&EPA
United States
Environmental Protection
Agency
Office of Water
(Mail Code 4305)
EPA 823-B-95-007
September 1995
Technical Guidance Manual
for Developing Total
Maximum Daily Loads
Book II: Streams and Rivers
Part 1: Biochemical Oxygen Demand/Dissolved
Oxygen and Nutrients/Eutrophication
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TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
Book II: Streams and Rivers -
Part 1: Biochemical Oxygen Demand/Dissolved Oxygen and
Nutrients/Eutrophication
EPA DOCUMENT NUMBER: EPA-823-B-97-002 DATE: March 1997
ABSTRACT
As part of ongoing efforts to keep EPA's technical guidance readily accessible to
water quality practitioners, selected publications on Water Quality Modeling and
TMDL Guidance available at http://www.epa.gov/waterscience/pc/watqual.html
have been enhanced for easier access.
This document is part of a series of manuals that provides technical information
related to the preparation of technically sound wasteload allocations (WLAs) that
ensure that acceptable water quality conditions are achieved to support
designated beneficial uses. The document:
• Emphasizes the need for water quality managers to consider key water
quality interactions and ecological responses to point and nonpoint source
loadings in streams and rivers;
• Provides technical guidance on modeling, reaction rate coefficients, and
field measurement techniques and
• Provides the recommended TMDL procedures for biochemical oxygen
demand (BOD), dissolved oxygen (DO), and nutrients discharged into
streams and rivers.
Book II Part 1 presents the technical basis for analysis of BOD, DO, nutrient, and
eutrophication impact. It also discusses some of the mathematical models
available to perform TMDL calculations, provides guidance on model selection,
and uses case studies to illustrate key steps in constructing a site-specific for a
TMDL. Detailed appendices provide additional discussions of important fate and
transport processes, quality assurance for field monitoring, and uncertainty
analysis.
KEYWORDS: Wasteload Allocations, Rivers, Streams, Biochemical Oxygen
Demand, Dissolved Oxygen, Eutrophication, Nutrients, Modeling,
Water Quality Criteria
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MEMORANDUM
SUBJECT: Final Technical Guidance Manual for Developing
Total Maximum Daily Loads (TMDLs)
FROM: Tudor T. Davies, Director
Office of Science and Technology (4301)
TO: Regional Water Division Directors
Regional Environmental Services Division Directors
Regional TMDL Coordinators
Attached for national use, is the final Technical Guidance manual for Developing Total Maximum Daily
Loads, Book II: Streams and Rivers, Part 1: Biochemical Oxygen Demand/Dissolved Oxygen and Nutri-
ents/Eutrophication. We are sending extra copies of this manual to the Regional TMDL coordinators for
distribution to the States to use on performing TMDLs.
Section 303(d) of the Clean Water Act requires States to perform wasteload allocations (WLAs) and Total
Maximum Daily Loads (TMDLs) for waters where technology-based treatment is found to be inadequate
to meet State water quality standards (WQS). As a part of our technical assistance effort in performing
WLAs, primarily involving controls of point source discharges, the Office of Water issued a series of techni-
cal guidance manuals. More recently, we issued guidance for the 303(d) program Guidance for water
quality-based decisions: The TMDL Process, 1991 in response to the U.S. General Accounting Office
(GAO) report Water Pollution - Greater EPA Leadership Needed to Reduce Nonpoint Source Pollution,
October 1990.
We are issuing this TMDL technical guidance manual to support the implementation of the 1991 TMDL
guidance mentioned above. This document provides guidance on how to assess water quality impacts of
point and nonpoint source discharges of biochemical oxygen demanding (BOD) pollutants and nutrients to
streams and rivers. More details of what this guidance includes are stated in the document under the
heading "To the Reader" on page iii.
The earlier drafts of this document have been reviewed by your staff, and some of them made signifi-
cant contribution to its development. Also, the document has been peer reviewed by technical ex-
perts. This final guidance reflects all comments and suggestions received on the earlier drafts.
If you have any questions, comments or desire additional information, please contact Hiranmay Biswas,
Standards and Applied Science Division (4305), Telephone: (202) 260-7012.
Attachment
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TO THE READER
This guidance manual represents the consolidation of the following two documents in the U.S. Environmental
Protection Agency's series of Technical Guidance Manuals for Performing Waste Load Allocations:
USEPA. 1983. Technical Guidance Manual for Performing Waste Load Allocations, Book II: Streams
and Rivers, Chapter 1: Biochemical Oxygen Demand and Dissolved Oxygen.
USEPA. 1983. Technical Guidance Manual for Performing Waste Load Allocations, Book II: Streams
and Rivers, Chapter 2: Nutrients and Eutrophication.
The revised single manual, renamed Technical Guidance Manual for Developing Total Maximum Daily
Loads, Book II: Streams and Rivers, Part I: Biochemical Oxygen Demand/Dissolved Oxygen and Nutri-
ents/Eutrophication, eliminates duplicative information on hydrodynamics and physical characteristics of
streams and rivers, and on the interactions of nutrients and dissolved oxygen dynamics, that was included
in the above- cited manuals. The availability of a single manual also helps to meet the needs of water
quality managers to adequately consider the key water quality interactions and ecological responses to
pollutant loadings in streams and rivers. In addition, this manual includes updated information on model-
ing, reaction rate coefficients, field measurement techniques, etc. and includes several examples using
EPA-supported models. More specifically, these changes and updates include:
Integration of principles and concepts on waste load and load allocations for nutrients/eutrophication with those for
carbon (BOD) and oxygen balances in aquatic ecosystems (see Chapter 2 - Basic Principles and Concepts).
• Update of model identification and selection, with emphasis on the EPA-supported water quality model
QUAL2E (see Chapter 3 - Model Selection and Review) and additional mention of watershed models.
• Update of water quality reaction rate coefficients and field measurement techniques (see Chapter 4
- River and Stream Modeling Procedures, Appendix A - Development of Model Coefficients and
Constants, and Appendix C - Quality Assurance for TMDL Studies).
• Update of technical literature citations (see Chapter 5 - References and Appendix E, Supplemental
Bibliography).
• Inclusion of a TMDL example using QUAL2Eand WASPS (see Appendix B - Example Total Maximum
Daily Load Analys\s).
• Inclusion of an uncertainty analysis example using QUAL2E-UNCAS (see Appendix D - Uncertainty
Analysis).
Comments and suggestions from the user community help us in improving our guidance manuals, and we
invite the user community to send their comments and suggestions to:
Hiranmay Biswas
U.S. EPA
Office of Science and Technology
Standards and Applied Science Division (4305)
Washington, DC 20460
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ACKNOWLEDGEMENTS
The contents of this section have been removed to comply with current EPA practice.
IV
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TABLE OF CONTENTS
MEMORANDUM i
TO THE READER iii
ACKNOWLEDGMENTS iv
1. . . INTRODUCTION 1-1
1.1 Purpose 1-1
1.2 Relationship to Other Guidance Documents 1-2
1.3 Organization and Scope of Manual 1-4
2. BASIC PRINCIPLES AND CONCEPTS 2-1
2.1 Purpose 2-1
2.2 Overview 2-1
2.3 Concepts in Biochemical Oxygen Demand, Dissolved Oxygen, and Nutrient
Analyses 2-2
2.3.1 Pollution Source Characteristics 2-2
2.3.2 In-Stream Fate and Transport of Pollutants 2-3
2.3.3 Receiving Water Conditions 2-4
2.3.4 Biochemical Oxygen Demand and Dissolved Oxygen Reaction Kinetics . . 2-8
2.3.5 Eutrophication Kinetics 2-15
2.4 Governing Equations 2-20
2.4.1 Mass Balance Principle 2-20
2.4.2 Dissolved Oxygen Equation 2-22
2.4.3 Separate Mass Balance Equations by Constituent 2-24
3. MODEL SELECTION AND REVIEW 3-1
3.1 Purpose 3-1
3.2 Overview 3-1
3.3 Model Selection 3-1
3.3.1 Study Objectives and Constraints 3-3
3.3.2 Pollutant Loadings, Spatial and Temporal Resolution, and
Transport Mechanisms 3-3
3.3.3 Water Quality Pollutant Interactions 3-8
3.4 Model Review 3-9
4. RIVER AND STREAM MODELING PROCEDURES 4-1
4.1 Purpose 4-1
4.1.1 Modeling Goals 4-1
4.1.2 General Requirements of a Stream Water Quality Modeling Analysis .... 4-3
4.2 Initial Assessment 4-3
4.2.1 Study Area Evaluation 4-3
4.2.2 Compilation and Review of Existing Data 4-7
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4.2.3 Preliminary Analysis 4-7
4.2.4 Selection of Modeling Framework 4-14
4.3 Site-Specific Stream Survey 4-16
4.3.1 Hydraulic Geometry Survey 4-16
4.3.2 Time-of-Travel Study 4-17
4.3.3 Stream Water Quality Sampling 4-17
4.3.4 Wastewater Monitoring 4-17
4.3.5 Biological Assessment 4-21
4.4 Model Calibration 4-21
4.4.1 Model Coefficient Assignment 4-21
4.4.2 Component Analyses 4-22
4.4.3 Quantifying the Comparison Between Model Results and Data 4-22
4.5 Model Validation 4-25
4.5.1 Model Coefficient Adjustment 4-25
4.5.2 Model Sensitivity Analysis 4-25
4.5.3 Model Accuracy 4-25
4.6 Model Application and Total Maximum Daily Loads 4-25
4.6.1 Development of Management Scenarios 4-27
4.6.2 Total Maximum Daily Loads 4-27
4.6.3 Uncertainty Analysis 4-29
5. REFERENCES 5-1
APPENDICES
Appendix A: Development of Model Coefficients and Constants A-1
Appendix B: Example Total Maximum Daily Load Analysis B-1
Appendix C: Quality Assurance for TMDL Studies C-1
Appendix D: Uncertainty Analysis D-1
Appendix E: Supplemental Bibliography E-1
Appendix F; Glossary F-1
Appendix G: Abbreviations G-1
Appendix H: Conversion Factors H-1
Appendix I: Symbols 1-1
Appendix J: BOD-DO Nutrient Guidance input files for QUAL2E
and WASP5-EUTRO5 example problems. Diskette EPA 823-C-95-004 .. J-1
VI
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LIST OF FIGURES
2-1 Interaction of transport mechanisms for loads in a stream 2-5
2-2 Interrelationship of major kinetic processes for BOD and
DO as represented by water quality models 2-7
2-3 Comparison of stream BOD and laboratory BOD for various incubation times 2-10
2-4 Steps in nitirification and utilization of dissolved oxygen 2-10
2-5 Interrelationship of major kinetic processes for BOD, DO, and nutrient analysis
as represented by water quality models 2-14
2-6 Specific algal growth rate as a function of temperature 2-16
2-7 Effect of light intensity on algal growth 2-16
2-8 Effect of nutrients of algal growth 2-17
2-9 Effects of nutrient limitation on algal growth 2-18
2-10 Ammonia preference structure for algal growth 2-20
2-11 Mass balance equations for dissolved oxygen 2-21
2-12 Components of DO profile (sag curve) downstream of waste discharge 2-23
3-1 Dissolved oxygen response as a function of estuary number 3-8
3-2 Effect of pH and temperature on un-iodized ammonia 3-10
4-1 Steps in the use of a water quality model for a site-specific TMDL application 4-2
4-2 Range of chlorophyll a average concentrations and target "objectives" to
regulatenutrient inputs for eutrphication control for various water bodeis 4-5
4-3 Time and space scales for assessment of water quality problems 4-6
4-4 Diurnal model vs. observed oxygen in Senix Creek, Long Island 4-15
4-5 Catawa River study area and major point sources 4-18
4-6 Preliminary water quality sampling network 4-19
4-7 Component analysis of DO for Rock Creek, Pennsylvania 4-23
4-8 Numerical tagging of James River 4-24
4-9 Some relative errors of dissolved oxygen models 4-26
4-10 TMDL procedure for BOD/DO problem 4-28
VII
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VIM
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LIST OF TABLES
1-1 Technical Guidance Manuals for Performing Waste Load Allocations 1-3
1-2 Available guidance and other references for TMDL development 1-4
2-1 Comparison of typical point and nonpoint sources 2-2
2-2 Decision situations requiring watershed models 2-3
2-3 Nonpoint source modeling options 2-4
2-4 Separate mass balance equations used for each constituent in BOD, DO, and
nutrient analyses 2-25
3-1 Methods of analysis for phytoplankton and aquatic plants 3-10
3-2 Comparison of models: constituents modeled 3-13
3-3 Comparison of models: summary of capabilities 3-14
3-4 Comparison of models: reaeration formulations 3-15
3-5 Comparison of models: input data requirements 3-18
3-6 Comparison of models: ease of application-output form and content 3-20
3-7 Comparison of models: ease of application-sources, support, and documentation 3-21
3-8 Comparison of models: ease of application-equipment and programming requirements . . 3-22
3-9 Comparison of models: operating costs 3-22
3-10 Hierarchy of models based on selected features 3-23
4-1 Identification of potential water quality problems: Dissolved oxygen depletion,
nutrient enrichment, and eutrophication 4-5
4-2 Data types and possible sources for stream total maximum daily load 4-7
4-3 Data for stream eutrophication calculation 4-11
4-4 Water quality survey for the Catawba River 4-20
4-5 Point source sampling program 4-20
IX
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1. INTRODUCTION
1.1 PURPOSE
The purpose of this guidance manual is to present the
most recent information and techniques for use in pre-
paring total maximum daily loads (TMDLs) when exces-
sive biochemical oxygen demand (BOD), low dissolved
oxygen (DO), and excessive nutrients and eutrophica-
tion impair the water quality of streams and rivers. This
manual reflects current policy on TMDL development
as outlined in the Guidance for Water Quality-based
Decisions: The TMDL Process (USEPA, 1991 a), and
represents the consolidation of the following two docu-
ments in the U.S. EPA's series of Technical Guidance
Manuals for Performing Waste Load Allocations:
USEPA. 1983. Technical Guidance Manual for
Performing Waste Load Allocations, Book II:
Streams and Rivers, Chapter 1: Biochemical Oxy-
gen Demand and Dissolved Oxygen
and
USEPA. 1983. Technical Guidance Manual for
Performing Waste Load Allocations, Book II:
Streams and Rivers, Chapter 2: Nutrients and Eu-
trophication.
This revised manual, renamed Technical Guidance
Manual for Performing Total Maximum Daily Loads,
Book II: Streams and Rivers, Part 1: Biochemical Oxy-
gen Demand/Dissolved Oxygen and Nutrients/Eutro-
phication, eliminates duplicated information on
hydrodynamics and physical characteristics of streams
and rivers. The objectives of the manual are (1) to
emphasize the needs of water quality managers to
adequately consider the key water quality interactions
and ecological responses to both point and nonpoint
source loadings in streams and rivers; (2) to provide
technical guidance on modeling, reaction rate coeffi-
cients, and field measurement techniques; and (3) to
provide the recommended TMDL procedures for bio-
chemical oxygen demand, dissolved oxygen, and nutri-
ents for point sources and nonpoint sources discharging
into streams and rivers. This manual includes several
examples using EPA-supported models. Much of the
information needed by the water quality analyst to
design and develop a TMDL for a stream or river (i.e.,
model selection and design, field measurements,
assignment of reaction rate coefficients, and analysis
of the TMDL) is contained within this manual.
This guidance reflects the current policy on TMDL
development for streams and rivers, which requires
the consideration of pollutant loads from all sources
within a watershed. TMDLs should be developed
to provide more stringent water quality-based con-
trols when technology-based controls are inade-
quate to achieve water quality standards (USEPA,
1991 a). TMDLs are composed of waste load allo-
cations (WLAs) for point sources, load allocations
(LAs) for nonpoint sources, and a margin of safety
(MOS). The MOS accounts for scientific uncer-
tainty involved in establishing the TMDL. This un-
certainty can be caused by insufficient or
poor-quality data or a lack of knowledge about the
receiving water and pollution effects. The TMDL
process consists of the following steps:
(1) Identifying water quality-limited waters still
requiring TMDLs.
(2) Prioritizing and targeting water quality-limited
waters.
(3) Developing the TMDL.
(4) Implementing the TMDL through control ac-
tions.
(5) Assessing whether step 4 actions are suffi-
cient to meet water quality standards.
The Guidance for Water Quality-based Decisions:
The TMDL Process (USEPA, 1991 a) discusses
these procedures for TMDL development within the
context of a water quality-based watershed ap-
proach. The following guidance is intended primar-
ily to assist the water quality analyst in the third step
of the TMDL process with regard to developing
TMDLs to control BOD, DO, and nutrients in
streams and rivers.
The level of effort required to develop a TMDL is
highly dependent on the complexity and magnitude
of the receiving water problems. In general, to assess
the anticipated level of effort, site-specific conditions
1-1
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need to be evaluated in terms of the type and com-
position of loads, the variability and characteristics of
pollutant sources and their response to local hydro-
logic events, and the characteristics of receiving
water. Additional considerations may also involve
the local or regional value of the resources being
protected and the phase of the TMDL process. Since
the TMDL program has directed water and watershed
managers toward adoption of a phased approach to
address controls on both point and nonpoint source
loads under both dry-weather and wet-weather con-
ditions, simplified modeling techniques for low-flow
conditions may be of limited use for developing first-
phase TMDLs. As water quality goals for a water-
shed are more clearly defined by first-phase
assessments and additional monitoring efforts, inter-
mediate or complex modeling techniques may be
required for advanced phases of the TMDL process.
This manual calls for an intermediate level of effort to
develop a TMDL for typical cases associated with
oxygen depletion and nutrient loadings. Although the
models reviewed in this manual accommodate multi-
ple discharges and complex inflow characteristics,
the emphasis is limited to less complex scenarios.
More detailed modeling techniques are described in
the Compendium of Watershed-scale Models for
TMDL Development (USEPA, 1992b), Principles of
Surface Water Quality Modeling and Control
(Thomann and Mueller, 1987), and Water Quality
Modeling, Volume 1, Transport and Surface Ex-
change in Rivers (McCutcheon, 1989). In special
cases where a level of effort less than that presented
in this document is deemed necessary, the following
documents may be of interest: Water Quality Assess-
ment: A Screening Procedure for Toxic and Conven-
tional Pollutants in Surface and Ground Water (Mills
et al., 1985), and Simplified Analytical Method for
Determining NPDES Effluent Limitations for POTWs
Discharging into Low Flow Streams (USEPA, 1980).
1.2 RELATIONSHIP TO OTHER
GUIDANCE DOCUMENTS
Table 1-1 summarizes the relationship of the various
documents that make up the series of technical guid-
ance manuals for waste load allocations. These manu-
als describe approaches for allocating point source
waste loads in rivers and streams, lakes and impound-
ments, and estuaries. The pollutants addressed in the
manuals listed in Table 1-1 include biochemical oxygen
demand/dissolved oxygen, nutrients, and toxic sub-
stances (ammonia, organic chemicals, and metals).
The manual Simplified Analytical Method for Determin-
ing NPDES Effluent Limitations for POTWs Discharging
into Low-Flow Streams (Table 1-1) may be used to
assist in waste load allocation procedures when such
simplifications are valid. In addition, ammonia toxicity
is addressed in more detail in the Simplified Methods
Manual, which now includes methods for evaluating the
interactions of multiple discharges.
Table 1-2 lists available guidance for TMDL develop-
ment. These documents include guidance on the
allocation of nonpoint source loads. These docu-
ments assist the water quality analyst in selecting and
using appropriate models for development of TMDLs.
In addition, an EPA report entitled Technical Guidance
for Estimating Total Maximum Daily Loads (TMDLs):
Integrating Nonpoint and Episodic Point Source Load-
ing from Stormwater and Combined Sewer Overflows
(CSOs) is currently in development and should be
available by October 1994. This document is intended
to provide technical guidance on the integration of
point and nonpoint, steady state and episodic dis-
charges into a waterbody. The guidance will provide
several examples of evaluating these discharges
within the TMDL process.
Users of this manual also can consult the latest State
water quality standards before developing TMDLs.
These standards provide applicable water quality
criteria for pollutants of concern in the state. Federal
water quality criteria for many pollutants are listed in
the EPA "Gold Book":
USEPA. 1987. Quality criteria for 1986 (with up-
dates 1 and 2 included). "Gold Book." EPA
440/5-86-001. U.S. Environmental Protection
Agency, Office of Water Regulations and
Standards, Washington, DC.
The "Gold Book" is available from:
U.S. Government Printing Office
Superintendent of Documents
North Capitol and H Street, NW
Washington, DC 20401
(202) 783-3238
Order No. 955-002-00000-8
Usually, however, TMDL developers consult state
water quality standards first. Several manuals on
modeling and parameter selection are also available.
These documents, listed in Table 1-2, are available
from:
1-2
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TABLE 1-1. TECHNICAL GUIDANCE MANUALS FOR PERFORMING WASTE LOAD ALLOCATIONS
Technical Guidance Manual for Performing Waste Load Allo-
cations - Book II Streams and Rivers - Chapter 1 Biochemi-
cal Oxygen Demand/Dissolved Oxygen (EPA 440/4-84-020)
This chapter presents the underlying technical basis for perform-
ing WLA and analysis of BOD/DO impacts. Mathematical mod-
els to calculate water quality impacts are discussed, along with
data needs and data quality.
Technical Guidance Manual for Performing Waste Load Allo-
cations - Book II Streams and Rivers - Chapter 2 Nutrient/Eu-
trophication Impacts (EPA 440/4-84-021)
This chapter emphasizes the effect of photosynthetic activity
stimulated by nutrient discharges on the DO of a stream or river.
It is principally directed at calculating DO concentrations using
simplified estimating techniques.
Technical Guidance Manual for Performing Waste Load Allo-
cations - Book II Streams and Rivers - Chapter 3 Toxic Sub-
stances (EPA 440/4-84-022)
This chapter describes mathematical models for predicting toxi-
cant concentrations in rivers. It covers a range of complexities,
from dilution calculations to complex, multi-dimensional, time-
varying computer models. The guidance includes discussion of
background information and assumptions for specifying values.
Technical Guidance Manual for Performing Waste Load Allo-
cations - Simplified Analytical Method for Determining
NPDES Effluent Limitations for POTWs Discharging into
Low-Flow Streams
This document describes methods primarily intended for "desk
top" WLA investigations or screening studies that use available
data for streamflow, effluent flow, and water quality. It is in-
tended for circumstances where resources for analysis and data
acquisition are relatively limited.
Technical Guidance Manual for Performing Waste Load Allo-
cations - Book IV Lakes and Impoundments - Chapter 2 Nu-
trient/Eutrophication Impacts (EPA 440/4-84-019)
This chapter discusses lake eutrophication processes and some
factors that influence the performance of WLA analysis and the
interpretation of results. Three classes of models are discussed,
along with the application of models and interpretation of result-
ing calculations. Finally, the document provides guidance on
monitoring programs and simple statistical procedures.
Technical Guidance Manual for Performing Waste Load Allo-
cations - Book IV Lakes, Reservoirs and Impoundments -
Chapter3 Toxic Substances Impact (EPA 440/4-87-002)
This chapter reviews the basic principles of chemical water qual-
ity modeling frameworks. The guidance includes discussion of
assumptions and limitations of such modeling frameworks, as
well as the type of information required for model application.
Different levels of model complexity are illustrated in step-by-
step examples.
Technical Guidance Manual for Performing Waste Load Allo-
cations - Book VI Design Conditions - Chapter 1 Stream De-
sign Flow for Steady-State Modeling (EPA 440/4-87-004)
Many state water quality standards (WQS) specify specific de-
sign flows. Where such design flows are not specified in WQS,
this document provides a method to assist in establishing a
maximum design flow for the final chronic value (FCV) of any
pollutant.
Final Technical Guidance on Supplementary Stream Design
Conditions for Steady State Modeling
WQS for many pollutants are written as a function of ambient en-
vironmental conditions, such as temperature, pH, or hardness.
This document provides guidance on selecting values for these
parameters when performing steady-state WLAs.
Technical Guidance Manual for performing Waste Load Allo-
cations - Book VII: Permit Averaging (EPA 440/4-84-023)
This document provides an innovative approach to determining
which types of permit limits (daily maximum, weekly, or monthly
averages) should be specified for the steady-state model output,
based on the frequency of acute criteria violations.
Handbook - Stream Sampling for Waste Load Allocation Ap-
plications (EPA 625/6-86/013)
This handbook provides guidance in designing stream surveys
to support modeling applications for waste load allocations. It
describes the data collection process for model support, and it
shows how models can be used to help design stream surveys.
In general, the handbook is intended to educate field personnel
on the relationship between sampling and modeling require-
ments.
Technical Guidance Manual for Performing Waste Load Al-
locations - Book III Estuaries - Part 1 - Estuaries and Waste
Load Allocation Models (EPA 823/R-92-002)
This document provides technical information and policy guid-
ance for preparing estuarine WLAs. It summarizes the impor-
tant water quality problems, estuarine characteristics, and the
simulation models available for addressing these problems.
Technical Guidance Manual for Performing Waste Load Al-
locations Book III Estuaries - Part 2 - Application of Estu-
arine Waste Load Allocation Models (EPA 823-R-92-003)
This document provides a guide to monitoring and model calibra-
tion and testing, and a case study tutorial on simulation of WLA
problems in simplified estuarine systems.
Technical Support Document for Water Quality-based Tox-
ics Control (EPA 505/2-90-001)
This document discusses assessment approaches, water qual-
ity standards, derivation of ambient criteria, effluent charac-
terization, human health hazard assessment, exposure
assessment, permit requirements, and compliance monitoring.
An example is used to illustrate the recommended procedures.
Technical Guidance Manual for Performing Waste Load Al-
locations - Book III - Estuaries - Part 4 - Critical Review of
Coastal Embayment and Estuarine Waste Load Allocation
Modeling (EPA 823-R-92-005)
This document summarizes several historical case studies of
model use in one freshwater coastal embayment and a number
of estuarine discharge situations.
Technical Guidance Manual for Performing Waste Load Al-
locations - Book III: Estuaries - Part 3 - Use of Mixing Zone
Models in Estuarine Waste Load Allocations (EPA 823-R-92-
004)
This technical guidance manual describes the initial mixing
wastewater in estuarine and coastal environmental and mixing
zone requirements. The important physical processes that gov-
ern the hydrodynamic mixing of aqueous discharges are de-
scribed, followed by application of available EPA-supported
mixing zone models to four case study situations.
These documents are available from the Office of Science and
Technology (4305), Washington, DC 20460. See Standards
and Applied Science Division Clearinghouse Request Form for
document completion dates.
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TABLE 1-2. AVAILABLE GUIDANCE AND
OTHER REFERENCES FOR
TMDL DEVELOPMENT
Rates, Constants, and Kinetics Formulations in Surface
Water Quality Modeling (Bowie etal., 1985, EPA/600/3-85/040)
This report provides formulations used in surface water quality
modeling along with accepted values for rate constants and coeffi-
cients. Topics covered include dispersion, heat budgets, dis-
solved oxygen saturation, reaeration, alkalinity, nutrients, algae,
zooplankton, and coliform bacteria.
Water Quality Assessment: A Screening Procedure for Toxic
and Conventional Pollutants in Surface and Groundwater,
Parts I and II (Mills et al., 1985, EPA 600/6-85/002a and EPA
600/6-85/002b)
Part I of this series describes the aquatic fate of toxic organic sub-
stances, waste loading calculations, and the assessment of water
quality parameters in rivers and streams. Part II describes the as-
sessment of impoundments, estuaries, and groundwater.
Compendium of Watershed-scale Models for TMDL Develop-
ment (USEPA, 1992b, EPA 841-R-92-002)
This document identifies and summarizes the most widely used
watershed-scale models and is intended to assist in model selec-
tion.
Modeling ofNonpoint Source Water Quality in Urban and
Non-urban Areas (Donigan and Huber, 1991, EPA/600/3-91/039)
This document presents detailed reviews of established nonpoint
source assessment procedures, methodologies, and modeling
techniques. Simple procedures (e.g., constant concentration, re-
gression, statistical, and loading function approaches) and com-
plex models (e.g., SWMM, HSPF, CREAMS, SWRRB) are
described.
A Quick Reference Guide: Developing Nonpoint Source
Load Allocations for 7/WDLs (USEPA, 1992a, EPA841-B-92-
001)
This document directs TMDL developers to existing technical guid-
ance from other programs while more detailed TMDL technical
guidance is developed.
TMDL Case Study Series
This series of case studies published by EPA illustrates real-world
TMDL applications that the user may consult when appropriate.
The Enhanced Stream Water Quality Models QUAL2E and
QUAL2E-UNCAS: Documentation and User Manual (Brown
andBarnwell, 1987, EPA/600/3-87/007)
This manual describes the water quality models QUAL2E, which
can be operated as a steady-state or dynamic model, and
QUAL2E-UNCAS, which is an enhancement of QUAL2E that in-
cludes uncertainty analysis. QUAL2E allows the user to model
the effects of diurnal variations and to examine diurnal dissolved
oxygen variations caused by algal growth and respiration.
The water quality analysis simulation program, WASPS, Part
A: Model documentation, Version 5.10 and The water quality
analysis simulation program, WASPS, Part B: The WASPS in-
put dataset, Version 5.10 (Ambrose, et al., 1993a and 1993b)
This manual describes the use of the Water Quality Analysis
Simulation Program Version 5.10 (WASP5). The WASP5 model-
ing system covers hydrodynamics, conservative mass transport,
eutrophication-dissolved oxygen kinetics, and toxic chemical-sedi-
ment dynamics.
USEPA Center for Exposure Assessment
Modeling (CEAM)
Environmental Research Laboratory
960 College Station Road
Athens, GA 30605-2720
(706) 546-3549
Bulletin Board (706) 546-3402
1.3 ORGANIZATION AND SCOPE OF
MANUAL
The remainder of this document is organized into three
chapters and five appendices, as summarized below.
Chapter 2, Basic Principles and Concepts, presents the
underlying technical basis for analyzing stream bio-
chemical oxygen demand (BOD), dissolved oxygen
(DO), nutrient, and eutrophication impacts. The basic
theory on transport and fate and the nature of stream
system responses to oxygen-demanding loads are de-
scribed using equations and basic relationships.
Chapter 3, Model Selection and Review, discusses
mathematical models available to perform TMDL cal-
culations, with emphasis given to EPA-supported
models including Multi-SMP, QUAL2E-UNCAS, and
WASP5. Guidance is also provided to assist in iden-
tifying and selecting appropriate models for varying
levels of complexity (e.g., steady-state vs. dynamic).
Chapter 4, River and Stream Modeling Procedures,
presents the following procedures to construct a site-
specific model for a TMDL: initial assessment, site-
specific stream survey, model calibration, model
validation, and model application. Examples from
actual case studies are given to illustrate key steps in
the procedures.
Appendix A, Development of Model Coefficients and
Constants, provides a detailed discussion on various
fate and transport processes and reaction rates af-
fecting biochemical oxygen demand, dissolved oxy-
gen, and nutrients in rivers and streams such as
reaeration, oxidation, nitrification, photosynthesis,
respiration, settling, sediment oxygen demand, and
ammonia flux. Environmental factors that influence
fate and transport processes and technical ap-
proaches for determining model parameters are pre-
sented. This appendix supplements the overview
material presented in Chapter 2.
Appendix B, Sample Total Maximum Daily Load
Analysis, presents an example that illustrates the
TMDL process applied in settings using an analytical
1-4
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solution and the EPA-supported QUAL2E and
WASPS models. The example TMDL problem in-
cludes problem setting, river characteristics, treatment
plant and effluent characteristics, ambient river water
quality data review, model calibration, and model pro-
jections. The example illustrates an analysis of the
same water quality problem using two different
models: an analytical, screening level model and
the WASPS model. The solutions consider non-
zero background sources, nonpoint source in-
puts, and eutrophication problems. The second
example problem is based on a study of the Wil-
lamette River basin in Oregon. The Willamette River
example highlights the use of the QUAL2E model in
assessing water quality for a large river.
Appendix C, Quality Assurance for Field Monitor-
ing Programs, provides an overview of objectives
and components of a quality assurance plan for
field monitoring.
Appendix D, Uncertainty Analysis, provides a dis-
cussion on uncertainty analysis as it applies to
waste load allocation modeling. An example demon-
strating various aspects of uncertainty analysis using
QUAL2E-UNCAS is included. Also, through this ex-
ample, techniques in uncertainty analysis, first-order
error analysis, and Monte Carlo simulation are de-
scribed.
Appendix E, Supplementary Bibliography, includes ad-
ditional references relevant to oxygen depletion, nutri-
ent enrichment, and eutrophication processes in
freshwater and marine ecosystems. These references
are not cited in the guidance manual.
Appendix F presents a glossary of technical terms
related to the guidance document.
Appendix G presents a list of abbreviations used in
the document. Appendix H provides a list of conver-
sion factors for metric and US equivalent units.
Appendix I provides a list of symbols used as nomen-
clature in the document.
Appendix J provides an attached MS-DOS 3.5 inch
diskette containing input files for the QUAL2E and
WASPS example problems presented in Appendix B.
1-5
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2. BASIC PRINCIPLES AND CONCEPTS
2.1 PURPOSE
This chapter provides an introductory discussion of
the primary concepts in conducting analyses of river
and stream dissolved oxygen responses to loadings
of BOD and nutrients. Section 2.2 provides an over-
view of the basic principles of the total maximum
daily load (TMDL) process. Section 2.3 presents a
discussion of the key relationships (i.e., loading, fate
and transport by physical and chemical/biological
processes) that determine the effect of a pollutant
load on oxygen demand and eutrophication in a
stream or river. Section 2.4 presents the mass bal-
ance principle and governing equations that form the
basis for most water quality models used to simulate
the key processes of interest.
2.2 OVERVIEW
EPA defines the total loading capacity (LC) or total
maximum daily load (TMDL) as the greatest amount of
pollutant loading that a waterbody can receive without
violating water quality standards. A TMDL is the portion
of the LC or TMDL that is allocated to one of its existing
or future point sources of pollution. A load allocation
(LA) is the portion of the TMDL that is allocated to one
of its existing or future nonpoint sources of pollution and
natural background. The sum of the individual WLAs
for point sources and LAs for nonpoint sources (includ-
ing natural background sources and tributaries) plus the
margin of safety (MOS) is equivalent to the TMDL (i.e.,
TMDL= LC = WLA+LA+MOS). TMDL studies utilizing
field monitoring data and predictive models provide
quantitative information to assist managers in making
effective decisions to protect water quality. Models and
water quality equations are used to establish cause-
and-effect relationships correlating incremental
changes in stream water quality to changes in pollutant
loading. From this correlation, optimum and desirable,
but not required cost-effective treatment levels can be
specified to achieve water quality standards and criteria.
The MOS can be included implicitly in the TMDL model
calculations to account for the uncertainty about the
relationship between the allocated waste loads and
loads and the predicted quality of the receiving water-
body. A reserve capacity for future development can
be included in the TMDL at this stage. Wastewater
treatment plant designers can then evaluate various
combinations of alternative unit processes to select
an optimum treatment scheme to meet the require-
ments of the WLA. Likewise, land use planners and
engineers may need to analyze various management
scenarios to meet the requirements of the nonpoint
source LA. This analysis may include an evaluation
of the cost-effectiveness of different combinations of
best management practices (BMPs).
Knowledge of the quantitative cause-and-effect rela-
tionship between receiving water quality and pollutant
loads is the key to making reliable determinations of the
total loading capacity. This relationship is quite sensi-
tive to natural environmental conditions. These condi-
tions include physical characteristics such as stream
flow, velocity, depth, slope, time of travel, and tempera-
ture and chemical/biological characteristics such as
in-place sediment oxygen demand, algal photosynthe-
sis and respiration, and nitrification. The determination
of the rates at which various water quality reactions take
place in the receiving waterbody introduces additional
complications in establishing cause-and-effect relation-
ships and projecting water quality impacts. In some
instances, the water quality response can be as sensi-
tive to the reaction rates as it is to the total amount of
pollutant loadings. This is particularly important in
BOD/DO reactions where the resulting dissolved oxy-
gen concentration is determined by competing reac-
tions of oxygen consumption from BOD, nitrification,
and sediment oxygen demand (SOD) and oxygen re-
plenishment from reaeration and photosynthesis.
Models not only are used to determine rigorous relation-
ships between pollutant loads and the resulting water
quality response, but also are necessary to predict
future water quality conditions and conditions that may
not have been monitored for in the past (e.g., 7Q10
critical low-flow conditions).1 Models are also useful to
IThere is a 10 percent chance that the 7Q10 critical low flow (7-day average low flow that occurs once in 10 years) will occur during a 1-year monitoring period. In a 10-year
monitoring period, there is only a 65 percent chance that critical low-flow conditions will occur.
2-1
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evaluate the array of variables (temperature, stream
flow, load, reaction rates, etc.) that simultaneously
influence water quality response, especially where
the system is relatively complex as a result of multiple
sources, varying stream geometry, flow changes due
to tributaries and storm events, and other factors.
2.3 CONCEPTS IN BIOCHEMICAL
OXYGEN DEMAND, DISSOLVED
OXYGEN, AND NUTRIENT
ANALYSES
This section examines the relationships between pol-
lutant fate and transport processes in natural waters
and the response of dissolved oxygen in streams and
rivers to point and nonpoint source loads. An appre-
ciation of these relationships and related factors
should help regulatory staff and water quality and
watershed managers to assess the technical com-
plexity associated with the development of a given
site-specific TMDL and to recognize the level of mod-
eling and monitoring effort that may be required.
Factors that govern the fate and transport processes
of pollutant loadings in streams and rivers and deter-
mine the effects on dissolved oxygen include those
factors related to the magnitude and variability of the
pollution sources, the hydrologic conditions of the
receiving water, and the in-stream transport of pollut-
ants. Detailed discussion of these factors can be
found in Appendix A. In addition, detailed derivation
of BOD, DO, and nutrient relationships can be found
in Thomann and Mueller (1987).
2.3.1 Pollution Source Characteristics
An important task in watershed and water quality
modeling is to characterize the pollution sources and
estimate the associated pollutant loadings. Pollution
sources can be characterized as either point sources
or nonpoint sources. These two categories of sources
are governed by different mechanisms, resulting in
different impacts on the receiving water. Table 2-1
identifies typical differences between point and non-
point source characteristics.
Point Sources - Point source pollutant loads include
effluent discharges from municipal and industrial
wastewater treatment plants. Point sources are also
characterized by pollutant inputs to surface waters
from tributaries and other watercourses that aggre-
gate into major surface water systems. Point sources
are defined in the Clean Water Act ) as ". . . any
TABLE 2-1. COMPARISON OF TYPICAL POINT
AND NONPOINT SOURCES
Point Sources
Fairly steady flow
Variability changes less than
one order of magnitude
Most severe impacts occur
during low flow conditions
Fairly predictable
concentrations
Nonpoint Sources
Highly dynamic flow occurring
at random intermittent intervals
Variability changes several
orders of magnitude
Most severe impacts occur
during or following storm
events
Unpredictable, variable
concentrations
discernible, confined, and discrete conveyance, in-
cluding but not limited to, any pipe, ditch, channel, tunnel,
conduit, well, discrete fissure, container, rolling stock, con-
centrated animal feeding operation, landfill leachate collec-
tion system, vessel or otherfloating craftfrom which pollutants
are or may be discharged. This term does not include return
flows from irrigated agriculture or agricultural storm water
runoff "(40 CFR Vol. 1 7-1-1990 edition).
Point source loading rates from permitted discharges,
such as publicly owned treatment works (POTWs)
and combined sewer systems, may be determined
from discharge monitoring reports (DMRs) available
from many state regulatory agencies or EPA regional
offices. Most of these DMRs contain information on
many conventional pollutants such as BOD, ammo-
nia, Kjeldahl nitrogen, suspended solids, and fecal
coliform bacteria. Not all nutrients are reported in
DMRs. For example, facilities that do not have phos-
phorus removal (e.g., secondary treatment plants)
may not measure or report total phosphorus and/or
orthophosphate concentrations in their effluents. In
this case, the field monitoring program should include
measuring these effluents. When plant-specific data
are not available, literature values (see Appendix A)
can be used for first approximations.
Nonpoint Sources - Nonpoint loading of pollutants
results from the transport of pollutants into receiving
waters via overland surface runoff within a drainage
basin. Land use and hydrologic characteristics of a
basin are major determinants of the magnitude of
pollutant loading contributed from nonpoint source
inputs. The general long-term trend of deforestation
and the subsequent transition to agricultural, urban,
2-2
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and suburban land uses has resulted in large-scale
changes in nonpoint source pollutant loading to the
Nation's rivers and coastal waters.
As the magnitude of the nonpoint source pollution
problem has become better understood over the past
10-20 years, a number of urban and agricultural
management practices have been proposed, investi-
gated, and implemented to reduce pollutant loading
from these very diverse sources. A major emphasis
of ongoing and future national water quality manage-
ment objectives for EPA and the states will be the
basin-scale implementation of best management
practices to reduce nonpoint source pollutant loads.
Several modeling techniques have been developed
for estimating pollutant loadings from diffuse and
storm-driven sources. Recent reviews of these tech-
niques are presented in USEPA (1992b) and
Donigian and Huber (1991). Although watershed
modeling techniques were originally developed to
estimate loading and to provide input to receiving
water models, the TMDL program has widened the
range of application of these models to include the
development and evaluation of various components
of watershed management plans. Since not all deci-
sion situations regarding the development of TMDLs
are the same, some models are more suitable than
others under certain conditions. Simple and screen-
ing watershed models have been extensively used to
support preliminary assessment and planning-level
activities, while applications of detailed simulation
models are most cost-effective when dealing with
TABLE 2-2. DECISION SITUATIONS
REQUIRING WATERSHED MODELS
Screening Level (simple models)
Relative comparison of watersheds
Preliminary estimates of discharge quantity and quality
Delineation of the geographical extent and analysis of the
temporal variability of major pollution sources
Identification of pollutants and governing processes of
concern
Identification of modeling and monitoring needs
Planning Level (mid-range to detailed models)
Prioritization and targeting of specific watersheds or
pollution sources
Evaluation and selection of control strategies
Post-Planning Level (detailed models)
Siting criteria for implementation of management measures
Design criteria for sizing control practices
development of design criteria or evaluating manage-
ment programs. Table 2-2 presents a set of com-
monly encountered decision situations associated
with TMDL development for which the use of a water-
shed model may be considered. These situations are
presented in increasing order of complexity and mod-
eling requirements.
Other nonpoint pollution sources that may influence
the development of TMDLs include groundwater
seepage, atmospheric deposition, and natural weath-
ering of rocks and soils. These sources are difficult to
control, and under natural conditions they represent
the background concentrations of the waterbody.
When developing TMDLs, uncontrollable sources
need to be identified and their magnitude evaluated
to characterize the available assimilative capacity of
the waterbody. The weathering and dissolution pro-
cesses of rocks and soil are natural mechanisms and
should be considered as part of the uncontrolled
loads. Atmospheric deposition is in part a result of
industrial and development activities at the regional
or national scale. Therefore, their control at the site-
specific or watershed scale is not possible. The con-
trol of atmospheric deposition is usually addressed in
regional and national programs and should be con-
sidered as part of the uncontrollable load for typical
TMDL development.
Groundwater contributions to the nonpoint source
loads are a main concern if the groundwater is con-
sidered contaminated. In general, since groundwater
interfaces natural geological formations that undergo
dissolution and weathering processes under natural
conditions, pollutant discharges caused by noncon-
taminated groundwater seeping to surface water-
bodies should be considered a part of the
uncontrollable load. When dealing with contaminated
groundwater, seepage to surface water can repre-
sent a major concern requiring an identification of
contamination sources and the pollutant(s) of con-
cern and an evaluation of the magnitude of the dis-
charge. Potential groundwater assessment methods
are summarized in A Review of Methods for Assess-
ing Nonpoint Source Contaminated Ground-water
Discharges to Surface Water (USEPA, 1991c).
2.3.2 In-Stream Fate and Transport of
Pollutants
When a pollutant load is discharged into a flowing
stream or river, it is subject to fate and transport
processes that modify stream concentrations. The
2-3
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principal factors determining stream concentrations
are advection, dispersion, and reaction.
Advection - Advection represents the primary trans-
port process of pollutant inflow in the downstream
direction. Lateral advective transport across a
stream is typically neglected. Usually complete mix-
ing between the pollutant load and the ambient
stream flow in the vertical and lateral direction has
been achieved within a relatively short distance
downstream of the outfall.
Dispersion - If all water elements in a stream were
traveling at a uniform speed over each cross-section
of the river, they would arrive at a given location at
the same time. In reality, however, lateral velocity
differences cause each element to arrive at a different
time, resulting in an apparent mixing due to vertical
and lateral velocity gradients. For example, the cen-
ter of the stream near the surface moves faster than
the flow near the banks and streambed. This phe-
nomenon is called longitudinal dispersion (see Fis-
cher et al., 1979). When analyzing the effects of a
continuous pollutant load, the effect of dispersion
may be ignored since the contribution of dispersion
to the resulting in-stream pollutant concentration is
usually small in comparison to the contribution from
advection. On the other hand, when analyzing trans-
port of storm-driven loadings during wet-weather pe-
riods, longitudinal dispersion also must be considered
since the pollutant loading is represented as a single
"pulse" input rather than a continuous series of
"pulse" inputs. When a water quality-analysis is con-
ducted over a "long" distance with a short time "pulse"
interval of discharge, then longitudinal dispersion
must be considered in the analysis (Thomann and
Mueller, 1987).
Reaction - The biodegradable materials discharged
to a stream or river (e.g., oxygen-demanding or-
ganics) undergo decomposition by bacteria in the
water column. In the presence of dissolved oxygen,
bacteria convert organic materials to end products
such as CO2, NO3, and H2O, stabilizing the pollutant
load. In addition, algae take up nutrients such as
inorganic phosphorus and nitrogen during photosyn-
thesis and reduce the nutrient concentrations in the
stream. Algal biomass is then recycled back into
inorganic nutrients. A number of chemical, biological,
and biochemical reactions contribute to the flux and
attenuation of waste material concentrations.
The interactions of these factors are shown schemati-
cally in Figure 2-1, which presents what would be
observed if a single slug of waste load were injected
and could be followed downstream over a period of
time. Conservative materials in the waste (those not
subject to reaction and decay, such as chloride)
would track as shown in the sketch of advection, or
advection and dispersion. Reactive materials, such
as oxygen-consuming materials, would behave as
shown in the sketches that include reaction. Thus,
the behavior of a dissolved substance in the stream
is the result of the velocity and mixing action of the
water and the resulting transformation from biological
and chemical reactions.
2.3.3 Receiving Water Conditions
The local impact of pollutant loadings to receiving
waters is largely determined by the relative magni-
tudes of the loading and the receiving water flow rate.
Assimilation of the pollutant load is a function of the
hydrologic conditions of the stream or river defined in
terms of flow rate, transport characteristics, and back-
ground water quality. As a result, seasonal and storm-
driven variations in the watershed hydrology and
pollutant buildup and washoff characteristics can ex-
ert very different impacts on the receiving water dur-
ing and immediately following wet-weather episodes.
The significance of storm-driven discharges from
nonpoint sources on dissolved oxygen is very site-
specific and difficult to characterize explicitly. During
wet-weather conditions, stream flow rate is generally
high, allowing for higher transport and assimilative
capacity. However, pollutant deposition and accumu-
TABLE2-3. NONPOINT SOURCE
MODELING OPTIONS
Stochastic/Probabilistic models: Mathematical models that
include consideration of hydrologic uncertainty and probability.
Models rely on statistical characteristics of the hydrologic
process to predict the behavior of the hydrologic system.
Transport and fate processes are represented using
compounded parameters describing multiple processes.
Deterministic models: Model variables are thought to follow a
predictable, certain behavior, and the probability of hydrologic
data is generally ignored. Models rely on series of algorithms
that simulate actual physical or chemical processes, and are
sometimes referred to as physically based models.
Design storm simulation: Focuses on a detailed simulation of a
single storm event, often selected as representative, with a
given frequency and duration of rainfall (e.g., 1-year, six -hour
storm).
Continuous simulation: Simulates the behavior of a system over
an extended period of time (months to years) with relatively
short time steps, providing continuous runoff and loading values.
2-4
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ADVEC11GN
ADVECT1ON AMD BEftCtiON
LIJQ
IT
T MB
T
THI
ADVECT1QMAND DISPERSiOM
L-3*3
1
I
1ME
ADVECT1ON, REACTION
AND DISFEflSI ON
•nut
FIGURE 2-1. INTERACTION OF TRANSPORT MECHANISMS FOR LOADS IN A STREAM
(After USEPA, 1983a)
2-5
-------
lation on streambed and pool areas may exert a
critical demand on dissolved oxygen during low flow
conditions. When nonpoint sources are identified as
the major sources of oxygen depletion, storm event
or continuous and time-dependent modeling may be
required. Nonpoint source modeling options that cap-
ture, to a certain extent, the impacts of wet-weather
conditions are summarized in Table 2-3.
Often when oxygen demand is the mechanism of
concern, the modeling effort focuses primarily on
pollutant discharges during dry periods and the base
flow rate, which depends on the magnitude of the flow
recession following wet-weather recharge conditions.
Although pollution discharges during dry periods are
characterized by fairly constant rates and composi-
tion, the base flow rate fluctuates seasonally and
annually. In the continental United States, seasonally
high flow normally occurs during the colder period of
winter and in early spring from snowmelt and spring
rains, while seasonally low flow typically occurs dur-
ing the warmer summer and early fall drought peri-
ods. Because of these seasonal hydrologic and
climatological patterns of low flow, minimum dilution,
and high temperature, summer and early fall are
typically the critical periods for evaluating the worst-
case impact of pollutant loads on water quality. Dur-
ing this period, flow conditions approaching steady
state are achieved. The analysis and evaluation of
data collected during this period become more mean-
ingful because the mathematical assumption of
steady state is frequently made when evaluating dis-
solved oxygen in streams and rivers due to fairly
constant point sources.
Rapid transport of pollutants by high flow and mixing
conditions results in a short residence time with typi-
cally minimal ecological damage. Conversely, slow
removal of pollutants in waters characterized by a
long residence time because of low-flow conditions
can result in adverse ecological impacts such as
severe oxygen depletion, nutrient enrichment, and
eutrophication problems.
Factors that affect the time of travel in a natural
stream include stream depth, width, cross-sectional
area, and bed slope-hydraulic geometry. In some
cases, stream hydraulic geometry and time-of-travel
information are available from studies performed by
the U.S. Geological Survey (USGS), the U.S. Army
Corps of Engineers, or other State and Federal agen-
cies. Sometimes a field program may be needed to
collect the hydraulic geometry data and measure the
time of travel (usually by a dye study).
Projections of water quality impacts for some future
critical low-flow condition are normally required in
TMDL studies. The change in hydraulic geometry
caused by flow fluctuation must be predicted. Flow
variance, in turn, results from changes in stream
velocity and depth (both of which strongly affect the
stream reaeration capacity).
Basically, two approaches are used to quantify hy-
draulic geometry and time of travel for future condi-
tions. First, Leopold and Maddock (1953) have
examined various rivers and developed empirical
relationships between flow (Q), velocity (U), depth
(H), and width (W) using the following functions with
flow as the independent variable.
(2-1)
(2-2)
(2-3)
,m
where a, b, and c are constants for the stream and n,
m, and f are exponents defining the basic relation-
ships.
These constants vary with size of the river basin.
More detailed information on these constants can be
found in Appendix A.
The second approach is to independently calculate
stream velocity, depth, and width for different flows.
Typically, hydrodynamic models based on momen-
tum and continuity equations are used. Many stream
water quality models (see Chapter 3) include hydrau-
lic components that can be used to model flow in
addition to water quality.
A simpler modeling approach is to use the Manning
equation relating velocity, depth, slope, and a chan-
nel roughness coefficient (Brown and Barnwell, 1987;
McCutcheon, 1989) to simulate the velocity and
stream flow rate for different depths. It is typically
easier to estimate and extrapolate the Manning
roughness coefficient than to estimate the hydraulic
constants and exponents in Equations 2-1 through
2-3. However, the Manning equation is an empirical
formulation that may not reflect actual conditions of
natural streams. While both equations are semi-em-
pirical, the Manning equation involves only one co-
efficient (vs. six in the Leopold and Maddock
equations), and that coefficient is well understood by
hydraulic engineers. The Manning equation also pro-
vides better physical insight by integrating the effect
2-6
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Atmospheric Ot
j """" ^
NH;
f
Nifrlfieatten
.
I i
V
NO;
PhotoiyrrtlM
0 _ S*ttilr»i
I S*d!n*«rt W
Si 0*tnt«f — -» —
^- SOD
O
L
¥
E
D
O
X
Y
G
E
N 1
i
• It FUtplratlon
Chi a
; ALGAE I
FIGURE 2-2. INTERRELATIONSHIP OF MAJOR KINETIC PROCESSES FOR BOD AND DO
AS REPRESENTED BY WATER QUALITY MODELS
(After McCutcheon, 1989)
2-7
-------
of slope and elaborate stream geometry information.
EPA Region 6, however, has shown Manning's n to
greatly overestimate velocity. Although not exten-
sively used in TMDLs, other backwater and dynamic
routing simulations are feasible (see McCutcheon
(1985) and French (1985) for a review).
2.3.4 Biochemical Oxygen Demand and
Dissolved Oxygen Reaction Kinetics
Figure 2-2 shows the interrelationship of the following
major BOD/DO kinetic processes for a water column
as commonly represented by water quality models:
• Carbonaceous deoxygenation
• Nitrogenous deoxygenation (nitrification)
• Reaeration
• Sediment oxygen demand
• Photosynthesis and respiration
Prior to describing these processes, a brief discus-
sion of the biochemical oxygen demand concept is
necessary. BOD is a measure of the amount of
oxygen required to stabilize organic matter in waste-
water. As such, BOD is an equivalent indicator rather
than a true physical or chemical substance. It meas-
ures the total concentration of dissolved oxygen that
would eventually be demanded as wastewater de-
grades in the stream. The validity of BOD as a gauge
of wastewater quality has often been questioned;
nevertheless, the concept of BOD remains the stand-
ard for dissolved oxygen modeling analysis.
BOD is determined from a standardized test measur-
ing the amount of oxygen available after incubation
of the sample at 20 °C for a specific length of time,
usually 5 days. The oxidation process is usually
carried out in two stages: carbonaceous and nitroge-
nous (nitrification). The first stage is accomplished
by saprophytic organisms, which derive their energy
from the breakdown of organic carbon compounds;
the second stage, by autotrophic bacteria, which
require simple inorganic nitrogen compounds.
Each stage is characterized by two steps: synthesis
and respiration. In the carbonaceous stage, the en-
ergy required for synthesis is obtained from the de-
struction of complex organic carbon compounds,
liberating carbon dioxide and water. After the organic
matter has been converted to bacterial cells, the
endogenous respiration of the synthesized organ-
isms occurs, also yielding carbon dioxide, water, and
usually ammonia. In the BOD test, there is a pro-
nounced lag between the carbonaceous oxidation
and the nitrification step, the latter following by as
much as 10 days. The lag is less for treated (stabi-
lized) wastewaters and is on the order of 1 to 2 days
for highly treated effluents. In streams, the two
stages frequently proceed simultaneously, although
there may be lags in the nitrification stage for highly
polluted streams or those with low dissolved oxygen.
2.3.4.1 Carbonaceous Deoxygenation
The first phase of the BOD reaction involves the
oxidation of the carbonaceous organic material. The
reaction is approximated by a first-order reaction.
The oxygen required, y, approaches the total demand
of the overall process, Lo, and the rate is assumed to
be proportional to the amount of oxygen-demanding
material (Lo - y), either substrate or cells:
dt
= Ki (L0-y)
Integration of this expression yields:
(2-4)
(2-5)
or, if the relationship is put in terms of the organic
matter remaining,
L=L0e
-Kit
(2-6)
where
K1 =
y
L =
Lo =
BOD reaction rate coefficient (day-1)
oxygen consumed
oxygen equivalence of the organic
matter remaining
total oxygen demand
time (day)
Equation 2-4 indicates that the rate at which the
oxygen is consumed (dy/dt) is proportional to the
concentration of biologically degradable organic ma-
terial, as well as chemically oxidizable substances.
The coefficient, K1, depends on the state of the
material and the degree of treatment. A typical do-
mestic wastewater may have the following values:
raw sewage (0.35 day ), settled sewage (0.40 day"
), and treated effluent (0.25 day" ). Because of the
nature and composition of wastewater, these values
vary significantly. Industrial wastewaters are known
for their widely varied Ki rates. Coefficients deter-
mined from samples taken from rivers indicate
2-8
-------
that many factors affect the rate at which the reaction
proceeds. In many natural settings, the reaction rate
coefficient for river water is usually less than that of
an undiluted wastewater sample and decreases with
distance downstream (Thomann and Mueller, 1987).
Decreasing coefficients indicate the progressive re-
sistance to the oxidation of the more stable (refrac-
tory) end products.
By U.S. convention, BOD measurements are typically
conducted for 5 days. In fact, regulatory agencies
write wastewater discharge permits (NPDES) in
terms of 5-day BOD. In addition, many of the tests
are run with a nitrification inhibitor so that the test
measures the oxidation of carbonaceous material
only. When total BOD is measured after 5 days (an
inhibitor is not used), these tests are designated as
BODs. When the 5-day BOD test employs a nitrifica-
tion inhibitor, the results are designated as CBODs
(Hall and Foxen, 1984). More and more frequently,
long-term tests of 20 to 30 days are employed to
measure ultimate BOD (BODU) to reflect the potential
strength of the oxygen consumption. Some pulp and
paper mill wastewater samples are analyzed for
much longer periods (in excess of 100 days), but
measurements over an extended period of time are
of limited value in streams where the time of travel
from the waste source to the dissolved oxygen sag is
only a few hours or days, or where the stream is
diluted by tributaries within a few hours or days. Such
tests are very useful, though, in converting model
results in CBODU to a CBODs NPDES limit. In a
standard test, the values of oxygen used, y, at the end
of specified intervals of time, t, are determined. Given
a set of such values, the coefficient, Ki, and the
ultimate value, l_o, may be determined (Metcalf and
Eddy, 1991).
Another important concept for stream BOD is illus-
trated in Figure 2-3. When water samples are taken
from a stream to the laboratory for analysis of their
biochemical oxygen demand, the results may be
represented by a family of curves (Equation 2-5) of
oxygen consumed vs. time of incubation (see Figure
2-3b). Each of these curves has a different KI value.
