jffe
Unlttfi Statot
Environmental Protection
Agency
Office of Wntor Regulation!
and Standards
Monitoring and Data Support
Dlvldon (WB-5S3I
EPA-440/4-04-020
Soptomber 1983
Final
Water
Waste Load Allocations
Book II
Streams and Rivers
Chapter 1
Biochemical Oxygen
Demand / Dissolved Oxygen
-------
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
1 WASHINGTON. D.C. 20460
OCT 3
MEMORANDUM
SUBJECT: Technical Guidance Manual for Perforating Waste Load Allocations
Book II, Streams and Rivers, j^apter 1, BOJ
FROMu^wSteven Schatzow, Director!
T Office of Water Regulations and Standards (WB-551)
U
TO: Regional Water Division Directors
Regional Environmental Services Division Directors
Regional Wasteload Allocation Coordinators
Attached, for national use, is the final version of the Technical
Guidance Manual for Performing Waste Load Allocations Book II, Streams and
Rivers, Chapter 1, BOD/DO. Wa are sending extra copies of this manual to
the Regional Wasteload Allocation Coordinators for distribution to the
States to use in conducting wasteload allocations.
Modifications to the March 1983 draft include:
o Deleting Appendix A and making the Simplified Analytical Method
for Determining NPDES Effluent Limitations for POTWs Discnarging
into Low-Flow Streams available as a separate document.
o Adding a discussion relating the detail of analysis with the
anticipated cost of treatment.
o Clarifying the selection of the critical period for the example
presented in section 2.
o Warning users against substituting values from the example into
real-life situations.
o Adding a note that effluent characteristics used in modeling
should reflect the performance expected of the proposed facility
during the critical period.
If you have any questions or caonents or desire additional information
please contact Tim S. Stuart, Chief/ Monitoring Branch, Monitoring and
Data Support Division (lfi-553) on (ETS) 382-7074.
Attachment
-------
TECHNICAL GUIDANCE MANUAL FOR
PERFORMING WASTE LOAD ALLOCATIONS
by
Eugene D. Driscoll (E.D. Driscoll and Assoc., Inc.)
John L. Mancini (Mancini and DiToro Consulting, Inc.)
Peter A. Mangarella (Woodward-Clyde Consultants)
Contract No. 68-01-5918
Project Officer
Jonathan R. Pawlow
Office of Water Regulations and Standards
Monitoring and Data Support Division
Monitoring Branch
U.S. Environmental Protection Agency
401 M Street, SW
Washington, D.C. 20460
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11 Vil
Revision Ntf.
ACKNOWLEDGEMENTS
The authors acknowledge che following individuals who contributed in various
ways to this chapter.
Jonathan R. Pawlow, the EPA Project Officer, USEPA, Washington, D.C., provided
guidance and direction on the basic content and emphasis, and coordinated
input from EPA Regional Offices.
Robert B. Ambrose, Jr., USEPA Environmental Research Laboratory, Athens,
Georgia; George Nossa, USEPA Region II; and Dr. Quentin Martin, Texas Depart-
ment of Water Resources, provided review of selected model descriptions.
Drs. Donald J. O'Connor and Robert V. Thooann, serving on a Board of
Consultants, provided technical input and review on certain parts of the
chapter.
Thomas W. Gallagher contributed to the organization and content of the
chapter section dealing with basic concepts and the example analysis.
Dr. Dominic DiToro and Larry Neal provided technical information that was
incorporated into the chapter.
Individuals from EPA Headquarters, EPA Regional Offices and States reviewed
and commented on draft versions.
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Revision No.
CONTENTS
ACKNOWLEDGEMENTS ....................... i
FIGURES ............................ v
TABLES ............................ «
1.0 INTRODUCTION
1.1 Purpose ....................... 1-1
1.2 Relation to Other Books and Chapters ........ 1-1
1.3 Organization and Scope of Chapter .......... 1-3
1.4 Appropriate Levels of Effort in Performing WLAs . . . 1-4
2.0 BASIC PRINCIPLES FOR PERFORMING STREAM BOD/DO WLAs .... 2-1
2.1 General ....................... 2-1
2.2 Concepts in River BOD/DO Analysis .......... 2-3
2.3 Development of BOD/DO Equations for Rivers ..... 2-34
2.4 Example Waste Load Allocation Analysis ....... 2-44
3.0 MODELS: SELECTION AND USE ................ 3-1
3.1 Selecting a Model .................. 3-1
3.2 Available Models and Model Features ......... 3-32
3.3 Modeling Procedures ................. 3-57
3.4 Assessing Adequacy of Model Verification ...... 3-108
3.5 Allocating Waste Loads ............... 3-110
4.0 TECHNICAL CONSIDERATIONS
4.1 Water Quality Problem Identification ........ 4-1
4.2 Data Requirements .................. &~8
4.3 Quality Assurance for Waste Load Allocation Studies . 4-20
REFERENCES
ill
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FIGURES
Number Page
2-1 Transport mechanisms for waste leads 2-5
2-2 Steady state responses 2-9
2-3 Stream dispersion effects 2-11
2-4 BOD decay: range of reaction rates 2-15
2-5 Effect of elevation on dissolved oxygen saturation
concentration 2-19
2-6 Reaeration rate coefficient related to depth and
velocity 2-23
2-7 Stream reaeration relationships 2-2S
2-8 Effect of rates on stream DO impacts 2-29
2-9 Basic relationships for BOD equations 2-37
2-10 Basic relationships for DO equations 2-41
2-11 Problem setting 2-47
2-12 Treatment facilities and effluent characteristics 2-49
2-13 River flow, temperature, geometry, and velocity 2-51
2-14 Dissolved oxygen, BOD, and nitrogen data 2-57
2-15 Ammonia, pH, and un-ionized ammonia data 2-59
2-16 Percentage of un-ionized ammonia 2-61
2-17 Model calibration analysis 2-67
2-18 Projected DO, ammonia, and un-ionized ammonia
(present wastewater load) 2-69
2-19 Projected DO, ammonia, and un-ionized ammonia
(design wastewater laod) 2-71
2-20 DO component unit responses 2-77
3-0 DO response as a function of K. E/U 3-15
3-1 Combinations of variables for DO analysis 3-19
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FIGURES (concluded)
Number Page
3-2 Feedback reaction sequence 3-25
3-3 Typical BOD removal curves 3-75
3-4 Deoxygenaeion coefficient (Kd) as a function of depth .... 3-81
3-5 Steps in development of site-specific water quality model . . 3-93
3-6 Illustration of the use of calculation to define
survey periods 3-97
3-7 Unit responses at two conditions 3-103
3-8 Probability of absolute difference in calculated vs
observed dissolved concentration 3-115
3-9 Example of the calculation procedure for alloeatable load . . 3-121
3-10 Example of allocation procedure to minimize cost 3-125
3-11 Example of variable load response system 3-129
3-12 Example of allocations for variable load response system . . . 3-133
4-1 Sampling station locations 4-13
4-2 Quality assurance elements and responsibilities . 4-23
vii
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TABLES
Number Page
1-1 Organisation of Guidance Manual for Performance
of Waste Load Allocations 1-2
2-1 Solubility of Oxygen in Water Exposed to Water-
Saturated Air 2-17
2-2 Calibration Analysis 2-65
2-3 Projection Analysis (design load) 2-73
3-1 Steps for Documenting Inclusion of Time-variable
or Quasi Steady-state Water Quality Analysis 3-9
3-2 Methods of Analysis for Phytoplankton and Aquatic Weeds . . . 3-24
3-3 Capabilities: Temporal and Spatial Features 3-37
3-4 Capabilities: Hydraulic Features 3-37
3-5 Capabilities: Waste Loads, Sinks, and Sources of
DO Waste Loads 3-38
3-6 Capabilities: Constituents 3-39
3-7 Capabilities: Physical and Biochemical Processes
'Simulated 3-40
3-8 Capabilities: Reaeration Formulations 3-41
3-9 Accuracy: Principal Assumptions 3-42
3-10 Data Requirements: Input '. 3-43
3-11 Data Requirements: Calibration and Verification 3-44
3-12 Ease of Application: Output Form and Content 3-45
3-13 Ease of Application: Sources, Support, and Documentation . . 3-46
3-14 Ease of Application: Equipment and Programming
Requirements 3-47
3-15 Operating Costs 3-48
ix
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SECTION 1.0
INTRODUCTION
1.1 PURPOSE
This chapter is one in a series of manuals whose purpose is to
provide technical information and policy guidance for the preparation of
Waste Load Allocations (WLAs), which are as technically sound as current
state of the art permits. The objectives of such load allocations are to
ensure that quality conditions that protect designated beneficial uses
are achieved. An additional benefit of a technically sound VLA is that
excessive degrees of treatment, which are neither necessary nor result in
corresponding improvements in water quality, can be avoided. This can
result in a more effective utilization of available funds.
This chapter addresses Biochemical Oxygen Demand/Dissolved Oxygen
(BOO/DO) impacts in streams and rivers.
1.2 RELATION TO OTHER BOOKS AND CHAPTERS
Table 1-1 summarizes the relationship of the various "books" and
"chapters" that make up the set of technical guidance manuals.
1-1
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TABLE 1-1
ORGANIZATION OP GUIDANCE MANUAL FOR PERFORMANCE OF WASTE LOAD ALLOCATIONS
BOOK I GENERAL GUIDANCE
(Discussion of overall WLA process, procedures and considerations)
BOOK II STREAMS AND RIVERS
(Specific technical guidance for these water bodies)
Chapter 1 - BOD/Dissolved Oxygen Impacts and Ammonia Toxicity
2 - Nutrient/Eutrophication Impacts
3 - Toxic Substances Impacts
BOOK III ESTUARIES
Chapter 1 - BOD/Dissolved Oxygen Impacts
2 - Nutrient/Eutrophication Impacts
3 - Toxic Substances Impacts
BOOK IV LAKES. RESERVOIRS. AND IMPOUNDMENTS
Chapter 1 - BOD/Dissolved Oxygen Impacts
2 - Nutrient/Eutrophication Impacts
3 - Toxic Substances Impacts
Note: The manual may be expanded to include design conditions, permit
averaging periods, screening procedures, and innovative permits. In
addition, other water bodies (e.g., groundwaters, bays, and oceans)
and other contaminants
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These technical chapters should be used in conjunction with the
material in Book I, General Guidance, which provides general information
applicable to all types of water bodies and to all contaminants that must
be addressed by the WLA process.
Users of this manual should also be aware that other reports and
processes may affect the wasteload allocation process. For instance,
criteria and standards for dissolved oxygen, ammonia and other parameters
are in a continuous process of change. Therefore, any standards used in
examples contained in this chapter should not be applied to real-life
situations without first consulting the latest applicable criteria and
standards documents.
1.3 ORGANIZATION AND SCOPE OF CHAPTER
The remainder of this chapter is organized into three parts, as
summarized below.
Section 2.0 presents the underlying technical basis for performing
WLAs for the analysis of stream BOD/DO impacts. Both the basic theory
and the nature of stream system responses to oxygen demanding loads are
described. An example analysis is presented that illustrates the WLA
process applied in a simple setting. The object of this section is to
provide to technical personnel having limited experience with WLAs, an
1-3
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example that highlights the important issues in performing technically
sound analyses and a framework for structuring a consistent approach to
more complex problem settings.
Section 3.0 is devoted to a discussion of mathematical models that
are required to perform the calculations of water quality impacts on
which the WLAs will be based. Guidance is provided to assist in
selecting an appropriate model; applying the model to the local situation
in a technically sound, consistent manner; and assessing the "goodness"
of the final form of the model.
Section 4.0 addresses some key technical considerations that strongly
influence the technical adequacy of any analysis performed with the water
quality models. The importance of effectively identifying and
characterizing water quality problems is discussed, since it will define
the focus of the analysis, monitoring programs, and treatment
approaches. Data needs are critical and vary with the type of problem
and with the model selected. The nature of the data available, even more
than the amount of data, will determine the extent to which models can be
verified, and the confidence with which WLAs can be established.
1.4 APPROPRIATE LEVELS OP EFFORT IN PERFORMING WLAs
The level of effort that can be applied to the performance of a waste
load allocation covers a broad spectrum in terms of resources assigned to
1-4
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collect water quality data and the extent of analysis efforts to
calibrate and verify mathematical models. At one extreme, simple
preliminary analyses would rely on existing data and estimates of
additional information needed to perform the analysis. At the other
extreme, VLA studies could be quite thorough and comprehensive.
While an effort approaching either of these extremes could be
reasonable and appropriate under a particular set of circumstances, the
general case would entail an intermediate level of effort. The degree of
confidence desired for identifying the magnitude of water quality impacts
for treatment alternatives under consideration will typically require
that adequate site-specific data be secured and analyzed. On the other
hand, sufficiently reliable engineering analyses can usually be made to
support the necessary decisions without the necessity of establishing
absolute scientific truth.
The level of effort specified in this manual reflects this
intermediate level, which should be sufficient for developing WLAs in the
majority of cases. For situations requiring a lesser or greater level of
effort, justification should be provided to support such approaches. For
many situations involving interacting arrangements of multiple
dischargers and complex waste characteristics, the level of effort
requires an advanced approach and understanding beyond the scope of this
document.
1-5
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In addition, the complexity of the VLA analysis should also be a
function of the anticipated treataent costs; therefore, advanced
treatment generally requires more complex WLA analysis including
site-specific data collection. However, a level of effort, less than
that described in this manual, has been deemed appropriate by EPA for
small municipal sewage treatment plants where the discharge is less than
10 HGO and the stream _Q . low flow is less than the discharge. For
these special conditions, the Simplified Analytical Methodology for
Determining NPDBS Effluent Limitations for POTVs Discharging into
Low-Plow Streams (September 26, 1980) and its Addendum (June 25, 1982)
can be used.
1-6
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SECTION 2.0
BASIC PRINCIPLES FOR PERFORMING STREAM BOD/DO ULAs
2. 1 GENERAL
Waste Load Allocation (WLA) studies provide information to assist in
making effective decisions on levels of treatment required for a source or sources
of pollutant load. WLAs are water quality oriented and are directed at estab-
lishing a quantitative relationship between a particular waste load and its
impact on water quality. These relationships make it possible to compare
Incremental changes in concentration of specific constituents in the receiving
water system. With this capability, one is able to identify the maximum waste
load that can be discharged without violating a water quality standard, and to
thereby determine a cost-effective level of treatment. Cost-effectiveness, in
this sense, relates to the minimum level of treatment that will achieve a
specified water quality objective, and assumes that costs are proportional to
level of treatment. It should be recognized that further cost-optimization is
possible, since a number of treatment system designs exist that produce the
same level of treatment at different costs.
A preferred approach to developing cost-effective treatment systems is to
use the WLA procedures to define allowable loads. These loads are then
compared with existing or projected waste loads to determine the level of control
(% removal) required. Alternative treatment approaches are then examined and
priced to identify the nest effective approach.
2-1
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Revision No.
The key co making reliable decisions on control requirements necessary to
achieve specific water quality objectives lies in the reliability with which
waste loads can be related quantitatively to receiving water Impacts. These
relationships are quite sensitive to natural environmental conditions, such as
stream flow and temperature. Because of the variability of such environmental
•
factors, the data available will generally not correspond to all possible
conditions (for example, a future population and a critical low-flow condition)
Thus, an ability to predict what will happen under the conditions selected for
analysis is required.
An additional complication in determining cause-effect relationships and
projecting impacts results from the fact that Che rate at which various
reactions take place is as important as the total amount of waste load
generated. This is particularly important in BOD/00 reactions where the
resulting dissolved oxygen concentration is determined by competing reactions
of oxygen consumption from 300, ammonia and organic nitrogen decay, and
oxygen replenishment from reaeration.
Because of the array of variable elements (temperature, stream flow, load
level, reaction rates) that must be considered to establish rate coefficients
and examine alternate conditions, computerized mathematical models are gene-
rally employed to isake the necessary calculations. In the simplest situations
(such as employed in the illustrative example at the end of this section),
manual calculations can be performed. In most cases, however, the use of
computerized mathematical models will be much more convenient. Where the
system is relatively complex because of multiple waste Load sources, varying
stream geometry, flow changes due to tributary inflows, ecc., the use of coo-
puter nodeIs becomes a practical necessity.
2-2
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One of che disadvantages of using mathematical models is their tendency to
prevent the development of an understanding of the system and its responses by
most involved parties other than the model analyse. This is because all perti-
nent interactions are embodied "within the model," and often only the final
output is presented for review. However, mathematical models that are properly
utilized can contribute greatly to our understanding of the system. This role
is emphasized in the discussions in Section 3.0 of this chapter, which
addresses the issues in greater technical depth.
2.2 CONCEPTS IN RIVER BOD/DO ANALYSIS
To aid in the general understanding of the nature of river and stream sys-
tem dissolved oxygen responses to organic waste loads, important relationships
are discussed briefly here. An appreciation of the nature and significance of
the factors discussed should help an administrator develop a recognition of
the significance of certain aspects of the analysis and assist in understand-
ing and evaluating the technical output of a mathematical model analysis.
Transport
When a waste load is discharged into a flowing stream or river, it is
subjected to three characteristic factors that tend to modify the concentra-
tions resulting from the initial dilution. The factors that determine the
concentration at any particular time or location are:
« Adveetion - This represents the downstream transport of a discrete
element of the waste load by the stream flow.
• Reaction - The biodegradable materials in the waste (BOO) undergo
decay under the action of naturally occurring bacteria in the stream.
In the presence of dissolved oxygen, bacteria convert the BOD to
oxidized end products (e.g., CO?, NO^, and HjO), the result being that
the mass of organic matter (BOD; in a discrete element of the waste
load gradually diminishes.
2-3
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Revision No.
• Dispersion - Under Che influence of turbulence, eddy currents, and
similar nixing forces, a discrete element of the waste load tends
not to remain intact, but to mix with adjacent upstream and down-
stream elements. Dispersion is a predominant factor in tidal
waters. In rivers and streams its influence is usually relatively
small compared with advection and reaction; however, it can be
important in some circumstances. For example, when a slug load
results from a spill or accidental dump, dispersion effects can
have an important influence on resulting peak concentrations, par-
ticularly at longer distances from the point of discharge. Inter-
mittent discharges, such as storm runoff, are also influenced by
dispersion. However, for continuous discharges (e.g. from waste-
water treatment plants) and steady-state conditions, dispersion
effects are usually insignificant, for reasons discussed later in
the section.
These factors are shown schematically in Figure 2-1 to illustrate the
behavior of a waste load discharged into a stream. A discrete element of the
waste load is shown as it is transported downstream. The picture presented is
what would be observed if a single slug of waste load were injected and could
be followed downstream over a period of time. Conservative constituents in the
waste (those not subject to reaction and decay, such as chloride) would crack
as shown in the sketch for advection only, or advection and dispersion.
Reactive constituents, such as BOD, would behave as shown in the sketches that
include reaction.
While the sketches represent the behavior of a discrete pulse of waste
load, they can be extended to provide a representation of steady-state condi-
tions. Waste load allocations are often performed to examine lapaces under a
steady-state condition. An extended period of some critical low flow and
associated maximum temperature is often selected to represent the design condi-
tion. Such conditions normally provide a close enough approximation co a
true steady-state to make this type analysis entirely appropriate. For this
illustration under steady-state conditions, scream flow and environmencal
factors affecting reaction rate are constant, and the waste load discharges
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Revision Ho. 0
ADVECTION
AOVECTION AND REACTION
OLOAO
OT
OlSTANCE
TIME
0
OT
OlSTANCEi
I !
TIME
AOVECTION AND DISPERSION
AOVECTION. REACTION
AND DISPERSION
OUOAO
Q—-1
0-r
OISTANCE
TIME.
Tl
<
— »
1
ME
>LOAO
!
i
[
DISTANCE
fl
SL
Figure 2-1. Transport mechanisms for waste loads.
2-5
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continuously at a conscant Loading race. The load pulses shown in figure 2-1
as diffe'rent conditions of a single pulse in space and time can also be con-
sidered co represent che condition of separate elements of Che continuous load
being discharged. Under a true steady-state condition, each pulse will behave
exactly the same as preceding and following ones. Thus they can be taken (as
shown by Figure 2-2) to represent individual points on a continuous profile.
Typical concentration profiles are shown for a conservative substance and for
a reactive substance such as BOD.
Dispersion has been ignored in these plots. To illustrate why under
steady-state conditions, and for conservative constituents it is valid to
ignore it in single calculations or why it will not affect results when a
computer model which includes dispersion is used, consider Figure 2-3. This
presents a set of calculated profiles for a conservative substance (Reaction
- 0) under an assumed set of conditions (loading, advection and dispersion).
As described earlier, they can represent che concentration profile in the
hypothetical stream selected, at successive intervals of 0.1, 0.2, 0.3...
days after a load was introduced as a single pulse.
It also represents the group of concentration profiles that would exist
in che scream reach shown at any time if the load were introduced in a
sequence of pulses spaced 0.1 day apart. At any point along the scream length,
the total concentration at that point is made up of components of a number of
pulses. By graphically adding up the appropriate individual pulse components,
it will be seen that total concentration will be approxiaately the sane at
each point in the stream. As pulses are spaced closer together approaching a
continuous discharge, che approximation of total concentration at all points
will approach the single value represented by W/Q (i.e., mass discharge
2-7
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ADVECTION
Mi
OLOAO
t
TIME
DISTANCE
ADVECTION AND REACTION
Mi
o-r -*1
TIME
DISTANCE
STEADY-STATE CONDITION
OLOAO
o
H
I
I-
LU
U
O
K
c
UJ
U
— 1»
«•
CONSERVE
CONSTITUI
TP
•N1
TRAVEL TIME OR DISTANCE
"01-0*0
O
U
O
u
O
H
oc
U
o
U
— ^>
•
*_ r
_^ ,
H W
;
REACTIVE
CONSTITU
mm «
EN
—
I I I \
TRAVEL TIME OR DISTANCE
Figure 2-2. Steady-state responses.
2-9
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II (1)
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River
10
12
14
DISTANCE (miles)
Figure 2-3. Stream dispersion effects.
2-11
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race/scream flow rate), shown as the steady-state profile for a conservative
constituent in the lower left plot in Figure 2-2.
This is true for conservative constituents, and approximately for reactive
ones. For most advective streams, the impact of longitudinal dispersion on the
profile of a reactive substance can be ignored. There are exceptions, however,
and procedures for estimating the magnitude of dispersive forces and their
effect on water quality impacts are presented in section 3.1.
BOD Reactions
BOD (biochemical oxygen demand) is a measure of biodegradable material in
terms of the oxygen utilized in stabilizing it. Both carbonaceous organic
compounds (CBOD) and nitrogenous forms (NBOD), principally ammonia and organic
nitrogen, are subject to b.io-oxidation. For convenience, the oxygen equiva-
lent of. biodegradation over a 5-day period is usually measured (BODj) rather
than the full oxygen equivalency (Ultimate BOD, ULT BOD, BODU), which commonly
rer-.uires in excess of twenty or thirty days for completion. In some cases, such
as with pulp and paper mill effluents, the BODy test can require over one hundred
days. The rate at which biodegradable material (CBOD or NBOD) is removed in a
stream may be determined from an analysis of river BODs or BODU, since both are
suitable indicators of biodegradable material present. The analysis of BOD
(whether ultimate or 5-day) referred to in this manual utilizes a nitrification-
inhibited test, unless stated otherwise; thus ratios of ultimate oxygen demand
to 5-day oxygen demand are for carbonaceous demands only. Table 3-20 gives a
range of values appropriate for the CBODu/CBOD5 ratio.
2-13
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The actual shape of the BOO profile would be a result of the rate of
removal In a particular stream system, although this removal rate may
actually represent a composite of several effluent decay rates. BOD exertion,
like many biological reactions, is considered to follow "first-order" kinetics;
that is, the rate of removal at any specific time is proportional to the amount
remaining.
