03)5\« 2.35
I 0.062+0.03 ) I'"e /
then from Equation V-40:
ot - oo -
0, • 12.7 - 1.30 - 2.35 - 9.05
-96-
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I Solving the same equations with Increasing t gives the data in Table V-16. |
| If 1t has been necessary to develop more data for the remainder of the stratified I
j period, appropriately updated coefficients might be used starting at the beginning j
! of each month. i
TABLE V-16
DO SAG CURVE FOR QUIET LAKE HYPOLIMNION
j Date ^j. _c t
j t « 0 0 0 12.70
j 5/5 2.35 1.30 9.05
j 5/10 4.68 2.13 5.89
j 5/15 6.99 2.65 3.06
5/20 9.22 2.98 0.50
! 5/25 11.54 3.18 0.00 !
| I
; Finally, if It is desired to evaluate the Impact of altered BOO or phosphorus ;
j loadings, the user must go back to the appropriate step in the evaluation process j
I and properly modify the loadings. !
i •
i !
: —- END OF EXAMPLE V-15 '•
5.6 TOXIC CHEMICAL SUBSTANCES
Although reasonably accurate and precise methods have been prepared for screening
only a few of the many priority pollutants (Hudson and Porcella, 1981), a reasonable
approach for assessing priority pollutants 1n lakes based on the methods presented 1n
Chapter 2 can be made 1f certain assumptions are made:
t The major processes affecting the fate and transport of toxicants
in aquatic ecosystems are known
• That reasonable safety factors are incorporated by making reasonable
most case analyses
• Because 1t is a screening approach, prioritlzatlon can be done to
identify significant constituents, lakes where human health or ecological
problems can realistically be expected, and processes which might
require detailed study.
The major processes affecting toxicants are listed 1n Table V-17. The primary
measure of the impact of a toxic chemical 1n a lake depends on Its concentration in
the water column. Thus, these screening methods are primarily directed at fate and
-97-
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TABLE V-17
SIGNIFICANT PROCESSES AFFECTING
TOXIC SUBSTANCES IN AQUATIC ECOSYSTEMS
Processes
Rate Coefficient Symbol, time
-1
Physical-Chemical Processes
Sorption and sedimentation
Volatilization
Hydrolysis
Photolysis
Oxidation
Precipitation
SED
k.
not assessed
not assessed
Biological Processes
Biodegradation
Bioconcentration
B
BCF (unltless)
transport of toxic chemicals. A secondary target 1s the concentration in aquatic
biota, principally fish. Because of the complexity of various routes of exposure and
bioaccumulation processes, the approach of bioconcentration 1s used to Identify
compounds likely to accumulate 1n fish. These can be applied to lakes using the
following method:
• A fate model is used that incorporates sediment transport, sorption,
partitioning, and sedimentation
• Significant processes include the kinetic effects of sedimentation,
volatilization and biodegradation
• Significant biochemical processes can affect the fate of a toxic chemical
as well as affect biota, such, as, bioaccumulation, biodegradation, and
toxicity
• In keeping with the conservative approach of the toxics screening
methodology, some important processes are neglected for simplicity;
for example, lake stratification, photolysis, oxidation, hydrolysis,
coagulation-flocculation, and precipitation are neglected. Also,
it 1s assumed that the organic matter 1s associated with Inorganic
particles and therefore organic matter settles with the Inorganic
particles.
Generally the toxic chemical concentrations are calculated conservatively,
that is, higher concentrations are calculated than would occur 1n nature because of
the assumptions that are made. The water column concentrations are calculated as the
-98-
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primary focus of the screening method. Then bloconcentration 1s estimated, based on
water concentration. To determine concentration and bioaccumulation, point and
nonpoint source loadings of the chemicals being studied are needed. Other data
(hydrology, sediments, morphology) are obtained from the problems previously done in
earlier chapters or sections of this chapter. The person doing the screening would
have to compile or calculate such data.
Occasionally, such Information must be estimated based on production, use. and
discharge data. Information on chemical and physical properties 1s important to
determine the significance of these estimates.
5.6.1 Overall Processes
Several processes affecting distribution of toxic chemicals are more significant
than others. Equilibrium aquatic processes Include suspended sediment sorption of
chemicals. Organics in sediments can have a significant effect on chemical sorption.
Hydrolysis and acid-base equilibria can alter sorption equilibria. Volatilization is
an equilibrium process that tends to remove toxic chemicals from aquatic ecosystems.
Removal processes include settling of toxics sorted on sediments, volatilization, and
biodegradation. Chemical reactions for hydrolysis and photolysis are included and
precipitation and redox reactions could be included 1f refinement of the method were
desired. Generally, bioaccumulation will be neglected as a removal process.
These removal processes are treated as first-order reactions that are simply
combined for a toxicant (C, mg/1 ) to give:
dC/dt « - K x C (V-44)
where
K • SEO + B + k + k + k.
v p h
SED « sedimentation rate, toxicant at equilibrium with sediments
ky » volatilization rate
B • biodegradation rate
k • photolysis rate
*h - hydrolysis rate.
This equation is analogous to the BOD decay rate equation used in the hypolimnetic
00 screening method.
The input of toxic chemical substances is computed simply (refer to Figure
V-23):
d£ . Q
dt 7
x C1n - (V-45)
where
C-n- the concentration in the Inflow (tributary or discharge);
flow (Q), volume of reservoir (V) and time (t) are as defined previously.
-99-
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At steady state, accounting for Inflow (Q*C1n) and outflow (Q-C), and
using Q/V « I/T^:
dC , I (c.n - c) - K x C - 0 (V-46)
w
and solving:
C • Cin/(l + TW x K) (V-47)
To determine the concentration at any time during a non-steady state condition
(assuming c. 1s a constant):
C • -p (1 - e" t/Tw) + co e~ft/T* (V-48)
where
f • 1 + T^ x K
C - reservoir concentration at t « 0.
5.6.1.1 Sorption and Sedimentation
Suspended sediment sorption 1s treated as an equilibrium reaction which Includes
partitioning between water (C¥) and the sediment organic phases (Cs). The
concentration sorbed on sediment can be computed as follows:
Ce
•^ • a x Kp x S (V-49)
where
C • the total concentration (c + C ), mg/1
S • input suspended organic sediment • OC x So, mg/1
OC • fraction of organic carbon.
So • input of suspended sediment, mg/1
K • distribution coefficient between organic sediment and water
a • fraction of pollutant in solution
If K 1s large, essentially all of the compound will be sorbed onto the sediments.
Note that S and C must be estimated or otherwise obtained.
The organic matter content of suspended sediment and the lipld solubility
of the compound are important factors for certain organic chemicals. Other sorption
can be ignored for screening. A simple linear expression can be used to calculate
the sediment partition coefficient (K ) based on the organic sediment carbon
concentration (OC) and the octanol-water coefficient (kow) for the chemical:
-100-
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kp - 0.63 (kow) (OC)
The sedimentation rate (SED) of a toxic chemical 1s computed as follows:
SED - a x D x K (V-50)
where
D « P x S x Q/V, sedimentation rate constant
P • sediment trapping efficiency
Q/V « I/TW
5.6.1.2 B1odegradat1on
The blodegradatlon rate (B) 1s obtained from the literature or 1s computed as
follows:
Modification to the rate can be made for nutrient limitation using phosphorus
(C ) as the limiting nutrient:
B (0.0277)0,,
a n«it.H . ' P^ (v-52)
1 * 0.177 x C
Temperature correction can be performed using the following equation:
B(T) - 8(20'C) x 1.072(T'20) (V-53)
Previous exposure to the pollutant 1s important for most toxic organic compounds.
Higher rates of degradation occur in environments with frequent or longterm loading
(discharges, nonpoint sources, frequent spills) than infrequent loadings (one-time
spills). In pristine areas, rates of one to two orders of magnitude less should be
used.
It is assumed that the suspended sediment decay rate 1s the same as aqueous
phase decay. Also benthic decay is disregarded because bottom sediment release may
be negligible.
5.6.1.3 Volatilization
Many organics are not volatile so this process is applied only to those which
are. It is assumed that the mass flux of volatile organics Is directly proportional
to the concentration difference between the actual concentration and the concentra-
tion at equilibrium with the atmosphere. The latter can be neglected 1n lakes.
-101-
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Also, only the most volatile are assessed.
Thus:
IT •
where
ky » volatilization rate constant, hr
The rate coefficient 1s derived from the 2 resistance Model for the 11 quid-gas
Interface, but It can be estimated using correlation with the oxygen reaeratlon
coefficient (based on Z1son et_al_., 1978):
k • Ka (Dw/Do) (V-5S)
and estimate (Dw/Do) • (32/mw)1/2
and the surface film thickness, SFT » (200-60 • Ww ) x 10"6
and Kal « Oo/SFT
Ka • Kal/ZB
where
Ka * reaeration rate, hr"
Dw • pollutant d1ffus1v1ty 1n water
Do • dlffuslvHy of oxygen In water (2.1 x 10"9 m2/sec, 20*C)
mw - pollutant molecular weight
U~ « wind speed, in/sec
7 • mean depth, m.
The volatilization rate coefficient (ky, hr"1) 1s determined by ky • Ka x k where k
Is obtained from literature values or computed as above (VDw/Oo). The rate should be
correct*
effect:
corrected for temperature (kyt) even though temperature has only a relatively small
x 1.024(T"20) (V-56)
5.6.1.4 Hydrolysis
Not all compounds hydrolyze and those that do can be divided Into three groups:
acid catalyzed, neutral, and base catalyzed reactants. A pseudo first-order hydrolysis
constant (*h) Is estimated for the hydrolysis of the compound:
IT • -kh ' c
The rate constant Uh) 1s pH dependent and varies as discussed 1n Chapter 2.
The typical pH of the lake for the appropriate season should be obtained for the
-102-
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necessary calculations. Generally, the pH 1s a common Measurement and 1s available
for most lakes. If not, pH values for most open lakes He between 6-9 and can be
estimated based on the following empirical values based on HutcMnson, (1957):
Hardness
(or Alkalinity) £H
add lakes <25 6 - 6.5
neutral lakes 25 - 75 6.5 - 7.5
hard water lakes 75 - 200 7.5 - 8.5
eutrophic and alkaline lakes 0-300 8.0 - 10.0
Median values on a range of values can be used to evaluate the significance of
hydrolysis as a factor affecting the fate of compounds.
5.6.1.5 Photolysis
Generally, photolysis 1s a reaction between ultraviolet light (UV, 260 to 380 nm
is most Important) and photosensitive chemicals. Not all compounds are subject to
photolysis nor does UV light penetrate significantly 1n turbid lakes. In the absence
of turbidity data, light transmission can be estimated by seasonally averaged SeccM
disk readings according to the following equation:
In (ISD/Io) « -ke(SD) - In 0.1 • -2.3
ke » 2.3/SD
where
ke » the extinction coefficient
SD • the Secchi depth in meters
(ISD/Io « 0.1) • relative intensity based on Hutchinson (1957).
Photolysis for appropriate chemicals (discussed in detail in Chapter 2) depends
on a first order rate constant (k ) incorporating environmental variables (solar
irradiance, Io) and chemical variables (quantum yield, *, and absorbance, E).
Turbidity effects are included as estimated as above since turbidity data are generally
not available. These values are Incorporated into the rate constant and the concen-
tration reduced as described in Chapter 2:
£ ' V (V-58)
where
kr • f (Io. *, E. ke, Z)
and
k . i.
P ke-I
-103-
-------
where
k « photolysis rate constant unconnected for depth and turbidity
of the lake.
Depth (Z) 1s generally applied only to the photic zone; mean depth (Z)
1s an appropriate measure since It approximates the mixed depth and the photic
zone.
5.6.1.6 Bloconcentratlon
B1 concentration 1s a complex subject that depends on many variables. The
simplest approach has been developed for organic compounds using the octanol-water
coefficient (kow) to calculate tissue concentrations (Y):
Y • BCF x C, g/kg fresh weight of fish flesh (V-59)
where
BCF « Bloconcentratlon factor
log BCF • 0.75 log kow - 0.23
(The coefficients for the equation (0.75. - 0.23) are median estimates obtained
from correlation equations and are default values for occasions where no other data
are available.)
5.6.2 Guidelines for Toxics Screening
Generally metals do not biodegrade nor volatilize. However, pK, hardness,
aUalinity and other ions are very important and can cause their removal by precipi-
tation. The conservative approach is taken here and metals are calculated without
removal (K • 0).
Organics may have variable sorption, volatilization, and biodegradatlon rates.
If data are available in the literature, these should be used. Otherwise, a conserva-
tive approach should be used and calculations made without removal (K • 0). For
chlorinated (and other halogens) compounds or refractory compounds, biodegradation
should be assumed to be zero.
EXAMPLE V-16
I Estimating Trichloroethylene and Pyrenc
| Concentrations in an Impoundment
I
• An impoundment with a single tributary is located in a windy valley.
The following conditions are known for E.G. Lake:
Mean tributary flow rate « 3.6 x 104m3/hour
I Total volume - 1.1 x 108m3
-104-
-------
I Mean depth • 11 m
j Tributary average sediment load » 200 mg/1
j Sediment average organic carbon content • .05
j Inlet average pyrene concentration • 50 wg/1
Inlet average trlchloroethylene concentration « lOOng/1
; Lake average phosphorus concentration • 50 ug/1
Mean water temperature • 15"C
Mean wind speed • 6 m/sec (35 mph)
Seech1 depth • 1 m
Determine the steady state concentration of pyrene and trlchloroethylene in the
lake, assuming V max for the sediment (mostly clay) 1s 3.2 x 10 feet/second.
The trapping efficiency 1s obtained from Figure V-34..
Other data Pyrene Trlchloroethylene
kow 148000 190
B IxlO"4
ky - 0.45xKa
The processes of photolysis and hydrolysis can be neglected because turbidity
prevents photolysis (SO « 1 meter) and these compounds have negligible hydrolysis
(see Chapter 2).
We use the summary equation V-47 for the analysis:
| The hydraulic residence time of E.G. Lake 1s:
j T^ - 1.1 x 108m3/(3.6 x loV/hr)
I - 3048 hours
j « 127 days
j « .349 year
j « 1.1 x 106 seconds
, Sedimentation
First, the suspended sediment concentration in E.G. Lake must be estimated.
, The trapping efficiency of the impoundment is estimated from Figure V-34.
j Da*a;
V max • 5 x 10 fps
! TW « 1.1 x 10 sec
D1 • 11 m • 36.1 ft 1.56
) A value of 101*95 is obtained which yields:
P » 90 • 0.9
-105-
-------
1C
V
.,1
10
-ex
1C
-51
: ic
-24.
Toxics
Example
Settling velocity in feet/
second
Hydraulic residence time
\n seconds
Flowing layer depth
Mass of sedim-nt tracped
of setf-.T.ert eru-nng
FIGURE V-34 NOMOGRAPH FOR ESTIMATING SEDIMENT TRAP EFFICIENCY
-106-
-------
In the Inflowing stream, the toxicants are assumed to be at equilibrium
with the organic matter. Thus:
S - OC x So • .05 x 200 x 10"6 • 1 x 10"5 kg/1
Therefore, for pyrene:
K - 0.63 x 148000 x 0.05 - 4660
aP - 1/(1 * 4660 x 1 x 10'5) • 0.955
£| - 0.955 x 4660 x 1 x 10"5 • 0.044
and !
SED - a x D x K \
D - P x S x Q/V I
D - 0.9 x 200 x 10'6 x ^jjj hours j
D • 5.91 x 10'8 hour I
SED * .955 x 5.91 x 10'8 x 4660 \
SED • 2.63 x 10'4 hr'1 j
For trlchloroethylene: j
Kp • .63 x 190 x 1 x .05 - 6 j
a - 1/{1 * 6 x 1 x 10"5) • 1 j
^ • 1 x 6 x 1 x 10'5 • 6 x 10"5 * 0 j
I and I
SED - 1 x 5.91 x 10'8 x 6 j
! SED - 3.54 x 10'7 hr"1
j Biodegradation '
Assume that the presence of trichloroethylene does not affect the
| biodegradation of pyrene. Trlchloroethylene does not biodegrade. The
I temperature corrected and nutrient limited rate constant for microblal decay J
| of pyrene are: I
I Bo » 1. x 10'4 hr'1 !
B - .0277 x 50/ (1 * .0277 x 50)
• .58
B(15) - .58 x 1. x 10"4 x 1.072(15"20)
- 4.1 x 10'5 hr'1
Volatilization
The reaeration coefficient for E.G. Lake will be estimated for trichloro-
ethylene only, because pyrene does not volatilize:
Kal • 2.1 x 10"9 / (200 - 60 x 61/2 ) 10'6
- 3.96 x 10"5 m/sec
« .143 m/hr
-107-
-------
I Ka • (.143 m/nr) / 11 • • .013 hr'1 j
j For trlchloroethylene (TCE): |
1 k - [HW(TCE)/NW(OO] • Ka • .45 x .013 » .0058 hr'1 '
1 i
| When adjusted for temperature: J
I ky • .0058 x 1.024<15-20) !
j - .0052 hr"1 |
| Volatilization for pyrene may be neglected. I
j Pollutant Mass Balance |
| The overall decay rate constants are: K • SED + B * ky I
j Pyrene: K - 2.63 x 10~4 + 4.1 x 10'5 j
j • .000304 hr'1 j
TMchloroethylene: K • 3.54 x 10"7 + 0 * 0.0051
! • .0052 hr"1 '
I Using the steady state equation: !
• C ' C1n' j
I For Pyrene: !
1 -1 I
' C • 50^9/l / (1 * 3048 hr x .000304 hr *) j
! C • 27 Kg/T !
I Note: WQC for human health Is 0.0028 ng/1 at 10"6 Risk (FR: \
I 11/28/80 p. 79339). j
j For Trrehloroethylene: I
j C • 100 K9/1 / (1 * 3048 hr x .0052 hr"1) j
j • 5.9 HQ/1 I
j Note: WQC for human health Is 2.7 ng/1 at 10"6 Risk (FR: 11/28/80 j
j P. 79341) j
Tissue burdens (Y) can be calculated: !
I I
j Y « BCF x C j
i where i
• log BCF • .75 log kow - 0.23 j
• For Pyrene: ;
| J I
j Y • 4330 x 27 • 120000 ^g/kg fish flesh j
• For Tr1chloroethylene:
j Y • 30 x 6 • 180 »*g/kg fish flesh j
• Comments
Several conclusions are apparent from this analysis:
! • Certain processes dominate the overall fate for a specific toxic ,
-108-
-------
I chemical so that, practically speaking, errors In estimating coeffic- I
j 1ents are negligible except for the Important processes. After |
j Identifying the Important processes, the coefficients can be varied j
to determine the range of concentrations. For example, sedimentation •
! of trlchloroethylene can be Ignored; however, volatilization should
! be studied.
I • The more stringent Water Quality Criteria are for toxicants that have I
i *
I significant bloconcentratlon; e.g. compare pyrene to trlchloroethylene. I
{ • Volatilization of trlchloroethylene would be Investigated in detail |
j since this process might not be significant In this lake because of j
j Its depth. Also, the physical properties are Important; e.g. •
trlchloroethylene has a specific gravity of about 1.5. Thus, It may
! accumulate on the bottom of the reservoir and remain there unless It '
! Is completely dispersed. j
I • Based on this analysis, sources of pyrene would be assessed first. I
| then trlchloroethylene. I
j • What other observations can you draw from this analysis? j
i i
I I
END OF EXAMPLE V-16
5.7 APPLICATION OF METHODS AND EXAMPLE PROBLEM
This chapter has presented several approaches to evaluation of five impoundment
problem areas. These are thermal stratification, sediment accumulation, eutrophica-
tion, hypolimnion DO/BOD, and toxic chemicals. Figure V-35 shows how the different
approaches are linked together with their data needs. In studying any or all of the
potential problem areas in an impoundment, the user should first define the potential
problems a* clearly as he can. Often the nature of a problem will change entirely
when its various facets are carefully described and examined en masse.
Once the decision is made that an aspect of impoundment water quality should be
evaluated and the problem is clearly stated, the user should examine available
solution techniques presented both in this document and elsewhere. The examination
should address the questions of applicability, degree of accuracy, and need for data.
The user will generally know what funds are available for data collection as well as
the likelihood of procuring the needed data from previously developed bases. Also,
the decision concerning needed accuracy rests with the user, and he should make
decisions based upon the way in which his results will be used.
Once appropriate methods have been selected, the next task is to set down
the data and to manipulate It according to computational requirements. Data are best
displayed first in tabular form and then plotted 1n some meaningful way. Careful
tabulation of data and graphing can themselves sometimes provide a solution to a
-109-
-------
iiti«cvt
IOTA l«i» '••
VOUM. MfA. Ml MVTH
MO •»>•*•! C»"»ITI«"1
HIM »«IUtl»t*
MfMl •!•» »IIOC!TT*
tirr-
i(»IH(»T LMM l*tO
FIGURE V-35 GENERALIZED SCHEMATIC OF LAKE COMPUTATIONS
problem, negating need for further analysis. To Illustrate these Steps, a conpre-
hensive application to a river basin system was performed in this section.
5.7.1 The Qccoquan Reservoir
The Occoquan River basin in Virginia was used to demonstrate the screening
approach. A basin map is shown in Figure V-36. Because the Occoquan Reservoir
is a public drinking water supply downstream from metropolitan areas, water quality
data were available to compare to the screening method's outputs.
-110-
-------
LOUOOUN
COUNTY
Fairfax
OCOOQUOO
Dam
KLOMCTCR*
I I I I I I
01 1 » 4 •
FIGURE V-36 THE OCCOQUAN RIVER BASIN
5.7.2 Stratification
Occoquan Reservoir is about 32 kin southwest of Washington, D.C. and has
the following morphemetrie characteristics:
-3 • 3.71 x 107
,6
Volume, m'
o
Surface area, m • 7.01 x 10"
Maximum depth, m « 7.1 (Occoquan Dam)
Mean depth, m • 5.29
Based upon the above geometry and the thermal plots, determine whether the
lake will stratify, the thickness of the epilimnlon and the hypol1mn1on, the depth to
the thenmocline, and the interval and starting and ending date of stratification.
Also note the temperature of the hypolimnion at the onset of stratification.
Predicting the extent of shielding from the wind requires use of topographic
maps. The reservoir is situated among hills that rise 25 meters or more above the
lake surface within 200 meters of the shore. The relief provides little access for
wind to the lake surface. Average annual wind speeds are 15.6 km/hr in Washington,
O.C. and 12.6 km/hr in Richmond, VA. Inflow comes essentially from two creeks, the
-111-
-------
Occoquan River and Bull Run River (Figure V-35).
First, determine needed Information and then do metric/English conversions
as necessary.
The first step 1n assessing Impoundment water quality is to determine whether
the Impoundment thermally stratifies. This requires knowledge of local climate.
Impoundment geometry, and Inflow rates. Using this Information, thermal plots likely
to reflect conditions 1n the prototype are selected from Appendix D.
For the thermal plots to realistically describe the thermal behavior of the
prototype, the plots must be selected for a locale climatically similar to that of
the area under study. Because the Occoquan Reservoir 1s within 32 kilometers of
Washington, D.C., the Washington thermal plots (Appendix D) should best reflect the
climatic conditions of the Occoquan watershed.
The second criterion for selecting a set of thermal plots 1s the degree of
wind stress on the reservoir. This 1s determined by evaluating the amount of pro-
tection from wind afforded the reservoir and estimating the Intensity of the local
winds. Table V-2 shows annual wind speed frequency distribution for Washington, D.C.
and Richmond, Virginia. The data suggest that winds 1n the Occoquan area are of
moderate intensity.
Predicting the extent of shielding from the wind requires use of topographic
maps. The reservoir is situated among hills that rise 25 meters or more above
the lake surface within 200 meters of the shore. The relief provides little access
for wind to the lake surface. The combination of shielding and moderate winds
implies that low wind stress plots are appropriate.
The geometry of the reservoir 1s the third criterion used 1n the selection
of thermal plots. Geometric data for the Occoquan Reservoir are summarized in
the problem. The volume, surface area, and maximum depth are all nearly midway
between the parameter values used in the 40-foot and 75-foot maximum-depth plots.
However, the mean depth is much closer to the mean depth of the 40-foot plot.
The mean depth represents the ratio of the volume of the impoundment to its
surface area. Because the volume and surface area are proportional to the thermal
capacity and heat transfer rates respectively, the mean depth should be useful in
characterizing the thermal response of the impoundment. It follows that the 40-foot
thermal profiles should match the temperatures in the Occoquan Reservoir more closely
than the 75-foot profiles. However, it is desirable to use both plots in order to
bracket the actual temperature.
Flow data provide the final information needed to determine which thermal
plots should be used. The inflow from the two tributaries adds up to be 20.09
m /sec.
-112-
-------
The hydraulic residence time can be estimated by using the expression:
TW . V . 3.71 x IQf m3
20.09
-------
AT*
IX
12
o **T o a*-
12
C 10 20 I* 0 10 39 M 0 10 20 It 0 10 20 10
unr. C TCnr. c Ttnr. c Ttnr. c
Iff
»CT
b.
UJ
O
i:
o 10 ?e J3
TEMP. C
12
0 10 20 JO
TErtP. C
0 10 20 10
TE«P. C
12,
0 10 20 10
TE«P. C
X
>—
o.
ta>
O
12
0 10 !• II O 10 JC »•
Unr. C UnP. C
WASHINGTON, D.C.
40' INITIAL «oxinun
30 D«T MYOR- RES. T1«E
MlNlnun nixiwc
FIGURE V-37 THERMAL PROFILE PLOTS FOR OCCOQUAN RESERVOIR
-114-
-------
TABLE V-18
COMPARISON OF MODELED THERMAL PROFILES TO
OBSERVED TEMPERATURES IN OCCOQUAN RESERVOIR
Mean Epi 1 imnion Temp., *C
Month 40-foot Plot*
March
April
May
June
July
August
September
October
November
December
7
13.5
19
24
26
26
22
17
11
7
Observed0
8.4
12.6
20.5
24.8
26.6
26.5
23.8
17.2
12.2
6.2
Mean Hypo limn ion Temp., *C,
40-foot Plot6
6
10
15
18
20
21
20
16
10
7
Observed0 *
6.3
9.2
14.4
17.2
21.2
23.7
20.2
15.8
11.6
5.8
Epi 1 imnion
Depth
(•)
10-foot Plotb
—
--
4.5
5.0
6.5
7
--
—
--
--
Source: Northern Virginia Planning District Commission. January, 1979.