As suggested above, the Ki value decreases in the
downstream direction. If CBODs values (either
measured during the analysis or calculated using
Equation 2-5) are plotted against the longitudinal
stream distance (Figure 2-3a), a decreasing trend for
CBODs is obtained. This trend follows an exponen-
tial decay and usually can be approximated by the
following equation in terms of ultimate CBOD:
L (CBODu) = L0 (CBODu) e Kru (2-7)
where
L(CBODu) = oxygen equivalence of the
organic matter at any given
location in the stream
(measured as CBODU)
Lo(CBODu) = total oxygen demand
measured at the source of
waste load following
complete mixing (measured
as CBODu)
Kr = CBODu removal rate in the
stream (day"1)
x = distance below the
wastewater discharge
U = average stream velocity
The time of travel, t, is equal to x/U. The meaning of
Equation 2-7 is that the oxygen-consuming materials
are removed from the water column at an overall loss
rate of Kr. It should be noted that Kr is used to
characterize the overall loss of dissolved organic
materials in the water column due to biochemical
oxidation and settling. It is highly empirical and,
therefore, is usually quantified by fitting an exponen-
tial decay curve through the field data.
The rate of removal of organic material from the water
column is not necessarily equal to the rate at which
dissolved oxygen is utilized. The coefficient describ-
ing this oxygen utilization may be identified as K
-------
w
f
0 -»-
Laboratory
{Nitrification Suppressing
to
CBOO
L
CBOO.
Jffj ^
CBOD
(mg/L)
L =
River Data
Tlm» of Trav»l (dayi)
or D!*tanc*
(Figure 2-3a)
•»- x or t
- L_ fx) •' J - s
0 5 10 IS
Tim* of lncufc.itIon (dayi)
(Figure 2-3b)
FIGURE 2-3. COMPARISON OF STREAM BOD AND LABORATORY BOD
FOR VARIOUS INCUBATION TIMES
(Manhattan College, 1983)
20
0' i«u:
T!(Pt, f
NlIritm>Ni;iBi> Ni
fff/mfff.
FIGURE 2-4. STEPS IN NITRIFICATION AND UTILIZATION OF DISSOLVED OXYGEN
(After Thomann and Mueller, 1987)
2-10
-------
may also contribute to the difference between the
laboratory rate, Ki, and the field rates, Kr and K NO 3
Stoichiometrically, 3.43 and 1.14 grams of oxygen
are required to transform each gram of ammonia
nitrogen to nitrite nitrogen (Equation 2-8) and nitrite
nitrogen to nitrate nitrogen (Equation 2-9), respec-
tively. The decay of organic nitrogen indirectly re-
quires oxygen after the organic nitrogen is hydrolyzed
into ammonia. Some researchers (e.g., Wezernak
and Gannon, 1967; Adams and Eckenfelder, 1977)
have suggested that the oxygen requirement could
be reduced to 3.22 and 1.11 grams, respectively, due
to cell synthesis.
The most common approach to modeling nitrification
is to use first-order kinetics (similar to BOD described
earlier) to characterize Equations 2-8 and 2-9. That
is, the rate of accumulation or depletion is linearly
dependent on the amount of nitrogen available in a
specific pool. Factors affecting the rate of nitrification
include temperature, pH, nitrogen concentrations,
dissolved oxygen, suspended solids, and organic and
inorganic compounds.
Because of the ease of measuring organic nitrogen,
ammonia, nitrite, and nitrate, waste load allocation
modeling of nitrification involves a mass balance and
a description of each species decay. Nitrification is
best simulated as a cascade process involving hy-
drolysis of organic nitrogen, oxidation of ammonia,
and oxidation of nitrite. In some models, the interme-
diate step of nitrite oxidation is combined with the
overall oxidation of ammonia to nitrate, but only little
computational efficiency is gained. Furthermore, the
conversion of nitrite to nitrate is very rapid; therefore,
the combination of the corresponding rates is not
unreasonable.
A number of studies have demonstrated that nitrifica-
tion and denitrification in the water column may be
dominated by benthic processes, particularly in fast-
moving shallow streams and rivers. Enumerations of
nitrifier organisms have demonstrated that benthic
populations can be two to three orders of magnitude
greater than water column populations (Williams and
Lewis, 1986). Several studies have shown that up to
80 to 95 percent of total nitrification can be accounted
for by benthic processes. Selected studies include
the James River in Virginia (Cerco, 1981), shallow
streams in North Carolina (Kreutzberger and Fran-
cisco, 1977; Lewis, 1983), the Trent River in England
(Curtis et al. 1975; Garland, 1978), and the Passaic
River in New Jersey (Matulewich and Finstein, 1978).
The sequential forward reactions of mineralization of
organic nitrogen and nitrification suggest that nitrate
should accumulate as an end product of the reactions.
Several data sets, however, suggest the removal of
nitrate from the water column along with the conver-
sion of ammonia to nitrite and nitrate (see Seitzinger,
1988). Simultaneous benthic nitrification and denitri-
fication have been observed in the James River
(Cerco, 1981) and in shallow streams in North Caro-
lina (Williams and Lewis, 1986) and incorporated into
water quality models of oxygen and nitrogen distribu-
tions (Cerco, 1981; Williams and Lewis, 1986).
Seitzinger (1988) has observed that measured rates
of denitrification in most river, lake, estuarine, and
coastal sediments (i.e., production of NzO gas) are
higher than the corresponding rates of nitrate loss to
2-11
-------
the sediments. The major source of nitrate for sedi-
ment denitrification underlying an aerobic water col-
umn is nitrate produced in the sediments during
nitrification rather than nitrate diffusing from the over-
lying water column into the sediments.
Some earlier stream models made the cascade proc-
ess a single process by combining Equations 2-8 and
2-9 and combining all nitrogenous oxygen demands
(3.43 + 1.14 = 4.57 grams of oxygen per gram of
nitrogen) as NBOD. Modeling NBOD and CBOD as
separate demands is not as useful as modeling
CBOD, organic nitrogen, ammonia, nitrite, and nitrate
as separate demands to track the sequential reac-
tions of the nitrogen cycle, which is widely used in
waste load allocation studies. Nevertheless, NBOD
modeling has been determined to be useful. For
example, the Simplified Analytical Method for Deter-
mining NPDES Effluent Limitations for POTWs Dis-
charging into Low-Flow Streams (see Table 1-1) uses
this approach after ensuring that none of the con-
straints of the method are violated.
2.3.4.3 Reaeration
In general, oxygen may be removed from or added to
water by various physical, chemical, or biological
reactions. If oxygen is removed from the water col-
umn and the concentration drops below the satura-
tion level, there is a tendency to make up this deficit
by the transfer of the gas from the atmosphere
through the surface into the stream at a certain rate.
If oxygen is added and the water column concentra-
tion is greater than the saturation level, the supersatu-
ration is reduced by the transfer of oxygen from the
stream to the air. Such interactions between the gas
phase and liquid phase are driven by the partial
pressure gradient in the gas phase and the concen-
tration gradient in the liquid phase (see Thomann and
Mueller, 1987). In general, oxygen transfer in natural
waters depends on:
• I nternal mixing and turbulence due to velocity
gradients and fluctuation.
• Temperature.
• Wind mixing.
• Waterfalls, dams, and rapids.
• Surface films.
• Water column depth.
The rate of transfer to be quantified in stream
BOD/DO modeling analyses is expressed as:
where
dC/dt
Cs
C
Ka
(2-10)
rate of change of oxygen
concentration
saturation concentration of
dissolved oxygen
dissolved oxygen concentration
in stream
stream reaeration rate
coefficient (day"1)
Many empirical formulations have been developed
for estimating stream reaeration rate coefficients.
For example, the QUAL2E model offers eight differ-
ent formulations reported in the literature. Stream
reaeration rate coefficients span a wide range of
values (typically 0.1 to 10 day" or even greater) and
have a greater magnitude than BOD reaction rate
coefficients. Appendix A presents reaeration rate
coefficients reported in the literature for a number of
waterbodies with guidance for selection of an appro-
priate equation.
2.3.4.4 Sediment Oxygen Demand
Benthic decomposition of organic material is defined
as the stabilization of the volatile suspended solids
that have settled to the streambed. These deposits
are stabilized by the biological activity of many different
organisms including bacteria. As these organic ma-
terials are associated with suspended solids, the
discharge of settleable waste components may form
a sludge blanket below a wastewater outfall. After a
period of time, organic materials may accumulate,
since the deposition rate of particulate material is
greater than the decomposition and physical loss
rate.
The demand of oxygen by sediment and benthic
organisms can, in some instances, be a significant
fraction of the total oxygen demand. This is particu-
larly true in small streams. The effects may be par-
ticularly acute during low-flow and high-temperature
conditions. Decomposition of organic matter and
respiration of resident invertebrates form the major
oxygen demands from the sediment. In addition to
biological decomposition and respiration of benthic
invertebrates, net photosynthetic oxygen production
of attached benthic algae (periphyton) can also be a
significant component of the total SOD. The oxygen
balance of shallow streams, in particular, can be
2-12
-------
influenced by this process since attached algae are
frequently present in shallow streams (see Terry and
Morris, 1986; Jeppesen and Thyssen, 1984). Al-
though these processes are distinct, they are typically
quantified together because in situ measurements
combine oxygen uptake and separation of the proc-
esses would result in added model complexity.
Because of its complexity, it is difficult to estimate
SOD analytically and independently. In situ meas-
urements of SOD are usually conducted using a
chamber at the bottom of the stream. Continuous
measurement of oxygen uptake over a certain period
of time provides data to derive the oxygen consump-
tion rate. In some cases, samples of river sediments
(undisturbed) are taken to the laboratory to measure
the oxygen uptake of bottom muds. The amount of
oxygen used over the test period is calculated as
grams of oxygen per square meter per day (g O2/m2-
day). In a modeling analysis, SOD is typically formu-
lated as a zero-order process:
at
(2-11)
where
dC/dt
SOD
H
rate change of oxygen
concentration (g O2/m3-day)
sediment oxygen demand (g
O2/m2-day)
average river depth (m)
Appendix A presents various values of SOD reported
in the literature for a number of streams and rivers.
Like many other reaction rate coefficients, the SOD
values can be determined by model calibration if
direct measurements from the field are not available.
The difficulty arises when SOD values need to be
predicted for future conditions. In recent years, cred-
ible interactive sediment-water column models have
appeared to independently quantify the oxygen up-
take rates of sediments. For example, Di Toro et al.
(1990) have developed a SOD model based on di-
agenesis of paniculate organic materials to predict
the production of hydrogen sulfide (H2S), ammonium
(NhU), phosphate (PO4), and silicon (Si). Such a
framework explains some, but not all, of the proc-
esses associated with SOD and is still being tested.
As a result, EPA recommends that conservative es-
timates of SOD be used for future conditions in
TMDLs.
2.3.4.5 Photosynthesis and Respiration
Through photosynthesis and respiration, phyto-
plankton, periphyton, and rooted aquatic plants
(macrophytes) could significantly affect the dis-
solved oxygen levels in the water column. Because
phytoplankton growth requires sunlight and nutri-
ents, quantifying photosynthetic oxygen production
would need to address phytoplankton-nutrient dy-
namics. That is, phytoplankton and nutrients
should be modeled concurrently to address this
problem. In many simple stream BOD/DO models,
however, the oxygen production rate due to photo-
synthesis and consumption rate due to respiration
are assigned, thereby uncoupling the calculation
from the phytoplankton-nutrient dynamics. In this
section, the simple approach is presented; the full
discussion of phytoplankton-nutrient dynamics is
provided in Chapter 4.
In a stream water quality model, the daily average
oxygen production due to photosynthesis and reduc-
tion due to respiration is formulated as follows:
where
dC/dt
R
(2-12)
rate of change of oxygen
concentration (mg O2/L-day)
average gross
photosynthesis production
(mg O2/L-day)
average respiration (mg
O2/L-day)
Note that R is considered to be plant respiration
only, excluding microbial respiration for carbona-
ceous deoxygenation and nitrification. In a
model such as QUAL2E, the mass flux term for
the aquatic plant contributions to the oxygen bal-
ance is typically modeled as a zero-order proc-
ess:
- = (0.3 \i ~ OC4 p ) Ag
(2-13)
where
dC/dt
Aa
rate of change of oxygen
concentration (mg O2/L-day)
algal biomass concentration
(mg/L)
2-13
-------
Atmoaphvrle
/w_t
Organic
Sic1«rt«i
Mirtr:*rt Uptik*
la iarttMc S«dlm*nt
Cirbon*o*CKj«
•%
- /'/',' 7'
1
H -*—
3 I
j rr^m-
/ V / ','' '
r
°*
f
°'
?
S :
S
o
L
V
E
D
O
X
Otnmttd
CBOO
**""«
7777
SOD
FIGURE 2-5. INTERRELATIONSHIP OF MAJOR KINETIC PROCESSES FOR BOD, DO, AND
NUTRIENT ANALYSES AS REPRESENTED BY WATER QUALITY MODELS
(After McCutcheon, 1989)
2-14
-------
p
as
04
algal growth rate coefficient
(day^
algal respiration rate
coefficient (day"1)
the stoichiometric ratio of
oxygen production per unit
of algal photosynthesis
(mg/ mg)
the stoichiometric ratio of
oxygen uptake per unit of
algae respired (mg/mg)
2.3.5 Eutrophication Kinetics
Figure 2-5 shows the major kinetic processes
usually considered in a complete DO, BOD, and
nutrient analysis. The reader should note the
similarities between Figures 2-2 and 2-5. The
following processes are discussed in this section:
• Algal growth and nutrient uptake
• Algal death and settling
• Nutrient mineralization
• Sediment nutrient release
2.3.5.1 Algal Growth and Nutrient Uptake
Phytoplankton growth is directly related to tempera-
ture in moderate climates, nutrient effect, and light
intensity up to a saturating condition:
Gp = GT
rn
(2-14)
where
Gp = phytoplankton growth rate
(day'1)
GT = temperature dependent
growth rate (day'1)
ri_ = light effect (dimensionless)
rn = nutrient effect
(dimensionless)
Temperature dependence, GT, is approximated by:
Gr=Gmax(1.066)T-20
where
Gmax
T
maximum growth rate(day ~1)
temperature (°C)
The value suggested for Gmax under average condi-
tions for a mixed phytoplankton population is ap-
proximately 1.8 day"
1987).
(Thomann and Mueller,
Auer and Canale (1980) and Canale and Vogel
(1974) summarized data from phytoplankton growth
experiments conducted at various temperatures.
These results, plotted in Figure 2-6, illustrate the
different temperature optimums for different phyla
(species groups) of phytoplankton (diatoms, green
and blue-green algae) as well as the influence of
temperature on the growth rate. The growth rate at
saturating light condition can be expected to be spe-
cies group dependent, as shown in Figure 2-7. Be-
cause light energy available to phytoplankton varies
with depth and time of day, an appropriate expression
of light availability for use in models should account
for these changes.
Averaging relative photosynthesis as a function of
light intensity over a given depth of water and over a
fixed interval of time yields
2.718 /
KeHT
[e
- e
']
0.2 =
Jr_
lsf
(2-15)
(2-15a)
(2-15b)
where
Is
IT
f
Ke
H
T
light effect
saturating light intensity (ly/
day)
total daily solar radiation (ly)
photoperiod (day)
extinction coefficient (m~1)
depth (m)
average period (day)
The extinction coefficient, Ke, is dependant on inor-
ganic solids, detrital particles, and phytoplankton
biomass in the water body. Values of Ke in natural
water bodies typically vary from 0.05 to 6.9 m"1.
Typical values for IT range from 250 to 500 ly. The
corresponding range of values for ri_ is 0.1 to 0.5, so
the overall daily effect of light extinction with depth is
to reduce the growth rate by about 50-90 percent
(Thomann and Mueller, 1987).
2-15
-------
G ,= 1,SU,066)
'
T~aCl
EC
9
Q.
V}
x
rfl
s
Diatoms
o t-
10
•
C)
FIGURE 2-6. SPECIFIC ALGAL GROWTH RATE AS A FUNCTION OF TEMPERATURE
(After Canale and Vogel, 1974)
I
*
a
w
I
] ' j- 1 n i i f « i TO
FIGURE 2-7. EFFECT OF LIGHT INTENSITY ON ALGAL GROWTH
(After Ryther, 1956)
2-16
-------
0.0
Nutrient Concentration (pg/L)
FIGURE 2-8. EFFECT OF NUTRIENTS ON ALGAL GROWTH
(After Ambrose et al., 1993a)
The phytoplankton growth rate is also a function of
nutrient concentrations up to a saturating condition,
greater than which it remains constant with nutrient
concentration (Figure 2-8). At zero nutrient concen-
tration, there is no growth. As the nutrient level is
increased, the growth rate is linearly proportional to
the availability of nutrients. However, as nutrient
levels continue to increase, the effect on the growth
rate of the phytoplankton is saturated. Such a rela-
tionship is described by a Michaelis-Menton formula-
tion where the nutrient reduction factor, or nutrient
effect, for algal growth, rn, is:
rn =
Nut
Km + Nut
(2-16)
where
Nut
K
= the nutrient concentration
half saturation (Michaelis)
constant (|ig/L)
The Michaelis half-saturation constant, a function of
the algal species group, is the nutrient concentration
for which the nutrient reduction factor is 0.5 or half the
maximum growth rate. The value usually ranges
from 5 |ig/L to 25 |j,g/L for nitrogen and from 1 |j,g/L to
5 |ig/l_ for phosphorus, depending on the species.
With more than one nutrient accounted for in the
model (i.e., nitrogen, phosphorus, silica), the nutrient
effect is given by:
rn= min
DIN
DIP
Si
where
DIN
DIP
Kmn
Kmp
Si
Ksi
Kmn + DIN ' Kmp + DIP ' KS! + Si""
/
(2-17)
limiting nutrient reduction
factor
inorganic nitrogen
concentration (sum of
ammonia, nitrate, and nitrite)
dissolved inorganic
phosphorus concentration
Michaelis-Menton constant
for nitrogen (|ig/L)
Michaelis-Menton constant
for phosphorus (jj,g/l_)
dissolved inorganic silica
concentration (|ig/L)
Michaelis-Menton constant
for silica (|ig/L)
The minimum ratio of the nutrients considered in the
model thus controls the computation of the nutrient
2-17
-------
10.0
7.5
5.0
2.5
Nitrogen
Limitation
Phosphorus
Limitation
60 120
DIN (ug/L)
180
0.1
o
to
LL
0.15 I
o
TJ
0)
0,2 g
QC
0.3 i
0.4 2
0.5 U
240
FIGURE 2-9. EFFECTS OF NUTRIENT LIMITATION ON ALGAL GROWTH
(After Ambrose et al., 1993a)
reduction factor and is described as the nutrient lim-
iting algal growth. Nitrogen and phosphorus are re-
quired by all algal species while silica is required only
by diatoms.
Figure 2-9 shows the Michaelis-Menton formulation
in a slightly different format. In this figure, Kmn = 25
|ig/L and Kmp = 1 |^g/L are used. For a stream with
a DIN concentration of 100 |ig/L, this corresponds to
a 20 percent reduction in the growth rate (rn = 0.8).
For phosphorus to become the limiting nutrient in the
stream, dissolved inorganic phosphorus must reach
a level of 4 |ig/L or less. It should also be pointed out
that if upstream nitrogen controls were instituted such
that DIN was reduced to 60 |ig/L for the same stream
reach, a further reduction in DIP to 2.5 |ig/L would be
required to keep phosphorus as the limiting nutrient.
In other words, as the water column concentrations
of DIP begin to approach growth-limiting levels due
to continued reduction in point source phosphorus
effluents, any nitrogen control strategies that might
be instituted would require additional levels of phos-
phorus removal to keep phosphorus as the limiting
nutrient by keeping an upstream N/P ratio below 10.
2.3.5.2 Algal Death
Decreases in algal biomass are brought about by two
processes: algal respiration and death. Algal respi-
ration is caused by endogenous respiration, in which
algal biomass is oxidized to generate CO2. Algal
death includes grazing by zooplankton (for diatoms
and greens only) and cell destruction through bacte-
rial attack, disease, physical damage, the natural
aging process, or other mechanisms. The distinction
between phytoplankton reductions through death
and reductions through respiration, grazing by
zooplankton, or settling is that upon death all the
carbon, nitrogen, and phosphorus contained in the
algal biomass is returned to the carbonaceous BOD
(CBOD), organic nitrogen, and organic phosphorus
pools, respectively. During respiration, carbon is
2-18
-------
given off as CO2 rather than CBOD; through grazing,
only a portion of the organic contents of the algal cells
is returned to the respective organic pools. (The
remaining portion is lost from the phytoplankton mass
balance as zooplankton biomass.)
The algal reduction rate, Dp, can be expressed as:
DP=DP1(T) + DZ (2-18)
where
DP1(T)
Dz
temperature-dependent
endogenous respiration rate
(day1)
death rate (day'1) (grazing
and natural mortality)
The phytoplankton death rate, Dz, is a function of
zooplankton population and zooplankton grazing
rate. Zooplankton control the population of phyto-
plankton through predation. They also recycle the
nutrient content of their prey. Limited data on
zooplankton usually do not allow elaborate formula-
tion of zooplankton grazing. Given the concentration
of zooplankton and their filtering rate, the loss rate of
phytoplankton due to zooplankton grazing may be
formulated.
2.3.5.3 Algal Settling
Phytoplankton are lost from the water column through
settling. In a vertically mixed water column, the net
settling rate (i.e., settling to the bottom less resuspen-
sion from the bottom) is expressed as:
where
S
Vs
H
H
net settling rate (day ),
phytoplankton settling
velocity (m/day)
average depth (m)
(2-19)
Through settling, none of the organic cell material is
returned to the organic nutrient pools in the water
column unless the model incorporates an explicit
dynamic link between the sediments and the water
column (e.g., Di Toro et al. 1990). As with other
parameters in a eutrophication model, the phyto-
plankton settling velocity is dependent on the algal
species group and size of the organism. Settling
velocities can range from 0.1 to 10.0 m/day with small
cells (e.g., chlorophytes) characterized by low veloci-
ties of 0.1 m/day and larger cell size diatoms by
higher velocities (1-10 m/day).
2.3.5.4 Nitrogen Components
The major components of the nitrogen system are
detrital organic nitrogen, ammonia, nitrite, and ni-
trate. In natural waters, there is a stepwise transfor-
mation from organic nitrogen to ammonia, nitrite, and
nitrate, yielding nutrients for phytoplankton growth as
shown in Figure 2-5. The kinetics of the transforma-
tions are temperature-dependent.
During algal respiration and death, the cellular nitro-
gen is returned to the organic nitrogen pool. Organic
nitrogen undergoes a bacterial decomposition whose
end product is ammonia. Ammonia, in the presence
of nitrifying bacteria and oxygen, is oxidized to nitrite
and to nitrate (nitrification). Both ammonia and ni-
trate are available for uptake and use in algal growth;
however, for physiological reasons the preferred form
of nitrogen is ammonia (Conway, 1977; Garside,
1981). The ammonia preference term is charac-
terized in Figure 2-10. As the available nitrate in-
creases above approximately the Michaelis
limitation, for a given ammonia concentration, the
preference for ammonia reaches a plateau. Also, as
the concentration of available ammonia increases,
the plateau levels off at values closer to unity, i.e.,
total preference for ammonia.
2.3.5.5 Phosphorus Components
In many stream water quality models, phosphorus is
accounted for in two forms: dissolved and paniculate.
A fraction of the phosphorus released during phyto-
plankton respiration and death is in the inorganic form
and readily available for uptake by other viable algal
cells. The remaining fraction released is in the or-
ganic form and must undergo a mineralization or
bacterial decomposition into inorganic phosphorus
before it can be used by phytoplankton.
There is an adsorption-desorption interaction be-
tween dissolved inorganic phosphorus and sus-
pended paniculate matter in the water column. The
subsequent settling of the suspended solids together
with sorbed inorganic phosphorus can act as a sig-
nificant loss mechanism in the water column and is a
source of phosphorus to the sediment. Compared
with the reaction rates for the algal and biological
2-19
-------
- 25/jg/L
c
Q
£
c
u_
o
t—
o
J3
al
1,0
0.8 -'
0,6 -
0,4 -
0.2
NH - 200
100 /jg/L
SO jugfi.
25
SO
N0
150
200
FIGURE 2-10. AMMONIA PREFERENCE STRUCTURE FOR ALGAL GROWTH
(After Thomann and Fitzpatrick, 1982)
kinetics, which are on the order of days, the adsorption-
desorption rates are much faster, permitting an in-
stantaneous equilibrium assumption for the
calculation. In the model formulation, the concentra-
tions of dissolved and paniculate phosphorus need to
be repartitioned at every time step. A wide range of
partition coefficients for phosphorus have been found
in the literature. Schreiber and Rausch (1979) re-
ported partition coefficients ranging from 4,540 to
15,900 for a flow detention reservoir (see also
Thomann and Fitzpatrick, 1982).
2.3.5.6 Sediment Nutrient Release
In addition to the external sources of nutrients, the
release of nutrients from the sediments may also be
important. Such releases occur as a result of a
gradient in nutrient concentration between the over-
lying water and the interstitial water of the sediment.
In some systems, the impact of sediment nutrient
release can be significant and can result in continuing
eutrophication problems even after point sources
have been substantially reduced through control
measures. Sediment nutrient releases can be
treated as nutrient sources to the stream in waste
load allocation modeling studies. In the absence of
site-specific field data describing sediment nutrient
release, approximations can be made on the basis of
sediment oxygen demand estimates (see Appendix
A).
2.4 GOVERNING EQUATIONS
2.4.1 Mass Balance Principle
The basic principle used to formulate a stream water
quality model is mass balance. That is, for a given
segment of the stream, the accumulation of a water
quality constituent over a finite period of time is equal
to the mass entering the segment plus the mass
added to the segment, less the mass leaving the
segment and the mass lost within the segment (Fig-
ure 2-11).
Accumulation = Mass In - Mass Out
+ Source - Sink (2-20)
2-20
-------
Oxyger. aadM 10 segment by
• Atmosphere feaerattsfi
K] a :
= river flow rate (LIT)
Dimension Code
L = length
M = mass
T = time
Q
C = concentration of dissolved oxygen (M/LJ)
Cs = saturation concentration of dissolved oxygen (MIL3)
L = CBOD concentration (MIL3)
H = mean water depth (L)
dV = segment volume AAx(L3)
as = the stoichiometric ratio of oxygen production per unit of algal photosynthesis (M/M
014 = the stoichiometric ratio of oxygen uptake per unit of algae respired (M/M)
as, ae = the stoichiometric ratio of oxygen uptake per unit of ammonia and nitrite-nitrogen oxidation,
respectively (M/M)
PI, f>2 = ammonia and nitrite oxidation rate coefficient, respectively (T 1)
|i = algal growth rate coefficient (T1)
p = algal respiration rate coefficient (T 1)
Ni, N2 = ammonia and nitrite-nitrogen concentration, respectively (MIL3)
Ag = algal biomass concentration (MIL3)
SOD = temperature-adjusted rate constant for SOD (M/L2T)
Ka = atmospheric reaeration rate: reflects first-order reaction whereby a fraction of oxygen deficit is
satisfied, eK*l= e~^w(T~1)
Ka(Cs-C) = change in dissolved oxygen concentration in a segment that when, multiplied by segment volume
(dV), yields change in dissolved oxygen mass in segment (M/L3T)
Kd = BOD oxidation rate where oxidation accounts for all CBOD removal (T 1 )
FIGURE 2-11. MASS BALANCE EQUATIONS FOR DISSOLVED OXYGEN
(See Equations 2-21 and 2-24)
(After USEPA, 1983a)
2-21
-------
Applying the mass balance principle and considering
a small segment of a stream, one may develop:
d VAC = QCAt- [Q + AQ] [C- Ax] Af
dx
+ WAt-dVKCAt
(2-21)
where
dV
AC
Q
C
At
AQ
ac
dx
w
K
volume of the segment and
is equal to AAx(L3)
change of concentration
(MIL3)
= flow rate (L3/t)
concentration (MIL3)
small increment of time (t)
change of flow rate over the
length
concentration gradient over
Ax (MIL4)
direct loading rate (Mt~1)
first-order reaction rate (t"1)
Dividing Equation 2-21 by dVAf results in
d£ = ^<3dC_£dQ W__Kr
dt~ A dx A dx + dV
(2-22)
Assuming steady-state conditions and neglecting the
flow gradient, the above equation becomes
QdC W
(2-23)
Note that the reaction term KC may represent formu-
lations for carbonaceous deoxygenation, nitrogenous
deoxygenation, reaeration, or any other first-order
reactions.
2.4.2 Dissolved Oxygen Equation
Using the notation in Figure 2-11, the distribution of
dissolved oxygen may be formulated by including all
dissolved oxygen sources and sinks described in
Section 2.3:
- 0.5 (3l A/1 - OC6 (32 A/2
SOD
H
(2-24)
The terms on the right side of Equation 2-24 repre-
sent, respectively: the downstream transport of oxygen
with the stream flow, atmospheric reaeration, biologi-
cal oxidation of CBOD, biological oxidation of ammo-
nia, biological oxidation of nitrite photosynthesis less
respiration, and the biological oxidation of sediment
materials. If CBOD is removed only by direct oxida-
tion, the deoxygenation rate coefficient, K
-------
wut« Biiehkr-g* :>: * 0, T • o)
Q
O
o «-
V^-l
(K
3 Z * * • 10 12 14 it tg 20
TIME Ways)
Distance (Miles) (U = 2mJ/day)
fl 4 a 12 IV 29 !•* 39 32 36
„ ., , j .... __._._
3,,-\ '
O5 \ 3»««t
j
Z 8 - •-, i
LU
0
X *
o
o
yj
f
O i x-^
C/3 ' """---_ DOProlll* wl1*N»
Q
fer>
2 4 fl 8 10 12 14 If II 26
TIME (days)
FIGURE 2-12. COMPONENTS OF DO PROFILE (SAG CURVE)
DOWNSTREAM OF WASTE DISCHARGE
2-23
-------
0, the initial CBODU concentration is 10 mg/L fol-
lowing complete mixing between the waste load and
stream flow. After 10 days all of the CBODU has
been exerted. Since the CBOD test measures the
amount of organic material present in terms of the
amount of oxygen required for its stabilization by
bacteria, the reduction of CBOD concentration is
equivalent to the dissolved oxygen consumption.
The bottom plot in Figure 2-12 shows two calculated
dissolved oxygen profiles associated with the CBOD
profile in the top plot. The lower profile represents the
dissolved oxygen concentration in the river if oxygen
were not replenished by reaeration. In this case, the
assumed initial dissolved oxygen concentration of 12
mg/L is ultimately reduced to 2 mg/L to compensate
for the CBOD reduction (in top plot). The upper
profile indicates the net effect of reaeration providing
a source of oxygen.
The characteristic shape of the stream dissolved
oxygen profile (called the DO sag curve) is the result
of interplay of the biological oxidation and reaeration
rates. Each is represented by first-order kinetics. In
the early stages, oxidation greatly exceeds reaeration
because of high CBOD concentrations and river dis-
solved oxygen concentrations close to saturation
(i.e., small deficit). Oxygen is used faster than it is
resupplied, and stream dissolved oxygen concentra-
tions decrease. As the waste moves downstream,
the consumption of oxygen decreases with the stabi-
lization of waste and the supply of oxygen from the
atmosphere increases because of greater deficits.
The driving force to replenish oxygen by atmospheric
reaeration is directly proportional to the oxygen defi-
cit, (i.e., low oxygen concentration). At some point
downstream from the waste discharge, the decreas-
ing utilization and the increasing supply are equal.
This is the critical location, where the lowest concen-
tration of dissolved oxygen occurs. Further down-
stream, the rate of supply exceeds the utilization rate,
resulting in a full recovery of the dissolved oxygen
concentration. The above discussion is a simple
illustration of the BOD/DO modeling analysis concept
when it is assumed that organic decomposition and
reaeration are the dominant pro-cesses affecting the
organic balance. In reality, many other factors such
as nitrification and SOD can significantly change the
shape of the profile. Many streams receive nonpoint
sources upstream or other point sources that depress
the upstream dissolved oxygen below a saturation
value. Natural background loading also may depress
dissolved oxygen in certain streams. Note that con-
stant hydraulic geometry is also assumed in the
above illustration. In a natural stream, it is difficult to
find constant hydraulic geometry for more than a few
miles. In this case, the stream is divided into a
number of reaches with uniform geometry.
2.4.3 Separate Mass Balance Equations by
Constituent
Dissolved oxygen dynamics depend on the interac-
tions of several constituents and processes. The
constituents that directly influence oxygen include
BOD, ammonia nitrite, and nitrate. Nitrogen and
phosphorous determine growth of phytoplankton,
periphyton, and aquatic plants and subsequently af-
fect dissolved oxygen via photosynthesis and respi-
ration. For each constituent that is in the dissolved
oxygen mass balance, a separate mass balance
equation is used to account for the reactions of that
parameter. Using the notation developed thus far,
these constituents may be modeled by the mass
balance equations summarized in Table 2-4. The
mass balance equations in Table 2-4 can be found in
many stream water quality models (e.g., QUAL2E)
that have been used inTMDL studies. Thomann and
Mueller (1987) present a simplified version of the
eutrophication equation for river and stream eutrophi-
cation analysis.
One should note that the major difference between
the BOD/DO modeling and nutrient/eutrophication
modeling is in terms of the model formulations. That
is, the equations governing phytoplankton growth are
nonlinear functions of nutrients and light availability,
whereas the BOD/DO equations are all linear. In fact,
the phytoplankton/nutrient problems are the most
difficult models to work with because of the complex-
ity of the algal biology, the nonlinear interactions
between nutrients and aquatic plants, and the inter-
actions of the sediment-water column interface. As
a result, the superposition of results from BOD/DO
equations is appropriate to isolate the effects of the
various linear reaction terms, whereas the same is
not true of the eutrophication results.
2-24
-------
TABLE 2-4. SEPARATE MASS BALANCE EQUATIONS USED FOR EACH CONSTITUENT IN BOD,
DO, AND NUTRIENT ANALYSES
Carbonaceous BOD (CBOD)
Ammonia Nitrogen
Nitrite Nitrogen
Nitrate Nitrogen
Organic Nitrogen
Algae
Organic Phosphorus
Dissolved Phosphorus
d{ = ps A/4 - Pi A/1 +-fi- Fa^iAg
C/A/2
dt
dN3
dt
C/A/4
= pi A/1 - p2 A/2
= p2 A/2 - (1 - F)ai |i Xlfl
- PS A/4 - 04 A/4
cff
dt
= OC2 p Ag - P4 Pi - 05 Pi
= P4Pl+^-(
Variables and coefficients not previously identified in Figure 2-11:
A/3
A/4
Pr
0.2
Ks
nitrate nitrogen concentration F
(MIL3)
organic nitrogen concentration pg
(MIL3)
organic phosphorus concentration $4
(MIL3)
dissolved phosphorus concentration 02
(MIL3)
fraction of algal biomass that is o3
nitrogen (M/M)
phosphorus content of algae 04
(M/M)
effective loss rate due to settling (T ~1) 05
fraction of algal nitrogen uptake
from ammonia pool
organic nitrogen hydrolysis rate
coefficient (T"1)
organic phosphorus decay rate
(I'1)
benthos source rate for dissolved
phosphorus (M/L2T)
benthos source rate for ammonia
nitrogen (M/L2T)
rate coefficient for organic nitrogen
settling (T"1)
rate coefficient for organic
phosphorus settling (T ~1)
2-25
-------
-------
3. MODEL SELECTION AND REVIEW
3.1 PURPOSE
The purpose of this chapter is to provide general
guidance and some specific procedures for selecting
an appropriate model(s) to support the development
of TMDLs for BOD, DO, and nutrients in streams and
rivers. Section 3.2 presents an overview of Chapter
3. Section 3.3 identifies and discusses the steps of
model selection. A brief review of selected models is
presented in Section 3.4. As stated earlier, the mod-
els reviewed in this guidance emphasize the fate and
transport of BOD, DO, and nutrients in streams and
rivers.
3.2 OVERVIEW
The success of a modeling effort to support the
development of TMDLs is highly dependent on under-
standing the complexity of the water quality problems.
This understanding will assist in defining the required
accuracy, analyzing the implication of various simpli-
fying assumptions, and eventually selecting an ap-
propriate modeling strategy and modeling tools. It is
generally known that the preferred and most cost-ef-
fective approach is to use the simplest model that
includes all the important processes affecting water
quality in the stream or river. Problem understanding,
normally gained through characterization studies us-
ing available data, provides answers to questions
such as the following: Are nonpoint sources an impor-
tant contributor to water quality impairment? Are non-
point sources or a portion of nonpoint sources
controllable? Is watershed modeling necessary, and
if so, what is the sufficient level of detail? What are
the temporal and spatial boundaries of impaired wa-
ters? In general, the results of watershed and water
quality characterization define the modeling needs as
well as the need for monitoring, field surveys, and
other support activities. The selection of too simple
a model may result in inaccurate predictions of man-
agement needs and their implications on water qual-
ity. The cost implications of decisions are also
important factors. Furthermore, inaccurate projec-
tions from present to future cond itions may be caused
by an insufficient sensitivity of the selected model(s)
to changes in watershed or water quality processes
such as the balance of sediment oxygen demand in
specific reaches or seasons.
On the other hand, the selection of too complex a
model can result in misdirected resources, delays in
the study, and unnecessary costs. Predictive uncer-
tainty may increase because of extra "free" model
parameters that cannot be estimated with available
data and resources. Study costs will increase be-
cause of the additional data needs, as well as model
calibration and validation requirements. When water
quality impairment is characterized as the result of
both controllable point and nonpoint loadings, the
selection of the modeling tools should be compatible
so that watershed modeling results provide the data
necessary for analysis of the water quality in the
receiving water.
3.3 MODEL SELECTION
Successful model selection results from achieving a
close match of the primary site-specific physical,
hydrologic, and water quality features of interest to a
model's capabilities to simulate these features. Two
categories of models are available for use throughout
the TMDL process. The first category consists of
watershed models that can be used to derive pollut-
ant loadings from both point and nonpoint sources.
Watershed models rely on (1) hydrologic processes
and water balance over the watershed and (2) the
physiographic characteristics of the watershed in-
cluding land use and land cover, soils, topography,
water uses, and discharges from municipal and in-
dustrial facilities. A detailed review of these models
in terms of their potential application in the develop-
ment of TMDLs is presented in USEPA (1992b). The
second category consists of receiving water models
that can be used to assess the impact of pollutant
loadings on the waterbody. These models rely on
(1) transport characteristics of the receiving water
including flow rate, stream morphology and bounda-
ries, and reaeration and dispersion parameters and
(2) fate of the pollutant within reaches of the receiving
water. Available watershed and water quality models
range from simple empirical and statistical proce-
3-1
-------
dures to more deterministic and multidimensional
models. In addition, these models can be differenti-
ated based on a number of criteria including:
• Water quality constituents modeled.
• Spatial and temporal resolution of the results.
• Level of detail used to simulate hydrologic
and water quality processes.
• Level of effort and data requirements for the
specific application.
• Ease of application including input and out-
put data processing, user support, documen-
tation, and operating requirements.
Most importantly, the selection process should focus
on determining which watershed and water quality
processes closely match the site-specific charac-
teristics. As mentioned earlier, the results of the
characterization of watershed and water quality con-
ditions can facilitate this selection process by provid-
ing information for (1) establishing the study
objectives and constraints, (2) determining the
needed detail to represent the pollutant loadings and
the problem boundaries and identifying the critical
conditions in terms of their temporal and spatial reso-
lution, and (3) determining the pollutant of concern
and the required mathematical formulations of hydro-
logic and water quality interactions.
A preliminary step of the characterization study con-
sists of reviewing existing information about the water
body so that the dominant physical and chemical
processes can be defined. This information includes
available site-specific analyses, monitoring data, past
modeling studies that identify pollution sources and
their magnitude, stream flow data, hydrologic and
statistical characteristics, and ambient water quality
impairment. In certain instances, simple calculations
and statistical procedures may be required prior to the
modeling selection process. These procedures may
include pollutant loading estimates using simple load-
ing functions, pollutant transport predictions using
analytical steady-state methods, and prediction of
water quality violations using standard excursion and
trend analysis techniques. The result of this step is
a detailed description of the modeling objectives and
the potential and anticipated constraints. The mag-
nitude of nonpoint source loadings and the signifi-
cance of their impact on the receiving water may
dictate whether a watershed model is necessary or
whether a steady-state water quality model is suffi-
cient to represent the dominant transport processes.
A second step may involve further evaluation of the
variability of pollution sources and the hydrologic
regime to assess the level of modeling effort required
to represent the temporal and spatial resolution of the
water impairment under consideration. Analysis of
the variability of pollution loadings from various
sources and identification of critical water quality
impairment conditions will result in identification of the
temporal and spatial resolution to be considered in
model development in order to ensure an accurate
representation of the system. At this stage, the analy-
sis should ensure that the watershed model and the
receiving water quality model are properly addressing
the key decisions and that all assumptions are within
the acceptable range. Although most streams and
rivers can be represented using a one-dimensional
steady-state model, certain wide or deep reaches
may exhibit significant lateral and vertical water qual-
ity gradients, therefore requiring a two-dimensional
configuration. In both of these cases, a simple wa-
tershed loading model may be sufficient to provide
input data for the water quality model. However, a
more detailed continuous or design storm watershed
simulation model may be required if water impairment
is characterized as storm-driven events, if a dynamic
representation of water quality is required to capture
daily variabilities, or if conditions where specific pol-
lutant concentrations violate certain criteria must be
defined.
In a third step, an initial assessment of the dominant
water quality interactions is necessary to ensure that
the proper combination of constituent and kinetics
formulation is represented by the model. For exam-
ple, where algal photosynthesis and respiration are a
small component of the dissolved oxygen balance,
the corresponding terms and rate coefficients can be
ignored in the model equations. Similarly, sequential
reaction of the various forms of organic and inorganic
nitrogen may be highly nonlinear, resulting in time and
space lags in the resultant dissolved oxygen profile
and therefore making it inadvisable to select a model
that combines all nitrogen reactions in a single term.
The steps listed above are addressed in more detail
in the following sections, with special emphasis on
BOD, DO, and nutrients in streams and rivers. Model
selection may require a phased approach in which
simple formulations are considered initially in Phase
1 ofTMDLdevelopment. As new monitoring data and
characterization studies become available, a more
detailed modeling effort can be considered.
3-2
-------
3.3.1 Study Objectives and Constraints
The first step in selecting an appropriate model to
support the development of TMDLs is to review the
existing data on pollutant loadings, stream flows, and
ambient water quality regarding the designated uses
of the stream and the applicable water quality stand-
ards. Estimation of pollutant loadings from a water-
shed may also require land use distribution data, soil
characteristics, information on existing management
practices, and pollutant buildup and washoff parame-
ters in addition to climatic and hydrologic charac-
teristics. These data should be reviewed to indicate
whether standards violations or water quality prob-
lems are associated with diel fluctuations, storm
events, flow variations, or seasons of the year.
In selecting a receiving water quality model, the
modeler can use this information to determine the
temporal resolution (steady-state, quasi steady-
state, real time) and to specify the magnitude and
variability of point and nonpoint sources that must be
included in the selected modeling approach. Ambi-
ent water quality data should also indicate where
violations or impairment problems are occurring and
whether significant spatial gradients in concentra-
tions exist. The combined information collected on
the watershed and hydrologic characteristics and
water quality problems will help determine the level
of effort needed and the type of water and water
quality processes that must be considered. Exam-
ples of processes of major concern when modeling
BOD, DO, and nutrients in stream and rivers include
CBOD oxidation, nitrite oxidation, sediment oxygen
demand, ammonia oxidation, atmospheric reaera-
tion, and algal photosynthesis and respiration.
The modeling framework should include preliminary
mass balance calculations using simple models or
analytical equations to help define water quality proc-
esses. These simple models provide analytical solu-
tions for various load scenarios under varying flow
conditions. In-stream sinks and sources can also be
represented using simplified formulations such as
zero- and first-order decay equations.
It is also desirable to anticipate the technical issues
associated with pollution control scenarios, overall
control levels, and other changes in watershed char-
acteristics such as changes in land use and the
addition of new sources of pollution. These issues
can be summarized in terms of how these changes
affect the magnitude of pollutant problems and there-
fore the modeling and monitoring needs. These
needs actually represent the project objectives and
define a number of criteria to assist in selecting the
appropriate model.
3.3.2 Pollutant Loadings, Spatial and Temporal
Resolution, and Transport Mechanisms
3.3.2.1 Pollution Sources
Various loads, sources, and sinks influence the dis-
solved oxygen distribution in streams and rivers. Up-
stream sources of oxygen demand or dissolved
oxygen deficit can be caused by point source dis-
charges from municipal and industrial waste treat-
ment plants; combined and separate sewer system
discharges and urban runoff; and runoff from for-
ested, agricultural, and suburban drainage areas.
In-stream processes that affect dissolved oxygen
distribution include sediment oxygen demand, ben-
thic regeneration, and oxygen production and utiliza-
tion by phytoplankton and other aquatic plants.
All sources that are explicitly included in the TMDL
analysis require direct measurements on appropriate
time and space scales to define the magnitude of the
individual source by contaminant. Under diverse
conditions, receiving water quality data are required
to evaluate the effects of both point and nonpoint
sources.
The primary contaminants of concern associated with
point sources are organic carbon compounds that
produce carbonaceous biochemical oxygen demand
(CBOD) and the reduced forms of nitrogen that result
in nitrification. For each source type, it is necessary
to define the magnitude of the ultimate oxygen de-
mand for both classes of contaminants. In addition,
field and laboratory data may be required to distin-
guish between the forms of organic nitrogen that can
hydrolyze to ammonia and the nitrogen that is effec-
tively refractory. This distinction can be important
when nitrification is a concern. The effluents from
treatment plants without nitrification can contain po-
tentially significant concentrations of organic nitro-
gen. The degree of nitrification required can be
influenced by the organic nitrogen level in the effluent
that can be transformed to ammonia and sub-
sequently oxidized in the stream or river. Although
considered point sources, combined sewer overflows
(CSOs) are storm-driven and contribute additional
pollutants of concern to stormwater discharges.
Groundwater may also contribute a significant portion
of nitrate to surface water, although unless proven
3-3
-------
contaminated, this portion of the loading is uncon-
trollable within the short term.
Nonpoint source pollutants come primarily from agri-
cultural lands, forested watersheds, and urban storm-
water runoff. Agricultural areas can contribute a
significant amount of nutrients depending on fertiliza-
tion programs. Organic loads also can be significant
during certain periods of the year. The main concern
associated with agricultural sources is the storm-
driven aspect of the pollutant loadings and the direct
relationship between the occurrence of storm events
and agricultural practices (e.g., timing and rate of
fertilizer application, soil plowing and tillage tech-
niques, etc.). Many researchers recognize that for-
ested watersheds represent pristine conditions and
that pollutant loadings from these areas are the result
of natural processes. These loads represent the
background condition and should be considered un-
controllable. However, some silvicultural activities
(e.g., road construction, timber harvesting, pre-
scribed burning) may result in soil disturbance and
erosion processes that represent concerns similar to
those for agricultural areas. Pollutants of concern
include high suspended sediment and organic debris
from destruction of topsoils. Urban stormwater runoff
is also a complex, storm-driven source. Stormwater
runoff transports significant amounts of metals.
Build-up of dust and dirt on impervious areas repre-
sents a major process characterizing urban sources.
Where combined sewer overflows (CSOs) are con-
tributing to stormwater runoff, additional pollutants of
concern involve those associated with municipal
waste.
the need to simulate the three-dimensional mixing of
an effluent in a stream. This is especially true for
CBOD and dissolved oxygen, for which it can be
shown that only small errors result from treating the
effluent plume as being immediately mixed at the
point of discharge (McCutcheon, 1989). For ammo-
nia toxicity, as well as other toxic constituents, it is the
usual practice to meet chronic toxicity criteria at the
edge of the mixing zone and acute criteria at the end
of the discharge pipe and in the mixing zone of initial
dilution (ZID). However, it is also important to ac-
count for the far-field effect of a potentially toxic
discharge, since the extent of the toxicity is related to
ambient and effluent levels of pH, temperature, and
hardness. An effluent discharge from an activated
sludge municipal wastewater plant that is charac-
terized by low pH in the effluent may not cause an
ammonia toxicity problem in the near-field mixing
zone. However, further downstream, after the pH has
returned to ambient conditions, ammonia toxicity can
occur in the far-field region. Refer to the Technical
Support Document for Water Quality-based Toxics
Confro/(USEPA, 1991b) for additional information.
Certain rivers may require a framework that encom-
passes a two-dimensional analysis. These situations
are generally associated with deep rivers or run-of-
the-river impoundments where vertical or lateral gra-
dients can be significant. Depending on the
geomorphology, the upstream regions of lakes and
impoundments may be characterized by significant
lateral, as well as longitudinal, variations in dissolved
oxygen that would require a two-dimensional analy-
sis.
3.3.2.2 Model Dimensions
Most receiving water modeling projects that address
dissolved oxygen in streams and rivers under sum-
mer, low-flow conditions can be adequately repre-
sented as one-dimensional, steady-state
calculations. Both theory and practice demonstrate
that dissolved oxygen gradients in streams and rivers
are most significant along the longitudinal axis. There
are only relatively minor vertical and lateral gradients
except in the initial mixing zone at the point of dis-
charge. Near the shore of streams and rivers, lateral
gradients can occur from low oxygen conditions re-
sulting from groundwater inflow depleted of oxygen,
photosynthetic and respiratory processes of attached
algae, elevated temperature, and reduced velocity
(and atmospheric reaeration) of the shallower near-
shore area. Most, if not all, State laws and regula-
tions have defined initial mixing zones that alleviate
If a second dimension (i.e., depth or width) is re-
quired, the analyst should provide justification in
terms of the specific decision-making elements relat-
ing to controls and treatment. This requirement is
necessary since the additional dimension in the
analysis for streams or rivers will usually require
substantially more data collection efforts and gener-
ally will result in a more complex model whose pa-
rameter values cannot be determined reliably in all
cases. Thus, if the study is not done well, the addi-
tional dimension can tend to weaken the analysis and
may adversely affect the ability to make decisions.
However, if significant vertical or lateral oxygen gra-
dients are apparent in observed data, a two-dimen-
sional model should be used.
Three-dimensional analysis of stream and river sys-
tems is still under development. These complex mod-
els are recommended only for TMDL decisions that
3-4
-------
cannot be addressed in any other fashion. If three-
dimensional models are required, they must be de-
veloped by experts in the field.
3.3.2.3 Spatial Extent
The spatial extent of the modeling analysis should
extend downstream of the dissolved oxygen recovery
zone (see Figure 2-12). This spatial coverage is
necessary for several reasons:
• Reaeration is a dominant factor in the zone
of recovery, and analysis can provide infor-
mation on the value of the reaeration coeffi-
cient.
• In many situations, a key issue is the pres-
ence of nitrification and the rate at which it
may occur following treatment upgrades.
Observations of nitrification in the zone of
dissolved oxygen recovery could be valuable
in defining bounds for nitrification rates to be
considered in making projections under fu-
ture conditions.
• Indications of phytoplankton or other aquatic
plant growth can be obtained by examining
the dissolved oxygen recovery zone after
treatment upgrades.
The information obtained from the zone of dissolved
oxygen recovery will depend, to a large extent, on the
uniformity of the stream.
3.3.2.4 Time Scale
The time scale selected for the analysis should be a
function of both the observed water quality and the
dissolved oxygen standards or criteria for the system
being analyzed. Dissolved oxygen analysis in
streams and rivers usually can be performed on a
seasonal time scale, employing either a steady-state
or time-variable analysis. It is desirable to evaluate
water quality data collected during several seasons
to determine the critical period to be analyzed. The
most frequent critical period is the low-flow, high-tem-
perature summer period. Winter periods, however,
may also be critical because of ice cover (physical
restriction of reaeration). Fall may be significant if
upstream organic carbon sources from phytoplank-
ton and/or aquatic plants result in large depressions
in dissolved oxygen. Also, spring floods that pick up
large amounts of organic debris from adjacent flood-
plains can result in severe dissolved oxygen deple-
tion or phytoplankton blooms. Some Great Plains
streams experience a low flow in spring before snow-
melt occurs. A rigorous hydraulic analysis is needed
to define the critical flow periods in relation to the
oxygen balance.
Next, the analyst must determine the time interval to
be used in the water quality analysis. Several
choices available are listed below in order of increas-
ing complexity:
• Steady-state.
• Quasi-steady-state, including
Constant loads—constant stream flow
and diel dissolved oxygen production
by phytoplankton or aquatic plants
Constant loads—variable stream flow
Variable loads—constant stream flow
Other combinations of the above
• Fully time-variable dynamic analysis.
In a steady-state analysis, a spatial profile of concen-
tration is calculated, such as would result at equilib-
rium (stream flows, waste loads, temperature, etc.).
To the extent that actual variations in pollutant load,
stream flow, and other factors can be realistically
approximated by constant conditions for the period
covered by the analysis, the calculated receiving
water concentration profile will approximate an aver-
age of the actual concentrations during that period.
A fully time-variable analysis performs successive
calculations at relatively short time steps and accepts
variable input values for parameters such as stream
flow, pollutant load, and temperature. The results are
a record of both temporal and spatial fluctuations in
the calculated water quality concentrations. Practical
considerations of cost and operating time usually limit
the duration that can be covered by such an analysis
to critical conditions.
"Continuous" versions of time-variable models ex-
tend the calculations over longer periods of time by
using larger time steps and averaging the variable
input over that period. As a result, the calculated
receiving water concentrations will not reflect short-
term variations but will reproduce the longer-term
fluctuation trends. Also available are complex kinetic
systems that relate oxygen levels to phytoplankton
populations (chlorophyll a), which in turn are control-
led by light, nutrients, zooplankton, and other factors.
These latter frameworks are time-variable and re-
quire extensive data for model calibration and valida-
tion.
3-5
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Quasi-steady-state analyses usually have one time-
variable element incorporated into what basically re-
mains a steady-state calculation. For example, the
QUAL2E program assumes that flow and loads are
constant and simulates the dynamic effect of sunlight,
temperature, and wind. Quasi-steady-state analyses
that use steady-state calculations supplemented by
time-variable calculations of diel oxygen variations
are also available for streams and rivers (Chapra and
DiToro, 1991).
Continuous monitoring data (usually dissolved oxy-
gen and flow measurements) are useful to determine
the time resolution required for TMDL modeling. For
example, if dissolved oxygen levels reach a constant
low value for long periods and if flow and loads are
relatively constant, then a steady-state analysis
should be employed. Accordingly, if dissolved oxy-
gen levels fluctuate, then a quasi-dynamic or dynamic
analysis may be in order. However, steady-state
averaging using a daily averaging period should be
attempted before complex dynamic models are ap-
plied. If an average condition is investigated, then the
fluctuations about the mean and relationships be-
tween the standard (i.e., daily or hourly average
dissolved oxygen standard) and the mean values
must be investigated as well. If necessary, some
safety factor must be incorporated when using a
steady-state analysis to estimate the mean trends in
a dynamically varying stream.
Variability in loads and upstream conditions does not
necessarily dictate a dynamic analysis. Only a sig-
nificant variable response in water quality during criti-
cal low dissolved oxygen periods justifies a dynamic
analysis to determine the exact critical conditions.
Diel variability due to photosynthesis also does not
necessarily justify a dynamic or quasi-dynamic simu-
lation. It has been consistently proven possible to
simulate the average net effect of dissolved oxygen
production minus respiration (P-R). However, the
fluctuation about the mean must be measured or
estimated by alternative means and taken into ac-
count (see Thomann and Mueller, 1987).
In general, a steady-state analysis should be widely
useful. Point sources, sediment oxygen demand,
groundwater inflows, and upstream background
loads are approximately constant or can be ade-
quately averaged. A dynamic analysis may be justi-
fied only if standards require that minimum dissolved
oxygen levels be maintained at all times or for a
significant portion of the time (i.e., 95 percent of the
time) and loads are known to cause variable dis-
solved oxygen levels in the stream. The effects of
photosynthesis can normally be taken into account
with a steady-state analysis, or a dynamic analysis
may occasionally be useful. The dynamic simulation
is expected to provide more reliable predictions but
will require more data collection and more computa-
tions. The increased amount of data input to perform
a dynamic analysis also creates difficulty with proper
interpretation of the results.
The issue of the time interval of the analysis is in part
controlled by the major pollution sources. Point
sources, sediment oxygen demand, and upstream
conditions usually can be represented by steady-
state modeling, which employs time-averaged values
for the loads from these sources. The same type of
analysis can be appropriate for some nonpoint
sources, such as those associated with groundwater
inflow, leaching from bottom deposits, and drainage
not directly related to transient events such as storm
runoff or spills. By contrast, event-related inputs of
mass, such as those associated with storms that
produce urban runoff and runoff from other land use
types, can require either a time-variable analysis or a
quasisteady-state analysis. The quasi-steady-state
analysis often can be considered in situations when
the receiving water is large and the incremental flow
associated with the study area being modeled is
small. For most of these situations, however, a time-
variable analysis has been necessary.
The time-variable analysis can be applied satisfacto-
rily if sufficient data exist or can be obtained. Projec-
tions present a special set of problems in terms of
identifying the storms or storm sequences to be used
to develop the TMDL. Furthermore, the event-related
dissolved oxygen problem can be influenced strongly
by the hydrograph after the event and the geomor-
phology of the downstream segments of the water-
body. In addition, the basic technical, economic, and
environmental issues associated with wet-weather
standards for dissolved oxygen have not yet been
addressed fully.
3.3.2.5 Transport Mechanisms
The transport mechanisms that influence the distribu-
tion of wastes discharged into free-flowing streams
and tidally mixed streams include advective transport
and dispersive transport. Advective transport repre-
sents the bulk transport, by flow, and is often the
dominant net transport mechanism except in certain
3-6
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tidally mixed streams where strong flow reversals
occur. Dispersive transport represents the mixing
(lateral and longitudinal) caused by local velocity
gradients within the bulk fluid and is normally a small
portion of the net transport except in tidally mixed
streams where the net advective transport is over-
shadowed by the longitudinal mixing caused by peri-
odic, strong tidally reversing flows.
Dispersion is present, to some extent, in all bodies of
water. However, water quality profiles, such as dis-
solved oxygen concentrations, may not be influenced
when the dispersive mixing is small and/or the advec-
tive transport is large. In these situations, decisions
will not be influenced by inclusion of dispersion in the
analysis. For certain slow-moving streams with com-
plex configurations (e.g., bayous), the dispersion
process may be a major transport component. Con-
sequently, the complexity of the calculations and data
collection programs will be reduced. The importance
of dispersion is site-specific and can be estimated by
the following procedure:
STEP 1 - Calculate the approximate longitudinal dis-
persion coefficient (Fischer et al., 1979).
c = 0.011 U2W2/HU*
(3-D
where
U
W
H
U*
longitudinal dispersion
coefficient (ft2/sec)
average stream velocity
(ft/sec)
stream width (ft)
stream depth (ft)
shear velocity (ft/sec)
The Shear velocity (O) for many streams is approxi-
mately one-tenth of the average stream velocity and
can be estimated by:
where
9
S
= gravitational constant (32.2
ft/sec2)
= stream slope (ft/ft)
- Calculate the estuary number (n) as de-
fined by O'Connor (Hydroscience, 1971). The longi-
tudinal dispersion coefficient can be employed with
stream velocity and oxidation rate (Kd) to develop this
dimensionless number.
n =
U
(3-2)
The estuary number (n) and the ratio (O) of the
reaeration rate coefficient (Ka) to the oxidation rate
coefficient (Kd) or
0= Ka/Kd
(3-3)
can be used, with Figure 3-1, to provide a basis for
judging the significance of dispersion in calculations
of dissolved oxygen concentration.