-kt
fraction remaining - e (2-1)
The time (t) is generally expressed in days; the reaction rate coefficient (k)
in terms of "per day." As discussed in a later section of the chapter, BOD
exertion rates in natural vater systems typically fall in the range 0.01 to 1.0
per day. Sample profiles for BOD decay at several rates within this range are
shown by Figure 2-4. The plots provide a sense of the time (and by inference)
space scales characteristic of BOD/DO reactions in a river or stream system. If
we consider the BOD to have exerted a significant impact when the amount remaining
falls below 10Z of that initially present, it is evident that periods of from
1 to 4 or more weeks are important. The spatial scale of significance would be
estimated from stream velocity to determine the distance traveled during that
time interval. The substantial difference in profiles indicates the importance
of an accurate assignment of this rate in a model study for waste load
allocation.
Atmospheric Reaeration
There are no standards for ambient BOD concentrations in streams. But our
main interest in BOD oxidation rates lies in their impact on dissolved oxygen levels
in the stream. An important aspect of stream dissolved oxygen resources is oxygen's
relatively low solubility limit in natural waters; saturation concentrations of
8 to 12 mg/1 for typical conditions. While salinity in coastal areas and altitude
in mountainous regions can influence solubility to an important degree, the effect
2-14
-------
100
Ul
Percent Remaining = e"kl
Figure 2-4. BOD decay: range of reaction rates.
n
o
o
-------
Table 2-1. Solubility of Oxygen in Water Exposed to
Water-Saturated Air (mg/i)**
Tcnipnum
C
0
1
I
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
IS
19
20
:i
^•r
23
24.
a
26
2T
3
29
30
31-
3T
33
34.
33.
36
37
ft
39
40
41
4.
43
44.
45
4
47
4
49
JO
mff/L
0
14.60
14.19
1341
13.44.
13.09
12.75
12.43
12,12
II J3
IIJ5
11.27
11.01
10.76
10.32
10.29
10.07
9.83
9.6.1
9.4)
9.26
9.07
8.90
8.72.
8J*.
8.40
U4
8.09
7.93
7.1!
7.67
7.34
r.4i
7.2S
7.16
7.03
6.97
6J2
6.71
6.61
6JI
4.41
6JI
62.
6.13
6.04.
5.9S
5.36
5.TS
5.70
5.62
5J4
5.000
13.72
I3J3
12.99-
12.65
12J3
12.02
11.72
11.43-
11.16
10.90
10.63
10.40
10.17
9.95
9.73
9.33
9.33
9.14
8.93
8.77
8.60
8.44
8.21.
8.127
7.9T
7.13
7.69-
7J5
7.42
7.30
7.17
r.os*
6^4
6.C.
6.71
6.61.
6J1
6.4ft
6J1
Ul
6.11
6.03
3.94.
5.85
5.7T
5.69
5.61
5.53
5.43
5.38
5.31
10.000
I2JO
12J6
1233
11.91
11.61
11J?
11.05*
10.7T
ioja
10.29-
10.03
9.83
9.61
9.41
9.21
9.01
8.83
8.63
8.48
8.32
8.16
8.00-
7.83.
r.TT
TJT
7.44
7J1
7. IS
7.06
6.9*
6.83
6i7T-
6.61
OO
6.40
fcj*
6J9
&.II
6.02.
5.93
5.M
5.7«
5.6*
5.60
5.J2
5.44.
5.3T
5.^
5.22
5.13
5.01
15.000
12.13
11 Jl
IIJI
I1J2
10.94-
10.67.
10.41
10.17
9.93
9.71
9.49
9.28
9.0S
8.89
8.71
8J3
8.36
8.19
8.03
7.8S
7.73
7J9
7.43
7J2'
7.19
7.06
6.94
6.83
6.71
6.60
6.49
6J9»
6.29
6.19
6.10
6.or
3.92
3.S3
5.74
5.66
5_58
5JO
5.4Z.
5.35
3.27
5.10
5.13
3.06
5.00
4.93
4.87
20.000
11.41
11.11
10.83
10J6
10JO
10.03
9^2
9J9
9J7
9.16
8.96
8.77
8JI
8.41
8J4
8.07
7.91
7.78
7.61
7.47
7J3
7.20
7.J7
6.93
6J3
6.71
6^0
6.49
6JS
6JS
4.11
6.08.
5.9»
5.99
5J1
J.TT
1M-
5J«
5.41
5.«0
5J3
5.25
5. IS
5.11
5.0*
4.91
4.91
4.83
4.7S
4.71
4.66
STANDARD
METHODS
** Aiaioui
S (m*U fnm thr
of 101J kPt. U
760-p
a the Miutaiiity it 101J kPt «od p n the prauune (mm) of suuraicd
tempenniic. For titvtoan kn Uua 1.000 n mod n
11 UJ
Revision No
rrtftr
S' -S
Dry «r is asaoMwd to
J. Amir. O*m. Sac. 33O62.)
below 25 C
try Whipp*. Md
-------
II (1)
it No. _
of water temperature on saturation concentrations is the factor of major practical
significance. Table 2-1 summarizes the effects of salinity and temperature.
Freshwater streams, which can experience temperatures between 0 and about 30°C,
will have dissolved oxygen saturation concentrations between about 15 and 7.5 mg/1,
respectively.
Figure 2-5 illustrates the effect of altitude on the saturation concentration of
dissolved oxygen. Saturation values for DO in rivers and streams at elevations of
4000 to 5000 feet will be about 1 to 1.5 mg/1 lower Chan in lowland streams at
similar temperatures.
A stream's ability to exhibit self-purification is related to the ability
of naturally occurring bacteria to decompose the organic waste materials,
utilizing the oxygen resources of the stream, coupled with the ability of the
stream to replenish these resources by natural reaeration processes. Transfer
of atmospheric oxygen to the water column occurs through diffusion and turbulence.
Of critical importance to the protection of water quality—one aspect which
is usually defined in terms of a minimum acceptable concentration for dissolved
oxygen—is the rate at which reaeracion takes place and the magnitude of this
rate in relation to the rate of oxygen consumption.
Most analytical methods are based on the concept of oxygen deficit (D),
defined as the difference in concentration between the saturation value (Cg)
and the actual DO concentration (C).
Like BOD, reaeration is considered to follow "first-order" kinetics,
such that the rate of reaeration at any time is proportional to the dissolved
oxygen deficit at that time. An equation of fraction of the initial deficit
remaining versus time would have the same form as that presented previously
for BOD decay, except that the reaction rate coefficient would be the reaeration
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II (1)
Revision No.
100
I 90
S
I
1 70
*
§
60
'Water
'Temperature
2 4 6 8 10
ELEVATION (1000 feet above mean sea level)
12
Figure 2-5. Effect of elevation on dissolved oxygen saturation concentration.
j_i Q
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II (1)
Revision No.
race. In an artificial environment, that is, starting at zero dissolved oxygen,
and with no significant influences other than reaeration, a plot of fraction of
the initial deficit remaining versus time would resemble the BOD plot shown
in Figure 2-4.
Reaeration rate coefficients, however, span a wider range of values and
have a greater magnitude (typically O.I to 5.0 or even greater) than BOD
exertion rates. While influenced by temperature, they are most strongly
correlated with depth and velocity of the stream. Figure 2-6 summarizes the
influence of velocity and depth on reaeration.rates. This figure associates
different reaeration formulas at the regimes of depth and velocity which were
used to develop the individual formulations. Alternatively, the reaeration
rate-can be measured for each reach. See also the part of Section 3.3 which
deals with the reaeration rate.
Dissolved Oxygen Profile
In natural waters, the oxygen consumed by bacteria in oxidizing the
biodegradable organic matter in a wastewater discharge (BOD) is taken from the
dissolved oxygen originally present in the water and from the additional
amounts transferred into the water by atmospheric reaeration. This is illus-
trated graphically in Figure 2-7.
The top figure is a calculated BOD profile in a river with a BOD removal
rate of 0.5 per day. At time t • 0, there is in this example, a concentration
of 10 mg/1 present, and after about 10 days all of the biochemical oxygen
demand (BOD)'has been exerted. Since the BOD test measures the amount of
organic matter present directly in terms of the amount of oxygen required for
its stabilization by biological action, the reduction in BOD concentration is
equivalent to dissolved oxygen consumption.
2-21
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II (1)
Revision No.
0.1 0.2 0.3 0.4 0.6 0.8 1 2
VELOCITY (ft/sec)
3456
Cued m EPA-600/3-78-105 "Rates. Connanii. and Kinetic Formulations
m Surface Water Qualify Modeling" (2) in modified form.
Figure 2-6. Reaeration rate coefficient (Ka)
related to depth and velocity.
2-23
-------
Q
i
12
10
8-
6-
2-
Oxygen Consumed
by Bacteria
BOO t
Remaining I
II (1)
Revision No. 0
Kf - 0.5/day
6 8 10 12 14 16 18 20
TIME (days)
12
Saturation
DO Profile with Reaeration
(Ka • 0.2/day)
Oxygen Consumed
by Bacteria
Oxygen Supplied
by Reaeration
00 Profile with No Reaeration
6 8 10 12 14 16 18 20
TIME (days)
Figure 2-7. Stream reaeration relationships.
2-25
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II (1)
Revision No.
The bottom figure shows two calculated dissolved oxygen profiles associ-
ated with the BOD removal profile in the upper plot. The profile indicated by
the solid line represents conditions that would occur in a river if oxygen
were not replenished by reaeration. In this case, the assumed initial dissolved
oxygen concentration of 12 mg/1 is ultimately reduced to 2 mg/1 to satisfy the
ultimate BOD of 10 mg/1. The dotted profile illustrates the net effect
of reaeration providing an additional source of oxygen.
The characteristic shape of the stream dissolved oxygen profile (the DO
sag curve) is the result of the interplay of the oxidation and reaeration
reaction rates. Each is represented by first-order kinetics: the rate of
oxygen consumed is proportional to the concentration of BOD remaining at any
time, and the rate of oxygen supplied is proportional to the magnitude of the
deficit at any time.
In- the early stages, oxidation greatly exceeds reaeration because BOD
concentrations are high and river dissolved oxygen concentrations are close to
saturation (i.e., deficits are small). Oxygen is used faster than it is re-
placed, and stream dissolved oxygen concentrations decrease. As time pro-
gresses, the consumption of oxygen decreases as the amount of BOD remaining is
reduced, and the supply of oxygen increases as stream concentrations drop and
deficits become greater. At some point the decreasing utilization and the
increasing supply are equal since oxygen is supplied at the same rate it is
utilized. This situation defines the "critical" point when the lowest concen-
tration of dissolved oxygen will be reached in the stream. Although the rate
of supply gradually diminishes after this, it always exceeds the utilization
rate, which continues to drop. River dissolved oxygen concentrations increase
thereafter, though at a decreasing rate as concentrations approach saturation.
Figure 2-8 presents a set of computations performed to illustrate the nature
of stream system responses under the influence of a range of reaction rate
-------
-K.-0.2
INCREASING REAERATION RATES
•K.-1.0
CASE 1
CASE 2
K>
SO
O
I
ffi
ff
o
h-
g
x
o
o
8
z
55
c
u
m
CASE 3
20
n>
<
Figure 2-8. Effect of rates on stream DO impacts.
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II (1)
98/12 Revision Mo.
values for BOD oxidation (Dd) and reaeration rates OO. For simplicity,
in these examples the initial deficit 'DQ) is assumed to be zero;
that is, the stream is at saturation concentration (assumed to be 10 mg/1)
after initial mixing of the waste load. It is also assumed that all BOD
removal occurs through oxidation* The initial BOD concentration (L_) is
assumed to be 10 mg/1; corresponding, for example, to a BOD load of 10,000
Ibs/day discharged into a stream with a flow of 185 cfs.
Figure 2-8 presents a range of stream DO responses that would result from
various combinations of high and low values for these rate coefficients. For
any given BOD waste load (and hence initial stream concentration), both the
magnitude of the maximum DO depression, and the location in the stream at which
it occurs will be determined by the particular combination of rate coefficients
which apply for that system. The race coefficients also affect the total length
of the river over which impact is detected.
Shallow, swift-flowing streams tend to have higher values of both Ka and
Kd, and tend to be represented by Case 4 in Figure 2-8. In contrast, deep,
slow-moving rivers tend to have lower values of K^ and Ka, as illustrated
by Case 1. In such streams the reaction is spread over a longer time, and
usually a correspondingly longer distance, and the DO sag becomes less pro-
nounced, making it more difficult to readily observe the effect of the waste
discharge from stream water quality data because of the potential to be masked
by reactions from other loads or sources occurring farther downstream (refer
also to the parts of Section 3.3 dealing with Ka and
The dissolved oxygen values plotted were obtained by subtracting the
calculated deficit concentration from the saturation concentration (in the
example assumed to be 10 mg/1, corresponding to a stream temperature of about
15°C). If the saturation value was 9 mg/1 (stream temperature about 20°C),
-------
II (1)
Revision Mo.
Chen each point on the dissolved oxygen curves would be 1 mg/1 lower. The
principal effect of temperature is on dissolved oxygen saturation values,
but temperature also affects reaction rates. Higher temperatures increase
both BOD exertion and reaeration rates. The effect on the BOD exertion
rate is more pronounced, so that higher stream temperatures produce a net
decrease in dissolved oxygen.
Variations in River Velocity. Depth, Area with Flow
Projections of water quality impacts for some future critical low-flow
condition are normally required in waste load allocation studies. The
predominant impact of reduced stream flow is usually to reduce dilution
provided for Che waste load. Thus initial concentrations of BOD (LQ) become
significantly higher. However, reduced scream flows also result in changes in
scream velocity and depth—factors which both strongly affect Che reaeration
race coefficient. Therefore, Che effect of stream flow changes on depth and
velocity must be determined.
In some cases stream cross-sectional measurements and time of passage
(cravel time) information will be available from studies performed by USGS
or state environmental agencies. In addition, data nay be available from
the Corps of Engineers in locations where projects have been designed.
Time of passage daca can be used to compute averages of velocity (U) and
depth (H). Each set of data will be related co a specific scream flow regime,
and different values can be expected for other flow regimes. In seeking infor-
mation on depth/velocity relationships in a scream reach, it is important co
distinguish between time of Cravel study daca and information that night be
derived from USGS flow gaging stations. Gaging stations are usually located
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II (1)
Revision No.
at places where the geometry favors the accurate determination of flow rate,
and as a result, depth and velocity ac such locations are not typical of
general stream conditions.
Leopold and Maddox (3) have suggested the following empirical relationship
between the pertinent physical stream factors and stream flow.
U . aQn (2-3)
H - bQB (2-4)
W - cO/ (2-5)
where:
a, b, c are constants for the stream in question
ra, n, f are exponents defining the basic relationships
Recognizing that stream flow is the product of cross-sectional area and
velocity (Q • A f U), and that cross-sectional area is the product of width and
depth (A • W + H), it can be shown that the sum of the exponents (m + n + f)
is 1. Using this and experience from a variety of streams, the value of the
exponents can be approximated as follows:
n - range (0.4 - 0.6); typical 0.5
m » range (0.3 - 0.5); typical 0.4
f - range (0 - 0.2); typical 0.1
Where the analyst has more than one set of data, a log-log plot of area (A),
depth (H) and_ velocity (U) against stream flow (Q) will permit extrapolation
to other flows of interest. The slope of such plots provides the local value
of the exponents. When data at only a single flow regime is available,
-------
velocity : U2/Uj "
depth : H2/Hj -
cross-sect. : A2/Aj •
area
travel : T2/Tj »
time
(Ql/Qi)0'5
(Q2/Q!)0'4
(Q2/Ql)°-5
(Q2/Ql)"°-5
II (1)
Revision No.
estimates for other flows of interest can be developed by the following ratios,
derived from the foregoing relationships:
(2-6)
(2-7)
(2-8)
(2-9)
It should be recognized that these relationships exist only in free-flowing
streams, and that the exponents may vary by 50% for any river. Impounded
reaches in rivers have exponents m and f«0, and n»l. Thus, acquiring
data to develop site-specific relationships of this type is normally ap-
propriate.
Because of the nature of the .relationships, reduced stream flows tend
to result in increased reaeration rates, principally due to the beneficial
effect of shallower depths. For example, a 50% reduction in stream flow may
increase Ka by about 30%. However, the net effect on stream 00 impacts is
negative because the improved reaeration is outweighted by increases in ini-
tial BOD concentations (L ), which would double for a 50% reduction in stream
flow.
2.3 DEVELOPMENT OF BOD/DO EQUATIONS FOR RIVERS
The principle upon which the equations in all water quality models are
based is a simple mass balance: mass leaving a river segment is equal to
mass entering the segment plus mass added directly to the segment, less any
mass lost within the segment. No matter how complicated the final water quality
equations appear, they are all a mathematical statement of this mass balance
principle. The applications of the mass balance principle to BOD and dissolved
2-34
-------
II (1)
Revision No.
oxygen in streams follows. For instructive purposes, more detail is given
in the development of the BOD equation.
BOD. To develop the basic BOD equation, consider a small segment of a
stream at any arbitrary location (x) along its length, as illustrated by
Figure 2-9. A BOD mass balance can be made on the small segment of length
AX as follows. At steady state, the following mass balance applies:
MASS OUT - MASS IN - LOSS
Q(L + dLax) QL K_LV
d£
QL + QdlAX QL KrLV (2-10)
dx
note that: U B Q/A; V • AAX
and therefore QaxdL = UAaxdL » UVdL
dx dx dx
divide 2-10 by volume -V:
KLV
QL + UVdL
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II (1)
Revision No.
Watte Uoad
Segment Volume. V " A-Ax
BOO Loo In Segment
' (KrU(V)
Segment
Cross-sectional
Area A
Flow out * Q
BOO out - L+
Q • River flow rate
L * BOO concentration entering tegment; i.e. concentration at location x
QL • BOO mass entering tegment
^=- • Raw of change of BOO(L) with distance (x); equivalent to rate of change
. f*
with time
-------
Revision No.
concentration of BOD immediately after dilution by the stream flow. This initial
concentration is designated LQ. Thus,
L • LQ at x - 0
substitr---''^%/?{>'fcr L and 0 for x in equation (2-12) yields
'' '/' -Krx
' ' L • ce ~~U~ • C e° - C(l)
o
Lo " C
substituting for C in equation (2-12)
-Krx
L LQ e ~~U~ (2-13)
Equation (2-13) provides the means for calculating the BOD concentration
(L) at any stream location (x) under the influence of advective transport (de-
fined by velocity, U) and the removal reaction (represented by rate coefficient,
Kr). It can be applied for-any substance that oxidizes or is removed at first-
order rates. Such reactions include oxidation of BOD and ammonia, or the die-off
of coliform bacteria.
The value of the initial BOD concentration (LQ) can be derived from a simple
mass balance. Where the upstream flow (qu) has a significant concentration
it is incorporated in the calculation.
5?
L0 -
• LQ o ^ River
Q - qu
2-39
-------
Revision No.
«^
In the above development, the rate of BOD removal was defined by the param-
eter (Kr). However, in a natural body of water, the rate of BCD removal does not
necessarily equal the rate at which oxygen is utilized to satisfy the BOO.
This parameter (the rate of BOD oxidation) is defined as (K^). The^ parameter
(Kj) defining oxidation of BOD can be equal to or less than the pan*** Ivw ' "*"""•-*.
\ '"«' i l
\ "*4- •
(K_) which defines total removal. The difference reflects removal Sy physical "
X
processes, settling for example.
Dissolved Oxygen. The dissolved oxygen equation is developed with the same
procedure used for the BOD equation. The basic elements for the DO equation
development are illustrated in Figure 2-10. A dissolved oxygen mass balance
can be made on the small segment of length &x, as follows. At steady state,
the following mass balance applies.
MASS IN - MASS OUT + SOURCES - SINKS - 0
QC - Q(C+dC ax) + Ka(Cg-C)V - KjLV - 0
dx
- qdC AX + Ka(Cs-C)V - KdLV = 0 (2-14)
dx
Note that U - Q/A; V - AAX
and therefore QdCax - (QAx)dC - (UAax)dC - UVdC
dx dx dx dx
Divide equation 2-14 by volume V
- UdC + Ka(Cs-C) KdL = 0 (2-15)
dx
For mathematical convenience, express equation (2-15) in teras of oxygen deficit
(D), where:
D • Cg - C or C » Cs - D
- Ud(Cc-D) + KaD - KdL = 0 (2-16)
dx
2-40
-------
Revision No,
Segment Volume
V • A-Ax
Oxygen added
to segment
by atmospheric
wee ration
Ka(C,-C)V
or
Ka(DtV
^•»»
t
Oxygen consumed
in segment
IKd L) (V)
Segment
Cross-sectional
Area
Q • River flow rate
C « Concentration of dissolved oxygen entering segment; i.e. concentration at location x
C, • Saturation concentration of dissolved oxygen
QC * Mass of oxygen entering segment
•^ " Rate of change of oxygen (C) with distance (x); equivalent to rate of change with time (t)
when converted by velocity (Ul
dC
dx
C + -
Ax - Change in oxygen concentration during time of passage through segment of length Ax
« Dissolved oxygen concentration leaving segment; i.e. at location (x +Ax).
This term multiplied by flow IQ) yield* mass of 07 leaving segment.
Ka • Atmospheric reaeration rate; reflects first-order reaction whereby fraction of oxygen
deficit satisfied - e-*«l - e~K»*/u
Ka D or Ka(Cs-C)' Change in dissolved oxygen concentration in segment;
this term, multiplied by segment volume (V) yields change
in dissolved oxygen mess in segment.
K(j • BOO oxidation rate: where oxidation accounts for all BOO removal, K
-------
Revision No. 0
This can also be written
-U[dC£
Ldx
+ KaD
(2-17)
When C is constant with respect to x;
dx
and the expression reduces to
+ U dD + K,D
KdL
(2-18)
Substitute for L the expression in equation 2-13 and rearrange terms
-Kr x/U
UdD + K.D
dx"
(2-19)
Integrating and solving equation (2-19) for the condition that D = DQ at x = 0,
yields:
X/U
D e
Ka-Kr
-K^x/U
- e
-Ka x/U
(2-20)
2-43
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II (1)
Revision No.
2.4 EXAMPLE WASTE LOAD ALLOCATION ANALYSIS
The following waste load allocation analysis is designed to provide an
example that is reasonably realistic but not so complex that it detracts
from the example's principal intent, which is to:
• demonstrate the major steps in a waste load allocation
analysis,
t show how the mathematical equations presented in previous
sections are applied, and
t present the relationship between water quality impacts and
the overall task of performing a waste load allocation.
Readers are cautioned that site-specific data must be used when performing
wasteload allocation analyses, and that values presented in this (or any
other) example, must not be substituted for site-specific data. When such data
is not available, applicable values should be developed by following, the pro-
cedures detailed in the text. Because the purpose of this example is to present
an overview of the steps required for a waste load allocation, emphasis is not
placed on providing details on data requirements and calibration-validation pro-
cedures. These technical aspects are discussed more thoroughly in other sections
of the manual.
Problem Seccing. In this example, a city of approximately 60,000 people
discharges its wastewater into a relatively small river with an average an-
nual flow of about 250 cfs. The city's wastewater is presently treated by a
trickling filter plant that provides about 85% BOD removal and has reached
its design capacity of 7.5 MGD. The population is projected to increase by
more than 50% 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 are proposed.
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ii v i;
Revision No.
The river, for thirty miles downstream of the treatment plant discharge,
is classified as Bl, which has a designated water use for fish and wildlife
propagation. The pertinent State water quality standards for this example
are a minimum dissolved oxygen level of 5.0 mg/1 and a maximum un-ionized aancnia
concentration of 0.02 mg/1. The river is used locally for fishing and is
bordered by several campgrounds and a state park. No water quality problems
are documented, and the limited water quality data do not show any standards
violations. A summary of the problem setting and treatment plant data is
presented in Figures 2-11 and 2-12.