*Mean temperatures in epilimn ion from thermal plots with T • 30 days and a maximum
depth of 40 feet. *
Mean temperatures 1n thermocline and hypolimnion from thermal plots with ^ « 30
days and a maximum depth of 40 feet. w
cMeans of observed temperatures in "upper" and "lower" layers of Occoquan Reservoir for
1974-1976. at Sandy Run.
thermal plots should predict results relatively close to the two low-flow years. The
differences expected for 1975 would be less pronounced when averaged with the other
two.
In conclusion, Occoquan Reservoir does apparently stratify, the depth to
the thermocline or the epllimnion approximates the mean depth (5.29), the hypolimnion
has a depth of 11.8 m (17.1-5.3), and the Interval of stratification approximates May
1 to mid September or 138 days. The hypolimnetic temperature 1s about 11 degrees C,
typical ly.
5.7.3 Sedimentation
To evaluate potential sedimentation problems. Appendix F 1s examined to see 1f
any data exist on the upstream reservoir (Jackson) or Occoquan Reservoir (Figure
V-36). Some data exist for Jackson but not for Occoquan Reservoir (Figure V-38 taken
-115-
-------
OATA
INI IT ICUVVOI* IT,
f»u»*o
V,. U.. ..,.«.« r,,.. ..
- ** _ f
V* MIW • 1
».l •». •»!.. .. .. ».
V4» I..-..H U._ 1.14 .»
4» • ••>
— to. _...to~
"" _-Tto. .--to-
44 4««4>M •. ^ toiiBnin
Vl» *rl»4«l|»l« 1. (IrlfklM 1.1- HiMMt
to .--.to--
<•• (W.4.1-. l.ltl.C.
Vt TW... 4— U.. to-
VII V>~(. tt— 0- «.-..•!
jj _
••>- * 4*
Wtl .W*. We. *1I. 1*. l-rt oV*.
«, 4*
V| •,.«•_ IL. »>~«l «.M, .~
"""" JT.^ »^ JT
- — •- —to-
y •»! MtlMptl t**4ft«>*}4 l*»t «»** •»» ***.» ••). •*.
t»|« »)VM «•* ••«« t« i** t*4( ««lt«l»llW«».
V/ *W*I**4 •f»«» IW1 •*»*•?.
& C*M**MM««II**> •» •«4ll*MNt (Ml mtf.
p •••••) *M *>tl|lMl •*>ltt«f «r**4 *|»*«I|M 04 r
r***lll*>« '»— « I• •' «»•.
Hllfl Iff A HUT TOWN CNUOTAGC AftCA
I9QUARI HLtt)
TOTAL ] MCT
MfOWC, •ftPMM.MkA, MM. M* t
HI*.** it*** — rm« o»*»>. H. u.f u.)
4MMMI. ll.w lll~ tfrl««. •• n.l H.tT
!-,..£,-..--. fc— ..H. *l |»/.l» .Tt
-»
_._to-: " H
-.-to.
„. e-»~i.~ . ». u iyt
» M H.I
— ii«-^.«. «.. imo IM.U
*«• Ml
' ' '
~"'~^ " ""
9VM*. M«*1*C, ttt, fttVU. •« C4ff F»M I
** 'fc
4 C.^.M^.. i. e. ni Ti.4
r* _
1 I* IHI. * tMlMBI
t>cnoo
CAM Of MtntH
WlTVIT M/tVITI
ITCAM)
r*fi
ITOtACt J«
CAfAOTf ™'J
(ACtf -Ft , ™"
Itl
ACM
»«i turn mm
M>. 1*11 - t/*!*1'
1*. KM »ll tt.TM
4^. itii it.i y>.*t>
»». l«7» - I.IM
!•». KM M !.!»>
• | KM - III
«r. KM T.I tt
I.I, Kit - IM
• •». KM l.t IM
k<. Itll K.I III
/•. ItM 10. 1 U/lil
l««. K»l ~ Ml
>... IHI U ITI
J«M IHT II. 1 IM
l«, KM ~ 1 Ml
4«. KIT T.I 4 IM
J~. IHI - U/» III
•rl. ItM 1.) 10 Mt
»•»• ItM l.t K III
4>(. ItM l.t K Ml
to**. Itl) _ ) in
4fl. ItM M.I 1 004
Mr. If)) - T HI
•n. IHI I.I T IH
*>r. Itt) — » Ml
ll.r. ItM I.I M Ul
to.. ItM — • MO
4^. KM M.4 M Wt
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to., itw u.i tor.*
»•»«. itM ~ itt.tr
4^! ItM it III.TI
i«u Him
— K»1 - IM
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"»J KM 111 1.1
• to. KM •- ».«W
U,. KH U.I >.tH
M.. KM .. I.IM
4>«. KH I.I I.IM
•»>. KM I.T1 4,*»
ItM.
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l«4cl tiiltoMl to talk *Mto* Uk* MH •«•
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"" «0»IC
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ACCIMUaTTO*)
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•.m *M i.ti ii. in
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. »>4 H* I.W I.HI
.IH —
.•II -
H* .IU IM
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IT l.ll I.IM
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ill! HO l!tl l'.tn
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MT*
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on
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FIGURE V-38 SUMMARY OF RESERVOIR SEDIMENTATION SURVEYS MADE IN THE UNITED STATES THROUGH 1970
-116-
-------
from Appendix F). Thus, we can detenrlne the trapping of sediment 1n Jackson Reservoir
but trapping must be calculated for the Occoquan. To refine the analysis, calculations
on Jackson Reservoir will also be made and the results calibrated.
To apply the Stokes1 law approach to a reservoir, we need to know the loading
first. The necessary sediment loading estimates for the tributaries were provided by
the methods 1n Chapter 3 and are listed in Table V-19 (Dean «* al_.t 1980) Before they
are used 1n further computations, a delivery factor must be applied to these values.
This factor {the sediment delivery ratio or SDR) accounts for the fact that not all
the sediment removed from the land surface actually reaches the watershed outlet.
Nonpoint loads from urban sources are presumed to enter the reservoir through Bull
Run River since most of the urbanized portion of the watershed lies In this sub-basin.
Computing the annual sediment load Into Occoquan Reservoir 1s complicated
by the presence of Lake Jackson Immediately upstream from the reservoir. The
trap efficiency must be computed for Lake Jackson as well 1n order to determine
the amount of sediment entering the Occoquan Reservoir from Lake Jackson. The
steps involved are to compute the sediment delivered (Table V-20) , the size range,
the fraction trapped for each size range and the total amount trapped. A table has
been devised to simplify these steps (Table V-21).
Soil types provide an Indication of the particle sizes in the basin under
study. Soils in the Occoquan basin are predominately silt loams. Particle size data
on the principal variety, Penn silt loam, are given in Table V-22. These data and
all calculations are transcribed Into Table V-23.
Some effort can be conserved by first calculating the smallest particle size
that will be completely trapped 1n the Impoundment. To do so, P, the trap efficiency,
must first be computed. Because both reservoirs are long and narrow and have rela-
tively small residence times, the flow will be assumed to approximate vertically
mixed plug flow (Case Bl). In this case, P is found from the expression:
where
I
D • mean flowing layer depth, m.
To calculate the smallest particle that 1s trapped in the Impoundment, P
is set equal to unity and the above equation 1s solved for V :
Ma A
v
* Tw
This expression for V(Mx is then substituted Into the fall velocity equation
(Stokes1 law), which in turn is solved for d:
-117-
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TABLE V-19
ANNUAL SEDIMENT AND POLLUTANT LOADS IN OCCOOUAN
WATERSHED IN METRIC TONS PER YEAR*
Type of Load
•Sediment
Total Nitrogen
Available Nitrogen
Total Phosphorus
Available
Phosphorus
BOD5
Rainfall Nitrogen
Kettle
Run
46.898
164.46
16.45
39.01
2.18
328.92
0.72
Cedar
Run
396,312
1.457.42
145.74
341.95
14.95
2.925.63
5.50
Broad
Run
142.241
518.91
51.89
114.22
5.57
1.042.45
2.00
Bull
Run
232,103
789.24
78.92
202.71
12.50
1.578.47
3.92
Occoquan
River
139,685
469.46
46.05
119.42
8.43
925.85
2.48
Urban
Runoff
12,699
12.88
5.38
2.59
1.27
77.47
-
* Estimates provided by Midwest Research Institutes Honpoint Source Calculator.
These values have not yet had a sediment delivery ratio (SOR) applied to
them. We will use 0.1 and 0.2 as lower and upper bounds. The SDR does not
apply to rainfall nitrogen.
Note: A large number of significant figures have been retained in these
values to ensure the accuracy of later calculations.
TABLE V-20
SEDIMENT LOADED INTO LAKE JACKSON,
1,000 Kg/Year
Tributaries
to
Lake Jackson
Kettle Run
Cedar Run
Broad Run
Total
Total
Available
Sediment
46,898
396,312
142,241
Sediment
Lake
Case I
(SOR-0.1)
4,690
39,fi30
14.220
58,540
Delivered to
Jackson
Case II
($DR«0.2)
9,380
79,260
28.440
117,080
-118-
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TABLE V-21
CALCULATION FORMAT FOR DETERMINING SEDIMENT ACCUMULATION IN RESERVOIRS (NOTE UNITS)
Size
Fi.ict ion
Percent
Coni|K)$ it ion
Density
Absolute
bulk
(lean
Particle
Diameter
Vniax
Fraction
Irappoil (P)
A
0
Test Case
i ncoHi i ng
Sediment
Trapped
Sediment
-119-
-------
TABLE V-22
PARTICLE SIZES IN PENH SILT LOAM
Particle Size - °f Particles Smaller Than
(ran) (By Height)
4.76
2.00
0.42
0.074
0.05
0.02
0.005
0.002
4.8 x 10* (Dn - D } d* n,
V p w / D
u
The resulting expression is:
' D' u
100
99
93
84
78
50
26
16
* 4.8 x 106 (0 - D^) • TW
The trap efficiency of Lake Jackson is calculated first. The data required
for these calculations are:
V - 1.893 x 106m3
Q - 12.47 n»3sec
U • 3.34 n
H- • l.ll (Assuming T « 16*C as in Occoquan Reservoir)
T. . V . 1.893 x 106 «3 . , ,(
>
w 12.47 m3 • sec"1 • 86400 sec - day*1
The »ini*u» particle size for 100 percent trapping is computed as:
1.34 m x 1.11 A
~" ~ 5.14 x 10"^ or
x 10b (2.66 - 1.0) • 1.76
-120-
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TABLE V-23
CALCULATION FORMAT FOR DETERMINING SEDIMENT ACCUMULATION IN RESERVOIRS (NOTE UNITS)
Mean
Size Percent Density Particle
Fraction Composition Absolute Bulk Diameter
cin
.000514 0.3 2.66 2.24 N/A
.00050 5 2.66 2.24 N/A
.00035 5 2.66 2.24 N/A
.00020 16 2.66 1.28 N/A
>. 000518 73.7 2.66 2.33 N/A
(average)
Example
Calculation SDR - 0.115
Vo) • 24750 m3/yr
Vol of Jackson Reservoir
(75 yrs lifetime)
Fraction
Trapped (P)
'max A B
m/day
1.90 N/A 1.00
1.79 N/A 0.94
0.88 N/A 0.46
0.29 N/A 0.15
N/A 1.00
Totals
Trapped
last per year «
Test Case
I
11
1
11
1
11
1
II
I
11
I mtons/yr
II mtons/yr
I m3/yr
11 m*/yr
24750m3/yr -
1893000m3
m
Incoming
Sediment
176
352
2927
5854
2927
5854
9366
18732
43144
8628S
48822
97644
21523
43046
1.3X/year
ton/vr
Trapped
Sediment
•^/yr
176 79
352 158
2751 1228
5502 1356
601
2582 1209
1405 1098
2810 2196
43144 19000
86288 37000
-121-
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The amount trapped of each size fraction 1$ computed separately for Case
6-1 from the equation:
p » V>na* T*
D'
For example, for size fraction 0.00035 on:
p . (0.88)(1.76) . Q.46
(3.34) u
A composite trapping efficiency can be obtained by determining the total percent
trapped (48822/58540 • 0.83).
The sediment accumulated in Lake Jackson for each Size range 1s determined
from the expression:
St ' ' ' S1
where
P » trap efficiency
S1 • sediment load from tributary 1
S * sediment trapped.
For the two cases (I, II):
St • (0.1, 0.1} x 0.83 [46898 * 132241] metric tons/year
« (48822. 97644) metric tons/year.
Data obtained from Appendix f of the screening manual show that the estimated
rate of sedimentation in Lake Jackson is 56,153 metric tons/year. This indicates
tnat an SDR of 0.115 would be appropriate.
Bulk density (g/cc) includes the water that fills pore spaces in sediment
that has settled to the bottom and this must be accounted for when determining
volume lost due to sedimentation. Bulk density varies with particle size and
some approximate values for the size ranges for sand (0.005-0.2 cm), silt (0.0002-
0.005 cm), and clay (<0.0002 cm) are as follows: 2.56 for sand, 2.24 for silt and
1.28 for clay. Thus, using an SDR of .115, 24,750m3 (or 1.31) of reservoir
volume would be lost per year. In comparing to Appendix F data, we find that this
value is conservative. The loss of volume was estimated by the SCS to be 47.5 acre
feet/year while these calculations snow only 20 acre feet/year being lost. The
estimated bulk density used by the SCS was 0.93 g/cc and we used a more conservative
value. If the SCS figure is used, the volume lost is determined to be 46.4 acre
feet /year .
Now we compute the sedimentation in Occoquan Reservoir. The minimum particle
size that is completely trapped is computed using the following values:
D' - 5.29
K • 1.11 (T - 16"C • mean of Table V-18)
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D - 2.66 g on'
D^ • 1.0 g on"
T • 21.4 days.
Under stratified conditions, the epllimnlon thickness should be used for 0'.
Since stratification 1s uncertain In this case and the predicted average hypolimnion
thickness, 5.75 m, 1s greater than the mean depth, the latter value trill be used. All
particles with diameter, d. such that:
r—
V 4.
25 « i-*1 - 1.86 x 1(T4 en
3 x 10° (2.66 - 1.0) • 21.4
will be completely trapped 1n the Occoquan Reservoir. Because this value 1s smaller
than the smallest size calculated for Lake Jackson (2 x 10* cm), our computations
are simple, we assumed that 84 percent of the sediment 1s totally trapped and the
remainder is trapped at an efficiency calculated for particle sizes of 0.0001 cm:
v
max
. 1-3 x 1C6 (2-66 - 1.) (1 x IP"4)'
» O.C72
p « V* T* „ 0.072 ' 21.4 „ Q 29
f —tf ^g U.M
The annual sediment trapped 1s:
St ' P ' S1
but corrections for sources and SDR must be made:
S^ • SDR x sediment from each source.
S1 - 13390 (Lake Jackson, already corrected for SDR) 0.115 (232103)
(Bull Run) + 0.115 (139685) (Occoquan River) + 12699 (Urban Runoff
S.j • 68845 metric tons/year
Assuming the distribution of particle sizes for all sources are essentially the
same and accounting for the fractions (f) of material that are In the two different
size ranges:
S, - fj Pj S, * f2 P2 S<
St - (0.84) (1.0) (68845) * (0.16) (0.29) (68845)
St - 57830 ; 3194 • 61024 metric tons
The volume lost is ^^ - 65620 m3/year or 0.2 percent per year of the reservoir volume.
5.7.4 Eutrophication
What would be the consequences to eutrophlcatlon in Occoquan Reservoir of
instituting 90 percent phosphorus removal at the treatment plant? If, in addition to
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phosphorus removal, nonpolnt source (NPS) phosphorus was reduced by 90 percent by
Instituting urban runoff and erosion control, green belts, and other NPS controls,
would an Improvement 1n lake quality occur?
Several assumptions concerning pollutants 1n the Occoquan watershed-reservoir
system are necessary In order to calculate the desired annual loads:
• The unavailable phosphorus 1s adsorbed on sediment particles. Therefore,
of the unavailable forms coming Into Lake Jackson, only the fraction (1
- PC [Jackson]} 1s delivered to the Occoquan Reservoir; available P
gets through Jackson,
• All of the phosphorus and nitrogen from the sewage treatment plants
(STPs) 1s 1n available form.
9 The output of STPs outside the Bull Run sub-basin Is negligible compared
to that of the STPs 1n Bull Run. This 1s justified by the fact that
during the period: under study, the plants In Bull Run had a combined
capacity several tiees larger than tne few plants outside the sub-basin.
• The problems of eutrophlcatlon depend on loading of phosphorus.
By applying these assumptions to the nonpolnt source data 1n Tables V-19
and V-24 the total load of each pollutant type may be calculated (Table V-25).
The computation for the total annual phosphorus load 1n Occoquan Reservoir 1s
computed in the following paragraphs. First the quantity of total phosphorus
coming Into the Occoquan Reservoir through Lake Jackson 1s calculated by:
TP, . enn - (i - p ) x [Total P - Available P] * Available P
Jacicson cjackson
The total phosphorus from Broad run, Cedar Run, and Kettle Run are summed and
the available phosphorus loads are subtracted to give the unavailable load. This
load is multiplied by the trap efficiency of the lake, P • 0.83, which yields
the unavailable load passing through. This value, plus the available load, 1s an
estimate of the total phosphorus entering Occoquan Reservoir from Lake Jackson. This
quantity is 103.24 metric tons yr"1 (Table V-25). This value 1s added to the
non-urban, nonpolnt source loads from Bull Run and areas adjacent to the Occoquan
Reservoir (Table V-18):
TNPNU - 202.71 * 119.42 * 103.24
• 425.37 metric tons yr"1
This quantity is modified by the sediment delivery ratio. The urban nonpolnt
loads and STP (Table V-24) loads are added to complete the calculation:
TP - (0.115) (425) * 2.59 * 11.92
• 63.3 metric tons yr
Similarly the SDR was applied to nonpolnt sources of nitrogen and BOD . The results
of load calculations are summarized in Table V-25.
The calculated annual total phosphorus and nitrogen loads (Table V-25) may
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TABLE V-24
SEWAGE TREATMENT PUNT POLLUTANT LOADS
IN BULL RUN SUB-BASIN IN METRIC TONS PER YEAR*
Total Nitrogen Total Phosphorus BOD5
108.0
11.92
54.80
Source: Northern Virginia Planning District
Commission, March 1979.
'Averages for July 1974 - December 1977
TABLE V-25
CALCULATED ANNUAL POLLUTANT LOACS TO OCCOQUAN RESERVOIR
Load Source
Urban runoff
Sewage treatment
Rainfall
Other fJonpoint Source*
TOTAL
Total N
12.38
103.00
14.62
391.00
525.50
Metric
Avail. N
5.38
108.00
14.62
39.10
167.10
Tons /Ve»"
Total P
2.59
11.92
-
48.83
63.34
Avail.?
1.27
11.92
-
2.65
15.84
BODc
77.47
54.30
-
802.00
934.27
Nonpoint Source %
80
35
81
25
94
Point Source *
Used SDR of 0.115.
20
65
19
75
be compared with the observed loads listed in Table V-26. The loads observed
are 1.5 to 6 times higher than highest calculated loads for nitrogen. Compari-
son of loadings (kg/ha year) with literature values suggest that Grizzard 1s most
accurate (Likens et^ a_l_., 1977).
The first method of predicting algal growth is known as the Vollenweider
Relationship. In the graph of total phosphorus load (g nf2 vr"1) versus mean
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TABLE V-26
OBSERVED ANNUAL POLLUTANT LOADS TO OCCOQUAN RESERVOIR
Mean Flow*
Rate
Period (m3 sec"1 )
10/74
7/75
7/76
- 9/75 24.7
- 6/76 24.0
- 6/77 10.4
Total Nitrogen Load Total Phosphorus Load
(metric tons year ) (metric tons year" )
805* 110b
1905° 188C
4763° 454C
* Source: USGS Regional Office, Richmond, Virginia.
* Grizzard et. a1_., 1977
e Northern Virginia Planning District Commission, Karch, 1979.
Data gathered by Occoquan Watershed honitoring Laboratory.
depth (m) divided by hydraulic retention time (yrs) (see Figure V-24), areas can *e
defined that roughly correspond to tne nutritional state of the Impoundment. For the
Occoquan Reservoir, the values of the parameters are:
Lp . (63.34) x 10s g/yr . g Q4 g .-2 yr-l
7.01 x 106 oi2
. S.29 a
0.0585 yr
vr
yr
-l
According to the Vollenweider Relationship, Occoquan Reservoir is well Into tne
eutrophic region for loading of total phosphorus. Based on these predictions a more
in-depth study of the algal productivity seems to be in order.
Solving for the phosphorus concentration in this reservoir:
1
Lp
p • —
z
9.04 g m
P « 0.0305 g/«» 80.5 ug/1.
Calculated and observed pollutant concentrations are list»d in T»ble v-?-.
The mean summer concentrations of phosphorus and nitrogen are closer to tfe concen-
trations calculated tnan would be expected on the basis of the comparison of ar-~'*'
loads.
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TABLE V-27
CALCULATED AND OBSERVED MEAN ANNUAL POLLUTANT
CONCENTRATIONS IN OCCOQUAN RESERVOIR
Total b Available Total
Nitrogen Nitrogen Phosphorus
(g m-3) (g ,-3) (9 m"3)
Calculated (SDR - 0.115) 0.831 0.264 0.08
Observed Values8
Mean 0.88 0.16 0.08
Max. 1.50 0.24 0.12
M1n. 0.35 0.10 0.04
a Assuming no removal processes for nitrogen.
b Averages for April-October between 1973 and 1977.
Source: Northern Virginia Planning District Conuiission,
March, 1979.
The ratio of nitrogen to phosphorus concentration 1n the reservoir can be used
to estimate which nutrient will limit the rate of plant growth. For the Occoquan
Reservoir, the N:P ratios are 10 to 1 for total N to total P. The calculated nutri-
ent ratios and the N:P ratio of the observed data (11.0) Indicates that phosphorus Is
probably growth limiting.
The available data also permits the estimation of the maximal primary production
of algae from the Chiaudani and Vighi Curve (Figure V-26). The theoretical phosphorus
concentration should be about 0.08 g m according to calculations. The maximal
primary production of algae is found from Figure V-26 to be about 2500 mgC m"2
day . This level of algal production is roughly the maximum production shown on
the curve. Both this result and the VoMenweider Relationship suggest algal growth
will contribute significantly to the BOD load in the impoundment.
Effects of 90 percent P removal at treatment plant on TP loading:
M • 52.61 m ton/yr
i 52.6! x 10 n/vr -, cn -2 -1
L • , ;,, iJi 7" /.50gm y
7.01 x ltf> m* y J
qs « 90 m yr"1
Although improved, we conclude that \oad1ng 1s still too great according to Figure
V-24.
Effects of 90 percent STP removal of TP plus 90 percent NPS removal of TP:
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M • 6.334 n ton/yr
_ -. Q A «
L . 6;3r * 'Tg • 0.90 g m y
This would move Occoquan Reservoir Into the bottom of the mesotrophlc range.
Lake concentrations of total P would be:
p ' (5.25i7:5i21.2-J ' 66-9 «/]
, .,,
(5.19) • (21. Z)
8 ug/1
P8/
Although the screening method shows narked Improvement In Occoquan eutro-
phlcatlon, 90 percent control of phosphorus UPS would be very expensive. Careful
analysis of assumptions made 1n the screening method and of control alternatives
would be necessary before proceeding to map such a control strategy. Moreover,
careful study of reservoir TP sources and sinks and of algal productivity would be
necessary. The screening method has served to Illustrate the feasibility and
potential value of such further analysis.
5.7.5 Hypolimnetlc DO Depletion
Excessive nutrient loading plus Inputs of BODs suggest that 00 problems 1n
the hypo 11 ran Ion could result, we will use the data obtained 1n the first three
problems to determine the hypolimnetlc DO. These data are summarized below.
All rate coefficients listed have already been corrected for temperature.
Physical /Biological
Area • 7.01 x 106m2
Volume • 3.71 x 107m3
Q • 20.09 m3 sec"1 • 1.74 x 106m3 day"1
Depth to thermocHne • 5.29 m (average depth)
Interval of stratification (May to mid-September) « 138 days
BOD loading • 934.27 106g . yr"1
Algal loading • 1800 mgCm day!
BOD concentration - 934.27 x 10 g/yr „ Q_069 }
3.71 x 10 m x 365 days/yr
Temperature • 10*C
Rates and Input Values
M • 0.8 k1 • 0.063 day"1
S « 2.67 k • 0.0378 day"1
P - 0.824 gC m"2 day"1 k4 - 0.0019 day"1
V • 5.29 m 00$at - 11.3 mg/1
- 21.4 day t -138
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The simplified model used to predict hypoHnmlon dissolved oxygtn levels assumes
that the only substantial dissolved oxygen sinks are Mater column and benthic deposit
BOD (Section 5.5). Additionally, all sources of oxygen, photosynthesis, etc., are
neglected 1n the hypol1mn1on after the onset of stratification. Thus, the procedure
requires that pre-stratification levels of BOO and dissolved oxygen be estimated in
order to compute the post-stratification rates of oxygen disappearance. The pre-
stratification concentration of water column BOD 1s determined first. A simple mass
balance leads to the following relationship, if steady state conditions are assumed:
where
GSS • steady state concentration of BOD in water column, mg/l~
k * mean rate of BOD loading from all sources g •" day"
s - •*, • ki -4
where
kc ' vc/^ " mean rate of BOD settling out onto
-1
impoundment bottom, day
k, • mean rate of decay of water column BOD, day"
31
Q • mean export flow rate, tn day"
V * impoundment volume, m
Vs • settling velocity, m day"
7 • impoundment mean depth, m.
The BOD load to the impoundment originates in two principal sources: algal
growth and tributary loads. The algal BOD loading rate is computed from the expression:
ka (algae) ' SMP'7
where
S • stoichiometric conversion from algal biomass as carbon to BOD •
2.67
M • proportion of algal biomass expressed as oxygen demand
P « algal primary production, g m day.