Figure 3-1 indicates that for advective streams with
values for n of about 0.1 or less, neglecting dispersion
effects will affect the calculation of the maximum
dissolved oxygen deficit (critical deficit, Dc) by less
than 10 percent. When considering steady-state
conditions, dispersion can be ignored. Where
reaeration is high relative to deoxygenation rates
(high values of O), the lack of sensitivity to dispersion
extends to higher values of n, as indicated by the
essentially horizontal lines for the higher values of O.
It should be noted that the estimates of the dispersion
coefficient and the ratio of the maximum DO deficit to
the initial BOD concentration (DC/L0) incorporate sev-
eral simplifying assumptions. The foregoing ap-
proach must therefore be considered to be an
approximation. It should, however, be adequate for
use in most studies.
There may be situations where dispersion is consid-
ered significant by the investigator even though the
foregoing analysis suggests otherwise. Examples
could include swamps, tidal rivers, or upstream seg-
ments of impoundments. If the computational frame-
work employed in the analysis introduces dispersion
due to spatial segmentation or numerical approxima-
tions (called numerical dispersion or numerical mix-
ing), the study should contain an evaluation of the
influence of dispersion on calculations of water qual-
ity. Finally, the influence of dispersion on TMDL
decisions should also be supplied in this situation.
The requirement relating to numerical mixing can
often be met by comparisons of analytical solutions
with computer output under comparable conditions.
A flow balance is required for the modeling effort;
3-7
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o i-
£ z
UJ Vi
1,4
24.
2.0 L
0.01
100.0
FIGURE 3-1. DISSOLVED OXYGEN RESPONSE AS A FUNCTION OF ESTUARY NUMBER,
n = KdDx/U2 (Equation 3-2), = Ka/Kd (Equation 3-3)
(Hydroscience, 1971)
tial importance of groundwater inflow and outflow. In
addition, flow from significant tributaries and waste
sources must be included in the model. The compu-
tation of a flow balance is not a trivial aspect of model
development. Since USGS stream-flow gauge data
are often used to compute time-averaged steady-
state streamflow (e.g., monthly) at successive down-
stream station locations, the flow balance can
become somewhat difficult because of the down-
stream travel time required for propagation of the flow
wave and the transient response of a drainage basin
to precipitation events between two successive
stream gauges. Any discrepancy in the downstream
balance of the USGS gauge time-averaged stream-
flow data with known (or estimated) point source
inputs from waste discharges and gauged tributaries
is usually attributed to either ungauged tributaries or
groundwater flow. Each of the sources included in
the model must also be supported by data (or best
estimates) to characterize the concentrations of sig-
nificant constituents, such as dissolved oxygen,
BOD, and NH3, to compute the pollutant mass flux
rate.
Data on the cross-sectional area, depth, and time of
travel (or velocity), as a function of flow, are required
for the flows at which observed water quality data are
collected and at the critical flow regimes used for
projections.
3.3.3 Water Quality Pollutant Interactions
Dissolved oxygen dynamics depend on the interac-
tions of several constituents and processes. The
constituents include dissolved oxygen, carbona-
ceous BOD, ammonia, nitrite, nitrate, temperature,
and in some cases phytoplankton, periphyton, and
aquatic plants.
These constituents and processes may be modeled
by a set of coupled mass balance equations such as
those in Table 2-4. The selection of constituents and
processes should be based on site- and problem-
specific factors. Documentation of the rationale for
selection of a particular combination of variables
should be provided in an early stage of the study and
should include an examination of observed water
quality data, considering each variable supplemented
3-8
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by calculations and relating the selected analysis
framework to the decisions to be made at the conclu-
sion of the project.
Ranges of the specific first-order rates for the various
reactions are discussed in Appendix A, as are the
procedures for defining site-specific reaction rates for
various levels of treatment. The necessity for depar-
tures from this norm should be documented at an
early point in the project and should particularly ad-
dress the additional information required in the deci-
sion-making process.
There are circumstances, particularly in systems with
low dissolved oxygen, in which nonlinear kinetic for-
mulations can be considered. The nonlinear formu-
lation usually employed is Michaelis-type kinetics, in
which the overall rate of reaction decreases as a
chemical species is depleted. Dissolved oxygen is
one of the chemical species that controls these types
of kinetic formulations. In particular, the rate of nitri-
fication has been shown to be controlled by dissolved
oxygen levels at and below 2 mg/L (Hydroscience,
1971; Carlucci and MacNally, 1969).
One method of approximating the nonlinear nitrifica-
tion reactions has been to use lower values for first-
order reaction rates in areas of low dissolved oxygen
concentrations. Low dissolved oxygen concentra-
tions can also reduce the rate of BOD oxidation and
sediment oxygen utilization and increase the release
of contaminants from the benthos. These latter reac-
tions are influenced only at very low dissolved oxygen
levels such as 0.1 mg/L or lower. In bodies of water
with large detention times, feedback reaction se-
quences have occasionally been employed
(Thomann, 1972). For example, the death and de-
composition of algal cells returns organic nitrogen to
the system. Feedback reactions can utilize first-order
kinetics in dissolved oxygen analysis and have been
used to model larger estuaries (see Thomann and
Mueller, 1987; O'Connor et al., 1973). The usual
reaction sequence employed for dissolved oxygen
investigation is shown in Figures 2-2 and 2-5. This
feedback reaction sequence may be appropriate for
larger river systems.
Many models use a simplified framework that ignores
or combines some of the processes in Figure 2-5. For
example, in systems where photosynthesis and res-
piration are small components of the overall oxygen
balance, the corresponding terms and equations can
be left out of the analysis (e.g., Wu and Ahler, 1979).
Simple models and hand calculation techniques often
represent the nitrogen cycle using a single nitrification
equation (e.g., Wu and Ahler, 1979) or combine the
nitrogenous and carbonaceous BOD into a single
constituent representing total BOD.
Even when the nitrogen cycle is not combined into a
single BOD equation, models differ in the number of
stages included in the cycle. The complete sequence
should include hydrolysis of organic nitrogen to am-
monia and oxidation of ammonia to nitrite and nitrite
to nitrate. However, many models do not include
organic nitrogen as a separate constituent (e.g., Wu
and Ahler, 1979; Johanson et al., 1984). It will be
important in many situations to distinguish between
organic nitrogen and ammonia concentrations, rather
than to define the nitrogenous oxygen demand (NOD
or NBOD) load on the basis of total Kjeldahl nitrogen
(TKN) concentrations, which are composed of both
these forms. Time and space lags in the resultant
dissolved oxygen profile, due to this sequential reac-
tion, may be significant. If the two species of nitrogen
are combined in the calibration and validation effort,
the apparent nitrification rate (Kn) will be lower than
the actual first-order nitrification rate of ammonia.
The ratio of TKN to NHs-N affects the value of the
overall oxidation rate. Where this ratio changes after
treatment, the modeler is faced with additional uncer-
tainty. Several models (e.g., Brown and Barnwell,
1987; Ambrose et al., 1988) include both organic
nitrogen and organic phosphorus capability. Many
models also leave out nitrite so that ammonia is
oxidized directly to nitrate in the model equations
(e.g., Ambrose et al., 1988). In many situations, the
NO2 concentration level observed and calculated is
very low or tends to be uniform, reducing the uncer-
tainty of this simplification. It should also be noted
that where algal problems are severe, NHs may be
taken up directly by algae.
Several levels of analysis can be used for considering
the influence of phytoplankton and other aquatic
plants. These are summarized in Table 3-1. Level
A, which uses measured values of photosynthesis
and respiration (P-R) and diel dissolved oxygen data
may be satisfactory in many cases. When significant
changes in nutrients or light extinction coefficient are
anticipated, the Level B analysis should be consid-
ered.
Level C represents a full-scale eutrophication ap-
proach, which increases the project costs for data and
modeling by several orders and should be used when
the problem is dominated by photosynthetic oxygen
3-9
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TABLE 3-1. METHODS OF ANALYSIS FOR
PHYTOPLANKTON AND AQUATIC PLANTS
A. Measure P-R and/or diurnal swings in DO: employ
measured value in steady-state or quasi-steady-state
models.
B. Measure chlorophyll a, light, light extinction, nutrients:
employ the results in steady-state or quasi-steady-state
models.
Calculate P-R.
Compare to P-R data and diurnal swings.
C. Model chlorophyll a, nutrients, dissolved oxygen, etc.
With calibration and validation, a time-variable,
nonlinear modeling framework is required.
production and utilization and where environmental
or control costs are significant.
Eutrophication analyses require models that simulate
nutrient and algal dynamics. Phosphorus and nitro-
gen are generally the only nutrients considered, al-
though silica can be considered if diatoms are a
dominant component of the phytophankton commu-
nity. The major processes include algal uptake, algal
excretion, sediment release, and nitrification.
Periphyton and aquatic plants are rarely included in
water quality models because of the difficulty in pre-
dicting biomass of these parameters although these
photosynthetic organisms can be significant compo-
nents of the oxygen and nutrient balance, specifically
in shallow rivers (e.g., Jeppesen and Thyssen, 1984;
Horner and Welch, 1981). An analytical framework
described by Level A in Table 3-1 can be used to
estimate the diel fluctuations in dissolved oxygen due
to aquatic plants. More quantitative modeling ap-
proaches would require equations analogous to
those used for algae except that the settling term is
replaced by a sloughing or nonpredatory mortality
term (e.g., Welch et al. 1989). The alternative ap-
proach is to use field data to account for the net
photosynthetic contributions of water column algae,
periphyton, and rooted aquatic plants as a combined
(P-R) term in the oxygen balance model.
In addition to dissolved oxygen analyses, ammonia
toxicity may be important. Ammonia toxicity is due to
the un-ionized form of ammonia. The un-ionized
fraction of total ammonia increases with pH and tem-
perature. Figure 3-2 shows this relationship. Most
currently available water quality models do not simu-
late un-ionized ammonia or pH. Therefore, TMDLs
that involve ammonia toxicity must usually be based
on total ammonia simulations in combination with field
measurements of pH and temperature (e.g., Szumski
5 10 IS 20 25 TO
•3.015
O.O1
Q.OO1
FIGURE 3-2. EFFECT OF pH AND TEMPERA-
TURE ON UN-IONIZED AMMONIA
(Novotny and Krenkel, 1975)
et al., 1982; Yake and James, 1983). Un-ionized
ammonia concentration can be calculated from
mod el-projected total ammonia and a relationship
such as that shown in Figure 3-2. There are models
available for ammonia toxicity (e.g., STREAM DO
from EPA Region VIM).
3.4 MODEL REVIEW
In this section the term model, following commonly
used terminology, is used to describe computer pro-
grams. However, computer programs are not models
until the user structures them with site-specific
boundaries, topography, hydrology, pollution buildup
and washoff, stream configuration, and pollutant in-
teractions representative of the contributing water-
shed, sources, and the receiving waterbody being
analyzed.
As stated earlier, TMDL development may require the
development of a watershed or water quality model
or both, depending on the results of the charac-
terization study. The TMDL process creates a frame-
work for considering the management of both point
and nonpoint pollution sources that contribute to wa-
terbody impairment. Although in most cases dis-
3-10
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solved oxygen problems are observed during low-
flow conditions in streams and rivers where point
sources are the major pollutant load contributor, spe-
cial consideration may be required in instances where
nonpoint sources have a significant impact on dis-
solved oxygen levels. In these cases, the review and
selection of appropriate watershed models are nec-
essary. The model selected should represent the
dominant processes inthewaterbody, should provide
the necessary management information on the mag-
nitude and variability of pollutant loading, and even-
tually should allow for an evaluation of the
implications of various watershed management alter-
natives. Watershed models are not considered in the
present review. However, interested readers are re-
ferred to USEPA (1992b) and Donigian and Huber
(1991), where detailed reviews of these models are
presented to assist water quality analysts in selecting
the appropriate model for a specific TMDL problem.
Selected receiving water quality models with potential
application to analysis of dissolved oxygen variations
in streams and rivers are reviewed in this section.
The criteria used for reviewing these models as part
of this document are as follows:
• They are in the public domain.
• They are available at a minimal cost from
various public agencies.
• They are supported on a limited basis by
Federal and/or State agencies. The form of
support is generally telephone contact to a
staff of engineers and programmers who
have experience with the model and provide
guidance (usually free of charge).
• They have been used extensively for various
purposes and are generally accepted profes-
sionally.
• They represent a wide range of complexity.
The more complicated models take into ac-
count additional processes and simulate a
given process in more detailed manner.
The selection procedure should not be limited to
those models discussed in this document. Other
computer programs (models) that are available to a
project or organization should be given consideration.
USEPA (1979c) and Hinson and Basta (1979) de-
scribe many other available water quality models.
The discussions and criteria presented in this docu-
ment can be employed as major elements in the
selection process. One additional consideration in
this process is the experience and familiarity of the
technical staff with a particular computer program.
It is suggested, however, that where project staffs do
not have access to or familiarity with other computer
programs, effort would be most effectively focused on
the computer programs selected for discussion in this
document. A brief description of the selected com-
puter programs follows. The models are listed in
order of increasing complexity. Source code, ex-
ecutable files and sample input files for EPA-sup-
ported models can be downloaded from E PA'sCEAM
electronic Bulletin Board Service (BBS); the phone
number for the BBS is (706) 546-3402. The BBS
system operator (SYSOP) can be contacted by tele-
phone at (706) 546-3524.
Simplified Method Program for Multiple Dis-
chargers (Multi-SMP) (USEPA, 1992d) is a steady-
state, one-dimensional water quality model that
implements EPA's Simplified Analytical Method for
Determining NPDES Effluent Limitations for POTWs
Discharging into Low Flow Streams (see Table 1-1).
The model predicts four water quality variables: dis-
solved oxygen, CBOD, NBOD, and un-ionized am-
monia. Water quality processes include reaeration,
deoxygenation, nitrification, and sediment oxygen
demand. The model considers up to 10 point source
discharges. Multi-SMP can be obtained from the
Center for Exposure Assessment Modeling (CEAM),
Athens, Georgia (requires one diskette).
Enhanced Stream Water Quality Model QUAL2E
and QUAL2E-UNCAS (Brown and Barnwell, 1987)
are one-dimensional (longitudinal) water quality mod-
els that assume steady flow (steady-state hydraulics)
but allow simulation of diel variations in temperature
or algal photosynthesis and respiration. QUAL2E
simulates a series of piecewise, nonuniform seg-
ments that make up a river reach. The effects of
withdrawals, branches, and tributaries can also be
included. Water quality variables simulated include
conservative substances; temperature; bacteria;
CBOD; DO; ammonia; nitrite, nitrate, and organic
nitrogen; phosphate and organic phosphorus; and
algae. QUAL2E is widely used for stream TMDLs
and discharge permit determinations in the United
States and other countries. It has a 15-year history
of application and is a proven, effective analysis tool
(e.g., Crabtree et al., 1986). QUAL2E Version 3
incorporates several uncertainty analysis techniques
useful in risk assessment. This model can be ob-
tained from CEAM (requires four diskettes).
3-11
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Water Quality Analysis Simulation Program
(WASPS) is a dynamic compartment modeling sys-
tem that can be used to analyze a variety of water
quality problems in one, two, or three dimensions
(Ambrose et al., 1993). WASPS simulates the trans-
port and transformation of conventional and toxic
pollutants in the water column and benthos of ponds,
streams, lakes, reservoirs, rivers, estuaries, and
coastal waters. The WASPS modeling system cov-
ers four major subjects: hydrodynamics, conservative
mass transport, eutrophication-dissolved oxygen ki-
netics (EUTRO5), and toxic chemical-sediment dy-
namics (TOXI5). The modeling system also includes
a stand-alone link-node hydrodynamic program,
DYNHYD5, that simulates the transport of water.
WASPS, along with the associated programs TOXI5,
EUTRO5, and DYNHYD5, can be obtained from
CEAM.
Hydrological Simulation Program-FORTRAN
(HSPF) is a comprehensive package that performs
continuous simulation of watershed hydrology and
water quality for both conventional and toxic organic
pollutants. HSPF incorporates the watershed-scale
Agriculture Runoff Model (ARM) and Non-Point
Source model into a basin-scale analysis framework
that includes fate and transport and transformation in
one-dimensional stream channels (Johanson et al.,
1984). It is the only comprehensive model of water-
shed hydrology and water quality that allows the
integrated simulation of land and soil contaminant
runoff processes with in-stream hydraulic and sedi-
ment-chemical interactions. HSPF, however, is an
extremely complex model that requires enormous
resources for development and application. HSPF
can be obtained from CEAM (requires six diskettes).
CE-QUAL-RIV1 (US Army Corps of Engineers, 1990)
is a fully dynamic one-dimensional riverine water
quality model. The model comprises two submodels:
a hydrodynamic model, RIV1H, which can stand
alone, and a water quality model, RIV1Q, which re-
quires output from Rl V1H or another routing model to
drive it. Ten water quality variables can be simulated:
temperature, DO, carbonaceous BOD, organic nitro-
gen, ammonia, nitrate, phosphate, dissolved iron,
dissolved manganese, and coliform bacteria. Addi-
tionally, algae/macrophyte photosynthesis, respira-
tion, and nutrient interactions are included.
CE-QUAL-RIV1 can be obtained from the US Army
Corps of Engineers, Waterways Experiment Station,
Vicksburg, Mississippi.
RIVMOD is a numerical, hydrodynamic, and sedi-
ment transport riverine model that describes the lon-
gitudinal distributions of flows and sediment
concentrations in a one-dimensional waterbody
through time. It can be used as an alternative to the
EPA-supported link-node model, DYNHYD5.
RIVMOD is based on a 4-point implicit numerical
integration scheme whereas DYNHYD5 is based on
an explicit numerical scheme. RIVMOD is available
from CEAM, although EPA does not currently provide
support or documentation for the model. RIVMOD
has been used by CEAM to link the transport output
data files as input to the previous version of the
general WASP model, WASPS.
Three of the models discussed (WASPS, HSPF, and
CE-QUAL-RIV1), when operated in the fully dynamic
modes, are quite complex and require well-trained
analysts.
The salient features of the first five models selected
for discussion are summarized in Tables 3-2 through
3-10. Since QUAL2E is probably the most widely
used computer model for predicting the effects of
conventional pollutants in streams, the tables use
QUAL2E as a reference point against which other
models can be compared. The tables presented are
as follows:
Table 3-2 Constituents Modeled
Table 3-3 Summary of Capabilities
Table 3-4 Reaeration Formulations
Table 3-5 Input Data Requirements
Table 3-6 Ease of Application—Output Form and Content
Table 3-7 Ease of Application—Sources, Support, and
Documentation
Table 3-8 Ease of Application—Equipment and
Programming Requirements
Table 3-9 Operating Costs
Table 3-10 Hierarchy of Models Based on Selected Features
Information presented under the first four table sub-
jects (Constituents, Capabilities, Reaeration Formu-
lations, and Input Data Requirements) is primarily
technical and is required to evaluate whether the
model simulates the important physical and bio-
chemical features of a problem. Information pre-
sented under the table subjects Ease of Application
and Operating Costs is primarily nontechnical or re-
lated to operational features of the models. This infor-
mation is needed to evaluate the cost associated with
and the ease of acquiring the model, getting the
model running on the user's system, calibrating and
validating the model, and finally applying the model.
3-12
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-------
TABLE 3-4. COMPARISON OF MODELS: REAERATION FORMULATIONS
Model
QUAL2E
CE-QUAL-RIV1
WASPS
HSPF
Multi-SMP
Number of Options
Options
A, B, F (after L), G, H, I, J, K, model
accounts for C
E (after M), F (after H), C (after N)
A, D, E (after M)
A, D, E, K
A, F (after H), J
Sources of Stream Reaeration Options
A Input directly
B As a power function
C Structural reaeration due to dams
D Covar's method (automatic selection among H, I, and L)
E Wind-driven reaeration
F Calculated as a function of velocity and depth
G Langbien and Durum (1967)
H O'Connor and Dobbins (1958)
I Owens etal., (1964)
J Thackston and Krenkel (1969)
K Tsivoglou-Wallace method (Tsivoglou and Wallace, 1972)
L Churchill etal., (1962)
M O'Connor (1983)
N Wilhelms and Smith (1981)
The information provided in these tables is primarily
qualitative and sufficient to determine whether a
model may be suitable for a particular application.
For some of the models, more quantitative informa-
tion is given in Evaluation of Water Quality Models: A
Management Guide for Planners (USEPA, 1976b).
For complete information the potential user must
consult the appropriate user's manuals and other
supporting documentation. The Center for Exposure
Assessment Modeling (CEAM, EPA Environmental
Research Laboratory, Athens, Georgia) is a source
of information and limited technical support. Brief
descriptions of the contents of Tables 3-2 through
3-10 follow.
Table 3-2. Constituents Modeled. As a basis for
comparison, QUAL2E simulates the following con-
stituents:
• Dissolved oxygen
• Carbonaceous biochemical oxygen demand
• Temperature
• Algae (as chlorophyll a)
• Organic nitrogen
• Ammonia
• Nitrite
• Nitrate
• Organic phosphorus
• Dissolved phosphorus
• Coliforms
• Arbitrary nonconservative constituents
• Three conservative constituents
Table 3-2 compares QUAL2E with other models com-
monly used in TMDL analyses with respect to the
constituents simulated. The models vary signifi-
cantly in terms of the number and type of constituents
for which calculations are performed. The number of
constituents analyzed usually reflects the number
and complexity of biochemical processes simulated
and is shown in Table 3-3. In the more complex
models (e.g., QUAL2E, WASPS), provision is made
for selecting only those constituents (and therefore
processes) of interest.
Table 3-3. Summary of Capabilities. The model
equations and process formulations in QUAL2E are
the same as those discussed in Section 2.3 for dis-
solved oxygen, nutrients, and phytoplankton. Figure
3-15
-------
2-5 shows the interactions of the various constituents
inQUAL2E.
Table 3-3 compares the general features of QUAL2E
(i.e., temporal and spatial resolution, hydraulics,
types of loads, and processes simulated) with other
computer models used in TMDL analyses. Multi-
SMP is limited to steady-state DO/BOD analyses,
whereas QUAL2E, WASPS, and CE-QUAL-RIV1 can
be used for eutrophication analyses as well as dis-
solved oxygen analyses. The latter three models
simulate the effects of photosynthesis, respiration,
and temperature on diel variations of dissolved oxy-
gen. WASPS, HSPF, and CE-QUAL-RIV1 are truly
dynamic since they simulate continuous temporal
variations in stream hydraulics and waste loadings.
QUAL2E assumes these features remain constant,
but allows the meteorology and water quality condi-
tions downstream of the upstream boundaries to
vary, making it a quasi-dynamic model.
Table 3-4. Reaeration Formulations. Most models
permit direct input of the reaeration coefficient or
selection from several commonly used correlations or
methods. Appendix A provides a discussion of this
parameter.
Table 3-5. Input Data Requirements. All models re-
quire data for input, calibration, and validation. It is
best if model selection is not restricted by availability
of data and the decision is made to acquire the
specific type of data required for the model. On the
other hand, if data availability is a constraint, selection
of a less sophisticated model than would be war-
ranted on technical grounds may be appropriate.
Table 3-5 compares the input data requirements for
the models discussed. Input data requirements in-
crease with the complexity of the stream hydraulics
and water quality mathematical formulations. For
example, Multi-SMP, QUAL2E, and WASPS (de-
scriptive transport mode) assume steady-state hy-
draulics formulas which then require specification of
regression coefficients (see Equations 2-1 through
2-3) to estimate velocity and depth required in the
reaeration formulas. The more complex models such
as WASPS (linked with DYNHYD5) or CE-QUAL-
RIV1 solve a form of the momentum equation, which
requires more detailed characterization of the stream
geometry and roughness. Similarly, extensive data
are required to simulate the nonlinear nutrient-algal-
DO linkage.
Table 3-6. Ease of Application—Output Form and
Content. All of the computer programs print results
of the simulation and the input data to standard ASCII
files. The more complex programs require scratch
disks or tapes for storing intermediate results to be
read subsequently in submodels or for storing infor-
mation to be plotted. Post-processing of model out-
put is a major task in the application of a model,
requiring software for statistical data summaries and
graphical display of observed and modeled data sets
(Stoddard, 1988; Stoddard et al., 1990).
Table 3-7. Ease of Application—Sources. Support.
and Documentation. Two of the most important fac-
tors in facilitating the use of a new model are the
adequacy of the documentation and the adequacy of
the support available. The documentation should
state the theory and assumptions in adequate detail,
describe the program organization, and clearly pre-
sent the input data requirements and format. A well-
organized input data scheme is essential. Limited
technical support is typically provided by agencies
responsible for distribution of models. For example,
EPA's Center for Exposure Assessment Modeling
(CEAM) in Athens, Georgia and the U.S. Army Corps
of Engineers, Waterways Experiment Station in
Vicksburg, Mississippi will provide very limited tech-
nical consultation to users experiencing problems
with operations of models. It may be possible that
special support arrangements (including short
courses or informational or personnel exchanges) are
available under existing intra- or interagency agree-
ments or could be made available to the potential
user. The support agency may also be able to pro-
vide the potential user with a list of local users who
could be contacted for information regarding their
past or current experience with the computer program
associated with the model.
Table 3-8. Ease of Application—Equipment and Pro-
gramming Requirements. The models are written in
FORTRAN 77, with the exception of Multi-SMP,
which is written in Turbo Pascal. Most models are
machine-independent though pre- and post-proces-
sors are important to ease of application. Storage
requirements increase with program complexity.
Table 3-9, Operating Costs. It is difficult to estimate
overall costs involved in a model application because
applications differ in scope and complexity and the
ability to solve or avoid certain problems is highly
dependent on the experience and technical back-
ground of the analysts involved. However, machine
requirements and costs associated with typical runs
are usually estimated in the program documentation.
As a rule, the simpler the model, the less expensive
3-16
-------
it is to apply. It is essential that the support agency
and other experienced professionals be contacted for
information or assistance.
Once the cost of application has been estimated, it
should be compared with the benefits of using the
program as part of the water quality modeling effort
and the overall importance of the problem. The
TMDL study costs should be consistent with the
economic, social, or environmental values associ-
ated with the problem and its solution.
Table 3-10. Hierarchy of Models Based on Selected
Features. To assist in initial model selection, TableS-
10 shows a hierarchy of models based on important
distinguishing features. As shown in this table, the
programs increase in complexity. One of these pro-
grams should be adequate for most TMDL studies and,
in general, the simpler program should be chosen if it
contains all the features needed to simulate the impor-
tant processes in the prototype. On the other hand, use
of a more complex model may be justified. Often, a
complex model can be used with no more additional
effort than that required for a simple model by "turning
off processes (i.e., set coefficients to zero values).
This procedure allows easy upgrading of the model as
more information becomes available. QUAL2E, for
example, can be used at the same analysis level as
Multi-SMP and requires no additional information.
3-17
-------
TABLE 3-5. COMPARISON OF MODELS: INPUT DATA REQUIREMENTS
Mtxlri
Hydrwlle
DUMf
m*L2t Blrem lenglh. lopltonalt Claud Headwaler and
oonnedion setiania, exw6«. isaramatrtc bibulaiy «ftows,
ptessurt. aef and withdrawals
iiii-iiniyiil
CE.
DUAL-
HIV I
COfliieclioii schuing
00
o>
Channel fanpri,
i and dlraciKsn,
! Surface
area and daptti
i, evapOTBlfon
, r*1 solar
reach-vBiirtbte
chratotogy inpul tof
sleady- state.
ir. biirotrmlri;
piessure, dry awl
h-ja-Sy,-dl'jr ai>J
liilfultiiY iiillows.
wtrsdrawate
lime senas ol soter Tima sanas o)
radifiiKo wind EHSMJ hciairv-atsr and
and dlracbon, mbulary inll&ws
photo pa Jtod,
tempera tura
CoerAcients lor
re§res£tofi, or bottom 6OQ,
FlfiM 1 Jt'J'i
.DO,
rvalive
, initial
ft's ft).
l:oundai>'
Icftian
I M.inn i IIJ'K ;i'|, liirHi
series ol tew.
velocity-ttow
regre&Kjn
cross ^
, bo-Horn
How, i
rmidjinass
(Mannng's n|
Irttow CMoanlraiion,
llXflparaniia, CO.
ROD, inJitol and
Flow rites and
tor al conduits to*
ii I riiuiiilu.:! :
I Fiila
oo«ific»rts;
hart- salurattin
oaertictanls, and
corrBcfiw te-dors
Baaeraliop,
o»dAlk>n, leac&on,
•jiiHjsuiiinrjnm*
liall-saluralion
, and
InMow tonosnlralion, lime series erf
lemperatiite, OO, loadǤs tor al water owdalon, readion.
BOD, initial and quality stele ranablas antf settling rale
boyndary condltlwia cxserfioanls, ruinem
tor ai modeled stale hall-saliiralion
oaerhoents, and
ElH-llfHM.lhir^
ai>d etevaton ol
Lj.d!;m, day at yL'di,
9, tiirgui
minimum DO
i::yii::
-------
ModiH
TABLE 3-5. COMPARISON OF MODELS; INPUT DATA REQUIREMENTS {Continued)
Maln-orolayii;
Hydjaulk
Watitr Quality
ElflU«nt
Rancllara Rates
Other
Note: Waleo;cik:.:iii: inpu! Is optional.
IISPF R?i&ig laftlss. length Sotar rwJalioni, dcwd Iniamglly computed Volurnaarid Inttow and runoi'
of cwnpuiatjonal cover, air diwlwsjaAteiMh (or cfficerrtralon,
ataman), diainage iBrnperaliurs, de-w ea* neaoti, avarige lemperatura, twntrvc
area pC'Inl lempanalure, chanrwl slope, domand, and toxic
towthraugri *na lor organic pdulart
n, aad mean How, v«toefly
JP ah
Flow ralss suxl
fly* rales and
concentrabon
MulU-
SMP
Stream Jengttis,
•.iniluirii i(i,ji:lii!:;
(Miimng's n\
I't^Kfw^til^ unij Intkyw cofic^inlriiiiori, Fkiw ^lii^ ^n
-------
TABLE 3-6. COMPARISON OF MODELS; EASE OF APPLICATION—OUTPUT FORM AND CONTENT
Model
Output Fonn
Output Content
QUAL2E
Compyter pnntout, plots, screen graphics
Gi-QUAL-fNV1
WASPS
Computer printout lahte and output plel
lila
Computer printoul/ASCII iile. screen
graphics, and screen tables.
aj Listing of input data
b) Concentrations and temperature ty reach and computational elements at spedfted
time steps
c) Maximum, minimum, and average concentration, temperature, flow, velocity, and
(fepft al reaches
d) Final summary, which inclucfes components of DO ctelieit and plot ol DO isfti BOD
e) Local cllmatotogical data
fj Detailed summary oi hyckatulic calculations
9) Pfols of observed and pireciicted DO concentrations (option)
a) Listing of input dale
DS Coficenlraiion of a oonsttluenl at any bnoeflocalion
a Usiing ol input daia
b) Concenlraiion of constituent arid otriw water quality variablwsj. al any lhfWi1c«aion
c) pQst-pfoces£ar is. available to create tables for import io graphics routines
d) values of brar/ispon and varirtles al any time/locaiion
e) Mass balance table lar selected cortslituanls
rv:
O
HSPF
Mul5i-SMP
Computer printout
Con^puler printout of graphs and tables
displayed (o sown or printer
a) Time iiisuxy of rurtoffi flow rat* sediment load, nuirieni CGooerifra&ons and toads
D) Water quality and quantity at any pdnt in a wateished
c) Display of on« at more Uirne series on a plottei and tabular display o1 inpul/ouipui
iraqpency LaDlcE
a) ualirig D( input data
b) DO, CBOD, and MBOO cowentrallws a? munipl«i points along slrearn reach
-------
00
tVi
TABLE 3-7. COMPARISON OF MODELS: EASE OF APPLICATION—SOURCES, SUPPORT,
WotW SourewM o< Mo*t
QUAU2€ Caniar for Exposure
Assessment Modeling
U.S. ErwifrqnmentBl
Athens, QA 30605
(J7CN3S S46-3649
CE-QUAL-RIV1 US Army Engineer
Waterways Experiment
Station
Vsckstouna, MS 39180
{601)634-3670
WASPS Caniar for Exposure
Assessment Modeling
U.S.Enwwi menial
Protection Agsncy
Attws, CiA 30505
1706) 546-3549
HSPF Centef for Exposure
Assessment rvtedaing
U.S.Environmantel
Pr-oiedion Agency
Alhans, GA 30605
{706) 546-3549
Multi-SMP Canlar (or Ettpo&ura
Ass&ssment Modfiing
U.S.ErtvirWMWiiaJ
Proteclioo Agency
Athens, GA 30605
(706) 54&-3S49
OocurmniUitJijn S
-------
Model
TABLE 3-8. COMPARISON OF MODELS: EASE OF APPLICATION-EQUIPMENT AND
PROGRAMMING REQUIREMENTS
Requirements
QUAL2E QUAL2E is written in FORTRAN 77 and is compatible with both mainframe and personal computer systems
equipped with 640 KB RAM. Can be executed from floppy disk. User interface and capabilities to interface
with graphics display, laser printers or dot matrix printers, or pen plotters.
CE-QUAL-RIV1 The program is written in FORTRAN 77 and is compatible with mainframe and personal computers.
WASPS The program is written in FORTRAN 77 and is compatible with mainframe and personal computer systems
equipped with 640 KB RAM. A 10-MB hard disk and a printer are generally required. A math coprocessor is
highly recommended.
HSPF The program is written in FORTRAN 77 and is compatible with mainframe and personal computer systems
equipped with 640 KB RAM. A 10-MB hard disk and a printer are generally required. A math coprocessor is
needed.
Multi-SMP Executable Turbo Pascal file. Requires IBM-compatible PC and EGA card for graphic capability.
TABLE 3-9. COMPARISON OF MODELS: OPERATING COSTS
Dimensionality
Water Quality Problem
Approximate Level of Effort
1-D steady state
1-D, 2-D, steady state
DO, BOD, nutrients
DO, BOD, nutrients,
phytoplankton, toxics
1-6 person-months
0.5-1 person-years
1-D, 2-D time variable
DO, BOD, nutrients,
phytoplankton, toxics
0.5-2 person-years
3-D time variable
DO, BOD, nutrients,
phytoplankton, toxics
1-5 person-years
3-22
-------
TABLE 3-10. HIERARCHY OF MODELS BASED ON SELECTED FEATURES
Models Multiple
(Ordered from Point
Least to Sources of
Most Complex) BOD
Multi-SMP X
QUAL2E X
CE-QUAL-RIV1 X
WASPS X
HSPF X
X Available feature
Distributed Benthic
Sources of Oxygen Net Algal Longitudinal
CBOD Demand Production Dispersion
V •
X « D X
x • •
X * A
XXX
Time-
variable
Waste Loads
BOD and Water
Settling Quality
.
X
X X
X X
Time-
variable
Flow
X
X
X
» Specified (i.e., input to the model as forcing function)
A Simulated in a nutrient-algal cycle
V Can be simulated approximately by input of load at beginning of each multiple segment
Can be simulated by making Kr
Meteorology only
3-23
-------
-------
4. RIVER AND STREAM MODELING PROCEDURES
4.1 PURPOSE
The purpose of Chapter 4 is to review briefly the
various steps associated with the development of a
site-specific water quality model. These steps are
generic and can be modified according to available
data and the type and complexity of the water impair-
ment being analyzed. Furthermore, the level of detail
required within each step may depend on the phase
of the TMDL. Simple analyses are usually sufficient
during the first phase of TMDL development, whereas
more detailed analysis may be required for later
phases. Examples illustrating the use of these steps
using the EPA-supported water quality models
QUAL2E and WASPS are provided in Appendix B.
The five steps suggested for model development,
illustrated in Figure 4-1, are as follows:
• Initial assessment
• Site-specific stream survey
• Model calibration
• Model validation
• Model application
4.1.1 Modeling Goals
Prior to detailing each step, it is necessary to present
the overall goals of model development. A phased
TMDL may require only simple modeling tools in the
early stages of development. However, an increas-
ing level of model complexity may be needed in later
phases when additional data become available. At
either stage, the overall modeling goals should re-
main consistent. For determining a TMDL for
streams and rivers, the following goals are applicable:
• Development of a technically credible quan-
titative cause-effect representation of in-
stream processes.
• Ensuring that modeling results are defensi-
ble for use in determining the loading capac-
ity and load and TMDLs.
• Provision of analytical or modeling tools suf-
ficient for evaluating the implications of vari-
ous pollution reduction alternatives.
• Definition of the level of uncertainty for deter-
mination of the margin of safety.
When developing TMDLs, it is reasonable to separate
the water quality impacts caused by a given pollution
source. This is best achieved through the use of one
model or a combination of models (watershed and/or
receiving water models). For example, in some sys-
tems where nonpoint source loadings are significant,
control of point sources may provide only a marginal
improvement in water quality.
Consider a typical case in which the dissolved oxygen
profile does not meet a water quality standard of 5 mg/L
using summer temperatures and a 7Q10 low flow.
Separation of the dissolved oxygen profile into com-
ponent responses may show that the discharger is
responsible for a minor portion of the predicted dis-
solved oxygen depression. The major depression in
dissolved oxygen could be created by upstream con-
ditions and sediment oxygen demand, for example.
This perspective is important because it demon-
strates that the discharger may have a minor impact
on the dissolved oxygen resources, and increased
treatment at the point source may have only a minor
effect on the dissolved oxygen balance.
Consider a second case in which critical conditions
for both dissolved oxygen and un-ionized ammonia
occur during the summer when the flow is low and the
river temperature is high, and where nitrification is
occurring in the river. In this case, it is necessary to
be able to separately evaluate the effects of carbona-
ceous and nitrogenous BOD on dissolved oxygen
and the effects of nitrification on ammonia in order to
optimize decisions on controlling nutrient loads and
on selecting wastewater treatment schemes (i.e.,
nitrification facilities vs. advanced CBOD removal).
Appendix B presents an example TMDL modeling
analysis using QUAL2E that illustrates this type of
optimization.
In this context, typical questions to be addressed in a
stream BOD/DO and nutrient/eutrophication TMDL
may include the following:
• How can the effects of two or multiple pollut-
ant loads be differentiated?
4-1
-------
INITIAL ASSESSMENT
Study Area Evaluation
Compilation and Review of Existing Data
Preliminary Analysis
Selection of Modeling Framework
SITE-SPECIFIC STREAM SURVEY
Hydraulic Geometry Survey
Time-of-Travel Study
Stream Water Quality Sampling
Wastewater Monitoring
Biological Assessment
MODEL CALIBRATION
Model Coefficient Assignment
Component Analysis
Quantifying Comparison Between Model Results and Data
I
MODEL VALIDATION
Model Coefficient Adjustment
Model Sensitivity Analysis
Model Accuracy Check
I
MODEL APPLICATION AND TMDL
Development of Evaluation Scenarios
Waste Load Allocations
Load Allocations
Margin of Safety
Uncertainty Analysis
FIGURE 4-1. STEPS IN THE USE OF A WATER QUALITY MODEL
FOP A QiTF.QPFriFir TMni APPI
4-2
-------
• How can the individual impacts of sediment
oxygen demand, nonpoint sources, and point
sources be quantified?
• Is nitrification occurring in the stream, and
would it occur under future conditions?
• Which nutrient should be controlled to reduce
the algal biomass?
• What is the magnitude of dissolved oxygen
fluctuations that cannot be accounted for by
the present analysis?
• How do these fluctuations vary with time and
space?
• Is dissolved oxygen or ammonia toxicity (un-
ionized ammonia) the limiting water quality
parameter?
In summary, the goal of the TMDL modeling analysis
is to obtain a quantitative assessment of system
behavior that will support decision making. To ac-
complish this task, a number of general requirements
are listed below.
4.1.2 General Requirements of a Stream
Water Quality Modeling Analysis
The following are examples of the basic requirements
of a TMDL study:
• A quantitative analysis of all pollutant loads
and inputs.
• Sufficient data to support the derivation of
model coefficients.
• A consistent set of model coefficients deter-
mined from independent derivation, model
calibration, and validation using available
data.
• Assignment of reasonable values for model
coefficients in model projections under future
conditions.
The suggested requirements should be flexible to
meet site-specific needs.
4.2 INITIAL ASSESSMENT
An essential element of a TMDL study is a quantita-
tive assessment of the relative impacts of different
types and sources of pollutant loads on specific water
quality parameters. This assessment will help to en-
sure that all participants in the TMDL process under-
stand the relative importance of various pollutant
sources at an early stage and that appropriate priori-
ties are defined. Another advantage of an initial
assessment is to provide a check that all significant
waste loads have been identified. It will also help to
ensure that subsequent field monitoring programs are
cost-effective and responsive to planning and deci-
sion-making requirements. The following analysis
particularly addresses water quality in streams and
rivers.
4.2.1 Study Area Evaluation
The study area evaluation defines the study area and
problem by determining applicable water quality
standards as well as existing and potential water
quality problems. A more detailed description of the
evaluation is presented in the following subsections.
4.2.1.1 Water Quality Standards
First, a desirable water use, or uses, for the stream
system (e.g., recreation, water supply, agriculture)
must be designated. State regulatory agencies
should be consulted to define the designated uses,
as well as specific water quality criteria. In addition,
EPA has published a series of water quality criteria
since the first "Green Book" issued by the Federal
Water Pollution Control Administration in 1968. The
current edition is EPA's "Gold Book," Quality Criteria
for 79S6(USEPA, 1987). In all cases, however, State
criteria should be consulted first.
In the United States there are no standards regulating
CBOD concentrations in streams. Instead, there are
extensive standards for dissolved oxygen levels that
are affected by CBOD deoxygenation. As a result,
CBOD and oxidizable nitrogen (NBOD) are regulated
on the basis of dissolved oxygen standards. Dis-
solved oxygen standards have been set by State
regulatory agencies to protect designated use(s) for
individual streams or segments of streams. State
dissolved oxygen standards may be expressed as
any one or all of the following:
• Average daily concentration.
• Minimum or lower percentile concentration
(usually used for streams that have signifi-
cant diel variations due to algae).
• Percent saturation.
There are no specific algal biomass standards for
eutrophication analyses since it is difficult to deter-
mine whether a particular chlorophyll a concentration
will be a problem. Figure 4-2 compares chlorophyll a
concentration ranges with perceived water quality
4-3
-------
conditions and target objectives for several different
waterbodies. These cases may be used as a guide
to regulate nutrient inputs for eutrophication control.
4.2.1.2 Identifying Existing and Potential Water
Quality Problems
Table 4-1 summarizes the constituents, waste
sources, and consequences associated with dis-
solved oxygen, nutrient enrichment, and eutrophica-
tion problems. Nutrient enrichment and subsequent
algal growth are a concern in rivers and streams
because of their effect on dissolved oxygen concen-
trations. Growing plants provide a net addition of
dissolved oxygen to the stream on an average daily
basis, yet respiration can cause low dissolved oxygen
levels at night that can affect the survival of less
tolerant fish species. Also, if environmental condi-
tions cause a die-off of either microscopic or macro-
scopic plants, the decay of biomass can cause severe
oxygen depressions. Therefore, excessive plant
growth can affect a stream's ability to meet both
average daily and instantaneous dissolved oxygen
stream standards.
Biological assessments can also be designed to es-
tablish baseline conditions and assess impacts from
point and nonpoint pollution sources. They can play
a fundamental role in establishing biocriteria, which
are numerical or narrative expressions that describe
the reference biological condition of aquatic commu-
nities inhabiting waters of a given designated aquatic
life use (Barbour et al., 1992). Biocriteria are often
presented as measures such as species composi-
tion, abundance, and diversity (Gallant et al., 1989).
Biological communities reflect overall biological integ-
rity and integrate the effects of different pollutant
stressors. In cases where specific impacts are ab-
sent or unknown (e.g., nonpoint source impacts that
degrade habitat), bioassessments may be the only
practical assessment tool.
The individual water quality problems can be associ-
ated with specific time and space scales, which can
be used to identify the most appropriate method of
analysis. Several different time and space scales are
required for effective water quality evaluation (see
Figure 4-3). In general, the dissolved oxygen prob-
lem associated with organic waste discharges has a
significant time scale of days to weeks, with a signifi-
cant space scale of impacts up to 20 miles. Nutrients
are usually associated with a longer time scale of
seasons to years and a space scale of up to 100
miles. It is essential to recognize these time and
space scales in order to address questions and prob-
lems in the most economical manner and to provide
meaningful analysis. The selection of a steady-state
or time-variable model should be determined on the
basis of the water quality variable, the available data
base, and the major mechanisms affecting that vari-
able.
In evaluating dissolved oxygen water quality effects,
including situations where algal influences are impor-
tant, a steady-state analysis can be used. Phyto-
plankton chlorophyll a concentrations will commonly
be sufficiently constant over the period covered by a
steady-state analysis tojustify this approach. In such
cases, a steady-state analysis of dissolved oxygen
response to point source BOD discharges is super-
imposed over the algae-induced diel fluctuations.
These fluctuations can be calculated by simplified
analytical approximations. QUAL2E uses steady-
state hydrology and allows simulation of diel vari-
ations in temperature or algal photosynthesis and
respiration.
Time-variable approaches to eutrophication prob-
lems are sometimes employed when a time-variable
data base exists (or can be developed) to calibrate
the model dynamically over a range of conditions.
Models such as HSPF, CE-QUAL-RIV1, and WASPS
are run in the time-variable mode. When using these
models, the computation can be continued, using
constant input values, until a steady-state condition is
reached.
A general guideline for determining the appropriate-
ness of a steady-state vs. a time-variable approach is
summarized below:
• If phytoplankton chlorophyll a concentrations
are relatively constant over a time period of
1 or 2 weeks, then a steady-state approach
is justified. This period should coincide with
the critical season in terms of stream flow and
temperature for dissolved oxygen analyses.
Spatial variations in algal biomass can be
handled by averages over appropriate river
reaches.
• Where the principal water quality issue is the
level of biomass rather than oxygen deple-
tion, longer time periods (covering one or
more seasons) are usually selected. On
such a time scale, expected changes are
large and time-variable eutrophication mod-
els are the most appropriate modeling ap-
proach.
4-4
-------
140
120
Asprerf-
, nmt*
i
f
4
EPA f
40
X A
Wsi»m
i_ak» Erie
Sin Joaqun
Datta, Calif.
PotomsG
««u«ry
FIGURE 4-2. RANGE OF CHLOROPHYLL a AVERAGE CONCENTRATIONS AND
TARGET "OBJECTIVES" TO REGULATE NUTRIENT INPUTS FOR
EUTROPHICATION CONTROL FOR VARIOUS WATER BODIES
(After Thomann and Mueller, 1987)
TABLE 4-1. IDENTIFICATION OF POTENTIAL WATER QUALITY PROBLEMS: DISSOLVED
OXYGEN DEPLETION, NUTRIENT ENRICHMENT, AND EUTROPHICATION
Sources:
Consequences:
Organic material, ammonia in:
wastewater
runoff and CSOs
benthic oxidation
algal production
marinas, boating
heated effluent
Fish kills
Reduced fish productivity
Less desirable aquatic community
Nitrogen, phosphorus, carbon in:
wastewater
runoff and CSOs
atmospheric deposition
benthic recycling
marinas, boating
Nuisance levels of phytoplankton
Less desirable aquatic community
Large dissolved oxygen fluctuations
Dissolved oxygen depletion
4-5
-------
ID
_
10s
Hour
OxvOIH
SCUOi
NUTRIITfTa
Month Y**r
S*«ton
Time Sea ISA
Effsctlva Distance (mites)
tr1 icP 1Q1 to*
FLOATAtLIt
•HUTP.IINTI
(5 ft) (SO ft) (500 ft)
•OUBI
.-^—Rtgig?
!--•
Spies Scal*t
FIGURE 4-3. TIME AND SPACE SCALES FOR ASSESSMENT OF WATER QUALITY PROBLEMS
(After USE PA, 1983b)
4-6
-------
4.2.2 Compilation and Review of Existing Data ily queried using interactive tools and the Reach File.
A thorough characterization of the river or stream is
necessary for any water quality study. Table 4-2 lists
the types of data to be gathered and their possible
sources.
Stream flow and geometry are typically available at
specific gaging stations for large rivers through the
USGS and/or the US Army Corps of Engineers.
For analysts with access to EPA's mainframe com-
puter, USGS streamflow data available can be eas-
The EPA STORE! system is a good source for
water quality data. STORE! data are usually ap-
propriate to describe long-term trends for water
quality problem identification. However, STORET
does not always have synoptic surveys of the
stream system, which are most useful for water
quality modeling.
EPA's Permit Compliance System (PCS) is the re-
pository of NPDES permitted loads and all reported
TABLE 4-2. DATA TYPES AND POSSIBLE DATA SOURCES FOR STREAM
TOTAL MAXIMUM DAILY LOADS
Data Type
Source
Federal Agencies
State Agencies
Local Groups
Stream Geometry USGS Special studies
US Army Corps of Engineers'
Division/District Offices
EPA
Planning agencies
Stream Flow
USGS gage records
and low flows (available
through EPA)
Publications on low flows
Basin plans
Universities
Planning agencies
Water Quality Data EPA STORET
USGS
US Fish & Wildlife Service
Regulatory agencies'
TMDL studies
State Dept. of Health
Studies by regional
planning groups
Discharger's studies
Universities
Wastewater Loads
EPA Permit Compliance
System (PCS)
Discharge Monitoring
Reports (DMR)
Municipal and industrial
discharger's plant records
Nonpoint Loads
EPA STORET, USGS and
US Fish & Wildlife Service;
urban runoff data available
from EPA National Urban
Runoff Program (NURP);
precipitation and meteoro-
logical data available from
Urban runoff data
from special studies;
precipitation and
meteorological data
from State planning
agencies and local
airports; land use and
soils characteristics
NOAA National Climatic Data
Center; land use data available data from State planning,
from USGS; soils charac- agricultural and geological
teristics data available from agencies.
USDA Soil Conservation Service.
Urban runoff data from
regional, city and county
studies; precipitation and
meteorological data from
local and county planning
agencies and local airports;
land use and soils
characteristics data from
regional and county
planning, agricultural and
geological agencies.
4-7
-------
information from NPDES discharge monitoring re-
ports (DMRs).
4.2.3 Preliminary Analysis
Preliminary screening analysis of available informa-
tion described in the previous section may be per-
formed by employing analytical equations, simplified
models, or a preliminary version of the water quality
model. Several simplified analyses are presented in
the following paragraphs.
4.2.3.1 Screening Procedure for Determining Algal-
Nutrient Relationship
This simple procedure may be used to provide an
appropriate indication of a nonproblem. That is, if the
maximum possible chlorophyll a level that could be
achieved is extremely low, it will usually be safe to
conclude that nutrients do not pose a problem in
relation to water column algae. The guidance in
Section 2.3.4.5 and Section A.9 of Appendix A, which
relates chlorophyll a levels to dissolved oxygen ef-
fects, can be used to determine how low the concen-
tration of chlorophyll a must be in a particular situation
to be considered insignificant.
On the other hand, it is not appropriate to use this
screening procedure to conclude that there is a prob-
lem. In most natural systems, especially flowing
streams, the actual chlorophyll a levels that occur will
be substantially less than the maximum potential
under a combination of ideal conditions. Collection
of chlorophyll a data could be used to verify the
estimated chlorophyll a levels and to determine
whether a problem exists.
in the presence of light to synthesize algal proto-
plasm. Nitrogen and phosphorus are the only essen-
tial elements that can be controlled since carbon is
often (but not always) readily available in solution and
the various trace elements are usually plentiful in
natural systems. When considering cell stoichiometry
of aquatic plants or phytoplankton, for example, cells
contain approximately 0.5 - 2.0 jig phosphorus per jig
chlorophyll a and 7 -10 |ig nitrogen per \ig chlorophyll
a. Although the weight ratio of each nutrient to chlo-
rophyll a varies with the age of an algal population,
species composition, and nutritional state, the follow-
ing ratios are commonly used to represent typical
conditions:
7 jig N/ jig chlorophyll a
1 jig PI jig chlorophyll a
The chlorophyll a-to-carbon and carbon-to-nutrient
stoichiometry of algal cells is not precise, and ratios
that are somewhat different from those used in this
manual may be preferred by other analysts (see
Bowie et al., 1985). Such preferences are usually
based on local data, which should be used whenever
possible.
For example, consider the following nutrient concen-
trations:
N =0.35 mg/L = 350 \ig NIL
P = 0.02 mg/L = 20 jig P/L
Using the above stoichiometric ratios, the maximum
potential chlorophyll a concentration would be either:
350 \
N/L) - - AJ = 50 \ig Chi a/L
/ \ig N/\ig Chi a
(Nitrogen)
or
(20 tig P/L)
Stoichiometric ratios can be used in preliminary
screening analyses to make two useful initial assess-
ments that can help focus subsequent data acquisi-
tion, testing, and analysis activities. The first of these
is to determine the limiting nutrient (nitrogen or phos-
phorus) and therefore the most appropriate for con-
trol. The second is an estimate of the maximum
potential chlorophyll a level that could result and the
implications on the need for nutrient control. In either
case, it should be recognized that such a screening
is relatively imprecise and results should be inter- (Phosphorus)
preted with care. When indicated conditions are mar-
ginal rather than being dramatically in favor of one
result over another, additional analyses should be
performed as indicated in the discussion that follows.
1
1 \ig P/\ig Chi a
= 2Q\ig Chi a/L
Algae require inorganic carbon, nitrogen, phospho-
rus, silica (for diatoms), and various trace elements
Since each concentration represents a maximum po-
tential, the lower of the two is the maximum result and
phosphorus is therefore the limiting nutrient. The
maximum possible chlorophyll a concentration that
could result from the waste discharge in combination
with the background stream concentration is 20 jig/L
4-8
-------
This level might be achieved if there is adequate
residence time in the study area, optimal environ-
mental conditions (i.e., temperature and light) exist,
and all of the phosphorus is in a form available for
algal uptake. Stream conditions, however, are usu-
ally considerably less than optimal. Stream turbidity,
shading by a forest canopy, or self-shading by the
algae usually restrict the available light.
If the ratio of ambient nitrogen (mg N/L) to phospho-
rus (mg P/L) is greater than 12 to 1, phosphorus is
considered to be the limiting nutrient; if the N-to-P
ratio is less than 5 to 1, nitrogen is considered limiting.
However, a number of factors must be considered
when interpreting the results of the type of analysis
illustrated above, particularly when the outcome is not
at one extreme or the other.
• Nutrient availability is an important issue.
Organic and paniculate forms of the nutrients
cannot be used directly by algae. Although
a relatively slow conversion to available
forms takes place in natural water systems,
the residence time in most stream systems
is too short to make this a significant factor.
• The lack of precise stoichiometric ratios can
be an important consideration when N-to-P
ratios are only marginally in favor of one or
the other as a limiting nutrient.
• Nitrogen-fixing blue-green algae may negate
the impact of a control program based on
nitrogen being the limiting nutrient because
they can draw on a source (atmospheric)
other than the wastewater discharge.
The first two of these issues can be addressed more
reliably by the use of algal growth potential (AGP) tests
to supplement or substitute for the simple analysis
based on stoichiometric ratios. Properly performed
AGP tests are generally preferred because they will
provide more accurate results than the use of
stoichiometric ratios. The Selenastrum capricornu-
tum Printz Algal Assay Bottle Test described by Miller
et al. (1978) is an example of a suitable AGP test.
4.2.3.2 Phytoplankton Analysis of Short Streams
The previous section describes the estimation of
maximum chlorophyll a concentrations based on
given nutrient concentrations under optimum light
and temperature conditions. This section illustrates
procedures to develop estimates of maximum chloro-
phyll a concentrations in a stream under specific light,
temperature, and nutrient conditions. A short stream
is defined as one in which nutrients are in excess of
growth-limiting concentrations over the entire length
of interest. The distance and hence the time of travel
for stream nutrient problem contexts generally tend to
be short, perhaps on the order of less than 10 days.
This travel time is equivalent to distances of less than
160 miles for streams with a velocity of about 1 ft/sec
(0.3 m/sec). As a result, the phytoplankton biomass
may not have enough time to grow to the maximum
level calculated from the N-to-P ratio. The rate of
growth of the phytoplankton and the travel time of the
stream length are therefore of specific importance.
Thomann and Mueller (1987) describe a simplified set
of differential equations for chlorophyll a and inor-
ganic phosphorus and nitrogen under a steady-state
condition:
where
A
P,N
r
X
U
ap
a/v
Gn
GP
DP
dA
off*
= Gn A
— = aP Gp A
dt*
— = a/v GP A
dt*
(4-1)
(4-2)
(4-3)
= concentration of chlorophyll a
(H9/L)
= concentrations of inorganic
phosphorus and nitrogen (mg/L)
= travel time in stream (= x/U)
(days)
= distance downstream of effluent
(miles)
= stream velocity (miles/day)
phosphorus:chlorophyll ratio
(0.001 mg P/jig A)
= nitrogen:chlorophyll ratio (0.007
mg N/|ig A)
phytoplankton net growth rate
(day ^)
= [Gp -Dp - Vs/H]
= phytoplankton growth rate (PN =
1.0) (day'1)
= phytoplankton death rate (day ~1)
4-9
-------
Vs = phytoplankton net settling velocity
(ft/day)
H = average stream depth (ft)
In these equations, inorganic phosphorus is assumed
not to settle and is not recycled from respired algae.
Solutions of Equations 4-1 through 4-3 are:
A = Ao e
Gnt
(4-4)
G,,,^
( for P > 0.025mg/L )
and
(4-5)
(for N>0.-\25 mg/L)
(4-6)
Note that these equations are valid only in the region
where nutrients are in excess of phytoplankton
growth needs. A0, Po, and No are the in-stream
concentrations of chlorophyll a (|ig/L), inorganic
phosphorus (mg/L), and inorganic nitrogen (mg/L) at
the outfall after mixing of the upstream and effluent
flows. The travel time to the location in the stream
where nutrients begin to significantly affect the phy-
toplankton growth rate can be calculated from Equa-
tion 4-5 or 4-6 by substituting P = 0.025 mg/L for
inorganic phosphorus and N = 0.125 mg/L for organic
nitrogen:
In summary, "short" streams are defined as those
streams where actual travel times are less than t*p or
t*N as calculated from Equations 4-7 and 4-8. For
such streams, phytoplankton concentrations vary ex-
ponentially according to Equation 4-4 and are essen-
tially independent of nutrient concentrations (which
are in excess of growth-limiting concentrations). Nu-
trient removals at a point source will reduce the
in-stream concentrations P0 and/or N0 and will de-
crease the travel times t*p and/or t*N. If t*p or t*N
becomes less than the actual stream travel time, peak
chlorophyll concentrations will be reduced.