River Characteristics. The river flow is gauged by the USGS immediately
upstream of the treatment plant discharge. The average monthly flows for a
thirty-year period are summarized in Figure 2-13. The 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 dissolved oxygen
standards must be met for a minimum seven-consecutive-day flow with a return
period of once met for a minimum seven-consecutive-flow with a return period of
once every 10 years (yP^)) • ^As discussed in Book VI, Design Conditions other
design flows may apply under summer conditions.) From a statistical analysis of
the flow records, the ;QiQ is determined to be 30 cfs and occurs between August
and October (for further discussion of critical conditions, refer to Tine Scale
in Section 3.1).
Critical conditions of dissolved oxygen and un-ionized ammonia concen-
tration in the river occur during the summer when the flow is low and the
river temperature is high. From eleven years of river temperature data collec-
ted as part of a limited river monitoring program by treatment plant person-
nel, the maximum average monthly river temperature is 27"C and occurs in August.
2-45
-------
Revision No.
Therefore, design critical river conditions for water quality impact analyses
are a river flow of 30 cfs and a river temperature of 27'C.
Note that for the example, both the critical low flow (jQjo) and Cne
maxin van average monthly temperature have been used in the projection, even
though historical records (summarized in Figure 2-13) 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 yQjQ could occur in August, the month of maximum average temp-
eratures. In areas where it can be shown that the jQjQ will occur in a
month with lower temperature, then the appropriate 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 7Qig and temperature condition
for each of the critical months (say June-October), determine which aonth is
most critical, and use that month in WLA calculations.
For this example, assume that three surveys have been conducted chat
measured stream cross-sectional area under different flow regimes. Cross-
sections were measured at 20 locations within the 30-mile long study area.
From cross-sectional area measurements, it is concluded chat Che river is
relatively uniform in the study area and, therefore, one average cross-
sectional area and length can characterize Che study area for each flow
condition. If the river cross-sectional area varied significantly with dis-
tance, the river would have been divided into smaller reaches, each of which
would have approximately uniform geometry for each prevailing flow condition.
Dye scudy techniques provide~an alternative means of accurately determining
average velocity for a given river section.
2-46
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II (1)
Revision No,
A. STUDY AREA
f STP
River Flow
Highway
USGS
Gage
5 10 15 20 25 30
RIVER MILEPOINT
B. POPULATION PROJECTIONS
•3
o
150-
100 H
50-
D
Q.
2
o
1900
Present (60)
Maximum (120)
Design (92)
..«••• Minimum (75)
1920 1940 I960 1980
YEAR
2000
2020
C. RIVER CLASSIFICATION AND USE
1. State Classtfication-BI
2. Designated Use-Fish and Wildlife Propogation
3. Water Quality Standards (partial)
a. DO Concentration-Greater than 5.0 mg/£
b. Un-ionized Ammonia-Less than 0.02 mg/C
4. Activities and Use
a. Active and Locally Popular Fishery
b. Several Campgrounds and State Park Have River
as an Attraction
5. Problems
No Documented Problems; Limited Water Quality
Data Do Not Show Violations
Figure 2-11. Problem setting.
2-47
-------
itevision NO.
XL TREATMENT FACILITIES
Present: Trickling Filter Plant Constructed in 1958
Plant Now at Design Capacity of 7.5 MGO
Effluent Does Not Meet NPDES Permit for
Secondary Treatment
Proposed: Activated Sludge System to Provide
Secondary Treatment
B. EFFLUENT CHARACTERISTICS
Flow
BODs
CBODu®
NH3-N®
NBOD
MGD
mg/8
Ib/day
mg/B
Ib/day
mg/8
Ib/day
mg/E
Ib/day
Present
7.5
40
2502
80
• 5004
15
938
68
4221
Design^
11.5
30
2877
60
5754
15
1439
68
6475
© Preliminary Basis-Standard Secondary Treatment
Note that the 30 mg/1 BOD. used in this example represents the secondary
treatment effluent standard, and that better performance may occur
during warm weather. Therefore, effluent characteristics used in
modeling real-life situations should reflect the performance expected
of the proposed facility during the critical period.
(D Long-term BOO Tests Indicate Ratio of C80DU/BOD5= 2.0
(D NBODBStoichiometric Oxygen Requirements for Oxidation
of Reduced Nitrogen Forms"4.57 x NH3-N
(effluent oxidizable organic nitrogen is negligible)
Figure 2-12. Treatment facilities and effluent characteristics.
2-49
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A. RIVER FLOW
auu
400-
w
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II (1)
Revision No.
The average river velocity during each of the cross-sectional area
survey periods was computed by applicaton of the continuity equation
VELOCITY - FLOW/AREA. The average flow for each survey period was obtained
from USGS records.
River cross-sectional area, depth and velocity generally form linear
correlations with flow when the data are plotted on log-log scales. Figure
2-13 presents these log-log plots for the example problem. Interpolations and
extrapolations of river geometry and velocity at specific flows can be made
directly from the log-log plots or 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 (inches/inch). As shown in Figure 2-13, these log-log rela-
tionships are summarized as follows:
AREA (ft2) - 19.5 Q (cfs)°'6 (2-21)
DEPTH (ft) =• 0.312 Q (cfs)0'5 (2-22)
VELOCITY (fps) - 0.0513 Q (cfs)0'4 (2-23)
Using the above equations, river area, depth and velocity can be computed
for any river flow. If river geometry data are available at only one flow
regime, the relationship presented in Section 2.2 (equations 2-3, 2-4, and
2-5) would be used to calculate river depth, area, and velocity at other flows.
Review of River Water Quality Data. Historical 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 samples
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Revision No.
are periodically collected at stations located at river milepoints 11 and
25. These data represent approximately one grab sample per month during the
summer over a five-year period. A review of these data does not reveal any
water quality problems with regard to dissolved oxygen and un-ionized ammonia.
Because there is no evidence of a water quality problem, only secondary
treatment at the expanded plant has been proposed. No additional funds for
Advanced Treatment (AT) have been proposed.
Considering the relatively good water quality, an appropriate level of
effort for a waste load allocation (WLA) study initially can be limited to
the analysis of a single river water quality data set collected during sum-
mer low flow conditions. Accordingly, a survey was conducted during two
days in August when the ri-ver flow averaged 100 cfs and the river water tem-
perature was 25°C. The results of this survey are presented in Figures 2-14
and 2-IS.
The dissolved oxygen data in Figure 2-14, both August 1979 data and
historical data, show river dissolved oxygen levels above the standard of
5.0 mg/1. The increase in river BODj and ammonia concentrations at milepoint
1.0 show the impact of the treatment plant discharge. The gradually decreasing
ammonia profile and increasing nicrite plus nitrate profile suggest -that nitri-
fication is occurring in che river. There is evidence that a natural denitri-
fication process, in which nitrate and some oxygen-demanding material are
removed from.the water, may occur in some streams. At this time che natural
process is neither fully understood nor proven to exist.
2-54
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Revision No. 0
UJ
x
O
o
UJ
>
0-
•
0
August 23-24. 1979
• * J.
T State Environmental
Department Data (1949-1979)
Saturation j
• . i
Standard A
Flew at Rt.64 Bridge-
Temperature' 25 *C
•
100 CFS
0 5
STP Diicharge at x • 0
10 15 20 25 30
MILEPOINT
8
| 6
54
9 2
10 15
MILEPOINT
I
20 25 30
—
01
Z
4
3-
2-
1-
' * * T
'I '
0 5 10 15
* I
i i
20 25
•
31
MILEPOINT
1-
0
10 15
MILEPOINT
20
25 30
Figure 2-14. Dissolved oxygen, BOD, and nitrogen data
(August 23-24,1979).
2-55
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Revision No.
z
o
3
4-
3-
2-
1-
0
August 23-24. 1979
• • •
•
•
•
10 15
MILEPOINT
20
25
30
a
"S
Si
-i <
3*
"1
z
a. 9
8.0-
7.5-
7.0-
6.5-
6n
n nc
U.U9
0.04-
0.03-
n n^
0.01-
.•••." • • •
6 5 10 15 20 25 3(
MILEPOINT
Average Temperature • 25 C
Average pH • 7 8
Standard
* * «
0 5 10 15 20 25 3(
MILEPOINT
Figure 2-15. Ammonia, pH, and un-ionized ammonia data.
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The concentration of un-ionized ammonia, the species of ammonia that is
toxic to biological life, is dependent on the total river ammonia concentration,
river pH, and river temperature. The higher the river pH and temperature, the
higher the percentage of total ammonia that is in the un-ionized form. Figure 2-15
presents the measured total river aomonia concentration. The un-ionized ammonia
concentration is determined from the relationship summarized in Figure 2-16,
which relates un-ionized ammonia to pK and temperature. For a river temperature
of 25°C and a pH of 7.2 (point A), un-ionized ammonia is 0.9 percent of the
total ammonia concentration. During the August 1979 survey, the river un-ionized
ammonia concentration was less than the standard of 0.02 mg/1.
Model Calibration Analysis. For this analysis, model calibration is the de-
termination of the coefficients (reaction rates) of the equations (some'of
which were previously'presented in sections 2.2 and 2.3) that describe the
spatial distribution of BOD, ammonia, nitrite plus nitrate,.and dissolved
oxygen. The equations for each of these constituents are summarized as fol-
lows:
BOD5
-K.
L5 - (L5)0 e IT * (2-24)
x
Ammonia (as N)
NH3 - (NH3)Q e ~U° X (2-25)
Nitrite plus Nitrate (as N) (2-26)
—K
(N02 + N03) - (N02 + N03)0 +((NH3) (1 - e"""
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0.02-
0.01
TEMPERATURE (°C)
Note: Redrawn from
William T. Willlnghcm
Ammonia Toxiclty
USEPA 908/3-76-001
Fab. 1976 (4)
Figure 2-16. Percentage of unionized ammonia in
ammonia-water solution at various pH
and temperature values.
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Dissolved Oxygen Deficit
-K
D -
KdLo
U
-e
U
V V
~S "^a
IF x T x
e u -e
-K.
U
(2-27)
In all these equations, the variables with the zero subscript are the con-
centrations at x - 0 (after integrating the upstream concentration and the
treatment plant load). U is river velocity and Kr, Kd, 1^, and Ka are the BOD
removal rate coefficient, BOD oxidation rate, nitrification rate, and
atmospheric reaeration rate coefficients, respectively. LQ and NQ represent
(respectively) the ultimate carbonaceous BOD and nitrogenous BOD at x a 0, and
DQ is the initial oxygen deficit at x • 0.
Note that the oxidation of ammonia (as expressed by equation 2-25) is
analogous to the oxidation of BOD. Whereas the oxidation of carbonaceous BOD
produces carbon dioxide as the end product, the end product of ammonia oxidation
is nitrite plus nitrate. Thus, the equation for nitrite plus nitrate states
that the nitrite plus nitrate in the river is equal to the concentration at
x • 0 plus the amount gained from ammonia oxidation. When all forms of nitrogen
are expressed as N, the terms in equation 2-26 are directly additive.
The coefficients in equations 2-24 through 2-27 are determined by the
following steps. The river velocity is calculated for the August 23-24,
1979 river flow using equation 2-23. The initial conditions (x - 0) are
determined from a mass balance with the upstream concentration and the plant
load. The BOD removal coefficient (Kf) is the value of Kr that provides the
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••M
best fie of the August 1979 BOD data with equation 2-24; for secondary
effluents Kd • Ky (no settling). The nitrification rate (KQ) is the value
of KQ that simultaneously yields the best fit of both the ammonia and
nitrite plus nitrate data with equations 2-25 and 2-26 respectively. The
atmospheric reaeration rate is determined in accordance with Figure 2-6 in
Section 2.2. In addition, long-term BOD tests have been performed and indi-
cate the ratio of ultimate to S-day carbonaceous BOD to be 2.0. A summary of these
calculations is shown in Table 2-2, and the calibration results are presented
in Figure 2-17.
In this example, the calculation of the dissolved oxygen profile agrees
with the measured data quite favorably and without any adjustments. Often
the calculated dissolved oxygen profile does not initially agree with the
data due to other sources and sinks of oxygen, such as nonpoint source loads,
algal photosynthesis and respiration, ana benthal oxygen demands. For the
sake of simplicity, these complications have been omitted. Section 3 includes
a discussion of procedures to use when these complications are present.
Model Projections. Having calibrated a model for BOD, DO, and nitrogen,
i.e., defining site-specific coefficients and accepting that some reserva-
tions on reliability exist because the model was not tested against an inde-
pendent data set, the model may be used to project water quality impacts
that might be expected under conditions of interest. Two specific cases
of interest are the water quality impacts of existing wastewater loads and
for future design wastewater loads for the minimum river flow (jQ^g) of 30
cfs. Dissolved oxygen, ammonia, and un-ionized ammonia profiles are presen-
ted for both cases in Figures 2-18 and 2-19. The model calculations for the
design load condition are shown in Table 2-3.
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TABLE 2-2. CALIBRATION ANALYSIS
STP
x, Hr River Temperature* 25° C
Q• 100CFS » // * » 0-111.6CFS
GAGE
UPSTREAM CONDITIONS PLANT EFFLUENT
BOD5 • 1.0 mp/B Q - 7.5 MGO (11.6 CFS)
NH3 (N) - 0.2 mg/B BODfi • 40 mgft (2502 Ib/day)
00 - 8.2 mg/B (SAT.) NH3 (N) • 15 mg/£ (938 Ib/day)
DO - 8.2 mg/B (SAT.)
A. DETERMINATION OF RIVER DEPTH AND VELOCITY
(from equations in Figure 2-13)
Depth • 0.312 Q0'5 • 0.312 (111.6)°'S " 3.3 ft.
Velocity - 0.0513 0° 4 - 0.0513 (111.6/3'4 - 0.34 ft./sec. (5.6 mi./day)
B. DETERMINATION OF REACTION RATES
1. Reaeration (from Figure 2-6 or K, - 13 U%/H% I
Ka - 13 (0.34)%/(3.3)% - 1.26/day. at 20* C
Ka at 25°C • 1.26 x 1.024s - 1.42/day
2. BOD Removal and Oxidation Rates (from fit of river BOD data)*
Kr-Kd-0.30/dayat20>C
Kr and Kd at 25°C - 0.30 x 1.047s • 0.38/day
3. Nitrification Rate (from fit of river ammonia and nitrate data)*
Kn-0.1S/dayat20°C
Kn at 25°C - 0.15 x 1.08s • 0.22/day
• Note: Since data were collected atriver temperature of 25°C,Kd and Kn determined
from data fit would be 0.38 and 032 respectively.' It is auumed hem that ana-
lyst has converted to rates at 20°C for convenience (a) In comparing with pub-
lished data, and (b) in subsequent calculations which may be at temperatures
other than 2«fC and 25°C.
C INITAL CONDITIONS (atx-0)
CoBeentraelaa, • (UpetXMB eancatcatlm tag/1) > Opttrua flev (cfe)}
» {Plant load (lb/d»y) » 0.185*1
{Dpitxua flow (cf>) 4 nut flev
(Wee: 0.1834 ia • coaverilfla factor having ualta of
B0»3(»-0) " 0-5)0 ' (1-0 « »00) * (»
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II (i)
Revision No. 0
U!
(3
X
O
o
12
10H
8
6
4
2-
r 0
Saturation = 8.2
Flow it Rt.64 Bridge • 100 CFS
Temperature • 2S°C
10 15
MILEPOINT
20
25
30
8
& K
1
10 15 20
MILEPOINT
25
30
— 4
57
I 3
- 2
0 «—r
10 15 20
MILEPOINT
25
30
1<
~ 3
I 2
Z ,
0 «—r
10 15 20
MILEPOINT
25
30
Figure 2-17. Model calibration analysis.
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I
s
12
10
8
6
uj 4'
I 2.
5 o
Saturation
Flow ai Rt.64 Bridge- 30 CFS
Temperature-27eC
10 15
MILEPOINT
20
25
30
1 10
1 8
I 6H
O
I
10 15
MILEPOINT
20
25
30
- 0.10
50.08
0.06
Temperature • 27*C
pH - 7.2
Unionized Ammonie • IX Ammonia Concentration
10 15
MILEPOINT
20
25
30
Figure 2-18. Projected dissolved oxygen, ammonia, and
un-ionized ammonia (present wastewater load).
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X
o
o
12
10
8
6-1
4
2
0
II (1)
Revision No.
Saturation
Flow at Ht. 64 Bridge-30 CFS
Tempera tu re • 27*C
10
15
20
25
MILEPOINT
I I0
I 8
I 6
< 4
O
<
10 15
MILEPOINT
20
25
30
1 0.10
0-08-
Temperature • 27 °C
pH - 7.2
Un-ionized Ammonia • 1% Ammonia Concentration
10 15 20 25
MILEPOINT
Figure 2-19. Projected dissolved oxygen, ammonia, and
un-ionized ammonia (design wastewater load).
30
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Revision No.
TABLE 2-3 PROJECTION ANALYSIS (design load)
STP
// HT Rivef Temperature • 27°C
Q • 30 CFS -=-» // * » Q = 47.8 CFS
GAGE
UPSTREAM CONDITIONS PLANT EFFLUENT
BOD5-1.0mg/« Q- 11.5 MGD (17.8 CFS)
NH3 (N) " 0.2 mg/8 BOD5 - 30 mg/6 (2877 Ib/davl
00 • 8.0 mg/e (SAT.) NH3
-------
Revision No,
The calculated profiles in Figure 2-18 shew than present wastewater
loads would result in dissolved oxygen and un-ionized ammonia wacer quality
standards violations over approximately ten miles of river, if design drought
flow conditions were so occur (;Q^Q flow sad A river ccspcrszurs cf 27'C).
The lowest daily average dissolved oxygen concentration is about 3.0 mg/1,
and the highest daily average un-ionized ammonia is twice the standard of 0.02
mg/1. At 27"C and with a pH of 7.2, un-ionized ammonia is 1 percent of the
total ammonia concentration (point B - Figure 2-16).
Calculated dissolved oxygen and un-ionized ammonia profiles for yQjg
flow conditions and the design wastewater load are presented in Figure 2-19.
For the design.load, the carbonaceous BOO is only slightly greater than the
present load, but the ammonia and nitrogenous BOD loads are about SOZ greater
than present loads (see Figure 2-12). The minimum dissolved oxygen is about
2.6 mg/1, and the maximum un-ionized' ammonia about 0.06 mg/1.
The projected dissolved oxygen and un-ionized ammonia profiles in Fig-
ures 2-18 and 2-19 indicate that whether or not the treatment plant expands
from 7.5 MCO to 11.5 MOD, sorae reduction of wastewater BOD (carbonaceous
and/or nitrogenous) and ammonia is required to meet water quality standards
during critical low flow conditions. One method of computing the required
reduction in wastewacer BOD and anoonia is Co calculace a series of dissolved
oxygen and un-ionized ammonia profiles and, through trial and error, arrive
at the proper combination of wastewacer load reductions chat meets water
quality standards. An alternative to the trial and error method for dis-
solved oxygen is to separately calculate the dissolved oxygen deficit due
to each BOD source (upstream BOD, plant carbonaceous BOD, plant nitrogenous
2-74
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BOD). This has been done for the design vastewater load case and is shown
in Figure 2-20. (See also section 3.5 for further discussion and examples.)
The top profile is the calculated dissolved oxygen distribution in
which the lowest daily average dissolved oxygen concentration of 2.6 mg/1
(maximum deficit of 5.4 mg/1) occurs at oilepoint 4. The next three profiles
are the components of the total dissolved oxygen deficit produced individually
by the oxidation of upstream BOD, treatment plant carbonaceous BOD, and treat-
ment plant nitrogenous BOD, respectively. On each deficit profile, the deficit
produced at the critical point in the river, milepoint A, is indicated. Note
that the deficits of the component parts at milepoint 4 add up to the total
deficit of 5.A mg/1. Inspection of equation 2-27 shows that the carbonaceous
and nitrogenous deficits are additive. The upstream BOD may be considered
as a fraction of the total carbonaceous BOD in the river and thus separable
from the plant carbonaceous BOD.
Knowing the relative contribution of each BOD source to the total def-
icit, it is an easy task to select combinations of wastewater BOD reductions
that will achieve water quality standards. For the sake of simplicity, the
use of a safety factor in the allocation procedure is omitted in this example.
However, the first example in Section 3.5 demonstrates the application of a
margin of safety. At 27°C, dissolved oxygen saturation is 8.0 mg/1; therefore,
for a dissolved oxygen standard of 5.0 mg/1, the allowable maximum deficit is
3.0 mg/1. Assuming that the upstream BOD deficit of 0.2 mg/1 is uncontrollable,
2.8 mg/1 of deficit would be available for the total of carbonaceous and nitro-
genous plant BOD oxidation. Considering the un-ionized ammonia standard and the
economics of nitrification versus advanced carbonaceous BOD removal suggests that
2-75
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Flown Ri.64 Bridge-30 CFS
Temperature • 27*C
MILEPOINT
O
u.
ui
O
O
Q
B
6-
4-
2-
n
Upstream BOO
BOOg-I.Omg/8
0.2
O
8
I
a
s
8
6
4-
2-
10 15
MILEPOINT
20.
25
Treatment Plant Carbonaceous BOO
Plant Q - 11 S MOD
EFF BOO.-30mg/C
10 15
MILEPOINT
20
25
30
8
6-
4-
2-
Treatment Plant Nitrogenous BOO
Plant Q • 11 s MGO
- N - 15 mg/«
10 15
MILEPOINT
20
25
30
Figure 2-20. Dissolved oxygen component unit responses.
2-77
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Revision No.
providing nitrification facilities for the expanded treatment plant is a cost-
effective step towards achieving water quality standards. Assuming that nitrifi-
cation removes 90% of the ammonia (i.e., nitrogenous BOD) the un-ionized ammonia
standard would be met and the nitrogenous BOD deficit would be reduced to
0.2 mg/1, yielding a total deficit of 3.4 mg/1 (DO of 4.6 mg/1) at milepoint 4.
Although calculations show that nitrification and standard secondary
treatment for the design plant flow of 11.5 MGD will not meet dissolved
oxygen standards, the waste load allocation analysis should not be carried
any further with currently available information. Planning for a summer nitri-
fication facility can proceed since the process provides for a significant
reduction in ultimate BOD at a relatively low cost compared to other types of
AT. However, before the model is used to calculate the additional carbonaceous
BOD removal beyond secondary treatment that may be required, some additional
steps should be taken. First, the model should be calibrated and validated agai'nst
one or two more data sets to check the model coefficients under different flow
regimes, especially lower flows than the first survey, if possible. A sensitivity
analysis should be performed to relate the cost of required wastewater treatment to
changes in population estimates. For example, if the population in the year
2000 is 75,000 people (projected minimum), will additional carbonaceous BOD
treatment be required? A sensitivity analysis of the effect of different
reserve policies on required treatment should also be performed. For example,
what is the increase in wastewater treatment costs if the dissolved oxygen
reserved for future development is set at 0.5 mg/1 versus 0.25 mg/1? It is
clear from these questions that a final waste load allocation should be the
result of more than a model projection. Such a decision takes many factors
into consideration, one of which is the impact of a design wastewater load on
water quality.
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SECTION 3.0
MODELS: SELECTION AND USE
3.1 SELECTING A MODEL
Introduction
Three basic components collectively constitute a site-specific dissolved
oxygen water quality model. These are:
• The types of reactions which are included (i.e., the phenomena
considered) and the equations used to represent these reactions.
Examples of phenomena that may be included in a water quality model
include: oxidation of BOD in the water column, oxygen demand from
benthal deposits, oxidation of ammonia, atmospheric reaeration,
diurnal changes in oxygen production and depletion (P-R) due to
algal activity, provision for input of distributed loads, etc.
• The calculation framework. This may range from a single equation
providing an analytical solution for the DO deficit to the array
of equations, calculation instructions and input/output processes
that collectively comprise the software of a generalized receiving
water quality model (DOSAG, QUAL II, etc.).