Since the Chiaudani and Vighi curve (Figure V-26) gives the maximal algal pro-
duction, a correction should be made for the actual epilimnion temperature. If the
maximal rate occurs at 30"C and the productivity decreases by half for each 15"C
decrease in temperature, the algal production can be corrected for temperature using
the expression:
'IT,' ',30, » 1.0«7
According to the data in Table 1, the epilimnion temperature during the month
prior to stratification is approximately 13°C. Thus:
P{13., - (1.8) gC m-2 day"1 x i.^13^30^
• 0.824 gC m"2 day"1
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If M 1$ assumed to be 0.8, then:
k . 2.67 x 0.8 x 0.824 qC m"2 day'1
a(algae)
« 0.333 g »"3 day'1
The BOD load bome by tributaries 1s found by the expression:
k . Mean Dally BOD fro« Tributaries (Table V-18)
a(tr1b) Impoundment Volt'
. 034.27 x 106 q yr"1 1 yr
3.7! , IOV ' *
« 0.069 g m"3 day
The total BOO load to Occoquan Reservoir 1s then:
ka ' kt<»19««) * *a (tr1b)
« 0.33 9 m"3 day"1 * 0.069 g »~3 day"1
• 0.402 g m day"1
Before the water column BOO concentration can be computed, the constants
comprising kfa must be evaluated. The first of these, k$, requires knowledge
of the settling velocities of BOO particles. Ideally these would be determined by
using values of the physical properties of the particles and the water 1n the settling
velocity equation, V-6. Because such data are lacking, a settling velocity of 0.2 m
day" reported for detritus will be substituted. The reported values He between
0 and 2 meters day , with most values close to 0.2 m day"1 (Z1son et^ al_. ,
1978). Then:
k$ - 0.2 m day"l/5.29 m -0 .0378 day"1
The second constant comprising k& 1s the first-order decay rate constant for
water column BOD. Reported values of kj vary widely depending on the degree of waste
treatement. 21 son et_ al_. (1978) presents data for rivers, but contains only two
values for kj In lakes and estuaries. Both are kj • 0.2 day"1. Camp (1968) reports
values from 0.01 for slowly metabolized industrial wastes to 0.3 for raw sewage.
Because there is considerable sewage discharge Into the Occoquan Reservoir, k.
may be assumed to be 1n the upper range of these values, between 0.1 and 0.3 or 0.15
day" . Like the algal production rate, kj must be corrected for the water
temperature. In April, the mean water temperature Is about ll'C.
Then:
k • 0.095 day"1 x 1.047 (n*c-20'C)
» 0.063 day"1
Finally, kfa is evaluated as follows:
kb » -0.0378 day"1 - 0.063 day"1 -
« -0.148 day"1
Next, k and k may be substituted Into the following equation to obtain C
ss
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C - -a
ss 1T
*
0.402 -3
Once the water column BOD concentration 1s known, the benthic BOD 1s
computed from the expression:
L» • ^
where
k. « mean rate of benthic BOD decay, day"
Values for the benthie SOD decay rate constant span a greater range than
those for water column BOD. Camp (1968), however, reports values of k^ very
near 0.003 day" for a range of benthic depth from 1.42 to 10.2 cm (Table
V-10). Assuming this to be a good value, a temperature-corrected value of k.
may be computed at an April hypolimnion temperature of 10°C (Table V-18):
k4 - 0.003 day"1 x 1.047(10"20) « 0.0019 day"1
0.0378 day"1 x 2.72 g m"3 x 5.29 m
Lss " 0.0019 day"1
- 286 g m"2
Prior to stratification the impoundment 1s assumed to be fully mixed and
saturated with oxygen. During April, the hypolimnion temperature is 10°C. Saturated
water at this temperature contains 11.3 ppm oxygen (Table V-12).
Finally, the dissolved oxygen level in the hypolimnion may be predicted during
the period of stratification. The applicable expressions are:
A B C E 8
AOL • (1.04) [(53.1) (0.231) - (1/53.1)]
M)L • 12.74
F E
AOC « (1.7) (1) - 1.7
Ot • 11.3 - 12.74 - 1.7
Therefore the hypolimnion Is depleted of oxygen at the end of the stratification
period (138 days). By selecting different conditions for decay rates and for time of
stratification a family of curves was generated that can be compared with actual
observations (Figure V-39). As car be seen situations 3 and 4 (BOD decay of 0.3
later corrected for temperature and a total BOD loading of 0.36 or 0.57 g • m
day' ) gave a reasonable fit of observed data at the deepest station (Occoquan
Dam, 1973}.
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o i
o i
0}
03
High Oam (ItfOt
Oceoquan Oam (19/3)
• • Calculaftd
• • Ohservtd Potnl t
30 40 M CO ?0
TIME AFTER SinATIFICATION (DAYS)
FIGURE V-39
DISSOLVED OXYGEN DEPLETION VERSUS TIME IN THE
OCCOQUAN RESERVOIR
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Interpretation of the dissolved oxygen-time data at High Dan 1n 1970 presented
1n Figure V-39 1s complicated by the Introduction of fresh oxygen after the onset of
stratification. Although a direct comparison of oxygen depletion tines 1s not
possible, the rates of oxygen level follows curve 2 of Figure V-39 very closely,
while during the second period of oxygen consumption the oxygen concentrations
closely match those of curve 1. Since the reservoir 1s shallowest at High Dam and
the substantially lower than average flow rate 1n 1970 resulted 1n strongly stratified
conditions, the oxygen depletion rates 1n this case should be among the highest
likely to be observed 1n the Impoundment. Curve 1 represents the fastest decay rates
predicted by the model. Thus, the observed oxygen consumption times should be
greater than the lower limit predicted by the model 1n nearly all cases.
The above agreement of the observed with the predicted limits for the range of
oxygen depletion times in Occoquan Reservoir Implies that the typical or average time
must also fall within the predicted range. Since 1t was for "average" conditions
that the impoundment was modeled, it may be concluded that the model does accurately
describe the behavior of the Occoquan Reservoir.
5.7.6 Toxicants
It was not possible to obtain data on toxicants in Occoquan Reservoir. In
order to provide a problem with some realism, published data on a priority pollutant
in another reservoir were obtained. In Coralville Reservoir, Iowa, commercial
fishing was banned in 1976 because of excessive accumulation of dleldrln residues in
flesh of commercially important bottom feeding fish (Schnoor, 1981). The dieldrln
arose from biodegraded aldrin, an insecticide in wide use along with dleldrln before
cancellation of registration of both pesticides by USEPA in 1975.
After 1976 there was steady diminution of dieldrin in the waters, fish, and
bottom sediments of Coralville Reservoir, until the late 1970's when dleldrln levels
in fish flesh declined to less than 0.3 mg/kg (Food & Drug Administration guideline).
In 1979, the fishing ban was rescinded.
Using the screening methods and data abstracted from Schnoor's paper, the
potential dieldrin problem can be evaluated in Coralville Reservoir. Available
and back-calculated data include the following values:
Reservoir Dleldrln
Tw - 14 days • 336 hrs kow • 305000
1 • 8 feet - 2.4 n koc - 35600
C - 0.05 ng/1 dieldrin solubility 1n fresh water » 200
OC « 0.05 (estimate)
So • 200 jig/1 (estimate)
- 200 x 10'6 kg/kg
P • 0.9 (estimate)
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Assuming that conditions retained constant, the steady state concentration
of dleldrln can be computed using the approach described 1n Section 5.6 as follows:
where
C • Cin/ (1 * TW . k,
K • SED + B + k + k + kh
V p n
Evaluation of K depends on estimation of the separate rate constants. Informa-
tion 1n Chapter 2 and 1n Callahan, et^ al_. (1977) Indicate that the blodegradatlon
rate (6) in aquatic systems 1s extremely small. Similarly volatilization (ky) and
hydroloysls (kh) are negligible processes affecting the fate of dleldrln. Photoly-
sis (k ) can be significant In some circumstances but the high turbidity 1n
Coralv1lie Reservoir Indicates that minimal photolysis takes place. Consequently, K
» SED. These assumptions are supported by Schnoor (1961).
Calculation of the sedimentation rate constant (SED) 1s as follows:
SED - 4 x D x K
k • 0.63 x kow x OC
- 0.63 x 305000 x 0.05
• 9610
D • P x 50 x ^
0 - 0.9 x 200 x 10'6 x -33^ • 5.36 x 10'V1
a - I/ (1 + kpS)
S • OC x 50 • .05 x 200 x 10'6 - 1 x 10"5
a • 0.912 x 5.36 x 10'5 x 9610
• 0.0047 m~l
The steady state concentration of dieldrin in Coralvilie Reservoir is estimated
to be:
C • 0.05 Kg/1 (1 + (0.0047 hr"1 x 336 hr))
C • 0.019 ng/1
This value is much greater than the present fresh water quality criteria of 0.0023
dieldrin ng/1 (Federal Register: 79318-79379. Nov. 26, 1980) and would indicate a
serious potential problem in the reservoir that would require significant action and
study.
Evaluation of bioconcentration supports this conclusion:
Y • BCF x C
If the default estimate is used (Section 5.6.1.6):
log BCF - 0.75 log KOW - 0.23
- 3.88
BCF • 7642
Y • 7642 x 0.019 • 145 ng/kg fish flesh
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This value would be less than the FDA guideline. However, two published BCF values
are available: 35600 from Chapter 2; 70000 from Schnoor (1981). These values
produce much higher tissue burdens, both of which violate the FDA guideline:
Y - 35600 x 0.019 • 676
Y • 70000 x 0.019 • 1330
In 1979, H 1s estimated that C1n « 0.01 (calculated frow Schnoor, 1981).
Therefore, assuming other conditions are constant:
C • 0.01/ (1 + (.0047 x 336))
- 0.0039 ng/1
A value about double the water quality criterion. Flesh concentration would be
(using BCF • 70000):
Y - 70000 x 0.0039 • 270 ng/kg
This value (0.27 Mg/kg) would be less than the FDA guidelines of 0.3 Kg/kg and
support the conclusion to 11ft the fishing ban. Schnoor (1981) shows the following
measured data that can be compared to the screening results:
1970 1979
Screening
Measured
Water
0.019
0.015
Fish
1300
1100
Water
0.04
0.005
F1sh
270
250
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REFERENCES
Callahan, M.. M. Slimak. N. Gabel, I. May, C. Fowler. R. Freed, P. Jennings, R.
Durfee, F. WMtmore, B. Maestri, W. Mabey, B. Holt, C. Gould. 1979. Water-
Related Environmental Fate of 129 Priority Pollutants, Volumes 1 and 2. U.S.
Environmental Protection Agency Report. EPA 440/4-79-029a, b. NTIS Reports:
PB80 204373, PBBO 204381.
Camp, T.R. 1968. Water and Its Impurities. Relnhold Book Corporation. New York.
Carlson, R.E. 1977. A Trophic State Index for Lakes. Llmnol. Oceanogr. 22:361-369.
Chen, C.W., and G.T. Orlob. 1973. Ecologlc Study of Lake Koocanusa L1bby Oam. U.S.
Army Corps of Engineers, Seattle District.
Chiaudanl, G.. and M. V1gh1. 1974. The N:P Ration and Tests with Selenastrum
to Predict Eutrophicatlon 1n Lakes. Water Research 8:1063-1069.
Cowen. W.F., and G.F. Lee. 1976. Phosphorus Availability 1n Paniculate Materials
Transported by Urban Runoff. JWPCF 48:580-591.
Dean, J.D., R.J.M. Hudson, and W.B. Mills. 1979. Chesapeake-Sandusky: Non-designated
208 Screening Methodology Demonstration. Midwest Research Institute, Kansas
City, MO. U.S. Environmental Protection Agency Rept. for Env. Res. Lab,
Athens, GA. In Press.
Dillon, P. 1974. A Manual for Calculating the Capacity of a Lake for Develop-
ment. Ontario Ministry of the Environment.
Dillon, P., and F. Rlgler. 1975. Journal Fisheries Research Board of Canada
32(9).
Dorich, R.A., D.W. Nelson, and L.E. Sommers. 1980. Algal Availability of Sediment
Phosphorus in Drainage Water of the Black Creek Watershed. J. Environ. Qual.
9:557-563.
Drury, O.D., D.B. Porcella, and R.A. Gearheart. 1975. The Effects of Artificial
Destratlfication on the Water Quality and Microbial Populations of Hyrmn
Reservoir. PRJEW011-1. Utah State University, Logan, UT.
Grizzard, T.J., J.P. Hartigan, C.W. Randall, J.I. Kim, A.S. Librach, and M. Derewlanka.
1977. Characterizing Runoff Pollution-Land Use. Presented at MSDGC-AMSA Workshop,
Chicago. VPISU, Blacksburg, VA. 66 pp.
Hudson, R.J.M., and D.B. Porcella, 1980. Selected Organic Consent Decree Chemicals:
Addendum to Water Quality Assessment, A Screening Method for Non-designated 208
areas. U.S. Environmental Protection Agency Rept. for Env. Res. Lab, Athens,
&A. In Press.
Hutchinson, G.E. 1957. A Treatise on Limnology, Volume I. John Wiley ft Sons, New
York. 1015 pp.
Hydrologic Engineering Center (HEC), Corps of Engineers. 1974. Water Quality
for River-Reservoir Systems. U.S. Army Corp of Engineers.
Jones, J.R., and R.W. Bachmann. 1976. Prediction of Phosphorus and Chlorophyll
Levels in Lakes. JWPCF 48:2176-2182.
-136-
-------
Larsen, D.P., and K.W. Malueg. 1981. Whatever Became of Shagawa Lake? In: Inter-
national Symposium on Inland Waters and Lake Restoration. U.S. Environmental
Protection Agency. Washington, D.C. p. 67-72. EPA 440/5-81-010.
Larsen, D.P., and H.T. Herder. 1976. Phosphorus Retention Capacity of Lakes. J.
Fish. Res. Board Can. 33:1731-1750.
Likens, 6.E. et^ al_. 1977. B1ogeochem1stry of a Forested Ecosystem. Springer-
Verlog, New York. 146 pp.
Llnsley. R.K.. M.A. Kohler, and J.H. Paulhus. 1958. Hydrology for Engineers.
McGraw-Hill, New York.
Lorenzen, M.W. 1978. Dhosphorus Models and Eutrophication. In press.
Lorenzen, M.W. 1980. Use of Chlorophyll-Secchl Disk Relationships. Llmnol.
Oceanogr. 25:371-3727.
Lorenzen, M.W., and A. Fast. 1976. A guide to Aeration/Circulation Techniques
for Lake Management. For U.S. Environmental Protection Agency, CorvalUs,
OR.
Lorenzen, M.W. et^ al_. 1976. Long-term Phosphorus Model for Lakes: Application
to Lake Washington. In: Modeling Biochemical Processes In Aquatic Ecosystems.
Ann Arbor Science, Ann Arbor, MI. pp. 75-91.
Lund, J. 1971. Water Treatment and Examination 19:332-358.
Marsh, P.S. 1975. Slltatlon Rates and Life Expectancies of Small Headwater Reser-
voirs 1n Montana. Report No. 65, Montana University Joint Water Resources
Research Center.
Megard, R.O., J.C. Settles, H.A. Boyer, and W.S. Combs, Jr. 1980. Light, Secchl
Disks, and Trophic States. Limnol. Oceanogr. 25:373-377.
Porcella, D.B., S.A. Peterson, and D.P. Larson. 1980. An Index to Evaluate Lake
Restoration. Journal Environmental Engineering Division ASCE 106:1151-1169.
Rast, W., and G.F. Lee. 1978. Summary Analysis of the North American (US Portion)
OECO Eutrophication Project. U.S. Environmental Protection Agency, Corvallis,
OR. 454 pp. EPA-600/3-78-008.
Sakamoto, M. 1966. Archives of Hydrobiology 62:1-28.
Schnoor, J.L. 1981. Fate and Transport of Oieldrin in Coralville Reservoir:
Residues in Fish and Water Following a Pesticide Ban. Science 211:804-842.
Smith, V.H., and J. Shapiro. 1981. Chlorophyll-Phosphorus Relations in Individual
Lakes: Their Importance to Lake Restoration Strategies. Env. Sci. and Tech.
15:444-451.
Stumm, W., and J.J. Morgan. 1970. Aquatic Chemistry. Wiley-Interscience. New
York.
Vollenweider, R.A. 1976. Advances in Defining Critical Loading Levels for Phosphorus
in Lake Eutrophication. Mem. 1st. Hal. Idrobiol. 33:53-83.
Vollenweider, R.A., and J.J. Kerekes. 1981. Background and Summary Results of the
OECD Cooperative Program on Eutrophication. In: International Symposium on
Inland Waters and Lake Restoration. U.S. Environmental Protection Agency,
Washington, D.C. p. 25-36. EPA 440/5-81-010.
-137-
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U.S. Department of Commerce. 1974. Climatic Atlas of the United States. U.S.
Department of Commerce, Environmental Sciences Services Administration, Environ-
mental Data Service, Washington, D.C.
U.S. Environmental Protection Agency. 1975. National Water Quality Inventory,
Report to Congress. EPA-440/9-7S-014.
Zison, S.W., W.B. Hills. D. Deimer, and C.W. Chen. 1978. Rates, Constants, and
Kinetics Formulations in Surface Water Quality Hodellng. U.S. Environmental
Protection Agency, Athens, GA. 316 pp. EPA-600/3-78-105.
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GLOSSARY OF TERMS
Significant variables are shown with typical units. Units must be compati-
ble or use conversion factors (Chapter 1). Note that son* symbols are used for
more than one tern.
2 2
A Lake surface area. m - sediment area, •
a Fraction of pollutant In solution • 1/(1+K x S)), unltless
B B1odegradat1on rate, hr"
B(T) B1odegradat1on rate, corrected for temperature T, hr
BCF 61 oconcent ration factor, unltless
Bo Initial nricroblal biodegradatlon rate, uncorrected for temperature
or nutrient concentration, hr
C Reservoir concentration at time, t, mgl
C Initial concentration, mgl"
-1
C Concentration of phosphorus, tigPl
P .3
C Total exchangeable phosphorus concentration 1n the sediments, g m
5 .1
C, Toxicant concentration sorted on sediment, mg 1
» _i
C. Concentration of BOD at time t, mg 1
1 _i
C Concentration in water phase, mg 1
* -1 -3
C Steady-state water column phosphorus concentration, mg 1 , gm
C^ Steady state influent concentration, mg/1
-3
C Steady-state water column BOD. g m
C Weight concentration
wt
C , Volumetric concentration
D Depth, m
D Discharge channel depth, ft
D Sedimentation rate constant • P x S x Q/V, mg 1 day
D Dilution rate, day"1
D1 Flowing layer depth, ft
D" Inflow channel depth, ft
U Mean depth, m
TT Depth to thermocline, m
D. Mean hypolimnion depth, m
Dj Depth at the 1th cross-section, m
Do Diffusivity of oxygen in water (2.1xlO~9 m2 sec"1, 20*C)
D Weight density of a particle, Ib ft"3
33
DW Weight density of water, Ib ft" , g cm
DW Pollutant diffusivity in water, m2 sec"1
d Number of days per time period, days
d Particle diameter, cm
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f 1 * (TW x K), unltless)
g Acceleration due to gravity, 32.2 ft sec"
I Intensity of light at Secchl depth, relative units
I Initial Intensity of light at surface, relative units
K Pollutant removal rate, • SED + B + ky + kp + k^, hr"1
K Net rate of phosphorus removal, hr"
K. Specific rate of phosphorus transfer to the sediments, m yr"
J _i
10 Specific rate of phosphorus transfer from the sediments, m yr
K. Fraction of total phosphorus Input to sediment that 1s available
for the exchange process, unltless
K Reaeratlon rate, hr"
a .1
Ka, Reaeratlon coefficient, m hr
K Distribution coefficient between organic sediment and water,
unitless
K. First order decay rate for water column 800 at 20*C, day"
* ,1
K. Benthlc BOD decay rate at 20*C, day
-3 -1
K Mean rate of BOD loading from all sources, g m day
a -3-1
K < 1 a ) Al9al contribution to BOD loading rate, g • day
Tributary or point source contribution to BOD loading rate,
•*
g m day
a \ i •* ,
S --Ks -K1 -d/Tw), day"1
k Extinction coefficient, IB"
e _i
*h Hydrolysis rate, hr
k Photolysis rate, hr'1
* Photolysis rate constant uncorrected for depth and turbidity
of the lake, m"1
k Hean rate of BOD settling out onto the impoundment bottom,
"""'
ky Volatilization rate, hr
koc Organic carbon based partition coefficient, unltless
kow Octanol-water coefficient, unitless
L Areal BOD load, gm"2
L Phosphorus loading, g m" yr"
LSS Steady-state benthic BOD load, g m"2
H Total annual phosphorus loading, g yr
M Proportion of algal biomass expressed as an oxygen demand (unltless)
HW Molecular weight, g mole"
OC Sediment organic carbon fraction, unltless
^°c Dissolved oxygen decrease due to hypollmnion BOO, mg 1
A\ Dissolved oxygen decrease due to benthic demand, mg l"1
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0 Dissolved oxygen at time t • 0, mg l"
0+ Dissolved oxygen at time t, mg l"
p Sediment trapping efficiency, unltless 1 _> P _> 0
P Primary productivity rate, g Carbon • day"
P Total phosphorus 1n the water column, mg m"
PI Influent phosphorus, mg 1
QI Mean annual Inflow, m yr
Q Mean annual outflow, • yr"
q Hydraulic loading (7/Tw),myr~
R Reynolds number, unltless
r Radius, ft
S Sto1ch1ometr1c conversion from algal blomass as carbon to BOD,
2.67, unltless
S Input suspended organic sediment • OC x So, mg 1
S, Mass of sediment In Inflow per unit time, mg l"
1 _i
SQ Input of suspended sediment, mg 1
S Sediment trapped, metric tons yr"
SO Secchl depth, m
SDR Sediment delivery ratio, unltless
SED Sorptlon and sedimentation rate (toxicant at equilibrium with
sediments), hr
T Temperature, degrees centrlgrade
V Lake or impoundment volume, m
Vu Hypolimnlon volume, 1
3
V Sediment volume, m
5 1
Vmmw Terminal velocity of a spherical particle, ft sec
TTiaX «
W Wind speed, m sec"
Y Tissue concentration of pollutant, g kg"1 fish flesh
y Number of years
Z Depth, m
7 Mean depth, m
n Absolute vlscosdty of water, Ib sec ft"2, g sec on"2
P Mass density of a particle, slugs ft
_3
pw Mass density of water, slugs ft
T Mean hydraulic residence time (V/Q), days
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CHAPTER 6
ESTUARIES
6.1 INTRODUCTION
6.1.1 General
Estuaries are of primary social, economic, and ecologic importance to America.
Forty-three of 110 of the Department of Commerce's Standard Metropolitan Statistical
Areas are or estuaries (DeFalco, 1967). Estuaries are the terminal or transfer point
for essentially all waterborne national and international commerce in this country,
and biologically are more productive on a mass per unit area basis than any other
type of water body. Essentially all conservative wastes and much of the nonconserv-
ative wastes discharged into any inland stream in America eventually pass into an
estuary. Yet these coastal formations on which there is such a demand for services
are less stable geologically than any other formation found on the continent (Schubel,
1971). Sedimentation processes, for example, are filling, destroying, or at least
altering all estuaries. While this process is always rapid in a geological sense,
the actual length of time reouired for complete estuarlne sedimentation is a function
primarily of the stability of the sea level, the rate of sediment influx, and the
intra-estuarine circulation pattern (Schubel, 1971). The instability, variation, and
complexity of estuaries make water quality assessment and prediction especially
difficult, yet the demands placed on estuaries require a most active water quality
management program.
This chapter will describe a systematic approach which may be used to provide
estuarine water quality assessment and prediction. Its purpose is two-fold. First,
the planner wi11 be provided the capability of making elementary assessments of
current estuarine water quality. Second, methodologies are presented by which the
planner can evaluate changes in water quality which might result from future changes
in waste loading.
Chapter 3 provided methodologies for assessing the waste load directly entering
an estuary. Chapter 4 provided methodologies which can be used to assess the water
quality of a river or stream as it enters an estuary. The output of these chapters
will provide information about present and projected estuarine water quality which
can be used to identify regions having greatest water quality problems, water quality
parameters of special concern, and areas for which subsequent computer study is nec-
essary. Methods presented below comprise a screening tool which may be used by the
planner to focus attention on critical spatial regions and water Quality parameters.
These can then be fully assessed using computer models or other techniques, as
desired.
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6.1.2 Estuarine Definition
It 1$ difficult to provide a concise, comprehensive definition of an estuary.
The basic elements included In most current definitions are that an estuary is:
o A semi-enclosed coastal body of water
o Freely connected to the open sea
o Influenced by tidal action
o A water body In which sea water 1s measurably diluted with fresh
water derived from land drainage (Prltchard, 1967; Pritchard and
Schubel, 1971).
The seaward end of an estuary is established by the requirement that an estuary
be semi-enclosed. Because this boundary 1s normally defined by physical land features,
it can be specifically identified. The landward boundary 1s not as easily defined,
however. Generally tidal influence in a river system extends further Inland than
does salt intrusion. Thus the estuary is limited by the requirement that both salt
and fresh water be measurably present. Accordingly, the landward boundary may be
defined as the furthest measurable inland penetration of sea salts. The location of
this inland boundary will vary susbstantial1y from season to season as a function of
stream flows and stream velocities and may be many miles upstream from the estuarine
mouth (e.g., approximately 40 miles upstream on the Potomac River, 27 miles on the
James River, and approximately 16 miles upstream for the small Alsea Estuary in
Oregon) (Pritchard, 1971). This definition also separates estuaries from coastal
bays (embayments) by the requirement for a fresh water Inflow and measurable sea
water dilution.
6.1.3 Types of Estuaries
While the above definition provides adequate criteria for segregating estuaries
from other major types of water bodies, it does not provide a means to separate the
various types of estuaries from one another. The variations in estuarine circulation
patterns and resulting variations in pollution dispersion from estuary to estuary
make classification a necessary part of any water quality assessment. Two basic
estuarine classification systems have been used in recent years to accomplish
estuarine subclass separation: a topographical system and a physical processes
system (Dyer, 1973, Chapter 2 or Ippen, 1966, Chapter 10).
6.1.3.1 Topographical Classification
Under a topographical system, estuaries are divided into four subclasses.
These are briefly described below.
• Drowned River Valley (Coastal Plain Estuary). These estuaries are
the result of a recent (within the last 10,000 years) sea level rise
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which has kept ahead of sedimentation processes at a river's mouth.
Such estuaries are, quite literally, rivers whose lower basins have been
drowned by the rising oceans. Coastal plain estuaries are characteris-
tically broad, relatively shallow estuaries (rarely over 30 m deep) with
extensive layers of recent sediment.
• Fjord-Uke Estuaries. These estuaries are usually glacial ly formed and
are extremely deep (up to BOO «) with shallow sills at the estuarine
mouth. Fjord-like estuaries are restricted to high latitude mountainous
regions and are not found in the United States outside of Alaska and
Puget Sound in the state of Washington.
0 Bar-built Estuaries. When offshore barrier sand islands build above sea
level and form a chain between headlands broken by one or more inlets, e
bar-built estuary is formed. These estuaries are characteristically
very shallow, elongated, parallel to the coast, and frequently are fed
by more than one river system. As a result bar-built estuaries are
usually very complex hydrodynamically. A number of examples of bar-built
estuaries can be found along the southeast coast of the United States.