For small streams, 10 to 20 miles long with velocities
of 0.5 to 1.0 ft/sec (8 to 16 miles/day), resulting travel
times are from 1 to 2.5 days. If a high-rate activated
sludge (HRAS) plant flow with effluent P = 5 mg/L (75
percent of which is available for uptake) mixes with
an equal upstream flow with ambient P = 0.02 mg/L,
Po = 25 |j,g/L, Gp = 1/day, and Gn = 0.5/day, t*p will
equal approximately 7 days. If phosphorus removal
were instituted and the effluent were reduced to 1
mg/L, t*p would become approximately 4 days. In
both cases, t*p exceeds the actual travel time and the
stream would be classified as a "short" stream, with
phytoplankton concentrations varying exponentially
throughout its length.
The following procedure for analysis is suggested:
1.
2.
.
tp = -pr In
Gn
tN = -7- In
Gn
1_ |n [Ao + Po - 0.025 1 (4-7) pirical relationships.
Determine the limiting nutrient (inorganic phos-
phorus or nitrogen). Include an estimate for the
fraction of the inorganic nutrients available for
uptake (for example, 0.75).
For present conditions, estimate Gn, Gp, Dp, and
Vs using observed phytoplankton data and
irii~al rolatinnchinc
em-
3.
Ao" + No - 0.125
Ao"
(4-8)
where
t*P, t*N =
travel times to stream locations where
inorganic phosphorus and nitrogen con-
centrations begin to significantly limit phy-
toplankton growth (days)
Calculate t*p or t*N for present conditions from
Equation 4-7 or 4-8.
• If t*p (or t*i\i) is greater than the actual travel
time in the stream reach under consideration
(t*a), then nutrients are in excess and
A max « A0eGnta
• If t*p or t*N is less than t*a, nutrients have the
potential to limit at t*p or t*N and
Ao' =
ap GpAp
G~n
(mg/L)
i max :
Ao e
Gn(tPortN)
a/y GpA0
7^
Gn
(mg/L)
4-10
-------
TABLE 4-3. DATA FOR STREAM EUTROPHICATION CALCULATION
Parameter
Flow Rates:
Ambient Stream
Wastewater
Total Flow
Hydraulic Geometry:
Stream Depth
Velocity
Velocity
Water Temperature
Solar Radiation:
Daily Solar Radiation (If)
Optimum Light Intensity (ls)
Photoperiod (/)
Averaging Period (T)
Light Extinction Coef. (Ke)
KeH
Inorganic Phosphorus Cone:
Upstream
Wastewater
Maximum Limiting Phosphorus Cone
Chlorophyll a Cone:
Upstream (x < 0)
Downstream (x = 20 mi)
Algal Growth Rate, Gmax(20 °C)
Algal Respiration Rate, \IR (20 °C)
Net Algal Settling Rate, Vs
Unit
cfs
cfs
cfs
ft
ft/sec
mi/day
°C
iy
ly/day
day
day
ft'1
mg/L
mg/L
H9/L
jig/L
day'1
day'1
ft/day
Present
20.0
0.39
20.39
3.0
0.5
8.2
23.0
600
300
0.5
1.0
0.33
0.99
0.02
5.0
0.025
25.0
65.0
1.8
0.1
0.327
Design
12.0
0.49
12.49
2.2
0.4
6.56
25.0
600
300
0.5
1.0
0.33
0.73
0.02
1.0
0.025
25.0
7
1.8
0.1
0.327
4. Under projected conditions and future removal
programs, repeat steps 1 through 3. If the new
t*p (or t*i\i) is greater than the new t*a, nutrients
would still be in excess.
The data given for the example calculation for a short
stream are summarized in Table 4-3 and Thomann
and Mueller (1987). The underlying assumption is
that nutrients are not limiting the algal growth in the
stream.
Analysis
Use observed chlorophyll a data at x= 0 and
x = 20 miles and assume an exponential
increase. P(x=20) = P(x=0)exp(+Gn x/U)
Travel time for reach: x/U= t* = 20 mi/8.2
mi/day = 2.44 days
Chlorophyll a at end of 20 miles: P(x=20)= 65
= 25 e<2-*4)(Gn)
Net growth rate: Gn = [In (65/25)] / 2.44 =
0.391 day'
,-1
Estimate net phytoplankton growth rate (Gn):
• Determine algae population dynamics rate
factors:
4-11
-------
Gp = Gmax 1 .066
r\erl I
= GT ri_ rn
Nut
rn = 1.0
(assuming no nutrient limitation)
Km + Nut
(2-14)
(2-17)
GT= (1 .8day~1) (1 .066) (23~20) = ~1
= 2.18 day~ (Figure 2-6)
OC1 =
0.2 =
600 ly
e-(0.33)(3) = r47 (2_15a)
/L =
300 ly/day (0.5day)
^04 = 4.00 (2-15b)
300 /y/day (0.5day)
(2.718X0.5) (e-i.47_e-4.oo) = 0287
(0.33)(3.0)(1.0)
Gp = (2.18day~1)(0.287)(1) = 0.626 day'1
Dp = (0.1day~1)1.C
= 0.1 26 day
,-1
Since Gn = [Gp - Dp - VS/H], the net settling loss
rate can be estimated from
Vs = H (Gp - Dp - Gn) = 3.0 (0.626-0. 126-0.371)
Vs = 0.327 ft/day
Summary of population dynamics rates:
-1
-1
,-1
-1
Specific growth rate, Gp = 0.626 day
Respiration loss rate, Dp = 0.126 day
Algal settling loss rate, Vs/H = 0.109 day
Net algal growth rate, Gn = 0.391 day'
• Check for nutrient limitation:
Using a phosphorus-to-chlorophyll a ratio
(ap) of 1 .0, the amount of inorganic phospho-
rus required to generate a net 40 |ig/L chlo-
rophyll a is
Po' = Ao'/ap= apGPA°aP= 40
Gn
The initial phosphorus concentration follow-
ing complete mixing between the waste input
and stream flow is
- = 0.115 mg/L= 115
By the end of the 20-mile reach, the inorganic
phosphorus concentration would be equal to
115 - 40 or 75 \ig/L, which is much higher than
the maximum limiting concentration of 25
[ig/L (see Table 4-3). Thus, the above analy-
sis is appropriate.
Estimate algal population dynamics rate fac-
tors under future design conditions:
Assume that the phytoplankton settling rate
(Vs) and light extinction coefficient (Ke) will
not change under future design conditions.
Modify pertinent rate factors for design
stream flow, temperature, and depth.
Using design conditions summarized in Ta-
ble 4-3 and the pertinent relationships de-
fined earlier, the rate factors for algal growth
dynamics become:
Light limiting factor, ri_ = 0.236
Nutrient limiting factor, rn = 1.0
(initial assumption)
Specific algal growth rate, Gp = 0.585 day"1
Algal respiration rate, Dp = 0.147 day"1
Algal settling rate, Vs/H = 0.149 day"1
Net algal growth rate, Gn = 0.289 day"1
The projected algal chlorophyll a concentra-
tion at x = 20 miles would be
25e(0.289cfay )(20m//6.56 mi/datf = 6Q 3 ng/L
which would require the following amount of
inorganic phosphorus to support it:
00)^X25)
= 50.6
Yet, the inorganic phosphorus concentration
following complete mixing at x= 0 is only
(12.0)(0.02)+(0.47)(1.0)
12.0+0.49
- = 0.0568 mg/L = 56.8 \ig/L
Although this inorganic phosphorus concen-
tration is slightly more than the amount re-
quired for algal growth, it is not sufficient to
maintain a no limitation condition while ap-
proaching the end of the 20-mile stream.
[Note that an inorganic phosphorus concen-
tration of 25 |ig/L (see Table 4-3) is required
for a no limitation condition in the water col-
umn.] In other words, phosphorus limitation
will occur in the stream prior to the end of the
20-mile reach. Because of this limitation, the
chlorophyll a concentration at x = 20 miles,
60.3 |ig/L as calculated earlier, will be the
upper bound for the algal biomass. A lower
4-12
-------
bound can be estimated by first calculating where
the time it takes to reach a potential phospho- n
rus limitation (i.e., inorganic phosphorus
cone. = 25 \ig/L):
= number of days
n = cos(nnf/T)
1 50.6+56.8-25
Gn
50.6
= 1.628 days
(nT/f)2 - (2nn)2
and the average daily value of this function is equated
The lower bound of the chlorophyll a concen- |° the average daily algal oxygen production calcu-
tration is therefore
lated as:
Based on the above analysis, the maximum chloro-
phyll a concentration at x = 20 miles would be be-
tween 41 and 60 |j,g/L. The analysis also indicates
that the short stream assumption is violated under
future design conditions. More rigorous analyses
(i.e., using a computer model) are required to address
this issue.
4.2.3.3 Diel Dissolved Oxygen Variation Due to Al-
gae
If only average daily dissolved oxygen concentrations
are of concern in a TMDL, the above analysis may be
used to determine the daily average net dissolved
oxygen production due to algal photosynthesis and
respiration. In cases where minimum daily standards
are of concern, an estimate of the diel variation in
dissolved oxygen must be made. A brief theoretical
analysis is presented in the following paragraphs and
followed by an example using the data from the
previous example in Section 4.2.3.1.
Algal oxygen production as a function of time during
the day can be approximated as (Di Toro, 1975;
Chapra and Di Toro, 1991):
P(t) = PM sin(?i t/f)
P(0 =
0
-------
(Cmax-Cmin)
[1-6
fKal"\ -
(4-12)
where Cmax and Cmin represent the maximum and
minimum daily (24 hr) oxygen levels.
Thomann and Mueller (1987) and Chapra and Di Toro
(1991) present complete documentation of derivation
of the diel oxygen production model and Di Toro's
(1975) delta method of determining the diel range of
oxygen from algal photosynthesis.
In shallow streams and rivers, attached epiphytic
algae and benthic macrophytes can account for sig-
nificant components of observed primary production
and oxygen and nutrient distributions (Jeppesen and
Thyssen, 1984). In particular, steep gradient reaches
of rivers with high current velocity (ca. 50 cm/s) and
sufficient nutrient supply are typically characterized
by maximum rates of benthic primary productivity
from periphyton (Hynes, 1970; Horner and Welch,
1981; Welch et al. 1989). Consistent with other stud-
ies reported in the literature, stream velocity in-
creases of up to -50 cm/s have been observed to
result in enhanced biomass accumulation and pro-
ductivity of attached periphyton (Horner and Welch,
1981). Velocities higher than -50 cm/s tend to result
in reduced biomass accumulation because of physi-
cal scouring and removal of attached biomass.
Since data to describe benthic biomass or benthic
primary productivity in a river are typically not avail-
able, literature values can be used to estimate pa-
rameter values for gross benthic algae production
and production/respiration ratios (P/R) (e.g., Bott et
al., 1985). From these literature values, gross ben-
thic algae productivity appears to be on the order of
0.5 to 5.0 g C/m2-day. Based on photosynthetic
efficiency and assuming that 1 mole 62 = 112 kcal,
gross benthic production is on the order of 0.5 to 5.0
percent of total incoming solar radiation (Thomann
and Mueller, 1987).
In a comparative long-term seasonal study of four
rivers across the United States (Oregon, Michigan,
Pennsylvania, and Idaho), Bott et al. (1985) reported
summer benthic algae productivity rates of 0.25 to 2.5
g C/m -day. Bott et al. (1985) also reported a range
of values of P/R ratios consistent with the "River
Continuum Concept" (Williams, 1981) where transi-
tions in community metabolism (i.e., P/R) tend to
occur over the domain of a river as small streams
develop into larger rivers over a drainage basin. In
general, the data of Bott et al. (1985) tend to support
this hypothesis, as summarized below:
• Upper reach of river: predominant heterotro-
phy (P/R <1 )
• Middle reach of river: predominant autotro-
phy(P/R> 1)
• Lower reach of river: predominant heterotro-
phy (P/R <1 )
In shallow systems, accurate representation of the
observed diel oxygen range might require a daily
average and diel benthic algae component in addition
to the phytoplankton component.
In order to account for benthic algae, or macrophytes,
Equation 4-11 can be easily modified to include addi-
tional daily average and diel terms. This approach has
been used with hydrographic data for Flanders Bay and
Senix Creek (Tetra Tech, 1989; Morton et al. 1990),
shallow estuarine ecosystems in eastern Long Island .
Data from a 48-hour time series in Senix Creek (Ryther
et al., 1958) are presented for comparison to the diel
model results assuming (a) phytoplankton production
only and (b) phytoplankton and benthic macrophyte
production (Figure 4-4).
Using the hydrographic and nutrient data obtained for
Senix Creek, the computed average phytoplankton
primary production rate of 5.3 g C/m2-day falls within
the observed range of 3.2-6.2 g C/m2-day. If phyto-
plankton were the dominant primary producer, then
the diel analysis should have adequately reproduced
the observed 48-hour time series of oxygen data where
sediment oxygen demand was assumed constant at
4.1g O2/m2-day at the ambient temperature of 25 °C.
Like the diel oxygen model results reported for the
Shenandoah River (Deb and Bowers, 1983), the com-
puted amplitude and phase of the phytoplankton diel
oxygen model do not adequately reproduce the ob-
served data (Figure 4-4(a)). Incorporation of an aver-
age benthic macrophyte production (4 g C/m2-day) and
respiration (3.75 g C/m2-day), however, results in
much better agreement with the observations from
Senix Creek (Figure 4-4(b)).
The results of the diel analysis clearly demonstrate
that benthic photosynthetic oxygen production can be
a significant factor in the observed diel variability of
oxygen in shallow systems such as Senix Creek. It
is also likely that benthic macrophytes would account
for a significant component of total nutrient uptake in
the water column.
4.2.4 Selection of Modeling Framework
Obtaining a simulation model that effectively imple-
ments the conceptual model is important. If availab
4-14
-------
s
I
a
* !-
Ryttwf « nix 1958) Jua a&-27, S9S7
SUNRISE
u
Diuraal
(a) ONLY ALGAL PRODUCTION INCLUDED IN MODEL (BENTHIC MACROPHYTE
PRODUCTION AND RESPIRATION EQUAL TO ZERO)
Rytber tlri41958) Jun 26-27.19S7
S
e
c
\
\
\&
\
\
TME FROM SUNRISE (flay)
DiutMl & Ot»
(b) BOTH ALGAL AND MACROPHYTE PRODUCTION INCLUDED IN MODEL (BENTHIC
MACROPHYTE PRODUCTION AND RESPIRATION GREATER THAN ZERO)
FIGURE 4-4. DIEL MODEL VS. OBSERVED OXYGEN IN SENIX CREEK, LONG ISLAND
(After Tetra Tech, 1989)
4-15
-------
models do not fully implement a specific conceptual
model, the analyst may:
• Refine the model code.
• Make calculations or assumptions external to
the model code.
• Explore consequences with model sensitivity
analyses.
It should be pointed out that how a modeling frame-
work is used is typically more important to a TMDL
modeling study than exactly which model is used.
Selection of an appropriate modeling framework in-
creases the probability of accurate results.
The nature of the problem and, specifically, the time
and space scales of the problem dictate the simplicity
or complexity of the modeling analysis. Given or
assuming these scales, a specific question is posed,
and the purpose of the modeling analysis is to answer
this question in the simplest, most efficient, and most
realistic manner. For example, if the dissolved oxy-
gen depression in the stream is primarily due to point
source BOD discharges and no significant algae have
been detected in the study area, a simple model of
BOD/DO without eutrophication is sufficient for the
analysis. By contrast, if the dissolved oxygen prob-
lem is caused by decomposition of algal biomass
following nutrient inputs, the next level of analysis,
incorporating algal-nutrient dynamics, should be con-
sidered.
Furthermore, many stream water quality problems
can be and have been answered by a steady-state
analysis with linear kinetics and simple transport
(one-dimensional) components. The simple dis-
solved oxygen models of streams are typical exam-
ples. Such problems may be approximated with
sufficient accuracy to yield an analysis that is ade-
quate for making decisions regarding the treatment
level of wastewater. On the other hand, at this stage
of development, an analysis of the eutrophication
problem usually requires time-variable and nonlinear
terms in order to determine the effect of nutrient
removal from wastewaters.
The relative complexity of the model is an important
factor in TMDL studies—the more complex, the
greater the degree of model validation required. The
complexity of the model is determined by the number
of transport, kinetic, and input terms in the model
equations. Compare the simplicity of the equations
used to describe the steady-state distribution of dis-
solved oxygen in streams to the complexity of those
describing the time-variable distribution of nutrients
and phytoplankton in streams. For each additional
component included in the analysis, an additional
degree of validation is necessary. As a conse-
quence, additional data are required. If data are not
available on a specific component, it is questionable
whether the component should be included in the
analysis.
Most of the stream water quality models for TMDLs
can be run on personal computers. Therefore, it is
essential that the modeling framework selected be
user-friendly. Technical support to operate the model
is also crucial. Finally, graphic display of the model
results can significantly increase the productivity of
the TMDL study. With the rapid advancement of
microcomputer hardware and software, user-friendly
features should be considered in model selection.
4.3 SITE-SPECIFIC STREAM SURVEY
Following the initial assessment, including review of
existing data, preliminary analyses, if any, and the
selection of a modeling framework, a field survey may
be conducted to fill any data gaps. The additional
data are key to the model calibration and validation
for the TMDL study. In fact, the initial assessment
should determine:
• What pollution sources will be monitored?
• What is the extent of water quality data to be
collected?
In general, a stream survey includes three basic
components:
• Measuring stream physical parameters such
as hydraulic geometry, velocity, flow, and
time of travel.
• Receiving water quality (physical, chemical,
and biological) data collection.
The following special studies may be conducted, as
needed, if the budget and time schedule allow:
• Time-of-travel and dye dispersion studies.
• Measurement of reaeration coefficients.
• Light and dark bottle tests.
• Diel oxygen measurements.
4-16
-------
• Nitrifying bacteria counts in the water column
and sediments.
• Long-term BOD tests of wastewater and re-
ceiving water.
• Field measurements of sediment oxygen de-
mand and nutrient fluxes.
It is extremely important that these components be
synchronized to form a synoptic survey, making the
data most useful for the water quality modeling analy-
sis. The handbook on stream sampling for wasteload
allocation applications by Mills et al. (1986) provides
complete information for designing a stream survey
program for point sources. A complete QA program
for the stream survey should be developed in ad-
vance of any sampling activities to ensure docu-
mented evidence that a data product of known and
acceptable quality is produced. Appendix C presents
the basic elements of a quality assurance program for
field monitoring programs.
4.3.1 Hydraulic Geometry Survey
Physical stream data include stream cross-sectional
area, average stream depth, stream flow, and aver-
age stream slope. These data must be collected at
each of the sampling stations selected. If the river is
constricted or not reflective of the natural channel at
these stations, then area and depth data should be
measured slightly upstream of the location or where
the channel is reflective of natural conditions.
About 5 percent accuracy should be required for
cross-sectional area data, while 10 percent accuracy
should be required for flow measurements. In addi-
tion, some self-checking procedure should be estab-
lished so that any vandalism or change in staff gage
elevation can be determined and corrected.
4.3.2 Time-of-Travel Study
Time-of-travel data are useful to define the time of
passage between various sampling stations and to
determine the magnitude of longitudinal dispersion in
the stream. Time-of-travel studies should be con-
ducted under different flow conditions (see Figure
A-4). These flow conditions could be low flow or dry
weather flow, and high flow. Each time-of-travel
study should take place during a constant flow period
of a few days. During the survey, fluorescent dye is
released at each selected location on the river and
fluorescence is measured at the next downstream
station. Stations should be selected to take into
account any features in the river basin that might
change the time of travel such as present and future
wastewater inputs, tributary inputs, and changes in
channel characteristics. The dye is released instan-
taneously at the upstream station and collected over
time at the downstream station. Dye samples can be
collected by an automatic sampler for fluoresence
measurement. The sampling interval from start of
sampling to end of sampling should be determined
before the dye is released, based on the river flow and
the length of the stream reach. Although most dye
studies are conducted using a single instantaneous
dye dump, continuous dye injection can also be used.
When conducting a time-of-travel study for multiple
reaches in a river, the analyst must always start with
the most downstream reach and proceed in the up-
stream direction to avoid any influence from upstream
dye releases.
Rhodamine WT dye is normally used in stream sur-
veys. This dye should be diluted, one to one, with
methyl alcohol to bring the solution to a specific
gravity of approximately 1.0. The mass of dye re-
leased should be recorded, as well as the instantane-
ous flow at the upstream and downstream stations.
After dye samples have been collected, they should
be analyzed for percent transmittance. In addition, a
calibration curve should be presented, showing the
percent transmittance vs. dye concentration (Wilson
etal., 1986).
4.3.3 Stream Water Quality Sampling
Water quality sampling should be conducted to as-
sess the point and nonpoint source impacts on
BOD/DO levels in a stream or river. When monitoring
water quality, all samples should be checked for
residual chlorine. If substantial levels are found, then
BOD samples must be dechlorinated and reseeded.
In addition, when planning a stream water quality
survey, three key items should be determined: (1)
sampling locations, (2) sampling time and frequency,
and (3) sampling protocols.
A survey program designed for the Catawba River,
South Carolina, illustrates the scope of a stream
survey to support a BOD/DO TMDL study (Lung,
1990). Figure 4-5 shows the study area and major
point sources along the Catawba River. Figure 4-6
presents the sampling network along the river. Note
that the water quality sampling stations were selected
to reflect the major point source discharges and non-
point source tributary inputs. The receiving water
quality parameters sampled are shown in Table 4-4,
including the sampling frequency. The number and
locations of the stations could vary slightly depending
4-17
-------
s
riilis PLictt- S.34
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s,
—r **>y
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«. ST?
aawnter*
Man*tt* Mills
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35,.50 15.000
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FIGURE 4-5. CATAWBA RIVER STUDY AREA AND MAJOR POINT SOURCES
(Lung, 1990)
4-18
-------
4
5
of the »yil«
sf €
Hill-
r STP
S-igar Creek
Ucscreaa of jurctton with
Craek
of junccton
Caw Cre«k
FIGURE 4-6. PRELIMINARY WATER QUALITY SAMPLING NETWORK
(Lung, 1990)
4-19
-------
TABLE 4-4. WATER QUALITY SURVEY FOR THE CATAWBA RIVER
Parameter
Stations
Sampling Frequency
Temperature3
pHa
Dissolved Oxygen3
Specific Conductivity3
Diurnal Dissolved Oxygen
CBODu
TBODud
CBODs
Total Kjeldahl Nitrogen
Ammonia Nitrogen
Nitrite and Nitrate
Total Suspended Solids
All
All
All
All
3, 5, 7,9
3, 5, 7,9
3, 5, 7,9
All
All
All
All
All
Twice a day for 2 days
Twice a day for 2 days
Twice a day for 2 days
Twice a day for 2 days
Grab samples every 2 hr for 24 hr
Grab samples0
Grab samples0
Twice a day for 2 days
Twice a day for 2 days
Twice a day for 2 days
Twice a day for 2 days
Twice a day for 2 days
3 Using field sampling unit.
Light and dark bottle rig was used.
c Both total BOD and nitrification inhibited BOD for days 1, 2, 3, 5, 7, 10, 15, 20, 30, 40, and 50.
d Total BOD.
TABLE 4-5. POINT SOURCE SAMPLING PROGRAM
Parameter
Sources
Sampling Frequency
Temperature
pH
Flow
Dissolved Oxygen
CBODs
Total Kjeldahl Nitrogen
Ammonia Nitrogen
Nitrite and Nitrate
Total Suspended Solids
CBODu
TBODu
All
All
All
All
All
All
All
All
All
All
All
Instantaneous
Instantaneous
24-hour composites taken 4 times during
the survey
Same as above
Same as above
Same as above
Same as above
Same as above
Same as above
Grab samples3
Grab samples3
3 Both total BOD and nitrification inhibited BOD for days 1, 2, 3, 5, 7, 10, 15, 20, 30, 40, and 50.
4-20
-------
on the actual field conditions. A similar summary is
shown in Table 4-5 for point source sampling. The
survey lasted for approximately 4 days to cover the
entire length of time required for dissolved sub-
stances to travel the designated section of the river.
The sampling of the upstream stations began 2 days
prior to the stream sampling to establish accurate
boundary conditions for the modeling analysis.
4.3.4 Wastewater Monitoring
Different types of point sources require an analysis of
wastewater characeristics to accurately determine
the ultimate dissolved oxygen demand. The most
important factor for this determination is the CBODu-
to-CBOD5 ratio. In the Catawba River, a number of
municipal and industrial point sources were sampled
during dry weather conditions. Table 4-5 lists the
water quality parameters sampled and the sampling
frequency.
Because of insufficient CBODu and CBOD5 data,
conservative values (high ratio) were used during the
study to avoid criticism. An overly conservative
CBODu-to-CBOD5 ratio would result in wasteload
allocations more stringent than necessary. There-
fore, if industries want to have adequate allocations,
sufficient data are required to justify a lower CBODu-
to-CBOD5 ratio. A long-term BOD test of the efflu-
ents and the stream samples is needed. Long-term
BOD tests usually take about 90 to 100 days and are
very straightforward, but time-consuming.
4.3.5 Biological Assessmen*
Several methods exist for evaluating the biological
attributes of a stream system (USEPA, 1993a). Habi-
tat Evaluation Procedures (HEPs) are used to docu-
ment the quality and quantity of available habitat by
providing information for comparing in-stream and
riparian habitat in different areas or in one area under
different conditions. Rapid Bioassessment Protocols
(RBPs) for habitat are screening tools for determining
whether a stream is supporting a designated aquatic
life use. One component of these protocols is an
in-stream habitat assessment procedure that meas-
ures physical characteristics of the stream reach.
RBP III, an RBP for benthic macroinvertebrates, fo-
cuses on quantitative sampling in riffle/run habitat or
on other submerged, fixed structures where riffles
may not be available. The data collected are used to
calculate various metrics pertaining to benthic com-
munity structure, community balance, and functional
feeding groups. The Index of Biological Integrity (IBI)
has been used in many States to assess a wide range
of impacts in streams and rivers. The IBI includes 12
matrices in three major categories offish assemblage
attributes: species composition, trophic composition,
and fish abundance and condition. Any of these
methods can be useful in determining the effects of
pollutant loadings on biological communities in
streams and rivers.
4.4 MODEL CALIBRATION
Model calibration is the first stage of testing and tuning
a model to a set of field data, preferably a set of field
data not used in the original model construction
(Thomann and Mueller, 1987). Given the external
parameters of a modeled stream system, an initial
estimate is made of the appropriate transport and
reaction rate coefficients in the model. These coeffi-
cients may be determined from a fundamental analy-
sis relating to each specific coefficient (i.e., hydrologic
or hydraulic analyses). The coefficients may also be
determined from a statistical analysis, as is usually
done with biological and chemical kinetic terms. In
any case, if a range of these values is known, a best
estimate is made for each, the model is run, and the
output is compared to the data. Successive iterations
and adjustments are required to obtain a reasonable
fit of the model and data. This procedure is known as
model calibration.
4.4.1 Model Coefficient Assignment
Model calibration is also part of the process of deter-
mining model coefficients. A simple example is the
derivation of the stream deoxygenation coefficient,
Kd, using the measured CBOD5 or ultimate CBOD
data (e.g., CBOD20).
In many stream BOD/DO modeling analyses, sedi-
ment oxygen demand was not included in the models.
To calibrate the model to actual in-stream dissolved
oxygen data, the effect of SOD was incorporated into
other modeling rates such as Kd, Kn, and Ka. In
cases where Ka was determined using a reaeration
formula and was not adjusted, the oxygen demand
from SOD could be incorporated into the Kd or Kn
rates. This approach would have the effect of over-
estimating the dissolved oxygen impact from removal
of nitrogenous or carbonaceous BOD. Sub-
sequently, this derived value must be incorporated
into the site-specific model to check the model-com-
puted CBOD5 and dissolved oxygen profiles against
the field data.
4-21
-------
Incorrect calibration of models could also arise from
wrong steps in model calibration. For example, Kd
can be adjusted until the calculated dissolved oxygen
matches the measured data, rather than adjusting Kd
to correspond to the CBODu data. Sediment oxygen
demand, not considered in the model, was measured
at a certain value. In this case, the effect of SOD
could inadvertently be included in the Kd rate in order
to match the model output with the observed data.
Thus, the Kd rate used in the model could be sub-
stantially higher than the Kd estimated from the
CBOD data. Since the Kd used in the model exceeds
its likely value, the dissolved oxygen increase result-
ing from CBOD removal would be overestimated.
In model calibration analyses, adjustments of model
coefficients should not exceed a predetermined
range for each individual rate constant. For example,
if CBOD5 data show that Kd could range from 0.25
to 0.30 day-1 (depending on how the slope of the
CBOD decay curve was drawn), Kd should not be
adjusted beyond this range. Another approach in
calibrating a model is to set all rates other than Ka
equal to their most reasonable value based on avail-
able data, and then to vary Ka under various flow
regimes within the range indicated by the applicable
reaeration formulas. If adjustments within this range
of Ka do not produce a good match with the data, then
the other rate constants may be adjusted further
within their range of uncertainty. If these adjustments
still do not produce a good match, the analyst should
reevaluate available data, the reaeration formulas
used, and the receiving stream itself to identify factors
that may be preventing model results from correspond-
ing with actual in-stream data. It should be noted,
however, that if Ka is calculated or measured using
site-specific data, it is not advisable to vary Ka values
and other estimated coefficients such as SOD should
be adjusted.
A more difficult case is the assignment of the model
coefficients involving eutrophication. As indicated in
Section 2, many kinetic processes related to phyto-
plankton growth and nutrient recycling in the water
column are difficult, if not impossible, to obtain inde-
pendently because of cost or time constraints. The
practical approach of assigning them in a TMDL
analysis is to rely on model calibration and sensitivity
analyses. That is, model coefficient values are se-
lected from literature values, preferably from previous
studies at the specific site location, or from water
bodies with similar problem settings. Subsequent
model runs are performed to fine tune these model
coefficients by matching the field data. Although a
number of model coefficient values are derived from
literature data, independent estimates of the exoge-
nous variables such as streamflows, time of travel,
boundary conditions, and environmental conditions
should still be derived from the field data to minimize
the degree of tuning.
When field measurements are available, model coef-
ficients can be determined using curve-fitting proce-
dures. However, it should be pointed out that model
calibration is not a curve-fitting exercise. The model
coefficients (e.g., algal growth rate) are also adjusted
through a series of model runs with reasonable and
narrow ranges of their values derived from the litera-
ture. The model is designed to mimic the steady-state
algal growth and nutrient dynamics and should be
shown to accomplish the task of reproducing the algal
biomass and nutrient concentrations in the stream. I n
model sensitivity analyses, adjusting the kinetic coef-
ficients and constants (within their predetermined
ranges) to improve the calibration of certain water
quality constituents often results in adverse outcomes
for other water quality constituents. These are the
constraints in the model calibration process that
would eventually lead to the determination of a unique
set of credible model coefficients.
4.4.2 Component Analyses
In the steady-state stream BOD/DO modeling analy-
sis, the amount of dissolved oxygen deficit produced
by each of the oxygen-demanding components can
be calculated. The dissolved oxygen deficit is calcu-
lated for each source of deficit and then is plotted.
Figure 4-7 shows the component analysis results from
the modeling analysis of Rock Creek, Pennsylvania,
for the August 1979 conditions (Lung, 1990). The
results suggest that the Gettysburg wastewater treat-
ment plant and the sediment oxygen demand contrib-
uted the most oxygen deficit in the stream. All other
sources had a much smaller effect on the dissolved
oxygen concentrations. This type of analysis is impor-
tant in both the model calibration/validation and was-
teload allocation analyses. The component analysis
gives the analyst a graphical presentation of the
cause-and-effect relationship for in-stream water qual-
ity-
While component analyses are routinely performed to
quantify the contribution of individual sources to dis-
solved oxygen deficits, a similar component analysis
is not appropriate for eutrophication modeling analy-
sis because of the nonlinear nature of the phytoplank-
ton growth-nutrient dynamics in the model. That is,
results from a component analysis would not predict
algal biomass accurately in terms of the various
4-22
-------
1 I
TJ
C
"l;
s
f— ™ "T-
CP
5
J3
-i1
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ft C
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2
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(I> Curr oer ana
© GeHysburg Plant
. 4 5 6
Mia* (roffi Cumb«irlan4
11
Plant
FIGURE 4-7. COMPONENT ANALYSIS OF DO FOR ROCK CREEK, PENNSYLVANIA
(Lung, 1990)
sources of phosphorus without taking into considera-
tion other factors that also control algal production.
Lung and Testerman (1989) have demonstrated a
technique called numerical tagging to determine how
much phosphorus in the algal biomass at a certain
location in the James River, Virginia, is from a par-
ticular wastewater source. The technique is similar to
using a radioactive tracer in limnological studies to
track the fate and transport of phosphorus in systems.
Instead of using a radioactive tracer such as 32PO4,
Lung and Testerman used a numerical tracer injected
at the particular wastewater source studied. That is,
that source of phosphorus was numerically labeled
and added to the river. Figure 4-8 shows the numeri-
cal tagging results for the James River. The results
show that POTWs in the James River are major
contributors of orthophosphate as well as algal
biomass. One interesting observation is that while
the Richmond POTW contributes more than 80 per-
cent of the orthophosphate to the river, its contribution
to the biomass is only about 50 percent (a dispropor-
tionate share compared with its phosphorus input).
Such a result further emphasizes the nonlinear nature
of eutrophication models.
4.4.3 Quantifying the Comparison Between
Model Results and Data
Research activities (Thomann, 1982,1987) in model-
ing eutrophication in lakes have begun to explore the
use of simple statistical comparisons in an attempt to
quantify model adequacy. These techniques could
be a supplement to the qualitative comparisons of
observed and calculated water quality profiles. Three
techniques that have been used are:
• Comparison of means
• Regression analysis
• Relative error
In the first technique, the mean of the observed data
is compared to the mean of the computed profile for
the comparable conditions of loading, transport, and
temperature. The Student's t-probability density
function is employed for the comparison of the
means.
In regression analysis, calculated concentrations and
observed data are considered as paired points in the
test equation:
4-23
-------
Freshwater Flow: 1100 cfs (31.2 m'/s) T«nnp«raturt; 26*C
0
Upstream & Ncmpoint Input
Bey Exchange
50 40 30
upstream at NonoQint Input
Other POTWs
Richmond
POTW
Appomcrttox Rwer Input
Upstreqm at Nanpcfrrt Phoaphorua Input
Indiatrfd Phosphorus input
from Other POTWs
Richmond
ROTW .
Bay Exdwnga
30 20 10 0
70 60 50 40
River Mtea from Mouth
FIGURE 4-8. NUMERICAL TAGGING OF JAMES RIVER
(After Lung and Testerman, 1989)
4-24
-------
= a
C + E
where and o are the true intercept and slope, respectively,
between the calculated value Cand the observed data X Eis the
error associated with the observed dataX The regression analysis
assumes that the calculated value C is known with certainty and
that the error Eis in the measured data, which is not necessarily
a realistic assumption. Standard linear regression methods can
be used to compute the square of the correlation coefficient (r2\
and the standard error of estimate representing the
residual error between data and model. Estimates of
the slope and intercept are calculated and a test of
significance developed. Well-calibrated models
would have a zero intercept and a slope of one.
Relative error is the absolute value of the difference
between the observed and the calculated values
divided by the observed value. The relative error may
be aggregated across time or space, and the cumu-
lative frequency of error can be computed. Estimates
can be made of the median relative error as well as
the 10 percent and 90 percent frequency of error.
This statistic is poorly behaved at the upper tail and
at low values of X. The median error can be easily
understood; therefore, it is the suggested measure if
statistical representations of model adequacy are to
be employed in a TMDL study.
Statistical measures of adequacy are in the early
stages of research and should be employed recog-
nizing that they provide, at the very best, a lower
bound on the magnitude of the error.
4.5 MODEL VALIDATION
4.5.1 Model Coefficient Adjustment
Once a set of coefficients representative of one set
of external conditions (e.g., with respect to tempera-
ture, flow, and loading inputs) has been established,
the model is rerun for a different set of input condi-
tions. If the model output agrees in a reasonable,
qualitative way with the second set of data, the model
is considered to be validated in the first degree.
In some instances, if sufficient data are available, a
quantitative comparison is possible. Then a measure
such as the standard error of the mean can be used,
and the model is considered validated if the model
results fall within one standard error. Additional com-
parisons with different combinations of the exoge-
nous parameters yield higher degrees of validation.
In some cases, a model coefficient value may have
to be varied slightly to match the data in the validation
process. Then the changed value must be tested
again with the data set for the model calibration run.
A good example of such an exercise is the calibration
of the nitrification rate, Kn. When data from a winter
survey are first used to calibrate a model, the dis-
solved oxygen balance is not sensitive to the nitrifica-
tion rate and, therefore, Kn cannot be determined
accurately. During model validation, another set of
data collected in the summer months is used. Since
the nitrification process is highly sensitive to tempera-
ture, the modeling analysis is able to tune the nitrifi-
cation rate with greater accuracy. Now, this modified
Kn should be checked again with the winter run.
Because of the cold temperature in the winter months,
the model results are not affected. This procedure is
also valid for model calibration and validation analy-
ses between two drastically different stream flow
conditions. Under high flows, some kinetic coeffi-
cients may not be important and, therefore, cannot be
accurately calibrated until the low-flow conditions,
when the kinetics become much more significant in
relation to stream flow.
4.5.2 Model Sensitivity Analysis
When validating or calibrating a mathematical water
quality model, the analyst selectively determines
some model input parameters that, when used in the
model, yield reasonable simulations of observed
water quality data. Some of these input parameters,
such as stream geometry, cross-sectional areas, and
depths, are directly measured. Other model parame-
ters, such as system transport, oxidation rates,
reaeration rates, and nitrification rates, are not directly
measured. These parameters are determined from
empirical formulations, literature searches, or itera-
tive model simulations. The purpose of a sensitivity
analysis is to test the sensitivity of the model to some
of these input parameters. Some of the common
model sensitivity analyses in a stream TMDL include:
• Sensitivity of model to transport coefficients.
• Sensitivity of model to Ka rates.
• Sensitivity of model to Ka rates.
• Sensitivity of model to Kn rates.
• Sensitivity of model to the net algal oxygen
production rate (P-R).
• Sensitivity to SOD
4-25
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Rity pcicev
had met&aii relative
FIGURE 4-9. SOME RELATIVE ERRORS OF DISSOLVED OXYGEN MODELS
(Thomann, 1980)
4-26
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4.5.3 Model Accuracy
The question of model accuracy is often crucial in
situations where a given allocation is being negoti-
ated or contested. Thomann (1980) has discussed
this question and compiled a distribution of relative
errors between model calibration results and the ob-
served data. Figure 4-9 displays the median relative
error in measured versus simulated (modeled) dis-
solved oxygen for waterbodies of varying complexity.
The models represented in Figure 4-9 generally rep-
resent state-of-the-art models, applied by experi-
enced practitioners using best judgment on loads,
parameters, and model structure. That is, the calibra-
tions were conducted based on defensible theoretical
assumptions rather than simply an attempt to match
the measured dissolved oxygen values by arbitrarily
adjusting model coefficients. With this consideration
in mind, Figure 4-9 indicates that for the 20 models
represented, 50 percent had a median relative error
in dissolved oxygen of 10 percent (plus or minus),
with maximum errors of up to 60 percent occurring in
the smaller streams/estuaries simulated. This com-
parison is useful in suggesting the present ability to
reproduce the observed data with a credible model.
4.6 MODEL APPLICATION AND
TOTAL MAXIMUM DAILY LOADS
An integral part of the TMDL process is the analysis
of cause-effect relationships via a mathematical
model of loading input and resulting water quality
response. The TMDL rests heavily on the credibility
and predictive capability of the mathematical model-
ing framework (Thomann and Mueller, 1987). How-
ever, the adequacy of the modeling framework is only
one of many issues that must be considered in a
TMDL process (Chadderton and Kropp, 1985). To
develop an actual TMDL, a number of tasks need to
be conducted. The following sections provide a brief
description of these tasks.
4.6.1 Development of Management Scenarios
In many cases, management alternatives can be
evaluated by using model applications, particularly in
river systems that receive loadings from multiple
sources. Usually a regional or State planning agency
is responsible for soliciting input from dischargers, the
public, and other interested parties to determine the
most feasible management alternatives. In all cases,
depending on scenario, all point and nonpoint
sources should be considered when developing allo-
cation scenarios.
When developing an allocation scenario for a TMDL, the
water resource manager should select the best combi-
nation of point and nonpoint source controls that
achieves water quality standards. The selection of an
allocation alternative largely depends on available tech-
nical and financial resources. The best combination of
pollution reduction controls is that which is the most
cost-effective and feasible to implement. Allocation
scenarios typically reduce point source discharges
through NPDES permitting, reduce nonpoint source
loads through the implementation of best management
practices (BMPs), or use a combination of both.
Cost trade-offs are an important consideration when
developing alternative pollution allocation scenarios.
Point and nonpoint source trading is one cost-effec-
tive alternative for meeting water quality criteria or
other appropriate TMDL endpoints. Although it can
be implemented in many different forms, essentially
trading allocates pollutant loading reductions across
point and nonpoint sources using least cost as the
criterion (USEPA, 1992c). For example, in lieu of
upgrading their pollution control technology, point
source dischargers may be allowed to pay for equiva-
lent or greater reductions in nonpoint source loadings
within their watersheds. Trading is applicable when
implementation of nonpoint source BMPs is less
costly per unit of pollution reduction than upgrading
point source treatment technology.
4.6.2 Total Maximum Daily Loads
Application of a model to allocate waste loads and
nonpoint loads is usually done under 7-day, 10-year
low-flow conditions depending on the WQS being im-
plemented, and the type of waterbody (see Section
A.3.2). A temperature condition needs to be estab-
lished as well. There is no standard procedure in the
model application analysis. Figure 4-10 is a suggested
allocation procedure for BOD/DO in streams, the steps
of which are discussed below. The procedure does not
address cost/benefit issues.
The determination of the dissolved oxygen standard or
endpoint as the first step includes an evaluation of the
statistical requirements of the standard. Thus, if the
standard indicates that the dissolved oxygen should
never be less than 5 mg/L, then recognition should be
given to random uncontrollable variations in dissolved
oxygen. For streams and rivers, these fluctuations may
be on the order of a standard deviation of 0.25 mg/L.
Thus, if 0.5 mg/L is added to the standard, then the
4-27
-------
YES
ALLOCATION IS AS
GIVEN BY APPLIED LOADS
INCREMENT TREATMENT
LEVEL UNTIL DO
STANDARD IS VIOLATED
I
"EQUIVALENT"
RESERVE CAPACITY'
"See glossary for definition
DO STANDARD
I
DETERMINE UPSTREAM
AND BACKGROUND FLOW,
BOD AND DO CONDITIONS
I
INPUT ALTERNATIVES
LOADINGS SOURCES
I
APPLY WATER QUALITY
MODEL
i
7S DO STANDARD
ACHIEVED?
I
NO
NO
INCREMENT TREATMENT
LEVEL WITH EACH
SOURCE LOAD
IS DO STANDARD
ACHIEVED?
YES
I
MAXIMUM ALLOWABLE
LOAD
1
SELECT
"MARGIN OF SAFETY"
I
CHECK FOR UPPER
TECHNOLOGICAL
CONSTRAINT
FIGURE 4-10. TMDL PROCEDURE FOR BOD/DO PROBLEM
4-28
-------
resulting level of 5.5 mg/L represents the target mini-
mum level that, if attained, will meet the absolute
minimum level of 5 mg/L with only a 2.5 percent
chance of dropping below the standard. This does
not imply that the short-term fluctuations may or may
not be damaging to the ecosystem. That determina-
tion is part of the interpretation of the standard.
The selection of a background dissolved oxygen defi-
cit is subject to wide variation depending on the spe-
cifics of the area, such as urban, suburban, or rural
land use. Some States have determined background
percent saturation for specific ecoregions. The deficit
may be determined from upstream BOD and dis-
solved oxygen conditions and calculated through the
region of interest. This approach requires assignment
of BOD deoxygenation coefficients. A minimum effort
analysis would simply assign a constant dissolved
oxygen deficit throughout the river reach of 0 -1 mg/L
depending on the problem conditions. This step is
clearly subject to potentially widely varying engineer-
ing judgment. It should be noted that the use of a
1 -mg/L dissolved oxygen deficit may result in a signifi-
cantly higher degree of required treatment than that
resulting if no background is assigned.
The inputs from each of the point source discharges
are then estimated following general guidelines for
expected effluent concentrations. Nonpoint source
loadings are estimated from existing or collected wa-
tershed data. Often, nutrient budget studies are con-
ducted as part of the TMDL process to determine
approximate pollutant loadings contributed by non-
point sources. The remaining steps are as indicated.
The application of the water quality model may also
vary widely, depending on the level of effort involved,
from simplified desktop calculations to full-scale field
and calibration studies. If the dissolved oxygen stand-
ard is achieved with presently mandated effluent lev-
els, then the allocation is as given by those levels and
an equivalent reserve capacity can be estimated. In
some cases the dissolved oxygen standard may be
achieved by incrementing point source treatment by
discrete levels. However, nonpoint source controls
may be needed when further reductions in point source
waste loads are not possible or are cost-prohibitive.
The technological upper bound should be checked
here. The maximum allowable discharge load is then
the load needed to achieve the standard. However, this
is not necessarily the load to be allocated.
If relatively rapid growth is forecasted for an area,
then it is recommended that some fraction of the
maximum allowable load be placed in reserve for
future growth. A fraction of the maximum allowable
load can be set aside explicitly, or implicitly, as a
margin of safety to account for scientific uncertainty
about whether the TMDL reflects the actual loading
capacity of the waterbody. This uncertainty can be
caused by insufficient or poor-quality data or a lackof
knowledge about the water resource and pollutant
effects. Thus, if a margin of safety of 0.8 is chosen,
then 20 percent of the allowable load is placed in
reserve. The allocation is given by the margin of
safety times the maximum allowable load. However,
a final check should be made to ensure that the
required treatment level is technologically feasible. If
an upper technological treatment bound has been
exceeded, the margin of safety may have to be ad-
justed.
4.6.3 Uncertainty Analysis
Uncertainty analysis should be included as an integral
component of water quality modeling. One of the
primary purposes is to quantify the error in predicting
water quality and evaluate the effect of input parame-
ters on model output. Better management decisions
can be made by quantifying this error. Such quanti-
fication also facilitates subsequent studies, such as
risk assessments, to evaluate alternative allocations.
In addition, uncertainty analysis may provide insight
into the need for additional data collection to refine
the estimate of certain loads, initial conditions, or
reaction rates. For example, if the model is sensitive
to the reaeration rate (that is, a small change in
reaeration rate results in large changes in the predic-
tion of critical water quality parameters such as dis-
solved oxygen), it may be appropriate to allocate
resources to more accurately estimate the reaeration
rate of that stream or river.
Appendix D presents a discussion of the three tech-
niques for performing uncertainty analysis: sensitivity
analysis, first-order error analysis, and Monte Carlo
simulation. Each technique has advantages and dis-
advantages in terms of applicability and computa-
tional burden that will make one method more suitable
than another for a particular analysis. In many in-
stances, the modeler may need to explore the results
from all three procedures. The three methods may
produce discrepancies in their results because the
methodologies and assumptions differ. Each of
these techniques is available in QUAL2E-UNCAS,
and the discussion and example in Appendix D is
limited to the features available in that model.
4-29
-------
-------
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APPENDIX A. DEVELOPMENT OF MODEL
COEFFICIENTS AND CONSTANTS
A.1 OVERVIEW
As demonstrated in Chapter 2, a number of model coef-
ficients and constants are formulated in a stream water
quality model. Coefficient values can be obtained in four
ways:
• Direct measurement
• Estimation from field data
• Literature values
• Model calibration
Model calibration is usually required regardless of the
approach selected. However, coefficients that are site-
specific or those that can take on a wide range of values
should be measured directly or estimated from field
samples. The purpose of Appendix A is to provide
sufficient information and data to develop a consistent set
of model coefficients and parameter values for a TMDL
model analysis. For some model coefficients, additional
discussions are presented to address subtle technical
issues associated with the determination. This appendix
is organized to follow the materials presented in Chapter
2 and is summarized below.
A.1 Overview
A. 2 Loads
A.3 Physical Parameters
A.4 Carbonaceous Deoxygenation Rate
A.5 Nitrogenous Deoxygenation (Nitrification)
Rate
A.6 Stream Reaeration Rate
A.7 Sediment Oxygen Demand
A.8 Photosynthesis and Respiration
A.9 Phytoplankton Kinetic Rates
A.10 Nutrient Recycling Rates
A.11 Sediment Nutrient Release Rate
A.12 Temperature Effects on Reaction Rate
Coefficients
A.2 LOADS
A.2.1 Effluent Concentrations
As suggested in Chapter 2, point source inputs from
municipal wastewater treatment plants or publicly owned
treatment works (POTWs) and industrial facilities should
be measured for site-specific situations. However, if the
data are not readily available, typical effluent charac-
teristics reported for POTWs in the literature may be
used as a first approximation. In a study by Leo et al.
(1984), an extensive amount of POTW effluent infor-
mation was gathered and compiled to assess effluent
BOD5, CBODs, ammonia, CBODu-to-BODs ratios, and
CBODu-to-CBODs ratios for various treatment levels. In
total, information on these parameters was available from
approximately 114treatmentfacilities. TableA-1 presents
a summary of the effluent BODs, CBODs, and ammonia
concentrations for POTWs with various treatment levels.
Effluent BODs and CBODs concentrations are signifi-
cantly different (see Table A-1), reinforcing the findings by
Hall and Foxen (1984) that significant nitrification occurs
during BOD tests for many POTWs with secondary treat-
ment. For the 26 secondary treatment facilities in the
above study, the ammonia data were gathered during
intensive summer water quality surveys, indicating that
many secondary POTWs achieve some nitrification dur-
ing summer periods. It is likely that with in-plant nitrification
occurring, nitrifying bacteria present in the effluent can
cause oxygen consumption during the BODs test. The
BODs test would therefore tend to underestimate the
ability of the POTW to remove carbonaceous oxidizing
materials.
In general, only POTWs that practice phosphorus removal
to meet their NPDES permit effluent limits measure and
report phosphorus concentrations in the effluent. Lung
(1986b) reported an average total phosphorus concentra-
tion of 6.25 mg/L in the effluents of 18 secondary POTWs
in the Chesapeake Bay area (plants in Virginia, Maryland,
and Pennsylvania) that did not have phosphorus removal.
Phosphate detergents have been progressively banned
in the Chesapeake Bay region since that study. Recent
data collected from a number of POTWs in Hampton
Roads Sanitation District, Virginia, indicated up to a 50
percent phosphorus load reduction following the phos-
phate detergent ban, which became effective on January
1,1988 (Virginia Water Control Board, 1989). One should
note that phosphate detergent bans would have no effect
on the effluent concentrations at POTWs that remove
phosphorus to meet NPDES permits.
A number of texts, technical reports, and other literature
document influent and effluent characteristics of munici-
pal wastewater for various treatment levels. Tables A-1
through A-17 present data summarized by a number
A-1
-------
TABLE A-1. SUMMARY OF EFFLUENT CHARACTERISTICS
(After Leo et al., 1984)
POTW Effluent Concentrations (mg/L)
BODs
CBODs
Ammonia-N
Treatment Type
Primary
Trickling Filter
Secondary
Secondary + P-Removal
Secondary + Nitrification
Secondary + P-Removal + Nitri-
ficaton
Secondary + P-Removal + Fil-
ters
Number of
Locations3
2
13
38
9
10
3
3
Mean
101.0
41.2
19.1
16.2
11.5
13.6
3.9
Standard
Deviation Mean
21.2 —
27.8 —
16.3 10.3
14.0 14.6
11.8 4.8
18.6 —
2.0 —
Standard
Deviation Mean
— —
— 16.6
6.4 8.9
9.3 7.9
3.9 1.0
— 0.9
— 4.8
Standard
Deviation
—
12.2
6.3
8.9
1.4
0.7
8.2
s Number of locations with BODs data. In some cases, number with CBODs or Nhb data may be less.
of investigators that can be used to estimate effluent
characteristics.
A.2.2 Effluent CBODu-to-BODs or CBODu-to-
CBODs Ratios
The effluent CBODu-to-BODs or CBODu-to-CBODs ra-
tio is required in dissolved oxygen modeling analyses
to estimate POTW CBODU from effluent BODs or
CBODs data. This data is also needed to convert model
output (as CBODu) to NPDES permit limits (as CBODs).
A summary of this information is presented in Figure A-1
(Leo et al., 1984), suggesting a mean value of 2.47 for
CBODu-to-BODs and 2.84 for CBODu-to-CBODs.
Thomann and Mueller (1987) summarize the CBODu-
to-CBODs ratios for municipal wastes as 1.2 for no
treatment, 1.6 for primary/secondary, 3.2 for activated
sludge, and 2.84 for advanced primary. In the absence
of site-specific data, these ratios are reasonable ap-
proximations for a dissolved oxygen modeling analysis.
EPA strongly recommends that, whenever possible,
data from existing plant or pilot plant effluents be used
in the modeling analysis. In this case, long-term BOD
tests should be run to determine the Ki coefficient from
Equation 2-5 and consequently the CBODu-to-CBODs
ratio. However, caution should be exercised when
using data from an existing plant that has a treatment
level significantly less than that of a proposed plant.
In this case, the existing data should be used as a
guide. A model sensitivity analysis of the final WLA
with respect to the ratio should help the analyst to
judge the need for additional data.
The CBODu-to-CBODs ratio of industrial wastewater is
highly dependent on the type of industry manufacturing
processes, treatment schemes or operation, measure-
ment techniques, and other factors. Pulp and paper mill
effluent, for example, is characterized by very high ratios
of CBODu to CBODs because of the refractory nature
of the cellulose and compounds in the wastewater. For
many industrial wastewaters, the ratios also may vary
with BOD concentration.
A.2.3 Nonpoint Source Loads
Other loading rates for nonpoint loads such as combined
sewer overflows, urban storm runoff, and upstream back-
ground loads vary from one study area to another.
Thomann and Mueller (1987) and Novotony (1991,1992)
provide a brief summary of these loading rates. Mills et
al. (1985) present information on determining these
loads. Table A-2 lists some of the typical ranges as
described in the literature.
A-2
-------
TABLE A-2. TYPICAL RANGES OF POLLUTANT LOAD FOR SOURCES
Source
Range
Supplemental References
Domestic and Industrial
Point Sources
Upstream Background Levels:
Dissolved Oxygen Deficit
BOD5
NH3
N03
Organic N
Combined Sewer Overflow, BOD
Organic N
TN
Nonpoint sources (kg/ha/yr)
Urban
General
TN
TP
BODS
Residential
TN
TP
BODS
Commercial
TN
TP
BODS
NPDES Permits
Compliance Reports
0.5-2.Omg/L
0.5-3.0 mg/L
0.05-.27 mg/L
0.07-0.37 mg/L
0.05-0.50 mg/L
115 mg/L
3.8 mg/L
9.1 mg/L
6.69
6.37-8.00
8.12
5.62-7.14
17.23
1.57
0.40-3.19
1.20
0.89-4.46
1.33
58.97
34.23
0.87
4.77-7.16
6.69
0.17
0.48-0.79
1.03
28.55
28.67
7.34
2.39-9.56
17.83
0.55
0.07-0.71
2.70
13.03
78.03
a, b, c, d, e
g, i, Use STORET
f, g, h, Use STORET
f, g, h, Use STORET
f, Use STORET
f, g, Use STORET
d, h,j
d, h,j
d, h,j
m
n
o
k
I
m
n
o
k
m
m
k
I
m
k
m
m
k
I
m
k
m
A-3
-------
TABLE A-2. (Continued)
Source
Agricultural
General
TP
Cropland
TN
TP
Improved Pasture
TN
TP
Pasture
TN
TP
Forested TN
Range
0.63-59.71
0.08-7.16
20.46
4.77-47.77
0.09-10.35
18.71
0.83
0.24-5.58
0.04-2.32
5.45
5.02
3.98-11.95
0.92
0.08-0.48
4.17
2.31
0.24
0.44
2.44
0.79-6.37
2.41-10.35
Supplemental References
I
I
k
I
n
o
k
I
n
0
k
I
k
I
k
0
k
0
k
I
n
a Leo et al., 1984
b Metcalf and Eddy, 1972
c Mueller et al., 1976
d Thomann and Mueller, 1987
e Mueller et al., 1982
f Hydroscience, 1975
g Hydroscience, 1968
h Metcalf and Eddy, 1977
i Manhattan College, 1980
j USEPA, 1976a
k Shahane, 1982
I Novotny and Chesters, 1981
m NURP, 1983
n Sweeten and Melvin, 1985
o Haith and Shoemaker, 1987
A-4
-------
TABLE A-3. REPORTED VALUES OF SELECTED WASTE INPUT
PARAMETERS IN THE UNITED STATES
(after Thomann and Mueller, 1987)
Variable
Average daily flow
Total suspended solids
CBODs9
CBODu9
NBOD9
Total nitrogen
Total phosphorus
Total coliforms
Cadmium
Lead
Chrome
Copper
Zinc
Total PCB
Units3
gcd
mg/L
mg/L
mg/L
mg/L
mg-N/L
mg-P/L
106/100mL
mg/L
mg/L
M9/L
|ig/L
mg/L
mg/L
Municipal
Influent"
125
300
180
220
220
50
10
30
1.2
22
42
159
241
0.9
csoc
410
170
240
290
9
3
6
10
190
190
460
660
0.3
Urban Agriculture
Runoff11 (Ib/mi2-day)e
610 2500
27 40
2.3 15
0.5 1.0
0.3
13
280
22
110
500
Forest Atmosphere
(Ib/mi2-day)e (Ib/mi2-day)f
400
8
4 8.9-18.9
0.3 0.13-1.3
0.015
1.3
0.088
1.8
0.002-0.02
Units apply to municipal influent, combined sewer overflow (CSO), and urban runoff sources; gcd = gallons per capita per day.
b Thomann (1972); heavy metals and PCB, HydroQual (1982).
c Thomann (1972); total coli, Tetra Tech, (1977); heavy metals DiToroetal. (1978); PCB, Hydroscience (1978).
d Tetra Tech (1977); heavy metals, Di Toro et al. (1978).
e Hydroscience (1976).
f Nitrogen and phosphorus, Tetra Tech (1982); heavy metals and PCB, HydroQual (1982).