• The site-specific values assigned to the rate coefficients employed
in the calculations, stream geometry, the location of input loads,
etc., i.e., the details that convert the generalized model framework
to a model of a specific receiving water system.
All three components are necessary to define a site-specific water quality
model.
The preferred approach is to use the simplest model that can be applied
in a particular case. Ideally, the model should include only those phenomena
that are operative and important in the river or stream being modeled. The
most appropriate procedure for selecting a model is to first define the phe-
nomena that are important for the particular site-specific analysis to be per-
3-1
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Revision Xo.
formed. Activities that help to define phenomena that should be incorporated
include the following: (a) reviews of existing data on waste loads, stream
flows, and water quality; (b) preliminary mass balance calculations using simple
models or equations that provide analytical solutions for various load sources
(combined sewer overflows, nonpoint sources, sediment) and reaction phenomena
(nitrification, algal photosynthesis and respiration, etc.).
It is also desirable to attempt to anticipate the technical issues
with respect to control actions (level of treatment, alternate discharge
locations, etc.) and determine whether this will Influence the types of
reactions that will be important. From the foregoing, the analyst will generally
be able to establish the phenomena that should be included in the selected model
and the time and space scale of the analysis which is most appropriate.
Under ideal circumstances, one would select a formal -model or analysis
approach that included all the phenomena determined Co be important in the study
area, and which excluded those reactions chat are insiginificant in the case
in question. Qhile this guidance should be followed as much as possible, in
practice a calculation framework or model often will be selected because it is
available or familiar to the analyst.
In such cases, two criteria are important to apply. First, the model
selected must be capable of handling all of the important sice-specific
phenomena considering the tine and space scale of the analysis and using
the equations and formulations specified. Secondly, provision should be
made, where possible, to eliminate from the calculation framework the effect of
3-2
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TT (1)
Revision No.
any phenomenon chat are insignificant in the site-specific analysis. In some
cases inclusion of phenomena judged to be unimportant on a site-specific basis
can increase the level of uncertainty of the analysis and thus directly affect
decisions. In these situations, additional data collection, sensitivity runs,
and other aspects of the overall waste load allocation program must be consid-
ered, in order that phenomena contained in the calculations are adequately
addressed.
Additional evaluation criteria for model selection include completeness of
computer program documentation, costs for manpower, and computer time.
The third component of the water quality model is the most significant in
the context of decision making. The activities of model calibration and veri-
fication, which are discussed in Section 3.3., are key elements that essentially
consist of comparisons of observed water quality and calculated responses under
a range of conditions that are diverse enough to test the level of understand-
ing of individual phenomenon and define site-specific model coefficients and
parameters. In this regard, data collection programs form an essential element
of the analysis.
The overall process of modeling is discussed in the context of the three
components of a water quality model. First, some general and specific consid-
erations that should be addressed in selecting a model are discussed. Next,
available models and their important features are described, and finally an
approach and considerations for calibrating and verifying a model are presented.
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Important Considerations in Selecting a Model
Selecting the Number of Dimensions* Most waste load allocation projects
that address dissolved oxygen in streams and rivers employ one-dimensional
steady-state calculations. Both theory and experience demonstrate that
dissolved oxygen gradients in streams and rivers are largest along the
longitudinal axis of the system with relatively minor variations in the
lateral and vertical dimensions. This results from the time scale for the
dissolved oxygen response. Generally, near-field analysis is not important
and only far-field problems need to be examined (i.e., mixing zone calcula-
tions are usually ignored). The number and definition of spatial dimensions
that oust be considered can usually be determined by an examination of his-
torical water quality data. Field data to be examined should include dissolved
oxygen and other variables such as temperature, conductivity, BOD, NH-j, etc.
Certain river situations may require a framework that encompasses a
two-dimensional analysis. These situations are generally associated with deep
rivers or run of the river impoundments when vertical or lateral gradients
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 analysis.
Water quality observations and the problem setting will determine the
number of spatial dimensions required for a site-specific analysis.
In particular* if a second dimension is considered, the investigator should
provide justification in terms of the specific decision-making elements
with regard to controls and treatment that require the information resulting
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from inclusion of a second dimension in the analysis. This requirement is
necessary since the additional dimension in the analysis for streams or rivers
will usually require substantially more data collection efforts and generally
will result in generation of "free" modeling parameters whose site-specific
values cannot be determined reliably. Thus, the additional dimension can tend
to weaken the analysis and may adversely affect the ability to make decisions.
Three-dimensional analysis of stream and river systems is considered to
be more of a research and development activity and generally does not appear
appropriate for inclusion in the context of projects addressing WLA decisions.
Loads, Sources, and Sinks. Loads, sources and sinks that can influence the
dissolved oxygen distribution in streams and rivers are:
• point source discharges from waste treatment plants
• urban runoff from combined and separate sewer systems
• nonpoint sources
• sediment oxygen demand
• oxygen production and utilization by phytoplankton or aquatic weeds
• upstream sources of oxygen demand or dissolved oxygen deficit
These will be collectively defined as sources in this subsection.
All sources that are explicitly included in the analysis require direct
measurements on appropriate time and space scales to define the magnitude of
the individual source by contaminant* In addition, as discussed in Section
3.2, receiving-water quality data is required under diverse conditions in order
to evaluate the effect of individual sources. Therefore, it is suggested that
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Time Scale. The tine scale selected for the analysis should be « ;.:r.c:ion
of both the observed water quality and the dissolved oxygen standards or cri-
teria for the system being analyzed. Dissolved oxygen analysis in srra^.as and
rivers usually can be performed on a seasonal time scale, employing sicher
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-
temperature summer period. However, winter periods may also be critical when
ice cover is important. In some situations, the fall may be significant if
upstream sources of organic carbon from phytoplankton and/or aquatic weeds
result in large depressions in dissolved oxygen levels. Also, spring floods
that pick up large amounts of organic debris from adjacent floodplains may
result in severe DO depletion.
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
increasing complexity:
• steady-state
• quasi steady-state
- constant loads—constant stream flow—diurnal 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 analysis
In a steady-state analysis, a spatial profile of concentration is
calculated, such as would result at equilibrium under a constant set of
input conditions (stream flows, waste loads, temperature, etc.). To the extent
that actual variations in waste load, stream flow, etc. can be realistically
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approximated by constant conditions for the period covered by the analysis,
the calculated receiving water concentration profile will approximate an
average of the actual concentrations during that period.
A fully time-variable analysis performs successive calculations at rela-
tively short time steps and accepts variable input values for parameters
such as stream flow, waste load, and temperature. Its output is 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.
"Continuous" versions of time-variable models extend 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 concentra-
tions will not reflect short-term variations but should track the longer-term
fluctuations.
Quasi steady-state analyses usually have one time-variable element
incorporated in what remains as basically a steady-state calculation.
Table 3-1 presents a series of steps, related questions, and output that
can be employed to determine the appropriate tine interval for the analysis.
The decision on the time interval to be used in the analysis is critical to
overall project success and should be documented in terms of the impact on
water quality control decisions. Complex analysis frameworks associated with
time-variable, (dynamic) models will require more data collection and increased
study costs for model runs, input and output analysis, and sensitivity runs.
The degree of uncertainty in the analysis can also increase due to "free"
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Table 3-1. STEPS FOR DOCUMENTING INCLUSION OF TIME-VARIABLE OR QUASI STEADY-
STATE WATER QUALITY ANALYSIS
Review existing
water quality data
Review flow data
Review rainfall
data.
Typical Questions
When are standards
violations observed?
Are violations associated
with diurnal fluctuations,
rainfall, flow variation,
or season of the year?
Output
Documentation
Plots of data
Regression analysis
or plots
Define probable
or possible causes
of observed quality
problems. (Use
experience supple-
mented 'by calcula-
tions.)
Do point source waste loads
control water quality?
What loading types control
quality (event, continuous,
etc.)?
How important are factors
other than loads?
Tabulate loads and
probable range of
effects defined by
calculations.
Direct statement
showing how control
is possible
Is water quality controll-
able?
List typical control
options.
For control options,
list information
needed from model-
ing study to make
decisions.
What planning or treatment
decisions are affected by
output from non-steady state
analysis?
Tabulate decisions
and information that
requires non-steady
state analysis
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model parameters. In general, Che least complicated analysis that will provide
the information required to make water quality control decisions should be
selected. As more complex analyses are built into a study, the requirements
for documentation and justification in terms of decisions will increase.
Several levels of analysis are available for situations that are influ-
enced by oxygen production and utilization from phytoplankton and/or aquatic
weeds. Steady-state analysis may be employed using average oxygen production
and respiration (P-R) terns. Quasi steady-state analyses are also available
for streams and rivers (5) that use steady-state calculations supplemented by
time-variable calculations of diurnal oxygen variations. Complex kinetic sys-
tems are also available that relate oxygen levels to phytoplankton populations
(chlorophyll) that in turn are controlled by light, nutrients, zooplankton,
etc. These latter frameworks are time variable and require extensive data for
model calibration and verification. Combinations of modeling frameworks and
data collection programs can provide a spectrum of analyis to fit most problem
settings. In most situations, it is suggested that a steady-state or quasi
steady-state analysis be considered as a reasonable framework. Because of the
complexity of the technical and management issues involved in using time vari-
able models, they should be used only in cases where sufficient data exists and
where this level of understanding of water quality problems is essential to
determining treatment needs.
The issue of the time interval of the analysis is in part controlled by
the sources considered in category I. Point sources, sediment oxygen demand,
and upstream conditions usually can be adequately represented by steady-state
modeling, which employs time-averaged values for the loads from these sources.
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each project create two categories for sources. Category I should consist of
major sources controlling water quality under existing and projected condi-
tions, and all sources that are to be controlled. Sources in this category
will require thorough data collection and modeling analysis to define both
the magnitude and effect of the individual sources. Category II will contain
background sources; small to moderate data collection and analysis would be
required for sources in this category. The basic distinction is that sources
in the second category should not influence decisions on load allocations;
i.e., even if the magnitude and effect of individual sources in category II
were incorrectly identified, the basic decisions resulting from the project
would not change. This requires that category II sources be a small portion
of the total. Historical data on sources can be combined with information in
the Literature and calculations to place sources in the appropriate category.
The primary contaminants of concern associated with sources are organic
carbon compounds that produce carbonaceous biochemical oxygen demands (CBOO) and
the reduced forms of nitrogen that produce nitrogenous biochemical oxygen demands
(NBOD). For each source type, it is necessary to define the magnitude of the ul-
timate oxygen demand for both classes of contaminants. Long-term BOD data are
required. The carbonaceous demand alone is measured by using a nitrification-
inhibited test. In addition, experimental information may be required to distin-
guish between the forms of organic nitrogen that can hydrolize to ammonia and the
nitrogen that is, in a sense, refractory and is not transformed to ammonia. This
distinction can be important if nitrification is of concern. The effluents from
treatment plants without nitrification can contain potentially significant concen-
trations of organic nitrogen. The degree of nitrification required can be in-
fluenced by the organic nitrogen level in the effluent that can be transformed
to ammonia and subsequently oxidized in the stream or river.
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The same type of analysis can be appropriate for some nonpoint sources, such as
those associated with groundvater inflow, leaching from bottom deposits, and
drainage not directly related to transient events such as storn 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 quasi steady-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. However, for most of these situations, a
time-variable analysis has been necessary. While expensive, the time-variable
analysis can be applied satisfactorily to analyze observed data provided suf-
ficient data exists or can be obtained. Projections present a special set of
problems in terms of identifying the storms or storm sequences to be used Co
develop the waste load allocation. Furthermore, the event-related dissolved
oxygen problem can be influenced strongly by the hydrograph after the event
and the geomorphology of the downstream segments of the water body. In addi-
tion, the basic technical, economic, and environmental issues associated with
wet weather standards for dissolved oxygen have not yet been addressed fully.
As a result of these complexities, and in order to permit timely action on
decisions that must be made regarding control of point source loads, EPA has
adopted the following basic strategy for developing waste load allocacions for
point sources. As a first approach for the general case, WLA calculations will
ignore storm-induced loads and the issue of wet weather standards and will
concentrate "on point source impacts under critical low-flow conditions. While
it is recognized that wet weather effects and the possible need for control of
Storm runoff loads need to be considered (at least in some locations, possibly
in most) such considerations can be deferred until the results of current EPA
investigations of these issues can be incorporated into policy guidance to be
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This approach is most appropriate for the issue of BOD/DO effects in
rivers and streams. In advective river systems (unlike estuaries) the residual
effects of storm loads on BOD/DO can be ignored. Point source impacts under
critical flow conditions, therefore, represent a design situation that oust
be addressed independently of any separate consideration that may ulitmately
prove appropriate to apply to storm loads.
Spatial Extent. The spatial extent of the modeling analysis should be well
into the zone of dissolved oxygen recovery. This spatial coverage should
be considered for several reasons.
• Reaeration is a dominant factor in this region, and analysis can
provide information on the value of the reaeration coefficient.
• In many situations, a key issue in decision making concerns the
presence of nitrification and the rate at which it may occur fol-
lowing upgrading of treatment. Observations of nitrification in
the zone of dissolved oxygen recovery could be valuable in defining
bounds for nitrification rates to be considered for making projec-
tions under future conditions.
• Indications of the growth of phytoplankton and aquatic weeds, after
treatment has been upgraded, often can be obtained by examining
the dissolved oxygen recovery zone.
The information obtained from the analysis of the zone of dissolved
oxygen recovery will depend, to a large extent, on the uniformity of system
geomorphology.
Transport Systems. Dispersion is present, to some extent, in all bodies
of water. However, water quality profiles, such as dissolved oxygen concen-
trations, may not be influenced when the dispersive mixing is small and/or the
advective transport is large. In these situations, which will characterize
most WLA projects on streams and rivers, decisions will not be influenced by
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inclusion of dispersion in the analysis. This will reduce che complexity of
the calculations and data collection programs. The importance of dispersion
is site-specific, and can be estimated by the following procedure:
STEP 1 - Calculate the approximate Longitudinal Dispersion Coefficient
(Ref 6).
E • o.on
(3-1)
where:
U
W
H
U*
Longitudinal Dispersion Coefficient (ft/sec)
Average Stream Velocity (ft/sec)
Stream Width (ft)
Scream Depth (ft)
Shear Velocity (ft/sec)
The Shear Velocity (U*) for many -streams is approximately one tenth of
.the average stream velocity, and can be estimated by:
where:
8
S
Gravitation Constant (32.2 ft/sec2)
Stream Slope (ft/ft)
STEP 2 - Calculate the "estuary number (n)" as defined by O'Connor (7).
The longitudinal dispersion coefficient can be employed with stream
velocity and reaction race (Kd), co develop this dimensionless number.
11.
2
U
(3-2)
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The O'Connor Number (n), and Che ratio (0) of Che reaeracion race
coefficient (Kfl) to deoxygenacion rate coefficient (K^) . . .
9 - Ka/Kd (3-3)
can be used with Figure 3-0, Co provide a basis for judging the signifi-
cance of dispersion in calculations of dissolved oxygen concentration.
Inspection of this figure 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,
D ) by less than 102. For WLA studies, dispersion can be ignored in such
cases. Where reaeration is high relative to deoxygenation rates (high
values of 0), the lack of sensitivity to dispersion extends to higher
values of n, as indicated by the essentially horizontal lines for the
higher values of 0.
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 several simplifying assumptions. The foregoing
approach must therefore be considered to be an approximation. It should,
however, be adequate for use in most WLA studies.
There may be situations where dispersion is considered significant by the
investigator even though the foregoing analysis suggests otherwise. Examples
could include swamps, tidal rivers, or upstream segments of impoundments.
Detailed documentation defining the magnitude of dispersion and relating these
phenomena to waste load allocation decisions should be developed early in the
study to support inclusion of dispersion in the modeling studies. If the
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RIVERS
0.01
STREAMS
Figure 3-0. Dissolved oxygen response as a function of Kd E/U .
too.
wt
o
o
•
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computational framework employed in the analysis introduces dispersion due to
spatial segmentation or numerical approximations (called numerical dispersion
or numerical mixing), the study should contain an evaluation of the influence
of dispersion on calculations of water quality. Finally, the influence of
dispersion on decisions and waste load allocations 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, and, therefore, consid-
eration should be given to the potential importance of groundwater inflow and
outflow. In addition, flow from significant tributaries and waste sources must
be included in the model. Each of the sources of flow included in the model
must also be supported by data.on the concentrations of significant constit-
uents, such as dissolved oxygen, BOD, NH^, etc.
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 qual-
ity data are collected and at the critical flow regimes used for projections.
Variables to be Considered and Formulations. Several combinations of var-
iables can be significant in dissolved oxygen analysis in streams and rivers.
The most common are shown in Figure 3-1. Each of the four combinations of
variables has been employed to develop waste load allocations. The selection
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 by
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Carbonaceous BOO
(CBOO)
-W TR
Temperature
Dissolved Oxygen
Deficit - CBOD
Dissolved Oxygen
Saturation (C$)
Dissolved Oxygon
Concentration
II.
Carbonaceous BOD
(CBOD)
Organic Nitrogen
Temperature
Dissolved Oxygen Deficit
CBOD
Dissolved Oxygen
Saturation (Cs)
NOD Dissolved
Oxygen Deficit
'
'
Temperature
t
Dissolved Oxygen
Concentration
TR - Transformation Rate
Figure 3-1. Combinations of variables which can be considered
for 00 analysis in streams and rivers (continued).
30
ro
u»
o
-------
III.
^aruonaceous HUL
I
y
i
I
P. a
\ ,
\ '
LWIICII 1.DUU
DO Deficit due to
Phytoplankton
r-
. Dissolved Oxygen 1
Concentration |
IV.
Carbonaceous BOD
Nutrients
Chlorophyll
Organic Nitrogen
Temperature
P-R
Deficit CBOD
Cs
DO Deficit due to
Phytoplankton
Dissolved Oxygen
Concentration
TR • Transformation Rate
90
n>
F igure 3-1. (concluded).
o —»
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calculations and relating the selected analysis framework to the decisions
to be made at the conclusion of the project.
It should be pointed out that the illustrated reaction sequences in combi-
nations II and IV show sequential oxidation of NH^ to N02» w^ictl oxidizes to
NO3. In many situations the NO2 concentration level observed and calculated
is very low or tends to be uniform. Under these circumstances, the analysis
could consider a single reaction sequence for ammonia oxidation, converting
NH-j directly to NO-j. It should also be noted that where algal problems are
severe, NHj may be taken up directly by algae.
It will be important in many situations to distinguish between organic
nitrogen and ammonia concentrations, rather than define the nitrogenous oxygen
demand (NOD or NBOD) load on the basis of TKN concentrations, which are com-
posed- of both these forms• Organic nitrogen must first hydrolyze to ammonia
before its oxygen demand will be exerted. Time and space lags in the resul-
tant dissolved oxygen profile, due to this sequential reaction, may be
significant. If the two species of nitrogen are combined in the calibration
and verification effort, the apparent oxidation rate (KQ) will be lower than
the actual first-order oxidation rate of ammonia. The ratio of TKN to NHj-N
affects the value of the overall oxidation rate. Where this ratio changes after
treataent, the aodeler is faced with additional uncertainty.
Several levels of analysis can be used for considering the influence of
phytoplankton. These are summarized in Table 3-2. Level A, which uses measured
values of P-R and diurnal 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 considered. Level C analysis
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- • \ -
?.«?•• ; 1 0 "
TABLE 3-2. METHODS OF ANALYSIS FOR PHYTOPLANKTON AND AQUATIC WIZDS
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 che
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 Verification: A time-variable, nonlinear modeling framework is
required.
increases the program costs for data and modeling by several orders and should
be used when the problem is dominated by phytoplankton oxygen production and
utilization and environmental or control costs are significant.
When aquatic weeds are the cause of diurnal fluctuations, the only analy-
tical framework available is level A in Table 3-2. Other quantitative aquatic
weed analysis frameworks are essentially in the research stage and do not
appear to be appropriate for use in a decision-oriented project.
First-order rates employing sequential reactions generally have proven
adequate for waste load allocation analysis. Most of the available comput-
erized solution techniques employ these formulations. Therefore, the four
combinations of variables defined in Figure 3-2, which are most frequently
employed in dissolved oxygen analysis, can be characterized by first-order
transformation functions (TR1, TR2, TR3, TR4, etc.). Ranges of the specific
first-order rates for the various reactions are discussed in Section 3.3 as
are the procedures for defining site-specific reaction rates for various levels
of treatment. There are circumstances, particularly in systems with low
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Dissolved Oxygen Analysis
ui
I
N>
DO Deficit CBOD
DO Saturation
NOD Deficit
Temperature
PR Deficit
Dissolved Oxygen
Concentration
Figure 3-2. Feedback reaction sequence.
SO
(D
O •
3 »
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dissolved oxygen, where nonlinear kinetic formulations can be considered. The
nonlinear formulation usually employed is Michaelis-type kinetics in which the
overall rate of reaction reduces 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 nitrification has been shown (8, 9)
to be controlled by dissolved oxygen levels at and below 2 mg/1. One method
of approximating the nonlinear nitrification reactions has been to use lower
values for first-order reaction rates in areas of low dissolved oxygen concen-
trations. Low dissolved oxygen concentrations can also reduce the rate of BOD
oxidation, sediment oxygen utilization, and increase the release of contaminants
from the benthos. These latter reactions are influenced only at very low dissolved
oxygen levels such as 0.1 mg/1 or lower. In bodies of water with large deten-
tion times, feedback reaction sequences have occasionally been employed (10).
For example, the death and decomposition 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. The
usual reaction sequence employed for dissolved oxygen investigation is shown
in Figure 3-2. This feedback reaction sequence may be appropriate for larger
river systems. In systems where dissolved oxygen levels are controlled by
phytoplankton populations that are internally controlled by nutrients and available
light, nonlinear phytoplankton kinetic models may be appropriate. In past
applications these taodels usually have not been supported by the data base
needed for calibration and verification and have employed literature values
rather than site-specific reaction rate coefficients. While this type of
kinetic structure can be found in available computational software, its use
should be limited to dissolved oxygen problems that are controlled by phytop-
plankton levels and to nutrient removal decisions involving large costs. The
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data base required to make the analysis meaningful in decision making is very
extensive and needs to be collected in support of studies using this modeling
framework.
For dissolved oxygen analysis in streams and rivers, the basic modeling
framework should consider sequential reactions with first-order kinetics, as
illustrated in Figure 3-1. The necessity for departures from this norm should
be documented at an early point in the project and should particularly address
the additional Information required in the decision-making process.
Guidelines for Selecting a Model. Selecting a model involves so many site-
specific considerations that a detailed selection procedure that quantita-
tively ranks the acceptability of the model against selected criteria may
be appropriate. An example of such a procedure is given in Reference 11.
Herein, we have chosen to provide a series of practical guidelines that may
assist in selection.
The guidelines fall under two categories: technical and operational.
The technical guidelines previously discussed in this section ultimately are
concerned with matching the model capabilities to the important physical and
biochemical processes of the prototypical system. The operational guide-
lines are concerned with the ease and cost associated with model operation.
The following is the sequence of guidelines with a brief discussion of the
considerations involved.
Technical Guideline 91: Determine Important Features of Prototypical
System that are Required in the Analysis. The important mechanisms that
generally govern the DO distribution in streams have been discussed in Section
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2.2 and Che means of identifying the site-specific analysis required are out-
lined in this section and in other publications (e.g., 11). With this back-
ground, site-specific data should be collected and reviewed to understand
the system and establish the important factors associated with the identified
problem (problem identification is discussed in Section 4.1). Valuable
information can also be obtained from other experienced professionals,
especially those who have modeling experience or site-specific field exper-
ience, and from personal site visits.
Technical Guideline #2; Review Available Models and Model Capabilities.
Section 3.2 outlines the capabilities for several models selected primarily on
the basis of professional acceptance, availability, and support. Many other
models are available that contain the same capabilities as those presented
here and should not be excluded from consideration.