• Tectonic Process Estuaries. Tectonic estuaries exist as the result of
major tectonic events (movement of tectonic plates with associated
faulting or subsidence and coastal volcanic activity). San Francisco
Bay 1s a good example of an American estuary of this type.
Based on this topographic classification system, the vast majority of American
estuaries fall into the drowned river class. As a result, this system is not
functional for categorization of American estuaries. The classification system
described below is based on physical processes and is more useful. Further, the
parameters used in physical classification are directly applicable to estuarine
pollution analysis. Consequently, a physical parameter classification system will be
used for the water quality assessment approach to be presented.
6.1.3.2 Physical Process Classification
Physical process classification systems are generally based on the velocity
and salinity patterns in an estuary. Using these two parameters, estuaries can
be divided into three classes, each of which is of potential importance to planners
concerned with American coastal plain estuaries. The classes are: stratified,
partial 1y mixed, and well mixed.
The general behavior of salinity and velocity regimes in the three types
of estuaries has been described by a number of researchers (Glenne, 1967, Ouxbury,
1970, Pritchard, I960, and Dyer, 1973, among others) and is summarized below:
t Stratified (Salt Wedge) Estuary. In this type of estuary, large
fresh water inflows ride over a salt water layer which intrudes landward
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along the estuary bottom. Generally there is a continuous inland flow
1n the salt water layer as some of this salt water is entrained into the
upper seaward-moving fresh water flow. Tidal action is not sufficient
to mix the separate layers. Salinity (S) and Velocity (U) profiles and
a longitudinal schematic of this flow pattern are shown in Figure VI-1.
The Mississippi River Estuary is usually a salt wedge estuary.
• Well Mixed. In a well mixed estuary, the tidal flow (or the tidal
prism*) is much greater than the river outflow. Tidal mixing forces
create a vertically well mixed water column with flow reversing from ebb
to flood at all depths. Typical salinity and velocity profiles and a
longitudinal flow schematic for a well mixed estuary are shown in Figure
VI-2. As examples, the Delaware and Raritan River estuaries are both
normally wel1 mixed.
• Partially Mixed. Partially mixed estuaries lie between stratified
and well mixed in terms of flow and stratification characteristics.
Tide-related flows in such estuaries are substantially greater than
river flows. Significant salinity gradients exist as in fully strati-
fied estuaries, but are much less steep. While velocity at all depths
normally reverses with ebb and flood tide stages, it is possible for net
inland flow to be maintained in the lowest layers. Typical salinity and
velocity profiles and a longitudinal schematic flow diagram are shown in
Figure VI-3. There are many partially mixed coastal plain estuaries in
the United States; the lower James River Estuary is typical.
Classification primarily depends on the river discharge at the time of classi-
fication. Large river flows result in more stratified estuaries while low flow
conditions in the same estuaries can lead to full mixing. Thus the classification of
any single estuary is likely to vary from season to season as river flows vary. As
examples, many West Coast estuaries are partially mixed in winter when river flows
are high and are well mixed in summer when river flows are very low.
6.1.4 Pollutant Flow in an Estuary
The importance of understanding the basic types of estuarine systems may
be appreciated by briefly reviewing the general advective movements of a pollutant
released Into each of the three types of estuaries (summarized from Prltchard, 1960).
The associated spatial and temporal variability of pollutant levels have water system
management as well as water quality implications.
If a pollutant flow of density greater than the receiving water column is
introduced into a salt wedge type estuary, the pollutant tends to sink into the
•The tidal prism is that volume of water which enters an estuary during an
incoming (flood) tide and equals high tide estuarine volume minus low tide volume.
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SURFACE
BOTTOM
VELOCITY
0
SALINITY
corr«i*o*« to creti ttctiofit
FIGURE VI-1 TYPICAL MAIN CHANNEL SALINITY AND VELOCITY
FOR STRATIFIED ESTUARIES
bottom salt water layer and a portion can be advectively carried Inland toward
the head of the estuary. Frictlonally Induced vertical entrainment of the pollutant
into the surface water flow is slow, residence time of the pollutant is high, and the
time required to flush the pollutant from the estuary is also high. Some pollutants
which are sufficiently dense and stable remain in or settle to the bottom layer of
water, and are not transported out of a salt wedge estuary. Such constituents bu^d
up in the estuarine sediment layer.
Conversely, if a pollutant of lower density than the receiving water column is
introduced into a salt wedge estuary, it remains 1n the surface layer and is readily
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vELOcrrr
o
il
SALINITY
SURFACE
BOTTOM
C,0
•L»tt«ri correspond to crt«nn«l cross-icctions.
FIGURE VI-2 TYPICAL MAIN CHANNEL SALINITY AND VELOCITY
PROFILES FOR WELL NIXED ESTUARIES
flushed from the system. This is the case because seaward flows strongly predominate
in this layer.
At the opposite end of the estuary classification scale, a pollutant introduced
into a well mixed estuary is advectively transported in a manner independent of the
pollutant's density. Tidal forces cause turbulent vertical and lateral mixing. The
pollutant is carried back and forth with the oscillatory motion of the tides and is
slowly carried seaward with the net flow.
Pollutants introduced into partially mixed estuaries are dispersed in a manner
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JL --:
SAUNITY
ch«nn«l
FIGURE VI-3 TYPICAL MAIN CHANNEL SALINITY AND VELOCITY
PROFILES FOR PARTIALLY MIXED ESTUARIES
intermediate between the transport patterns exhibited in well mixed and stratified
estuaries. Pollutant transport is density dependent but nevertheless Involves
considerable vertical mixing. Eventual flushing of the pollutant from an estuary in
this case depends on the relative magnitudes of the net river outflow and the tidal
seawater inflow.
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6,1,5 Estuarine Complexity and Major Forces
Before outlining the complexities of estuarine systems, a brief review of
the nomenclature used in this chapter will be helpful. This information 1s shown in
Figure Vl-4. This figure shows top, side, and cross sectional views of an estuary
and indicates the basic estuarine dimensions. Additionally, the relationship between
tidal elevation (or tidal stage) and surface water velocity 1s shown 1n the upper
right quadrant of Figure Vl-4.
The complexities of estuarine hydrodynamics are evident from even the brief
qualitative descriptions presented above. Many variations in flow pattern and many
of the forces acting on an estuarine water column have beer omitted In order to
permit a verbal description of the normally predominant phenomena, and it should be
understood that the descriptions do not fully account for the complexities of estuarine
motion. Estuarine circulation may be conceived as a thre^-dimenslcnal flow field
with variations possible in salinity and velocity along the longitudinal, the vertical,
and the lateral axes. As a result of this complexity, and because an estuary 1s a
transitional zone between fresh water and marine systems, great variations in a
number of major water quality and physical parameters are possible. For example:
• £H. Typical concern pH is 7.8 to 8.4. Typically, rivers are slightly
acidic (pH<7). Thus the pH can change from slightly acidic to basic
across an estuary with resulting major changes in chemical characteris-
tics of dissolved and suspended constituents. pH variations from 6.8 to
9.25 across an estuary have been recorded (Perkins, 1974, p. 29).
• Salinity. Over the length of an estuary, salinity varies from fresh
water levels (typically less than 1 ppt) to oceanic salinity levels
(usually 32 ppt to 34 ppt)*. Moreover, salinity at any given location
in an estuary may vary substantially over one tidal cycle and over the
depth of the water column at any single point in time. Salinity varia-
tions are especially significant in estuarine calculations for a variety
of reasons. First, salinity distribution can be used to predict the
distribution of pollutants; second, salinity is a prime determinant of
water density; and third, variations in salinity affect other major
water quality parameters. For example, the saturated dissolved oxygen
concentration normally diminishes by 2 mg/1 as salinity increases from
0 to 35 ppt.
• River Flow. River flow is a major determinant of estuarine circulation
and flushing characteristics. Instantaneous flow rates for some western
rivers vary by orders of magnitude from winter high flow to summer low
flow periods (Goodwin, Q _a_K, 1970). These differences In river flow
result in major variations in estuarine water quality characteristics.
*ppt represents parts per thousand by mass. Sometimes the symbol °/oo is used.
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TOP VIEW
Lint
SIDE VIEW
V
Meon High Tide (MHT)
M«on Low Tidt (MLT)
-Low Tide Volumt
ESTUARY LENGTH __ \
CROSS SECTIONAL VIEW
-Tidol Prism
VMHT //-LowTidtVolumi
TIDE
HEIGHT
11* ••» — jfc.ii •-> '*•'-*> ".•*
FIGURE VM ESTUARINE DIMENSIONAL DEFINITION
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• Time. Estuarine water quality parameters vary over several separate
time scales. First, variations occur with each tidal cycle over a
period of hours. Second, tidal cycles vary in mean amplitude from
spring (maximum amplitude) to neap tides (minimum amplitude) every two
weeks. This affects water quality since flushing characteristics are in
part dependent on the tidal prism which is, in turn, dependent on tide
stage. Third, there are seasonal variations in river flow, temperature
and waste loadings.
The four factors just listed affecting the range and rate of variation of
estuarine parameters pose part of the difficulty in analyzing estuarine water
quality. In order to avoid large errors, both small time increments and small
spatial increments must be used. This, in turn, necessitates a large number of
individual calculations to fully analyze the variation of even a single parameter
over the estuary and sometimes requires the use of a computer model.
Further complicating the analytical process is the large number of independent
forces acting on the estuarine water column which should be considered. This group
includes (from Harleman and Lee, 1969):
• Ocean tides
• Local wind stresses
• Bottom roughness and bottom sediment types
• Channel geometry
• Coriolis forces*
• Nearby coastal features and coastal processes.
6.1.6 Methodology Summary
A variety of techniques are presented in this chapter to assess water quality in
estuaries. Table Vl-1 summarizes the techniques and indicates if they are applicable
to one-dimensional (well-mixed) or two-dimensional (vertically stratified) estuaries.
Many of the techniques can be applied to conventional or toxic pollutants. If decay
rates for toxic pollutants are needed. Chapter 2 can be used.
It is redundant to describe in detail each method at this point in the chapter,
because the procedures are presented later. As a general statement, however, most of
the methods for prediction of water quality apply to continuous, steady-state dis-
charges of pollutants. The discharges can be located anywhere within the estuary,
*Cor1olis forces reflect the effect of a rotating reference plane (the earth) on
particle motion. The net effect is to cause a water flow to drift to one side as 1t
moves down a channel. The same effect tends to laterally segregate fresh water
flows (moving from head to mouth) and salt water inflows '.moving from mouth to head)
in an estuary and in the northern hemisphere to create a counterclockwise flow
pattern with fresh water to the right (looking from the head of the estuary toward
the mouth) flowing toward the sea and salt water on the left flowing toward the head
of the estuary.
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TABLE VI-1
SUMMARY OF METHODOLOGY FOR ESTUARINE WATER QUALITY ASSESSMENT
Calculations
Methods
Type of Estuary Applicable*
Estuarine Classification
Flushing Time
Pollutant Distribution
Thermal Pollution
Turbidity
Sedimentation
• Hansen and Rattray
• Flow ratio
• Fraction of freshwater
• Modified tidal prisai
• Fraction of+freshwat«r (conservative
pollutants)
• Modified tidal prisai (conservative or
first-order decay pollutants)'
• Olspersion-advectlon equations
(conservative.first-order decay pollutants,
and dissolved oxygen)
• Pritchard's^Box Model (conservative
pollutants)*
• Initial dilution
• Pollutant concentration at completion
of initial dilution (conservative
pollutants/ DH. dissolved oxygen)
• Farfield distribution (Conservative and
first-order pollutants, tnd dissolved
oxygen)
• AT of water passing through condenser
• Maximum discharge temperature
• Thermal block, criterion
• Surface area criterion
• Surface temperature criterion
• Turbidity at completion of Initial
dilution
• Suspended solids at the completion of
initial dilution
• Light attenuation and turbidity
relationship
• Seechi disk and turbidity relationship
• Description of sediment movement
• Settling velocity determination
• Null zone calculations
one- or two-dimensional
one- or two-dimensional
one-dimensional
one-dimensional
one-dimensional
one-dimensional
one-dimensional
two-dimensional
one- or two-dimensional
one- or two-dimensional
two-dimensional
not applicable
not applicable
one- or two-dimensional
one- or two-dimensional
one- or two-dimensional
one- or two-dimensional
one- or two-dimensional
one- or two-dimensional
one- or two-dimensional
one- or two-dimensional
one- or two-dimensional
two-dimensional
•One c.mensiona! means a vertically well mixed system. A two dimensional estuary is vertically stratified.
These wethods apply to either conventional or toxic pollutants.
-152-
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from head to mouth. Multiple sources of pollutants can be analyzed by applying the
method of superposition, which is illustrated subsequently.
Although no single sequence of calculations must be followed to use the method-
ology. Figure VI-5 shows a suggested procedure. It 1s often useful to begin by
classifying the estuary by season to find out when it 1s well mixed and when it is
stratified. If the estuary is never well mixed, then the tools listed in Table VI-1
pertaining to one-dimensional estuaries should not be used.
Users are cautioned that the methods in this chapter are of a simplified
nature, and consequently there are errors inherent in the calculations. Additionally,
inappropriate data can produce further systematic errors. Data used should be
appropriate for the period being studied. For example, when salinity profiles are
needed, they should correspond to steady flow periods close to the critical period
being analyzed.
Even though the methods presented in this chapter are amenable to hand calcula-
tions, some methods are more difficult to apply than others. The fraction of fresh-
water and modified tidal prism methods are relatively easy to apply, while the
advective-dispersion equations offer greater computational challenge. Since the
advective-dispersion equations require numerous calculations, the user might find 1t
advantageous to program the methods on a hand calculator (e.g. TI-59 or HP-41C).
6.1.7 Present Water-Quality Assessment
The first step in the estuarine water quality assessment should be the evaluation
of existing water quality. Before an analysis of the impact of future waste load
changes is made, the planner should know whether or not current estuarine water
quality is acceptable, marginal, or substandard.
By far the best way to assess existing water quality is to measure it. The
planner should attempt to locate other agencies which might have already collected
acceptable samples and/or data. Candidate organizations include the United States
Geologic Survey, the U.S. Army Corps of Engineers, state water quality control and
monitoring agencies, and engineering and oceanographic departments of local colleges
and universities. If such data cannot be located, a data collection program could be
undertaken. If at all possible, high tide, and especially low tide in-situ measure-
ments and samples should be collected along the full length of the estuary's main
channel and in all significant side embavments. Analyses should then be made in an
appropriate laboratory facility. If funds for such data collection efforts are not
available, the use of a mathematical estimation of existing water quality is an
alternative. The methods presented in subsequent sections and applied to the exist-
ing discharges can be used. However, it should be remembered that actual data are
preferable to a mathematical estimate of existing water quality.
-153-
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U.11II'' Cl'V
£«y*ri«Mt uoMOvtnvt
TOIIC 1XX.HtMiTI H
• lIMtrt* «I'M«'
-^/£it^,
V Siuii'iu
IJUIXM1I*!
iMi UtIM SlTCMU'l
[ \f» «• fetfiilM A
V t4tC4*»fiMt )
\
P
C^lflCAv **|«t *••
^
' ^
•two*
FIGURE VI-5 SUGGESTED PROCEDURE TO PREDICT ESTUARJNE WATER QUALITY
-154-
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6.2 ESTUARINE CLASSIFICATION
6.2.1 General
Section 6.1.7 discussed making a first estimate of current estuarine water
quality. This section begins a calculation methodology designed to look at the
effect of future changes in waste loading patterns.
The goal of the classifications process presented below is to predict the
applicability of the hand calculations to be presented. The classification
process is normally the first step to be taken in the calculation procedure
since it reveals which techniques can be applied.
6.2.2 Classification Methodology
The classification system recommended for purposes of hand calculations is
based on salinity and velocity profiles within the estuary. As both of these
parameters vary seasonally and spatially for each estuary, their use will result in a
range of values rather than in one single classification number. The following
section will describe in detail the procedure for use of this system, and show
examples of the procedure.
6.2.3 Calculation Procedure
Hansen and Rattray (1966) developed an estuarine classification system using
both salinity stratification and water circulation patterns (based on water column
velocities). This procedure involves the calculation of values for two parameters at
various points along the main estuarine channel and the plotting of these intersec-
tions on the graph shown in Figure VI-6. Figure VI-7 shows plots made by Hansen and
Rattray for various estuaries at a single point in time. It should be noted that
each estuary is not represented by a point but by a line connecting the points
calculated for the mouth and head areas.
The area designations (e.g. la, Ib, 2b) on Figure VI-6 were related by Hansen
and Rattray to previously used classification titles (e.g. stratified, well mixed).
In general, area la corresponds to well mixed estuaries. Area Ib has the water
circulation pattern of a well mixed estuary yet shows increased stratification.
Areas 2 and 3 correspond to the "partially mixed" class of estuaries with area 3
showing more significant vertical circulation within the estuary. Designations 2a/b
and 3a/b, as was true of la and Ib, indicate increasing degrees of vertical strati-
fication. Type 3b includes fjord-type estuaries. Area 4 represents highly stratified
salt wedge estuaries.
-155-
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Increasing longitudinal circulation
to
A
10
FIGURE VI-6 ESTUARINE CIRCULATION-STRATIFICATION DIAGRAM
{Station code: M, Mississippi River mouth; C, Columbia
River estuary; J. James River estuary; MM, Narrows of
the Mersey estuary; OF, Strait of Juan de Fuca; S,
Silver Bay. Subscripts h and 1 refer to high and low
river discharge; numbers indicate distance (in miles)
from mouth of the James River estuary,
FIGURE VI-7 EXAMPLES OF ESTUARINE CLASSIFICATION PLOTS
(FROM HANSEN AND RATTRAY, 1966)
-156-
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6.2.A Stratification-Circulation Diagram Interpretation
The closer an estuary falls to the lower left hand corner of a stratification-
circulation diagram, the more vertically and laterally homogeneous It 1s. On the
stratification-circulation diagram (Figure VI-6), two types of zonal demarcation can
be seen. First are the diagonally striped divisions between adjacent estuarine
classifications used by Kansen and Rattray to indicate a transitional zone between
separate classifications. The second is a wide solid band arching around the lower
left corner of the diagram. Estuaries falling primarily Inside of this band (to the
lower left of the band) are those for which the one dimensional calculation methods
may be applied to obtain reasonably accurate results. If an estuary falls outside of
this band, the planner should use only the methods presented which pertain to strati-
fied estuaries, or use computer analyses. Within the band 1s a borderline of marginal
zone. Calculations for one-dimensional estuaries can be used for estuaries falling
principally within this zone, however the accuracy of the calculations will be
uncertain.
The two parameters used with the stratification-circulation diagram are described
below:
a. Stratification Parameter: The stratification parameter Is defined as:
AS
Stratification Parameter = »- (VI-1)
o
where
&S • time averaged difference in salinity between surface and bottom
water I
S « cross-section mean salinity, ppt.
The diagrammatic relationship of these values 1s shown in Figure VI-8.
b. Circulation Parameter: The circulation parameter is defined as:
Us
Circulation Parameter - — (VI-2)
uf
where
Us • net non-tidal sectional surface velocity (surface velocity
through the section averaged over a tidal cycle) measured in
ft/sec. See Figure VI-8 for a diagrammatic representation of
V
Uf. « mean fresh water velocity through the section, ft/sec.
In equation form:
-157-
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CIRCULATION PARA
Velocity *
4 ?
MtTtR
• v
ftmT Tfffc*
STRATIFICATION
Salinity *
y AS ^
1 K 7
N
f. . *• \ V
PARAMETER
-4
!
i
°f A
*6oth velocity and salinity values for these profiles are averaged over a tidal cycle
(net velocity and salinity) rather than being Instantaneous values. Of the two the
stratification parameter is much less sensitive to variations over a tidal cycle and
can be approximated by mean tide values for salinity. Surface velocity (Us) must be
averaged over a tidal cycle.
FIGURE VI-8 CIRCULATION AND STRATIFICATION PARAMETER DIAGRAM
where
R » fresh water (river) inflow rate, ft /sec
A ' cross-sectional area of the estuary through the point being
used to calculate the circulation pattern and stratification
parameters based on a mean tide surface elevation, ft .
If good cross-sectiona) area data are not available, cross-sectional profiles
can be approximated from the U.S. Geological Survey (USGS) coastal series topographical
maps, or, more recently, from NOAA National Ocean Survey charts. The circulation and
stratification parameters should be plotted for high and low river flow periods and
for stations near the mouth and head of the estuary. The area enclosed by these four
points should then include the full range of possible instantaneous estuary hydro-
dynamic characteristics. In interpreting the significance of this plotted atea, by.
far the greater weight should be given to the low river flow periods as these periods
are associated with the poorest pollutant flushing characteristics and the lowest
estuarine water quality. The interpretation of the circulation-stratification
diagrams will be explained more fully after an example of parameter computation.
-158-
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EXAMPLE VI-1
Calculation of Stratification and Circulation Parameters
The estuary for this example 1s the Stuart Estuary which is shown in Figure
VI-9. The estuary is 64,000 feet long, is located on the U.S. west coast, and is
fed by the Scott River. Two stations were selected for parameter calculation (A
and B) with station A located on the southern edge of the main channel 6,500 feet
from the estuary's mouth and station B in center channel 47,500 feet from the
mouth (16,500 feet from the head of the estuary).
Necessary salinity data were obtained from the coastal engineering department
of a nearby university. USGS gage data were available for river flow, and, as a
result of Its own dredging program, the local district office of the U.S. Corps
of Engineers could provide cross-sectional profiles 1n the approximate areas of
both stations. The cross-sections are labeled (1) and (2) on Figure VI-9. The
mean low tide depth reading on NOAA Coastal charts was used to verify Corps data.
Current meters were tied to buoy channel markers at A and B to provide velocity
data. The information obtained from these various sources is shown 1n graphical
form in Figure VI-10.
The calculations proceed as follows:
a. Stratification Parameter:
STATION
AS
bottom " surface
33 - 30 _
\\ e w .u«
31.5 - 24.2 _
27.8 ^
14.5 - 10.5 . „
TV K " "*
4 - 2A - 5B
3.25 ^°
SUMMER
WINTER
Circulation Parameter:
1. Calculate A.'s using cross sectional information on Figure VI-10:
I
Afl « (630 ft) (20 ft) (1/2) * (630 ft) (20 ft) + (1590 ft) (20 ft) (1/2) |
« 34,800 ft j
Ab - (2580 ft) (16 ft) (1/2) + (1720 ft) (16 ft) (1/2)
« 34,400 ft I
For most cross-sections it is advisable to use more finely divided j
segments than in the simple example above In order to reduce the error I
associated with this approximation. The method for this calculation, i
-159-
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OCEAN
FIGURE VI-9 THE STUART ESTUARY
! however, 1s Identical regardless of the number of regular segments
I used.
I 2. Calculate Uf's (with R and A1 values obtained from Figure VI-10):
! STATION
I
; A B
R
*1
550 ft3/sec ,_ , SB , iff2ft/-cr
3.48 x 10'ft"
1800 ft3/ sec . , .. j0-2ft,MC
3.48 x lO'ft^
550 ft3/sec . . ,0 10-3ft/
3.44 x l(Tft"
1800 ft3/sec . f „, 10-2f
3.44 x 10 ff
SUMMER
WINTER
3. Calculate i 's:
Uf
U$ values are read fro* Figure VI-10. The precise value for
U$ 1s the Integral of the velocity curve (area under "ebb"
velocity curve minus the area under the "flood" velocity curve)
divided by the elapsed time period (length of one tidal cycle).
If the elapsed time for flood flow at a station Is only slightly
below the elapsed time for ebb flow U may be approximated as
(L)ebb(max) ' uflood(max)
-160-
-------
S(%.) AT MEAN TIDE
Swrfi
Bottom
2000
J F MAMJUlASlO
N 0
MONTHS
• Monthly *»»rog< Dtsctwry* ftotw
Flood
U« 0
(FT/SEC)
WINTER ,
SUMMER
ebb
CROSS SECTION OF A
CROSS SECTION OF.
S 4300'
F
1
I FIGURE VI-10 STUART ESTUARY DATA FOR CLASSIFICATION CALCULATIONS '
STATION
0.15 ft/sec _ a F
1.58 x 10"2 ft/sec ^^
0.2 ft/sec , 3 9
5.17 x 10"2 ft/sec
0.3 ft/sec _ ,n „
1.60 x 10~* ft/sec
0.4 ft/sec _ , „
1 " /.OD
5.23 x 10"^ ft/sec
r i IMMTD
bUrflcR
UT UTTD
WINTcR
-161-
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10
10
"L
Uf
FIGURE VI-11 ESTUARINE CIRCULATION-STRATIFICATION DIAGRAM
The circulation-stratification plots for the Stuart Estuary are shown
in Figure Vl-11 with points A$ (station A, summer value), A^ (station A,
winter Value), B (station B, summer value), and B (station B, winter
value).
As indicated, this estuary shows a significant amount of vertical strati-
fication (especially at station A) but little evidence of major vertical
variations in net circulation.
END OF EXAMPLE VI-1
Turning to Figure VI-11, the Stratification-Circulation diagram for the Stuart
Estuary, it is apparent that this estuary lies principally within the marginal area.
Moreover, the low flow classification (line A -8 ) also lies primarily within
the marginal area. Thus, the planner for the Stuart Estuary should calculate an
additional criterion (see below) to help determine the suitability of using the
calculation procedures for well mixed estuaries. If the Stuart Estuary plotted more
predominately below the marginal zone, the planner could proceed with flushing time
calculations since the estuary would then meet the well mixed classification criteria.
It should be noted that the data for the Stuart Estuary produced a fairly
tight cluster of data points. As can be seen in Figure Vl-12, the salinity profiles
for one west coast estuary (the Alsea River and Estuary along the central Oregon
coast) vary considerably more from season to season than those of the Stuart Estuary.
-162-
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ALSEA RIVER
a
UJ
o
S(%.) AT HIGH TIDE
2515
i"P ?
WINTER-Ftb.9,1968
20
33 302S|t5lp5
'.,.'i'.jf l •;.>".:<*••, '- ; /«"l£«* '•:.
SPRING -Moy 9,1968
0
10
20
33 30 25 20
15
10 5
SUMMER-Aug. 9,1968
[
0 I 2 3 4 5 6 7 B 9 10 II 12 13 14
MILES UPSTREAM
FIGURE VI-12 ALSEA ESTUARY SEASONAL SALINITY
VARIATIONS (FROM GIGER, 1972)
This increased variation would produce a far greater spread in the summer and winter
AS/S parameter values.
6.2.5 Flow Ratio Calculation
If application of the above classification procedure results in an ambiguous
outcome regarding estuary classification, another criterion should b« applied.