9 CBOD5 = 5 day carbonaceous biochemical oxygen demand (CBOD); CBODu = ultimate CBOD; NBOD = nitrogenous BOD.
TABLE A-4. APPROXIMATE COMPOSITION OF AN AVERAGE DOMESTIC WASTEWATER (mg/L)
(after Clark etal., 1977)
Before Sedimentation
After Sedimentation
Biologically Treated
Total solids
Total volatile solids
Suspended solids
Volatile suspended solids
BOD
Ammonia nitrogen as N
Total nitrogen as N
Soluble phosphorus as P
Total phosphorus as P
800
440
240
180
200
15
35
7
10
680
340
120
100
130
15
25
7
530
220
30
20
30
20
20
7
7
A-5
-------
TABLE A-5. MUNICIPAL WASTE CHARACTERISTICS BEFORE TREATMENT
(after Thomann, 1972)
Variable
Unit
Approx. Average
Normal Range
Avg. Daily Flow
Solids -Total
Total Volatile
Total Dissolved
Total Suspended
Volatile Suspended
Settleable
CBOD (5-day)a
CBOD (ultimate)
NBODb
Total Nitrogen
Organic Nitrogen
Ammonia Nitrogen
Nitrate + Nitrite
Total Phosphate
Ortho Phosphate
Poly-Phosphate
Total Coliforms
Fecal Coliforms
gal/cap/day
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/L
mg/LN
mg/L N
mg/LN
mg/L N
mg/L PO4
mg/L PO4
mg/L PO4
million/1 OOmL
million/1 OOmL
125
800
400
500
300
130
150
180
220
220
50
20
28
2
20
10
10
30
4
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
CBOD - Carbonaceous oxygen demand.
bNBOD - Nitrogenous oxygen demand, ultimate; exclusive of CBOD.
TABLE A-6. TYPICAL COMPOSITION OF RAW DOMESTIC SEWAGE
(All values except settleable solids are expressed in mg/L)
(after Metcalf & Eddy, 1972)
Concentration Before Treatment
Constituent
Solids, total
Dissolved, total
Fixed
Volatile
Suspended, total
Fixed
Volatile
Settleable solids, (mL/L)
Biochemical oxygen demand, 5-day, 20
°C (BOD5@20°C)
Total organic carbon (TOC)
Chemical oxygen demand (COD)
Nitrogen, (total as N)
Organic
Free Ammonia
Nitrites
Nitrates
Phosphorus (total as P)
Organic
Inorganic
Chlorides8
Alkalinity (as CaCO3)a
Grease
Strong
1200
850
525
325
350
75
275
20
300
300
1,000
85
35
50
0
0
20
5
15
100
200
150
Medium
700
500
300
200
200
50
150
10
200
200
500
40
15
25
0
0
10
3
7
50
100
100
Weak
350
250
145
105
100
30
70
5
100
100
250
20
8
12
0
0
6
2
4
30
50
50
Values should be increased by amount in carriage water.
A-6
-------
TABLE A-7. TYPICAL MUNICIPAL WASTEWATER CHARACTERISTICS
(After Mueller et al., 1976)
Concentration (mg/L)
Parameter
NYC
Raw Sewage
NJ
Primary Effluent
NYC
Secondary Effluent
SS
ALK
BOD5
COD
TOC
MBAS
Oil & Grease
NH3-N
Org-N
NO2+NO3-N
Total N
Ortho-P
Total P
Cd
Cr
Cu
Fe
Hg
Pb
Zn
Fecal Coll (cells/100ml_)
Total Coll (cells/1 OOmL)
Total Coll after Chlorination
(cells/100mL)
139
190
131
2.5xBOD5
83
10
36
10.6
10.4
0.68
21.7
3.27
4.70
0.018
0.15
0.23
2.5
0.033
0.26
0.39
0.44xT.Coli
50x1O6
93
190
158
2.5XBOD5
0.68x BODs
10
23
0.58xTot.N
0.69xNH3-N
0.02 x Tot. N
22
0.7xTot.P
6.14
0.012
0.057
0.105
0.70
0.025
0.190
0.185
0.44xT.Coli
15x106
357
43
170
36
4.7xBOD5
0.94XBOD5
1.0
15
0.64xTot.N
0.53xNH3-N
0.02 x Tot. N
22
0.7xTot.P
3.30
0.012
0.057
0.105
0.70
0.025
0.190
0.185
0.44xT.Coli
2.5X106
357
A-7
-------
TABLE A-8. TYPICAL MUNICIPAL WASTEWATER CHARACTERISTICS
FOR CONVENTIONAL POLLUTANTS AND MOST METALS
(after Mueller et al., 1982)
Parameter
SS
BOD
TOC
NH3-N
ORG-N
N02-N
NO3-N
Ortho-P
Total-P
Fecal Coliform
(MPN/100ml_)e
Winter
Summer
Cadmium
Chromium
Copper
Cyanide
Lead
Mercury
Nickel
Zinc
NYC Raw
Sewage3 (mq/L)
110
104
93
10
13
0.07
0.38
2.0
3.2
3x106
3x106
1.2
42
159
92
22
1.3
45
241
Middlesex County
NJ Primary Secondary
Effluent" (mq/L) Effluent0
105
218
151
22
13
0.06
0.51
7.7
9.3
33
33
14
68
185
92'"
211
0.62
105
365
43
39
128
11
17
0.16
3.6
3.5
2.3
33
33
12
34
334
57
77
0.2
37
4800
NYC
Secondary
Effluentd (mq/L)
20
15
39
7.9
6.1
0.19
1.3
1.6
2.1
1.5x105
33
1.1
16
93
52
11
0.57
37
101
Not including Newton Creek and Bowery Bay (high industry).
14 New Jersey plants.
SS, BOD, TOC, ORG-N, and ortho-P from ISC data. All other from Middlesex County (NJ) quarterly reports.
Not including Coney Island, Newton Creek, and Owls Head (intermediate treatment) and Bowery Bay (high industry).
NYC raw from 208 study, NJ primary, Middlesex County, and NYC secondary from NYC summer 1980 and NYC winter
from Lake Tahoe, California.
NYC raw concentration assumed.
A-8
-------
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A-9
-------
TABLE A-10. MASSACHUSETTS WATER RESOURCES AUTHORITY (MWRA)
BOSTON HARBOR PILOT PLANT WASTEWATER EFFLUENT LEVELS
(After Metcalf & Eddy, 1989)
(in mg/L unless otherwise specified)
Effluent Parameter
Total CBODs
Soluble CBODs
Paniculate CBODs
Particulate/Total CBODs
Total COD
Soluble COD
Particulate COD
Particulate/Total COD
Total SS
TKN
NH3-N
Total N
N03-N + N02-N
Total P
MWRA Primary
Effluent
112
44.80
67.20
60%
253
93.61
159.39
63%
136
16
11
16.33
0.33
4.13
MWRA Secondary
Effluent
9
3.05
5.94
66%
50.50
37.87
12.62
25%
15
11
8.10
11.22
0.22
1.88
Data Source
MWRA Pilot
TotarParticulate
Total'Particulate/Total
MWRA Pilot
MWRA Pilot
TotarParticulate
Total'Particulate/Total
MWRA Pilot
MWRA Pilot
MWRA Pilot
MWRA Pilot
TN=TKN/0.98
NO3=TN*0.02
MWRA Pilot
TABLE A-11. EFFECT OF VARIOUS TREATMENT OPERATIONS AND
PROCESSES ON PHOSPHORUS REMOVAL3
(after Metcalf & Eddy, 1991)
Treatment Operation or Process
Removal of Phosphorus Entering System (%)
Conventional treatment
Primary
Activated-sludge
Trickling-filter
Rotating biological contactors
Biological phosphorus removal only
Mainstream treatment
Sidestream treatment
Combined biological nitrogen and phosphorus removal
Chemical removal
Precipitation with metal salt
Precipitation with lime
Physical removal
Filtration
Reverse osmosis
Carbon adsorption
10-20
10-25
8-12
8-12
70-90
70-90
70-90
70-90
70-90
20-50
90-100
10-30
Adapted in part from Ref. 24 cited in Metcalf & Eddy (1991).
A-10
-------
TABLE A-12. EFFECT OF VARIOUS TREATMENT OPERATIONS
AND PROCESSES ON NITROGEN COMPOUNDS3
(After Metcalf & Eddy, 1991)
Nitrogen Compound
Treatment Operation
or Process
Conventional treatment
Primary
Secondary
Organic Nitrogen
10-20% removed
15-50% removed0 urea
— > NH3-NH4d
NH3-NH4
No effect
< 1 0% removed
N03
No effect
Slight effect
Removal of Total
Nitrogen Entering
Process, %b
5-10
10-30
Biological processes
Bacterial assimilation
Denitrification
Harvesting algae
Nitrification
Oxidation ponds
Chemical processes
Breakpoint chlorination
Chemical coagulation
Carbon adsorption
Selective ion exchange for
ammonium
Selective ion exchange for
nitrate
No effect
No effect
Partial transformation to
NH3-NH4d
Limited effect
Partial transformation to
NH3-NH4
Uncertain
50-70% removed
30-50% removed
Slight, uncertain
Slight effect
40-70% removed
No effect
—> Cells
—> N03
Partial removal by
stripping
90-100% removed
Slight effect
Slight effect
80-97% removed
Slight effect
Slight 30-70
80-90% removed 70-95
—> Cells 50-80
No effect 5-20
Partial removal by 20-90
nitrification/denitrification
No effect 80-95
Slight effect 20-30
Slight effect 10-20
No effect 70-95
75-90% removed 70-90
Physical operations
Filtration
Air stripping
Electrodialysis
Reverse osmosis
30-95% of suspended
organic N removed
No effect
100% of suspended
organic N removed
60-90% removed
Slight effect
60-95% removed
30-50% removed
60-90% removed
Slight effect
No effect
30-50% removed
60-90% removed
20-40%
50-90%
40-50%
80-90%
A-11
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o
JE;
1
P
A-12
-------
TABLE A-14. REMOVAL OF NITROGEN FROM SEWAGE EFFLUENTS
(After Ketchum, 1982)
Effect on Constituent
Treatment process
Organic-N
Ammonia-N
Nitrate-N
Removal of Total
Nitrogen Entering
Process (%)
Conventional treatment processes
Primary
Secondary
10-20% removed no effect no effect
15-20% removed <10% removed nil
urea —> NH3/NH4
5-10
10-20
Advanced wastewater treatment
processes
Filtration
Carbon sorption
Electrodialysis
Reverse osmosis
Chemical coagulation
Other nitrogen removal processes
Selective ion exchange for nitrate
Oxidation ponds
Algae stripping
Bacterial assimilation
30-95% removed
30-50% removed
100% of suspended
organic N removed
100% of suspended
organic N removed
50-70% removed
nil
partial
transformation to
NH3/NH4
partial transforma-
tion to Nhb/NhU
no effect
nil
nil
40% removed
85% removed
nil
nil
partial removal by
stripping
— > cells
40-70% removed
nil
nil
40% removed
85% removed
nil
75-90% removed
partial removal by
nitrification-
denitrification
— > cells
limited effect
20-40
10-20
35-45
80-90
20-30
70-90
20-90
50-85
30-70
TABLE A-15. TOTAL NITROGEN AND PHOSPHORUS CONCENTRATION (MEDIAN) IN WASTE-
WATER EFFLUENTS FOLLOWING FOUR CONVENTIONAL TREATMENT PROCESSES
(After Ketchum, 1982)
Primary
Treatment Type
Trickling Filter
Activated Sludge
Stabilization Pond
No. of plants sampled 55
Total P (mg/L) 6.6 ± 0.66
Total N (mg/L) 22.4 ±1.30
N:P (weight) (mg N/mg P) 3.39
N:P (atoms) 7.52
(mg-at N/mg-at P)
244
6.9 ±0.28
16.4±0.54
2.38
5.26
244
5.8 ±0.29
13.6 ±0.62
2.34
5.19
149
5.2 ±0.45
11.5± 0 .84
2.21
4.90
A-13
-------
TABLE A-16. AVERAGE WASTE REDUCTION EFFICIENCIES OF VARIOUS
CONTROLS OPERATING ON MUNICIPAL WASTE
(After Metcalf & Eddy, 1991)
Percent Reduction3
Control
Conventional Treatment
Primary settling
Intermediate-chemical treatment
Secondary-primary and trickling filter
Secondary-primary and
conventional activated sludge
Advanced Treatment
Secondary, nitrification and
denitrification
Secondary and coagulation,
settling filtration
Secondary and coagulation and
adsorption
Secondary and coagulation and
adsorption and electrodialysis
CBOD
25-40
40-65
65-85
85-90
90-95
95
99C
99C
Suspended
Solids
20-60
60-80
60-80
90
95
99
99
99
Total
Nitrogen
10-20
20-30
20-40
20-40b
90
50
55
75
Dissolved
Solids
-
-
-
5
5
10
15
50
Total
Phosphorus
-
-
-
10
10
95
95
97
Percent reduction based on raw waste concentration.
Longer aeration times convert oxidizable nitrogen to nitrate.
Minimum CBOD of about 2-5 mg/L.
TABLE A-17. MEDIAN AND MEAN PHOSPHORUS AND NITROGEN CONCENTRATIONS AND
MEDIAN LOADS IN WASTEWATER EFFLUENTS FOLLOWING FOUR
CONVENTIONAL TREATMENT PROCESSES
(After Gakstatter et al., 1978)
Number of Sampled Plants
Total Population Served
Ortho-P Cone, (mg/l)
Total-P Cone, (mg/l)
Total-P Load (cap-y)
Total-N Load (kg/cap -y)
Inorganic-N Cone, (mg/l)
Total-N Cone, (mg/l)
Total-N Load
TN:TP Ratio
Per Capita Flow (1/cap • d)
Median
Mean
Median
Mean
Median
Median
Median
Mean
Median
Mean
Median
Median
Median
Primary
55
1,086,784
3.5±0.29a
4.0 ±0.62
6.6 ±0.66
7.7±1.19
1.1 ±0.10
3.7
6.4 ±1.00
8.3 ±1.40
22. 4± 1.30
23. 8 ±3. 48
4.2 ±0.40
3.4
473 ±72
Treatment Type
Trickling
Filter
244
3,459,893
5.1 ±0.21
5.4 ±0.38
6.9 ±0.28
7. 2 ±0.50
1.2 ±0.05
2.9
7.1 ±0.38
8.2 ±0.60
16.4±0.54
17. 9 ±1.23
2. 9 ±0.1 7
2.4
439 ±19
Activated
Sludge
244
4,357,138
4.6 ±0.24
5. 3 ±0.40
5. 8 ±0.29
6.8 ±0.51
1.0 ±0.06
2.4
6.5 ±0.45
8.4 ±0.69
13.6±0.62
15.8±1.16
2.2±0.15
2.4
394 ±26
Stabilization
Pond
119
270,287
3. 9 ±0.34
4.8 ±0.62
5. 2 ±0.45
6.6 ±0.81
0.9 ±0.10
2.0
1.3±0.29
5. 5 ±1.95
11. 5 ±0.84
17.1 ±3.59
2.0 ±0.26
2.2
378 ±38
A-14
-------
(a)
nj.U
5.5
O1 4.0
O
£0 3,0
•s,
J 2.0
3
O
00
u 1.0
0,8
1.
« 50
0 4'°
e 3.0
*v
5 2,0
3
Q
O
CO
u 1.0
rt«l
•
- *
rM{.&H +S $TQ OEV A
" 1 ..----... •
mm * * »
~~ » r-ME&N- 2.4?
. • •••• ... . ••
* »
I ^.MEAN-I STO, DEV.
JL i I 1 I i ( | J t I 1 1 ! 1 1 !
0 3.0 10.0 50.O SOO.O
EFFLUENT B008 (mi/1 )
(b)
•
[_ r-MEAM4§l STO.D6V. * «
^* * • * * ^-MEAN= 2.84
_ » . • • •
""**" V **^-*-% **
^-MEAN -i STO, DEV, *
i i i 1 i ' i i 1 i i i 1 i i i i
5.0 10.0 50.0 IOO.O
EFFLUENT CSOOS (mg/l 1
FIGURE A-1. POTW EFFLUENT ULTIMATE CBOD AS A FUNCTION OF CBODs AND BOD5
(After Leo et al., 1984)
A-15
-------
These loading rates represent those rates found at
specific sites across the country. In any water quality
modeling analysis, site-specific data should be col-
lected.
A.3 PHYSICAL PARAMETERS
A.3.1 Hydraulic Geometry Data
Hydraulic data include the velocities, flows, and water
depths. Flows include the flows at upstream bounda-
ries of all channels, as well as all significant tributary
inflows, lateral inflow (from groundwater or runoff),
flow diversions, return flows, and stage at some loca-
tions. If wastewater flows represent a significant
portion (i.e., greater than 5 to 10 percent) of the total
stream flow, they should be included in the hydraulic
analysis.
While the upstream boundary, tributary, and diver-
sion flows can be measured directly, lateral inflows
from groundwater or runoff can be estimated from
differences in measured flow at different locations
along the stream channel. USGS official flow records
are annually published several months to a year after
the end of the water year, which ends September 30.
All USGS flow data are available through EPA's
mainframe computer. Under special contract, USGS
is able to furnish the records for the period of a stream
study as soon as the stream stage data can be
converted to flow. These records may be designated
as tentative or provisional, but are adequate for all but
the strictest legal uses. The U.S. Army Corps of
Engineers and the U.S. Bureau of Reclamation main-
tain stream flow records on streams for which they
have special responsibilities. In addition, some State
regulatory agencies only rarely make stream flow
measurements for selected streams.
As indicated in Section 2.3.3, mathematical models
such as Manning's Equation and stream hydrody-
namic models can be used to quantify the stage-flow
relationships for each channel reach in a stream.
One of the simple stream hydrodynamic models is
RIVMOD (USEPA, 1990). Power functions may also
be developed relating flow with velocity, depth, and
cross-sectional area (see Equations 2-1 through 2-3).
It can be shown that the sum of the exponents (m +
n + f) and the product of the coefficients (abc) from
Equations 2-1 through 2-3 are unity because of the
continuity equation. Using this and experience from
a variety of streams, the value of the exponents can
be approximated as follows (Barnwell et al., 1989):
n = range (0.4 - 0.6); typical 0.43
m =
range (0.3 - 0.5); typical 0.45
f = range (0 - 0.2); typical 0.12
Impounded reaches in rivers have exponents m and
f = 0, and n = 1. Where the analyst has more than
one set of data, a log-log plot of area, depth, and
velocity against stream flow will permit extrapolation
to other flows of interest. The slope of such plots
provides the local value of the exponents (see Figure
A-2). When data at only a single flow regime are
available, estimates for other flows can be developed
by the following ratios, derived from the foregoing
relationships:
velocity:U2/Ui =
0.43
depth:
H2/Hi = (Q2/Qi)
0.45
cross-sect. A2/Ai = (Q2/Qi)
area:
0.43
travel time: T2/Ti = (Q2/Qi)
0.43
(A-1)
(A-2)
(A-3)
(A-4)
It should be recognized that these relationships exist
only in free-flowing streams and care should be exer-
cised when upstream dams or hydropower facilities
are present that may interfere with the assumption of
the analysis. It is also common to collect site-specific
data since the exponents may vary by 50 percent for
any river.
A.3.2 Low-Flow Analysis
Generally, the minimum average 7-day flow expected
to occur once every 10 years is used in modeling
analyses depending on the state WQS and water
body assessed. However, several different types of
flows can be estimated from a hydrologic record. For
example, the minimum average 7-day flow occurring
at any time in a year can be estimated, or the mini-
mum average flow in a given month or season can be
computed. Figure A-3 shows the low-flow frequency
curves for the Potomac River at Point of Rocks de-
veloped using the USGS flow records from 1891 to
1981. Table A-18 presents a summary of data ob-
tained from Figure A-3. The analysis to determine the
low-flow frequency curve is simple and straightfor-
ward; Thomann and Mueller (1987) provide an easy-
to-follow procedure.
A-16
-------
River Geometry
10
1 -r
Shallow Channel
Depth =0,565
•vQ.48
0,1 1.0 10.0 100.0
Flow (m1,'*)
Deep
10
1
I
1
Depth «1,412 Qfl
0.1 1.0 IO-.0 100-0
100
I
River Velocity sha||ow
1,00
I
0.10
0.01
Velocity « 0.065 Q'
0,1
Rovrtm1/*)
1000
10.0 100JO
1COO
1
100
Araa -S7.6Si QQSf
Deep Channel
i.oo
I
I
0.10 • •
0,01
Velocity » 0,017
0.1
1.0 10.0
Flowfn'lk)
O.I 1.0 10.0 100.0
1CO.O
FIGURE A-2. EMPIRICAL RELATIONSHIPS FOR HYDRAULIC GEOMETRY
A-17
-------
"""" " ^— "" •! - 1 1 <- W |
r^ -— |p~U-i '
" ' — —• _L: - -L- - '
_. .' - \\~ "i~: "
\1
. „_. ^*^3
^ , »'^ i'=«- -"'-=» r- .i..«i.^i.-a .
t \ ' ' ' '
rbt= ~t===
\i X . ,.
V : - -i li \
, — y v ^ ,---. ;-r^ _._;
:t|
1 "'" ""
_: vi iv
— -VM-V—^ i
Ct
a
o>
O
O
00
2
LU LU
> D
o
Q.
A-18
-------
TABLE A-18. LOW FLOW RECURRENCES, POTOMAC RIVER
AT POINT OF ROCKS, MARYLAND
(1891 -1981)
Recurrence
Interval
(years)
5
10
50
Probability
of Occurrence
(% time flow
< flow plotted)
20%
10%
2%
7-day
950
825
625
Mean Annual Low Flow (cfs)
30-day 90-day
1200 1500
1005 1250
800 910
365-day
6600
5600
4000
A.3.3 Time-of-Travel Survey
Time of travel can be determined by several different
methods. The three principal methods involve use of
surface floats, use of a tracer such as a dye or
radionuclide, and measurement of cross-sectional
areas.
Surface floats can be followed downstream and timed
for known distances to determine times of travel. This
approach requires considerable judgment since
floats tend to travel into eddies or become trapped on
tree limbs, stream banks, or other obstacles. The
floats must be frequently retrieved and returned to the
current of the stream. The principal judgment factors
are how long the floats should be left in quiet areas
before retrieval and where they should be placed in
the current. The surface water velocity is greater than
the average for the entire stream, and a correction
factor must be applied to the surface velocity; an
average velocity equal to 85 percent of the surface
velocity is a reasonable rule of thumb. Oranges make
very good floats since their density is such that they
float with only a small portion of their tops exposed to
wind action and their color is easily detected and
followed in the water.
Measurement of cross-sections at frequent longitudi-
nal intervals and calculation of average velocity from
the average cross-section and stream flow at the time
of measurement constitute a time-consuming method
of obtaining time of travel. This method does, how-
ever, produce information that is useful for other
purposes. For example, reaeration coefficients may
be calculated by one of the formulas based on aver-
age depths and velocities.
The most accurate method of measuring time of
travel, and a good way to measure velocity, involves
following a tracer downstream. An industrial waste
may include an occasional discharge of some con-
stituent that can serve as a tracer. Radioisotopes
have given good results, but their safe handling can
present problems. Several kinds of dyes have been
used, including the recent trend of using Rhodamine
WT. This dye can be detected in concentrations as
low as 0.05 part per billion (|ig/L) by a fluorometer.
The dye is distributed across the stream at the up-
stream point, as nearly instantaneously as possible.
Because of longitudinal mixing (see Figure 2-1), the
dye arrives downstream in a wide band. The time of
travel to a downstream point is the difference be-
tween the time the dye was released to the stream
and the time the centroid of the dye mass arrives at
the downstream point. Two handbooks by the USGS
(Hubbard et al., 1982 and Wilson et al., 1986) provide
step-by-step procedures to conduct a time-of-travel
study. Figure A-4 shows the hydraulic geometry and
time-of-travel data for the Kalamazoo River in Michi-
gan under various stream flow conditions.
A.3.4 Longitudinal Dispersion Coefficient
Although the mechanics of longitudinal dispersion are
well understood, general analytical treatment is ex-
tremely difficult, if not impossible. Theoretical devel-
opment has led to a number of equations to calculate
longitudinal dispersion in one-dimensional stream
models. One equation suggested by Fischer et al.
(1979) is:
Dx
0.011L/2 I/I/2
HU*
(A-5)
where
Dx
= longitudinal dispersion
coefficient (ft2/sec)
U = average velocity (ft/sec)
I/I/ = river width (ft)
H = river depth (ft)
U* = shear velocity (ft/sec)
Since the exact effect of irregularities cannot be in-
cluded and, for most applications, results are insen-
sitive to the exact value used, it is generally not
A-19
-------
§1
H* ^
*
u
tt >
O
o
Al
O
JWU
FIGURE A-4. HYDRAULIC GEOMETRY AND TIME OF TRAVEL
A-20
-------
necessary to achieve a high accuracy in predicting
dispersion coefficients (Fischer et al., 1979). Equa-
tion A-5 provides a good approximation to longitudinal
dispersion coefficients for a number of rivers, as
shown in Table A-19.
A.4 CARBONACEOUS
DEOXYGENATION RATE
A.4.1 Using Field Data to Determine Krand Kd
The carbonaceous deoxygenation rate coefficient
can be estimated from field data by plotting CBOD
measurements versus time of travel on semi-log pa-
per, based on Equation 2-7. The rate of deoxygena-
tion is estimated as the slope of the line that best fits
the data points:
Kr=-
In (L/Lo)
t
(A-6)
where
L
oxygen equivalence of the
organic matter at any given
location in the stream (mg/L)
Lo = total oxygen demand measured
at the source of waste load
following complete mixing
(mg/L)
t = time of travel (day)
The above equation, based on concentrations, is
applicable for constant hydraulic geometry. In prac-
tice, the river channel changes frequently and addi-
tional flow from tributaries may provide dilution to the
river flow, all affecting the BOD concentrations. A
more practical approach to estimating the deoxy-
genation rate coefficient is to plot the mass loading
rate (kg/day) of BOD instead of concentration. The
mass loading rate at any given location in the river is
the product of measured BOD concentration and river
flow. Figure A-5 shows such a plot for Rock Creek,
Pennsylvania. Note that the tributaries provide dilu-
tion along the stream.
In Rock Creek, a two-stage curve is obtained. The
first part of the curve is steep, showing that the total
removal rate (Kr) results when both settling and bio-
logical oxidation are significant. The second part, a
more gradual slope, generally represents the CBOD
deoxygenation rate (Kd) after most of the settling has
taken place. The settling rate (Ks) can then be esti-
mated as the difference between Krand Kd.
The above procedure is valid for either CBODs or
CBODu provided that the laboratory coefficients, Ki,
are identical for all stations. If Ki values vary from
station to station, it is necessary to use CBODU.
Leo et al. (1984) evaluated the change in Kd following
the installation of higher treatment levels at POTWs.
The data indicate that Kd values associated with
advanced treatment levels are generally lower than
those determined for lesser treatment levels.
Algae can affect the CBOD data used to calculate Kd.
Algal respiration and decay in the CBOD bottle can
TABLE A-19. LONGITUDINAL DISPERSION COEFFICIENT IN RIVERS
(After Fischer et al., 1979)
River
Missouri River
Clinch River,
Tennessee
Bayou Anacoco
Nooksack River
Wind/Bighorn Rivers
John Day River
Comite River
Sabine River
Yadkin River
H
(m)
2.70
0.85
2.10
2.10
0.94
0.91
0.76
1.10
2.16
0.58
2.47
0.43
2.04
4.75
2.35
3.84
W
(m)
200
47
60
53
26
37
64
59
69
25
34
16
104
127
70
72
U
(m/sec)
1.55
0.32
0.94
0.83
0.34
0.40
0.67
0.88
1.55
1.01
0.82
0.37
0.58
0.64
0.43
0.70
if
(m/sec)
0.074
0.067
0.104
0.107
0.067
0.067
0.27
0.12
0.17
0.14
0.18
0.05
0.05
0.08
0.10
0.13
Dx(m2/sec)
Measured
1500
14
54
47
33
39
35
42
160
14
65
14
315
670
110
260
Dx(m2/sec)
Using Eq. A-5
5290.8
43.7
100.2
94.7
13.6
39.5
98.6
224.6
342.7
86.4
23.5
17.9
392.4
191.2
42.4
66.0
References
Yotsukura et al.
(1970)
Godfrey and
Frederick (1970)
(predicted Dx
from Fischer,
1968)
McQuivey and
Keefer(1974)
(predicted Dx
from
Fischer, 1975)
A-21
-------
93
•q
C3
3
Q
O
CO
u
19
J3
O
en
1
August 8-9,1979
Temperatyri =•
i •-
2 « * t ia.
MILiS FROM CUMBERLAND WASTEWATER TREATMENT PLANT
FIGURE A-5. DETERMINATION OF CBOD REMOVAL AND DEOXYGENATION RATES FOR ROCK
CREEK, PENNSYLVANIA
A-22
-------
cause higher measured CBOD values and thus
higher Ki rates compared to samples without algae.
In addition, if the concentration of suspended algae
is not constant in the stream below the discharge, the
measured CBOD concentrations would not indicate
a defined Kd. Where the concentration of suspended
algae increases in the stream, there may be a net
increase of measured CBOD below the discharge.
To minimize these effects, filtered CBOD and total
CBOD samples should be analyzed at several loca-
tions downstream of the discharge. The oxygen de-
mand resulting from settleable (i.e., filtered) organics
is then accounted for separately in establishing the
Ks (BOD settling) and SOD rates. However, even
with filtered and unfiltered CBOD data, it is difficult to
select rates for model calibration and projection
analyses of algae-dominated streams. Where large
concentrations of algae occur in the receiving stream,
a range of Kd rates should be estimated based on
filtered and unfiltered CBOD data. Some general
rules of thumb follow:
• Algal impacts on Kd occur wherever high
concentrations of chlorophyll a or large diur-
nal dissolved oxygen fluctuations are meas-
ured.
• 10 |j,g/L of chlorophyll a will increase the
CBODu concentration by 1 mg/L above lev-
els without algae. Rough estimates can be
obtained from multiples of this relationship;
i.e., 100 |j,g/L of chlorophyll a may increase
the concentration by 10 mg/L.
• If the stream is effluent-dominated with most
of the CBOD originating from the discharge
rather than algae, filtering may not be needed
or the number of filtered CBOD analyses may
be decreased. If the stream is not effluent-
dominated and most of the CBOD is from
algae, filtered and unfiltered samples should
be run.
A.4.2 Projection of Carbonaceous
Deoxygenation Rates
In wasteload allocations, Kd rates are projected for
future conditions. Literature data have been com-
piled (Figure A-6) to correlate Kd with the stream
depth in lieu of any other parameters. The rationale
behind this correlation is that the greater the wetted
perimeter, the greater the contact with the biological
community in the streambed, the most important
factor in natural oxidation processes. The tendency
for this relation to hold is greater for rocky streambeds
than for silty beds. However, the general trend ap-
pears reasonable up to depths of about 5 to 10 ft.
Hydroscience (1971) developed the following rela-
tionship:
. n o \H-. -0.434
f= U.6 [—\
forO8
(A-7a)
(A-7b)
where H is the depth in feet. Wright and McDonnell
(1979) suggested the following:
Kd=10.3Q
-0.49
(A-8)
where Q is stream flow in cfs. They also indicated
that for flow conditions greater than 800 cfs, Kd rates
were consistent with Ki for the effluent. In other
words, for larger and deeper streams (greater than
10 ft), the characteristics of the streambed become
less of a factor and the level of treatment would
dictate the following Kd values:
• Primary 0.4 day"1
• Intermediate 0.3 day"1
• Secondary 0.2 day"1
• Advanced 0.1 day"1
That is, for increasing levels of treatment, the residual
waste contains a large proportion of refractory organ-
isms and will be less easily oxidized since the treat-
ment processes are designed to oxidize the labile
components of the organic matter.
A.4.3 Literature Values of Kd
Bowie et al. (1985) summarized a large number of
carbonaceous deoxygenation rate coefficients re-
ported in the literature (Table A-20). Leoetal. (1984)
provided a comparison of Kd rates before and after
the improvement in stream dissolved oxygen condi-
tions following treatment upgrades (Table A-21).
A.5 NITROGENOUS DEOXYGENATION
(NITRIFICATION) RATE
A.5.1 Using Field Data to Determine Kn
The procedure described in Section A.4.1 (see Figure
A-5) may be used to develop the nitrification coeffi-
cient, Kn, for NBOD. Either the nitrogenous compo-
nents of the laboratory BOD test or the directly
measured ammonia concentrations at the various
locations in the stream may be used. Each should
yield the same value of Kn following the first-order
reaction. The displacement of the curves is due to
the stoichiometric relation between oxygen and am-
A-23
-------
0.3 0.5 1 1,6 5 10
DiPTH IHH'Mt)
SO 100
O'Connor Dili
0*t*
FIGURE A-6. DEOXYGENATION COEFFICIENT (Kd) AS A FUNCTION OF DEPTH
(A benthic deoxygenation component is included in these values)
(After Hydroscience, 1971)
A-24
-------
TABLE A-20. VALUES OF KINETIC COEFFICIENTS FOR DECAY OF CARBONACEOUS BOD
(After Bowie et al., 1985)
Location
Potomac Estuary 1977
Potomac Estuary 1978
Willamette River, OR
Chattahoochee River, GA
Ganga River, India
Yamuna River, India
S. Fork, Shenandoah River
Merrimack River, MA
Gray's Creek, LA
Onondaga Lake, NY
Yampa River, CO
Skravad River, Denmark
Seneca Creek
Kansas (6 rivers)
Michigan (3 rivers)
Truckee River, NV
Virginia (3 rivers)
N. Branch, Potomac, WV
South Carolina (3 rivers)
New York (2 rivers)
New Jersey (3 rivers)
Houston Ship Channel, TX
Cape Fear R. Estuary, NC
Holston River, TN
New York Bight
White River, AR
N. Fork Kings River, CA
Lake Washington, WA
Ouachita River, AR
36 U.S. river reaches plus
laboratory flume
San Francisco Bay Estuary
Boise River, ID
W. Fork, Trinity River, TX
Wilamette River, OR
Arkansas River, CO
Lower Sacramento River, CA
Delaware River Estuary
Wappinger Creek Estuary, NY
Potomac Estuary
Speed River, Ontario
Kd
(day 1 @20 °C,
base e)
0.14±0.023
0.16±0.05
0.1-0.3
0.16
3.5-5.6(Kr)
1.4
0.4(Kr)
0.01-0.1
1.44(Kr)
0.10
0.40
0.15
0.90(Kr)
0.008
0.20-0.60
0.56-3.37
0.36-0.96
0.30-1.25
0.4
0.3-0.35
0.125-0.4
0.2-0.23
0.25
0.23
0.4-1.5
0.05-0.25
0.004-0.66(Ki)
0.2
0.2
0.15
0.17(Ki)
0.02(Ki)
0.08-4.24
0.2
0.75
0.06-0.30
0.07-0.14
1.5
0.41
0.31
0.31
0.16, 0.21
1.0
Method
Determining
Coefficient
field study
field study
field study
field study
model calibration
model calibration
model calibration
field study
various methods
model calibration
laboratory study
calibration
laboratory study
field studies
laboratory study
lab and field study
field study
Reference
USEPA(1979b)
USEPA(1979a)
Bacaetal. (1973)
Bauer etal. (1979)
Bhargava (1983)
Deb and Bowers (1 983)
Camp (1965)
Crane and Malone (1 982)
Freedman etal. (1980)
Grenney and Kraszewski (1981)
Hvitved-Jacobsen (1982)
MWCOG (1982)
Reported by Bansal (1975)
Novotny and Krenkel (1975)
O'Connor etal. (1981)
Terry etal. (1983)
TetraTech (1976)
Chen and Orlob (1975)
Hydroscience (1979)
NCASI(1982a)
Wright and McDonnell (1979)
Chen (1970)
Chen and Wells (1975)
Jennings etal. (1982)
McCutcheon (1983)
Hydroscience (1972)
Thomann and Fitzpatrick (1982)
Gowda (1983)
A-25
-------
TABLE A-21. SUMMARY OF PRE- AND POST-IMPROVEMENT OXIDATION RATES
(After Leo et al., 1984)
Pre-lmprovement
River
Main Stem
Patuxent
Wilsons Creek
Hurricane Creek
Cibolo Creek
Clinton River
Hudson River
South River
Treatment
Secondary
Secondary
Trickling Filter
Secondary
Secondary
Primary
Secondary
CBOD
Oxidation
Rate (day 1)
0.61a
0.30
0.10-0.50
0.18
2.20
0.25
NBOD
Oxidation
Rate (day 1)
0.76a
0.40
0.10-0.50
0.25
0
0
1.6-2.0
Treatment
Secondary and
Nitrification
Secondary and
Nitrification and
Polishing
Secondary15
Secondary0
Secondary and
P- Removal
Secondary
Secondary and
Nitrification
Post-Improvement
CBOD
Oxidation
Rate (day 1)
0.30a
0.30
0.35
0.18
0.20
0.15
NBOD
Oxidation
Rate (day 1)
0.46a
0.40
0.70
0.25
2.5-3.8
0
1.6-2.0
From reference (23) cited in Leoetal. (1984), not from calibration analysis.
b Oxidation ditch achieving nitrification.
c New facility achieving nitrification.
monia, which is approximately 4.57. Figure A-7
shows the determination of Kn for the Shenandoah
River.
Benthic ammonia regeneration, benthic nitrification,
and large concentrations of algae, either suspended
or attached, markedly affect values obtained for Kn.
The approach shown in Figure A-7 to determine Kn
reflects only the net loss of ammonia. Such an ap-
proach can result in the overestimation of Kn where
significant algal or attached periphyton effects occur.
Algae consume ammonia as a nutrient; therefore, a
Kn determination based only on the loss of ammonia
would include uptake of ammonia by algae as well as
ammonia oxidation. In some cases, using the rate of
nitrate increase is a better approach for estimating Kn
because nitrate increases result directly from ammo-
nia oxidation. However, as a cautionary note, under
some conditions algae can consume nitrate as well
as ammonia. In addition, benthic denitrification can
account for a significant component of the total nitro-
gen balance as a loss mechanism for nitrate (Seitz-
inger, 1988). Therefore, the Kn rate derived from
nitrate data would represent the minimum Kn. A
critical issue in determining Kn involves the time of
year. Although ammonia and nitrate data may indi-
cate relatively high Kn rates during July and August,
Kn rates for the same stream may be negligible during
the winter months and even during transitional peri-
ods such as April, May, June, September, October,
and November. Seasonal adjustments in Kn using
the temperature correction relationships can be found
in Section A.12. During months when the tempera-
ture falls below 20 °C, nitrogen series data collected
during these cooler periods may be necessary to
select appropriate Kn rates to support cool-weather
nitrification.
A.5.2 Projection of Nitrogenous
Deoxygenation Rates
Kn rates applied to deep and slow-moving rivers,
without site-specific data, are higher than those nor-
mally expected for such rivers. The availability of
surfaces for nitrifier attachment can affect Kn rates.
These surfaces include the stream bottom and sus-
pended particles in the water column. Therefore,
shallow streams with rocky bottoms favor the growth
of nitrifying bacteria with associated high Kn rates.
Deep rivers composed of sands, silts, or clays gen-
erally have fewer attached nitrifiers. Although these
streams may support significant populations of nitrifi-
ers in the water column, they tend to have lower Kn
values than shallow streams.
One of the difficult issues related to the determination
of Kn is the onset of the nitrification process. It is
known that there are lags in the nitrification process
in highly polluted streams or those with low dissolved
oxygen. In projection analyses, a critical question is
A-26
-------
4.0 T
3.0-
2,0-
1,0
0.9
0,8
0.5
•Kn-l.25/day
OJ 1.0 1,5 2,0
TIME OF TRAVEL.LWS
2,5
FIGURE A-7. NITROGENOUS BIOCHEMICAL OXYGEN DEMAND VERSUS
TRAVEL TIME IN SHENANDOAH RIVER
(Deb and Bowers, 1983)
A-27
-------
when and where nitrification should occur following
improved treatment such as nitrification at the plant.
A.5.3 Literature Values of Kn Rates
A large body of literature exists for case studies of Kn
rates in streams and rivers. Tables A-22 and A-23,
taken from Bowie et al. (1985), summarize Kn rates
measured in the field and used as parameter values
for models from a number of investigations.
A.6 STREAM REAERATION RATE
A.6.1 Measuring Stream Reaeration Rate
Several methods of measuring Ka rates have been
reported in the literature. These methods are dis-
cussed in detail by Bennett and Rathbun (1972).
Churchill et al. (1962) used a dissolved oxygen bal-
ance method to measure reaeration in several Ten-
nessee rivers. Owens et al. (1964) used a similar
technique for small English streams. Both required
that all other factors influencing the oxygen balance
be known or negligible. Because of the difficulty in
accurately measuring the other factors, these tech-
niques are subject to considerable error. Tsivoglou
(1967) developed a gas-tracer method for directly
measuring gas transfer in streams, eliminating the
need for the oxygen balance information. In this
method, a fluorescent tracer is used for determining
time of travel and longitudinal dispersion, tritium is
used as an indicator of total dispersion, and krypton-
85 is used as a gaseous tracer. Of the various
methods, the gas-tracer method is superior since it
does not require estimating any other factor affecting
the oxygen balance. This method, however, requires
the handling and the injecting of radioactive tracers
into streams. Application of the method is limited
because the use of radioactive tracers in the natural
environment is subject to public health restrictions.
Rathbun et al. (1975) modified Tsivoglou's method to
use nonradioactive hydrocarbons (ethylene or pro-
pane) as the gaseous tracers. Additional information
about the method is given in Rathbun and Grant
(1978). Whittemore (1990a) has recently reported a
nonradioactive technique for determining reaeration
rates.
A.6.2 Predicting Stream Reaeration Coefficient
Various predictive equations are discussed in Ben-
nett and Rathbun (1972) and Rathbun (1977). One
of the most popular theoretical formulas was that of
O'Connor and Dobbins (1958):
Ka =
12.9LT
(A-9)
where
U = average stream velocity (ft/sec)
H = average stream depth (ft)
This formulation was derived from theoretical consid-
erations regarding surface renewal of the liquid film
through internal turbulence. Table A-24 lists a
number of other conceptual, empirical, and semi-em-
pirical predictive equations found in the literature.
The model QUAL2E offers eight different formula-
tions.
The variability of Ka estimates using these formulas
is illustrated in Figure A-8. As shown in this figure,
the range of Ka values calculated with the O'Connor,
Owens, Churchill, and Tsivoglou equations is signifi-
cant at all flow levels in the Muskingum River. Al-
though these formulas may not be equally applicable
to this particular river, this result illustrates the differ-
ences in the Ka values calculated using these four
equations. For some allocations, Ka values derived
from empirical formulas could result in the degree of
uncertainty exceeding the degree of projected water
quality improvement from the proposed treatment
plant upgrades. Using a predictive equation devel-
oped for the receiving water conditions similar to
those being modeled is extremely important (see the
applicability column in Table A-24).
In additiontothe numerous studies compiled in Bowie
et al., (1985), Whittemore (1990b) has compiled a
data base of stream reaeration measurements ob-
tained over a 30-year period under a wide range of
environmental and hydraulic conditions. The data
base and computer software for querying the data
base are available to interested investigators from
NCASI for a modest cost. Using a personal com-
puter, the data base can be queried to extract field
study measurements obtained under a range of en-
vironmental criteria specified by the analyst (i.e.,
depth, velocity, temperature, etc.).
A.6.3 Dam Reaeration
The QUAL2E model uses the following equation de-
scribed by Butts and Evans (1983) to estimate oxy-
gen input from dam reaeration:
Da-Db= 1-
1 + 0.116 a £>H(1-0.034H) 0+0.0467)J a
(A-10)
A-28
-------
TABLE A-22. SUMMARY OF NITRIFICATION RATES (day )
(After Bowie et al., 1985)
River
Grand River, Ml
Clinton River, Ml
Truckee River, NV
South Chickamaugo Creek, TN
Oostanaula Creek, TN
Town Branch, AL
Chattahoochee River, GA
Willamette River, OR
Flint River, Ml
Upper Mohawk River, NY
Lower Mohawk River, NY
Barge Canal near Upper
Mohawk River, NY
Ohio River, OH
Big Blue River, NB
Delaware River Estuary, DE
Willamette River, OR
Ouachita River, AR and LA
Potomac Estuary
Lake Huron and Saginaw Bay
New York Bight, NY
Maximum
3.9
15.8
4.0
2.4
1.9
0.8
0.7
2.5
0.3
0.3
0.25
0.25
0.25
0.54
-
Average
2.6
5.7
1.9
1.9
-
-
0.7
0.44
-
1.4
0.25
0.3
0.25
0.25
0.11
0.3
0.75a
1.05b
0.1a
0.5b
0.09-0.13
0.20
0.025
Minimum
1.9
2.2
0.4
1.1
0.1
0
0.4
0.1
0.25
0.3
0.25
0.25
0.03
0.09
-
Reference
Courchaine (1968)
Wezernak and Gannon (1968)
O'Connell and Thomas (1965)
Ruane and Krenkel (1978)
Ruane and Krenkel (1978)
Ruane and Krenkel (1978)
Stameretal. (1979)
Rinellaetal. (1981)
Bansal (1976)
Bansal (1976)
Bansal (1976)
Bansal (1976)
Bansal (1976)
Bansal (1976)
Bansal (1976)
Alvarez-Montalvo et al.
(undated)
NCASI(1982a)
Thomann and Fitzpatrick (1982)
DiToro and Matystik (1 980)
O'Connor etal. (1981)
Note: Nitrification rates are in units of day"
a Ammonia oxidation.
b Nitrate oxidation.
A-29
-------
as
2 $Q
^'•5 S
*Z C -ni
CL O ,£T
Cl t? ,*s
111
a c at c '
•s 2S 1
*** CE?
II
X *
— E
Q- •&
i§
o .£
c
"5
.J1 Of T*
m ^ ^p,
> « O
c a "5
c s o
B _
et
u, a
s i
TABLE A-23. CASE STUDIES OF NITRIFICATION IN NATURAL WATERS
(Bowie etal., 1985)
A-30
-------
II
o
.8
CJ
c
e
Uk
"C
c:
01
%
S>
&
ajr
^ h-
S »
^ ^.
e*
<5
1
O
2
•D
i/: r-
S 5
o
5
£
c
O
O
O- 2
z
o
s
«3
9
o
£ S
1 | .5
111
oil
I- TJ S
I
W
O w
>
£
.9
a. z
o
a.
IABLL A-23. (Continued)
A-31
-------
TABLE A-24. REAERATIQN COEFFICIENTS FOR RIVERS AMD STREAMS
(Bowfe ei al,, 1 MS)
K(1 base e (day"1 at 20 "C)
23.3 O5
7.fi 0
H
Ll-O-^^K
H
s ...J*35
24.9 < IT
H
234
Units
U-lps
U-lps
H-ISit
U-lps
U-lps
H-lwt
U-nVa
S-nvWi
U-tps
H-lMt
u-lpa
w-ipa
U-ips
S-l¥?t
Oi-tffmr
LMps
Applicability
Auttior(s)
'Cewnw anil Daebfea ft 9SS J
to deep channels:
i 30 ft, 0 5_£ U i.i.a ips.
0-S ^ te i.T2.a'aav. O'Comof snd
afet> -slLi;hi.
Ri^rission analysis psrlwrr^d on. 0-sts
ii362)
w*d Ortob (1 962)
P'addon arhJ CSIflyna 1 1 97 1 J
S-IMl
B^Sed On m iltt'.'ri.Tnlrj ;i-,Tlyr,L-. of rixia: alion Ca.d\vu.liiJ'Ji and
aata. I^Dcfirwl r, 1369}
A-32
-------
TABLE A-24. (Continued)
K., base e {day -1 at 20 °C) U nits
, , I
.««
H-fart
S-ltfl
H-fe«
AppJicabJIity
Author(s)
Ess*! on -aaralysis of raewrati&i daia in Bansal (<973)
nLfrHrujs nvarS.
These t*o eauattsfra art ijaseo w a
rMnalysis 0! hiSlos'iSal daia, vsilh CIQ
equation 5«wg abnj^ as good a pradctor
as *.a first, bud run hawng the slcea arm.
Swnffft arel
i'i973)
1 17 I 1 H-F % 6'Sl3 a?*
,5
0
*1
-in
1-2
)- 0.0052
° ra "J-
W-leet
U-fca
Q-tF/see
^teel
Ct-
T-aC
U-nv'wc
i n>*asur»r«nte m Oob&nB (1964]
nalurtl sa^aim, ana llyin* dam ol Kninkel
arx! •
in sflvenu small *C9 and B^w (1979)
Sasad on Ssl3
streams.
Based on me VB*I nwfliod (1 970) ar«J
for JiS rnix irrtKnpl I nrs
on an aooumuMon ol aKHteauofls of tfw
af 25 "C
tot q> 1
D.4J {Q.63 i"' 0-4S )
<& fi 1
S-ltfrrt
flJvfwt
ftadkjacflva
5tr*arn4 m Kentucky.
0 < $*
on wrall
Pom's f l W6J (tea
Baa«l «i sunmaiy s< redtoacdva iracw
;ippscal:ann la 5 rfvfifl.
Bae«J on dasa coflectee on ?4
streaf« using radssacUve Iras&r imlhod.
Wnllacs (1972)
Tsivoglou and Naa! 11976)
0.09
25* C
Based on data from iO sm^y stfoains in Grant [1876}
Wisconsin uwrg radtoactwa tracer techniqmw:
1.25 S 5 70 Wmilii
0.3
A-33
-------
TABLE A-24. {Continued)
'1 at 2®
OJOS'^5 '»t2S-C
046;
Units
Mays
L-tfaya
Applicability
3as«J en
an flock
0.0"
0.25 S U<1.€lpB
0.2 < S £ 3.5
260
tracer data
, 'Wisconsin antf Illinois;
AuUiorfs}
3raoc(197B)
L!;L:;I>I qn r«-.nr--r.l
(x»tfoents l
-------
•IS
_
*
o
it
9 O
| I
• I
1 1
1 <3
t l
i
XI
i
4
Q
i
b
•z
1 *"
_*
FIGURE A-8. STREAM REAERATION ACCORDING TO SIX FORMULAS
A-35
-------
where
Da
Db
T
H
= dissolved oxygen deficit above
dam (mg/L)
= dissolved oxygen deficit below
dam (mg/L)
= temperature (°C)
= height through which water
falls (ft)
a = 1.80 in clean water
= 1.60 in slightly polluted water
= 1.00 in moderately polluted water
= 0.65 in grossly polluted water
b = 0.70 to 0.90 for flat, broad
crested weir
= 1.05 for sharp crested weir with
straight slope face
= 0.80 for sharp crested weir
with vertical face
= 0.05 for sluice gates with
submerged discharge
The parameters H, a, and b need to be assigned for
each dam.
A.6.4 Saturated Dissolved Oxygen
Concentration
The solubility of oxygen in water is dependent on
water temperature, barometric pressure (i.e., alti-
tude), and the concentration of dissolved solids in the
water. Oxygen saturation concentration decreases
with the increase in temperature and salts and in-
creases with barometric pressure. Freshwater
streams, where temperature ranges from about 0 to
30 °C, typically have oxygen saturation concentra-
tions ranging from 7.5 to 15 mg/L. The following
equation is recommended to calculate the saturated
dissolved oxygen concentrations as a function of
temperature for freshwater streams:
Cs =
468
316.6+7
(A-11)
where Tis water temperature in degrees Celsius (°C).
This equation is accurate to within 0.03 mg/L com-
pared with the Benson-Krause equation on which the
Standard Methods tables are based (see McCutch-
eon, 1985).
A.7 SEDIMENT OXYGEN DEMAND
A.7.1 Field Measurement of SOD
Direct field measurement of sediment oxygen con-
sumption upstream and downstream of the discharge
is the preferred approach for obtaining model input
data. Consistent field techniques for determining
SOD in natural waters are evolving with investigators
in the southeast United States using an approach
developed by Murphy and Hicks (1986). The two
basic measurement techniques are (1) in situ cham-
bers and (2) sediment core extraction and laboratory
measurement (see Bowie et al., 1985; Hatcher, 1986;
and Whittemore, 1986). The in situ method requires
submersion of a chamber on the bottom with periodic
measurements of oxygen to determine the uptake
rate in the chamber. Laboratory measurements are
based on a sample core from the sediment (hopefully
undisturbed) being placed in a well-oxygenated col-
umn with oxygen measurements taken over time to
determine the uptake rate. Different investigators
have varying opinions on the relative merits of each
technique; however, the use of in situ chambers, with
minimal disturbance of the natural sediments, ap-
pears to be the preferred technique (Murphy and
Hicks, 1986).
A.7.2 Predicting SOD
Projections of the expected water quality impact of a
waste discharge alternative for some future low-flow
condition are normally required during waste load
allocation studies. Projections of the expected
change in SOD that might result from a change in
waste loading to a stream is a complex evaluation
(e.g., DiToro et al., 1990). HydroQual (1987), for
example, demonstrated that a reduction of total or-
ganic carbon loading to the Potomac estuary from
92,540 Ib/day (1.56 g C/m2-day) in 1969 to 57,800
Ib/day (0.98 g C/m2-day) in 1985 resulted in a reduc-
tion of the mean SOD from 2.2 to 1.8 g O2/m2-day.
The relationship used to infer the long-term coupling
between carbon loading and SOD in the Potomac is
not a simple formulation.
Until such time when models (such as that of Di Toro
et al., 1990) are readily available to explicitly couple
paniculate carbon deposition and sediment oxygen
demand, it is beyond the scope of most waste load
allocation studies to predict future SOD rates with any
credibility since SOD is not linearly proportional to the
waste loading of organic carbon in freshwater sys-
tems. For projecting future water quality conditions,
it is preferable to use the same SOD parameter
values that were used in verification of the model. At
the least, this approach will result in a somewhat
conservative projection of future oxygen levels since
SOD is likely to be reduced following improvements
in waste management.
A-36
-------
A.7.3 Literature Values of SOD
Model parameter values for SOD could be specified
using field measurements reported for streams and
rivers with similar hydraulic and waste loading char-
acteristics. A fairly large body of literature (e.g.,
Phoel, 1982; Butts and Evans, 1978; Butts, 1974) is
available for the analyst to review actual field meas-
urements obtained under a wide range of conditions
that might be similar to the study area for a waste load
allocation. Table A-25, taken from Bowie et al.
(1985), summarizes a large number of investigations
of SOD rates that have been reported for streams and
rivers in the literature. Table A-26, taken from Mur-
phy and Hicks (1986), also summarizes a large
number of in situ chamber SOD measurements ob-
tained from 1977 to 1984.
A.8 PHOTOSYNTHESIS AND
RESPIRATION
A.8.1 Estimation Techniques
Three methods for estimating photosynthesis (P) and
respiration (R) in waste load allocation modeling stud-
ies are:
• Estimation from observed chlorophyll a lev-
els.
• Measurements of diel variations of dissolved
oxygen concentrations.
• Light and dark bottle measurements of dis-
solved oxygen.
The first method is addressed by the following prob-
lem: given the concentration of phytoplankton in a
stream, estimate the average daily oxygen produc-
tion. A technique for performing this estimate, devel-
oped by Di Toro (1975), can be found in Thomann
and Mueller (1987). In summary, the following equa-
tions are used:
P= 0.25 Chi a
(A-12)
and
Pi = 0.025CWa (A-13)
in which Chi a is the chlorophyll a concentration in
For the second method, Di Toro (1975) has devel-
oped an analytical method to calculate P based on
the measured diurnal dissolved oxygen range:
where
f
Ka
= photo period (0 < f < 1)
= stream reaeration rate coefficient
(day1)
fKa(\-e-KsT)
(A-14)
T =1 -day period
A = diurnal dissolved oxygen range
(mg/l_)(max-min)
Note that Equation A-14 can be used to estimate the
diurnal range of dissolved oxygen with an estimate of
P from the first two methods (Thomann and Mueller,
1987). Table A-27 presents a summary of stream
photosynthesis studies compiled by Bowie et al.
(1985).
The light and dark bottle method is described in detail
by Standard Methods (APHA, 1989). As shown in
Figure A-9, clear glass (light) and foil-wrapped glass
(dark) bottles are stationed or suspended at various
fixed depths in a stream and filled with water collected
at their respective depths. Usually, an attempt is
made in deep rivers to suspend the bottles at least to
the depth of the euphotic zone, taken to be the 1 percent
light penetration depth. Based on Equation A-20, the
depth to 1 percent remaining light can be estimated
as 4.6/Ke. Since Ke is approximated by I.HSecchi
depth (Equation A-21), the approximate depth of the
euphotic zone is 2.9 times the Secchi depth.
Dissolved oxygen measurements are made at regu-
lar time intervals, with the light bottles that receive the
solar radiation, measuring net photosynthetic oxygen
production (P-R). The dark bottles, in the absence of
light, measure gross respiration (R) as shown in
Figure A-9. It should be noted that:
• In contrast to the diurnal method where water
column and benthic algae or macrophytes
contribute to the observed oxygen balance,
only the photosynthetic activity of the algae
in the water column (phytoplankton) is meas-
ured by this technique. If there are significant
attached algae or rooted plants, no measure-
ment of their photosynthetic contribution is
made.
• The estimate of respiration (R) made from
the dark bottle studies includes both algal
respiration and bacterial respiration from oxi-
dation of carbonaceous and nitrogenous
compounds.
• Both P and R are temperature-dependent.
Since they are essentially expressions of
growth rate and respiration rate in oxygen
equivalents, the temperature-rate relation-
ships discussed in Sections 2.3.5 and A.9 for
growth and respiration apply directly to Pand
A-37
-------
TABLE A-25. MEASURED VALUES OF SEDIMENT OXYGEN DEMAND
IN RIVERS AND STREAMS
(After Bowie etal., 1985)
SOD, g02\m2 day
0.022-0.92
0.09 ±0.02 (@12°C)
0.1 5 ±0.04 (@20°C)
0.20 ±0.03 (@28°C)
0.29 ±0.07 (@36°C)
0.18±0.05 (@12°C)
0.55 ±0.22 (@20°C)
0.60 ±0.28 (@28°C)
0.87 ±0.23 (@36°C)
3.2-5.7
0.52-3.6
Environment
Upper Wisconsin river
Eastern U.S. river
Southeastern U.S. river
Fresh shredded tree bark
Aged shredded tree bark
Experimental Conditions
60-hour laboratory core incubation
periodic mixing, 4 °C, dark
45-day incubation of 0.6 liter
sediment in 3.85-liter BOD
dilution water, light
10-liter incubations in aged tap
water, room temperature, light
References
Sullivan et al. (1978)
NCASI (1981)
NCASI (1971)
2-33
0.9-14.1
<0.1-1.4(@20°C)
0.27-9.8
0.1-5.3 (@20°C)
1.1-12.8
0.3-1.4
0.2-1.2
1.7-6.0
1.5-9.8
4.6-4.4
Four eastern U.S. rivers In situ chamber respirometers,
downstream of paper mill 22-27 °C, light, stirred at varying
discharges rates
Open-ended tunnel respirometer,
in situ 22-27 °C, dark
NCASI (1978)
Eastern U.S. river
downstream of paper
mill discharge
Northern Illinois rivers
(N = 89 stations)
Six stations in eastern
Michigan rivers
New Jersey rivers
(10 stations)
Swedish rivers
Swedish rivers
Spring Creek, PA
74 samples from
21 English rivers
Streams
In situ respirometer stirred at
various rates, 9-16 °C, dark,
0 = 1.08
In situ respirometer, dark,
T = 5-31 °C, time = 1 1/2-3 hours
In situ respirometer in stirred
chambers, 15-27 hours, dark,
19-25 °C, 0 = 1.08 0 = constant
for temperature adjustment
In situ respirometer, dark 30
minutes-8 hours, stirred.
