EPA-600/9 77 023a
AUGUST 1977
Property of
US Environmental Protection Agency
Library Rigson X
1200 Sixth Avenue
Suaitk WA 98101
DLC >*. iWi
WATER QUALITY ASSESSMENT:
A SCREENING METHOD
FOR NONDESIGNATED
208 AREAS
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
environmental Research Laboratory
Athens, Georgia 30605

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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series These nine broad cate-
gories .ere established to facilitate further development and application of en-
viro r ental technology. Elimination of traditional grouping was consciously
pi? 5d to foster technology transfer and a maximum interface in related fields.
The .line series are:
1	Environmental Health Effects Research
2	Environmental Protection Technology
3	Ecological Research
4.	Environmental Monitoring
5.	Socioeconomic Environmental Studies
6	Scientific and Technical Assessment Reports (STAR)
7	Interagency Energy-Environment Research and Development
8	"Special" Reports
9	Miscellaneous Reports
I If
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.

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EPA-600/9-77-023
August 1977
WATER QUALITY ASSESSMENT
A Screening Method
for Nondesignated 208 Areas
by
Stanley W.	Zison
Kendall F.	Haven
William B.	Mills
Tetra Tech, Inc.
Lafayette, California 94549
Grant No. R804450-01-0
Project Officer
James W. Falco
Environmental Research Laboratory
Athens, Georgia 30605
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30605

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DISCLAIMER
This report has been reviewed by the Environmental Research Laboratory,
U.S. Environmental Protection Agency, Athens, Georgia, and approved for publi-
cation. Approval does not signify that the contents necessarily reflect the
views and policies of the U.S. Environmental Protection Agency, nor does men-
tion of trade names or commercial products constitute endorsement or recommen-
dation for use.
ii

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FOREWORD
As environmental controls become more costly to implement and the
penalties of judgment errors become more severe, environmental quality
management requires more efficient analytical tools based on greater
knowledge of the environmental phenomena to be managed. As part of this
Laboratory's research on the occurence, movement, transformation, impact, and
control of environmental contaminates, the Technology Development and
Applications Branch develops management or engineering tools to help
pollution control officials achieve water quality goals through watershed
management.
Basin planning requires a set of analysis procedures that can provide an
assessment of the current state of the environment and a means of predicting
the effectiveness of alternative pollution control strategies. This report
contains a description of a set of consistent analysis procedures that
accomplish these tasks. It is directed toward local or state government
planners who must interpret technical information from many sources and
recommend the most prudent course of action that will maximize the environ-
mental benefits to the community and minimize the cost of implementation.
David W. Duttweiler
Director
Environmental Research Laboratory
iii

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ABSTRACT
The objective of this study is to develop a methodology for the
preliminary screening of surface water quality applicable for use by
nondesignated 208 planning agencies. Analytical methods are included
for the assessment of rivers, impoundments, and estuaries. Additionally,
methods are provided by which point and nonpoint sources can be
evaluated.
The water quality parameters analyzed for all three water body
types are biochemical oxygen demand, dissolved oxygen, temperature,
and sediment accumulation. Other constituents, more pertinent to
a particular water body type, are also addressed. The analyses are
designed to be performed with, at most, the assistance of a desk top
calculator and with a minimal amount of data input.
This report is submitted in partial fulfillment of Grant No.
R804450-01-0 by Tetra Tech, Inc. Work was completed March 31. 1977.
iv

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TABLE OF CONTENTS
Page
Foreword	i
Abstract	iv
List of Figures	v111
List of Tables	xvil
Chapter
1	Introduction	1
1.1	Background	1
1.2	Problem Definition	2
1.3	Purpose and Scope	2
2	Overview of Methodology	4
2.1	PIanning Steps	4
2.2	Base Map	5
2.3	Data Collection	5
2.4	Plotting Data on Maps	8
2.5	Analysis of Hydrologic Data, Estimation
of Waste Loads, Data Supplementation	9
2.6	Stream Analyses	9
2.7	Impoundment Analyses	10
2.8	Estuarine Analyses	11
2.9	Presentation of Results	12
2.10	Limitations of Methodology	12
3	Waste Loading Calculations	14
3.1	Introduction	14
3.2	Sediment Loading Function for Surface
Erosion	16
3.3	Nitrogen Loading Function	67
3.4	Phosphorus Loading Function	76
3.5	Organic Matter Loading Function	80
3.6	Accuracy of Nutrient and Organic Matter
Loading Functions	84
3.7	Loading Values for Salinity Loads in
Irrigation Return Flow	86
3.8	Pollutants from Urban Runoff	91
v

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Page
104
123
127
127
141
160
196
221
234
240
244
259
266
270
270
271
289
332
355
386
393
395
395
417
421
445
463
506
518
540
544
A-l
TABLE OF CONTENTS (Continued)
3.9 Point Source Waste Loads
References
Rivers and Streams
4.1	Introduction
4.2	Carbonaceous and Nitrogenous Oxygen
Demand
4.3	Dissolved Oxygen
4.4	Temperature
4.5	Nutrients and Eutrophication Potential
4.6	Total Coliform Bacteria
4.7	Conservative Constituents
4.8	Sedimentation
4.9	Presentation of Results
References
Impoundments
5.1	Introduction
5.2	Impoundment Stratification
5.3	Sediment Accumulation
5.4	Eutrophication
5.5	Impoundment Dissolved Oxygen
5.6	Application of Methods and Presentation
of Results: Some Recommendations
References
Estuaries
6.1	Introduction
6.2	Present Water Quality Assessment
6.3	Estuarine Classification
6.4	Flushing Time Calculations
6.5	Calculation of Pollutant Concentrations
in Estuaries
6.6	Thermal Pollution
6.7	Turbidity and Sedimentation
6.8	Tidal Prism/Throat Cross-Sectional
Area Relationships
References
Monthly Distribution of Rainfall Erosivity
Factor R
VI

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TABLE OF CONTENTS (Continued)
Appendices	Pa9e
B	Methods for Predicting Soil Erodibility
Index k	B-l
C	River and Stream Data	C-l
D	Impoundment Hydrothermal Profiles for
10 Locations in U.S.	D-l
E	Hydrothermal Profile Simulation Method	E-l
F	Sediment Accumulation in Selected
Impoundments in U.S.	F-l
G	Equivalents of Commonly Used Units of
Measurement	G-l
vii

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LIST OF FIGURES
Figure	Page
:il-l	Flow Diagram for Calculating Sediment Loading
from Surface Erosion	19
11-2	Average Annual Values of the Rainfall--
Erosivity Factor, R (U.S.D.A. and EPA, 1975)	23
11-3	Mean Annual Values of Erosion Index (in
English Units) for Hawaii (U.S. Dept. of
Agriculture, 1974)	24
11-4	Soil Moisture--Soi1 Temperature Regimes of
the Western United States (U.S. Dept. of
Agriculture, 1974)	25
11-5	Relationships between Annual Average Rainfall
Erosivity Index and the 2-Year, 6-Hr. Rainfall
Depth for Three Rainfall Types in the Western
United States (U.S. Dept. of Agriculture, 1974)	28
11-6	Storm Distribution Regions in the Western
United States (U.S. Dept. of Agriculture, 1974)	29
11-7	Slope Effect Chart Applicable to Areas A-l
in Washington. Oregon, and Idaho and All of
A-3 (U.S. Dept. of Agriculture, 1974)	33
11-8	Slope Effect Chart for Areas Where Figure 111-7
is not Applicable (U.S. Dept. of Agriculture)	34
11-9	Slope Effect Chart for Irregular Slopes
(Forter and Wischmeier, 1973)	37
11-10	Sediment Delivery Ratio for Relatively
Homogeneous Basins (McElroy, et al , 1976)	50
11-11	Projected Variation of Soil Erosion for Lands
with Constant Cover Factor, in Parts of Michigan,
Missouri, Illinois, Indiana, and Ohio
(McElroy, et al , 1976)	62
Vlll

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12
13
14
15
16
17
18
19
1
2
3
4
5
6
7
8
9
LIST OF FIGURES (Continued)
Page
Projected Variation of Soil Erosion on
Continuous Corn Lands in Central Indiana
(McElroy, et al, 1976)	66
Percent Nitrogen (N) in Surface Foot of Soil
(Parker, et al , 1946)	70
Soil Nitrogen vs. Humidity Factor and Temperature	72
Nomograph for Humidity Factor, H	73
Nitrogen (NH^-N and NO^-N) in Precipitation	75
Phosphorus Content in the Top 1 Foot of Soil
(Parker, et al, 1946)	78
Climate Zone for the Cities from Which Data are
Available and Used in the URS Study (Amy,
et al , 1974)	97
Correlation between Population Density and Curb
Length Density (American Public Works
Association, 1975)	100
Mechanisms of BOD Removal from Rivers	145
Deoxygenation Coefficient as a Function of Depth,
(After Hydroscience, 1971)	146
Example of Computation of k. from Stream Data
(From Hydroscience, 1971)	148
Hypothetical BOD Waste Loadings in a River	154
Variability of Dissolved Oxygen by Season for
22 Major Waterways, 1968-72 (EPA, 1974)	161
Reaeration Coefficient as a Function of Depth
(From Hydroscience, 1971)	164
Reaeration Coefficient for Shallow Streams,
Owen's Formulation	166
Flow Process of Solution to Dissolved Oxygen
Problem in Rivers	173
Nomogram for Solution to the Dissolved Oxygen
Sag (After Thomas, 1948)	174
ix

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LIST OF FIGURES (Continued)
Figure	Page
IV-10	Characteristic Dissolved Oxygen Profile
Downstream from a Point Source of Pollution	175
IV-11	Flow Process in Reach by Reach Solution to
Critical Dissolved Oxygen Values	188
IV-12	Hypothetical River Used in Example IV-5	193
IV-13	Idealization of a Run-of-the-River Power
Plant	198
IV-14 Mechanisms of Heat Transfer Across a Water
Surface (Parker and Krenkel, 1969)	202
IV-15 Schematic of Site No. 3 Cooling Lake
(From Edinger, et al , 1968)	203
IV-16 Observed Temperatures, Site No. 3, July 18-
July 24, 1965 (Edinger, et al, 1968)	204
IV-17	Comparison of Computed Equilibrium and
Ambient Temperatures with Observed Mean
Diurnal Temperature Variations for Site No. 3
July 18-July 24, 1966 (Edinger, et al , 1968)	205
IV-18 Mean Daily Solar Radiation (Langleys)
Throughout the United States for July and
August (U.S. Department of Commerce, 1968)	207
IV-19 Downstream Temperature Profile for Completely
Mixed Stream, T-E/T -E vs. r (From Edinger,
1965)	m	219
IV-20	Flow Duration Curve, Hatchie River at
Bolivar, Tenn. (From Cragwall, 1966)	222
IV-21	Frequency of Lowest Mean Discharges of
Indicated Duration. Hatchie River at Bolivar,
Tenn. (From Cragwall, 1966)	223
IV-22	Total Coliform Profiles for the Willamette
River (EPA, 1974)	236
IV-23	Salinity Distribution in a Hypothetical
River	244
x

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LIST OF FIGURES (Continued)
Fi qure	Page
IV-24 Y and tc for DuBoys Relationship as Functions
of Median Size of Bed Sediment (Task
Committee on Preparation of Sedimentation
Manual, 1971 )	248
IV-25 Hydraulic Radii for Different Channel Shapes
(From King, 1954)	250
IV-26 Sediment Discharge as a Function of Water
Discharge for the Colorado River at Taylor's
Ferry (Task Committee on Preparation of
Sedimentation Manual, 1971)	257
IV-27	Sediment Discharge as a Function of Water
Discharge for the Niobrara River at Cody,
Nebraska (Task Committee on Preparation of
Sedimentation Manual, 1971)	258
IV-28 Graphical Presentation of Results of
Example IV-5	261
IV-29 Graphical Results of Example IV-4	263
V-1	Water Density as a Function of Temperature
and Dissolved Solids Concentration (from
Chen and Orlob, 1973)	272
V-2	Water Flowing into an Impoundment Tends to
Migrate Toward a Region of Similar Density	273
V-3	Annual Cycle of Thermal Stratification and
Overturn in an Impountment	275
V-4	Plots Used in Example V-l Thermal Profile	287
V-5	Thermal Profile Plots Appropriate for
Use in Example V-2	291
V-6	Sediment Rating Curve Showing Suspended
Sediment Discharge as a Function of Flow
(After Linsley, Kohler, and Paulhus, 1958)	294
V-7	A Relationship Between the Percent of Inflow-
Transported Sediment Retained within an
Impoundment and the Ratio of Capacity to
Inflow (From Linsleyk Kohler, and Paulhus,
.1958)	296
xi

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LIST OF FIGURES (Continued)
Fi qure	Page
V-8	Plot of C/R and CR2 versus R (From Camp,
1968)	301
V-9	The Drag Coefficient (C) as a Function of
Reynolds' Number (R) and Particle Shape
(From Camp, 1968)	302
V-10 Schematic Representation of Hindered
Settling of Particles in a Fluid Column	303
V-11	Velocity Correction Factor for Hindered
Settling (From Camp, 1968)	305
V-12	Upper and Lower Lakes and Environs, Long
Island, New York	310
V-13	Impoundment Configurations Affecting
Sedimentation	314
V-14	Kellis Pond and Surrounding Region,
Long Island, New York	317
V-15	Hypothetical Depth Profiles for Kellis
Pond	318
V-16	Hypothetical Flow Pattern in Kellis Pond	319
V-17	Hypothetical Depth Profiles for Kellis
Pond Not Showing Significant Shoaling	320
V-18 Lake Owyhee and Environs	322
V-19	New Millpond and Environs	323
V-20 Significance of Depth Measures D, D1, and
D11, and the Assumed Sedimentation Pattern	326
V-21	Settling Velocity for Spherical Particles	327
V-22	Nomograph for Estimating Sediment Trap
Efficiency	328
V-23 The Vollenweider Relationship	336
V-24	Plot of the Vollenweider Relationship Showing
the Position of 133 Eastern U.S. Impoundments
Impacted by Municipal Sewage Treatment Plant
(MSTP) Effluents (National Eutrophication
Survey, 1976)	337
xii

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LIST OF FIGURES (Continued)
Figure	Page
V-25	Relationship Between Summer Chlorophyll
and Spring Phosphorus (from Lorenzen,
unpublished)	343
V-26	Maximal Primary Productivity as a Function
of Phosphate Concentration (After
Chiandani, et al, 1974)	345
V-27	Conceptualization of Phosphorus Budget
Modeling (Lorenzen, et al , 1976)	347
V-28	Geometric Representation of a Stratified
Impoundment (From HEC, 1974)	358
V-29	Quality and Ecologic Relationships (From
HEC, 1974)	359
V-30	Rate of BOD Exertion at Different
Temperatures Showing the First and Second
Deoxygenat'ion Stages	364
V-31	Quiet Lake & Environs	373
V-32	Thermal Profiles for 20-Foot Deep
Berlington, Vermont, Impoundment	381
V-33	A Possible Approach to Displaying Sediment
Deposition Rates as a Function of Time and
Axial Distance Downstream	389
V-34	Displaying Trap Efficiency as a Function
of Grain Size	390
V-35	An Example of a Plot of DO Versus Time	391
VI-1	Typical Main Channel Salinity and Velocity
Profiles for Stratified Estuaries	400
VI-2	Typical Main Channel Salinity and Velocity
Profiles for Well Mixed Estuaries	402
VI-3	Typical Main Channel Salinity and Velocity
Profiles for a Partially Mixed Estuary	403
VI-4	Estuarine Dimensional Definition	406
Xlll

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LIST OF FIGURES (Continued)
Fi qure	Page
V1-5	Saturation Temperature Salinity Relationships
(Green, 1963)	408
VI - 6	Schematic Diagram of Estuarine Water Quality
Calculation Process	415
VI - 7	Estuarine Classification Schematic	423
VI-8	Examples of Estuarine Suitability for Hand
Calculations	424
VI-9	Estuarine Circulation-Stratification Diagram	426
VI-10	Examples of Estuarine Classification Plots
(From Hansen and Rattray, 1966)	426
VI-11	Circulation and Stratification Parameter
Term Diagram	428
VI-12	The Typical Estuary	429
VI-13	Typical Estuary Data for Classification
Calculations	431
VI-14	Estuarine Circulation-Stratification Diagram	434
VI-15	Alsea Estuary Seasonal Salinity Variations
(From Giger, 1972)	436
VI-16. Estuary Cross-Section for Tidal Prism
Calculations	439
VI-17	Alsea Estuary Summer High Tide Salinity
Profile	451
VI-18	Alsea Estuary Fraction of Fresh Water
Segmentation	451
VI-19	Alsea Estuary Cross-Sectional Areas	452
V1-20	Alsea Estuary Cross-Sectional Areas	458
VI-21	Alsea Estuary Upstream Intertidal Volume	458
V1-22	Dispersion Methodology Schematic	465
VI-23	River Borne Pollutant Concentration for One
Tidal Cycle	471
xiv

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LIST OF FIGURES (Continued)
Figure	Page
VI-24 Alsea Estuary River Borne Conservative
Pollutant Concentration	473
VI-25	Pollutant Concentration from an Estuarine
Outfall	476
V1-26 Alsea Estuary Salinity and f Profile	477
V1-27 Alsea Estuary Example Heavy Metal
Concentration for Two Outfalls	480
VI-28	Example Estuarine Non-Conservative Pollutant
Concentration	488
VI-29 Incremental BOD Loading--D0 Response in
Estuaries	488
VI-30	Contributing Factors to Dispersion Coefficients
in the Estuarine Environment	492
V1-31	Additive Effect of Multiple Waste Load
Additions	495
VI-32	Single Event Pollutant Flow into an Estuary	500
VI-33 Estuarine Heat Budget (After Parker and
Krenkel, 1970)	508
VI-34	Initial Thermal Plume Mixing	512
VI - 3 5 Mean Suspended Solids in San Francisco Bay
(From Pearson, et al, 1967, pg V-15)	522
V1-36	Sediment Movement in San Francisco Bay System
(Million Cubic Yards) (From U.S. Engineering
District, San Francisco, 1975)	529
VI-37	Idealized Estuarine Sedimentation	530
V1-38	Particle Diameter vs Settling Fall per Tidal
Cycle (12.4 hrs) Under Quiescent Conditions
(Spheres with density 2.0 gm/cm^)	535
V1-39 Estuarine Null Zone Identification	538
VI-40 Tidal Prism vs Cross-Sectional Area, Regression
Curves for all Inlets	542
XV

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LIST OF FIGURES (Continued)
Figure	Page
VI-41	Tidal Prism vs Cross-Sectional Area,
Regression Curves for Inlets with One
or No Jetties	543
VI-42	Tidal Prism vs Cross-Sectional Area,
Regression Curves for Inlets with Two Jetties	544
xvi

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LIST OF TABLES
Table	Page
111-1	Applicability of Rr and Rs Factors in the
Areas West of the Rocky Mountains
(U.S. Dept. of Agriculture, 1974a)	26
111-2	Relative Protection of Ground Cover Against
Erosion (In Order of Increasing C Values)	41
111 - 3	"C" Values for Permanent Pasture, Rangeland,
and Idle Land (Wischmeier, 1972)	42
111-4	"C" Values for Woodland (Wischmeier, 1972)	44
111 - 5	"C" Values for Construction Sites (Water
Resources Administration, 1973)	45
111-6	"P" Values for Erosion Control Practices on
Croplands (U.S. Dept. of Agriculture. 1974a)	46
111 - 7	Typical Values of Drainage Density	52
111-8	Summary of Applicability of Characteristic
Factors	53
111-9	Estimated Range of Accuracy of Sediment Loads
from Surface Erosion	56
111-10	Nutrient and Sediment Losses (Viets. 1971)	69
111-11	Sediment Yield in Example	82
111-12	Available Nitrogen Loading (Lb/Day)	82
111-13	Available Phosphorus Loading (Lb/Day)	83
111-14	Organic Matter Loadings (Lb/Day)	84
111-15	Probable Range of Loading Values for Nutrients
and Organic Matter	85
111-16 Salt Yields from Irrigation in Green River
Subbasin (EPA, 1971)	87
xvii

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LIST OF TABLES (Continued)
Table
111-17 Salt Yields from Irrigation in Upper Colorado
Main Stream Subbasin (EPA, 1971)
111-18 Salt Yields from Irrigation in San Juan River
Subbasin (EPA, 1971)
11-19	Salt Yields from Irrigation in Lower Colorado
River Basin (EPA, 1971)
11-20	Salt Yields from Irrigation for Selected Areas
in California (Water Resources Councilv 1971)
11-21	Solid Loading Rates and Composition-
Nationwide Means and Substitutions of the
Nationwide Means at 80% Confidence Level
(Amy, et al, etc.)
11-22 Mean Concentrations of Mercury and Chlorinated
Hydrocarbons in Street Dirt from Nine U.S.
Cities (Amy, et al, 1974)
11-23	Equivalent Curb-Length per Unit Area of
Street Surface, Arranged by Land Use Types
(Amy, et al , 1974)
11-24 General Land Consumption Rates for Various Land
Uses (American Public Works Association, 1974)
11-25 Typical Municipal Waste Concentrations
(Metcalf and Eddy, 1972)
11-26a Examples of Municipal Discharges
11-26b Point Source Loadings of Six Major Wastewater
Treatment Facilities in One North Carolina
208 Area
11-27 Municipal Wastewater Flow Rates
11-28	Municipal Effluent Concentrations Corresponding
to EPA Best Available Technology (BAT)
Treatment Levels (Tetra Tech, Inc., 1975)
11-29	Characteristic Values for Urban Stormwater ant.
Sewer Overflow Water Quality (Field, 1975)
11-30	Comparison of Quality of Storm Sewer Discharges
for Various Cities (Lager and Smith, 1974)
xviii

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LIST OF TABLES (Continued)
Table	Page
11-31	Comparison of Quality of Combined Sewage for
Various Cities	113
11-32	Summary of Stormwater Pollutant Concentrations
(Kaiser Engineers, 1969)	114
11-33	Typical Industrial Discharge Pollutant
Concentrations	115
11-34a Selected San Francisco Area Industrial
Dischargers	116
11-34b Selected San Francisco Area Industrial
Dischargers	117
11-35	Summary of Current and Projecte'd Waste Loads
in One Region 208 Area (By SIC)	118
11-36	Typical Industrial Effluent Concentrations
BPT - "1977" Approximate Mean Effluent
Characteristics (EPA, 1974)	119
11-37	Typical Industrial Effluent Concentrations
BAT - "1983" Approximate Mean Effluent
Characteristics (EPA, 1974)	120
11-38	EPA BAT Guidelines for Selected New Source
Industrial Discharges (30 Day Average)	121
IV-l	Reference Level Values of Water Quality
Indicators for U.S. Waterways (EPA, 1974)	129
IV-2	Condition of Eight Major Waterways (EPA, 1974)	130
IV-3	Water Quality Problem Areas Reported by
States Number Reporting Problems/Total
(EPA, 1975)	133
IV-4	Water Quality Parameters Commonly Monitored
by States (EPA, 1975)	134
IV-5	Annual Phosphorus and Nitrogen Load for
Selected Iowa River Basins (EPA, 1975)	137
IV-6	Major Waterways: Seasonal and Flow Analysis,
1968-72 (EPA- 1974)	140
IV-7	Interrelationships between Sections of
Chapter 4	142
xix

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LIST OF TABLES (Continued)
Table	Page
IV-8	Municipal Waste Characteristics before
Treatment (Thomann, 1972)	143
IV-9	Solubility of Oxygen in Water (Standard
Methods , 1971)	169
IV-10 D /I Values Versus D /L and k,/k.	178
CO	0 0	a L
IV-ll	k t Versus D /L and k ,/k,	179
a	0 0	a L
IV-12	Some Average Values of Gross Photosynthetic
Production of Dissolved Oxygen (After Thomann,
1972, and Thomas and O'Connell, 1966)	183
IV-13	Chlorophyll a_ and Assimilation Number of
Various Communities (After Odum, et al , 1958)	184
IV-14	Average Values of Oxygen Uptake Rates of
River Bottoms (After Thomann, 1972)	185
IV-15	Compilation of Information in Example IV-4	190
IV-16	Critical Travel Time Results, Example IV-4	192
IV-17	Net Long Wave Atmospheric Radiation, HI	209
an
IV-18	Water Vapor Pressure (mmHg) Versus Air
Temperature, T , and Relative Humidity	210
a
IV-19	B and C(B) as Functions of Temperature	211
IV-20	Summary of Solar-Radiation Data for Mineola,
Brookhaven, and the Connetquot River Sites	213
IV-21	Eutrophication Potential as a Function of
Nutrient Concentrations	226
IV-22 Predicted Mean Total Phosphorus (TP)
Concentrations (mg/1) (From EPA, 1976)	229
IV-23	Predicted Total Nitrogen (TN) Concentrations
(mg/1) (From EPA, 1976)	230
IV-24	Total Nitrogen Distribution in a River in
Response to Point and Non-Point Source Loading	233
XX

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LIST OF TABLES (Continued)
Table	Page
IV-25	Total Coliform Analysis (EPA, 1 976)	235
IV-26	Salinity Distribution in a Hypothetical River	243
IV-27	Relationship of Total Suspended Sediment
Concentration to Problem Potential (After
EPA, 1976)	246
IV-28	Sediment Grade Scale (Task Committee on
Preparation of Sedimentation Manual, 1971)	249
IV-29	Computing D/T for Determining the Hydraulic
Radius of a Parabolic Section (From King, 1954)	251
IV-30	Relationship between Width to Depth Ratio of
a Graded Stream and the Suspended and Bed
Load Discharge (After Fenwick, 1969)	252
IV-31	Characteristics of the Colorado and Niobrara
Rivers (Task Committee on Preparation of
Sedimentation Manual, 1971)	255
IV-32	Summary of Preliminary Water Quality Analysis
of the Hypothetical Rappahan River from
Rivermile 280 to Rivermile 40	265
V-l	Parameter Values Used in Generation of
Thermal Gradient Plots (Appendix C)	279
V-2	Temperature, Cloud Cover, and Dew Point Data
for the Ten Geographic Locales Used to
Develop Thermal Stratification Plots
(Appendix D)	280
V-3	Limpid Lake Characteristics	286
V-4	Physical Characteristics of Lake Smith	288
V-5	Comparison of Monthly Climatologic Data
for Shreveport, Louisiana,and Atlanta,
Georgia	290
V-6	Hypothetical Physical Characteristics of
Upper Lake, Brookhaven, Suffolk County,
New York	311
XXI

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LIST OF TABLES (Continued)
Table	Page
V-7	Hypothetical Physical Characteristics of
Lower Lake, Brookhaven, Suffolk County,
New York	313
V-8	Hypothetical Physical Characteristics
(Assuming an Epilimnion Depth of 10 Feet)
of Lower Lake, Brookhaven, Suffolk County,
New York	31 5
V-9	Sources and Sinks of Impoundment Dissolved
Oxygen	356
V-10	Oxygen Demand of Bottom Deposits
(After Camp, 1968)	366
V-ll	Saturation DO Levels in Fresh Water as a
Function of Temperature (Chruchill, et al ,
1961)	368
V-12	Characteristics of Quite Lake	374
V-13	Water Quality and Flow Data for Tributaries
to Quiet Lake	374
V-14	Precipitation and Runoff Data fot Quiet
Lake Watershed	377
V-15	DO Sag Data for Quite Lake Hypolimnion	386
VI-1	Tidal Prisms for Some U.S. Estuaries	440
VI-2	Alsea Estuary Salinity and Volume by
Segments	452
VI-3	Alsea Estuary Segmentation for Modified
Tidal Prism Method	460
VI-4	Calculation of Segment Conservative Pollutant
Quantity for Alsea Estuary	470
VI-5	Conservative Pollutant Concentrations above
an Estuarine Outfall	479
VI-6	Comparison of Pollutant Concentrations for
Alternate Outfalls in Alsea Estuary	479
VI-7	Typical Values for Decay Reaction Rates 'k'	482
xxii

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LIST OF TABLES (Continued)
Table	Page
VI-7a	Temperature Correction for Selected
Temperatures	483
VI-8	Tabulation of Values for Non-Conservative
Pollutant Concentration	486
VI-9	kE Values for Several Types of Estuaries	493
VI-10	E Values for Selected Estuary
(From Hydroscience, 1971 )	493
VI-11	Gradiation of Candle Turbidimeter	521
VI-12 Maximum Allowable Channel Velocity to
Avoid Bed Scour (FPS) (King, 1954)	527
VI -13	Sediment Particle Size Ranges (After
Hough, 1957)	533
VI-14	Rate of Fall in Water of Spheres of Varying
Radii and Constant Density of 2a as
Calculated by Stokes' Law& (Mysels, 1959)	534
VI-15 Throat Area--Tidal Prism Relationships	542
xxiii

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ACKNOWLEDGMENTS
The authors would like to acknowledge the many individuals within Tetra
lech and the U.S. Environmental Protection Agency who provided support and
(telpful suggestions in the preparation of this document. Especial thanks go
to the Project Officer, Dr. James W. Falco of the EPA Environmental Research
Laboratory, Athens, Ga., and to Mr. Steve Gherini of Tetra Tech for their
technical and editorial suggestions. The authors would also like to thank
Mr. Paul Johanson and Mr. Kenneth Day for their work on impoundment stratifi-
cation, and Dr. Carl Chen and Dr. Marc Lorenzen for their criticisms and
suggestions.
xxiv

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CHAPTER 1
INTRODUCTION
1.1. BACKGROUND
One of the primary and potentially far reaching concepts set forth
in the Federal Water Pollution Control Act Amendments of 1972 (PL 92-500)
is contained in Section 208 of that Act. As originally proposed, this
section was to facilitate the development and implementation of waste
treatment management plans at the areawide level. Congress envisioned
208 as a process of creating comprehensive regional water quality planning
to replace state planning in areas of severe water quality problems. The
areal scope of 208 planning was originally limited to areas characterized
by high urban-industrial concentrations, generally standard metropolitan
statistical areas (SMSA's). Areas contiguous to SMSA's having substan-
tial water quality problems could also be included.
On July 25, 1975 the U.S. District Court for the District of
Columbia handed down a final decision which increased state responsi-
bility for 208 planning to include nondesignated areas as well. This
meant that 208 planning would be accomplished in all areas of each
state, and not just those defined as "designated". Additionally this
ruling obligated EPA to fund state programs for planning in the non-
designated areas. The Court decision set November 1, 1978 as the final
deadline for submission to EPA of complete 208 plans for nondesignated
areas. Although the 208 program was largely stalled during the first two
and one-half years after the passage of the 1972 Act, it is now a high
priority program and should continue"as such through Phase II (1977-83)
of planning.
1

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1.2 PROBLEM DEFINITION
The area! extent of nondesignated 208 areas is extensive.
Consequently, each area may contain a large number, as well as a wide
spectrum, of surface water bodies. Additionally, data available to
assess the severity of existing problems are often severely limited.
Hence, there exists a need to facilitate the assessment of water quality
problems occurring within these areas. By performing a preliminary
analysis, areas of potential problems can be identified and screened
from those areas where problems do not exist. Using more sophisticated
techniques (e.g., computer models) the planner can then accurately and
efficiently assess suspected problem areas. A subsequent report by
Tetra Tech will provide this more advanced methodology.
1.3 PURPOSE AND SCOPE
This report contains a simplified methodology which nondesignated
208 planners can use to perform a preliminary assessment of surface
water quality. Analyses require little data, and in most cases, can be
accomplished with the assistance of a desk top calculator. Desk top
calculation procedures are provided for the following subject categories:
1.	Wasteload estimation, including point and non-point
source pollutants.
2.	Stream analyses for water temperature, biochemical
oxygen demand, dissolved oxygen, total suspended
solids, coliform bacteria, plant nutrients, and
conservative constituents.
3.	Lake analyses for thermal stratification, sediment
accumulation, phosphorus budget, eutrophication
potential, and hypolimnion DO.
2

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4. Estuarine analyses for estuarine classification,
temperature, BOD, DO, turbidity, sediment
accumulation, and conservative constituents
(e.g., salinity).
This report is intended to be used with little external input.
Consequently, abundant data are included as tables, figures, and appendi-
ces. This is meant to increase the day-to-day utility of the document.
Where instructive, introductory material has preceded the actual
presentation of water quality assessment methodologies. This was done
to orient the planner toward pertinent background material, as well as
to clearly state limitations of the methodologies due to assumptions
and simplifications. Further, example calculations of the major emphases
within each chapter are included to illustrate the ideas being presented.
These examples are designed to unify the theory that has preceded it,
as well as in some cases to introduce new, but related ideas.
The units most commonly used in this report are those that histori-
cally appear in the literature. Most often, the units are not metric.
Consequently an english-metric conversion appendix is included at the
end of this report.
3

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CHAPTER 2
OVERVIEW OF METHODOLOGY
2.1 PLANNING STEPS
The initial 208 planning process should proceed with the following
steps:
1.	Preparation of a base map, delineating the planning area and
the water system composed of lakes, streams and estuaries.
2.	Data collection
3.	Identification and mapping of land uses, population centers
and industrial complexes.
4.	Analysis of hydrologic data for annual runoff, monthly runoff,
and critical flow for different parts of the water system.
5.	Estimation of waste loads including point and non-point sources
of pollutants.
6.	Supplementation of data base.
7.	Analysis of stream water quality and comparison of the results
to water quality criteria and/or acceptable water quality
objectives.
8.	Analysis of lake water quality and evaluation of their accep-
tability.
9.	Analysis of estuarine water quality.
4

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This sequence of analysis is designed to follow the natural pro-
gression of a water system from upstream to downstream. Thus, estimates
of waste loads are made to provide necessary input to streams, lakes,
and estuaries. Some waste loads may enter a stream which feeds a lake,
or an estuary. In this case, the stream analysis provides additional
inputs to the calculations for the downstream water body.
2.2	BASE MAP
The first step in the planning process can be to obtain large scale
topographic maps of the study area. These can be used to determine which
water bodies are to be examined and to establish an order of study.
Once this has been done, selected small scale (7 1/2 minute or 15 minute
series) topographic sheets can be obtained. On these the planner can
locate and mark point source discharges, regions of specific kinds of
land use, population centers, and industrial complexes. Use of overlays or
push pins may be helpful in preparing these displays.
The maps are also very important in showing the relationships among
water bodies and the flow patterns for stormwater runoff. Finally,
control strategies may be displayed for examination on the maps.
2.3	DATA COLLECTION
Once the base maps are prepared, the kinds of data needed should
be fairly clear in most cases. In general terms, data needs will fall
into two categories. These are hydrologic data and waste loading data.
2.3.1 Hydrologic Data
Hydrologic data includes such items as:
	Runoff quantity and quality
	Stream flows (low flows, statistical flows such as 7Q-jq,
critical flows to be protected as decreed by law)
5

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	Impoundment residence times, inflows and outflows, stagnant
regions, stratification, internal flow patterns
	Estuarial tidal prism, flushing time
Much of the necessary hydrologic data will be available from the
USGS, state geological survey, state environmental protection agencies,
and other governmental organizations. In addition, data may be
available from the private sector, as from universities, local citizens
groups, and private firms.
Hydrologic data must usually be analyzed to serve as a basis for
subsequent water quality analyses. Statistical methods may be applied
to determine the annual runoff, monthly runoff and critical flow for
a stipulated return frequency, on a selected time basis.
To select critical flow, for example, one must have some base
knowledge of the seasonal distribution of stream flow and quantity -
quality relationships. In general, the summer low flow is considered
as the critical condition for stream and estuarine analyses. Average
annual runoff is to be used for lake analyses, even though wet years
are generally more critical from the standpoint of lake water quality.
To counter the lack of gaged hydrologic data, runoff may be esti-
mated from rainfall information either through.the rational method using
a hand calculation or through a computerized runoff model such as
EPA's SWMM or ARM.
Another type of data which may be needed is climatology data.
Generally these are available from the National Climatic Center in
Ashville, North Carolina. This agency can provide data summaries of
various kinds for a large number of weather stations. Data include
precipitation, cloud cover, humidity and other important parameters.
Also, computer tapes can often be provided.
6

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2.3.2 Waste Loads
Waste loads can usually be categorized as follows:
1.	Point sources from cities and industries that discharge
waste water at a number of concentrated points to the
waterway.
2.	Non-Point sources with diffuse areas of entry. These include:
	Urban stormwater runoff
t	Agriculture drainage
	Animal farms and feedlot drainage
	Forest and other natural watershed runoff.
For municipal point sources, the flow and mass emission rate of
various pollutants can best be obtained by requesting information
directly from responsible city officials.
For industrial discharges, it is often difficult to obtain data.
Many plant managers are reluctant to release data for a number of
reasons including protection of proprietary processes. Accordingly,
the planner often must seek sources of information other than the
industrial plant itself. Sources include NPDES permits and process
description references. The latter can be used in conjunction with
work force figures to estimate waste loads. A similar approach may be
used to estimate municipal discharge levels where data are unavailable.
Here population data are a good indicator of raw sewage production, and
the type of treatment (e.g., secondary treatment, trickling filter,
holding pond) provides an estimate of the treatment efficiency. Also,
national average wastewater characteristics are available for different
categories of population centers and industries. Care must be exer-
cised, however, to determine the potential errors of applying national
averages to local situations.
7

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For non-point sources, information is generally not available.
Estimates may be made, however, using loading functions. These are
discussed later in this report.
After wasteload estimates are made, it is important to display
the magnitudes and entry points of the various waste loads on the base
map. The display will provide a perspective for the problems at
hand.
2.3.3 Other Data Categories
Many other kinds of data may be of use to the planner. These
include, for example, in situ stream water quality data, rates of
sediment accumulation in impoundments, and heavy metal concentrations
in estuaries. Note that these are the areas to which the hand calcu-
lations developed in later chapters are addressed. It cannot be over-
emphasized that where data are already available, these should be used.
Methods to be presented below are only meant to supplement existing
data so that the planner can analyze his study region. Accordingly,
all of the types of data implicit in methods presented below are
candidates for the planner's data collection efforts.
2.4 PLOTTING DATA ON MAPS
Following data collection, the planner should plot important data
on the base maps. Colored push pins (map pins) are especially useful
here. As an example, where in situ data have been obtained, black
tacks can represent areas of known high BOD levels. Coliform problems
can be denoted by yellow pins, and DO problems by blue pins. Color
coding may be functional. Green pins can represent algal blooms while
white (sterility) can denote regions of very high heavy metals concen-
trations .
Point sources, such as industrial discharges can be denoted by
8

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numbered pins keyed to an accompanying detailed discharge quantity and
quality index.
Other data not amenable to affixing to maps should not be neglected.
These should be summarized carefully in tabular form. Such data might
include various rates and coefficients, detailed population data, thermal
profiles and other kinds of data which either cannot be associated with
a specific geographic location or are too extensive to place on a map.
2.5	ANALYSIS OF HYDROLOGIC DATA, ESTIMATION OF WASTE LOADS, DATA
SUPPLEMENTATION
In preparation for analysis, the planner should examine the
available data to decide on the methods to be used. Generally, many
analytical needs will be revealed during the data collection process
itself. For example much DO data are likely to be available where
severe DO problems are believed to exist. Other needs will be revealed
upon inspection of the data. For example, where a particular point
source is high in BOD, BOD and DO analysis are desirable. This, in
turn, points to specific methods presented in later chapters. Use of
those, in turn, should lead the planner either to the conclusion that
no problem exists, or that further, more sophisticated analysis is
necessary.
2.6	STREAM ANALYSES
While there are numerous other water quality parameters that may
be considered important, analyses for the following parameters can
usually pinpoint important problems rapidly.
t	Biochemical Oxygen Demand
	Dissolved Oxygen
t	Temperature
	Nutrients
	Total Coliforms
9

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	Conservative Constituents, (total dissolved solids), and
	Suspended sediment and bed load
Basically, the stream analyses are performed in the following
manner.
1.	Selection of a critical flow for planning.
2.	Segmentation of the river into reaches for calculation.
3.	Determination of in-stream water quality concentrations
based on the mass balance consideration, taking into
account dilution, point sources, non-point sources, and decay.
4.	Comparison of the resulting water quality concentrations
against the water quality concentration objectives.
The water quality problem areas identified should be displayed on
the base map. Such a display can provide a quick overview of areas
requiring more detailed analysis.
2.7 IMPOUNDMENT ANALYSES
Delineation of water quality problems in lakes and impoundments,
requires as a minimum, analysis of the following:
	Thermal stratification
	Sediment Accumulation
	Nutrient Budget - Eutrophication
	Hypolimnion Dissolved Oxygen
A computer model was used to calculate the thermal regimes of some
hypothetical lake configurations in various geographic locations and
under their respective typical climatological conditions. The planner
can select the appropriate temperature profile by simply matching
10

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applicable conditions.
Sedimentation rates for a large number of impoundments have been
studied by the U.S. Soil Conservation Service. Again, the planner can
obtain answers by use of a look-up table, or he can make estimates of
sedimentation rates based on several computational approaches.
The	nutrient budget of an impoundment is basically a mass balance
problem.	Based on nutrient balance and hydraulic characteristics, the
eutrophic	state of an impoundment may be ascertained by the use of
empirical	curves. Such curves are presented in Chapter 5.
Because of the accumulation of oxygen-consuming materials and
the lack of reoxygenation mechanisms in the hypolimnion, undesirable
anoxic conditions may develop. Evaluation of hypolimnion dissolved
oxygen requires an estimate of:
1.	Initial DO at the onset of thermal stratification
2.	Initial BOD at the onset of thermal stratification
3.	Benthic BOD
4.	DO sag over time
The final section of Chapter 5 provides a means to evaluate hypolimnion
DO.
2.8 ESTUARINE ANALYSES
The complexity of estuarine hydrodynamics requires the use of
computer models for a definitive water quality analysis. Only a
limited number of problems are amenable to hand calculations. Such
calculations, in many instances, help focus on problem areas for subse-
quent computer analysis.
Simple calculations that can be performed for an estuarine system
i nclude:
11

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1.	A gross estimate of mean water quality concentration.
2.	Estuary classification. This can be accomplished based on
some simple rules so as to define the applicability of sub-
sequent hand calculation methods.
3.	Flushing time calculations to determine the length of
time required to replace the existing water mass within
an estuary, or within a segment of an estuary. The total
concentration of pollutants in the estuary may then be
estimated.
4.	Dispersion calculations for conservative and non-conserva-
tive pollutant concentrations. These groups include heavy
metals, hydrocarbons, oil and greases, BOD, DO, nutrients, and
coliform bacteria, etc.
5.	Temperature calculation for heated discharges.
6.	Analysis of sediment budget, sediment transport, its effect
on turbidity, and location of critical sedimentation areas.
2.9	PRESENTATION OF RESULTS
It is important to emphasize the need for graphical presentation
of analytical results. A simple display of when and where water
quality problems are expected to occur for BOD, DO, temperature, heavy
metals and other parameters can help decision-makers bring the problems
and their potential solutions into focus. Such a display can be made
on a base map in concert with accepted planning methods
2.10	LIMITATIONS OF METHODOLOGY
Factors that can influence system water quality include waste loads,
climatology, hydrology, hydrodynamics, biology, chemistry and others.
12

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Very complex phenomena occur in any real water system. Many assumptions
and simplifications are clearly necessary for hand calculation methods.
Users of this manual must be aware of the limitations and the
potential errors associated with the methodologies proposed and utilized.
This tool is to be used only as a screening procedure and not as a method
for definitive water quality assessment.
13

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CHAPTER 3
WASTE LOADING CALCULATIONS
3.1 INTRODUCTION
This chapter outlines basic procedures that can be used to
generate estimates of diffuse (non-point) and point-source loading rates.
Loading functions for the following pollutants will be considered for
non-point sources:
	Sediment
t	Nutrients (phosphorus and nitrogen)
	Organic matter
	Salinity in irrigation return flow
	Urban related pollutants
Both cultivated and noncultivated agricultural land as well as urban
areas are addressed in this report. For agricultural lands, sediment
loading is calculated by use of the Universal Soil Loss Equation (USLE)
(Section 3.2). This method has been adopted for a number of reasons,
principal among them being the large data base that exists for the
terms in the USLE. The loading of both nutrients and organic matter
can be quantitatively related to sediment loading and this is done in
this report. Thus, the discussion of nutrients and organic matter
(Sections 3.3 through 3.5) logically follows the sediment loading
calculations. These selected water quality parameters were chosen for
inclusion in this report because they represent commonly occurring
problems of major concern to planners.
Salinity in irrigation return flow is important in many areas in
the arid western states. Considerable data are included in this
report especially for the Colorado River basin, and the irrigated
regions in California (Section 3.7).
14

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For urban areas (Section 3.8) solids loading rates are first
calculated and then the loading rates of other pollutants are related
to them. Pollutants considered in this section include BOD, phosphorus,
nitrogen, coliforms, and heavy metals.
Each of the major divisions on nonpoint source calculations
(agriculture, salinity, and urban areas) in this chapter is essentially
independent of every other. Accordingly, they can be used in any order.
Within each section, the calculations performed can be used in two
different ways. First, the magnitude of loadings can be compared for
various alternatives (e.g., different land use schemes) to ascertain
the significance of the changes. Second, the loadings can be used in
calculations presented in Chapter 4 to assess the water quality impacts
of nonpoint source pollutants on river and streams.
Finally, Section 3.9 presents estimates of typical point source
pollutant loads for municipal and industrial discharges. Whenever
possible, however, local data should always be used, if available, in
lieu of the "typical" loadings given here.
The developments for non-point source loading presented in this
chapter have been largely taken from a recent handbook developed by
the Midwest Research Institute (McElroy, et al., 1976). That document
provides supplemental background information on each of the loading
functions presented here. For a more comprehensive presentation of
the material in this chapter it is suggested the MRI handbook be
consulted.
The units in which the loading functions are expressed need
minor modifications for use in the non-point source loading expressions
used in Chapter 4. Generally the loading functions in this chapter
are expressed in units of kg/year or lb/year. In Chapter 4 the
distributed loading terms are in units of lb/unit length/unit time,
where the unit time may be, for example, a day and the length (in
miles) is measured along the longitudinal axis of a water course. In
15

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general a change in the units in which time is expressed, as well as
a division of the loading function by the number of river miles over
which the loading occurs, will produce the proper units for use in
Chapter 4.
3.2 SEDIMENT LOADING FUNCTION FOR SURFACE EROSION
Sediment loading is defined in this report as the quantity of
soil material that is eroded and transported into the watercourse.
Sediment loading is dependent on (a) on-site erosion, and (b) delivery,
or the ability of runoff to carry the eroded material into the receiving
waters.
The sediment loading function is based on the mechanisms of gross
erosion and sediment delivery. The Universal Soil Loss. Equation
(Wischmeier and Smith, 1965) has been chosen to predict the on-site
surface (including sheet and rill) erosion, for the following reasons:
1.	This equation is applicable to a wide variety of land uses
and climatic conditions.
2.	It predicts erosion rates by season, in addition to annual
averages.
3.	Data have been collected nationwide for factors included
in the equation.
The sediment loading function has the form:
n
Y(S)e - E [Ai-(R-K-L-S-C-P-Sd)i]
d; i
(III-l)
where
Y(S)^ = sediment loading from surface erosion, tons/year
n
number of subareas in the area
16

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Source area! factor:
A'. = acreage of subarea i, acres
Source characteristic factors:
R = the rainfall factor, expressing the erosion
potential of average annual rainfall in the
locality, is a summation of the individual
storm products of the kinetic energy of rainfall,
in hundreds of foot-tons per acre, and the maximum
30-min. rainfall intensity, in inches per hour,
for all significant storms, on an average annual
basi s
K = the soil-erodibility factor, commonly expressed
in tons per acre per R unit
L = the slope-length factor, dimensionless ratio
S =	the slope-steepness factor, dimensionless ratio
C =	the cover factor, dimensionless ratio
P =	the erosion control practice factor, dimensionless ratio
S^ =	the sediment delivery ratio, dimensionless
The R factor in the above equation can be expressed in metric
units((hundreds of meter-metric tons/ha-cm) multiplied by (maximum
30-min. intensity, cm/hr)) by multiplying the English R values by 1.735.
The factor for conversion of K in English units to metric-tons per
hectare per metric R unit is 1.292 (Wischmeier, 1972).
Equation 111-1 can be used to predict sediment loading resulting
from sheet and rill erosion from cultivated and non-cultivated lands.
Parameter values for silviculture, construction, and mining are less
well documented than for agriculture, however. The user will thus
17

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find it relatively easy to use Equation 111-1 for agriculture, and
substantially more difficult for other sources. The equation does not
predict sediment contributions from gully erosion, streambank erosion,
or mass soil movement.
The sediment loading section will present the following informa-
tion :
	procedures and examples for estimating sediment
loadings based on the above described loading function
	methodology for predicting minimum and maximum erosion
rates.
3.2.1 General Procedure for Use of the Sediment Loading Function
The following procedure is to be used to calculate sediment
loading from an area based on the loading function in Equation III-l.
The terminology applies to agricultural lands, but the procedure is
applicable to other non-point sources. This procedure is shown as a
flow diagram in Figure 111-1 and is summarized in Sections 3.2.1.1 through
3.2.1.3. Then a more detailed discussion of the procedure follows with
example problems being presented in Section 3.2.4.
Estimation of surface erosion should be made for each land-use
type. For a given land-use type, if 90% or more of the area is made up of
one soil type, one may calculate soil loss for the land use based on
that soil type. If there is less than 90% of one soil type, one should
calculate soil loss for each soil type that makes up at least 10% of
the land use, and then obtain a weighted average for the entire land-
use area (U.S. Dept. of Agriculture, 1974).
18

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Land Use Acreage, A: 's
Local Drainage
Density Soil
Texture, and
Figure III-10,
or Eq. (Ill-2)
CD
Sediment
Delivery
Ratio S(j
Soil Names,
or Soil
Properties
Soil Erodibility
Factor K, from
Published Lists
or Nomographs
Land Use Types,
Dates of Cropstages,
Canopy, ground
Cover Density
Cover Factor C,
from Table 3H-2
to M-5, or Others
Types of
Conservation
Practice
Practice
Factor P,
from
Table m-6
n r

-|
v (s)E= z *
 (R-
K  LS  C  P  Sd )j
i = i

-J
Slope Lengths,
and Slope
Gradients
Topographic
Factor LS,
from Figure
3H-7 to m-9
Local Rainfall Erosivity
Factor R from Iso-erodent
Maps or by Calculation
Figure III-l Flow Diagram for Calculating Sediment Loading from Surface Erosion

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3.2.1.1 Obtain Basic Land Data
The following should be obtained:
	total area, and land use acres in the area: cropland,
pastureland, and woodland, etc.
	soil characteristic information including soil name, soil
texture, etc. for each land use.
	information about canopy and ground cover condition for each
land use.
	topographic information, such as slope gradient and slope
length of the land.
	information about the type and extent of conservation practices.
3.2.1.2 Determine Factor Values
Determine R: Use the appropriate isoerodent map (see Figures
111-2 and 111-3), or procedures described for the western United States
(see Section 3.2.2.1).
Obtain K: Obtain the K values of the named soils from published
lists from SCS, or determine K values on nomographs (Figures B-l and
B-2 in Appendix B) from soil properties.
Determine LS: Refer to Figures 111-7 or III-8 for uniform
slopes, or Figure 111-9 for irregular slopes.
Obtain C: Refer to the appropriate table for the crop or ground
cover condition for C value.
20

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Obtain P: Refer to Table 111-6.
Determine sediment delivery ratio, S^: Obtain from local sources
or from Figure 111-10 by using drainage density and soil texture for
homogeneous watersheds.
3.2.1.3 Calculations
Multiply R, K, LS, C, and P, and to obtain sediment loadings
for cropland, pasture, and woodland in annual yields per unit area of
source.
Multiply loading rates by source sizes (total hectares or acres)
for cropland, pastureland, and woodland to obtain total loading per
source.
Sum source loadings calculated in the item above to obtain total
loading from land uses (total loading in the watershed will require
summation of other sources within the watershed).
3.2.2 Determination of Source Characteristic Factors
3.2.2.1 The Rainfall Factor (R)
R is a factor expressing the erosion potential of precipita-
tion in a locality. It is also called index of erosivity. erosion
index, etc. It is the summation of the individual storm products of
the kinetic energy of rainfall (denoted by E), and the maximum 30 min.
rainfall intensity (denoted by I) for all significant storms within the
period under consideration. The product EI reflects the combined
potential of raindrop impact and runoff turbulence to transport dis-
lodged soil particles from the site (Wischmeier and Smith, 1965).
21

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Values of average annual rainfall-erosivity index, R, are
shown in Figure 111-2 for the continental U.S. and Figure 111-3 for
islands of Hawaii. On these maps, the lines joining points with the
same erosion index value are called isoerodents. Points lying between
the indicated isoerodents may be approximated by linear interpolation.
Interpolation for values of R factors in the mountainous
areas, particularly those west of the 104th meridian may not be
appropriate because of the sporadic rainfall pattern. Values of the
erosion index at specific areas can be computed from local recording
rain gage records with the help of a rainfal1-energy table and the
computation procedure presented by Wischmeier and Smith (1958).
ARS recently recommended that 350 be the maximum used in
the Gulf and southeastern states, shown in Figure 111-2, until further
research can validate values higher than 350.
In the northwestern United States, runoff from snowmelt
contributes significantly to surface erosion. The annual index of
R for some portions of this region is the combined effect of rainfall
and snowmelt designated by and Rs, respectively. The snowmelt
factor (Rs) is important in Areas A-l, B-l, and C on Figure III-4
(also refer to Table III-l). The map values in the shaded region of
the Northwest (see Figure 111-2) represent values for the rainfall
effect (R ) only, and must be added with appropriate Rs values to
account for the effect of runoff from thaw and snowmelt.
Interim procedures for calculating annual R values, which
include both R and R_, for the northwestern U.S. are described in
r	s'
Conservation Agronomy'Technical Note No. 32, USDA/SCS, Portland,
Oregon (1974), and are briefly presented below.
22

-------
Figure 111-2 Average,Annual Values of the Rainfall-Erosivity Factor, R
(I'.S.D.A. AND EPA, 1975)

-------
150
M0L0KA

Scole:
for
0 5 10 Miles
200
PACIFIC OCEAN
KAUAI
LANAI
MAUI
MOLOKAI
OAHU
HAWAII
OAHU
Scale-0 10 20Miles
PACIFIC OCEAN
LANAI
&
KAUA
MAUI
o
Figure 111-3 Mean Annual Values of Erosion Index for Hawaii (!!.S.n.A1974)

-------
SCALE
100 200 MILES
Figure 111-4 Soil Moisture-Soil Temperature Regimes of the
Western United States (U.S.P.A., 1974)
25

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TABLE 111 -1
APPLICABILITY OF Rp AND R$ FACTORS IN THE AREAS
WEST OF THE ROCKY MOUNTAINS (U.S. DEPT. OF AGRICULTURE, 1974a)
Areas (see	R
Figure 111-4)	Typical Locations	r	s
A-l	Washington, Idaho. Nevada,	X^'	X
California, western Utah
A-2	Cascades, Sierra, Tetons of	X
Idaho, Wasatch Mountains
A-3	West of Cascades, San Joaquin	X
Valley, west of Sierras
A-4	Areas of southern California,	X
east of Santa Anas, southern
Nevada, intermountain Nevada,
Salt Lake area, Utah
B-l	Western Montana, Colorado,	X
eastern Utah, high elevations
of Arizona
B-2	Great plains area of eastern	X
Montana, Wyoming, Colorado
(includes gently sloping
mesas and upland at lower
elevations of Monticello,
Utah area)
C	Rainfall during summer is	X
high; high elevations
a/ X needed
b/ - not needed
b
26

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The annual Rr factor is obtained by using as base the two
year, six hour rainfall (2-6 rainfall). Relationships between R^ and
2-6 rainfall vary to conform to specific local climatic characteristics.
These relationships are designated as Type I, Type IA, and Type II,
and are shown in Figure 111-5. Specific areas applicable to these
curves are shown in Figure 111-6. Type I curve is for the central
valley and coastal mountains and valleys of southern California.
Type IA curve applies to the coastal side of the Cascades in Oregon
and Washington, the coastal side of the Sierra Nevada Mountains in
northern California, and the coastal regions of Alaska. Type II
curve applies to the remainder of the region. For 2-6 rainfall data,
refer to Technical Paper No. 40, U.S. Department of Commerce, Weather
Bureau, Washington, D.C. (1961), or other suitable rainfall frequency
analysis reports.
To obtain the annual R factor for a given location, obtain
s	3
the average annual total precipitation by snowfall (in inches of water
depth) and multiply it by the constant 1.5 to give annual Rs.
There are numerous sources of snowfall data for the United
States. Some of the major sources are:
	The 1941 Yearbook of Aoriculture, USDA,
Washington, D.C.,
 "Climates of the States," Water Information
Center, Inc., Port Washington, New York (1974), and
	Data resulting from the Western Federal-State-
Private Cooperative Snow Surveys, coordinated by
SCS/USDA, Portland, Oregon.
27

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2-Year, 6-Hour Rainfall, cm

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0
600
1 1 1 l 1 1 1 1 1 1 1




m





c 500
/

p





m


9


u 400
/ /




e
/

o
9, / /

o
o 300
\
1

li.
/ \ /
X n / >

ac
\
\




 200


c


c


<


100


n
i i I I I I i

u

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

2-Year, 6-Hour Rainfall, inch
Figure 111-5 Relationships between Annual Average Rainfall Erosivity Index and the
2-year, 6 hour Rainfall Depth for 3 Rainfall Types in Western H.S.
(U.S.D.A., 19/4)

-------
LEGEND - Storm Distribution
|	J TYPE IA
EI53 type i
Rasa type n
Figure 111-6 Storm Distribution Regions in Western M.S,
(U.S.H.A., 1974)
29

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Data on snow density is necessary to convert depth of snow
to depth of meltwater. Snow at the time of fall may have a density
as low as 0.01 and as high as 0.15 g/ml. The average snow density
for the United States is taken to be 0.10 (Garstka, 1964). If
snowfall is recqrded as inches of precipitation, no conversion is
required.
The annual R factor for the western United States is the
summation of effect of rainfall, Rr, and snowmelt, R . Where Rg is
not significant, values of R and R^ are the same.
The monthly distribution of the erosion, index for the
37 states east of the Rocky Mountains has been reported in USDA-ARS
Agriculture Handbook No. 282 (Wischmeier and Smith, 1965). Average
monthly erosion index values are expressed as percentages of average
annual values and plotted cumulatively against time in Appendix A.
The monthly distribution of erosion index for the islands
of Hawaii also has been developed (U.S. Dept. of Agriculture, 1974b).
These curves are shown in Appendix A.
For the areas west of the Rockies in the continental United
States, the monthly distribution of erosion index R is the summation
of R and R . Where R values are not needed, the R and R curves
r	s	s	r
are the same.
As of June 1974, the monthly R distribution curves for
portions of the area west of the Rockies had been made available (U.S.
Dept. of Agriculture, 1974a). The reader should contact the state Soil
Conservation Service for such information. Procedures suggested by
SCS for computing and plotting monthly R distribution curves for the
western United States are described in Appendix A.
30

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3.2.2.2	The Soil-Erodibility Factor (K)
K factor is a quantitative measure of the ratd at which a
soil will erode, expressed as the soil loss (tons) per acre per unit
of R, for a plot with 9% slope, 72.6 ft. long, under continuous
cultivated fallow.
K factors for topsoils, as well as subsoils, for most soil
series have been developed. Values of K for soils studied thus far
vary from 0.12 to 0.70 tons/acre/unit R.
The K values for named soils at different locations of the
nation can be obtained from the regional or state offices of the
Soil Conservation Service.
K values of soils can be predicted from soil properties.
In Appendix B of this report, two nomographs are presented from which
K values may be determined for topsoils and subsoils when the governing
soil properties are known.
3.2.2.3	The Topographic Factor (LS)
Soil loss is affected by both length (L) and steepness of
slope (S). These factors affect the capability of runoff to detach
and transport soil material.
The slope length factor is the ratio of soil loss from a
specific length of slope to that length (72.6 ft) specified for the
K factor in the equation. Slope length is defined as the distance
from the point of origin of overland flow to either of the following,
whichever is limiting, for the major part of the area under considera-
tion: the point where the slope decreases to the extent that deposi-
tion begins; or the point where runoff enters a well-defined channel
31

-------
that may be part of a drainage network, or a constructed channel that
may be part of a drainage network, or a constructed channel such as a
terrace or diversion. Slope length can be determined accurately by
on-site inspection of a field, or by measurements from aerial photographs,
or topographic maps. When the land is terraced, the terrace spacing
should be used. All slope lengths are compared to a slope length of
72.6 ft, which has a factor value of 1.
The slope gradient or percent slope factor is the ratio of
soil loss from a specific percent slope to that slope (9%) specified
for the K value in the USLE. A 9% slope has a factor value of 1.
Slope data may be obtained from topographic maps, engineering or
land level surveys, and other sources. A widely used method is to
estimate slope from soil survey maps in which the soils have been
mapped by slope range.
The slope length (L) and slope gradient (S) are combined in
the USLE into a single dimensionless topographic factor, LS, which
can be evaluated using a slope-effect chart.
The slope-effect chart in Figure 111-7 is designed for the
following areas shown in Figure III-4: A-l in Washington, Oregon, and
Idaho; and all of A-3 (U.S. Dept. of Agriculture, 1974a).
For the remainder of the U.S., the slope-effect chart,
Figure III-8, is to be used (U.S. Dept. of Agriculture, 1974a).
Slope-effect charts in Figure 111-7 and 111-8 can be used
when uniform slopes are assumed. The following steps are to be used
for obtaining LS values from these charts:
1. Enter the chart on the horizontal axis with the
appropriate value of slope length.
32

-------
* -^0 S'ope , ,
soL
CO '0-0 L 60
^ /		
.  6,0/mi
o . /	i*5
^ *0 f.	*0
 i	?
. .o/	/
& /	:	'
o	/	/J
A? '/	'0
-6
/ _	
/
0.a
0,/ ^CLT			'
^^Oo^Zl	-5
^Oo
'C/G^C ;.	S/0 400 Soo"
'll-7	t 'o-
"v 7 f^t r^"'
4/ 5^^ 4-J	4
^Sl,	f f r	(7/, C ^fGO/j C^&i j.
TeH" uf Ill~1	D<*T A"D u  -W,
'"'  "' ; ,,  " : "= '
""""  ,s *"* 4"
*

-------
Slope Length, Meters
3.5 6.0 10	20	40 60 100 200 400 600
20.0
10.0
8.0
6.0
4.0
W
-1 3.0
tS
o
o 2.0

o
f 1.0
O" 0.8
O
jO 0.6
0.4
0.3
0.2
0.1
10	20	40 60 100 200 400 600 1000 2000
Slope Length, Feet
Figure 111-8 Slope--Effect Chart for Areas Where Figure 111-7
is not Applicable (U.S. Dept. of Agriculture)
&/ The dashed lines represent estimates for slope dimensions
BEYOND THE RANGE OF LENGTHS AND STEEPNESSES FOR WHICH DATA
ARE AVAILABLE.
34

-------
2.	Follow the vertical line for that slope length to
where it intersects the curve for the appropriate
percent slope.
3.	Read across the point of intersection to the vertical
axis. The number on the vertical axis is the LS value.
An irregular slope should be divided into a series of
segments such that the slope gradient within each segment can be
treated as uniform. The slope segments need not be of equal length.
The total soil loss from the entire slope is calculated based on the
effective LS value for the entire length of the irregular slope.
A family of curves shown in Figure 111-9 was designed to
facilitate the determination of the LS factor for the irregular
slopes ranging from 2 to 20%. The quantity plotted on the vertical
scale is designated by the symbol U. Slope lengths, designated by A,
are plotted on the horizontal scale.
Assume an irregular slope with n segments illustrated as
fol1ows:
Segment I
35

-------
distance from the top of the entire slope (the point at
which overland flow begins) to the lower end of the jth
segment
Aj 1= length of entire slope above segment j
Ag = overall slope length
S. = the slope gradient of segment j, in percent
J
The steps taken for calculating LS for irregular slopes
using Figure 111 -9 are (Foster and Wischmeier, 1973):
1.	Enter on the horizontal axis with the value of A. ^
(the slope length above segment j).
2.	Move vertically to the curve with the appropriate
percent slope for segment j.
3.	Read on the vertical scale the value of U-jj.
4.	Enter the figure with the value of A. (the distance
from the top of the entire slope to the lower end of
the jth segment), repeat Steps 1 through 3 to obtain
the value of U^j.
5.	Subtract from U-j ..
6.	Repeat Steps 1 through 5 for each of the slope segments.
7.	Sum n values of - U-jj, divide the sum by Ag (the
overall slope length). The result is the effective LS
value for the entire length of the irregular slope.
36

-------
X( Meters)
20
30 40
ZOO 250
60 80 100
1000
800
Steepness of	/
Slope Segment: 20%
600
500
400
300
200
ZD 100
80
5%
60
50
40
30
20
200 300
20
30 40
60 80 100
X (Feet)
Figure 111-9 Slope Effect Chart for Irregular Slopes
(Forter and Wischmeier, 1973)
37

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Examples of the use of the above procedure to calculate LS
factors for irregular slopes are given in Appendix C of the Midwest
Research Institute (McElroy, et al., 1976) handbook.
The percentage of the total sediment yield that comes from
each of the n segments can be obtained through a similar procedure.
The relative sediment contribution of segment j, assuming constant
soil erodibility for the entire slope, is given by:
U9 . - U, 
2j 1J
n
Z
j = l
(U2j - U )
For constructed slopes or mined slopes that cut into
successive soil horizons, the soil erodibility K may vary considerably
fron upper to lower parts of a slope. When variations in slope
gradient are associated with variations in soil erodibility along an
irregular slope, K and - U-j must be combined as follows to estimate
the relative sediment contribution of segment j.
J
K,
n
Z
j = l
(U
2j
-v
K.
J
(U2j -Ulj>
3.2.2.4 The Cover Management Factor (C)
In the USLE, the factor C represents the ratio of soil
quantity eroded from land that is cropped or treated under a specified
condition to that which is eroded from clean-tilled fallow under
identical slope and rainfall conditions. C ranges in value from near
zero for excellent sod or a well-developed forest to 1.0 for contin-
uous fallow, construction areas, or other extensively disturbed soil.
38

-------
In order to evaluate the cover management factor for crops,
five crop stage periods have been selected for relative uniformity of
cover and residue effects within each period. These five periods are
defined as follows (Wischmeier and Smith, 1965):
Rough fallow - turn plowing to seeding.
Seedbed - seeding to 1 month thereafter.
Establishment - from 1 to 2 months after
seeding. (Exception: for fall-seeded grain,
Period 2 includes the winter period and
extends to 30 April in the North and 1 April
in the South, with intermediate latitudes
1	nterpolated.)
Growing crop - from Period 2 to crop harvest.
Harvest, residue or stubble - from crop harvest
to turn plow or new seedbed. (When meadow is
established in small grain, Period 4 ends
2	months after grain harvest. Thereafter, it
is classified as established meadow.)
The average cover factor C for the entire year or years of
crop rotation is computed by crop stages. Input for calculation of
C includes average planting and harvesting dates, productivity,
disposition of crop residues, tillage, and monthly distribution of
the erosion index R. The C value for each of these time periods is
weighted according to the percentage of annual rainfall factor
occurring in that period. The summation of these RC products for the
entire year or years of crop rotation is then converted to a mean
annual C.
Period F:
Period 1:
Period 2:
Period 3:
Period 4:
39

-------
Values of factor C for croplands are highly variable with
rainfall pattern, planting dates, type of vegetative cover, seeding
method, soil tillage, disposition of residues, and general management
level. Ranges of C value for several types of vegetation and ground
cover are listed in Table 111 -2, in order of decreasing protection
against erosion (increasing C value from near zero to 1).
The reader is advised to consult with state conservation
agronomists of SCS for appropriate C values for crops in the local
area. The reader is also referred to USDA-ARS Agriculture Handbook
No. 282 (Wischmeier and Smith, 1965) for a listing of approximated C
values for various crops at each crop stage, as we-11 as a working
table for derivation of average C value for periods of crop rotation.
C values typical of permanent pasture, range,.and idle
lands, with varying cover and canopy conditions, are given in Table
111- 3. These values were developed by Wischmeier (1972).
Wischmeier (1972) also estimated factor C for some woodland
situations. Data are presented in Table 111 - 4.
For urban and road areas, as well as construction sites, the
factor C represents the effect of land cover or treatment that may be
used to protect soil from being eroded. Table 111-5 (Water Resources
Administration, 1973) lists values of the factor C for various soil
covers and treatments.
3.2.2.5 The Practice Factor (P)
The factor P accounts for control practices that reduce the
erosion potential of runoff by their influence on drainage patterns,
runoff concentration, and runoff velocity.

-------
TABLE 111-2
RELATIVE PROTECTION OF GROUND COVER AGAINST EROSION
(IN ORDER OF INCREASING C VALUES)
Land-Use Groups
Examples
Range of "C" Values
Permanent vegetation
Protected woodland
Prai rie
Permanent pasture
Sodded orchard
Permanent meadow
0.0001-0.45
Established meadows
Alfalfa
CI over
Fescue
0.004-0.3
Small grains
Rye
Wheat
Barley
Oats
0.07-0.5
Large-seeded legumes
Soybeans
Cowpeas
Peanuts
Field peas
0.1-0.65
Row crops
Cotton
Potatoes
Tobacco
Vegetables
Corn
Sorghum
0.1-0.70
Fallow
Summer fallow
Period between plowing
and growth of crop
1.0
41

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TABLE
111-3




"C" VALUES
FOR PERMANENT PASTURE, RANGELAND, AND IDLE LAND (WISCHMEIER,
1972)7

Veqetal Canopy
Type and Height . ,
of Raised Canopy-
Canopy
Cover/
(%)



Cover that Contacts the Surface




Percent
Ground Cover


Type-7
0
20
40
60
80
95-10(
Column No.
2
3
4
5
6
7
8
9
No appreciable canopy

G
0.45
0.20
0.10
0.042
0.013
0.003


W
0.45
0.24
0.15
0.090
0.043
0.011
Canopy of tall weeds
25
G
0.36
0.17
0.09
0.038
0.012
0.003
or short brush

W
0.36
0.20
0.13
0.082
0.041
0.011
(0.5 m fal 1 height)
50
G
0.26
0.13
0.07
0.035
0.012
0.003


W
0.26
0.16
0.11
0.075
0.039
0.011

75
G
0.17
0.10
0.06
0.031
0.011
0.003


W
0.17
0.12
0.09
0.067
0.038
0.011
Appreciable brush
25
G
0.40
0.18
0.09
0.040
0.013
0.003
or brushes

W
0.40
0.22
0.14
0.085
0.042
0.011
(2 m fall height)
50
G
0.34
0.16
0.085
0.038
0.012
0.003


W
0.34
0.19
0.13
0.081
0.041
0.011

75
G
0.28
0.14
0.08
0.036
0.012
0.003


W
0.28
0.17
0.12
0.077
0.040
0.011
(conti nued)

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TABLE 111-3 (Continued)
Vegetal Canopy
Type and Height . ,
of Raised Canopy-
Canopy
Cover-^
(%)



Cover that Contacts the
Surface




Percent
Ground Cover

r d/
Type
0
20
40
60
80
95-100
Column No.
2
3
4
5
6
7
8
9
Trees but no appreci-
25
G
0.42
0.19
0.10
0.041
0.013
0.003
able low brush

W
0.42
0.23
0.14
0.087
0.042
0.011
(4 m fal1 height)
50
G
0.39
0.18
0.09
0.040
0.013
0.003


W
0.39
0.21
0.14
0.085
0.042
0.011

75
G
0.36
0.17
0.09
0.039
0.012
0.003


W
0.36
0.20
0.13
0.083
0.041
0.011
a/ All values shown assume: (1) random distribution of mulch or vegetation, and (2) mulch of
appreciable depth where it exists.
b/ Average fall height of waterdrops from canopy to soil surface: m = meters.
zj Portion of total-area surface that would be hidden from view by canopy in a vertical
projection (a bird's-eye view).
d/ G: Cover at surface is grass, grasslike plants, decaying compacted duff, or litter
at least 5 cm (2 in.) deep.
W: Cover at surface is mostly broadleaf herbaceous plants (as weeds) with little
lateral-root network near the surface and/or undecayed residue.