This is the flow-ratio calculation. Schultz and Simmons (1957) first observed
the correlation between the flow ratio and estuary type. They defined the flow
ratio for an estuary as:
'•*
(VI-4)
-163-
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where
F « the flow ratio,
R « the river flow measured over one tidal cycle (measured in fir or
ft3)
P • the estuary tidal prism (in nr or ft ).
Thus the flow ratio compares the tidally induced flow in an estuary with
the river induced flow. Schultz and Simmons observed that when this ratio was
on the order of 1.0 or greater, the associated estuary was normally highly strati-
fied. Conversely, ratios of about 0.1 or less were usually associated with very
well-mixed estuaries and ratios in the range of 0.25 were associated with partially
mixed estuaries. A flow ratio of 0.2 or less warrants inclusion of the estuary in
the hand calculation process for one dimensional estuaries. Flow ratios in the range
0.2 to 0.3 should be considered marginal. Estuaries with flow ratios greater than
0.3 should not be included in the one-dimensional category.
EXAMPLE VI-2
Calculation of the Flow Ratio for an Estuary i
i
I
The following data appply to the Patuxent Estuary, Maryland: •
R, total river discharge over one tidal cycle » 1.42 x 10 m (low flow)
3.58 x 106m3 (high flow) \
P, estuary tidal prism volume « 3,51 x 10 m3 I
The flow ratios for the Patuxent Estuary at low and high river flows are thus: I
1.42 x 105m3
3.51 x 10V
0.004
3.56 x 106m3
3.51 x IflV
« 0.10
Values of FjCO.l are usually associated with well mixed estuaries. The F values
calculated above indicate a well mixed estuary. However, historical data indicate
the Patuxent River Estuary is partially stratified at moderate and high river
flows.
END OF EXAMPLE VI-2
When tidal data are not available, NOAA coastal charts may be used to estimate
the difference between mean high tide and mean low tide estuary surface areas. As
-164-
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/-MHT Surface*
Mean Tide—y /
\ / ^MLT Surface*
TIDAL
HEIGHT"*
P, (section 1) « section Length * tidal height K (™T width » NIT ,1dth j
P estuary « £p for all sections
1
• widths obtained from NOAA tide table for the area
"Available from local Coast Guard Stations
FIGURE VI-13 ESTUARY CROSS-SECTION FOR TIDAL PRISM CALCULATIONS
can be seen 1n the cross-section diagram in Figure VI-13 the estuarlne tidal prism
can be approximated by averaging the MLT and MHT surface areas and multiplying this
averaged area by the local tidal height. Mean tidal heights (approximately 1 week
before or after spring tides) should be used for this calculation. As indicated in
Figure VI-13, the estuary can be conveniently subdivided into longitudinal sections
for this averaging process, to reduce the resulting error. Table VI-2 lists tidal
prisms estimated for many U.S. estuaries. These values may be used as an alternate
to tidal prism calculations.
6.3 FLUSHING TIME CALCULATIONS
6.3.1 General
Flushing time is a measure of the time required to transport a conservative
pollutant from some specified location within the estuary (usually, but not always,
the head) to the mouth of the estuary. Processes such as pollutant decay or sedimen-
tation which can alter the pollutant's distribution within the estuary are not
considered in the concept of flushing time.
It was mentioned earlier in this chapter that the net non-tidal flow in an
-16S-
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TABLE VI-2
TIDAL PRISMS FOR SOME U.S. ESTUARIES
(FROM O'BRIEN, 1969 AND JOHNSON, 1973)
Estuary
Plum Island Sound, Mass.
Fire Island Inlet, N.Y.
Jones Inlet, N.Y.
Beach Haven Inlet {Little
Egg Bay), N.J.
Little Egg Inlet (Great
Bay), N.J.
Brigantine Inlet, N.J.
Absecon Inlet (before
jetties), N.J.
Great Egg Harbor Entr, N.J.
Townsend Inlet, N.J.
Hereford Inlet, N.J.
Chincoteague Inlet, Va.
Oregon Inlet, N.C.
Ocracoke Inlet, N.C.
Drum Inlet, N.C.
Beaufort Inlet, N.C.
Carolina Beach Inlet, N.C.
Stono Inlet, S.C.
North Edisto River, S.C.
St. Helena Sound, S.C.
Port Royal Sound, S.C.
Cali bog tie Sound, S.C.
Wassaw Sound, Ga.
Ossabaw Sound, Ga.
Sapelo Sound, Ga.
St. Catherines Sound, Ga.
Doboy Sound, Ga.
Altamaha Sound, Ga.
Hampton River, Ga.
St. Simon Sound, Ga.
St. Andrew Sound, Ga.
Ft. George Inlet, Fla.
Old St. Augustine Inlet,
Fla.
Coast
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Tidal Prism (ft3)
1.32 x 109
2.18 x 109
1.50 x 109
1.51 x 109
1.72 x 109
5.23 x 108
1.65 x 109
2.00 x 109
5.56 x 108
1.19 x 109
1.56 x 109
3.98 x 109
5.22 x 109
5.82 x 108
5.0 x 109
5.25 x 108
2.86 x 109
4.58 x 109
1.53 x 1010
1.46 x 1010
3.61 x 109
8.2 x 109
6.81 x 109
7.36 x 109
6.94 x 109
4.04 x 109
2.91 x 109
1.01 x 109
6.54 x 109
9.86 x 109
3.11 x 108
1.31 x 109
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TABLE VI-2 (Cont.)
Estuary
Ponce de Leon, Fla.
(before jetties)
Delaware Bay Entrance
Fire Island Inlet, N.Y.
East Rockaway Inlet, N.Y.
Rockaway Inlet, N.Y.
Masonboro Inlet, N.C.
St. Lucie Inlet, Fla.
Nantucket Inlet, Mass.
Shinnecock Inlet, N.Y.
Moriches Inlet, N.Y.
Shark River Inlet, N.J.
Manasguan Inlet, N.J.
Barnegat Inlet, N.J.
Absecon Inlet, N.J.
Cold Springs Harbor
(Cape May), N.J.
Indian River Inlet, Del.
Winyah Bay, S.C.
Charleston, S.C.
Savannah River (Tybee
Roads), Ga.
St. Marys (Fernandina
Harbor), Fla.
St. Johns River, Fla.
Fort Pierce Inlet, Fla.
Lake Worth Inlet, Fla.
Port Everglades, Fla.
Bakers Haulover, Fla.
Captiva Pass, Fla.
Boca Grande Pass, Fla.
Gasparilla Pass, Fla.
Stump Pass, Fla.
Midnight Pass, Fla.
Big Sarasota Pass, Fla.
New Pass, Fla.
Longboat Pass, Fla.
Coast
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Tidal Prism (ft3)
5.74 x 106
1.25 x 1011
1.86 x 109
7.6 x 108
3.7 x 109
8.55 x 108
5.94 x 108
4.32 x 108
2.19 x 108
1.57 x 10-J
8.46 x 108
1.48 x 108
1.75 x 108
6.25 x 108
1.48 x 109
6.50 x 108
5.25 x 108
3.02 x 109
5.75 x 109
3.1 x 109
4.77 x 109
1.73 x 109
5.81 x 108
9.0 x 108
3.0 x 108
3.6 x 108
1.90 x 109
1.26 x 1010
4.7 x 108
3.61 x 108
2.61 x 108
7.6 x TO8
4.00 x 108
4.90 x 108
-167-
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TABLE VI-2 (Cont.)
Estuary
Sarasota Pass, FT a.
Pass-a-Grille
Johns Pass, Fla.
Little (Clear-water)
Pass, Fla.
Big (Ounedin) Pass, Fla.
East (Destin) Pass, Fla.
Pensacola Bay Entr., Fla.
Perdido Pass, Ala.
Mobile Bay Entr., Ala.
Barataria Pass, La.
Caminada Pass, La.
Calcasieu Pass, La.
San Luis Pass, Tex.
Venice Inlet, Fla.
Galveston Entr. , Tex.
Aransas Pass, Tex.
Grays Harbor, Wash.
Willapa, Wash.
Columbia River, Wash. -Ore.
Necanicum River, Ore.
Nehalem Bay, Ore.
Tillamook Bay, Ore.
Netarts Bay, Ore.
Sane Lake, Ore.
Nestucca River, Ore.
Salmon River, Ore.
Devils Lake, Ore.
Siletz Bay, Ore.
Yaquina Bay, Ore.
Alsea Estuary, Ore.
Siuslaw River, Ore.
Umpqua, Ore.
Coos Bay, Ore.
Caquil le River, Ore .
Floras Lake, Ore .
Coast
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Tidal Prism (ft3)
8.10 x 108
1.42 x 109
5.03 x 108
6.8 x 108
3.76 x 108
1.62 x 109
9.45 x 109
5.84 x 108
2.0 x 1010
2.55 x 109
6.34 x 108
2.97 x 109
5.84 x 108
8.5 x 10
1.59x 1010
1.76 x TO9
1.3 x 1010
1.3 x 1010
2.9 x 1010
4.4 x 107
4.3 x 10B
2.5 x 109
5.4 x 10fl
1.1 x 108
2.6 x 108
4.3 x 107
1.1 x 108
3.5 x 108
8.4 x 108
5.1 x 108
2.8 x 108
1.2 x 109
1.9 x 109
1.3 x 108
6.8 x 107
-168-
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TABLE VI-2 (Cont.)
Estuary
Rogue River, Ore.
Chetco River, Ore.
Smith River, Ca.
Lake Earl, Ca.
Freshwater Lagoon, Ca.
Stove Lagoon, Ca.
Big Lagoon, Ca .
Mad River, Calif.
Humbolt Bay, Calif.
Eel River, Calif.
Russian River, Calif.
Bodega Bay, Calif.
Tomales Bay, Calif.
Abbotts Lagoon, Calif.
Drakes Bay, Calif.
Bolinas Lagoon, Calif.
San Francisco Bay, Calif.
Santa Cruz Harbor, Calif.
Moss Landing, Calif.
Morro Bay, Calif.
Marina Del Rey, Calif.
Alamitos Bay, Calif.
Newport Bay, Cal if.
Camp Pendleton, Calif.
Aqua Hedionda, Calif.
Mission Bay, Cal if.
San Diego Bay, Calif.
Coast
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Tidal Prism (ft3)
1.2
2.9
9.5
5.1
4.7
1.2
3.1
2.4
2.4
3.1
6.3
1.0
1.0
3.5
2.7
1.0
5.2
4.3
9.4
8.7
6.9
6.9
2.1
1.1
4.9
3.3
1.8
xlO8
x 107
xlO7
xlO8
x 107
xlO8
x 108
x 107
x 109
x 108
x 107
x 108
x 109
x 107
x 108
x 108
xlO10
xlO6
xlO7
xlO7
xlO7
xlO7
xlO8
xlO7
x 107
x 108
x 109
estuary is usually seaward* and Is dependent on the river discharge. The non
tidal flow is one of the driving forces behind estuarine flushing. In the absence of
this advective displacement, tidal oscillation and wind stresses still operate to
*While net flow is always seaward for the estuaries being considered here, it
is possible to have a net upstream flow in individual embayments of an estuary.
While this occurrence Is rare in the United States, an example of such a situation
is the South Bay of San Francisco Bay where freshwater Inflows are so small that
surface evaporation exceeds freshwater inflow. Thus, net flow is upstream during
most of the year.
-169-
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disperse and flush pollutants. However, the advective component of flushing can be
extremely important. Consider Tomales Bay, California as an example. This small,
elongated bay has essentially no fresh water inflow. As a result there is no advective
seaward motion and Pollutant removal is dependent upon dispersion and diffusion
processes. The flushing time for the bay is approximately 140 days (Johnson, et al. ,
1961). This can be compared with the Alsea Estuary In Oregon having a flushing time
of approximately 8 days, with the much larger St. Croix Estuary in Nova Scotia
having a flushing time of approximately B days (Ketchur and Keen, 1951), or with the
very large Hudson River Estuary with a short flow flushing time of approximately 10.5
Cays (Ketchum, 1950).
6.3.2 Procedure
Flushing times for a given estuary vary over the course of a year as river
discharge varies. The critical time is the low river flow period since this period
corresponds with the minimum flushing rates. The planner might also want to calcu-
late the best flushing characteristics (high river flow) for an estuary. In addition
to providing a more complete picture of the estuarine system, knowledge of the full
range of annual flushing variations can be useful in evaluating the Impact of seasonal
discharges (e.g., fall and winter cannery operation in an estuary with a character-
istic summer fresh water low flow). Further, storm sewer runoff normally coincides
with these best flushing conditions (high flow) and not with the low flow, or poorest
flushing conditions. Thus analysis of storm runoff is often better suited for high
flow flushing conditions. However, the low flow calculation should be considered for
use in primary planning purposes.
There are several ways of calculating flushing time. Two methods are presented
here: the fraction of freshwater method and the modified tidal prism method.
6.3.3 Fraction of Fresh Water Method
The flushing time of a pollutant, as determined by the fraction of freshwater
method is:
where
V^ « volume of freshwater in the estuary
T^ - flushing time of a pollutant which enters the head of the estuary
with the river flow.
Equation VI-5 is equivalent to the following concept of flushing time which is
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more intuitively meaningful:
T, - " (VI-6)
f M
where
M • total mass of conservative pollutant contained in the estuary
M - rate of pollutant entry into the head of the estuary with the river
water.
Since the volume of freshwater in the estuary is the product of the fraction of
freshwater (f) and the total volume of water (V), Equation VI-5 becomes:
Tf - ™ (VI-7)
If the estuary is divided into segments the flushing time becomes:
fiV1
Tf " l V~ (VI-8)
1
Equation VI-8 is more general and accurate than the three previous expressions
because both f^ (the fraction of freshwater in the ith segment) and R^ (the fresh-
water discharge through the ith segment) can vary over distance within the estuary.
Note that the flushing time of a pollutant discharged from some location other than
the head of the estuary can be computed by summing contributions over the segments
seaward of the discharge.
A limitation of the fraction of freshwater method is that it assumes uniform
salinity throughout each segment. A second limitation is that it assumes during
each tidal cycle a volume of water equal to the river discharge moves into a given
estuarine segment fron the adjacent upstream segment, and that an equal volume of the
water originally in the segment moves on to the adjacent one downstream. Once this
exchange has taken place, the water within each segment is assumed to be instantane-
ously and completely mixed and to again become a homogeneous water mass. Proper
selection of estuarine segments can reduce these errors.
6.3.4 Calculation of Flushing Time by Fraction of Freshwater Method
This is a six step procedure:
1. Graph the estuarine salinity profiles.
2. Divide the estuary into segments. There is no minimum or maximum number of
segments required, nor must all segments be of the same length. The divisions
should be selected so that mean segment salinity is relatively constant over
-171-
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the full length of the segment. Thus, stretches of steep salinity gradient
will have short segments and stretches where salinity remains constant may
have very long segments. Example VI-3 provides an illustration.
Calculate each segment's fraction of fresh water by:
f1
where
f^ « fraction of fresh water for seqment "I"
S • salinity of local sea water*. °/oo
S, • mean salinity for segment "1", °/oo.
4. Calculate the quantity of fresh water 1n each segment by:
Wf - f1 x V1 (VI-10)
where
W1 « quantity of fresh water 1n segment "1"
Vj . total volume of segment "1" at MIL.
5. Calculate the exchange time (flushing time) for each segment by:
where
T, » segment flushing time, 1n tidal cycles
R » river discharge over one tidal cycle.
6. Calculate the entire estuary flushing time by sumroinq the exchange times for
the individual segments:
I T (VI-12)
where
T^ « estuary flushing time, in tidal cycles
n - number of segments.
Table VI-3 shows a suggested method for calculating flushing time by the fraction of
freshwater method.
*Sea surface salinity along U.S. shores vary spatially. Neuman and Pierson (1966)
mapped Pacific mean coastal surface salinities as varying from 32.4 °/oo at Puget
Sound to 33.9 °/oo at the U.S. -Mexico border; Atlantic mean coastal surface
salinities as varying from 32.5 °/oo in Maine to 36.2 °/oo at the southern
extreme of Florida; and Gulf coast salinities as varying between 36.2 °/oo and
36.4 °/oo. Surface coastal salinities in Long Island Sound (Hardy, 1972) and off
Long Island south coast (Hydroscience, 1974) vary between 26.5 and 28.5 °/oo.
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TABLE VI-3
SAMPLE CALCULATION TABLE FOR CALCULATION OF FLUSHING TIME
BY SEGMENTED FRACTSON OF FRESHWATER METHOD
Segment
Number
Mean
Segment
Salinity
S^ppt)
Mean
Segment
Length
(«)
Mean Segment
Cross-sectional
Area (m'j
Segment Mean
Tide Volume
V1 (m*)
Fraction of
River Water
. Ss-Sl
ft Ss
River Water
Volume
W « f xV
"l 11
On3)
n
EV
1=1 '
Segment
Flushing Time
T1 - Wj/R
(tidal cycles)
I/I
u>
Q.
-173-
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------------------- EXAMPLE VI-3
Flushing Time Calculation by Fraction of Fresh Water Method
This example pertains to the Patuxent Estuary. This estuary has no major
side embayments, and the Patuxent River is by far Its largest source of fresh
water. This estuary therefore lends itself well to analysis by the segmented
fraction of fresh water method.
Salinity profiles for July 19, 1978 are used to find segment salinity
values. Chesapeake Bay water at the mouth of the Patuxent Estuary had a salinity
of 10.7 ppt (Sj). The Patuxent River discharge over the duration of one tidal
cycle is:
R - (12 m3/sec) (12.4 hr/tidal cycle) (3600 sec/hr)
« 5.36 x I0*m /tidal cycle
A segmentation scheme based on the principles laid out above is used to divide the
estuary into eight segments; their measured characteristics are shown Table VI-4.
The segmentation is shown graphically on the estuary salinity profile (Figure
VI-14).
The next step is to find the fraction of fresh water for each segment.
For segment 1:
j where
j f, « fraction of fresh water, segment 1
: S$ « salinity of local seawater
S » measured mean salinity for segment 1
The calculation is reported in Table IV-4 for segments 2 through 8.
The volume of fresh water (river water) in each segment is next found
' using the formula: j
Wi ' fi * Vi
i x vi j
For segment 1: ;
H, • f, x V, - 0.93 (0.79 x 107m3)
A -J I
« 7.35 x 10V i
The flushing time for each segment is next calculated by:
T. . w./R ;
-174-
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TABLE VI-4
PATUXENT ESTUARY SEGM£NT CHARACTERISTICS FOR
FLUSHING TIME CALCULATIONS
I
I
Segment Mean Segment Salinity Segment Length
Number S4, ppt meters
Mean Tide
Mean Segment Segment Volume I
Cross-Sectional Area V^ . ;
meter2
meters
8
7
6
5
4
3
2
1
10.3
9.5
8.7
7.6
5.8
3.3
1.8
0.8
10.400
10.400
6.100
6.100
5,800
5,000
4.650
4.650
16,000
12,500
11,400
7.500
4,300
3,100
2,200
1,700
16.6xl07
13.0xl07 j
6.95xl07 j
4.58x107 I
•
2.49xl07 |
l.SSxlO7 !
1.02xl07 !
0.79xl07 :
10 20 30 40 - - i i
DISTANCE FROM HEAD OF ESTUARY (Km) CHESAPEAKE BAY /
50 /i
FIGURE VI-14 PATUXENT ESTUARY SALINITY PROFILE AND SEGMENTATION SCHEME:
USED IN FLUSHING TIME CALCULATIONS,
-175-
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I For segment 1:
1 Tj • Wj/R • 7.35 x 106m3/(5.36 x I05m3/t1dal cycle)
j - 13.7 tidal cycles
I Fraction of freshwater, river water volume and flushing time values for the
j eight segments are compiled in Table VI-5.
The final step is to determine the flushing time for the estuary. In
! this case:
1 8
! Tf " Z T1 "
I f 1-1 1
1 11.4 * 27.2 + 24.6 + 24.8 + 21.5 + 20.0 + 15.8 + 13.7
i « 159 tidal cycles, or 2.74 months
6.3.5 Branched Estuaries and the Fraction of Freshwater Method
Branched estuaries, where more than one source of freshwater contributes
to the salinity distribution pattern, are common. The fraction of freshwater
method can be directly applied to estuaries of this description. Consider the
estuary shown in Figure VI-15, having two major sources of freshwater (River 1,
R,; and River 2, R,). The flushing time for pollutants entering the estuary
with river flow R- is:
Tf (R,) " T, + T2 + T, + T, + Ts + T» »
fiV, fjV2 f.,V, fvVk f$V5 f.V.
R2 R2 R2 R2 Ri+R2 Ri+Rj
For the pollutants entering with R., the flushing time is:
T (RlJ. V* t fbVb , Vc , f»V» , f^
f R1 RI RI Ri+R2 Rt*R2
The flushing time computations are similar in concept for the case of a single
freshwater source, modified to account for a flow rate of R, + R. in segments 5
and 6.
6.3.6 Modified Tidal Prism Method
This method divides an estuary into segments whose lengths are defined by
the maximum excursion path of a water particle during a tidal cycle. Within each
segment the tidal prism is compared to the total segment volume as a measure of the
-176-
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TABLE VI-5
FLUSHING TIME FOR PATUXENT ESTUARY
Segment Nunber
8
;
6
5
4
3
2
V
ffe*n Segment
Salinity
Sj. ppt
10. J
9.5
8.7
7.6
5.8
3.3
1.8
0.8
Segment Length
meterj
10.400
10,400
6.100
6.100
5.800
5.000
4.650
4.650
Mean Segment
Cross-Sectional Area
peter1
16.000
12.500
11.400
7.500
4.300
3.100
2.200
1.700
Segment Mean
Tide Volume
VI
meter'
16.6x10'
13.0x10'
6.95x10'
4.58x10'
2.49x10'
1.55x10'
1.02x10'
0.79x10'
fraction of
River Water
. Ss-Si
ft " ~V^
(5, -S10.7)
0.037
0.112
0.19
0.29
0.46
0.69
0.83
0.93
River Water
Volume
W, • f, x V.
Vtirs')1
6.14x10*
14.6x10'
13.2x10*
13.3x10*
11.5x10*
10.7x10*
8.47x10*
7.35x10*
Segment
flush Time
7« * "i/B
tidal cycles
11. <
27.2
24.6
24.8
21.5
20.0
15.8
13.7
•In this numbering scheme segment I is the most upstre** segment.
Sow • 159 tidal cycles
or 2.74 months
END OF EXAMPLE VI-3
-177-
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FIGURE VI-15 HYPOTHETICAL TWO-BRANCHED ESTUARY
flushing potential of that segment per tidal cycle (Dyer, 1973). The method assumes
complete mixing of the incoming tidal prism waters with the low tide vo limes within
each segment. Best results have been obtained In estuaries when the number of seg-
ments 1s large (i.e. when river flow is very low) and when estuarine cross-sectional
area increases fairly quickly downstream (Dyer, 1973).
The modified tidal prism method does not require knowledge of the salinity
distribution. It provides some concept of mean segment velocities since each
segment length is tied to particle excursion length over one tidal cycle. A dis-
advantage of the method is that in order to predict the flushing time of a pollutant
discharged midway down the estuary, the method still has to be applied to the entire
estuary.
The modified tidal prism method is a four-step methodology. The steps are:
1. Segment the estuary. For this method an estuary must be segmented so that
each segment length reflects the excursion distance a particle can travel
during one tidal cycle. The innermost section must then have a tidal prism
volume completely supplied by river flow. Thus:
where
P
tidal prism (intertidal volume) of segment "0"
river discharge over one tidal cycle.
-178-
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The low tide volume in this section (VQ) 1s that water volume
occupying the space under the intertidal volume PQ (which has Just
been defined as being equal to R). The seaward limit of the next seaward
segment is placed such that its low tide volume (Vj) is defined by:
Vj • PO+ V0 (V
P, is then that intertidal volume which, at high tide, resides
above V . Successive segments are defined in an identical manner to
this segment so that:
V1 • Pi-l * Vi-l (VI-14)
Thus each segment contains, at high tide, the volume of water contained
in the next seaward section at low tide.
2. Calculate the exchange ratio (r) by:
Thus the exchange ratio for a segment is a measure of a portion of
water associated with that segment which is exchanged with adjacent segments
during each tidal cycle.
3. "Calculate segment flushing time by:
r (VI-16)
ri
where
T. « flushing time for segment "i", measured in tidal cycles.
4. Calculate total estuarine flushing time by summing the individual segment
flushing times:
where
Tf « total estuary flushing time
n « number of segments.
Table VI-6 shows a suggested method for calculating flushing time by the modified
tidal prism method.
-179-
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TABLE VI-6
SAMPLE CALCULATION TABLE FOR ESTUARINE FLUSHING TIME BY
THE MODIFIED HDAL PR ISM HETHOO
Seoroent
Number
Segment Dimensions
Starting
Distance
Above Mouth
f»)
Ending
Distance
Above Mouth
(m)
Distance
of Center
Above Mouth
(m)
Segment
Length
(m)
Subtidal
Water
Volume, V)
(i-M
Jntertfdal
Mater Volume
'I',
Segment
Exchange
Ratio
ri
n
£ T' '
Segment
Flushing
Time, Tj
(Tidal Cycles)
>>
8
-180-
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EXAMPLE VI-4
Estuary Mushing Time Calculation by the •
Modified Tidal Prism Method
I - I
i i
J The Fox Mill Run Estuary, Virginia, was selected for this example. During j
I low flow conditions, the discharge of Fox Mill Run has been measured at 0.031 m3/sec.l
J R » river discharge over one tidal cycle J
I - 0.031 m3/sec x 12.4 hrs/tidal cycle x 3600 sec/hr I
I • 1384 m3/tidal cycle j
j The estuary flushing time is found in four steps: j
j 1. Segmentation
j From bathymetric maps and tide gage data, cumulative upstream
volume was plotted for several positions along the estuary (see Figure !
! VI-16). I
Since: !
P0 '
Reading across the graph from "a" to the intertidal volume curve, then down !
the subtldal volume curve and across to -b": '
V0 » 490 m3 !
I
The known cumulative upstream water volume also establishes the downstream !
segment boundary. Reading downward from the subtidal volume curve to "c", a'
VQ of 490 m3 corresponds to an upstream distance of 2.700 meters for I
the segment 0 lower boundary. j
The low tide water volume tor the next segment can be found by the j
equation:
vi ' "o * vo i
or i
Vj » 1384 * 490 • 1874 m3 j
Since the graphs of Figure VI-16 are cumulative curves, it is necessary, j
when entering a V^ value in order to determine a P. value, to sum
the upstream V^'s. For V, the cumulative upstream low-tide volume !