It is important to be aware of those capabilities that involve a substan-
tial increase in complexity. In simulating physical processes, a significant
increase in complexity is associated with simulating time-variable hydraulics.
This is because the model must solve the more complex equation of motion rather
than, in the case of steady flow, the continuity equation. In simulating the
biochemical processes, a significant increase in complexity is required to sim-
ulate (as opposed Co prescribe) the photosynthecic process, water temperature,
and nitrification.
Technical Guideline #3; Match Important Features of Prototypical System
with Model Capabilities. An important step in model selection is comparing the
important features of the prototypical system with Che model capabilities and
selecting, as techncially acceptable, those models whose capabilities match the
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features of the system. A rule of thumb is to select the simplest model(s)
that retains all important features in the prototypical system. Choosing a
aore complex model is not cost effective since data requirements and computer
cost tend to increase rapidly. An overly complex program will not usually
result in an improved simulation and may increase uncertainty in the analysis.
Technical Guideline 9k i Confirm Selection of Technically Acceptable
Models. The information given in this report only permits a preliminary
selection of a technically acceptable model(s). To confirm that the models are
indeed technically appropriate, the potential user should consult the user's
manual and other support documents, contact and discuss the potential applica-
tion vith members of the support agency, and consult with other experienced
professionals.
Operational Guideline #1; Selection of Candidate Models Based on Ease of
Application. Once a technically acceptable model has been selected, it is
necessary to estimate the ease of applying it. However, it is very difficult
to evaluate the adequacy of documentation and support and realistically
estimate costs without prior experience with the model. Therefore, it is
recommended that the support agency be consulted. 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 otherwise could be made available to the potential user. The support
agency may also be able to provide 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.
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Operational Guideline £2; Selection of Candidate Models Based on Cost of
Application and Problem Significance. It is difficult Co estimate overall
coses involved in a model application because each application differs in scope
and complexity, and the ability to solve or avoid certain problems is very
dependent on the experience and technical background 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 it is to apply. Again, it is essential that the
support agency and other experienced professionals be contacted for information
or assistance.
Once an estimate of the costs of application has been made, 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. In other words,
the WLA study costs should be consistent with the economic, social, or environ-
mental values associated with the problem and its solution.
Operational Guideline //3; Selection of Candidate Models Based on Data
Availability and Data Acquisition Costs. All models require data for input,
calibration, and verification. 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 warranted on
technical grounds may be appropriate.
Summary.' The first step in model selection is to determine which programs
are technically acceptable, based on an understanding of the important physical
and biochemical processes in the prototypical system. The second step is to
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determine the ease and costs of application of chose which are technically
acceptable. The result of the second step is a list of candidate models which
nay or may not be ranked according to convenience and cost. The final selec-
tion of the preferred model from the list of candidates is based on the over-
all judgment of the potential user taking into account all of the factors
discussed.
3.2 AVAILABLE MODELS AND MODEL FEATURES
In this section the term model, following commonly used terminology,
is used to describe computer programs. However, strictly speaking, programs
are not models until the user structures them with the geometry, hydrology,
loading and reaction rate factors that are representative of the particular
receiving water system being analyzed. It is only when this is done that the
computer programs described can be considered to be mathematical models of the
user's system.
Numerous models are available to analyze DO variations in a stream for a
waste load allocation study. The models described in this section have been
selected for discussion because:
• They are in the public domain.
• They are available at a minimal cost from various public agencies.
• They are supported to various extents 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, particularly
waste load allocation studies, and are generally accepted by the
profession.
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• They form a sequence of more technically complex models,
i.e., each model Cakes into account additional phenomena
and/or simulates a given phenomenon in a 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. The discussions and criteria
presented in this document can be employed as major elements in the selection
process* One additional consideration in this process can be 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 effec-
tively focused on Che computer programs selected for discussion in this document.
A brief description of the selected computer programs follows.
DOSAG-I is a program.chat solves the steady-state, one-dimensional equa-
tions that simulate the dissolved oxygen response in a stream network. The
original model was developed by the Federal Water Pollution Control Administra-
tion (subsequently the US EPA Water Quality Office) and later modified by the
Texas Water Development Board (12). The model solves the Streeter-Phelps equa-
tion, modified to include both carbonaceous and nitrogenous oxygen demands,
for a series of uniform reaches thac are assembled Co simulate the stream
network. Waste loads enter at Che upstream ends of each reach. The model also
can simulate the effects of two 00 control options. An analyst can specify
one of five treatment levels governing the waste load BOO and the model will
estimate required flow augmentation to meet a specified DO standard.
SNSIM is a computer program chat solves the steady-state, one-dimensional
form of the scream equation. The code was developed by Robert E. Braster,
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Steven C. Chapra, and George A. Nossa of the US EPA Data Systems Branch in New
York (13). The model solves the Streeter-Phelps equation, modified for NBOD and
CBOD loads, for a series of uniform reaches that represent the stream network.
Waste loads enter as point sources at the upstream end of the reach or as
uniformly distributed nonpoint sources along the stream reach. The user may
specify values for benthic oxygen demand and for net P-R from photosynthesis.
QUAL-II solves either the steady-state or time-variable stream equations.
The program simulates CBOD, DO, temperature, chlorophyll a, phosohorus, NH.,
nitrate, nitrite, coliform bacteria, radioactive material, and any three
conservative constituents in a stream network. It can be run in two modes:
completely steady state, or dynamic in terms of water quality with steady-
state hydraulics. The program ta'kes into account longitudinal dispersion,
sediment oxygen demand, CBOD settling, and nitrification. A version that simu-
lates denitriffcation has been developed for EPA Region IV. Photosynthesis is
based on a simplified nutrient-light-algal cycle. Steady-state or dynamic stream
temperatures can also be simulated. QUAL-II was developed by Water Resource Engi-
neers for the EPA (14) and further improved for the Southeast Michigan COG in a 208
Study (15). It is an adaption of QUAL-I developed by the Texas Water Development
Board (16, 17).
RECEIV II solves the time-variable one or quasi two-dimensional (verti-
cally well-mixed) stream or estuary equations. The program contains separate
hydraulic and water quality subroutines. The hydraulic program solves the
continuity equation and the one-dimensional equation of motion for a series of
volumetric elements'connected by hypothetical links that serve as flow paths.
The following eleven constituents are considered: phosphorus, coliform
bacteria, ammonia nitrpgen, nitrite nitrogen, nitrate nitrogen, total nitrogen
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(assumed conservative), CBOD, chlorophyll a, DO, salinity (assumed conserva-
tive) and one metal ion. The program considers the effects of photosynthesis,
nitrification, settling, and sediment demand on DO and is, therefore, similar in
water quality simulation capability to QUAL-II. However, unlike QUAL-II, water
temperature cannot be simulated. The code can also accommodate dynamic waste
loads. Unlike the other three models previously discussed, RECEIV-II uses
metric units. RECEIV-II, developed by Raytheon Company (9,18) under contract to
the Water Planning Division, US EPA, is an adaption of the RJECEIV module con-
tained in the EPA Storm Water Management Model (SWMM) (19).
The models selected here represent the typical range available. However,
on technical grounds, many other models are comparable indeed, some are
related to those described. Other available computer programs can be generally
grouped into one of the following categories:
• variants of the nodels discussed here
• proprietary models held by consulting firms
• models developed for research purposes
Most of the models selected are one in a sequence or family of versions
originating from some source. Any member of this family tree may be a logical
candidate for program selection. For example, a metric version of DOSAG-I,
called DOSACM, was developed for Sao Paulo, Brazil (20); and an updated version
of DOSAG-I, referred to as DOSAG-III, was developed by Duke and Masch of
Water Resource Engineers (21) to include many of the water quality features of
QUAL-II.
Many proprietary models are held by consulting firms and some individual
consultants. One of the better known models in this category is the
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Hydrocomp Simulation Model HPSF developed by Hydrocomp, International, Palo Alto,
California (22). The quality portion of the model simulates temperature,
BOD, coliform bacteria, zooplankton, sediment oxygen demand, organic nitrogen,
DO, TDS, nutrients, and conservative constituents. The model also can be run
continuously and the output can be frequency analyzed to determine, for example,
the probability distribution of dissolved oxygen in the stream. A nonproprietary
version of this program, the Hydrologic Simulation Model (FORTRAN [HSPF]) is now
available from EPA Athens Environmental Research Laboratory (Ambrose, personal
communication 1980). These programs are quite complex and require well-trained
analysts. Another proprietary model is Raytheon's RECEIV III, an updated version
of RECEIV-II, which, unlike its predecessors, includes longitudinal dispersion
as well as other effects.
Numerous analytical frameworks cited-in the technical literature have been
developed for research purposes to stimulate DO. These models either have been
developed from scratch or are modified versions of existing models. For ex-
ample, Wu and Ahlert (23) discussed a steady-state BOD, NH-j-N, DO model that
takes into account photosynthesis, sedimentation, and nonpoint source distri-*
buted loads; Lin, Fan & Erickson (24) included the effects of transient in-
stream temperature in a program that solves the DO and BOD equations; Novotny
and Krenkel (25) modified DOSAG-I to include settling and benthic demand; and
Sparr (21) applied QUAL-I to the lower Mississippi to investigate the effect of
longitudinal dispersion.
Salient features of the models selected for discussion in this manual are
summarized in*Tables 3-3 through 3-15. References 27 and 28 describe many
other available water quality models. The categories and subject of tables,
modified from Evaluation of Water Quality Models: A Management Guide for Planners
(11), are as follows:
3-36
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1 * \ * *
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TABLE 3-3. CAPABILITIES: TEMPORAL AND SPATIAL FEATURES
Model
DOSAG-I
SNSIM
QUAL-II
RECEIV-II
Time
Variability
Steady State1
Steady State
Steady State or
Dynamic Water Quality
Dynamic
Spatial
Dimensions
One Dimensional
One Dimensional
One Dimensional
One or Quasi-Two
Dimensional
Event or
Continuous
Not Applicable2
Not Applicable2
Not Applicable2
Event or
Continuous
*Set up but not restricted to simulate mean monthly conditions.
Any steady state (usually low flow) condition.
TABLE 3-4. CAPABILITIES: HYDRAULIC FEATURES
Model
DOSAG-I
SNSLM
QUAL-II
Receiving Water
Type
Stream
Stream
Stream or
Single Reach
or Network
Both
Both
Both
Other
Features
RECEIV-II
Completely Mixed
Reservoir
Stream or
Completely Mixed
Estuary
Both Considers wind-stress,
control structures
(dam), tidal boundary
condition
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0/14
TABLE 3-5. CAPABILITIES: WASTE LOADS1, SINKS, AND SOURCES OF DO
Model
DOSAC-I
SNSIM
QUAL-I1
RECEIV-II
Waste Load Characteristics
Single or Loading Dissolved
Types Multiple Rate Sinks
Point Multiple Constant CBOD
NBOD
Point & Multiple Constant CBOD
Nonpolnt NBOD
(distributed) benthal
demand,
Algal
respiration
Point & Multiple Constant CBOD
Nonpoint NHOD
benthal
demand ,
Algal
respiration
Point Multiple Constant or CBOD
Variable NHOD
benthal
demand,
Algal
respiration
Oxygen
Sources
Reaeration
Reaeratlon,
photosynthesis
(specify P-R)
Reaeration,
photosynthesis
(nutrient-algal)
Reaeratlon
photosynthesis
(nutrient-algal)
Special Features
and/or Limitations
Can specify treatment
levels; model will
estimate required flow
augmentation to meet
specified DO standard.
Allows for settling of
BOD material, will
estimate required flow
augmentation to meet
specified DO standard.
Allows for settling
of nitrate
Commonly refer to municipal and industrial waste discharges but may also
apply to tributary or upstream Inflows and agricultural or urban runoff.
70
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m*»
a
u
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TABLE 3-6. CAPABILITIES: CONSTITUENTS
Model Modeled Specified
DOSAG-I DO, NBOD, CBOO (conservative constituents via Temperature
zero reaction rate)
SNSIM DO, NBOD, CBOD (conservative constituents via Temperature
zero reaction rate)
QUAL-II DO, CBOD, temperature, chlorophyll a, phosphorus,
NHj, nitrate, nitrite, coliform bacteria, radio-
active material, and any three conservative con-
stituents
RECEIV-II DO, CBOD, chlorophyll a, phosphorus, NH Temperature
nitrate, nitrite, total nitrogen, coliform
bacteria, salinity & one metal ion.
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VIA
TABLE 3-7. CAPABILITIES: PHYSICAL AND BIOCHEMICAL PROCESSES SIMULATED
Model
Physical
Processes
Biochemical
Processes
DOSAG-I
Advectlon, dilution, reaeration
Ist-order decay of CBOD, NBOU; coupled DO with
CBOD and NBOD
SNSIM Advection, dilution, reaeration
QUAL-1I Advection, dilution, reaeration,
longitudinal dispersion, stream
heat balance
RECEIV-II Advection, dilution, reaeration
Ist-order decay of CBOD, NBOD; coupled DO with
CBOD and NBOD, benthie demand, net photosynthesis
(specified)
Ist-order decay of CBOD, CBOD removal by deposi-
tion; coupled DO with CBOD, benthal demand,
photosynthesis and nitrification (based on
nutrient-algal model)
Ist-order decay of CBOD; coupled DO with CBOD,
benthal demand, photosynthesis & nitrification
(based on nutrient algal model)
n
o
a
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TABLE 3-8. MODEL CAPABILITIES: REAERATION FORMULATIONS
Model
Options
DOSAG-I Four options: input directly; calculated as a function
of velocity and depth fallowing Churchill et al., Langbein
& Durum, O'Connor & Dobbins, or Owens & Gibbs; calculated
as a function of flow; method of Thackston & Krenkel
SNSIM Three options: input directly; calculated as a function
of velocity and depth as above; method of Tsivoglou et al.
QUAL-II Multiple options similar to DOSAG-I, including Tsivoglou's
equation.
RECEIV-II Churchill et al.
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430
TABLE 3-9. ACCURACY: PRINCIPAL ASSUMPTIONS
Model
Quantity
Quality
DOSAG-I
SNS1M
*-
N*
QUAL-I1
RECEIV-II
Assumes steady state; geometry and velocity
are unifonn throughout reach; no lateral or'
vertical variation in velocity; velocity and
depth can be expressed as power functions of
flow, completely mixed.
Assumes steady state; geometry and velocity
are uniform throughout reach; no lateral, or
vertical variation In velocity; velocity and
depth can be expressed as power functions of
flow, completely mixed.
Assumes steady state; geometry and velocity
are uniform in a reach; no lateral or vertical
variation in velocity; velocity and depth
can be expressed as power functions of flow,
completely mixed.
Assumes receiving water can be broken down into
a system of completely mixed volumetric units
called nodes connected by a series of links
along which flows occur; no lateral variation
in velocity.
Assumes Ist-order decay of NBOD and CBOD
(both specified), constant waste loads,
neglects benthic demand and photosynthe-
sis; reaction rates constant In a reach;
well mixed laterally and vertically, no
longitudinal dispersion.
Assumes Ist-order decay of NBOD and CBOD
(both specified); constant waste loads;
constant benthal and photosynthetic
demand; reaction rates constant in a
reach; well mixed laterally and verti-
cally; no longitudinal dispersion.
Assumes CBOD Ist-order decay; well mixed
laterally and vertically; includes effects
of benthic demand (specified), algal
production (modeled), and nitrification
(modeled) on oxygen; allows for CBOD
settling (specified); includes longi-
tudinal dispersion.
Assumes CBOD Ist-order decay; includes
effects of benthic demands (specified),
algal production (modeled), & nitrifi-
cation (modeled) on oxygen; model volume
is well mixed; no longitudinal dispersion.
70
n>
o -
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TABLE 3-10. DATA REQUIREMENTS: INPUT
tllllMt
O.C.,
•*!••
lllaaa laaflbi.
MllufBj faaChaa.
C0M1MIM KlMM,
iiallum raafbaa.
mim lot
mm*»*ftmi m*t
Iflfcilaff lallaaw.
lflkul»ry lallo««t
I.I la. c.«..lc.ll
•!!•«• •«
flaw tmlmm mmt •*••*•! IM aaj immtmlmm
tmmtmmnatmu til* (MllKlwtl. mmt
mmmjmtm*mS9 mutmtmmmm tMCMIlMlct
V|OH tmlmm mmm §•••!•« la* ««4 faactla*
(MMMnilM f«i« . mmm
Ullav CMCUlfallra • lav lato u4 •««.!«!•«. nacilM
CMCwifMlM ••• MiiIlM Ml* mmm mlnmltmm ml
(MIIUIMI*. mmt tmw kola, tmt mt (a*r.
QIUL-II Slrcma Icafta.. CluiU ciiv«i. at«a«* ll«*aM«l«f «a4 C««lllcl«ala tmw
caaaaccle* crhcaa. pbaflc ar««a«f*. 4rf Iflhilalv lalloml. v«laIM
IKCKIV-II kaibywirv •• aruv!4« lalalall iMlaaally. Haaartalaf aa4 luuglioa.a foalllcltal lallcw caacaalfallaa. VlaM falaa aa4 ••aarallaa. raacllwi. Hf4*a«llc mmt
«>>lb«. cbaaaal >l.a aaaaa «4 41- •ilo«i
aaurcaa ml (!•»
O —
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TABLE 3-11. DATA REQUIREMENTS: CALIBRATION AND VERIFICATION
Model
DOSAG-I
SNSIM
QUAL-II
Hydrologic
Scream flow
Scream flow
Scream flow
Hydrodynamlc
Scream velocity
Scream velocity
Scream velocity
Water Quality
Concentrations
Concentrations
Concentrations
and temperature
RECEIV-II Stream flow Scream velocity, Concentrations
depth
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TABLE 3-12. EASE OF APPLICATION: OUTPUT FORM AND CONTENT
Model
Output Form
Output Content
DOSAG-I
Computer printout
SNSIM
Computer printout
QUAL-II
Computer printout
RECEIV-II
Computer printout, velocities
also written on scratch tape/disk
for quality mode (optional tape/
disk storage of results for plotting)
a) Listing of input data
b) DO, CBOD and NBOD concentrations
at start and end of each reach,
and magnitude and location of mini
mum DO concentration in each react
a) Listing of input data
b) Variation of DO, CBOD and NBOD
concentrations and DO deficit
and source of deficit along
stream reach
a) Listing of input data
b) Concentrations and temperature
by reach and computational ele-
ments at specified time steps
c) Maximum, minimum and average
concentration, temperature, fl
velocity and depth for *ach reach
a) Input data listing
b) Channel flows and velocities,
junction depths and concentra-
tion of constituents at prescribes
time intervals
-------
TABLE 3-13. EASE OF APPLICATION: SOURCES, SUPPORT AND DOCUMENTATION
Source(s) of
Model
Source(s) of Nature of
Support Support
Documentation Source(s) of
(Reference 0) Documentation
Adequacy of
Documentation
-I EPA Planning
Assistance
Branch, Wash. D.C.
Data Systems Section Same
Texas Dept. of Water
Resources, P.O. Box 13087
Austin, Texas 78711
EPA Data Systems Same
Branch,
26 Federal Plaza
New York, N.Y. 10007
II Center for Water Quality
Modeling
U.S. Environmental
Protection Agency
Athena, GA 30613
(404) 546-3585
Texas Dept. of Water Same
Resources
(see above)
V- EPA Planning Same
Assistance Branch
Wash. D.C. 20460
Raytheon Company Same
P.O. Box 360
Portsmouth, R.I. 02871
12
NT IS
PB 202 974
Telephone
contact
Telephone
contact
13
NT IS
PB 241 923
Software 14
Maintenance,
Workshop,
Technical
Assistance
through Official
EPA Channels
Telephone
contact
Telephone 18
contact
Telephone
contact
EPA Planning
Assistance Branch
Wash. D.C. 20460
Adequate theory
and user's manual,
good input data
format
Adequate theory
and user's manual,
well-organized
input data format
Good discussion
of theory, and
assumptions
Adequate user's
manual, includes
good input data
information
Excellent descrip-
tion ot Input data
needtt; well-organ-
ized input format
yo
HP
-s
o —-
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TABLE 3-14. EASE OF APPLICATION: EQUIPMENT AND PROGRAMMING REQUIREMENTS
Model
Requirements
DOSAG-I Requires any computer with about 27,000 word storage and a FORTRAN-
IV compiler. No tapes or disks needed.
SNSIM Written in FORTRAN IV, version SNSIM-1 compatible with IBM 370/155;
SNSIM-2 compatible with IBM 1130. Storage requirements similar to
DOSAG-I. No tapes or disks needed.
QUAL-II Written in FORTRAN IV (level G) to be compatible on UNIVAC 1108,
COC 6400, and RCA Spectra 70/45 and therefore is almost machine
independent; requires 45,000 word storage. No capes or disks needed.
RECEIV-II Written in FORTRAN IV (level G)a to be compatible on IBM 370/155 and
Honeywell 6000/60; requires approximately 50,000 words of storage;
tapes or disks may be necessary depending on application.
aAlso compatible to ANSI Standard FORTRAN.
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TABLE 3-15. OPERATING COSTS
Model
DOSAG-I
SNSIM
QUAL-II
RECEIV-II
Acquisition
Nominal
Nominal
Nominal
Nominal
Machine Costs3'
Per Run
(dollars)
1-5
1-5
1-5 or less
15-100 (quantit
b Labor Costs (person weeks)
Set Upc
2-6
2-6
2-10
y) 5-20
Running3
Negligible
Negligible
Negligible
Routine runs
Analysis3
1
1
ld
The complexity
10-50 (quality)
take minimal
time
of model re-
quires at least
several hours of
analysis for eac
run to be evalu-
ated
a For each run, including those used for calibration, verification and projections.
Approximate range for a single run on a typical application using a commercial
IBM 370/55 during daytine hours. These costs are dependent on many factors
and should be used in a relative sense.
c Set-up time for each model depends on the complexity of the application, the
form of the available data, and staff capabilities.
Runs including nutrient-algal simulation initially require at least several
hours.
Partial Source: Reference (11).
3-48
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Capabilities: Table
Temporal and Spatial Features 3-3
Hydraulic Features 3-4
Waste Loads, Sinks and Sources of 00 3-5
Constituents Modeled 3-6
Physical and Biochemical Processes Simulated 3-7
Reaeration Formulations 3-8
Principal Assumptions 3-9
Data Requirements:
Input 3-10
Calibration and Verification 3-11
Case of Application:
Output Form and Content 3-12
Sources, Support, and Documentation 3-13
Equipment and Programming Requirements 3-14
Operating Costs 3-15
Summary Tables:
Summary of Features 3-16
Heirarchy of Models Based on Selected Features 3-17
Information presented under the first three cable subjects (Capabilicies,
Assumptions, and Data Requirements) is primarily technical and required to
evaluate whether the model simulates Che important physical and biochemical
features of the problem. Information presented under Che table subjects, Ease
of Application and Operating Coses, is primarily nontechnical or related co
operational features of Che models. This information is needed Co evaluate che
cose associated with and che ease of acquiring Che oodel, getting che model
running on your system, calibrating and verifying the model, and finally apply-
ing che model.
The information provided in these cables is primarily qualitative and
sufficient to determine whether a model may be suitable for a particular
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410/1*
•TABLE 3-16. SUMMARY OF FEATURES
I
Ul
o
DOSAG-I
SNS1H
qilAL-II
RECEIV-II
Tlae Space Event or
Scale Scale Continuous
•teady 1
•tall
•teady 1
atate
steady 1
•tale
hydraulic.