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TABLE 111-4
"C" VALUES FOR WOODLAND (WISCHMEIER, 1972)
Forest
Tree Canopy Litter
Percent of Percent of
Stand Condition Area^	Area-^ Undergrowth^ "C" Factor
Well stocked	100-75 100-90 Managed^	0.001
Unmanaged^ 0.003-0.011
Medium stocked
70-40
85-75
Managed
Unmanaged
0.002-0.004
0.01-0.04
Poorly stocked
35-20
70-40
Managed
Unmanaged
0.003-0.009
0.02-0.09-7
a/ When tree canopy is less than 20%, the area will be considered as
grassland or cropland for estimating soil loss.
b/ Forest litter is assumed to be at least 2-in. deep over the percent
ground surface area covered.
cj Undergrowth is defined as shrubs, weeds, grasses, vines, etc., on
the surface area not protected by forest litter. Usually found
under canopy openings.
d/ Managed - grazing and fires are controlled.
Unmanaged - stands that are overgrazed or subjected to repeated
burning.
e/ For unmanaged woodland with litter cover of less than 75%, C values
should be derived by taking 0.7 of the appropriate values in
Table III-3. The factor of 0.7 adjusts for the much higher soil
organic matter on permanent woodland.
44

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TABLE II1-5
"C" VALUES FOR CONSTRUCTION SITES
(WATER RESOURCES ADMINISTRATION, 1973)
Type of Cover	C Value
None (fallow)	1.00
Temporary seedings
First 60 days	0.40
After 60 days	0.05
Permanent seedings
First 60 days	0.40
After 60 days	0.05
After 1 year	0.01
Sod (laid immediately)	0.01
Rate of Application
Maximum A11owable
In Metric Tons
Mulch Per Hectare
In Tons
Per Acre
C Value
SI ope
(ft)
Length
(m)
Hay or straw
1/2
1/2
0
.34
20
6

1
1
0.
.20
30
9

1-1/2
1-1/2
0.
.10
40
12

2
2
0.
.05
50
15
Stone or gravel
14
15
0.
.80
15
5

55
60
0.
.20
80
24

120
135
0.
.10
175
53

220
240
0.
.05
200
61
Chemical mulches






First 90 days

a/
0.
.50
50
15
After 90 days

a/
1 .
.00
50
15
Woodchi ps
2
2
0.
.80
25
8

4
4
0.
30
50
15

6
7
0.
20
75
23

11
12
0.
10
100
30

18
20
0.
06
150
46

23
25
0.
05
200
61
a/ As recommended by manufacturer.
45

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For croplands, control practices refer to contour tillage.,
cross-slope farming, and contour strip-cropping. The practice value P
is the ratio of soil loss from a specified conservation practice to
the soil loss occurring with up-and-downhil1 tillage, when other
conditions remain constant. Table 111- 6 (U.S. Dept. of Agriculture,
1974a) shows P values for up-and-downhi 11 farming, cross-slope farming
without strips, contour farming, cross-slope farming with strips, and
contour strip-cropping.
TABLE 111-6
"P" VALUES FOR EROSION CONTROL PRACTICES
ON CROPLANDS (U.S. DEPT. OF AGRICULTURE, 1974a)

Up-and-
Cross-slope

Cross-stope


Down-
Farmi ng
Contour
Farming with
Contour
SI ope
hill
Without Strips
Farming
Stri ps
Stri p-croppi ng
2.0-7
1 .0
0.75
0.50
0.37
0.25
7.1-12
1.0
0.80
0.60
0.45
0.30
12.1-18
1 .0
0.90
0.80
0.60
0.40
18.1-24
1 .0
0.95
0.90
0.67
0.45
Terracing is also an effective practice to reduce soil
erosion. The quantitative effect of terracing is accounted for in
the slope length factor, since the horizontal terrace interval becomes
the slope length, after the terraces are constructed.
3.2.2.6 Sediment Delivery Ratio (S^)
The sediment-delivery ratio, in this report, is defined as
the fraction of the gross erosion which is delivered to a stream. The
classical method for determining an average delivery ratio is by
46

-------
comparing the magnitude of the sediment yield at a given point in a
watershed (generally at a reservoir or a stream sediment measuring
station), and the total amount of erosion. The quantities of gross
erosion from sloping uplands are computed by erosion prediction
equations for surface erosion, and estimated by various procedures
for gullies, stream channels, and other sources. The sediment yield
at a given downstream point is obtained through direct measurements.
Measurements of sediment accumulations in reservoirs and
sediment-load records in streams show wide variations in sediment
yields from watersheds. Estimates show that as little as 5% and as.
much as 100% of the materials eroded in some watersheds may be
delivered to a downstream point. Estimates of the delivery ratio
for some specific watersheds, particularly in the humid sections of
the country, can be obtained from the Soil Conservation Service, USDA.
Many delivery-ratio analysis studies have been aimed at
finding measurable influencing factors that can be related to sediment-
delivery ratio. A popular means of developing such information is by
statistical analysis using the sediment-delivery ratio as the dependent
variable and measurable watershed factors as the independent, or control-
ling variables. Many physical and hydrologic factors may influence
sediment-delivery ratios. Some lend themselves to quantitative expres-
sion whereas others do not. At present, the science of sedimentology
does not delineate the relative degree of influence of each of the
individual factors on the delivery ratio of sediment. Nevertheless,
empirical relationships for delivery ratios have been proposed and are
presented below. Estimates of sediment loading can be made through the
use of these relationships, but such estimates should be tempered with
judgment and consideration of other influencing factors not included in
the quantitative expressions. The user is encouraged to consult with
local experts and should use local data when available.
47

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The MITRE Corporation (1974) reported that the sediment-
delivery ratio for construction sites can be approximated by a function
of the overland distance between the construction site and the receiving
water.
The format of the sediment delivery ratio proposed by MITRE
for construction sites has the following form:
Sd = D~0'22	(II1-2)
where
D = overland distance between the erosion site and the
receiving water, in ft
The e^ove equation was empirically derived from available
data. The data base for the derivations includes values of D from 0
to 800 ft. MITRE suggests that this function should be further
tested, particularly in areas of the Midwest and Central U.S.
For mining sites, logging roads and fire lanes, sediment
delivery ratio relationships have not yet been established due to lack
of systematically measured data. It is suggested that the delivery
ratio developed by MITRE and expressed in Equation 111-2 be used as
the first approximation for these sites. This needs to be verified
when appropriate data become available.
Sediment delivery ratios have been evaluated in many areas
of the country, particularly the eastern half of the United States.
The delivery ratio usually depicts a general trend in basins that are
relatively homogeneous with respect to soils, land cover, climate,
and topography. The Soil Conservation Service (1973) analyzed
data from stream and reservoir sediment surveys from widely scattered
areas.
48

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This analysis shows that sediment delivery ratios vary
inversely with "drainage basin size". It also indicates the effect
of soil texture of upland soil on the sediment deljvery ratio.
The delivery ratio relationships reported by SCS (1973)
were used by the MRI study group in developing delivery ratios for
sediment loading to watercourses. The result is shown in Figure 111-10.
The horizontal scale of the figure is the reciprocal of drainage
density which is defined as the ratio of total channel-segment lengths
(accumulated for all orders within a basin) to the basin area. The
reciprocal of drainage density may be thought of as an expression of
the closeness of spacing of channels, or the average distance for soil
particles to travel from erosion site to the receiving water.
The delivery ratio relationship shown in Figure 111-10 also
takes into account the effect of soil texture. For example, if soil
texture of UDland soil is essentially silt or clay, the sediment
delivery ratio will be higher than when the soil texture is coarse.
The delivery ratio relationships in Figure 111-10 need to
be verified by acquisition of new data and improved by including other
factors relative to deposition mechanisms.
The following steps are to be used to obtain the delivery
ratio (Sj) from Figure 111-10.
1.	Enter the figure on the horizontal axis with the value
of the reciprocal of drainage density (1/DD).
2.	Move vertically from the value of 1/DD to where it
intersects the curve for the appropriate soil texture.
3.	Read across from the point of intersection to the
vertical axis. That number represents the delivery
ratio, Sj.
49

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1/Drainage Density, Kilometers
500
100
200
100
Silty Clay
-^Predominantly Silt
400
100
0.02
I/Drainage Density, Miles
Figure 111-10 Sediment Delivery Ratio for Relatively Homogeneous Basins
(McElroy, et al., 1976)

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A great range of values of drainaqe density exists in the
2	2
United States, from 2 km/km (3 miles/mile ) for the Appalachian
Plateau Province (Smith, 1950) to 500 km/km^ (800 ini les/mi 1 e^) in
Badlands at Perth Amboy, New Jersey (Schumm, 1956). In general,
according to Strahler (1964), low drainage density is found in regions
of highly resistant or highly permeable subsoil materials, under dense
vegetative cover, and where relief is low. High drainage density is
favored in regions of weak or impermeable materials, sparse vegetation,
and mountainous relief.
Some typical values of drainage density for various locales
in the U.S. are given in Table 111 -7. Local drainage density figures
may be obtained from agencies such as the U. S. Geological Survey and the
Army Corps of Engineers.
Measurements of drainage density can be made from a topo-
graphic map with a planimeter and chartometer. Care must be taken to
include all permanent stream channels to their upper ends by checking
in the field or aerial photographs in verification of topographic maps.
A rapid approximation method for determining drainage density is suqgest-
ed by Carlston and Langbein (1960).
3.2.2.7 Summary of Applicabilities of Source Characteristic Factors
The preceding paragraphs indicate that assessment of sediment
loadings from surface erosion requires quantitative information on soil
erodibility, rainfall and snowmelt erosivity, topography, vegetative
cover, conservation practices, and sediment delivery ratio. Applica-
bility of each factor varies with specific location of the site and
also with type of land disturbance. Table III-8 gives a total surmary
of variations in application of those factors.
51

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TABLE II1-7
TYPICAL VALUES OF DRAINAGE DENSITY

Drainage density

Locati on
km/ km^
2
mi 1e/mi1e
Reference
Appalachian Plateau
Province
1.9-2.5
3.0-4.0
Smith (1950)
Central and eastern
United States
5-10
8.0-16.0
Strahler (1952)
Dry Areas of the Rocky
Mountain Region
31-62
50-100
Melton (1957)
The Rocky Mountain Region
(except the above)
5-10
8.0-16
Melton (1957)
Coastal ranges of
Southern California
12-25
20-40
Smith (1950)
Melton (1957)
Maxwell (1960)
Badlands in South Dakota
125-250
200-400
Smith (1958)
Badlands in New Jersey
183-510
310-820
Schumn (1956)
3.2.3 Limitations of the Loading Function
The USLE predicts soil losses from sheet and rill erosion. It
does not predict sediment from gullies, streambank erosion, landslides,
road ditches, irrigation, or from wind erosion. The USLE was developed
primarily for croplands, and has been chiefly based upon experimental
plot data from the areas east of the Rocky Mountains. The loading
function therefore is best defined for these areas of use. For crop-
lands in the western United States and sources outside agriculture such
as silviculture, construction, and mining, the factors have not been
systematically developed, which seriously affects the ease of using the
USLE for such sources.
52

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TABLE 111-8
SUMMARY OF APPLICABILITY OF CHARACTERISTIC FACTORS
Land use
Extent of land
disturbance
Zero to moderately
disturbed
Example
Growing forests
Rangeland
Pastureland
Cropland
Orchards
Source
characteristic
factor
Regions in the United States
LS
Eastern states and Hawaii
Western states
Affected by rainfall only; use Affected by rainfall, some
Figures 111-2 or 111-3.	areas also by snowmelt (see
note below).
Erodibility of topsoils.	Erodibility of topsoils.
Use Figure 111-8 for natural
slope steepness and slope
length (except terracing).
Use Figure 111-7 for some
areas in Washington, Oregon,
Idaho, and California; the
remainder use Figure 111-8
(except terracing).
For croplands and orchards, C's	For croplands and orchards,
are determined locally by SCS. C's are determined locally
For forests, use Table 111 - 4; by SCS. For forests, use
rangeland and pastureland, use Table 111-4; rangeland and
Table 111 - 3. pastureland, use Table 111 - 3
For croplands, use Table 111- 6;	For croplands, use Table 111-6
others = 1.0. others = 1.0.
Assume relatively homogeneous
land use components; use
Figure 111-10.
Assume relatively homogeneous
land use components; use
Figure III-10.

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TABLE 111-8 (Continued)
Land use
Extent of land
disturbance
Intensively
disturbed
Example
Construction
si tes
Mining sites
Logging roads
Fire lanes
Source
characteristic
factor
Regions in the United States
Eastern states and Hawaii
Affected by rainfall only; use
Figure 111-2 or III-3.
Erodibility of topsoils and
subsoils.
Western states
Affected by rainfall, some
areas also by snowmelt
(see note below).
Erodibility of topsoils and
subsoils.
LS	Use Figure II1-9 for irregular Use Figure 111-9 for irregular
slopes.	slopes.
Use Table 111- 5.
Use Table II1-5.
Equals 1.0.
S^	Use Equation 111-2.
Equals 1.0.
Use Equation 111-2.
Note: To develop annual R values for the western United States see Section 3.2.2.1.

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3.2.3.1 Specific Limitations
R: Research is needed to determine the effective R values more
accurately throughout the continental United States.
L and S: The relationships on which the slope effect charts
are based were derived from data taken on slopes not exceeding 20% and
length not exceeding 400 ft. How far these dimensions can be exceeded
before those relationships change has not been determined.
C: More work is needed to improve definitions of cover factor,
particularly for areas outside agriculture, such as undistrubed forest,
harvested or burned forests, logging roads, mining sites, rangeland,
and construction sites.
P: The reported values of the practice factor have been
limited to cropland. Definitions of practice factor values are needed
for various conservation practices on silviculture, mining, construction
and other areas outside agriculture.
S^: The science of sedimentology has not progressed to the
state where the sediment-delivery ratio can be predicted to the degree
of accuracy desired.
The loading function in Equation 111-1 and supporting data in
tables and figures were designed to predict lonqterm average loadings
for specific conditions. Sediment loading for a specific year may be
substantially greater or smaller than the annual averages because of
differences in number, size, and timing of erosive rainstorms, and in
other weather parameters. Table 11 of USDA Agriculture Handbook 282
(1965) contains a listing of 50, 20, and 5% probability values of R
factor at 181 key locations in the area east of the Rocky Mountains.
These may be used for further characterization of soil-loss hazards.
55

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Due to the uncertainties embedded in factor values, sediment
loadings computed by Equation III-l should be considered as reasonable
estimates rather than as absolute data. Table 111-9 lists the best
estimate of the range of accuracy for Equation III-l and available
supporting data. The range pertains to annual average. For a specific
year, the range may be much larger than those given.
TABLE II1-9
ESTIMATED RANGE OF ACCURACY OF SEDIMENT LOADS
FROM SURFACE EROSION
Predicted loading
(MT/ha/.year)
0.1
1
10
100
1 ,000
Estimated range of accuracy
	(MT/ha/.year)	
0.001 - 1.0
0.1 ~ 5
5-15
50 - 150
500 - 1,500
3.2.4 Source Characteristic Factors for Predicting Maximum and
Minimum Sediment Loadings
The loading function in Equation III-l can be used to predict
sediment loading other than annual averages. Variations of the loading
rate are embedded in rainfall factor R and cover factor C. The evalua-
tion procedure is illustrated in the following examples.
		EXAMPLE III-l 	
Assessing Sediment Loading from Surface Erosion
The watershed of interest has an area of 830 acres. It is
located in Parke County, Indiana. Compute sediment loading from the
watershed from sheet and rill erosion in terms of average daily loading,
maximum daily loading during a 30 consecutive day period, and minimum
during a 30 consecutive day period.
56

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Basic Information
Land use types:
	Cropland
	Pasture
	Woodland
Delivery	ratio: 60%
Land information: (Cropland - 180 acres)
e	Continuous corn
	Conventional tillage, average yield ^ 40 to 45 bu
	Cornstalks are left after harvest
	Contour strip-cropped
	Soil - Fayette silt loam
	Slope - 6%
	Slope length - 250 ft
Pasture: (220 acres)
	No appreciable canopy
	Cover at surface - grass and grasslike plants
	Percent of surface or ground cover - 80%
	Soil - Fayette silt loam
	Slope - 6%
	Slope length - 200 ft
Woodland: (430 acres)
t	Medium stocked
	Percent of area covered by tree canopy - 50%
	Percent of area covered by litter - 80%
	Undergrowth - managed
	Soil - Bates silt loam
	Slope - 12%
	Slope length - 150 ft
57

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Maximum and Minimum Rates
The ratios between 30-day maximum and average daily rates, and
30-day minimum and average daily rates for continuous corn, pasture,
and woodland for this area are evaluated in Examples 111-2 and
111-3. They are:
Continuous corn: Ratio--30 day maximum/average daily = 3.2
Ratio--30 day minimum/average daily = 0.25
Pasture and woodland: Ratio--30 day maximum/average daily = 2.5
Ratio--30 day minimum/average daily = 0.25
Calculations of Loading Per Acre
Cropland:
R
= 200 (Figure 111-2)
K =
= 0.37 (USDA-SCS)
LS =
= 1.08 (Figure 111-8)
C =
= 0.49
P
= 0.25 (Table 111-6)
Sd s
= 0.60
Calculate average annual loading per acre.
Y(s)annuai = 200 x -37 x 1.08 x 0.49 x 0.25 x 0.6
= 5.87 tons/acre/year
Calculate average daily loading per acre.
Y(s)avg.daily = 5-87 tons/acre/year " 365 days
= 0.016 tons/acre/day = 32 lb/acre/day
58

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Calculate maximum loading per acre during a 30 consecutive day period.
Y(S)on ,	= 0.016 tons/acre/day x 3.2
v '30 day max	J
- 0.052 tons/acre/day = 104 lb/acre/day
Calculate minimum loading per acre during a 30 consecutive day period.
Y(S) i	= 0.016 tons/acre/day x 0.25
v '30 day mm	J
= 0.004 tons/acre/day = 8 lb/acre/day
Pasture:
R =
200
K =
0.37
LS =
0.95
C =
0.013 (Table 111-3)
P =
1.0
Sd =
0.60
Y(s)annuai = 200 x -37 x -95 x -013 x 1- x -6
= 0.548 tons/acre/year = 1,100 lb/acre/year
Y(S)avg daily = 0.548 tons/acre/year t 365 days
= 0.0015 tons/acre/day = 3 lb/acre/day
Y(S)on ,	= 0.0015 tons/acre/day x 2.5
v y30 day max	J
= 0.0038 tons/acre/day =7.6 Ib/acre/day
y(S)-3A a	= 0.0015 tons/acre/day x 0.25
v '30 day min	J
= 0.0004 tons/acre/day = 0.8 lb/acre/day
59

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Woodland:
R =
200
K =
0.32
LS =
2.75
C =
0.003 (Table 111-5)
P -
1.0
Sd =
0.60
Y(s)annual = 200 x -32 x 2*75 x -003 x 1- x -60
= 0.3168 tons/acre/year
Y(S) , -n 0.3168 tons/acre/year = 365 days
v avg.daily	J	J
= 0.0009 tons/acre/day = 1.8 lb/acre/day
Y(s)30 day max = 0.0009 tons/acre/day x 2.5
= 0.0022 tons/acre/day = 4.4 lb/acre/day
Y^30 day min = 0-0009 toris/acre/day x	0.25
= 0.0002 tons/acre/day =	0.4 lb/acre/day
Calculations of Gross Loading
Average daily:
Cropland - 180 acres x 0.016 tons/acre/day = 2.88	tons/day
Pasture - 220 acres x 0.0015 tons/acre/day = 0.33	tons/day
Woodland - 430 acres x 0.0009 tons/acre/day= 0.39	tons/day
Total	Y(S)avg. total = 3'60 tns/dal'
60

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30 day maximum:
Cropland - 180 acres x 0.052 tons/acre/day =9.36 tons/day
Pasture - 220 acres x 0.0038 tons/acre/day = 0.84 tons/day
Woodland - 430 acres x 0.0022 tons/acre/day = 0.95 tons/day
Total	y(s)3o max total = 11.15 tons/day
30 day minimum
Cropland - 180 acres x 0.004 tons/acre/day =0.72 tons/day
Pasture - 220 acres x 0.0004 tons/acre/day = 0.09 tons/day
Woodland -430 acres x 0.0022 tons/acre/day = 0.09 tons/day
Total Y^30-min total = 0.90 tons/day
	 END OF EXAMPLE III-l 	
	 EXAMPLE II1-2 	
Variations Caused by Rainfall Factor Alone
The rainfall erosion index R varies within a year, as shown in
percent erosion index curves in Appendix A. For lands where cover
factor is relatively constant, such as woodland and grassland, temporal
distribution of rainfall factor R governs temporal variations in erosion.
Figure 111-11 shows an example of monthly distribution of percentages
of annual R values. This distribution curve is for parts of M'ichigan,
Missouri, Illinois, Indiana, and Ohio based on Curve 16 in Figure A-2d.
The following steps are required for evaluating monthly variation of
R values.
61

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0.8
0.7
30-Day Maximum
>*
o
"O
a>
CL
c
o
CO
o
LU
a>
o
a
0.4
in

O
O
Average Daily
<4
O
c
a>
a
L_

-------
1.	Read the percent of annual erosion index, at the pre-
determined time interval, on the appropriate erosion
index distribution curve (for this specific example,
Curve 16 on Figure A-2d in Appendix A).
2.	For each time interval, subtract the reading of the
first date from that of the last date.
3.	Results of Step 2 are the percents of annual index that
are to be expected within the particular periods. Use
these data for plotting distribution curve. The percent
average daily is 0.274, which is obtained by dividing
100 (percent) by 365 (days in a year).
The curve in Figure 111-11 indicates that, if other factors hold
constant, soil erosion in this area would have its maximum from 20
June to 20 July, and minimum from late December to late January.
One estimates that, based on the R distribution in Figure 111-11,
the maximum daily loading rate during a 30-consecutive-day period for
woodland and grassland in this particular area is approximately 2.5
times that of average daily loading rate for 1 year; the minimum
daily rate during a 30-consecutive-day period is approximately one-fourth
of the average daily rate.
	 END OF EXAMPLE 111-2 	
63

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EXAMPLE 111-3
Variations Caused by the Combined Effects
of Rainfall Factor and Cover Factor
For croplands, where soils are tilled and surface conditions
change drastically from one crop stage to another, evaluation of erosion
variation should include both the R factor and C factor.
Required steps to achieve such evaluations are:
1.	Determine average dates of each crop stages.
2.	Determine C factor values for each crop stage from such
information as productivity, disposition of crop residues
and tillage.
3.	Obtain monthly distribution of R.
4.	Multiply C factor values by the R value of the correspond-
ing period.
Variations of RC products are the temporal variations of sediment
loading.
In this example, temporal variation of surface erosion rate for
continuous cornland in central Indiana was calculated. Again, the
erosion index distribution Curve No. 16 on Figure A-2d was used.
Assumptions were conventional tillage, a yield average of 40 to 59 bu
of corn per acre, and cornstalks left on the field after harvesting. The
dates, C values, and percent of erosion index for five-crop stages, and
RC products are:
64

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Percent R
Crop stage,
starting-
ending date
Cover
factor,
C7
Reading7'
Percent
in the
Period
RC
product
Turn plowing, 5/1-5/19
0.55
13.8
5.7
3.14
Seeding, 5/20-6/19
0.70
19.5
16.5
11.55
Establishment, 6/20-7/19
0.58
36.0
21 .3
12.35
Growing crop, 7/20-10/9
0.32
57.3
33.7
10.78
Harvest and
0.50
91.0
22.8
11.40
stubble, 10/10-4/30




Total


100
49.22
aj Reference source: USDA-Agricultural Research Service Handbook No.
282-' Table 2.
b/ Reading from Figure A-2d (Curve 16) for starting date.
The annual C factor is estimated at 0.49. Temporal variation of sur-
face erosion rate, in terms of percent of annual total, is shown in Figure
111-12. It is seen that the maximum erosion from this continuous cornland
would occur in mid-June through mid-July, nearly identical to the period of
maximum erosion with constant soil cover (Figure 111-11). The 30-day
maximum is approximately 3.2 times average daily, which is higher than the
previous (constant C factor) estimate due to the magnifying effect caused
by the overlapping of a high R period with a high C period. Figure 111-12
also shows that minimum erosion would occur during the winter season; the
30-day minimum is one-fourth of the average daily load.
	END OF EXAMPLE 111-3 	
65

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I.o I-
30-Day Maximum
CROPSTAGE
F - Turn Plowing
CI - Seedling
C2-Establishment
C3-Growing Crop
C4-Harvest and Stubble
/> 0.4
Average Daily
a! 0.2
30-Day Minimum
l/l 2/1 3/1 4/1 5/1 6/1 7/1 8/1 9/1 10/1 Il/l 12/1 l/l
Date Month/Day
Figure 111-12 Projected Variation of Soil Erosion
on Continuous Corn Lands in Central
Indiana (FIcElroy et al,, 1976
66

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3.3 NITROGEN LOADING FUNCTION
While the complex interactions in soil, air, water and plants are
reasonably well understood, methods for quantifying movements within
the system are still in the research stage. Methods which are suitable
for general use often oversimplify the problem. They must be used with discretion
and may be quite inadequate in certain cases. In particular, it is not
presently possible to describe leaching processes for soluble forms of
nitrogen. The nitrogen loading function is made up of two sources:
(a) erosion; and (b) precipitation. Total nitrogen loading is obtained
by adding the yields from both sources. The loading functions exclude
leaching losses, and predict the amount of total nitrogen that is released
to surface waters by runoff and erosion. The nitrogen in precipitation
is mostly in available form.
3.3.1 Nitrogen Loading Function for Erosion Loss
The nitrogen loading from erosion is computed as:
Y(NT)e - a  Y(S)e  CS(NT)  rN	(III-3)
where
V(NT)E = total nitrogen loading from erosion, kg/year (lb/year)
a = dimensional constant (10 for metric units, 20 for English units)
C^(NT) = total nitrogen concentration in soil, g/100 g
Y(S)E = sediment loading from surface erosion, MT/year (tons/year)
r.. = nitrogen enrichment ratio
Available nitrogen can be obtained by using a fraction f^ which is
the ratio of available N to total N in sediment. Thus, the available
nitrogen in sediment is
Y(NA)e = Y(NT)E  fN	(111-4)
67

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3.3.2 Nitrogen Loading Function for Precipitation
The nitrogen loading from precipitation is computed as:
Y(N)p = A-21M .N -b	(III_5)
Kr Q(Pr) Pr
where
Y(N)pr = stream nitrogen load from precipitation, kg/year (lb/year)
A = area, ha (acres)
Q(0R) = overland flow from precipitation, cm/year (in/year)
Q(Pr) = total amount of precipitation, cm/year (in/year)
Npr = nitrogen load in precipitation, kg/ha/year (1b/acre/year)
b = attenuation factor (use b = 0.75 for metric and English units
unless better information is available).
Almost all of Y(N)pr will be in the available form so that the total
available nitrogen from both erosion and precipitation may be obtained
by adding Equations 111-4 and III - 5. Thus,
Y(NA) = Y(NT)E-fN + Y(N)pr	(III-6)
3.3.3 Evaluation of Parameters in the Nitrogen Loading Function
The value of Y(S)^ can be evaluated from the sediment loading
function presented in Section 3.2. The value of the enrichment ratio
r^ is variable according to the soil texture and cultural treatment.
Viets (1971) presented the values of r^ using data from small experimental
plots (see Table 111-10). Hagin and Amberger (1974), as well as
Stoltenberg and White (1955) have proposed an r^ value of 2.0. Massey,
et al., (1953) estimated the value of r^ as 2.7. Because of wide
variations in the properties of erodible soil, a single value of r^ is
not probable; the values reported range from less than 2.0 to greater
than 4.0 and an appropriate value should be selected for a specific
location from local knowledgeable sources such as the State Agricultural
Experiment Stations.
68

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TABLE III-10
NUTRIENT AND SEDIMENT LOSSES (VIETS, 1971)
Source
Check
Rye winter cover crop
Manure (45 MT/ha)
Rye and manure (45 MT/ha)



Enri chment
Total
loss (kq/haj
rati o,
r
Soi 1
N
P
N
P
29,100
74.5
75.8
3.88
1.59
13,160
38.9
37.7
4.08
1.56
18,390
52.8
44.3
4.28
1 .47
8,130
21.5
19.6
3.35
1 .47
The value of CS(NT) in the plowed layer of soil is variable from
location to location and from time to time. Estimates of native soil
nitrogen in the U.S. indicate a range between 0.02 and 0.4% (Jenny, 1930).
Parker et al* (1946) published a map in 1946 showing the nitrogen
content in the top 1 - ft layer in trie U.S. (see Figure 111 -1 3). Data
in Figure 111-13 should be viewed in general terms; for specific sites,
local sources such as SAES and SCS Soil Survey should be consulted.
Precipitation also contributes to the soil nitrogen. Atmospheric
nitrogen extracted by soil microbes becomes incorporated into soil
organic matter; animal manures, crop residues, and other wastes contribute
significant amounts of nitrogen to the soil. Jenny (1930) expressed the
nitrogen content of the soil in terms of temperature, T, and a humidity
factor, H. Jenny's equation is:
CS(NT) - O.SS/0-087 (1 - e-'005H)	O11"7'
H = 	-		(111-8)
fl - ^ ) cup
U 100; iVht
* Note that in areas of heavy antecedent cultivation, particularly where
large amounts of anhydrous ammonia or other nitrogen sources are
applied, these estimates may not be valid.
69

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* # vXvrt*v'** \
* pAvIvJ.vSr'v.v.h
nvi'i'i'i
*-r a  */   FVNMUbLVA'    
> r. 	 .v.v
64T * * i JWVVf.v.v.vlJf-.
NITROGEN
Percent N
*~3 Highly Diverse

-------
where
P = precipitation, mm/year
C^(NT) = concentration of soil nitrogen, g/100 g
T = annual average temperature, C
RH = relative humidity, %
SVPt = saturated vapor pressure at given temperature, mm
of Hg
Equation 111-9 shows the relation between SVP^ and T.*
SVPt = 10 [9-2992 -2360/(2" ~ T)]
The solution of Equation 111-7 is shown graphically in Figure II1-14.
The value of humidity factor, H, can be determined from Equations 111-8
and 111-9. A nomograph solution of H is shown in Figure 111-15.
For given values of precipitation, relative humidity and temperature,
the value of H can be quickly and accurately established from Figure
111 -15. For example, given = 500 mm/year (19.7 in/year), RH = 60%,
and T-| = 5C (41F), the value of H factor can be determined as follows:
using a straight-edge ruler, align P^ and RH^ to intersect on the index
line at "a" as shown on the inset of Figure 111 -1 5. Align "a" with T-j
on the temperature scale to intersect the H scale. The result on the H
scale is 194.
Data in Figure 111-13 may be used as a check on current data.
Equations (III-8) and (111-9) may be used to calculate nitrogen
content of soil more precisely if necessary data are available for using
these equations. Again data from State Agricultural Experiment Stations,
and SCS Soil Surveys are much more dependable than the above sources and
should be consulted whenever possible.
* Modified from Gladstone, S., Elements of Physical Chemistry, D. Van
Nostrand Company, Inc., New York, New York (1946)
71

-------
.00
- 5C
0.80
0.60
0C
0.40
 0.30
o
cn
0.20
o
cn
c
c
o
a>
o
20C
Z 0.08
o
 0.06
25 C
30 C
h-
? 0.04
(O
O
0.03
0.02
500
600
700
100
400
0
200
300
H. Humidity Factor
Figure 111-14 Soil Nitrogen vs. Humidity Factor and Temperature
72

-------
80
70
60 -
50-1
40 -
30 V
20-i
15 - =
- 1000
800
700
600
-500
400
>
s
c
c
o
*-
o
Q.
u

Q.
Q."
10
9
8 i
7 -j
6 v
5
4 -
r 200
3 -F
2
I.5tI
1.0-r
8
0.7
0.6
0.5H
2000
1500
300 -
>%
E
E
c
o
150 ~
-100
80
70
60
50
40
30
20
15
l>

a
qT
0.4 -1 10
100-
p- 10,000
-5,000
4,000
3,000
2,000
95 -
 90
o
4>
Q.
>: 85
5
I 80
-1,000
-500
400
300
200
o
ioo S.

 70

t_
3
2 15-
a
E
a>
*" 20
25-
30
35-t
o
50 
3
O
60 |
E
o
-70
80
E-90
Figure 111-15 Nomograph for Humidity Factor, H

-------
The fraction of available nitrogen to total nitrogen in soil, f^
is variable, depending upon many factors such as soil chacteristics,
degree of mineralization, and organic matter content. The most important
forms of available nitrogen are NH^+, NO^ , and certain simple organic
compounds containing free amide or amino groups. Nitrate is only a
minor source of available nitrogen in soil.
The available nitrogen in soil rarely exceeds 15% of total nitrogen.
Data from Lopez and Galvez (1958) suggest that about 8% of total nitrogen
in soil is available in mineralized form for plant growth. For more
precise values, local expertise should be consulted for a given area.
The values of Q(0R) and Q(Pr) may be obtained from local data sources.
The value of Q(Pr) (annual average precipitation) is usually obtained
from the weather bureau statistics for the area. The value of overland
runoff can be roughly estimated from stream flow data. A user unfamiliar
with hydrology should consult with qualified personnel in state conser-
vation services, agricultural extension service, the Corps of Engineers,
or the Agricultural Research Service for assistance in interpretation of
stream flows. These resources will also have historical information on
overland runoff in relation to precipitation.
Values of Np^ are usually available from measurements made in the
local research stations. In the absence of actual data, data in Figure
111-16 may be used.
74

-------
Figure 111-16 Nitrogen (NHf|-N and NO^-N) in Precipitation. (Personal Communication
with MRI, J.H. Cravens, Regional R.orester, C.SAA.-FS, Eastern
Region, 197^)

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3.4 PHOSPHORUS LOADING FUNCTION
Phosphorus occurs naturally in soil from weathering of primary
pnosphorus-bearing minerals in the parent material. Additions of plant
residues and fertilizers by man enhances the phosphorus content of the
surface soil layer.
Phosphorus in soils occurs either as organic or inorganic phosphorus.
The relative proportion of phosphorus in these two categories varies
widely. Organic phosphorus is generally high in surface soils where
organic matter tends to accumulate. Inorganic forms are prevalant
in subsoils. Soil phosphorus is readily immobilized due to its
affinity to certain minerals. In strongly acid soils the formation
of iron and aluminum phosphates, and in alkaline soils, the formation
of tricalcium phosphate reduces the availability of sch'1 phosphorus.
Once it enters a stream, the nature of phosphorus existing in
sediment or in solution becomes significant in the nutrition of aquatic
mi croorgani sms.
Phosphorus transport from a given site to stream can occur either
by erosion or by leaching. The predominant mode of transport is via
soil erosion. Soil solution usually contains less than 0.1 pg of
phosphorus per milliliter; the leaching losses are thus extremely low
even in well-drained soils. Exceptions are sands and peats which have
little tendency to react with phosphorus.
The loading function for phosphorus is based on the soil erosion
mechanism. The loading function is;
Y (PT) = a-Y(S)E-Cs(PT).-rp	(111-10)
76

-------
where
Y(PT) = total phosphorus loading, kg/year (lb/year)
a = a dimensional constant (10 metric, 20 English)
Y(S)e = sediment loading, MT/year (tons/year)
(PT) = total phosphorus concentration in soil, g/100 g
r^ = phosphorus enrichment ratio
Available phosphorus may be computed from Equation 111-11:
Y(PA) = Y (PT)  f p	(.111-11)
where
Y(PA) = yield of available phosphorus, kg/year (lb/year)
fp = ratio of available phosphorus to total phosphorus
3.4.1 Evaluation of Parameters in Phosphorus Loading Function
Sediment loading, Y(S)^, may be obtained from procedures outlined
in Section 3.2.
The value of C^(PT), the total phosphorus content of the soil, is
variable. For any given location, current and local data are preferred
to generalized values given in this report. No central repository of
current nationwide data exists. Parker, et al., (19.46) published data
on the phosphorus content of soil in the top 30 cm (1 ft) for the 48
states, as shown in Figure 111 -17. Parker's data, although obtained
30 years ago, will serve as a check on current data. Soil surveys
periodically made by the Soil Conservation Service contain more recent
information on soil phosphorus content. State agricultural extension
service personnel can also provide reasonable estimates of soil phosphorus
content in a given area. These sources should be given priority in
77

-------
v&5 >::
rivAvV\-v.^
ESI^KMV
['>;?! "vXVav*.v;, vvawV.
&MM&&
EiMl^sHi
r*V# VAVAVaM1 IWU nil
PHOSPHORIC ACID
Percent P2O5
^ 0.0-0.04
vTI 0.05-0.09
Figure 111-17 Phosphorus Content in the top 1 ft of Soil (Parker, et al., 1946)

-------
determining the phosphorus content of the soil.
The enrichment ratio, r , has been the least researched parameter
in the loading function. As shown in Table III-10, thp reported r^
values average about 1.5. Massey, et al., (1953) obtained an r^ value
of 3.4, and Stoltenberg and White (1955) reported a value of 2.0. Hagin
and Amberger (1974) have used a value of rp of 2.5 in their simulation
model for nutrient losses from agricultural sources. Massey, et. al.,
(1955) have developed an empirical equation to determine rp:
log rp = 0.319 + 0.25 (-log X) + 0.098 (-log Y) (111-12)
where
X = sediment loss/unit of runoff, tons/acre-in
Y = sediment loss, tons/acre
The determination of available phosphorus in the soil is difficult.
Most reported data fail to distinguish between soluble phosphorus,
absorbed or particulate phosphorus and organic phosphorus in sediment
runoff. Total phosphorus is not always a useful parameter, since
only the soluble orthophosphate form is immediately available for uptake
by aquatic organisms. However, other forms of phosphorus in sediment
can act as a source or sink for subsequent release in available form.
Schuman, et. al., (1970) have reported an empirical relation between
sediment phosphorus (concentration in ppm, C<.(PT)) and soluble phosphorus
(concentration in ppm, Cq(P) ) for Iowa soils. The relation may be
stated as:
Cq(P) = a + b-CS(PT)	(111-13)
where a and b are regression coefficients. The reported values of a
and b are 0.018 and 0.047, respectively. Equation 111-13 shows that the
ratio of solution phosphorus to sediment phosphorus is just under 1:20.
79

-------
Taylor (1967) suggested that about 10% of the total phosphorus in
eroded soil is ordinarily available for aquatic plant growth.1
3.5 ORGANIC MATTER LOADING FUNCTION
The loading function is:
Y(0M)e - a-Cs(0M)-Y(S)E*r0M	(111-14)
where
Y(0M)e = organic loading, kg/year (lb/year)
a = a dimensional constant (10 metric, 20 English)
C^(OM) = organic matter concentration of soil, g/100 g
Y(S)e = sediment loading, MT/year (tons/year)
r0M = enr"'c'iment ratio for organic matter in eroded soil
3.5.1 Evaluation of Parameters in the Organic Matter Loading Function
The value of Y(S)E can be obtained from procedures discussed
previously. The value of C^(OM) should be obtained preferably from
current or historical data for a given area, (e.g. from the extension
service). For approximate values, C-(0M) may be taken as equal to
20 x CS(NT), where C<.(NT) is the total nitrogen concentration in the
soil. (Buckman and Brady, 1969).
The value of rAM, the enrichment ratio, is more difficult to assess
0M?
due to lack of research data. Values of rQ^ are in the range of 1 to
5. The enrichment ratio for sandy soils will be high. Conversely,
the enrichment ratio will be low when the mineral fraction of the soil
is finely divided and highly erodible. The user should consult with
local soil experts and should use local data when available.
80

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EXAMPLE II1-4
Example of Loading Computation for
Nitrogen, Phosphorus, Organic Matter
The watershed used in Example 111-1 (Section 3.2.4) for Parke County
. Indiana will be used to illustrate the methodology presented in this
section for computing the pollutant loads. It is required to compute
available nitrogen, available phosphorus, and organic matter loading
for the given area for the following conditions:
Average daily loading;
Maximum daily loading during a 30 consecutive day period; and
Minimum daily loading during a 30 consecutive day period.
The following data, plus soil data, are required:
Soil nitrogen content.
Soil phosphorus content.
The preferred source of data is local records. Jenny's
equation (Eq. 111-7) and Figure 111-17 are alternate sources from
which general values may be estimated.
Nitrogen Loading
Using the following data, soil nitrogen content is calculated;
Average annual temperature = 10C
Average annual precipitation = 96.5 cm
Average annual relative humidity = 70%
Using the nomograph given in Figure 111-15, the value of H factor
was determined to be 350. From Figure 111-14, and using H = 350 and
T = 10C, the value of C^(NT), the soil nitrogen content was estimated
to be 0.204% or 0.204 g/100 g. Assume that 6.% of total nitrogen is
81

-------
available, and rM is 2.0. Using Equations 111-3 and III-4
Y(NA)e = 20-Y(S)e-0.204-2.0*0.06
(111-15)
= 0.49Y(S),
The values of areal sediment yield as given in Example 111 -1 are
shown below in Table 111-11.
TABLE III-ll
SEDIMENT YIELD IN EXAMPLE
Land Use
Cropland
Pasture
Woodland
Total
Sediment yield (tons/day)
Daily Average
2.88
0.33
0.39
3.60
Maximum 30 days
9.36
0.84
0.95
11.15
Minimum 30 days
0.72
0.09
0.09
0.90
The nitrogen loadings are shown in Table 111-12 using the data in
Table III-ll and Equation 111-15.
TABLE 111-12
AVAILABLE NITROGEN LOADING (LB/DAY)


Nitrogen Loading (lb/day)
Land Use
Daily Averaqe
Maximum 30 days
Minimum 30 days
Cropland
1.41
4.59
0.35
Pasture
0.16
0.41
0.04
Woodland
0.19
0.47
0.04
Total
1 .76
5.47
0.43
82

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Phosphorus Loading
Assume C<-(PT) = 0.255 g/100 g for the area, 10% of C^(PT) is
available phosphorus, c<.(PA); and rp is 1.5, and using Equation 111-10;
Y(PA)e = 20-Y(S)E-0.255-1.5-0.10	(111-16)
= 0.765 Y(S)e
Phosphorus loadings computed from Table 111-9 and Equation 111-10
are shown in Table 111-13.
TABLE 111-13
AVAILABLE PHOSPHORUS LOADING (LB/DAY)
Land Use
Daily Average

Maximum 30 days
Minimum 30 days
Cropland
2.20

7.16
0.55
Pasture
0.25

0.64
0.07
Woodland
0.30

0.73
0.07
Total
2.75

8.53
0.69
Organic Matter Loading



Us i ng
Equation 111-14,
data
for Cs(0M), Y(S)e,
rAM are needed.
0M
Assume
that the value
of Cs
(0M)/C$(NT) equals
2 and rQM =2.5,

y(om)e -
20-2.
5 * Y(S)E- 20 * Cs(NT)


=
1000 -
Cs(NT)-Y(S)e

Using C$(NT) = 0.2%,
Y(0M)E =200-Y(S)e	(111-17)
The values of organic loading are computed from Equation 111-17 and
presented in Table 111-14.
83

-------
TABLE 111-14
ORGANIC MATTER LOADINGS (LB/DAY)
Land Use	Daily Average Maximum 30 days
Minimum 30 days
144
18
18
Cropland
Pasture
Woodland
576
66
78
1 ,872
168
190
2,230
Total
720
180
END OF EXAMPLE 111-4
3.6 ACCURACY OF NUTRIENT AND ORGANIC MATTER LOADING FUNCTIONS
The accuracy of predicting loads using the loading functions
presented in the preceding sections depends, to a large extent, on
the availability of reasonably accurate data for evaluating the various
parameters in the functions. For example, the nitrogen loading function
is composed of several parameters, each of which is in turn a function
of several other variables. In addition, several options are available
to the user to develop the parameter values from his own sources of
information which may alter the prediction accuracy. However, if the
used values reflect the longterm average rather than a specific year,
and if reasonably large areas are used such as large watersheds (> 100
square miles) rather than individual plots or small watersheds, the
expected accuracy can be reasonably estimated. Using the logic that
the error in individual parameters will tend to accumulate to a larger
error, the expected ranges of predicted values for given "true" or
estimated values of load are presented in Table 111-15.
These estimates are more accurate for nitrogen when erosion
is moderate to extensive, and are less accurate when erosion is slight
or when surface runoff is negligible. In the latter cases dissolved
84

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TABLE III-15
PROBABLE RANGE OF LOADING VALUES FOR
NUTRIENTS AND ORGANIC MATTER

Estimated value
Probable range
Loading Function
(kg/ha/year)
(kq/ha/.year)
Total N sediment^
1
0.1-10
Total N sediment
10
5-20
Total N sediment
50
30-75
Total N precipitation^
0.3
0.1-0.6
Total
1.0
0.5-3.0
Total P
5.0
2-10
Total P
10.0
5-20
Organic matter
10.0
5-20
Organic matter
100
50-200
a/ Available N in sediment will range from 3 to 8% of total N.
b/ Available N is equal to total N in precipitation,
c/ Available P in sediment will range from 5 to 10% of total P.
85

-------
forms of nitrogen are the principal nitrogen pollutants. The$e forms
are transported either to subsurface waters or directly to surface
waters in runoff. Functions which describe either of the latter
phenomena are not yet available, and the approach to estimating dis-
solved forms of nitrogen accordingly involves a combination of local
or regional experience supplemented by measurements of soluble nitrogen
forms in runoff and baseflow.
Nutrient and organic matter loading functions presented in this
section are accordingly based on the sediment loading function
developed previously. It is assumed that the nutrients and organic
matter are carried through surface runoff and that most of these
materials are removed with sediment.
Because the currently available data applicable to the entire U.S.
may not reflect the local conditions, it is suggested that local data
whenever available be used in preference to the general data presented
in this section.
3.7 LOADING VALUES FOR SALINITY LOADS IN IRRIGATION RETURN FLOW
Perhaps the most useful method of establishing salinity loads is
through loading values determined for particular regions. Lists of
such values are presented in Tables 111-16 through 111-20 for subbasins
in the Colorado River basin, and for irrigated regions in California.
Studies in the Twin Falls area and the Colorado River basin
indicate that the range of values for salt pickup from irrigated lands
is roughly 1.3 to 22 MT/ha/year (0.5 to 8 tons/acre/year) (Skogerboe
and Law, 1971). An average salt pickup rate might be 5 MT/ha/year
(2 tons/acre/year). On a per day basis, the range becomes 3 to 50
kg/ha/day (3 to 44 lb/acre/day), and the average becomes 12 kg/ha/day
(11 lb/acre/day).
86

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TABLE 111-16
SALT YIELDS FROM IRRIGATION IN GREEN RIVER SUBBASIN (EPA, 1971)

Average sal t yield

Area
(tons/acre/yr)
(kg/ha/day)
(lb/acre/day)
Green River above New Fork River
0.1
0.6
0.5
Big Sandy Creek
5.6
34.3
30.7
Blacks Fork in Lyman area
2.4
14.7
13.2
Hams Fork
0.3
1.8
 1.6
Henry's Fork
4.9
30.1
26.9
Yampa River above Steamboat Springs
0.2
1.2
1.1
Yampa River, Steamboat Springs to Craig
0.4
2.5
2.2
Mill Creek
0.1
6.1
5.4
Williams Fork River
0.3
1.8
1.6
Little Sanke above Dixon
0.3
1.8
1.6
Little Sanke, Dixon to Baggs
0.5
3.1
2.7
Ashley Creek
4.2
25.8
23.0
Duchesne River
3.0
18.4
16.4
White River below Meeker
2.0
12.3
11.0
Price River
8.5
52.2
46.6
San Rafael River
2.9
17.8
15.9

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TABLE II1-17
SALT YIELDS FROM IRRIGATION IN UPPER COLORADO MAIN STREAM SUBBASIN (EPA, 1971)
Area
Main stem above Hot Sulphur Springs
Main stem, Hot Sulphur Springs to
Kremmling
Muddy Creek Drainage Area
Brush Creek
Roaring Fork River
Colorado River Valley, Glenwood Springs
to Silt
Colorado River, Silt to Cameo
Grand Valley
Plateau Creek
Gunnison River above Gunnison
Tomichi Creek.above Pari in
Tomichi Creek, Pari in to mouth
Uncompahgre above Dallas Creek
Lower Gunnison
Naturita Creek near Norwood
Average salt yield
(tons/acre/yr) (kg/ha/day) (lb/acre/day)
0.3	1.8	1.6
0.9	5.5	4.9
2.4	14.7	13.2
0.7	4.3	3.8
3.5	21.5	19.2
2.3	14.1	12.6
3.5	21.5	19.2
8.0	49.1	43.8
0.9	5.5	4.9
0.3	1.8	1.6
0.3	1.8 	1.6
0.3	1.8	1.6
4.5	27.6	24.7
6.7	41.1	36.7
2.8	17.2	15.3

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TABLE 111-18
SALT YIELDS FROM IRRIGATION IN SAN JUAN RIVER SUBBASIN (EPA, 1971)
Fremont River above Torrey, Utah
Fremont River, Torrey to
Hanksville, Utah
M'jddy Creek above Hanksville, Utah
San Juan above Carracas
Florida, Los Pinos, Animas drainage
Lower Animas Basin
LaPlata River in Colorado
LaPlate River in New Mexico
	Average salt .yield	
(tons/acre/yr) (kg/ha/day) (1b/acre/day)
0.4	2.5	2.2
5.8	35.6	31.8
3.1	19.0	17.0
2.7	16.6	14.8
0.2	1.2	1.1
3.5	21.5	19.2
1.4	8.6	7.7
0.3	1.8	1.6

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TABLE 111-19
SALT YIELDS FROM IRRIGATION IN LOWER COLORADO RIVER BASIN (EPA, 1971)
Average salt yield
Area
Virginia River
Colorado River Indian Reservation
Palo Verde Irrigation District
Below Imperial Dam
(Gila and Yuma projects)
(tons/acre/.yr) (kg/ha/day) (lb/acre/day)
2.3
0.5
2.1
variable
14.1
3.1
12.9
12.6
2.7
11.5
TABLE 111-20
SALT YIELDS FROM IRRIGATION FOR SELECTED AREAS IN CALIFORNIA
(WATER RESOURCES COUNCIL, 1971)
	Average salt yield
Area	(tons/acre/yr) (kg/ha/day) (lb/acre/day)
North coastal	0.353	2.2	1.9
Central coastal	0.808	5.0	4.4
Sacramento	0.707	4.3	3.9
Delta-Central Sierra	0.974	6.0	5.3
San Joaquin	0.827	5.1	4.5
Tulare	0.768	4.7	4.2
Colorado Desert	10.9	67	60

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3.8 POLLUTANTS FROM URBAN RUNOFF
From established urban areas, stormwater may pick up various wastes
ranging from settled dust and ash to debris coming directly from man
himself. The quantities of solids from urban nonpoint sources are quite
significant in quantity. Fly ash and dust from industrial processes
such as steel mills, cement manufacturing, and certain chemical pro-
cesses are known to be profuse. Dusts from the burning of organic fuels
are a significant factor, and solids in sizable quantities also result from
off-street mud, automotive exhaust, organic debris from tree leaves and
grass trimmings, and discarded litter.
In this report, the nonpoint pollutant loading function for urban
areas is formulated from pollutant loading values obtained in a recent
URS study (Amy, et al., 1974) for the U.S. Environmental Protection
Agency. In that study URS reviewed a large number of published reports,
extracted and statistically analyzed data, and presented average solid
loading values and chemical and biological composition of solids.
In analyses of urban runoff data, URS assumed that only the runoff
from street surfaces contributed to urban nonpoint pollution. The
resulting loading values for solid wastes are given in terms of pounds
per curb-mile per day. The user should note that these values represent
contributions from both street and nonstreet surfaces.
Data developed in the URS study include nationwide means of solids
loading rates and pollutant composition of street solids, as well as
a more detailed breakdown of data into major source categories. Table
111-21 shows data from the URS report which are divided into 13 subsets
among three major source categories including climate, land use,
and average daily traffic. These data may be different from the means
which are given in the last column of the table, at the 80% confidence
level. Whenever the mean of any parameter (solid loading rates or
composition) in any subset differs significantly from the mean
of the set of all data, that number may be substituted for the mean
91

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TABLE 111-21
SOLID LOADING RATES AND COMPOSITIONNATIONWIDE MEANS AND
SUBSTITUTIONS OF THE NATIONWIDE MEANS AT 80% CONFIDENCE LEVEL* (AMY, ET AL., 1974)
CO
CO
Concentrations in micrograms per gram of dry solid	No /gram
CIimate
Land Use
Traffic
No./day
Category
Loading
bod5
COD
O
CL.
O
no3
OrgN
Cd
Cr
Cu
Fe Pb
Mn
Mi
Sr
Zn TC0LI+
FCOL 1+
Northeast
291
c




5,970c
2.6b
139b

17,700. 870.
b c
363
a
2,c
27b
260.
b
4.45:5c
Southeast
103b
29,100.
b

2,240
a

1,970,
a


137.
b
1,370.
b

21b
28b

7.0^
Southwest
50c


470b



241
a
78a
2,520.
b

57b
15a
5.716 .
d

Northwest
30c






246
a

34,500b 2,600b


10c
480g 6.8Z5f
l.U4f
Openspace















Residential

14,000b
82,000.
b
850b
550
c
1,800
a


93a
l,430b

28b



Commercial
74c
58,700c
269,000c
2,250c
1,580c
6.430
a


133b
3,440b

48b

520.
b

Light Industry















Heavy Industry







278b

28,600b 1,160c
570b


8.2E5
e

500









1,2!0d



252.
b
6.9Z4 f
500-5,000

9,500c
83,000c
741d
419b




18,900, 1,060
a C

17d
34c

3.4?:5d
5,000-15,000












18a


15,000
82d









357
a


3.8JC5
a

All data**
156.
b
19,900.
b
140,000.
D
1,280.
D
804.
b
2,950.
b
3.4b
211
a
104
a
22,000 1,810
3 d
418
d
35a
21
a
370 2.55:6
a C

Freedom > 10). Total number of permitted substitutions = 103. Percent Standard Error of the Mean Subscripting Code: a=0-9, b=10-19 c=20-29 d=30-39
e=40-49, f=50-62.
+Coliform counts are expressed in computer notation, i.e. 5=10"*.
** Average TPO4 is 2,930c and NH4 is 2,640c

-------
of the set of all data. Table 111-21 also gives the percent standard
error of the mean which indicates the degree of confidence that may be
placed on the mean.
Table 111-22 presents the means and standard deviations of
concentrations of mercury and several pesticides, which resulted
from a set of data that were characterized as "very small and unreliable."
No other data were obtained.
3.8.1 Loading Functions for Solids
Y(S)U = L {S) u - l_st	(111-18)
where
Y(S) = daily total solids loading, kg/day (lb/day)
L(S)u = daily solids loading rates, kg/curb-km/day (Ib/curb-
mi 1e/day)
L ^ = steet curb-length (approximately 2.0 x street length),
curb-km (curb-miles).
3.8.2 Loading Functions for Other Pollutants
Y(i) = a *Y(S) -C(i)	(111-19)
where
Y(i)M = daily total loading of pollutant i, kg/day (lb/day);
MPN(x 10"'
coliform.
u	6
MPN(x 10 ) per day for total coliform and fecal
= conversion factor, 10"6 (metric and English).
Y(S)U = daily total loading of solids, kg/day (lb/day), cal-
culated in Equation 111-18.
C(i)u = concentration of pollutant i in solids, ug/g; MPN/g
for total coliform and fecal coliform.
93

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TABLE 111-22
MEAN CONCENTRATIONS OF MERCURY AND CHLORINATED
HYDROCARBONS IN STREET DIRT FROM NINE U.S. CITIES (AMY, ET AL., 1974)
	Concentrations in micrograms per kilogram of dry solid	
CD
^	Methoxy-	Methyl

Hg.
Endrin
Dieldrin
PCB
chlor
DDT
Li ndane
parathion
DDD
Mean
83
0.2
28
770
500
76
2.9
2
82
Standard
111
-
28
770
1,050
118
7.1

78
deviation

-------
Equations 111-18 and 111-19, along with solid loading values and
compositions in Tables III-21 and III-22, provide the means to assess
daily average pollutant loadings from urban areas.
It is important to note that pollutant loadings so calculated are
street surface loadings rather than loadings at outfalls to the
receiving waters. The transport of storm runoff in sewers and removal
of pollutants in some treatment systems would reduce pollutant loads
to some extent. Such effects are not included in loading factors
suggested in Tables 111 -21 and III-22. Furthermore, the methodology
presented above does not reflect the effect of housekeeping practices
in the urban area. Good housekeeping practices such as cleaning of
street solids by sweeping, and the use of catchment basins to remove
solids and organic matter, will reduce pollutant loads from streets to
receiving waters (Startor, 1972).
3.8.3 Procedure for Loading Calculations
Data in Tables 111-21 and 111 -22 represent two options as well as two
levels of accuracy for a user to assess pollutant loadings from a given
urban area. Application of the "subset" data may result in higher
accuracy, but require more data and more computation effort, than if
"nationwide means" are used.
Option I - In this option the user will use nationwide means
presented in Tables 111-21 and 111 -2 2. Proceed as follows:
1.	Determine solids loading rate and solids composition from
tables.
2.	Determine street length (include that of primary and
secondary streets but not driveways, alleys, or parking
lots).
95

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3.	Calculate daily solids loading using Equation 111-18.
4.	Calculate daily loading of other pollutants using
Equation 111-19.
Option II - In this option the user will make use of data presented
for source categories in Table III-21. Steps needed for loading calcula-
tions are:
1.	Characterize the study urban area. When applicable, the
entire area should be divided into individual homogeneous
sections with unique characteristics. Each individual
section is then defined as a subarea (e.g., residential
area).
2.	Determine street length in each subarea.
3.	Enter the Table 111-21 at the line labeled "All Data."
4.	Select a category of climate, land use, or average daily
traffic, which best applies to an area and move upward to
the line of data to the right of the category heading.
5.	Substitute those values available in the row selected for
the corresponding values in the row labeled "All Data."
In choosing the substitute loading factors, the following
priority sequence of source categories is suggested:
(a) climate; (b) land use; (c) average daily traffic.
The climatic zones of the U.S. delineated by the URS are
shown in Figure 111-18. Caution: it is not permissible
to use more than one row of substitutions at a time, i.e.,
to use a BOD value for land use and COD for climate in
order to form a new row of loading rate and composition
data. It is both proper and useful, however, to repeat
the above process to obtain several new rows of data to
96

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NORTHEAST
MIDWEST
NORTHWEST
(INSUFFICIENT DATA) i
tImore
act
; Lawrences \
San Jo^e {southWESt!
Durham
Tulsa
Tucs
Figure III-18 Climate Zone for the Cities from Which Data are Available
and Used in the URS Study (/Yiy, et al,, 1974)
97

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present a range of composition and loading rates. Use
data from Table III-22 if desired.
6.	Repeat Steps 4 and 5 for all subareas.
7.	Use Equation 111-18 to calculate total solid loading in
a subarea.
8.	Use solid loading (Step 7), Equation 111-19 and selected
composition data to calculate total loading of other
pollutants in a subarea.
9.	Sum up loadings of subareas to obtain the loading of
entire study area.
The calculation procedure delineated for Option I and Option II above
is illustrated in Example III-5.
Option III - In this option, the user will make use of site specific
data.
The recent URS study has assembled all presently available data on
the rates of accumulation of solids and on the concentrations of
various pollutant constituents in those solids that collect on street
surfaces. These data are probably adequate for most urban planning
operations. The user, however, may alternatively replace these
loading factors by site specific data to obtain better prediction.
If site specific data are lacking, users are encouraged to
conduct sampling and analytical programs of their own. The data from
site specific tests, if handled properly, may be used in analyzing the
area's runoff problems instead of using values given in this report.
This would be desirable in most instances, especially in areas or under
specific conditions that were not documented in the URS study.
98

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Recommended procedures for conducting site specific tests are given
in Appendix B of the URS Report (Amy, et al. , 1974).
With the lack of site specific data, the user may wish to examine
the available published data for source and reliability. The user is
referred to Appendix A of the URS Report for description of available data
sources, as well as procedures for processing these data.
3.8.4 Street Length and Land Use Data for Urban Areas
Street length data are available from local public works
departments or street departments. They can also be obtained by measure-
ment on aerial photographs.
Survey statistics for the U.S. indicate that street surfaces
occupy on the average about one-sixth of the urban area (Manuel, et al.,
1968). The American Public Works Association (American Public Works
Association, 1974) recently developed a regression relationship between
curb length of urban area versus population density. Data from many
cities across the country were used. The resulting regression equation is:
CL -	413.11 - (352.66)(0.839)PD	(111-20)
where
CL =	curb length density, ft/acre
PD =	population density, number/acre
The correlation coefficient for the equation is 0.72. The
regression curve is shown in Figure 111-19.
Curb length can be estimated if street surface acreage is known.
Table 111-23 presents equivalent curb length per unit area of street
surface, suggested by URS. However, if actual values are known, it
is best to use known values.
99

-------
cm
U
<
>
to
z
LLI
Q
X
l
O
z
(33
3
U
600
550
500
450
400
350
300
250
200
150
100
50
0
GROSS POPULATION DENSITY, POP/HECTARE
0 20 40 60 80 ICC 120 140 160 180 200 220 240
	r v  i
--i i 

V " 
1 I	1	1






-











-





^,
























- 7 





J 





 /





/ 





/ * *




-
/ 





/ 





-I *





/ 





1





/ 











 





1











 "
i i
i

1 1 1

797
750
700
650
600
550 S
<
u
0 10 20 30 4C 50 60 70 80
GROSS POPULATION DENSITY, POP/ACRE
90 100
500
to
450 
400 ^
350 to
Z
LU
300 Q
x
250 o
200
CO
150 U
100
50
0
Figure 111-19 Correlation between Population Density and Curb
Length Density, (American Public Works Associa-
tion., 1975)
100

-------
TABLE II1-23
EGUIVALENT CURB-LENGTH PER UNIT AREA
OF STREET SURFACE, ARRANGED BY LAND USE
TYPES (AMY, ET AL., 1974)

Equivalent curb-km Equivalent curb-miles

per hectare of
per acre of

street surface street surface
Open land
2.11
0.53
General residential
2.15
0.54
General commercial
1 .63
0.41
Light industrial
1.71
0.43
Heavy industrial
1 .59
0.40
All land use types
1 .83
0.46

TABLE 111-24

GENERAL LAND CONSUMPTION RATES
FOR VARIOUS LAND USES
(AMERICAN PUBLIC WORKS ASSOCIATION,
1974)

Land consumption (acres/capita)

<100,000 >100,000
>250,000
Land Use
Population Population
Population
Residential
0.1049 0.0714
0.0585
Commerci al
0.0101 0.0084
0.0073
Industri al
0.0177 0.0083
0.0077
Park
0.0146 0.0093
0.0078
101

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The following references provide survey data and analysis results
relative to land uses in major urban areas of the U.S.:
Bartholomew, H., Land Use In American Cities, Harvard University
Press, Cambridge, Massachusetts (1955).
Niedercorn, J. H., and E. F. R. Hearle, "Recent Land-Use Trends in
Forty-Eight Large American Cities," The RAND Corporation, Santa Monica,
California, Memorandum RM-3664-FF, June 1963.
Manuel, A. D., R. H. Gustafson, and R. B. Welch, "Three Land
Research Studies," National Commission on Urban Problems, Research
Report No. 12, Washington, D.C. (1968).
The American Public Works Association (1974) estimated land con-
sumption rates for various land uses in American cities, shown in
Table III- 24. These rates can be used to estimate acreages in different
land uses if the number of population is known.
	 EXAMPLE 111-5 	
The study area is a 250-acre urban watershed in Atlanta, Georgia.
The area is mainly residential and has 17 curb-miles of primary and
secondary streets. Predict the average daily loadings of BOD and
lead in runoff from the entire area.
Option I - Use nationwide means of solid loading rate and compositions
gi ven i n Table 111- 21.
Calculate solid loading:
L(S)u = 156 lb/curb-mile/day
Y(S) = 156"17 - 2,652 lb/day
102

-------
Calculate BOD and Pb loadings:
C(BOD)u = 19,900-TO-6 lb/lb solid
C(Pb)u = 1,810-10"6 lb/lb solid
Y(BOD)u = 2,65219,900*10"6 = 52.8 lb/day
Y(Pb)u = 2,652-1 ,810*10~6 = 4.8 lb/day
Option II - Use substitutions at 80% confidence level.
Atlanta is in the southeast. Move upward in Table 111-21 to
southeast climate category. A loading substitution is available. Make
all available substitutions into the row labeled "All Data." The new
row has, among others:
Solid loading rate, L(S)U = 103 1b/curb-mi1e/day
BOD concentration, C(B0D)u = 19,900-10 ^ lb/lb solid
Pb concentration, C(Pb)u = 1,370*10"^ lb/lb solid
Calculate solid loading:
Y(S) - 103-1 7 = 1 ,751 lb/day
Calculate BOD and Pb loadings:
Y(B0D)u = 1 ,751 -19,900-10"6 = 34.8 lb/day
Y(Pb)u = 1,751 -1 ,370-10"6 = 2.40 lb/day
Pollutant loadings calculated in Option II are lower than those in
Option I and probably better represent the real situation in Atlanta,
Georgia.
	 END OF EXAMPLE III-5 	
103

-------
3.9 POINT SOURCE WASTE LOADS
3.9.1	General
The purpose of this section is to discuss sources of information
concerning point source discharges and to provide a reasonable range of
values for discharge concentrations when no direct source data can be
located. When available, direct data concerning an existing or proposed
discharge is preferable to the use of the information presented here.
The point-source information presented here is divided into three
catergories: municipal discharges, urban storm water discharges, and
industrial discharges. Three basic sources of information were used in
collecting the data: EPA guidelines for future discharges, the results of
recent attempts (e.g., Tetra Tech, Kaiser Engineers) to characterize point
source waste loads, and data from a number of actual continuous flow dis-
charges. These types of information are identified as they appear in the
subsequent tables.
3.9.2	Sources of Direct Data
Before using these guidelines and estimates a planner should
exhaust the sources of actual point source waste loading information
available to him. The discharger may be the best source of information
since many states require dischargers to maintain a self monitoring
program. Pollutant load per day and pollutant concentration data are
usually included in this information. Second, essentially all point
source discharges are now required to obtain a discharge permit. The
state or federal agency issuing these permits will have on file maximum
allowable limits for the discharge. These limits can be used as an
upper bound waste loading rate. Third, state water quality or water
resource agencies often have conducted sample collection programs for
significant discharges. Fourth, data for a similar facility within the
local region (same activity, same general size) may be used as an esti-
mate for an unknown waste load. If none of these are available the
104

-------
data presented here may be used as a reasonable "ball park" estimate.
3.9.3 Municipal Discharges
Total municipal discharge loads show a strong connectivity with
population levels. Additionally, municipal discharge concentrations are
reasonably consistant from one municipality to another. Thus municipal
waste load estimates presented here represent better estimates for a
specific discharge than do urban stormwater or industrial discharges.
Table 111-25 lists typical concentrations of basic water quality
parameters which generally concern the planner. This table is based
on assessment of a large number of individual discharges. Based on
the existing level of a specific municipal wastewater treatment system,
one of the three columns in the table could be used to approximate
municipal waste loadings. The breath of variety which exists in actual
municipal discharges is shown in Tables III-26a and III-26b where
fifteen municipal discharges and six discharges in a designated 208 area
in North Carolina are characterized, respectively. Table III-26b also
indicates relative treatment levels by listing both inflow and outflow
concentrations.
Table 111-27 lists average daily flow rates for various contributors
to municipal systems on a per capita basis. Multiplying this per capita
flow rate times the municipal waste load concentrations (from Table
111-25) produces a waste load per capita per day. Using this figure
either total present municipal waste loading (population multiplied by
waste load per person per day) or future municipal waste loading
increases (projected population increase multiplied by waste load per
person per day) may be estimated.
Finally, Table III-28 shows major pollutant effluent concentra-
tions which conform to BAT treatment (1983 standard). 'Comparison of this
105

-------
TABLE II1-25
TYPICAL MUNICIPAL WASTE CONCENTRATIONS (METCALF AND EDDY, 1972)
Constituent
Concentration inq
/I
Strong
Medium**
Weak
Solids, total
1 ,200
700
350
Dissolved, total
850
500
250
F i xed
525
300
145
Volatile
325
200
105
Suspended, total
350
200
100
Fi xed
75
50
30
Volatile
275
150
70
Settlable solids, (ml/liter)
20
10
5
Biochemical oxygen demand, 5-day, 20C (B0Dg-20)
300
200
100
Total organic carbon (TOC)
300
200
100
Chemical oxygen demand (COD)
1 ,000
500
250
Nitrogen, (total as N)
85
40
20
Organic
35
15
8
Free ammonia
50
25
1 2
Nitri tes
0
0
0
Ni trates
0
0
0
Phosphorus (total as P)
20
10
6
Organic
5
3
2
Inorgani c
15
7
4
Chiorides*
100
50
30
Alkalinity (as CaCO^)*
200
100
50
Grease
150
100
50
*Values should be increased by amount in carriage water.
**In the absence of other data use medium strength data for planning purposes.
106

-------
TABLE III-26a
EXAMPLES OF MUNICIPAL DISCHARGES
Discharge
Flow .Rate
Mqd
BOD
mg/1
' 	   1
BOD
g/cap/day
, -
TSS
mg/1
TDS
mg/1
Turbidity
JTU
Total N
mg/1
Total P
mq/Y
COD
mg/1
2
Los Angeles City , Ca.
350.4
320
--
330

7.1
107
52
610
2
Los Angeles Hyperion,Ca
332.2
113
--
85.7
--
54
17.3
20
240
2
Huntington Bch. , Ca.
154.7
180
--
96.4
2611
100
48.2
--
646
San Diego2, Ca.
100.1
172
--
134
1986
256
42
--
. 626
2
Terminal Island , Ca.
9.1
165
--
135
--
--
33
10
--
Vallejo San. Dst.^, Ca.
5.3
124
31.3
--
--
--
32
47
336
Marin County #5"*, Ca.
0.4
91
28.5
--
--
--
30
27
272
Richmond (City)^, Ca.
6.2
138
50.3
--
--
--
23
23
435
San Francisco , Ca.
47.9
158
69.9
--
--
--
33
21
389
3
San Francisco S.E. , Ca
19.1
158
71.2
--
--
--
33
21
445
3
Belmont , Ca.
3.5
87
28.8
--
--
--
22
24
280
Petaluma , Ca.
1.0
36
9.1
--
--
--
28
55
190
Islip5, N.Y.
0.168
29.3
--
48
--
--
9.1
--
--
Huntington^, N.Y.
1.77
29.8
--
32
--
--
18.1
5.3
--
Port Jefferson^, N.Y.
1.44
68.8
--
54.2
--
--
19.4
5.9
--
Based on systems receiving primary treatment
Tetra Tech, Inc., 1975
3
Pearson, Storrs and Selleck, 1969
4.
All data is for one year only and is designed to indicate a range of probable values.
5" Weston, 1976..

-------
TABLE III-26b
POINT SOURCE LOADINGS OF SIX MAJOR WASTEWATER TREATMENT FACILITIES IN ONE NORTH CAROLINA 208 AREA
1
FACILITY NAME
FLOW
(MGD)
BOD (
b/day)
S.S.
(lb/day)
Sludqe Production
INFLUENT
EFFLUENT
INFLUENT
EFFLUENT
(lb/day Dry Solids)
Northside
8.4
16,673
1,331
13,731
2,522
4,300
Third Fork
3.4
7,231
993
5,189
2,410
3,300
New Hope
3.4
5,473
1,758
4,197
1 ,361
318
Chapel Hill
3.8
5,166
824
5,071
1,363
3,000
Walnut Creek
20.3
64,673
11,005
23,702
7,111
6,255
Hillsborough
0.56
957
383
934
234
0 - See Text
SUB-TOTAL
39.9
100,173
16,294
52,824
15,001
17,173
Percent of TOTAL
84.8%
90.7%
95.3%
84.4%
93.0%


-------
TABLE 111-27
MUNICIPAL WASTEWATER FLOW RATES
Category
Waste Flow Per Day
Domestic - Single Dwelling^
Domestic - Multiple Dwelling^
Industrial - Major Cannery Activity^
Industrial - Diversified^
Industrial - Minimal Activity^
Commercial Activity^
2
Total Municipal System
57 gcd3
55 gcd
500 gmd^
400 gmd
175 gmd
100 gcd5
140 - 170 gcd
^ Tetra	Tech, Inc. 1975
~ Metcalf and Eddy, 1972
3	gcd =	gallons per capita per day
4
gmd =	gallons per manufacturing employee oer day
5
ged =	gallons per commercial employee per day
TABLE 111-28
MUNICIPAL EFFLUENT CONCENTRATIONS CORRESPONDING TO
EPA BEST AVAILABLE TECHNOLOGY (BAT) TREATMENT LEVELS
(TETRA TECH, INC. 1975)
Consti tuent
BAT Concentration (mg/1)
BOD
10
TSS
10
Total N
5
Total P
3
Grease
3
109

-------
data with data on influent concentrations in Table 111-25 indicates
the degree of treatment necessary to conform to these standards.
3.9.4	Urban Stormwater Waste Load Estimation
Stormwater waste loads enter a natural water body either through
a storm sewer system or through a combined sewer system. Typical values
of pollutant concentrations for the stormwater overflow through each of
these systems is shown in Table III-29. Tables III-30 and 111-31 show
data collected for a number of actual storm sewer and combined systems
respectively. Finally, a summary table of pollutant loading for storm-
water discharges is shown in Table III-32.
3.9.5	Industrial Waste Loadings
Industrial waste loadings are difficult to accurately assess
from either national averages or published guidelines. Both flow rate
and pollutant concentrations will vary substantially as a function of
plant size, processes involved, primary and secondary product mix, etc.
Waste discharge data for a number of individual plants is provided in
Tables 111-33, III--34aand b, and 111-35. Plants within a local region
which are similar to any of the listed plants may be used as a guide
to local plant discharge concentrations. These data are further
generalized in Tables III-36 and 111 -3 7 which report Best Practical
Technology (BPT) and Best Available Technology (BAT) guidelines for
six types of industrial activities. Individual processes for these
industries will have different guidelines. Table III-38 defines BAT
guidelines for selected parameters and industrial processes.
110

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TABLE 111-29
CHARACTERISTIC VALUES FOR URBAN STORMWATER
AND SEWER OVERFLOW WATER QUALITY (FIELD, 1975)
Water Quality
Parameter
Combined Sewer
Overflow Characteristic
Concentration (mg/1)
Urban Stormwater
Characteristic
Concentration (mg/1)
BOD5
100 - 500
11
-
500
TSS
100 - 1500
500
-
11 ,300
Total Solid
300 - 2000
1000
-
14,600
Organic N
3
5 - 30.1
0.9
-
16
NH-N
1
1 - 11.5
0.4
-
2.5
P04

1 - 62
10
-
125
Total coliform
5xl04 -
30x106 MPN/ml
2xl03
-
14xl05
PH
4
9 - 8.4

~

Fecal coliform
5xl04 -
llxl06 MPN/ml



Chloride


200
-
25,000
Oils


10
-
110
Phenols


0
-
0.2
Lead


0
-
1 .9
*No data available
111

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TABLE 111-30
COMPARISON OF QUALITY OF STORM SEWER DISCHARGES FOR VARIOUS CITIES3
(LAGER AND SMITH, 1974)
Type of wastewater,
location, year,
Ref. No.
bod5,
mg/1
COD,
mg/1
DO,
mg/1
ss,
mg/1
Avg Range Avg Range Avg Avg
Range
Total
coliforms,
MPN/100 ml
Avg
Range
Total	Total
nitrogen, phosphorus,
mg/1 as N mg/1 as P
Avg
Avg
Typical untreated
municipal
Typical treated
municipal
Primary effluent 135
Secondary effluent 25
200 100-300 500 250-750
70-200 330
15-45 55
165-500
25-80
Storm sewer
discharges
Ann Arbor, Mich.,
1965 (2)	28 11-62
Castro Valley,
Calif., 1971-72 (14) 14 4-37
Des Moines, Iowa,
1969 (6)	36 12-100 -
Durham, N.C.,
1968	(1)	31 2-232 224
Los Angeles,
Calif., 1967-66 (19) 9.4 -
Madison, Wis.,
1970-71 (17)		
New Orleans, La.,
1967-69"	(16)	12
Roanoke, Va.,
1969	(12)	7
Sacramento, Calif.,
1968-69	(37)	106 24-283 58
Tulsa, Okla.,
1968-69 (33)	11 1-39 85
Washington, D.C.,
1969 (5)	19 3-90 335
40-660
8.4
6.9
4.5
21-176
12-405
200 100-350 5xl07 Ixl07-lxl09
80 40-120 2xl07 5xl06-5xl08
15 10-30	lxlO3 Txl0Z-lxl04
2,080 650-11,900
505 95-1,053
1,013
81 10-1,000
26
30
71 3;211
247 84-2,052
2xl04 4x103-6x104
3x105 3x103-2x106
3x103-2x106
lxlO6 7x103-7x108
,5
40
35
30
3.5
1.9b
2.2
4.8
10
7.5
5.0
1.7
0.87
0.18
1.1
8x10 2x10-1x10'
lxlO5 1x103-5x108 0.3-1,5e 0.2-1.2f
29-1,514 - 1,697 130-11,280
6xl05 1x10^-3x10
2.1
0.4
a.	Data presented here are for general comparisons only. Since different sampling methods, nunber of samples, and other
procedures were used, the reader should consult the references before using the data for specific planning purposes.
b.	Only ammonia plus nitrate.
c.	Only fecal.
d.	Median values from 1 sampling station.
e.	Only organic (Kjeldahl) nitrogen.
f.	Only soluble orthosphosphate.