1s: I
VQ * Vj • 490 + 1874 - 2364 m3 )
Entering the graph where the subtidal volume is equal to 2,364 m3 j
(across from "d"), we can move upward to read the corresponding cumulative I
Intertidal volume "e" on the vertical scale, and downward to read the i
-181-
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1000-,
mt»rtidal volume
10 15 ' 20 ' 25 " 30
Distance above mouth (100's of maters)
FIGURE VI-16 CUMULATIVE UPSTREAM WATER VOLUME,
Fox MILL RUN ESTUARY
-182-
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I downstream boundary of segment 1 at "f" on the horizontal scale. The
| cumulative upstream intertldal volume Is 5900 m .
j Since:
j 5900 m3 - PQ + Pj
.3
I PL - 5900 - 1384 - 4516 m"
I For segment 2:
I V. « P. + V. » 1874 + 4516 • 6390 m3
| To find P., it is necessary to enter the graph at a cumulative
| subtidal volume of:
I Vn + V. + V, • 490 + 1874 + 6390 - 8759 m3 (across from "g")
i U 1 t -5
I This yields a cumulative intertidal volume of 14,000 m (across from
j "h") and a downstream segment boundary of 1,650m "1".
j The tidal prism of Segment 2 is found by:
j 14000 • PO + Pj + P2
I °r
| P2 + 14000 - 1384 - 4516 * 8100 m3
I The procedure is identical for Segment 3. For this final segment:
j V3 • 14,490 m3
| P3 • 36,000 m3
j Dimensions and volumes of the four segments established by this procedure
are compiled in Table VI-7.
2. The exchange ratio for segment 0 is found by:
! r - Pn . 1384 m3
I ° P0*V0 1384 m3 + 490 m3
( Exchange ratios are calculated similarly for the other three segments.
i 3. Flushing time for each segment "i" is given by:
so
Exchange ratios and flushing times for the four segments are shown
in Table IV-7.
4. Flushing time for the whole estuary is found by:
-183-
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1
i DATA ANJ FLUSHING
4
1
TABLE VI-7
TIME CALCULATIONS FOR FOX MILL RUN ESTUARY
; Segment Dimensions Mater
1
Starts at this Stops at this
1 Segment Distance Above Distance Above
' Number Mouth-meters Mouth -meters
j 0 3.200 2.700
1 2.700 2.240
2 2.240 1.650
3 1.650 180
1
i
I or
' T - 1.35 + 1.41 * 1.79
1 • 5.96 tidal cycles
| • 73.9 hours
j « 3.1 days
i
Volume it Jntertldal Exchange
Center Point Segment Low Tide Volume Ratio for
Distance Above Length Vj Pj Segment 1
Mouth-meters meters meterj3 meters3 r(
2.950 500 490 1.384 0.74
2.470 460 1.874 4.516 0.71
1.945 590 6.390 8.100 0.56
915 1.470 14.490 36.000 0.71
Hushing
Time for
Segment 1
1.35
1.41
1.79
1.41
IT • 5.96 tidal cycles
+ 1.41
6.4 FAR FIELD APPROACH TO POLLUTANT DISTRIBUTION IN ESTUARIES
6.4.1 Introduction
Analysis of pollutant distribution 1n estuaries can be accomplished in a
number of ways. In particular, two approaches, called the far field and near
field approaches, are presented here (Sections 6.4 and 6.5, respectively). As
operationally defined in this document, the far Held approach Ignores buoyancy
and momentum effects of the wastewater as it 1s discharged into the estuary.
The pollutant Is assumed to be instantaneously distributed over the entire cross-
section of the estuary (in the case of a well-mixed estuary) or to be distributed
over a lesser portion of the estuary in the case of a two-dimensional analysis.
Whether or not these assumptions are realistic depends on a variety of factors,
including the rapidity of mixing compared to the kinetics of the process being
analyzed (e.g. compared to dissolved oxygen depletion rates). It should be noted
that far field analysis (either one- or two-dimensional) can be used even 1f actual
mixing is less than assumed by the method. However, the predicted pollutant concen-
trations will be lower than the actual concentrations.
-184-
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Near field analysis considers the buoyancy and momentum of the wastewater
as it is discharged into the receiving water. Pollutant distribution can be calcu-
lated on a smaller spatial scale, and assumptions such as "complete mixing" or
"partial mixing" do not have to be made. The actual amount of mixing which occurs is
predicted as an integral part of the method itself. This is a great advantage in
analyzing compliance with water quality standards which are frequently specified in
terms of a maximum allowable pollutant concentration in the receiving water at the
completion of initial dilution. (Initial dilution will be defined later in Section
6.5.2.)
The following far field approaches for predicting pollutant distribution
are presented in this chapter:
• Fraction of freshwater method
• Modified tidal prism method
t Oispersion-advection equations
• Pritchard's Box Model.
The near field analysis uses tabulated results from an initial dilution model called
MERGE. At the completion of initial dilution predictions can be made for the following:
• Pollutant concentrations
• pH levels
• Dissolved oxygen concentrations.
The near field pollutant distribution results are then used as input to an analytical
technique for predicting pollutant decay or dissolved oxygen levels subsequent to
initial dilution. The remainder of Section 6.4 will discuss those methods applicable
to the far field approach.
6.4.2 Continuous Flow of Conservative Pollutants
The concentration of a conservative pollutant entering an estuary in a continuous
flow varies as a function of the entry point location. It is convenient to separate
pollutants entering an estuary at the head of the estuary (with the river discharge)
from those entering along the estuary's sides. The two impacts will then be addressed
separately.
6.4.2.1 River Discharges of Pollutants
The length of time required to flush a pollutant from an estuary after it
is introduced with the river discharge has already been calculated, and is the
estuarine flushing time. Now consider a conservative pollutant continuously dis-
charged into a river upstream of the estuary. As pollutant flows into the estuary,
it begins to disperse and move toward the mouth of the estuary with the net flow.
If, for example, the estuary flushing time is 10 tidal cycles, then 10 tidal cycles
following its initial flow into the estuary, some of the pollutant is flushed out to
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the ocean. Eventually, a steady-state condition 1s reached 1n which a certain amount
of pollutant enters the estuary, and the same mount 1s flushed out of the estuary
during each tidal cycle. The amount of this pollutant which resides in the estuary
at steady-state 1s a function of the flushing time. From the definition of flushing
time, the amount of fresh water (river water) in the estuary may be calculated by:
Tf R
(Vl-18)
where
We • Quantity of freshwater in the estuary
Tf • estuary flushing time
R « river discharge over one tidal cycle.
Using the same approach, the quantity of freshwater in any segment of the estuary is
given by:
T1R
(VI-19)
where
V
Ti -
quantity of freshwater in the i segment of the estuary
flushing time for the i segment calculated by the fraction
of freshwater method.
If a conservative pollutant enters an estuary with the river flow, it can be assumed
that its steady-state distribution will be identical to that of the river water
itself. Thus:
(VI-20)
and
(VI-21)
Cr
Ci
where
M^ « quantity of pollutant in estuary segment "i"
concentration of pollutant in the river inflow
concentration of pollutant in estuary segment "1" assuming
all of pollutant "i" enters the estuary with the river discharge.
Thus direct discharges into the estuary are excluded.
V- « water volume segment "i".
The same values for C^ and M1 may also be obtained by using the fraction of
-186-
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freshwater, f., for each segment by:
Ci • f1 Cr (VI-22)
and
M^ - C1 V1 (VI-23)
Thus both the quantity of a pollutant 1n each segment and Us concentration
within each segment are readily obtainable by either of the above methods. The
use of one of these methods will be demonstrated in Example Vl-5 below for calculation
of both C^ and M..
EXAMPLE VI-5 ,
I I
J Calculation of Concentration of Conservative I
I River Borne Pollutant in an Estuary |
i
j Th« Patuxent Estuary is the subject of this example. The problem is to
predict the incremental concentration increase of total nitrogen (excluding N? j
gas) in the estuary, given that the concentration in river water at the estuary
head is 1.88 mgN/1. !
Assume that total nitrogen is conservative and that the nitrogen concentration j
in local seawater is negligible. The segmentation scheme used in Example VI-2 I
(fraction of freshwater calculation) wi11 be retained here. For each segment, the |
total nitrogen concentration is directly proportional to the fraction of freshwater I
in the segment:
C1 ' fi Cr I
The total nitrogen concentration for the uppermost segment is therefore given j
i
Cj • 0.93 (1.88 mgN/1) j
• 1.75 mgN/1
For the next segment It is:
I
C? • 0.83 (1.88 mgN/1) « 1.56 mgN/1
and so on. Nitrogen concentrations for all the segments are compiled in Table
VI-8. Note that these are not necessarily total concentrations, but only nitrogen J
inputs from the Patuxent River. I
4
The incremental mass of nitrogen in each segment is found by: |
M ' W C '
-187-
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TABLE VI-8
POLLUTANT DISTRIBUTION IN THE PATUXENT RIVER
Segment Nuaber*
8
7
6
5
4
3
2
I
River
•From Example
"These are the
Fraction of Freshwater*
1n Segaent f<
0.037
0.112
0.19
0.29
0.46
0.69
0.83
0.93
1.00
VI-2
Increment concentrations of total
Resultant Pollutants**
Concentration
•f1 x 1.88 mgN/1
0.07
0.21
0.36
0.55
0.86
1,30
1.56
1.88
1.68
nitrogen 1n the estuary
due to the river-borne input.
TABLE VI-9
INCREMENTAL TOTAL NITROGEN IN PATUXENT RIVER,
EXPRESSED AS KILOGRAMS
(See Problem VI-5)
Segment Number
8
7
6
5
4
3
2
1
River Water
Volume
vvv
meters
6.14xl06
14.6 xlO6
13.2 xlO6
13.3 xlO6
11.5 xlO6
10.7 xlO6
8.47xl06
7.35xl06
Incremental Total N
M. - W1 (1.88)
kilograms
11,500
27.400
24,800
25,000
21.600
20,100
15,900
13,800
-188-
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I The H. values for the eight segments were determined in Example VI-2. For
| segment 1, the incremental nitrogen is given by:
l " Hl Cr
• (7.35 x 10V)(1.88 mgN/l)(103l/Bi3)
I
j - 1.38 x 1010 ng or 13,800 kg |
I Increased total nitrogen (in kilograms) for the entire estuary is shown in Table i
j «-'• i
I END OF EXAMPLE VI-5 '
In this example, low tide volumes were used to calculate H. since low tide
volumes had been used to calculate f^'s. The approach assumes that C^'s are
constant over the tidal cycle and that M^'s are constant over the tidal cycle.
This leads to the assumption that calculation of a low tide C, and M^ will
fully characterize a pollutant in an estuary. This, however, is not strictly true.
Figure VI-17 depicts one tidal cycle in an estuary and shows the periods of the cycle
during which a pollutant is flushed out of the estuary and during which river discharge
brings pollutants into the estuary. During periods of high tide, rising tidal
elevation tlodcs river discharge and backs up river flow in the lower stretches of
the river. Figure VI-17 also shows the resulting quantity of a pollutant in residence
in the estuary (W_J over the tidal cycle. This variation over the tidal cycle
™
as a percentage of M- is dependent on the flushing time but is usually small. The
change in the total volume of water in an estuary over a tidal cycle is equal to the
tidal prism which is often of the same magnitude as the low tide volume. As an example,
the Alsea Estuary in Oregon has ?t • 5.1 x 108 ft3 while Vt - 2.1 x 108 (Goodwin,
Emmet, and Glenne, 1970). Thus the variation in estuarine volume is 2.5 times the
low tide volume. As a result, estuarine volume variations over a tidal cycle have a
much greater impact on variations in pollutant concentrations in the estuary than do
changes in the quantity of pollutant present in the estuary over a tidal cycle. It
is important to note, however, that low tidal volume and low Mr nearly coincide,
so that variations in mean pollutant concentrations are less severe than are estuarine
water mass changes.
This qualitative description of pollutant flow into and out of an estuary
is somewhat simplistic since it assumes that high tide and low tide at the mouth of
an estuary coincide with those at the head of the estuary. This is usually not the
case. There is normally a lag time between tidal events at an estuarine mouth and
those at its head. Thus river discharge into the estuary which depends on tidal
conditions at the head, and tidal discharge which depends on tidal conditions at the
mouth, are not as directly tied to each other as indicated in Figure VI-17.
While Wr does not vary substantially over a tidal cycle under steady-state
-189-
-------
TIDAL
ELEVATION
W,
PE
FIGURE VI-17 RIVER BORNE POLLUTANT CONCENTRATION
FOR ONE TIDAL CYCLE
conditions', the mean concentration of a pollutant in an estuary (Cp) does. Alsea
Estuar> data can be used to show this C^ variation over a tidal cycle. Using
data for the estuary as a whole (mean concentration), the equations for this compari-
son are:
(VI-24)
and
with
or
Then:
and
ME/(Vt * Pt)
Wr - (566.4ng/ft3) (4.64 x 106ft3/tidal cycle)
Wr • 2.628 x loVg/tidal cycle.
« (2.628 x 10>g/tidal cycle)(20.8 tidal cycle)
- 5.466 x 101CVg
CE(low) * 5'466 x 1010Hg/2.1 x 108ft3
(VI-25)
-190-
-------
or
CCM , * 260.31 Kg/ft3, or 46 percent of river concentration.
c.( low;
However:
CE(high) * 5'466 x ""Wtt.l x 108ft3 + 5.1 x 108ft3)
Cf... h» « 75.92 ng/ft or 13 percent of river concentration.
In an actual estuary, the concentration of a pollutant is not a stepwise
function as indicated by segment C, values, but is more realistically a contin-
uous spectrum of values. By assigning the longitudinal midpoint of each segment a
concentration value equal to that segment's C^, a resulting continuous curve can
be constructed as shown in Figure VI-18. This type of plot is useful 1n estimating
pollutant concentrations within the estuary. It can also be used, however, to
estimate maximum allowable C to maintain a given level of water quality at any
point within the estuary. This latter use of Figure VI-18 1s based on determining
the desired concentration level (C ) and then using the ratio of C to C
to calculate an allowable Cr.
6.4.2.2 Other Continuous Conservative Pollutant Inflows
In the previous section, an analysis was made of the steady-state distri-
bution of a continuous flow pollutant entering at the head of an estuary. The
result was a graph of the longitudinal pollutant concentration within the estuary
(Figure VI-18). This section addresses a continuous, conservative pollutant flow
entering_along the side of an estuary. Such a pollutant flow (e.g. the conservative
elements of a municipal sewer discharge, industrial discharge, or minor tributary) is
carried both upstream and downstream by tidal mixing, with the highest concentration
occurring in the vicinity of the outfall. Once a steady state has been achieved, the
distribution of this pollutant is directly related to the distribution of fresh river
water (Dyer, 1973).
The average cross-sectional concentration at the outfall under steady-state
conditions is:
Qn
C «-£f (VI-26)
o R o
where
CQ • mean cross-sectional concentration of a pollutant at the point of
discharge, mass/volume
Qp » discharge rate of pollutant, mass/tidal cycle
fQ « segment fraction of freshwater
R « river discharge rate, volume/tidal cycle.
Downstream of the outfall, the pollutant must pass through any cross section at
-191-
-------
10 120 30 40 50 60 TO ISO
DISTANCE U) FROM HEAD OF ESTUARY (in 1000FT)
FIGURE VI-18 ALSEA ESTUARY RIVERBORNE CONSERVATIVE
POLLUTANT CONCENTRATION
a rate equal to the rate of discharge. Thus:
vO
f
90
x
0
V$0
(VI-27)
where
Sx, CK and fx denote downstream cross-sectional values
S , C. and f denote the cross-sectional values at the discharge
point (or segment into which discharge is made).
Upstream of the outfall, the quantity of pollutant diffused and advectively
carried upstream is balanced by that carried downstream by the nontidal flow so
that the net pollutant transport through any cross section is zero. Thus, the
pollutant distribution is directly proportional to salinity distribution and (Dyer,
1973):
CX-C0^ (VI-28)
5o
Downstream of the outfall, the pollutant concentration resulting from a point
discharge is directly proportional to river-borne pollutant concentration. Upstream
from the discharge point, 1t is inversely proportional to river-borne pollutant
concentrations. Figure VI-19 is a graph of fx versus distance from the estuary
-192-
-------
f, 00
-p*
0 '- 10.5
DISTANCE FROM HEAD »
110
*L • Totol E»toonn« Ungth
FIGURE VI-19 POLLUTANT CONCENTRATION FROM AN
ESTUARINE OUTFALL (AFTER KETCHUM, 1950)
head for a typical estuary. The solid f line Is also a measure of pollutant
concentration for all points downstream of a pollutant outfall (either discharge
location A or B). The actual concentration (C ) for any point is equal to this
fx value multiplied by Q /R which is a constant over all x. Upstream concen-
trations decrease from C in a manner proportional to upstream salinity reduction
(see dotted lines). It is important to note how even a small downstream shift in
discharge location creates a very significant reduction in upstream steady-state
pollutant concentration. Table VI-10 shows a suggested format for tabulating pollutant
concentrations by the fraction of freshwater method.
- EXAMPLE VI-6
Calculation of Conservative Pollutant Concentration
for a Local Discharge
This example will again utilize the eight-segment scheme devised for the
Patuxent Estuary in Example VI-2. The objective is to predict the concentration
distribution of total nitrogen in the estuary resulting from a discharge of 80,000
mgN/sec Jnto segment 4.
The first step is to determine the nitrogen concentration in segment 4.
-193-
-------
TABLE VI-10
SAMPLE CALCULATION TABLE FOR DISTRIBUTION OF A LOCALLY DISCHARGED
CONSERVATIVE POLLUTANT BY THE FRACTION OF FRESHWATER METHOD
From Table VI-3
Segment
Number
Segment
Containing
Discharge
Fraction of
Freshwater
fi
Mean Segment
Salinity
(ppt)
fi
~o
I
S1
S
1
Pollutant
Concentrations*
(mg/1)
*Po "Mutant concentration -«
where Cn«
f .
C0 — , down estuary of the discharge
o
C0 — , up estuary of the discharge
1
• From Equation VI-26:
c m Op f0 f (8xlQ4 mgN/sec x 12.4 hrs/tidal cycle x 3600 sec/hr)(0.46)
5.36xl05m3/tida) cycle
3.065 mgN/1
I For segments 1-3, upstream from the discharge, nitrogen concentration is
J found by Equation VI-28:
! ci • c.
i
-194-
-------
1 For segment 1:
1
! S, - 0.8%.
1
1 5 * 5 4 * b.o 7oo
<
i
j CA » 3.065 mgN/1
1 so
I \5.8700/
; Nitrogen concentrations in segments 2
j VI-11 summarizes the information used
i
i
i
i
i
*
|
« 0.42 mgN/1
1
and 3 are found in an identical way. Table
I
in the calculation. [
1 For the segments downstream of the discharge, total nitrogen concentration is 1
| found using Equation VI-27:
i c. - c i-
• 1 0 T
' In segment 5:
1 f, - 0.29
1 f . f . 0.46
1
,
1
i
»
1
i
1
i
1
i
1
•
1 TABLE VI-11 !
1 NITROGEN CONCENTRATION IN PATUXENT ESTUARY !
| BASED ON
1
Fraction of
1 Segment Freshwater
! Number f ^
i
1 8 0.037
<
1
j 7 0.112
j 6 0.19
1 5 0.29
! Discharge _ 4 0.46
! 3 0.69
1
2 0.83
j 1 0.93
LOCAL DISCHARGE |
i
|
Mean Si f< j
Segment »- -r- Concentration \
Salinity o o mgN/1 |
1
10.3 - 0.08 0.25 I
1
1
9.5 - 0.24 0.74 j
8.7 - 0.41 1.26 j
7.6 - 0.63 1.93 1
5.8 1 1 3.06 !
3.3 0.57 - 1.75
1
1.8 0.31 - 0.95 j
0.8 0.14 - 0.43 j
-195-
-------
and
3.065 mgN/1
so
C5 • 3.065 mgN/1
,.93 mgN/1
I
The same procedure yields nitrogen concentrations in segments 6-8, also downstream |
of the discharge. j
Figure VI-20 below shows the nitrogen concentration distribution over the
entire estuary. Note that the nearer a discharge is to the estuary's mouth, the
greater the protection rendered the upstream reaches of the estuary. j
4.0-1
3.CT-
z
Oi
\ 2.0H
0
9
o
1.0-
10
i
20
i
30
I
40
discharge
Distance above estuary mouth UOOO's of meters)
FIGURE VI-20 HYPOTHETICAL CONCENTRATION OF TOTAL NITROGEN
IN PATUXENT ESTUARY
END OF EXAMPLE VI-6
-196-
-------
6.4.3 Continuous Flow Non-Conservative Pollutants
Most pollutant discharges into estuaries have some components which behave
non-conservatively. A number of processes mediate the removal of compounds from
natural waters, among these:
• Sorption by benthic sediments on suspended matter
• Partitioning
• Decay (by photolysis or biologically mediated reactions)
• Biological uptake
• Precipitation
• Coagulation.
The latter two processes are particularly significant in estuaries. Thus, in addition
to dispersion and tidal mixing, a time-dependent component is incorporated when
calculating the removal of non-conservative pollutants from estuarine waters. The
concentrations of non-conservative pollutants are always lower than those of conserva-
tive pollutants (which have a decay rate of zero) for equal discharge concentrations.
The results of the previous section for conservative constituents serve to set upper
limits for the concentration of non-conservative continuous flow pollutants. Thus,
if plots similar to Figure VI-17 for river discharges and to Figure Vl-19 for other
direct discharges have been prepared for flow rates equal to that of the non-conserva-
tive pollutant under study, some reasonable approximations can be made for steady-
state non-conservative pollutant concentrations without requiring additional data.
Assuming a first order decay rate for the non-conservative constituent, its concentra-
tion is given by:
Ct « C0e'kt (VI-29)
where
C^ • pollutant concentration at time "t"
CD « initial pollutant concentration
k « decay rate constant.
For conservative pollutants k • 0 and C « CD under steady-state conditions.
Decay rates are determined empirically and depend on a large number of variables.
Typical decay rates for BOD and coliform bacteria are shown in Table VI-12. If data
are not available for a particular estuary, the use of these average values will
provide estimates.
It should be noted that decay rates are dependent upon temperature. The values
given assume a temperature of 20*C. Variations in k values for differing temperatures
are given by Equation VI-30:
T-20- (VI-30)
kT *20' 9
-197-
-------
TABLE Vl-12
TYPICAL VALUES FOR DECAY REACTION RATES 'k1*
Source BOD Collforn
Dyer, 1973 .578
fetchem, 1955 .767
Chen and Orlob, 1975 .1 .5
Hydrosdence, 1971 .05-.125 1-2
McGaughhey, 1968 .09
Harletnan. 1971 .069
*k values for all reactions given on a per
tidal cycle basis, 20* C.
where
ky « decay rate at temperature T
k20 « decay rate at 20*C (as given 1n Table Vl-12)
6 « a constant {normally between 1.03 and 1.05).
Thus an ambient temperature of 10"C would reduce a k value of 0.1 per tidal cycle to
0.074 for a-6 • 1.03.
Decay Affects can be compared to flushing effects by setting time equal to
the flushing time and comparing the resulting decay to the known pollutant removal
rate as a result of flushing. If kt in Equation VI-29 1s less than 0.5 for t •
Tf, decay processes reduce concentration by only about one-third over the flushing
time. Here mixing and advective effects dominate and non-conservative decay plays a
minor role. When kTf > 12 decay effects reduce a batch pollutant to 5 percent of
Us original concentration in less than one-fourth of the flushing time. In this
case, decay processes are of paramount importance in determining steady-state concen-
trations. Between these extremes, both processes are active in removing a pollutant
from the estuary with 3 < kTf < 4 being the range for approximately equal contri-
butions to removal. Dyer (1973) analyzed the situation for which decay and tidal
exchange are of equal magnitude for each estuarine segment. Knowing the conservative
concentration, the non-conservative steady-state concentration in a segment is
given by:
(W-31)
-198-
-------
and
S. / r \ for segments upstream (VI-32)
V Co S^ i-l^-.n I j (1.r )c-kJ of the outfall
where
non-conservative constituent mean concentration in segment "1
L1
C - conservative constituent mean concentration in segment of discharge
o
r1 • the exchange ratio for segment "i- as defined by the modified
tidal prism method
n « number of segments away from the outfall (i.e. n » 1 for segments
adjacent to the outfall; n « 2 for segments next to these segments,
etc.)
Other parameters are as previously defined.
In the case of a non-conservative pollutant entering from the river, n « 1, and
the only concentration expression necessary is:
!« (VI-33)
where
(VI-34)
Table VI-13 shows a suggested format for tabulating pollution concentrations by
the modified tidal prism method.
j. EXAMPLE VI-7 1
i i
Continuous Discharge of a Non-Conservative Pollutant j
! into the Head of an Estuary
I I
i '
| The Fox Mill Run Estuary (see Example VI-3) is downstream of the Gloucester, j
Virginia, sewage treatment plant. Knowing the discharge rate of CBOD in the plant |
effluent, the purpose of this example is to determine the concentration of CBOD |
throughout the estuary. j
It is first necessary to determine the concentration of CBOD in Fox Mill Run •
as it enters the estuary (assume no CBOD decay within the river). The following •
information has been collected: \
Cr, Background CBOD in river » 3 mg/1
-199-
-------
TABLE VI-13
SAMPLE CALCULATION'TABLE FOR'DISTRIBUTION OF A LOCALLY DISCHARGED
MOW-CONSERVATIVE POLLUTANT BY THE MODIFIED TIDAL PRISM METHOD
From Table VI-6
Segment
Number
Distance of
Center Above
Mouth
(m)
Segment
Exchange
Ratio
Mean Salinity
(from salinity
plot)
Si
ppt
Fraction of
River Water
f - *'
B1
Pollutant
Concentration
(mg/1)
i.
1C
a
-200-
-------
i Q , River flow below treatment plant discharge - 0.031 m /sec
j Qd, Treatment plant discharge rate « 0.006 m /sec
j Cd, Treatment plant effluent CBOD « 45 mg/1
The CBOD concentration 1n the river downstream of the treatment plant is found j
using the equation: j
I Cr(Qr-Qd) * CdQd
I C" % !
| or I
j c „ 3 mg/1(.031-.006 m3/sec)+45 mg/l(0.006 m3/sec) j
• 0.031 m3/sec j
! - 11.1 mg/1
! To find the CBOD concentration distribution in the estuary, the following additional.
j data are used: '
! S Chesapeake Bay salinity « 19.0 °/oo (at the mouth of
j Fox Mill Run Estuary) (
I k, CBOD decay constant « 0.3/day j
j T, Tidal cycle - 12.4 hours I
i so |
| kt « 0.3/day x 12.4 hr x 1 day/24 hours I
j • 0.155 I
I Also necessary are mean salinity values for each estuary segment. Values for J
| the Fox Mill Run Estuary are summarized in Table VI-14. Fraction of freshwater I
j values for each segment are found using the formula: |
Vsi
f'"ir
| The variables are as previously defined.