•teady a
dynaalc
quality
dynaalc 1,1 event or
continuous
Uaicr
Body
atreaa
network
atreaa
network
streaa
network
streaa
network or
well-ailed
estuary
Typea of Loading
Loads Rale
Accepted Accepted
•ultlple conalani
point
•ource
•ultlple conatant
point
eource a
distributed
•ource
•ulllple conatant or
point llae
•ource a variable
nonpolnl
•ource
•ultlple constant or
point llae
•ource variable
Water Quality
Paraaeter
Modeled
DO. CBOD. NBOD
conservative*
DO. CBOD. NBOD
conservative*
DO. CBOD. iiraperature,
aononla, nitrate.
nitrite, alg.ic, phoa-
uliurua col If ara.
radioactive aubatancee.
three coneervatlve
aubstancei
DO. CBUD. aanonla. nitrate.
nitrite, total nitrogen.
phosphorous roll lorn, algae.
aa Unity, one aelal Ion
Procesaee Slaulated
Chealcal/Blolgolcal
let-order decay
ol NBOD, CBOD
coupled DO
1 si-order decay
of NBOC. CBOD.
coupled DO,
benthlc deaend (a).
photoayntheele (e)
let-order decay
of NBOO. CBOD,
coupled DO, benthlc
denand (a), CBOD
aetlllng (a).
nutrient-algal
cycle
lei-order decay
of CBOB, coupled DO
benthlc deaand (a).
CBOD aetlllng (e).
nutrient-algal
cycle
Physical
dilution,
•dvectlon.
reeeratlon
dilution.
advect Ion,
reaeral Ion
dilution.
advectlon,
reaeratlon,
heal balance
dilution.
advect Ion,
reaeratlon
Calibration/
Verification
Parameters
Q. V. C
Q. ». C
Q. », C
Q. ». C
*Use CBOD or NBOD with icro or low decay ralea
(a) - epeclfled
<
^.
I/I
o
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J/1A
TABLE 3-17. HEIRARCIIY OF MODELS BASED ON SELECTED FEATURES
Multiple Constant
Jel
JAC-I
JIM
AL-II
UEIV-1I
Point
NBOD
X
X
X
X
Sources of
COOD
X
X
X
X
Distributed
Sources of
BOD
Xc
X
X
xc
Benthal
Demand
Xa
Xa
Xa
Algal
Production
Xa
Xb
Xb
Longitudinal BOD
Dispersion Settling
Xd
Xd
X Xa
xd
Tine-
variable
Waste Loads
(and
quality)
Xe
X
Time-
variable
Flow
X
Specified (i.e., input to the model)
Simulated in a nutrient-algal cycle
Can be simulated approximately by input of load at beginning of -each multiple segment.
Can be simulated by making Kf > Kfl
Meteorology only
in
o
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application. For some of the models, more quantitative information is given in
Reference (11). For complete information the potential user must consult the
appropriate user's manuals and other supporting documentation. The Center for
Water Quality Modeling, EPA Environmental Research Laboratory, Athens,
Georgia (Mr. Thomas 0. Barnwell) is a source of information and technical
support. A brief description of the contents of each of these tables follows.
Table 3-3 Model Capabilities; Temporal and Spatial Features. The diff-
erence between static and dynamic models, single versus multidimensional
models and the significance of various time and space scales in the context
of the water quality problem have been discussed in Section 3.1. The models
considered in Table 3-3 are all deterministic, one or two dimensional, and
can calculate steady-state or dynamic solutions. RECEIV-II may be run either
In (1) an event mode (i.e., the simulation period'is limited to the duration
of a relatively short-lived event of interest, e.g., a storm, a diurnal or
weekly pattern of waste load discharge, or a weekly period of changing stream
flow) or in (2) a continuous mode in which numerous events over larger periods
(e.g., monthly, seasonal, or annual) are simulated. The operational difference
is associated with the time step used in the calculation and the associated
requirements for data on flow, loads, etc. as a function of time. Event simu-
lations require data at smaller time steps - than continuous simulations.
Table 3-6 Model Capabilities; Hydraulic Features. All of the models
selected are appropriate for a stream network, i.e., a system of individual
stream segments connected together. Additional capability is found in the
RECEIV-II model, which may be applied to well-mixed estuaries. The first
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three models use inputted upstream, tributary and wasteload flow3 to compute
downstream flows assuming steady state* RECEIV-II simulates time-variable
hydrodynamics and, therefore, requires downstream depth-flow control. In
RECEIV-II the control is a dam or a tidal boundary condition.
Table 3-5 Model Capabilities; Waste Loads. Sinks, and Sources of DO. The
models vary in ability to simulate point versus nonpoint source waste
loads, constant or time-variant loading (or discharge) rate and DO demands
from benthal deposits, photosynthesis, and nitrification. QUAL-II also allows
for BOD settling. In most cases if a aodel does not permit distributed loads,
such loads can be approximated by a series of point sources.
Table 3-6 Model Capabilities; Constituents. 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 3-7.
In the more complex programs, i.e., QUAL-II and RECEIV-II, provision is made
for selecting only those constituents (and therefore processes) of interest.
Therefore, it is relatively easy to "zero out" constituents that are not
applicable. Sometimes it is possible to change the number or type of con-
stituents simulated by minor modifications in the code. For example, conser-
vative constituents may be simulated by setting reaction rates to zero; or
direct oxidation of Nh^ to ^03 may be simulated by assigning a large value to
the MO2 to NO-j oxidation rate coefficient.
Table 3-7 Model Capabilities: Physical and Biochemical Processes
Simulated. The physical processes simulated are usually advection, dilution,
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and reaeration since these are considered essential to describe most physically
related DO variations. Settling may also be simulated directly, or by adjust-
ment of rates such as K and K.. The biochemical processes simulated are quite
varied and can be classified in the following increasing order of complexity:
• BOD-DO coupling (usually first-order reactions)
• NBOD-CBOD-DO linkage (i.e., inclusion of nitrogenous biochemical oxygen
demand in DO balance—usually first-ordered reactions)
• Prescribed sediment oxygen demand and/or photosynthetic related oxygen
production and demand (usually first-order reactions)
• Simulated nutrient-algal-dissolved oxygen linkage (usually nonlinear
reactions)
Sometimes it is possible to consider certain effects even though the
effects are not explicitly contained in the program. For example, if the pro-
gram makes a distinction between .Che BOD decay rate (K ) and the oxidation rate
associated with BOD decay (K^) [see Section 2.3] then settling can be considered
by making Kf greater than K^. If the program does not make such a distinction,
it may be relatively easy to modify the code accordingly.
Table 3-8 Capabilities: Reaeration Formulations. Most models permit
direct input of the reaeration coefficient or selection from several commonly
used correlations or methods.
Table 3-9 Accuracy; Principal Assumption. Each model makes a number of
assumptions. The simpler computer program simulation techniques, by neglecting
certain effects, assume that such effects are not important for the case being
considered. The more complex models, although they may consider additional
effects, also incorporate assumptions in mathematically representing the proto-
typical system.
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Revision No. C
In the context of water quality modeling, two components should be con-
sidered in judging the accuracy of computer programs. The first consideration
deals with the accuracy of the numerical solution technique for the differential
equations representing water quality employed by the program, as compared to
analytical solutions of the same differential equations. The second consider-
ation is concerned with the adequacy and accuracy of the formulations of rates
and transport that are employed in the differential equation that is being
used in the analysis. In most cases, the computer programs can be operated to
provide adequate accuracy for decision making, considering both of the com-
ponents indicated above.
Table 3-10 Model Data Requirements-- Input. The input data reouirenents
increase with the complexity of che flow and quality mathematical formulations.
•The first three models assume steady-state hydraulics formulae, which then require
specification of regression coefficients (see equations 2-3 through 2-5) to estimate
velocity and depth required in che reaeration formulae. The aore complex models
such as RECEIV-II solve a form of the momentum equation, which requires more
detailed characterization of the stream geometry and roughness. Similarly, the
data required to simulate the nonlinear nutrient-algal-DO linkage is extensive.
Table 3-11 Daca Requirements: Calibration and Verification. The tyse and
amount of data required for calibration and verification increases as che
complexity of che computer program becomes greater. Daca requirements tend
co increase rapidly wich increasing complexity of analysis. Dynamic models
require that data be obtained synoptically at a number of stations and over
relatively short time incervals (e.g., minutes Co hours).
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Table 3-12 Ease of Application: Output Form and Content. All of the
computer programs print results of the simulation and the input data. The more
complex ones require scratch disks or tapes for storing intermediate results to
be read subsequently in submodels or for storing information to be plotted.
Table 3-13 Ease of Application; Sources, Support, and Documentation.
Two of the most important factors 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 present the input data require-
ments and format. A well-organized input data scheme is essential. The sup-
port provided by the support agency should include user access via telephone to
programmers and engineers familiar with the model.
Table 3-14 Ease of Application; Equipment and Programming Requirements.
All models are written in FORTRAN IV and most are machine independent. Storage
requirements increase with program complexity.
Table 3-15 Operating Costs. Computer costs and labor requirements vary
significantly depending on numerous factors as discussed in the notes at the
bottom of Table 3-15. Therefore, these results are only to be used for compar-
isons between models.
Table 3-16 Summary of Features. For initial screening purposes, a
summary of model capabilities is given in Table 3-16. For more detail the
reader may then refer to Tables 3-3 through 3-8.
Table 3-17 Hierarchy of Models Based on Selected Features. To assist
in initial model selection, Table 3-17 shows a hierarchy of models based on
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important distinguishing features. As shown in this table, the programs
increase in complexity. One of these programs should be adequate for most waste
load allocation scudies and, in general, the simpler program should be chosen
if it contains all the features needed to simulate the important 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 a simple
model by "turning off" processes. This procedure allows easy upgrading of the
model as more information becomes available. QUAL-II, for example, can be
used at the same analysis level as DOSAG-I and SNSIM, and requires no additional
information.
3.3 MODELING PROCEDURES
Objectives of Site-specific Modeling
Assume that the water quality problem has been identified, the components of
a water quality model have been defined, and a computational framework, such as
a computer program, selected. The next task is to develop a site-specific water
quality model that is directed towards each of the following objectives in the
context of the water quality problem:
• Confirm that water quality problems do or will exist.
• Develop a quantitative understanding of system response to each
significant load, source, and sink.
• Develop a quantitative understanding of system response to impor-
tant constituents in the loads.
• Define the level of uncertainty in the quantitative understanding
of system response.
The modeling work is directed towards defining the quantitative effects
of the components that contribute to water quality problems. Critical
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examination of the residual uncertainties in the water quality analysis is
usually of prime importance in the engineering and decision-making process.
Therefore, it is necessary to include in the calibration and verification
program a series of calculations and data sets that permits the analyst to
check and cross-check the water quality effects ascribed to individual loads
and constituents. In this context, the following questions are typical of
those that will be helpful in setting up and evaluating the study program:
• How can the effect of two sources be differentiated using data
and calculations?
• How can the effect of sediment oxygen demand, nonpoint sources, and
point sources be differentiated?
• What data and calculations can be developed that will provide an
assessment of the differences in reaction rates (such as BOO oxida-
tion rates) between various sources?
• Is nitrification occurring in the system, and should it be antici-
pated under future conditions?
• What is the magnitude of dissolved oxygen fluctuations that cannot
be accounted for by the present analysis?
• How do these fluctuations vary with time, seasonally and spatially?
In summary, the goal of the water quality analysis is to obtain an assess-
ment of system behavior that will support decision making. Each study has
unique requirements that may modify the modeling procedures suggested below;
however, they are presented as a basis for meeting many project requirements
and as a point of departure for development of individualized site-specific
study programs.
Verify Model Calculations
The first step in any modeling analysis is to verify that the calculation
technique to be used is functioning correctly. This can be accomplished by
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employing analytical solutions for specific simplified representations of Che
individual components to be included in the analysis effort. Table 3-13 is
reproduced from the Areawide Assessment Procedures Manual (29) and contains
analytical solutions to the stream dissolved oxygen equations. That aanual
also provides example calculations illustrating the use of these equations.
Equation 3-1 can be employed to check the more complex computerized solutions
to the dissolved oxygen equation in streams. Note that in equation 3-1, the
convention for concentrations at x»0 (DQ, LQ, NQ) reflects concentrations after
mixing with the waste load, in contrast to the convention employed in Table
3-18, in which the subscript "o" represents concentrations in the stream
immediately upstream of the waste load.
D - * D0 c *
f -Jr4>(*> -Ja$<*)"|
* P, I e - e
+ *n •
- e
- e
1 - e
-Pmf(xft)
(b)
(c)
(d)
(e)
in which
F -
1
f(x.t) -
Kr.n.
2(Ka2 +TT2/P2)
sin t.
C08 t.
[*-
C08 »
cos 2t
| +
-------
TABLE 3-18. SUMMARY OF SOLUTIONS FOR POLLUTANT CONCENTRATIONS
IN THE RECEIVING WATERS
Conservative C
Reactive L
Coupled D
Point Source
"" L segment length V
0 ' 1 0
° ~v~~~~
f!n 1 „" IV, i ! *
Hl« SJ« U0 —| f—
C-CQ+W/O
L-L..-".-^,.-"-
^ KA X/U
^J B ^}ffc 0
Kd , -KfW -K.X/U
+ L0 • K _K le - e 1
Distributed Source
W 1
0
^J • ^}A 0
Kv y j] • svw/ii
ft • ^KfAfW •• n*M/U .
K§-Kr
* TuT • iT^c ^ e"K"X/U- «"K'X/U+ -^-r 1
''•*•• ^a "» A A
NOTE:
Q • Flow
X • Distance
C • Conservative Substance Concentration
L » Reactive Substance Concentration (BOD)
D ° Coupled Substance Concentration (DO Deficit)
U <• Velocity
A *• Cross-sectional Area
Kr <• BOD Removal Coefficient
K,j °> BOD Oxidation Coefficient
Ka o DO Reaeration Coefficient
Co. LO. DQ •> Concentration at X - 0
W = Point Surface Loading Rate
w = Non-point Source Loading Rate
ro
<
-*.
vt
o
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This equation calculates Che dissolved oxygen deficit distribution in space
for:
• Initial deficit from upstream and/or waste flow - Equation 3-la.
• BOD input from a waste load - Equation 3-lb.
• NH^ oxidation from a waste load - Equation 3-lc.
• Sediment oxygen demand - Equation 3-Id.
• Phytoplankton oxygen production and respiration - Equation 3-le.
The recommended approach is to use constant geometry and temperature (other
than 20°C) in a simplified representation of a site-specific system and then to
compare the dissolved oxygen deficit as calculated by the computer program and
by the equations. Do this either for all loads, or preferably individually for
each type of load, source, and sink. All computer codes for stream analysis
can yield the dissolved oxygen deficit as output. This may require some pro-
gramming effort, depending on the program version. The effort will prove a
worthwhile investment in time both for this activity and for subsequent require-
ments to examine unit responses. It should be noted that Equation 3-1 can be
employed to calculate the time-variable (quasi-steady state) dissolved oxygen
response due to phytoplankton oxygen production and utilization. Therefore,
this equation can be employed as partial confirmation of the dissolved oxygen
calculations in the more complex time-variable phytoplankton models for streams.
The approach is to run the time-variable model to steady state and, using the
documentation, calculate FO and R, internally generated by the model. These
values can then be substituted into Equation 3-1. The stream equations in
Table 3-18 and Equation 3-1 can be used in this manner to assess the accuracy
of numerical solutions and the segmentation used in the computer program. As
a final check, sum all deficits calculated employing Equation 3-1 and/or
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Table 3-18 formulations and compare the cocal deficit to that obtained from a
comparable computer run with the computer doing the summation. The same reaeration
equation and temperature adjustments should be employed in each computation.
The exercise suggested above will verify the validity and accuracy of a
specific program code as set up in a particular computer installation. This
activity will also provide valuable insights and experience for the individual
who has not been involved in hands-on modeling of dissolved oxygen.
Identify Inputs; Loads. Rate Coefficients, Transport
At this point in a project, the equations and formulations that are to be
used in the analysis have been selected. A computational technique has been
chosen and placed on a computer facility. The computer program outputs for
each of the reactions and loading types have been checked against the appropriate
analytical solutions. The next step in the project is to unravel the cause
and effect relationships that are controlling dissolved oxygen concentrations
in the stream or river. The first step, model calibration, essentially consists
of comparing dissolved oxygen, BOD, NH^, NO2, and NO3 profiles calculated
by the model to observed data.
General—Due to the critical importance tfiat input parameter selection has in
any modeling effort, the utmost care must be taken to use the best possible
estimates for values. The reader should refer to the discussion of this sub-
ject in the early part of Section III-C, Dissolved Oxygen Analysis, in Appendix A.
Loads—The loads, sources and sinks in category I (i.e., those that are
significant for the site-specific situation) should be defined from direct
measurements corresponding to each set of receiving water quality data secured.
Loads, sources, and sinks in category II (those that are considered to control
background conditions) can be estimated from a combination of isolated measure-
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TABLE 3-19. TYPICAL RANGES OF LOAD FOR SOURCES*
Source
Range
Supplemental
References
Domestic and Industrial
Point Sources
Upstream Background Levels:
Dissolved Oxygen Deficit
BOD5
NH3
N03
Organic N
Urban Storm Runoff, BOD
Organic N
TN
Combined Sewer Overflow, BOD
Organic N
TN
Nonpolnt Loadings, BODj
TN
Benthal Oxygen Demand, S
(gm/nr/day)
Average Gross Photosynthetic
Oxygen production Pa
(gm/nr/day)
Assimilation Number,
(gm 02/hr/gm Chi a)
Average Algal-Respiration Ra
(gm/nr/day)
NPDES Permits
Compliance
Reports
0.5 - 2.0 mg/1
0.5 - 3.0 mg/1
0.05 - .27 mg/1
.07 - .37 mg/1
.05 - .50 mg/1
20 mg/1
1.4 mg/1
3. 1 mg/1
115 mg/1
3.8 mg/1
9.1 mg/1
6 - 60 mg/1
0.8 - 1.3mg/i
1 - 10
.3 - 18
.7 - 4.5
.025 (Chi a)
7, 5, Use Storet
30, 31, 32, Use Storet
30, 31, 32, Use Storet
30, Use Storet
30, 31, Use Storet
32, 29
32, 29
32, 29
32, 29
32, 29
32, 29
29
33
5, 10, 2
2, 5, 10
2
"These can be used for Category II Sources with confirmation by site-specific
data.
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ments, for confirmation, supplemented by information in the literature. Table
3-19 presents data on typical ranges of values for loads, sources, and sinks
and lists references that nay be employed with confirming measurements and
local study results to develop estimates for background conditions for category
II sources. Category I sources usually require direct site-specific
measurements.
Point source inputs from domestic and industrial waste treatment plants
will usually be in category I sources and should be measured during each
period that receiving water quality data are collected in an allocation study.
For historical data, compliance reports for NPDCS permits can be used. Data
on upstream contributions can often be obtained from Storet and 208 or other
studies. Runoff loads from combined and separate sewer systems, if these are
necessary to include as category II sources, can be estimated from Table 3-19,
supplemented by a modest amount of local data from the allocation study or a
recent 208 program study.
Reaction Coefficients. Reaction rate coefficients, in contrast to loads,
sources, and sinks, generally cannot be directly measured under natural condi-
tions. Indirect measurements, supplemented by calculations, provide one of
the most reliable techniques for estimating reaction rates. In addition, lab-
oratory and field experiments can provide information on the relative range of
reaction rates. However, laboratory conditions usually are sufficiently dif-
ferent from natural conditions that direct application of experimentally derived
reaction rates to natural streams is not valid. Illustrations of this dif-
ficulty are found in measurements of BOD oxidation and nitrification rates
under laboratory conditions, which generally cannot be directly used to
estimate these reaction rates in natural systems.
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Assuming that inputs to the stream or river are adequately characterized
by direct measurement, the basic objective of the model calibration process
is to define a system of reaction rates that when combined with the mea-
sured inputs, yield calculated contaminant profiles that are consistent
with observed data. The reaction rates employed in water quality modeling
are based on physical, chemical, and biological principles or approximations
Co processes that can be examined under more or less controlled laboratory
or field conditions. Therefore, two significant constraints must be imposed
upon the values for reaction rates employed in water quality modeling calcula-
tions. These constraints are:
• All reaction rates oust be uniform in space and in time unless
variations are systematically related to identifiable system char-
acteristics or processes.
• The rates and the formulations for systematic variation used in
specific water quality modeling projects should fall within the
range reported in the literature.
As an example, the first constraint allows variation of reaction rates as
a function of temperature and factors such as stream depth or bed character-
istics, light, nutrients, etc., but prohibits spatial variation of reaction
rates to "fit the data" or changes in reaction rates used to characterize
different sets of data or periods within a data set. This constraint is
basically an outgrowth of the deterministic approach to water quality modeling
that has classically been employed and is suggested for waste load allocation
studies. The first constraint can be tested readily by application of the
question: Do reaction rates vary in a systematic manner that can be identi-
fied and demonstrated to be phenomenologically realistic?
In one sense, the second constraint is easier to test since the range of
reaction rates reported in the literature has been summarized (2). In a more
fundamental sense, this constraint is really very difficult to evaluate. The
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objective of the modeling effort is to develop a quantitative assessment of
factors controlling water quality. An evaluation of the portion of the water
quality responses that is quantitatively undefined should be included in this
assessment. These latter responses will usually be important in the decision-
making process. The range of values reported in the literature for indi-
vidual reaction rates is usually quite large. Thus, while a series of
reaction rates may be technically within the numerical range reported in
the literature, there may be a consistent bias in the values assigned
that attempts to compensate for the effects of a phenomenon not fully
incorporated in the analysis. This concern is the essence of the second
constraint and is very difficult for both analyst and reviewer to identify.
The following segments of this report present tabulated ranges of
reaction coefficients, formulations to calculate probable values, and dis-
cussions of methods for defining site specific reaction rate coefficients.
It should be recognized by the analyst and included in the decision-making
process that the level of available technical know-how will not provide a
basis for _a priori assignment of site-specific reaction coefficients. This
results from two factors.
The first factor is associated with an incomplete technical understanding
for particular reactions, of the processes, pathways, and system character-
istics that influence the speed of the reaction. Examples of reactions
where incomplete tech-ical understanding is of importance are the nitrifi-
tion reactions and sediment oxygen utilization. For both of these reactions
there are qualitative hypotheses available describing the pathways and
probable influence of system characteristics, but quantitative a priori
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402/20
prediction of reaction.rates even in controlled laboratory experiments have
not been made.
The second factor that limits the ability to assign site-specific
reaction rates in waste load allocation projects is associated with the need
to properly average reaction rates or system characteristics over segments of
a natural stream or river. The process of atmospheric reaeration is an
example where the second factor is probably of major significance. There is
general agreement that liquid film resistance at the air-water interface
determines the reaeration coefficient. Various formulations have been devel-
oped that attempt to relate system characteristics such as depth, velocity,
rate of energy loss, etc. to the reaeration coefficient. The liquid film
resistance is controlled by local system characteristics such as depth,
velocity, rate of energy loss, etc., therefore, the various formulations
really provide different approximations for the process of averaging local
phenomena over a segment of a stream or river.
In view of the limitations in technical knowledge and the associated
difficulties in properly averaging local processes over large segments of a
stream or river, _a priori assignment of reaction rate coefficients in waste
load allocation projects carries considerable uncertainty. The process of
model calibration and verification is the preferred method for narrowing
the probable range of site-specific reaction rates. The ranges of coeffi-
cients presented in this section may also be reduced based upon the judge-
ment of the analyst derived from calculations and data on the site-specific
project or experience with other similar systems. In any event it is
unlikely that a single set of coefficients can be developed; thus, there is
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Revlslcn No. Q
the r.esd co carry out a formal or info—.a! sensitivity analysis. The range
of pro:a'.'j.-i responses from this sensitivity analysis should be carried into
the deiiston-making process.