Temperature unknown
In situ respirometer, light,
stirred, 0-10 °C
Laboratory incubations,
stirred, dark, 20 °C
Laboratory incubators in dark,
stirred, 20 °C
Laboratory incubation of
cores; 15 °C
Oxygen mass balance
NCASI (1979)
Butts & Evans (1978)
Chiaro & Burke (1980)
Hunter etal. (1973)
Edberg & Hofsten (1973)
Edberg & Hofsten (1973)
McDonnell & Hall (1969)
Rolley & Owens (1967)
James (1974)
A-38
-------
TABLE A-26. SOD RATES MEASURED USING EPA IN SITU CHAMBERS, 1977-1984
(After Murphy and Hicks, 1986)
Location
Indian River, FL
Sykes Creek at Merritt Is, FL
Description
High-salinity lagoon
Saltwater tidal creek subjf
Mean
g 02/m2-hr
.12
=ct to urban .31
SOD Rates
Range
g 02/nr-hr
.10-. 14
.12-. 69
C,V
%
23.6
81.0
Mean
Temp. °C
30.0
31.8
Turkey Creek at Melbourne, FL
Inidan River at Turkey Creek,
Melbourne, FL
Sugarloaf Key, FL
Wilson Creek, SC
Wilson Creek, SC
Wilson Creek, SC
Mobile Bay, AL
St. Andrews Bay, FL
Savannah River at Savannah, GA
Savannah River at Savannah, GA
Savannah River at Savannah, GA
Hillsborough River at Tampa Bay, FL
Hillsborough River at Tampa Bay, FL
Hillsborough River at Tampa Bay, FL
Hillsborough River at Tampa Bay, FL
Sarasota Bay, FL (Summer)
Sarasota Bay, FL (Summer)
Sarasota Bay, FL (Summer)
Sarasota Bay, FL (Summer)
Sarasota Bay, FL (Winter)
Sarasota Bay, FL (Winter)
Sarasota Bay, FL (Winter)
Sarasota Bay, FL (Winter)
Whitaker Bayou, FL (Summer)
Whitaker Bayou, FL (Summer)
Sarasota Bay, FL at Whitaker Bayou
(Summer)
Whitaker Bayou, FL (Winter)
Whitaker Bayou, FL (Winter)
Sarasota Bay, FL, at Whitaker Bayou
(Winter)
Lake Myakka, FL (Summer)
Lake Myakka, FL (Winter)
Lake Myakka, FL (Winter)
Gulf Shores, AL
Gulf Shores, AL
Gulf Shores, AL
Guntersville Reservoir, AL
Guntersville Reservoir, AL
Pickwick Reservoir, AL
Pickwick Reservoir, AL
runoff and STP
Density-stratified tidal creek stream,
residential development, heavy organic
deposit
Estuary
Dead-end canal, hypersaline
Shallow, flashy, piedmont creek
Shallow, flashy, piedmont creek
Shallow, flashy, piedmont creek
Low-salinity estuary
Estuary
Density-stratified, high-velocity river/estuary
Density-stratified, high-velocity river/estuary
Density-stratified, high-velocity river/estuary
Density-stratified river/estuary
Density-stratified river/estuary
Density-stratified river/estuary
Density-stratified river/estuary
Shallow bay, grass flat
Open bay, sandy bottom
Open bay, sandy bottom
Deep bay channel, coarse sand
Shallow bay, grass flat
Open bay, sandy bottom
Shallow bay, grass flat
Deep bay channel, coarse sand
Density-stratified creek, thick organic
deposits. Subject to urban runoff and STP
Density-stratified creek, thick organic
deposits. Subject to urban runoff and STP
Bay near mouth of tidal creek. Subject to
urban runoff and STP
Density-stratified creek, thick organic
deposits. Subject to urban runoff and STP.
Density-stratified creek, thick organic
deposits. Subject to urban runoff and STP
Bay near mouth of tidal creek. Subject to
Urban runoff and STP
Shallow freshwater lake with bottom of
dense organic matter
Shallow freshwater lake with bottom of
dense organic matter
Shallow freshwater lake with bottom of
dense organic matter
Gulf Intracoastal Waterway
Gulf Intracoastal Waterway
Gulf Intracoastal Waterway
TVA lake
TVA lake
TVA lake
TVA lake
.54
.12
.49-.60
.13-.22
14.3
36.4
32.4
32.0
.12
.10
.08
.12
.12
.05
.027
.061
.036
.41
.18
.11
.17
.165
.227
.156
.128
.122
.106
.077
.086
.155
.140
.264
.154
.240
.160
.049
.070
.124
.086
.070
.112
.163
.099
.037
.099
.10-. 14
.09-. 11
.05-. 14
.07-. 18
.10-. 13
.03-.04
.21-. 32
.38-. 78
.25-. 44
.37-. 45
.16-. 19
.09-. 14
.12-. 19
.148-. 183
.172-. 357
.145-. 166
.107-. 152
.070-. 202
.094-. 116
-
.063-. 110
.050-. 121
.117-. 157
.098-. 604
.138-. 169
.134-. 300
.123-. 214
.020-.064
.063-0.75
.081-. 172
.070-. 109
.066-.078
.072-. 154
.136-. 222
.078-. 120
.028-.056
.093-. 104
23.6
10.7
36.0
30.4
16.7
40.0
22.2
29.5
19.4
8.37
6.55
19.72
14.92
14.9
34.3
9.6
17.5
39.6
9.5
-
27.2
43.0
12.9
66.0
14.3
35.4
26.3
51.0
7.1
36.3
18.8
9.9
32.7
20.0
18.4
27.0
5.7
25.0
23.4
24.6
25.1
28.0
20.0
24.8
21.2
23.2
22.8
22.8
22.9
23.2
29.6
29.0
28.2
28.9
20.3
21.1
21.1
22.0
28.9
27.7
28.4
22.0
20.5
20.5
28.5
19.7
19.2
22.5
21.5
22.0
25.5
24.8
23.5
23.0
A-39
-------
TABLE A-26. (Continued)
Location
Hillsborough Bay, FL
Hillsborough Bay, FL
Hillsborough Bay, FL
Sowashee Creek, MS
Sowashee Creek, MS
Hillsborough Bay, FL
Tampa Bay, FL
Hillsborough Bay, FL
Tampa Bay, FL
Old Tampa Bay, FL
Tampa Bay, FL
Manatee River, FL
Manatee River, FL
Manatee River, FL
Boone Lake
Boone Lake
Boone Lake
Boone Lake
Boone Lake
Boone Lake
Boone Lake
Boone Lake
Boone Lake
Boone Lake
Calcasieu River
Calcasieu River
Calcasieu River
Calcasieu River
Calcasieu River
Calcasieu River
Calcasieu River
Charlotte Harbor
Pine Island Sound
Ft. Loudoun Res.
Ft. Loudoun Res.
Ft. Loudoun Res.
Tellico Reservoir
Tellico Reservoir
Description
Density-stratified bay, dynamic murk
Density-stratified bay, sand/silt
Density-stratified bay at river mouth and
STP density
Shallow creek, upstream of STP
Shallow creek, downstream of STP
Shallow bay, dark sand & silt
Open Bay, sand
Shallow bay, dark sand & silt
Open bay, sand
Shallow bay, nearshore
Shallow bay, nearshore
Tidal stratified river
Tidal stratified river
Tidal stratified river
TVA lake, sludge bank
TVA lake, upstream of sludge bank
TVA lake, downstream of sludge bank
TVA lake, HRM19.7
TVA lake, HRM 26
TVA lake, HRM 29
TVA lake, HRM 31
TVA lake, WRM 3
TVA lake, WRM 7
TVA lake, WRM 11. 2 5
Stratified river/estuary
Stratified river/estuary
Stratified river/estuary
Stratified river/estuary
Stratified river/estuary
Stratified river/estuary
Stratified river/estuary
Estuary; seasonal stratification
Estuary; shallow
TVA Lake, TRM-608
TVA Lake, TRM-608
TVA Lake, TRM-638
TVA Lake, LTRM-16.5
TVA Lake, LTRM-21
Mean
g 02/m2-hr
.033
.046
.094
.097
.102
.131
.074
.131
.195
.111
.203
.077
.181
.075
.346
.072
.041
.031
.064
.078
.109
.050
.023
.072
.027
.027
.027
.067
.055
.027
.035
.062
.044
.046
.044
.043
.048
.047
SOD Rates
Range
g 02/nr-hr
.025-.048
.039-.052
.085-. 100
.079-. 116
.090-. 124
.074-. 176
.061-.087
.074-. 176
.161-. 276
.107-. 114
.137-. 284
.064-. 107
.160-. 193
.062-.087
.171-. 465
.071-.073
.037-0.44
.018-.036
.055-.077
.062-. 10
.066-. 14
.040-.060
.020-.027
.64-. 81
.019-.031
.019-.039
.019-.039
.061 -.083
.038-.073
.024-.038
.029-.043
.054-.070
.038-.048
.045-.049
.033-.050
.038-.051
.042-.054
.028-.065
c,v
%
39.3
20.2
8.4
19.2
18.7
33.2
24.8
33.2
21.5
3.2
26.5
25.9
10.2
13.7
44.7
1.4
8.8
11.9
12.1
30.7
30.7
17.3
13.3
8.4
20.1
32.8
22.0
13.9
27.3
22.3
14.6
10.4
11.8
5.0
17.2
13.9
12.5
33.3
Mean
Temp. °C
16.5
16.0
18.0
26.2
29.5
30.2
30.2
31.0
31.0
30.5
31.5
32.0
31.0
14.0
10.5
10.5
10.5
11.8
14.3
24.8
24.1
24.0
24.2
24.2
26.0
24.5
23.0
17.0
19.5
24.2
24.8
24.2
18.1
A-40
-------
TABLE A-27. PHOTOSYNTHETIC OXYGEN PRODUCTION AND RESPIRATION RATES IN RIVERS
(After Bowie et al., 1985)
River
Grand, Michigan
Clinton, Michigan
Truckee, Nevada
Ivel, Great Britain
Flint, Michigan
North Carolina Streams
Laboratory Streams
Charles, Massachusetts
Shenandoah, Virginia
Baker, Virginia
Rappahannock, Virginia
S. Fork Rivanna, Virginia
Rivanna Virginia
South, Virginia
Mechums, Virginia
Havelse, Denmark
Experimental Channels
T Pm Pav
°C g/m2-day g/m2-day
28 12.7-37.6 4.4-13.0
21 13.2-22.9 4.2-7.3
28 12.9-26.0 4.8-9.6
16 24 9.0
28 4.0-40.0 1.3-18.
9.8
3.4-4.0
19-25 - 0.0-12.0
23 4.8-17.4
0.45
6.1
2.1
2.3
2.0
1.3
0.2-25.9C
9-24 5-45 1.5-14.8
R
g/m2-day
9.3-12.73
9.3a
3.6-6.2a
. ra
4.6
4.-203
21. 5b
2.4-2.9b
0.0-36.b
0.9-5.93
1.9b
7.3b
3.4b
5.4b
5.3b
2.6b
4.8-22.9b
2.6-10.7b
Reference
O'Connor and Di Toro (1970)
O'Connor and Di Toro (1970)
O'Connor and Di Toro (1970)
O'Connor and Di Toro (1970)
O'Connor and Di Toro (1970)
Thomas and O'Connell (1966)
Thomas and O'Connell (1977)
Erdmann (1979a, b)
Deb and Bowers (1983)
Kelly etal. (1975)
Kelly etal. (1975)
Kelly etal. (1975)
Kelly etal. (1975)
Kelly etal. (1975)
Kelly etal. (1975)
Simonsen & Harremoes (1978)
Gulliver etal. (1982)
aAlgal respiration only.
bTotal community respiration.
cMeasurements were made over the period of 1 year, and solar radiation varied by more than a factor of 10.
A-41
-------
EJGHT
BOTTLB
* O
*f. "*
c O
I
12
10 -
Chi a - 14 uf/L
S Id fit
12
j 10 -
pa,
TIME
EXAMPLE CALCULATION (for each bottle)
(1) Slope of light DO data
6 hr 1 day
(2) Slope of dark bottle DO data
(6.1-7.5) v (24 hr) , A ,. .
X = 1.4 mq/L-day
10 hr 1 day M J
(3) R = Slope of dark bottle data = 1.4 mg/L-day
(4) P = Slope of light bottle + Slope of dark bottle
P = 22.0 + 1.4 = 23.4mg/L/day
(5) Calculate P for each depth sampled
(A, B, C, D) and plot as shown
(6) Equate area under curve Ai to A2 to determine
depth averaged production rate
P Cmi/L) 0,
X
Q C -
FIGURE A-9. LIGHT AND DARK BOTTLE STUDIES
(After Thomann and Mueller, 1987)
A-42
-------
R measurements derived from light and dark
bottle tests.
The productivity vs. depth relationship developed
from the light and dark bottle test data, shown in
Figure A-9, provides a determination of the depth-av-
eraged primary productivity rate. The extent to which
it is time-averaged depends on the period of the day
covered by the measurements. Because of the sig-
nificant variations in Pwith depth and time, care must
be taken that light and dark bottle test results are
interpreted correctly.
When conducting the light and dark bottle work, it is
essential that the light bottles not be allowed to pro-
gress to the point where saturation is exceeded.
Losses of dissolved oxygen during sample handling
and performing the analytical measurements would
introduce errors into the test results. The maximum
hourly increase in dissolved oxygen in the light bottle
can be computed as follows:
.„
AC =
Gmax 1 .066( '
(1000) (24)
Ch
(A-15)
where
AC
= maximum hourly increase in
dissolved oxygen (mg/L-hr)
aoc = stoichiometric ratio of oxygen to
carbon = 2.67 (mg O2/mg C)
ac = stoichiometric ratio of carbon
to chlorophyll a (mg C/mg Chi)
Gmax = maximum algal growth rate (day-1)
T = water temperature (°C)
Chi = instantaneous chlorophyll a
concentration (|ig/L)
Equation A-15 can be used to estimate appropriate
sampling intervals and maximum duration of light
bottle measurements.
A.8.2 BOD Deoxygenation in Bottles
The following example illustrates how to calculate the
algal respiration from the light and dark bottle results
with significant BOD: The initial DO in a light and dark
bottle test is 7.0 mg/L. After 1 day, the DO in the dark
bottle is 2.0 mg/L and the DO in the light bottle is 9.0
mg/L. The BODs of the water sample without algae
is 10 mg/L and Ki is 0.3 day"1. Using Equation 2-5,
- e
yielding BODU equal to 12.9 mg/L. Thus, BODi can
be calculated as
= 1 2.9 [1 - e ~
= 3.34
That is, the amount of oxygen consumed by bacteria
for BOD decay is 3.34 mg/L. The algal respiration is
then equal to 7.0 - 2.0 - 3.34 or 1.66 mg/L.
A.9 PHYTOPLANKTON KINETIC
RATES
A.9.1 Growth Rate
Eppley (1972) summarized algal growth data from a
variety of sources as a function of temperature and
developed the following equation:
GT= Gmax©
T-20
(A-16)
where
GT
Gmax
0
r
temperature-adjusted growth rate
(day1)
maximum growth rate at 20°C
(day1)
constant for temperature
adjustment
temperature (°C)
Both GT and Gmax are specific growth rates under
optimum light and nutrient conditions. Reported
ranges for Gmax and 0 are:
Gmax = 1 to 3 day"1 at 20°C
0=1.01 to 1.18
As a first approximation, Gmax = 1.8 day'1 and 0 =
1.066 may be used (Thomann and Meuller, 1987).
Thus,
GT= 1.8 (1.066) (T~20)
(A-17)
Equation A-17 is shown in Figure 2-5. This relation-
ship (Eppley, 1972) can be viewed as an envelope
representing the maximum growth rate at any tem-
perature, under optimum light and nutrient condi-
tions.
A.9.2 Light Effect on Phytoplankton Growth
A depth- and time-averaged effect of available light
energy on phytoplankton growth rate can be obtained
(Di Toro et al., 1971), by integrating the light intensity
relationships over depth and time. This reduces to
KeHT
' - e
-OC2N
(A-18)
where
A-43
-------
-KeH
_
oci = is
0.2= -
IT
Is
r\_ = light limitation factor
f = photoperiod - daylight fraction of
averaging period (day)
T = averaging period (day)
Ke = light extinction coefficient (m~1)
H = average depth of segment (m)
la = average of incident light on water
surface over a 24-hour day (ly/day)
IT = average of incident light over
photoperiod (=la/f)0y)
Is = saturated light intensity (ly/day)
(see Figure 2-6)
The full expression for algal growth can be synthe-
sized from Equations A-16, A-17, and A-18 as fol-
lows:
Gp=Gmax1.066(T-20^
AS
DIN DIP
mm
Si
Kmn + DIN ' Kmp + DIP ' KSi + si (A-19)
Solar radiation is measured routinely at selected
weather stations in the United States. It is usually
reported as langleys (ly), which is a measure of the
total radiation of all wavelengths that reach the sur-
face of the earth. One ly is equal to 1 g cal/cm2.
Algae and other photosynthetic plants respond to
solar radiation in the visible range of the spectrum.
Visible light energy was historically measured in
terms of intensity as footcandles. A common conver-
sion used in calculations is 2000 ft-candles = 350
ly/day. Contemporary primary production studies
generally report incident light intensity with units of
jj£m~2- sec (micro einstein) where the appropriate
conversion factors are:
TABLE A-28. TYPICAL LIGHT EXTINCTION
COEFFICIENTS
Ke = 1.5/SD
(m1)
0.02 - 0.06
0.2
0.2 -0.5
0.5-5.0
Secchi
Depth (m)
30-80
8-10
3 -8
0.3-3.0
Types of Waterbodies
Clear, mid-ocean
oligotrophic waters
Clear lake waters
Coastal zone marine waters
Rivers and estuaries
condition for algal growth when compared with turbid
and deep waters. KeH, a dimensionless number, is
also referred to as the light extinction factor.
Typical /
-------
The nonvolatile suspended solids (the inorganic par-
ticulates) both absorb and scatter the light, whereas
the organic detritus and phytoplankton chlorophyll
mainly absorb the light. Di Toro has shown that
Equation A-22 applies to Ke values of approximately
less than 5.0 m" and phytoplankton biomass up to
approximately 15 jj,g/l_.
A.9.3 Death Rate
The endogenous respiration rate, Dpi (Equation 2-
16) is given approximately by
Dpi = [IR (1.08)
T-20
(A-23)
where |j,f? varies from 0.05 to 0.25 day" (Thomann
and Mueller, 1987). A value of 0.15 day"1 is usually
used as a first approximation.
A.9.4 Settling Rate
Phytoplankton settling rate is estimated by dividing
the settling velocity by the stream depth. Phytoplank-
ton settling velocities are presented in Table A-29.
Additional data are available in a review by Smayda
(1970). Some phytoplankton such as blue-green al-
gae develop gas vacuoles, which result in buoyancy
and subsequent aggregation at the water surface.
The proliferation of such species is a particular prob-
lem because the settling velocity may be zero or even
negative and phytoplankton tend to remain in the
water column or at the surface (e.g., 1983 Microcystis
bloom in Potomac estuary).
A.9.5 Biomass Stoichiometry
Dry weight biomass is related to the major nutrients
(carbon, nitrogen, and phosphorus) and chlorophyll a
through stoichiometric ratios that give the ratios of
each nutrient to the total biomass. Typical algal
nutrient compositions are summarized in Table A-30.
Ratios for different algal groups or species (e.g.,
blue-green, diatom, etc.) can be found in the literature
(O'Connor et al., 1973; Bowie et al., 1985) but are not
included in Table A-29 as this manual addresses the
algal modeling only on a total population basis.
A.9.6 Half Saturation Constants
Half saturation constants are required to describe the
nutrient dependence of the phytoplankton growth rate
(Equation A-19). Table A-31 summarizes an exten-
sive compilation of phytoplankton half saturation con-
stants for populations of diatoms, flagellates,
chlorophytes and chrysophytes.
A.10 NUTRIENT RECYCLING RATES
A.10.1 Phosphorus Mineralization Rate
The rate of transformation from paniculate phospho-
rus to orthophosphate in the water column ranges
from 0.02 to 0.10 day"1 (Bowie etal., 1985). As a first
approximation, a value of 0.03 day"1 may be used.
A.10.2 Organic Nitrogen Hydrolysis Rate and
Ammonia Nitrification Rate
Table A-32 presents the rate coefficients for nitrogen
transformations reported in a number of modeling
studies.
A.11 SEDIMENT NUTRIENT RELEASE
RATE
Sediment nutrient releases measured in the field are
usually reported in mg/m2-day. Table A-33 (from
Thomann and Mueller, 1987) shows some reported
nutrient fluxes from the sediments under both aerobic
and anaerobic conditions. When the overlying water
is anaerobic, the flux of phosphorus from the sedi-
ment increases significantly as a result of increased
diffusion between the sediment and the water. Such
increased diffusion results from changes in the iron
complexes at the water-sediment interface. Table
A-34 presents data for two stations in the Peconic
Bay in Long Island (Garber, 1990).
Since data are usually not available to characterize
sediment nutrient processes for many streams and
rivers, aerobic sediment flux rates of ammonia and
phosphate can be estimated as the stoichiometric
equivalent of the biochemical component of SOD
using Redfield ratios (by weight) for O:C:N:P
(109:41: 7.2:1) (Redfield etal., 1963). UsingtheO:N
ratio of 109 mg 62: 7.2 mg N benthic regeneration of
ammonia can be estimated as:
jNHs = SOD [1000 mg O2/g 02] [1 mg N/15.14 mg
02]
where SOD is in units of g O2/m2-day and jNHs has
units of mg N/m~2-day. Di Toro (1986) has summa-
rized paired measurements of SOD and jHNs flux to
substantiate the relationship of SOD and jHNs under
aerobic conditions.
Although the sediment-water interactions for phopho-
rus recycling are complex, Redfield Stoichiometry is
appropriate for a preliminary estimate of phosphate
flux from the sediments under aerobic conditions.
A-45
-------
TABLE A-29. TOTAL PHYTOPLANKTON SETTLING VELOCITIES
(After Bowie etal., 1985)
Settling Velocity (m/day) References
0.05 - 0.5 Chen and Orlob (1975)
TetraTech (1976)
Chen (1970)
Chen and Wells (1975, 1976)
0.05 -0.2 O'Connor et al. (1975, 1981)
Thomann et al. (1975, 1979)
Di Toro and Matystik (1980)
Di Toro and Connolly (1980)
Thomann and Fitzpatrick (1982)
0.02-0.05 Canale etal. (1976)
0.4 Lombardo(1972)
0.03-0.05 Scavia(1980)
0.04 Bierman etal. (1980)
0.2 - 0.25 Youngberg (1977)
0.04 - 0.6 Jorgensen (1976)
Jorgensen et al. (1978, 1981)
0.01 - 4.0 Baca and Arnett (1976)
0.0 - 2.0 Chen and Orlob (1975)
Smith (1978a)
0.15-2.0 Duke and Masch (1973)
Roesneretal. (1977)
0.0-0.2 Brandes (1976)
0.0 - 30.0 Jorgensen (1979)
A-46
-------
TABLE A-30. NUTRIENT COMPOSITION OF ALGAL CELLS - RATIO TO CHLOROPHYLLa (as \igl\ig)
(After Bowie et al., 1985)
C N P Si
Algal Type Cr|l a Chi a Ch la Chi a
Total Phytoplankton 50 - 1 00 7-15 0.5-1.0
0.5
7.2 0.63
25-112a 7-29a 1.0a
10-100a 2.7-9.18
Diatoms 100 1.-15 0.5-1.0 40-50
0.5
5.-200b
18-500a 2.2-74.6a 0.27-1 9.2a 2.4-50.7a
Green Algae 20-1 00b
Blue-green Algae 14-67b
Dino flagellates 275 19.3
Dry Weiaht (ma/ma DW) percentaae of five phvtoplankton function aroups. (O'Connor et al.
Total
Phytoplankton % Carbon % Nitrogen
Average % SD(N=5) 39 % 4.4 6.1 % 1 .9
Range 19150 2.719.1
References
Thomannetal. (1975, 1979)
O'Connor etal. (1981)
DiToro&Matystik(1980)
DiToro & Connolly (1980)
Salas and Thomann (1978)
Salisbury etal. (1983)
Larsenetal. (1973)
Jorgensen (1979)
O'Connor etal. (1981)
DiToro & Connolly (1980)
Di Toro & Matystik (1 980)
Thomann etal. (1979)
Salisbury etal. (1983)
Baca& Arnett (1976)
DiToro etal. (1971)
Baca& Arnett (1976)
Baca& Arnett (1976)
O'Connor etal. (1981)
, 1973)
% Phosphorus
1.6% 0.8
0.4I3.3
3 Literature values.
b Model documentation values.
N = available inorganic nitrogen concentration, mass/volume
C = available inorganic carbon concentration, mass/volume
Si= available inorganic siliconcentration mass/volume.
A-47
-------
TABLE A-31. LITERATURE SUMMARY OF PHYTOPLANKTON HALF-SATURATION CONSTANTS
FOR NITROGEN, PHOSPHORUS, AND SILICA
(After Tetra Tech, Inc., 1992)
Species
mixed/natural populations
mixed/natural populations
mixed/natural populations
mixed/natural populations
Skeletonema costatum
Skeletonema costatum
Skeletonema costatum
Skeletonema costatum
mixed/natural populations
mixed/natural populations
mixed/natural populations
mixed/natural populations
Dunalliella tertiolecta
Dunalliella tertiolecta
Dunalliella tertiolecta
Dunalliella tertiolecta
Monchrysis lutheri
Monchrysis lutheri
Monchrysis lutheri
Monchrysis lutheri
Taxa
DIATOM:AVG
DIATOM:MIN
DIATOM:MAX
DIATOM:OBS
DIATOM:AVG
DIATOM:MIN
DIATOM:MAX
DIATOM:OBS
FLAG ELL: AVG
FLAGELLMIN
FLAGELLMAX
FLAGELL:OBS
CHLORO:AVG
CHLORO:MIN
CH LORD: MAX
CHLORO:OBS
CHRYSO:AVG
CHRYSO:MIN
CHRYSO:MAX
CHRYSO:OBS
N03
HgN/L
15.25
1.40
71.40
43
6.30
5.60
7.00
2
64.12
1.40
144.20
5
7.14
1.82
19.60
4
7.14
5.88
8.40
2
NhU-N
ngN/L
22.46
0.28
130.20
30
19.74
6.16
50.40
4
56.47
15.40
79.80
3
2.17
0.28
4.90
6
4.37
0.42
7.42
9
Si(OH>4
jigSi/L
55.00
2.46
158.20
39
24.98
11.76
50.68
9
ND
ND
ND
PCM-P
ngP/L
27.46
10.00
53.32
5
ND
ND
ND
ND
TABLE A-32. NITROGEN TRANSFORMATION RATES IN WATER COLUMN (day-1).
(After Bowie etal., 1985)
PONa to NH3
0.035
0.03
0.03
0.03
0.075
0.1-0.15
0.1
0.003
0.1
0.1-0.4
0.02-0.04
NH3 to N02
0.05
0.02
0.02
0.1-0.5
0.1-0.5
NH3 to N03
0.04
0.12
0.20
0.09-0.13
0.05-0.15
NO2 to NOs
0.25
0.25
5.0-10.0
3.0-10.0
Reference
Thomann etal. (1975)
Thomann etal. (1979)
Di Toro and Connolly (1 980)
Di Toro and Matystik (1 980)
Thomann and Fitzpatrick (1982)
Lung (1986a)
Lung and Paerl (1988)
Tetra Tech, Inc. (1980)
Porcella et al. (1983)
Bacaetal. (1973)
Bacaand Arnett (1976)
PON = particulate organic nitrogen.
A-48
-------
TABLE A-33. SEDIMENT NUTRIENT RELEASE RATES
(After Thomann and Mueller, 1987)
Flux-Aerobic Conditions
(mg/m2 -day)
Flux-Anaerobic Conditions
(mg/m2 -day)
Location
Total Dissolved
Phosphorus
NH3-N
Total Dissolved
Phosphorus
NH3-N
Si-silicon
Reference
Muddy River, Boston,
MA
Lake Warner, Amherst,
MA
Lake Ontario
Lake Erie
Western Basin
Central Basin
Eastern Basin
White Lake, Muskegon
Co., Ml
Cape Lookout Bight,
NC
LaJolla Bight
Potomac Estuary
9.6 (96 Max)
1 .2 (26 Max)
0.2
6.0 44
3.0 30
2.0 22
34 32
40 (winter)
325 (summer)
2.4
(-13to 16)
1-10
Fillos and
Swanson (1975)
Bannerman
etal. (1975)
DiToro and
Connolly (1980)
297 Freedman and
Canale (1977)
Martens et al.
(1 980)
Hartwig (1975)
Calendar and
Hammond
(1982)
TABLE A-34. SELECTED MEASUREMENTS
OF SOD AND BENTHIC AMMONIA
FLUX IN PECONIC BAY,
JULY 1989 (after Garber, 1990)
rates of benthic nitrification and benthic denitrification
are summarized in Table A-35.
Region
Gardiner Bay
Little Peconic
Bay
Station
BT-6A
BT-3
SOD
(g 02/m2
-day)
0.76
0.8
NH3 flux
(gN/m2
-day
14.6
33.3
Temp
(°C)
23.7
24.8
Using the N:P ratio of 7.2 mg N:1.0 mg P, benthic
regeneration of phosphate can be estimated as:
j PCM =JHN3 (1mg P/7.2 mg N)
wherejPO4 is in units of mg P/m2-day and jNHs has
units of mg N/m2-day. In addition to benthic release
of nitrogen, benthic uptake of ammonia and nitrate
can be a potentially significant component of the
overall nitrogen balance in a stream or river (e.g.,
Williams and Lewis, 1986). Reported measured
A-49
-------
TABLE A-35. REPORTED RATES OF BENTHIC NITRIFICATION AND BENTHIC NITRATE LOSS
(as mg N/m2-day)(Negative values indicate water column loss to the sediments; positive
values indicate sediment source to the water column)
Study Site Range Reference
Benthic Nitrification
Lake Mendota -540to-900 Kaushiketal. (1981)
Sewage-enriched stream Oto-150 Kaushiketal. (1981)
Laboratory stream -29a to - 69b Kaushik et al. (1981)
Benthic Nitrate Loss
Sewage effluent/canals -913c Kaushik etal. (1981)
Swifts Brook/Ontario -480 Kaushik etal. (1981)
Duffin Creek/Ontario -40 to-300 Kaushik etal. (1981)
Laboratory columns -61 to-166 Kaushik etal. (1981)
Silt-enriched columns -100to-251 Kaushik etal. (1981)
Sand/gravel columns -20 to-60 Kaushik etal. (1981)
Streams -50a to-90b Kaushik etal. (1981)
Upper Potomac estuary -266 to +23 MWCOG (1987)
Gunston Cove, Potomac .35 Seitzinger (1988)
Notes:
3 Absence of tubificid worms.
b Presence of tubificid worms enhances nitrification and denitrification/nitrate loss rates.
c Reported units are mg NO3-N/m2-day.
TABLE A-36. REPORTED VALUES FOR ATMOSPHERIC REAERATION
TEMPERATURE COEFFICIENT (After Bowie et al., 1985)
Temperature
Coefficient, B Reference
1 -047 Streeter (1926)
1-0241 Elmore and West (1961)
1-0226 Elmore and West (1961)
1 -020 Downing and Truesdale (1955)
1 -024 Downing and Truesdale (1955)
1-016 Downing and Truesdale (1955)
1-016 Streeter (1926)
1.018 Truesdale and Van Dyke (1958)
1.015 Truesdale and Van Dyke (1958)
1 -008 Truesdale and Van Dyke (1958)
1.024 Churchill etal. (1962)
1-022 Tsivoglou (1967)
1-024 Committee on Sanitary Engineering Research (1960)
A-50
-------
A.12 TEMPERATURE EFFECTS ON „ „ nr-2o ,A N
REACTION RATE COEFFICIENTS "T= Kw & (A 24)
in which KT and Kzo are values of the kinetic coeffi-
Water temperature plays an important role in affect- cient at temperatures T and 20 °C, respectively.
ing many first-order kinetic coefficients because the Tables A~36 tnrou9n A-41 Present ran9es of © values
reactions are temperature-dependent following the for a varietV of kmetlc coefficients.
usual van't Hoff-Arrhenius temperature correlation:
A-51
-------
TABLE A-37. VALUES OF THE TEMPERATURE COEFFICIENT
FOR CARBONACEOUS BOD DECAY
(After Bowie et al, 1985)
Temperature coefficient, Q
Temperature
Limits (°C)
Reference
1.047
1.05
Chen (1970)
Harleman et al. (1977)
Medina (1979)
Genet etal. (1974)
Bauer etal. (1979)
JRB Associates (1983)
Bedford etal. (1983)
Thomann and Fitzpatrick (1982)
Velz(1984)
Roesneretal. (1981)
Crim and Lovelace (1973)
Rich (1973)
1.03-1.06
1.075
1.024
1.021-1.06
1.04
1.05-1.15
(0-5)-(30-35) Smith (1978b)
Imhoff etal. (1981)
MWCOG (1982)
Bacaand Arnett (1976)
Bacaetal. (1973)
Di Toro and Connolly (1980)
5-30 Fair etal. (1968)
TABLE A-38. TEMPERATURE COEFFICIENT, 0, FOR NITRIFICATION
(After Bowie etal. 1985)
Reference
Stratton (1 966)
Knowlesetal. (1965)
Buswelletal. (1957)
Wild etal. (1971)
Bridle etal. (1979)
Sharma and Ahlert (1977)
Ammonia Oxidation
1.0876
1.0997
1.0757
1.0548
1.1030
1.0689
Nitrite Oxidation
1.0576
1.0608
-
-
-
1.0470
Laudelout and Van Tichelen (1960)
Mean
1.0850
1.0689
1.0586
A-52
-------
TABLE A-39. TYPICAL VALUES OF THE TEMPERATURE COEFFICIENT FOR
SOD USED IN WATER QUALITY MODELS
(After Bowie et al., 1985)
Model
0
Qioa
Reference
DOSAG-3
QUAL-II
Vermont QUAL-II
Lake Erie Model
WASP
WASP
LAKECO
WQRRS
ESTECO
DEM
EAM
EAM
USGS - Steady
AQUA-IV
EXPLORE-I
Laboratory/Field Studies
1.047
1.047
1.047
1.08
1.08
1.1
1.02
1.02-1.04
1.02-1.04
1.04
1.02
1.047
1.065
1.02-1.09
1.05
1.040-1.130
1.58
1.58
1.58
2.16
2.16
2.59
1.22
1.22-1.48
1.22-1.48
1.48
1.22
1.58
1.88
1.22
1.63
1.5-3.4
Duke and Masch (1973)
Roesneretal. (1977)
JRB Associates (1983)
Di Toro and Connolly (1980)
Thomann and Fitzpatrick (1982)
O'Connor etal. (1981)
Chen and Orlob (1972, 1975)
Smith (1978)
Brandes (1976)
Genet etal. (1974)
Bowie etal. (1980)
Tetra Tech (1980); Porcella et al.
Bauer etal. (1979)
Baca and Arnett (1976)
Bacaetal. (1973)
(1983)
Zison etal. (1978); Whittemore (1984)
1 Qio = ratio of K (20°C)/K(10°C) = e10from K(T) = K2o OT 20
forT = 10°C
TABLE A-40. TYPICAL EXPERIMENTAL VALUES OF THE EFFECT OF TEMPERATURE ON SOD
(After Whittemore, 1986)
Reference
Edbergand Hofsten (1973)
Edwards and Rolley (1965)
Karlgren (1968)
McDonnell and Hall (1969)
Pamatmat (1971)
Thomann (1972)
Fair etal. (1941)
Baity (1938)
Masch etal. (1971)
Range, °C
5-15
10-20
15-25
10-20
2-22
5-25
5-10
10-30
10-25
22-29
_
Coefficient, 0
1.130
1.180
1.040
1.077
1.090
1.067
1.088
1.065
(1.07)a
(1.05)a
1.0159
Estimated based upon author's conclusion.
A-53
-------
TABLE A-41. TEMPERATURE DEPENDENCE OF BENTHIC AMMONIA REGENERATION
IN ESTUARINE WATERS
Location
Narragansett Bay
Peconic Bay
mean
range (N = 8)
Chesapeake Bay
(Anoxic mainstem)
Qio
4.48
7.0
0.8-11.6
3.0
0
1.16
1.215
0.98-1.28
1.116
Reference
Kremerand Nixon (1978)
Garber (1990)
Garber (1990)
Note: Relationship of Qio to & and reaction rates at 10°C (Kio) and 20°C (K2o)
Qio = K2o/Kio
0 = 10allogQ10
0 = exP(0.1 In Qio)
A-54
-------
APPENDIX B: SAMPLE TOTAL MAXIMUM DAILY
LOAD ANALYSES
B.1 INTRODUCTION
Two studies, the Rivanna River study and the Willamette
River study, are included in this appendix to illustrate the
application of WASPS and QUAL2E—two EPA supported
stream water quality models. Additionally, an analytical
solution approach is included in the Rivanna River study to
demonstrate how different water quality parameters can be
directly calculated, without the use of a complex simulation
model, for a relatively simple BOD-DO and eutrophication
problem. The Willamette River Basin modeling study high-
lights the use of the QUAL2E model in assessing dissolved
oxygen (DO), nutrients, and phytoplankton biomass for a
large river system in Oregon.
Readers are cautioned that site-specific data must be used
when performing TMDL analyses, and that values pre-
sented in this (or any other) example must not be substi-
tuted for site-specific data. When such data are not
available, applicable values should be developed by follow-
ing the procedures detailed in the text.
B.2 RIVANNA RIVER STUDY
B.2.1 Problem Setting
This example is based on the earlier example problem
presented in the Technical Guidance Manual for Perform-
ing Waste Load Allocations (USEPA, 1983) in calculating
simple biochemical oxygen demand and dissolved oxygen
conditions in streams. This example extends further to
include a eutrophication problem and assessment of vari-
ations in channel geometry. Addressing the algal growth
as a component of this example provides a more compre-
hensive analysis of production and respiration processes
and their effect on dissolved oxygen in rivers.
A city of approximately 60,000 people discharges its waste-
water into a relatively small river, Rivanna River, with an
average annual flow of about 250 cfs. The city's wastewa-
ter is presently treated by a trickling filter plant that provides
about 85 percent BOD removal and has reached its design
capacity of 7.5 mgd. The population is projected to increase
by more than 50 percent to 92,000 people (with a range of
75,000 to 120,000 people) by the year 2000. Expansion
of the treatment plant to a capacity of 11.5 mgd and
provision of an activated sludge system for secondary
treatment has been proposed.
Rivanna River, for 60 miles downstream of the treatment
plant outfall, is classified as B1, which has a designated
water use of fish and wildlife propagation. The pertinent
State water quality standards for this example are a mini-
mum DO level of 5.0 mg/L, a maximum un-ionized ammo-
nia concentration as specified by EPA Ambient Water
Quality Criteria for Ammonia (USEPA, 1984), and a narra-
tive nutrient criteria as specified in the State water quality
standards. The river is used locally for fishing and is
bordered by several campgrounds and a State park. Ap-
proximately 30 miles downstream of the treatment plant
outfall is a wider, slow moving section of the river, which
under low flow conditions has experienced algal blooms,
with chlorophyll a proliferation in the range of 30-40 ug/L.
Occasional violations of DO and un-ionized ammonia have
been observed downstream of the wastewater treatment
plant. The watershed consists of approximately 60 per-
cent agricultural, 35 percent forested, and 5 percent urban
areas under existing conditions. The size of the urban
portion of the watershed is 9.4 square miles which is
projected to increase to 14.4 square miles under future
conditions (2000 A.D.). Future land use conditions are
expected to show a conversion of a portion of agricultural
land to urban areas. This more developed watershed is
estimated to consist of 58 percent agricultural, 35 percent
forested, and 7 percent urban areas. A summary of the
problem setting and treatment plant data is presented in
Figures B-1 and B-2.
B.2.2 River Characteristics
The river flow is gaged by the United States Geological
Service (USGS) 5 miles upstream of the treatment plant
discharge. The average monthly flows for a 30- year period
are summarized in Figure B-3(A). The
B-1
-------
POPULATION PROJECTION: •
-
1900 If25 :S*6
mm USE
1980 2000 29W
ftW
5,
DC- CcrowtraEcn • O^-jaw ^an 5 1 ^
-JfM€P-z«I Atnncnia • L*SS sfan o -32
and Use
a. Active and locally poputof fishery
b. Several campgrounds aod parks have river as an attfftctton
Limited water quality thaw occasional violations ot
DO and un-ionized ammonia Biandards under low flow
conditions; parlodic Wo0ms occur in the wide
section of the stream.
B-2
-------
A/TREATMENT FACILITIES
Tn ck! ing filler plant constructed in
Plant -now at design capacity of 7.5 MGO
Effluent does not meet iNPQES permit for
treatment
Present:
Proposed; Activated sludge s^aiam to provide s-econdary treatment
B. EFFLUENT CHARACTERISTICS
Fit™
MQD
ODD*
Kg/day
n*g,'l
rrgrt
NEJOQ
nxj;1
Present Deafgn • •'
7.5
40
1136
80
2271
15
426
68
1930
111.5
30-
.1306
60
2612
15
653
2960
PrBlimiruiry baais • fitDr.dnriS M^LiJidjri,1 Irontmont
oat Ifie SQ-fn^fi. BOO? u«6d in *i§ eitaitfihS repfMfiflB l» ieconSanf !T&a(mgrY) 0ffluvil standard, and tha? bertlnr parfann.
a niay occur during wdrfn weather. TIjarBloro. affluanl Cha«C5arrSliea uSWiwn nwdilir!g rsal-lilo sfeaftsn^ shogld rflftncl Hi a pa"
ffl Old prcpaaafl Tanlity dunng ffi6 crilkaJ parked.
=2,0.
SOD tfl?1» l
NQOD m SlDklvidnMilrlc oxygan f o-q uirenmn'j for aiidatl
nitrogen fornu = 4.JS? z NH^N (atfluvnt axldiuifilo organic ni1ro-g«n if
FIGURE B-2. TREATMENT FACILITIES AND £f FLUENT CHARACTERISTICS.
B-3
-------
.
Vbmfa
10
1
Depth =0,565 Q
**
us
Deep Charm*)
10
I
f
i
C.I
*"
t« W.0
(«« y,',,
s
st 10
wte
C.
I
Q.td -
a m
Velocity «• 0. 065 a
"*1
pw*<»|
"
1
• O.i0
DO1
Q1
«4 C
flow Wl'
IDG 1DC.O
B-4
-------
average annual flow is about 250 cfs with a minimum
monthly average low flow of 100 cfs, which occurs in
September. However, the State requires that minimum
DO standards must be met for the minimum 7 consecu-
tive-day flow with a return period of once every 10 years
(7Q10). (As discussed in Book VI, Design Conditions,
other design flows may apply under summer conditions.)
From a statistical analysis of the flow records, the 7Q10 is
determined to be 30 cfs and occurs between August and
October. (For further discussion of critical conditions, refer
to Section 3.3 of this document.)
Critical conditions of DO, un-ionized ammonia concentra-
tion and nutrient enrichment in the river occur during the
summer when the flow is low and the river's water tempera-
ture is high. From 11 years of water temperature data
collected as part of a limited river monitoring program, the
maximum average monthly river temperature is calculated
to be 27°C and occurs in August. The river condition
selected to represent critical conditions assume a river flow
of 30 cfs and a river temperature of 27°C.
Note that for this example, both the critical low flow (7Q10)
and the maximum average monthly temperature have
been used in the projection, even though historical records
(summarized in Figure B-3A) show minimum average
monthly flow and temperature to occur in different months.
This tacitly assumes that although the minimum average
monthly flow occurs in September, the critical 7Q10 could
occur in August, the month of maximum average tempera-
tures. In areas where it can be shown that the 7Q10 will
occur in a month with lower temperature, then the appro-
priate combination should be used rather than each of the
extreme values. For example, critical low flows frequently
occur during October in the northeast. An appropriate
approach in such cases would be to define the 7Q10 and
temperature conditions for each of the critical months (e.g.
June-October), determine which month is most critical, and
use that month in allocation calculations.
For this example, assume that three surveys were con-
ducted to measure stream cross-sectional area under
different flow conditions. Cross-sections were measured
at 20 locations within the 65-mile long study area. From
analysis of cross-sectional area measurements, it can be
concluded that the study area may be divided into three
relatively homogeneous reaches as shown in Figure B-1.
The first and the third reaches have almost the same
channel geometry, while the second reach has a wider and
deeper channel. Throughout the length of each of these
reaches the river is assumed to have uniform geometry.
The first reach stretches from the STP outfall to 30 miles
downstream. The second reach is 10 miles long and
begins 30 miles downstream of the STP outfall. The final
reach is 20 miles long. Two representative cross-sectional
areas are used to characterize the reaches for each set of
flow conditions; one cross-sectional area at a given flow
represents the first and the third reaches, and another
represents the second reach.
The average river velocity during each of the cross-sec-
tional area survey periods was computed by application of
the equation VELOCITY = FLOW/AREA. The average
flow for each survey period is obtained from USGS records.
Alternatively, dye study techniques could be used to more
accurately determine average velocity for a given river
section.
River cross-sectional area, depth, and velocity generally
form linear relationships with flow when the data are plotted
on log-log scales. Figure B-3B shows two sets of log-log
plots derived from stream cross-sectional data. One set
represents the relationships between the channel geome-
try and flow for the narrow and shallow sections between
0-30 miles and 40-60 miles downstream of the discharge.
Another set represents the wide and deep channel be-
tween 30-40 miles. Figure B-3C shows the relationship
between stream velocity and flow. Interpolations and ex-
trapolations of river geometry and velocity at specific flows
can be made directly from the log-log plots or can be
computed from the equation of the line of best fit. The
equation for the line of best fit has the form Y =IQs where
I is the intercept at Q = 1 cfs and s is the slope scaled directly
from the plot. A summary of the mathematical expressions
of the graphs presented in Figure B-3 are as follows:
For the narrow and shallow sections
AREA (m2) = 15.358 [Q (m3/s)f'57 (B'1>
3,_\i0.45
DEPTH (m) = 0.565 [Q (m3/s)]
(B-2)
VELOCITY (mis) = 0.065[Q (m3/s)f'43 (B-3)
For the wide and deep sections
AREA (m2) = 57.659 [Q (m3/s)]0.57 (B-4)
DEPTH (m) = 01.413 [Q (m3/s)]0.45 (B-5)
VELOCITY (mis) = 0.017 [Q (m3/s)]0.43 (B-6)
B-5
-------
River area, depth, and velocity can be computed for any
flow in the appropriate section of the river by using the
equations listed above. If river geometry data are available
for only one flow condition, the relationship presented in
Section A.3.1 (Equations A-1 through A-4) can be used to
calculate river depth, area, and velocity at other flows.
B.2.3 Review of Water Quality Data
Historic river water quality data within the study area are
limited. As part of the State environmental department's
overall monitoring program for this river basin, water sam-
ples are periodically collected at stations located at river
miles 25 and 55. These data represent approximately one
grab sample per month during the summer over a 5 year
period. A review of these data reveal occasional water
quality problems with regard to dissolved oxygen and
un-ionized ammonia. Further downstream, periodic algal
blooms violate the State's narrative nutrient criteria. Prob-
lems appear to occur only under extreme low flow condi-
tions. Since there are indications of occasional violations
of water quality criteria, a TMDL is needed to assess load
allocations under future conditions. The TMDL should
address the occasional DO, un-ionized ammonia prob-
lems, and the eutrophication in the downstream recrea-
tional area. The TMDL should consider both upstream
nonpoint source loadings and the local point source dis-
charge.
Considering the conditions under which problems occur,
an appropriate level of effort for a TMDL study initially can
be limited to the analysis of a single river water quality data
set collected during summer low-flow conditions. Accord-
ingly, a survey was conducted during two days in August
when the river flow averaged 100 cfs and the river water
temperature was 25oC. The results of this survey and the
State environmental data are presented in Figure B-4.
The DO data in Figure B-4, both August 1979 data and
historical data, show stream DO levels above the standard
of 5.0 mg/L at a flow condition of 100 cfs. The increase in
river BOD5 and the ammonia concentrations at zero mile
point showthe impact of the treatment plant discharge. The
gradually decreasing ammonia profile and increasing nitrite
and nitrate profile suggest that nitrification is occurring in the
river. There is evidence that a natural nitrification process,
in which nitrate and some oxygen-demanding material are
removed from the water, may occur in some streams.
Un-ionized ammonia has been demonstrated to be the
principal form of ammonia toxic to biological life. Tempera-
ture and pH have been shown to affect ammonia toxicity.
The EPA Ambient Water Quality Criteria for Ammonia
(USEPA, 1984) requires two conditions to be met—a 4-day
average for chronic toxicity and an 1 -hour average concen-
tration for acute toxicity. For a river temperature of 25°C
and pH of 7.75, with salmonids or other sensitive coldwater
species absent, the 4-day average standards are 0.043
mg/L un-ionized ammonia (0.0353 mg/L un-ionized NH3-
N) and 1.39 mg/L total ammonia (1.142 mg/L NH3-N). For
a 1 -hour averaging period standards are 0.32 mg/L un-ion-
ized ammonia (0.263 mg/L un-ionized NH3-N) and 10.384
mg/L total ammonia (8.384 mg/L NH3-N). During the
August 1979 survey, the ambient total ammonia concen-
tration was less than the standard of 8.384 mg/L total
NH3-N for the 1 -hour average condition. The 1 -hour aver-
age values are used for calibration so that the worst case
scenario can be portrayed. Historical river water quality
data collected near the USGS gage provides concentra-
tions under 7Q10 flow conditions. Table B-1 shows esti-
mated data for upstream boundary conditions used in
modeling. The boundary conditions take into account the
proportionally highly nonpoint source loads under the 100
and 250 cfs flow conditions. Monitored concentrations of
water quality constituents inthewastewater treatment plant
effluent are listed in Table B-2. Table B-2 also shows
estimated effluent concentrations for management alterna-
tives used in modeling (e.g., activated sludgetreatmentand
advanced water treatment). These values were obtained
through a literature search of typical loadings from various
levels of treatment.
B.2.4 The Simplified Analytical Solution
Approach
The Simplified Analytical Solution Approach uses the exact
solutions to differential equations presented in this docu-
ment to analyze the Rivanna River example. This approach
provides a better insight into the fundamentals of modeling
DO and eutrophication problems in rivers. The analytical
solution approach is similar to the methods described in the
Technical Guidance Manual for Performing Waste Load
Allocation, Simplified Analytical Method for Determine
NPDES Effluent Limitation for POTWs Discharging into
Low FlowStreams (USEP'A, 1980) in calculating ammonia
toxicity and DO concentrations. The analytical solution
presented for DO presented here expands on the modified
Streeter-Phelps equation to account for phytoplankton
production and respiration
B-6
-------
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z L * * »
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10 •) tO 10 j<3 tO io 'X5 r
Dist^oe (ttulet)
-? ~~*- - — "=™
1 2 —
1
\ .-
i . • T
t * *^.«.
= L,....i.. , .«.. , .." f -.
• iO fO 10 2*3 3O *Q SO ^
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Dissolved
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Pattwoe (suJe)
30 -
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10 1 T f
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-id ** t<> r, 50 *? 50 to *;
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• 10 0 10 20 30 4t} SO 60 70
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DistMJM <£Bilei DwtuBce *,i
SjlTSiOGEN AND PHOSPHORUS, CHUWPHYLL. A,
AWO ^O DATA i August 23-24 1'
B-7
-------
TABLE 8-1. UPSTREAM BOUNOARV CONDITIONS.
1
$>
P
Pargurre'er Uncs
L,
CBOD., . mg/L
TN 2 mg/L
(S*H , " mg/L
NO, ^ NQj i mg/L,
Og N j mg/L
ITQT - PAR ^ y,'d
PholQpenoc ' 'Jays
Temperature I :C
pH
PO4 mg/L
Pl-ylwjlarnton ^g/L
Existing Faw Ccndil.ons1
2SO ds*
{7.070 mVs)
9.6^CO
2.5782
0.1437
0,7779
1 .6565
144.1
0.61
15
7.75
o.osa
2409
1 30 c4s"
(2.932 nj,'s;.
S.C663
2.^126
C.134S
0,728
1.SS01
94.6
0.55
25
7.7S
0.099
2.702
30 Sis1
(C.B49 m'/s)
20C72
1.7907
0.10
R.1'-rB Flew
Contfrtions^
30 cfas
«;0,849 mVs)
2.CO?2
1.7907
0.10
0.5*02 i 0.5403
1.1505
1136
1.1505
113.6
0.5 SS [ 0.58S
arc
7,75
0.14
3.80
37'=C
7.76
0.14
3.BO
" Existing Conditions (Plant sflluanl = 7,5 mgd; Land usos: AgncuNuffl 60%, Fixeslry 35%. Urban S%) Pop. = &3.QQQ
: Future CondiiiorfS i Plant atfluani = * 1.5 mgd; Land uses: Agriculture 5B%. Fcirescrv 35%, Uftjan 7%J Pop, = 92,000
1 Repr0$rJfliaiivQ May data
' Repreaeri1a1iva September data
5 Eslimaled August data
TABLE B-2. CHARACTERISTICS OF EFFLUENT TREATMENT FOR DIFFERENT PROCESSES.
Water Quality
Constituent '
NH3
NO3
PC*
Clil_a (iiglL)
caoo*
CBOO^
: Oxygen
OrgN
\ Org P
I
TM
TP
Tricklirg Ffflar
15.0
,0-
4.6S8
,3.
^0
SO
a.o
-3-
I.SS3
15.0
625
Activated Sludge Trealmenl
1S.O
-0-
4.B69
-0-
3C
60
B.O
-0-
1.379
15.0
5.§4
AdvAncetl Waler Trealmenl
I
1.3
-0-
0.70
-0-
30
60
a.o
-0-
0.3
1
..5
1
B-8
-------
as well as, BOD, SOD, and reaeration (Thomann and
Mueller, 1987). Although ammonia toxicity is likely to occur
near the vicinity of the wastewater treatment plant dis-
charge, this approach also shows how to calculate the
ammonia concentrations at downstream locations. The
allowable instream total ammonia concentration is based
on the un-ionized ammonia concentration as a function of
pH and temperature. The EPA Ambient Water Quality
Criteria for Ammonia—1984 (USEPA, 1984) describes
how to calculate allowable chronic and acute toxicity levels
for un-ionized and total ammonia at a given pH and
temperature. This approach also shows clearly the effect
of changing channel geometry on DO sag. A simplified
analysis calculates the location of DO sag due to a waste-
water discharge for BOD decay only. If the problem is
further compounded by conditions associated with lower
reaeration coefficients and phytoplankton growth, a sec-
ond DO sag may occur. Which of the two sags produces
the minimum DO depends on overall conditions. The
analytical solution approach provided here includes a more
elaborate process for dealing with nonuniform channels
and eutrophication issues. In the absence of phytoplank-
ton growth and any significant variation in channel geome-
try, the analytical approach reduces to the method
presented in the above mentioned document.
The analytical solution approach also addresses some of
the limitations of reaeration models. The method pre-
sented here uses a discrete segment approach similar to
that employed by more sophisticated computer simulation
programs. To avoid the tedious work of repetitive calcula-
tions, a spreadsheet or a short computer program can be
set up to solve the appropriate mathematical equations.
Repeated solutions of the equations presented here were
used to generate solutions at desired locations of the
stream. Application of this approach is, however, limited
to steady state conditions. A set of sample calculations are
shown in Table B-3. The first step in the analytical model
application is to divide the system under study into reaches
with relatively uniform physical characteristics. The stream
is divided into four reaches based on wastewater treatment
plant discharge location and channel geometry. The up-
stream boundary conditions were used as initial conditions
for the first reach. Concentrations of water quality constitu-
ents at the downstream end of each reach are used as
initial conditions for the next reach. Therefore, for the
second reach, initial conditions are the concentrations
resulting from mixing of the treatment plant effluent with
instream concentrations at the end of the first reach. Efflu-
ent from the wastewater treatment plant is assumed to mix
completely with stream water immediately after discharge.
Since the second reach is 30 miles long, a more detailed
assessment could be performed by calculating concentra-
tions at various locations along the stream, possibly more
densely near the discharge. The calculations shown in
Table B-3 can be grouped into six steps, 1) calculating
physical parameters, 2) calculating net phytoplankton
growth rate, 3) checking nutrient limits for phytoplankton
growth, 4) estimating reaction rates, 5) calculating DO
components and DO concentration, and 6) calculating
concentrations of nutrients, BOD, and chlorophyll a. This
simplified approach does not include analysis of organic
nitrogen, organic phosphorus, and exchange of nutrients
between water and sediment. Additional equations can be
used to incorporate these factors in the analysis of phyto-
plankton growth. Alternatively, more detailed water quality
models, such as WASPS, can explicitly consider a wider
range of nutrient species, interactions, sources, and sinks.
As stream water quality data are available for 100 cfs flow
conditions, it is used for calibration. For an analytical solu-
tion approach, calibration consists of the determination of
the reaction rate coefficients (presented in Chapter 2 and
Appendix A) that describe the spatial distribution of CBOD,
ammonia, nitrite and nitrate, phytoplankton growth, and
DO. The first set of calculations must be made based on
an educated guess of reaction rates. Then a comparison
between the calculated values and observed data will allow
the modeler to make a better estimate of reaction rates.
The overall loss rate of N BOD can be estimated solely by
matching observed ammonia and nitrate data. The overall
loss rate of CBO D and the effective deoxygenation rate can
be estimated by matching observed CBOD and DO data,
respectively. Calibration of the analytical solution model,
as shown in Figure B-5, provides 0.15 day-1, 0.30 day-1,
0.30day-1 and0.20day-1 for the overall loss rate of N BOD
(Kn), the effective deoxygenation rate (Kd), the overall loss
rate of CBOD (Kr) and endogenous respiration of phyto-
plankton, respectively. Loss rates are determined by finding
a value that provides the best fit with the August 1979
CBOD data. The CBOD removal rate by settling (Ks) is
assumed to be zero for the secondary effluent, and the
CBOD oxidation rate (Kd) equals the total removal rate (Kr).