-------
TABLE 111-31
COMPARISON OF QUALITY OF COMBINED SEWAGE FOR VARIOUS CITIES3,
(LAGER AND SMITH, 1974)
Type of wastewater,
location, year,
Ref. No.

bod5,
mg/1
COO
mg/1
DO,
mg/1

SS
mg/1
Total
coli forms,
MPN/100 ml
Total
nitrogen,
mg/1 as N
Total
phosphorus,
mg/1 as P
Avg
Range
Avg
Range
Avg
Avg
Range
Avg
Range
Avg
Avg
Typical untreated
municipal
200
100-300
500
250-750

200
100-350
5xl07
Ixl07-lxl09
40
10
Typical treated
municipal








5xl0-5xl08


Primary effluent
136
70-200
330
165-500

80
40-120
2x10
35
7.5
Secondary effluent
25
15-45
55
25-80
-
15
10-30
1 xlO3
Ixl02-lxl04
30
5.0
Selected combined











Atlanta, Ga.,
1969 (31)
100
48-540

--
8.5
--

lxlO7
--
--
1.2b
Berkeley, Calif.
1968-69 (34)c
60
18-300
POO
20-600

100
40-150


--
--
Brooklyn, N.y.,
1972 (8)
180
86-428
__


1,051
132-8,759
--

--
1.2b
Bucyrus, Ohio
1958-69 (35)
120
11-560
400
i 3-923

470
20-2,440
lxlO7
Zx105-5xl07
13
3.5
Cincinnati, Ohio,
1970 (36)
200
80-380
250
190-410
--
1 .100
500-1,800
--

--
--
Des Moines, Iowa,
1968-69 (6)
115
29-158
	

--
295
155-1,166


12.7
11.6
Detroit, Mich.,
1965 (2)
153
74-685
115

--
274
120-804

--
16.3d
4.3
Kenosha, Wis.,
1970 (18)
129

464

__
458
__
2x10

10.4d
5.9
Milwaukee, Wis.,
1969 (7)
55
26-182
177
118-765
--
244
113-848

2xl05-3xl07
3-24
0.8b
Northampton, U.K.,
1960-62 (22)
150
80-350
__
	
--
400
200-800
--

10C
--
Racine, Wis.,
1971 (18)
119



--
439




--
Roanoke, Va.,
1969 (12)
115



--
78

7xl07

--

Sacramento, Calif.,
1968-69 (37)
165
70-328
238
59-513

125
56-502
5x10
5 7^
7x10-9x10


San Francisco, Calif.,
1969-70 (3) 49
1.5-202
155
17-626

68
4-426
3x10
2xl04-2xl07

--
Washington, D.C.,
1969 (5)
71
10-470
362
80-1,760
--
622
35-2,000
3x10
4x10^-6x10
3.5
1 .0
a. Data presented here are for general comparisons only. Since different sampling methods, number of samples, and other
procedures were used, the reader should consult the references before using the data for specific planning purposes.
b.	Only orthophosphate.
c.	Infiltrated sanitary sewer overflow.
d.	Only ammonia plus organic nitrogen (total) Kjeldahl).
e.	Only aimionia.
f.	Only fecal.
113

-------
TABLE II1-32
SUMMARY OF STORMWATER POLLUTANT CONCENTRATIONS
(KAISER ENGINEERS, 1969)
Pol 1 utant^
Stormwater Overflow Concentrations
Separate Drainage Areas^ Combined Areas^
Standard Standard
Mean Deviation Mean Deviation
B0D5
COD
S.S.
Total Coliforms^
Total Nitrogen
(as N)
Total Phosphorus
(as P)
27 25 108 36
205 118 284 110
608 616 372 275
3xl05 - 6xl06
2.3 1.4 9 6
0.5 0.4 2.8 2.9
(a)	Summary of 20 cities, storm sewers and unsewered areas
(b)	Summary of 25 cities, combined sewer areas
(c)	All units mg/1 except coliforms, MPN/100 ml
(d)	Geometric mean
114

-------
TABLE 111-33
TYPICAL INDUSTRIAL DISCHARGE POLLUTANT CONCENTRATIONS
Industry
Flow
Rates ,
mq/1000 lb1
BOD
lb/1000 lb
COD
lb/1000 lb
TSS
lb/1000 lb
Total N
lb/1000 lb
Total P
lb/1000 lb
Heavy
Metal
lb/1000 lb
Oil &
Grease
lb/1000 lb
 p
Primary Metal'
0.2-1.6
-
-
-
32
15
55-242
-
Cu, Brass Rods-*
0.04
0.1
0.5
0.02
0.07
-0
-
-
Roofing Materials^
0.01
13.6
25.7
14.2
0.34
-0
0.13
0.68
Steel Plate, Wire^
0.004
0.56
2.7
5.1
0.04
0.01
1.2
0.12
Petroleum (General
0.005
1.3
3.7
-
0.4
_
0.003
0.15
Oil Production(#l)3
0.003
0.57
2.1
0.58
0.33
0.01
0.05
0.14
Oil Production(#2)3
0.003
0.45
1.3
0.86
0.16
0.01
0.03
0.09
Oil Production(#3)3
0.001
0.45
2.9
 0.65
0.24
0.01
0.04
0.31
Paper (General)2
0.015
18
55
28
-
-
-
-
Paperboard^
0.017
19.6
64.8
37.9
0.05
-
-
-
Paper^
0.024
12.6
43
33.1
0.03
-
-
-
Primary Inorganic^
0.002
0.2-3.5
 -
5-30
0.03-0.7
' 0.8-9.0
0.05-0.3
0.06-2
Alky Lead Fluoro
Hydrocarbons-*
0.002
0.39
0.89
0.15
0.03
-
-
0.1
Inorg. Acids^
0.004
0.08
0.52
5.37
0.04
0.02
0.33
0.06
Primary Organic^
0.002
1-1.9
-
-
3-7
0.15-0.3
0.01-0.02
0.05-0.08
Caustic Chemicals^
0.021
1.24
4.9
19.9
1.27
0.3
1.69
0.24
Plant Food-*
0.001
0.03
1.43
0.01
1.17
0.14
0.02
0.02
1	Units are million gallons of pollutant per 1000 lb. of finished product
2	Kaiser Engineers, 1969
3	Pearson, Storrs, Sellech, 1969

-------
TABLE III-34a
SELECTED SAN FRANCISCO AREA INDUSTRIAL DISCHARGERS
DISCHARGER
FLOW
BOO
SS
OIL &
GREASE
ORGANIC
NITROGEN
TOTAL
PHOSPHATE
TOTAL
COL I FORM
pH
LEAD
ZINC
PHENOLIC
COMPOUNDS

MGC
Cone* Load**
Cone
Load
Cone
Load
Cone
Load
Cone Load
MPN
Per 100 ml

Cone
Load
Cone
Load
Cone Load
Shell Oil
3.4
9
250
28
800
15
430
NR
_
NR
< 100
7.0
NR
_
80
2
20 0.6
C4H Sugar
21
51
9000
3
470
2
320
NR
-
NR -
NR
7.8
NR
-
NR
-
NR
Hercules
1.6
NR
-
30
380
3
37
5
62
NR -
< 10
-
NR
-
NR

NR -

0.2
9
17
50
95
3
5
5
9
NR -
< 100
7.6
NR
-
NR
-
NR -
Standard
Oil
109
9
8200
14
13,000
3
2700
NR
_
NR -
NR
_
NR
_
20
22
14 13
Stauf fer
Co.
0.1
NR
_
5
5
4
4
NR
_
NR -
NR
_
30
0.02
NR
_
NR
Stauffer
Co.
0.08
NR

7
4
2
1
NR

NR
NR

_
_


NR

36.5
NR
-
Net
Loss
-
NR
-
1
300
1 300
NR
7.8
Net
Loss
-
180
56
NR -
U.S.
Steel
22
NR

6
1,200
1
200
NR


NR

10
2
120
2
30 5
DeLavol
Turbine
0.6
15
75
14
70
0.6
3
NR

NR -
NR
7.0
NR
_
NR
_
NR -

0.15
3
4
7
9
1
1
NR
-
NR
NR
7.0
NR
-
NR
-
10 0.01
N. Elec..
0.16
7
9
3
4
1
2
NR
-
NR -
< 10
-
9
0.01
160
0.2
NR -
*Conc = Concentration in mg/1
**Load = Load in lb/day

-------
TABLE III-34b
SELECTED SAN FRANCISCO AREA INDUSTRIAL DISCHARGERS
DISCHARGER
FLOW
BOO
SS
OIL 8
GREASE
ORGANIC
NITROGEN '
TOTAL
PHOSPHATE
TOTAL
COL I FORM
pH
LEAD
ZINC
PHENOLIC
COMPOUNDS

MGD
Cone
* Load**
Cone
Load
Cone
Load
Cone
Load
Cone Load
MPH
Per 100 ml

Cone Load
Cone
Load
Cone
Load
Allied
Chemical
3.3
5
140
Net
Loss



NR

NR -
NR
7.8
100
3
60
1.5
NR

Dow
Chemical
22.2
2

28

_
_
NR
_
NR -
NR
7.3
7
1.3
NR
_
NR
-
Exxon Oil
2.3
24
400
23
300
1
20
NR
-
NR -
NR
7.2
NR
-
20
0.4
190
2.5
FMC
0.7
NR
-
11
75
NR
-
NR
-
26 160
NR
7.6
NR
-
NR

NR
-
Marine
World
1.4
2
15
Net
Loss
_
3
35
1
15
0.5 7
7000
7.8
NR
-
NR
-
NR
-
Merck Co.
3.2
NR
-
740
21,000
18
530
NR
-
NR -
NR
10.1
NR
-
NR
-
NR
-
G&E, it)
0.3
NR
-
75
200
1
3
NR
-
NR -
NR
9.0
NR
-
NR
-
NR
-

0.03
NR
-
0.6
2
NR
-
NR
-
NR -
NR
11
NR
-
NR
-
NR
-
GSE, #2
12.2
NR
-
75
8,000
1
85
NR
-
NR -
NR
7.8
5
0.5
50
5
NR
-

0.005
NR
-
0.3
0.01
2
0.1
MR
-
NR -
NR
9.9
NR
-
NR
-
NR
-
Sequoia
Oil
0.1
13
9
47
40
8
7
MR
_
NR -
NR
7.8
NR
-
70
0.05
40
0.04
Ph i11i ps
Oil
10.5
9
800
33
3,000
2
180
NR
-
NR -
<100
-
-
-
20
2
10
1
S. F.
Airport
0.8
28
190
82
420
2
11
NR
-
NR -
<100
-
10
0.06
120
0.7
7
0.04
*Conc = Concentration in mg/1
**Load = Load in lb/day

-------
TABLE 111-35
SUMMARY OF CURRENT AND PROJECTED WASTE LOADS IN ONE REGION 208 AREA (BY SIC)
SIC GROUP
CURRENT LOADINGS
BEST PRACTICABLE WASTE REDUCTION TECHNOLOGY
PROJECTED LOADINGS


BOD
(lb/day)
SS
(lb/day)

Expected
Reductions
BOD
(lb/day)
SS
(lb/day)
No.
Descri ption
Sewer
Sewer
Description
B0D(%)
SS(%)
Sewer
Sewer
201
Meat Products
1,523
1,059
Anaerobic Lagoon to Stabilization Pond
90
85
152
117
202
Dairy Products
973
400
Anaerobic Digestion & Clarification
85
90
71
40
204
Grain Mill Prods.
180
50
Oxidation Ditch & Clarification
85
75
27
13
205
Bakery Prods.
935
910
Rotating Bio-Filters & Clarification
85
65
140
319
208
Soft Drinks
330
40
Fixed Activated Sludge
84
65
53
14
211
Tobacco Man.
2,024
1,750
Activated Sludge (E.A.) & Clarification
85
75
304
438
22_
Textile Mill
2,530
2,173
Activated Sludge & Alum-Aided Clarif.
85
75
380
543
226
Dyeing & Fin.
0
0
Carbon Adsorption & Clarification
75
60


251
Furniture
0
0





265
Paperboard Con.
245
150
Screening, Ext. Aeration, Clarification
35
65
159
53
27_
Print. & Pub.
0
0


--


28_
Chem. & Allied P.
64
29
Activated Sludge & Clarification
85
75
10
18
32_
Stone, Clay P.
0
0
Stilling Ponds, Water Recycle
30
70


35_
Machinery.
32
79
Oil & Grease Traps
50
65
16
28
36_
Elect. Equip.
659
402
Ion Exchange (for Plating Process)
10
90
593
40
379
Transp. Equip.
100
100
Oil & Grease Traps
50
65
50
50
...
Non-Manuf.
1,374
170
See Text
70
90
412
17
9999
Mun. W.W.T.P.
0
0
Upgrade Six Largest Plants
Varies for
Each Plant



TOTALS
10,459
7,312
--

2,367
1,690

-------
TABLE II1-36
TYPICAL INDUSTRIAL EFFLUENT CONCENTRATIONS
BPT - "1977"
APPROXIMATE MEAN EFFLUENT CHARACTER 1ST ICS'a' (EPA, 1974)
(in mg/1)

20
22
26
28
29
33
Parameter
Food
Textiles
Paper
Chemi cals
Petroleum
Metals
TSS
40^
49(b)
58^
40^)
l0(b)
20(b)
B0Dc
29 (b)
22(b)
39(b)
30^
15(b)
38^
5
COD
135
225^
156
1400^
102^
-
TDS
-
700
3785
4350
-
i
CI
565
25
135
-

1
_ 1
1
Total-P
17
2
-
5

.50 1
/  \ 1
Total-N
50
2
-
20
70
62
Lead
_
.03

2(b)

.25^
Zinc

5
_
0.25(b)

.25(b) j
Cadmi um
_
.005
_
0.225^

,15(b)
Oil
,0
10

l5(b)
5(b>
5
L






^ ^Represents an approximate estimate of the mean effluent concentrations
for each industry. The pollutant concentration could vary widely within
an industry as a result of varying water usages.
Concentrations developed from effluent guidelines which exist for
these parameters, other concentrations were obtained from existing
treatment plant data.
119

-------
TABLE II1-37
TYPICAL INDUSTRIAL EFFLUENT CONCENTRATIONS
BAT - "1983"
APPROXIMATE MEAN EFFLUENT CHARACTERISTICS^9' (EPA, 1974)
(in mg/1)

20
22
26
28
29
33
Parameter
Food
Textiles
Paper
Chemicals
Petroleum
Metals
TSS
l0(b)
8
BODr
7(b)
ll(b)
22(b)
15
5{b)
4(b)
b
COD
48
72(b)
88
460*b)
26
-
TDS
-
700
3785
4350
-
-
CI
565
25
135
-
-
-
Total-P
1.2
2
_
3
-
0
Total-N
9(b)
2
_
3
28
5(b)
Lead
_
.03
__
-| (b)
_
0(b)
Zinc
_
5
_
.25^

0(b)
Cadmi urn
_
.005

-O
LO
O
_
0(b)
Oil
io
10
-
3
1.35C''
5(b)
^Represents an approximate estimate of the mean effluent concentrations
for each industry. The pollutant concentration could vary widely
within an industry as a result of varying water usages.
^Concentrations developed from effluent guidelines which exist for
these parameters, other concentrations were obtained from any existing
treatment plant data found in the EPA Development Documents (2-14).
120

-------
TABLE 111-38
EPA BAT GUIDELINES FOR SELECTED NEW
SOURCE INDUSTRIAL DISCHARGES (30 DAY AVERAGE)
Industry
BOD
TSS
PH
Dairy - Fluid, Cultured Products
0.37 lb/100 lb. BOD1
0.046 lb/100 lb. BOD
6.0-9.0
Dairy - Butter, Cheese Processing
0.008 lb/100 lb. BOD
0.01 lb/100 lb. BOD
6.0-9.0
Dairy - Ice Cream Processing
0.47 lb/100 lb. BOD
0.059 lb/100 lb. BOD
6.0-9.0
Wet Corn Milling
20 lb/1000 bu. corn2
10 lb/1000 bu. corn
6.0-9.0
Parboiled Rice Processing
0.007 lb/100 wt. rice
0.003 lb/100 wt. rice
6.0-9.0
Tuna Processing
8.1 lb/1000 lb. tuna
3.0 lb/1000 lb tuna
6.0-9.0
Cane Sugar Refining
0.18 lb/ton of melt
0.07 lb/ton of melt
6.0-9.0
Wool Finishing (Textile)
11.2 lb/1000 lb. wool
11.2 lb/1000 lb. wool
6.0-9.0
Woven Fabric Finishing
3.3 lb/1000 lb. fabric
3.3 lb/1000 lb. fabric
6.0-9.0
Carpet mill
3.9 lb/1000 lb
3.9 lb/1000 lb.
6.0-9.0
Cement manufacturing
--
0.005 lb/1000 lb. product
6.0-9.0
Electro plating
--
327 lb/106 ft2
6.0-9.5
Organic Chemicals (aqueous)
0.2 lb/1000 lb.
0.12 lb/1000 lb.
6.0-9.0
Plastics (Polyvinyl Chloride) Manufacture
0.19 lb/1000 lb.
0.13 lb/1000 lb.
6.0-9.0
Rayon manufacture
2.0 lb/1000 lb.
1.28 lb/1000 lb.
6.0-9.0
Acrylics manufacture
0.87 lb/1000 lb.
0.27 lb/1000 lb.
6.0-9.0
Soap Production (by Batch Kettle)
0.40 lb/1000 lb.
0.40 lb/1000 lb.
6.0-9.0
Petroleum cracking
3.1 lb/1000 bbl. feedstock3
2.0 lb/1000 bbl. feedstock3
6.0-9.0
Petrol chemical processing
4.1 lb/1000 bbl. feedstock3
2.7 lb/1000 bbl. feedstock3
6.0-9.0
Iron & Steel (Coke By Product)
--
0.104 lb/100 lb.
6.0-9.0
Iron (Blast Furnace)
--
0.13 lb/1000 lb.
6.0-9.0
Primary Alumnium Smelting
--
0.05 lb/1000 lb. product
6.0-9.0
Hide Tanning and Finishing
1.6/1000 lb.
2.0 lb/1000 lb.
6.0-9.0

-------
TABLE III-38 (continued)
Industry
BOD
TSS
pH
Asbestos - Cement Pipe
Rubber Tire Production
Kraft Paper Process
Slaughterhouse Operation
3.1 lb/ton
0.12 lb/1000 live weight
0.38 lb/1000 lb.
0.064 lb/1000 lb.
7.5 lb/ton
0.2 lb/1000 lb. live weight
6.0-9.0
6.0-9.0
6.0-9.0
6.0-9.0
^nits are in lbs of effluent BOD per 100 lbs of influent BOO.
2
Reference to weight of products are to weights of raw input product.
3
Actual limits equal listed limits times facility size dependent multipliers

-------
REFERENCES
American Public Works Association, 1974. Nationwide Characterization,
Impacts and Critical Evaluation of Stormwater Discharges, Non-
sewered Urban Runoff and Combined Sewered Overflows. Monthly
Progress Report to the U.S. Environmental Protection Agency.
Amy, G., Pitt, R., Singh, R., Bradford, W. L., and LaGraff, M. B.,
1974. Water Quality Management Planning for Urban Runoff. U.S.
Environmental Protection Agency, Washington, D.C., (EPA 440/9-
75-004) (NTIS PB 241 689/AS).
Association of Bay Area Governments, 1?7C.	i ishec.
California Regional Framework Study Committee for Pacific Southwest
Inter-Agency Committee, Water Resources Council, 1971. Com-
prehensive Framework Study, California Region, Appendix XV, Water
Quality, Pollution, and Health Factors. Water Resources Council,
Washington, D.C.
Carlston, C. W., and Langbein, W. C., 1960. Rapid Approximation of
Drainage Density: Line Intersection Method. U.S. Geological
Survey, Water Resource Division, Bulletin 11.
Buckman, H. 0., and Brady, N. C., 1969. The Nature and Properties of
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Field, R., 1975. "Coping With Urban Runoff in the United States,"
Waste Research. Vol. 9, pp. 499-505.
Forter, G. R., and Wischmeier, W. H., 1973. Evaluating Irregular
Slopes for Soil Loss Prediction. American Society of Agricul-
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Garstka, W. U., 1964. "Snow and Snow Survey," in Handbook of Applied
Hydro!ogy. ed: Chow, V. T. McGraw-Hill, Inc.; New York,
New York.
Hagin, J., and Amberger, A., 1974. Contribution of Fertilizers and
Manures to the Nitrogen and Phosphorus Load of Waters. A Compu-
ter Simulation. Technion^Israel Institute of Technology,
Haifa, Israel.
Jenny, H. , 1930. A Study on the Influence of Climate Upon the Nitrogen
and Organic Matter Content of the Soil. Missouri Agr. Exp. Sta.,
Res. Bui. 152.
123

-------
REFERENCES (continued)
Kaiser Engineers, 1969. Final Report to the State of California San
Francisco Bay Delta Water Quality Control Program. Chapter VII.
California Water Quality Control Board, Sacramento, Cal.
Lager, J. A. and Smith, W. G., 1974. Urban Stormwater Manaaement
and Technology: An Assessment. USEPA National Environmental
Research Center, Cincinnati, Ohio.
Lopez, A. B., and Galvez, N. L., 1958. "The Mineralization of the
Organic Matter of Some Philippine Soils Under Submerged Condi-
tions," Phi 1ippine Agr-, 42:281-291.
Manuel, A. D. , Gustafson, R. H., and Welch, R. B. , 1968. Three Land
Research Studies. National Commission on Urban Problems,
Washington, D.C., Report No. 12.
Massey, H. F. , Jackson, M. L., and Hays, 0. E. , 1953. "Fertility
Erosion on Two Wisconsin Soils," Agron. J. , 45:543-547.
Maxwell, J. C., 1960. Quantitative Geomorphology of the San Dimas
Experimental Forest, California. Columbia University, Depart-
ment of Geology, New York, Project No. NR389-042, Report No. 19.
McElroy, A. D. , Chiu, S. V., Nebgen, J. W. , Aleti, A., and Bennett,
F. W., 1976. Loading Functions for Assessment of Water Pollu-
tion from Nonpoint Sources. U.S. Environmental Protection
Agency, Washington, D.C., (EPA-600/2-76-151 ).
Melton, M. A., 1957. An Analysis of the Relations Among Elements
of Climate, Surface Properties and Geomorphology. Columbia
University, Department of Geology, New York, Project No.
NR389-042, Technical Report No. 11.
Metcalf and Eddy, Inc., 1972. Wastewater Engineering: Collection,
Treatment, Disposal. McGraw-Hill Book Company; New York.
Parker, C. A. et al., 1946. Fertilizers and Lime in the United States.
USDA Misc. Pub. No. 586.
Pearson, E., Storrs, P. and Sellech, R., 1969. Final Report, A
Comprehensive Study of San Francisco Bay. Volume IV: Waste
Discharges and Loadings. University of California Sanitary
Engineering Research Laboratory.
Pitt, R., 1976. Control Measures for Reducing the Accumulation of
Street Surface Contaminant. NSF, Washington, D.C.
124

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REFERENCES (continued)
Schuman, G. E., Spomer, R. G. , and Piest, R. F., 1970. "Phosphorus
Losses from Four Agricultural Watersheds on Missouri Valley
Loess," Soil Science Society of America, Proceedings. 37(2):424.
Schumm, S. A., 1956. "The Evolution of Drainage Systems and Slopes in
Badlands at Perth Amboy, New Jersey." Geo. Soc. Amer. Bull.,
67:597-646.
Skogerboe, G. V. , and Law, J. P., Jr., 1971. Research Needs for Irri-
gation Return Flow Quality Control. U.S. Environmental Protec-
tion Agency, Report No. 13030-11/71.
Smith, K. G., 1950. "Standards for Grading Texture of Erosional
Topography," Amer. J. Sci., 248:655-668.
	. 1958. "Erosional Processes and Landforms in Badlands
National Monument, South Dakota," Geo. Soc. Amer. Bull.,
69:975-1008.
Strahler, A. N., 1952. "Hypsometric (Area-Altitude) Analysis of
Erosional Topography," Geo. Soc. Amer. Bull. , 63:1 117-1142.
	. 1964. Quantitative Geomorphology of Drainage Basin and
Channel Network. Handbook of Applied Hydrology, ed: Chow, V. T.
McGraw-Hill, Inc.; New York, New York, pp.4-39 to 4-76.
Startor, J. D., and Boyd, G. B. , 1972. Water Pollution Aspects of
Street Surface Contaminants. U.S. Environmental Protection
Agency, Washington, D.C. EPA-R2-72-081.
Stoltenberg, N. L., and White, J. L., 1953. "Selective Loss of
Plant Nutrients by Erosion," Soil Science Society of America,
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Taylor, A. W., 1967. "Phosphorus and Water Pollution," J. Soil, and
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Tetra Tech, Inc., 1975. Draft Final Report Study Areas II and VI-C
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Washington, D.C.
URS Corporation, 1976. Areawide Water Quality Management Plan - 208
Pollution Source Analysis. Triangle J Council of Governments,
Research Triangle Park, N.C.
125

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REFERENCES (continued)
U.S. Department of Agriculture., 1973. Engineering Technical Note
No. 16. Soil Conservation Service, Des Moines, Iowa.
U.S. Department of Agriculture., 1974. Soils Technical Note No. 3.
Soil Conservation Service, Honolulu, Hawaii.
U.S. Department of Agriculture Conservation., 1974. Agronomy Techni-
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U.S. Environmental Protection Agency, Regions VIII and IX., 1971.
"Natural and Man-Made Conditions Affecting Mineral Quality,"
Mineral Quality Problem in the Colorado River Basin. Appendix A.
Environmental Protection Agency, Washington, D.C.
U.S. Environmental Protection Agency., 1974. Effect of Hydrologic
Modifications on Water Quality. (Draft.) MITRE Corporation.
Viets, F. G., Jr., 1971. "Fertilizer Use in Relation to Surface and
Groundwater Pollution," Fertilizer Technology and Use (2nd ed.).
Soil Science Society of America, Madison, Wisconsin, pg. 517.
Water Resources Administration., 1973. Technical Guide to Erosion and
Sediment Control Design (Draft). Maryland Department of Natural
Resources, Annapolis, Maryland.
Weston, R. F., 1976. Nassau-Suffolk 208 Domestic and Industrial Point
Source Inventory and Evaluation. Nassau-Suffolk Regional
Planning Board; New York.
Wischmeier, W. H., and Smith, D. D., 1958. "Rainfall Energy and Its
Relationship to Soil Loss," Transaction, American Geophysical
Union, 39:285-291.	"
Wischmeier, W. H., and Smith, D. D., 1965. "Predicting Rainfall--
Erosion Losses from Cropland East of the Rocky Mountains,"
Agriculture Handbook 282. U.S. Department of Agriculture,
Agriculture Research Service.
Wischmeier, W. H., 1972. "Estimating the Cover and Management Factor
for Undisturbed Areas," Proceedings, USDA Sediment Yield Work-
shop. U.S. Department Agriculture, Oxford, Mississippi.
	., 1972. "Upland Erosion Control," Environment Impact
on Rivers, ed: Shen, H. W., Fort Collins, Colorado,
pg 15-1 to 15-26.
126

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CHAPTER 4
RIVERS AND STREAMS
4.1 INTRODUCTION
The main purpose of the formulations presented in this
chapter is to allow the user to predict responses of rivers and
streams to selected waste loading schemes. It is suggested that the
planner read this introductory section completely to gain a feel for
the scope of problems that will be covered and the limitations of
formulations presented.
Rivers throughout this country are subject to a wide
spectrum of geological, biological, climatological, and man-induced
impacts, and the result is a variety of water quality problems. Any
approach providing guidance to the solution of these problems,
especially one restricted to hand calculations, must be limited in
scope. The following guidelines have been used in selecting topics
to be considered within this section: 1) widely occurring problems,
2) those amenable to hand calculations, and 3) those for which
planners will be able to obtain sufficient data.
4.1.1 Scope
The major problem areas to be considered are:
	Carbonaceous (CBOD) and Nitrogenous (NBOD) Biochemical
Oxygen Demand
	Dissolved Oxygen
	Temperature (with a discussion of low flow)
	Nutrients and Eutrophication Potential
	Total Coliforms
	Conservative Constituents
	Sedimentation and Suspended Solids
127

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Since 1974, the U.S. Environmental Protection Agency has annually
published the National Water Quality Inventory which is a compilation
of current water quality conditions and recent trends in the nation's
rivers and lakes. Several of the tables in that report series are
relevant to this document and are included here. Table IV-1 illus-
trates reference water quality levels used to define acceptable
pollutant limits in U.S. waterways. Table IV-2 shows water quality
conditions in eight major waterways in the United States, while Table IV-3
summarizes the most widely observed water quality problems in the U.S.
These tables will frequently be cited throughout this chapter.
4.1.2 Significance of Problem Areas
Oxygen depletion is often the result of excessive CBOD and
NBOD loadings particularly in combination with high temperature, low
flow conditions. Increased nutrient loadings to streams producing
elevated ambient concentrations pose substantial potential for
eutrophication. The nutrient problem is currently one of the most
widespread areas of concern regarding river water quality. The health
hazards category in Table IV-3 lists elevated coliform levels, a
problem of particular concern in northeastern and Great Lakes States.
Salinity also has been identified as a major problem, particularly in the
central and southwestern states.
Because of their importance, each of the problem areas just
described will be addressed in this chapter. As shown in Table IV-4,
many states routinely measure the parameters associated with these problems.
The total number of states responding to the survey was 47. Because of
the routine surveys conducted, data are commonly available for performing
hand calculations. NBOD, though not directly measured, can be found
from measurements of organic and ammonia nitrogen. Chloride concen-
tration measurements can be directly converted to salinity.
128

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TABLE IV-1
REFERENCE LEVEL VALUES OF WATER QUALITY
INDICATORS FOR U.S. WATERWAYS (EPA, 1974)
Parameter
Suspended solids
Turbidity
Temperature
Col or
Reference Level, Receptor,
and Information Source
80 mg/1 - aquatic life+
50JTU - aquatic life*
90F - aquatic life*
75 platinum-cobalt units - water supply+
Ammonia +

0.89 mg/1
- aquatic 1ife+
Nitrate (e
s N)
0.9 mg/
-
eutrophication
Nitrite plus nitrate t
0.9 mg/
-
eutrophication
Total phosphorus +
0.1 mg/
-
eutrophicati on
Total phosphate t
0.3 mg/
-
eutrophication
Dissolved
phosphate t
0.3 mg/
-
eutrophication
Di ssolved
solids (105C)
500 mg/
-
water supply*
Di ssolved
solids (180C)
500 mg/
-
water supply*
Chloride

250 mg/
-
water supply+
Sulfate

250 mg/
-
water supply+
PH

6.0-9.0
-
aquatic life*
Di ssolved
oxygen
4.0 mg/
-
aquatic life*
Total coli
forms (MFD)**
10,000/
00
ml - recreation*
Total coli
forms (MFI)**
10,000/
00
ml - recreation*
Total coli
forms (MPN)**
10,000/
00
ml - recreation*
Fecal coli
forms (MF)**
2,000/
00
ml - recreation*
Fecal coli
forms (MPN)**
2,000/
00
ml - recreation*
Phenols

0.001 mg/1
- water supply+
*Guidelines for Developing or Revising Water Quality Standards,
EPA Water Planning Division, April 1973.
+Criteria for Water Quality, EPA, 1973 (Section 304(a)(1) guidelines).
ttBiological Associated Problems in Freshwater Environments,
FWPCA, 1966, pp 132-3.
**Membrane filter delayed, membrane filter immediate, most
probable number, membrane filter.
t Original reference did not specify whether as N or NO-,, or P or PO,.
129

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TABLE IV-2
CONDITION OF EIGHT MAJOR WATERWAYS (EPA,1974)
Ri ver
Mi ssi ssi ppi
Mi ssouri
Ohio
Tennessee
Detroit area
rivers
Columbia
Snake
Harmful
Substances
Trace metals
present in middle
river
High*; increasing
iron and
manganese
Cyanide present
but improving
Severe gas super
saturation; some radio-
activity in lower river
Severe gas super-
saturation, signif-
cant pesticides
Physical
Modification
High* turbidity and
solids below
Missouri River
High* suspended solids,
turbidity in middle and
lower river
High* suspended solids
in lower river, some
improvements
Suspended solids
improving, local
temperature effects
from discharges
Occasional high*
temperatures
Turbidity from
natural erosion,
agricultural practices,
reservoir flushing
Eutrophication
Potential
High* increasing
nutrients but no
al gae
High*, increasing
nutrients but no
al gae
High* nutrients but
no algae
Small increase in
nutrients but no
algae
Nutrients discharged
to Lake Erie
decreasing
High* nutrients but
no algae, except for
slime growths in
lowet? river
Nuisance algal
blooms each
summer

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TABLE IV-
Harmful
River	Substances
Willamette	Significant sulfite
waste liquor from
pulp and paper wastes
Ri ver
Mississippi
Salinity, Acidity,
and A1 kal init.y
High* salinity, acidity
below major
tributaries
Mi ssouri
High* dissolved salts
in middle and lower
ri ver
Ohio
Low* alkalinity
especially in upper
ri ver
Tennessee
Detroit area
ri vers
Acids and chloride low,*
improving despite
large discharges
(continued)
Physical
Modi fication
High* turbidity at
high flow, high
temperature in summer
Eutrophication
Potential
High* level of
nutrients but
not excessive algae
Oxygen
Depletion
Oxygen-demanding
loads from large
cities evident
High* organic loads
from feedlots,
improved near cities
Occasional low*
dissolved oxygen near
Cincinnati and Pittsburgh
Low* BOD and
decreasing COD in
reservoi rs
Low* dissolved oxygen
only at mouths of
area tributaries
Health Hazards and
Aesthetic Degradation
Commercial fishing
eliminated in lower
river by phenols,
bacteria near cities
High* bacteria and
viruses present in wet and
dry periods
High* bacteria especially
in high population
areas
High* bacteria in small
areas near cities, low
radionuclides
Phenols decreasing,
bacteria unchanged-
to-higher

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TABLE IV-2 (continued)
Ri ver
Columbia
Snake
Willamette
Salinity, Acidity,
and A1kalinity
Approaches ideal
for fresh waters
High* dissolved
solids from irrigation
in middle river
Low* dissolved mineral
salts, improved pH
Oxygen
Depletion
Dissolved oxygen
close to saturation
Dissolved oxygen
close to saturation
Improved dissolved
oxygen, no standards
violations
Health Hazards and
Aesthetic Degradation
Very low* bacteria
High* bacteria
below population
centers
High* bacteria, but
improving
*High (or low) relative to other rivers, or relative to other sections of river, or to
national reference levels. Does not necessarily imply standards violations or
dangerous condition.

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TABLE IV-3
WATER QUALITY PROBLEM AREAS REPORTED BY STATES*
NUMBER REPORTING PROBLEMS/TOTAL (EPA,1975)

Middle
Atlantic,
Northeast
South
Great
Lakes
Central
Southwest
West
Islands
Total
Oxygen
depletion
11/13
9/9
6/6
6/8
4/4
6/6
4/6
46/52
Eutrophi-
cation
potential
11/13
6/9
6/6
8/8
2/4
6/6
4/6
43/52
Health
hazards
11/13
8/9
5/6
8/8
3/4
5/6
5/6
45/52
Salinity,
acidity,
alkalinity
3/13
6/9
2/6
6/8
4/4
' 4/6
2/6
27/52
Physical
modification
7/13
3/9
3/6
8/8
3/4
6/6
5/6
35/52
Harmful
substances
6/13
6/9
5/6
4/8
4/4
2/6
3/6
30/52
* Localized or statewtde problems discussed by the States in their reports.

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TABLE IV-4
WATER QUALITY PARAMETERS
COMMONLY MONITORED BY STATES* (EPA,1975)

Number
Parameter
of States
Flow
47
Dissolved oxygen
47
Coliform bacteria
45
Nitrogen (any form)
39
Phosphorus (any form)
35
pH
35
B0D/C0D/T0C
27
Water temperature
29
Turbidity
26
Solids (any type)
27
Metals (any type)
17
Chiori des
19
A1kalini ty
15
Conductivity
16
Col or
11
Sulfate
14
*Only parameters listed by at least 10 States and specified as being
part of each State's monitoring program are included.
134

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4.1.3 Applicability to Other Problems
The basic theories to be presented are aimed at reaching solutions
to particular water quality problems. Generally, however the theories
have broader applicability than will be presented, in terms of additional
water quality parameter analysis. The approach most often utilized
below is the law of mass conservation. In the case of temperature, an
energy balance is performed which is analogous to a mass balance. The
degree of commonality of source and sinks of a particular pollutant
(e.g., nutrients) or water quality indicator (e.g., dissolved oxygen) is
responsible for the similarities and differences among the specific
equations. For example, CBOD and NBOD produce a similar general effect
(oxygen depletion), generally have similar sources and sinks, and for
purposes of this study, are assumed to follow first order decay
kinetics. Coliforms, also assumed to decay by first order kinetics,
are handled by the mass-balance approach. Conservative substances are
different from BOD and coliforms in that they do not decay. Finally,
there are also some instances where a more subjective analysis is
indicated, and neither a mass nor energy balance is presented.
Once the similarities among water quality parameters are under-
stood, handling two seemingly different problems may be accomplished in
a straightforward fashion. More generally, it is possible to apply
the tools presented here to other problems which, although not specifi-
cally discussed, can be analyzed using the same basic tools. For
example, the distribution of toxic substances that are either conserva-
tive or follow a first order decay may be evaluated using techniques
described for conservative substances and coliforms, respectively.
4.1.4 Sources of Pollutants
Pollutant loadings can be classified as originating from three
general sources: point, nonpoint, and natural. Each of these can
constitute a major hurdle in meeting the 1983 goals of fishable and
135

-------
swimmable waters. Specifically, point sources (30 states), nonpoint
sources (37 states), and natural conditions (21 states) are all major
contributors to water quality problems (EPA, 1975).
It is imperative that the capacity to accommodate nonpoint
sources be a part of the hand calculation tool for rivers. Table IV-5
illustrates, for example, the importance of nonpoint source nutrient
loading for selected rivers in Iowa. Up to 95.9% of the annual phosphorus
load and up to 99.1% of the total nitrogen are from nonpoint sources.
Admittedly, quantification of these loads is often difficult. Neverthe-
less, simplified nonpoint source terms will be included in some of the
mass-balance formulations since Chapter III has supplied a methodology
for estimating nonpoint source loading rates.
4.1.5 Assumptions
In deriving the mass-balance equations, it is necessary to make
certain assumptions. The planner should have an understanding of
these in order to prevent the misapplication of developed formulations.
The major assumptions are:
	steady-state
	plug flow
	vertically and laterally mixed system
	first order decay rates (when decay occurs)
The steady-state assumption means that conditions are not changing
with time. Changes are considered only as a function of distance along
the river, and the time scale to be considered for steady-state generally
should be on the order of a week or longer. For example, summer low
flow conditions can be assumed to represent a steady-state. However,
storm events, and the dynamic responses of a river to them, must be
considered a transient situation.
136

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TABLE IV-5
ANNUAL PHOSPHORUS AND NITROGEN LOAD FOR SELECTED IOWA RIVER BASINS (EPA,1975)
ANNUAL PHOSPHORUS LOAD
Ri ver
Total
(lbs/year)
Point Sources
(1bs/year)
Nonpoint Sources
(lbs/year)
Percent of
Total from
Nonpoint Sources
Floyd
720,207
29,807
690,400
95.9
Little Sioux
1,851,632
129,088
1,722,544
93.0
Chariton
879,916
48,203
831,713
94.5
Des Moines
5,621,007
586,015
5,034,992
89.6
Iowa
1 ,723,975*
103,445*
1 ,620,530*
94.0
Cedar
5,099,507
1,526,775
3,572,732
70.1
*Orthophosphate

ANNUAL NITROGEN LOAD


River
Total
(lbs/year)
Point Sources
(lbs/year)
Nonpoint Sources
(lbs/year)
Percent of
Total from
Nonpoint Sources
Floyd
1,705,984
65,171
1,640,813
96.2
Little Sioux
9,609,556
35,308
9,522,248
99.1
Chariton
1,585,427
24,795
1 ,560,632
98.4
Des Moines
41,334,897
695,235
40,639,662
98.3
Iowa
2,075,830
91,287
1 ,984,543
95.6
Cedar
6,804,881
1 ,552,334
5,252,547
C\J
r-*.

-------
Plug flow assumes that the effects of dispersion can be neglected.
If an instantaneous slug of dye were injected into a stream with purely
plug flow, there would be no tendency for the plug to spread out due
either to a concentration gradient between the dye and the surrounding
water or to velocity gradients. In actuality, some mixing does occur.
Since the effect of dispersion is to spread pollutants, concentrations
predicted along a river may be higher under the plug flow assumption
than would actually be observed.
The fully-mixed assumption presupposes a well mixed system. That
is, concentration gradients exist only in the direction of flow (longi-
tudinal direction) and not in either the vertical or lateral direction.
The final major assumption is that all decay rates can be approximated
by first order decay. This means that the decay rate of a substance is
proportional to the amount present. First order decay is traditionally
used in CBOD computations, and occasionally in nitrogen oxidation. The
oxidation of inorganic nitrogen actually proceeds in stages from
ammonia-N to nitrite-N to nitrate-N. However, for purposes of this
report, the first order decay rate is acceptable for NBOD and coliforms,
as well as CBOD. Before applying first order decay to other substances,
however, care should be taken to determine the validity of this
assumption.
4.1.6 Spatfa1 Variation
For the analysis of spatial variation, the portion of the river
under investigation is divided into reaches. Generally within each reach
a fairly constant stream temperature, velocity, depth, and cross-
sectional area must be assumed. In the discussions below, some
exceptions will occasionally be made. These are noted wherever they
occur.
Any incoming point source or major tributary should constitute the
beginning of a new reach. If a distributed source is included, its
influence is assumed to extend over the entire reach. The more complicated
138

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the situation the planner wants to simulate, the larger the number of
reaches into which a given portion of river will have to be divided.
4.1.7	Data Requirements
Associated with any of the water quality problems to be considered
is the compilation of a small amount of data. For example, stream
velocity (U), volumetric flow rate (Q), and stream temperatures (T) are
needed in the analysis of many water quality problems. Specific to
each problem are numerous other parameters, such as decay rates and
incoming biochemical oxygen demand, for which estimates are
needed.
When it is necessary to gather data, such as stream velocity (UQ)
at the upstream end of a reach, caution and judgment should always be
exercised. U0, for example, should be measured downstream from any
incoming waste flow or tributary entering at the upper end of the reach.
The location of measurements should be representative of the river con-
figuration in the vicinity of the upstream end of the reach. The same
judgment should apply to measurements of stream cross-sectional areas
where needed. In such cases, representative areas should be chosen.
By attempting to understand the significance of each parameter utilized,
the user is more likely to arrive at a meaningful and realistic
solution than if he proceeds mechanically.
4.1.8	Selection of Season
It is reasonable to expect that a particular water quality prob-
lem may be more severe at one time of the year than another. Table IV-6
shows that pollutant levels can depend on season (summer or winter) and
flow rate (high flow or low flow). Dissolved oxygen problems, for
example, are clearly associated with summer, low flow conditions. Conse-
quently, for any particular pollution problem, the planner should strive
139

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TABLE IV-6


MAJOR
WATERWAYS:
SEASONAL AND
FLOW ANALYSIS,
1968-72 (EPA,
1974)

Winter,
Summer,
Wi nter,
Summer,
Domi nant
Parameters
Hiqh Flow
Low Flow
Low Flow
Hiqh Flow
Effect


(number of reaches exceeding reference levels)**
Suspended sol ids
9
5
0
4
High flow
Turbidi ty
13
4
1
7
High flow
Color
11
6
3
4
High flow
Ammonia
14
3
7
1
Cold weather
Ni tri te
3
7
5
1
Low flow
Nitrate(as N)
12
4
8
1
Cold weather
Nitrate(as NO3)
8
3
6
1
Cold weather
Nitrite plus nitrate
2
3
2
1
Inconclusive
Organic nitrogen
3
6
0
3
Warm weather
Total Kjeldahl nitrogen
3
5
0
3
Warm weather
Total phosphorus
10
3
5
2
Cold weather
Total phosphate
8
3
5
1
Cold weather
Dissolved phosphate
6
3
4
0
Cold weather
Dissolved sol ids(105C)
4
7
6
3
Low flow
Dissolved solids(l80C)
3
8
6
2
Low flow
Chlorides
4
15
10
0
Low flow
Sulfates
5
13
5
5
Warm weather.low flow
A1kalinity
6
12
10
0
Low flow
ph
15
4
6
4
Cold weather,high flow
Dissolved oxygen
0
19
0
9
Warm weather
BODc
11
6
8
1
Cold weather
COD (.025N)
6
5
3
2
Cold weather
Total coliforms(MFD)*
4
10
2
5
Warm weather
Total coliforms(MFI)*
8
6
2
4
High flow,warm weather
Total coliforms(MPN)*
4
2
3
3
Inconclusive
Fecal coliforms(MF)*
6
6
3
4
Inconclusi ve
Fecal coliforms(MPN)*
4
0
1
0
Cold weather
Phenols
5
0
1
0
Inconclusive
Odor
4
0
0
0
Inconclusive
'Membrane filter delayed, membrane filter immediate, most probable number, membrane filter.
-Reference levels are available in Table IV-1. Thirty reaches were analyzed during each season.

-------
to perform the analysis under critical conditions normally encountered.
Where planning is performed with consideration of the aggrevated
situation, and where proper abatement action is taken, it is likely
that pollution concentrations will be below problem levels during
other times of the year. If a problem in fact exists, then it is
under these conditions that it will be most pronounced.
In the following sections, hand calculation methods for each
problem area are described with illustrative examples. Table IV-7
provides a cross-reference of the material presented.
4.2 CARBONACEOUS AND NITROGENOUS OXYGEN DEMAND
4.2.1 Introduction
Many wastes discharged into waterways contain biologically oxi-
dizable materials that exert an oxygen demand on waterway resources.
This biochemical oxygen demand (BOD) can be subdivided into carbo-
naceous (CBOD) and nitrogenous (NBOD) components. Table IV-8 illu-
strates typical concentrations of NBOD and CBOD in untreated munici-
pal waste. The NBOD can be estimated by:
NBOD = 4.57 (TON)
where TON represents total oxidizable nitrogen. TON can be estimated
by the sum of organic plus ammonia nitrogen. For example, a typical
TON from Table IV-8 is 20 + 28 = 48 mg-N/1. This represents an NBOD
of 219 mg/1, the same as the approximate average in that table.
141

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INTERRELATIONSHIPS
TABLE IV-7
BETWEEN SECTIONS
OF CHAPTER 4

Section
Prerequi site
Section
Related
Sections
Relationship
Illustrative
Examples
BOD
Introducti on
Coliforms
First order
decay
IV-1
DO
BOD, Introduction
Temperature
Critical DO
1evels
IV - 2 IV - 5
Temperature
Introduction
DO
Temperature
dependence
IV-6 + IV-8
Nutrients
Introduction
Conservative
consti tuents
Nutrients considered
conservative
IV-9
Total
Coliforms
Introduction
BOD
First order
decay
IV-10
Conservati ve
Constituents
Introduction
Nutrients
Nutrients considered
conservative
IV-11
Sedimentation
Introduction
Conservative
constituents
Suspended solids
conservative over
long term
IV-12

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TABLE IV-8
MUNICIPAL WASTE CHARACTERISTICS
BEFORE TREATMENT (THOMANN, 1972)
Approx.
Variable	Uni t	Average
Average Daily Flow	gal/cap/day	125
Sol ids
Total	mg/1	800
Total Volatile	mg/1	400
Total Dissolved	mg/1	500
Total Suspended	mg/1	300
Volatile Suspended	mg/1	130
Settleable	mg/1	150
BOD
Carbonaceous (5 day)	mg/1	180
Carbonaceous (ultimate)	mg/1	220
Nitrogenous*	mg/1	220
Ni trogen
Total	mg/1 N	50
Organic	mg/1 N	20
Ammonia	mg/1 N	28
Nitrite + Nitrate	mg/1 N	2
Phosphate
Total	mg/1 PO-^	20
Ortho	mg/1 P04	10
Poly	mg/1 PO^	10
Coli forms
Total	million org./lOO ml	30
Fecal	million org./lOO ml	4
*Ultimate, Nitrogenous	oxygen demand, exclusive of CBOD.
Normal
Range
100-200
450-1200
250-800
300-800
100-400
80-200
100-450
120-580
15-100
5-35
10-60
0-6
10-50
5-25
5-25
2-50
0.3-17
143

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CBOD is a commonly measured characteristic of waste water. The
CBOD used in the formulations presented below is the ultimate CBOD,
the oxygen required for complete stabilization of the waste. Often
CBOD is expressed as CBOD^, the oxygen utilized in a 5 day test. The
relationship between ultimate (CB0DL) and 5-day CBOD can be approximated
by:
CB0Dc
The mass balance equation used in the CBOD analysis is exactly
analogous to the NBOD equation. The first order decay rate assumption
for NBOD stabilization is necessary to maintain this analogy, and is
sufficient for hand calculations.
Nitrification (the process by which ammonia is oxidized to nitrite,
and nitrite to nitrate) is pH dependent with an optimum range of 8.0 to
8.5 (Wild, 1971). To be more conservative, however, if the pH is
between 7.0 and 8.5, significant nitrification may be assumed. If the
pH is much lower than 7.0, nitrification is not likely to be important.
4.2.2 BOD Decay Rate
The decay rate for CBOD will be denoted by and for NBOD by k^.
Typical values of both k^ and k^ lie between 0.1 and 0.6/day, with
0.3/day being typical, k^ values can, however, exceed the range given
here. Values of 1 to 3/day have been computed for shallow streams
(Thomann, 1972). A figure to be presented shortly will show how
depends on depth. The following discussion will be directed toward
k^, but in general will also apply to k^.
The disappearance of BOD from a river is a reflection of both
settling and biochemical oxidation, as shown in Figure IV-1. Biochemical
oxidation can consist of instream oxidation (k^L) as well as absorption by
attached organisms (k^L). The total oxidation rate then, is k^, where
kd = kl + k4
144

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The total loss rate is
kL = kd + k3
where reflects settling.
FLOW-
^ ?K3lj
Sedimentation
f
\

X
<
/Ax\
~
X

-J
k4l
/
deoxygenation
L- ULTIMATE B.O.D.
.Absorption by
attached organisms
Figure IV-1
Mechanisms of BOD Removal
from Rivers
Settling of BOD is generally more prevalent just below a sewage
discharge where the discharged material mav contain a large suspended
fraction. As this material is transported downstream the settling
component becomes less important and the reaction rate k^ approaches
the oxidation rate k^. In this chapter, the settling component will
not be explicitly considered. Neglecting settling will tend to cause
instream BOD levels to be somewhat higher than they actually might be
along certain portions of a river. It should be noted that if instream
BOD data are used to determine k^ (one such method will be explained in
Figure IV-3) then the effect of settling is automatically included in
k^. A further discussion of benthic demand (as associated with dis-
solved oxygen utilization) can be found in Section 4.3.10.
Figure IV-2 illustrates the dependence of k^ on river depth. The
highest deoxygenation rates occur in shallow streams with stable, rocky
beds, reflecting the significance of attached biological organisms. Appendix
C contains observed and predicted values of kL for various natural streams.
145

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10.0
.0
o
o
8

5 -'
0.05
0.3
DEPTH (FT.)
Stable,Rocky Bed
Moderate Treatment
Some Ammonia
MEAN
Unstable, Sandy Channel
Highly Treated Effluent
with Nitrification
10.0
100.0
Figure IV-2 Deoxygenation Coefficient as a Function of
Depth, (after Hydro-science, 1971)
The decay coefficients and k^ are both temperature dependent
and this dependence can be estimated by:
kT = k2Q 1.047(T"20)	(IV-1)
146

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where
k2Q = kL at 20C
kT = kL at TC
T = water temperature, C
Numerous methods for computing k^ from observed data are available
(Nemerow, 1974). One method entails the use of a semi-log plot. The
stretch of the river containing the data to be plotted must have a
constant stream area and flow rate, and the BOD loading must be from a
point source located at a position that will be called x = 0. Plotting the
log of BOD concentration versus distance generally produces a straight
line with slope of -k^/ll. An example is shown in Figure IV-3. Either
CBODg or CBOD^ can be plotted as the ordinate. Caution must be exercised
to convert the slope from base 10 logarithms as given in the semi-
log plot to base e logarithms as needed in the formulations used in
this chapter. The conversion may be made by multiplying the value
for log base 10 by 2.303.
4.2.3 Mass Balance of BOD
The general mass-balance equation for BOD with the first order
decay process is
It = 0 = T h i()L) - kL L + Lr	+ Lrd 
-------
10.0
5.0
Slope = 2.3 (-^11
U = 4 Miles/Day
K. = -Slope x U
= 2 3 ( 017* '4 Mjles
_J
\
CD
Miles
KL = 0.16/Day
Day
in
O
O
00
O
24
32
36
DISTANCE (MILES)
INPUT
Figure IV-3 Example of Computation of ki from Stream
Data (from Hydroscience, 19/1)
148

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Lr = concentration of CBOD entering through an incremental
sideflow (distributed source), mg/1
Lrd = mass	of CBOD entering, with no associated flow,
mg/l/sec
x = stream distance
3L
gY = 0 indicates that steady-state conditions are being assumed and
thus no accumulation of material takes place at any point
within the reach.
The NBOD equation is completely analogous in form to Equation IV-2:
I? = 0 = " Ih (QN)  V +	+ Nrd	(IV-3)
where N is the NBOD.
N ^ represents purely a mass flux of nitrogenous material, while
Nr (lxVA is a source of entering the river reach through an
incremental sideflow. Thus, in cases where a known distributed source
of BOD significantly contributes to a river reach under study, and the
distributed flow (flow associated with a distributed source) can be
neglected, N ^ can be used in lieu of	. N^d can be estimated
by determining the mass M of BOD entering a volume of river water V in
time T. N ^ is given by:
M
N = 
"Yd V T
For any particular reach of a river under investigation the stream
cross-sectional area can be expressed by:
 = A0( (-^) x = Ao + V	
-------
where
A
'A
Aq =	stream area at upstream end of the reach
=	stream area at downstream end of reach
x =	distance downstream from beginning of reach
x^ =	length of reach
The cross-sectional area need not be measured directly, but can be
computed from:
The cross-sectional area change is a reflection of a change in
stream velocity, perhaps due to a bed slope increase or decrease.
The length of the reach under investigation, x^, is measured in river
miles along the river's centerline. If use of a constant stream area
is assumed, tyfen A^ = 0 and A = AQ throughout the reach.
4.2.4 Typical Solutions
Case 1: The only source of CBOD occurs as a point source at
x = 0. The CBOD distribution is then expressed by:
(IV-5)
where
-k
L
U
o
U = stream velocity at x = 0
o	J
L = ultimate BOD at the upstream end of the reach
o
L = ultimate BOD at a distance x downstream
150

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The other terms have previously been defined. The initial CBOD, L ,
must reflect both CBOD upstream of the reach as well as that contributed
by the point source in question. It is given by:
where
W =	mass rate of discharge of CBOD, lb/day
Qu = upstream river flow, cfs
Q.. =	waste flow rate, cfs
L =	upstream CBOD concentration, mg/1
Case	2: For a point source of CBOD at x = 0 and a distributed
mass	influx of CBOD entering the river throughout the reach, the
solution is
(IV6)
where
L , = mass rate of CBOD entering.the reach per unit
volume of river water, mg/l/day
Case 3: A distributed flow enters the river carrying CBOD
and a point source of CBOD exists at x = 0. The flow rate
Q at a distance x is:
Q = Q +
w vo
- Q
xf vo
x,
X - Qo + flgX
where
151

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The BOD distribution is given by (the river cross-sectional area
is assumed constant throughout the reach):
where
E
k. A + An
L o Q
1	AQ
L = concentration of CBOD entering the river in the distributed
r
flow, mg/1
Case 3 can also be usea to establish the effect a purely
diluting inflow (i.e. Lp = 0) would have on the CBOD distribution,
Case 4: For a point source at x = 0, a distributed source
with associated inflow, and a mass flux with no associated
flow (constant river cross-sectional area), the solution is
L = Lofir) ' + ^vV'f'Cr) ') 
-------
Perhaps the simplest method is assuming that BOD does not decay. An
upper limit of the instream concentration at any point can then be
determined by incorporating all known sources, and using the methods
presented in Section 4.7. If the computed instream concentrations are
below a threshold pollution level, then there is no need to apply
Equations IV-5 through IV-8 because the inclusion of C; decay rate can
only lower the concentrations.
It may also be feasible, as a first estimate, to combine the CBOD
and NBOD equations into one, and use that equation to estimate the
distribution of the total oxygen-demanding material. To do this, all
source terms must include both CBOD and NBOD. One decay coeffi-
cient is used for both CBOD and NBOD decay. The larger decay coeffi-
cient of the two might be used since that will produce the larger
oxygen deficit.
In deciding which of Equations IV-5 through IV-8 to use for any
analysis, the purpose of the analysis as well as data availability
should be considered. If the main purpose is to relate differences
in stream concentrations caused by various levels of abatement at a
sewage treatment plant, the diffuse sources of BOD need not be
considered. The resulting concentration difference can be expressed
as:
AL exp
o
AL =
"J.
('
. A
)X AA 2~
)]
AL ^
fr)
(IV-9A)
(IV-9B)
where AL is the change in BOD concentration due to a change, ALq, in
the initial concentration. Equation IV-9A should be used for a Case 1
or Case 2 situation, and Equation IV-9B for Case 3 or Case 4. If an
estimate of the absolute level of BOD is desired, however, then the
appropriate expression containing the significant sources should be
utilized. It should be noted that if the diffuse sources of BOD are
153

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large then the improvement of instream BOD concentrations by point
source control will be relatively minor. In that case the planner
should focus on nonpoint source control.
EXAMPLE IV-1
Estimating BOD Distribution in a River
Suppose the user wants to calculate the BOD distribution in the river
shown below in Figure IV-4. There are nine point sources contributing
U0= I.I fps
d = 4'
BOD = I mg/l
Q = 300 cfs
Q = 200cfo
iBOD = l mg/l
75 Ml.
I \
mt  mm    jL  w 
Uf
(D
>
50 Ml.
"7

i	" n ' m
Figure IV-^ Hypothetical BOD Waste Loadings in a River
BOD in the stretch of river under consideration. The ninth source is
actually a tributary, and contributes substantially more flow than the
other eight. The initial, problem is to divide the river up into reaches.
The first reach (I) should include the first 75 miles in which there is
one point source of BOD at the upstream end (source (1)). Equation IV-5
154

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is applicable to that reach. Now, there are several choices available
regarding the division of the river between sources (2) and (8). One
choice is to-divide the 50 miles into mini-reaches similar to reach I,
and reapply Equation IV-5 seven more times. A second alternative is
to group adjacent point sources into fewer and larger sources, thereby
requiring fewer applications of Equation IV-5. A third alternative is
to assume that sources (2) through (8) comprise one continuous distrib-
uted source, the total pollutant loading of this equivalent source being
equal to the sum of the individual loads. For this representation to be
valid the sources should be both evenly spread spatially and be dis-
charging comparable loads. The third alternative will be examined here,
and reach II will consist of the 50 miles following reach I. Equation
IV-7 will be used to analyze reach II. Reach III then, will begin just
downstream from the tributary (source (9)).
For reach I, Equation IV-5 is first solved.* Suppose the follow-
ing characteristics of waste source (1) are known:
Q = 20 MGD = 1.55 (20) cfs = 31 cfs
W = 5000 lb. B0D5/day
* Perhaps the most persistent problem encountered in perform-
ing an analysis similar to this is that of ensuring all units in the
calculations are consistent. Two commonly used conversion factors in
analyses of this type are:
1 mg/1 = 8.34 lb/MG
1 MGD = 1.55 cfs
155

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Recall that
L Q + W
_ iru
' - %
W must be in lb. BOD ultimate/day
5000
W =
.68
7353 lb. B0DL/day
Then
(1) (300) + 7353
(1-55)
8.34
300 + 31
= 5.0 mg/1
The decay coefficient is estimated from Figure IV-2 as 0.4/day. No
correction will be made for temperature. Equation IV-5 can
now be expressed as (for constant cross-sectional area):
5 exp ^(1.1)(24)(3600)
where x is the downstream distance in feet. Note the correction
needed to convert the decay coefficient from units of 1/day to 1/sec
The results of the above equation for selected distances down-
stream can be expressed as follows:
x (miles)
L (mq/1)
0
5.0
30
2.6
60
1.3
75
0.9
156

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For reach II, sources (2) through (8) are assumed to contribute
the following loading.
BOD = 8000 lb/day
Q = 120 MGD = 186 cfs
The flow distribution, Q, in reach II is then:
q = q + Qf Q x = 331 + If! x
y yo x.	50
where x is in miles (from 0 to 50). Lr, the average BOD^ concentration
in the incoming flow is:
. = 8000 lb/day 1 mq/1 = a n ma/1
r 120 MGD 8.34 lb/day 8- mg/1
If the average depth in reach II is assumed to be 5 feet, then:
L = .3/day
Finally, E-j is computed:
K.Ao + An	ooi	o
E = 9-	fl =  = = 301 ft
bl\ An	o U 1.1 U 1
Q	o
(0.3)(301)
E = (24) (3600) + ! = 2 5
186
(50)(5280)
157

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Then, using L from the 75 mile point of Reach I as Lq:
In tabulated form:
x (mi)
Q (cfs)
L (mg/1)
0
331
0.9
20
405
1.8
40
480
2.3
50
517
2.5
Note that the BOD concentration is increasing within this reach.
For reach III, only enough information is given to compute the
initial concentration, which proportions the BOD at the end of reach
II with that entering through the tributary (source (9)).
= 200(1) + 517(1.9) = 1 7 
o	200+517	1' mg/1
-END OF EXAMPLE IV-1-
158

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4.2.6 Interpretation of Results
The most frequent use of BOD data in river water quality
analyses involves their relationship with the dissolved oxygen
balance. This relationship will be discussed more fully in Section
4.3. At this point it is sufficient to say that it is necessary to
predict the BOD distribution in a river in order to compute dissolved
oxygen concentrations.
When a river receives a heavy load of organic matter, the normal
processes of self purification result in a series of zones of decreas-
ingly severe conditions succeeding one another downstream. Each zone
contains characteristic animals and plants (Nemerow, 1974). A sapro-
bicity system (saprobicity is a measure of biodegradable organic
matter) has been developed that relates BOD concentrations in streams
to the degree of pollution there. Correlations have been found, for
example, among BOD concentrations, coliform bacteria, and dissolved
oxygen in rivers (Sladecek, 1965). Sladecek (1969) has assigned 5-day
BOD values of 5 ppm to mildly polluted conditions and 10 ppm to sub-
stantial pollution.
Sources of drinking water a're subject to restraints on the maximum
allowable BOD that can be contained in raw water and still qualify as
a drinking water source. Further, the degree of treatment of the raw
water is dependent on the concentrations of certain constituents, such
as BOD. One reference (HEC, 1975) has stated that water having a 5-day
BOD over 4 mg/1, in combination with high levels of other constituents,
represents a poor source of domestic water supply.
As discussed above, the concentration of BOD in a river can come
from a number of sources, both point and nonpoint. It is important to
have the capability of predicting what effect a reduction in waste
loading will have on the instream concentration. One particular point
159

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source may, for example, contribute only a relatively small amount to
the overall problem. Hence a BOD reduction from that particular point
source, although it might be easiest to accomplish, might only produce
negligible improvement.
4.3 DISSOLVED OXYGEN
4.3.1. Introduction
Historically dissolved oxygen has been and continues to be the
single most frequently used indicator of water quality in streams and
rivers. Figure IV-5 shows the seasonal variability of dissolved
oxygen in 22 major waterways throughout the country (EPA, 1974) from
1968 to 1972. Invariably the levels observed from June o October
are lower than those observed in January to March. This is due
primarily to the influence of temperature on the dissolved oxygen
levels. Due to the effect of temperature, summer is the most critical
season in terms of pollutant assimilation in rivers.
The dissolved oxygen calculations presented below range in
complexity from a simple CBOD-DO relationship to a more general dis-
solved oxygen mass balance including CBOD, NBOD, photosynthesis,
respiration, and benthic demands. It should be stressed, however,
that the results calculated from any of the relationships only
provide estimates since each procedure incorporates various assump-
tions that are never fully met. For example, all natural rivers and
streams exhibit varying degrees of dispersional effects, while the
methods presented below do not include any dispersion. Also, waste
loading inflows are assumed to remain constant in quality and quantity
over time. In reality loadings may vary diurnally. Furthermore,
160

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Number
of
Stations
Hudson
Delaware
Susquehanna
Potomac
Alabama
Upper Ohio
Middle Ohio
Lower Ohio
Upper Tennessee
Lower Tennessee
Upper Missouri
Middle Missouri
Lower Missouri
Upper Mississippi
Mississippi near Minneapolis
Middle Mississippi
Lower Mississippi
Upper Arkansas
Lower Arkansas
Upper Red
Lower Red
Bra:os
Rio Grande
Upper Colorado
Lower Colorado
Sacramento
Columbia
5nake
Willamette
Yukon
8oston Harbor
Chicago Area-Tributaries
Chicago Area-Lake Michigan
Detroit Area-Tributaries
Detroit Area-Rivers
19
17
21
15
59
29
7
6
24
23
4
3
17
12
4
4
4
3
4
2
5
4
17
12
12
7
6
7
4
3
5
5
7
5
U
9
23
11
ia
15
28
23
16
65
11
9
7
7
56
2
0.00
1.75 3.50
300 SEASONAL
5.25 7.00 8.75
X
Greater
Than
10.50 12.50 14.00





KEY:
Jun-Oct
Jan-Mar	
Mean 15th
Percentile
Mean
Median
Mean 85th
Percentile




Figure IV-5 Variability of Dissolved Oxygen by Season for
22 Major Waterways, 1968-72 (EPA, 1974)
161

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the choice of system parameters involves a certain degree of judgment.
Thus for any given situation, the planner should establish an envelope
of possible outcomes by different realistic choices of system parameters.
4.3.2 Dissolved Oxygen Mass-Balance
The general dissolved oxygen mass-balance equation that will be
utilized here is given by:
8C = 0 = - 1 9(QC) -kL-kN+k (C -C) - S + P-R	(IV-10)
ST	A 3x	L Y1 a {Ls Lj bb V R
where the new symbols introduced are:
C = dissolved oxygen concentration, mg/1
k = reaeration coefficient, 1/day
a
C$ =	saturation value cf dissolved oxygen, mg/1
=	benthic oxygen demand, mg/l/day
P =	rate of oxygen production due to photosynthesis, mg/l/day
R = rate of oxygen consumption due to algal respiration,
mg/l/day
Stated in words, Equation IV-10 expresses the following relationship:
At steady state, the rate of addition of dissolved oxygen to a river
due to reaeration and photosynthesis equals the depletion rate caused
by the net advective flow, carbonaceous oxidation, nitrogenous oxidation,
benthic demands, and algal respiration.
Commonly, the dissolved oxygen mass-balance equation is expressed in
terms of the deficit, D, which is the difference between the saturation
and actual concentrations.
162

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4.3.3 Reaeration Rate
The atmosphere provides the major source for replenishing the
dissolved oxygen resources of rivers. This mechanism tends to equili-
brate the dissolved oxygen concentration in a river to its saturation
value. Most conmonly, the dissolved oxygen concentration is below
saturation and there is a net influx of oxygen into the river from the
atmosphere. On occasion, due to the production of dissolved oxygen by
algae, rivers or streams can become supersaturated, in which case there
is a net loss of oxygen to the atmosphere.
A number of expressions for the reaeration coefficient, kfl> have
been developed. Two are presented here. O'Connor's formulation
(T(iona;in, 1972) states cnot:
k = (Dl U)1/2 at 20C	(rv-u).
where
9	A
= oxygen diffusivity = 0.000081 ft /hr at 20 C
H = stream depth in ft
U = stream velocity in ft/sec
Expressed in English units,
k = 12.9 U1/2 at 20C
h3/2
The above formula was verified on streams and rivers ranging in average
depth from 1 foot to 30 feet with velocities ranging from 0.5 to 1.6 fps.
Its use should be limited to streams where the reaeration coefficient
is less than 12/day. Figure IV-6 illustrates how ka changes with depth
and velocity.
163

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10.0
Rapid Turbulent
1.0-2.0 FPS
Moderate
0.5-1.0 FPS
Slow Stagnant
0.1-0.5 FPS
ii i i
0.3
DEPTH (FT.)
100.0
Figure IV-6 Reaeration Coefficient as a Function of Depth
(from Hydroscience, 1971)
164

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For shallow (0.4 - 2.4 feet), fast moving streams the following
expression developed by Owens (Thomann, 1972) is preferable, as the
experimental work to devel.op this expression was done almost
exclusively on shallow streams:
k, = 21.6 U0'67 at 20C	(IV*12)
where U is in ft/sec and H in feet. A graphical representation of
Equation IV-12 is shown in Figure IV-7.
Temperature changes affect the reaeration rate, and the relation-
ship can be approximated by;
(k ) = (k ) 1.024(T"20)	(IVr-13)
a T	a 20
where (k ) is the reaeration coefficient at T C.
a T
In addition to temperature, substantial suspended sediment concen-
trations can appreciably alter the reaeration rate in streams (Alonso,
et al, 1975). As an approximation, k decreases by 9% per 1,000 ppm
a
increase in suspended sediment up to a 4,000 ppm load. Beyond that,
concentration data are not available to assess the response of k,. It
a
is suggested that a 40% decrease be used for higher suspended sediment
loads. Rivers with high suspended sediment loads are generally found
in the western central states. Measured values of k for various streams
a
and rivers are included in Appendix C.
4.3.4 Effect of Dams on Reaeration
Many rivers or streams have small to moderate sized dams crossing
them in one or more places. Reaeration occurs as the water flows over
the dam. Based on experimental data (Gameson, et al., 1958), and later
verified with field data (Barrett, et al., 1960), the following relation-
ship for reaeration over dams has been developed:
165

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40
V=2.0
V=I.O
V-Stream Velocity (ft/sec)
V=0.5
o
o
O
CO
6
V=0.l
o
4.0
DEPTH (FT.)
Figure IV-7 Reaeration Coefficient for Shallow Streams,
Owen's Formulation
166

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n n = 1	]	_l n	(IV-14)
a - b [ T + 0.11 ab(l + 0.046T)H J Da
where
Dg = dissolved oxygen deficit above dam, mg/1
= dissolved oxygen deficit below dam, mg/1
T = temperature, C
H = height through which the water falls, ft
a =1.25 in clear to slightly polluted water: 1.00 in
polluted water
b = 1.00 for weir with free fall: 1.3 for step weirs or cascades
An alternate equation developed from data on the Mohawk River
and Barge Canal in New York State (Mastropietro, 1968) is as follows:
Dg - Db = 0.037H Da	(IV-15)
Equation IV-15 is valid for dams up to fifteen feet high and for
temperatures in the range of 20 to 25C. It is recommended that this
equation be used within its stated range of applicability.
In handling the problem of a dam, a new reach can be started
just below the dam. D can be calculated as the value that occurs at
a
the end of the old reach. The new deficit D^, which will become the
deficit at the beginning of the next reach, is calculated from one
of the above two formulas.
4.3.5 Dissolved Oxygen Saturation
The rate at which atmospheric reaeration occurs depends not
only on k , but also on the difference between the saturation concen-
d
tration C$ and the actual concentration C. The saturation value of
dissolved oxygen is a function of temperature, salinity, and barometric
167

-------
pressure. The effect of salinity becomes important in estuarine
systems, and to a lesser degree in rivers where high irrigation return
flow can lead to substantial salinity values. Table IV-9 depicts the
relationship between oxygen saturation and chlorinity. The expression
relating salinity and chlorinity concentration is:
Salinity (/Q0) ~ 0-03 + 0.001805 chlorinity (mg/1)
where /oo represents parts per thousand.
The temperature dependence (at zero salinity) can be expressed as:
Cs = 14.65 - 0.41022T + 0.00791T2 - 0.0007774T3 (IV-16)
where T is in C. This relationship is also expressed in Table IV-8
for zero chloride concentration.
Barometric pressure affects C$ as follows:
(IV -1 7)
760-P.
b
where
Cs = saturation value at sea level, at the temperature
of the water, mg/1
Cs' = corrected value at the altitude of the river, mg/1
P^ = barometric pressure at altitude, mm Hg
saturation vapor pi
temDerature, mm Hg
Pv = saturation vapor pressure of water at the river
As an approximation of the influence of altitude. Cs decreases about
7% per 2,000 feet elevation increase.
168

-------
i
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
TABLE IV-9
SOLUBILITY OF OXYGEN IN WATER (STANDARD METHODS, 1971)
Chloride Concentration
in Water - mg/1
Difference





per 100 mg
0
5,000
10,000
15,000
20,000
Chloride
Dissolved Oxygen - mg/1
14.6
13.8
13.0
12.1
11.3
0.017
14.2
13.4
12.6
11 .8
11 .0
0.016
13.8
13.1
12.3
11.5
10.8
0.015
13.5
12.7
12.0
11.2
10.5
0.015
13.1
12.4
11.7
11.0
10.3
0.014
12.8
12.1
11.4
10.7
10.0
0.014
12.5
11 .8
11.1
10.5
9.8
0.014
12.2
11.5
10.9
10.2
9.6
0.013
11.9
11.2
10.6
10.0
9.4
0.013
11.6
11 .0
10.4
9.8
9.2
0.012
11.3
10.7
10.1
9.6
9.0
0.012
11.1
10.5
9.9
9.4
8.8
0.011
10.8
10.3
9.7
9.2
8.6
0.011
10.6
10.1
9.5
9.0
8.5
0.011
10.4
9.9
9.3
8.8
8.3
0.010
10.2
9.7
9.1
8.6
8.1
0.010
10.0
9.5
9.0
8.5
8.0
0.010
9.7
9.3
8.8
8.3
7.8
0.010
9.5
9.1
8.6
8.2
7.7
0.009
9.4
8.9
8.5
8.0
7.6
0.009
9.2
8.7
8.3
7.9
7.4
0.009
9.0
8.6
8.1
7.7
7.3
0.009
8.8
8.4
8.0
7.6
7.1
0.008
8.7
8.3
7.9
7.4
7.0
0.008
8.5
8.1
7.7
7.3
6.9
0.008
8.4
8.0
7.6
7.2
6.7
0.008
8.2
7.8
7.4
7.0
6.6
0.008
8.1
7.7
7.3
6.9
6.5
0.008
7.9
7.5
7.1
6.8
6.4
0.008
7.8
7.4
7.0
6.6
6.3
0.008
7.6
7.3
6.9
6.5
6.1
0.008
7.5





7.4





7.3





7.2





169

-------
4.3.6 DO-BOD Interactions
The most widely used dissolved oxygen predictive equation is the
Streeter-Phelps relationship which predicts the dissolved oxygen concen-
tration downstream from a point source of BOD being discharged into the
river. Assuming a constant river cross-sectional area, the dissolved
oxygen deficit (Cs~C) cari be expressed as:
k = reaeration coefficient, 1/day
a
Dq =	initial deficit (at x = 0), mg/1
D =	deficit at x, mg/1
l_Q =	initial BOD (at x = 0), mg/1
=	BOD decay coefficient, 1/day
Lq and Dq are found by proportioning BOD and DO deficit concentrations
just upstream of the waste discharge with the influx from the dis-
charge itself. As presented earlier in the BOD section, Lq is given by:
W = discharge rate of BOD, lb/day
L = concentration of BOD in the river upstream of the
waste discharge, mg/1
Qu = river flow rate upstream of discharge, cfs
Q = flow rate of waste discharge, cfs
w
Qw + Qu = flow rate of river in the reach under consideration, cfs
D = D exp ^
o p U
where
(IV -19)
where
170

-------
W in Equation IV-19 should be expressed in terms of ultimate BOD,
and not 5-
-------
4.3.7 Dissolved Oxygen Calculations
Calculation of dissolved oxygen in rivers can proceed as
shown in Figure IV-8. The planner needs to estimate the waste
loading scheme for the prototype, whether it be a 20 year projection
or the current condition. Based on the waste load distribution, the
river can then be divided into reaches. By repeated use of Equation
IV-18, dissolved oxygen calculations can be performed for one reach
after another, starting from some upstream point and proceeding down-
stream. All data and calculations should be succinctly and clearly
recorded to minimize errors.
Equation IV-18 can be solved graphically, as well as analyti-
cally, as illustrated in Figure IV-9. The abscissa in Figure IV-9 is
proportional to the product of the reaeration coefficient (k ) and
cl
the travel time (t) in days. The following example (Nemerow, 1974)
should serve to illustrate the use of the nomogram.
	 EXAMPLE IV2	
Use of Figure IV-9
Assume that the following information has been calculated:
k = 0.12/day
_JS = l .o
kL
DQ = 0.77 mg/1
L = 12 mg/1
172

-------
Criteria Met for
Determine projected waste loading
scenario (source/sink distribution)
YES
Hand Calculations
Divide river into reaches
Determine temperature independent
Use Computer
Model
parameters for each reach:
Determine reaction rates at 20 C:
for each reach
Incorporate temperature corrections
Determine C for each reach
Begin reach^
Calculate conditions at x=o
(upstream end of present reach)
Perform and record
by-reach
desired calculations
Calculations
Go to next
Another
YES
reach
reach
Figure IV-8 Flow Process of Solution to Dissolved Oxygen
Problem in Rivers
173

-------
2.0
2.0
CkO
D,
o
0.80
= 1.00
L,
0
0.8
0.6
(D>
0.8
0.6
2.00
0.4
4.00
0.2
500

to
Figure IV-9 Nomogram for Solution to the Dissolved Oxygen
Sag (after Thomas, 1948)
Suppose the user wants to obtain the deficit for a travel time
of 2.3 days. Using a straight edge, a straight line can be formed
connecting 0.77/12 = 0.064 (Point on the DQ/ Lq scale) with the
point representing kgt/2.3 = 0.12 (point  at the intersection of
the line 0.12 on the k t scale with the k /k, = 1.0 curve). Next
_	d	a L
0.265 (point (3) ) is read on the D/Lq scale at the intersection of
the straight line. The value of the deficit at the end of 2.3 days
is then:
D	(LQ) = 0.265 (12) =	3.2 mg/1
The use of points and (5) will be explained subsequently.
	 END OF EXAMPLE IV-2		
174

-------
The dissolved oxygen profile downstream from a waste discharge
characteristically has a shape shown in Figure IV-10. If the reach
Waste Inlet
o
c~
o
ci
TC(XC)
TIME (DISTANCE)
Figure IV-10 Characteristic Dissolved Oxygen
Profile Downstream from a Point
Source of Pollution
is long enough, the dissolved oxygen will decrease to some minimum value,
D , at a distance x (termed the critical distance). D is called the
c	c	c
critical deficit. Within any reach there will always be a minimum dis-
solved oxygen value that occurs, but it may not be the critical deficit,
which is defined as the minimum point on a dissolved oxygen sag. The
difference between the minimum and critical values should be kept in
mind. As. one example of the difference between the values, a reach may
have a dissolved oxygen profile where concentrations are monotonically
decreasing throughout the reach. The minimum DO will then occur at the
downstream end of the reach, but this will NOT be the critical DO value,
since DO is still decreasing in the downstream direction.
The travel time to the critical deficit point is given by:
175

-------
The distance downstream can be computed by knowing the travel time and
flow velocity:
~ u *
c	c
-k
The critical deficit can be found from:
Do(ka"kL)\l VkL
c =

kLLo
-k.
Lokl
ka"kL
Ik MW)
kL V kLLo /
k -k.
a L
(IV-23)
(IV-24)
Equations IV-22 and IV-24 are limited to those cases where the Streeter-
Phelps type relationship of Equation IV-18 is valid. Dc can also be
found by solving Equation IV-22 for t and then using the nomogram
(Figure IV-9) by entering the abscissa at the critical travel time. As
a second alternative, use Figure IV-9 exclusively as described in the
next example.
	 EXAMPLE IV-3 	
Determining Critical Deficit from Figure IV-9
From the previous example (Example IV-2) the dissolved oxygen
deficit for a specified travel time was found. Suppose now the
critical deficit and the travel time associated with that deficit
is desired. Using the information in the previous example
^a^L = 'V'o = 0.064), a straight edge is used to draw a line
from point  to a tangent on the ka/k^ = 1 line.
176

-------
The point where this line crosses the D/LQ axis (point  ) is the
maximum deficit that can occur. From the nomogram,
Dc = (0.4) (12) = 4.8 mg/1
On the ka/k^ line, point (4) indicates that
k t/2.3 = 0.4
a
t = (0.4)(2.3) = 7.7 days
c .12
	 END OF EXAMPLE IV-3 			
Solutions to both Equations IV-24 and IV-22 for a
broad range of values are presented in Tables IV-10 and IV-11,
respectively. Observe that there exist practical limitations to the
solutions of both equations, governed by the conditions that the
solutions be both positive and real. If in solving Equation IV-22 t
is negative, the minimum dissolved oxygen concentration actually
occurs at x = 0, and DO conditions will improve proceeding downstream.
Tables IV-10 and IV-11 are particularly useful for computing the
waste assimilative capacity of a river under a given set of conditions.
Waste assimilative capacity (WAC), as defined here, is the amount of
BOD that can be discharged into a river without causing the minimum
dissolved oxygen to go below a desired value. The process of computing
this is explained in Example IV-4. In constructing Tables IV-10 and
IV-11 more detail was incorporated for DQ/L0 between 0.0 and 0.5.
This is because most practical, problems fall into this range.
It should be noted that the methods for DO computation first presented
differ mainly in degree of resolution and convenience. Selection by
the user should be made accordingly.
177

-------
TABLE IV-10
D /L VALUES VERSUS D /L AND k /k,
r' ft	r\' r\	a'

0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
ka
1.9
'*L
2. J
2.3
2.5
2.7
2.9
3.1
3.3
3.5
3.7
3.9
4.)
4.3
4.5
4.7
4.9
0.00
.77
.60
.50
.44
.39
.35
.32
.30
.28
.26
.24
.23
.22
.21
.20
.19
.18
.17
.17
.16
.15
.15
. 14
.14
. 14
0.02
.79
.61
.51
.44
.40
.36
.33
.30
.28
.26
.25
.23
.22
.21
.20
.19
.18
.18
.17
.16
.16
.15
.15
.14
.14
0.04
.81
.62
.52
.45
.40
.36
.33
.31
.29
.27
.25
.24
.23
.22
.21
.20
.19
1.8
.17
.17
.16
.16
.15
.15
.14
0.06
.82
.63
.53
.46
.41
.37
.34
.31
.29
.27
.26
.24
.23
.22
.21
.20
.19
. 18
.18
.17
.17
. 16
.15
.15
.15
0.08
.84
.65
.54
.47
.42
.38
.35
.32
.30
.28
.26
.25
.24
.23
.21
.21
.20
.19
.18
.18
.17
.16
.16
.15
.15
0.10
.85
.66
.55
.48
.43
.39
.36
.33
.31
.29
.27
.26
.24
.23
.22
.21
.20 '
.19
.19
.18
.17
.17
.16
.16
.15
0.12
.87
.67
.56
.49
.44
.40
.36
.34
.31
.29
.28
.26
.25
.24
.23
.22
.21
.20
.19
.19
MO
.17
.17
.16
.16
0.M
.88
.68
.57
.50
.45
.40
.37
.34
. 32
.30
.28
.27
.25
.24
.23
.22
.21
.21
.20
.19
.19
.18
.18
.17
.17
0.16
.90
.69
.58
.51
.45
.41
.38
.35
.33
.31
.29
.27
.26
.25
.24
.23
.22
.21
.21
.20
.19
.19
.18
.18
.17
0.18
.91
.71
.59
.52
.46
.42
.39
.36
.33
.31
.30
.28
.27
.^6
.25
.24
.23
.22
.21
.21
.20
.20
. 19
.19
.19
0.20
.93
.72
.60
.53
.47
.43
.39
.37
.34
.32
.30
.29
.28
.26
.25
.24
.24
.23
.22
.22
.21
.21
.20
.20
.20
0.22
.95
.73
.62
.54
.48
.44
.40
.37
. 35
.33
.31
.30
.28
.27
.26
.25
.25
.24
.23
.23
.22
.22



0.24
.96
.75
.63
.55
.49
.45
.41
.38
.36
.34
.32
.31
.29
.26
.27
.26
.26
.25
.25
.24
.24




0.26
.98
.76
.64
.56
.50
.46
.42
.39
.37
.35
.33
.31
.30
.29
.28
.27
.27
.26
.26 .