Next, values of the coefficient B. must be calculated for each segment
"1." For segment 0:
r^, the segment exchange ratio, « 0.74
and
B rO °-74
° " l-(l-r0)e-" " l-(l-0.74)e-u-1"
« 0.95
Coefficient values for all segments are compiled in Table VI-14.
Finally, CBOD concentrations for the individual* segment are calculated, beginning
with the uppermost segment and working downstream. The concentration in segment
"i" is found by:
-201-
-------
TABLE VI-14
SALINITY AND CBOD CALCULATIONS FOR FOX MILL RUN ESTUARY
from Problem VI -3
Center Point
Distance Above Exchange Ratio
Est. Mouth, For Segment
Segment Number Meters r^
River (>3200)
0 2950 0.74
1 2470 0.71
2 1945 0.56
3 915 0.71
Fraction of
Mean Segment Fresh (River)
Salinity , s" i
Si, ppt ri S«
(From Sal. Plot) (Sj- 19.0)
-0 I. 00
4.7 0.75
8.6 0.55
11.6 0.39
15.3 0.19
Concentration of
CBODU
f .
n r «r a
Bi C1 ci-l fM 8i
(mg/1 )
11.1
0.95 8.1
0.94 5.5
0.90 3.6
0.94 1.6
-202-
-------
I For segment 0, the river 1s taken as segment "1-1", and the calculation 1s as j
j follows: !
I
! For segment 1:
CQ » 11.13 mg/1 f ~] 0.95 - 8.1 mg/1
/•55\
C, • 8.1 mg/1 (— I 0.94 « 5.6 mg/1
j and so on. 1
j Figure VI-21 depicts this estimate of the distribution of CBOD in the estuary, j
In addition, hypothetical concentrations of a conservative pollutant (k » 0) and •
! conform bacteria (k • 1.0) are plotted. Downstream concentration diminishes
' faster for substances having larger decay constants, as might be expected.
i !
i I
|2
u
o
U
conservative
pollutant
coWorma
10
20
Distance Above Mouth Of Eatuary (100'* of meters)
30 river 36
mouth
FIGURE VI-21 RELATIVE DEPLETIONS OF THRES POLLUTANTS ENTERING THE !
Fox MILL RUN ESTUARY, VIRGINIA I
END OF EXAMPLE VI-7
.J
-203-
-------
6.4.4 Multiple Waste Load Parameter Analysis
The preceding analysis allowed calculation of the longitudinal distribution
of a pollutant, either conservative or non-conservative, resulting from a single
waste discharge. However, the planner will probably want to simultaneously assess
both conservative and non-conservative elements front several separate discharges.
This can be accomplished by graphing all desired single element distributions on one
graph showing concentration versus length of the estuary. Once graphed, the resulting
concentration may be linearly added to obtain a total waste load.
The pollutant concentration increment from each source is calculated by assuming
the source is the sole contribution of pollution (i.e. other waste loadings are
temporarily set equal to zero). This method, called superposition, is valid as the
long as volumetric discharge from any of the sources does not significantly influence
the salinity distribution within the estuary. This assumption is typically true,
unless the estuary is extremely small and poorly flushed, and the volumetric discharge
is targe relative to tidal and advective flushing components.
An example of the superposition procedure is shown in Figure VI-22. Three local
z
Ul
a
Water Quality Standard
New Pollutant
Concentration
•Current Pollutant
Concentration
Sum
DISTANCE FROM HEAD
FIGURE VI-22 ADDITIVE EFFECT OF MULTIPLE HASTE LOAD ADDITIONS
-204-
-------
point sources of pollutants discharge at locations A, 8, and C. A background source
enters the estuary with the river discharge. The contribution due to each source can
be found from the fraction of freshwater method (assuming the pollutants act conserva-
tively) as follows:
WR
C • - f, x > 0, where x 1s aeasured from the head of the estuary
WA
-^f
R x
X>A
O £ A _
T f B T ' x < B
cc'
Tfx '
wc sx
where
Cfe • concentration due to river discharge
CA, Cg, CQ • concentrations due to sources A, B, and C, respectively
R • river flow rate
f», f», ff • fraction of freshwater at locations A, B, C, respectively
SA, Sg, S^ • salinity at locations A, 6, C, respectively.
-205-
-------
The pollutant concentration (above background) at any location in the estuary is:
Sum • CA + Cg + G£
and is shown in Figure VI-22. When this 1s added to the background level, the
total pollutant concentration becomes:
CT • (CA + CB + Cc) «• Cb
The dotted line in Figure VI-22 depicts Cj.
The technique of graphing outfall location and characteristics with resulting
estuarine pollutant concentration can be done for all anticipated discharges. This
will provide the planner with a good perspective on the source of potential water
quality problems.
Where the same segmentation scheme has been used to define Incremental pollutant
distributions resulting from several sources, the results need not even be plotted to
determine the total resultant concentrations. In this case, the estuary is evaluated
on a segment-by-segment basis. The total pollutant concentration in each segment is
calculated as the arithmetic sum of the concentration increments resulting from the
various sources.
EXAMPLE VI-8
The previous two example problems involved calculations of nitrogen concentra- •
tion in the Patuxent Estuary resulting from individual nitrogen sources. The '
objective of this example is to find the total nitrogen concentration In the j
estuary resulting from both nitrogen sources. I
The eight-segment scheme of Examples VI-6 and VI-7 is retained for this |
problem. For each segment, the incremental nitrogen increases are summed to give j
the total concentration: j
c • cb * CA i
where j
C^ » concentration resulting from the H source discharging into the
estuary at point A.
For segment 1, the calculation is: |
C « 1.75 mg/1 (from river) + 0.43 mg/1 (from local source)
« 2.18 mg/1 total nitrogen j
Necessary data and final concentrations for each segment are shown in Table I
Vl-15. i
-206-
-------
TABLE VI-15
DISTRIBUTION OF TOTAL NITROGEN IN THE PATUXENT
ESTUARY DUE TO TWO SOURCES Of NITROGEN
Segment Number
8
7
6
5
4
3
2
1
River
Results From
Problem VI -4
Total Nitrogen
From River
ngN/1, Cj,
0.07
0.21
0.36
0.55
0.80
1.30
1.56
1.75
1.88
Results From
Problem VI-5
Total Nitrogen
From Point A Source
(Segment 4)
mgN/1, CA
0.25
0.74
1.26
1.93
3.06
1.74
0.95
0.43
0.00
Resultant
Concentration
c"cb * CA
rooN/l
0.32
0.95
1.62
2.48
3.92
3.04
2.51
2.18
1.88
i !
: END OF EXAMPLE VI-8 '
6.4.5 Dispersion-Advection Equations for Predicting Pollutant Distributions
Disperslon-advect1on equations offer an attractive method, at least theoretically,
of predicting pollutant and dissolved oxygen concentrations in estuaries. However,
from the point of view of hand calculation, the advection-dispersion equations are
usually tedious to solve, and therefore mistakes can unknowingly be Incorporated into
the calculations.
Dispersion-advection equations have been developed in a variety of forms,
including one-, two-, and three-dimensional representations. The equations in this
section are limited to one-dimensional representations in order to reduce the amount
of data and calculations required.
One-dimensional dlspersion-advectlon equations can be expressed In quite diver-
gent forms, depending on boundary conditions, cross-sectional area variation over
distance, and source-sink terms. O'Connor (1965), for example, developed a variety
of one-dimensional advection-dispersion equations for pollutant and dissolved oxygen
analyses in estuaries, some of which are infeaslble for use on the hand-calculation
level.
-207-
-------
The advection-dispersion equations to be presented subsequently In this chapter
can be used to predict:
• Distributions of conservative or non-conservative pollutants
• Pol Mutant distributions 1n embayments
• Dissolved oxygen concentrations.
Solutions from advect1cm-dispersion can be superposed to account for multiple
discharges. Example VI-9, to be presented subsequently, will illustrate this
process.
As the name of the equations implies, dispersion coefficients are needed in
order to solve advectIon-dispersion equations. Tidally averaged dispersion coeffic-
ients are required for the steady-state formulations used here. The tidally averaged
dispersion coefficient (EL) can be estimated from the following expression:
r . RS_ (VI-35)
L A dS/dx
(VI'36)
x+Ax
where
S • tidal ly and cross sectional ly averaged salinity in vicinity of
discharge
2Ax » distance between the salinity measurements $4 (at a distance
Ax down estuary) and Sx (at a distance of AX up estuary)
R « freshwater flow rate in vicinity of discharge.
The distance interval 2Ax should be chosen so that no tributaries are contained
within the interval .
In the absence of site specific data, the dispersion coefficients shown in
Tables VI-16 and VI-17 can provide estimates of dispersion coefficients.
For pollutants which decay according to first order decay kinetics, the steady
state mass balance equation describing their distribution is:
• - « • 0 (V.-37)
The solution to Equation VI-37 is:
x > 0(down estuary) (VI-38a)
C •
£ e J|X x < 0(up estuary)
o
-208-
-------
TABLE VI-16
TIDALLY AVERAGED DISPERSION COEFFICIENTS FOR SELECTED
ESTUARIES (FROM HYDROSCIENCE, 1971)
Estuary
Delaware River
Hudson River (N.Y.)
East River (N.Y.)
Cooper River (S.C.)
Savannah R. (Ga. , S.C.)
Lower Raritan R. (N.J.)
South River (N.J.)
Houston Ship Channel (Texas)
Cape Fear River (N.C.)
Potomac River (Va. )
Compton. Creek (N.J.)
Uappinger and
Fishkill Creek (N.Y.)
*1 mi2/day « 322.67 ft2/sec
rtiere
J2 « fl -\/l + -
2AEL \^ V
Freshwater
Inflow
(cfs)
2,500
5,000
0
10,000
7.000
150
23
900
1,000
550
10
2
F A2\
bL\
R1 /
Low Flow
Net Uontidal
Velocity ( fps)
Head - Mouth
0.12-0.009
0.037
0.0
0.2G
0.7-0.17
0.047-0.029
0.01
0.05
0.48-0.03
0.006-0.0003
0.01-0.013
0.004-0.001
f)i spers ion
Coeff ic icnl
? *
5
2U
10
3D
10-20
5
5
?7
2-10
1-10
1
0.5-1
j,
R / /
[1 +W
2AE v
Co- -
0 R ./l+(4kEL/ir)
U » net velocity
k « decay rate
W » discharge rate of pollutant (at x • 0).
For Equations VI-38a and VI-38b to accurately estimate the pollutant distribution
in an estuary, the cross-sectional area of the estuary should be fairly constant over
-209-
-------
TABLE VI-17
TIDALLY AVERAGED DISPERSION COEFFICIENTS
(FROM OFFICER. 1976)
Estuary
Dispersion Coefficient
Range (ft2/sec)
Comments
San Francisco Bay
Southern Arm
Northern Arm
Hudson River
Narrows of Mercey
Potomac River
Severn Estuary
Tay Estuary
Thames Estuary
Yaquina Estuary
200-2,000
500-20,000
4,800-16,000
1,430-4,000
65-650
75-750
(by Stomnel}
580-1,870
(Bowden)
530-1,600
(up estuary)
1,600-7,500
(down estuary)
600-1,000
(low flow)
3,600
(high flow)
650-9,200
(high How)
140-1,060
(low flow)
Measurements were made at slack
water over a period of one to a
few days. The fraction of
freshwater method was used.
Measurements were taken over
three tidal cycles at 25
locations.
The dispersion coefficient was
derived by assuming Ei to be
constant for the reach studied,
and that it varied only with
flow. A good relationship
resulted between EL and flow,
substantiating the assumption.
The fraction of freshwater
method was used by taking mean
values of salinity over a tidal
cycle at different cross
sections.
The dispersion coefficient was
found to be a function of dis-
tance below the Chain Bridge.
Both salinity distribution
studies (using the fraction of
freshwater method) and dye
release studies were used to
determine E, .
Bowden recalculated L values
originally determined by
Stommel, who had used the
fraction of freshwater method.
Bowden included the fresh-
water inflows from tributaries,
which produced the larger
estimates of E, .
The fraction of freshwater
method was used. At a given
location, EL was found to vary
with freshwater inflow rate.
Calculations were performed
using the fraction of fresh-
water method, between 10 and
30 miles below London Bridge.
The dispersion coefficients for
high flow conditions were sub-
stantially higher than for low
flow conditions, at the same
locations. The fraction of
freshwater method was used.
-210-
-------
distance, and the estuary should be relatively long. For screening purposes the
first constraint can be met by choosing a cross-sectional area representative of the
length of estuary being investigated. If the estuary 1s very short, however, pollut-
ants might be washed out of the estuary fast enough to prevent attainment of a
steady-state distribution assumed by Equations VI-38a and VI-38b. For shorter
estuaries the fraction of freshwater method, modified tidal prism method, or near
field approach are more appropriate.
At times when the freshwater flow rate in an estuary 1s essentially zero pollutant
concentrations might increase to substantial levels, if tidal flushing 1s small.
Under these conditions the mass-balance expression for a pollutant obeying first
order kinetics is:
E. d2C - kc
L -
(VI-39)
The solution to this equation is:
exp
CQ exp
where
for x > 0 {down estuary)
for x <0 (up estuary)
(Vl-40a)
(VI-40b)
(VI-41)
When the pollutant is conservative (i.e., k • 0), Equation VI-39 reduces to:
d2C
The solution is:
E. - 0
L dxj
CQ , x < 0 (up estuary)
(VI-42)
(VI-43a)
(L-x) + C. , x > 0 (down estuary) (vi-43b)
ELA
where
Co * CL
HI
CL « background concentration of the pollutant at the mouth of the
estuary
L « distance from the discharge location to the mouth of the estuary.
-211-
-------
Equation Vl-43 Illustrates the important concept that the concentrations of conserva-
tive pollutants are constant up estuary from the discharge location (when the river
discharge is negligible) and decrease linearly from the discharge point to the mouth
of the estuary. Equations VI-40 and VI-43 apply to estuaries of constant, or approxi-
mately constant, cross-sectional area (e.g. sloughs). If the cross-sectional area
increases rapidly with distance toward the mouth, the methods presented in Section
6.5 are more appropriate.
The dissolved oxygen deficit equation (where deficit is defined as the difference
between the saturation concentration and the actual dissolved oxygen concentration)
for one-dimensional estuaries at steady-state conditions is:
L'-D
— L n - kP * kL
cx dx* *
where
D • dissolved oxygen deficit
L • BOO concentration
k, « reaeration rate
k « BOO decay rate.
Using Equation IV-38 to represent the BOD distribution, the expression for the
deficit D u:
exp * I - —=z exp
- (»:&\
* Tr exp\~l— /
(VI-45)
where
The plus sign (*) is used to predict concentrations up estuary (x < 0)
The minus sign (-) is used to predict concentrations down estuary (x > 0)
a, - U^
a2 » U2 t
M • mass flux of dissolved oxygen deficit contained in the discharge.
W « mass flux of ultimate BOD contained in the discharge, (Cs - Ce)^e.
Cs » saturation concentration of dissolved oxygen.
Cf « effluent concentration of dissolved oxygen.
*e « effluent flowrate.
The advantage of expressing the dissolved oxygen concentration in terms of the
deficit is that the principle of superposition can be invoked for multiple discharges
within a single estuary. Specifically:
D • L D (Vl-46)
-212-
-------
and
cs - z o,
(VI-47)
where
0, « dissolved oxygen deficit resulting from the i— discharge
C • final dissolved oxygen concentration
Cs » dissolved oxygen saturation level.
Figure VI-23 shows the relationship between dissolved oxygen saturation and temperature
and salinity.
FIGURE VI-23 DISSOLVED OXYGEN SATURATION AS A FUNCTION
OF TEMPERATURE AND SALINITY
EXAMPLE VI-9
Dissolved Oxygen Concentration Resulting from Two Sources of BOD I
i
Two municipal wastewater treatment plants discharge significant quantities of |
BOD into the James River in Virginia. One discharges near Hopewell, and the j
second 10 miles further down estuary, near West Point. Calculate the dissolved
oxygen concentration in the estuary as a function of distance. Pertinent data
are: I
-213-
-------
BOD, in Hopewell plant effluent • 69,000 Ibs/day 1
* i
BOD, 1n West Point plant effluent, located 10 miles downstream from |
Hopewell • 175,000 Ibs/day I
Freshwater flow rate » 2,900 cfs |
Dissolved oxygen saturation » 8.2 mg/1 j
Cross sectional area • 20,000 ft2 j
Reaeration rate • 0.2/day
Deoxygenatlon rate • 0.3/day J
Dispersion coefficient • 12.5 m12/day I
i
Effluent dissolved oxygen - 0.0 mg/1. |
The dissolved oxygen deficit due to each of the two contributions can be j
determined independently of the other using Equation IV-45. The results are j
plotted in Figure VI-24. The deficits are added to produce the total deficit
(D(x)) due to both discharges (Figure VI-24a). The distance scale in Figure
VI-24a Is referenced to the Hopewell plant. The West Point plant 1s placed at !
mile 10. When the deficit at this location due to the West Point plant 1s calcu- j
lated, set x • 0 in Equation VI-45. The dissolved oxygen concentration then I
becomes C(x) • 8.2-D(x), and is shown in Figure VI-24b. |
One example calculation of dissolved oxygen deficit will be shown to Illus- j
trate the process. Consider the deficit produced at mile 0.0, due to the Hopewell j
plant. The waste loading front the Hopewell plant is:
69,000 x 1.46 « 100,000 Ibs/day, BOD-ultimate j
• 1.16 Ibs/sec
When x - 0, Equation VI-45 simplifies to: !
I
/2900\2 4(.3)(12.5)(5280)(5280) ft2 ;
I a, • IT «• 4k E. ( 1 + • .077
j L \20000/ 81400 • 86400 sec2 j
j so j
I j
j \TaT - .278 ft/sec \
I , I
j a2 - U2 * 4k2EL « 0.058 ft2/sec2
! » j
!
1 -242 ft/sec |
-214-
-------
0>
O
O
•o
•
"5
n
7.0-
6.0-
5.0-
4.0-
3.0-
2.0-
1.0-
Deficit due to Hopewell
Deficit due to West Point
— — Total deficit
-15 -10
0 10
Hopewell WestrPomt
20
30
40
50
Miles Below Hopewell
(a)
8.0-
§ 7.0-
g
u
6
TJ
0)
"5
at
10
5.0 H
4.0-
3.0-
_di£8£jved_px^pen ^saturation
-15 -10
10
20
30
40
50
Miles Below Hopewell
(h)
FIGURE VI-24 PREDICTED DISSOLVED OXYGEN PROFILE
IN JAMES RIVER
-215-
-------
1 The deficit 1s:
I (.3){1.16)
1 n *
r i IT
. o t v m-5 iK/ft
! 20000(.2-.3) L -278 .242 _
• This value 1s then plotted in Figure VI-24 at mile point 0.0.
. at this location due to West Point is evaluated at x • -10 ml
! VI -45, since West Point 1s located 10 miles down estuary of H
1 of 0.6 mg/1 is found, and 1s plotted In Figure VI-24 at mile
I deficit at Hopewell is 1.5 + 0.6 • 2.1 mg/1, as shown 1n the
t
I
'. run nr PYAMPI P VT.Q
1
i
3 « 1.5 mg/1 j
i
The deficit :
les in Equation
opewell. A deficit !
point 0.0. The total '
*
figure. |
i
6.4.6 Prltchard's Two-Dimensional Box Model for Stratified Estuaries
Many estuaries 1n the United States are either stratified or partially mixed.
Because the circulation of stratified systems 1s fairly complex, few hand calculation
methods are available for their analysis. Instead computerized solutions are gener-
al ly used.
One method developed by Pritchard (1969) which predicts the distribution
of pollutants In partially mixed or stratified estuaries is suitable for hand
calculations provided the user does not require too much spatial resolution.
This method, called the "two-dimensional box model," divides the estuary horizontally
from head to mouth into a series of longitudinal segments. Each segment is divided
into a surface layer and a bottom layer. The analysis results 1n a system of n
simultaneous linear equations with n unknowns, where n equals twice the number of
horizontal segments. The unknowns are the pollutant concentrations in each layer.
Division of the estuary into only two horizontal segments results in four
simultaneous equations, which is probably the most one would like to solve entirely
by hand. However, many programmable hand calculators contain library routines for
solving systems of 10 or more simultaneous equations, which would allow the estuary
to be divided into 5 or more horizontal segments. If many more segments are desired,
the solution could be easily implemented on a computer using a numerical technique
such as Gaussian elimination to solve the resulting system of simultaneous linear
equations.
The following information is required for the two-dimensional box analysis:
1) the freshwater flow rate due to the river; 2) the pollutant mass loading rates;
and 3) the longitudinal salinity profiles along the length of the estuary in the
upper and lower layers, ana the salinity at the boundary between these two layers.
The upper layer represents the portion of the water column having a net nontidal flow
directed seaward, and the lower layer represents the portion of the water column
having net nontidal flow directed up to the estuary. If no velocity data are avail-
-216-
-------
able, these layers can generally be estimated based on the vertical salinity profiles.
Figure Vl-25 shows the parameters used in the analysis, which are defined
as follows:
n « segment number, Increasing from head toward mouth
(S ) » salinity in upper layer of segment n
($,) - salinity in lower layer of segment n
(Sy)n « salinity at the boundary between the upper and
lower layers of segment n
(Sy)n , n « salinity In the upper layer at the boundary
between segments n-1 and n
(Sj)n_j n « salinity in the lower layer at the boundary
between segments n-1 and n
(Qu)n_^ n « net nontidal flow rate in the upper layer from
segment n-1 to n
(Qi)n i n " net nontidal flow rate in the lower layer from
A n ™ i t i
segment n to n-1
^v^n * nc* uP*ard vertical flow from the lower to the
upper layer of segment n
E » vertical exchange coefficient between the lower and
upper layers of segment n
R » freshwater flow rate due to river
(qu)n » pollutant mass loading rate to upper layer of
segment n (from external sources)
(Qj)n • pollutant mass loading rate to lower layer of
segment n (from external sources)
^u^n * Poll0**"* concentration in the upper layer of
segment n)
(C^)n « pollutant concentration in the lower layer of
segment n.
Pritchard's two-dimensional box analysis as presented here requires the following
assumptions:
• Steady-state salinity distribution
• The pollutant is conservative
• The concentration of the pollutant is uniform within each layer of
each segment and
• The pollutant concentration at the boundary between segments or layers
is equal to the average of the concentrations in the two adjacent
segments or layers.
Application of the two-dimensional box model involves six steps. These are:
1. Plot the longitudinal salinity profiles in the upper and lower
-217-
-------
n-1
«Mn
n-M
Jn-1,n
t (Svl —
__ — -• — — "" r- — ~~
.•.,*• • ..•: ••"•'•i ••••'•
•.••..*•••••«. •.•••.•'•.
, ,,
';•••.'••••::'••.•.;
.•»••.••.•••• •••.
'.«•'..* •;•'«;• ".»..•".'• •'. » •
•;^ ; ••• :•••.• «'.•.•/•.».. •;.:.•••'.••.»'.
:-'-V.i'..-*';..y-:V:.>:-.-.'.:-.''-'i---:v:V
FIGURE VI-25 DEFINITION SKETCH FOR PRITCHARD'S TWO-DIMENSIONAL Box MODEL
layers, and at the interface between the two layers. If informa-
tion on the net nontidal velocity distribution is not available to
define the layers, the boundary may be estimated for a given
section of the estuary as the depth at which the vertical salinity
gradient is maximum. The resulting plots wi11 be used to determine
the average salinities in each segment and layer, and the salini-
ties at the boundaries between each segment and layer.
Segment the estuary. The number of segments will depend on the
degree of spatial resolution desired, and the limitations of the
hand calculators used to solve the system of simultaneous equations.
The accuracy of the results will generally Increase with the number
of segments used, since the assumptions of the analysis are better
satisfied. A minimum of three horizontal segments should probably
be used to obtain even a rough estimate of the pollutant distribution
in the estuary. This will require the solution of six equations
and six unknowns.
Compute the net nontidal flows in the upper layer and lower layer
at the boundary between each horizontal segment using Knudson's
-218-
-------
Hydrographlcal Theorem {Dyer, 1973):
(Q''"-'-"
<*.>„... .-'Vn-l. n
(VI-4S)
(Q,)
1 "• "-1 n *
-------
n-1
(VI-53)
- E.
for the lower layer of segment n.
Since oust pollutant discharges are buoyant, they should be considered as
loadings to the upper layer, even though they My be physically Introduced at
the bottom. Pollutants which are denser than the upper waters and which would
sink to the bottom should be considered as loadings to the lower layer. However, the
analysis 1s not applicable to pollutants which tend to remain near the bottom and
accumulate 1n or react with the bottom sediments.
The above mass balance equations can be simplified and rearranged Into the
following form:
(Q
u n-]
u>n + [2En +
*v n
.
(VI-54)
for the upper layer of segment n and
- (Q..).
n *^v n
). +
u n
-2E.
Vl
(VI-55)
for the lower layer of segment n. This pair of equations Is written for each
segment, resulting 1n a system of simultaneous equations where the concentra-
tions, (Cu)n and (Cj)n, *^« the unknowns, the terms enclosed in square brackets
are the coefficients, and the terns on the right hand side of the equations are the
constants.
However, since each equation involves both the upstream and downstream segments
-E20-
-------
for a given layer, the boundary conditions at both the upstream and downstream end of
the estuary must be applied so that there will not be more unknowns than equations.
At the upstream end of the estuary, the following boundary conditions apply:
(0 ) j n " R * river fl°* rate
n. Alternatively,
the concentration outside the mouth may be assumed to equal some fraction of the
concentration Inside the mouth, or:
- fc (Cu)n
-221-
-------
where f is the selected fraction. The previous assumption (Cu)n+1 • {Cy)n
1s one case of this second assumption where the fraction equals one (f * 1).
Using the second more general assumption, the equation of the upper layer of the last
downstream segment simplifies to:
. „]
' fc
«n
(VI -60)
Step (6) of the two-dimensional box analysis Involves computing all of the
coefficients and constants in the system of equations defining each segment and
layer (Equations VI-54 and VI-55) and applying the boundary conditions to produce
equations for the first upstream and last downstream segments 1n the estuary (Equations
Vl-56 through VI -60). The coefficients and constants are functions of the variables
previously computed in steps (3) through (5). The resulting equations are then
solved using library routines in programmable hand calculators, or by programming an
appropriate numerical technique such as Gaussian elimination on either a programmable
hand calculator or a computer.