These values can be adjusted for simulating water quality
constituents under different management conditions. The
atmospheric reaeration rate (Ka) is determined in accord-
ance with Table A-24.
B-9
-------
TA3LE B-3. SAMPLE CALCULATIONS FOR REACH 1,
Lei us a$wrne IM a $ttgi-sp«cific investigation provided followm^ additional
Background Light sxtinraion oMffitierrt, K, = I -SO at'
Endogenous respra1ic.il of phytoptonkton, y f = 0,20 dby"'
Pfiytoplankloni settling rate, Vt =05 m>'" day
Cartson 1o chlorophyll a raila, ac - 33 tzg C/ ,T^ C"W a
Nitrogen la chlorophyll a ratio, a v = 5 & W£ iV / JJf CW «
Phosphorus, to clilOTOp*)iyll a ranc-, a^ = 0 "9 ng P f fsg Cki a
Phytoplanklon maximumgrawlh rate, (!M - ISdrt' ' af 30'"C
At x = S.O miles, wltldi is |r-!D = 1.8- L066':I3-3IJ| = 1.47* (Ay-1 12-
Ligrit extinction coflfficient considering Ihe self shading or a(ga« (Rn«y, 1956).
^ = K.i + 0.008 S X9 + 0.054 . A^ , wh»w Aa n the Chi a
= L5 -t- Q.QQ8S- 2.702 4- 0,054 • 2 7-Q2" = I 63 w"1
Ugiil dependent gfowtlt redudii«i factor,
-*« l136
^ = 0 223 <
12-1 Sb)
t
\25 + (I3S+- 728} ]+• 99.2
(2-17)
= mMi{G971,G99) = 0971
B-10
-------
TABLE B-3. (CONTINUED)
growth rait after adjusting farlernperatu™. liphl arxi nutrianl liffirt
6' P = (JrfLrx =2478- 0.4 56 • 097 1. = 1.097 itoy ' '
Temperature adjusted endogenous feiara-ion raw
D,. = .HJ, • LOS**"" =02-10*'= 0294
death tut,
D 31 0 294 + 0,0 = 0.294
aretwih raw,
C =6*?-D,<-— =
? P H
ni] Ch«ek nutrtont limn
O.S
0.902
= 02
{2- 1 4)
-------
TABLE 8-3, (CONTINUED)
f'.v = --In
?" artd t\ > t' no nutrient WmH occurs in the flrS reach,
(4-9)
nt«*
Almoapheilc reaeratlon rala using Bennett and RaChburj i1§72j famiula :
202
01017
'— -
1-3281 i-
{ ft
[m
adjuiiment maerailon rale.
0.902m -3.281
\ m
- = 1.66 day~
A'24)
U 45 important to check lh« valy* of nsieratien f»t* at eacft raaeft. Hydres4S«iiea (19?1) suggeas a
minimum value of the owpen transftr «effici«fH (ojc^^fl iffl^tor ewfflcieni , K<_ « K, H) ol D.s to 1 .0
rwday. if KL H IMS than 0.6 m/diy at »y (*«eli, ¥* shOuW 6« adjust^
TM folitswirw valuis of Kg. Kt arid K v^ere deiennined ihrouoh cainaraftlon j
K, =
l 2QX
J^tf = 0,22 • 1 OT:^" = 0.
JC, =038- 1,047 &1S = 0,
JC., = O.J8 • l.047ilj"" = 0,30
B-12
-------
TABLE B-3. (CONTINUED)
v) Disioivid
Saturated cancenif alien of Do al mem s«a level and z«ra salinily is given in APHA (1985) as,
,-_,,_
Al T » 25
L^i**' *" -* *: '*** "' j
:r*:7! i »;• ii'iT, y,' I
. initial
a = c, - q, = a 263 - a 3 = -o 017 «^ / /.
DO deficit at 1fie end of the reach ts gwcn by
" -K-EX
« ST = -0.00646 m£ / £.
CEOD
CBODU, L» = 2 0 /„ = 2 0 • 4;03 = 8.06 mg f L
L-*.'1 »e-*V j
*,-A;
0,38-8.06 r H:H*O*ISJ -19*0*1^1
_ 1^-,,-OU _ g < F, , I
= 0.53l5rag/L
NBOD
», IJ' = 4.S7 [ Ar//j ] - 4.S 7 • 0. t J 5 = 0 6 1 1 mg t L
if rw t
^,v^> -*^' _ -K
"5*
0.22-0.617 r^ji, », 3 r _ -
1.906- 022
= 0.051 8 mg/L
(i.e.
rallo.
a0 s 1.67 ^ a 2.67-33 (J4^ O, t tig Q (wr C i m Chf} = 88 1 1 tig Q f
B-13
-------
TABLE B-3. (CONTINUED)
0*7-0 2fl«l-
•
I
(. L
(1906-024?);
_ -
|Jt 1
SOQ eai^rti
= 05
^
£3
^
-[I-.
.906
Sybstltuling the values in lh« DO
/> = ^O.OO646 + 05315 + O.OS ] S - Q.04fi + 0.3 59 = d.*9 my / L
TTlsnjforB. Ihe dissolvad oxygen coneertration ju«t upttrtam of tti* discfiai^e (i.e. x * 5 miles)
C = Ct - D = S.263, - O.S? = 737 M^ f L
vi) COirte»nUitiQ« of oth*r w«t»r quality eenftHutoll*
CBODS Oincantrailon
as
f =403e"1'3i:<"'!S"=2S46m^.,'£
= O.I I tag ft' f L
Nitrate and nitrita
= O.L35«H"-
JSJUUMM
= I NO - NO 1 4- r VJV 1 -rw 1 - SH^fAL13-"' - i\
^j T'.J'I J * l,,jrt JL.rt ' I > T4 J j,ju.«fl I J TJ!,I! i J.™fl _ 1 ^ L J
* . M J 1 J^^^U * l-i-lTM! ^J ^ jp
T
= 0.72S 4 0135 - 0 JI - •"• "}m 'l^LJtoi4w^»7 __ ^
0146-1000 x '
B-14
-------
TABLE B-3. (CONTINUED)
inorganic Qhostfiorus fs$sti«riifna no recycling from
••?. .1" si
~
~
G
0246-1000
= 0 0966 ing P ; L
N'ole that whusn a nulnerti limitirtg siluasion -0«aj*S due 10 -3^-pleiiQn of inofBJrtie pho$pfeOH4S H
critical to include recycling of TO^tere ptosphonj* from ftspifKl algas Otherwise,
population will drop atonistly due io nytrient limrted gncwrth.
population
= 2 704 • ^=*3""> = 1388 «y CM /
H1Jief« were no effluent di-so'iange from Iji* was«ewat*f treaimunl planl al the end of first naacii, all
DQtneantraliOTS cateulaled at llie end of first react* w3uW h*v* been u£*d as boundary eo«i«n(r*1i4*
for ?he $«00nd reach &«aus* of the wastewalar ireatmant plant discharge i1 x = 5 miles, all water
quality constituent concentration* JiHv* l.o b* cal&lafad assumirsa a campjet* rnlxlrtg of efnuenrt
wrth stream walec and the new values will b® «s«o<« 50 th«
Tli« foil-owing forrrtula is u&ad 10 calculated
r«5._ T Ud
, »c«S- and x=S* indicate upareim and dovrtisartirn of milt peirtt 5, i.s. tha disdwQa looiton,
B-15
-------
- L
t
£
5
I ,
* r-
•**
20
W
3 t
* ~ r
i ~ r
1
«
2
'
-ly § 10 20 3O 40 SO fiO TO
(tmle)
O £
> ^
L:S-
*
a
•= 20 \-
10 i-
>
,J 10
s
§ s
n
-
:
i 1 1
*~ i \
= M ^^
• X -
Ciii, i , , , , I , M , 1 , ,', .trtftLk-u^j^lii i Jj
f.
c
i
o
1
1
a
"" r-
12 E-
10 ^-
-a " » 1
a ~ ' „.— —'*' 1
""* »* *'~ 1
6 L J'l,^*-^'l ^"£ _ _ . -
4 1, * DO Standard
~
2 p-
rt bjOjJjJAlliJJLLlj_LLj.l,l 1 i >> 1 ' 1 1 1 M 1 1 1 U U-
40 0 i§ 20 JO 40 SO 60 70
B-&. CALJBfiATiON OF
-10 0 10 20 M 40 50 56 TO
DiitHiee (mile)
B-16
-------
(Ka) is determined in accordance with Table A-24. In the
wider section of the river, Ka drops below 0.5 day-1.
Hydroscience (1971) suggests that the minimum value for
oxygen transfer coefficient is 0.6 to 1.0 m/d. The minimum
Ka is then determined by dividing the minimum oxygen
transfer coefficient by the corresponding river depth.
Inthis example, the calculation of the DO profile agrees with
the measured data quite favorably without any adjust-
ments. In some cases, the calculated DO profile does not
initially agree with the data because of sources and sinks
of oxygen which may not be accounted for, such as SOD.
Benthic oxygen demand, phytoplankton production and
respiration are included in the analytical calculations. Be-
cause no exchange is considered between the benthic
layer and the water column, observed NH3 data are found
to be higher than model predicted values in Figure B-5. A
good agreement between observed and simulated data is
found in the chlorophyll a calibration. The observed inor-
ganic phosphate data shows a decline with distance down-
stream which is not matched by the analytical solution. This
difference is probably due to the assumption that only
dissolved phosphate is considered in the analytical solution
approach. The loss of phosphate by settling is therefore
omitted.
Having calibrated a model for CBOD, DO, nutrients, and
chlorophyll a (i.e., having defined site-specific coefficients
and accepting that some reservations on reliability exist
since the model is not tested against an independent data
set), an analyst may use the model to project water quality
impacts that might be expected under conditions of interest.
Three different flow conditions are modeled for existing
loading conditions to evaluate the range of conditions under
which problems may occur. For each of the three flow
conditions, the upstream boundary condition is varied to
account for changes in nonpoint source loading contribu-
tions. Under the 30 cfs case, upstream flow is considered
to be comprised wholly of baseflow. Ammonia, nitrate,
inorganic phosphate, chlorophyll a, BODS, and DO profiles
are presented in Figure B-6.
The calculated profiles in Figure B-6 show that present
wastewater loads would result in DO water quality standard
violations over approximately 8 miles of the river under
design 30 cfs drought flow conditions (7Q10 flow and a river
temperature of 27oC). The lowest DO concentration is
about 3.4 mg/L under 7Q10 flow conditions. Total ammo-
nia violates the standard for approximately 25 miles down-
stream of discharge. For a river temperature of 27oC and
pH of 7.75, the total ammonia standard that corresponds
to an acceptable un-ionized ammonia level is 1.14 mg/L
NH3-N. The highest predicted total ammonia concentra-
tion is more than three times the standard. It is important
to note here that if the observed effluent ammonia concen-
tration and the 100 cfs flow condition persists for 4 days,
violations of the standard would occur over a 25-mile
section of river downstream of the discharge. The BOD5
profile shows a significantly higher concentration immedi-
ately downstream of discharge, but it decreases rapidly
within first 30 miles downstream. Another major concern
is the growth of phytoplankton. The total chlorophyll a
profile shows that under 7Q10 flow eutrophic conditions
exist in the downstream reaches of the river. Accelerated
growth of algal is likely to result in a reduction of the
recreational value of the river.
The analysis of the three flow conditions shows that the
initial selection of 30 cfs as the critical condition is justified.
Developing the TMDL for the 30 cfs flow condition should
be protective of other flow conditions and result in a con-
servative estimate of required load reduction.
The next step in the analysis is to consider three alternative
levels of treatment for the wastewater treatment plant. The
three different treatment scenarios are simulated using
future population and land use conditions for the low flow
critical condition (e.g., 30 cfs). For each management
alternative, boundary conditions were defined by baseflow
concentrations (equivalent to 30 cfs case under existing
conditions). Each treatment alternative is then compared
with the water quality criteria for DO and un-ionized ammo-
nia. The narrative nutrient standard must be equated to a
numeric measure for comparison with model results.
Based on a review of similar rivers in the State a chlorophyll
a threshold of 20 g/l is selected as a target goal. Continued
monitoring should be used to reevaluate the target in future
years.
Calculated ammonia, nitrate, phosphate, chlorophyll a,
BOD5, and DO profiles for the projected wastewater loads
are presented in Figure B-7. No significant difference
exists between the effluent nutrient concentrations that
result from trickling filter and activated sludge treatment
processes under simulated future loading conditions.
Therefore, ammonia, nitrate and chlorophyll a profiles for
these two alternatives coincide. Effluent discharged from
the
B-17
-------
&
.*•««, nr
* ?
§ 6
§ c
•= >
is
1 4
o
,o 3
Z 2
i i
n,
U1
-1
•1
4 |
j^* 15
'S***'
^v
'•»*•
f"»
'•™* i
o_ 1
-1
^ c
35
30
^ 25
^ji
f 20
•-«»*
1 1S
a 10
s
fi
100 tfs j
ZSO cfs
_
r~ \
I X
— : \
:
i_ \ 4^ay avg. Standard
: """- X\ (pH.-=7,75,"I = 259C)
=- -| ^ -"-=— st^--
0 0 10 20 30 40 50 60 ?
Dwl™C* fm'1**>
—
_
_
r ""*"----_
-"— -
*i • Ttl 1 i 1 1 L 1 I..J i 1 1 « i * 1 * i i i 1 i 1 i i 1 ' " t 1 1 1 I I J
00 10 2fl 30 40 50 60 7
Di«4»*>
i
L i
* \
'— i
- \t
— \
: \
ij-i^^t,,^,^! , , ,,
0
fj
sh '
7 *
a
L» 5
2 .
'« 4
'-«-• 1
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RGURE B-6, CONCENTRATIONS OF NUTRIENTS, CHLOROPHYLL A, BODs AMD CO FOR DIFFER-
ENT FLOW CONDITIONS UNDER EXISTING LOADS,
B-18
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FIGURE B-7, PROJECTED NUTRIENTS. CHLOROPHYLL 4, BQOs AND DO FOR DIFFERENT TREAT-
MENT OPTIONS UNDER FUTURE LOADS,
B-19
-------
trickling filter or an activated sludge treatment process is
estimated to violate the total ammonia and the DO stand-
ards under the low flow critical condition. The minimum DO
simulated for trickling filter and activated sludge processes
are 2.4 and 3.5 mg/L, respectively. An algal bloom is
predicted to continue up to the end of 65-mile study area
and reaches 30 ug/L of chlorophyll a. Advanced water
treatment is the only option which allows the river to meet
total ammonia and DO standards at 30 cfs. It also controls
the algal growth to a maximum of 18.6 ug/L. The lowest
daily average DO concentration of about 5.0 mg/L occurs
at 3 miles downstream of discharge location. A sensitivity
analysis is recommended when differences between dif-
ferent options are small. Sensitivity analysis can also be
used in the determination of Margin of Safety (MOS). More
refined analysis can be used to reduce the MOS and in
some cases increase the allowable discharge.
B.2.5WASP5 EXAMPLE
This example shows an alternative approach to analysis of
the Rivanna River example and considers in greater detail
the in-stream impacts of changes in the contributions from
nonpoint source runoff, baseflow, and effluent concentra-
tions to the river reaches. WASP5 includes more detailed
transformation and exchange processes than an analytical
approach. For example WASP5 can account for the
settling of inorganic paniculate material, recycling of organic
nutrients to the inorganic pool, and nutrient flux from the
bottom sediment layer to the water column. This applica-
tion illustrates the capabilities of a steady state WASP5
model application, similar to the previous example. In
addition, the development of a WASP5 model allows the
user the flexibility to examine continuous simulation results
should further examination of dynamic nonpoint sources
loadings prove necessary.
The WASP5 model is developed based on the data
provided in Problem Setting and River Characterization
(Sections B.2.1 and B.2.2). The WASP5 model is config-
ured as 45 segments. The first 35 miles are represented
by 15 one-mile segments followed by 10 two-mile seg-
ments. The wider portion of the river is divided into 10
one-mile segments followed by 20 miles divided into 10
two-mile segments. Additional data required by the
WASP5 model includes downstream boundary conditions,
geometric data for each segment, and air temperature.
Downstream boundary conditions and initial conditions are
estimated based on observed stream data. Depth and
width for each segment are derived as a function of flow
and hydraulic coefficients.
The model is executed using a timestep of 0.05 days (1.2
hours) for the three flow conditions and three treatment
scenarios considered earlier. A 30-day simulation period
is used to allow sufficient time for the model to reach
steady-state conditions. The modeling results are based
on the final 5 days of the simulation period.
The first step in any model application is to calibrate the
model with existing data. For this example, the WASP5
model is calibrated to the observed data gathered from
August 23-24,1979. Figure B-8 shows the model calibra-
tion analyses for WASP5 with the observed data. The
analytical solution, described in the previous section, pro-
vides an additional check for model calibration. Analytical
solutions are generally recommended for evaluation of
model performance. This comparison demonstrates the
ability of each model to mimic the water quality responses
of the river and shows the similarity between the results of
each model for a steady-state application. Although the
results agree with the measured data, the WASP5 run has
significantly higher input requirements and demand a
greater level of effort for application. Table B-4 shows a
listing of the WASP5 input file.
Similar to the analytical solution, once calibrated, WASP5
was run for three different flow scenarios (30 cfs, 100 cfs,
and 250 cfs) and three treatment scenarios for future point
source loading (30cfs flow only) foratotalof6runs. Figures
B-9 and B-10 show the resulting (based on the last 5 days
of the simulation period) in-stream concentrations of oxy-
gen, BOD5, ammonia, nitrate, total organic nitrogen, and
total nitrogen for existing and future conditions, respec-
tively. The worst case, with DO below the recommended
limit of 5 mg/l, occurs under the 30 cfs low flow condition
(Figure B-9). Under low flow conditions, the baseflow
contribution is assumed to be constant and changes are
attributed solely to the increase in load from the treatment
plant. WASP5 simulation results show problems very
similar to those of analytical solution approach for ammo-
nia, nitrate, chlorophyll a and DO. Interestingly, with a 20
percent paniculate phosphate and a 0.5 m/d settling rate,
WASP5 is well calibrated for instream phosphate concen-
trations. This is important because it causes nutrient inhibi-
tion for phytoplankton growth and a resulting decline of
chlorophyll a
B-20
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B-21
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FIGURE B-9. WASPS PREDtCTION OF INORGANIC NITROGEN. PHOSPHORUS,
CHLOROPHYLL A BOD AND DISSOLVED OXYGEN FOR DIFFERENT FLOW CONDITIONS UNDER
EXISTING LOADS.
B-28
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FIGURE B-tO. PROJECTiD INORGANIC MTRQGEN, PHOSPHORUS, CHLOROPHYLL A, BODs,
AND DO UNDER DIFFERENT FUTURE LOADINGS UNDER LOW FLOW CONDITIONS.
B-29
-------
concentration at approximately 40 miles downstream for
existing 30 cfs flow conditions.
B.3 WILLAMETTE RIVER EXAMPLE
QUAL2E MODEL
B.3.1 Introduction
For the low flow condition, the WASPS run results in
approximately the same oxygen and ammonia concentra-
tions as that of the analytical example under both existing
and future conditions. Oxygen concentrations drop to
approximately 4 mg/L and ammonia concentrations reach
approximately 4.2 mg/L, resulting in predicted violations of
both oxygen and ammonia standards. The BODS plot
shown in Figure B-10 includes the demand exerted by
decaying algae which was not considered in the analytical
solution approach. In the WASPS model, benthic denitrifi-
cation is not accounted for since it is assumed to be
negligible.
B.2.6 Conclusions
For this example, the results showed that low flow condi-
tions (7Q10) represent a critical condition for maintenance
of DO and NH3 standards. Critical conditions occurred
primarily under low flow (30 cfs) when the system was
dominated by point source loads. Recommended man-
agement for implementation of a TMDL is to pursue a load
reduction from point sources. As the flow decreases, an
increasing percentage of the CBOD and nutrient load can
be attributed to the sewage treatment plant. Low flow
conditions are also critical for augmented algal growth. For
other types of pollutants or other site specific conditions,
analyses may result in different conclusions. In some
cases a continuous simulation of storm inputs and receiving
water response may be required to determine the fre-
quency and duration of stream impacts. As shown here,
steady state examination of several flow conditions using
a analytical solution or WASPS can assist in screening for
the range of flow conditions where problems may occur.
For development of an actual TMDL, some additional
investigations are recommended. Calibration and valida-
tion of a nonpoint source loading model and river response
model may need to be conducted and additional data
collected if possible. Future development that may cause
an additional expansion of the treatment plant should be
considered. Any model uncertainty and future conditions
should be built into a margin of safety for the TMDL. A final
TMDL should not be assigned until all of these factors are
considered carefully.
The Willamette River basin modeling study was selected
to show a recent example of a QUAL2E application. This
example highlights the use of the QUAL2E model in
assessing DO (DO), nutrients, and phytoplankton biomass
for a large river system in Oregon. For additional discussion
on the use of QU AL2E in the development of TMDLs, see
Sections 2.3 and 3.4. TheuseofQUAL2E for uncertainty
analysis is shown in Appendix D.
The Willamette River Basin Water Quality Study
(WRBWQS) is an ongoing interdisciplinary study that in-
cludes investigations of river hydrology, sediment transport,
toxic organic compounds and trace elements, point and
nonpoint pollution sources, and aquatic ecosystems. The
development of predictive computer models under low flow
conditions of late summer was one goal of the Phase I
study. The low-flow period coincides with the critical period
for DO and is suitable for steady-state DO modeling. A
model was needed to more fully assess the interactions
among nutrients, phytoplankton, and DO, which had not
previously been undertaken. A summary of the selection,
calibration, and preliminary evaluation of the Phase I DO
model is presented below. A water quality management
case scenario involving the effect of variation of the river
flow regime on DO and phytoplankton biomass is also
presented. A more complete description of the develop-
ment and evaluation of the WRBWQS Phase I DO model
has been provided in a number of technical reports (Tetra
Tech, 1993a, b,c).
B.3.2 Problem Setting
The Willamette River drainage basin area is approximately
30,000 km2 in area and is bounded by the Coast and
Cascade mountain ranges (Figure B-11). The mainstem
of the river meanders in a northerly direction through an
alluvial valley approximately 300 km to the Columbia River.
The problem setting and essential characteristics of the
river system are summarized in Figure B-12.
Although the drainage basin contains the majority of the
State's inhabitants, approximately half of the basin is for-
ested. However, significant changes have occurred in the
drainage basin since the arrival of European immigrants
beginning in the early 1890s
B-30
-------
a
Major Poinl Sourca
Wa;*r Quaiiiy Sampling
FIGURE B-11. THE WJLUWIETTE RIVER BASIN STUOV AfiEA, LOCATIONS OF MAJOR POINT
SOURCE DISCHARGES ALONG THE MAINSTEM OF THE RIVER, AND LOCATIONS
Of THE AUGUST 1S92 SYNOPTIC SURVEY STATIONS,
B-31
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LEGEND
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FIGURE B-l 2, RIVER SEGMENTATION, POINT SOURCE ^*JD
TRIOUTARY LOCATION SCHEMATIC
B-32
-------
Gleeson, 1972; Sedell and Frogatt, 1984). Approximately
one-third of the basin is currently used for agriculture, and
the forests have been exploited for timber production.
About 10 percent of the basin has been urbanized or is in
residential use. The river receives direct inputs of treated
municipal wastes and industrial effluents—primarily from
pulp and paper processing facilities. Although nonpoint
source inputs are significant during winter rainfall runoff, this
source is considered minor relative to point sources during
the dry critical period for DO.
Oregon water quality standards relevant to the modeling
study include the state standards for DO and an "action
level" for chlorophyll a (Oregon Administrative Rules,
Chapter 340, Division 41). The state DO standards vary
for each reach of the river:
• The Tidal Reach [river kilometer (RK) 0-43] -
5 mg/L
• Newberg Pool (RK 43-80) - 6 mg/L
• Newberg Pool to Salem (RK 80-137) - 7 mg/L
Above Salem, the DO standard is a minimum of 90 percent
of the saturation concentration for DO.
The state action level for chlorophyll a is 15 g/L. This action
level applies to natural lakes that do not thermally stratify,
and to reservoirs, rivers, and estuaries. The action level is
intended to identify water bodies where phytoplankton
might impair beneficial uses. If it is determined that the
action level is exceeded in a particular water body, addi-
tional studies might be conducted to determine the causes
of the exceedances and impacts on beneficial uses. Con-
trol strategies, including additional standards or pollutant
load limitations, could then be developed.
The need for predictive water quality models was under-
scored by the continued industrial and agricultural devel-
opment and population growth withinthe basin. As of 1990,
the population within the nine counties that cover the basin
had almost reached 2 million. Highest population growth
rates have occurred in the counties that encompass the
large urban centers of Eugene, Salem, and Portland.
These urban centers and other smaller towns and industrial
facilities are found along the banks of the mainstem of the
river.
Currently there are 21 major dischargers to the mainstem
of the Willamette River. Twelve additional facilities dis-
charge to tributaries of the Willamette. Discharger name,
type, receiving water, and river mile location are summa-
rized in Table B-5. Pollutant loading information for the
various facilities is shown in Table B-6.
B.3.3 River Characteristics
At its mouth, the Willamette is the 10th largest river in the
continental U nited States, in terms of total discharge (Sedell
and Frogatt, 1984), and the discharge per unit area is the
highest of the large rivers in the Nation due to the heavy
winter rainfall at lower elevations in the basin during the
winter months (Rickert and Mines, 1978). At higher eleva-
tions the winter precipitation occurs as snow, which con-
tributes to extended high flow as spring snowmelt runoff.
The climate is temperate and characterized by wet, mild
winters and dry, moderately warm summers. Most of the
rainfall occurs in the fall, winter, and spring, with little rainfall
during June, July, and August. The period of low river flow
during the late summer coincides with the period of low
rainfall and highest air temperatures.
River discharge is managed for flood control, irrigation, and
navigation purposes by impoundments located on a
number of the large tributaries. Nonetheless, river dis-
charge varies seasonally, with greatest runoff occurring
during the winter months (December-February) (ca. 1,800
m3/see) and lowest flows occurring in summer (July-Sep-
tember) (ca. 283 m3/sec), with a mean annual flow of
approximately 943 m3/sec (Moffatt et al., 1990). Low
summer flows are augmented by controlled releases from
tributary impoundments to provide for commercial naviga-
tion. A natural flow control occurs at RK 42—Willamette
Falls—although a lock, powerhouse, and fish ladder have
also been constructed at this location. Below the falls, the
river is tidally influenced via the confluence with the Colum-
bia River which flows to the Pacific Ocean approximately
160 km to the west. Due to the great d istance to the ocean,
flow reversals in this 42-km reach cause intrusion of only
fresh Columbia River water into the Willamette. Flow in the
reach below the falls is further complicated by the presence
of two channels—the main channel, which enters the
Columbia River at RK 162, and the Multnomah Channel,
which passes between Willamette RK 5 and Columbia RK
140.
Based on hydraulic and physical characteristics, the main-
stem of the river may be divided into three distinct reaches
(Rickert et al., 1976). The upstream reach is 217 km long
and is characterized by fast-moving currents flowing over
a shallow, meandering
B-33
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riverbed composed of cobbles and gravel. The middle
reach (Newberg Pool) is a 54-km-long, deep and slow-
moving portion of the river formed by the natural impound-
ment behind Willamette Falls. The tidally influenced reach
below the falls (Tidal Reach) is also relatively deep and has
the longest estimated travel time—241 hours during critical
flow conditions (Rickert et al., 1975).
B.3.4 Model Application
The objective of the WRBWQS was to develop and cali-
brate a predictive DO model for the Willamette River to
evaluate river basin management alternatives and meet
regulatory mandates. To first identify appropriate predictive
models, several DO models of varying complexity were
identified and evaluated using a number of selection crite-
ria: 1) Dimensionality—a one-dimensional model was con-
sidered adequate; 2) Temporal characteristics—a
steady-state model was considered appropriate for the
summer low-flow period of interest; 3) Consideration of
relevant processes—these processes included the capa-
bility to model phytoplankton growth and nutrient interac-
tions; 4) Suitability for a range of
applications—temperature or bacteria modeling is an ex-
ample; 5) Data requirements—the data required for model
calibration had to be within the resources of the study; and
6) Ease of use—the selected model needed to be suffi-
ciently easy to use so water quality managers could prac-
tically apply the model as a decision-making tool.
Based on these selection criteria, the model QUAL2E
(Version 3.14) was selected. This one-dimensional,
steady-state model incorporates all of the relevant proc-
esses and has a menu-driven input and output system that
facilitates use of the model. Additionally, the model in-
cludes applications for component, sensitivity, first-order
error analysis, and Monte Carlo simulations.
B.3.4.1 Database Development and Model
Calibration
Historical water quality data and previous DO modeling
efforts were reviewed to identify relevant data and modeling
approaches that could be incorporated into the QUAL2E
model calibration effort (Tetra Tech, 1992a, b). The histori-
cal data review also identified data gaps to support the
design of a synoptic field sampling effort to provide a data
set for calibration of the model.
The field sampling effort was conducted in August 1992
and included diurnal DO and temperature measurements
at 15 stations and measurements of nutrients and CBOD
at 24 stations along the mainstem (Tetra Tech, 1992c).
ODEQ collected single grab samples from 10 locations,
and Tetra Tech collected samples at approximately 6-hr
intervals over a 24-hr period at 15 stations. Data were also
collected by the USGS at RK 20.6 as part of its National
Stream Quality Assessment Network (NASQUAN) on
August 17,1992. USGS data were also incorporated into
the model calibration effort. Point source loading data were
compiled for the 21 major municipal and industrial effluent
discharges to the mainstem of the Willamette River using
the permit-required monitoring reports submitted to ODEQ
and additional data collected during the synoptic field study
(Tetra Tech, 1992c, d) (Table B-4).
The QUAL2E model was first discretized based on river
hydraulic information provided by USGS (M. Fretwell, May
20,1992, personal communication). The river was divided
into 35 model segments with similar physical charac-
teristics, resulting in a model consisting of 35 reaches
divided into elements 1.2 km long for a total of 249 model
elements. The tributaries and major municipal and indus-
trial point sources were modeled as point sources inputs to
the mainstem of the river.
Since river depths, velocities, and cross-sectional areas in
each model segment vary under different hydrologic con-
ditions, discharge coefficients and exponents were esti-
mated for the model calculation of these variables as a
function of discharge. (Note: It was assumed that the
effective channel width would not change under low flow
conditions.) To estimate the coefficients and exponents for
each model segment velocity- and depth-discharge rela-
tionship, low- and high-flow stream channel hydraulic infor-
mation provided by USGS was used (M. Fretwell, May 20,
1992, personal communication). The resulting QUAL2E
model output for discharge, velocity, depth, and cross-sec-
tional area are compared to the channel hydraulics data
provided by USGS for the 2-yr, 60-day recurrence interval
flow in Figure B-13. The model-predicted discharge, ve-
locity, depth, and cross-sectional area are also shown in
Figure B-14 for the August 1992 sampling period. A
sample of the model input file is shown in Table B-7.
The model was then calibrated to the 1992 synoptic water
quality survey data using a combination of visual best-fit
and error minimization techniques. A preliminary calibra-
tion was conducted first using best
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FtGURE B-13. WILLAMETTE RIVER FLOW, VELOCITY, DEPTH, AND CROSS-SECTION
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professional judgment and a visual best-fit technique to
arrive at reasonable values for the rate constants in the
following steps:
• Nitrogen balance: Adjustment of the ammo-
nia oxidation nitrification and organic nitro-
gen hydrolysis rates to fit the model
predictions to the nitrate, ammonia, and or-
ganic nitrogen data.
• Phytoplankton growth:
1) Variation of the model options for algal
growth limitation and photosynthesis.
2) Adjustment of the specific maximum algal
growth rate, algal respiration rate, and the
phytoplankton settling rate to fit the model
predictions to the chlorophyll a and nutrient
data.
• Phosphorus balance: Adjustment of the or-
ganic phosphorus decay rate to fit the or-
ganic phosphorus and soluble phosphorus
data.
• DO balance: Fixing of the instream ultimate
CBOD decay rate and the atmospheric
reaeration coefficient based on previous
studies of the Willamette River (reported by
McKenzie et al., 1979) and adjustment of the
SOD to fit the DO field data.
Final model calibration was achieved by minimizing the
cumulative absolute relative error (CARE) between model
output and field data using the ammonia oxidation rate, the
organic phosphorus decay rate, the maximum specific
algal growth rate, the algal settling rate, and the sediment
oxygen demand rate.
The calibrated model's fit to the synoptic survey data are
shown in Figures B-14, B-15, and B-16. The location and
concentration of the minimum DO measured during the
synoptic survey at RK 43 was matched by the model (7.3
mg/L) (Figure B-16). The model-predicted DO concentra-
tions ranged up to 8.6 percent of the 24-hour average DO
concentrations measured at 15 stations, with a mean and
median relative difference of 2.5 and 1.7 percent, respec-
tively. The model-predicted DO concentrations did not fit
the concentrations measured using single grab samples
collected by ODEQ. In general, single grab samples for
DO were considered inadequate for the calibration of a
steady-state model, especially for the upper river reach
where large diurnal fluctuations in DO occur.
The maximum chlorophyll a concentrations measured in
the lower river were also predicted well by the model,
although the model prediction increased exponentially to
much higher levels below RK 11 (Figure B-17). The model
did not predict the relatively high chlorophyll a levels meas-
ured in the upper river. Suspended algal biomass in the
upper river reach is considered to be derived from slough-
ing of periphyton in this relatively shallow stretch of river.
Because the model does not consider the influence of
periphyton growth, the model DO predictions for the upper
river reach reflect only variation in the steady-state DO
concentration due to point source inputs and reaeration.
B.3.4.2 Model Validation
Validation of a calibrated model with an independent data
set is meant to substantiate the model's predictive power
under environmental conditions similar to those under
which the model was calibrated. With this goal in mind, the
calibrated model was applied to August 1990 conditions
using point source data provided by HydroQual (1990) and
water quality data available as part of ODEQ's Ambient
Monitoring Program. Although model-predicted and
measured conditions were in relatively good agreement
(Figure B-17 shows the model's fitto the DO and chlorophyll
a data), the model was not considered to be fully validated
because the DO concentrations reported by ODEQ are for
single grab samples. These types of samples were not
considered adequate for the calibration or validation of a
steady-state model. The model was considered suffi-
ciently tested for management analysis. Full validation will
be achieved upon completion of additional monitoring and
future updates of the model.
B.3.5 Conclusions
Figure B-18 shows the effect of variation in the Willamette
River flow regime on Willamette River DO and chlorophyll
a concentrations. The relative effect of various flow re-
gimes, ranging from 135 to 218 m3/sec measured at
Salem, on the calibrated-model prediction of DO at RK 43
(using the August 1992 model inputs) and chlorophyll a at
RK 16, are presented. In general, variation in river flow had
a noticeable effect on DO throughout the river and on
chlorophyll a below RK 80 where the river enters the
Newberg Pool reach. This analysis substantiates the as-
sumption that flow augmentation of the Willamette River
during the low-flow period of July through September can
be an effective means of water quality
B-43
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FIGURE B-15, COMPARISON OF CALIBRATED OUAL2E MODEL OUTPUT
TO THE AUGUST 1992 FILE DATA FOR ULTIMATE CBOD AND PHOSPORUS COMPOUNDS
B-44
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FIGURE B-16. COMPARISON OF THE CALIBRATED QUALSE MODEL OUTPUT TO THE AUGUST
19952 FIELD DATA FOR CHLOROPHYLL A AND DISSOLVED OXYGEN,
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management. A minimum flow of 170 m3/sec atthe Salem
gauge (RK134) is maintained during these months to allow
for navigation, and also, to maintain adequate DO levels in
the river (Rickert et al. 1980). The model-predicted DO
concentrations at RK 43 vary almost linearly from 7.0 to 7.5
mg/L over the range of flow regimes evaluated. The
model-predicted effect of flow on chlorophyll a concentra-
tion was not linear. The chlorophyll a concentration is
predicted by the model to increase rapidly when river flow
at Salem falls much below 150 m3/see. These results
support the hypothesis of Rickert et al. (1977) that phyto-
plankton biomass in the lower river is most strongly con-
trolled by variation in the flow (i.e., the water residence time)
and that management of the flow regime is not only an
effective means to control DO levels, but should also be
effective in the control of phytoplankton biomass.
None of the assumptions associated with the model devel-
opment precluded its application and use as a predictive
tool.
Future work includes a field study conducted during the
summer of 1994 by ODEQ and USGS, including meas-
urements of SOD that will allow further refinement of the
QUAL2E-UNCAS DO model. Planned Phase II model
improvements include updating the model to QUAL2E
Version 3.20, which will allow for the incorporation of minor
point sources and the evaluation of the model-specified
SOD rates. Depending on the results of this evaluation, the
model will be recalibrated and validated using the more
recently collected field data. The update of the model will
refine estimation and predictive capabilities.
There are several assumptions inherent to the modeling
analysis that should be considered in interpretation of the
calibrated model results.
B.4 REFERENCES
1) The model does not incorporate the effect of
periphyton production on DO. The effect of
periphyton production on DO might be signifi-
cant in the upper reach of the river above RK 80.
2) The model does not account for tidal mixing
with the Columbia River. Therefore, the model
output below RK 16 should be interpreted with
caution.
APHA (American Public Health Association), 1985. Stand-
ard Methods for the Examination of Water and Waste
Water, 16th ed., Washington, DC., 874 pp.
Bowie, G.L., W.B. Mills, D.B. Porcella, C.L. Campbell, J.K.
Pagenkopf, G.L. Rupp, K.M. Johnson, P.W.H. Chan, and
S.A. Gherini. 1985. Rates, constants and kinetics formula-
tions in surface water quality modeling. 2nd ed.
EPA/600/3-85/040. U.S. Environmental Protection
Agency, Environmental Research Laboratory, Athens, GA.
3) The model does not consider high-flow
events or dynamic conditions. The model as-
sumes steady-state conditions that are appropri-
ate for representing the low-flow conditions
present when problems in the Willamette River
typically occur.
4) The model does not explicitly consider mi-
nor point sources of nutrients or oxygen-de-
manding substances. Preliminary estimates
suggest that minor point sources could contrib-
ute as much as an additional 10 percent to the
estimated CBOD demand load to the mainstem
of the river (Tetra Tech, 1992d).
5) The model-predicted DO concentration in
the lower river was very sensitive to the model-
specified rate of SOD. However, no field data
were collected to establish the reliability of the
rates of SOD specified in the model.
Fretwell, M.O. 20 May 1992. Personal Communication
(letter to Mr. Robert Baumgartner, Water Quality Section,
Oregon Department of Environmental Quality, Portland,
OR). District Chief, U.S. Geological Survey, Portland, OR.
Gleeson, G.W.. 1972. The return of a river. The Wil-
lamette River, Oregon. The Willamette River Advisory
Committee on Environmental Science and Technology
and Water Resources Institute, Oregon State University,
Corvallis, OR.
HydroQual. 1990. DO data analysis and modeling for the
Willamette River, Oregon. HydroQual, Inc., Mahwah, NJ.
McKenzie.S.W., W.G. Hines, D.A. Rickert and F.A. Rinella.
1979. Steady-state DO model of the Willamette River,
Oregon. U.S. Geological Survey Circular 715-J.
Moffatt, R. L, R.E. Wellman and J.M. Gordon. 1990.
Statistical summaries of streamflow data in Oregon:
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Volume 1 — Monthly and annual streamflow, and flow
duration values. U.S. Geological Survey, Open-File Re-
port 90-118, Prepared in cooperation with Oregon Water
Resources Department.
Rickert, DA, and W.G. Mines. 1978. River quality assess-
ment: implications of a prototype project. Science,
200:1113-1118.
pared for Oregon Department of Environmental Quality,
Portland, OR. Tetra Tech, Inc., Redmond, WA.
TetraTech. 1992d. Willamette River Basin Water Quality
Study. Component?: Point source discharges and waste
loading to the Willamette River basin during 1991. Pre-
pared for Oregon Department of Environmental Quality,
Portland, OR. Tetra Tech, Inc., Redmond, WA.
Rickert, D.A., W.G. Mines and S.W. McKenzie. 1975.
Methods and data requirements for river-quality assess-
ment. Water Resources Bulletin 11:1013-1039.
Rickert, D.A., W.G. Mines and S.W. McKenzie. 1976.
Methodology for river-quality assessment with application
to the Willamette River Basin, Oregon. U.S. Geological
Survey Circular 715-M.
Rickert, D.A., R. Petersen, S.W. McKenzie, W.G. Mines
and S.A. Wille. 1977. Algal conditions and the potential for
future algal problems in the Willamette River, Oregon. U.S.
Geological Survey Circular 715-G.
Rickert, D.A., F.A. Rinella, W.G. Mines and S.W. McKenzie.
1980. Evaluation of planning alternatives for maintaining
desirable dissolved-oxygen concentrations in the Wil-
lamette River, Oregon. U.S. Geological Survey Circular
715-K.
Riley, G.A., 1956. Oceanography of Long Island Sound
1952-1954. II. Physical Oceanography, Bulletin Bingham.
Oceanog. Collection 15, pp. 15-46.
Sedell, J.R. and J.L. Frogatt. 1984. Importance of stream-
side forests to large rivers: The isolation of the Willamette
River, Oregon, U.S.A., from its floodplain by snagging and
streamside forest removal. Verh. Internal Limnol.
22:1828-1834.
TetraTech. 1992a. Willamette River Basin Water Quality
Study. Components: Data review and summary for DO
modeling on the Willamette River. Prepared for Oregon
Department of Environmental Quality, Portland, OR. Tetra
Tech, Inc., Redmond, WA.
TetraTech. 1992b. Willamette River Basin Water Quality
Study. Component 4: Review and summary of nutrient
and phytoplankton growth data for the Willamette River.
Prepared for Oregon Department of Environmental Qual-
ity, Portland, OR. Tetra Tech, Inc., Redmond, WA.
TetraTech. 1992c. Willamette River Basin Water Quality
Study. Component 11: Water quality survey data. Pre-
TetraTech. 1993a. Willamette River Basin Water Quality
Study. Summary report. Prepared for Oregon Depart-
ment of Environmental Quality, Portland, OR. Tetra Tech,
Inc., Redmond, WA.
TetraTech. 1993b. Willamette River Basin Water Quality
Study. Willamette River DO modeling component report.
Volumes 1 and 2. Prepared for Oregon Department of
Environmental Quality, Portland, OR. Tetra Tech, Inc.,
Redmond, WA.
TetraTech. 1993c. Willamette River Basin Water Quality
Study. Willamette River nutrient and phytoplankton growth
modeling component report. Volumes 1 and2. Prepared
for Oregon Department of Environmental Quality, Portland,
OR. Tetra Tech, Inc., Redmond, WA.
Thomann, R.V., and J.A. Mueller. 1987. Principles of
surface water quality modeling and control. Harper & Row,
New York, NY.
USEPA. 1980. Technicalguidance manual'forperforming
waste load allocation, Simplified analytical method for de-
termine NPDES effluent limitation for POTWs discharging
into low flow streams. U.S. Environmental Protection
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Washington, D.C.
USEPA. 1983a. Technical guidance manual for performing
waste load allocations, Book II: Streams and rivers, Chap-
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EPA-440/4-84-020. U.S. Environmental Protection
Agency, Office of Water Regulations and Standards,
Washington, DC.
USEPA. 1983b. Technical guidance manual for perform-
ing waste load allocations, Book II: Streams and rivers,
Chapter2: Nutrinet/eutrophication imacts. EPA-440/4-84-
021. U.S. Environmental Protection Agency, Office of
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USEPA. 1984. EPA Ambient water quality criteria lor
ammonia. U.S. Environmental Protection
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Agency, Office of Water Regulations and Standards, USEPA. 1992. Compendium of watershed-scale models
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USEPA. 1987. Quality criteria lor 1986. EPA 440/5-86- ton, D.C.
001. U.S. Environmental Protection Agency, Office of
Water Regulations and Standards, Washington, D.C.
B-50
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APPENDIX C: QUALITY ASSURANCE FOR FIELD
MONITORING PROGRAMS
C.1 OVERVIEW
As used here, quality assurance (QA) is a system of
activities used to provide documented assurance that a
data product of known and acceptable quality is produced.
The importance of QA should be evident. However, be-
cause of the additional effort required to provide QA (ad-
vance planning, management, supervision, and
resources) it is often neglected or overlooked. This manual
has addressed, at some length, guidelines for the analysis
of data that will lead to the performance of technically
sound, defensible TMDL studies. This is particularly impor-
tant where decisions derived from TMDL studies have
serious economic and environmental impacts.
A properly planned and implemented QA program will
enable the substantiation of data accuracy and precision
by an outside, impartial review and forestall any attempts
to discredit or impeach the data produced. This section
outlines the minimum QA effort required to ensure a reliable
TMDL study. Its aim is to assist the user in developing a
reliable and effective quality assurance program that will
meet data user requirements for completeness, precision,
accuracy, and comparability of data. Note that the QA
requirements given herein are the minimum requirements;
they are to serve as a foundation on which the user can
build a viable QA program.
C.2 ACCURACY AND PRECISION
Accuracy refers to agreement between the measurement
and the true value of the measurand, with the discrepancy
normally referred to as error. Precision refers to the repro-
ducibility (repeatability) of the measurement, when re-
peated on a homogenous, time-stationary measurand,
regardless of the displacement of the observed value from
the true value.
The statistical measures of location or central tendency
(e.g., the various averages, mean, median, and mode) are
related to accuracy. The statistical measures of dispersion
or variability (e.g., variance, standard deviation, coefficient
of variation, and other measures derived from central
moments of the probability density function) are related to
precision.
Discrepancies between the results of repeated observa-
tions, or errors, are inherent in any measurement process
since it is recognized that the true value of an object of
measurement can never be exactly established. These
errors are customarily classified into two main groups:
systematic and random (or accidental) errors. Systematic
errors usually enter into records with the same sign and
frequently with either the same magnitude (e.g., a zero
offset) or an establishable relationship between the mag-
nitude of the measurement and the error. The methods of
symmetry and substitution are frequently used to detect
and quantify systematic errors. In the method of symmetry,
the test is repeated in a symmetrical or reversed manner
with respect to the particular condition that is suspect. In
the method of substitution, the object of measurement is
replaced by one of known magnitude (a calibration stand-
ard); an instrument with a known calibration curve is sub-
stituted for the measuring instrument in question, and so
on. Thus, systematic errors bear heavily on the accuracy
of the measurement.
Random errors, on the other hand, are due to irregular
causes, too many in number and too complex in nature to
allow their origin to be determined. One of the chief char-
acteristics of random errors is thatthey are normally as likely
to be positive as negative and, therefore, are not likely to
have a great effect on the mean of a set of measurements.
The chief aim of a data quality assurance effort is to account
for systematic errors and thereby reduce errors to the
random class, which can be treated by simple probability
theory, in order to determine the most probable value of the
object of observation and a measure of the confidence
placed in this determination.
C.3 ELEMENTS OF A QA PROGRAM
The basic elements of any quality assurance program
include the following:
• Management's commitment to provide the
resources necessary to implement quality
C-1
-------
assurance activities (approximately 10 to 20
percent of total water monitoring resources).
• Designation of a quality assurance coordina-
tor responsible for coordinating and imple-
menting necessary quality assurance
activities.
• Documentation of a quality assurance plan
outlining the specifics of and responsibilities
for the development and implementation of
internal and external quality assurance
checks.
A complete QA program for water quality measurements
would incorporate a variety of specific elements. These
can be depicted on a quality assurance wheel, as shown
in Figure C-1. The wheel arrangement illustrates the nature
of a quality assurance system that addresses all elements
and at the same time allows program managers the flexi-
bility to emphasize those elements which are most appli-
cable to their particular program. Quality assurance
elements are grouped on the wheel according to the
organizational level to which responsibility is normally as-
signed. These organizational levels are the quality assur-
ance coordinator (normally a staff function), supervisor (a
line function), and operator. Together the supervisor and
quality assurance coordinator must see that all these
elements form a complete and integrated system and
achieve the desired program objectives.
The following specific elements are suggested as minimal
requirements for structuring a QA program for a TMDL
study. Any proposed program should be compared
against these criteria to determine its acceptability.
• A written quality assurance plan should be
prepared. It should define the oversight role
of management; identify personnel responsi-
ble for the quality assurance program; and
specify proper sample collection, use of ap-
proved measurement techniques, calibration
standards and their verification, internal qual-
ity control practices, and appropriate data
management controls.
• An estimate of costs associated with the
quality assurance program in terms of per-
centage of overall project cost should be
developed. Normally, a minimum of 10 per-
cent of the estimated sample collection and
analysis costs will be necessary for adequate
quality control.
• A program for demonstration of acceptable
performance through the use of audit sam-
ples should be established and used
throughout the duration of the study.
Provision should be made for performing on-
site field and laboratory audits at the option
of and on a schedule established by the
project officer. Such audits would evaluate
performance and document the availability of
all equipment and supplies necessary for
successful execution of the study.
Documentation of quality control perform-
ance should be submitted with the final report
and otherwise as directed by the project offi-
cer.
C.4 ASPECTS OF A QA PROGRAM
A number of aspects of a QA program must be addressed
by the QA plan if the minimal requirements are to be met.
These aspects can be aggregated into three general cate-
gories: water chemistry (laboratory), field data collection,
and data handling and reporting.
C.4.1 Water Chemistry
The minimum QA requirements for water chemistry are as
follows:
• Quality control management manual
- Outline of quality assurance program ob-
jectives
- Outline of the administrative structure of
the laboratory (including an organiza-
tional chart)
Clear identification of the responsibilities
for implementing the specific quality con-
trol activities
Commitment of resources by manage-
ment to implement the necessary quality
control activities
Description of laboratory training pro-
gram
Designation of a laboratory quality assur-
ance coordinator, including a statement
addressing coordination responsibilities
and duties
• Laboratory operations manual
- Description of analytical methodologies
and procedures
Description of laboratory quality control
activities
C-2
-------
FIGURE C-1. QUALITY ASSURANCE ELEMENTS AND RESPONSIBILITIES
(THE QUALITY ASSURANCE WHEEL)
C-3
-------
- Description of the laboratory's internal
chain-of-custody procedures
- Description of general laboratory re-
quirements
- Description of laboratory communication
and coordination
• Sample log manual
• Quality control records manual
• Blind duplicate and spiked field samples
Sample audits
Parameters included in the program
• Audit sample preparation procedures
• Data evaluation
- Audit follow-up and corrective action
• Estimation of limits for laboratory accuracy
checks
C.4.2 Data Collection
The minimum QA requirements for field data collection are
as follows:
• Sampling network design
• Sampling procedures
• Calibration of direct-reading field instruments
and fixed continuous monitoring devices
• Record keeping
• Quality assurance checks in field sampling
• Personnel training
• Flow measurements
• Records, data storage and retrieval
• Sample handling and identification proce-
dures (chain of custody)
• Collection of samples/field investigations
C.4.3 Handling and Reporting
The minimum QA requirements for data handling and
reporting are as follows:
• Preprinted forms and labels
• Data sheets
• Data flow
• Significant figures and rounding procedures
• Calculation checks
• Data corrections
• Data reviews
• Reasonableness and consistency checks
• Data acceptance
• Data storage and retrieval
C-4
-------
APPENDIX D: UNCERTAINTY ANALYSIS
D.1 INTRODUCTION
Uncertainty analysis should be included as an inte-
gral component of water quality modeling. One of the
primary purposes is to quantify the error in predicting
water quality and evaluate the effect of input parame-
ters on model output. By quantifying this error, im-
proved management decisions can be made. Such
quantification also facilitates subsequent studies
such as risk assessments to evaluate alternative
waste load allocations. In addition, uncertainty analy-
sis may provide insight into the need for additional
data collection to refine the estimate of certain loads,
initial conditions, or reaction rates. For example, if
the model is sensitive to the reaeration rate (that is,
a small change in reaeration rate results in large
changes in the prediction of critical water quality
parameters such as dissolved oxygen), it may be
appropriate to allocate resources to more accurately
estimate the reaeration rate of that stream or river.
There are three techniques for performing uncertainty
analysis: sensitivity analysis, first-order error analy-
sis, and Monte Carlo simulation. Each technique has
advantages and disadvantages in terms of applicabil-
ity and computational burden that will make one
method more suitable than another for a particular
analysis. In many instances, the modeler may need
to explore the results from all three procedures. The
three methods may produce discrepancies in their
results since the methodologies and assumptions
differ. Each of these techniques is available in
QUAL2E-UNCAS, and the following discussion is
limited to the features available in that model. An
example uncertainty analysis using QUAL2E-
UNCAS is provided at the end of this appendix.
D.2 TECHNIQUES IN UNCERTAINTY
ANALYSIS
D.2.1 Sensitivity Analysis
Sensitivity analysis is the simplest of the three tech-
niques for assessing the effect of an input variable on
the output variable. This analysis technique can be
used to evaluate simple alternatives and projections
such as the effect of reducing all pollutant loads by
10 percent. Simple what-if scenarios are particularly
useful for managers who must make decisions
among alternative load reduction strategies. For the
modeler, the same analysis can serve as a useful
guide for model calibration.
In the single-factor approach, the modeler varies one
of the input variables, X, and observes the effect in a
particular output variable, Y. A sensitivity coefficient
is then computed as the percentage change in Y
divided by the percentage change in X. In general, a
sensitivity coefficient can be estimated at all points
where the output variable is predicted. However, this
process can result in an enormous interpretation
burden and it is generally recommended that the
analysis be limited to critical points along the modeled
stream. This process can then be repeated for a
number of different perturbations inXaswell as other
input variables. By evaluating the relative change in
the sensitivity coefficients for different input variable
perturbations, the modeler can determine the model
nonlinearity for that input variable.
Similarly, several input variables can be varied simul-
taneously. As the number of input variables and
combinations is increased, the interpretation of re-
sults is complicated. Experimental design strategies
can be applied in this situation to elicit main and
interaction effects of input variables. Specifically, in
QUAL2E-UNCAS, the modeler may specify a 22 or
23 factorial design. In other words, the modeler may
be able to examine the main and interactive effects
of two or three variables evaluated at two levels (e.g.,
perturbations). The statistical significance of the in-
teraction and main effects are evaluated by compar-
ing an appropriate ratio of the sum of squares to a
critical F ratio.
To perform sensitivity analysis with QUAL2E-
UNCAS, the user must specify the type of analy-
sis (single/multiple variable or factorial design),
the input variables to be modified, and the pertur-
bation as a percent of the input variable.
D.2.2 First-Order Error Analysis
First-order error analysis can be used in a manner
similar to that used for sensitivity analysis. In addition
D-1
-------
to estimating the change of an output variable with
respect to an input variable, first-order error analysis
provides an estimate of the output variance. A first-
order approximation (from the Taylor series expan-
sion) to the relationship for computing variances in
multivariate situations is used. Input variables are
assumed to be independent, and the model is as-
sumed to respond linearly to the input variables. (In
some instances, the assumptions may not be cor-
rect.) The linear assumption can be evaluated by
computing the normalized sensitivity coefficients for
several different input parameter perturbations. If the
normalized sensitivity coefficients are similar or the
difference is small, the model can be assumed to be
linear for that input parameter. If the difference in
normalized coefficients is large, it may be more accu-
rate to use the Monte Carlo simulation approach to
estimate output parameter variance.
In this analysis, the sensitivity coefficients are normal-
ized such that
Sij=(AYj/Yjy(AXi/Xi)
(D-1)
where
Sij
AX\
Yj
AYj
normalized sensitivity coefficient
for output Yy to input X\
base value of input variable
magnitude of input perturbation
base value of output variable
sensitivity of output variable
The components of variance for each output variable
(Y) are the percentages of output variance attribut-
able to each input variable (X) and are computed in
the following manner.
tainty caused by factors such as spatial and temporal
variation, sampling and analytical error, and bias in
measurement or estimation techniques. A file of
typical variance estimates is provided with the model.
D.2.3 Monte Carlo Simulation
Monte Carlo simulation is a numerical procedure that
can be used to evaluate linear and nonlinear systems.
Each input variable is defined to have a certain prob-
ability density function (pdf). Before each model run,
an input variable is randomly selected from each
predefined pdf. By combining the results from nu-
merous model runs, a pdf can be developed for the
output variable. The pdf is useful in evaluating overall
model predictions and in assessing the likelihood of
violating a water quality standard.
In general, the linear and independence assumptions
of first-order error analysis can be relaxed when using
Monte Carlo simulation techniques. In QUAL2E-UN-
CAS, only the linear assumption is relaxed. To use
QUAL2E-UNCAS, the user must specify the variance
of the input variable (a file of typical variance esti-
mates is provided), the probability distribution as
either normally or lognormally distributed, and the
number of simulations to perform. As one would
expect, the number of model runs is relatively large
as compared to the number of runs typically done for
sensitivity or first-order error analysis. Preliminary
experience indicates that about 2000 simulations are
required to achieve estimates of output standard
deviations with 95 percent confidence intervals of
5 percent.
D.3 EXAMPLE APPLICATION
Var(Yj)= £ (AY/AX,)2 Var(Xj)
/'=1 (D-2)
where
Var(Yj) = variance of output variable Yy
Var(Xj) = variance of input variable Xj
Each term in the summation of Equation D-2 is a
component of the total variance of the output variable.
A particular input variable may be a large (small)
contributor to the output variance if it has either a
large (small) input variance or a large (small) sensi-
tivity coefficient. This analysis can be used as a guide
for additional field work. To apply this analysis tech-
nique using QUAL2E-UNCAS, the user must specify
the magnitude of input parameter perturbation and
variance. The variance term is a measure of uncer-
This section provides an example of how the uncer-
tainty methodologies in QUAL2E-UNCAS can be ap-
plied to a QUAL2E data set. The sole purpose of this
section is to demonstrate the utility of uncertainty
analysis rather than to provide a definitive analysis of
the river system from which the data were obtained.
This appendix is a condensation of Appendix C of the
QUAL2E and QUAL2E-UNCAS User Manual (Brown
and Barnwell, 1987), entitled QUAL2E-UNCAS Ex-
ample Application. The reader is referred to that
manual for a more detailed explanation of QUAL2E-
UNCAS.
The data used to demonstrate the capabilities of
QUAL2E-UNCAS were obtained from a U.S. EPA
Region 4 survey of the Withlacoochee River during
October 1984 (Koenig, 1986). In this study, water
D-2
-------
quality simulations were examined for portions of the
river subjected to both municipal and industrial waste
loads. In addition, there is a significant accretion of
flow from groundwater inputs. The river has a uni-
form low slope but is characterized by alternating
shoals and pools (often in excess of 25 feet deep).