0.28
.99
.77
.65
.57
.51
.47
.43
.40
.38
.36
.34
.32
.31
. 30
.29
.29
.28
.28







0.30
1.01
.78
.66
.58
.52
.48
.44
.41
. 39
.37
.35
.34
.32
.31
.31
.30
.30








0.32
1.03
.80
.67
.59
.53
.49
.45
.42
.40
.38
.36
.35
.34
.33
.32
.32









0.34
1.04
.81
.68
.60
.54
.50
.46
.43
.41
.39
.37
.36
.35
.34
.34










0.36
1.06
.82
.70
.61
.55
.51
.47
.44
.42
.40
.38
.37
.36
.36











0.38
1.07
.84
.71
.62
.56
.52
.48
.45
.43
.41
.40
.39
.38












0.40
1 .09
.85
. 72
.63
.57
.53
.49
.46
.44
.42
.41
.40













0.42
1.1)
.86
.73
.65
.58
.54
.50
.47
.45
.44
.43
.42













0.44
1.12
.88
.74
.66
.60
.55
.51
.49
.47
.45
.44














0.46
1.14
.89
.76
.67
.61
.56
.53
.50
.48
.47
.46














0.48
1.15
.90
.77
.68
.62
.57
.54
.51
.49
.48















0.50
1.17
.92
.78
.69
.63
.59
.55
.53
.51
.50















0.6
1.25
.99
.84
.7
.69
.65
.62
.60

















0.7
1.33
1.06
.91
.82
.76
.72
.70


















0.8
1.41
1.13
.98
.89
.84
.81



















0.9
1.50
1.20
1.05
.97
.92
.90



















1.0
1.58
1.27
1.12
1.04
1.00




















1.1
1.66
1.35
1.20
1.13
1.10




















1.2
1.75
1.43
1.28
1.21





















1.3
1.83
1.50
1.36
1.30





















1.4
1.92
1 .58
1.44
1.40





















1.5
2.00
1.66
1.53






















1.6
2.09
1.75
1.62






















1.7
2.17
1.83
1.71






















1.8
2.26
1.91
1.80






















1.9
2.34
2.00
1.90






















2.0
2.43
2.08























2.1
2.52
2.17























2.2
2.60
2.26























ka/kL
5.1 5.3 5.5 5.7 5.9 6.1
6.3 6.5 6.7 6.9 7.1 7.3 7.5 7.7
8.3 8.5 8.7 8.9 9.1 9.3 9.5 9.7 9.9
0.00
.13
.13
.12
.12
.12
.11
.11
.11
.11
.10
.10
.10
.10
.10
.09
.09
.09
.09
.09
.09
.08
.08
.08
.08
.08
0.02
.13
.13
.13
.12
.12
.12
.11
.11
.11
.11
.10
.10
.10
.10
.10
.09
.09
.09
.09
.09
.09
.08
.08
.08
.08
0.04
.14
.13
.13
.13
.12
.12
.12
.11
.11
.11
.11
.10
.10
.10
.10
.10
.09
.09
.09
.09
.09
.09
.08
.08
.08
0.06
. 14
.14
.13
.13
.13
.12
.12
.12
.12
.11
.11
.11
.11
.10
.10
.10
.10
.10
.09
.09
.09
.09
.09
.09
.09
0.08
.15
. 14
. U
.13
.13
.13
.12
.1?
.12
.12
.11
.11
.11
.11
.11
.10
.10
. 10
.10
. 10
.10
.09
.09
.09
.09
0.10
.15
.15
.14
.14
.14
.13
.13
.13
.12
.12
.12
.12
.11
. 11
.11
.11
.11
.11
.11
. 10
.10
.10
.10
.10
.10
0.12
.16
.15
.15
.14
. 14
.14
.14
.13
.13
.13
.13
.12
.12
.12
.12
.12
.12








0.14
.16
.16
.16
.15
.IS
. 1 :
.14
.14
.14
.14
.14














0.16
.17
.17
. 17
.16
. lo
.16



















0.18
.18
.18
. 18






















178

-------
TABLE IV-11
kflt VERSUS Dq/Lo AND ka/kL
0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9
0.00
.26
.52
.69
.83
.95
1.05
1.14
1.22
1 .29
1.36
1.42
1 .47 1
53
1.58
1 .S3
1.67
1.71
1.75
1.79
1 .83
1.87
1.90
1.93
1.97
2.00
0.02
.25
.51
.68
.82
.93
1.03
1.11
1.19
1.25
1.32
1.37
1 .43 1
48
1.52
1.57
1.61
1 .65
1.68
1 .72
1 .75
1 .78
1.81
1.84
1 .87
1.89
0.04
.25
.50
.67
.80
.91
1.00
1.08
1.16
1.22
1.28
1 .33
1.38 1
42
1.47
1.50
1.54
1 .57
1 .61
1 .64
1 .66
1.69
1.72
1.74
1.76
1.78
0.06
.25
.50
.66
.79
.89
.98
1.06
1.13
1.18
1.24
1 .29
1.33 I
37
1.41
1.44
1.47
1.50
1.53
1.55
1.57
1.59
1.61
1.63
1.65
1.66
0.08
.25
.49
.65
.78
.88
.96
1.03
1.09
1.15
1.20
1.24
1.28 1
31
1.35
1.37
1.40
1.42
1 .44
1.46
1.48
1.49
1.50
1.51
1.52
1.53
0.10
.25
.49
.64
.76
.86
.94
1.00
1.06
1.11
1.16
1.19
1.23 1
26
1.28
1.30
1.32
1.34
1.35
1.36
1.37
1.38
1.38
1.38
1.38
1.38
0.12
.24
.48
.63
.75
.84
.92
.98
1.03
1.08
1.11
1.15
1.17 1
20
1.22
1.23
1.24
1.25
1.25
1.26
1.26
1 .25
1.24
1.23
J .22
1.20
0.M
.24
.48
.63
.74
.82
.89
.95
1.00
1.04
1.07
1.10
1.12 1
13
1.15
1.15
1.16
1.16
1.15
1.14
1.13
1.11
1.09
1.07
1 .04
1.00
0.16
.24

.62
.72
.81
.87
.92
.97
1.00
1.03
1.05
1.06 1
07
1.07
1.07
1.07
1.05
1.04
1 .02
.99
.96
.92
.68
.83
.77
0.18
.24
.47
.61
. 71
.79
.85
.90
.93
.96
.98
1.00
1.00 1
00
1.00
.99
.97
.95
.92
.88
.84
.79
.73
.66
.57
.48
0.20
.24
.46
.60
.70
.77
.33
.87
.90
.92
.94
.94
.94
93
.92
. 9C
.87
.83
.78
.73
.66
.59
.49
.39
.25
.09
0.22
.24

.59
.68
.75
.80
.84
.87
.88
.89
.89
.88
86
.83
. oc
.76
.70
.64
.56
.46
.35
.21
.04


0.24
.23
.45
.58
.67
.73
.78
.81
.83
.84
.84
.83
.81
78
.74
. 7C
.64
.56
.47
.36
.23
.06




0.26
.23

.-57
.66
.72
.76
.79
.80
.80
.79
.77
.74
70
.65
.59
.50
.41
.28
.13






0.28
.23

.56
.64
.70
.74
.76
.76
.76
.74
.71
.67
62
.55
.7
.36
.23
.07







0.30
.23

.55
.63
.68
.71
. 73
. 73
.72
.69
.65
.60
53
.44
.34
.20
.03








0.32
.23

.54
.62
.66
.69
.70
.69
.67
.64
.59
.52
44
.33
.2C
.02









0.34
.23
.42
.54
.61
.65
.67
.67
.66
.63
.58
.52
.44
34
.21
.04










0.36
.22
.42
.53
.59
.63-
.65
.64
.62
.58
.53
.45
.36
23
.07











0.38
.22
.41
.52
.58
.61
.62
.61
.58
.54
.47
.38
.27
12












0.40
.22
.41
.51
.57
.60
.60
.58
.55
.49
.41
.31
.18













0.42
.22
.41
.50
.56
.58
.53
.55
.51
.44
.35
.23
.08













0.44
.22
.40
.49
.54
.56
.55
.52
.47
.39
.29
.15














0.46
.22
.40
.49
.53
.54
.53
.49
.43
.34
.23
.07














0.48
.22
.39
.48
.52
.53
.51
.46
.39
.29
.16















0.50
.21
.39
.47
.51
.51
.48
.43
.35
.24
.09















0.6
.21
.37
.43
.45
.42
.37
.28
.15

















0.7
.20
.35
. 39
.39
.34
.25
.12


















0.8
.20
.33
.36
.33
.26
.13



















0.9
.19
.31
.32
.27
.17
.01



















1.0
1.
.18
.18
.29
.27
.29
.25
.22
.17
.09
.01




















1.2
.17

.22
.11





















1.3
.17
.24
.19
.06





















1.4
.17
.22
.16
.01





















1.5
.16
.21
.13






















1.6
. 'o
.19
.11






















1.7
1.8
.15
.15
.18
.17
.08
.05






















: .9
.15
.15
.03






















2.0
.14
. 14























2.1
.14
.13























2.2
.13










ka/k














5.1
5.3
5.5
5.7
5.9
6.1
6.3
6.5
6.7
6.9
7.1
7.3
7.5
7.7
7.9
8.1
8.3
8.5
8.7
8.9
9.1
9.3
9.5
9.7
9.9
0.00
2.03
2.06
2.08
2.11
2.14
2.16
2.19
2.21
2.24
2.26
2.28
2.30 2
.32
2.35
Z.37
2.39
2.41
2.43
2.44
2.46
2.48
2.50
2.52
2.53
2.55
0.02
1.92
1.94
1.97
1.99
2.01
2.03
2.05
2.07
2.09
2.11
2.13
2.15 2
.16
2.18
1.20
2.21
2.23
2.24
2.26
2.27
2.28
2.30
2.31-
2.32
2.33
0.04
1.80
1.82
1.84
1.86
1.87
1.89
1.90
1.92"
1.93
1.94
1.96
1.97 1
.98
1.39
L. 00
2.01
2.01
2.02
2.03
2.03
2.04
2.05
2.05
2.06
2.06
0.06
1.68
1.69
1.70
1 .71
1.72
1.73
1.73
1. 74
1.74
1.75
1.75
1.75 1
.75
1.75
1.75
1.75
1 .75
1.75
1 .74
1.74
1.73
1 .73
1 .72
1 .71
1.70
0.08
1 .53
J. 54
1.54
1.54
1.54
1.54
1.53
1.53
1.52
1 .51
1.50
1.49 1
.48
1 .46
1.45
1 .43
1 .41
1 .39
1 .36
1.34
1.31
1 .28
1.24
1.21
1.17
0.10
1.37
1.36
1.35
1.34
1.33
1.31
1.29
1.27
1.24
1.22
1.19
1.15 1
.11
1 .07
1.03
.97
.92
.85
.78
.70
.62
.51
.40
.26
.09
0.12
1.18
1.16
1.13
1.10
1.07
1.03
.99
.94
.88
.82
.75
.67
.58
.47
.35
.21
.03








0.14
.97
.92
.87
.81
.74
.67
.58
.48
.36
.21
.04














0.16
.70
.62
.53
.42
.29
.14



















0.18
.36
.22
.05






















179

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4.3.8 General Dissolved Oxygen Deficit Equation
The most general dissolved oxygen mass-balance formulation to be
presented is as follows:
D =
(A) (L- y) [exp ("4 f(x)) exp(^f(x))
N ) (No - y) [ex" (t f(x>) - exP (-^f(x))
ka"kN / V" " kN
+ R + Sd + L, + N j-P
B rd rd
1 - exp
ft f(x))
+ D exp
o H
(- f(xl)
(IV-25)
where
B
oxygen production rate due to photosynthesis, mg/l/day
oxygen utilization rate due to respiration, mg/l/day
benthic demand of oxygen, mg/l/day
The distance function f(x) expresses the cross-sectional area relation-
ship throughout the reach. The area can increase or decrease linearly
or remain constant. The general form of the relationship is:
f(x) Aqx + Aa x /2 , Aa Af Aq
180

-------
where
A
f
area at x = x
L
A = area at x = 0
o
xL = length of reach
For a reach of constant cross-sectional area, = n.
In developing Equation IV-25 the following relationship for
CBOD was used (as originally presented in the BOD section):
1  ( - )"( !?
(IV-6)
An analogous expression for NBOD was also used.
In Equation IV-25, the distributed sources and sinks (P, R, Sg,
L ., N ,) are all mass fluxes, and no volumetric flow rate is
rd rd'
associated with any of these sources and sinks of dissolved oxygen.
4.3.9 Photosynthesis and Respiration
The difficulty of accurately assessing the impact of photosynthesis
and respiration on the dissolved oxygen resources of streams is not
readily apparent from the single terms appearing in Equation IV-25.
Of concern are both free floating and attached algae, as well as aquatic
plants. The extent to which algae impact the dissolved oxygen resources
of a river is dependent on many factors, such as turbidity, which can
decrease light transmittance through the water column. Additionally,
the photosynthetic rate constantly changes in response to variations in
sunlight intensity. Photosynthetic rates are not truly constant as shown
in Equation IV-25. Hence if algal activity is known to be a significant
181

-------
factor affecting the dissolved oxygen balance, the use of a computer
model is recommended in order to accurately assess such influences. For
example, in the Truckee River in California and Nevada,- the diurnal
variation of dissolved oxygen has a range of from 150 percent saturation
during the daylight hours to 50 percent saturation at night due to algal
photosynthesis and respiration, respectively. At the most, hand calcula-
tions can only give estimates of net dissolved oxygen production rates
that then can be compared to the other source/sink terms in Equation IV-10v
From this comparison the significance of each can be estimated.
Table IV-12 presents some observed values of oxygen production by
photosynthesis. As shown, dissolved oxygen production is often given
in terms of rate per unit area. To convert to units of concentration
per unit time, divide by the average depth:
where
o
P = production rate of dissolved oxygen, gm/m /day
H = average river depth, meters
P = production rate of dissolved oxygen, mg/l/day
P can now be directly compared to other terms in Equation IV-10.
182

-------
TABLE IV-12
SOME AVERAGE VALUES OF GROSS PHOTOSYNTHETIC PRODUCTION OF
DISSOLVED OXYGEN (AFTER THOMANN, 1972 AND THOMAS AND O'CONNELL, 1966)
Water Type
Aver.Gross Production
(qrams/m -day)
Average Respiration
(qm/m^-day)
Truckee River - Bottom
attached algae
9
11.4
Tidal Creek - Diatom Bloom
(62-109.105 diatoms/1)
6

Delaware Estuary - summer
3-7

Duwamish River estuary -
Seattle, Washington
0.5-2.0

Neuse River System -
North Carolina
0.3-2.4

River Ivel
3.2-17.6
6.7-15.4
North Carolina Streams
9.8
21.5
Laboratory Streams
3.4-4.0
2.4-2.9
The assimilation number (not the same as assimilative capacity),
is defined as the grams of oxygen produced per hour per gram of
chlorophyll a^. This number may be useful in estimating oxygen
production. Table IV-13 gives observed chlorophyll ^concentrations
and assimilation numbers for various communities. Multiplying the
chlorophyll ^concentration by the assimilation number yields the
oxygen production rate per unit area. A generally low but acceptable
estimate of assimilation number is 1 gm oxygen per hour per gram of
chlorophyll a^.
183

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TABLE IV-13
CHLOROPHYLL a AND ASSIMILATION NUMBER OF
VARIOUS COMMUNITIES (AFTER ODUM, et al ., 1958)
Plankton Communities
Euphotic Zone*
Chlorophyll a_
gm/m ^
Assimilation
Number, gm Oxygen
Per Hour Per gm
Chlorophyll a
(Not including bottom plants)
Long Island Sound
UD
O
1
O
1-3
Diatom bloom, Moriches Bay
one meter
0.20
4.5
Sewage Pond, Kadoka, S.D.
1 .5
2
Shallow Aquatic Communities
with Bottom Plants


Rocky Mountain Stream, Utah
0.3-1.5
0.7-2.0
Blue-green algal mat, polluted
stream, Mission River, Texas,
August, 1957
2.5

*From the surface to the depth where light intensity = 1% of
surface light.
Values of photosynthetic respiration vary widely, ranging from
2	2
0.5 gm/m /day to greater than 10 gm/m /day. One suggested relationship
between respiration and chlorophyll a^ is given as (Thomann, 1972):
R(mg/l/day) = 0.024 (chlorophyll aj (ug/1) (IV-26)
where
1 pg/1 = 10"3 mg/1
Chlorophyll ^concentration is most commonly expressed in terms of
Mg/1 
184

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4.3.10 Benthic Demand
In addition to oxygen utilization by respiration of attached algae,
benthic deposits of organic material and attached bacterial growth
can utilize dissolved oxygen. Table IV-14 illustrates some uptake
rates. As with photosynthesis, the uptake rates are expressed in
2
gm/m /day. To use these values in Equations IV-10 or IV-25, division
by stream depth (in meters) is necessary. Temperature effects can be
approximated by
(SB) = (SB) 1.0651-20	(IV-27)
TABLE IV-14
AVERAGE VALUES OF OXYGEN UPTAKE RATES OF
RIVER BOTTOMS (AFTER THOMANN, 1972)

2
Uptake (gms 02/m -day)

0
20C
Bottom Type and Location
Ranqe
Approximate
Averaqe
Sphaerotilus - (10 gm dry Wt/M^)
-
7
Municipal Sewage Sludge -
Outfall Vicinity
2-10.0
4
Municipal Sewage Sludge -
"Aged" Downstream of Outfall
1-2
1.5
Cellulosic Fiber Sludge
4-10
7
Estuarine mud
1-2
1.5
Sandy bottom
0.2-1.0
0.5
Mineral soils
0.05-0.1
0.07
185

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The areal extent of significant oxygen demanding benthic
materials is often limited to the region just below the outfall
vicinity. Although the oxygen demand may be great over a short
distance, it may be insignificant over larger distances. .The
response of rivers to areally limited benthic deposits is generally
to move the critical deficit upstream, but not to lower its value
signi ficantly.
4-3.11. Simplifying Procedures in Dissolved Oxygen Calculations
The usage of Equation IV-25 may be untenable for	several
reasons, such as lack of available data, or because of	the voluminous
calculations required to apply it to a large number of	reaches.
Numerous suggestions are offered that should lead to a
simplification of the analysis of the dissolved oxygen	problem.
Since the general scope of this section is to facilitate the
determination of existing or potential problem areas, the analysis
should proceed from a simple approach to the more complicated.
It may be adequate to analyze the dissolved oxygen response to only
the most severe loadings, neglecting those of secondary importance.
If such an analysis clearly indicates dissolved oxygen problems,
then the inclusion of any other pollutant discharges would only
reinforce that conclusion. More rigorous procedures (e.g., a
computer model) could then be employed to perform a detailed
analysis.
Suppose the improvement of river dissolved oxygen over a reach
due to decreased loading from a point source is of interest. This
situation is common, as in the design of waste loading abatement
schemes. Such improvement can be estimated by:
186

-------
AD = AD[) exp [--] ~	(AL0)[exP ( f<*>)
- exp(-jp f(x)
V o
where
ALq = the change in the initial BOD, mg/1
AD = change in deficit in response to ALq
Equation IV-28 was formulated from Equation IV-25 assuming that Lq
and Dq are the only changes of significance.
Many rivers have a large number of point sources. Although this
is not necessarily a complicating factor, a detailed analysis might be
too time consuming for hand calculations. There are several possible
alternatives to deal with this situation in order to reduce the number
of reaches to be analyzed. The first, already mentioned, is to
consider only the significant pollutant sources. Second, as was illus-
trated in Example IV-1, a number of uniformly distributed point sources
can be considered as a single distributed source. Third, combining
several adjacent point sources is also possible, if the length of the
reach under consideration is long relative to the distance of separation
between the point sources. Analogously, a distributed source can be
approximated as a point source, contributing the same waste loading and
located at the center of the distributed source.
It may be that the planner wants only to determine the critical
dissolved oxygen concentration in each of a series of reaches. In this
case no more than two values of dissolved oxygen per reach need be
calculated. Figure IV-11 shows the solution process to be followed.
)
187

-------
Q BEGIN ))
Determine k and k
d
for each reach
Begin reach
calculations
Another
reach
^ Go to next
/ reach
Find t
Find D at
Find D
at x '
YES
and
YES
Figure IV-11 Flow Process in Reach by Reach Solution to
Critical Dissolved Oxygen Values
188

-------
One final note on dissolved oxygen evaluations should be made here.
It may be that if the planner is interested only in locating DO problems,
he need not perform any computations. This is especially likely where
dissolved oxygen data are available at various locations on the river.
Plotting dissolved oxygen time trends may reveal when, as well as where,
annual dissolved oxygen minima occur.
Suppose the user wants to determine waste assimilative capacity
(WAC) for a river reach that has the following characteristics:
First, ka and need to be found. From Figure IV-6, kfl (20) =
0.8/day, and from Figure IV-2, kL = 0.4/day. At any other tempera-
ture then, kfl and k^ can be found from the temperature relationships
previously developed:
EXAMPLE IV-4
Determining River Assimilative Capacity from
Tables IV-10 and IV-11
critical dissolved oxygen concentration = 5.0 mg/1
(user establishes this)
initial deficit = 1.0 mg/1
average velocity =0.5 fps
average depth = 4 feet
chloride concentration = 0
temperature range 10C to 35C
k
a
(k ) 1.0241"20
a 20
(IV-13)
k
L
(k, ) 1.0471"20
L 20
(IV-1)
189

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Using Table IV-8 the dissolved oxygen saturation concentration within
the temperature range of interest can be found. This information
can be then compiled into a table an example of which is shown below
(Table IV-15).
TABLE IV-15
COMPILATION OF INFORMATION IN EXAMPLE IV-4
1 o
o
C
s
(mg/1)
cc
(mg/1)
Dc
(mg/1)
D /D
o c
ka/kL
10
11.3
5.0
6.3
0.16
2.5
15
10.2
5.0
5.2
0.19
2.2
20
9.2
5.0
4.2
0.24
2.0
25
8.4
5.0
3.4
0.29
1 .8
30
7.6
5.0
2.6
0.38
1 .6
35
7.1
5.0
2.1
0.48
1 .4
Using the values of D /D and k /k., L can be found, which in this case
0 C	a L 0
is the WAC.
Procedure
1.	Table IV-15 is entered at the appropriate k /k. column.
a L
This is 2.5 at 10C.
2.	Next, the entry within the kQ/k^ column in Table IV-10
is found such that
190

-------
Since the left-most column of Table IV-10 is D0/L0 and the entries
are D /L , the ratio of these values is taken until that ratio equals
c o
0 16.
For example, try DQ/Lo = 0.05. Then DC/LQ = 0.23 and
q'23 ~ 0-22 >0.16, too big
try Do/Lq = 0.04. Then Dc/Lq = 0.23 and
0-04 17 ,
q 23 = '' close enough
Dr	ft
then = .23, or Lq =	= 27.4 mg/1
The results are tabulated below for the temperature range 10C to 35C.
T(C)
WAC (mg/1)
D /L
0 0
10
27.4
0.04
15
20.0
0.05
20
15.0
0.07
25 '
11.3
0.09
30
7.6
0.13
35
5.4
0.19
lQ is directly related to the loading rate of BOD, as expressed
earlier in Equation IV-19:
WAC = (L )	= L"Q" +Wcritica1
^ o' ... -i Q +0
critical Mu vw
191

-------
From equation IV-19 the critical waste loading W can be found. If
desired, this procedure can be repeated for different river flow rates,
and WAC an-d W	found for the various flows. To do this, diff-
cnti cs 1
erent average depths and velocities will be needed. Generally this
analysis is most useful carried out under minimum flow conditions, as
this is the most critical situation, but higher flows may be of interest
to assess the benefits of flow augmentation decisions. Novotny and
Krenkel (1975) have used a 20 year, 3-day low flow in analyzing the
Holston River in Tennessee. For further discussion of low flow cal-
culations refer to Section 4.4.6.
In interpreting the results of this example the user should be
looking more at trends rather than particular results. For example,
notice how the WAC decreases with increasing temperature. For every
10 increase the WAC is approximately halved. A similar relationship
between WAC and flow rate could also be determined.
Finally, using Table IV-11, the travel time t can be determined
to the point of critical deficit. The appropriate D /L and k /k,
0 0	8 L
values are used to find t . Table IV-16 illustrates these results.
TABLE IV-16
CRITICAL TRAVEL TIME RESULTS, EXAMPLE IV-4
T(C)
	1
ra
D /L
0 0
t k
c a
ka
tc(days)
10
2.5
0.04
1.4
.63
2.2
15
2.2
.05
1.3
.71
1 .8
20
2.0
.07
1.2
.8
1.5
25
1 .8
.09
1.13
.9
1.2
30
1 .6
.13
1 .0
1.0
1.0
35
1 .4
.19
0.9
1.1
0.8
END OF EXAMPLE IV-4
192

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EXAMPLE IV-5-
Critical Deficit Calculations for Multiple
Reaches (Illustrating Use of Figure IV-11)
Suppose the critical deficit in each of the three reaches of the
river illustrated in Figure IV-12 is to be determined. The conditions
upstream of the first discharge are:
T - 27 C
Q - 600 cfs
U = 0.4 fps
depth = 5.0 feet
Du = 1 mg/1
Lu - 2 mg/1
Using these data, along with the solution process outlined in
Figure IV-11, the following procedure can be used:
1. Determine k
for each reach. For this example it will
be assumed that the average depth, velocity, and temperature remain
relatively constant over the three reaches, so that k, and k. are
a	L
also the same.
1
1
1
0
! 0
i
()
1
Du=lmg/I |

I
i
1

>
Qu= 600cfs

12 Ml.
B.O.D.L=40mg/l
Q=50MGD

4 Ml.

B.0.D.|_=50mg/l B.0.D|=20mg/l
Q = 60MGD Q = IOMGD
Figure IV-12 Hypothetical River Used in Example IV-5
193

-------
k (20) = 0.5, (from Figure IV-6)
a
k. (20) = 0.35, (from Figure IV-2)
Using the temperature correction:
k (27) = 0.60, (from Equation IV-13)
d
kL (27) = 0.48, (from Equation IV-1)
The saturation dissolved oxygen concentration at 27C and 0%o salinity
is (from Table IV-9) 8.1 mg/1.
2. For the first reach, calculate L and D .
0 0
L = (2)(600)+(40) (50) (1.55) _
0	600 +(50)(1.55)	- 6.35 mg/1
For lack of better information about the dissolved oxygen
characteristics of the waste, it can be assumed that DQ = Du = 1 mg/1.
The location of where the critical deficit occurs can now be calculated
using Table IV-11, or Equation IV-23. In this example Table IV-11 will
be used. To use that table, the following ratios are needed:
Do/Lo = 1/6-35 = -16
and
k Jk. = 0.60/0.48 = 1.3
a L
- From Table IV-11, then, k t = .92 or
a C
t = .92/0.6 = 1.53
xc .	('-53yo3600) (24) - 10.0 miles
194

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Since xc < 12, the critical deficit actually exists, and is located 10
miles downstream. From Table IV-10 Dc can be found by entering it with
the same ratios used in Table IV-11. The result is:
D
p- = .38 - Dc = JL4 mg/1
o
3. Before the critical conditions in reach 2 can be calculated,
the conditions at the upstream end of that reach must be established.
The conditions at the downstream end of reach 1 are
D = 2.3 mg/1, from Equation IV-18
L = 2.6 mg/1 from Equation IV-5
The conditions at the upstream end of reach 2 are thus:
JMli677jji60i_lK55) = g	,
o	677 +93	a/
Dq = 2.3 can be used for lack of better information on the dissolved
oxygen concentration in the effluent to reach 2. For use in
Table IV-10, it is found that
VLo = *28
So
k t = .76
a
t - .76/0.6 - 1.3
c
xc = 8.3 mi 1es
195

-------
Since reach 2 is only 4.0 miles long, the critical deficit is not
reached. Instead the maximum deficit will occur at the downstream
end of reach 2, where:
D - 3.3 mq/1, Equation IV-18
L = 6.22 mq/1, Equation IV-5
4. For the beginning of reach 3, L and D must be found.
o o
(20) (10 ) (1 -55) +(770.5 ) (6.22)
o = 	770.5 +(10 )11.55)	9
For Dq, it can be assumed that Cw = 5.0 mg/1. From Equation IV-20,
then
n - n i (8.1 - 3.3) (770. 5 )+ (5.0 ) ( 1 0) (1. 55)_ - .
Do 8-1 "	770.5 + 15.5	J 9/
The calculations of critical conditions can now be made for
this reach, as done in the previous two.
	 END OF EXAMPLE IV-5 	
4.4 TEMPERATURE
4.4.1 Introduction
The biota comprising an established aquatic ecosystem generally
respond negatively to significant abnormal temperature fluctuations.
Man-induced modifications of rivers and streams can alter the thermal
regime, most often by elevating the maximum and mean water temperatures.
Repercussions of elevated temperatures are manifested through a shift
196

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in the ecological balance and the water quality of rivers. For
example, there is a progression in the predominance of algal species
from diatoms to green algae to blue-green algae as water temperature
increases through a specific range. Thermal discharges can increase
the ambient temperature enough to alter the predominant species to
the undesirable blue-green algae. Increased metabolic activity of
aquatic organisms, such as fish, also accompanies elevated tempera-
ture. If the increase is high enough, the results can be lethal. Much
data are available today (e.g., Committee on Water Quality Criteria,
1972) delimiting lethal threshold temperatures for aquatic organisms.
Water quality may be adversely affected through decreased
solubility of dissolved oxygen and increased biochemical reaction
rates. Adequate dissolved oxygen levels, particularly at elevated
temperatures, are critical because of the increased metabolic acti-
vity. Yet, as previously discussed (see Table IV-9) the saturation
concentration of dissolved oxygen diminishes with rising temperature.
Worse still, is the concurrent low flow condition which is associated,
in many parts of the country, with the warm summer months. For
example, in a recent study (EPA, 1974) of 30 river reaches in the U.S.,
20 had lower flows in the summer months than in the winter. This
situation further reduces assimilative capacity and usually results
in the most critical dissolved oxygen levels over the year.
Man can alter the thermal regime of rivers by removing trees
(shading), changing the flow regime,and by increasing thermal dis-
charges. Diversions of water from a river can reduce the water depth,
and increase the mean and diurnal fluctuation of stream temperature.
In Long Island (Pluhowski, 1968), modification of the natural
environment of streams has increased average stream temperatures
during the summertime by as much as 9 to 14F. Concurrent temperature
differences of as much as 14 to 18F between sites on the same stream
197

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were observed on days of high solar radiation. A principal factor
involved in these occurrences was the removal of vegetation along the
banks of 'the streams, permitting significantly greater penetration of
solar radiation. Other contributing factors cited by Pluhowski
included increased stormwater runoff, a reduction in the amount of
groundwater inflow, and the introduction of ponds and lakes.
4.4.2 Ambient Temperature Increase Due to Thermal Discharge
Figure IV-13 shows an idealization of a run-of-the-river power
plant that pumps river water through an intake channel to a condenser,
and then discharges the heated effluent directly back into the river.
Assuming that the heated effluent has completely mixed with the river
water at section A-A, the new ambient river temperature T^, at that
point, can be estimated by:
Tf - T. + ^o AT
1 Qr	(IV-29)
where the terms in Equation IV-29 are defined in Figure IV-13.
Intake Channel
	
*
-Ti >*.r Tn=Ti + AT
Plant ^0" ' i
w
Or

t
.Outlet
Channel
R
^Li.
Skimmer Wall
River
lA
PLAN VIEW
Figure IV-13 Idealization of a Run-of-the-River
Power Plant
198

-------
In many cases the heated effluent may only spread a fraction of
the distance across the river. In this case the ambient temperature
at A-A is (within that portion of the river affected by the thermal
discharge):
Q (T.+AT-^T.)+^Q T.
j _ wo x i	w v w xr i
f	q (i_ ) + X. Q
xo w w r
where y/w is the fractional distance across the river over which the
thermal plume spreads. Both Equations IV-29 and IV-30 will tend to
underestimate the maximum temperature rise because in actuality, the
warmer effluent may not mix completely in the vertical direction, but may
tend to ride atop the cooler river water.
	 EXAMPLE IV-6 			
Estimating AT Across a Power Plant Heat Exchange Unit
Suppose the user wants to determine AT to use in Equation
IV-29 for the Hartford Electric Light Company's South Meadow Steam
Electric Power Plant (a fossil fuel plant) located on the Connecticut
River. Data available are (Jones, et al., 1975):
capacity	217 MW
cooling water	341 ft /sec
waste heat discharged to cooling water . . .422 MW
Since the waste heat being dissipated through the cooling water is
known, AT can be calculated directly using that value in conjunction
with the known Qq. Assume, however, that the waste heat
199

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being discharged is not known. It can be estimated from the plant
capacity as follows. First, assume the plant efficiency is 33%. The
rate at which fuel is burned when at capacity then, isf'
* 658 MW
If 10% of the total energy is lost up the stacks, then approximately 58%
is dissipated through the cooling water, or
658 (.58) = 382 MW
Compared with the known 422 MW of heat discharged to the cooling water,
the above calculation would underestimate AT.
AT is calculated by
thermal loading rate to coolinq water in megawatts
Al "	yC Q	a
r p
(3-4,4o6 ssfrXMM
where yCp= 62.4 BTU/ft3/F
Qo = flow rate, ft3/sec
Substituting the appropriate values into the above equation, it is found
that (using the known thermal loading to the cooling water):
.T (422) (3.414) (106)/3600 _ or
AT - 	 (62.4) (341)	 18-8 F
	 END OF EXAMPLE IV-6 	
200

-------
4.4.3 Equilibrium Temperature
If a body of water at a given initial temperature is exposed
to a set of constant meteorological conditions, it will tend to
approach some other temperature asymptotically. It may warm
by gaining heat or cool by losing heat. Theoretically, after an
infinite period of time the temperature will become constant and
the net heat transfer will be zero. This final temperature has been
called the equilibrium temperature, E. At equilibrium, the heat
gained by absorbing solar radiation and long-wave radiation from the
atmosphere will exactly balance the heat lost by back radiation,
evaporation, and conduction.
These heat fluxes are illustrated in Figure IV-14, which also
shows typical ranges for the fluxes. Some of these terms (H ,H ,H ,
\ S' a' sr
H ) are independent of water temperature, while the remainder
a r
(Hbr,Hc,He) are dependent upon water temperature. At equilibrium then,
Hn (net transfer) equals zero, or
Hs - Hsr + Ha - Har " Hbr " Hc " He = 0	
In actuality, the water temperature rarely equals the equilibrium
temperature because the equilibrium temperature itself is constantly
changing with the local meteorological conditions. The equili-
brium temperature will rise during the day when solar radiation is
greatest, and fall to a minimum at night when solar radiation is absent.
A daily average equilibrium temperature may be computed using a
number of factors including daily average values of radiation, temp-
erature, wind speed, and vapor pressure. The daily average will
reach a maximum in midsurrmer and a minimum in. midwinter. Other time
periods, such as one month, may also be used for averaging. Since the
actual water temperature always tends to approach, but does not reach
the equilibrium temperature, it will usually be less than equilibrium
201

-------
Hs = Shortwave solar radiation (400-2800 BTU ft"2 day"1)
H = Long wave atmospheric radiation (2400-3200 BTU ft"2 day"1)
Hfar= Long wave back radiation (2400-3600 BTU ft"2 day-1)
^Hg = Evaporative heat loss (2000-8000 BTU ft-2 day"1 )
H = Conductive heat loss or gain (-320-+400 BTU ft-2 day"1)
-1
A
sr
= Reflected solar (40-200 BTU ft-2 day"1)
A^ar = atmospheric reflection (70-120 BTU ft-2 day"1)
-1
NET RATE AT WHICH HEAT CROSSES WATER SURFACE
(n = [<"s +
Ha " Hsr
Har) " (Hbr  Hc + H2)
Independent of Water Temperature
BTU ft"2 day"1
Absorbed Radiation (Hd)	Temperature Dependent Terms
Hbr~ (Ts + 460)
H
(T.
V
He ~ W(es " ea
Figure IV-14
Mechanisms of heat transfer across a
Water Surface (Parker and Krenkel, 1969)
in the spring when temperatures are rising, and greater than equilibrium
in the fall when temperatures are dropping. During a one day
period, the equilibrium temperature usually varies from above the
actual water temperature during the day to below the actual water
temperature at night, forcing the water temperature to assume a
diurnal cycle.
202

-------
The amplitude of the actual diurnal water temperature cycle is
generally dampened significantly in comparison to the amplitude of
the equilibrium temperature cycle due to the large heat capacity of
water. A thermal discharge into a water body will usually increase
the actual daily amplitude because of the water temperature dependent
terms in Equation IV-31, as well as elevate the maximum diurnal
temperature. This situation is illustrated in the following example
(Edinger, et al., 1968). Figure IV-15 illustrates a flow through
cooling pond into which a thermal effluent is discharged (at
Station B).
Sta. H
Sta. G.
430
ACRES
Sta. E
POWER
PLANT
Sta. B.
Sta. D.
Sta. C
Figure IV-15 Schematic of Site No. 3
Cooling Lake (from Edinger.
et al,, 1968)
Temperature observations were recorded at Stations B through H at four-
hour periods for one week. The findings are depicted in Figure IV-16.
203

-------
120
U_
o
110-
0> 100--.
LU
Q_
LU
- 90
7/20
7/18
DAY (4 HOUR PERIODS)
7/19
7/21
7/22
7/24
7/23
Figure IV-16 Observed Temperatures, Site No, 3,
July 18 - July 24, 1965 (Edinger,
et al,, 1968)
Not only are the highest temperatures recorded at Station B, but so
are the largest diurnal variations (decreasina from an
amplitude of 12.5 at Station B to approximately 2F at Station H).
The peak temperature at Station B is just after noon, corresponding
to the peak loading from the plant. At Station C the peak loading
is at 1800 hours, indicating the lag in flow time from Station B to
C. The peak temperatures at the remaining stations are more
influenced by meteorological conditions, and less by the thermal
discharge. The relationship of the observed temperatures to the
equilibrium temperature over a 24-hour period is shown in Figure IV-17.
Note the amplitude of the equilibrium temperature E (33F amplitude).
The average equilibrium temperature, F, is approximately 91F.
A progression from Station B to Station H indicates that the daily
water temperature tends to approach the average equilibrium temperature.
204

-------
Sta.B -~45
110
Sta. C
40
Sta. E
100
Sta. G
Li_
Sta. H
LlI
Tn (Ambient Temp.)
uj 90--
--30 H
E (Equilibrium)
UJ
a. 80--
0
24
4
8
12
16
20
TIME OF DAY (HRS.)
Figure IV-17 Comparison of Computed Equilibrium and
Ambient Temperatures with Observed Mean
Diurnal Temperature Variations for Site
No. 3, July 18-July 24, 1366 (Edinger,
et al., 1963)
Stations G and H, and the ambient temperature T^, all reflect the
predominating influence of meteorological conditions. When the water
temperature is above the instantaneous equilibrium temperature E, it
tends to decrease downward, and when the temperature is below E, it
tends to increase. In the early morning and late evening hours, when
E is low, the water temperature decreases at these stations. During
midday when E is higher, however, the temperatures at these stations
increase.
4.4.4 Calculation of Equilibrium Temperature
Studies (Edinger and Geyer, 1965) have shown that the equilibrium
temperature of a well mixed body of water can be estimated by:
205

-------
E = -
0.05E
K
1801
K - 15.7
K (,26+B)
[ea - C(B) + 0.26T
a (IV-32)
where
E = equilibrium temperature, F
K = thermal exchange coefficient, BTU/ ft^/day/F
Hd = net incoming short (H ) and long (H ) wave radiation
k	s n 2	on
(see Figure IV-14), BTU/ ft /day
T = air temperature, F
d
eo = water vapor pressure of ambient air at air temperature,
a
mmHg
B = proportionality coefficient, mmHg/F
C(B) = value dependent on B, mmHg
The thermal exchange coefficient K is expressed as:
K = 15.7 + (0.26+B) f(u)	(IV-33)
where f(u) is a function of wind speed. Different relationships for
f(u) have been developed. For purposes of hand calculations, the '
following relationship will be used:
f(u) = 11.4u
where u is the daily average wind speed in mph.
To calculate E using Equation IV-32, an iterative procedure is
needed, since K, B, and C(B) depend on E. The following steps outline
a solution procedure.
1. Data needed with which to start the procedure include:
T, relative humidity, wind speed, and net shortwave
a
solar radiation. Figure IV-18 illustrates daily average
solar radiation reaching the continental United States
206

-------
CANADA
IVT750 /
\V>v
[ r
MEXICO
CANADA
MEXICO
AUGUST
2
NOTE: To convert Langleys/day to BTU/ft /day, multiply by 3.7.
Figure IV-18 Mean Daily Solar Radiation (langleys) throughout
the U.S. for July and August (U.S. Department
of Commerce, 1968)
207

-------
for the months July and August. It is during these
months that stream temperatures usually reach their
annual maxima. These values do not account for the
albedo of water (the percent of incoming solar radiation
that is reflected), but since this is small, it can be
ignored. Because of the variability caused by
topography, vegetative cover, and other factors, it
is strongly suggested that local sources of information
be used when possible for solar radiation values.
2.	Calculate HD = H + H (BTU/ft2/day). If Figure IV-18
K Sri ail	n
is utilized for Hsn, convert from langleys/day to BTU/ft /day
by multiplying by 3.7. H can be estimated from Table IV-17
an
by knowing the air temperature and the cloud cover fraction
(0.1 to 1.0).
3.	Determine e, from Table IV-18 by entering with T and
a	a
relative humidity.
4.	Choose an initial value for E. The air temperature Tq
can be the first guess.
5.	Enter Table IV-19 for B and C(B) at E (F).
6.	Knowing u, f(u), and B, calculate K from Equation
IV-33.
7.	From Equation IV-32 make the next estimate of E (Epew)
by evaluating the right hand side of that equation
(call this result F(E)).
208

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TABLE IV-17
NET LONG WAVE ATMOSPHERIC RADIATION, H
an
Cloud
Tempera- H
ti/rp
tUre (BTU/Sq.
Cover ( F) Ft/Day)
Tempera-
ture
an
(BTU/Sq.
( F) Ft/Day)
Tempera- H_
turp
^re	(BTU/Sq.
(F)	Ft/Day)
Tempera- Han
ture (BTU/Sq.
Ft/Day)
(F)
Tempera- H
turp
ture	(BTU/Sq.
( F)	Ft/Day)
Tempera-
ture
an
(BTU/Sq.
(UF) Ft/Day)
.1
35
65
1685
2400
40
70
1790
2540
45
75
1900
2688
50
80
2016
2842
55
85
2138
3004
60
90
2266
3173
35
65
1694
2412
40
70
1799
2553
45
75
1910
2701
50
80
2026
2857
55
85
2149
3019
60
90
2277
3190
35
65
1708
2432
40
70
1814
2575
45
75
1926
2724
50
80
2043
2881
55
85
2167
3045
60
90
2296
3216
35
65
1728
2461
40
70
1335
2605
45
75
1949
2756
50
80
2067
2914
55
85
2192
3080
60
90
2323
3254
35
65
1754
2497
40
70
1863
2644
45
75
1978
2797
50
80
2098
2958
55
85
2225
3126
60
90
2358
3303
35
65
1785
2542
40
70
1896
2691
45
75
2013
2847
50
80
2136
3011
55
85
2265
3182
60
90
2400
3362
35
65
1822
2595
40
70
1936
2747
45
75
2055
2907
50
80
2180
3074
55
85
2312
3249
60
90
2450
3432
35
65
1865
2656
40
70
1981
2812
45
75
2103
2975
50
80
2232
3146
55
85
2366
3325
60
90
2508
3513
.9
35
65
1914
2725
40
70
2033
2885
45
75
2158
3053
50
80
2290
3228
55
85
2428
3412
60
90
2573
3604
1.0
35
65
1968
2803
40
70
2091
2967
45
75
2220
3139
50
80
2355
3320
55
85
2497
3509
60
90
2646
3707

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TABLE IV-18
WATER VAPOR PRESSURE (mmHg) VERSUS AIR TEMPERATURE, T , AND RELATIVE HUMIDITY
a
Ta
e *
s



R E L
A T I V E
H U M I
D I T Y



(F)
(mmHg)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
35
5.2
0.5
1.0
1 .6
2.1
2.6
3.1
3.6
4.2
4.7
5.2
40
6.3
0.6
1.3
1.9
2.5
3.2
3.8
4.4
5.0
5.7
6.3
45
7.6
0.8
1.5
2.3
3.0
3.8
4.6
5.3
6.1
6.8
7.6
50
9.1
0.9
1.8
2.7
3.6
4.6
5.5
6.4
7.3
8.2
9.1
55
11.0
1.1
2.2
3.3
4.4
5.5
6.6
7.7
8.8
9.9
11.0
60
13.1
1.3
2.6
3.9
5.2
6.6
7.9
9.2
10.5
11.8
13.1
65
15.6
1.6
3.1
4.7
6.2
7.8
9.4
10.9
12.5
14.0
15.6
70
18.6
1.9
3.7
5.6
7.4
9.3
11.2
13.0
14.9
16.7
18.6
75
22.0
2.2
4.4
6.6
8.8
11.0
13.2
15.4
17.6
19.8
22.0
SO
26.0
2.6
5.2
7.8
10.4
13.0
15.6
18.2
20.8
23.4
26.0
85
30.5
3.1
6.1 
9.2
12.2
15.3
18.3
21.4
24.4
27.5
30.5
90
35.8
3.6
7.2
10.7
14.3
17.9
21.5
r 
LO
CVJ
28.6
32.2
35.8
95
41.8
4.2
8.4
12.5
16.7
20.9
25.1
29.3
33.4
37.6
41.8
100
48.7
4.9
9.7
14.6
19.5
24.4
29.2
34.1
39.0
43.8
48.7
* es = saturated vapor pressure

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TABLE IV-19
B AND C(B) AS FUNCTIONS OF TEMPERATURE
Temperature
(F)
B
(mmHq/ F)
C(B)
(mmHq)
Temperature
(F)
B
(mmHq/F)
C(B)
(mmHq)
45
.286
-5.5
70
.660
-22. 9
46
.296
-4.5
71
.680
-23.6
47
.306
-4.1
72
.701
-24.4
48
.317
-4.2
73
.722
-25.4
49
.328
-4.6
74
.743
-26.5
50
.340
-5.4
75
.765
-27.8
51
.352
-6.3
76
.787
-29.3
52
.365
-7.5
77
.810
-31 .0
53
.378
-8.7
78
.833
-33.0
54
.391
-10.0
79
.857
-35.1
55
.405
-11.2
80
.881
-37.6
56
.419
-12.5
81
.905
-40.3
57
.433
-13.6
82
.930
-43.2
58
.448
-14.7
83
.955
-46.4
59
.464
-15.8
84
.980
-49.7
60
.479
-16.7
85
1 .006
-53.3
61
.496
-17.6
86
1 .033
-57.1
62
.512
-18.3
87
1 .060
-61 .0
63
.529
-19.0
88
1 .087
-64.9
64
.547
-19.6
89
1.114
-68.9
65
.564
-20.1
90
1 .142
-72.9
66
.583
-20.7
91
1 .171
-76.7
67
.601
-21 .2
92
1 .200
-80.4
68
.620
-21 .7
93
1 .229
-83.8
69
.640
-22.3
94
1 .259
-86.8



95
1 .289
-89.3
211

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8.
The next estimate of E is:
E = 0.3E + 0.7 F(E)
new	v '
(Note: this choice of E_ brings about a more
new 3
rapid convergence to the answer than would use
of E alone).
9. If |E - EI<1F, then E . , = E
new 1 '	actual new
o
If E - .E >1 F, return to step 5 with E and
1 new 1	v	new
repeat procedure until convergence criterion is
met, namely, Eac;ua, = Eew.
Instantaneous, daily average, weekly average, or even longer
term average equilibrium temperature, E, can be calculated by
using mean meteorological conditions over the period of interest
and following the solution procedure just outlined. The daily
equilibrium temperature is a useful concept because it is the
temperature about which the instantaneous temperature tends to
oscillate. Calculating the daily average E under the most crucial
annual meteorological conditions (usually occurring in July or
August) yields the highest temperature about which that water body
tends to naturally oscillate. The repercussions of man's activities
in terms of altering E can thus be estimated and analyzed for potential
impact.
	 EXAMPLE IV-7 	
Calculation of Equilibrium Temperature
On Long Island, New York, studies done by Pluhowski (1968) have
indicated that shading of streams by a natural vegetative canopy
can drastically affect the shortwave solar radiation reaching those
streams. The results of some of his findings are presented in
Table IV-20. In the summer, when leaves are on the trees, the
actual solar radiation reaching the Connetquot River can be as low
as 29% of that reaching unobstructed sites at nearby Mineola or
Brookhaven.
212

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TABLE -20
SUMMARY OF SOLAR-RADIATION DATA
FOR MINEOLA,.BROOKHAVEN, AND THE CONNETQUOT RIVER SITES
Solar
Site
(1)

Dates
(2)
Mean-Daily Solar Radiation in Langleys:
for the Indicated Periods
Ratio=
Connetquot River
Observed
Mineola
(3)
Brookhaven
(4)
Connetquot
River
Estimated
(5)
Connetquot
River
Observed
(6)
Connetquot
Ri ver
Unobstructed
(7)
1
Jan.
30, 31, 1967
235
244
240
148
0.62
2
Jan.
28, 29, 1967
148
130
137
96
.70
3
Jan.
25, 26, 1967
135
135
135
104
.77
1
Apr.
21-23, 1967
466
464
465
343
.74

Apr.
16-18, 1968
452
502
502
389
.77
2
Apr.
19, 20, 1967
436
386
429
384
.90
3
Apr.
24-26, 1967
408
411
410
401
.98
1
June
9-11, 1967
600
599
599
254
.42
2
June
7, 8, 1967
664
671
669
531
.79
3
June
12-14, 1967
527
523
525
443
.84
1
Aug.
26-28, 1967
275
260
266
78
.29
2
Aug.
22-24, 1967
277
328
308
162
.53
3
Aug.
29, 30, 1967
504
484
492
338
.69
1
Nov.
28, 29, 1967
204

204
86
.42
Note 1 - Radiation data in column 5 are estimated unobstructed horizon values for Connetquot River
based on data from Mineola and Brookhaven (cols. 3,4).
Note 2 - Solar site 1 is typically heavily forested, solar site 2 is moderately to heavily forested,
and solar site 3 is moderately forested.

-------
Suppose the user is interested in calculating how the removal of
the vegetative cover might affect E. Consider the period 22-24 August,
1967, when the Connetquot River received 162 langleys/day
of a possible 308 langleys/day of shortwave solar radiation.
Representative meteorological conditions during this time were:
T = 65F
a
u = 2 mph
cloud cover fraction =0.5
relative humidity = 80%
The steps in solving for E are as follows:
1.	Data have been gathered, as previously listed.
2.	Hsn = 162 (3.7) = 600 BTU/ ft2/day. This value
assumes that the vegetation canopy blocks 47% of the
solar radiation. From Table IV-17, H is
rpn
(.5 cloud cover at 65F) 2497 BTU/ft /day. Thus,
Hr - 2497 + 600 = 3097 BTU/ft2/day.
3.	At 80% relative humidity and an air temperature
of 65F, e, = 12.5 mmHg from Table IV-18.
a
4.	As an initial guess of E, assume E-j = 65F,
the air temperature.
5.	From Table IV-19, B = .56, C(B) = -20.1
6.	K = 15.7 + (.26 + .56) (11.4) (2) = 34.4
214

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7
F(E1) = -0.05(65)2 , 3098-1801 34.4-15.7
1	34.4	34.4 34.4(.26+.56)
X |^12.5 + 20.1 + .26(65)J = -6.1 + 37.7 + 33.0 = 64.6
8.	E2 - .3(65) + .7(64.6) = 64.7
9.	Since |E2-E1|-1F	E = 64.7F
Now suppose the user wants to find E for no reduction in Hsn due
to shading. Steps 1 through 9 again are repeated, using Hgn =
308(3.7) = 1140 BTU/ft2/day, with otherwise the same meteorological
conditions. Without detailing the calculations here, it is found that
E" = 73.7, a 9F increase.
It is evident then that altering the solar radiation penetrating
to the stream can significantly change E. Even more severe cases of
repression of shortwave radiation (as noted by the 71% reduction on
26-28 August, 1967, Table IV-20) are possible, exemplifying the
large differences which may be observed.
	 END OF EXAMPLE IV-7 	
To estimate the effects of shading over the day, the incoming
solar radiation should be calculated, first assuming no shading, but
otherwise using existing meteorological conditions for the time of
the year of interest. The effects of shading should be superimposed
upon this result as a percent reduction. The following (Pluhowski,
1968) can serve as guidelines in estimating solar radiation reduction:
 0-25% reduction: shading generally restricted to
early morning and late afternoon.
215

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25-50% reduction: some sunshine penetration in morning
and evening. Considerable sunshine between 1000 and
1400 hours.
	50-75% reduction: very little sunshine penetration in
morning or late afternoon. Some sunshine between 1000
and 1400 hours.
	Greater than 75% reduction: very little penetration
even at noon.
If the diurnal variation of E is desired (such as given in
Figure IV-17), it can be estimated by a sinusoidal curve:
where
Emax = maximum daily equilibrium temperature (occurs
at noon, solar time)
E . = minimum daily equilibrium temperature (occurs
nun	^
at approximately midnight)
T = time of day, from 0 to 24 hours
Both E and E . can be found by applying Equation IV-32 for the
max	mm	j rr j ?
instantaneous meteorological conditions occurring at noon and midnight,
respectively. The maximum instantaneous solar shortwave radiation can
be estimated by:
(IV-34)
(H )
v sn'max
= (12) (3.14) H
N
sn
(IV-35)
216

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where
^sn = avera9e daily shortwave solar radiation for the day
under consideration
N = number of daylight hours, from sunrise to sunset
The shortwave radiation at midnight is, of course, for nil practical
purposes zero.
4.4.5 Longitudinal Temperature Variation
If the temperature at a particular location in a iriver is known,
the steady-state temperature distribution downstream from that point
can be estimated by:
YT~jf = exP ( pc Ud ^	(IV-36)
m	VP/
where
Tm = temperature at x = 0, F
T	=	stream temperature at a distance x
E	=	equilibrium temperature, F
K	=	thermal transfer coefficient, BTU/ ft^/day/F
U	=	stream velocity, ft/sec
d	=	stream depth, feet
P	=	water density, lb/ft"*
Cp	=	heat capacity of water, BTU/lb/F
(pCn = 62.4 BTU/ft3/F)
Since the equilibrium temperature E is constantly changing, question:?
arise as to which equilibrium temperature should be used in
Equation IV-36, and what elapsed time is acceptable. In general the
time elapsed (i.e., the travel time) should not exceed the time
217

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base for which E i.'s calculated. For example, if an average daily E
is calculated and used in Equation IV-36, then this equation should
be restricted to analyzing cases where the travel time is less than
one day. If it is desired to determine the temperature distribution
downstream from a thermal discharge in the afternoon hours, Equation
IV-34 can be used to calculate an E valid for the afternoon in
question.
An important fact is revealed upon inspection of Equation IV-36.
Suppose that a thermal discharge heats the ambient water to a
temperature T , but T is less than the instantaneous equilibrium
^	m	m
temperature. E. In that instance the stream temperature will continue
to rise exponentially downstream, approaching E. The rate at which
T approaches E is dependent on the thermal transfer coefficient, as
well as stream velocity and depth. Equation IV-36 is graphically
illustra.ted in Figure IV-19.
	EXAMPLE IV-8 	
Use of Figure IV-19
Suppose an average daily thermal transfer coefficient, K, of
200 BTU/ft2/day has been calculated. The river of interest has an
initial temperature "excess" (i.e., Tm-E>0). How far downstream will
that excess be 50% of the original? Other stream data:
U = .5 fps
d =4 feet
pCp = 62.4 BTU/ft3/F
From Figure IV-19, r is to be found (from Figure IV-15) such that
T - E = .5
218

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1.0
0.8
0.6
0.5
0.4
0.3
LU
i
h-
0.08
0.06
0.05
0.04
2.0
2.5
0.5
3.0
Figure IV-19 Downstream Temperature Profile for Completely
Nixed Stream,, T-E/Tm-E vs, r (from Edinger,
1965)
219

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The correct r equals 0.68. Solving for x in terms of r it is found:
x
rpCdU (0.68) (62.4) (4) (.5)(24)(3600)
K
200
= 3.6 x 104 feet = 6.9 miles
= 3.6 x 10
.5
,4
The associated travel time is T =
x 3gQQ hr = 20.4 hours
Since T is less than the time of averaging for E (1 day) the result
does not violate the steady-state assumptions of Equation IV-36.
	 END OF EXAMPLE IV-8 	
4.4.6 Low Flow and Temperature
Evidence has previously been cited 1n this chapter to show that
in many parts of the country high temperature conditions are concomi-
tant with low flow. The planner needs to be able to quantify better
the nebulous term "low flow" to fruitfully use this concept as a
planning tool. For example, suppose a decision is made based on the
low flow condition of this year. What are the chances that this low
flow will be exceeded in the future? If they are high, then any
decision (e.g., a particular level of waste abatement at a sewage
treatment plant) based on the observed conditions could have unexpected
deleterious results at a future time. It is paramount then, to predict
how often flow will fall below a specified rate.
Two measures or indexes of low flow that have been found useful
are flow duration and low-flow frequency. Although it is beyond the
scope of this report to explain in detail how to develop these
measures, examples of each will be presented that explain their
utility. The majority of the material in this section is from
220

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Cragwall (1966) who provides a discussion on low flow, and cites
additional references. Many texts on engineering hydrology
(e.g., Linsley et al., 1958) also discuss low flow.
Figure IV-20 shows a flow duration curve for the Hatchie River
at Bolivar, Tennessee. The vertical axis is the daily discharge
and the horizontal is the percent of time a flow is equaled or
exceeded. For example, 95 percent of the time from 1930-58 the flow
exceeded 177 cfs. It can also be assumed that this flow (177 cfs)
will probably be exceeded 95% of the time in other years. Thus this
concept offers one means by which to quantify "low flow".
A second concept is the low flow frequency curve, illustrated
in Figure IV-21. This depicts the relationship between discharge
and recurrence interval of different duration flows. For example
the 7 day mean flow of 100 cfs c^.n be expected to occur once each 19
years. Stated another way, since probability is the reciprocal of
recurrence interval, in any one year there is about a 5 percent
probability that a seven day mean flow of less than 100 cfs will
occur. A commonly used flow for analyses is the 7 day mean flow at
a recurrence interval of 10 years, or 7Q^q.
4.5 NUTRIENTS AND EUTR0PHICATI0N POTENTIAL
4.5.1 Introduction
Within the past few years the elements most often responsible for
accelerating eutrophication - nitrogen and phosphorus - have shown
generally increasing levels in rivers (EPA, 1974). Median concentra-
tions increased in the period from 1968 to 1972 over the period from
1963 to 1967*in 82 percent of the reaches sampled for total phosphorus,
74 percent for nitrate, and 56 percent for total phosphate.
221

-------
10,000
1930-58
1,000
PERCENT OF TIME INDICATED DISCHARGE
WAS EQUALLED OR EXCEEDED
Figure IV-20 Flow Duration Curve, Hatchie River at Bolivar,
Tenn. (from Cragwall, 1966)
222

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10000
120 Day
60 Day
30 Day
~ 100
L-L-LU	I
100
RECURRENCE INTERVAL (YEARS)
Figure IV-21
Frequency of Lowest Mean Discharges of
Indicated Duration, Hatchie River at
Bolivar, Tenn. (from Cragwall, 1966)
223

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These increasing concentrations afford more favorable conditions
for eutrophication, although many rivers with high nutrient levels do
not have algal blooms (see Table IV-2). Algal growth cn be inhibited
in numerous ways. For example, turbidity can decrease light trans-
mittance through water and effectively stop growth. Decreasing
turbidity could, however, have a deleterious side effect of promoting
excessive algal growth, unless stream nutrient levels are concur-
rently decreased. High water velocity can also prevent algae from
reaching bloom proportions before they are carried out of the river
system. The eutrophication problem, then, is transferred to the water
body into which the river empties.
4.5.2 Basic Theory
Stumm and Morgan (1970) have proposed a representation for the
stoichiometry of algal growth:
106C0 + 16N0" + HPO 2~ + 122H 0 + 18H+(+ trace
9	1	"	2
elements; energy)
*	(IV-37)
\C h" 0 N P I + 138 0
106 263 110 16 1'	2
algal protoplasm
where P and R represent photosynthesis and respiration, respectively.
Observe that in the algal protoplasm the ratio of C:N:P is
C:N:P = 106:16:1, by atomic ratios	(IV-38)
C:N:P = 41:7:1, by weight ratios	(IV-39)
224

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From the above two equations it can be inferred that only small
amounts of phosphorus are needed to support algal growth in relation
to the amounts of carbon and nitrogen required. If phosphorus is not
present in the amount required for algal growth then algal production
will be curtailed, regardless of how much of the other nutrients is
available. Phosphorus is then termed growth limiting. It is possible
for other elements, particularly nitrogen, and occasionally carbon or
trace metals, to be growth limiting as well (Stumm and Stumm-Zollinger,
1972).
Nitrogen uptake by algae is generally in the nitrate form if
nitrate is available. However, different types of fresh water algae
can utilize either organic nitrogen or inorganic nitrogen in the form of
arrmonia, depending on what is available (Stumm and Stumm-Zol 1 inger,
1972). Algae typically require phosphorus in an inorganic form,
usually as orthophosphate ion (Kormondy, 1969).
Some indication of whether nitrogen or phosphorus is growth
limiting may be made by determining the weight ratio of the appro-
priate forms of nitrogen and phosphorus found in a river, and
comparing that with the stoichiometric ratio required for growth.
This gives an idea regarding the nutrient on which control efforts
should focus. Specifically, let
R = [op10, phosphorus is more likely to limit than N.
If R<5, nitrogen is more likely limiting than P.
If 5
-------
Since the N:P ratio in algal biomass can vary from species to species,
this makes the determination of the limiting nutrient somewhat uncer-
tain, and leads to the indeterminate range of 5
-------
For example, algae utilize nutrients, die, and settle to the bottom
Although there is a recycling of algal cell-bound nutrients, the
settling rate may surpass the rate of recycling. Assuming total
nitrogen and total phosphorus to be conservative should give an
estimate of the upper limit of the instream concentrations of these
nutrients.
The instream concentration of total nitrogen (TN) or total
phosphorus (TP) resulting from a point discharge is (formulas will
presented for TN only; those for TP are exactly analogous):
TN - TNuQu + wq'
o 	
^	(IV-41A)
or
Q + Q
Mu vw
TN'Q + w
TN = 	B.	(IV-41B)
o
Q + Q
vu w
where
TNu = instream TN upstream of discharge, mg-N/1
TNw = concentration of TN in point discharge, mg-N/1
Qu = flow in river upstream of point discharge, cfs
Qw ~ ^ow rate f point discharge, cfs
TNq = resulting instream TN concentration, mg-N/1
Wp = loading rate of point source, lb/day
The expression for TNq is given by either Equation IV-41A or IV-41B.
The appropriate form to use will depend on the form of the available
data.
227

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To determine the instream concentration of total nitrogen due to
a distributed discharge, use:
(IV-42A)
or
TO,
0^0 + wx
(IV-42B)
TN
Q
Q
where
TN^ = TN entering with the distributed flow, mg-N/1
TNq = instream TN at x = 0, mg-N/1
x = distance downstream from the point source discharge
Q = stream flow rate at x, cfs
Q	=	stream flow rate at x = 0, cfs
o
Aq	= incremental flow increase per unit distance, cfs/mile
w	= mass flux of TN entering the stream through the
In general. Equation IV-42B will probably be the more useful of the above
two equations, since the influx of TN is expressed in terms of a total
influx per unit distance. The expressions (McElroy, et al. 1976)
utilized in Chapter III for TN and TP loadings can be used directly
in these expressions by dividing the loading by the number of stream
miles over which it occurs. The flows Qq and Q should reflect average
flows over the period the analysis is designed to cover.
The Environmental Protection Agency (1976) has performed studies
relating land use to stream nutrient levels. The geographic area for
which the data were collected encompassed most of the United States
ea^t of the Mississippi River. As a result of these studies, expressions
distributed source, lb/day/mile
228