Since the analysis requires application of the boundary conditions at the
freshwater^ head of the estuary and the coastal mouth of the estuary to obtain
the same number of equations as unknowns, the entire estuary must be Included
In the first cut analysis. The initial analysis will yield the overall pollutant
distribution throughout the entire estuary. Once this is determined, the analysis
could be repeated to obtain more detail for smaller portions of the estuary by using
the first cut results to estimate the pollutant boundary conditions at each end of
the region of concern, and then rearranging equations (7) and (8) so the terms
involving the concentrations outside the specified regions are treated as constants
and moved to the right hand side of the equations.
The Pritchard Model theoretically allows external pollutant loading to be
introduced directly into any segment along the estuary. By moving external loadings
from the head to near the mouth of the estuary, the planner can predict how pollutant
levels are affected. However, experience with the model has shown that when external
side loadings are considerably larger than those which enter at the head of the
estuary, model instabilities can arise. When this occurs, the pollutant profile
oscillates from segment to segment, and negative concentrations can result. It is
recommended that the user first run the Pritchard Model by putting all pollutant
loading into the head of the estuary. This situation appears to be always stable,
and, as the following example shows, reasonable pollutant profiles are predicted.
-2?2-
-------
I EXAMPLE VI-10 '
i !
! Pollutant Distribution 1n a Stratified Estuary |
i i
The Patuxent River 1n Maryland 1s a partially stratified estuary, where j
. the degree of stratification depends on the freshwater flow rate discharged
! at the head of the estuary. Table VI-18 shows the salinity distribution within !
j the estuary under low flow conditions for each segment and layer. The location of j
I each layer Is shown In Figure Vl-26. Also shown 1n the table 1s the pollutant I
| distribution by layer and segment for a Mass flux of 125 Ibs/day (57 kg/day) of |
j conservative pollutant Input at the head of the estuary. j
j The pollutant distribution was predicted by solving on a computer the
12-segment, 2-1ayer system (24 simultaneous equations). The salinity distribution <
! shown 1n Table VI-18 was used as Input data. As a point of Interest, the same !
! network was solved using the model WASP (courtesy of Robert Ambrose, ERL, U.S. {
I Environmental Protection Agency, Athens, Georgia), which 1s a dynamic two-d1men- I
» i
| slonal estuary model. Instead of using salinity directly. WASP predicts the |
j salinity distribution based on dispersive and advectlve exchange rates. The j
j salinity distribution predicted by WASP 1s the same as shown 1n Table VI-18, which j
was u*ed n Input to PHtchard's Model. After running WASP to steady-state '
, conditions,, the pollutant distribution throughout the estuary was virtually the
I same as predicted by PrUchard's Model.
I The pollutant distribution 1n the Patuxant estuary will be solved In detail
| using 4 segments Instead of 12. The resulting system of 8 simultaneous equations
j can be solved on a variety of hand-held calculations. The tabulations below show
j salinities at each segment boundary, and the horizontal flow rates 1n the upper
and lower layers.
Boundary (Vn-l,n (Vn-l,n
-------
, TABLE VI -18 j
1 SALINITY AND POLLUTANT DISTRIBUTION IN PATUXENT !
j ESTUARY UNDER LOW FLOW CONDITIONS f
i
! Salinity
| {as Chloride, mg/1)
1 Segment Number Upper Layer
1
j 1 496.
j 2 1831 .
i
1 3 3771.
1 4 6050.
! 5 8040.
6 9310
1
7 10010.
1
j 8 10790.
j 9 11240.
1 '10 11830.
1 El 12100.
! 12 12750.
boundary 13500.
1
i
1
| The salinities within each layer,
Lower Layer
524.
1940.
3970.
6280.
8220.
9910.
10660.
11070.
11760.
12120.
12650.
12850.
13500.
the salinity and
Pollutant Concentration
Upper Layer
0.193
0.173
0.144
0.100
0.081
0.062
0.051
0.040
0.033
0.025.
0.021
0.011
0.0
Lower Layer J
i
0.192 j
0.171 1
0.141 J
0.108 !
0.078
1
0.053
0.042 j
0.036 j
0.025 1
0.020 !
0.013 !
I
0.009 j
0.0 j
1
i
flow rate between the interface j
1 of each layer, and the exchange coefficients are tabulated below. 1
i
1 C A — M + ' ^. t / «fc ^ ^ J _
i oegment u n v n
n mg/l-Cl mg/l-Cl
! 1 1830 1890
j 2 8040 8130
j 3 10790 10930
{ 4 12100 12380
mg/l-Cl m /sec
1940 113.
B220 23.
11070 -45.
12650 63.
' The flow rates were found from Equation VI-50, and
1 from Equation VI-51.
1 Substituting these data into
the pollutant ma;
m /sec
3260.
3140.
930.
280.
the exchange
is balance exp
I
i
i
i
i
i
coefficients
1
resslons (Equations 1
-224-
-------
FIGURE VI-26 PATUXENT ESTUARY MODEL SEGMENTATION
-225-
-------
t VI-54 through VI-59), the following system of equations result:
-6528.
6411.
117.
0.
0.
0.
0.
6638.
-6525.
0.0
0.
0.
0.
0.
-117.
0.0
-6275.
6252.
139.
0.
0.
0.
0.
113.
6297.
.6275.
0.0
-136.
0.
0.
0.
0.
-139.
0.0
.1856.
1901
94.
0.
0.
0.
0.
136
1811.
.1856.
0.0
-91.
o.
0.
°-
0.
-94.
0.0
-561
499.
0."
0.
0.
0.
0.
91.
624.
.561
(cu>;
(c])1
(CU>2
3
4
2
3
4
OF EXAMPLE VI-10 -•
6.5 POLLUTANT DISTRIBUTION FOLLOWING DISCHARGE FROM A KARINE OUTFALL
6.5.1 Introduction
Numerous coastal states have enacted water quality standards which limit
the maximum allowable concentration of pollutants, particularly metals and organic
-226-
-------
toxicants, which can be discharged into estuaMne and coastal waters. The standards
normally permit that an exempt area, called a mixing zone, be defined around the
outfall where water quality standards are not applicable. For example, the Water
Quality Control Plan for Ocean Waters of California (State Hater Resources Control
Board, 1978) sets forth the following statement directed at toxic substance limitations:
"Effluent limitations shall be imposed in a manner prescribed
by the State Board such that the concentrations set forth ... as
water quality objectives, shall not b* exceeded in the receiving
water upon the completion of initial dilution."
The mixing zone, or zone of initial dilution (ZID), 1s non-r1gorously defined as
the volume of water where the wastewater and ambient saline water mix during the
first few minutes following discharge, when the plume still has momentum and buoyancy.
As the wastewater 1s discharged, it normally begins to rise because of Its buoyancy
and momentum, as Illustrated 1n Figure VI-27.
If the ambient water column is stratified and the water depth is great enough,
the rising plume will not reach the surface of the water, but rather will stop at the
level where the densities of the plume and receiving water become equal. This level
is called the plume's trapping level. (See Figure Vl-27.) Due to residual momentum,
the plume might continue to rise beyond the trapping level, but will tend to fall
back aftar the momentum 1s completely dissipated. Once the plume stops rising, the
waste field begins to drift away from the ZID with the ambient currents. At this
time, initial dilution is considered complete. Section 6.5.2, which follows, shows
how initial dilution is calculated, and then Sections 6.5.3 and 6.5.4 Illustrate how
pollutanv concentrations at the completion of initial dilution can be predicted.
Sections 6.5.5 and 6.5.6 explain methods of predicting pollutant and dissolved oxygen
concentrations, respectively, as the waste field migrates away from the ZID.
The methods presented 1n Sections 6.5.2 through 6.5.6 are applicable to strati-
fied or non-stratified estuaries, embayments, and coastal waters. The methods assume
that reentrainment of previously discharged effluent back into the ZID is negligible.
Reentrainment can occur if the wastewater 1s discharged into a confined area where
free circulation is impaired or because of tidal reversals in narrow estuaries.
6.5.2 Prediction of Initial Dilution
6.5.2.1 General
Discharge to bodies of water through submerged diffusers is a common waste
water management technique. A diffuser 1s typically a pipe with discharge ports
spaced at regular intervals. Such discharges are often buoyant with high exit
velocity relative to the ambient velocity. The resulting waste streams act as plumes
or buoyant jets. The velocity shear between ambient and plume fluids results in the
-227-
-------
Ptrticutite*
(which settle out
of dntt field)
Effluent leaving
difruser ports
FIGURE VI-27 WASTE FIELD GENERATED BY MARINE OUTFALL
Incorporation of ambient fluid into the plume, a process called entralnment. Initial
dilution results from the entrainment of ambient fluid Into the plume as the plume
rises to Its trapping level.
The magnitude of Initial dilution depends on a number of factors including,
but not limited to, the depth of water, ambient density stratification, discharge
-228-
-------
rate, buoyancy, port spacing (I.e. plume merging), and current velocity. These
factors may be referred to collectively as the dlffuser flow configuration or simply
the flow configuration. Depending on the flow configuration, the Initial dilution
may be less than 10 or greater than 500. As attaining water quality criteria may
often require relatively high Initial dilution, the need to be able to estimate
Initial dilution for various flow configurations becomes apparent.
Other than actually sampling the water after a facility 1s In operation,
there are various ways to estimate pollutant concentrations achieved in the vicinity
of a particular dlffuser. A scale model faithful to all similarity criteria could
yield the necessary dilution Information. Dimensional analysis and empirical formulae
may also be very useful. Alternatively, a numerical model based on the laws of
physics may be developed. This method is chosen to provide initial dilution estimates
here because it is more cost-effective than field sampling and more accurate than a
scale model.
Any numerical model used to provide dilution estimates should faithfully
replicate the relevant plume relationships and should be verified for accuracy.
The plume model MERGE (Frlck, 1981c) accounts for the effects of current ambient
density stratification and port spacing on plume behavior. In addition, it has been
extensively verified (Frick, 1981a, 1981b; Tesche et_ a]_., 1980; Pollcastro et^ al_.,
1980; Cawiar! et_ aj_., 1981).
There are several ways of presenting the initial dilution estimates. MERGE may
be run for specific cases or run for many cases spanning a range of conditions and
presented in nomogram or tabular form. The latter method Is the most compact. The
resulting inRial dilution tables display values of dilution achieved at the indicated
depths and densimetric Froude numbers. One hundred tables are presented in Appendix
G for various combinations of port spacing, density stratification, and effluent-to-
current velocity ratio.
Before describing the tables in more detail and discussing examples, it may be
helpful for some users to read the following, occasionally technical, discussions of
the plume model MERGE (Section 6.5.2.2) and of basic principles of similarity (Section
6.5.2.3). Others may want to advance directly to Section 6.5.2.4 describing table
usage.
6.5.2.2 The Plume Model MERGE
MERGE 1s the latest in a series of models whose development began in 1973.
Various stages of model development have been recorded (Winiarski and Frick, 1976 and
1978; Frick, 1981c). In the realm of plume modeling, MERGE belongs to the Lagrangian
minority since more models «re Eulerian. The model can be demonstrated to be basically
equivalent to its Eulerian counterparts (Frick and Winiarksi, 1975; Frick, 1981c).
Time is the independent variable which is incremented in every program iteration
based on the rate of entrainaent.
-229-
-------
To simplify the problem, many assumptions and approximations are made 1n
plume modeling. In MERGE, steady-state 1s assumed and the plume 1s assumed to
have a round cross section everywhere.
The MERGE user may Input arbitrary current and ambient density profiles.
The model Includes a compressible equation of continuity so that the predictions
are also valid for highly buoyant plumes. It accounts for merging of adjacent
plumes but only when the ambient current dilution 1s normal to the dlffuser pipe. In
many cases, this 1s not a significant restriction as many dlffusers are oriented to
be normal to the prevailing current direction.
The model contains an option for using either constant or variable coefflents
of bulk expansion 1n the equation of state. The water densities 1n Table VI-19
are generated using the model's density subroutine based on actual temperatures
and salinities (I.e. effectively using variable coefficients). If temperature
and salinity data are unavailable then the model can be run based on density data
alone. The latter method Is satisfactory for relatively high temperatures and
salinities because the equation of state 1s relatively linear with these variables 1n
that range. However, for low densities and temperatures gross Inaccuracies may
result. Unfortunately, the Initial dilution tables are based on the latter method.
A nore accurate representation would greatly Increase the number of tables necessary
to cover all the cases. Users with applications Involving cold, low salinity water
are urged ro run the more accurate form of the model.
The success of MERGE In predicting plume behavior 1s primarily attributable
to two unique model features. The first of these relates to the expression of
forced entralnment. Entralnment may be attributed to the velocity shear present even
1n the absence of currents. I.e. aspiration, and to current-Induced entrainment,
sometimes called forced entrainment.
The forced entrainment algorithm In MERGE 1s based on the assumption that
all fluid flowing through the upstream projected area of the plume 1s entrained.
This hypothesis 1s based on we11-established principles and observations (Rawn
«!«!., I960; Jlrka and Harlman 1973). Paradoxically, the hypothesis has never
been implemented In numerical models before. The projected area normally contains
linear and quadratic terms 1n plume diameter, whereas in conventional modeling,
forced entrainment is generally expressed as a linear function of diameter. It 1s
necessary to Include additional sources of entrainment to make up the difference when
so expressed.
The second feature 1s the use of a constant aspiration coefficient. This
coefficient 1s often considered to be variable (e.g. Fan, 1967). The need for
a variable coefficient 1s attributable to the fact that many models predict centerllne
plume values. For plumes discharged vertically upward Into density stratified
ambient water, such models are expected to predict the maximum penetration of the
plume. To achieve agreement requires a relatively small aspiration coefficient.
-230-
-------
WATER DENSITIES (EXPRESSED AS SIGMA-T)* CALCULATED
USING THE DENSITY SUBROUTINE FOUND IN NEKGE
Salinity
(°/oo) 0
0
5
10
IS
20
-0.093
.721
1.535
2.348
3.159
3.970
4.781
5.590
6.399
7.207
8.015
8.822
9.628
10.434
11.240
127015-
[?.850
13.654
14.459
15.263
I6.06F
16.870
17.674
18.478
19.281
-0.034
.776
1.586
2.395
3.203
4.010
4.817
5.623
6.428
7.233
8.037
8.840
9.643
10.446
11.248
12.019
12.851
H.652
14.453
15.254
16.051
16.855
17.655
18.455
19.225
2 4
.007 .031 .039 .030
.814 .835 .839 .827
1.620 1.637 1.638 1.623
2.425 2.439 2.437 2.419
3.230 3.240 3.234 3.213
4.033 4.040 4.031 4.007
4.836 4.840 4.818 4.800
5.639 5.639 5.623 5.593
6.441 6.437 6.418 6.385
7.242 7.235 7.213 7.176
8.042 8.032 8.007 7.967
8.842 8.829 8.801 8.758
9.642 9.625 9.594 9.548
10.441 10.421 10.387 10.338
11.240 11.217 11.179 11.127
12.038 12.012 11.971 11.916
12.836 12.807 12.763 12.705
13.634 13.602 13.555 13.494
14.432 14.396 14.346 14.282
15.229 15.190 15.137 15.071
16.027 15.985 15.929 15.859
16.824 16.779 16.720 16.647
17.621 17.573 17.511 17.436
18.418 18.367 18.302 18.224
19.255 19.161 19.093 19.012
TEMPERATURE (°C)
5 8
.006
.800
1.593
2.385
3.177
3.968
4.758
5.548
6.337
7.125
7.913
8.701
9.488
10.275
11.062
11.848
12.634
13.420
14.205
14.991
15.777
16.562
17.347
18.133
18.919
-0.032
.758
1.548
2.338
3.126
3.914
4.701
5.488
6.274
7.060
7.845
8.630
9.415
10.199
10.983
11.766
12.549
13.332
14.115
14.898
15.661
16.464
17.247
18.030
18.813
-0.086
.702
1.489
2.276
3.061
3.847
4.631
5.415
6.199
6.982
7.764
8.546
9.328
10.109
10.890
11.671
12.452
13.232
14.013
14.793
15.573
16.354
17.134
17.914
18.694
-0.154
.632
1.416
2.200
2.983
3.765
4.547
5.329
6.109
6.890
7.670
8.449
9.228
10.007
10.786
11.564
12.342
13.120
13.898
14.676
15.453
16.231
17.009
17.787
18.565
10
-0.235
.548
1.329
2.111
2.691
3.671
4.450
5.229
6.007
6.785
7.563
8.340
9.116
9.893
10.669
11.445
12.220
12.996
13.771
14.547
15.322
16.097
16.873
17.648
18.424
-0.330
.450
1.230
2.006
2.786
3.564
4.341
5.117
5.893
6.668
7.443
8.218
8.992
9.766
10.540
11.313
12.087
12.860
13.633
14.406
lb.179
15.952
16.725
17.498
18.271
12
-0.438
.340
1.117
1.893
2.669
3.444
4.218
4.992
5.766
6.539
7.312
8.084
8.856
9.628
10.399
11.170
11.941
12.712
13.483
14.254
15.025
15.796
16,566
17.337
18.108
-0.558
.217
.992
1.766
2.539
3.312
4.064
4.856
5.627
6.398
7.168
7.939
8.708
9.478
10.247
11.016
11.785
12.554
13.322
14.091
14.860
15.628
16.397
17.166
17.935
14
-0.691
.082
.854
1.626
2.397
3.16tJ
3.938
4.708
5.477
6.245
7.UI4
7.782
8.549
9.317
10.1)84
10.851
11.618
12.384
13.151
13.917
14.684
15.451
16.217
16.984
17.751
-231-
-------
TABLE Vl-19a
(Continued)
Salinity
(o/oo) 0
25 20.055
20.838
21.692
22.496
23.300
30 24.104"
20.056
20.856
21.657
22.457
23.258
24.059
2
20.012
20.810
21.607
22.405
23.202
24.001
19.955
20.749
21.544
22.338
23.133
23.929
4
19.884
20.676
21.467
22.259
23.051
23.843
19.801
20.589
21.378
22.167
22.956
23.746
TEMPEHATUKE (°C
5
19.704
20.490
21.276
22.063
22.849
23.636
19.596
20.379
21.162
21.946
22.730
23.514
)
8
19.475
20.256
21.037
21.818
22.599
23.381
19.343
20.121
20.900
21.678
22.458
23.237
10
19.199
19.975
20.751
21.528
22.305
23.082
19.045
19.819
20.592
21.367
22.141
22.916
12
18.880
19.651
20.423
21.195
21.967
22.740
18.704
19.473
20.243
21.103
21.783
22.554
14
16.518
19.285
20.053
20.821
21.5B9
22.358
25.713 25.662 25.598 25.520 25.429 25.326 25.211 25.084 24.946 24.797 24.637 24.467 24.287 24.097 23.897
26.518 26.464 26.397 26.316 26.223 26.117 25.999 25.870 25.729 25.578 25.416 25.243 25.061 24.869 24.667
27.324 27.267 27.196 27.113 27.016 26.908 26.788 26.656 26.513 26.359 26.195 26.020 25.836 25.641 25.437
35 28.130 25.070 27.996 77^10 27.611 27.700 27.577 27.422 27.297 27.141 26.974 26.798 26.611 26.414 26.208
25.936 28.873 26.737 Zfl./OB 28.606 28.492 28.366 28.230 28.082 27.923 27.754 27.575 27.357 27.185 26.950
29.743 29.677 29.598 29.506 29.401 29.285 29.157 19.017 28.867 28.706 28.535 28.354 28.163 27.963 27.753
30.550 30.482 30.399 30.305 30.197 30.078 29.948 29.806 29.653 29.490 29.317 29.133 28.940 28.738 28.526
31.358 31.287 31.202 31.104 30.994 30.872 30.739 30.595 30.440 30.275 20.099 29.913 29.718 29.514 29.300
40 32.167 32.042 32.605 31.904 31.732 31.667 31.53? 31.3B5 31.227 31.060 30.682 30.694 30.497 36.290 30.075
•Stg«a-t (ff») is defined as: (densUy-1) x 103. For example, for seawater xlth a density of 1.02500 g/cm3, vt • 25.
-232-
-------
TABLE VI-19b
MATER UENSITIES {EXPRESSED AS SIGMA-T)* CALCULATED
USING THE DENSITY SUBROUTINE FOUND IN MERGE
Salinity
(°/oo)
0 -0.836
-0.065
.705
1.475
2.24*
5 3.012
3.780
4.548
5.315
6.082
10 6.848
7.614
8.379
9.145
9.910
15 10.675^
11.439^
12.204
12.969
13.733
20 14.498~
15. 26^
16.027
16.792
17.557
16
-0.993
-0.224
.544
1.312
2.079
2.845
3.611
4.377
5.142
5.907
6.671
7.435
8.198
8.962
9.725
10.488
11.251
12.013
12.776
13.539
14.301
15.064
15.827
16.590
17.353
-1.161
-0.394
.372
1.138
1.903
2.667
3.431
4.195
4.958
5.721
6.483
7.245
8.007
8.768
9.530
10.291
VI . 052
11.813
12.573
13.334
14.095
14.856
15.617
16.378
17.139
18
-1.341
-0.576
.189
.952
1.716
2.478
3.240
4.002
4.763
5.524
6.285
7.045
7.805
8.565
9.324
10.083
10.843
11.602
12.361
13.120
13.879
14.638
15.397
16.156
16.916
-1.532
-0.768
-0.006
.756
1.518
2.279
2.039
3.799
4.558
5.317
6.076
6.835
7.593
8.351
9.108
9.866
10.623
11.381
12.138
12.895
13.653
T4.410
15.168
15.925
16.683
20
-1.733
-0.971
-0.211
.550
1.309
?.06B
2.827
3.585
4.343
5.100
5.857
6.614
7.371
8.127
8.883
9.639
10.395
11.150
11.906
12.662
13.417
14.173
14.929
15.685
16.441
TEMPERATURE (°C
22
-1.945
-1.185
-0.426
.333
1.091
1.848
2.605
3.362
4.118
4.873
5.629
6.3B4
7.139
7.893
8.648
9.402
10.156
10.910
11.664
12.418
13.173
13.927
14.681
15.436
16.190
-2.167
-1.409
-0.651
.106
.862
1.618
2.373
3.128
3.882
4.636
5.390
6.144
6.897
7.650
8.403
9. 156^
9.908
10.661
11.413
12.166
12.919
13.671
14.424
15.177
15.931
)
-2.399
-1.642
-0.887
-0.131
.623
1.377
2.131
2.884
3.637
4.390
5.142
5.894
6.646
7.397
8.149
6.900
9.6M
10.402
11.153
H.904
12.656
13.407
14.158
14.910
15.662
24
-2.641
-1.885
-1.132
-0.378
.375
1.127
1.880
2.631
3.383
4.134
4.885
5.635
6.385
7.135
7.885
8.635
9.385
10.134
10.884
11.634
12.384
13.134
13.884
14.634
15.384
-2.893
-2.139
-1.387
-0.635
.117
.868
1.619
2.369
3.119
3.868
4.618
5.367
6.116
6.864
7.613
6.361
9.109
9.858
10.606
11.354
12.103
22.851
13.600
14.349
15.098
26
-3.154
-2.402
-1.651
-0.901
-0.150
.599
1.348
2.097
2.846
3.594
4.342
5.089
5.837
6.584
7.331
8.078
8.825
9.572
10.319
11.066
11.813
12.560
13.308
14.056
14.803
-3.425
-2.674
-1.925
-1.176
-0.427
.321
1.069
1.816
2.563
3.310
4.057
4.803
5.549
6.295
7.041
7.786
8.532
9.278
10.023
10.769
11.515
12.261
13.007
13.754
14.500
28
-3.704
-2.956
-2.208
-1.460
-0.713
.034
.780
1.526
2.272
3.017
3.763
4.507
5.252
5.997
6.741
7.486
8.230
8.975
9.719
10.464
11.208
11.953
12.698
13.443
14.189
-3.993
-3.246
-2.499
-1.753
-1.007
-0.262
.483
1.228
1.972
2.716
3.460
4.Z03
4.947
5.690
6.433
7.176
7.920
8.663
9.406
10.149
10.893
11.637
12.381
13.125
13.869
-233-
-------
TABLE Vl-195
(Continued)
Salinity
25 18.322
19.087
19.853
20.619
21.385
30 22.152
22.919
23.687
24.455
25.224
35 25.993
2 7 '.534
28.305
29.077
40 29.850
16
18.116
18.880
19.643
20.408
21.172
21.937
22.702
23.468
24.235
25.001
75.769
26.537
27.306
28.075
28.846
29.617
17.901
19.424
20.187
20.949
21.713
22.476
23.240
24.005
24.770
25.536
26. 302
27.069
27.837
28.605
29.375
18
17.676
18.436
19.196
19.957
20.718
21.479
22.241
23.003
23. 766
24.530
25.294
26. 058
26.824
27.590
28.357
29.124
17.441
18.200
18.958
19.717
20.477
21.236
21.997
22. 757
23.519
24.281
25.043
25.806^
26.570
27.334
28.100
28.866
20
17.198
17.955
18.712
19.469
20.227
20.985
21.744
22.503
23.263
24.023
?4.?84
25.545
26.308
27.071
27.834
28.599
TEMPERATURE (°C)
22
16.945
17.701
16.456
19.212
19.968
20.725
21.482
22.240
22.998
23.757
24.516
25.277
26.037
26. 799
27.561
28. 324
16.684
17.438
18.192
18.946
19.701
20.456
21.212
21.968
22.725
23.483
24.241
24.999
25. 759
26.519
27.280
28.042
16.414
17.166
17.919
18.672
19.425
20.179
20.934
21.669
22.444
23.200
23.957
24.714
25.472
26.231
26.991
27.751
24
16.135
16.886
17.637
18.389
19.141
19.894
20.647
21.401
22.155
22.910
23.665
24.421
25.178
25.936
26.694
27.453
15.848
16.597
17.347
18.098
18.849
19.600
20.352
21.104
21.857
22.611
23.365
24.120
24.876
25.632
26.390
27.148
26
15.552
16.300
17.049
17.798
18.548
19.298
20.049
20.800
21.552
22.304
23.058
23.811
24.566
25.321
26.078
26.835
15.247
15.995
16.742
17.490
18.239
18.988
19.738
20. 488
21.239
21.990
22.742
23.495
24.248
25.003
25.758
26.514"
28
14.935
15.631
16.428
17.175
17.922
18.670
19.419
20.168
20.917
21.668
22.419
23.171
23.923
24.677
25.431
26.186
14.614
15.359
16.105
16.851
17.597
16.344
19.091
19.840
20.588
21.338
22.088
22.839
23.590
24.343
25.096
25.651
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