Average depths during the survey periods were 5.2
to 14.8 feet; widths were 90 to 140 feet; and flows
varied from 150 cfs at the headwater to 660 cfs at the
end of the system. Water quality is affected by algae
activity resulting from municipal waste discharges
above the section of stream studied. The addition of
industrial waste at RM 24, however, dramatically
reduces light penetration to the extent that the algae
population diminishes in the downstream direction.
A location map of the basin is shown in Figure D-1,
and a plot of observed and modeled dissolved oxygen
concentrations is presented in Figure D-2. Ten state
variables were simulated in this study: temperature,
dissolved oxygen, carbonaceous BOD, four nitrogen
forms (organic, ammonia, nitrate, and nitrite), two
phosphorus forms (organic and dissolved), and algae
as chlorophyll a. A summary of the calibrated inputs
and their variance estimates for the uncertainty analy-
sis is shown in Table D-1. The calibrated values in
general were obtained by adjusting field or laboratory
measurements of the specific model inputs. The
variance estimates were computed from replicate
data taken during the survey period and by inference
from other published data (McCutcheon, 1985; Bowie
etal., 1985).
D.3.1 First-Order Error Analysis (FOEA)
Table D-2 shows the first-order error analysis (FOEA)
results for the output variables of CBOD and DO at
three locations in the Withlacoochee system: an
upstream location (RM 26), a midpoint near the dis-
solved oxygen sag (RM 20), and a downstream loca-
tion (RM 2). For the CBOD sensitivity coefficients in
Table D-2(a), it is clear that the input forcing functions
such as point load, headwater flows, and CBOD
dominate model sensitivity.
Table D-2(a) also presents the components of vari-
ance for the modeled CBOD output. These results
show a pattern similar to the sensitivity coefficients.
The headwater CBOD is the dominant contributor (99
percent) to CBOD variability in the upper reaches of
the basin. The point load CBOD values are the
primary variance component elsewhere in the river
(84 percent at RM 20 and 79 percent at RM 2). The
total variability in simulated CBOD estimated by the
first-order analysis, when expressed as a standard
deviation, varies from 0.35 mg/L to 0.76 mg/L to 0.27
mg/L proceeding through the basin.
The FOEA results for dissolved oxygen are presented
in Table D-2(b). The only forcing functions that have
large DO sensitivity coefficients are the headwater
inputs, not the point load inputs. DO is also very
sensitive to temperature inputs. Next in importance
of DO sensitivity are the reaeration rate and velocity.
Similar patterns are apparent in the components of
variance for dissolved oxygen (Table D-2(b)). CBOD
decay has a relatively small impact on DO variance,
whereas reaeration and SOD have large impacts.
Temperature inputs make a minimum contribution to
DO variance. The total variability in simulated DO,
when expressed as a standard deviation, increases
in the downstream direction varying from 0.18 mg/L
to 0.30 mg/L and averaging about 5 percent of the
simulated DO.
D.3.2 Effect of Model Nonlinearity
First-order error analysis uses a linear approximation
to compute an estimate of output variance. The
validity of that approximation can be assessed by
computing the sensitivity coefficients for both large
and small values of delta x, the input perturbation.
Small changes in the normalized sensitivity coeffi-
cient indicate near linearity of the state variable over
the range of perturbed input values, while large
changes in sensitivity reflect important nonlinear ef-
fects. Table D-3 contains values of the normalized
sensitivity coefficients for the state variables DO and
chlorophyll a for input perturbations, ranging from -20
to +20 percent. The input variables selected for
analysis are those having the largest sensitivity coef-
ficients.
For dissolved oxygen (Table D-3(a)), the reaeration
and headwater temperature have the largest non-
linear effects on DO. The other variables are consid-
ered linear for the conditions of the simulation. The
net effect from all model input nonlinearities is mani-
fest in the FOEA estimate of dissolved oxygen stand-
ard deviation, which decreases by 7 percent over the
range of input perturbations.
The more pronounced patterns are observed for the
state variable, chlorophyll a (Table D-3(b)). The ratio
of chlorophyll a to algal biomass and headwater flow
exhibit large nonlinear effects. The maximum algal
growth rate and the algal respiration rate show mod-
est nonlinearities, while headwater chlorophyll a is
essentially linear. The net FOEA estimate of stand-
D-3
-------
FIGURE D-1. LOCATION MAP OF THE WITHLACOOCHEE RIVER BASIN
n
a
RM 2
EK 20
Spring
mm
I
20 IS
Hlvw Location
10
FIGURE D-2. OBSERVED AND PREDICTED DISSOLVED OXYGEN CONCENTRATIONS
D-4
-------
TABLE D-1. SUMMARY OF INPUT DATA FOR QUAL2E-UNCAS SIMULATION-
WITHLACOOCHEE RIVER SURVEY 1984
Input Parameter or Base Case (Mean) Relative Standard
Coefficient Values Deviations (%)
Hydraulic Data (7)*
Flow (cfs) 150-660 3%
Depths (ft) 5.2-14.8 8%
Velocities (fps) 0.12-0.78 8%
Others a, b 10-20%
Reaction Coefficients (8)
CBOD Decay (day1) 0.04-0.10 15%
Reaeration (day ) 0.08-0.08 13%
SOD (g02/ft^ - day) 0.04-0.13 12%
N. p. AI9ae a,b 15-25%
Algae, Nutrient, Light Coefficients (17)
Maximum Growth Rate (day 1) 13 10%
Respiration Rate (day1) g ^g ig%
Otners a, b 10%
Climatology, Temperature Inputs (23)
Wet, Dry Bulb Air Temps (°F) 64 3 ?4 5 2%
Temperature Coefficients 1.00-1.083 3%
Others a,b 1-15%
Headwater, Incremental, Point Loads (27)
DO, Temperature
CBOD, N, P, Algae a 1"3/0
' ' ' * a 8-25%
(a) Basin-specific values from Koenig, 1986.
(b) Typical values from Table III-3 of Koenig, 1986.
'Value in parentheses is the number of input variables of the type indicated.
TABLE D-2. SUMMARY OF FIRST ORDER SIMULATIONS FOR WITHLACOOCHEE RIVER
(a) Simulation Variable:
Input
Variable
CBOD Decay
Incr Flow
HW Flow
HWTemp
HWCBOD
Ptld Flow
Ptld CBOD
Relative
St Dev (%)
15
3
3
1
15
3
15
CBOD (mg/L)
Sensitivity Coefficient
RM26
-0.06(3)a
-0.05
0.05
-0.11(2)
0.98(1)
0.00
0.00
RM20
-0.11
-0.22
-0.44(3)
-0.13
0.24
0.67(2)
0.74(1)
Standard Deviation of Simulated
Components of Variance (%)
RM2
-0.22
-0.37(3)
-0.05
-0.16
0.18
0.43(2)
0.69(1)
(CBOD) (mg/L)
(%)
RM26
1
1
1
1
99
0
0
0.35
15
RM20
2
1
1
1
9
3
84
0~76
12
RM2
8
1
1
1
6
1
79
0.27
12
(b) Simulation Variable: Dissolved Oxygen
Velocity
CBOD Decay
SOD
Reaeration
Incr Temp
HE Temp
HWDO
8
15
5
13
1
1
3
0.03
-0.02
-0.05(3)
0.04
-0.01
-0.25(2)
0.92(1)
0.05
-0.12
-0.23
0.31(3)
-0.15
-0.70(1)
0.55(2)
Standard Deviation of Simulated DO
-0.26(2)
-0.03
0.09
0.40(1)
-0.17(3)
-0.13
0.04
(mg/L)
(%)
1
1
5
4
1
1
84
0.18
3
2
9
5
45
1
1
8
O27
6
13
1
3
77
1
1
1
0.30
6
Value in parentheses is rank, with 1 being highest.
D-5
-------
TABLE D-3. NORMALIZED SENSITIVITY COEFFICIENTS FOR VARIOUS SIZES OF
INPUT PERTURBATIONS (WITHLACOOCHEE RM 20)
(a) Simulation Variable: Dissolved Oxygen (mg/L)
-20%
Input Variable
CBOD
SOD
Reaeration
HW Temp
HWDO
Std Dev. (mg/L)
Magnitude of Input Perturbation %
-1% +1%
-0.12
-0.23
0.33
-0.66
0.55
O28
-0.12
-0.23
0.31
-0.69
0.55
0.27
-0.12
-0.22
0.31
-0.69
0.55
0.27
+20%
-0.12
-0.23
0.30
-0.77
0.55
0.26
Relative
Change (%)
0
0
-9
+16
0
(b)
Simulation Variable: Chlorophyll a (|ig/L)
Max Growth Rate
Respiration
Chi a/Agy-B
HW Flow
HW Chl-a
Std Dev. (ng/L)
0.40
-0.37
-1.24
0.28
0.96
Jj2
0.41
-0.36
-1.01
0.24
0.95
3.12
0.42
-0.35
-0.98
0.25
0.96
3.06
0.43
-0.34
-0.83
0.21
0.94
2.64
+ 7
-8
-33
-25
-2
^29
TABLE D-4. DIFFERENCES IN STANDARD DEVIATION ESTIMATES FOR OUTPUT VARIABLES-
WITHLACOOCHEE RIVER SURVEY 1984
Output Variables
Between FOE A Input
Perturbations from
-20 to +20%
Between FOE A (5%)
and Monte Carlo
Simulations (2000)
Temperature
Dissolved Oxygen
CBOD
Nitrogen Forms
Phosphorus Forms
Chlorophyll a
Algal Growth Rate
5.4
7.7
0.8
a
a
29
6.9
1.8-4.3
0.6-4.5
1.4-2.6
a
a
16-21
2-4
Expected values of standard deviations are too small to compute meaningful relative differences, although values are certainly
less than 10% and likely less than 5%.
ard deviation of chlorophyll a decreases by 29 per-
cent over the range of input perturbations.
the magnitude of the input perturbation increases
over the range of -20 to +20 percent.
The results of the analysis of the other state variables
(Table D-4) show changes in FOEA estimates of
standard deviation of about 7 percent for algal growth
rate, 5 percent for temperature, and less than 5
percent for all others, including CBOD, the nitrogen
forms, and the phosphorus forms. In all cases, the
FOEA estimate of standard deviation decreases as
D.3.3 Monte Carlo Simulations
The Monte Carlo simulation output in QUAL2E-
UNCAS provides summary statistics and fre-
quency d istributions for the state variables at specific
D-6
-------
TABLE D-5. SUMMARY STATISTICS FROM 2000 MONTE CARLO
SIMULATIONS FOR WITHLACOOCHEE RIVER
Statistic
Dissolved Oxygen (mg/L)
RM26 RM20 RM2
Chlorophyll a (|ig/L)
RM26 RM20 RM2
Calibrated Mean
Simulated Mean
Minimum
Maximum
Range
Std. Deviation
Coef. Variation
Skew Coef.
Std. Deviation from FOEA
5.83
5.82
5.26
6.41
1.15
0.18
3.0%
0.01
0.18
4.48
4.47
3.47
5.31
1.84
0.28
6.2%
-0.15
0.27
5.06
5.05
3.69
5.89
2.20
0.31
6.2%
-0.20
0.30
18.1
18.9
10.2
53.8
45.6
4.25
23.5%
1.73
3.54
14.4
15.0
2.8
41.4
33.6
3.48
24.2%
1.6
2.94
6.6
6.6
3.0
22.2
19.2
1.87
28.4%
1.46
1.62
locations in the basin. Table D-5 contains the sum-
mary statistics, based on 2000 Monte Carlo simula-
tions. The same input variances employed in the
first-order error analysis were used. Input probability
distributions were assumed to be normal.
There is very good agreement between the cali-
brated mean and simulated mean for dissolved
oxygen. For chlorophyll a the differences average
3 percent and may be attributed to the nonlineari-
ties. For dissolved oxygen, the standard deviation
grows in the downstream direction. This is the
result of the fact that dissolved oxygen never recov-
ers to approach saturation, as well as the cumula-
tive effect of model input uncertainty. For
chlorophyll a, the standard deviation decreases
steadily in the downstream direction because the
algal biomass concentration is also decreasing.
This is the result of a lower algal growth rate due to
reduced light penetration caused by color in the
industrial waste discharge at RM 24 and due to the
dilution effects from groundwater inflow. As shown
in Table D-4, for the output variables of temperature,
CBOD, and algae growth rate, the Monte Carlo esti-
mate of standard deviation differs by less than 5
percent from the FOEA estimate. These differences
are within the 95 percent confidence interval for the
Monte Carlo estimates, thus implying negligible non-
linear effects for the conditions of this simulation.
The frequency distributions for dissolved oxygen
generated by the Monte Carlo analysis are shown
graphically in Figure D-2. These distributions are
useful in providing a visual representation of the
distribution of model output at different locations in
the system. In the case of dissolved oxygen shown
in Figure B-3, the distributions appear nearly sym-
metric and the dispersion in the upper reaches of the
basin is substantially smaller than that in the middle
and lower reaches. Similar plots (not shown) for
chlorophyll a data in Table D-5 clearly show the
decreasing dispersion and pronounced positive
skew in the simulated data.
D-7
-------
D-8
-------
APPENDIX E: SUPPLEMENTAL BIBLIOG-
RAPHY
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Bruno, S.F., R.D. Staker, G.M. Sharma, and J.T.
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Collins, C.D., and J.H. Wlosinski. 1983. Coefficients
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E-3
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E-4
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APPENDIX F. GLOSSARY
Activated sludge
Acute toxicity
Adsorption-desorpt
ion
Advanced primary
treatment
Advanced
secondary
treatment
Advanced waste
treatment (AWT)
Advection
Aerobic
Algae
Algal bloom
Algal growth
A secondary wastewater treatment process that removes organic matter by mixing
air and recycled sludge bacteria with sewage to promote decomposition.
A chemical stimulus severe enough to rapidly induce an effect; in aquatic toxicity
tests, an effect observed within 96 hours or less is considered acute. When referring
to aquatic toxicology or human health, an acute effect is not always measured in
terms of lethality.
Adsorption is the process by which nutrients such as inorganic phosphorous adhere
to particles via a loose chemical bond with the surface of clay particles. Desorption
is the process by which inorganic nutrients are released from the surface of particles
back into solution.
Waste treatment process that incorporates primary sedimentation of suspended
solids with chemical addition and flocculation to increase the overall removal of
organic solids. Advanced primary treatment typically achieves about 50% removal
of suspended solids and BOD.
Biological or chemical treatment processes added to a secondary treatment plant
including a conventional activated sludge to increase the removal of solids and BOD.
Typical removal rates for advanced secondary plants are on the order of 90%
removal of solids and BOD.
Wastewater treatment process that includes combinations of physical and chemical
operation units designed to remove nutrients, toxic substances, or other pollutants.
Advanced, or tertiary, treatment processes treat effluent from secondary treatment
facilities using processes such as nutrient removal (nitrification, denitrification),
filtration, or carbon adsorption. Tertiary treatment plants typically achieve about 95%
removal of solids and BOD in addition to removal of nutrients or other materials.
Bulk transport of the mass of discrete chemical or biological constituents by fluid
flow within a receiving water. Advection describes the mass transport due to the
velocity, or flow, of the waterbody.
Environmental conditions characterized by the presence of dissolved oxygen; used
to describe biological or chemical processes that occur in the presence of oxygen.
Any organisms of a group of chiefly aquatic microscopic nonvascular plants; most
algae have chlorophyll as the primary pigment for carbon fixation. As primary
producers, algae serve as the base of the aquatic food web, providing food for
zooplankton and fish resources. An overabundance of algae in natural waters is
known as eutrophication.
Rapidly occurring growth and accumulation of algae within a body of water. It usually
results from excessive nutrient loading and/or sluggish circulation regime with a long
residence time. Persistent and frequent bloom can result in low oxygen conditions.
Algal growth is related to temperature, available light, and the available abundance
of inorganic nutrients (N,P,Si). Algal species groups (e.g., diatoms, greens, etc.) are
typically characterized by different maximum growth rates.
F-1
-------
Algal respiration
Algal settling
Ambient water
quality
Ammonia
Ammonia toxicity
Anaerobic
Analytical model
Anoxic
Anthropogenic
Aquatic ecosystem
Assimilative
capacity
Attached algae
Autotroph
Process of endogenous respiration of algae in which organic carbon biomass is
oxidized to carbon dioxide.
Phytoplankton cells (algae) are lost from the water column by physical sedimentation
of the cell particles. Algal biomass lost from the water column is then incorporated
as sediment organic matter and undergoes bacterial and biochemical reactions
releasing nutrients and consuming dissolved oxygen.
Natural concentration of water quality constituents prior to mixing of either point or
nonpoint source load of contaminants. Reference ambient concentration is used to
indicate the concentration of a chemical that will not cause adverse impact to human
health.
Inorganic form of nitrogen; product of hydrolysis of organic nitrogen and denitrifica-
tion. Ammonia is preferentially used by phytoplankton over nitrate for uptake of
inorganic nitrogen.
Under specific conditions of temperature and pH, the un-ionized component of
ammonia can be toxic to aquatic life. The un-ionized component of ammonia
increases with pH and temperature.
Environmental condition characterized by zero oxygen levels. Describes biological
and chemical processes that occur in the absence of oxygen.
Exact mathematical solution of the differential equation formulation of the transport,
diffusion and reactive terms of a water quality model. Analytical solutions of models
are often used to check the magnitude of the system response computed using
numerical model approximations.
Aquatic environmental conditions containing zero or little dissolved oxygen. See also
anaerobic.
Pertains to the [environmental] influence of human activities.
Complex of biotic and abiotic components of natural waters. The aquatic ecosystem
is an ecological unit that includes the physical characteristics (such as flow or velocity
and depth), the biological community of the water column and benthos, and the
chemical characteristics such as dissolved solids, dissolved oxygen, and nutrients.
Both living and nonliving components of the aquatic ecosystem interact and influ-
ence the properties and status of each component.
The amount of contaminant load (expressed as mass per unit time) that can be
discharged to a specific stream or river without exceeding water quality standards
or criteria. Assimilative capacity is used to define the ability of a waterbody to
naturally absorb and use waste matter and organic materials without impairing water
quality or harming aquatic life.
Photosynthetic organisms that remain in a stationary location by attachment to hard
rocky substrate. Attached algae, usually present in shallow hard-bottom environ-
ments, can significantly influence nutrient uptake and diurnal oxygen variability.
Organisms that derive cell carbon from carbon dioxide. The conversion of carbon
dioxide to organic cell tissue is a reductive process that requires a net input of energy.
The energy needed for cell synthesis is provided by either light or chemical oxidation.
Autotroph that use light, phototroph, include photosynthetic algae and bacteria.
Autotroph that use chemical energy, chemotroph, include nitrifying bacteria.
F-2
-------
Background levels
Bacterial
decomposition
Benthic
Benthic ammonia
flux
Benthic
denitrification
Benthic
nitrification
Background levels represent the chemical, physical, and biological conditions that
would result from natural geomorphological processes such as weathering or
dissolution.
Breakdown by oxidation, or decay, of organic matter by heterotrophic bacteria.
Bacteria use the organic carbon in organic matter as the energy source for cell
synthesis.
Refers to material, especially sediment, at the bottom of an aquatic ecosystem. It
can be used to describe the organisms that live on, or in, the bottom of a waterbody.
The decay of organic matter within the sediments of a natural water results in the
release of ammonia nitrogen from the interstitial water of sediments to the overlying
water column. Benthic release, or regeneration, of ammonia is an essential compo-
nent of the nitrogen cycle.
Under anaerobic, or low oxygen conditions, denitrifying bacteria synthesize cellular
material by reducing nitrate to ammonia and nitrogen gas. Denitrification is a
component of the overall nitrogen cycle and has been shown to account for a
significant portion of the "new" nitrogen loading to freshwater and estuarine ecosys-
tems.
Under aerobic conditions, nitrifying bacteria synthesize cellular material by oxidizing
ammonia to nitrite and nitrate. Benthic nitrification is a component of the overall
nitrogen cycle and has been shown to account for a significant portion of the nitrogen
budget of shallow freshwater and estuarine ecosystems.
Benthic organisms Organisms living in, or on, bottom substrates in aquatic ecosystems.
Benthic
photosynthesis
Best management
practices (BMPs)
Biochemical
oxygen demand
(BOD)
Biological
Nutrient Removal
(BNR)
Biomass
Boundary
conditions
Calibration
Carbonaceous
Synthesis of cellular carbon by algae attached to the bottom of a natural water
system. Benthic photosynthesis typically is limited to shallow waters because of the
availability of light at the bottom.
Methods, measures, or practices that are determined to be reasonable and cost-ef-
fective means for a land owner to meet certain, generally nonpoint source, pollution
control needs. BMPs include structural and nonstructural controls and operation and
maintenance procedures.
The amount of oxygen per unit volume of water required to bacterially or chemically
oxidize (stabilize) the oxidizable matter in water. Biochemical oxygen demand
measurements are usually conducted over specific time intervals (5,10,20,30 days).
The term BOD generally refers to standard 5-day BOD test.
Waste treatment method that employs natural biological processes to reduce the
quantity of nitrogen and phosphorus discharged to natural waters. Treatment
processes employ the movement of primary effluent through aerobic, anoxic/an-
aerobic zones to facilitate bacterially mediated processes of nitrification and denitri-
fication.
The amount, or weight, of a species, or group of biological organisms, within a
specific volume or area of an ecosystem.
Values or functions representing the state of a system at its boundary limits.
Testing and tuning of a model to a set of field data not used in the development of
the model; also includes minimization of deviations between measured field condi-
tions and output of a model by selecting appropriate model coefficients.
Pertaining to or containing carbon derived from plant and animal residues
F-3
-------
Channel
Channel
improvement
Channel
stabilization
Chloride
Chlorophyll
Chronic toxicity
Coliform bacteria
Combined sewer
overflows (CSOs)
Complete mixing
Concentration
Conservative
substance
Contamination
Conventional
pollutants
Cross-sectional
area
Decay
Decomposition
Denitrification
Design stream
flow
Designated use
A natural stream that conveys water; a ditch or channel excavated for the flow of
water.
The improvement of the flow characteristics of a channel by clearing, excavation,
realignment, lining, or other means in order to increase its capacity. Sometimes used
to connote channel stabilization.
Erosion prevention and stabilization of velocity distribution in a channel usingjetties,
drops, revetments, vegetation, and other measures.
An atom of chlorine in solution, bearing a single negative charge.
A group of green photosynthetic pigments that occur primarily in the chloroplast of
plant cells. The amount of chlorophyll-a, a specific pigment, is frequently used as a
measure of algal biomass in natural waters.
Toxicity impact that lingers or continues for a relatively long period of time, often
one-tenth of the life span or more. Chronic effects could include mortality, reduced
growth, or reduced reproduction.
A group of bacteria that normally live within the intestines of mammals, including
humans. Coliform bacteria are used as an indicator of the presence of sewage in
natural waters.
A combined sewer carries both wastewater and stormwater runoff. CSOs dis-
charged to receiving water can result in contamination problems that may prevent
the attainment of water quality standards.
No significant difference in concentration of a pollutant exists across the transect of
the waterbody.
Amount of a substance or material in a given unit volume of solution. Usually
measured in milligrams per liter (mg/l) or parts per million (ppm).
Substance that does not undergo any chemical or biological transformation or
degradation in a given ecosystem.
Act of polluting or making impure; any indication of chemical, sediment, or biological
impurities.
As specified under the Clean Water Act, conventional contaminants include sus-
pended solids, coliform bacteria, biochemical oxygen demand, pH, and oil and
grease.
Wet area of a waterbody normal to the longitudinal component of the flow.
Gradual decrease in the amount of a given substance in a given system due to
various sink processes including chemical and biological transformation, dissipation
to other environmental media, or deposition into storage areas.
Metabolic breakdown of organic materials; the by-products formation releases
energy and simple organics and inorganic compounds, (see also respiration)
Describes the decomposition of ammonia compounds, nitrites, and nitrates (by
bacteria) that results in the eventual release of nitrogen gas into the atmosphere.
The stream flow used to conduct steady-state wasteload allocation modeling.
Uses specified in water quality standards for each waterbody or segment regardless
of actual attainment.
F-4
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Detritus
Diagenesis
Dilution
Discharge permits
(NPDES)
Discharge
Monitoring Report
(DMR)
Dispersion
Dissolved oxygen
(DO)
Dissolved oxygen
sag
Diurnal
Domestic
wastewater
Drainage basin
Dye study
Dynamic model
Dynamic
simulation
Ecosystem
Effluent
Effluent plume
Epiphyte
Any loose material produced directly from disintegration processes. Organic detritus
consists of material resulting from the decomposition of dead organic remains.
Production of sediment fluxes as a result of the flux of paniculate organic carbon in
the sediment and its decomposition. The diagenesis reaction can be thought of as
producing oxygen equivalents released by various reduced species.
Addition of less concentrated liquid (water) that results in a decrease in the original
concentration.
A permit issued by the U.S. EPA or a State regulatory agency that sets specific limits
on the type and amount of pollutants that a municipality or industry can discharge
to a receiving water; it also includes a compliance schedule for achieving those limits.
It is called the NPDES because the permit process was established under the
National Pollutant Discharge Elimination System, under provisions of the Federal
Clean Water Act.
Report of effluent characteristics submitted by a municipal or industrial facility that
has been granted an NPDES discharge permit.
The spreading of chemical or biological constituents, including pollutants, in various
directions from a point source, at varying velocities depending on the differential
instream flow characteristics.
The amount of oxygen that is dissolved in water. It also refers to a measure of the
amount of oxygen available for biochemical activity in water body, and as indicator
of the quality of that water.
Longitudinal variation of dissolved oxygen representing the oxygen depletion and
recovery following a waste load discharge into a receiving water.
Actions or processes having a period or a cycle of approximately one tidal-day or
are completed within a 24-hour period and which recur every 24 hours.
Also called sanitary wastewater, consists of wastewater discharged from residences
and from commercial, institutional, and similar facilities.
A part of the land area enclosed by a topographic divide from which direct surface
runoff from precipitation normally drains by gravity into a receiving water. Also
referred to as watershed, river basin, or hydrologic unit.
Use of conservative substances to assess the physical behavior of a natural system
to given stimulus.
A mathematical formulation describing the physical behavior of a system or a
process and its temporal variability.
Modeling of the behavior of physical, chemical, and/or biological phenomena and
their variation over time.
An interactive system that includes the organisms of a natural community associa-
tion together with their abiotic physical, chemical, and geochemical environment.
Municipal sewage or industrial liquid waste (untreated, partially treated, or com-
pletely treated) that flows out of a treatment plant, septic system, pipe, etc.
Delineates the extent of contamination in a given medium as a result of effluent
discharges (or spills). Usually shows the concentration gradient within the delineated
areas or plume.
A plant growing on another plant; more generally, any organism growing attached
on a plant.
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Estuary
Estuarine number
Eutrophication
Eutrophication
model
Extinction
coefficient
Factor of Safety
Fate of pollutants
Fecal coliform
bacteria
First-order kinetics
Flocculation
Flux
Forcing functions
Geochemical
Gradient
Groundwater
Half-saturation
constant
Heterotroph
Hydrodynamic
model
Brackish-water areas influenced by the tides where the mouth of the river meets the
sea.
Nondimensional parameter accounting for decay, tidal dispersion, and advection
velocity. Used for classification of tidal rivers and estuarine systems.
Enrichment of an aquatic ecosystem with nutrients (nitrates, phosphates) that
accelerate biological productivity (growth of algae and weeds) and an undesirable
accumulation of algal biomass.
Mathematical formulation that describes the advection, dispersion, and biological,
chemical, and geochemical reactions that influence the growth and accumulation of
algae in aquatic ecosystems. Models of eutrophication typically include one or more
species groups of algae, inorganic and organic nutrients (N,P), organic carbon, and
dissolved oxygen.
Measure for the reduction (absorption) of light intensity within a water column.
Coefficient used to account for uncertainties in representing, simulating, or designing
a system.
Physical, chemical, and biological transformation in the nature and changes of the
amount of a pollutant in an environmental system. Transformation processes are
pollutant specific. However, they have comparable kinetics so that different formu-
lations for each pollutant are not required.
Bacteria that are present in the intestines or feces of warm-blooded animals. They
are often used as indicators of the sanitary quality of water. See Coliform bacteria.
Describes a reaction in which the rate of transformation of a pollutant is proportional
to the amount of that pollutant in the environmental system.
The process by which suspended colloidal or very fine particles are assembled into
larger masses or flocules that eventually settle out of suspension.
Movement and transport of mass of any water quality constituent over a given period
of time. Units of mass flux are mass per unit time.
External empirical formulation used to provide input describing a number of proc-
esses. Typical forcing functions include parameters such as temperature, point and
tributary sources, solar radiation, and waste loads and flow.
Refers to chemical reactions related to earth materials such as soil, rocks, and water.
The rate of decrease (or increase) of one quantity with respect to another; for
example, the rate of decrease of temperature with depth in a lake.
Phreatic water or subsurface water in the zone of saturation. Groundwater inflow
describes the rate and amount of movement of water from a saturated formation.
Nutrient concentration at which the growth rate is half the maximum rate. Half-satu-
ration constants define the nutrient uptake characteristics of different phytoplankton
species. Low half-saturation constants indicate the ability of the algal group to thrive
under nutrient-depleted conditions.
Organisms that use organic carbon for the formation of cell tissue. Bacteria are
examples of heterotroph.
Mathematical formulation used in describing circulation, transport, and deposition
processes in receiving water.
F-6
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Hydrograph
Hydrologic cycle
Hydrolysis
In situ
Initial conditions
Initial mixing zone
Interstitial water
Kinetic processes
Light saturation
Loading, Load,
Loading rate
Load allocation
(LA)
Long stream
Longitudinal
dispersion
Low-flow (7Q10)
Macrophyte
Margin of Safety
(MOS)
Mass balance
Mathematical
model
Mineralization
A graph showing variation of in stage (depth) or discharge of water in a stream over
a period of time.
The circuit of water movement from the atmosphere to the earth and return to the
atmosphere through various stages or processes, such as precipitation, intercep-
tion, runoff, infiltration, storage, evaporation, and transpiration.
Reactions that occur between chemicals and water molecules resulting in the
cleaving of a molecular bond and the formation of new bonds with components of
the water molecule.
In place; in situ measurements consist of measurement of component or processes
in a full-scale system or a field rather than in a laboratory.
A state of a system prior to an introduction of an induced stimulus. Describe
conditions at the start-up of system simulations.
Region immediately downstream of an outfall where effluent dilution processes
occur. Because of the combined effects of the effluent buoyancy, ambient stratifica-
tion, and current, the prediction of initial dilution can be involved.
Water contained in the interstices, which are the pore spaces or voids in soils and
rocks.
Description of the rate and mode of change in the transformation or degradation of
a substance in an ecosystem.
Optimal light level for algae and macrophyte growth and photosynthesis.
The total amount of material (pollutants) entering the system from one or multiple
sources; measured as a rate in weight per unit time.
The portion of a receiving water's total maximum daily load that is attributed either
to one of its existing or future nonpoint sources of pollution or to natural background
sources.
A receiving water where nutrients are in excess of growth limiting conditions, and
where the travel time allows growth and physical accumulation of algal biomass.
The spreading of chemical or biological constituents, including pollutants, down-
stream from a point source at varying velocities due to the differential instream flow
characteristics.
Low-flow (7Q10) is the 7-day average low flow occurring once in 10 years; this
probability-based statistic is used in determining stream design flow conditions and
for evaluating the water quality impact of effluent discharge limits.
Large vascular rooted aquatic plants.
A required component of the TMDL that accounts of the uncertainty about the
relationship between the pollutant load and the quality of the receiving waterbody.
An equation that accounts for the flux of mass going into a defined area and the flux
of mass leaving the defined area. The flux in must equal the flux out.
A system of mathematical expressions that describe the spatial and temporal
distribution of water quality constituents resulting from fluid transport and the one,
or more, individual processes and interactions within some prototype aquatic
ecosystem. A mathematical water quality model is used as the basis for waste load
allocation evaluations.
The transformation of organic matter into a mineral or an inorganic compound.
F-7
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Mixing
characteristics
Monte Carlo
simulation
N/P ratio
Natural waters
Nitrate (NO3) and
Nitrite (NO2)
Nitrification
Refers to the tendency for natural waters to blend; i.e. for dissolved and paniculate
substances to disperse into adjacent waters.
A stochastic modeling technique that involves the random selection of sets of input
data for use in repetitive model runs. Probability distributions of receiving water
quality concentrations are generated as the output of a Monte Carlo simulation.
The ratio of nitrogen to phosphorus in an aquatic system. The ratio is used as an
indicator of the nutrient limiting conditions for algal growth; also used as indicator
for the analysis of trophic levels of receiving waters.
Flowing water within a physical system that has developed without human interven-
tion, in which natural processes continue to take place.
Oxidized nitrogen species. Nitrate is the form of nitrogen preferred by aquatic plants.
The oxidation of ammonium salts to nitrites (via Nitrosomonas bacteria) and the
further oxidation of nitrite to nitrate via Nitrobacter bacteria.
Nitrifier organisms Bacterial organisms that mediate the biochemical oxidative processes of nitrification.
Nitrobacter
Nitrogenous BOD
(NBOD)
Nitrosomonas
Nonconservative
substance
Nonpoint source
Numerical model
Nutrient
Nutrient limitation
One-dimensional
model (1-D)
Organic matter
Organic nitrogen
Type of bacteria responsible for the conversion of nitrite to nitrate.
Refers to the oxygen demand associated with the oxidation of nitrate.
Type of bacteria responsible for the oxidation of ammonia to the intermediate product
nitrite.
Substances that undergo chemical or biological transformation in a given environ-
ment.
Pollution that is not released through pipes but rather originates from multiple
sources over a relatively a large area. Nonpoint source can be divided into source
activities related to either land or water use including failing septic tanks, improper
animal-keeping practices, forest practices, and urban and rural runoff.
Models that approximate a solution of governing partial differential equations which
describe a natural process. The approximation uses a numerical discretization of
the space and time components of the system or process.
A primary element necessary for the growth of living organisms. Carbon dioxide,
nitrogen, and phosphorus, for example, are required nutrients for phytoplankton
growth.
Deficit of nutrient (e.g., nitrogen and phosphorus) required by microorganisms in
order to metabolize organic substrates.
A mathematical model defined along one spatial coordinate of a natural water
system. Typically 1-D models are used to describe the longitudinal variation of water
quality constituents along the downstream direction of a stream or river. In writing
the model, it is assumed that the cross-channel (lateral) and vertical variability is
relatively homogenous and can, therefore, be averaged over those spatial coordi-
nates.
The organic fraction that includes plant and animal residue at various stages of
decomposition, cells and tissues of soil organisms, and substance synthesized by
the soil population. Commonly determined as the amount of organic material
contained in a soil or water sample.
Form of nitrogen bound to an organic compound.
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Orthophosphate
(O_PO4_P)
Outfall
Oxidation
Oxygen demand
Oxygen depletion
Oxygen saturation
Partition
coefficients
Peak runoff
Periphyton
Photoperiod
Photosynthesis
Phyla
Phytoplankton
Plankton
Point source
Pollutant
Postaudit
Form of phosphate available for biological metabolism without further breakdown.
Point where water flows from a conduit, stream, or drain.
The chemical union of oxygen with metals or organic compounds accompanied by
a removal of hydrogen or another atom. It is an important factor for soil formation
and permits the release of energy from cellular fuels.
Measure of the dissolved oxygen used by a system (microorganisms) in the
oxidation of organic matter. See also biochemical oxygen demand.
Deficit of dissolved oxygen in a water system due to oxidation of organic matter.
Natural or artificial reaeration or oxygenation of a water system (water sample) to
bring the level of dissolved oxygen to saturation. Oxygen saturation is greatly
influence by temperature and other water characteristics.
Chemicals in solution are partitioned into dissolved and particulate adsorbed phase
based on their corresponding sediment-to-water partitioning coefficient.
The highest value of the stage or discharge attained by a flood or storm event, also
referred to as flood peak or peak discharge.
Attached benthic algae.
Time period of the seasonal response by organisms to change in the length of the
daylight period (e.g., flowering, germination of seeds, reproduction, migration, and
diapause are frequently under photoperiod control).
The biochemical synthesis of carbohydrate based organic compounds from water
and carbon dioxide using light energy in the presence of chlorophyll. Photosynthesis
occurs in all plants, including aquatic organisms such as algae and macrophyte.
Photosynthesis also occurs in primitive bacteria such as blue-green algae.
Species groups of same family of organisms. Phyla of phytoplankton include
diatoms, blue-green algae, dinoflagellates, and green algae.
A group of generally unicellular microscopic plants characterized by passive drifting
within the water column. See Algae.
Group of generally microscopic plants and animals passively floating, drifting or
swimming weakly. Plankton include the phytoplankton (plants) and zooplankton
(animals).
Pollutant loads discharged at a specific location from pipes, outfalls, and conveyance
channels from either municipal wastewater treatment plants or industrial waste
treatment facilities. Point sources can also include pollutant loads contributed by
tributaries to the main receiving water stream or river.
A contaminant in a concentration or amount that adversely alters the physical,
chemical, or biological properties of a natural environment. The term include
pathogens, toxic metals, carcinogens, oxygen demanding substances, or other
harmful substances. Examples of pollutant sources include dredged spoil, solid
waste, incinerator residue, sewage, garbage, sewage sludge, munitions, chemical
waste, biological material, radioactive materials, heat, wrecked or discharged equip-
ment, sediment, cellar dirt, hydrocarbons, oil, and municipal, industrial, and agricul-
tural waste discharged into surface water or groundwater.
A subsequent examination and verification of model predictive performance follow-
ing implementation of an environmental control program.
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Pretreatment
Primary
productivity
Primary treatment
plant
Priority pollutant
Publicly Owned
Treatment Works
(POTW)
Raw sewage
Reaction rate
coefficient
Reaeration
Receiving waters
Refractory
organics
Reserve capacity
Residence time
Respiration
Rotating
biological
contactors (RBCs)
Roughness
Coefficient
Scour
The treatment of wastewater to remove or reduce contaminants prior to discharge
into another treatment system or a receiving water.
A measure of the rate at which new organic matter is formed and accumulated
through photosynthesis and chemosynthesis activity of producer organisms (chiefly,
green plants). The rate of primary production is estimated by measuring the amount
of oxygen released (oxygen method) or the amount of carbon assimilated by the
plant (carbon method)
Wastewater treatment process where solids are removed from raw sewage primarily
by physical settling. The process typically removes about 25-35% of solids and
related organic matter (BODs).
Substances listed by the U.S. EPA under the Federal Clean Water Act as harmful
substances and having priority for regulatory controls. The list includes metals (13),
inorganic compounds (2), and a broad range of naturally occurring or artificial
organic compounds (111).
Municipal wastewater treatment plant owned and operated by a public governmental
entity such as a town or city.
Untreated municipal sewage.
Coefficient describing the rate of transformation of a substance in an environmental
medium characterized by a set of physical, chemical, and biological conditions such
as temperature and dissolved oxygen level.
Describe the net flux of oxygen occurring from the atmosphere to a body of water
with a free surface.
Creeks, streams, rivers, lakes, estuaries, groundwater formations, or other bodies
of water into which surface water and/or treated or untreated waste are discharged,
either naturally or in man-made systems.
A broad lumping of man-made organic chemicals that resist chemical or bacterial
decomposition, including many pesticides, herbicides, household and industrial
cleaners and solvents, photofinishing chemicals, and dry-cleaning fluids.
Pollutant loading rate set aside in determining stream waste load allocation account-
ing for uncertainty and future growth.
Length of time that a pollutant remains within a section of a stream or river. The
residence time is determined by the streamflow and the volume of the river reach
or the average stream velocity and the length of the river reach.
Biochemical process by means of which cellular fuels are oxidized with the aid of
oxygen to permit the release of the energy required to sustain life; during respiration
oxygen is consumed and carbon dioxide is released.
A wastewater treatment process consisting of a series of closely spaced rotating
circular disks of polystyrene or polyvinyl chloride. Attached biological growth is
promoted on the surface of the disks. The rotation of the disks allows contact with
the wastewater and the atmosphere to enhance oxygenation.
A factor in velocity and discharge formulas representing the effects of channel
roughness on energy losses in flowing water. Manning's "n" is a commonly used
roughness coefficient.
To abrade and wear away. Used to describe the weathering away of a terrace or
diversion channel or streambed. The clearing and digging action of flowing water,
F-10
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Secchi depth
Secondary
treatment plant
Sediment
Sediment oxygen
demand (SOD)
Sedimentation
Short stream
Simulation
Sorption
Spatial
segmentation
Stabilization pond
Steady-state
model
Stoichiometric
ratio
STORE!
Storm runoff
Stratification (of
water body)
Streamflow
especially the downward erosion by stream water in sweeping away mud and silt
on the outside of a meander or during flood events.
A measure of the light penetration into the water column. Light penetration is
influenced by turbidity.
Waste treatment process where oxygen-demanding organic materials (BOD) are
removed by bacterial oxidation of the waste to carbon dioxide and water. Bacterial
synthesis of wastewater is enhanced by injection of oxygen.
Particulate organic and inorganic matter that accumulates in a loose, unconsolidated
form on the bottom of natural waters.
The solids discharged to a receiving water are partly organics, and upon settling to
the bottom, they decompose anaerobically as well as aerobically, depending on
conditions. The oxygen consumed in aerobic decomposition represents another
dissolved oxygen sink for the waterbody.
Process of deposition of waterborne or windborne sediment or other material; also
refers to the infilling of bottom substrate in a waterbody by sediment (siltation).
A receiving water where nutrients are in excess of growth-limiting conditions and
where the time of travel within the stream reach is not sufficient to allow growth and
physical accumulation of algal biomass.
Refers to the use of mathematical models to approximate the observed behavior of
a natural water system in response to a specific known set of input and forcing
conditions. Models that have been validated, or verified, are then used to predict the
response of a natural water system to changes in the input or forcing conditions.
The adherence of ions or molecules in a gas or liquid to the surface of a solid particle
with which they are in contact.
A numerical discretization of the spatial component of a system into one or more
dimensions; forms the basis for application of numerical simulation models.
Large earthen basins that are used for the treatment of wastewater by natural
processes involving the use of both algae and bacteria.
Mathematical model of fate and transport that uses constant values of input variables
to predict constant values of receiving water quality concentrations.
Mass-balance-based ratio for nutrients, organic carbon and algae (e.g., nitrogen-to-
carbon ratio).
U.S. Environmental Protection Agency (EPA) national water quality database for
STORage and RETrieval (STORET). Mainframe water quality database that in-
cludes physical, chemical, and biological data measured in waterbodies throughout
the United States.
Rainfall that does not evaporate or infiltrate the ground because of impervious land
surfaces or a soil infiltration rate lower than rainfall intensity, but instead flows onto
adjacent land or waterbodies or is routed into a drain or sewer system.
Formation of water layers each with specific physical, chemical, and biological
characteristics. As the density of water decreases due to surface heating, a stable
situation develops with lighter water overlaying heavier and denser water.
Discharge that occurs in a natural channel. Although the term "discharge" can be
applied to the flow of a canal, the word "streamflow" uniquely describes the discharge
in a surface stream course. The term streamflow is more general than "runoff" as
F-11
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Substrate
Surface waters
Suspended solids
or load
Temperature
coefficient
Tertiary treatment
Three-dimensional
model (3-D)
Total Kjeldahl
Nitrogen (TKN)
Total Maximum
Daily Load (TMDL)
Total coliform
bacteria
Toxic substances
Transit time
Transport of
pollutants (in
water)
Travel time
Tributary
Trickling filter
Turbidity
Turbulent flow
Turbulence
streamflow may be applied to discharge whether or not it is affected by diversion or
regulation.
Refers to bottom sediment material in a natural water system.
Water that is present above the substrate or soil surface. Usually refers to natural
waterbodies such as rivers, lakes and impoundments, and estuaries.
Organic and inorganic particles (sediment) suspended in and carried by a fluid
(water). The suspension is governed by the upward components of turbulence,
currents, or colloidal suspension.
Rate of increase in an activity or process over a 10 degree Celsius increase in
temperature. Also referred to as the Qio.
Waste treatment processes designed to remove or alter the forms of nitrogen or
phosphorus compounds contained in domestic sewage.
Mathematical model defined along three spatial coordinates where the water quality
constituents are considered to vary over all three spatial coordinates of length, width,
and depth.
The total of organic and ammonia nitrogen in a sample, determined by the Kjeldahl
method.
The sum of the individual wasteload allocations and load allocations. A margin of
safety is included with the two types of allocations so that any additional loading,
regardless of source, would not produce a violation of water quality standards.
A particular group of bacteria that are used as indicators of possible sewage
pollution. They are characterized as aerobic or facultative anaerobic, gram-negative,
nonspore-forming, rod-shaded bacteria which ferment lactose with gas formation
within 48 hours at 35 degrees Celsius. (See also fecal coliform bacteria)
Those chemical substances, such as pesticides, plastics, heavy metals, detergent,
solvent, or any other material that are poisonous, carcinogenic, or otherwise directly
harmful to human health and the environment.
In nutrient cycles, average time that a substance remains in a particular form; ratio
of biomass to productivity.
Transport of pollutants in water involves two main process: (1) advection, resulting
from the flow of water, and (2) diffusion, or transport due to turbulence in the water.
Time period required by a particle to cross a transport route such as a watershed,
river system, or stream reach.
A lower order stream compared to a receiving waterbody. "Tributary to" indicates
the largest stream into which the reported stream or tributary flows.
A wastewater treatment process consisting of a bed of highly permeable medium to
which microorganisms are attached and through which wastewater is percolated or
trickled.
Measure of the amount of suspended material in water.
A flow characterized by irregular, random-velocity fluctuations.
A type of flow in which any particle may move in any direction with respect to any
other particle and in a regular or fixed path. Turbulent water is agitated by cross
current and eddies. Turbulent velocity is that velocity above which turbulent flow will
always exist and below which the flow may be either turbulent or laminar.
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Two-dimensional
model (2-D)
Ultimate
Biochemical
Oxygen Demand
(UBOD or BODu)
Uncertainty factors
Unstratified
Verification (of a
model)
Volatilization
Waste load
allocation (WLA)
Wastewater
Wastewater
treatment
Water quality
Water quality
criteria (WQC)
Water quality
standard (WQS)
Wind mixing
Zero-order kinetics
Zooplankton
Mathematical model defined along two spatial coordinates where the water quality
constituents are considered averaged over the third remaining spatial coordinate.
Examples of 2-D models include descriptions of the variability of water quality
properties along: (a) the length and width of a river that incorporates vertical
averaging or (b) length and depth of a river that incorporates lateral averaging across
the width of the waterbody.
Longterm oxygen demand required to completely stabilize organic carbon in waste-
water or natural waters.
Factors used in the adjustment of toxicity data to account for unknown variations.
Where toxicity is measured on only one test species, other species may exhibit more
sensitivity to that effluent. An uncertainty factor would adjust measured toxicity
upward and downward to cover the sensitivity range of other, potentially more or
less sensitive species.
Indicates a vertically uniform or well-mixed condition in a waterbody. See also
stratified.
Subsequent testing of a precalibrated model to additional field data usually under
different external conditions to further examine model validity (also called validation).
Process by which chemical compounds are vaporized (evaporated) at given tem-
perature and pressure conditions by gas transfer reactions. Volatile compounds
have a tendency to partition into the gas phase.
The portion of a receiving water's total maximum daily load that is allocated to one
of its existing or future point sources of pollution.
Usually refers to effluent from a sewage treatment plant. See also domestic
wastewater.
Chemical, biological, and mechanical procedures applied to an industrial or munici-
pal discharge or to any other sources of contaminated water in order to remove,
reduce, or neutralize contaminants.
The biological, chemical, and physical conditions of a water body. It is a measure of
a water body to support beneficial uses.
Water quality criteria comprised numeric and narrative criteria. Numeric criteria are
scientifically derived ambient concentrations developed by E PA or States for various
pollutants of concern to protect human health and aquatic life. Narrative criteria are
statements that describe the desired water quality goal.
A water quality standard is a law or regulation that consists of the beneficial
designated use or uses of a waterbody, the numeric and narrative water quality
criteria that are necessary to protect the use or uses of that particular waterbody,
and an antidegradation statement.
Refers to a physical process occurring when wind over a free water surface
influences the atmospheric reaeration rate.
Describe the rate of transformation or degradation of a substance; the reaction rate
of change is independent of the concentrations in solution.
Very small animals (protozoans, crustaceans, fish embryos, insect larvae) that live
in a waterbody and are moved passively by water currents and wave action.
F-13
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APPENDIX G.
ABBREVIATIONS
AGP algal growth potential
ARM agricultural runoff model
ASCII American Standard Code for Information
Interchange
AT advanced treatment
AWT advanced water treatment
BOD biochemical oxygen demand
BODs 5-day biochemical oxygen demand
BODu ultimate biochemical oxygen demand
BMPs best management practices
BNR biological nutrient removal
CBOD carbonaceous biochemical oxygen demand
CBODs 5-day carbonaceous biochemical oxygen
demand
CEAM Center for Exposure Assessment Modeling
(EPA)
CE-QUAL- fully dynamic one-dimensional riverine water
RIV1 quality model
Chi chlorophyll concentration
COD chemical oxygen demand
COE U.S. Army Corps of Engineers
CSO combined sewer overflow
DIN inorganic nitrogen concentration (sum of
ammonia, nitrate, and nitrite)
DIP dissolved inorganic phosphorus concentration
DMR discharge monitoring report
DO dissolved oxygen
DYNHYD5 hydrodynamic model; a submodel of WASP5
EUTRO5 eutrophication/dissolved oxygen kinetics; a
submodel of WASP5
EPA Environmental Protection Agency
EPA STORET U.S. Environmental Protection Agency (EPA)
national water quality data base for STORage
and RETrieval (STORET). Mainframe water
quality data base that includes physical,
chemical, and biological data measured in
waterbodies throughout the United States
FOIA Freedom of Information Act
FOEA first-order error analysis
FORTRAN FORmula TRANslation; revised high-level
programming language for solving problems
in science and engineering
FORTRAN77 FORmula TRANslation ANSI Standard of
1977; computer language often used in
writing scientific equations and models as
source code for water quality and
hydrodynamic models.
H surface-to-bottom depth of the water column;
units of length
HSPF Hydrologic Simulation Program - FORTRAN
HRAS high-rate activated sludge
LA load allocation
MBAS methyl benzene alkyl sulfonate
MGD million gallons per day
Multi-SMP Simplified Method Program for multiple
dischargers
NBOD nitrogenous biochemical oxygen demand
NPDES National Pollutant Discharge Elimination
System
NTIS National Technical Information Service
NTU nephelometry turbidity units
NVSS nonvolatile suspended solids concentration
O-PO4-P orthophosphate
P average gross photosynthesis production
PC personal computer; usually refers to IBM
DOS-compatible machines
PCS Permit Compliance System
PDF probability density function
POTW publicly owned treatment works
P/R production/respiration ratio
P-R photosynthesis and respiration
Q streamflow; units of volume/time
QA/QC quality assurance/quality control
QUAL2E stream water quality model
QUAL2E- stream water quality model
UNCAS
R average respiration
RIVMOD numerical, hydrodynamic, and sediment
transport riverine model
RIV1H hydrodynamic model; a submodel of CE-
QUAL-RIV1
RIV1Q water quality model; a submodel of CE-QUAL-
RIV1
SOD sediment oxygen demand
STP sewage treatment plant
TBOD total biochemical oxygen demand
TDS total dissolved solids
TKN total Kjedahl nitrogen
TMDL total maximum daily load
TOC total organic carbon
TOXI5 toxic chemical-sediment dynamics; a
submodel of WASP5
TP total phosphorus; sum of all forms of
phosphorus: dissolved, particulate, inorganic,
and organic phosphorus
TSS total suspended solids
USGS U.S. Geological Survey
VSS detritus concentration
W width across a stream channel; units of length
WASPS Water Quality Analysis Simulation Program
WLA waste load allocation
1-D one-dimensional water quality model
7Q10 7-day average low flow that occurs once in 10
years
G-1
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APPENDIX H: CONVERSION FACTORS
For readers who
Multiply
milimeter (mm)
Meter (m)
kilometer (km)
meter per second (mis)
nanometer (nm)
centimeter (cm)
square meter (m2)
cubic meter (m3)
liter (L)
cubic meter per second (m3/s)
millligram (mg)
gram (g)
kilogram (kg)
metric ton (Mt) (1000 kg)
gram per square meter (g/m2)
degree Celsius (°C)
milligram per liter (g/L)
grams per liter (mg/L)
langley (ly)
calorie/square centimeter day
Symbol
PAR
|imho
prefer to use U.S. equivalents of metric
for terms used in this report are listed
By
Length
0.03937
3.281
1.094
0.6214
0.5400
3.281
3.937X108
0.3937
Area
10.76
1.196
Volume
35.31
1.308
1.057
35.31
Mass
0.00003527
0.03527
0.002205
2,205
1.102
8.922
Temperature
1.8[°C] +32
Concentration
1.0
1.0
Energy
1.0
3.6867
Meaning
Photosythetically active radiation
(400-700 nanometer waveband).
Measured in microeinsteins per
square meter per second [|iE/m2/s]
Conductance in micromhos. A
measure of the amount of dissolved
ions present in water
units, conversion factors
below:
To
Obtain
inch (in)
foot (ft)
yard (yd)
mile (mi)
nautical mile (nmi)
foot per second (Ills)
inch (in)
inch (in)
square foot (ft2)
square yard (yd2)
cubic foot (ft3)
cubic yard (yd3)
quart (qt)
cubic foot per second (ft3/s)
ounce (oz)
ounce (oz)
pound (Ib)
ton (short)
pound per acre (Ib/acre)
degree Fahrenheit (°F)
parts per million (ppm)
parts per thousand (ppt)
calorie/square centimeter (cal/cm2)
British thermal units/square foor/day
(Btu/ft2/day)
Conversion
1 watt m 2~4.6|iEm 2s 1
1 ly day1-0.485 watt m 2
1 part per thousand is approximately
1,500|imhoat25°C
H-1
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APPENDIX I. SYMBOLS
SYMBOL DESCRIPTION (dimension)
SYMBOL DESCRIPTION (dimension)
3N
ap
A
Ag
bn
C
Cs
C(t)
dV
Dp
Dx
Dz
f
F
g
Gmax
Gn
Gp
GT
H
K
Ka
Kd
Ke
Km
Kmn
Kmp
Kn
Kr
Ks
Ksi
Ki
la
IT
L
n
N
Nut
Ni
N2
N3
N4
nitrogen:chlorophyll ratio (MM 1)
phosphorus:chlorophyll ratio (MM^)
chlorophyll a concentration (ML3)
algal biomass concentration (ML 3)
periodic coefficient
dissolved oxygen concentration in stream (ML 3)
saturation concentration of dissolved oxygen (ML )
time varying oxygen value (ML 3)
volume of the segment and is equal to AAX(L 3)
phytoplankton death rate (T 1)
longitudinal dispersion coefficient (L2T 1)
death rate (T 1)
photoperiod (T)
fraction of algal nitrogen uptake from ammonia pool
gravitational constant (L2 T1)
maximum growth rate (T 1)
phytoplankton net growth rate (T ^)
phytoplankton growth rate (T 1)
temperature effect (T 1)
average depth (L)
first-order reaction rate (T 1)
stream reaeration rate coefficient (T 1);
atmospheric reaeration rate: reflects first-order
reaction whereby fraction of oxygen deficit is
satisfied
BOD oxidation rate where oxidation accounts for
all CBOD removal (T 1)
extinction coefficient (L 1)
half saturation (Michaelis) constant (ML 3)
Michaelis-Menton constant for nitrogen (ML 3)
Michaelis-Menton constant for phosphorus (ML 3)
nitrification reaction rate (T 1)
CBODs removal rate in the stream (T 1)
effective loss rate due to settling (T 1)
Michaelis-Menton constant for silica (ML3)
BOD reaction rate (T 1)
average of incident light on water surface over a
24-hour period (ly/day)
saturating light intensity (ly/day)
total daily radiation (ly)
oxygen equivalence of the organic matter
remaining CBOD concentration (ML 3); length; liters
total oxygen demand (ML 3)
langley (incident light intensity)
estuary number (dimensionless)
nitrogen concentration (ML 3)
nutrient concentration (ML 3)
ammonia concentration (ML 3)
nitrite-nitrogen concentration (ML 3)
nitrate-nitrogen concentration (ML 3)
organic nitrogen concentration (ML 3)
Pav
PM
P(t)
Pi
P2
0
PL
rn
R
S
Sb
Si
t
t*
T
U
u*
Vs
w
x
y
a-i
OC2
as
OC4
as
ae
61
62
63
B4
02
03
04
05
average gross photosynthesis production
(ML 3 T1); phosphorus concentration (ML 3)
average daily rate of photosynthetic oxygen
production (ML 3 T 1)
maximum rate of photosynthetic oxygen
production (ML 3 T 1)
algal gross photosynthetic production of oxygen
(ML 3T 1)
organic phosphorus concentration (ML 3)
dissolved phosphorus concentration (ML 3)
river flow rate (L3T 1)
light effect (dimensionless)
nutrient effect (dimensionless); limiting nutrient
reduction factor
average algal oxygen respiration (ML 3T 1)
net settling rate (T 1); stream slope (LL 1)
sediment oxygen demand (ML2T 1)
dissolved inorganic silica concentration (ML 3)
time (T)
travel time in stream ; =x/U (T)
temperature (°); average time period
average stream velocity (LT 1)
shear velocity (LT 1)
phytoplankton settling velocity (MT 1)
direct loading rate (MT 1); stream width (L)
distance downstream of effluent (L)
oxygen consumed (ML 3)
fraction of algal biomass that is nitrogen (MM-1)
fraction of algal biomass that is phosphorus (MM 1)
the stoichiometric ratio of oxygen production per
unit of algal photosynthesis (MM-1)
the stoichiometric ratio of oxygen uptake per unit
of algae respired (MM-1)
the stoichiometric ratio of oxygen uptake per unit
of ammonium (MM-1)
the stoichiometric ratio of oxygen uptake per unit
of nitrite-nitrogen oxidation (MM-1)
ammonia oxidation rate coefficient (T 1)
nitrite oxidation rate coefficient (T 1)
organic nitrogen hydrolysis rate coefficient (T 1)
organic phosphorus decay rate (T 1)
benthos source rate for dissolved phosphorus (ML 2T 1)
benthos source rate for ammonia nitrogen (ML 2T 1)
rate coefficient for organic nitrogen settling (T -1)
rate coefficient for organic phosphorus settling (T 1)
algal growth rate coefficient (T 1)
algal respiration rate coefficient (T 1)
constant for temperature adjustment (dimensionless)
Dimension codes:
L=Length M=Mass T=Time
1-1
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