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were developed that related land use and stream nutrient concentrations.
The expressions can aid the planner in obtaining estimates of
nutrient concentrations. Data pertinent to the system under investi-
gation should be preferentially used when available, however.
The predictive equation for total phosphorus is given by:
Logio (TP =-1.831 + 0.0093 (% agric. + % urban) (IV-43A)
where
% agric. = percent of land used for agricultural purposes
% urban = percent of land used for urban activities
Experience by the Environmental Protection Agency has shown this
expression to be more appropriate when agriculture and/or forest
comprise the predominant land use type(s) (even though forested land
does not appear in Equation IV-43A). This equation is based on
regression analysis. Accordingly, it does not describe physical
mechanisms exactly. Hence there is a difference between observed
values and those predicted by the equation. Table IV-22 illustrates
this variability. For example, in streams draining areas with a
combined agriculture plus urban land use percentage of 50%, mean
TABLE IV-22
PREDICTED MEAN TOTAL PHOSPHORUS (TP)
CONCENTRATIONS (mg/1) (FROM EPA, 1976)
% Ag + % Urb
Avg. TP
67% Limits
95% Limits
0
0.015
0.008-0.027
0.004-0.050
25
0.025
0.014-0.046
0.007-0.086
50
0.043
0.023-0.079
0.013-0.146
75
0.074
0.040-0.135
0.022-0.249
100
0.126
0.068-0.231
0.037-0.427
229

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total phosphorus concentrations average 0.043 mg-P/1. However
because of data variability, there is a 67% probability that the true
value is between 0.023-0.079 mg-P/1, and a 95% probability the true
value is between 0.013-0.146 mg-P/1.
For orthophosphate the regression equation is:
Log]0 (0PC0NC) + -2.208 + 0.0089 (% agric. + urban) (IV-43B)
The coefficient of linear correlation (r) is 0.70.
The same type of predictive equation for total nitrogen has been
formulated. It is expressed as:
Log-|Q (TN) =-0.278 + 0.0088 (% agric. + % urban)	(iv-44)
Table IV-23 shows the predicted concentrations for different percentages
of agricultural and urban coverage.
TABLE IV-23
PREDICTED TOTAL NITROGEN (TN)
CONCENTRATIONS (mg/1) (FROM EPA, 1976)
% Ag + % Urb
Avg. TN
67% Limits
95% Limits
0
0.53
0.35-0.80
0.24-1.19
25
0.87
0.58-1.31
0.39-1.96
50
1 .45
0.97-2.18
0.64-3.26
75
2.41
1.61-3.62
1.07-5.42
100
4.00
2.67-6.00
1.78-9.00
230

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4.5.4 Nutrient Accounting System
It may be desirable to determine the "impa.ct of each nutrient
source on the total instream concentration in order to distinguish
among the major sources. An accounting procedure utilizing Equations
IV-41 and IV-42 can be developed to do this. The following steps
outline the procedure.
1.	Segment River. Divide the river into major segments.
These segment divisions may reflect waste loading distri-
butions or another convenient division scheme chosen at
the discretion of the planner. The segments are not
necessarily the same as the reaches that have previously
been discussed (see Section 4.1). The delineation of
reaches as described earlier is based upon lengths of
river having uniform hydraulic conditions. Segments,
as used here, are purely a convenience subdivision of
the river. If desired, furthermore, each segment can
again be subdivided when determining instream nutrient
concentrations.
2.	Quantify and Locate Sources o
-------
3. Perform Mass-Bcilance. Sum the known sources to determine
the total nutrient loading to each segment. Then make the
following comparisons:
a.	Compare the totcil loading with the nutrient input
from the mainstom at the upstream end of the segment.
This direct comparison permits an assessment of
the collective impact of the nutrient sources
entering a secjment and the upstream contribution
of the mainste.rn.
b.	Perform an intersource comparison to ascertain the
relative impact of each nutrient source. Express
the results for each source as a percent of the total
loading.
When a tributary has a high percent contribution steps 1
through 3 can be repeated for the tributary itself to
track the sources of this nutrients. Depending on its
length the entire tributary may be considered as a single
segment.
Apply Equations IV-41 and' IV-42 to each reach within the
segment to determine the in^tream nutrient concentration
throughout the segment. Gnce this is done this step can be
repeated for the next reach.
By applying this analysis one can determine the relative
impact of any discharge, determined jointly by the flux of
the nutrient and the discharge location.
232

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	 EXAMPLE IV-9 	
Computing Total Nitrogen Distribution
This example illustrates the use of Equations IV-41B and IV-42B
in calculating the total nitrogen distribution in a river. Suppose
the user has been able to estimate the point and non-point loading of
total nitrogen in a river as shown in Table IV-24.
TABLE IV-24
TOTAL NITROGEN DISTRIBUTION IN A RIVER IN
RESPONSE TO POINT AND NON-POINT SOURCE- LOADING
Reach
Number
Ri ver
Mi 1 e-
Po i n t
TN
Added*
(1bs/day)
TN
Cummulati ve
(1bs/day)
Q
Cummulati ve
(cfs)
TN Con-
tration
(mg-N/1)
1
0
400 L
400
300
0.25

9.99
500 D
900
400
0.42
2
10.0
0
900
400
0.42

14.99
700 D
1 ,600
600
0.50
3
15.0
800 L
2,400
700
0.64

20.99
650 D
3,050
900
0.62
4
21 .0
0
3,050
900
0.62

26.0
900 D
3,950
1,000
0.73
*"L" indicates a localized or point source. "D" indicates a diffuse
or non-point source whose range of input is over the entire reach.
If these loading rates are estimated over a year, then the flow
rates used should also be average annual flows. To compute the
concentration at mile 0, Equation IV-41B can be used:
TN
()(QU)
300
1 .55
400
_a^34
= 0.25 mg-N/1
233

-------
where the following conversions were used:
1 MGD = 1.55 cfs
1 mg/l= 8.34 lb/MG
To determine the concentration at milepoint 9.99, use Equation IV-42B:
500
TN = (0.25) + gjp - 0.42 mg-N/1
TT55
Note that wx in Equation IV-42B is the 500 lb/day shown in Table IV24.
By reapplying these two basic equations for each reach the user can work
downstream through the four reaches. Also note that the total
nitrogen concentration has decreased slightly through reach 3, even
though more TN has been added. This is because the incoming flow has
served to lower the concentration by dilution.
	 END OF EXAMPLE IV-9 	
4.6 TOTAL COL IFORM BACTERIA
4.6.1 Introduction
Total coliform bacteria are considered an indicator of the presence
of pathogenic organisms, and as such relate to the potential for public
health problems. Allowable levels of total coliform bacteria in rivers
vary from state to state and according to the water use description
characterizing the particular river segment. For example, in Montana
(Montana State Dept. of Health and Environmental Sciences, 1973) the
raw water supply may not have more than an average of 50 MPN/100 ml*
*MPN means "Most Probable Number". Coliform organisms are not counted
individually, but their densities are statistically determined and the
results stated as MPN/100 ml.
234

-------
total coliforms if it is to be used as a potable water supply
following simple disinfection. In water suitable for bathing,
swimming and recreation, as well as growth and marginal propagation
of salmonoid fishes, an average of 1,000 MPN/100 ml is allowable.
Concentrations of total coliforms vary with the season of the
year. Often the heaviest loadings occur during the summer months,
but this impact is somewhat offset due to the more rapid die-off
at higher temperatures. In the Willamette River (Figure IV-22), for
example, the highest counts were actually observed from November
through May.
Treated municipal sewage comprises a major source of coliform
pollution. Urban stormwater runoff can also be significant,
especially through combined sewer outflows. Rural storm water
runoff transports significant fecal contamination from livestock
pastures, poultry and pig feeding pens, and feedlots. Wildlife
both within refuges and in the wilds can contribute as well. For
guidance in the interpretation of preliminary coliform analyses,
Table IV-25 can be used.
TABLE IV-25
TOTAL -COLIFORM ANALYSIS (EPA, 1976)
If the Calculated
Concentration is:
Probability of
a Coli form Problem
Less than 100/100 ml
Less than 1,000/100 ml
More than 1,000/100 ml
More than 10,000/100 ml
Improbable
Possible
Probable
Highly Probable
235

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o
o
O)
a.
in
E
o
o
O
o
100,000
10,000
1,000
100
SEASONAL RIVER PROFILES
WILLAMETTE RIVER
Total Coliforms
JUN. TO OCT. 1972
10 -
O
o

a.
CO
E
o
o
o
o
I
100,000
10,000
1,000
100
10
I
LEGEND:
	 MEDIAN
	 85 %
	15%
OREGON
STANDARD-
J	L
J	L
0 20 40 60 80 100 120 140 160 180 200
River Miles
NOV. TO MAY 1971 /I972

J

/ \
\
/vy
^ /\
"A

OREGON \
STANDARD


J	L
	
0 20 40 60 80 100 120 140 160 180 200
River Miles
Figure IV-22 Total Coliform Profiles for
the Willamette River (EPA, 1974)
236

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4.6.2 Mass Balance for Total Coliforms
The mass balance equations applicable to total coliform organisms
are exactly analogous to Equations IV-5, IV-7, and IV-9A and IV-9B,
since first order decay is used for both. For purposes of hand
computations, the following decay coefficient is acceptable:
ktc = 1.0 + 0.02 (T-20)
(IV-45)
where
k^c = decay coefficient for total coliforms, 1/day
T = water temperature, C
Those equations with the widest applicability are listed below.
For a point source of coliforms:
TC = TCq exp
^ (Ao x + AA \ )
(IV-46)
For a point and distributed source of coliforms:
Ej

(IV-47)
For a change in coliform concentration due to a point source
modification:
ATC exp
o r
ATC =
-J
~A
f (v "A)
(t)
(IV-48A)
"tc
237

-------
where
TC = total coliform concentration, MPN/100 ml
TCq = initial total coliform concentration, MPN/100 ml
i = 
' tc U
o
TCp - Total coliform level in distributed flow, MPN/100 ml
p _ ktcAo + A0
tc	Ap
Because of the potential variability in coliform loadings, seasonal
analyses may be warranted. Typically the summer months are of primary
concern because loadings often increase during this time period and water
contact recreation is at its maximum. Major storm events may also be of
interest, because of the large coliform loading that may be associated
with them.
	 EXAMPLE IV-10 			
Estimating the Change in Total Coliform Levels
in Response to a Waste Loading Change
Suppose the user wants to compare the change in total coliform
levels, ATC, produced by a change ATCo at s given location in a river.
Further, he wants to determine how this change is affected by a distrib-
uted flow entering the river. Relevant data for the river are as
follows:
UQ =	1 fps
T =	20C
Qq =	500 cfs
Qf -	800 cfs
=	10 miles
238

-------
k. = 1.0/day at 20C
tc
First the computations will be performed assuming no distributed flow.
Equation IV-48A is then app
flow distance of 10 miles):
Equation IV-48A is then applicable. Computing the exponent x (at a
3f x _ (1.0) (10) (5280) _ ,
tc	(24) (3600) (1) Ub11
So
ATC
ATC
o
= exp (-.611) = 0.54
or
ATC = 0.54 ATC
o
For example if ATCq = -1,000 MPN/100 ml then ATC = -540 MPN/100 ml
(negative ATCq indicates that the coliform level has decreased from what
it previously was).
Now suppose the distributed flow of 300 cfs 1s included In the
computation. Then,
ktc Ao + Aq
^tC	Aq
Ao = VUo = 500/1 = 500 ft-2
300	2
AQ = 10(5280) = -0057 ft /sec
F - (1-0) (500)
tc (24) (3600) (0.0057)
= 2.02
239

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Then
ATC / 500 \ 2 02 _
ATCq y 800 J
or
ATC	= 0.39 ATCQ
For ATCQ	= 1,000 MPN/100 ml, ATC - -390 MPN/100 ml.
Note that this decrease is 150 MPN/100 ml less than if no distributed
flow existed.
To determine the absolute total coliform level, simply add to
the original level the resulting change caused by the waste loading
modification.
	 END OF EXAMPLE IV-10 	
4.7 CONSERVATIVE CONSTITUENTS
4.7.1 Introduction
Conservative constituents are those which are not reactive and
remain either in solution or in suspension. They are advected through
the water column at the velocity of the river with no loss of mass.
The analysis of nutrients, already discussed in this report, was
performed assuming they acted conservatively. Other substances, such
as salinity and suspended solids (on a long term basis), can also be
considered as conservative. Chapter 3 contains information on
salinity in irrigation return flow for many rivers with salinity
problems.
240

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Mass Balance for Conservative Constituents
Two simple mass balance equations are sufficient for analyzing
conservative constituents. The first relates the instream concentration
due to a point loading:
S Q + W
s = g %	(IV-49)
xu xw
where
S = resulting pollutant concentration, mg/1
S = upstream concentration, mg/1
Qu = upstream flow rate, cfs
Qw = point source flow rate, cfs
W = loading rate of pollutants, lb/day
The units of the loading rate W have to be made compatible with
the other terms in Equation IV-49. This is done by using W1, where
.,, _ 1.55 W
w 8.34
This relationship is obtained by using the following two conversions:
1MGD = 1.55 cfs
lmg/1 = 8.34 lb/MG
When a distributed flow is present along some length of the river, then
the distribution of the conservative pollutant is given by:
S = IP" + T	(IV-50)
where
w = distributed loading rate, lb/day/mi
241

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x = distance downstream, miles
SQ = initial concentration (at x = 0), mg/1
SQ in Equation IV-50 is identical with S in Equation IV-46.
	 EXAMPLE IV-11 		
Calculating Salinity Distribution in a River
Salinity problems are receiving increased attention in the
western United States, particularly relating to the economic issues in
the Colorado River Basin and international impacts with Mexico. In
the Colorado River Basin high salinity levels in the lower reaches
adversely affect nearly twelve million people and approximately one
million acres of fertile irrigated farmland (Bessler and Maletic, 1975).
The salinity now averages approximately 865 mg/1 at Imperial Dam and is
projected to be 1,160 mg/1 or more by the year 2000, unless firm
control actions are taken.
As an example, suppose one is interested in determining the
salinity distribution in the river shown in Figure IV-23. Assume the
data shown there are averaged over a period of a year. These data,
along with the salinity concentrations at different river mileposts are
tabulated in Table IV-26.
To calculate S (salinity at milepolnt 100) use Equation IV-49:
5 = -500 + <2x^(1'55/8'34) = 186 m9/1
At milepost 199.9, Equation IV-50 is appropriate and S is given by:
<- _ (186)(2000) (4x10 ) (1.55/8.34)	,,
0 c;nnn	snnn	~ m9/1
242

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TABLE IV-26
SALINITY DISTRIBUTION IN A HYPOTHETICAL RIVER

Ri ver
Sa 1 i n i ty

Sa1i n i ty
Q
Salini ty
Reach
Mi le
Added*

Cumulative
Cumulative
Concentration
Number
Point
(lbs/day)

(lbs/day)
(cfs)
(mg/1)
1
0
0

0
500
0

99.9
0 fi

0 fi
500
0
2
100
2x106
L
2x10
2000
186

199.9
4x10b
D
6x10
5000
223
3
200
0

6x10
5000
223

279.9
0 fi

6x10
5000
223
4
280
-1.2x10
L
4.8x1Oc
4000
223

359.9
0

4.8x10;?
4000
223
5
360
0 fi

4.8x10
4000
223

449.9
25x10
D
29.8x10
9000
615
6
450
0

29.8x10^
9000
615

499.9
0 6

29.8x10
9000
615
7
500
8 10
L
37.8x10?
12000
585

524.9
0 fi

37.8x10
12000
585
8
525
-7.9x10
L
29.9x10
9500
585

599.9
0 fi

29.9x1Oc
9500
585
9
600
-4.7x10
L
25.2x10^
8000
585

649.9
0

25.2x10^
8000
585
10
650
0 fi

25.2x10^
8000
585

750
20x10
D
45.2x10
10000
840
*'L' indicates a localized or point source at the milepoint shown in
the same row.
1D' indicates a diffuse or non-point source ending at the milepoint
shown in the same row and beginning at the milepoint in the above row.
243

-------
Q = l500cfs
Q = 3000cfs
W = 4xl06lb/day
Q = 5000cfs
W= 25xl06lb/day
Q = 2500cfs
W=2xl0^lb/day
Q= lOOOcfs W = 8xl0^lb/d
Q = 2000cfs
y W=20xl0^lb/day
0
100
200
300
400
500
600
700 750
RIVER MILES
Figure IV-23 Salinity Distribution in a Hypothetical River
At milepoint 280, 1,000 cfs of flow leaves the mairistem (perhaps for
irrigation purposes). The concentration of salinity in this flow is the
same as that in the mainstem. So the mass rate of withdrawal is
A negative sign is used to signify a withdrawal. Completing the
remainder of the table is solely a matter of reapplying these basic concepts.
4.8 SEDIMENTATION
4.8.1 Introduction
One of the more difficult classes of hydraulic engineering problems
associated with rivers involves the erosion, transportation, and
deposition of sediment. Sedimentation is important economically,
particularly relating to filling of reservoirs and harbors, and to
W =	(223 x 1000) = -1 .2x106 lb/day
END OF EXAMPLE IV-11
244

-------
maintaining channel navigability and stability. Table IV-2, located
in Section 4.1, documents some suspended solids problems encountered
in eight major U.S. waterways.
The sediment loading in a river can be divided into two components:
the bed material load and the wash load. The bed material load is
composed of those solid particles represented in the bed. The trans-
port of this material is accomplished both along the bed (bed load)
and suspended within the water (suspended load). Although there is no
sharp demarcation delineating bed load from suspended load, many
researchers have developed individual expressions for each transport
component. The total bed material load then is the sum of the bed
load and the suspended load. Other researchers have developed a
unified theory from which the total bed material load can be predicted
from a single expression.
The wash load is usually produced through land erosion, rather than
channel scour. Wash load is composed of grain sizes finer than the
bulk of the bed material. It readily remains in suspension and is
washed out of the river without being deposited. A definite relation-
ship between the hydraulic properties of a river and the wash load
capacity apparently does not exist, making it difficult to advance an
analytical method for washload prediction (Graf, 1971). Not all the
erodible material entering a stream is transported as wash load, but
a large portion may become part of the bed material and be transported
as bed material load.
As a guide in evaluating whether a river is carrying a significant
quantity of suspended sediment, Table IV-27 can be consulted. 100 mg/1
is the delineation between a potential and probable problem. In
a table previously introduced (Table IV-1), a reference level of 80 mg/1
was set for protection of aquatic life.
245

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TABLE IV-27
RELATIONSHIP OF TOTAL SUSPENDED SEDIMENT CONCENTRATION
TO PROBLEM POTENTIAL (AFTER EPA, 1976)
If Calculated
Concentration is:
Probabili ty of
a Problem
Less than 10 mg/1
Less than 100 mg/1
More than 100 mg/1
Improbabl e
Potential
Probable
4.8.2 Long-Term Sediment Loading from Runoff
The procedures outlined in Chapter III will permit an assessment
of the sediment loading to a river on a long-term basis. When using
those procedures care should be taken to incorporate the entire
drainage area of the watershed. As an estimate, the loading can be
assumed conservative (i.e. all sediment that comes into the river will
be washed out of the river over an extended time period). Under that
assumption the procedure outlined in Section 4.7 can be utilized for an
estimate of average yearly suspended solids concentrations at locations
throughout the river system. This result should be interpreted only as
an indicator of the impact of the runoff on sediment loads within a
river and not as actual suspended solids concentrations. Not all of
the incoming sediment will be transported as suspended load since a
large fraction can be transported as bed load. The transport process
is generally of an intermittent nature with higher concentrations
occurring during periods of high flow.
Care should be taken not to apply the conservative assumption at
points on a river where that assumption is clearly violated, such as
at reservoirs which can be efficient sediment traps. An example for
the computation of sediment loading to rivers has been considered in
Chapter 3.
246

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4.8.3 Bed Material Load
As previously mentioned, the estimation of bed material transport
poses a difficult problem, and is an area where there is no consensus
regarding the best predictive relationship to use. Numerous bed
material load relationships (Task Committee on Preparation of Sedimen-
tation Manual, 1971) have been developed over the past century, some
requiring considerably more input data than others. In this report
the DuBoys relationship (Task Committee on Preparation of Sedimentation
Manual, 1971) will be used in part because of its simplicity. The
relationship,which is restricted to uniform flow in alluvial channels,
is:
9st= % (T0 - Tc>	
-------
If dgQ can be estimated then y and xc can easily be evaluated,
leaving only tq to compute. A summary of hydraulic radii (the ratio
of cross-sectional area to wetted perimeter} for different channel
200
100
40 
3
O
MEDIAN SIZE OF BED SEDIMENT, d50
(MM)

Figure IV-24 * and tc for DuBoys Relationship
as Functions of Median Size of
Bed Sediment (Task Committee on
Preparation of Sedimentation
Manual, 1971)
geometries is shown in Figure IV-25. For very wide, shallow,channels,
the hydraulic radius approximately equals the depth of flow. Many
river cross-sections can be approximated by a parabolic section. To
calculate "c" in the relationship for hydraulic radius of a parabolic
section, refer to Table IV-29.
248

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TABLE IV-28
SEDIMENT GRADE SCALE (TASK COMMITTEE ON PREPARATION
OF SEDIMENTATION MANUAL, 1971)
Size Range
Class Name
Very large boulders
Large boulders
Medium boulders
Small boulders
Large cobbles
Small cobbles
Mil 1imeters
4096-2048
2048-1024
1024-512
512-256
246-128
128-64
Microns
Inches
160-80
80-40
40-20
20-10
5-2.5
Approximate Sieve Mesh
Openings Per Inch
Tyler
United States
Standard
Very coarse gravel
Coarse gravel
Medium gravel
Fine gravel
Very fine gravel
64-32
32-16
16-8
8-4
4-2
2.5 -1.3
1.3 -0.6
0.6 -0.3
0.3 -0.16
0.16-0.08
2-1/2
5
9
5
10
Very coarse sand
Coarse sand
Medium sand
Find sand
Very fine sand
2-1
1-1/2
1/2-1/4
1/4-1/8
1/8-1/16
2.000-1.000
1.000-0.500
0.500-0.250
0.250-0.125
0.125-0.062
2000-1000
1000-500
500-250
250-125
125-62
16
32
60
115
250
18
35
60
120
230
Coarse silt
Medium silt
Fine silt
Very fine silt
1/16-1/32
1/32-1/64
1/64-1/128
1/128-1/256
0.062-0.031
0.031-0.016
0.016-0.008
0.008-0.004
62-31
31-16
16-8
8-4
Coarse clay
Medium clay
Fine clay
Very fine clay
1/256-1/512	0.004-0.0020 4-2
1/512-1/024	0.0020-0.0010 2-1
1/1024-1/2048	0.0010-0.0005 1-0.5
1/2048-1/4096	0.0005-0.00024	0.5-0.24

-------
CHANNEL SLOPE
HYDRAULIC RADIUS
T
3
<	
<-HI K-H
>;
D
\1/
	0 + zx) D	^ x = D/b) z = e/D
1 +2 x V 1
+ x
Trapezoidal
If
T	\|
/
r b
7V
D
Rectangular
bD
b + 2D
1^
( ' X ' >
Triangular
zD
z = e/D
2 y/l
+ z
Parabolic
cD
(for c, see
Table IV-29)
Figure IV-25 Hydraulic Radii for Different Channel Shapes
(from King, 1954)
250

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If the bed slope is unknown it can be estimated by using a
topographic map and finding contour lines approximately five hundred
feet above and below the point on the river where the measurement is
to be made. Dividing this elevation difference by the horizontal
distance over which the difference is measured, produces the slope.
TABLE IV-29
COMPUTING D/T FOR DETERMINING THE HYDRAULIC RADIUS OF
A PARABOLIC SECTION (FROM KING, 1954)
*
D
T
.00
.01
.02
.03
.04
.05
.06
.07
CO
o
.09
.0
.667
.667
.666
.665
.664
.662
.660
.658
.656
.653
. 1
.650
.646
.643
.639
.635
.631
.626
.622
.617
.612
.2
.607
.602
.597
.592
.586
.581
.575
.570
.564
.559
.3
.554
.548
.543
.537
.532
.526
.521
.516
.510
.505
.4
.500
. 495
.490
.485
.480
.475
.470
.465
.460
.455
.5
.451
.446
.442
.437
.433
.428
.424
.420
.416
.412
.6
.408
.404
.400
.396
.392
.388
.385
.381
.377
.374
.7
.370
.367
.364
.360
.357
.354
.351
.348
.344
.341
.8
.338
.335
.333
.330
.327
.324
.321
.319
.316
.313
.9
.311
.308
.306
.303
.301
.298
.296
.294
.291
.289
*D
T
c









Adequate methods that are within the scope of this report and
which would provide a straightforward estimation of suspended sediment
discharge presently do not exist. Most relationships require a known
reference level concentration at some depth within the river to predict
the concentration at another depth (Morris and Wiggert, 1972). To
251

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determine the suspended sediment load, then, a summation of contributions
at each depth must be made. Since these formulas apply to one grain
size this procedure should be repeated for all grain sizes present.
Einstein (Graf, 1971) has developed a method for computing suspended
sediment discharge that does not require knowledge of a reference concen-
tration, but it is an advanced approach. For this report the contri-
bution of the suspended load will be estimated from the bed material
load by the relationship given in Table IV-30. The relationship in
Table IV-30 is valid for graded channels (by graded is meant that the
slope is stable over time, being neither steepened nor flattened by
flow or other influence).
TABLE IV-30
RELATIONSHIP BETWEEN WIDTH TO DEPTH RATIO
OF A GRADED STREAM AND THE SUSPENDED AND
BED LOAD DISCHARGE (AFTER FENWICK, 1969)
Suspended
Load % of Total
Bed Material Load
Bed Load % of
Total Bed
Material Load
Width-
Depth
Ratio
M %
35-100
0-15
7
30-100
65-85
15-35
7-25
0-30
30-65
35-70
25
0
There is a relationship between M (a weighted mean percent of the fine
sediments in the bed and bank) and the width to depth ratio for graded
channels (Schumm, 1960). (See Section 4.8.4 for a detailed discussion)
Once the width to depth ratio for the stream 1n ouestion is determined.,
the suspended load can then be approximated after first computing the
bed material load, and then using Table IV-30.
252

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Once the suspended load discharge is estimated the average
concentration at a section can be computed by:
(IV - 5 2 A)
or
(IV-52B)
where
Css	=	average suspended solids concentration, mg/1
Gss	=	suspended solids discharge, lb/sec
Q	=	flow rate, cfs
gss	=	suspended solids discharge per unit width, lb/sec/ft
q	=	flow rate per unit width, cfs/ft
4.8.4 Alluvial Channel Stability
Alluvial channel beds are not always graded, or in a state of
equilibrium. Physical modification of the stream, such as building
an upstream reservoir, or altering watershed characteristics can cause
a graded stream to depart from equilibrium. The stream will then
have a tendency to either erode the bed, or to deposit some of the
sediment being transported. These two conditions are known, respectively,
as degradation and aggradation. Schumm (1960) developed a relation-
ship based on data from alluvial channels that enables one to estimate
whether a stream is aggrading or degrading based on the presence of
silt-clay, designated M, composing the perimeter of a channel. For
a graded channel:
W/D = 255 M
-1.08
(IV-5 3 )
253

-------
where
S x W + S. x 2D
c	b
W + 2D
Sc = percent of silt and clay in channel alluvium
= percent of silt and clay in bank alluvium
D = channel depth
W = channel width
Equation IV-53 is the same relationship as expressed in Table IV-30
between W/D and M. Schumm (1960) chose silt and clay to be those
sediments with sizes less than 0.074 mm (200-mesh sieve). If a
channel is aggrading, then the W/D ratio is actually larger than
predicted by Equation IV-53. If it is degrading, the W/D ratio
will be smaller than expected. Appendix C contains M-values for
sixty-nine graded channel sections.
	 EXAMPLE IV-12 				
Estimation of Bed Material Load
Table IV-31 shows characteristics of the Colorado River at
Taylor's Ferry, California, and of the Niobrara River near Cody,
Nebraska. Suppose one desires to calculate the bed load for the
Colorado River at this location for flow ranges of 8-35 cfs/ft.
The following data will be used:
dj-Q = 0.33 mm
Y = 62.4 lb/ft3, at 60F
S = 0.000217 ft/ft
254
O

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TABLE IV-31
CHARACTERISTICS OF THE COLORADO AND NIOBRARA RIVERS
(TASK COMMITTEE ON PREPARATION OF SEDIMENTATION MANUAL, 1971)
Data
Stream
Depth range, ft
Range in q, in cubic feet per
second per foot of width
Mean width, in feet
Colorado
Ri ver
(Taylor's Ferry)
4-12
8-35
350
Niobrara
Ri ver
(Cody, Neb.).
0.7-1 .3-
1 .7-5
110
Slope, in feet per foot
Minimum value
Maximum value
Value used in calculations
0.000147
0.000333
0.000217
0.00116
0.00126
0.00129
Water temperature, in degrees
Fahrenhei t
Minimum value
Maximum value
Value used in calculations
48
81
60
33
86
60
Geometric mean*sediment size,
in mil 1imeters
35'
*50'
in millimeters
in mil 1imeters
dgg, in millimeters
dgg, in millimeters
0.320
0.287
0.330
0.378
0.530
0.283
0.233
0.277
0.335
Q. 530
Mean size, dm, in millimeters
0.396
0.342
*The geometric mean of a set of values X
" is(V") V
ihus the
geometric mean of the values 1, 2, 3, and 4 is (1x2x3x4)^** = 2.213.
Compare with arithmetic mean of 2.5.
255

-------
Using Figure IV-24 one finds
V = 64
rc - 0.019
All that remains is the computation of the hydraulic radius. Since
the width is much greater than the depth, you can assume Ru = D.
h
R _ j 4 ft at q = 8 cfs/ft
^ | 12 ft at q = 35 cfs/ft
Using Equation IV-51 it is found that the bed material load is
_ | 0.12 lb/sec/ft at q = 8 cfs/ft
st (1.5 lb/sec/ft at q = 35 cfs/ft
The actual bed material load observed at Taylor's Ferry has been
compared with the DuBoys prediction for a range of flow rates (Task
Committee on Preparation of Sedimentation Manual, 1971). This
relationship is shown in Figure IV-26. (The DuBoys curve in
Figure IV-26 does not quite match the calculations in this example
because slightly different data were used). Observe that the DuBoys
relationship overpredicts the bed material load for nearly all flow
ranges. This pattern is repeated for the Niobrara River (Figure IV-27).
This suggests that the bed material load estimated by the DuBoys
relationship will in general exceed the actual bed material load.
This is further substantiated by other work (Stall, et al . 1958).
The more accurate predictions of bed material load occur under high
flow conditions, which is generally when the prediction of bed
material load is most important.
256

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COLORADO RIVER
AT TAYLORS FERRY
Duboys
Observed
4 6 8 10 20 40 60 80100
WATER DISCHARGE (cfs/ft.)
Figure IV-26 Sediment Discharge as a Function
of Water Discharge for the Colorado
River at Taylor's Ferry (Task
Committee on Preparation of
Sedimentation Manual, 1971)
To estimate the suspended load contribution first calculate
the width-depth ratio:
kIP _ | 88 at q = 8 cfs/ft
I 29 at q = 35 cfs/ft
In both cases W/D >25. Referring to Table IV-30, the suspended load
should be between 30 and 65 percent of the	bed material load. Assume
it is on the lower end of the scale, about	40%. Then the suspended
load is
0.05 lb/sec/ft	at q = 8 cfs/ft
0.60 lb/sec/ft	at q = 35 cfs/ft
257

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or
ss
100 mg/1 at q = 8 cfs/ft
275 mg/1 at q = 35 cfs/ft
NIOBRARA RIVER
0.80I-
0.60
Duboys
0.40--
0.20- -
0.08- -
0.04- -
Observed
0.02- -
0.4 0.8
0.6
WATER DISCHARGE (cfs/ft)
Figure IV-27 Sediment Discharge as a Function
of Water Discharge for the
Niobrara River at Cody,
Nebraska (Task Committee on
Preparation of Sedimentation
Manual, 1971)
from Equation IV-52B. These concentrations indicate that suspended
sediment concentrations are excessively high throughout the range
of flows normally encountered at Taylor's Ferry. Data on suspended
sediment concentrations have been gathered at Taylor's Ferry (U.S.
258

-------
Bureau of Reclamation, 1958). The average of 30 measurements taken
there are as follows:
Q = 7350 cfs (or q = 21 cfs/ft)
C = 132 mg/1
ss	3
Observed range of suspended sediment
concentration: 40-277 mg/1
These values are generally within the range predicted in this example.
	 END OF EXAMPLE IV-12		
4.9 PRESENTATION OF RESULTS
In essence, the purpose of this chapter has been to predict
instream levels of various pollutants and water quality indices for
the purpose of identifying potential problem areas. The planner must
be concerned not only with the location of problem areas but the time
of year they occur as well. This is the case because as Table IV-6
has shown, the impact of pollutants is seasonally influenced. Further,
because of the comprehensive nature of the 1972 Water Pollution Control
Act Amendments, planners can not concentrate on one pollutant to the
exclusion of others, but rather, should methodically proceed to
determine the impact of a wide spectrum of pollutants.
As the analyses are done, a display of results becomes critical if
interpretation of findings is to be done rapidly and yet accurately.
A graphical presentation is often a very meaningful method of displaying
results. For example, suppose a dissolved oxygen analysis is to be
performed. The planner may want to answer the following questions:
 At what points do the instream DO concentrations fall
below the standard (for a selected loading scheme)?
259

-------
t What appears to be the major cause of the low levels?
	How do these levels relate to saturation?
	How do the DO levels respond to different loading schemes?
The answers to these and similar questions can be shown by graphs,
such as those which might be developed from Example IV-5 (see Figure
IV-28). The only points plotted in the figure are those tabulated in
the example. These are joined by straight lines. Actually, curved
lines should result, but this would have required finding DO values at
additional milepoints.
Only on the downstream end of the river reach studied, does the
DO level fall below the 5.0 mg/1 standard used. The cause of these
fairly low DO levels is directly related to the large waste discharge
at mile 12 on the river. Just above that point, the DO level is seen
to be increasing toward saturation.
It should be recalled from Example IV-5 that the DO would still
be decreasing downstream of milepoint 16 if there were no discharge
coming into the river at that point. Even though there is, it appears
certain that a further DO decrease will occur proceeding downstream,
and which would warrant further investigation of that reach.
Two important questions regarding low DO levels are resolved by
this graphical representation. These questions are: where do low DO
levels occur and what causes them? Also, by displaying the locations
and magnitudes of the waste inputs, an assessment can be made of the
relative magnitude of each. Although only point sources are shown
in Figure IV-28, nonpoint sources, such as those considered in Example
IV-11 can also be readily illustrated.
Results of alternative waste loading schemes and other stream flow
conditions can similarly be presented, and such display could supply an
260

-------
10
8

-------
answer to the question of potential impact on DO. It may not be
apparent, for example, which hydrologic conditions produce the most
critical results. By evaluating several candidate situations and
using overlays to compare results, the overall DO status can be
evaluated.
In addition to presentinq lonqitudinal concentration profiles,
plottinq families of curves can be informative when there are more
than two variables under consideration. For example, one miqht plot
waste assimilation capacity (WAC) versus temperature with stream flow
rate as a parameter. The results of Example IV-4 illustrate this con-
cept (see Fiqure IV-29a). The solid line depicts the results obtained
in the example, while the dashed lines are hypothetical results at
other stream flow rates.
For any flow-temperature combination the planner desires to
evaluate, he can determine the stream's WAC, and compare it to the
actual loading to determine the likelihood of a problem. Additionally
he can use Figure IV-29b to find out where the minimum DO would exist,
and how it miqht vary with stream temperature. (Only the results
from Example IV-4 are shown in Figure IV-29b. Curves for each flow
rate could be plotted as in Figure IV-29a).
Figures IV-28, IV-29a, and IV-29b are meant to suggest to the
planner ways of presentinq his results to obtain the maximum benefit
from his work. By applying his ingenuity he can produce similar
graphics that portray clearly the outcomes for particular situations
of interest. After completinq computations, therefore, it only remains
for the planner to succinctly tabulate an overall summary of his
findinqs. By doing this, he will have before him the essential points
of his analysis. He may then want to develop, from these results, a
priority system defining an order of further investigation. An
example of how such a table of results might look is Table IV-32.
Although a table can only contain the most germane information,
supplementing it with a more detailed description of problem areas
262

-------
3.0
2.0
m
S2..0
X 	
o
T3
O
<
^ 00
20
P	X\^
* \\fc \<3 \5) V&
\9> \o \
15
- ov
10

5

0





0
10
20
30
(/)
LlI
Oq
^ Q
LlI ,
O
?E
^ CC
Q O
STREAM TEMPERATURE (C)
Figure IV-29 Graphical Results of Example IV-4
263

-------
and incorporating graphics should give the planner fingertip recall
of his analyses.
264

-------
TABLE IV-32
SUMMARY OF PRELIMINARY WATER QUALITY ANALYSIS OF THE HYPOTHETICAL RAPPAHAN RIVER
FROM RIVERMILE 280 TO'RIVERMILE 40
Water Quality	Waste Loading	Waste Loads Estimated Criti-
Parameter	Conditions	Hydrologic Conditions Neglected	cal Values
Location
(Rivermile) Probable Cause Comments
Dissolved Oxygen Present Loading of CBOD	August low flow
and NBOD from point	(7 day duration,
sources	10 year recurrence)
Same as Above	Same as Above
BPT of all point
sources
Same as Above
All nonpoint
sources
Same as Above
4.1-4.9 mg/1
Same as Above 4.5-5.0 mg/1
None
260 - 240 Frederick STP
70 - 50 Saluda STP and
Ferguson's Cannery
All DO values
exceed 5.5 mg/1
Temperature
No significant thermal
loads, other than
natural
Removal of vegetation
in upper reaches
(urbanization)
August low flow
(7 day duration,
10 year recurrence)
Same as Above
80F
270 - 250 Meteorology
80 F is accept-
able
270 - 250 Additional	Potential increase
solar radiation significant
Nutrients	Present distribution of
point sources, agricul-
tural sources, and
duck farm
BPT and dry duck
farms
Spring low flow
Same as Above
All major known 0.1-0.8 mg/P/1
sources con- 0.3-1.5 mg/N/1
sidered
Same as Above
0.1-0.3 mg/P/1
0.1-0.6 mg-N/1
240 - 40 Agriculture and
duck farms
240 - 40 Agriculture
High concen-
trations
throughout
system
Runoff from agricultural
lands significant
Total Coliforms
Present distribution of
point sources and duck
farms
BPT and dry duck
farms
August low flow
(7 day duration,
10 year recurrence)
Same as Above
Agricultural & 10,000
one feedlot MPN/100ml
Same as Above
240 - 200 Duck Farms
Consider analyzing
below mile 40
10,000
MP/ 100ml
Conservative No analysis yet
Constituents See Comments
Perform salinity
analysis when more
data available

-------
REFERENCES
Alonso, C. V., McHenry, J. R. , and Hong, J.-C. S. , 1975. "The Influ-
ence of Suspended Sediment on the Reaeration of Uniform Streams,"
Water Research. Vol. 9 pp 695-700.
Bansal, M. K., 1975. "Deoxygenation in Natural Streams", Water
Resources Bulletin. Vol. 11, No. 3, pp 491-504.
Barrett, M. J., Gameson, A. L., and Ogden, C. G. , 1960. "Aeration
Studies of Four Wier Systems," Water and Water Engineering.
London.
Bessler, M. B., and Maletic, J. T., 1975. "Salinity Control and
Federal Water Quality Act," American Society of Civil Engineers,
Journal of the Hydraulics Division. Vol. 101, HY5, pp 581-594.
Committee on Water Quality Criteria, National Academy of Sciences and
National Academy of Engineering., 1973. Water Quality Criteria
1972. U.S. Environmental Protection Agency, Washington, D.C.,'
EPA-R3-73-033.
Cragwall, J. S., 1966. "Low-Flow Analysis of Streamflow Data," 5th
Annual Sanitary and Water Resources Engineering Conference.
Nashville, Tenn.
Edinger, J. E. , 1965. Heat Exchange in the Environinent. John Hopkins
University, pg 43.
Edinger, J. E. , Brady, D. K. , and Graves, J. C. , 1968. "The Varia-
tions of Water Temperature Due to Electric Cooling Operations,"
Journal of Water Pollution Control Federation. Vol. 40, No. 9,
pp 1637-1639.
Edinger, J. E., and Geyer, J. C., 1965. Heat Exchange in- the
Environment. Edison Electric Institute, Publication 65-902.
Fenwick, G. B. , 1969. State of Knowledge of Channel Stabilization in
Major Alluvial Rivers. Corps of Engineers, U.S. Army, Techni-
cal Report No. 7.
Gameson, A. L., Vandyke, K. G., and Oger, C. G., 1958. The Effect of
Temperature on Aeration at Wiers, Water and Water Engineering.
London.
Graf, W. H., 1971. Hydraulics of Sediment Transport. McGraw-Hill
Book Company; New York.
266

-------
REFERENCES (continued)
Hydrologic Engineering Center, Corps of Engineers., 19,75. Water
Quality Modeling of Rivers and Reservoirs. U.S. Army Corps
of Engineers.
Hydroscience, Inc., 1971. Simplified Mathematical Modeling of Water
Quality. U.S. Environmental Protection Agency, Washington,D.C.
Jones, H. G. M., Bronheim, H., and Palmedo, P. F. , 1975. "Electricity
Generation and Oil Refining," Mesa New York Bight Atlas.
New York Sea Grant Institute, Albany, New York, Monograph No.25.
King, H. W., 1954. Handbook of Hydraulics. McGraw-Hill Book Company,
Inc. ; New York.
Karmondy, E. J., 1969. Concepts of Ecology. Prentice-Hall, Inc.;
Englewood Cliffs, New Jersey.
Krenkel P. A., and Parker, F. L., 1969. Biological Aspects of
Thermal Pollution. Vanderbilt University Press.
Lehman, J. T., Butkin, D. B., and Likens, G. E., 1975. "The Assump-
tions and Rationales of a Computer Model of Phytoplankton
Population Dynamics," Limnology and Oceanoqraohv, Vol. 20(3k
pp 343-362.
Linsley, R. K., Kohler, M. A., and Paulhus, J. H., 1958. H.ydroloqy
for Engineers. McGraw-Hill Book Company; New York.
Lund, J. W. G., 1965. "The Ecology of Freshwater Phytoplankton,"
Biol. Rev. Vol. 40, pp 231-293.
Mastropietro, M. A., 1968. "Effects of Dam Reaeration on Waste
Assimilation Capacities of the Mohawk River," Proceedings of
the 23rd Industrial Waste Conference. Purdue University
McElroy, A. D., Chiu, S. Y., Nebjen, J. W., Aleti, A., and Bennett,
F. W. 1976. Loading Functions for Assessment of Water Pollution
from Nonpoint Sources. U.S. Environmental Protection Agency,
Washington, D.C., EPA-600/2-76-151.
Montana State Dept. of Health and Environmental Sciences., 1973.
Water Quality Standards. MAC 16-2.14(10)SI448Q.
267

-------
REFERENCES (continued)
Nemerow, N. L., 1974. Scientific Stream Pollution Analysis. Scripta
Book Company; Washington, D.C.
Novotny, V. and Krenkel, P. A., 1975. "A Waste Assimilative Capacity
Model for a Shallow, Turbulent Stream," Water Research.
Vol. 9, pp 233-241.
Odum, H. T., McConnell, W. and Abbott, W., 1958. "The Chlorophylla
of Communities," Insti. of Marine Sci. Vol. V, pp 65-69.
Parker, F. L., and Krenkel, P. A., 1969. Engineering Aspects of
Thermal Pollution. Vanderbilt University Press.
Pluhowski, E. J., 1970. Urbanization and its Effect on Stream
Temperature. U.S. Geological Survey Professional Paper 627-D,
pp 1-109.
Schumm, S. A., 1960. The Shape of Alluvial Channels in Relation to
Sediment Type. U.S. Geological Survey, Professional Paper
352-B, Washington, D.C.
Sladecek, V., 1965. "The Future of the Saprobity System,"
Hydrobiologia. Vol. 25, 518-537.
	., 1969. "The Measures of Saprobity," Verh. Int. Ver.
Limnol. Vol. 17, 546-559.
Stall, J. B., Rupani, N. L., and Kandaswamy, P. K., 1958. "Sediment
Transport in Money Creek," American Society of Civil Engineers,
Journal of the Hydraulics Division. Vol. 84, No. HY1, pp
1531-1 to 1531-27.
American Public Health Association., 1973. Standard Methods for the
Examination of Water and Waste Water. 13th Edition. American
Public Health Assn., Washington, D.C.
Stumm, W. , and Morgan, J. J., 1970. Aquatic Chemistry. Wiley-
Interscience; New York.
Stumm, W., and Stumm-Zollinger, E., 1972. "The Role of Phosphorus
in Eutrophication," Water Pollution Microbiology. Chapter 3,
Wiley-Interscience; New York.
Task Committee on Preparation of Sedimentation Manual, 1971.
"Sediment Discharge Formulas," Journal of the Hydraulic
Division. Vol. 97, No. HY4, Proc. Paper No. 7786.
268

-------
REFERENCES (continued)
Thomann, R. V., 1972. Systems Analysis and Water Quality Management.
Environmental Research and Applications, Inc.'; New York. '
Thomas, N. A. and O'Connell, R. L. , 1966. "A Method for Measuring
Primary Production by Stream Benthos," Limnology and Ocean-
ography. Vol. II, No. 3, pp 386-392.
U.S. Bureau of Reclamation, Interim Report., 1958. Total Sediment
Transport Program, Lower Colorado River Basin. USBR. Denver,
Colorado.
U.S. Department of Commerce., 1968. Climatic Atlas of the United
States. U.S. Dept. of Commerce, Environmental Sciences
Services Administration, Environmental Data Service;
Washington, D.C.
U.S. Environmental Protection Agency., 1974. National Water Quality
Inventory. Vol. 1. 1974 Report to Congress, EPA-440/9-74-001.
U.S. Environmental Protection Agency., 1975. National Water Quality
Inventory. Report to Congress, EPA-440/9-75-014.
U.S. Environmental Protection Agency., 1976. The Influence of Land
Use on Stream Nutrient Levels. Ecological Research Series,
EPA-60013-76-014.
Wild, H. E., Sawyer, C. N., and McMahon, T. C., 1971. "Factors
Affecting Nitrification Kinetics", Journal of the Water Pollu^
tion Control Federation. Vol. 43, pg 1845.
269

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CHAPTER 5
IMPOUNDMENTS
5.1 INTRODUCTION
This chapter contains several methods for assessing water quality
and physical conditions in impoundments. The general topics covered
are sediment accumulation, thermal stratification, DO-BOD, and
eutrophication. 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.
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 predicting eutrophication
are empirical and based upon correlations between historical water
quality conditions and algal productivity in a number of lakes and reser-
voirs. Because algal blooms are sensitive to the presence of toxicants
and factors other than those involved in the estimation methods, the
methods for predicting eutrophication will occasionally be inapplicable.
Since the planner may not be able to assess applicability in specific
cases, results may occasionally be inaccurate.
In using the techniques to be presented, it is important to apply
good "engineering judgement" particularly where sequential application
of methods is likely to result in cumulative errors. Such would be the
case, for example, in evaluating impoundment hypolimnion DO problems
resulting from algal blooms. If methods presented below are used to
evaluate hypolimnion DO, the planner should determine when stratifi-
cation occurs, the magnitude of point and non-point source BOD loads,
and algal productivity and settling rates. From all of this, he may
270

-------
then predict BOD and DO levels in the hypolimnion. Since each of these
techniques has an error associated with it, the end result of the compu-
tation will have a significant error envelope and results must be inter-
preted accordingly. The best way to use any of the techniques is to
assume a range of values for input parameters in order to obtain a
range of results within which the studied impoundment is likely to fall.
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 presentation is:
	Impoundment stratification
	Sediment accumulation
	Eutrophication
	Impoundment dissolved oxygen
It is strongly recommended that all materials presented be read
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.
5.2 IMPOUNDMENT STRATIFICATION
5.2.1 Pi scussion
The density of water is strongly influenced by temperature and
by the concentration 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 containing water of the same density. Figure
V-2 shows this effect schematically.
271

-------


60
,0
SO1-
\"DS


\jA

>SS>"



-------
STRATIFIED
IMPOUNDMENT
DENSITY
PROFILE
m Influent
Cool Influent
Density of
Warm Influent
Density
of Cool
Influent
Density
Figure V-2 Water Flowing into an Impoundment Tends to Migrate toward a Region
of Similar Density

-------
Where density gradients are very steep, mixing is inhibited.
Thus, where the bottom water of an impoundment is significantly more dense
than surface water, vertical mixing is li.kely to be unimportant. The
fact that low density water tends to reside atop higher density water
and that mixing is 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.
5.2.1.1 Annual Cycle in a Thermally Stratified Impoundment
Figure V-3 shows schematically the processes of thermal
stratification and overturn which occur in many impoundments. Begin-
ning at "a" in the figure (winter), cold water (at about 4C) flows
into the impoundment which may at this point be considered as fully
mixed. There is no thermal gradient over depth and the impoundment
temperature is about 6C. During spring ("b"), inflowing water is
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 impound-
ment. At the same time, the surface water of the impoundment is
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 temperature change, and ultimately
the surface may cool to the temperature of the bottom. Since continued
274

-------
LATE FALL-WINTER
-Wattr
Oisploctd Upward
fall
T
OVERTURN
0 15
f
Inflow
Temperature
10 15 20 25 30
T (C)
Epilimmon
Thermocline
0 5 10 15 20 25 : 30
TCC) i
Inflow
Temperotufe
fro
0
01
V
A
INFLOW
SPRING
w too
Q. 150
SUMMER
=>
STRATIFICATION
Epiiimnion
Tnermocime
a '50
15 20 25 30
TCC)
Inflow
Temperature
0 5 10 15 20 25 30
TCC) i
inflow
Temperoture
Figure V-3 Annual Cycle of Thermal Stratification and Overturn in an Impoundment

-------
increases in surface water density result in instability, the impound-
ment water mixes (overturns).
5.2.1.2	Monomictic and O-imictic Impoundments
The stratification and overturn processes described in
Figure V-3 represent what occurs in a monomictic or single-overturn
water body. Some impoundments, especially those north of 40N
latitude and those at high elevation may undergo two periods of
stratification and two overturns. Such impoundments are termed
"dimictic." In addition to the summer stratification and resulting
fall overturn, such impoundments stratify in late winter. This
occurs because water is most dense near 4C, and bottom waters may
be close to this temperature, while inflowing water is colder and
less dense. As the surface goes below 4C strata are established.
With spring warming of the surface to 4C wind induced mixing occurs.
CN
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 essentially limited to the epilimnion
(surface layer). Thus surface velocities are somewhat higher in an
impoundment when stratified than when unstratified. Since.vertical
mixing is inhibited by stratification, reaeration of the hypolimnion
(bottom layer) is virtually nonexistent. The thermocline (layer of
steep thermal gradient between epilimnion and hypolimnion) is often
at considerable depth. Accordingly, the euphotic (literally "good light")
276

-------
zone is likely to be limited to the epilimnion. Thus photosynthetic
activity doesn't serve to reoxygenate the hypolimnion. The water
that becomes the hypolimnion has some oxygen demand prior to the
establishment of strata. Because bottom (bethic) matter exerts a
further demand, and because some settling of particulate matter into
the hypolimnion may occur, the D.O. level in the hypolimnion will
gradually decrease over the period of stratification.
Anoxic conditions in the hypolimnion result in serious
chemical and biological changes. Microbial activity leads to hydrogen
sulfide (H2S) evolution as well as formation of other highly toxic
substances, and these may be harmful to indiginous biota.
It should be noted that the winter and spring strata and overturn
are relatively unimportant here since the major concern .is anoxic
conditions in the hypolimnion in summer. Thus all impoundments will
be considered as monomictic.
Strong stratification is also important in prediction of sedimenta-
tion 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 of thermal gradients is complicated by prevailing
physical conditions, physical mixing phenomena, and impoundment geom-
etry. Such factors as depth and shape of impoundment bottom, magnitude
and configuration of inflows, and degree of shielding from the wind are
very much more difficult to quantify than insolation, back radiation,
and still air evaporation rates. Since the parameters which are diffi-
cult to quantify are critical to predicting stratification characteris-
tics, no attempt has been made to develop a simple calculation pro-
cedure. Instead, a tested model (Chen and Orlob, 1975; Lorenzen and
Fast, 1976) has been subjected to a sensitivity analysis and the
277

-------
results plotted to show thermal profiles over depth and over time
for some representative geometries and climatological conditions.
The plots are presented in Appendix D.
To assess thermal stratification in an impoundment, it is
necessary only to determine which of the sets of plots most closely
approximates conditions in the impoundment studied. Parameters which
were varied to generate the plots and values used are shown in Table Vrl.
Table V-2 shows the climatological conditions used to
represent the geographic locales listed in Table V-l. For details
of simulation technique, see Appendix E.
5.2.2.1 Using the Thermal Plots
Application of the plots to assess stratification character-
istics 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
is not near one of the ten areas, then the user may obtain data for
the parameters listed in Table V-2 (climatologic data) and then select
the modeled locale wh.ich best matches the region of interest.
Next, the user must obtain geometric data for the impoundment.
Again, if the impoundment of interest is 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, if the studied impound-
7 2
ment is 55 feet deep (maximum), with a surface area of about 4x10 feet ,
then the 40 and 75 foot deep impoundment plots should be used.
Mean hydraulic residence time (t ) may be estimated using
the mean total inflow rate (Q) and the impoundment volume (V):
278

-------
TABLE V-l
PARAMETER VALUES USED IN GENERATION OF
THERMAL GRADIENT PLOTS (APPENDIX D)
Parameter
Geographic Locale
Geometry
Depth
(maximum,
feet)
20
40
75
TOO
200
Value
Atlanta, Georgia
Billings, Montana
Burlington, Vermont
Flagstaff, Arizona
Fresno, California
Minneapolis, Minnesota
Salt Lake City, Utah
San Antonio, Texas
Washington, D.C.
Wichita," Kansas
Surface 2
Area (feet )
8.28	x 106
3.31	x 107
1.16	x 10
2.07	x 10
8.28	x 10
Volume
(feet^)
7.66 x
107
6.13 x
SO i
o
4.04 x
109
9.58 x
109
7.66 x
1010
Mean Hydraulic Residence Time	Days
10
30
75
100
200
Wind Mixing*	High
Low
*See Appendix E.
279

-------
TABLE V-2
TEMPERATURE, CLOUD COVER, AND DEW POINT DATA
FOR THE TEN GEOGRAPHIC LOCALES USED TO DEVEOP THERMAL
STRATIFICATION PLOTS ( APPENDIX D). SEE FOOT OF TABLE FOR NOTES.


Temperature (F)

Dew
Cloud Cover
Wi nd

Max.
Mean
Min.
Point ( F)
Fraction
(MPH)

Atlanta (Lat:33.8N, Long:84.4W)


January
54
45
36
34
.63
11
February
57
47
37
34
.62
12
March
63
52
41
39
.61
12
April
72
61
50
48
.55
11
May
81
70
57
57
.55
9
June
87
77
66
65
00
LO
8
July
88
79
69
68
.63
8
August
88
78
68
67
.57
8
September
83
73
63
62
.53
8
October
74
63
52
51
.45
9
November
62
51
40
40
.51
10
December
53
44
35
34
.62
10

killings (Lat:45.8N,
Long:108.5W)


January
27
18
9
11
.68
13
February
32
22
12
16
.68
12
March
38
27
16
20
.71
12
Apri 1
51
38
26
28
.70
12
May
60
47
34
38
.64
11
June
68
54
40
46
.60
11
July
79
63
46
48
.40
10
August
78
61
45
46
.42
10
September
67
52
37
38
.54
10
October
55
42
30
21
.56
11
November
38
29
20
22
.66
13
December
32
22
14
15
.66
13
280

-------
Wiru
(MP!
10
10
10
10
9
9
8
8
8
9
10
10
8
9
11
12
11
11
9
9
8
8
8
7
TABLE V-2 - CONT.
Temperature (F) Dew	Cloud Cover
Max.	Mean	Min. Point ( F) Fraction
Burlington (Lat:44.5N, Lat:73.2W)
27
18
9
12
.72
29
19
10
12
.69
38
29
20
20
.66
53
43
33
32
.67
67
56
44
43
.67
54
66
77
54
.61
82
71
59
59
CO
LO
80
68
57
58
.57
71
60
49
51
.60
59
49
39
40
.65
44
38
29
30
.79
31
23
15
17
CO
Flagstaff (Lat:35.2N, Long:111.3W)
40
27
14
14
.59
43
30
17
16
.49
50
36
22
17
.50
59
43
28
20
.49
68
51
34
22
.41
77
60
&2
25
.24
81
66
50
43
.54
79
64
49
43
.53
75
59
42
35
.29
63
47
31
25
.31
51
36
21
20
.34
44
30
17
15
.44
281

-------
Win
(MP
6
6
7
7
8
8
7
6
6
5
5
5
11
11
12
13
12
11
9
9
10
11
12
11
TABLE V-2 CONT.
Temperature (F)	Dew	Cloud Cover
Max.	Mean Min. Point ( F) Fraction
Fresno (Lat:36.7N, Long:119.8W)
55
46
37
38
.67
61
51
40
41
.61
68
55
42
41
.53
76
61
46
44
.44
85
68
52
45
.34
92
75
57
48
.19
100
81
63
51
.11
98
79
61
52
.11
92
74
56
51
.15
81
65
49
46
CO
CM
68 
54
40
42
.44
57
47
38
40
.70
Minneapolis (Lat:45.0N,
Long:93.3W)

22
12
3
6
.65
26
16
5
10
.62
37
28
18
20
.67
56
45
33
32
.65
70
58
46
43
.64
79
67
56
55
.60
85
76
61
60
.49
82
71
59
59
.51
72
61
49
50
.51
60
48
37
40
.54
40
31
21
25
.69
27
18
9
13
.69
282

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TABLE V-2
CONT





Temperature (F)

DeW n
Cloud Cover
Wi nd

Max.
Mean
Mi n.
Point ( F)
Fraction
(MPH)

Salt Lake City (Lat:40.8N,
Long:111.9W)

January.
37
27
18
20
.69
7
February
42
33
23
23
.70
8
March
51
40
30
26
.65
9
April
62
50
37
31
.61
9
May
72
58
45
36
.54
10
June
82
67
52
40
.42
9
July
92
76
61
44
*.35
9
August
90
75
59
45
.34
10
September

65
50
38
.34
9
October
66
53
39
34
.43
9
November
49
38
28
28
.56
8
December
40
23
32
24
.69
7

San
Antonio (Lat:29.4N,
Long:98.5W)


January
62
52
42
39
.64
9
February
66
55
45
42
.65
10
March
72
61
50
45
.63
10
Apri 1
79
68
58
55
.64
11
May
85
75
65
64
.62
10
June
92
82
72
68
.54
10
July
94
84
74
68
.50
10
August
94
84
73
67
.46
8
September
89
79
69
65
.49
8
October
82
71
60
56
.46
8
November
70
59
49
46
.54
9
December
65
42
54
41
.57
9
283

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TABLE V-2 CONT.


Temperature (F)

Dew
Point ( F)
Cloud Cover
Wi nd

Max.
Mean
Min.
Fraction
. (MPH)

Washington, D.C. (Lat:38.9N, Long:77.0W)

January
44
37
30
25
.61
11
February
46
38
29
25
.56
11
March
54
45
36
29
.56
12
April
60
56
46
40
.54
11
May
76
66
56
52
.54
10
June
83
74
65
61
.51
10
July
87
78
69
65
.51
9
August
85
77
68
64
.51
8
September
79
70
61
59
.48
9
October
68
59
50
48
.47
9
November
57
48
39
36
.54
10
December
46
43
31
26
.58
10

Wichita (Lat:37.7N
, Long:97.3W)


January
42
32
22
21
.50
12
February
47
36
26
25
.51
13
March
56
45
33
30
.52
15
Apri 1
68
57
45
41
.53
15
May
77
66
55
53
.53
13
June
88
77
65
62
.46
13
July
92
81
69
65
.39
12
August
93
81
69
53
.38
11
September
84
71
59
55
.39
12
October
72
60
48
43
.40
12
November
34
55
44
33
.44
13
December
45
36
27
25
.50
12
284

-------
TABLE V-2 CONT.
Notes: Mean:	Normal daily average temperature, F.
Max.:	Normal daily maximum temperature, F.
Min.:	Normal daily 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.
285

-------
t = V/Q
w x
(V-l)
Again, the sets of plots bracketing the value of tw should be examined.
Where residence times are greater than 200 days, the residence time
has little influence on stratification (as may be verified in Appendix
D) and either the 200 day or infinite time plots mav 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 E).
. 	 EXAMPLE V-l	
Thermal Stratification
Suppose one wants to know the likelihood that hypothetical
Limpid Lake is stratified during June. The first step is to compile
the physical conditions for the lake in terms of the variables listed
in Table V-l. Table V-3 shows how this might be done. Next, refer
to the indexes provided in Appendix D to locate the plot set for con-
ditions 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 mixing rate would be chosen (see Table V-3). Figure V-4 is a
reproduction of the appropriate page from Appendix D.
TABLE V-3
LIMPID LAKE CHARACTERISTICS
Item
Limpid Lake
Available Plot
Location
Depth, ft (maximum)
Volume, ft^
Mean residence time (t )
Mi xi ng
Manhattan, Kansas
180
6 x 1010
500 days
high (windy)
Wichita, Kansas
200
7.66 x 1010
o (no inflow)
high coefficient
286

-------
no*
JUN
20
20
20-
20
Q.
iu
cd
40-
a_
Li_l
a
40-
a_
LU
CD
40-
Q_
Li_l
a
4 0-
60
20-
Q.
LU
a
40-
60.
20-
X
t
Q.
UJ
a
40-
60
10 20
TEMP. C
JUL
30
10 20
TEMP. C
NOV
10 zo
TEMP. C
60
20-
4 0
30
60
20
a_
U-J
CD
40-
30
60
10 20
TEMP. C
BUG
30
60
0 10 20 30
TEMP. C
SEP
20-
3C
a_
LU
CD
40
10 20
TEMP. C
OEC
30
60
60
20
a_
UJ
CD
4 0-
0 10 20 -30
TEMP, c
60
10 20
TEMP. C
OCT
30
10 20 30
TEMP. C
WICHITA . KRNSRS
200 ' INiriRL MAXIMUM DEPTH
I NFINITE HYDR . RES - T[ME
MAXIMUM MIXING
10 20
TEMP. C
30
Figure V-4 Thermal Profile Plots "sed in Example V-]
287

-------
According to the plots, Limpid Lake is likely to be strongly
stratified in June. Distinct strata form in May and overturn probably
occurs in December. During June, the epilimnion should extend down
to a depth of about eight or ten feet, and the thermocline should
extend down to about 30 feet. The gradient in the thermocline should
be about 1C per foot.
	 END OF EXAMPLE V-l 	
	 EXAMPLE V-2 	
Thermal Stratification
What are the stratification characteristics of Lake Smith?
The hypothetical lake is located east of Carthage, Texas, and
Table V-4 shows its characteristics along with appropriate values for
the thermal plots.
TABLE V-4
PHYSICAL CHARACTERISTICS OF LAKE SMITH
Item
Lake Smith
Plot Values
Location
Depth, ft (maximum)
Volume, ft^
Mean residence time
Mi xing
15 miles east of
Carthage Texas
23
3 x 108
250 days
low (low wind)
20
1.66 x 108
00
low mixing coefficient
288

-------
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 is somewhat warmer and insolation is 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 Atlanta may be used, bearing in mind that the
temperatures are likely to be biased uniformly low. Figure V-5 (repro-
duced 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, it is clear that the lake is likely to stratify from April
or May through September, .the epilimnion will be very shallow, and the
thermocline will extend down to a depth of about 7 feet. The thermal
gradient is in the range of about 7C per meter, as an upper limit,
during June. Bottom water warms slowly during the summer until the
impoundment becomes fully mixed in October.
	 END OF EXAMPLE V-2 	
5.3 SEDIMENT ACCUMULATION
5.3.1 Introduction
Reservoirs, lakes, and other impoundments are usually more quies-
cent than tributary streams, and thus act as large settling basins for
suspended particulate matter. Sediment deposition in impoundments
gradually diminishes water storage capacity to the point where lakes
fill in 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).
289

-------
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)
Cloud
Temperature, F	 Dew	Cover, Wind,

Max.
Mean
Mi n.
Point, F
Fraction
MPH
January
57/54
48/45
38/36
38/34
.60/.63
9/11
February
60/57
50/47
41/37
40/34
.58/.62
9/12
March
67/63
57/52
47/41
44/39
.54/.61
10/12
Apri 1
75/72
65/61
55/50
54/48
.50/.55
9/11
May
83/81
73/70
63/57
62/57
.48/.55
9/9
June
91/87
81/77
71/66
69/65
.44/.58
8/8
July
92/88
82/79
72/69
71/68
.46/.63
7/8
August
94/88
83/78
73/68
70/67
.40/.57
7/8
September
88/83
78/73
67/63
65/62
.40/.53
7/8
October
79/74
67/63
55/52
55/51
.38/.45
7/9
November
66/62
55/51
45/40
45/40
.46/.51
8/10
December
59/53
50/44
40/35
39/34
.58/.62
9/10
Shreveport Lat:32.5N, Long:94W
Atlanta Lat:33.8N, Long:84.4W,
290

-------
CL
UJ
a
a.
UJ
~
x
t
CL
UJ
~
10 20
TEMP . C
10 20
TEMP. C
NOV
10 20
TEMP. C
x:
Q_
UJ
CD
3D
2 
a.
LU
C3
30
2 
UJ
o
3D
10 20
TEMP. C
a_
UJ
C3
10 20 30
TEMP, C
BUC
0 10 20
TEMP. C
SEP
a_
UJ
a
0 10 20 30
TEMP. C
OEC
0 10 20
TEMP. C
2 
3=
a.
UJ
a
30
10 20 30
TEMP, c
0C1
2 
32
a_
UJ
CD
30
10 20 30
TEMP. C
RTLRNTH, GEORGIA
20' INITIAL MAX[MUM DEPTH
INFINITE HYOR. RES- TIME
MINIMUM MIXING
30
Figure V-5 Thermal Profile Plots Appropriate for I'se in Fxample V
291
-2

-------
Just how much suspended matter settles out as water passes
through an impoundment, 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 impoundment may
significantly reduce light penetration thus limiting algal and bottom-
rooted plant (macrophyte) growth. This, in turn, can adversely affect
food availability for indigenous fauna, or may slow plant succession,
a part of the natural aging process of lakes.
Settling of suspended matter may eliminate harborage on impound-
ment 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 deposition within an
impoundment allows for effective planning to be initiated. If sedimen-
tation rates are unacceptable, 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
erodible fields and transporting waterways, farming and crop management
practices may be changed, or zoning may be modified to prevent a
worsening of conditions.
292

-------
These considerations, along with others relating to se'diment
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 accumu-
lation (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.
5.3.2 Annual Sediment Accumulation
5.3.2.1 Use of Available Data
Data provided in Appendix F permit estimation of annual
sediment accumulation in acre-feet for a large number of impoundments
in 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 in terms of annual sediment accumulation.
Refer to the U.S. map included in the appendix and find the index
numbers of the region within which the impoundment is located. The
data tabulation in the appendix is arranged in order of index number,
and this will permit quick location of specific data. Referring to
the impoundment data section of the appendix, total annual sediment
accumulation in acre feet is given by multiplying average annual sediment
accumulation in acre feet per square mile of net drainage area ("Annual
Sediment Accum.") by the net drainage area ("Area") in square miles:
Total Accumulation = Annual Sediment Accum. x Area	(V-2)
293

-------
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. Note that this approach, as well as those pre-
sented 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 in 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 in Appendix F for a specific
impoundment, the following method will permit estimation of annual or
short-term sediment accumulation rates. The method is 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 is provided in Figure V-6.
10.000
1,000
Fitted
10,000
1,000
100,000
SUSPENDED SEDIMENT DISCHARGE, S: (tons/day)
Figure V-6 Sediment Rating Curve Showing Suspended Sediment
Discharge as a Function of Flow (After Linsley,
Kohler, and Paulhus, 1958)
294

-------
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,
it would be expected that:
where
S. = sediment transport rate to be determined in
tributary "i" in mass per unit time,
S. = known transport rate for comparable tributary
J
(j) in same units as ,
V.j = mean velocity for tributary i over the time
period, and
V. = mean velocity in tributary j over the same
\)
time period as
Once average transport rates over the time period of interest
have been determined, 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:
P = f(C/Qi)	(V-4)
295

-------
I
to
CD
cn>
100
90
~ 80
(L 70
60
"O
0)
O.
Q.
P 50
o>
E
"O

-------
whore
P =	percent of inflowing sediment trapped
C =	capacity of the impoundment in acre-feet, and
=	water inflow rate in acre-feet per year
Data used for development of the curves in Figure V-7 included
41 impoundments 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,
St = S.P	(V5)
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 evaluating sediment deposition in impoundments are
capable of providing reasonable estimates, but only where substantial
periods of time are involved - perhaps 6 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.
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
297

-------
passing through an impoundment. The steps are:
 Determine terminal fall velocities for th grain
size distribution
 Estimate hydraulic residence time
 Compute trap (sedimentation) rate
5.3.3.1 Fall Velocity Computation
When a particle is released in 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 is 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 particle.
v
max = T8i7(pp-pw'd2 = mr(Dp-D^d2
(V-6)
where
v
max
= terminal velocity of the spherical particle (ft sec
y
d
D
g
p
p,
_2
= acceleration due to gravity (32.2 ft sec )
_3
= mass density of the particle (slugs ft )
_3
= mass density of water (slugs ft )
= particle diameter (ft)
_2
= absolute viscosity of the water (lb sec-ft )
_ 3
= weight density of particle (lb ft )
298

-------
Dw = weight density of water (lb ft"3)
Stokes law is satisfactory for Reynolds numbers" between 1x10 ^
and 0.5 (Camp, 1963). Reynolds number is given by:
R = V	(V - 7)
where
R = Reynolds number
v = particle velocity
v = kinematic viscosity of water
-?
Generally, for particles of diameter less than 3 x 10 inches
(0.7 mm) this criterion is 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
is given by:
Fd= CAv2/2	
where
= the drag force
C = unitless drag coefficient
A = projected area of the particle in the direction
of motion
Equating the drag force to the gravitational (driving) force for the
special case of a spherical particle, velocity is given by:
299

-------
V
max =
1
"9 "
3C Pw
(V-9)
All variables in the expression for vmax (Equation V-9) may be easily
estimated except C, since C is dependent upon Reynold's number. Accord-
ing to Equation (V-7), Reynolds number is a function of v. Thus a
"trial and error" or iterative procedure would ordinarily be necessary
to estimate C. However, a somewhat simpler approach is available to
evaluate the drag coefficient and Reynolds number. First, estimate
CR2 using the expression (Camp, 1968):
Cr2 = 4pw (pp " pw) 9d3/3y2	(V-10)
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 Vmax 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 (in impoundments). 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.
300

-------
I05
10'
10
CM
5 '2
T3
C
O
o|cE jo
to
a>
= I
o
>
10"
10*
10
-3
~1





-





-





-





-





-





-





1 III
1 III
i in
i i j i
i in
i \i i
I0~3	I0-2
10"'
I
10
I02	I03
Values of R =
vd
Figure V-8 Plot of C/R and CR^ Versus R (Camp, 1963)
301

-------
-




LEGEND >
A - Stokes' Low
B - Spheres
C - Cylinders, L = 5d
D - Discs
-




-








-


v\
\\
\\
\
>
\
\ \
\ \


i
1
fe
1
i

1 III
1 III
1 III
i iii
\
A^\
\
\
i iii
i iii
i iii
^-c		
i iii
%
1 III
I0~3	I0~2	10"'	I	10	I02	I03	I04	I05	I06
Reynolds Number, R
Figure V-9 Drag Coefficient (C) as Function of Reynold's Number (R)
and Particle Shape (Camp, 1968)

-------
Particles which	
velocity is affected
by vertical velocity
field
-Region of disruption,
upward fluid motion
-Settling sphere

-------
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 however, and Figure V-ll is a plot of a velocity
correction factor, v'/V as a function of volumetric concentration .
Volumetric concentration is given by:
C
- cwtpw
vol -	(V-ll)
where
C = volumetric concentration
vol
C t = weight concentration
As an approximation, the curve for sand may be used to correct v as a
function of C .
vol
	 EXAMPLE V-3 	
Settling Velocity
Assume that a swiftly moving tributary to a large reservoir
receives a heavy loading of sediment which is mostly clay particles.
The particles tend to clump somewhat, and average diameters are on the
order of 2 microns. The clumps have a specific gravity of 2.2. Applying
Stokes1 law for 20C water,
vmax = T8^T (pp " PJ d
2
v = 32,2	=- X (2.2x62.4/32.2-62.4/32.2)x(6.56x10~6)
maX (18x2.lxlO"5)
= 8.53x10 ^ ft sec ^ = .03 ft hr ^
Thus the particles of clay might be expected to fall about 9 inches
per day in the reservoir. It should be noted that for such a low
304

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CO

01
1.0
0.9
0.8
>|> 0.7
0.6
0.5
0.4
0.3
0.2
0.1
o
o
o
0)
o
O
X
X,




LEGEND:
A - Red Blood Cells
B - Lucite Spheres, d = 0.0181 cm., P, = 1.194
C - Round Sand Grains, d=O.OI67 cm., P, = 2.66


4



+
\

+



tS.'

+
1













X




^6










7
M/
Xc
V














kC,.