The range of reported rate coefficients employed in dissolved oxygen
analysis of streams and rivers is summarized in Table 3-20. This table also
tabulates the range of temperature formulations available. Table 3-21 presents
a summary of the reaeration formulas available. A review of the supplemental
references indicated in Tables 3-20 and 3-21 would be useful. These references
provide discussions of the phenomena that control the values of the various
rate coefficients, and tabulations of the specific rates found in various field
studies, laboratory experiments, and modeling projects. Table 3-20 also pre-
sents some- indication of the usual range of the various coefficients*
BOD Oxidation and/or Removal Rate (K./K-). In most stream and river waste
load allocation studies, the BOD oxidation rate K^ is of primary importance.
The classical approach to evaluation of this rate is to obtain long-term stream
carbonaceous BODs at various locations. A nitrification-inhibited test procedure
is recommended. A semi-log plot of log BOD vs time of travel has a slope equal
to -K , or in cases where settling, volatilization, or other non-oxygen using
d
phenomena reduce BOD, the slope equals -K . This procedure has been modified
by plotting log BOD vs distance with a slope equal to -Kd/U. Kd may be directly
calculated from the slope and average velocity CU). Further modifications in
the procedure for evaluation of K involve plots of the log of BOD^ vs distance.
The various approaches can yield slightly different values for the BOD oxidation
rate. The values obtained by any of the methods are usually adequate for the
analysis in view of the usual scatter in measured oxygen demand (BOD^ or BOD
ultimate) encountered. In cases where the variation in K^ found with, the several
methods is significant, the approach using long-term BOD vs time of travel is
oreferable. ,_60
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TABLE 3-20. RANGE OF REACTION RATES FOR DISSOLVED OXYGEN ANALYSIS
Reaction Rates
Organic Nitrogen to NH3 (I/Day)
NH3 to NO2 (I/Day)
NH3 to N03 (I/Day)
NO2 to N03 (I/Day)
Setting Rate (I/Day)
BOD Oxidation "Kd" (I/Day)
BOD Removal "Kr" (I/Day)
KL Film Coefficient
Reaeration (Ft/Day)
Range
.COS - .4
.003 - .5
.040 - 2.5
.090 - 10.0
.001 - .1
Usual
Range
.05 - .3
.05 - .3
.05 - .3
.10 - 1.0
.01 - .1
.020 - 3.4 0.10 - 1.0
.020 - 3.4 0.10 - 1.0
1.5 - 50
Reaeration Rate (I/Day) K2 or Ka .1 - 50
1 - 5
Supplemental
References'
31, 34, 35, 9
31,'34, 35, 9
31, 32, 34, 35, 9
31
31
31, 34, 9
31. 34, 9
31, 34, 9
31, 34, 9 (use
formulation)
BODu/BOD5
Temperature correction
factor 6
NH3 Oxidation
Benthic Uptake
BOD Oxidation
Reaeration Rate
1.1
1.0548 -
1.041 -
1.02 -
1.008 -
4.0
1.0997
1.09
1.09
1.047
31
31,
31,
31,
31,
34,
34
34,
34,
9
9
9
Notes: (1) Formulation normally is: Kfi • &204C*
(2) All rates to base "e".
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TABLE 3-21. REAERATION COEFFICIENTS FOR STREAMS
Original Reference
O'Connor and Dobbins
(I9&8)
Churchill, et al.
(1962)
Owens, et al.
langbeln and Durui
(1967)
Isaacs and Gaudy
(I960)
Negulescu and Rojanskl
(1969)
Tslvoglou (1967. 1972)
Tslvoglou and Neal
(1976)
force (1976)
Gloyna. tl aj.. (1971)
formulation for kj (base e) Units of Variables
. Y *n> compatible set of units
1 |0-^
„'•*
U-fps
II til""'6' H-lert
U-fps
., ,U0.67 H-leel
^VBT~ V "/day
7.6U U-fps
~V.lJ H-leet
rpju u-fps
jTr H-leet
" fcj- I/day
/ %0 85 U'fp*
a >alul tl-ltel
'•MU; "?-""•'
(Ah\ Ah- feet
~ I MS*C t-liours
1 / k2- I/hour
0.10.0.I9S1'' MlJii"1"
u-ips
6.B6U0701 "•'««
HT.^T k2-|/d"
(continued)
Drvelnimicnt Conditions
for slrpains displaying lsntrni>ic
turbulence. Ilir observed djla
had Ilir following characteristics.
r-ll 10'. O.S-U'1.6 Ips;
Based on observed reaeratinn rates
below dans from which oxygen
deficient water was released.
2Is.
Oiygen recovery •nnltorpil for sli
Streams in [ngland following
deoiygenatlon with sndlua sulflle.
0. UU-4 fps
Based on synthesis of data Iron
O'Connor and Dobbins (I9SB).
Churchill, et al. (1962).
Krenkel and Grlbb (1961). and
Streeter. et al. (I9J6).
Developed using regression analysis
on data collected from a circular
trough with reclrculatlng water.
Developed fro* a reclrculallnq
Mine with depths less than O.S
feet.
Gas tracer technique used.
2S-Q<*lOO cfs
Gas tracer technique used on
small streams In Kentucky.
0-S 42 fcet/nile
.02
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Table 3-21. REAERATION COEFFICIENTS FOR STREAMS (concluded).
Origin*! Reference
luruulaliun for k, (base »)
Units of Variables
Conditions
Discussed By
IhacLston and Krenkel
(l!tt>9)
O'Connor and Dobbin*
o-ooom i.
V«lid for low velociiut and
Krcnkcl and Orlob
(196*)
nin
9.9.10-
on tritficUt channel
ob&ervaiions.
Thackslon and
Krenkel (I9b4)
Hydroloqic Cmjineer-
Iny Center (19/4)
(1975)
II-ft
Mout:
I. All eipreiilont ylven to base • and for 20°C unleii olherwKe noted
2. Definition of tyinbols:
OH • lolecular diffusion coefficient (B.I-IO"4 ft/hr 0 20"C) for oiygen In naler
U • Stream velocity
II • average stream depth
Ah • change in itrean elevation between two points
t • travel time between two points for which Ah wasured
S • flnpe (chamje in water surface elevation divided by distance)
q • specific discharge (cts per square nlle or drainage area)
DL • longitudinal dispersion coefficient
Uj • bed Shear velocity
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In situations where water quail:? is dominated by waste discharges
from well-operated secondary treataenc plants, the rate of BOD removal
Kr is usually equal to the rate of 303 oxidation K^. For other instances,
settling, volitalization, and other processes may remove BOD without directly
utilizing the oxygen resources of the system. As an illustration, urban
runoff loads from separate and combined sewer systems usually have signifi-
cant organic loads associated with solids. If these solids settle in the
stream or river, all of the observed BOD removed does not use oxygen
immediately. The organics that settle contribute to the oxygen demand of
the bottom, which may be exerted over a time frome of months to years.
Caution should be exercised when attributing BOD removal to settling when the
discharge is from a biological treatment system, in that TSS (Total Settleable
Solids) in such discharges often remain in suspension. This process can be
observed in the semi-log plots indicated previously. The slope of the plot
is initially large and then reduces as shown in Figure 3-3. Normally, the
large slope in the first part of the curve is employed to define K , the BOD
removal rate, while the second lesser slope is assumed to represent K the
deoxygenation rate. As shown on the figure, K > K for the first reach and
K - K, in the second reach. In these situations, observations of the stream
r d
bottom should be made to confirm that settling is responsible for the higher
removals observed in reach one. This confirmation is necessary as other phenomena
may produce similar BOD profiles. Comparable profiles could be observed in streams
where, for example, reach one was characterized by a shallow rocky bottom
stream and reach two was deeper with a silt bottom. In such a case;
&r • Kd in both reaches; the stream geomorphology produces a higher
deoxygenation rate in the first reach. The lower portion of Figure 3-3
3-73
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Revision No
Dissolved Oxygen Model
Segment 1
Segment 2
rmf
Urban Runoff
STP Waste Load
•3
o»
£
S
i
Reach 1
Reach2
- Slope-K,-y
• Slope-Kd-x
TIME OF TRAVEL
K1 Bottle Rate
Streambed
Factor
Stream
ICj Deoxygenation
Rate
Physical
Removal
Rate
(settling, etc)
Overall
Removal
Rate
Figure 3-3. Typical BOO removal curves with settling or other
non-oxygen using processes of BOD removal.
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illustrates schematically the relationship between various components of
the BOD removal rate.
A wide range of values for the carboneaceous (CBOD) deoxygenation rate
(Kj) has been observed in natural water systems. Two fundamental
factors are thought to Influence, or determine the magnitude of this rate
in rivers and streams. These are:
Stream Geometry and Geomorphology
Other things being equal (temperature, reactivity of the organic
compounds comprising the CBOD), the observed net overall deoxygenation
rate along a stream reach should be related to the number of microorganisms
that come into contact with the CBOD constituents. These organisms will
be present both in the water column and on the stream bed as attached
organisms. Under any set of conditions of temperature and reactivity,
the relative amounts of "attached" bacteria on the stream bed represent
the biggest variable from one stream system (or reach) to another.
Their relative numbers can be considered to be related to:
• The area of streambed, which can be defined by the wetted perimeter.
However, the "effective" relative numbers might be thought to include
some expression of the wetted perimeter in relation to the total
volume of water contained in the stream section—this to reflect the
opportunity for contact.
• The cross-sectional area divided by the wetted perimeter is desig-
nated the hydraulic radius (RR)—and is closely approximated by depth
for roughly rectangular streams in which the width is large compared
with depth. For example, where width/depth ratio is 20 or more, R^
is approximated by depth within 5 to 10Z.
• The nature of the stream bed, since this can influence the extent to
which a bacterial population can establish itself, and the stability
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of the population once Initially established. Stable rocky stream
beds are considered to provide more favorable conditions for main-
taining a large, effective population—than are unstable, sandy or
silty channels where hydrologic perturbations are prone to smother
or scour out populations that gain a foothold.
Based on these considerations, the deoxygenation rate (£4) could be ex-
pected to Increase with decreases in stream depth (or the relationships
for which depth is a surrogate) and to increase with the stability of the
stream bed.
Reactivity of Organic Compounds Comprising CBOD
Raw sewage and primary effluent will have a higher proportion of easily
bio-oxidized constituents than would a secondary effluent, which has been
exposed to intensive biological contact. Similarly, application of AWT to
a wastewater discharge can be expected to remove all but the more refractory
organic compounds—so that what remains for discharge to the stream consists
of organic compounds that will be biooxidized more slowly than those dis-
charged where lower levels of treatment are applied.
The reactivity of organic compounds from industrial waste discharges
com rising CBOD would depend on both the level of treatment applied and
the type of industry involved. For example, treated pulp mill effluents decay
at very slow rates, but have high ultimate CBOD /C30D, ratios. Although
u .*
different waste discharges exhibit individual decay rates it is often assumed
the decay rate for the river segment can be represented by a single decay rate.
Considering the number of factors that affect the rate of oxygen utili-
zation in natural streams, all of which are incorporated in the coeffi-
cients, Kd and 1^, it is not surprising that a large range of values has
been reported. It is also apparent why stream surveys are recommended to
quantify site-specific values for these coefficients, in spite of the
expense, time and difficulty of such projects.
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However, the occasion frequently arises when the available resources of
time, personnel and money are inadequate to conduct such a survey and the
question of assigning an appropriate stream coefficient is posed. Even
in a case where a survey is conducted, and the stream coefficient evaluated,
it will only be representative of the flow, loading and temperature at the
time of the survey. The problem then arises of projecting a value that
takes into account the effect of a different condition (higher treatment
levels, drought flow conditions). The difficulty is further compounded
when a development—municipal, industrial or agricultural—is proposed
for a river site on which there is no or little data. In all these cases,
the question of assigning an appropriate coefficient arises.
Figure 3-4 summarizes a carefully screened set of data on stream Kd values
that have been established with high levels of confidence (via well-verified
models).
A definite correlation between Kj and depth is evident in the range of
stream depths between 1 foot and 5 or 6 feet. No data is available at
stream depths less than one foot, and no clear relationship between K.
and depth is indicated for depths greater than 5 or 6 feet. Further, -the
range in potential values for K^ at any particular depth is quite broad—
with about 6 fold differences between high and low ends of the range
being observed.
A suggested relationship is shown by the band placed on the data in this
figure. This is based on an interpretation based on a somewhat crude, but
rational set of empirical rules. The rules have in turn been based on ob-
servations of stream system behavior in terms of K values made by a number
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10
0.3 0.5
1.5
5 10
DEPTH (H) (feet)
50 100
• O'Connor Data (7.39)
O Wright-McDonnell Data (36)
Figure 3-4. Deoxygenation coefficient (Kd) as a function of depth.
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of investigators, and an integration of approaches that attempt to account
for the independent effects of streambed characteristics, and level of treat-
ment reflected in the laboratory bottle rate (Kj).
In the suggested relationship, Kd is shown to be dependent on average
stream depth—over the range of stream depths between 1.0 to 1.5 feet and 5 or
6 feet. For depths less than 1 foot, the value of Kd is made independent of
depth, reflecting the expectation suggested by various investigators that some
limiting value will be reached. In this depth range, the value of Kd within
the range shown will be determined by streambed characteristics, as described
later.
For stream depths greater than about 5 or 6 feet, Kd is also made inde-
pendent of stream depth. In this range the principal determinant of Kd is the
relative biodegradability of the waste, determined for municipal wastes by the
level of treatment applied, and reflected by the laboratory derived reaction
rate (K,). Values for Kj can be determined from long-term BOD tests.
In the 1 to 6 foot depth range, a combination of waste reaction rate (Kj),
and benthic microorganism population, reflected by depth and streambed
characteristics, is important.
O'Connor has proposed an approach (5) that provides a basis for narrow-
ing the broad range of potential values, after estimating the order of the Kd
value from Figure 3-4. His approach provides a basis for making a rational
estimate based on coefficients derived from laboratory tests of the waste,
and background receiving water conditions, such that the stream coefficients
will reflect both of these effects. The framework is similar to procedures
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Chat have been proposed In the past and like them lacks the body of data
required to Independently evaluate the coefficients it incorporates. It
is accordingly not presented as a quantitative procedure—but rather as
a qualitative framework to aid the analyst's judgment in assigning values
for Kd in specific situations.
The approach relates stream deoxygenatlon rates (K^) to (1) the turbulence
of the flowing water, (2) the physical characteristics of the streambed
with respect to the volume of the water in contact with it, and (3) labor-
atory measurements of the BOD oxidation rate (Kj) from BOD bottle tests.
It is emphasized again that the approach is basically qualitative. How-
ever, some of the elements can be determined; long-term BOD tests can
be performed to establish a value or range for Kj, and reconnaissance can
determine the general characteristics of the streambed (e.g., rocky, stable,
intermediate or unstable). Furthermore, estimates of average depth
can be made together with calculations to estimate changes in depth with
stream flow. At worst—with no site-specific information on Kj under any
conditions—such efforts will assist in narrowing the probable range for
sensitivity analyses. This will probably prove to be important in many
cases because the range indicated by Figure 3-4 may prove to be too broad
for practical utility in performing a waste load allocation analysis. In
cases where a site-specific evaluation of K^ has been made under some con-
dition, estimates for other conditions will be significantly enhanced, be-
cause they will reflect the net effect at that site of the streambed factor.
The suggested integration of the three indicated effects is as follows.
The mass rate of reaction, K^LV, may be described in terms of the two com-
ponents, the planktonic microorganisms dispersed in the volume of flowing
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water (V), and the attached benthic microorganisms on the bed
surface (A).
Thus:
KdLV - aKjLV + bLA (3-2)
in which
Kd • overall stream deoxygenation coefficient, I/day
Kj ° BOD bottle reaction coefficient, I/day
L a BOD concentration, mg/1
a a mixing factor
b a streambed factor
V
and dividing through by LV, where H » —
A
b
Kd a aK, + (3-3)
H
Equation (3-3) is represented as a rather crude, but rational, empiricism
that can be used qualitatively to assist in estimating stream deoxygena-
tion coefficients on the basis of bottle rates and the substantial effects
of stream depth and bed conditions.
It is not presented as a quantitative mathematical expression for direct
calculation of K^ values. A rigorous analysis of an adequate data set would
be required to assign values to the coefficients a and b. It is not clear
whether an adequate data base, which includes information on all pertinent
parameters, exists* It has not been assembled to date.
However, while precise values for the above coefficients cannot be assigned,
their order can be inferred from Figure 3-4. If the assumption of an upper
limit to Kj in streams less than 1 to 1.5 feet deep, and dominated by bed
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characteristics, is correct, then values for the bed factor (b) will range
between about 0.8 and 5.0. The value is projected to increase with in-
creasing stability of the bed: O'Connor has suggested a range for (a) of
1.1 to 1.5, increasing with increasing stream turbulence.
The impact of BOD removal and/or oxidation rates that vary between
sources can have a substantial influence on waste load allocations and de-
cision making. The sensitivity of each individual system will be related
to the ultimate BOO load associated with the different sources and the
flow, system geometry, etc. Table 3-22 contains results of calculations
illustrating the influence of BOD oxidation rates that vary with type of
loading. The variations in reaction rates used are within the range that
could be anticipated. The average stream reaction rates calculated by the
two techniques indicated are reasonably close. The average stream K^ is
602 larger than that for load A and 80% of the load B value (Row 1).
Removal of portions of load A would result in an Increase in the average
stream Kj (Row 3), while treatment of load B results in a decrease in the
average stream K^ (Row 2). These calculations employ the basic first-order
BOD equations and do not consider the further complication that K^ may
change as a result of the treatment process. The basic procedures to be
discussed for model calibration and verification will provide a framework
for defining the significance of the differences in reaction rates and a
method for estimating the rates for individual sources if necessary.
Nitrogen Reaction Rates (KR)
The rate of conversion of organic nitrogen to ammonia may be calculated
in a fashion similar to that employed to define BOD removal and oxidation
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TABLE 3-22. ILLUSTRATION OF THE INFLUENCE OF BOD REACTION RATES WHICH
VARY BY LOADING TYPE ON THE CALCULATED AVERAGE STREAM "Kd"
Row
(1)
(2)
(3)
Load
Type
A
A
A<2>
UOD Kj Load
mg/1 I/day Type
5.0 .1 B
3* U • 1 O
2. 5 .1 B
KJ
UOD I/ Day
12 .2
3 .2
12 .2
Average
BODS
vs Time
I/Day
.175
.140
.180
Stream KJ
UBOD
vs Time
I/Day
.16
.13
.17
Notes: (1) 75Z removal of Source B; no change in reaction rate
(2) 50Z removal of Source A; no change in reaction rate
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rates* In this instance, the hydrolizable organic nitrogen fraction
should be employed. If significant quantities of organic nitrogen are
hydrolized to ammonia, then the ammonia oxidation rate can be obtained
only by trial and error calculations comparing calculated and observed
profiles of organic nitrogen, ammonia, nitrite, and/or nitrate. The
comparison of observed and calculated profiles for the oxidized
nitrogen forms is a key element in determining and confirming nitrifi-
cation rates. If nitrate is not formed, considering appropriate mass
balances, the presence and importance of nitrification has not been
demonstrated. Speculation on nitrate removal mechanisms, which almost
balance ammonia oxidation uniformly in space and time, such as bottom
denitrification or plankton uptake, should not be considered as adequate
justification for decisions in waste load allocations projects.
In systems where hydrolysis of organic nitrogen is not significant, the
nitrification rate may be approximated using a semi-log plot of ammonia
vs time of travel. Again, the oxidizable forms of nitrogen are a key
element in demonstrating the existence and importance of nitrification.
Projections of nitrification under future conditions can be characterized
by two basic questions:
• Will nitrification occur?
• If nitrification occurs, what is the rate at which it will occur?
For situations where nitrification is presently occurring, it may be
assumed that it will continue to be present in the future. This assumption
should be used if existing nitrification is confined to the downstream
oxygen recovery zones and present critical- dissolved oxygen levels are
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below approximately 2-3 mg/1, which can inhibit nitrification. Normally,
nitrification is assumed to occur under future conditions at the maximum
observed rates. The "normal" assumptions indicated above should be re-
viewed in the context of the individual stream. As an illustration, cur-
rent theory asserts that nitrifying bacteria may compete most effectively
if they can find sites on particles. Therefore, major differences in sus
pended solids levels, the ratio of wetted area to stream cross-section
or the nature of the stream bed (rocky or muddy), between reaches should
prompt reevaluation of these "normal" assumptions.
For situations where nitrification is not observed under existing condi-
tions, projections should be made with and without nitrification under
future conditions. The processes controlling nitrification are not
sufficiently understood so as to permit definitive projection of the
presence or rate of nitrification in the future if it is not currently
observed. The nitrification projections can be employed in a staged
approach to construction of facilities.
Reaeration Coefficient K
Procedures are available for estimating the reaeration coefficient.
Table 3-21 presents a summary of the formulations that have been developed.
In addition, existing field procedures, such as tracers, can be employed to di-
rectly measure the reaeration coefficient. For each major project, field measure-
ments should be obtained for at least one flow condition over the length of stream
to be studied. A distinction needs to be made between the technique for
measurement of &a and the equations used to project Ka for other conditions
of flow, depth, and temperature. Use of measurement techniques within a
project can be combined with several of the reaeration formulas to make
projections to other conditions.
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Sediment Oxygen Demand (SOD)
Bottom sediments of all rivers and streams utilize dissolved oxygen from
the water column. The range of reported values is presented in Table 3-19.
The oxygen utilized by sediment is associated with decomposition of organic
matter and may also be influenced by oxidation-reduction reactions that occur
in the interstitial waters of deep layers of sediment. Sediments that are
low in organic content can utilize dissolved oxygen at a rate of on the order
2
of 1 gm/m -day., or lower, while sediments with moderate organic content can have an
oxygen utilization rate that is from three to six times this value. Sediment
oxygen demand values above 6 gm/nr-day are usually associated with high organic
sediments that have continual additions of new organic matter. In general,
all waste load allocation projects should consider inclusion of a factor for
bottom oxygen utilization. This may be estimated from visual observation of
the sediment, or by direct laboratory or field measurement of the SOD. Field
measurements employing sediment capping and oxygen utilization data are preferred.
The importance of SOD in a site specific situation may be estimated by
employing the following equation:
Maximum SOD Deficit - S
•\
where: S • SOD (gm/m -day)
H - depth (m)
Kfl- reaeration coefficient (I/day)
For systems with large velocities and high rates of oxidation, the maximum
SOD dissolved deficit may not be reached in the critical region (xfi). The
SOD at this location may be calculated by:
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Deficit from SOD at
TA1
SOD effects should be considered in all waste load allocation studies,
and included in the calculations where these effects will be significant.
Omission tends to result in an overestimate of the benefits from point
source treatment.
Photosynthetic Activity
Plankton, periphyton, or rooted aquatic plants can cause significant
fluctuations in dissolved oxygen concentrations, over the course of a day,
when they are present in a stream reach in large enough concentrations.
Where the magnitude of the diurnal variation is appreciable, violations of
DO standards can occur for part of each day, even though the average daily
concentration may be acceptable. In such cases, the effect of photosynthetic
activity must be considered in performing a waste load allocation. The user
is referred to Chapter 2 - "Nutrient/Eutrophication Impacts" for rivers and
streams for guidance on procedures for incorporating photosynthetic effects
into a waste load allocation study.
Transport. Transport can usually be defined by a series of measurements.
There is a need to develop a reasonable flow balance with, if possible, some
internal checks for consistency. USGS gaging records are sufficiently accurate
for dissolved oxygen analysis and waste load allocations. It may be necessary
to supplement existing gages with flow measurements and bottom cross-section
profile surveys at additional locations. Furthermore, all major studies should
conduct a time of passage study using dye or other tracers. These studies
provide data to confirm flow balances, define stream velocities by reach, define
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the amount of longitudinal dispersion present, and indicate lateral mixing effects
to aid in locating sampling points.