T

+






X



Ql


































0.05
0.10	0.15	0.20	0.25
p
Volumetric Concentration, Ct-
^1
0.30
0.35
Figure V-1I Velocity Correction Factor for Hindered Settling (From Camp. 1968)

-------
settling rate, turbulence in the water can cause very significant
errors. In fact, the estimate is useful only in still waters having
a very uniform flow clacking substantial vertical components.
END OF EXAMPLE V-3
	 EXAMPLE V-4 	
Sett! ing., Velocity, for a Sand and Clay
Suppose a river is transporting a substantial sediment load which
is mainly sand and clay. The clay tends to clump to form particles
of 10 micron diameter while the sand is of 0.2 mm diameter. The
sand particles are very irregular in shape tending toward a somewhat
flattened plate form. The specific gravity of the clay is about
1.8 while that of the sand is near 2.8. Given that the water tempera-
ture is about 5C, the terminal velocity of the clay may be estimated
as in Example V-3:
x (0.8x62.4/32.2)x(3.28xl0"5)
2
v
max
18x3.17x10
9.4 xlO"^ ft sec ^
8 ft day-^
For the sand, apply Equation (V-10)
cr2 = 4ew (pp " p> 9dW
32.2 x (6.56xl0~4)
X	-
3
3x(3.17x10")
CR
2
82
306

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Referring to Figure V-8, a value of CR^ equal to 82 represents R-2.8
and C=10.3. From Figure V-9, the corrected drag coefficient for discs
is close to 10.3 (no correction really necessary). Then, using Equation
(V9) as an approximation,
v
max
49 (p - p ) d
VKp
3Cp
 _ 14x32.2x(1.8x62.4/32.2)x6.56xl0~4
max ^ 3x10.3x62.4/32.2
vmax = 0-^7 ^ sec ^ = 252 ft hr~^
Thus the clay will settle about 8 feet per day whiTe the sand will
settle about 6048 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 in estimating sediment deposi-
tion rates is 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 in 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 is 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?
307

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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 simpli-
fication 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 is computed as in Equation (V-l). That is,
t = V/Q
w
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 or promontory,
or whether they are isolated by a density gradient, as in the thermo-
cline and hypolimnion. Ignoring stagnant areas may result in a very
substantial overestimate of t , and in sediment trap computations, an
overestimate in trap efficiency. Actually tw computed in this way is
an adjusted hydraulic residence time. All references to hydraulic
residence time in the remainder of this chapter mean adjusted x .
w
Hydraulic residence time is directly influenced by such physical
variables as impoundment depth, shape, side slope, and shoaling,
as well as hydraulic characteristics such as degree of mixing, stratifi-
cation, 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.
308

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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 configu-
ration types are possible, the methods are perhaps best explained using
exampl es\
	 EXAMPLE V-5 			
Hydraulic Residence Time in Unstratified Impoundments
The first step in estimating hydraulic residence time for purposes
of sedimentation analysis is to determine whether there are signifi-
cant 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 im-
poundment 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
movinq river reach. With these assumptions, the computation of
hydraulic residence time is as shown in Table V-6.
309

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1/2
 o
MILES
YAPHANK
COUNTY
HOME
Figure V-I2 Upper and Lower Lakes and Environs, Long
Island, New York
310

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TABLE V-6
HYPOTHETICAL PHYSICAL CHARACTERISTICS
OF UPPER LAKE, BROOKHAVEN, SUFFOLK COUNTY, NEW YO'RK


D
U
CSA
Distance
Downstream
Average
Average
Cross-sectional
from
Inflow
Depth
Width
Area,_D x W
Mi 1 es
(feet)
ft.
ft.
ft2
0.05
(264)
3
63
189
0.10
(528)
4
110
440
0.15
(792)
6
236
1,416
0.20
(1 ,056)
7
315
2,205
0.25
(1,320)
7
340
2,380
0.30
(1 ,584)
8
315
2,520
0.35
(1,848)
7
550
3,850
0.40
(2,112)
8
550
4,400
0.45
(2,376)
7
354
2,478
0.50
(2,640)
10
350
3,500
Total length = 0.5 mi. (2,640 ft.)
Inflow from upstream = 380 cfs )
Outflow to downstream = 380 cfs (
(steady-state)
mean CSA = 2,338 ft
Computation
Volume (Vol) = Total length x mean cross-sectional area
Vol = 2,640 ft. x 2,338 ft2 = 6.17 x 106 ft3
Residence time (t) = Vol/flow
w
t = 6.17 x 10 ft3/(380 ft3/sec) = 1.62 x 10^ sec (4.5 hr)
w
Velocity (Vel) = length/Tw
Vel = 2,640 ft/1.62 x 10 sec = .163 ft/sec
311

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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, particularly 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 stratification very un-
likely, and that Lower Lake is a slow moving river reach. We then
compute hydraulic residence time as shown in Table V-7. Figure V-13
in particular diagram 1, shows what these assumptions mean in terms of
a flow pattern for both lakes.
	 END OF EXAMPLE V-5 	
	 EXAMPLE V-6 	
Assume for this example that Lower Lake is stratified during the
period of interest. This significantly changes the computation of res-
idence time. To a first approximation, one can merely revise the
effective depth of the impoundment to be from the surface to the upper
limit of the thermocline rather than to the 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 plot of the temperature profile over depth. Actually,
the profile could represent a salinity gradient as well as a thermal
gradient.
Table V-8 shows the procedure to estimate travel time for strati-
fied Lower Lake. The upper boundary of the thermocline is 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 assump-
tion is valid presuming that the thermocline and hypolimnion are
relatively quiescent. Thus once a particle enters the thermocline it
can only settle, and can not leave the impoundment.
	 END OF EXAMPLE V-6 	
312

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TABLF. V-7
HYPOTHETICAL PHYSICAL CHARACTERISTICS
OF LOWER LAKE, BROOKHAVEN, SUFFOLK COUNTY, NEW YORK
Distance Downstream
from Inflow
Miles (feet)
D
Average
Depth
ft.
U
Average
Width
ft.
CSA
Cross-sectional
Area,0D x W
ft2
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
396)
792)
1,188)
1,584)
1,980)
2,376)
2,772)
3,168)
3,564)
3,960)
4,356)
4,752)
5,148)
5,544)
5,940)
15
20
20
25
35
30
35
35
40
42
41
51
42
40
37
157
165
173
197
197
228
232
197
220
315
433
591
551
433
323
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
Total length = 1.125 mi (5,940 ft.)
Inflow from upstream 400 cfs
Outflow to downstream 390 cfs
Average flow = 395 cfs
i
mean CSA = 11,008
(surface rising)
Computation
Volume (Vol) = Total length x mean cross-sectional area
Vol = 5,940 ft. x 11,008 ft2 = 6.54 x 107 ft3
Residence Time (t, ) = Vol/flow
w
t,, = 6.54 x 107/(395 ft3/sec) - 1.65 x 105 sec (46 hr)
W
Velocity (Vel) = length/Tw
Vel = 5,940 ft/1.65 x 10 sec = .036 ft/sec
313

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LAAOC SUNfACrO, FASI-UOV1N0
IMPOUNOMINT
AfVYS.-.-y.
tf S'ratIfJcot)*
S#dit lqi*'v-
o|
T 
Trtfcrtory J
CkonMl {
LAROE SURFACEO, DEEP
IMPOUNDMENT
j Rc*i*:ng
I Channel
Epihmnion (Miatd, Flowing)
rmodint (Einntally Stogncnl
Hfpoll/nnton (Srognoni)
saimtm Lor

I LARGE SURFACED, MODERATELY SHALLOW ' .... .
IMPOUNDMENT, VERr LOW VELOCITIES ?! , '
f OMti j	j cnannti
(3)
Thcrmoclmt
Hypolimoiort
miiing
I Croduol der*e\ i Miiing
I In 4ptD vlrh 11 d#crtad
I tafft incrtaM i/ |
I Mr foe* trta ' j
SHALLOW, WIND MjXEO (TURBULENT) IMPOUNDMENT
I 1Vt4 S*or
(4)
T-
Ott* SUPERFICIALLY TURBULENT,
STRATIFIED IMPOUNDMENT
WM
o ( O f^p^cTO
		 fpilimmon
(3)
lri
T
Figure V-13 Impoundment Configurations Effecting Sedimentation
314

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TABLE V-8
HYPOTHETICAL PHYSICAL CHARACTERISTICS
OF LOWER LAKE, BROOKHAVEN, SUFFOLK COUNTY, NEW YORK
(ASSUMING AN EPILIMNION DEPTH OF 10 FEET)

D
W
CSA
Distance Downstream
Average
Average
Cross-sectional
from Inflow
Depth
Width
Area,0D x W
Miles (feet)
ft.
ft.
ft2
0.075
10
160
1,600
0.150
10
170
1,700
0.225
10
175
1 ,750
0.300
10
200
2,000
0.375
10
198
1 ,980
0.450
10
230
2,300
0.525
10
233
2,330
0.600
10
200
2,000
0.675
10
222
2,220
0.750
10
316
3,160
0.825
10
435
4,350
0.900
10
590
5,900
0.975
10
552
5,520
1 .050
10
435
4,350
1 .125
10
325
3,250
Total length = 1.125
mi (5,940 ft.
) mean
CSA = 2,961 ft2
Inflow from upstream
397 cfs )
(steady-state surface, difference
Outflow to downstream
393 cfs (
due to loss to water table)
Average flow = 395 cfs
Computation
Volume (Vol) = Total length x mean cross-sectional area
Vol = 5,940 ft. x 2,961 ft2 = 1.76 x 107
Residence Time (t ) = Vol/flow
xw = 1.76 x 107/(395 ft3/sec) = 4.46 x 104 sec (12.3 hr)
Velocity (Vel) = length/x
w
Vel = 5,940 ft/4.46 x 10 sec = 0.133 ft/sec
315

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EXAMPLE V-7
Large, Irregular Surface Impoundment
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 36 acres. From the surface shape of the pond, it is
clear that it cannot be considered as a stream reach.
Figure V-15 shows a set of hypothetical depth profiles for the
pond. From the profiles, it is evident that considerable shoaling
has resulted in the formation of a relatively well defined flow
channel through the pond. Peripheral stagnant areas have also formed.
Hypothetical velocity vectors for the pond are presented in Figure
V-16. Based upon them, it is reasonable to consider the pond as
being essentially the hatched area in Figure V-15. To estimate
travel times, the hatched area may be handled in the same way as for
the Upper Lake example presented above. It should be noted, however,
that this approach will almost certainly result in underestimation of
sediment deposition in later computations. This is true for two
reasons. First, estimated travel time will be smaller than the true
value since impoundment volume is underestimated. Second, since the
approach ignores the low flow velocities to either side of the central
channel and nonuniform velocities within it, heavier sedimentation
than computed is likely.
316

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SOUTHAMPTON
LONG POND
I BRIDGEHAMPTON
LITTLE LONG
\POND +
KELL/S POND to
HAYGROUND
WEST MECOX
VILLAGE
1/2
MILES
Figure V-14 Kellis Pond and Surrounding Region, Long Island,
New York
317

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v.v'-.ii.v:.: :

INFLOW
PLAN VIEW
feta


v

phd
0
TRANSECTS










v, w
(
	
4
"w
			  - w
V
 ^









k		\y
X7







w
<*1
V
tw

 
 :


B
0
0
Figure V-15 Hypothetical Depth Profiles for Kellis Pond
318

-------
STAGNANT
STAGNANT
Figure V-16 Hypothetical Flow Pattern In Kellis Pond
Still more difficult to evaluate is	the situation where shoaling
and scour have not resulted in 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, particu-
larly if the impoundment is of much importance. If such data are
not available but it is deemed worthwhile to do field studies,
methods available for evaluating flow patterns include dye tracing
and drogue floats. A simple but adequate method (at least to evalu-
ate 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 will permit estimation of hydraulic
residence time directly or generation of data to use in the prescribed
method. In the latter case, the data might be used to define the
major flow path through an impoundment of a form like Kellis Pond.
	 END OF EXAMPLE V-7 	
	 EXAMPLE V-8 	
Complex Geometries
The final hydraulic residence time example shows the degree of
complexity that sediment deposition problems may entail. Although
it is possible to make rough estimates of sediment accumulation, it
319

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^r

V
2.
V
R
5L
'"V~\Crrr7>-.:.n
-.. j W t. -  
_2	
PLAN VIEW

^
		y




17	q
TRANSECTS
0
0
0
0
0
0
Figure V-17 Hypothetical Depth Profiles for Kellis Pond Not
Showing Significant Shoaling
320

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is recommended that for such impoundments more rigorous methods be
used - mathematical modeling and/or detailed field investigations.
Figure V-18 shows Lake Owyhee in eastern Oregon. This impound-
ment is well outside the ranoe of complexity of water bodies which
can be evaluated using these calculation methods. Because of geometry,
the number of tributaries, and size, it isn't feasible to conceptually
reduce the impoundment in such a way as to estimate travel times. Flow
patterns are likely to be very complex, and bediment deposition is dif-
ficult to predict both in terms of quantity and location.
In contrast, Figure V-19 shows New Millpond near Islip, New
York and surrounding 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. Bearing in mind the limita-
tions imposed by wind mixing, stratification, and the presence of
stagnant regions described in earlier examples, deposition might
nevertheless be estimated in arms A, B, and C. Because of the diffi-
culty of predicting velocities and turbulence in section D, estimates
of sedimentation cannot be reliably made there. However, it is
likely that much of inflowing sediments will have settled out by the
time water flows through the arms and into section D.
	 END OF EXAMPLE V-8 	
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 is fully mixed as in turbulent flow, or that
it moves in a "laminar" flow through the impoundment. In terms of
sediment accumulation estimates, the fully mixed plug assumption is
321

-------
R.43E.
R.44 E.
R.45 E.
LAKE
OWYHEE
V
Ax
T 22 S
T 24 S
'elican Point

T 25 S
T 26
Miles
Figure V-18 Lake Owyhee and Environs
322

-------
WILLOW POND
SMITHTOWN
VAIL POND
County Park
NEW MILL POND
HAUPPAUGE
1/2
MILES
Figure V-19 New Millpond and Environs, New Millpond is
Subdivided for Purposes of Estimating Sedi-
mentation in Regions A, R, and C.
323

-------
handled in the same way as the fully mixed impoundment model,
we have two kinds of computations:
Thus
Cases
Plug flow with the plug not
mixed vertically
versus
t Plug flow assuming a vertically
mixed plug, or
 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.
where
S = S -P
t i
P =
^(twv) + D" -D^/D
P = VTw
P
St
Si
v
D
D'
D"
mean proportion of S. trapped (l^P>-0)
mass of sediment trapped per unit time
mass of sediment in inflows per unit time
particle settling velocity
discharge channel depth
flowing layer depth
inflow channel depth
(V-12)
(V-13)
(V-14)
324

-------
Figure V-20 shows the significance of the various depth measures
D, D1, and 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 available
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 P is a 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 is included to provide estimates
of vmax for spherical particles of 2.7 specific gravity. The data
are presented as a function of particle diameter and temperature.
Figure V-22 is a nomograph relating trap efficiency, P (in percent)
to depth D1, vmax, and x . The nomograph is useful only for case B
assumptions.
	 EXAMPLE V-9 	
Sedimentation in Upper and Lower Lakes
Using the data from Table V-6 and settling velocities for the
clay and sand of Example V-4, for case A,
x = 1.6x10^ sec
w
vmax for clay = 8 ft day_1
v , for sand = 252 ft hour"^
max
325

-------
Flow
PLUG FLOW, PLUG NOT MIXED VERTICALLY
Thermocline
PLUGS
H ypol i mnion
CASE A
Sediment Layer
- IMPOUNDMENT
Flow
PLUG FLOW, VERTICALLY MIXED PLUG
Sediment Layer
IMPOUNDMENT
Flow
FULLY MIXED IMPOUNDMENT OR STRATUM

ThermocIine
CASE B
Hypol i mnion ::
;Sediment Loyer X
IMPOUNDMENT
Figure 20 Significance of Depth Measures D, D1, and
D11, and the Assumed Sedimentation Pattern
326

-------
20
25
30
35
. I mm
. 075 mm
. 05 mm
. 025 mm
. 01 mm
.0075 mm
o
(A
.005 mm
, 0025 mm
.001 mm
o>
.00075 mm
.0005 mm
-5
CO
.00025 mm

-6
-4
o>
mm
7.5 x 10  mm
5xl0~ mm
-7
2.5x 10-5 mm
-8
x I0~ 5 mm
-9
F.gure V-21 Settl.ng Velocity for Spher,CAL Particles
327

-------
St/Sj (%)
Settling velocity in feet/
second
Hydraulic residence time
in seconds
Flowing layer depth
Mass of sediment trapped
Mass of sediment entering
impoundment
Pivot axis
10 --
699-
= 50
Figure V-22 Nomograph for Estimating Sediment Trap Efficiency
328

-------
Although it is not specified in Table V-6, the inflow channel depth
at the entrance to Upper Lake is 3 feet. The discharge channel depth
is 10 feet. Assuming "laminar" flow with minimal vertical components,
for clay:
[(Tw x v) + D" - D]
Tw "	d71
n _ [(1.6x1 04x9.3x10"5) +3-10]
^	3
P = -5.5
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 this example is very small (4.5 hours).
Many impoundments will have substantially larger values.
For the sand,
n _ [(1.6x104x7x10"2) +3-10]
3
P = 371
All of the sand will clearly be retained. Note that a clay or very
fine silt of vmax = 5x10 4 ft sec ^ would be only partially trapped.
n _ [(1.6x104x5x10"4) +3-10]
3
P = 0.33
329

-------
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
n _ [(1 .6xl04x5xl0~4) + 3 - 11] _ n
-	3	u
Thus with D=ll, all silt exits the impoundment. If D is only 9 feet, then
p = [(1,6x104x5x10"4) +3-9] = 6g
Two-thirds of the silt is retained. Remember that P represents a
mean value. Clearly during some periods none of the silt will be
retained (due to turbulence, higher velocities) while during other
periods, all of the silt will be trapped. The key here is the word
"mean."
If the impoundment is assumed to be vertically mixed (case B),
compute the mean depth D
n
D = Z D./n
i=l 1
where
n = the number of cross-sections
D.j = depth at the ith cross-section
For Upper Lake,
D = 6.7 = D'
330

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Then
v Tw
P = FTT^
For the clay,
p = 9.3xl0~5xl.6x104 = o 22
6.7
About one-fourth of the clay is retained.
For the sand,
n 7xl0~^xl .6xl04 c~i
P = 	0	 = 167
All of the sand will be trapped within about 1/167 times the length
of the lake. If the daily influent loading of sand is one ton, while
the loading of clay is fifteen tons, then the daily 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
size range of .002mm diameter, and that the water temperature is 5C.
Further, assume tw has been estimated as 2.77 days (10^ seconds), and
that D'=50 feet. From Figure V-21, the settling velocity is about
-4
1x10 feet per second.
-4	4
In Figure V-22, draw a line from 10 on the V axis to 10 on the
tw axis. The point of intersection with axis L is L'. Next, compute
logl050=l.699. Draw a line from this point on the D1 axis to L* .
Where this line crosses the St/Si- (%) axis gives the log of the percent
of the sediment trapped. This is 10 =1.99^2%.
	END OF EXAMPLE V-9 				
331

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5.4 EUTROPHICATION
5.4.1 Introduction
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, microscopic or macroscopic algae, or bottom-rooted or free-
floating macrophytes. The quantity of plant matter present in an impound-
ment is important for several reasons. First, plant cells produce oxygen
during the "light reaction" of photosynthesis, thereby providing an
important source of dissolved oxygen to the water column. Plant cells
also consume oxygen through the process of respiration. Respiration
occurs along with photosynthesis during the day, but also occurs at
night. 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. One such process,
called the "dark reaction", serves to store energy which was intercepted
by the plant cells during the "light reaction". The energy is usually
stored as the simple monosaccaride glucose or as glucose polymers.
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, in turn, pro-
vide food for predatory fishes, mammals, insects, and other higher forms.
Finally, plant development in impoundments is 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
332

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may ultimately support the growth of higher plants and trees.
The gradual filling in of an impoundment in this way reduces its.use-
fulness, and may finally eliminate the impoundment 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 nitrogen, potassium, and phosphorus, are
needed in large quantity. These are termed macronutrients. The
micronutrients, e.g. iron, cobalt, manganese, zinc, and copper, are
needed in very small amounts. In nature, the micronutrients are
usually in adequate supply (although not always), while nitrogen
and phosphorus are commonly growth limiting.
Nitrogen, particularly as nitrate and ammonium ions, is available
to water-borne plant cells to be used in synthesis of proteins,
chlorophyll a^ and plant hormones. Each of these substances is vital
for plant survival.
Phosphorus, an element found in a number of metabolic cofactors,
is also necessary for plant nutrition. The biosynthesis and function-
ing 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
metabolize properly.
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. 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 impoundments. Due to the fact that
333

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many impoundments have very low flow velocities, impoundments represent
excellent biological culturing vessels, and often become choked with
p-lant life.
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 and factors
are present in excess, we say that nitrogen is growth limiting. In
general, N:P ratios in the range of 5 to 10 by mass are usually
associated with plant growth being neither nitrogen nor phosphorus
limited. However, in this range, plant growth may well be limited by
N and P collectively. Where the ratio is greater than 10, phosphorus
tends to be limiting, and for ratios below 5, nitrogen tends to be
limiting. (Chiandani, et al., 1974).
In addition to nitrogen and phosphorus, any necessary nutrient
or physical condition may limit plant growth. For example, in
highly nutritious (eiithophic) waters, algal biomass may increase
until light cannot penetrate, and light is then limiting. At such
point, a dynamic equilibrium exists in which algal cells are
consumed, settle, or lyse (break) at the same rate as new cells are
produced.
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 calculations technique. Some relation-
ships regarding algal productivity have been derived, however, which
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.
334

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The methods presented below are based upon the fact that in most cases
(perhaps 60 percent) phosphorus is the biomass limiting nutrient (EPA,
1972). One such approach has been developed by Vollenweider (EPA, 1972,
Lorenzen, 1976). It may be used to predict the degree of impoundment
eutrophication as a function of areal phosphorus loading. It does not,
however, permit direct estimates of algal biomass to be made. Figure
V-23 shows the relationship as a plot of phosphorus loading ()
versus the ratio of impoundment mean depth (2) to hydraulic residence
time (t ). As indicated in the plot, it is possible to predict on a
w
preliminary basis, whether an impoundment will have eutrophication
problems. Figure V-24 shows where 133 eastern U.S. impoundments are
located on the same kind of plot.
Before considering application of any of the methods to assess
eutrophication, 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.
	 EXAMPLE V-10 	
Big Reservoir and
The Vollenweider Relationship
To use the Vollenweider relationship for phosphorus loading,
data on long-term phosphorus and nitrogen loading rates must be avail-
able. It is also important that the rates represent average loading
conditions over time because transient phosphorus loading pulses will
give misleading results. Big Reservoir has the following characteristics:
Big Reservoir
Available Data (all values are means):
20 mi =32.2 km
5 mi = 8.05 km
Length
Width
335

-------
10
EUTROPHIC
DANGEROUS
OLIGOTROPHY
PERMISSIBLE
z
'w
Figure V-23 The Vollenweider Relationship

-------
100.0
c\j
E
\
o>
a>
o
QT
o>
c
10.0
"O
o
o i.o
to
a.
V)
o
o
0.1
Eutrophic
u

Oligotrophy
JJLL
J	I I I I I ill
O = Oligotrophic
A = Mesotrophic
~ = Eutrophic
Open Symbols = P-limited
Solid Symbols = N-limited
~ = Present Load
= Present Load Minus 50% MSTP Load
= Present Load Minus 80% MSTP Load
i i i i i i in	|	i i I I mi	|	| | I
10.0	100.0
Meon Depth (m)
1000.0
Hydraulic Retention Time (yrs)
Figure V-24
Plot of the Vollenweider Relationship Showing the
Position of 133 Eastern U.S. Impoundments Impacted
by Municipal Sewage Treatment Plant (MSTP) Effluents
(Matioku. B.trophication Survey, 1976)
337

-------
Depth (Z)'	200 ft = 61 m
Inflow (Q)	500 cfs
Total phosphorus concentration in water column o.8 ppm
Total nitrogen concentration in water column 3.6 ppm
In order to apply the plot in Figure V-23, 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 3.6/.8 = 4.5. Presum-
ably, alqal qrowth in Big Reservoir is not phosphorus limited, and
the Vollenweider relationship for phosphorus is not a good one to use.
In this case, use of a rigorous model is suggested.
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 (Z) 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
338

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influent water, and since no additional data are available on impound-
ment water quality, N:P for influent water will be used.
N:P = 10.6/0.8 = 13.25
Thus algal growth in Bigger Reservoir is probably phosphorus
1imi ted.
Compute the approximate surface area, volume and the
hydraulic residence time (for technique, see sediment section above).
Volume (V) = 20 mi x 10 mi x 200 ft x 52802 =
1? 3	If) 3
1 .12 x 10 *ft = 3.16 x 10 m
Hydraulic residence time (t ) = V/Q =
1.12 x 1012ft3/500 ft3sec_1 = 2.24 x 109sec = 71 yr
Surface area (A) = 20 mi x 10 mi x 52802 =
5.57 x 109ft2 = 5.18 x loV
Next, compute qs
qc = Z/x
w
qs = 61 m/71 yr = 0.86 m yr 1
Compute annual inflow, Qy
Qy = Q x 3.15 x 107 sec yr'1
Qy = 1.58 x 1010ft3 yr"1
Phosphorus concentration in the inflow is 0.8 ppm, or 0.8 mg/1.
Loading (L ) in grams per square meter per year is computed
from the phosphorus concentration, in mg/1:
= 28-3U x .n(* 9 x MJH x	x l ,58xl010 ^
p ft3 lOOOmg I 5.18x10 M
339

-------
Lp = 0.70 gm ^yr~^
Now, referring to the plot in Figure V-23, we would expect that Bigger
Reservoir is eutrophic, possibly with severe summer algal blooms.
	 END OF EXAMPLE V-ll 					
	 EXAMPLE V-12			
The Vol 1enweider Relationship
Using Monthly Inflow Quality "Data
Is Frog Lake eutrophic? Frog Lake's physical characteristics
are as shown below:
Frog Lake
Available Data:
Mean length	2 mi
Mean width	1/2 mi
Mean depth	25 ft
Available Inflow Water Quality Data:
Q (monthly
Month 1972
mean, cfs)
1974
Total
1972
P (mg/1)
1974
Inorganic
1972
N (mg
1974
October
50
65
0.1
0.08
7.2
6.0
November
80
90
0.02
0.02
6.3
2.4
December
40
40
0.03
0.04
3.1
1.5
January
-
-
-
-
-
-
February
-
-
-
-
-
-
March
60
58
0.01
0.02
2.0
1.9
April
80
80
0.01
0.01
2.3
0.50
May
75
76
0.04
0.05
0.55
0.52
June
40
70
0.03
0.08
1 .20
1 .35
July
-
25
-
0.11
-
2.01
August
38
20
0.09
0.04
3.50
1 .29
September
38
25
0.06
0.05
2.80
o
o
340

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First, estimate the mean annual flow and the hydraulic residence
time. To compute mean annual flow,
n.
y i	y
Q = ( Z Z	Q. .)/ Z n.
i=l j=l	1,3 i=l 1
where
Q. . = the individual flow measurements
*  J
y = the number of years of data
n. = the number of observations per year
Q = 1050/19 = 55.3 cfs = 1.75 x 109 ft3/yr
Now estimate the volume, surface area, hydraulic residence time,
and qs
V = 2 mi x 1/2 mi x 25 ft x 52802 = 6.97 x 108ft3 =
1.98 x 107m3
A = 2 mi x 1/2 mi x 52802 = 2.79 x 107ft2 = 2.59 x 106m2
tw = V/Q = 6.97 x 108ft3/55.3 cfs = 1.26 x 107sec = 0.4 yr
qs = 25/0.4 = 62.5
Next, calculate the weighted mean inflow phosphorus and nitrogen
concentrations P and N as follows:
n.	n.
y t	y i
P (or N) = (  Z Q. x C. .)/( Z Z Q. .)
i=l j=l 1,J 1,J i=l j=l 1,J
P = 43.86/1050 = 0.042 ppm
N = 2671.92/1050 =2.54 ppm
341

-------
The N:P ratio in the inflows is 60. Therefore if one of the two is growth
5.4.4 Winter Phosphorus Levels in Predicting Algal Productivity
and Biomass
Another technique, which is also based upon phosphorus loading, may
be even more useful than the Vollenweider relationship because it
permits summer chlorophyll a^ concentrations to be estimated rather
than general impoundment trophic status. The method has been
advanced by several researchers including Sakamoto (1966), Lund (1971),
Dillon (1974), and Dillon,, et al. (1975). Briefly, the method relates mean
summer chlorophyll ^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. Using a least squares method
gives the equation of the line as (Lorenzen, in press):
limiting, it is probably phosphorus. Compute the phosphorus loading, L
28.3U .. 1 q 0.042 mq
p ft3 X 1000 mg x SL X
1 x 1.75x109ft3
2.59xl06m2	yr
L = 0.80
P
Now, referring to the plot in Figure V-23 with Lp = 0.80 and
qs = 62.5, the impoundment is well into the oligotrophic region
END OF EXAMPLE V-12
log (chl a_) = 1.5 log (P)-l.l
(V-15)
or
chl a = 0.08(P)1'5 P<250 mg/m3 = 0.25 ppm
(V-16)
342

-------
1000-
to
2
N
CD
100-
o
tr
LlI
3
CO
<
LlI
i.o-
0.1 |~
 Japanese Lakes
~ Other Lakes
I	10	100	1000
SPRING MEAN TOTAL PHOSPHORUS
MG/M3
Figure V-25 Relationship between Summer Chlorophyll and
Spring Phosphorus (From Lorenzen, Unpublished)
343

-------
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 a^ concentrations, the relationship appears to
be reasonably robust and therefore useful.
Because dried algae contain very roughly 3 percent chlorophyll a
(J.A, Flder, ners. comm., 1S77), dry algal biomass may be estimated from
chlorophyll ^concentration by multiplying by thirty-three. Similarly,
carbon productivity, as in the plot in Figure V-26, may be converted
to total algal biomass. Since a proximate analysis of dried algae has
been determined as (Stumm and Morgan, 1970):
C106H263110N16P1
3550
the gravimetric factor is j272 ~	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 pro-
ductivity with accuracy, more sophisticated approaches may be
necessary.
	 EXAMPLE V-l3 	
Winter Phosphorus and Summer Chlorophyll a
Lake Sara mean spring total phosphorus concentration = .03 mg/1 = 30 mg/m3
chl a = O.OS(P)1"5
chl a^ = 13.1 mg/m3
algal dry biomass =13.1 x 33 = 430 mg/m3
344

-------
2500-
2000-
o>
o 1500-
k.
 1000-
500
0.05
0.10
PO4- (as P, mg/l)
Figure V-26 Maximal Primary Productivity as a Function of Phosphate Concentration
(after Chianeiani, et al., 1974)

-------
Maximal carbon productivity in the impoundment may be estimated from
the curve in Figure V-26 to be about 1950 mgCm~2day_1 or about 5460 mq
-2 -1
dry algal biomass m day
Observe that the two methods may lead to contradictions. In this
case, if Lake Sara is 5 meters deep, the concentration is 5460/5 =
3	?
1092 mg/m . This does not compare well with the 430 mg/m value just
computed, and the discrepancy reflects one inadequacy in use of the
Chiandani curve, namely, that it really does not permit estimates of
concentration to be made. The discrepancy also reaffirms the importance
of applying good judgment in evaluating estimates and in using more
than one technique.
	 END OF EXAMPLE V-13 		
5.4.5 Water Column Phosphorus Concentrations
Two of the three relationships just described for predicting algal
biomass are predicated on phosphorus levels within the impoundment.
Often, phosphorus data will be available only in inflowing water, and
a mechanism is therefore needed to estimate impoundment phosphorus
levels from phosphorus loading. Additionally, it may be desired to
evaluate the effect of changes in loading on impoundment phosphorus
1evels.
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 Dhosphorus concentrations vields the coupled differential
equations:
dCw	M K?ACc Mc CwQ
_w = M 2 s _ J	w _ _w_	(V-17)
dt V V	V V	U)
dC K-, AC	K,AC	K-. K_AC
	s. _ _J	w	_2	s_	1 3 w /.. -1 q\
dt V "	V "	V (V-18)
s s	s
346

-------
Q(i>
K . _ . C . .
2 s
^ater Column
Sediment
/*' \
K (4) (K (l)C(s) )
Figure V-27 Conceptualization of Phosphorus Budget
Modeling (Lorenzen et al., 1976)

-------
C = average annual total phosphorus concentration in
3
water column (g/m )
C = total exchangeable phosphorus concentration in the
sediments (g/m )
M = total annual phosphorus loading (g/yr)
3
V = lake volume (m )
3
Vs = sediment volume (m )
2	2
A = lake surface area (m ) - sediment area (m )
3
Q = annual outflow (m /yr)
= specific rate of phosphorus transfer to the
sediments (m/yr)
= specific rate of phosphorus transfer from the
sediments (m/yr)
= fraction of total phosphorus input to sediment
that is unavailable for the exchange process
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:
C.
cw  rtkTa	
-------
where
by:
Cw = steady-state water column phosphorus
concentration in ppm
C^n = steady-state influent phosphorus
concentration in ppm
The steady-state sediment phosphorus concentration is then given
C. K (1 - K )
c: = 1" 1 /	1*-	(V-21)
s k2(i + (k1k3a/q)T
It is important to observe that these relationships are valid
only for steady-state conditions. Where phosphorus loading is changing
with time, where sediment deposition or physical characteristics are
changing, or where there are long-term changes in 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 coeffi-
cients had the following values:
K.| =43 m/yr
= 0.0014 m/yr
K3 = 0.5
It should be recognized, however, that this model is relatively untested
and that coefficient values for other impoundments will vary from those
cited here.
349

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Based upon the conceptualization (see Figure V-27), it is reasonable
that the coefficients interact. For example, , 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-| 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 = M
w Q + K-j k3a
and
Cw K2
Cs " K7rM9-
M-QC
From (V-22)	K.K., =
w
Computation of , therefore, requires a value for K^. This coefficient,
(K^) unfortunately, is usually unavailable. It represents the fraction of
phosphorus entering the sediment which is not available to return to
the water column. Phenomena contributing to this are steady-state
sediment accumulation, and steady-state chemical precipitation of phospho-
rus, such as with iron to form Fe-^PO^^ .8H2O (vivianite). Lorenzen's
value for Lake Washington was 50%. Because the fraction is likely to vary
significantly from system to system and because the coefficient is
difficult to evaluate, the planner is advised to use 30% as the lower
limit, 50% as a probable value, and 70% as an upper limit for estimating
sediment phosphorus content. The water column concentration is indepen-
dent of changes in because the product of K-j and is a constant.
(V-22)
(V-23)
(V-24)
350

-------
Using Equation (V-24), K~ uniquely defines K,. Then, from Equation
(V-23),
K9 is therefore also defined by fixing Kv providing C and C are known.
c	O	W	S
	 EXAMPLE V-14 	
A Comprehensive Example
Impoundment Water Column Phosphorus
What will be the steady-state concentration of phosphorus in the
water column of Lake Jones following diversion of flow? How will this
affect algal abundance? A first step might be to use the Lorenzen
model to evaluate K-| and and determine whether the impoundment
is at steady state with respect to phosphorus levels in the water column
and sediment. Generally, this is the case where K-jK^ lies in the range
of 20 to 40. If K-jKg is outside of this range, field data should be
obtained for current water column phosphorus.
Available Data (prior to diversion):
Inflows:
Mean Annual
Flow, cfs	Mean P, mg/1
1.	Janes River	75	.15
2.	Jennies River	22	.07
3.	Johns Creek	5	.21
4.	Direct stormwater influx	(nominal,	may be disregarded)
351

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Lake Jones:
Area, A	20 miles2 = 5.6xl08ft2 =5.2xl07m2
Volume, V.	3.08xl0nft3 = 8.73j<109m3
Sediment volume, Vg	Irrelevant for steady-state solution
Phosphorus (water column)	.01 mg/1
K3 = 0.5
M-QC
v -	w
l Kx~a
3 w
 [(-* *4^) ~	+(i^ *^)1
28.3l 1 q 3.16xl07sec
X 	o	 X i nnn 	 X		
ft3	1000 mg	yr
M = 1.24x107 gP yr-1
Q = (75+22+5)ft3 3.16x107sec = 3.22xl09ft3 = 9.13xl07m3
^ ""	sec	yr	yr	yr
Cw = .01 mg/1 = .01 g/m3
( 1 .24x107qP 9.1 3x107m3 0.01q\\ /
= I yr - yr	m3 ))/
/. 5 x	x 5.2 x 10 V ^ = 44^:
K-j K3 = 44 x 0.5 = 22
This approach, therefore, does not give reason to suspect non steady-
state conditions for water column phosphorus. Assuming there are no other
reasons for suspecting non steady-state phosphorus levels, it is feasible
to estimate the new water column P concentration after diversion.
352

-------
The diversion, which is for irrigation purposes, has resulted in
lowering the mean annual inflow from Jennies River to 1 cfs with an
average annual phosphorus concentration of 0.01 mg/1. Additionally,
there is a reduction of flow in Janes River to 55 cfs. The new
phosphorus concentration in the water column can be computed as follows
Q = 55+22+1 = 78cfs x 3-16x17sec = 2.46xl09  = 6.98xl07 
yr	yr	.yr
Compute the net equivalent inflow as M:
M =	JSmtL + lfti ^Olraa +
new lsec	1	Sec	1
28.31 1	1 g	3.16xl07sec
X ft3 X 1000 mg x yr
Then, applying Equation V-22,
C , x = 8'3^x16	T = 6.9xl0~3 mgl"1
w(new) 6.98x10 +22x5.2x10
Compare the new water column concentration, .0069, to the old
value, .01 mg/1. Now refer to the methods presented earlier in this
section. To apply the Vollenweider relationship, first to the pre-
diversion status of Lake Jones, compute q$:
5 ft3 -21 mg \
Sec x 1 /
8.33x106gPyr_1

Z =
8.73x109m3
5.2x10^
= 168 m
353

-------
xw = 8.73xl0^m^/9. 13x10^m^yr'^ = 95.6 yr
qs = 168/95.6 = 1.76 m yr"1
Compute phosphorus loading:
M
p A
7 ~ ""1	-2.-1
L = 1  24x10 pr_=Q 24 gm-2yr
p 5.2x10 jn
Referring to Figure V-23with qg = 1.76 and Lp =0.24, one can see
that this lake may have eutrophication problems under pre-diversion
condi tions.
After the diversion,
T. . =
8.73xl0^m^ _ 125 yr
w 6.98xl07m^/yr
Assuming the lake depth is not materially changed over the short term,
qs = 168/125 = 1.34 ^
For the new conditions,
M = 8.33 x 106 gP yr"1
I = 8.33x106 g yr 1 = ]6 qp/m2
P 5.2xl07 m2
354

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Now, according to the Vol 1enweider plot (Figure V-23), this is in the
region between "dangerous" and "permissible" - the mesotrophic region.
Under the new circumstances, algal blooms are less likely than before
the flow diversions were established, but blooms are by no means to
be ruled out.
Turning now to an estimate of algal biomass under pre-diversion
conditions,
chl a = O.OS(P)1'5
chl a_ = 0.08 ( 0.01x1000)^= 2.5 mg/m^
Dry algal biomass - 2.5x33 = 82.5 mg/m^
Under post-diversion conditions,
chl a_ = 0.08( .0069x1000)^"5 = 1.5 mg/m^
3
Dry algal biomass - 1.5x33=49.5 mg/m
Note that these low levels of chlorophyll a.almost certainly mean that the
lake is oligotrophia and that the Vollenweider method suggests worse
conditions than may actually exist in this case.
	 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, 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.
355

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BOD exertion is not the only sink for DO. Table V-9 lists
important sources and sinks of impoundment dissolved oxygen.
TABLE V-9
SOURCES AND SINKS OF
IMPOUNDMENT DISSOLVED OXYGEN
Sources
Sinks
Photosynthesis
Atmospheric reaeration
Inflowing water
Rai nwater
Water Column BOD
Benthic BOD
Chemical oxidation
Deoxygenation at surface
Plant and animal respiration
Many of the processes listed in Table V-9 have a complex nature.
For example, the atmospheric reaeration rate is dependent in part upon
the near-surface velocity gradient over depth. The gradient, in turn,
is influenced by the magnitude, direction, and duration of wind, as
well as the depth and geometry of the impoundment.
Photosynthetic rates are affected by climatological conditions,
types of cells Dhotosynthesizing, temperature, and a number of bio-
chemical 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
356

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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 strati-
fied impoundment and to gain an appreciation of both the utility and
limitations of the approach presented later, it is useful to briefly
examine a typical dissolved oxygen model. Figure V-28 shows a geo-
metric representation of a stratified impoundment. As indicated
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-29;
The phenomena usually taken into account in an impoundment DO
model include:
	Vertical advection
	Vertical diffusion
e Correction for element volume change
	Surface replenishment (reaeration)
	BOD exertion utilizing oxygen
	Oxidation of ammonia
	Oxidation of nitrite
	Oxidation of detritus
	Zooplankton respiration
	Algal growth (photosynthesis) and respiration
	DO contribution from inflowing water
	DO removal due to withdrawals
Many of the processes are complex and calculations in detailed
models involve simultaneous solution of many cumbersome equations.
357

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tributary
inflow,
evaporation
tributary	^
inflow
Vertical
advection
control
slice
outflow
Figure V-28 Geometric Representation of a Stratified
Impoundment (From Hec, 1974)
358

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ATMOSPHERE
CARBONACEOUS
BOD
DISSOLVED
OXYGEN
?t~b
/NITRATE \v_/
V^f.'l TRCGEM jT
ALGAE
ZOOPLANKTO?]
NITRITE
NITROGEN
FiSH
BENTHIC
ANIMALS
< ORGANIC	\d-
SEDIMENT	J
V	[
< SUSPENDED
DETRITUS	Jr1
A
CARBON
DIOXIDE
CARBON
AMMONIA
NITROGEN
PHOSPHATE
PHOSPHORUS
TOTAL
INORGANIC
CARBON
\
\ ^
e,m\
 R N-
\
E^
h^7
HARVEST
R r>
B
A	Aeration
B	Bacterial Decay
C	Chemical Equilbrium
E	Excreta
G	Growth
M	Mortality
P	Photosynthesis
R	Respiration
S	Settling
H	Harvest
Figure V-29 Quality and Ecologic Relationships
(From Hec, 1974)
359

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Among the processes simulated are zooplankton-phytoplankton interactions,
the nitrogen cycle, and advection-diffusion. Thus it is clear that a
model which is comprehensive and potentially capable of simulating DO
in impoundments with good accuracy is not appropriate for hand calcu-
lations. A large amount of data (coefficients, concentrations) are
needed 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 ^concentrations are very low.
Hand calculations must be based upon a greatly simplified model
to be practical. Since some DO-determining phenomena are more important
than others and if some assumptions are made about the impoundment
itself, it is feasible to develop such a model.
5.5.2 A Simplified Impoundment Dissolved Oxygen Model
For purposes of developing a model for hand calculations, the
following assumptions are made:
	The only condition where DO levels may become dangerously
low is in an impoundment hypolimnion and during warm
weather.
	Prior to stratification, the impoundment is mixed. After
strata form, the epilimnion 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 minor source is influent BOD.
Following formation of strata, sources and sinks of BOD are
BOD settling out onto the bottom, water column BOD at the time
360

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of stratification, and benthic BOD.
	Photosynthesis is unimportant in the hypolimnion as a
source of DO.
	Once stratification occurs (a thermocline gradient of
1C per meter of depth or greater) no mixing of thermo-
cline and hypolimnion waters occurs.
	BOD loading to the unstratified impoundment and to the
hypolimnion are in steady-state for the computation
period.
5.5.2.1 Estimating a Steady-State BOD Load to the Impoundment
Equation V-25 is an expression to describe the rate of change of BOD
concentration as a function of time:
$ = Ka - ksC - k,C - SC	(V-25)
where
C = the concentration of BOD in the water column in mgl'^d
-1
kQ = the mean rate of BOD loading from all sources in mgl
k = the mean rate of BOD settling out onto the impoundment
-1
bottom in day
k-j = the mean rate of decay of water column BOD in day"^
0 = mean export flow rate in lday"^
V = impoundment volume in liters
361

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Integrating Equation V-25 gives:
, _ (ka * kbCo'e'kbt) - ka (v-26)
4 "	kb
where
Ct =	concentration of BOD at time t
C =	initial concentration of BOD
k =	-k -k - 9-
b	Ks K1 V
To estimate the steady-state loading of BOD, we set dc/dt = 0 and
obtain
where
Css = steady-state water column BOD
Thus Equation (V-27) may be used to estimate a steady-state water column
BOD concentration and Equation (V-26) may be used to compute BOD as a
function of time, initial concentration of BOD, and the various rates.
5.5.2.2 Rates of Carbonaceous and Nitrogenous Demands
The rate of exertion of BOD and therefore the value of is
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 in-
volved. Nearly all of the biochemical oxygen demand in impoundments
is 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.
362

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Carbohydrates (celluloses, sugars, starches) and fats are essentially
devoid of nitrogen. Proteins, on the qther 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-30, which shows the difference graphically and as a function of
time and temperature, 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 nitrifiers 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 repre-
sented by first order kinetics. That is, the rate of oxidation is
directly proportional to the amount of material remaining at time t.
_ wr	(V- 28)
dt " ~kL
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 k^ was first determined by
Phelps in 1909 for sewage filter samples. The value was 0.1 (Camp,
1968). More recent data show that at 20C, 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 15C. The
relationship for correcting k-| for temperature is:
363

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20C
9C
C Q.
32 36 40 44 48
60
20 24
Period of Incubation, Days
Figure V-30 Rate of BOD Exertion at Different Temperatures
Showing the First and Second Deoxygenation
Stages

-------
kl,(j) kl ,(20C) 0^T"20^	(V-29),
where
T = the temperature of reaction
0 = correction constant = 1.047
However, Thereault has used a value for 6 of 1.02, while Moore
calculated values of 1.45 and 1.065 for two sewages and 1.026 for
river water (Camp, 1968).
Streeter has determined the rate of the nitrification or second
deoxygenation stage in polluted streams. At 20C, k-| for nitrification
is about 0.03 (Camp, 1968). Mobre found the value to be .06 at 20C
and .035 at 10C (Camp, 1968). For purposes of this analysis, BOD
exertion will be characterized as simple first order decay using a
single rate constant.
Benthic 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 very more than values for k-j
in 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-10) for a sludge depth of 1.42 cm up to 4.65 g/m2 day
for a sludge depth of 10.2 cm (Camp, 1968). 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
2	9
0.46 g/m day for 10.2 centimeter depth sludge up to 0.76 g/m day
for 1.42 centimeter depth sludge.
365

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TABLE V-10
OXYGEN DEMAND OF BOTTOM DEPOSITS
(AFTER CAMP, 1968)
Benthic
Depth
(mean) cm
Initial
Volume of _2
Solids, kqm"
Initial Area Demand
k4(20C)
L 'gm 2)
Initial
Demand
-2 . -1
qm day
10.2
3.77
739
4.65
.0027
4.75
1 .38
426
3.09
.0031
2.55
0.513
227
1.70
.0032
1.42
0.188
142
1.08
.0033
1.42
0.188
134
1.02
.0033
The constant loading rate (k ) used in Equation (V-25) is best esti-
a
mated 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, k may
a
be estimated using this value and adopting some percentage of maximal
primary productivity (see Figure V-25). Thus,
ka(algae) = SMP x 10"3/D	(V-30)
where
kfl(algae) = algal contribution to BOD loading rate
S = stoichiometric conversion from algal biomass as
carbon to BOD = 2.67
M = Proportion of algal biomass expressed as an
oxygen demand (unitless)
-2 -1
P = Primary production in mgCm day
366

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The difference between algal biomass and the parameter M repre-
senting the proportion of algal biomass exerted as BOD may be conceptu-
alized as accounting for such phenomena as incorporation of algal bio-
mass into fish tissue which either leaves the impoundment or is harvested,
loss of carbon to the atmosphere as CH^, and loss due to outflows.
The settling rate coefficient, kg in Equation (V-25) must be esti-
mated for the individual case. It represents the rate at which dead
plant and animal matter (detritus) settles out of the water column
prior to oxidation. Clearly, this coefficient 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 kg while turbulence
and small organic fraction particle sizes will give small values for kg.
5.5.2.3 Estimating a Pre-Stratificatjon 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 (D.J. Smith, pers. comm.,
November, 1976). Table V-ll shows saturation dissolved oxygen levels
for fresh water as a function of temperature, and DO levels may be
estimated accordingly.
367

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TABLE V-ll
SATURATION DO LEVELS IN FRESH WATER AS A
FUNCTION OF TEMPERATURE (CHURCHILL, ET AL., 1961)
(ATMOSPHERIC PRESSURE = 760 MM Hg, TDS = 0 mg/1)
Temperature
DO, ppm (Saturation)
0
14.65
5
12.79
10
11.27
15
10.03
20
9.02
25
8.18
30
7.44
5.5.2.4 Estimating Hypolimnion DO Levels
The final step in use of this model is preparation of a D0-
versus-time plot for the hypolimnion (or at least estimation of DO
at incipient overturn) and estimation of BOD and phosphorus loadings
which result in acceptable hypolimnion DO levels. An equation to
compute DO at any point in time during the period of stratification
is
jj& -k-jC-k^L/D	(V-31)
where
0 = dissolved oxygen in ppm
k^ = benthic decay rate in day"^
_2
L = areal BOD load in gm
D = depth in m
The second term in the equation requires that an estimate be made of
the magnitude of BOD loading in benthic deposits. To do this within
the present framework, it is assumed that BOD settles out prior to
368

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stratification and that following stratification, surface velocities
are adequately high and density gradients steep to ignore settling of
mass into the hypolimnion. The pre-stratification benthic demand
is a function of the amount of BOD settling and the rate of benthic
BOD decay. Based upon the rate of settling used earlier in estimating
a steady-state BOD concentration (Equation (V-25)) and rate of decay
for conditions prior to stratification, the rate of benthic matter
accumulation is:
t = ksCssD"k4L	
where
Css = concentration of BOD in the water column in gm
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:
Lt . (ksDCss-Vs* ^	(V 33)
For steady-state deposition (dL/dt = 0, DksCss= constant),
k C D
Lss  -TT-
where
_2
L$s = steady-state benthic BOD load in gm
Application of Equation (V-34) with and k^ appropriately
chosen for the month or two preceding stratification will give an
estimate of the benthic BOD load upon stratification. Application
369

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I
of Equation (V-33) gives the response of L to different water column
BOD (steady-state) loading rates and changes in rats'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
HF = ~k4L + DksC	(V-35)
Since
dC
dt
= -ksC -k^C = ~(k1+ks)C
1 (V-36)
and
C = C e"^kl + ks}t
t o
(V-37)
3T = -k1L + D*sCo 8" 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).
370

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The equation presented earlier (Equation V-31) for hypo 1 i-mnion
DO was:
3T = -k,C -k4L/D
Equation (V-31) is not integrable in its present form, but since L
and C are defined as functions of t (Equations (V-39) and (V-37)
respectively), it is possible to determine dissolved oxygen in the
water column. The equation for oxygen at time t is:
where
Ot =	dissolved oxiygen at time t
0Q =	dissolved oxygen at time t = 0
AO^ =	dissolved oxygen decrease due to benthic demand
A0C =	dissolved oxygen decrease due to hypolinminion BOD
From Equation (V-39), and using l_ss as Lq and Css as CQ,

Solution of Equation (V-40) gives an estimated DO concentration in
the hypolimnion as a function of time.
(V-40)
(V-41)
and from Equation (V-37),
(V-42)
371

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EXAMPLE V-l5
Quiet Lake
(Comprehensive Example)
Quiet Lake is located a few miles south of Col ton, New York. The
lake is roughly circular in plan view (Figure V-31) and receives
inflows from three tributaries. There is 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-12 shows
characteristics of Quiet Lake, Table V-l3 shows tributary discharge
data along with withdrawal and outflow levels, and Table V-l4
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 of the hypolimnion, and what is its volume,
and what is the distribution of hypolimnion mean temperatures during
the period? To answer these questions, either use field observation
data, or apply some computation technique such as that presented earlier
in this section. Assuming that methods presented earlier are used, the
selection of appropriate thermal profile curves hinges around three
factors. These are
	Climate and location
	Hydraulic residence time, and
	Impoundment geometry
372

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CO
SUUSVILLE
QUIETOWN
tori BoondQr*
*0,e hack R'dl3e
[o] PUMP HOUSE
~ STREAM QUALITY
AND FLOW STATION
RUNOFF QUALITY
lJ SAMPLING STATION
SAMPLES TAKEN FROM SMALL
EROSION CHANNELS NEAR LAKE
Figure V-31 Puiet Lake and Environs
373

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TABLE V-12
CHARACTERISTICS OF QUIET LAKE

Quiet Lake



Length (in direction of flow)
3.5 miles =
o
CO
CO
ft.
Wi dth

4.0 miles =
21 ,120
ft.
Mean Depth

22 ft.


Maximum Depth

27 ft.


Water Column P

0.014
-------
TABLE V-13 (Continued)


First Creek
(Station 5)


Month
Mean
Flow, cfs
Total N
Total P
BOD




Ppm

October

5
1 .0
.01
0.5
November

3
2.0
.01
1.0
December

2
0.5
.02
1.5
January

2
1.2
.01
1.0
February

3
1.3
.02
0.8
March

4
2.3
.01
0.6
Apri 1

6
2.0
.01
0.5
May

8
1.8
.02
0.6
June

10
1 .6
.01
0.8
July

8
1 .4
.01
0.8
August

6
1.5
.00
1.0
September

4
0.8
.00
1.2


Second Creek (Station 4)


Month
Mean
Flow, cfs
Total N
Total P
BOD




ppm

October

14.0
15
.15
7
November

13.0
16
.08
8
December ,

12.5
10
.20
10
January

5.0
9
.15
7
February

1.2
12
.12
7
March

2.0
13
.10
6
April

2.5
8
.11
7
May

4.0
6
.07
9
June

8.0
5
.08
12
July

12.0
7
.20
3
August

8.0
6
.22
4
September

5.5
8
.25
8
375

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TABLE V-13 (Continued)
Swi ft
River (Stations 2 and 3)
and Pumped Withdrawal

Pumped
Withdrawal, cfs
Mean Monthly
Flow, cfs
Month
Station 2
Station 3
October
22.6
69.5
77.0
November
22.0
50.0
55.0
December
3.5
20.0
?2.0
January
1.2
7.5
9.0
February
0.8
1.2
1.4
March
0.4
9.1
10.1
April
12.0
44.5
48.75
May
24.0
63.2
69.5
June
30.7
100.0
110.0
July
89.5
168.5
184.8
August
29.8
80.6
88.5
September
43.9
91 .3
100.25
Notes: All three tributaries have their headwaters within the shed.
The net inflow-outflow to the groundwater is known to be close to
zero in the two creeks. Swift River is usually about 10% effluent over
its entire length (10% of flow comes into the river from the
groundwater table).
376

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TABLE V-14
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 Precipi- 	Runoff Quality
Month
tation, inches
Total N
Total P
BOD



ppm

October
3.0
6.0
0.1
27
November
2.4
6.5
0.2
37
December
1.0
4.0
0.1
46
January
0.5
3.0
0.008
34
February
0.3
1 .0
0.07
33
March
0.6
1.5
0.1
30
April
2.0
2.5
0.15
40
May
2.8
3.2
0.25
50
June
4.2
3.6
0.20
40
July
7.6
7.0
0.40
37
August
3.5
7.8
0.60
45
September
4.2
9.2
0.80
50
Total
32.1



Note: Infiltration to the water table on a monthly basis accounts for
roughly 30% of precipitation volume.
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 pro-
vide good shielding, so the next task is to estimate the hydraulic
residence time to select a specific set of plots.
377

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Inspection of all Burlington plots indicates that stratification
is likely to occur at most from May to August. Accordingly, for pur-
poses of plot selection, we are most interested in a mean hydraulic resi-
dence time based on flows in the period from about March to August. Since
hydraulic residence time (x ) is given by x = V/Q, we compute mean Q
... "
(Q). Q represents the average of tributary inflows during this
period, computed as follows:
j=i _ 8+40+55+85+1 50-1-70 4+6+8+10+8+6 2+2. 5+4 '8+1 2+8
g _	6	+	6	.
(Swift River) (First Creek) (Second Creek)
Q = 68+7+6.08 - 81.1 cfs
However, in order to fully account for mass transport as well as properly
estimate hydraulic residence time, one more factor should be considered.
This is 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 computation is as follows:
Qs= APK(1-L)-^Q.(1-I.)j
where
Qs = stormwater or non-point inflow in cfs (excluding rivers and creeks)
A = area of shed in square miles
n = number of tributaries
Q.j = monthly mean pickup (in cfs) iri the ith tributary
P = monthly total precipitation, in inches per month
I- = percent (expressed as a decimal) of flow
contributed by exfiltration (from the water
table into the channel)
378

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L - the proportion of precipitation lost by infiltration
into the soil (expressed as a decimal)
3	_? _1 _i
K = unit correction = 0.895 ft mo mi in sec
As an example, the computation for October is:
Q = 55 mi2 x 3.0 ^
Ms	mo
**3
x 0.896  x (1-0.3) -
mi in sec
^54(1-0.1)+5(l-0.0)+14(1-0.0)+(77-69.5)(1-0.1)
-- 29.1 cfs
Now, since we know the pumped withdrawal rates as well as the difference
between flows at stations 2 and the sum of 1, 4, and 5, and that the im-
poundment surface is at steady-state over the mouth, we also can estimate
the net infiltration rate from the lake into the groundwater. The infil-
tration rate is (again, for October):
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 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 con-
tribution 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.
Net efflux = Q(sU 1+4+5) -Q2+VQw
- 73.0 - 69.5 + 29.1 - 22.6 = 10.0 cfs
^total
= 81.1 +
6.6+20.7+29.4+41.4+92.5+36.6
6
 - 119 cfs
379

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Then the hydraulic residence time is given by:
tw = V/Q = Trr2D/Q
r -	x 5280
where
L	=	length of the lake in mi.
W	=	width of the lake in mi.
D	=	mean depth in ft.
r	=	radius in ft.
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 tw would still be greater than 200 days. A reproduction of the
appropriate plot from Appendix D is presented in Figure V-32. As indi-
cated, Quiet Lake is likely to be weakly stratified from May to August
inclusive, with a thermocline temperature gradient of about lft~^. The
hypolimnion should extend downward to the bottom from a depth of about
3-1/2 meters, giving a mean hypolimnion depth of
= 5.69x10^ sec = 658 days
D
	Y - 3.5 m = 3.2 meters
3.28 ft ni
380

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X
CL
lu
o
0 10 20 3D
TEMP. C
JUL
2 
a.
UJ
a
x
t
a.
UJ
a
0 10 20
TEMP. C
	NOV	
2 
a_
UJ
a
3D
2 
6			1	
0 10 20 30
TEMP. C
dp*
10 20
TEMP. C
DEC
2 
0_
UJ
o
0 10 20 30
TEMP. C
nuc 	
UJ
CD
30
0 10 20 30
TEMP. C
nm
0 10 20 30
TEMP. C
SEP
10 20
TEMP. C
a_
UJ
a
30
JUN
0 10 20 30
TEMP. C
OCT
0 10 20 30
TEMP. C
BURLINGTON. VERMONT
20' INITIAL MAXIMUM DEPTH
INFINITE HYDR. RES- TIME
MINIMUM MIXING
Figure V-32 Thermal Profile Plots for Use in Quiet Lake Example
381

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The approximate hypolimnion volume, then, is
v" = X VTota1
VH =	x 1 .9xl0] 1- 9.2x101 Jl
Over the period of interest, the hypolimnion mean temperature dis-
tribution is:

Me a n
Temperature, C
Month
March
2.0
Apr i 1
5.5
May
9.5
June
12.5
July
14.0
August
15.5
The next step in use of the DO model is to determine a steady-
state or mean water column BOD loading (k ) and DO level prior to stratifi-
d
cation. This is a multi-step process because of the several 1301)
sources. The sources are tributaries, runoff, and primary productivity.
First, we estimate algal productivity using methods of this chapter
(or better, field data).
Using the curve in Figure V-26 and phosphorus data from Table V-12,
the maximal primary productivity should be in the range 1,400 mg
-2 -1	-2 -1	-1 -1
Cm day to 1,900 mgCm day . To convert to loading in mgl day ,
divide by (1000 lm~^ x 6.7m). This gives the loading as 0.21 to 0.28
mgl~^day~^.
382

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Now assuming that maximal productivity occurs at about 30C and
that productivity rates obey the same temperature rule as BOD decay,
temperature-adjusted estimates of productivity rates can be made. Using
the maximal rate range of 0.21 to 0.28 mgl'^day-^, the adjusted rates
are:
Productivity = (0.21, 0.28) x 1.047^375-3)
= (.06,.08) mgl ^ day ^
Then, according to Equation (V-30) and assuming M" = 1, k, due to algae
a
is estimated by:
k (algae) = 2.67 x (.06, .08) = (.16, .21 ) mgl^day"1
a
The next contributor to water column BOD is BOD leading of inflow-
ing waters. The value to be computed is the loading in milligrams per
liter of impoundment water per day.
/ n Li	\ / n
Daily BOD loading rate = (  L d-Q. . C.  I / VE d.
\ i = i j = l	1 'J / / k=1 k
where n	=	the number of time periods of measurement
V	=	volume of impoundment in liters
d	=	the number of days per time period
L	=	the number of inflows
For all inflows, the value is therefore approximately:
ka(Trib) = (2185 + 48'3 + 643-9 + 14240) x 2-45x1Q6* 1.9x10" = 0.22 mgl
(Swift (First (Second (Storm (Units (Impound-
River) Creek) Creek) water Conversion) ment
Runoff)	Volume)
Now, summing the two contributions:
^a ^a(algae) + ^a(Trib)
ka = (.16, .21 ) + .22 = (.38, .43) mgl^day"1
383

-------
The value of k-j will be assumed as 0.1 at 20C with 0 in Equation
(V-29) equal to 1.047. Then at 3.75C,
kl(3.75C) ^1(20C) X l-047(3-75 2^
= .1 x 1.047^6 -25) = 0.047
Now Q(discharge) (mean fr March and April) and V are known, with
^(discharge) = 26-8 (Swift River> Station 2)
+ 6.2 (pumped withdrawal) x 28-32^ = 935 sec"1
ftJ
V = 1.9 x 101
Then	C - 	-38, 	 = 4 94 5 58
SS (.03+.047+(935/1.9xl011)) " '
For further computations, Css = 5.25 will be assumed.
Since kg has been defined as .03, a steady-state areal concentra-
tion of benthic BOD prior to stratification can be estimated. If
k4(20C) =	anc' ^ss =	usin9 Equation (V-34),
ksCssD
"ss k
4(3.75C)
K4(3 75C) = -003x1.047(3-75_20) - .0014
, .03x5.25x6.7 -,c/1	-2
ss= 	70014	= 754 gra
The next step in evaluating hypolimnion DO depression is to
estimate pre-stratification DO levels. If we assume saturation at the
mean temperature in April (5.5C), the dissolved oxygen concentration
at onset of strata should be about 12.7 (from Table V-ll).
384

-------
Now we have all values needed to plot hypolimnion DO versus time
using Equations (V-40) through (V-42).
Using Lq = L$s
C = C
o ss
k, = 0.lxl.047^9"5_2) = .062, (T = 9.5C for May)
ks = 0.03,
k4 = .003x1.047(9-5"20) = .002, and
t = 5 days ,
and applying Equation (V-42),
k,C.
i0c = f
(1.e-(c1+ks)t)
. 0.062x5.25 /, -(0.062+0.03)5^ . ,
c " 0.062x0.03 ^"e	j - ^
Then, according to Equation (V-41),
L  (V<
1754 . 0.03x5.25 \ / -0.002x5 \ / 0.03x5.25 \
L I 3.2 0.03+0.062-0.002 )\	y y0.03+0.062-0.002 I
( 0.002 \ L -(0.062+0.03)5 \ = 2.35
0TO62+070TJ y	/
Then from Equation (V-40)
t = o -i0c-i0L
05 = 12.7 - by- - 1.94 = 10.26
Solving the same equations with increasing t gives the data in Table V-15.
385

-------
If it has been necessary to develop more data for the remainder of
the stratified period, appropriately updated coefficients might be used
starting at the beginning of each month.
TABLE V-15
DO SAG CURVE FOR QUIET LAKE HYPOLIMNION
Date
aol
>
o
n
t
O
II
+->
0
0
0
5/5
2.35
1 .30
9.05
5/10
4.68
2.13
5.89
5/15
6.99
2.65
3.06
5/20
9.22
2.98
0.50
5/25
11 .54
3.18
0.00
Finally, if it is desired to evaluate the impact of altered BOD or
phosphorus loadings, the user must go back to the appropriate step
in the evaluation process and properly modify the loadings.
	 END OF EXAMPLE V-15 	=	
5.6 APPLICATION OF METHODS AND PRESENTATION OF RESULTS: SOME RECOMMENDATIONS
This chapter has presented several approaches to evaluation of
four impoundment problem areas. These are thermal stratification,
sediment accumulation, eutrophication, and hypolimnion DO/BOD. In
studying any or all of the potential problem areas in an impoundment,
the user should first define the potential problems as clearly as he
can. Often the nature of a problem will change entirely when its
various facets are carefully described and examined en masse.
386

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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 in some meaningful way. Careful tabulation of data and
graphing can themselves sometimes provide a solution to a problem,
negating need for further analysis. Examples of plots of data include
those of the thermal profiles in Figures V-l, V-2, and V-32 above.
Where field observations of temperature are available, the data could
well be plotted in this way. Another approach is to plot the difference
between surface and bottom temperature over time.
Another example of data display is the sediment rating curve
shown in Figure V-6. Plotting the mass discharge rate against flow
for field data will produce a similar scatter plot. The degree of
scatter is an indication of the utility of the data. If the data
show high variability without an apparent trend, then the planner
should collect more data or use an alternative approach. If the
data appear to be well correlated, i.e., there is a clear trend and
little scatter, a line-fitting procedure may be used to obtain an
equation describing as a function of flow.
387

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Precipitation data may be displayed as hyetographs and long
term plots showing annual trends. Runoff data may be plotted as
runoff hydrographs (flow versus time) and tributary flows should
similarly be plotted as a function of time. Pol 1utographs developed
as concentration and as mass transport versus time should also be
prepared for use in such methods as DO-BOD evaluation and assessment
of eutrophication potential.
Following application of the methods discussed in this chapter,
various graphical display methods may be useful for showing computational
results. For example, in evaluating sediment accumulation in an
impoundment, particularly where there is reason to believe that compu-
tations are fairly accurate, a longitudinal profile of the impoundment
might provide the basis for a graphic display. The plot might show
rates of deposition of various grain sizes as a function of time and
distance through the impoundment. Accumulated sediment might be
represented by lines drawn above the bottom with distance from the
bottom of each line representing the magnitude of deposition. Figure
V-33 is an example of this kind of display. Another alternative,
might be to display the percent of inflowing sediment trapped as
a function of grain size. This plot, an example of which is shown
in Figure V-34, could easily contain curves for a number of
impoundments within the study area.
Data on DO sag in the impoundment hypolimnion might be displayed
graphically, although tabular results may be adequate. If a graphic
display is desired, it can be done as in Figure V-35. An alternative
might be to plot final DO (at overturn) as a function of loading.
Loading can be represented as PO^, algal biomass, or BOD.
In all cases, the user must determine how to best display
results. A general guide is to prepare a graphic display wherever
it will facilitate understanding of results, and the display should
388

-------
Five Year Loss of Capacity in an Impoundment
Due to Sediment Accumulation
IMPOUNDMENT
INFLOW
| DISCHARGE
CO
00
CD
2	Sand (100% Trapped)
3	Silt (100% Trapped)
3 Clay (43% Trapped )
Depth represents 5 year accumulation
Figure V-33 Possible Approach to Displaying Sediment Deposition
Rates as Function of Time and Distance Downstream

-------
100"
"O
0)
Q.
CL
o
c

o
0)
CL
IMPOUNDMENT
IMPOUNDMENT
2
IMPOUNDMENT 3
For each envelope, upper curve is for Case B,
Lower curve is for Case A.
Grain Diameter Increases
FIGURE V-34
Displaying Trap Efficiency as a Function of Grain Size

-------
CO
co
14
12
10
4
2
0
0
5
10
15
20
35
40
45
25
30
Time (days)
Figure V-35 An Example of a Plot of DO vs. Time in Impoundment Hypolimnion

-------
be carefully designed so as not to be misleading. Graphs, for example,
should not contain unnecessary breaks in scale, should have the origin
at coordinates (0,0) and should include all pertinent observations of
data set. That is, outlines should not be discarded unless it is
clear that they are, in fact, in error.
In closing, it cannot be overemphasized that display of results
is very important, and in the interest of clarity of results, should
be used to as great an extent as possible.
392

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REFERENCES
Camp, T. R., 1963. Water and Its Impurities. Reinhold Book Corporation.
New York.
Chen, C. W., and Orlob, G. T., 1973. Ecologic Study of Lake Koocanusa
Libby Dam. Corps of Engineers, U.S. Army, Seattle District.
Churchill, M. A., Elmore, H. L. and Buckingham, R. A., 1961. "The
Prediction of Stream Reaeration Rates", Tennessee Valley Authority.
Chiaudani, G. and Vighi, M., 1974. "The N:P Ration and Tests with
Selenastrum to Predict Eutrophication in Lakes", Water Research,
Vol. 8, pp 1063-1069.
Dillon, P., 1974. "A Manual for Calculating the Capacity of a Lake for
Development", Ontario Ministry of the Environment.
Dillon, P. and Rigler, F., 1975. Journal Fisheries Research'Board of
Canada, Vol. 32, No. 9.
Hydrologic Engineering Center, Corps of Engineers.. 1974. Water Quality
for River-Reservoir Systems. U.S. Army Corp of Engineers.
Linsley, R. K., Kohler, M.A., and Paulhus, J. H., 1958. Hydrology for
Engineers. McGraw-Hill Book Company; New York.
Lorenzen, M. W., 1976. "Long-Term Phosphorus Model for Lakes: Application
to Lake Washington", in Modeling Biochemical Processes in Aquatic
Ecosystems, Ann Arbor Science Publishers.
Lorenzen, M. W., 1977. "Phosphorus Models and Eutrophication", in press.
Lorenzen, M. W.,.and Fast, A., 1976. A Guide to Aeration/Circulation
Techniques for Lake Management: For U.S. Environmental Protection Agency
Corvallis, Oregon.
Lund, J., 1971. Water Treatment and Examination, Vol. 19 pp 332-358.
Marsh, P. S., 1975. Siltation Rates and Life Expectancies of Small Headwater
Reservoirs in Montana. Report No. 65, Montana University Joint Water
Resources Research Center.
Sakamoto, M., 1966. Archives of Hydrobiology, Vol. 62. pp 1-28.
Stumm, W., and Morgan, J. J., 1970. Aquatic Chemistry. Wiley-Interscience;
New York.
393

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U.S. Department of Commerce, 1968. Climatic Atlas of the United States
U.S. Department of Commerce, Environmental Sciences Services
Administration Environmental Data Service; Washington, D.C.
U.S. Environmental Protection Agency, 1975. National Water Quality
Inventory. Report to Congress, EPA-440/9-75-014.
394

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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 on estuaries (DeFalco, 1967).
Estuaries are the terminal or transfer point for essentially all water-
borne national and international commerce in this country, and biolog-
ically 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 nonconservative 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 geolog-
ically than any other formation found on the continent (Schubel, 1971).
Sedimentation processes, for example, are filling and destroying all
estuaries. While this process is always rapid in a geological sense,
the actual length of time required for complete estuarine sedimenta-
tion 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 estu-
aries 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 program which may be used
to provide initial estuarine water quality assessment and predicition.
Its purpose is two-fold. First, the planner will be provided the
capability of making elementary assessments of current estuarine water
quality. Second, a methodology is presented by which the planner can
395

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evaluate changes in water quality which might result from future
changes in waste loading Datterns.
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 this chapter 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 .necessary. 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 within a 208 area.
These should then be more fully assessed using computer models or other
sophisticated techniques, as required.
6.1.2 Estuarine Definition
It is difficult to provide a concise, comprehensive definition
of an estuary. The basic elements included in most current definitions
are that an estuary is:
a.	a semi-enclosed coastal body of water,
b.	freely connected to the open sea,
c.	influenced by tidal action, and
d.	a water body in which sea water is measurably diluted
with fresh water derived from land drainage {Pritchard,
1967 and 1971).
The seaward end of an estuary is established by the requirement
that c.n estuary be semi-enclosed. Because this boundary is normally
defined by physical land features, it can be specifically identified.
396

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The landward boundary is not as easily defined, however. Generally
tidal influence in a river system extends further inland than does
salt intrusion. Thus the estuary will be limited by the requirement
that both salt and fresh water be measurable present. Accordingly, the
landward boundary my be defined as the furthest measurable inland
penetration of sea salts. The location of this inland boundary will
vary substantially from season to season as a function of stream flows
and stream velocities and may be many miles upstream from the estuarine
mouth (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 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 segre-
gating 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 re-
sulting variations in pollutant dispersion from estuarine type.to type
make such a separation of estuaries 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.
a. Drowned River Valley (Coastal Plain Estuary). These
estuaries are the result of a recent (within the last
10,000 years) sea level rise which has kept ahead of
397

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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 characteristically broad, relatively
shallow estuaries (rarely over 30 meters deep) with
extensive layers of recent sediment.
b.	Fjord-like Estuaries. These estuaries are usually
glacially formed estuaries which are extremely deep
(up to 800 m) but have 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
Washi ngton.
c.	Bar-built Estuaries. When offshore barrier sand islands
build above sea level and form a chain between headlands
broken by one or more inlets, a 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 hydro-
dynamical ly. A number of examples of bar-built estuaries
can be found along the southeast coast of the United
States.
d.	Tectonic Process estuaries. Tectonic estuaries exist
as the result of major tetonic events (tectonic plates
with associated faulting or subsidence and coastal
volcanic activity). San Francisco Bay is a good ex-
ample of an American estuary of this type.
Based on this topographic classification system, the vast majority
398

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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 based on physical processes is more useful,
as described below. Further, the parameters used in calculating
physical process classifications 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 par-
ameters, 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, partially 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, Duxbury, 1970, Pritchard, 1970, and Dyer, 1973, among
others) and are summarized below.
a. Stratified (Salt Wedge) Estuary. In this type of estuary,
large fresh water inflows ride over a salt water layer
which intrudes landward along the estuary bottom. Gen-
erally there is a continuous inland flow in the salt
water layer as friction between the salt and fresh water
layers entrains some of this salt water up into the
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. As an ex-
ample of this type, the Mississippi River Estuary is
usually a salt wedge estuary.
399

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SURFACE
BOTTOM
V
SURFACE
BOTTOM
Freshwatsr
SALINITY
VELOCITY
0 ~
s
_ in
I UJ
*Letter correspond to cross section
Figure VI-! Typical PIain Channel Salinity and Velocity
Profiles for Stratified Fstijaries
400

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b.	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 normal-
ly well mixed.
c.	Partially Well Mixed. Partially well 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 strat-
ified estuaries, but are much less steep. While velocity
at all depths normally reverses with ebb and flood tide
stages, it is possible for net inward flow to be main-
tained in extreme lower layers. Typical salinity and
velocity profiles and a longitudinal schematic flow
diagram are shown in Figure VI-3. There are many par-
tially mixed coastal plain estuaries in the United States,
the James River Estuary being typical.
Classification primarily depends on the river discharge at the time
of classification. Large river flows tend to result in more stratified
estuaries while low flow conditions in the same estuary 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.
*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.
401

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SURFACE
Freshwater
Saltwater
BOTTOM
~Letters correspond to channel cross-sections.
Figure VI-2 Typical Main Channel Salinity and Velocity
Profiles for Well Mixed Estuaries
	a
surface
bottom
salinity
0	^
-o 
0) U)
1	UJ
VELOCITY
0 *
402

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Freshwater
Saltwater
SSSSfwSwwJsSSS
BOTTOM
SURFACE
BOTTOM
SALINITY
VELOCITY
0
-a 
o B
V (A
x uj
SURFACE
*Letters denote channel cross-sections
Figure VI-3 Typical Main Channel Salinity and Velocity
Profiles for Partially Mixed Fstuary
403

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6.1.4 Pollutant-Flow in an Estuarv
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 Pritchard, 1960). The associated spatial
and temporal variability of pollutant levels will have water system
management as well as water quality implications.
If a pollutant flow of greater density than the receiving water
column is introduced into a salt wedge type estuary, the pollutant
sinks into the bottom salt water layer and is advectively carried
inland toward the head of the estuary. Frictionally induced vertical
entrainment of the pollutant into the surface water flow is slow, re-
sidence 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 build 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 in
the surface layer and is readily 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 trans-
ported 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 behave be-
tween the transport patterns exhibited by a well mixed and a stratified
estuary. Pollutant transport is density dependent but is nevertheless
404

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subject to considerable vertical mixing. Eventual flushing of the pol-
lutant from an estuary in this case is dependent on the relative magni-
tude of the net river outflow.
6.1.5 Estuarine Complexity and Major Forces
Before outlining the complexities of estuarine systems, a brief
review of the estuarine dimensions and nomenclature as used in this
chapter will be helpful. This information is shown in Figure VI-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 is shown in the upper right quadrant of Figure VI-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 been 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 three-dimensional
flow field with independent 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 is a trans-
itional zone between fresh water and marine systems, great variations
in a number of major water quality and physical parameters are possible.
For example:
a. pH. Typical ocean pH is 7.3 to 8.4. Typically, rivers
are slightly acidic (pH<7). Thus the pH changes from
acidic to basic across an estuary with resulting major
changes in chemical characteristics of dissolved and
suspended constituents. Estuarine pH variations from
6.8 to 9.25 have been recorded (Perkins, 1974, p. 29)
405

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TOP VIEW
High Tide Line
Low Tide Line
SIDE VIEW
Mean HighTide (MHT)
Mean Low Tide (MLT)
Tidal Prism
Low Tide Volume
ESTUARY LENGTH
Figure VM
Estuarine Dimensional Definition

MHT
Mean
Tide
CROSS SECTIONALVIEW
-Tidal Prism
VMHT '//"Low Tide Volume
HEIGHT
LOW TIDE WIDTH
HIGH TIDE WIDTH

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with surface waters commonly having a higher pH than
bottom waters.
b.	Salinity. Over the length of an estuary, salinity
varies from fresh water levels (typically less than
1 ppt) to oceanic salinity levels (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 variations are especially significant
in estuarine calculations for a variety of reasons.
First, salinity distribution can be used to predict the
distribution of conservative pollutants; second, salin-
ity levels are a prime determinant of water density;
and third, variations in salinity affect other major
water quality parameters. As an example of this last
point, Figure VI-5 shows the effect of salinity varia-
tions on oxygen saturation concentration for a range
of water column temperatures.
c.	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, et al. 1970). These
differences in river flow result in major variations
in estuarine water quality characteristics.
d.	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
*ppt represents parts per thousand by mass. Sometimes the symbol /oo
is used.
407

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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.
O-Salinity (%o)
4.5
9.0
13.5
18.05
22.6
27.1
31.6
'
Z
o

I-
z
Ld
U
Z
o
o
z
o

z
UJ
o
>
X
o
20
'25
30
135
40
145
50
TEMPERATURE (C)
Figure VI-5 Saturation Temperature Salinity Relationships (Green,
1963)
408

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This, in turn, necessitates a large number of individual calculations
to fully analyze the variation of even a single parameter over the
estuary and normally requires the use of 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 of forces includes (from Harleman and Lee,
1969):
a.	Ocean tides
b.	Local wind stresses
c.	Bottom roughness and bottom sediment types
d.	Channel geometry
e.	Coriolis forces*
f.	Nearby coastal features and coastal processes
6.1.6 Simplifying Assumptions
A number of assumptions can be made which reduce the very
complex problem of estuarine hydraulics to something amenable to hand
calculations. Use of these assumptions results in a reduction in
the accuracy of the analysis, a loss of spatially and temporally
specific results (results will be averaged over large time segments and
over large areas of an estuary), and an equating of the number of
estuaries for which this methodology is valid to those meeting certain
qualifying criteria. However, for those estuaries meeting the
* Coriolis forces relate to 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 it propagates 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 counterclock-
409

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qualifications, the methodology will provide a valuable estimate for a
number of water quality parameters.
The basic assumptions involved in the simplifying' process are:
a.	Present salinity distribution can be used as a direct measure
of the distribution of all conservative, continuous flow
pollutants entering the estuary, and can be used as the basis
for calculating dispersion coefficients for one-time dis-
charges.
b.	The vertical water column is assumed to be homogenous.
Calculations will be based on vertically well mixed estuaries,
but can be empirically modified to account for the partially
mixed situation. However, the complexity and multi-dimensional
nature of stratified circulation excludes consideration of
these estuaries.
c.	All estuaries are assumed to be one-dimensional. This assump-
tion is the implicit result of assumptions b and c, which
assume lateral and vertical homogeneity.
d.	Coriolis forces may be ignored. This means that an estuary
may be assumed to be laterally homogeneous through any cross-
section and typically excludes consideration of very wide, slow
moving estuaries since the significance of the Coriolis forces
is inversely proportion to characteristic estuarine water
velocities. Dr. Ralph Cheng (1977) of the United States Geological
Survey has offered a criterion for checking compliance with
wise 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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this assumption using the Rossby number (Ro)*. For R0 values
less than 0.1, Coriolis forces will make a relatively small
contribution to water mass movements. Some error, however,
will be introduced for R0 values above 0.02 to 0.03. For
the level of calculation considered in this report it is
recommended that Coriolis forces be ignored. This assump-
tion is especially applicable to small U.S. estuaries.
However, it must be rememberd that the wider the estuary,
and especially the lower its range of typical velocities,
the greater the error introduced by ignoring Coriolis forces.
e. Only steady-state conditions will be considered. Calculations
will provide values averaged over a tidal cycle**. Further,
it will be assumed that for continuous flows, only the final
steady-state distribution of a pollutant is of concern to the
planner.
*The Rossby number is defined by (Neumann and Pierson, 1966)
R _ characteristic velocity
"typical water velocity". This may
be aproximated by 1/2 of the peak
surface velocity,
the length of the estuary,
earth's rotational rate at the
latitude of the estuary (earth's
rotational rate at the equator
multiplied by the sine of the
lati tude).
**This type of calculation will be called a "net non-tidal" calculation
and provides only the distribution of a pollutant mass at the end of
successive tidal cycles. It does not track variations in its distri-
bution during the tidal cycle from, for example, low slack water to
high slack water and back to low.
where: characteristic velocity =
L =
n =
411

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f.	Wind forces can be ignored. For large, shallow estuaries
(for example, most bar-built estuaries) wind forces are a
major mechanism for both lateral and vertical mixing. The in-
clusion of wind, however, cannot be readily accommodated in
hand calculations. Further, under all but strong and severe
wind conditions, wind is not a major controlling factor in
steady state conditions.
g.	Regular geometry is assumed. It is assumed that, at least over
the length of each segment, the estuary geometry is regular
and can be approximated by a constant cross-section. This means
that the calculations are not valid for many bar-built, fjord-
type, or complex estuaries with large side embayments.
h.	Only one river inflow is allowed. Estuaries with two
significant fresh water inflows have complex hydrodynamic
characteristics, and for these estuaries, computer models should
be used. However, when one fresh water flow is significantly
larger than all others, the dominant river may be considered to
be the only river inflow. All others may be considered as
point source pollutant inflows.
i.	No variations in tidal amplitude will be considered. In many
areas of the U.S., the two high and two low tides occurring
each, day are not equal. As a rule, they go from lower low, to
higher high, to higher low, to lower high, and back to lower
low (Ippen, 1966). Further, higher high tides vary signif-
icantly from spring to neap tide. For purposes of these
calculations all tidal cycles are assumed of equal amplitude.
j. All water leaving the estuary each tidal cycle is replaced by
"fresh" sea water. This assumes that none of the pollutant
flushed out of an estuary with one ebb tide will re-enter the
estuary on the subsequent flood tide. This approximation can be
accounted for in flushing time calculations by reducing the total
412

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tidal flow to an "effective" tidal flow if specific conditions
indicate that a significant percent of tidal water returns into
the estuary (see Section 6.4).
6.1.7 Methodology Summary
The techniques presented in this chapter are based on past investi-
gative work. While there is little in terms of new technique presented
below, this chapter represents a compilation of all major methodologies
applicable to the hand calculation process. There are techniques more
sophisticated than those presented here. However, it is felt that such
techniques are either too cumbersome or require too much input informa-
tion to be amenable to hand calculations.
This chapter constitutes a step-wise methodology. While the
goals and techniques of each step are separately discussed in the
appropriate sections, a summary of the goals of each step and their
sequential order is given here.
1. Existing Water Quality Assessment Determine which estuaries
Step
Goal
 Estimate present estuarine
water quality
have most severe water quality
problems; obtain estimate of
current "worst-case" estuarine
water quality.
2. Future Water Quality Assessment
 Classify Estuary
Determine whether hand calcu-
lations are appropriate for a
given estuary
 Estimate Flushing Time
Determine pollutant residence
time in the estuary; improve
estimate of pollutant concen-
tration
413

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 Calculate New Source
Pollutant Distribution
Estimate the distribution of
pollutants associated with
additional waste loadings;
estimate resulting changes in
estuarine water quality
 Calculate Waste Heat
Distribution
Estimate distribution of
excess heat resulting from a
single thermal discharge
 Estimate Sediment Transport
and Deposition
and bed load movement through
an estuary; identify areas of
critical sediment deposition,
and assess estuarine turbidity
Estimate suspended sediment
An overall schematic diagram for the procedures for the predictive
portion of the estuarine hand calculation methodology is shown in
Fiqure VI-6. The water quality parameters which will be addressed in each
major step of the analytical process are shown in the left hand column of
that fiqure. More detailed schematics for the various components
shown are contained in each associated section of this report. Note
from Figure VI-6 that the hand calculations do not represent a defini-
tive final analysis of estuarine water quality. The results obtained
here will serve only as a screening process to identify areas and
individual estuaries for which application of computer models is
indicated anc will allow the planner to set analytical priorities.
6.1.8 Data Requirements
One consideration in the selection of the techniques presented in
this report was a minimization of data requirements. Still, certain
data will be needed for each estuary in order to use any of the calcu-
lations. These data generally include:
414

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WATER QUALITY
PARAMETERS ANALYZED
DO-BOD
Nutrients
Toxicants
Dissolved Solids
Collform Bacteria
Clorophyl
Conservative Pollutants
Classify Estuary
Calculate
flushing time
calculations
Calculate dispersion
coefficients and
dispersion patterns
Suspended Solids
Sedimentation
Temperature
o-
Calculate
sedimentation
rates

'
Calculat
discharge
e thermal
dispersion
c
End of
Hand Calculations
)

Select marginal and
critical areas for
further study
J
1
EstuarlneI
Computer
Model
Figure VI-6 Diagram of Estuarine Water Quality Calculation
Process
415

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	Existing water quality: In order to assess the effect of
changes in water quality (for example, a population growth-
induced BOD increase through a municipal sewage treatment
system) knowledge of the existing water quality in each
estuary is essential. These basic water quality data should
include dissolved oxygen measurements from mean high tide (MHT)
and mean low tide (MLT)*, temperature distribution through
the estuary for each season, and turbidity levels for raising
river outflows and tidal stages. Measurements of total
dissolved solids (TDS), nutrient levels, and background levels
of pollutants of special concern in each area (e.g., petroleum
hydrocarbons, heavy metals, and radionuclides) will even-
tually be necessary but are not essential to the use of these
hand calculations.
	Estuarine topography: The general topography of each estuary
must be known. Topographical data required will be: cross-
sectional area over the entire length of the estuary, the
tidal prism or intertidal volume as a function of distance
from the mouth of the estuary, and the estuary length.
	Sa1inity: A mean high tide longitudinal salinity profile for
each estuary taken during low river discharge periods will be
required. Other seasonal profiles will be very useful
but will not be essential for these calculations. Without
salinity profiles for more than one season, it will not be
possible to plot stratification-circulation diagram data
for both summer and winter periods (see Section 6.3). This will
reduce the accuracy of the classification process but will not
invalidate it since a one season classification for the low flow
period can be used.
*These terms as used here are synonymous with the terms "mean higher-
high tide" (MHHT) and "mean lower-low tide" (MLLT).
416

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	River discharge: River discharge rates into the estuary
for annual low flow periods (normally measured in cubic feet
per second (cfs)) will be required. Again river discharge
rates throughout the year are desirable but not essential
for these calculations.
*	Velocity profiles: Finally, vertical velocity profiles* for
several stations in each estuary will be needed for at least a
one tidal cycle duration for both low and high river discharge
periods. These stations should be within the main estuary
channel and should include one station near the mouth and
one well upstream toward the head of the estuary.
Further detail on these data parameters and some potential sources
from which they may be obtained will be discussed in each section as
appropriate.
6.2 PRESENT WATER QUALITY ASSESSMENT
The first step in the estuarine water quality assessment must 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
* Surface and bottom velocities are acceptable if more detailed
vertical profiles cannot be obtained.
417

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collection program sponsored by the 208 planning agency should be
undertaken. If at all possible, high tide, and especially low tide
in-situ measurements and samples should be collected along the full
length of the estuary's main channel and in all significant side
embayments. Analyses should then be made in an appropriate laboratory
facility. If funds for such data collection effort are not available,
the use of a mathematical estimation of existing water quality is a
third alternative. One very coarse method for such water quality
estimation is presented here. However, it should be remembered that
actual data is always preferable to a mathematical estimate of water
quali ty.
This section will provide a method for estimating estuarine
water quality and will be useful where data are lacking. Chapter 3
presented methods for evaluating the total direct waste load. Chapter
4 presented methods for evaluating river water quality (concentrations
of pollutants in the river flow). Combining these allows evaluation
of the total waste load enterine an estuary over any time period. This
total load of each individual pollutant type (e.g., conservatives,
BOD) may be converted into average pollutant concentration in the
estuary through use of Equation VI-1 below.
F [E (QjS-j)
\j = 1	J /	(VI-1)
 1	VOL
where c- = average concentration of pollutant "i" in the estuary,
normally in mg/1
c . .= concentration of pollutant "i" in waste load source "j,"
^ J
normally in mg/1
0. = flow rate of discharge "j" (normally obtainable in cubic
feet per second (cfs) or in million gallons per day (mgd)
and must be converted as shown below
418

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n = number of discrete waste loads discharging into the
estuary
F = flushing time (normally measured in tidal cycles)
and VOL = water volume of the estuary at low tide (in cubic feet).
Low tide volumes are often obtainable from the sources of
potential estuarine water quality data previously discussed
or may be estimated from U.S. Coast and Geodetic Survey
coastal map series sheets.
In this equation, measurements of Q. must be converted from cfs or
J
mgd units to cubic feet per tidal cycle. Conversion from cfs units
involves only a time conversion (3600 sec/hour x 12.4 hour/tidal cycle).
From mgd units it involves both a time conversion (1 day/24 hr x
12.4 hr/tidal cycle) and a volumetric conversion (o/| cubic ft/7.8 gal).
Once the waste load is in units of cubic feet/tidal cycle, it may be

multiplied by the flushing time to obtain a total estuarine mass of
pollutant "i".
There are a number of methods available for estimation of flushing
time. This term represents the residence time of a mass of water
(or of a pollutant) within the estuary. In other words, the flushing
time represents the amount of time required to replace all of the fresh
water within the estuary by "new" water from the fresh water (river)
inflow. Two methods of estimating flushing time are presented here.
More explicit versions of both will be used later. (See section 6.4.5).
The more general versions presented below are applicable for this level
of analysis.
6.2.1 Estuarine Fraction of Fresh Water
This method requires average estuarine salinity data (averaged
longitudinally over the length of the estuary and temporally over a
tidal cycle). With this data, F is given by:

-------
where S = oceanic salinity (generally 32 /oo to 36 /oo depending
on location)
Sg = mean estuarine salinity (in parts per thousand, /oo)
and F = flushing time in tidal cycles
6.2.2 Tidal Prism Method
If salinity data are not available, flushing time may be
estimated by
V + P
F = ~~T~	(VI-2b)
where F = flushing time in tidal cycles,
V = low tide volume of the estuary,
and P = estuarine tidal prism (volume of water between low
tide level and high tide level)
These procedures may be repeated for each pollutant parameter to
obtain an overall assessment of estuarine water quality.
6.2.3 Interpretation of Results
The water quality data obtained by this analysis must be
considered as a first estimate. It has provided only an overall
relationship between the gross amount of pollutants entering an estuary
and the water mass within the estuary. In addition to the assumptions
discussed earlier, the following assumptions have been added to these
calculations:
1)	The estuary is assumed to be totally mixed.
2)	All inflows are assumed to disperse throughout the estuary
in exactly the same manner regardless of the discharge
location. In fact, as will be shown in subsequent sections,
420

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the location of discharge will have a major impact on both
the magnitude and peak location of resulting pollutant con-
centration.
3) Pollutant concentrations are assumed constant over time
(over a tidal cycle and from tidal cycle to cycle).
If these approximations result in unacceptably large uncertainties
in current pollutant load estimation the more detailed methods presented
in subsequent sections for the evaluation of changes in water quality
may be applied to the evaluation of present water quality. This process
requires the separate evaluation of each discrete discharge. To avoid
excessive effort in such a calculation, adjacent discharges should be
grouped wherever possible and treated as a single point source. Total
estuarine concentrations of the various pollutants are then estimated
by summing the steady state distributions of each discharge in order
to obtain total concentration over the length of the estuary.
6.3 ESTUARINE CLASSIFICATION
6.3.1 General
The previous section presented a method for making a first
estimate of current estuarine water quality when no actual data were
available. This section begins a calculation methodology designed to
look at the effect of future changes in waste loading patterns.
Because such an analysis will focus on a limited number of discharges
at once, the technique presented will be much more detailed and
sophisticated than those of the previous section.
The goal of the classification process presented below is to
predict the applicability of the hand calculations to be presented.
As described earlier, a number of limiting assumptions have been made
to reduce the complexity of computations. The classification process
is the first step to be taken in the calculation procedure since it
421

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selects those estuaries for which techniques to be presented can be
applied.
6.3.2	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.
A schematic of the classification process presented in this
section is shown in Figure VI-7. The following section will describe
in detail the procedure for use of this system; and show examples of
the procedure.
6.3.3	Calculation Procedure
6.3.3.1 Geometric Pattern
This first step is a subjective one. All of the calculations
used in this chapter assume a single "drowned river valley" estuarine
geometry. The presence of major side embayments not along the central
river channel or of more than one significant fresh water inflow
violates this assumption and means that hand calculations should not
be attempted for that estuary. As can be seen in Figures VI-1 through
VI-3 this does not mean that the estuarine channel must be completely
linear and uniform. However, the farther away from an idealized
channel an estuary is, the larger will be the error in the final water
quality estimations. Figure VI-8 shows examples of three estuaries
for which one might proceed with these calculations, and two estuaries
for which one should not.
422

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estuar^s
geometrically
acceptable .
Calculate circulation
and
stratification parameters
Does ^
estuary meet
criterion
BORDERLINE
	iL	
Calculate tidal prism -
river outflow ratio
^ Does ^
estuary meet
criterion ^
m.
Do not use
		
Proceed to flushing
time calculation
hand calculation.
Go directly to
computer model.
Figure VI-7 Estuarine Classification Schematic
423

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A.	Geometry marginal but could be used.
B.	Major side embayment-should not be used.
C.	Could be used ignoring minor side inflow.
D.	Two fresh water inflows-should not be used.
E.	Typical tidal coastal plain estuary-the type
for which this procedure was designed.
Figure VI-3 Examples of Fstuarine Suitability for Hand Calculations

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6.3.3.2 Stratification-Circulation Diagram
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 intersections on
the graph shown in Figure VI-9. Figure VI-10 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 plots calculated for the mouth and head areas.
The area designations (e.g., la, lb, 2a) on Figure VI-9 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 lb 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 lateral circulation within the estuary.
Designations 2a/b and 3a/b, as was true of la and lb, indicate
increasing degrees of vertical stratification. Type 3b includes
fjord-type estuaries. Area 4 represents highly stratified, salt wedge
estuaries.
The two parameters used with this diagram are described below:
a. Stratification Parameter: The stratification parameter
is defined as*:
Stratification Parameter =	(VI-3)
*The symbol = as used in this chapter implies a definition.
425

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Us
Uf
Figure VI-9 Estuarine Circulation-Stratification Diagram
10
1
3b


10

2o
3q
-2
10
3
10
(Station code: M, Mississippi River mouth; C, Columbia
River estuary; J, James River estuary; NM, Narrows of
the Mersey estuary; JF, 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-1G Examples of Estuarine Classification Plots
(from Hansen and Rattray, 13CC)
426

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where
AS = time averaged difference in salinity
between surface and bottom water
^bottom " ^surface^
and,
S0 = cross-section mean salinity ^bottom + Ssurface^
2
The diagramatic relationship of these values is shown in
Figure VI-11.
b. Circulation Parameter: The circulation parameter is defined
as:
Circulation parameter = ^	(VI-4)
Uf
where
and
Us = net non-tidal sectional surface velocity
(surface velocity through the section
averaged over a tidal cycle) measured in
ft/sec. See Figure VI-11 for a diagramatic
representation of Us>
= mean fresh water velocity through the section
In equation form,
Uf = 	(VI-4a)
i
427

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where
R = fresh water (river) inflow rate measured in
ft^/sec,
and	A. = 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
STRATIFICATION PARAMETER "
u*	s*
AS
SURFACE

BOTTOM
R
* Both U and S values for these profiles are averaged over a tidal cycle (net velocity
and salinity) rather than being instaneous values. Of the two the stratification
parameter is much less sensitive to variations over a tidal cycle and can be approxi-
mated by mean tide values for salinity. Surface velocity (Us) must be average over
a tidal cycle.
Figure VI-11 Circulation and Stratification Parameter Term Diagram
If exact cross-sectional area data are not available, cross-
sectional profiles can be approximated from the Coast and Geodetic
Survey coastal series topographical maps, or, more recently, from NOAA
National Ocean Survey map sheets.
These tv/o parameters should be plotted for high and low river
flow periods and for stations near the mouth and head of the estuary.
428

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The area enclosed by these four points should then include the full
range of possible instantaneous estuary hydrodynamics characteristics.
In interpreting the significance of this plotted area, by far the
greater weight should be given to the low river flow periods as these
periods are associated with the poorest pollutant flushing character-
istics and lowest estuarine water quality. The interpretation of the
circulation-stratification diagrams will be explained more fully
after an example of parameter computation.
	 EXAMPLE VI-1 	
Calculation of Stratification and Circulation Parameters
The estuary for this example is the Typical Estuary which is
shown in Figure VI-12. The estuary is 64,000 feet long, is located
on the U.S. west coast, and is fed by the Running 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).
. . ^Station ^
Station g
OCEAN
Figure VI-12 The Typical Estuary
429

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Necessary salinity data were obtained from the coastal engi-
neering department of the nearby university. USGS gage data were
available for river flow, and, as a result of their own dredging
program, the local district office of the U.S. Corps of Engineers could
provide cross-sectional profiles in the approximate areas of both
stations. The cross-sections are labeled (1) and (2) on Figure VI-12.
The mean low tide depth reading on USGS Coastal Topographic maps was
used to verify Corps data.* Current meters were borrowed from the
School of Engineering at the nearby university and tied to buoy
channel markers at A and B to provide velocity data not available
through the coastal engineering department. The information obtained
from these various sources is shown in graphical form in Figure VI-13.
The calculations proceeds as follows:
a. Stratification Parameter:
STATION
A
bottom surface
33 - 30
31 .5
.095
14.5 - 10.5
12.5
^32
SUMI1ER
31.5 - 24.2
v>!
CM
4 - 2.1
.58
WINTER
27.8
3.25
* While the sources of information mentioned here do not necessarily
have information for all U.S. estuaries, they are the best general
sources for the kinds of data estuarine hand calculations require.
430

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S(%o) AT MEAN TIDE
35
Surface,
53
Bottom
k.

w
O
w
V
2000
2 Years Ago
q*-Last Year
Average
1700
1400
0 
1100
w 00
"q: 500
MONTHS
~ Monthly Average Discharge Rates
WINTER
SUMMER
Flood
(FT/SEC)
~
Ebb
CROSS SECTION OF A	CROSS SECTION OF B
2650'
4300
MHT
MT
MLT
20
Figure VI-13 Typical Fstuary rATA for Classification Calculations
431

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b. Circulation Parameter
1.	Calculate A^'s using cross sectional information
on figure VI-12.
Afl = (630 ft) (20 ft) (H) + (630 ft) (20 ft) +
(1590 ft) (20 ft) (h) =
34,800 ft2
Ab = (2580 ft) (16 ft) {h) + (1720 ft) (16) (H) =
34,400 ft2

For most cross-sections it is advisable to use more finely
divided segments than in the simple example above in order
to reduce the error associated with this approximation.
The method for this calculation, however, is identical re-
gardless of the number of regular segments used.
2.	Calculate U^'s (with R and A. values obtained from
Figure VI-13)
STATION
A	B
3
550 ft /sec -i co ,-2,
	7y- 1.58x10 ft/sec
3
550 ft /sec -1 ,-A lri-3^-. ,
	= 1.60;'.10 ft/sec
3.44x1O^ft^
SUMMER
3.48x10 ft
1800 ft^/sec r t
	15- = 5.17x10 ft/sec
1800 ft3/sec c 00 	
	TP= 5.23x10 ft/sec
WINTER
3.48x10 ft
3.44x10 ft
432

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3.
us -s
Calculate r^
uf
Ug values are read from Figure VI-13. The precise
value for Us is 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
Us may be approximated as (Uebb(ma)<) - UF,ood (Max)
)/2.
A
STATION
0.15 ft/sec
1.58xl0~^ft/sec
= 9.5
0.3 ft/sec
1 .60x10 ^ft/sec
-- = 18.8
SUMMER
0.2 ft/sec
5.17x10~^ft/sec
= 3.9
0.4 ft/sec
5.23x10 ^ft/sec
= 7.65
WINTER
The circulation-stratification plots for Typical Estuary are shown
in Figure VI-14 with points Ag (station A, summer value), Aw (station
A, winter value), B (station B, summer value), and 3 (station B,
s	w
winter values).
433

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3b
AS
So
3a
2a
10-
U:
Uf
Figure VI-14 Estuarine Circulation-Stratification Diagram
As indicated, this estuary shows a significant amount of
vertical stratification (especially at station B) but little evidence
of major lateral non-homogeneity.
			END OF EXAMPLE VI-1 		
6.3.4 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
homogenous it is, and the better that estuary fits the assumptions
associated with this methodology. Thus the closer an estuary lies to
that corner, the smaller the error that will be produced by the use of
these hand calculations. On the stratification-circulation diagram
434

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(Figure VI-9 or VI-14), two types of zonal demarcation can be seen.
First are the diagonally striped divisions between adjacent estuarine
classifications used by Hansen and Rattray to indicate a transitional
period 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 (lower left) are those for which
the hand calculation method may be applied to obtain reasonably
accurate results. Those estuaries falling predominately outside of
this band violate the assumptions of this study to such an extent
that hand calculations should not be used. If an estuary falls within
this latter group, the planner should go directly to the use of computer
models or other methods of water quality analysis. Within the band is a
borderline or marginal zone. Hand calculations should be used for
estuaries falling principally within this zone, however the accuracy
of the calculations will be subject to increased uncertainty.
Turning to Figure VI-14, the Stratification-Circulation diagram
for the Typical Estuary, it is apparent that this estuary lies prin-
cipally within the marginal area. Moreover, the low flow classifica-
tion (line A -B$) also lies primarily within the marginal area. Thus,
from Figure VI-7 the planner for the Typical Estuary should calculate
additional criteria to help determine the suitability of using these
water quality hand calculations. If the Typical Estuary plotted more
predominately below the marginal zone, the planner could proceed with
flushing time calculations since his estuary would then have met
the classification criteria.
It should be noted that the data for the Typical Estuary produced
a fairly tight cluster of data points. As can be seen in Figure VI-15
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 did the Typical Estuary. This increased varia-
tion would produce a far greater spread in the summer and winter
AS/Sq parameter values.
435

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ALSEA RIVER
S(%o) AT HIGH TIDE
25 15
20
WINTER - Peb.9,1968
J
SPRING - May 9,IS WW
33 30 25 20 15 10 5 0
0
10
20
SUMMER - Aug.9,1968
0 I 2 3 4 5 6 7 8 9 10 II 12 13 14
MILES UPSTREAM
Figure VI-15 Alsea Estuary Seasonal, Salinity Variations
(from Giger, 1972)
6.3.5 Flow Ratio Calculation
If application of the above classification procedure results in
an ambiguous outcome regarding applicability of the hand calculation
approach, another criterion should be applied. This is the flow ratio.
Schultz and Simmons (1957) first observed the correlation between the
flow ratio and estuary type. They defined the flow ratio for an estuary
x
i-
Q_
LU
r*i
20
30 2511510 5
436

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as:
FR = 	(VI 5)
Kt
where
FR = the flow ratio,
R = the river flow measured over one tidal cycle
3
(measured in ft )
and
3
= the estuary tidal prism (in ft )
Thus the flow ratio compares the tidally indited 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 asso-
ciated estuary was normally highly stratified. 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. For the purposes of hand calculations,
a flow ratio of 0.2 or less warrants inclusion of the estuary in the
hand calculation process. Flow ratios in the range 0.2 to 0.3 should
be considered marginal. Such estuaries may be included but only
with the understanding that the hand calculations should produce
increased error in water quality estimates. Finally, estuaries
with flow ratios greater than 0.3 should not be included.
	 EXAMPLE VI-2 	
Flow Ratio Calculation
This example uses data for the Alsea Estuary in Oregon. River
outflow is calculated for the low flow period of the year. Associated
flow data were obtained from Oregon State University flow gages located
approximately 2 miles above the estuary. From these data.
437

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R = (104 ft3/sec) (3600 sec/hour) (12.4 hrs/tidal cycle) =
4.64 x lO^ft^/tidal cycle
Tidal prism data were available from previous work by Goodwin,
et al., (1970). From these data,
PT = 5.05 x 108ft3/tidal cycle
Thus
FR = B. = 4'64 x 10^ = 9.18 x 10"3< 0.1
HT 5.05 x 10a
Accordingly, Alsea Estuary should be considered well mixed in the
summer low flow period,^and would qualify for hand calculations.
END OF EXAMPLE VI-2
In Example VI-2, tidal prism data were available through a local
university. This will be the case for many estuaries, both large and
small, around the country. Where it is not the case, however, N0AA
coastal charts may be used to estimate the difference between mean
high tide and mean low tide estuary surface areas. As can be seen in
the cross-section diagram in Figure VI-16 the estuarine 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-16, the estuary
can be conveniently subdivided into longitudinal sections for this averag-
ing process, to reduce the resulting error. Table VI-1 lists tidal prisms
estimated for many U.S. estuaries. These values may be used as an
alternate to P calculations.
It should be emphasized that application of the flow ratio
criterion is not a refinement of the stratification-circulation diagram
method. In fact just the opposite is true. However, when the latter
438

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MHT Surface
Mean Tide
MLT Surface
nL- ;
TIDAL
HEIGHT**
P^ section = tidal height* MHT + MLT w-jdth ^ tidal height x MT width
Py estuary = V P^ for each section
* Widths obtained from or from MOAA tide table for the area
** Available from local Coast Guard Stations
Figure VI-16 Estuary Cross-Section for Tidal R?ism Calculations
method produces inconclusive results, use of the flow ratio which
employs somewhat different estuarine characteristics can reduce the
uncertainty of the outcome based on stratification-circulation data.
439

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TABLE VI-1
TIDAL PRISMS FOR SOME U.S. ESTUARIES*
(FROM O'BRIEN, 1969 AND JOHNSON, 1973)
Estuary
Coast
Tidal Prism
(ft3)
Plum Island Sound, Mass.
Atlantic
1.32
X
o9
Fire Island Inlet, N.Y.
Atlantic
2.18
X
o9
Jones Inlet, N.Y.
Atlantic
1.50
X
o9
Beach Haven Inlet (Little
Egg Bay), N.J.
Atlantic
1.51
X
o9
Little Egg Inlet (Great
Bay), N.J.
Atlantic
1.72
X
O9
Brigantine Inlet, N.J.
Atlantic
5.23
X
08
Absecon Inlet (before
jetties), N.J.
Atlantic
1.65
X
09
Great Egg Harbor Entr, N.J.
Atlantic
2.00
X
09
Townsend Inlet, N.J.
Atlantic
5.56
X
O8
Hereford Inlet, N.J.
Atlantic
1.19
X
09
Chincoteague Inlet, Va.
Atlantic
1.56
X
09
Oregon Inlet, N.C.
Atlantic
3.98
X
09
Ocracoke Inlet, N.C.
Atlantic
5.22
X
09
Drum Inlet, N.C.
Atlantic
5.82
X
O8
Beaufort Lnlet, N.C.
Atlantic
5.0
X
09
Carolina Beach Inlet, N.C.
Atlantic
5.25
X
08
Stono Inlet, S.C.
Atlantic
2.86
X
09
North Edisto River, S.C.
Atlantic
4.58
X
o9
St. Helena Sound, S.C.
Atlantic
1.53
X
010
Port Royal Sound, S.C.
Atlantic
1.46
X
qIO
Calibogue Sound, S.C.
Atlantic
3.61
X
o9
Wassaw Sound, Ga.
Atlantic
8.2
X
o9
Ossabaw Sound, Ga.
Atlantic
6.81
X
o9
Sapelo Sound, Ga.
Atlantic
7.36
X
o9
St. Catherines Sound, Ga.
Atlantic
6.94
X
o9
440

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TABLE VI-1 (Cont.)
Estuary
Coast
Tidal Prism
(ft3)
Doboy Sound, Ga.
Atlantic
4.04
X
o9
Altamaha Sound, Ga.
Atlanti c
2.91
X
o9
Hampton River, Ga.
Atlantic
1.01
X
o9
St. Simon Sound, Ga.
Atlantic
6.54
X
o9
St. Andrew Sound, Ga.
Atlantic
9.86
X
O9
Ft. George Inlet, Fla.
Atlantic
3.11
X
08
Old St. Augustine Inlet,
Fla.
Atlantic
1.31
X
O9
Ponce de Leon, Fla.
(before jetties)
Atlantic
5.74
X
08
Delaware Bay Entrance
Atlantic
1.25
X
o11
Fire Island Inlet, N.V.
Atlantic
1.86
X
O9
East Rockaway Inlet, N.Y.
Atl antic
7.6
X
08
Rockaway Inlet, N.Y.
Atlantic
3.7
X
09
Masonboro Inlet, N.C.
Atlantic
8.55
X
08
St. Lucie Inlet, Fla.
Atlantic
5.94
X
08
Nantucket Inlet, Mass.
Atlantic
4.32
X
08
Shinnecock Inlet, N.Y.
Atlantic
2.19
X
O8
Moriches Inlet, N.Y.
Atlantic
1 .57
8.46
X
X
8
08
Shark River Inlet, N.J.
Atlantic
1 .48
X
08
Manasguan Inlet, N.J.
Atlantic
1 .75
X
o8
Barnegat Inlet, N.J.
Atlantic
6.25
X
o8
Absecon Inlet, N.J.
Atlantic
1 .48
X
o9
Cold Springs Harbor
(Cape May), N.J.
Atlantic
6.50
X
o8
Indian River Inlet, Del.
Atlantic
5.25
X
o8
Winyah Bay, S.C.
Atlantic
3.02
X
o9
Charleston, S.C.
Atlantic
5.75
X
o9
Savannah River (Tybee
Roads), Ga.
Atlantic
3.1
X
o9
441

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TABLE VI-1 (Cont.)
Estuary
Coast
Tidal Prism
(ft3)
St. Marys (Fernandina
Harbor), Fla.
At! antic
4.77
x
109
St. Johns River, Fla.
Atlantic
1.73
X
o9
Fort Pierce Inlet, Fla.
Atlanti c
5.81
X
o8
Lake Worth Inlet, Fla.
Atlantic
9.0
X
o8
Port Everglades, Fla.
Atlantic
3.0
X
o8
Bakers Haulover, Fla.
Atlantic
3.6
X
o8
Captiva Pass, Fla.
Gulf
of
Mexico
1 .90
X
o9
Boca Grande Pass, Fla.
Gulf
of
Mexi co
1 .26
X
0io
Gasparilla Pass, Fla.
Gulf
of
Mexico
4.7
X
08
Stump Pass, Fla.
Gulf
of
Mexi co
3.61
X
08
Midnight Pass, Fla.
Gulf
of
Mexico
2.61
X
08
Big Sarasota Pass, Fla.
Gulf
of
Mexico
7.6
X
08
New Pass, F1 a.
Gulf
of
Mexico
4.00
X
08
Longboat Pass, Fla.
Gulf
of
Mexi co
4.90
X
08
Sarasota Pass, Fla.
Gulf
of
Mexi co
8.10
X
08
Pass-a-Gri11e
Gulf
of
Mexico
1.42
X
O9
Johns Pass, Fla.
Gulf
of
Mexi co
5.03
X
08
Little (Clearwater)
Pass, Fla.
Gulf
of
Mexico
6.8
X
08
Big (Dunedin) Pass, Fla.
Gulf
of
Mexi co
3.76
X
o8
East (Destin) Pass, Fla.
Gulf
of
Mexico
1 .62
X
o9
Pensacola Bay Entr., Fla.
Gulf
of
Mexi co
9.45
X
o9
Perdido Pass, Ala.
Gulf
of
Mexi co
5.84
X
o8
Mobile Bay Entr., Ala.
Gulf
of
Mexico
2.0
X
Qio
Barataria Pass, La.
Gulf
of
Mexico
2.55
X
o9
Caminada Pass, La.
Gulf
of
Mexico
6.34
X
o8
Calcasieu Pass, La.
Gulf
of
Mexico
2.97
X
o9
San Luis Pass, Tex.
Gulf
of
Mexico
5.84
X
o8
442

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TABLE VI-1 (Cont.)
Estuary
Coast
T~
Tidal Prism (ft )
Venice Inlet, Fla.
Gulf of Mexico
8.5
X
1
o
Galveston Entr., Tex.
Gulf of Mexico
1.59
X
1010
Aransas Pass, Tex.
Gulf of Mexico
1 .76
X
109
Grays Harbor
Pacific
1.3
X
1010
Willapa
Pacific
1.3
X
1010
Columbia River
Pacific
2.9
X
1010
Necanicum River
Pacific
4.4
X
107
Nehalem Bay
Pacific
4.3
X
108
Tillamook Bay
Pacific
2.5
X
109
Netarts Bay
Pacific
5.4
X
108
Sand Lake
Paci fic
1 .'l
X
108
Nestucca River
Pacific
2.6
X
108
Salmon River
Pacific
4.3
X
107
Devils Lake
Paci fic
1.1
X
108
Siletz Bay
Pacific
3.5
X
108
Yaquina Bay
Paci fic
8.4
X
108
Alsea Estuary
Paci fi c
5.1
X
108
Siuslaw River
Paci fic
2.8
X
108
Umpqua
Paci fic
1.2
X
109
Coos Bay
Pacific
1.9
X
109
Caquille River
Paci fic
1.3
X
108
Floras Lake
Pacific
6.8
X
107
Rogue River
Pacific
1 .2
X
108
Chetco River
Paci fic
2.9
X
107
Smith River
Pacific
9.5
X
107
Lake Earl
Paci fi c
5.1
X
108
Freshwater Lagoon
Pacific
4.7
X
107
Stove Lagoon
Pacific
1.2
X
108
Big Lagoon
Pacific
3.1
X
108
443

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TABLE VI-1 (Cont.)
Estuary
Coast
Tidal Prism
(ft3)
Mad River
Paci fic
2.4
X
o7
Humbolt Bay
Paci fic
2.4
X
o9
Eel River
Paci fic
3.1
X
o8
Russian River
Paci fi c
6.3
X
o7
Bodega Bay
Paci fic
1.0
X
o8
Tomales Bay
Pacific
1.0
X
09
Abbotts Lagoon
Pacific
3.5
X
O7
Drakes Bay
Pacific
2.7
X
08
Bolinas Lagoon
Paci fi c
1.0
X
08
San Francisco Bay
Pacific
5.2
X
o10
Santa Cruz Harbor
Pacific
4.3
X
O5
Moss Landing
Pacific
9.4
X
07
Morro Bay
Pacific
8.7
X
o7
Marina Del Rey
Paci fi c
6.9
X
o7
Alamitos Bay
Paci fi c
6.9
X
o7
Newport Bay
Pacific
2.1
X
o8
Camp Pendleton
Paci fi c
1.1
X
o7
Aqua Hedionda
Paci fi c
4.9
X
o7
Mission Bay
Pacific
3.3
X
o8
San Diego Bay
Pacific
1 .8
X
o9
*Inc1udes some estuaries not necessarily appropriate for application
of hand calculations.
444

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6.4 FLUSHING TIME CALCULATIONS
6.4.1. General
The most basic water quality calculation which can be made for an
estuary is the estuarine flushing time. The flushing time may be
defined as the length of time required to replace existing fresh (river)
water in an estuary at a rate equal to the river discharge. Thus, it
represents the length of time (normally measured in tidal cycles)
required to carry a pollutant out of the estuary (Dyer, 1973)*.
Unless otherwise specified, estuarine flushing time is taken as the
time required to flush a pollutant which was introduced into the
estuary at its head (i.e. with the river inflow).
As has been mentioned, the net non-tidal flow in an estuary is
always seaward and is dependent on the river discharge. This nontidal
flow is the driving force behind estuarine flushing. Were it not for
this advective displacement of pollutants only dispersion and diffusion
forces would dilute pollutant concentration within the oscillatory
motion of the tides. Tomales Bay, California, can be used as an
example to show the importance of this river induced net motion. This
~Actually this length of time will not remove aJJ_ of a dispersed
pollutant from an estuary. Some portion will remain behind.
However it is sufficiently small so that it can be ignored without
creating a significant error.
~ ~
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 occurance is very rare in the United States,
an example of such a situation is the South Bay of San Francisco Bay where
fresh water inflows are so small that surface evaporation exceeds inflow.
Thus, net flow is upstream during most of the year.
445

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small, elongated California bay has essentially no fresh water inflow.
As a result there is no advective seaward motion (and pollutant removal
j
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 Alsea Estuary in Oregon having a flushing time of
approximately 8 days (see example later in this section), with the
much larger St. Croix Estuary in Nova Scotia having a flushing time
of approximately 8 days (Ketchum and Keen, 1951), or with the very
large Hudson River Estuary with a low flow flushing time of approx-
imately 10.5 days (Ketchum, 1950).
6.4.2 Procedure
Flushing times for a given estuary will 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 slowest flushing
rates. The planner may also want to calculate ^e best flushinr
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 characteristic summer fresh water low flow).
Further, storm sewer runoff will more normally coincide with these best
flushing conditions (high flow) and not with the low flow, or poorest
flushing characteristic. Thus analysis of storm runoff is often better
suited for high flow flushing conditions. However, the low flow calcu-
lation should be used for primary planning purposes.
Several methods are available for approximate calculation of
flushing time (Dyer, 1973). Two will be presented here, and while
data requirements for both are minimal, one (fraction of fresh water
method) will normally overestimate flushing time, and the other
(modified tidal prism method) will normally slightly underestimate
446

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flushing time. The limitations and advantages of each are listed
below.
6.4.3 Fraction of Fresh Water Method
This method uses the mean salinity level in a segment of the
estuary. The fraction of fresh water within that segment is calcu-
lated by comparing segment mean salinity to ocean water salinity. The
resulting volume of fresh water is then compared to the river discharge
rate to calculate the length of tine required to replace all the fresh-
water within that estuarine sscnent.
The principal limitation of this method is that it assumes uniform
salinity levels throughout the segment. A second limitation is
that it assumes that during each tidal cycle a volume of water equal
to the river discharge moves into a given estuarine segment from the
adjacent upstream segment, end 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 instantaneously and completely mixed and to again become
a homogeneous water mass. Proper selection of estuarine segments can
reduce the error created by the first of these limitations. This error
will also be reduced by the use of low flow data since estuaries tend
to be closer to well mixed during low river discharge periods. The
second limitation described above is inherent in the methodology and
cannot be counteracted. Normally, however, the error it introduces is
acceptably smal1.
A primary advantage of this method is that the derived fraction
of fresh water coefficients will form the basis for later segment
dispersion coefficient calculations. Secondarily, this method is
quite accurate when used on truly well-mixed estuaries.
447

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6.4.4 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 flushing potential of that segment
per tidal cycle (Dyer, 1973). The method assumes complete mixing of
the incoming tidal prism waters with the low water volumes within each
segment. Best results have been obtained in estuaries when the number
of segments is 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 has the advantage of not requiring
knowledge of the salinity distribution and also will provide some
concept of mean segment velocities since each segment length is tied
to particle excursion length over one tidal cycle.
6.4.5 Calculation Methodology
6.4.5.1 Fraction of Fresh Water Method
This is a six step procedure. These steps are:
1)	Graph the estuarine salinity profiles.
2)	Divide the estuary into segments. There is no minimum or
maximum number of segments required, nor should each
segment be of the same length. The divisions should
be selected so that mean segment salinity is relatively
constant over 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.
448

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3) Calculate each segment's fraction of fresh water by:
,,.
where f. = fraction of fresh water for segment "i"
Ss = salinity of sea water* 34 /oo)
and	S. = mean salinity for segment "i"
4) Calculate the quantity of fresh water in each segment by:
W. = f, x vol.	(VI-7)
nil
where W. = quantity of fresh water in segment "i"
and	vol. = low tide volume of segment "i"
5) Calculate the exchange time (flushing time) for each
segment by:
T.=Wi/R	(VI-8a)
where	= segment flushing time
and	R = river discharge over one tidal cycle
*Sea surface salinity along US 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 US - 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.
449

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and 6) Calculate the entire estuary flushing time by
n
Tf = Z T,	(VI-8b)
T i = l 1
where	= estuary flushing time
n = number of segments.
	 EXAMPLE VI-3 	
Flushing Time Calculation By Fraction Of Fresh Water Method
This example pertains to Alsea Estuary in Oregon. Necessary
estuarine topographical data were obtained from a report by Goodwin,
Emmett and Glenne (1970). Salinity data were obtained from that report
as well as from a report by McKinsey (1974). Sea surface salinity was
estimated to be 34 /oo. The profile of high tide salinity levels along
the estuary is shown in Figure VI-17. The selected segmentation scheme
is shown in Figure VI-18 with mean salinity levels. Where the salinity
increases fairly regularly along the length of the estuary the dividing
lines between segments is somewhat arbitrary. Where changes in mean
salinity occur sharply, the location of these segment divisions is more
fixed. Data showing cross sectional areas were obtained as shown from
Goodwin, Emmett and Glenne (1970) (Figure VI-19), and segment divisions
are also shown on that figure. The data presented in the three Figures
VI-17, 18, and 19 are sumnarized in Table VI-2 for use in flushing time
calculations.
This effort completes steps 1 and 2 of the 6 step procedure.
450

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35
30
25
Bottom
Mean
20
Surface
S %o 0
DISTANCE FROM MOUTH (MILES)
Figure VI-17 /\lsea Estuary SumER High Tide Salinity Profile
Segment Number

35
30
25
20
0	2/10.6 4/21.1
DISTANCE ABOVE MOUTH (Ml LES / FT. x 1000)
6/31.7
8/42.2
0/52.8 12/63.4
14/73.9 .
Figure VI-18
Alsea Estuary Fraction of Fresh Water Segmentation
451

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TABLE VI-2
ALSEA ESTUARY SALINITY AND VOLUME BY SEGMENTS


Segment Low
Segment No.
Mean Salinity (/oo)
T ide-Volumn
8
31.3
7.92xl07 ft3
7
28.0
1.28x107 ft3
6
23.3
1.06x107 ft3
5
17.7
1.37x107 ft3
4
12.3
2.45xl07 ft3
3
8.1
2.30x107 ft3
2
4.9
1.32x107 ft3
1
1.8
3.59x107ft3
Segment Number
)IClXi)OXIXlXIX
40
u_
f	[0_ J
o	/
UJ	'
C/)	^
c/)	*5	r
cn
o
Mean Tide Level
Mean LowTide
o
0	10	20
DISTANCE FROM MOUTH (FT. x I03)
30
60
40
50
70
80
Figure VI-19 Alsea Estuary Cross Sectional Areas
452

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3) Calculate f.'s by:
Segment
S. (o/oo)
f.
8
31.3
0.0794
7
28.0
0.176
6
23.3
0.315
5
17.7
0.479
4
12.3
0.638
3
8.1
0.762
2
4.9
0.856
1
1.8
0.947
4) Calculate 's by:
W. = f. x Vol.
Segment.
f.
i
VoK (xlO7 ft3)
Q. (xlO7 ft3)
8
0.0794 
7.92
0.629
7
0.176
00
C\J
0.225
6
0.315
1.06
0.334
5
0.479
1.37
0.656
4
0.638
2.45
1.56
3
0.762
2.30
1.75
2
0.856
1.32
1.13
1
0.947
3.59
3.40
453

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5) Calculate T. by:
When R = (104 ft3/sec) (3600 sec/hr) (12.4 hr/tidal cycle)
R = 4.64x10^ ft3/tidal cycle (from McKinsey, 1974)
Segment
Qi (xio6 ft3)
Ti
8
6.29
1.36
7
2.25
0.485
6
3.34
0.720
5
6.56
1.41
4
15.6
3.36
3
17.5
3.77
2
11.3
2.41
1
34.0
7.33
6) Sum IVs to obtain T^. by:
8
Tf = (1.36 + 0.485 + 0.72 +1.41 + 3.36 + 3.77 + 2.41 + 7.33)
= 20.8 tidal cycles
or T^. = 10.7 days
END OF EXAMPLE VI-3
454

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In addition to producing a total estuarine flushing time this
method provides some feeling for the way that pollutants move through
an estuary. Note that the total flushing time for segments 6, 7, and
8 is approximately 2.5 tidal cycles while the distance covered by the
pollutant is 5 miles. Conversely, the 8 miles at the head of Alsea
Estuary require approximately 16.9 tidal cycles to flush a pollutant.
This indicates that once a pollutant gets near the mouth of Alsea
Estuary it is quickly flushed out of the estuary. However, pollutants
introduced near the estuary's head require a considerable length of
time to move downstream into the main body of the estuary. The
flushing capacity of an estuary.is much better at the mouth of the
estuary than at the head. While this is typical of all estuaries the
difference in flushing rate from mouth to head is not always as large
as in Alsea Estuary.
6.4.5.2 Modified Tidal Prism Method
This 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 an intertidal volume completely supplied by river flow. Thus,
PQ = R	(from Dyer, 1973)
Where PQ = Tidal prism (intertidal volume) of segment "0"
and	R = River discharge over one tidal cycle
The low tide volume in this section (V ) is that water volume below
o
low tide 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 (V-j) is defined by:
455

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P-j is then that intertidal volume which, at high tide, resides
above V-j. Successive segments are defined in an identical manner to
this segment so that:
vi = pi-i + vi-i	
-------
	 EXAMPLE VI-4 	=	
Estuary Flushing Time Calculation By Modified Tidal Prism Method
1) Estuary Segmentation: Again, the Alsea Estuary will be
used as an example. From previous calculations, R = 4.64x10^ ft3/tidal
cycle.
Thus PQ = R=4.64x106 ft3
The differences in area between high tide and low tide cross
sectional areas on Figure VI-20 (a reproduction of the basic cross
sectional information in Figure VI-19) is the intertidal area, or
tidal prism. Thus, from the head of the estuary you can measure the
equivalent of "R" in intertidal volume (intertidal cross sectional area
times segment length). Alternately, this intertidal volume can be
graphed as in Figure VI-21. In this figure the intertidal volume up-
stream of any point is plotted against the distance from the mouth of
Alsea Estuary. Also shown on Figure VI-21 is a horizontal line from R
fi O
(4.64 x 10 ft ) to Alsea Estuary intertidal volume and down to the
distance from the mouth of Alsea Estuary above which PQ = R. VQ may
now be calculated as the low tide volume above 68,500 ft from the
estuary's mouth. From Figure VI-20 VQ = 4.85 x 10^ ft3 and the length
of segment "0" is 74,000 ft* - 68,500 ft = 5,500 ft.
Then,
V, = P + V
1 o o
V] = 4.64xl06 ft3 + 4.85xl06 ft3
V1 = 9.49xl06 ft3
* The extent of mean summer salinity intrusion in Alsea estuary (i.e.,
it's length) is approximately 74,000 ft.
457

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40
20
Mean HighTide
Mean Tide Level
o
UJ
CO
CO
CO
Mean Low Tide
o
0	10	20
DISTANCE FROM MOUTH (FT. x I03)
30
40
50
60
70
I 80
Estuarin#
Head
Figure VI-20 Alsea Estuary Cross-Sectional Areas
UPSTREAM INTERTIDAL VOLUME (FT.3)
a>
O
CO
>
z
o
m
2
O
c
H
X
3
o
o
o
~n
H
Figure VI-21 Alsea Estuary Upstream Intertidal Volume
458

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From Figure VI-20 the length of segment 1 may be calculated by
6 3	'
measuring a low tide volume = 9.49x10 ft below 68,500 ft from the
estuary's mouth." From Figure VI-20 the distance below 68,500 ft
which corresponds to a Vn = 9.49x10 ft is approximately 8250 ft.
Thus, segment 1 extends from 60,250 feet above Alsea estuary's mouth
to 68,500 feet above the estuary.
From Figure VI-21 the intertidal volume between 60,250 and
68,500 ft above the estuarine mouth is:
P] = 2.75xl07 ft3 - 4.64xl06 ft3 = 2.286xl07 ft3
Then, V2 = P1 + V1 = 2-29xl7 ft3 + 9.49xl06 ft3
or	V2 = 3.24xl07 ft3
Following this same procedure, from Figure VI-20 the length of
segment 2 below 60,250 ft from the estuary's mouth which corresponds
7 3
to a V2 = 3.24x10 ft is 15,700 ft with a mean segment cross section
of 2050 ft2. Thus, segment 2 extends from 44,550 ft to 60,250 ft above
the mouth of Alsea Estuary. From Figure VI-21 this corresponds to:
P2 = 5.4x107 ft3 - 2.75x107 ft3 = 2.65xl07 ft3
Then,
V3 = P2 +V2 = 2.65x107 ft3 + 3.24x107 ft3
or	V3 = 5.89xl07 ft3
From Figure VI-20 the length of segment 3 is 22,250 ft with a
2
mean cross sectional area of 2650 ft and segment 3 extends from
22,300 ft to 44,550 ft above the estuary mouth.
459

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From Figure VI-21
Thus
P3 = 1.7xl08 ft3 - 5.4xl07 ft3 = 1.16x108 ft3
v4 = p3 + v3 = 1.16x108 ft3 + 5.89xl07 ft3
V4 = 1.74xl08 ft3
However, this V4 is greater than the remaining low tide volume
in Alsea Estuary. Thus, segment 4 extends from the mouth to 22,300 ft
above the mouth with a segment length of 22,300 ft, a mean cross
2
sectional low tide area of 3825 ft and,
V4 = 3825 ft2x22,300 ft = 8.525xl07 ft3
From Figure VI-21 the intertidal volume below 22,300 ft from
the estuary's mouth is:
P4 = 5.lxl08 - 1.7x108 = 3.4xl08 ft3
Table VI-3 summarizes these segment physical characteristics.
TABLE VI-3
ALSEA ESTUARY SEGMENTATION FOR MODIFIED TIDAL PRISM METHOD
Segment
length (ft)
vi (ft3)
Pi (ft3)
0
5,500
4.85xl06
4.64x106
1
8,250
9.49x106
2.286xl07
2
15,700
3.24x107
2.65x107
3
22,250
5.89xl07
1.16x1O8
4
22,300
8.525xl07
3.4x108
460

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2) Calculate-ry's by:
Segment
P. (106 ft3)
V.(106x ft3)
r.
l
0
4.64
4.85
0-489
1
22.86
9.49
0.707
2
26.5
32.4
0.450
3
116.0
58.9
0.663
4
340.0
85.25
0.800
3) Calculate T.'s by:
Segment
r.
l
T.
l
0
0.489
2.25
1
0. 707
1.62
2
0.450
2.32
3
0.663
1.61
4
0.800
.1.25
461

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4) Calculate
Tf = 2.25 + 1.62 + 2.32 + 1 .61 + 1.25
Tf = 9.05 tidal cycles
or	T^ = 4.7 days
	 END OF EXAMPLE VI-4 	
This flushing time estimate for Alsea estuary is less than 50%
of that by the fraction of fresh water method. The discrepancy is
unusually large and should be smaller for most U.S. estuaries. As was
stated earlier the modified tidal prism method produces best results
when the number of segments is large which is not the case for this
estuary.* A planner, of course, has no control over the number of
segments created in a specific estuary with a specific river outflow.
However, the larger the estuary with respect to river outflow, the
greater the number of segments and the greater the accuracy of the
flushing calculations. Based on these two flushing calculations the
planner for Alsea Estuary could estimate the flushing time for that
estuary to be about 8 days and could be reasonably assured that the
actual instantaneous flushing time would not vary significantly from
this figure without major changes in river discharge.
In addition to estimating pollutant residance times, the flushing
time for an estuary, or more particularly, for a segment of an estuary,
has a direct relationship with the concentration of a pollutant in that
segment. Segments with high flushing times will concentrate pollutants
and will thus tend to be the sites of the most severe water quality
* Ketchum (1955) obtained 13 segments in his analysis of the Raritan
River and got good agreement between predicted and observed values.
V
=.E Ti
1= o
462

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problems. This relationship will be explained in considerably more
detail in the next section of this chapter.
Both methods presented here for estimation of segment and estuarine
flushing times are somewhat empirical and are subject to considerable
error. However, the great utility of the flushing time and its relative
ease of calculation make it worth the effort. These simple procedures
for estimation of segment flushing times provides: pollutant residence
times, locations of peak pollutant storage concentration, segment flushing
time and estuarine flushing time. This information is extremely valuable
for both subsequent calculation of pollutant distribution and for
gaining a basic understanding of the kinetic operation of an estuary.
6.5 CALCULATION OF POLLUTANT CONCENTRATIONS IN ESTUARIES
6.5.1 ' General
The previous two major sections were preliminary sections to this
section. By.classifying each estuary and by calculating segment-and
estuarine flushing time, the basic ground work has been completed to
now directly address estuarine water quality. The methods presented
in this section will allow direct calculation of the concentration of .
a wide range of pollutants in the estuarine environment which will act
as primary water quality indicators (e.g., heavy metals, BOD, hydro-
carbons, coli.form bacteria, pesticides, oil and grease, and nutrients*).
Input waste loadings can be divided into four cases which will be
addressed separately: continuous flow conservative discharges, con-
tinuous flow non-conservative discharges, single event or one-time
conservative discharges, and one-time non-conservative discharges.
Actually, a continuous discharge will probably, contain both conservative
and nonconservative substances and thus an analysis of both cases will
~Nutrients will be treated in this section as a conservative pollutant.
While it is true that nutrients are consumer1 for piv/toplankton prMucticn
and are thus not fully conserved, light, and not nutrients, is normally
the limiting factor for estuarine production. Therefore, the assumption
that nutrients will be conservative will not introduce excessive error.
463

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be required for a full evaluation of its impact on estuarine water quality.
This methodology will address only one discharge at a time and is
thus designed primarily for use in assessing changes in water quality
resulting from changes (additions or deletions) in the waste loading
pattern. This type of analysis requires only that a few discharges be
evaluated and that the results of pollution dispersion be added to the
existing, or background, pollutant concentrations. The approach can
also be used to assess existing water quality. However, this requires
separate analysis of each waste load and generally will be quite time
consuming.
A simple schematic representation of individual steps is shown in
Figure VI-22, The types of discharges associated with each step in
this section are listed in Figure VI-22 as are water quality parameters
appropriate for the analysis in each of these steps.
As was true for estuarine hydrodynamics, pollutant dispersion
in the estuarine environment is a very complex process. In fact, this
is not a single process, but is the composite of a number of individ-
ual physical and chemical processes including advective dispersion,
eddy diffusion, and density gradient diffusion. The concern here is
to approximate only the cumulative effect of all of these separate
mixing processes. The methods presented in this section are designed
to approximate this steady state distribution of pollutants based on
known flushing times and on estimated decay rates for non-conservative
pollutants. Finally, single event discharges (non-steady state events)
will be estimated through the use of dispersion equation techniques.
6.5.2 Continuous Flow Conservative Pollutants
The concentration of a conservative pollutant entering an estuary
in a continuous flow will vary as a function of the location of the
entry point location. It will be convenient to separate pollutants
entering an estuary at the head of the estuary (with the river discharge).
464

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TYPES OF DISCHARGES
COVERED
Municipal Sewers 1
River Discharge >
Industrial DischargeJ
Storm Drains
Leaks
Major Spills
<
Contini
Consen
Discha
jous
/ative
rges


Continuous
Non-Conservative
Discharges


One Time
Conservative
Discharges


One Time
Non-Cons
Discharg
ervative
es
f
f
t
APPLICABLE
TYPES OF
POLLUTANTS
I Nutrients
J Conservatives
"S Most Toxicants
I TDS
DO-BOD
Coliform Bacteria
I Nutrients
J Conservatives
Most Toxicants
I TDS
DO-BOD
Coliform Bacteria
Figure VI-22 Dispersion Methodology Schematic
465

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from those entering along the estuary's sides. The two impacts will
then be addressed separately.
6.5.3 River Discharges
Based on calculations previously done only very simple calculations
are required to determine the concentration of a pollutant in each
estuarine segment (Cp^) when that pollutant enters the estuary with
the river inflow. It is then equally trivial to calculate the total
amount of each conservative pollutant residing within the estuarine
water column (Wpp).
The length of time required to flush a pollutant out of 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 discharged into a river upstream
of the estuary. After a single tidal cycle's worth of pollutant flows
into the estuary, it begins to disperse and work its way toward the
mouth of the estuary with the net flow. If, for example, the estuary
flushing time is 10 tidal cycles, 10 tidal cycles following intro-
duction into the estuary, a single batch of the pollutant has been
essentially flushed out to the ocean. However, during each of the
intervening tidal cycles, more of the pollutant enters the estuary
and smaller portions of these batches are also flushed out. Eventually,
a steady-state condition is reached in which a certain amount of
pollutant enters the estuary, and the same amount is flushed out of
the estuary during each tidal cycle. The amount of this pollutant
which then resides in the estuary is a function of the flushing time.
From the definition of flushing time, the amount of fresh water in
the estuary may be calculated by:
WE = Tp R	(VI-12)
where
= quantity of fresh water in the estuary
Tp = estuary flushing time
466

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and .
R = river discharge over one tidal cycle
Using the same approach, the quantity of fresh water in any segment'
of the estuary is given by:
W. = ^ R	(VI-12a)
quantity of fresh water in the i^*1 segment
of the estuary
flushing time for the i*^1 segment calculated by
the fraction of fresh water 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,
where
and
W.
l
T. -
l
and
where
and
wpi = "i v = Ti R V	(VI"13a)
cpi = wp1/v0'i	(VI-13b)
= quantity of pollutant in estuary segment "i"
c = concentration of pollutant in the river inflow
pr
c . = concentration of pollutant in estuary segment "i"
assuming all of pollutant "i" inflows to the
estuary with the river discharge. Thus direct
discharges into the estuary are now being dis-
regarded.)
vol. = water volume segment "i"
The same values for c . and W . may also be obtained by using the
pi	pi
467

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fraction of fresh water, f., for each segment by:
cpi = fi Cpr	(VI-14a)
and
wp1 - Cp1 vol,	(VI-14b)
Thus both the quantity of a pollutant in each segment and its
concentration within each segment are readily obtainable by either
of the above two methodologies. The use of one of these methods
will be demonstrated in Example VI-5 below for calculation of both
c . and W ..
pi	pi
It should also be noted that the total amount of a pollutant
in residence in an estuary may be estimated by summing the segment
W .1s by:
pi J
n
W c =Y] U .
pE ' pi
i = l
	 EXAMPLE VI-5 	
Calculation of Concentration of Conservative River Borne Pollutants
in an Estuary
For this example The Alsea Estuary again will be used since its
flushing characteristics have already been determined. Assume that
the State Department of Environmental Quality has just released that
a planned expansion of upstream agricultural activity will result
in a summer mean river concentration of 20 yg/1 of a certain
468

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pesticide*. The planner must now calculate the steady-state concentra-
tion of pesticide throughout Alsea Estuary so that local biologists may
determine if this activity will affect estuarine clam beds.
c o
From previous calculations, R = 4.64 x 10 ft tidal cycle.
Converting pesticide concentrations into appropriate units:
cpr = (20 yg/1) (28.32 1/ft3) = 566.4 yg/ft3
Using the segmentation scheme derived for the fraction of fresh water
flushing calculation, the tabular calculations shown in Table VI-4 can
be made for cp^ and Wpi
As a check on this result, WpE can alternately be calculated by
W c : Tr R C
pE f pr
using the fraction-of-fresh-water method T^ as a check,
Wp^ = (20.8) tidal cycles (4.64 x 10^ ft3/tidal cycle)
(566.4 yg/ft3)
Wp^ = 54.67 x 10^ yg
W r is within 0.41% of
PE
the previous estimate.
~Pesticides actually tend to absorb to particulates and settle
to the sediment layer. However the assumption made here that
they act conservatively will not create excessive error.
469

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TABLE VI-4
CALCULATION OF SEGMENT CONSERVATIVE POLLUTANT QUANTITY
FOR ALSEA ESTUARY
segment
f.
i
C
yg/ft*
Pi
yg/T
voli (107 ft3)
Wpi (yg)
1 (head)
.947
536.4
18.9
3.59
19.26x109
2
.856
484.8
15.8
1.32
6.40xl09
3
.762
431.6'
15.2
2.30
9.93xl09
4
.638
361.4
12.8
2.45
8.85x109
5
.479
271.3
9.6
1.37
3.72xl09
6
.315
178.4
6.3
1.06
1.89xl09
7
.176
99.7
3.5
1.28
1.28xl09
8 (mouth)
.0794
45.0
1.6
7.92
3.56xl09
WpE = 54.89xl09yg = 121.0 lbs
END OF EXAMPLE VI-5
In this example low tide volumes were used to calculate W . since
pi
low tide volumes had been used to calculate f^'s. The approach assumes
that 1) Cp-j's are constant over the tidal cycle and that 2) Wpi- 's are
constant over the tidal cycle. This leads to the assumption that cal-
culation of a low tide c . and W . will fully characterize a pollutant
pi	pi
in an estuary. This, however, is not strictly true. Figure VI-23
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 blocks river discharge and backs
up river flow into the lower stretches of the river. Figure VI-23 also
shows the resulting quantity of a pollutant in residence in the estuary
(Wp) over the tidal cycle. This variation over the tidal cycle as a
percentage of W ^ is dependent on the flushing time but is usually small
(approximately 1.5% for Alsea Estuary). The change in the total volume
470

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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. ' For Alsea
Estuary, = 5.1 x 10^ ft^ while V = 2.1 x 10^ (Goodwin, Errmet, 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 Wp^ nearly coincide, so that variations in
mean pollutant concentrations are less severe than are estuarine water
mass changes.
Period for tidal
flushing of
pollutant from
estuary \
MHT
TIME
TIDAL
ELEVATION
MLT-
Period of
river dis-
charge into
estuary
TIME
Nominal
II.. II
Mean
Figure VI-23 River Borne Pollutant Concentration For One Tidal Cycle
471

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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 will coincide with those at the head
of the estuary. This is usually not the case. There is normally a
significant lag time between tidal events at an estuarine mouth and
those at it's head. Thus river discharge into the estuary which de-
pends on tidal conditions at the head, and tidal discharge which de-
pends on tidal conditions at the mouth, are not as directly tied to
each other as indicated on Figure VI-23.
While Wp does not vary substantially over a tidal cycle under
steady state conditions, the mean concentration of a pollutant in an
estuary (Cp^) will. Alsea Estuary data can be used to show this Cp^
variation over a tidal cycle. Using data for the estuary as a whole
(mean concentration), the equations for this comparison are:
WpE Wpr TF,	(VI-15)
CpE(low) = wpE/vo1E'
and	CpE(high) = WPE/(v0lE+PT)	(VI-16)
with	Wpr = (566.4 yg/ft3) (4.64x10^ ft3/tidal cycle)
or	Wpr = 2.628x10^ yg/tidal cycle*
Then,	W ^ = (2.628x10^ yg/tidal cycle) (20.8 tidal cycle)
WpE = 5. 466x1010 yg,
and
CpE(low)= 5-6xl010 yg/2.1x108 ft3
3
or	cpE(low) ~ 260.31 yg/ft , or 46% of river concentration.
However, cpE(high) = 5.466xl010 yg/(2.1xl08 ft3 + 5.1xl08 ft3)
472

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CpE(high) = 75.92 yg/ft3, or 13% 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
continuous spectrum of values. By assigning the longitudinal centroid of
each segment a concentration value equal to that segment's c ., a resulting
continuous curve can be constructed as shown in Figure VI-24. This type
of plot is useful in estimating pollutant concentrations within the estuary.
It can also be used, however, to estimate maximum allowable cpr to main-
tain a given level of water quality at any point within the estuary. This
latter use of Figure VI-24 is based on determining desired cpx levels and
then using the ratios of cpx to cpr, to calculate an allowable cpr>.
20
0.9
0.8
0.7
0.6
px
(jug/l)
0.3
0.2
0.0
20 30 40 50 60 70
DISTANCE (x) FROM HEAD OF ESTUARY (in 1000FT.)
80
90
Figure VI-24 Alsea Estuary Riverborne Conservative Pollutant Concentration
473

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6.5.4. Other Continuous Conservative Pollutant Inflows
In the previous section an analysis was made of the steady state
distribution of a continuous flow pollutant entering at the head of an
estuary. The result was a graph of the longitudinal pollutant con-
centration within the estuary (Figure VI-24). This section will address 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)
will be carried both upstream and downstream by tidal mixing with the
highest concentration in the vicinity of the outfall. Once a steady
state has been achieved, the distribution of this pollutant will be
directly related to the distribution of fresh river water (Dyer,1973).
The average cross sectional concentration at the outfall under steady
state conditions is:
c = Qp f ~ Qp f
0 R+Q 0 R 0	(VI-17)
P
when	c = mean cross sectional concentration of a
o
pollutant at the point of discharge.
0	?
P = discharge rate of pollutant (ft /tidal cycle)
f = segment fraction of fresh water
R = river discharge rate (ft^/tidal cycle)
Downstream of the outfall the pollutant must pass through any cross
section at a rate equal to the rate of discharge. Thus,
(VI-18)
where sx, c^ and fx denote any downstream cross section.
and s , c and f denote the cross section at the discharge point
oo o
(or segment into which discharge is made)
474

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Upstream of the outfall, the quantity of pollutant diffused and advec-
tively carried upstream will be balanced by that carried downstream by
the non-tidal flow so that the net pollutant transport through any
cross-section is zero. Thus, the pollutant distribution will be
directly proportional to salinity distribution and, (Dyer, 1973):
c =c x
x o q-
o
(VI-19)
Downstream of the outfall, the pollutant concentration resulting from a
point discharge will be directly proportional to river borne pollutant
concentration. Upstream from the discharge point it will be inversely
proportional to river borne pollutant concentrations. Figure VI-25 is
a graph of f versus distance from the estuary head for a typical
estuary. This 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
px
to this f value multiplied by Q /R which is a constant over all x.
x	p
Upstream concentrations decrease from cQ in a manner proportional to
upstream salinity reduction (see dotted line). It is important to note how
even a small downstream shift in discharge location will create a very
significant reduction in upstream steady state pollutant concentration.
	 EXAMPLE VI-6 	
Calculation of Estuarine Pollutant Concentrations for Varying Discharge
Locations
A new industrial complex is to be built on the south shore of
Alsea Estuary. Two outfall locations (A and B) are being considered.
A is 18,5000 feet from the mouth, B is 31,000 feet. It must now be
determined what the differential impact of discharges from these two
points will be on each of three important ecological areas (1, 2, and
475

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3). Area 1 is centered 7,000 feet from the estuary mouth, area 2 is
centered 28,000 feet from the mouth and area 3 is centered 50,000 feet
above the mouth. The primary concern is with the heavy metal content
of the discharge. The concentration is listed as 800 yg/1 in a 2.5 MGD
discharge flow, and the pollutant may be assumed to act as a conserva-
tive constituent within the estuary.
First, longitudinal f and S values must be plotted. Figure VI-18
X	X
showed Alsea Estuary low river flow salinities, and Figure VI-24 showed
Alsea Estuary f values. These are repeated in Figure VI-26. Ad-
X
ditionally, both potential outfalls and the three study sites are
marked in Figure VI-26.
i.o
0.8
0.6
0.4
0.2
f
x
Bk
0.5
DISTANCE FROM HEAD x
L*
*L = Total Estuorine Length
Figure VI-25 Pollutant Concentration From An Estuarine Outfall
476

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0.8
0.6
0.4
0.2
35
30
25
20
Sx vrs X
75
0	10	20	30	40
DISTANCE (x) FROM MOUTH (in 1000FT.)
50
60
70
Figure VI-26 Alsea Estuary Salinity and fx Profile
c values were obtained by multiplying corresponding f values by
px	X
Qp/R as follows
Qp = (800 ug/1) (28.32 1/ft2) (1.54723 cfs/mgd)
(2.5 mgd) (3600 sec/hr) (12.4 hr/tidal cycle)
or	Qp = 3.912x10^ yg/tidal cycle
and
3.912xl09 pq = 843 -J pg/ft3
K 4.64x1O6 ft3
477

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thus	downstream of the outfall c values = (f ) (843.1 yg/ft3)
x	x
Upstream of each outfall,
Sx
C = C ^T-
X 0 S
0
From Fig. VI-25 and rquation VI-17,
r _Q_Pf	= (843.1 ng/1 ft3) (0.2)
A R (x=18,000 )
- 168.6 yg/ft3
CB = R* f
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TABLE VI-5
CONSERVATIVE POLLUTANT CONCENTRATIONS ABOVE AN ESTUARINE OUTFALL

OUTFALL
A
OUTFALL
B
Distance above
outfall (ft)
cx(yg/ft3)
~
X
cx(yg/ft3)
~
X
5,000
144.2
23,000
365. 3
36,000
10,000
113.2
28,000
309.1
41,000
15,000
85.5
33,000
219.2
46,000
20,000
70.9
38,000
154.6
51,000
25,000
52.7
43,000
88.5
56,000
30,000
41.7
48,000
56.2
61,000
35,000
23.8
53,000
35.1
66,000
40,000
16.1
58,000
19.7
71 ,000
T
x a distance from mouth in feet
TABLE VI-6
COMPARISON OF POLLUTANT CONCENTRATIONS FOR
ALTERNATE OUTFALLS IN ALSEA ESTUARY
outfall
mean cross section concentration
critical n. used
A
B

habitat number
yg/ft
yg/i
yg/ft3
yg/l
1,
62
2.19
62
2.19
2
112
3.95
370
13.07
3
32
1.13
166
5.86
479

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500
400
300
200
100
0	10	20	30	40
DISTANCE (x) FROM MOUTH (in 1000 FT.)
50
60
70
Figure VI-27 Alsea Estuary Example Heavy Metal Concentration for
Two Outfalls
The major advantage of using discharge points nearer to the estuary's
mouth is not in improvements in downstream Water quality but in the
large upstream improvemen-ts in water quality. Thus, it is advantageous
to locate estuarine outfalls as near the mouth of the estuary as
possible.
	 END OF EXAMPLE VI-6 	
6.5.5 Continuous Flow Non-Conservative Pollutants
Most of the discharges made into an estuary will have non-conser-
vative components, with BOD being the most common of these. In ad-
dition to dispersion and tidal mixing, these components will also decay
as a function of time. The concentration of the non-conservative pol-
480

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lutants will thus always be lower than that for conservative pollutants
(which have a decay rate of zero) for equal concentration of discharge
rates. The results of the previous section for conservative consti-
tuents will serve to set upper limits for the concentration of non-
conservative continuous flow pollutants. Thus, if plots similar to
Figure VI-24 for river discharges and to Figure V1-27 for other direct
discharges have been prepared for flow rates equal to that of the
non-conservative 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 non-conservative constituents, non-conservative concentration is
given by:
ct = coe~kt	(VI-20)
where	c^ = pollutant concentration at time
"t",
cQ = initial pollutant concentration.
k = decay or reaction constant
and	t = elapsed time (usually measured in days
or tidal cycles)
For conservative pollutants k = 0 and c^ = cQ under steady state
conditions, k values are determined empirically, and depend on a large
number of variables. Typical k values for the two major estuarine decay
phenomena to be addressed (BOD and coliform bacteria) are shown in
Table VI-7. If data are not available for a particular estuary, the
use of these average values will at least ensure reasonable estimates.
481

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TABLE VI-7
TYPICAL VALUES FOR DECAY REACTION RATES ' k' *
Source
BOD
coli form
Dyer, '73

.578
Ketchum, '55

.767
Chen and Orlob '75
.1
.5
Hydroscience '71
.05-.125
1-2
McGaughey '68
.09

Harleman '71
.069

*k values for all reactions given on a per
tidal cycle basis.
It should bo noted that decay rates arc dependent upon temperature.
The values crivon assume a temperature of 20 C. Variations in k values
for differing temperatures are given by equation VI-21.
T-20
ky ~ ^20 	(VI-21)
where
ky = decay rate at temperature "T",
^20 = decay rate at 20C (as given in table VI-7),
and
0 = a constant (normally between 1.03 and 1.04)
Thus an ambient temperature of 10 C would reduce a k value of 0.1
per tidal cycle to 0.074 for a 0=1.03. Table VI-7A shows the tempratur
correction for various temperatures. The actual k value is then the
product of the kOg0 value and the correction factor. Where temperature
data are not available for either an estuary as a whole or for a segment
of the estuary, use kQO values.
482

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TABLE VI-7A
TEMPERATURE CORRECTION FOR SELECTED TEMPERATURES
Temperature (C)
0T-2O*
6
0.661
8
0.701
10
0.744
12
0.789
14
0.838
16
0.889
18
0.943
20
o
o
0
	1	
22
1 .061
24
1.126
26
1 .194
28
1.267
30
1.344
*for 0 = 1.03
Decay effects can be compared to flushing effects by setting time
equal to the flushing time and comparing the resulting decay to the
known pollutant removal as a result of flushing.
If kt in equation VI-20 is less than 0.5 for t = T-, decay processes
would reduce concentration by only 1/3 over the flushing time. Here mixing
and advective effects dominate and non-conservative decay can be discounted.
When kT^ > 12 decay effects would reduce a batch pollutant to 5% of its
original concentration in less than 1/4 of the flushing time. In this case,
decay processes dominate and steady state concentrations will approximate
those resulting from decay alone. Between these extremes, both pro-
cesses are active in removing a pollutant from the estuary with
3 < kTf < 4 being the range for approximately equal contributions to
removal. Dyer (1973) analyzed the situation for which decay and
tidal exchange are of equal magnitude for each estuarine segment.
483

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Knowing the conservative concentration, the non-conservative steady-
state concentration in a segment is given by:
f. / r. \
c. = cQ T-(l-r.)ek) for se9ments downstream	(VI-22a)
1 / of the outfall
S.I r. Y
and	ci = cQ sM-[_(])e-kJ for segments upstream	(VI-22b)
0 ^ "* / of the outfal 1
where c. = non-conservative constituent mean
concentration in segment "i",
c = conservative constituent mean con-
o
centration in segment of discharge,
r.. = 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=l for segments adjacent to the
outfall; n=2 for segments next to these
segments, etc.)
and other parameters are as previously defined.
	 EXAMPLE VI-7 	
Continuous Discharge, Non-Conservative, Steady State Concentration
Calculation
Example VI-6 considered an agricultural runoff containing pesti-
cides. The flow entered Alsea Estuary from the river. In addition to
pesticide concentrations, however, BOD concentrations in an estuary as
a result of projected agricultural activity should be calculated.
484

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Based on DEQ data and previous calculations for river flow (see Chapter
4 for river related calculations) it is known that the summer mean river
concentrations of BOD resulting from this activity as it enters Alsea
Estuary is 3.2 mg/1.
It is reasonably apparent that decay and tidal mixing for BOD in
Alsea Estuary are both important.
From previous calculations, - 17 tidal cycles and thus it can be
estimated that kTf = 1.7 (see Table V1-7 for k values). For a kTf
value in this range it would be expected that tidal action predominates
but that decay significantly reduces steady state concentrations.
Values of f and S for Alsea Estuary are shown on Figure VI-26.
X	X
Since the current problem involves river borne introduction of pol-
lutants, there are no upstream segments in the estuary and salinity
values will not be needed. Values of r. and segment designations are
obtained from the Modified Tidal Prism Method flushing time calculations.
Table VI-8 summarizes this information and lists B. values where:
thus
f.
Given that cR = 3.2 mg/1,
then cq = cr f = (3.2 mg/1) (.970) = 3.104 mg/1
This c value is for conservative pollutants,
o
485

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Thus	f
cQ = c -j Bq = cQ Bq = (3.104 mg/1 ) (.9096) = 2.82 mg/l
o
for non-conservative pollutants.
TABLE VI-8
TABULATION OF VALUES FOR NON-CONSERVATIVE POLLUTANT CONCENTRATION
segment
n
f.
1
r.
~
B.
l
0
1
.970
.489
0.9096
1
2
.921
.707
0.9256
2
3
.805
.450
0.7189
3
4
.547
.663
0.8278
4
5
.119
.800
0.8891
*k- 0.1 is assumed for these calcula-
tions
Having calculated segment '0' concentration, remaining
segments are estimated by table VI-8 and:
f.
c . = c B .
486

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segment c. (mg/1)
0
2.82
4
2
3
2.48
1 .68
1.32
0.31
Figure VI-28 shows this estimate of non-conservative concentration
distribution. Additionally a plot of the concentration of a conservative
pollutant with the same discharge characteristics is shown for comparison.
Large segment exchange ratios result in lower amounts of pollutant decay
as residence time in the segment is reduced. The mass of pollutant de-
cayed with time increases directly with the decay rate k. To demon-
strate this, the dotted line on Figure VI-28 uses a k value of 0.578
(typical for coliform bacteria decay). The initial discharge rate is
equal to the previous BOD discharge rate. However, an increased decay
rate results in concentration in the mid-estuary section of approxi-
mately 1/3 the BOD concentration. Changes in moan section DO levels
could now Qualitatively be estimated as the inverse of the change in BOD
load throughout the. estuary. An example of this inverse relationship is
shown in Figure VI-29. As can be seen, there is longitudinal translation
of peak BOD to peak DO deficit due to net downstream advection. Addi-
tionally peak BOD is greater than peak DO deficit. The concept of DO
deficit was introduced in previous chapters of this report and will not
be expanded here. Because of the complexities of estuarine transport
and of the complete oxygen balance, and because many water quality reg-
ulations are now written for maximim allowable BOD, this chapter will not
go beyond BOD calculation. Where large BOD loads exist (5 mg/1 or more),
DO problems may be inferred. A complete analysis of the oxygen balance
in that spatial area should then be conducted using computer model tech-
487

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k= 0.578
(Coliform
Bacteria)
Non-conservative
Conservative
80
40
50
60
70
30
20
DISTANCE (x) FROM MOUTH (inlOOOFT.)
Figure VI-28 Example Estuarine Non-Conservative Pollutant Concentration
If
ESTUARY reach
x=o
Fresh-"^
water
Flow
I
W lbs/day BOD
3
Ocean
BOD
>
DO
DEFICIT
Saturation
Figure VI-29 Incremental BOD Loading - DO Response in Estuaries
488

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niques. The principle goal here is screen large estuarine areas and to
identify probable water quality problem areas. A BOD analysis is adequate
for this purpose.
END OF EXAMPLE VI-7
6.5.6 Use of Dispersion Equations
Until now the distributions of salinity and fresh water within
an estuary have been used as an indicator of the steady state results of
dispersion. Without knowledge of roughness coefficient, hydraulic
radius, and actual dispersion coefficients, this procedure is as good
an approximation as is practicable. If necessary data are available,
however, the use of a more formal dispersion equation for non-conserva-
tive pollutants is advisable.
Good reviews of this approach are provided by Harleman (1971),
O'Connorand Thomann (1971), and in summary form by Hydro^cience (1971).
Tiie approach and equational forms used by each researcher is the same.
The basic steady state equation of mass conservation for non-
conservative substances in an estuary is:
,2	,
0=E ^	U - kc (O'Connor and Thomann, 1971) (VI-23)
dx*-
where E = diffusion coefficient,
c = substance concentration
U = net velocity
and	k = decay, or reaction, coefficient as previously
defined.
The solution for equation VI-23 for.the concentration at any
point is:
-qx
c = co 6 '^or x<0 (downstream)
(VI-24)
c = co 6^X ^or x>0 (upstream)
and
489

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where: cQ is the concentration at the outfall point and is given by
w	=
C
it
w = waste discharge load
A = cross sectional area,
9 2E LU+ V U2 + 4kEJ
and	J = 2E [u- V U2 + 4kE]
The major unknowns in this set of equations are k and E. As was
covered in the previous section, k is an empirical approximation of
actual decay, consumption and mortality processes and can be approximated
by a range of values. E, the dispersion coefficient, is also an
empirical coefficient, and can be explicitly determined for any estuary
only by direct in-situ measurement. However, Harleman (1964) has
developed a formulation for approximating actual dispersion coefficient
values. This is:
E = 77 nv Rh5/6	(VI-28)
where: n = Mannings roughness coefficient*
v = velocity in fps
hydraulic radius in feet**
and E = dispersion coefficient in ft2/sec
* This coefficient is a function of the bottom surface. Typical estuarine
values range from 0.028 to 0.035 depending on bottom cover.
** The hydraulic radius is defined as the cross sectional area divided by
the wetted perimeter of that cross section.
w
A yju2+ 4kE
(VI-25)
5F [,+ Vl + |] (VI-26)
sr[i-Vi+44] (VI"27)
490

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Harlemari (1971) discussed this approach to estimating E and was
able to relate E to maximum tidal velocity by:
E = '3 n Umax Rh '6	(VI-29)
where
E = longitudinal dispersion coefficient (in mi /day)
n - Manning roughness coefficient
Umax= max"'mum tidal velocity (in feet/sec)
and
Rh = hydraulic radius (in feet)
Equation VI-29 can be written for E-j calculation in ft2/sec units by:
E - 100 n Ufflax Rh '6	(VI-29a)
Use of either Equation VI-29 or VI-29a has the advantage of using
maximum tidal velocity rather than net non-tidal flow. Umax is directly
measurable and is generally available for U.S. estuaries in existing
literature. Both of these equational forms assume constant density
over a cross-section. While this limits the applicability of these
E approximations, it is consistent with previous assumptions of this
chapter for uniform cross-sectional U and S distribution.
The dispersion coefficient wi-J-1- vary somewhat over the length of
an estuary, decreasing toward the head of the estuary. Evenson (19/7,
personal communication) has identified three principal components which
comprise a dispersion coefficient: tidal mixing, salinity gradient mix-
ing, and net fresh water advective flow. The relative location in an
estuary for which each of these factors is significant, and their
relative magnitude is shown in Figure VI-30. Compounding the variation
in causal forces, the datum used as a basis for the calculations (MHT,
MLT, tidally averaged) will result in very different estimates for E.
Nonetheless, some range of values for certain types of estuaries can
491

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be obtained. Table VI-9 shows a range of values for kE for several
qualitative types of estuaries compiled by Hydroscience (1971).
Knowing that k values vary over a range of values, the range of
potential values for E is expanded from the kE listed in Table VI-9.
For example, if k varies from 0.2 to 0.5 for a major estuary, E
2
could vary from 10 to 100 mi /day and still satisfy the listed kE
range. Additionally, Table VI-10 lists E values calculated by
Hydroscience (1971) for selected estuaries. As can be seen from
Table VI-10 variations in dispersion parameters are large over the lengths
of a typical estuary. Unless specific E values are available from field
experimentation it is felt that the potential error from incorrect value
selection is too large to justify the use of this approach. In a case
in which the previous methods independent of a dispersion coefficient
are inadequate and in which specific E values are not known, the use of
computer models or dye studies to determine actual E values are recom-
mended.
Freshwater
Mixing|
Tidal Mixing
HEAD
MOUTH
RELATIVE DISTANCE -
Figure VI-30 Contribitting Factors to Dispersion Coefficients
in the Estuarine Environment
492

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TABLE VI-9
kE VALUES FOR SEVERAL TYPES OF ESTUARIES
Estuary Description
kE (mi2/day2)
Average Value Range
Large, deep main channel, major
tidal action; near mouth of
many estuaries.
Moderate navigation channel,
large tidal tributaries; in
upstream saline intrusions.
10 5-20
3 2-5
TABLE VI-10
E VALUES FOR SELECTED ESTUARY
(FROM HYDROSCIENCE 1971)
Estuary
R (cfs)
Low flow net
non tidal velocity (fps)
head - mouth
E (mi2/day*)
Delaware River
2,500
0.12-0.009
5
Hudson River (N.Y.)
5,000
0.037
20
East River (N.Y.)
0
0.0
10
Cooper River (S.C.)
10,000
0.25
30
Savannah R. (Ga., S.C.)
7,000
0.7-0.17
10-20
Lower Raritan R. (N.J.)
150
0.047-0.029
5
South River (N.J.)
23
0.01
5
Houston Ship Channel (Texas)
900
0.05
27
Cape Fear River (N.C.)
1 ,000
0.48-0.03
2-10
Potomac River (Va.)
550
0.006-0.0003
1-10
Compton Creek (N.J.)
10
0.01-0.013
1
Wappinger and



Fishki11 Creek (N.Y.)
2
0.004-0.001
0.5-1
* 1 mi*7day = 322.67 ft2/sec
493

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6.5.7	Multiple Waste Load Parameter Analysis
The preceding analysis allowed calculation of the longitudinal
distribution of a pollutant, whether it is conservative or non-conserva-
tive, resulting from a single waste discharge. However, the planner
will probably want to simultaneously assess both conservative and non-
conservative elements from several separate discharges. This can be
accomplished by graphing all desired single element distributions on
one graph showing resultant concentration versus length of the estuary.
Once graphed, the resulting concentration may be linearly added to
obtain a total resultant incremental waste load.
An example of this procedure is shown in Figure VI-31. Note
that the sum of the new discharges may be added to original ambient
conditions to estimate new ambient concentrations along the length of
the estuary. This technique of graphing outfall location and charac-
teristics with resulting estuarine pollutant concentration should be
done for all anticipated discharges. This will provide the planner
with a good perspective on the source of potential water quality
problems.
6.5.8	Graphical Analysis
In an effort to develop simplified planning guidelines Hydroscience
(1971) applied the basic dispersion equations (Equation VI-24 through
VI-26) over a wide range of tidal conditions for a dissolved "oxygen anal-
ysis. The analysis covered the ranges of the basic variables which
might be expected under normal estuarine conditions and allowed for
variation in river discharge, net nontidal velocity, mean cross
sectional area, section mean salinity, local dispersion coefficients
and general estuarine topography. Additionally, water temperature,
reaeration coefficients and surface oxygen transfer coefficients were
included as major system variables to allow a more complete oxygen
balance analysis.
494

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Water Quality Standard


New Pollutant
Concentration

Current Pollutant
Concentration
o
en
I-
z
Sum
U
O
z
o
O

I-
z
p
ID
_J
_l
O
0.
I
DISTANCE FROM HEAD
Figure VI-31 Additive Effect of Multiple Waste Load Additions
495

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The results of the Hydroscience analysis were a series of se-
quential graphs which could be used to estimate ultimate BOD, maximum
oxygen deficit, and minimum estuarine mean DO levels as a function of
a single point source loading. The analysis does not directly provide
spatial definition of an oxygen deficiency profile. The goal of the
analysis was to identify DO minima for comparison with existing stan-
dards. Two factors make the Hydroscience analysis of marginal use
here. First, it was intended to serve as an end product, or as the sole
estimate of DO levels, whereas this document represents a part of
a more comprehensive tool. A second phase of this study which includes
various levels of sophistication of computer models will be issued at
a later date. All of the computer models will provide a higher level
of accuracy than either the hand calculations in this document or the
Hydroscience analysis. Thus, the incremental improvement in information
provided by the Hydroscience approach does not warrant the extensive
additional effort. Second, all of the assumptions, limitations,
and simplification listed for the parameter development and definition
in this report apply for the development of the corresponding para-
meters in the Hydroscience methodology. Further, the extensive use of
sequential graphical operations, each of which is directly dependent
on the results of the preceeding step, is subject to the generation of
a large error through step wise increases of an initial minor error.
If however, no follow-on site specific or computer studies are
anticipated, the Hydroscience study methodology is recommended as a
good alternative to those presented in this chapter for the estimation
of estuarie BOD-DO relationships under steady state conditions. The
documentation for that report should be available through county or
local university libraries or from the regional EPA offices.
6.5.9 Salinity Intrusion
Upstream intrusion of sea. salt into the lower reaches of a river
system is often of interest to local planners. Salt intrusion can
endanger municipal water supplies, greatly reduce agricultural pro-
496

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duction in riparian lands, change sedimentation patterns and alter
the spatial distribution of both fresh water and estuarine species.
In addition to the seasonal changes in the salinity intrusion length
previously mentioned, planned changes in either estuarine channel
configuration or in river discharge will alter salinity intrusion
patterns. Channel configuration changes are primarily associated with
dredging projects. An increased cross sectional area results in
increased advective upstream transport of bottom saline waters and
in decreased net non-tidal velocities with the associated increased
upstream salt diffusion. Planned river discharge reductions can result
from increased agricultural fresh water withdrawals, additional
municipal and industrial withrawals, water diversion programs or up-
stream water storage projects. The decreased river discharge will re-
sult in decreased net non-tidal velocities and thus in increased up-
stream diffusion transport.
In previous sections the steady state distribution of conservative
pollutants was analyzed by assuming that this distribution was similar
to the salinity distribution. If salt itself is now treated as a
conservative pollutant, these same fcasic methdologies could be used to
analyze a new unknown salinity distribution (Stommel, 1953). However,
the methods presented for a continuous flow conservative pollutant
are not applicable since they require a known salinity distribution.
Prediction of a new salinity intrusion length can be approached
by use of the dispersion equations presented in the previous section
(Equation VI-24 through VI-27). For conservative pollutants the form
of Equation VI-27 reduces to:
J = -rjjjl=	(Stommel, 1953)	(VI-30)
This may now be applied to the new salinity regime by setting cQ
at x = o (at the mouth of the estuary) equal to ocean surface salinity
497

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(~35/oo) and by setting l/oo as the upper end of the salinity intrusion.
Thus from Equation VI-24
Cx = 1/oo _ -(Rx/AE)
c0 ~ 350/oo
or 3.5554 =
and
3.5554 AE
X	R	(VI-31)
where
x = length of the salinity intrusion at l/oo or greater
and where A, E, and R are as previously defined.
The solution of equation VI-31 is an iterative process. A and E will
both vary with x. Thus, the procedure for use of VI-31 should be to
assume an x value, obtain the A and E values associated with that x
and then put the A and E values into equation VI-31 to see if the
calculated x equals the assumed x. Based on the magnitude and direction
of the resulting in-equality, select a new x value and repeat the proced-
ure until the resulting error is acceptably small (in the range of 5%
of x).
6.5.10 Non-Continuous (Single Event) Discharges
Single event discharges into an estuary are of much less concern
to the planner than are continuous discharges. This is true for several
reasons. First, single event discharges (storm drains, leaks, spills,
etc.) normally represent a small fraction of the total annual estuarine
498

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waste load. Second, the effects of such single event discharges are
relatively short-lived and will thus have a much smaller impact on the
estuarine ecosystem. Within these constraints however, major single
events (large storms, major oil spills, etc.) can have a significant
short term impact on estuarine water quality.
Analysis of conservative and non-conservative substances will be
approached separately as was the case for continuously discharged pollutants.
6.5.10.1 Conservative (Single Event) Pollutants
If a single event discharge enters an estuary with the river dis-
charge, the flushing time provides a measure of the total estuarine
residence time for that pollutant. As was evident from Figure V1-24
and Example VI-4, maximum pollutant concentration will occur near the
head of the estuary. Methods described for calculation of concentrations
of conservative pollutants are not applicable for single event pheno-
mena since such events will not reach a steady-state condition. The
concentration calculated by continuous flow methodology will, however,
act as an upper limit to the concentration of a single event pollutant
flow for a specified discharge rate. An additional estimation of
single event concentration can be made based on the following assumptions:
1.	Discharge period into the estuary equals one tidal cycle.
2.	All pollutant entering the estuary during the one tidal
cycle will remain in the inner-most estuarine segment
throughout the cycle(i.e. the pollutant will obey "plug
flow" theory).
The curve in Figure VI-32 represents the temporal flow of a pol-
lutant into an estuary over one tidal cycle. Combining this with
the two assumptions listed above, the following two estimates of
pollutant concentration for the inner-most segment can be made.
499

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One Tidal Cycle
o Qpr
~time
Figure VI-32 Single Event Pollutant Flow Into An Estuary
cPi(MLT) CPr 2  vol.	(VI-32a)
and
C Pi(MT) CPr vol^ + Pi/2	(VI-32b)
where
Pi (MLT) = concentration of pollutant in segment "i"
at mean low tide of the first tidal cycle
after pollutant entry
500

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cPi(MT) = concentrat"'on pollutant in segment "i",
at mean tide of the first cycle after
pollutant entry
Cpr = concentration of pollutant in river discharge
and R, vol^ and P.. are as previously defined.
The relative magnitude of these two concentrations will
depend on the relative magnitudes of P^ and R. Normally Cp^MLjj
will be larger and will thus represent peak concentration of
a conservative pollutant for this event.
Single event conservative pollutant flows entering either along
the sides of an estuary or directly into the central waters are not as
easy to analyze. A lower limit for estuarine residence time can be
estimated by adding the segment flushing times for the segment of entry
and all seaward segments. This, however, assumes that none of the
pollutant is transported upstream from the segment of entry which is
generally not true. This residence time and associated pollutant con-
centration is really a function of local dispersion characteristics,
estuarine flushing characteristics, length of the discharge period,
and the time of release with respect to tidal stages. A pollutant
released during an outgoing tide will have very different residence and
concentration characteristics than one-released during an incoming
tide. While it is obvious that a pollutant release during an ebb tide
is preferable to one during a flood tide it is equally obvious that
neither the time of storms nor that of leaks and spills is subject to
discretionary planning.
Peak concentration for a single event discharge will be at the
discharge point, or in the segment of discharge. By assuming that lateral
501

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~
and vertical dispersion is complete and instantaneous and that the
discharge occurs instantaneously, a peak pollutant concentration can
be estimated by:
cPi (max) = V01!	(VI-
where
i	= segment of discharge
cp./ \ = maximum potential concentration of the pollutant
i I y 1113 /\ /
Qp.j	= quantity of pollutant released
and
vol. = low tide volume of segment i
*This appears to be a reasonable assumption, especially for verticle
mixing. Work by Fisher (1968) estimated vertical mixing as:
E7 = 0.23 dU*
Z
where
= vertical dispersion coefficient
d = segment depth
and
U* = shear velocity
Resulting E7 values for typical estuaries are on the order of 0.2 to
1 ft/sec. Thus a 60 ft deep segment would be vertically mixed in
approximately 1 minute - a very short period with respect to a tidal
period.
502

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Ippen (1966) applied finite difference techniques to the
basic conservation of mass equation* in order to derive a stepwise
method for tracking longitudinal concentration of such an instantaneous
conservative discharge. Knowing an initial concentration in the
segment of entry, this technique may be applied by:
Cx,t+At x

Ax Ax2 { (AD ^x+Ax/2+ ^AD ^x-Ax/2}
'X +Ax
X -Ax
r_u
["u
'* [2I
(AD')
A
At
2Ax~
(AD')
A
tel]
!fe( ]
(VI-34)
where
Ax and
At
longitudinal distance from the discharge point
longitudinal and time steps
cross-sectional area at "x"
pollutant concentration
*This conservation of mass equation is:
i + u 
3t	3x
1 JL
a ax
(ADx i)
Kc
where
and
A	=
c
U	=
Kc	=
longitudinal dispersion coefficient
cross-sectional area
pollutant concentration
current velocity
decay term which is disregarded in an analysis of conservative
pol1utants.
503

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apparent longitudinal dispersion coefficient. D" includes
dispersion due to vertical instabilities as well as tidal
and dispersion effects. In areas of little vertical
instability (well mixed estuaries) verticle instability
mixing is minimal and D approximately equals dispersion
coefficients as previously defined in this chapter.
Application of Equation VI-34 requires that consecutive
calculations be made for points x defined by x = + nAx from the
point of discharge and then for each time step (t + At) from the
time of release until essentially all the pollutant has been removed
from the estuary. Thus a large number of calculations are required
for this analysis and computers are usually used in the process. It
is important to note, however, that the concentration at any point
for the next time step (cx t+At) is dependent on dispersion out of
that segment during this time step and on previous concentration at
both the adjacent upstream and downstream segments. This approach,
then,recognizes both upstream and downstream advection and dispersion.
6.5.10.2 Non-Conservative Single Discharge Pollutants
As shown on Figure VI-22 this category of discharge includes
perhaps the most important of the single event pollutants - storm
drain BOD loading. In addition to being dependent on flushing,
dispersion time and length of discharge, this group of pollutants
is also dependent on decay rates. It is felt that too many approxi-
mations and assumptions are involved here for reliable application
of hand calculations. Computer models can test a wide range of
possible coefficient values and then be calibrated to accurately
reflect conditions in a given estuary. Without this "tuning" process
the potential error is substantially larger than the predicted concen-
tration values.
and
D' =
504

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It is possible, however, to apply a first order decay term to
Equation VI-34 at each time and spatial step to arrive at an equation
of the form:
cx,t+At = F (c.AD',t,x) e"k(t+At)	(VI-35)
where
k	= first order decay coefficient
e k(t+At)_ decay term for the time step from t to t+At
and
F(c,A,D',t,x) represents the three terms on the right hand
side of Equation VI-34.
If dispersion and decay coefficients for a given pollutant
in a specific estuary are known over the full length of the estuary,
and if good estimates are available for probable initial pollutant
distribution in the estuary (preferably through actual field
measurement of a previous event), then Equation VI-35 should be
applied. Under these conditions it will give acceptable results.
A final suggestion is in order for the analysis of single
event discharges. Mathematical results for all of these discharges
are dependent on empirical coefficients. Accuracy and reliability
will be greatly enhanced, and the guesswork of selecting coefficient
values reduced, if they are measured for each estuary. Dye tracers
can be injected into an estuary and tracked over time. Surface and
bottom floats can be spread over a cross-section at various stages
of the tide and traced over time. A wide variety of experimental
low-cost techniques are available. The information they provide will
not only be the basis for input data to mathematical models but will
give the planner an intuitive feeling for the controlling processes
in each estuary which will allow him to intelligently interpret,
and analyze the results obtained from a model.
505

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6.6 THERMAL POLLUTION
6.6.1 General
The presence of one or more major heat sources can have a signifi-
cant impact on both the local biotic community and local water quality.
As a result, consideration of significant thermal discharges by the planner is
essential in any comprehensive water quality analysis. Thermal power
plants account for the vast majority of both the number of thermal dis-
charges and the total thermal load. However, some industrial process
generate significant amounts of excess heat. This discussion will not
attempt to address total heat budget calculations. This should be left
to computer modeling.
The most important of the impacts of heat discharge are:
1.	Ecological Effects: Water temperature increases change the
productivity levels for planktonic and many benthic species.
As a result local community structures are altered. By
itself, this is neither good nor bad. However, many of the
species benefited by warmer conditions (e.g., blue green
algae) may be considered to be undesirable. In addition, many
species can perform certain life cycle functions only within
a limited temperature range. Elevated temperatures
may prevent some species from completing one or more
life stages, thus disrupting the reproductive cycle and
destroying the stability of the population.
2.	Water Quality Effects: Figure VI-5 showed the relative ef-
fect of salinity and ambient temperature on oxygen saturation.
From this figure, note the impact on the oxygen saturation
0 *
concentration of a 10 C rise in temperature. This impact is
*Suc.h a rise is common near power plant thermal plumes.
506

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especially significant when ambient temperatures are in the
10C to 15C range which is typical of many estuaries.
3 Sediment Effects: Estuarine sedimentation rates will be increased by
increasing local water column temperature. The significance
of this increase was discussed by Parker and Krenkel (1970).
They concluded that not only will sedimentation rates be in-
creased, but vertical particle size distribution, particle
fall velocity, and thus bottom composition will also be affected.
4. Beneficial Effects: The effects of thermal discharges are
not all negative, however. It has been shown for example,
that marine biofouling is substantially reduced in warmed
waters (Parker and Krenkel, 1970). In fact, the recirculation
of heated discharge through the condensor has proven to be a less
expensive and equally effective method of biofouling control than
chlorination for several California coastal power plants.
Estuarine contact recreation potentials are increased by increasing
local water temperatures, and extreme northern estuaries will
have reduced winter ice coverage as a result of thermal discharges.
6.6.2 Approach
A schematic of the heat budget for a segment of an estuary is shown
in Figure VI-33. These heat transfer processes (Q , Q , Q , Q , Q . )
s	r	- xr> - ^win/
are a function of water temperature, cloud cover, time of day, wind
velocity, air temperature, relative humidity, water density and atmospheric
pressure. These can all be easily incorporated into a computer model
but are awkward for hand calculation. However, the prime concern at this
level of analysis is to assess changes in estuarine temperature resulting
from man induced changes in thermal loading (e.g., thermal discharges).
Therefore, the advective transport of heat through the estuarine water
column can be addressed without accounting for heat transport across the
water surface. jhe immediate loss of heat from a thermal plume across the
water surface is small and an analysis of advective transport alone
507

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will not result in major errors.
Q = Q - Q +0 - Q - Q - Q - Q . Q . + Q . + 0 . + 0
ws wr ya var ybs e h vwont uwin Vvin yvout
where
Qs = short wave incident radiation
Qr = short wave reflected radiation
Qa = incident long wave radiation
Qar = reflected long wave radiation
Qbs = ln9 wave back radiation
Qg = energy utilized in evaporation
= sensible heat loss
Qwout = heat carried away with evaporated water
Qwin = heat bought ir.to estuary with precipitation
^vin = net ac)vective heat inflow
Qvout = net advective heat outflow
and
Q = net change in water body stored heat
Figure VI-33 Estuarine Heat Budget (After Parker and Krenkel, 1970)
508

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Thus, the approach used here will be to treat excess temperature as
a conservative pollutant and to then measure the resulting excess tempera-
ture* distribution. Characteristically, thermal discharges are associated
with large volumetric water flow rates. As a result, jet and plume effects
are often present in the area of the outfall. Thus an analysis of thermal
discharges must be divided into two spatial categories - the area immedi-
ately surrounding the discharge point which is influenced by momentum
effects, and the surrounding nearby area. Consideration of distant points
will not be made. If the effects of a thermal discharge are measurably
very far away from the discharge point (several miles away, for example)
then the water quality effects immediately surrounding the outfall will be
extreme. Therefore, prediction of the close-in and intermediate area
thermal distribution will suffice to anticipate whether or not a thermal
discharge will have important water quality impacts.
Finally, it will be assumed that all discharges are continuous,
and only steady-state (non-tidal) conditions will be considered.
6.6.3 Initial Temperature Distribution
The temperature distribution in the immediate vicinity of a ther-
mal discharge is dependent on the discharge structure design. The
total advective and dispersive fields transporting heat in this region
are determined by the momentum and buoyancy of the discharge
Thermal discharges often have high momentum because of their high
velocity and flow rate. The high velocity discharge typically entrains
large volumes of ambient water. This will lower the average excess
temperature of the water. Entrainment is limited by the ability of
ambient water to move into the discharge region and by the spatial ex-
pansion patter of the discharge.
~
Excess temperature is a measure of the temperature of a water column
above levels measured without the effects of the thermal discharge.
509

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Momentum jet relationships are applicable to the calculation of the
thermal distribution in the immediate area of the outfall based on the
assumptions and limitations made above. Using dynamic similarity it
can be shown that for a jet expanding in two directions (laterally from
its center line and downstream) the characteristic velocity will decrease
as the square root of distance along the axis, and that for a jet ex-
panding in three directions (laterally and vertically and downstream)
the characteristic velocity will decrease linearly with distance
(Edinger, 1971).
From this, the following scaling factors between discharge
conditions and points downstream may be established for the two
dimensional case so that downstream conditions may be analyzed.
1. Momentum conservation:
2x U2x = o Uo	(V'"36)
2. Dynamic similarity:
u9v - / \ 1/2

(VI-37)
and 3. (from 1. and 2.):
^2x = / _x_ V/2	{VI-38)
% V xo >
where
x = any downstream point measured along plume center line
from the point of virtual discharge
510

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xQ = virtual discharge length (similarly Qq and IJ
are the flow rate and velocity at the virtual
discharge location
Q = plume volumetric flow rate,
o
U = plume flow velocity
The virtual discharge position (xQ) is that distance downstream
from the actual discharge point beyond which discharge jet flow character-
istics measurably change from the in-pipe conditions. This distance is
generally two to ten times the discharge diameter (Edinger, 1971, and
Brooks,1972). For discharges into flow fields generally perpendicular
to the discharge velocity (as is typical for river and estuarine discharge)
nearer the lower limit (two times the diameter) is a better estimate of xQ.
It is important to note in Equation VI-38 that the flow dilution
ratio ((^ /Q ) is independent of discharge characteristics for any
given distance downstream. Thus, if Qq is increased by increasing UQ,
entrainment processes will increase proportionately so that Q2X/Q0
will remain unchanged.
Excess temperature may be tracked through the initial mixing stage
by assuming excess heat is conserved over the time and space of
initial mixing. With this assumption,
and
Q2X and U2X denote 2 dimensional (downstream and lateral)
flow rates and velocities
H s constant = Qq 0q = Q2x 0x
(VI-39)
0
x
(VI-39a)
where
H = excess quantity of heat discharged at the outfall
per unit of time (same time units as used in
"Q" values),
511

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and	0 = excess temperature at the discharge
For application of these equations, is calculated from equation
VI-38 for some downstream point "x." Then equation VI-39 is used to
calculate 6 for that downstream cross section. It must be remembered
X
that 0 is averaged over the entire width of each cross section and
thus does not represent 0x for each location across the plume cross
section since there is substantial integrity in the central portion of
the plume during initial mixing. This is made more evident in
Figure VI-34.
Channel Width
DISCHARGE
Initial Mixing Range
(net velocity)
10--
PLUME WIDTH
Figure V 1-3*1 Initial Thermal Plume Nixing
512

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Within the following limitations, however, equations VI-36 through
VI-39 will provide a meaningful picture of plume mixing during this initial
momentum mixing process.
1- The equations are only applicable in the area dominated
by momentum mixing. While no exact criteria are given to
define this region, it is restricted to the immediate down-
stream area from the jet and typically extends on the order
of several hundred feet downstream.
2. The angle of discharge to the estuarine velocity field
has been ignored. While changes in the angle of discharge
will change xQ values and will change the reach over which
these equations are valid, it will not invalidate the use
of equations VI-36 through VI-39.
3. Tidal action has been ignored. The system's response to a
jet discharge will differ substantially during different
stages of the tide. However, this variance will not be
excessive in the immediate vicinity of the discharge.
4. Only the two dimensional case has been described. Thus
complete initial vertical mixing is assumed so that only
lateral and longitudinal plume spread need be addressed. In
three dimensional form, equation VI-38 is (Edinger, 1971):
Q3x = x
Qo *o
in this case, is still calculated using equation VI-39.
513

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6.6.4 Intermediate Temperature Distribution
Temperature distributions outside the region of momentum mixing
are governed by the advective and dispersive characteristics of the
receiving waterbody. The temperature distribution in the intermediate
region can be estimated no more precisely than the detail with which
velocity and dispersion can be specified for inclusion in a heat
conservation equation. The velocity field is no longer controlled
by the discharge jet and must be derived from either dynamic equations
of motion or from some net non-tidal calculations. Relative to the
intermediate temperature distributions, the initial temperature distri-
bution determined by momentum mixing acts like an extension of a thermal
plant condenser. The thermal distribution resulting from initial mixing,
either by surface or submerged discharges, gives the source thermal
distribution to be used as an initial condition for intermediate heat
distribution calculation (Edinger, 1971).
Previous simplifications prevent complete analysis of this inter-
mediate temperature distribution. However, Edinger (1971) describes
the derivation of a relationship for estimating the area within a given
excess heat contour for the two dimensional discharge flow. This relation-
ship is defined as:
_3
0 = 0.168^ j	( VI-40 )
n2
where: AQ = surface area with excess temperature >0 (area within a
U	
contour line defined by excess temperature = 0)
0 = the excess temperature to be used as a basis for
the calculation
0p= initial excess temperature of plume,
2
and An= a scaling area (in ft ) defined by:
514

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n2
0.715
E U2 d3
(VI-41 )
where	- plume volumetric flow rate after momentum mixing
(generally in cfs units)
E = local dispersion coefficient (in ft? sec)
U = net non-tidal current velocity (in ft/sec)
and d = average water depth of the plume over the area of
intermediate mixing (in ft).
Typically, intermediate mixing extends several thousand feet down-
stream (Edinger, 1971) so that water depth should be averaged over this
distance. Discharge configuration design will determine both whether
or not momentum mixing will occur and, if so, over what distance it will
dominate the mixing processes. In the absence of any other information,
momentum mixing may be assumed to occur over 100 feet to 200 feet. These
estimates may then be used as inputs to equations VI-40 and VI-41.
Edinger and Polk (1969) used these relationships to investigate
the assumption that excess heat would be conservative over these
initial and intermediate areas. They found that inclusion of the
various surface heat transport processes had little effect on the
resulting areas for excess temperature greater than 0.2 0 . Thus
equation VI-40 may be used to estimate AQ for 0 > -20p. This AQ
is then the limit of the capability of these calculations to reliably
predict an Ap and this 0 is the smallest 0 for which these hand calcu-
lations should be used. This 0 will typically be on the order of 2F
to 4F.
515

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It must be remembered that there are a large number of approximations
and assumptions built into equations VI-40 and VI-41 (E, xq, x, etc).
Thus the resulting areas will also be approximations and are best suited
to be "order of magnitude" guides toward the effects of a thermal
di scharge.
	EXAMPLE VI - 8 		
Initial and Intermediate Thermal Mixing
A thermal power plant will be located on the upper reaches of an
estuary. Here the net non-tidal flow velocity is 0.6 ft/sec under low
river outflow conditions and MLLW depth is 10 feet in the region of the
plant. Well-mixed conditions are assumed during this season for this
part of the estuary. The plant will discharge 1100 ft /sec through a
10 ft. diameter pipe and will have a plant AT of 20F at rated capacity
operation. From work associated with previous sections of this chapter
the dispersion coefficient (E) in this region has been estimated to be
2
100 ft /sec*. You want to know what area will be subjected to an
excess temperature of 5F or more.
According to equation VI-38.
"2x=rx v*
X bd
Arbitrarily setting x  200 ft as the limit of initial mixing, and
assuming that xq ^ 6 multiplied by Pipe Diameter,
*This value is compatable with equation VI-29a and may be typical for the
main channel portion of many estuaries.
516

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I2x_
1100 ft^/sec
200 ft
6x10 ft
1/2
or
Qx = 2008 ft /sec
From equation VI-41,
with Qp = Q2x = 2008 ft /sec
Q 3
 p
A = 0.751 .
n	1 E U2 d3
(w)
= 0
.751 ( -
v (1
(2008 ft3/sec)"
(100 ft^/sec.) (0.6 ft/sec)^ (10 ft)"*
)
or
A = 168,900 ft
n
Then for equation VI-40,
VsFf '168 A
(t)
-3
(0.168) (168,900 ft )
o:v-3

Thus,
Aq_5Qp = 1-816 x 106ft2 =41.7 acres
END OF EXAMPLE VI-8
Conditions outside this area of intermediate mixing may be inferred
from the outer fringes of the intermediate mixing area. In the above
example, 0.20 = 4F and AQ _ ,or = 81.4 acres, or twice the area
associated with an excess temperature of 5 F. It is unlikely that a plume
517

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of this surface area would extend much more than 2 to 3 miles downstream. If
the resulting thermal regime at that point is acceptable, then points
farther downstream in the estuary should also be acceptable as they will
be closer to ambient conditions. If thermal conditions farther downstream
must be analyzed for some special situation the use of computer models is
recommended.
If an estuary is either stratified or partially stratified this
procedure may still be used. However, the estuarine depth term (d)
in Equation VI-41 should be altered to reflect the depth of the surface
water layer providing that the discharge is not made below this surface
layer. If the discharge is made into bottom waters, computer or physical
models may be required.
6.7 TURBIDITY AND SEDIMENTATION
Turbidity and sedimentation rates are accorded great importance by
many decision makers and by much of the general public. Turbidity
affects water clarity and water color and hence is of esthetic signifi-
cance. It also affects light penetration, so that increased turbidity
results in a decreased photic zone depth and an associated decrease in
primary production. Sedimentation is also of direct economic importance.
Dredging and dredge spoil disposal costs represent a large portion of
many local and federal water projects. This is especially true for required
maintenance dredging in high sedimentation areas. Unfortunately, current
state-of-the-art ability to predict sedimentation patterns throughout an
estuary, or to predict actual estuarine turbidity levels, is very limited.
It is possible, however, to make some general predictions of sediment
patterns and to develop planning guidelines for estuarine management with
respect to turbidity and sedimentation. Therefore, each topic will be
separately addressed here.
518

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6.7.1 Turbi di ty
Turbidity is a measure of the optical clarity of water and is
dependent upon the light scattering and absorption characteristics
of both suspended and dissolved material in the water column (Austin,
1974). The physical definition of turbidity is not yet fully agreed
upon, and varies from being equal to the scattering coefficient
(Beyer, 1969), to the product of an extinction coefficient and measured
pathlength (Hodkinson, 1966), and to the sum of scattering and
absorption coefficients (VandeHulst, 1957).
Turbidity levels in an estuary are likely to vary substantially
in both temporal and spatial dimensions. Temporal variations occur
as a function of seasonal river discharge, seasonal water tempera-
ture changes, instantaneous tidal current, and wind speed and direc-
tion.
Spatially, turbidity varies as a function of water depth, distance
from the head of the estuary, water column biomass content, and salinity
level. Part of the reason for the wide range of parameters which can
affect turbidity levels is that turbidity is the result of both
scattering and absorption from both dissolved and suspended material
which can be either organic or inorganic in nature. Much of the com-
plexity in the analysis of turbidity results from these different
sources of turbidity responding differently to the controlling variables
mentioned above. As an example, increased river discharge will tend
to increase turbidity because of increased inorganic suspended sediment
load. However, such an increase will decrease light penetration,
thus reducing water column photosynthesis. This, in turn, will reduce
the biologically induced turbidity. In general, suspended sediment
loads of silts and clays are dependent upon river discharge. To a
lesser extent they result from resuspension of estuarine sediment and
from flocculation of very fine colloidal material.
519

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The historical methods employed to monitor turbidity are by the use
of a "turbidimeter" and especially by the use of a Jackson candle turbid
meter (Austin, 1974). Light extinction measurements using this instru-
ment are in Jackson Turbidity Units (JTU) which are based on a clay
suspension. Once standardized, this arbitrary scale* can be used as a
calibration basis to measure changes in turbidity. The calibration JTU
scale is shown in Table VI-11. From a measured change in turbidity
a relative change in water quality may be inferred. Estuarine water
is almost always extremely turbid, especially when compared to ocean,
lake, or river waters.
The JTU scale is not the only available turbidity scale. In 1926
Kingsbury and Clark devised a scale based on a Formazin suspension
medium which resulted in Formazin Turbidity Units (FTU's). More
recently volume scattering functions (VSF) and volume attenuation coeffi
cients (a) have been proposed (Austin, 1974). However, JTU's are
still most commonly used as an indicator of estuarine turbidity levels.
As a rough indication of the wide variations possible in turbidity.
Figure VI-35 shows suspended solid concentrations for the various sub-
bays of San Francisco Bay for one year (Pearson, et_ aj_, 1967). The
solid line shows station annual mean concentrations while the dashed
lines indicate concentrations exceeded by 20% and 80% of the samples
taken at each station over the one year time period. These variations
at stations located near bay heads (left and right extremities of
Figure VI-35) typically exceed 300% of the annual 20th percentile
values. Use of extreme high/low values would produce correspondingly
larger annual variations.
*The JTU scale is an arbitrary scale since it cannot be directly
related to physical units when used as a calibration basis for
turbidimeter measurement.

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TABLE VI-11
GRADIATION OF CANDLE TURBIDIMETER*
Light Path^
cm
Turbidi ty
Uni ts

Light Path^
cm
Turbidi ty
Uni ts
2.3
1000

11.4
190
2.6
900

12.0
180
2.9
800

12.7
170
3.2
700

13.5
160
3.5
650

14.4
150
3.8
600

15.4
140
4.1
550

16.6
130
4.5
500

18.0
120
4.9
450

19.6
110
5.5
400

21.5
100
5.6
390

22.6
95
5.8
380

23.8
90
5.9
370

25.1
85
6.1
360

26.5
80
6.3
350

28.1
75
6.4
340

29.8
70
6.6
330

31.8
65
6.8
320

34.1
60
7.0
310

36.7
55
7.3
300

39.8
50
7.5
290

43.5
45
7.8
280

48.1
40
8.1
270

54.0
35
8.4
260

61.8
30
8.7
250

72.9
25
9.1
240



9.5
230



9.9
220



10.3
210



10.8
200



~~Measured from inside bottom of glass tube,
~from Austin, 1969, pg. 38
521

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110
100
90
60th Percentile
80
70
60
50
? 40
co 20
20th Percentile
2 10
SOUTH
BAY
NORTH
' BAY 
SAN PABLO
BAY
BAY
SUISUN BAY
Figure VI-35 Mean suspended solids in San Francisco Bay
From: Pearson ei al., 1967, pg v-15
6.7.2 Sedimentation
Like turbidity, sedimentation is a multifaceted phenomenon in
estuaries. As in rivers, estuaries transport bed load and suspended
sediment. However with the time varying currents in estuaries, no
equilibrium or steady state conditions can be achieved. (Ippen, 1966).
Additionally, while any given reach of a river will have reasonably
constant water quality conditions, an estuary varies from fresh
water (<1 p.p.t. salinity) to sea water (> 30 p.p.t. salinity), and
from a normally slightly acidic condition near the head to a slightly
basic at the mouth. The responses of many dissolved and suspended
sediments vary substantially across these pH and salinity gradients.
Many colloidal sized particles* agglomerate and settle to the bottom.
*Colloidal particles are particles small enough to remain suspended by
the random thermal motion of the water.
522

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In general, all estuaries undergo active sedimentation which tends to
fill in the estuaries (U.S. Engineering District, San Francisco, 1975).
It is also true for essentially all U.S. estuaries that the rate of
accumulation of sediment is limited not by the available sources of
sediment but by the estuary's ability to scour unconsolidated sediments
from the channel floor and banks.
6.7.2.1 Qualitative Description of Sedimentation
Before presenting what quantitative information is available con-
cerning sediment distribution in an estuary, a qualitative description
of sediment sources, types and distribution will be helpful. Sediment
sources may be divided into two general classes: sources external to
the estuary and sources internal to the estuary (Schultz and Simnons,
1957). The major sources of sediment within each category are shown
below. By far the largest external contributor is the upstream water-
shed.
1. External:
	Upstream watershed
	Banks and stream bed of tributaries
	Ocean areas adjacent to the mouth of the estuary
t	Surface runoff
	Wind borne sediments
	Human input (M & I discharges)
2. Internal
	Estuarine marsh areas
	Wave and current resuspension of unconsolidated bed materials
	Flocculation
	Estuarine biological activity
	Human input (dredging)
523

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General characterizations of U.S. estuarine sediments have been
made by Ippen (1966) and by Schultz and Simmons (1957). Many individual
case study reports are available for sediment characterization of
most of the larger U.S. estuaries (i.e. Columbia River, San Francisco
Bay, Charleston Harbor, Galveston Bay, Savannah Harbor, New York
Harbor, Delaware River and Bay, etc.). In general, estuarine sediments
range from fine granular sand (0.01 in. to 0.002 in. in diameter)
through silts and clays to fine colloidal clay (0.0003 in. or less in
diameter) (Ippen, 1966). Very little, if any, larger material (coarse
sand, gravel, etc.) is found in estuarine sediments. Sand plays a
relatively minor role in East Coast, Gulf Coast and Southern Pacific
Coast estuaries. Usually it constitutes less than 5% by volume
(< 25% by weight) of total sediments for these estuaries with most
of this sand concentrated near the estuarine mouth (Schultz & Simmons,
1957). By contrast, sand is a major element in estuarine shoaling for
the north Pacific estuaries (i.e. Washington and Oregon coasts).
These estuaries are characterized by extensive oceanic sand intrusion
into the lower estuarine segments and by extensive bar formations
near the estuarine mouth. The relative distribution of silts and
clays of organic and inorganic material within different estuaries,
and, in fact, the distribution of shoaling and scour areas within
estuaries, varies widely.
6.7.2.2 Estuarine Sediment Forces and Movement
As sediments enter the lower reaches of a river and come under
tidal influence they are subjected to a wide variety of forces which
control their movement and deposition. First, net velocities in the
upper reaches of estuaries are normally lower than river velocities.
Additionaly, the water column comes under the influence of tidal action
and thus is subject to periods of slack water. During these periods
coarse sand and larger materials tend to settle. Once settled, the
scour velocity required to resuspend the material is higher than that
524

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required to carry a particle when in suspension. Thus, once the
coarser particles settle out in the lower river and upper estuarine areas,
they tend not to be resuspended and carried farther into the estuary
(U.S. Engineering District, San Francisco, 1975). Exceptions to this
principle can come during periods of extremely high river discharge
when water velocities can hold many of these particles in suspension
well into or even through an estuary. Table VI-12 lists approximate
maximum allowable velocities to avoid scour for various sizes of exposed
particles. Values are approximate and are for unarmored sediment
(sediment not protected by a covering of larger material).
Sediment are subject to gravitational forces and have size depend-
ent settling velocities. However, in highly turbulent waters these
particle fall velocities are small compared to background fluid
motion. Thus the influence of natural gravitational forces on sediment
distribution is primarily 1imited to the relatively quiescent, shallow
areas of estuaries and to periods of slack water. Some information can
be obtained, however, by comparing residence time and size dependent
settling velocities to known sedimentation patterns. This will be
covered further in subsequent paragraphs in this section.
As mentioned earlier, particle settling attains a maximum in each
tidal cycle during high water slack and low water slack tides. During
periods of peak tidal velocity (approximately half way between high
and low water) resuspension of unconsolidated sediment may occur. Thus
during a tidal cycle large volumes of sediment are resuspended, carried
upstream with flood flow, deposited, resuspended, and carried downstream
on the ebb tide. Only those particles deposited in relatively quiescent
areas have the potential for long term residence. Compounding this
cyclic movement of sediments are seasonal river discharge variations
which alter estuarine hydrodynamics. Thus, sediment masses tend to
shift from one part of an estuary to another (Schultz and Simmons,
1975).
525

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As fresh waters encounter areas of significant salinity gradients
extremely fine particles (primarily colloidal clay minerals) often
destabilize (coagulate) and agglomerate to form larger particles
(flocculate). The resulting floe (larger agglomerated masses) then settle
to the bottom. Coagulation occurs when electrolytes, such as magnesuim
sulfate and sodium chloride, "neutralize" the repulsive forces between
clay particles. This allows the particles to adhere upon collision
(flocculation), thus producing larger masses of material. Flocculation
rates are dependent on the size distribution and relative composition
of the clays and electrolytes and upon local boundary shear forces
(Ippen, 1966, and Schultz and Simmons, 1957). Flocculation occurs
primarily in the upper central segments of an estuary in the areas of
rapid salinity increase.
Movement of sediments along the bottom of an estuary does not
continue in a net downstream direction as it does in the upper layers
and in stream reaches. In all but a very few extremely well mixed
estuaries upstream bottom currents predominate at the mouth of an
estuary. Thus there is a greater upstream flow at the bottom than
downstream flow. This is counterbalanced by increased surface down-
stream flow. However, net upstream flow along the bottom results in
a net upstream transport of sediment along the bottom of an estuary
near the mouth. Thus., sediments and floes settling into the bottom
layers of an estuary near the mouth are often carried back into the
estuary rather than being carried out into the open sea. Consequently,
estuaries tend to trap, or to conserve sediments while allowing fresh
water flows to continue on out to sea (Strumm and Morgan, 1970). At
some point along the bottom, the upstream transport will be counter-
balanced by the downstream transport from the fresh water inflow. At
this point, termed the "null zone," there is essentially no net bottom
transport. Here sediment deposition is extensive. In a stratified
estuary this point is at the head of the saline intrusion wedge. In
a partially well mixed estuary it is harder to pinpoint. Nonetheless,
sedimentation is a useful parameter to analyze and will be handled in
a quantitative manner in subsequent paragraphs (Section 6.7.2.3.).
526

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TABLE VI-12
MAXIMUM ALLOWABLE CHANNEL VELOCITY TO AVOID BED SCOUR (FPS) (KING, 1954)
Original material excavated
CI ear
water,
no
detritus
Water
trans-
porting
colloidal
si 1 ts
Water trans-
porting non-
colloidal silts,
sands, gravels
or rock
fragments
Fine sand 	
1.50
2.50
1.50
Sandy loair	
1.75
2.50
2.00
Silt loam 	
2.00
3.00
2.00
Alluvial silts	
2.00
3.50
2.00
Ordinary firm loam	
2.50
3.50
2.25
Volcanic ash 	
2.50
3.50
2.00
Fine gravel 	
2.50
5.00
3.75
Stiff clay 	
3.75
5.00
3.00
Graded, loam to cobbles 	
3.75
5.00
5.00
Alluvial silt 	
3.75
5.00
3.00
Graded, silt to cobbles 	
4.00
5.50
5.00
Coarse gravel 	
4.00
6.00
6.50
Cobbles and shingles	
5.00
5.50
6.50
Shales and hardpans 	
6.00
6.00
5.00
To this point, flow in a fairly regular channel has been assumed.
However in many estuaries topographical irregularities exist. Such
irregularities (e.g., narrow headlands) create eddy currents in the
lee of the feature. These eddy currents, or gyres, slow the sediment
movement and allow local shoaling. Additionally, large shallow subtidal
or tidal flatlands exist in many estuaries. Such areas are usually well
out of the influence of primary currents. As a result local water
velocities are usually low and increased shoaling is possible.
527

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Wind and waves also have a major influence on estuarine sediment
distribution. Seasonal wind driven currents can significantly alter
water circulation patterns and associated velocities.  This in
turn determines, to a large extent, the areas of net shoaling and
scour throughout an estuary. Local wind driven and oceanic waves can
create significant scour forces. Such scour, or particle resuspension, is
particularly evident in shallow areas where significant wave energy is
present at the sediment/water interface. Local wind driven waves
are a major counterbalancing force to low velocity deposition in
many estuarine shallow areas (U.S. Engineering District, San Francisco,
1975).
Finally, oceanic littoral currents (long shore currents) interact
with flood and ebb flows in the area of an estuary mouth. Particularly
in the Pacific Northwest, sandy sediment fed from such littoral drift
is a major source of estuarine sediment, and the interference of
littoral drift with normal flood and ebb flows is the major factor
creating estuarine bars.
Figure VI-36 shows the schematic flow of annual sediment movement
through San Francisco Bay. With the exception of the magnitude of
annual dredging, this is typical for most U.S. estuaries. The most
important thing to observe is the dominance of resuspension and redeposi-
tion over all other elements of sediment movement including net inflow
and outflow. Also note that there is a net annual accumulation of
deposited sediment in the bay. This figure is also helpful in concep-
tualizing the sediment trap or sediment concentration characteristic of
estuaries. In any year, 8-10 million cubic yards flow into the estuary
and 5 to 9 million cubic yards flow out. However, over 180 million
cubic yards are actively involved in annual sediment transport within
the estuary.
Figure VI-37 is an idealized conceptualization of the various
sediment-related processes in an estuary. It must be remembered that
528

-------
Figure VI-36 Sediment Movement in San Francisco Ray System
(million cubic yards). From: U.S. Engineering
District, San Francisco, 1975)
these processes actually overlap spatially much more than is shown
and that the processes active at any given location vary considerably
over time.
From this qualitative analysis, there are some general statements
which can be made. Ippen (1966) drew the following conclusions on the
distribution of estuarine sediments:
a) The major portion of sediments introduced into suspension in
an estuary from whatever source (includes resuspension)
during normal conditions will be retained therein, and if
transportable by the existing currents will be deposited
near the ends of the salinity intrusion, or at locations
of zero net bottom velocity.
529

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PLAN VIEW
^uiwii
MAJOR EDDY DEPOSITION
CHANNEL BANK DEPOSITION
AREA OF LOW ENERGY DEPOSITION
o
in
PROFILE
AREA OF MAXIMUM
SALINITY GRADIENTS/
FLOCCULATION
SEDIMENT TRAP AREA
f-

HEAVY
PARTICLE
SETTLING
NULL ZONE
SETTLING
SEDIMENT MOVEMENT (NET)
WATER COLUMN MOVEMENT
Figure VI-37 Idealizfd Estuarine Sedimentation
530

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b)	Any measure contributing to a shift of the regime towards
stratification will cause increased shoaling. Such
measures may be: structures to reduce the tidal flow and
prism, diversion of additional fresh water into the estuary,
deepening and narrowing of the channel,
c)	Sediments settling to the bottom of an estuary will, on
the average, be transported upstream and not downstream.
Such sediments may, at some upstream point be resuspended into
the upper layers and carried back downstream.
d)	Sediments will accumulate near the ends of the intrusion
zone and form shoals. Shoals will also form where the net
bottom velocity is zero (in the null zone),
e)	The intensity of shoaling will be most extreme near
the end of the intrusion for stratified estuaries and will
be more dispersed in the well mixed estuary,
f)	Shoals will occur along the banks of the main estuarine
channel where water is deep enough to prevent wave induced
scour and where velocities are reduced from main channel
velocities sufficiently to allow settling.
Schultz and Simmons (1957) made similar conclusions but added the
presence of shoaling at the mouth where flood and ebb currents intercept
littoral drift.
6.7.2.3 Settling Velocities
As wars stated in the previous section, settling velocities do not
play as major a role in controlling sedimentation patterns in estuaries
as they do in lakes. However, it is informative to assess settling
rates for various size particles. The possible size classifications of
531

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I
particles and their general inclusive diameter sizes are shown in
Table VI-13. Table VI-14 lists terminal settling velocities for each
particle size assuming spherical particles and density of 2.0* in
quiescent water. From this table it can be inferred that particles
of the medium sand class and coarser will probably settle to the
bottom within a very short time after entering an estuary.
Turning to the other end of the particle size scale of Table VI-14,
-4	-3
particles with a diameter of 10 mm will fall only 3.1 x 10 inches
per hour in the most favorable environment (calm waters). Such a
settling rate is not significant in the estuarine environment. Figure
VI-38 shows the quiescent settling rates for particle sizes in between
these two extremes since this intermediate size group is of real sig-
nificance in estuarine management (primarily silts). For particles
smaller than those shown in Figure VI-36, gravitational settling will
not be a significant factor in controlling particle motion. Particles
substantially larger than the range shown in Figure VI-38 will tend to
settle above, or at, the head of an estuary.
Combining Figure VI-38 (fall per tidal cycle)** with known segment
flushing times (in tidal cycles) the size of particles tending to
settle out in each segment can be estimated. If such predictions
reasonably match actual mean segment sediment particle size, then this
method can be useful in predicting changes in sediment pattern.
Anticipated changes in river-borne suspended sediment load by particle
size can be compared to areas where each size of particle would tend
to settle. This would then identify areas which would either be subject
to increased shoaling or reduced shoaling and increased scour. This
type of analysis has been more successful when applied to organic
detritus material than for inorganic suspended loads.
*The density of many inorganic suspended particles is approximately equal
to that of sand (2.7 gm/cm ) while that of biomass and organic detritus
is usually much closer to that of water and can be assumed to be about
1.1 gm/cnw.
**Based on a 12.4 hour tidal cycle
532

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TABLE VI-13
SEDIMENT PARTICLE SIZE RANGES (AFTER HOUGH, 1957)

PARTICLE SIZE RANGE

Inches
Mil 1imeters

D
max.
D .
nun.
D
max.
D .
mm.
Derrick STONE
120
36


One-man STONE
12
4
--

Clean, fine to coarse GRAVEL
3
1/4
80
10
Fine, uniform GRAVEL
3/8
1/16
8
1.5
Very coarse, clean uniform SAND
1/8
1/32
3
0.8
Uniform, coarse SAND
1/8
1/64
2
0.5
Uniform, medium SAND
--
--
0.5
0.25
Clean, well-graded SAND AND GRAVEL
--
--
10
0.05
Uniform, fine SAND
--
--
0.25
0.05
Well-graded, silty SAND AND GRAVEL

--
5
0.01
Silty SAND
--
--
2
0.005
Uniform SILT
--
--
0.05
0.005
Sandy CLAY
--
--
1 .0
0.001
Silty CLAY
--
--
0.05
0.001
CLAY (30 to 50% clay sizes)
--
--
0.05
0.0005
Collodal CLAY (-2u>50%)
--
--
0.01
10" 6
(After B. K. Hough, Basic Soils Engineering, p. 69, Values listed are
approximate)
A number of simplifying assumptions have gone into this settling
velocity analysis. The most significant of these are:
1. Water column density changes have been ignored. Inclusion
of this factor would slightly reduce the settling velocity
with increased depth. This effect will be more significant
for organic matter because of its lower density.
533

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TABLE VI-14
RATE OF FALL IN WATER OF SPHERES OF VARYING RADII AND
CONSTANT DENSITY OF 2a AS CALCULATED BY STOKES' LAWb (MYSELS, 1959)
Radi us
Terminal
velocity, u
mm.
cm./sec.
cm./mi n.
10
(2.2xl04)

1
(220)

0.1
(2.2)

0.01
2.2xl0-2
1.3
10"3
2.2xl0"4
0.013
10"4
2.2x10-6
1. 3x10"4
10"5
2.2x10"8
1.3x10"6
10"6
2.2xl0"10
1 .3xlO-8
10"7
(2.2x10-12)

Tc apply to other conditions, multiply the u value
by the pertinent density difference and divide it
by the pertinent viscosity in centipoises.
k Values in parentheses are calculated by Stokes' law
under conditions where this law is not applicable.
c Stokes law states that the terminal velocity 1s pro-
portional to the particle radius squared, the differ-
ence in density and inversely proportional to the
liquid viscosity.
2. Dispersive phenomena and advective velocities have not been considered.
3. Table VI-13 and Figure VI-38 are based on the fall of
perfectly spherical particles. Non-spherical particles
will have lower settling velocities.
534

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12
FALL DISTANCE PER Tl DAL CYCLE (FT.)
Figure VI-33. Particle Diameter vs Settling Fall per Tidal Cycle (12.4 hrs)
Under Quiescent Conditions (Spheres with density 2.0 gm/cm^)
4. Interference between particles has not been considered.
However, in a turbulent, sediment-laden estuary such
interference is probable (hindered settling). The analysis
of the effect of interference on settling velocities was
covered in Chapter V for lakes. This analysis is also
basically valid for estuaries. The effects introduced
there can be applied to Figure VI-38 velocities to
adjust for particle interference.
6.7.2.4 Null Zone Calculations
It was previously mentioned that substantial shoaling will occur
in the area of the null zone. It is possible to estimate the location
535

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of this zone, and hence the associated shoaling areas, as a function
of water depth and river discharge. In addition to the importance of
the null zone to shoaling, Peterson and Conomos (Peterson, et al.,
1974) established the biological and ecological importance of this area
in terms of planktonic production. The null zone, therefore, is both
an area of potential navigational hazard and an area of major ecological
importance to the planner.
Silvester (1974) summarized the analysis for estimating the location
of the null zone with respect to the mouth of an estuary. The basic
equation used in this analysis is:
S	u 2
n _ 1000 _r	(VI-42)
So _0.7S F2 gd
o n
mean salinity (averaged vertically and over a
tidal cycle) at the null point (n), (ppt)
ocean surface salinity adjacent to the esturary
in parts per thousand (ppt),
fresh water flow velocity, (ft/sec)
gravational force = 32.2 ft/sec. ,
estuarine depth, (ft)
densimetric Froude number at the null zone
where F is defined by:
n	J
Fn = Ur/rf (Ap/Pn)gd	(VI-43)
where
Ap/pn = difference between fresh water density and
that at the null zone (averaged over the
depth of the water column) divided by the
density of the null zone. This value may be
approximated for estuarine waters by:
Where S
n
So
U
r
g
d
and	F
536

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Combining Equations VI-42 and VI-44 and solving for Ap/pn yields
Ap/pn = T500 n	(VI-44)
This formulation is particularly good for channels which are either
maintained at a given depth (dredged for navigation) or are naturally
regular as "d" represents mean cross section channel depth at the null
zone.
The use of these equations first requires location of the present
null zone. This can most easily be done by measuring and averaging
bottom currents over one tidal cycle to locate the point where upstream
bottom currents and downstream river velocities are exactly equal,
resulting in no net flow. This situation is schematically shown in
Figure VI-39.
When this point has been established for one set of river discharge
conditions, equation VI-44 can be substituted into equation VI-43 to
calculate F . This F value is an inherent characteristic of an estuary
n	n
and can be considered to be constant regardless of the variations in
flow conditions or null zone location (Silvester, 1974).
With this information and a salinity profile for the estuary (S
X
plotted against x from x=0 at the mouth of the esturary to X=L^ at the
head) the location of future null zones may be calculated. Given the new
conditions of (changes in river discharge) or of d (changes in channel
depth, as by dredging activity), Equation VI-42 will allow calculation
of a new Sn. This may be plotted on the salinity profile to calculate
the location of a new null zone position. Even through these changes
will produce a new estuarine salinity profile, the use of Equation VI-42
and the old (known) salinity profile will produce reasonably good
estimates of longitudinal shifts in the location of the null zone.
Salinity profiles for appropriate seasonal conditions should be used for
537

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Mouth
'0.9
NULL ZONE
NULL ZONE
tidal 1y veraged velocity at a depth equal
to 0.9 of the water column depth.
river flow velocity
Figure VI-39 Estuarine Null Zone Identification
0.9
**
538

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each calculation (e.g. low flow profiles for a new low flow null
zone calculation).
	 EXAMPLE VI- 9		
Estimation of Null Zone Location
An estuary has the tidally averaged salinity profile shown in the
Salinity Table below. Mean channel depth in the area of the existing
null zone is 18 feet and the salinity at that point is 10 parts per
thousand (ppt). Current (low flow) river discharge velocity is 0.5 ft/
sec. Normal winter (high flow) velocity is 1.8 ft/sec. It is desired
to know where the null zone will be located in summer and winter if a
30 ft channel is dredged up to 70,000 feet from the mouth.
SALINITY DATA FOR EXAMPLE VI-9
Distance from mouth (1000ft)
5 15
25
35
45
55
65 75 85
Salinity, (ppt)
30 28
25
20
13
8
6 4 1
From equation VI-43 and equation VI-44

Fn * V y (.7/1000) (sj (g) (d)
= 0.5 ft/sec// (7xl0-4) (10 ppt) (32.2 ft/sec?) (18 ft)
or,	F = 0.248
n
539

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From equation VI-42 the null zone salinity with a deeper channel
will be:
S 1000 U2
^ _ _o	r_
n 5 0.7 F2 gd
o	n 3
= (1000) (0.5 ft/sec)2 /o.7 (0.248)2 (32.2 ft/sec3) (30 ft)
Sn = 6.0 ppt
From Table VI-15 this will occur approximately 65,000 ft from the
mouth of the estuary.
Under winter flow conditions,
1000 U2
S = 	L_
n 0.7 F2 gd
= (1000) (1.8 ft/sec) /o.7 (0.248)2 (32.2 ft/sec2) (30 ft)
Sn - 77.9 p.p.t.
This Sn is greater than ocean salinity and will not actually be
encountered. Thus null zone shoaling will occur at the mouth if it
occurs at all. This condition is common for rivers with highly seasonal
dependent flow rates.
	 END OF EXAMPLE VI-9 	
6.8 TIDAL PRISM-THROAT CROSS SECTIONAL AREA RELATIONSHIPS
A useful planning relationship can be developed between an estuarine
tidal prism and the throat cross sectional area. The "throat" of an
estuary may be defined as the smallest cross section in the area of the
540

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mouth of an estuary. This usually corresponds to the point where the
entrance channel is narrowest. The maintenance of this cross sectional
area as an open, viable navigational channel is dependent on the volume
and velocity of tidal prism water movement through the throat. This
relationship has been studied using regression techniques by O'Brien
(1969), and Johnson (1973), and more recently by Jarrett (1976).
O'Brien developed a regression expression based on data from all
types of estuaries. This relationship is given by:
A = 4.69xl0"4 P0-85	(VI-45)
o
where,	A = throat cross sectional area at mean sea level (ft )
P = tidal prism (ft^)
Johnson analyzed west coast estuaries only, and segregated them
by the number of jetties existing at the mouth. His resulting
formulation was:
A = 2x10 ^ P for no jetties, ft^, P in ft"^ (VI-46)
and
A = 4.69x10"^ P for 2 jetties, ft^ P in ft^ (VI-47)
Estuaries with one jetty would lie between these two values.
Jarrett made separate analyses for estuaries with no jetties, with
one jetty and with two jetties for the Atlantic, Gulf and Pacific coasts.
His resulting regression relationships are shown in Table VI-15. Figures
VI-40, VI-41, and V1-42 show all of these equations in graphical form.
Knowning the estuarine tidal prism, Figures VI-40, VI-41, and VI-42
may be used to assess the impact on shoaling or scour in the throat area
of either jetty construction or of dredging activity (increasing A).
If jetties are constructed the "natural" supportable throat area will
be difined by a new equation depending on the final number of jetties.
541

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TABLE VI-15
THROAT AREA - TIDAL PRISM RELATIONSHIPS
Coast
*
A=
All estuaries
*
A=
0 or 1 Jetty
*
A=
2 Jetties
Atlantic
Gulf
Paci fic
7.75x10"5P1,05
5.02x10~4P0-84
1.19x10"4P*91
5.37x10"6P1'07
3.51x10"4P0'86
1.91x1 O-6?1 1
5.77x10"5P0'95
5.28x10~4P'85
Combi ned
5.74x10"5P0'95
1,04x10"5P13
3.76x10~4P'86
(from Jarrett, 1976)
*Values given are representation of right hand sides of equations in
the form of Equation VI-45, 46, or Equation VI-47, and are for A in
2	3
units of ft and for P in units of ft .
If throat area dredging is undertaken, the tendency of the estuary to
either maintain or to refill this increased area may be directly deter-
mined from the appropriate figure (VI-40, 41, or 42).
io'
: JARRETT (1976)
	All Three Coasts
~	Atlantic Coast
		Gulf Coast
	Pacific Coast
OBRIEN0969K
4'
io9


A
///
/

10
-
y
s/r


io7
^ /
/
1 1 1 1  1 1 1

	

io2
io3
io4
IO5
MINIMUM CROSS SECTIONAL AREA
OF INLET (FT2) BELOW MSL (A)
Figure VI-40. Tidal Prisk vs Cross-Sectional /\rea,
Regression Curves for all Inlets
542

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10
10'
10
Q_
to
I-
Li_
3
<
z.
or
Z)
O
cr
o
CD
cr
Q_
CO
CO
cr
CL
_i
<
Q
10
10
8
E= 10'
- JARRETT (1976)
	All Three Coasts
	Atlantic Coast
	Gulf Coast
	Pacific Coast
JOHNSON
(1973)
OBRIEN
(1969)
10
\cr
10
I or
icr
MINIMUM CROSS SECTIONAL AREA
OF INLET (FT2) BELOW MSL (A)
Figure VI-41 Tidal Prism vs Cross-Sectional Area, Regression Curves
for Inlets with One or No Jetties
543

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JARRETT (1976)
All Three Coasts
Atlantic Coast
Pacific Coast
/
JOHNSON (1973)
aOBRIEN(l969)
Ldjjjj
I	' i i i ' ii
MINIMUM CROSS SECTIONAL AREA
OF INLET (FT2) BELOW MSL(A)
Figure VM2 Tidal Prism vs Cross-Sectional Area, Regression
Curves for Inlets with Two Jetties
544

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545

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546

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547

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548

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