Structuring a Site-Specific Water Quality Model
The essential procedures for developing a site-specific water quality
model consist of a combination of data collection and analysis. A model is
used with the results of these activities to provide the information needed
for projections, waste load allocations, and decisions. The steps in the process
are identified in Figure 3-3. Before discussing each step, it is advantageous
to present some definitions and requirements. Both model calibration and
verification consist of comparisons of observed and calculated water quality
profiles. These comparisons are defined to include:
• Comparisons of all significant water quality variables at the same
time for each data set.
• Consistent loads, rate coefficients, and transport systems should.
be used for each data set and for all segments of a data set.
• Loads, sources, sinks, reaction rates, and transport should be con-
stant in time and space unless systematic variations can be assoc-
iated with definable processes or direct measurements (such as flow,
temperature, etc).
• Comparisons of calculations and observations for two or more dis-
similar conditions are required.
• The comparisons must be carried out on the same space and time scale
that will be used for projects.
To clarify this latter point, steady-state, quasi steady-state and time-
variable models must be compared to appropriate data. As an example, time-
variable models should be calibrated and verified against time-variable data.
This means that data at t=0 are used for initial conditions in the model, and
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(§) Initial assessment
Review
Historlcel
Data
Initial Assessment
1. Water quality problems
2. Important (cxjrcei
3. Important reactions
4. Transport issues
Initial Model Calculations Using
Historical Data to Define Field
Program Conditions
1. Loading conditions
2. flows
3. Temperatures
Define Field Program
1. Conditions of study
2. Variables to be measured
3. Field experiments
4. Laboratory experiments
Model calibration
vo
Modal Rum to Define
Additional Data Needs
Based on Sensitivity
and Projections
Initial Projections
1. Treatment by load
a. Point source
b. Storm
c. Non-point
Define critical water
quality issues
Model Calibration
Compare All Variables
with Consistent
1. Loads
2. Transport
3. Rates
Field
program
Carry out Field &
Lab Program
and Provide Data
Model verification
Carry out Field
Program for
Verification Data
Model Verification
Compare calculated & observed
profiles all variables and cell
data with consistent model
parameters
Define Water Quality Model
for Specific Site
1. Loads 3. Transport
2. Rates 4. Uncertainly
(may include additional
sensitivity runs)
-t> To Waste Load Allocation Slap
Figure 3-5. Steps in development of site-specific water quality model.
SO
ID
V>
•A
O
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comparisons of calculations and observations are made at t°tj, t=t2> £=£3 •••
t=tn, as appropriate. A computer program that solves the stream dissolved
oxygen equations by numerical integration in time should not be considered as
a verified or calibrated time-variable model if steady-state calculations are
used. A time-variable, site-specific model is defined as one that has been
compared to time-variable data.
Initial Assessment
The first three steps in Figure 3-5 contribute to the initial assessment
activity. The historical data are reviewed and employed in conjunction with
initial model runs, which compare calculated and observed water quality to:
• confirm existing or future water quality problems.
• define the loads, sources, and sinks that control water quality.
• define the important reactions that control water quality.
• define issues in the area of stream transport that must be resolved.
This initial assessment is the first step of the process aimed at under-
standing the factors controlling water quality. Sources are placed in the
appropriate category. The specific output from this activity is a defined
field program of data collection that specifically identifies and defines:
• what sources will be measured
• when and at what frequency source measurements will be obtained
• under what conditions of load, temperature, and stream flow will
data be obtained.
• under what seasonal flow regimes transport studies should be
performed.
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• what special studies are required and under what conditions
- sediment oxygen demand surveys
- reaeration evaluation
- long-term BOD studies
- nitrlfier organism counts
- light and dark bottle P-R studies
- diurnal oxygen measurements
- others
Each site-specific problem will require an individual analysis. As an
illustration, consider the following example:
Analysis of historical data using a model indicates that the important
category I sources are: 1) point loads, 2) upstream BOD, and 3) sediment
oxygen demand. Calculations using the model are shown in Figure 3-6.
These suggest that in addition to the usual summer low-flow survey, a
higher-flow survey would provide data that could differentiate the effect
of•the upstream BOD from the point source loads. Furthermore, sediment
oxygen demand measurements will be required. In addition, a fall-winter
lower temperature survey will provide data that differentiate the effects
of the sediment oxygen demand from the upstream and point source BODs.
This can be done because the temperature effect and spatial distributions
of dissolved oxygen deficit are different for sediment oxygen demand and BOD.
In addition, the calculations suggest that the system dissolved oxygen is
sensitive to the reaeration rate; therefore, reaeration experiments with
time of travel are required.
The initial assessment activity is a first full step in understanding
quantitatively the factors controlling water quality. It is not a preliminary
analysis; instead, the initial understanding is translated into a field and
experimental program whose data output begins to challenge and strengthen the
understanding of the system.
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SURVEY "A" CONDITIONS
Dissolved Oxygen
Temp • 25t
Q °200cfs
• Data
— Calculated
/Total DO Deficit
8 12 16 20 24 28
12-
10-
8-
6
4.
2-
0
SURVEY "B" CONDITIONS
Dissolved Oxygen
Temp»10t
Q -400cfs
DO Deficit
8 12 16 20 24 28
2000 Ib/day
2-01 2000 Ib/day
Existing
8 12. 16 20 24 28
8 12 16 20 24 28
8 12 16 20 24 28
8 12 16 20 24 28
Bottom demand
no allocation
0 4 8 12 16 20 24 28
DISTANCE (miles)
8 12 16 20 24 28
DISTANCE (mites)
Figure 3-6. Illustration of the use of calculation to define survey periods.
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Field Program. This task translates the results of the initial assessment
into a practical field program that can be carried out on the river and in the
laboratory using the resources and manpower required and/or available. The
output from these activities is the required data on:
• loads, sources and sinks of dissolved oxygen
• rate studies (deoxygenation and reaeration)
• transport studies
• water quality
More detailed discussions are presented in Section 4.2.
Model Calibration* In these activities, the data from the field program
are employed to define category I sources, reaction rates, and transport.
Water quality calculations using the model are developed for the conditions of
loading, flow, and temperature associated with each of the water quality data
sets. These conditions include those associated with the historical data and
the data collected in the waste load allocation study. Adjustments in the
value of reaction coefficients and category II loads must be made in a consis-
tent fashion for all conditions. The results of these activities are a set of
consistent model parameters, which are then employed to develop water quality
calculations for the conditions associated with all available data sets.
Comparisons of calculated and observed water quality profiles should be
developed. The model runs and calculations employed to search for
and define the series of consistent coefficients should be retained since
they can provide an indication of system sensitivity.
At this stage in the modeling process, a calibrated model has been devel-
oped. The next step involves a test of the adequacy of the model in terms of
decisions required in the waste load allocation study.
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Model Adequacy. Recent research activities (37) in modeling eutrophica-
tion in lakes have begun to explore the use of simple statistical comparisons
in an attempt to quantify model adequacy. These techniques could be a supple-
ment 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
Comparison of Means. 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-probabillty density function is employed
for the comparison of the means.
Regression Analysis. Calculated concentrations and observed data are
considered as paired points in the test equation:
X -a+flC + E (3-4)
a and 0 are the true intercept and slope, respectively, between the calcu-
lated values C and the observed data X. E is the error of X. The regression
analysis assumes that calculated value C is known with certainty and that
the error E is in the measured data X. Of course this is not necessarily
a realistic assumption. Standard linear regression statistics can compute
2
the square of the correlation coefficient r (% variance accounted for) and
the standard error of estimate representing the residual error between data
and model. Estimates of the slope and intercept may be obtained and a test
of significance developed.
Relative Error. Calculated concentrations and observed data are considered
as paired data and the relative error is calculated by:
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x- C
(3-5)
X
The relative error may be aggregated across time or space, and the cumula-
tive frequency of error can be computed. Estimates can be made of the median
relative error as well as the 10% and 90Z frequency of error. This statis-
tic is poorly behaved at the upper tail and at low values of X. The median
error can be easily understood; therefore, if statistical representations
of model adequacy are to be employed in a waste load allocation study, this
is the suggested measure.
Statistical measures of adequacy are in the early stages of research
and should be employed recognizing that they provide, at the very best, a
lower bound on the magnitude of the error.
It is imperative that the adequacy"of the model be tested in the con-
text of the loadings and reactions controlling water quality for each of
the conditions that observed data are available. This can be accomplished
by plotting the unit responses from each category I load for each condition.
Qualitatively, the adequacy of the model is associated with the difference
in magnitude of the water quality response to each source and the relative
impact of each source under the several conditions examined.
As an example, Figure 3-7 contains the results of calculated dissolved
oxygen and dissolved oxygen deficit profiles for two survey conditions.
The first observation is that the dissolved oxygen profiles are different
for each survey and, more importantly, the dissolved oxygen deficit profiles
differ in shape and magnitude. Furthermore, the calculated influence of
the point load discharge (2000 Ibs/day) is almost twice as large during the
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12-i
10-
S? •'
1 6-
§
4-
2-
SURVEY "A" CONDITIONS
Dissolved Oxygen
Temp-25°C
Q = 200cfs
• Data
— Calculated
DO
8 12 16 20 24 28
12
10-j
9
6-
4-
2-
0
SURVEY "8" CONDITIONS
Dissolved Oxygen
Temp-10°C
Q -400cfs
DO Deficit
12 16 20 24 28
2-01
2000lb/day
18 12 16 2024 28
2.0-1
12 16 20 24 28
SB - 1 gm/m'/day
1.0 -i
Sediment demand
no allocation o«.
4 8 12 16 20 24 28
DISTANCE (miles)
I I I I
8 12 16 20 24 28
DISTANCE (miles)
Figure 3-7. Unit responses at two conditions.
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summer low-flow survey, and the maximum deficit is calculated to occur eight
miles closer to the load. In general, the example contains dissolved oxygen
deficit profiles that are different in both magnitude and shape for each
of the source types and which have each source type contributing a different
proportion of the total observed dissolved oxygen deficit at various loca-
tions for the two surveys. If it is assumed that the comparison between
observed and calculated water quality is equivalent for each survey condition,
results comparable to those presented in Figure 3-7 would indicate that the
model has passed one test of adequacy. This test of adequacy of the model
is measured by the diversity of conditions and unit responses rather than
the number of data sets examined. Two data sets obtained under different
conditions can provide a basis for both model calibration and verification.
In contrast to the example illustrated on Figure 3-7, the unit response
for the point load could have been similar under the two survey conditions.
In that case, additional data would be required for model verification
since the level of documented understanding of the point source load under
different conditions would be weak.
The last test of the adequacy of the water quality model is in terms
of the waste load allocation decisions to be examined. In the example, it
could be assumed that the allocation decisions were centered between the
treatment of the point load (2000 Ibs/day) and control of upstream sources.
The analysis has satisfactorily differentiated the effect of the individual
sources and has also quantitatively accounted for what might be an uncontrol-
A
lable source associated with the 1 gm/nr-day bottom demand. A final series
of calculations would include projections of dissolved oxygen with feasible
levels of treatment for each source and include a measure of the difference
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between calculated and observed dissolved oxygen. Table 3-23 Illustrates
preliminary allocation calculations at this stage; the results are plotted
on Figure 3-7.
The basic objective of these calculations is to ascertain that satis-
factory quantitative understanding of the factors controlling water quality
is available to allow waste load allocation. In the example, the waste load
allocation problem is now reduced to an economic and water quality effects
trade-off study between the point source and upstream sources. The measure
of the variation between calculated and observed profiles D(o-c) can be
obtained in one of several ways. If a sufficient data base exists at each
point, the variation in dissolved oxygen can be defined in terms of the
difference between the mean and the individual observations. This assumes
that the model will represent the mean of the observations. Alternatively,
the difference between the model and observed data can be used to estimate
this quantity. The mean of the differences can be used, or for never less
than standards, the 90% or 9SZ occurrence can be considered. Figure 3-8
illustrates a typical method of analysis.
The basic order of the variation (i.e., 0.4 mg/1), and the impact of
uncontrollable sources (i.e., 0 to 2.0 mg/1 sediment oxygen demand
assigned) are reasonable and could be found in many practical situations.
In particular, it is unreasonable to anticipate that the total system
response can be accounted for in terms of measured sources or that the
model output will coincide with every data point. For example, data
collection errors can be significant, and model response is also imperfect.
The procedures indicated above are directed towards developing an
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430/16 Revision No. _0.
TABLE 3-23. ILLUSTRATIVE CALCULATIONS TO TEST MODEL ADEQUACY FOR ALLOCATIONS
Distance
0
4
8
12
16
20
24
28
DB<3'5>
0
.98
1.50
1.77
1.92
2.00
2.00
2.10
D1000
0
.55
.67
.60
.50
.37
.27
.20
CD DI
0
.45
.50
.45
.37
.28
.20
.10
-.75<2> D
—
.4
.4
.4
.4
.4
.4
.4
DEF
0
2.4
3.J
3.2
3.2
3.1
2.9
2.8
DO
8.2
5.9
5.2
5.0
5.1
5.2
5.4
5.4
Notes: (1) 50% removal at point source
(2) 25% removal at upstream sources
(3) No removal
(4) D(o-c), measures of the variation between calculated and observed
profiles
(5) DB: deficit caused by sediment oxygen demand.
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understanding of system responses and testing the resulting level of
knowledge. Variation or modifications of the approach will be necessary
on a site-specific basis. These should be encouraged while retaining
the essential objectives.
3.4 ASSESSING THE ADEQUACY OF MODEL VERIFICATION
In many cases, the procedures discussed in the previous subsection will
indicate the need for obtaining additional water quality data sets under
various conditions of loading, flow, and temperature. This will lead to data
collection activities after the model calibration process, as indicated on
Figure 3-5. This data collection should not be a random effort but should be
directed toward obtaining information under different conditions to increase
understanding of water quality responses and lead to the model verification
activities.
The adequacy of a modeling effort in terms of decisions for waste load
allocations is determined in part by the differences between calculated and
observed data, as measured qualitatively by a visual evaluation of graphic
representations in space and time. Statistical parameters, such as the
median relative error, may also be used. Further measures of model adequacy
are the diversity of conditions for which comparisons of data and calculations
can be made and the ability to make waste allocation decisions. A final consi-
deration is the sensitivity of the calculated water quality profiles to varia-
tions of reaction coefficients.
If calculated profiles are significantly changed by small variations in
the values of reaction coefficients, several additional steps are necessary
to evaluate model adequacy. The value of the coefficient to which the
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calculated profiles are sensitive should be perturbed in a sensitivity
analysis, and comparisons of calculated and observed water quality obtained
for all conditions associated with available data. If the comparisons obtained
in the sensitivity analysis between observed and calculated water quality
"deteriorate" relatively uniformly in a biased manner, using the perturbed
coefficient values, this is usually evidence that the diversity of conditions
under which the model has been tested is large enough to have defined a reason-
able value for the coefficient. If the comparisons do not deteriorate and the
waste allocations change, then data and calculations under different conditions
of flow, temperature, and load should be obtained to assist in defining the
reaction coefficient. In certain situations special field or laboratory
studies, such as reaeration measurements or bottom release rates of oxidizable
substances, may also be of value in defining the coefficient.
Model verification efforts should contain activities similar to those
discussed under model calibration. In general, reaction coefficients and
class II sources should not be altered in the verification analysis. If
changes in these model inputs are required, the changes should be entered
for all data sets including historical, calibration, and verification data.
Only one set of reaction coefficients and category II sources is appropriate
unless documented cause and effect variations can be defined. The Category I
sources are measured with each water quality data set.
Comparison between observed and calculated water quality for all data
sets should be developed. The measures of adequacy discussed under model
calibration are also appropriate for use in the verification activities.
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The next step in Che process is to define a site-specific water quality
model that consists of:
• A single set of model parameters that were developed and used in
the calibration and verification analysis. These parameters should
be uniform in space and time varying only as defined below.
• A set of rules for variation of model parameters in terms of
measured information, such as temperature, flow, loads, geometry,
etc. The rules for variations of parameters should be those used
in the calibration and verification activities.
• A range of values for model parameters that cannot be adequately
defined by a single value. The range of parameters, determined
from sensitivity analysis, should be used in all projections.
• The quantitative and qualitative measures of model adequacy, including
graphs, statistics and appropriate discussions. In most situations,
a quantitative measure of the difference in calculated and observed
profiles equivalent to "D(o-c)n in the example is also required.
Thus, the definition of a site-specific water quality model is developed
in the total context of the calibration and verification analysis. The level
of understanding of the factors controlling water quality is defined in terms
of the assessment of model adequacy. Both strengths and weaknesses of the
analysis are identified.
3.5 ALLOCATING WASTE LOADS
Objective of Waste Load Allocation
The purpose of the waste load allocation analysis is to define the quantity
of waste that may be discharged into a stream or river while meeting the water
quality objectives at the lowest cost. The allocation analysis has application
when two or more sources of waste affect water quality. The sources may be
combinations of point and nonpoint sources or exclusively point or nonpoint
sources, and all or some of the sources may be controlled.
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Definition of the Allocatable Load(s)
The initial requirement is to quantitatively define the critical conditions
of flow, temperature, and in some instances loading (such as wet weather events)
that will control waste load allocations. There may be one or more critical
conditions that should be considered as discussed under the problem identification
section. Traditionally, the critical stream flow is the seven-consecutive-day low
flow, which is anticipated to occur on the average once every ten years. The
critical temperature is usually associated with this summer low-flow period and the
flow and temperature should be consistent. EPA is currently investigating the subject
of design flow and temperature conditions as well as the concept of seasonal WLAs.
It is expected that technical policy guidance will be issued at some future time.
The critical conditions are employed in the calibrated and verified water
quality model to project critical dissolved oxygen profiles. These profiles are
developed, considering the projected wasteloads from all sources. If residual
uncertainties are associated with the model in terms of coefficients, projections
should also be made with the full range of model coefficients. The procedures
discussed in the remainder of the wasteload allocation section should be employed
to examine all the projected dissolved oxygen profiles. These projected profiles
should include the total dissolved oxygen and the unit dissolved oxygen deficit
responses associated with each load and source.
The total dissolved oxygen profile under critical conditions is employed
to define the locations in space and time where the water quality does not meet
standards or creates other water quality problems. A single location in space
and time associated with the minimum dissolved oxygen usually controls the
allocation process. In some instances, several locations in space or time
that are below standards will control the allocation. It should be observed
that questions relating to the frequency of the severity and extent of violations
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(and the appropriateness of specific standards) may become factors to be
considered at some future date. The procedures discussed should be employed
for all critical locations.
The waste load allocation process considers the critical locations(s),
and the saturation value at the critical temperature. The basic procedure
consists of subtracting, from the saturation value, all deficit responses
for sources and processes that will not be allocated and also subtracting
the difference in dissolved oxygen between the model and the observed data.
The water quality objective, such as a dissolved oxygen standard, is in turn
subtracted from the remainder. The resulting dissolved oxygen value is allo-
catable. The allocatable load is calculated by:
Da
La - Dp X Lp (3-6)
where: La - allocatable load (Ibs BOD/day)
Da • allocatable dissolved oxygen deficit (mg/1)
Dp - projected dissolved oxygen deficit at the critical
location from controllable sources (mg/1)
Lp - load from controllable sources used in the projection
for critical conditions (Ibs BOD/day)
Example Allocation Procedure for Single Source
Assume that a waste load allocation study has been performed in which several
data sets have been analyzed by a water quality model, that the model has been
calibrated and verified using procedures described earlier, and that the verifi-
cation is judged to be acceptable.
Assume that the following is indicated by use of the verified model to
project dissolved oxygen impacts in the river under design conditions (future
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point source waste load and critical stream flow and temperature conditions).
• Dissolved oxygen saturation at design temperature (28°C).. 7.8 ng/1
• Dissolved oxygen deficit at critical location
from uncontrollable upstream sources
Initial deficit 0.2mg/l
Oxidation of BOD (2.85 mg/1) 1.0
Oxidation of NH3 (0.15 mg/1) 0.3
TOTAL DUE TO UNCONTROLLED SOURCES 1.5
from point source waste load to be controlled
Oxidation of BOD 3.0
TOTAL DEFICT-all sources 4.5
• Projected minimum DO concentration 3.3 mg/1
Assume further that a statistical comparison of calculated vs observed
dissolved oxygen has been performed as described earlier on all data sets used
in model calibration and verification, using coefficients which were selected
and used in the projection (i.e., the verified model) and that a probability
plot of the absolute difference between calculated and observed concentrations
is as shown by Figure 3-8.
This plot can be considered to represent one measure of the level of
understanding of the system response to the waste loads identified, and in
addition reflects the influences of those factors that are not included in
the analysis and are causing dissolved oxygen variations. It should be cautioned
that, when a test of uncertainty involves comparisons between predicted and ob-
served values, the number and arrangement of sampling stations is critical to the
meaningfulness of the test.
If environmental risks associated with maintenance of a minimum DO concen-
tration of 5.0 mg/1 are considered to be sufficiently great, then the above
probability distribution, which reflects a level of uncertainty in the water
quality projections, may be considered as a basis for assigning a "safety factor"
-------
O
o
1.0
0.8-
0.6
O
Q
2 0.4
1C
Ui
0.2-
0-
NOTE: Data from all survey* u«ed
0.01 0.1 0.6 1 2
5 10 20 30 40 60 60 70 80 90
PERCENT PROBABILITY OF DIFFERENCES LESS THAN
99
09.9 99.99
Figure 3-8. Probability of absolute difference in calculated vs. observed dissolved concentration.
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in the allocation process. If one standard deviation about the mean difference
between observed and calcualted concentration were adopted as the basis for
selecting a safety factor as a hedge against residual uncertainty, then the 84%
probability value represents the dissolved oxygen deficit that would be selected
(842 of the values are less than the mean difference + 10). This criterion re-
sults in a deficit concentration of 1.0 mg/1. Similarly, if the mean difference
were used as the criterion, a "safety factor" of 0.6 mg/1 would be selected.
There are no "rules" that can be assigned to suggest what a reasonable
criterion should be in a particular case. Individual judgment would be required,
taking into account the environmental risk associated with the residual uncer-
tainity as well as other uncertainties in population growth, upstream changes,
etc., and reserve policies. However, the procedure should assist in forming
such judgments by providing a degree of quantification to the issue.
Allocation of waste load for BOD to the point source to be controlled can
then be summarized as follows:
SATURATION CONCENTRATION 7.8
TOTAL DEFICIT AVAILABLE 7.8
DO STANDARD -5.0
DEFICIT AVAILABLE w/o VIOLATION 2.8
DEFICIT USED BY UNCONTROLLABLE
LOADS -1.5
DEFICIT THAT CAN BE ALLOCATED 1.3
LESS RESERVE FOR UNCERTAINTY
IN PROJECTION OF WASTE LOAD
IMPACTS (USE MEAN 50Z DIFFERENCE) -0.6
LESS RESERVE FOR FUTURE GROWTH
(PER REGULATORY AGENCY POLICY) -0.4
DEFICIT TO BE ALLOCATED TO POINT
SOURCE BEING CONTROLLED 0.3 mg/1
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The maximum waste load (BOD) that can be discharged, without exceeding
the DO deficit that has been allocated to the point source in question,
can be readily calculated by the ratio to the deficit caused by the existing
load. Thus, under critical design conditions:
DO Deficit for 40000/day BOD -3.0 mg/1
Allowable waste load - 0.3 x 4000 0/day =» 400 It/day
3.0
In this case, the waste load allocation for the point source in question
would be 400 0/day; a treatment level that provides 90Z reduction would be
required.
It is convenient to observe at this point that "safety factors" developed
in the above manner, based essentially on residual uncertainties in the model
projections of impacts, will in some cases preempt a significant portion of an
otherwise allocatable load. The type of residual uncertainties in projected
impacts addressed by the indicated probability analysis will tend to be greater
when data and data acquisition are limited, and model verification efforts are
constrained as a result. Where the economic impact of providing treatment is
substantially influenced by the magnitude of such an assigned safety factor, and
if environmental risks do not justify neglecting this consideration, then addi-
tional model verification efforts (with attendant data acquisition) may be appro-
priate.
Waste Load Allocations for Multiple Sources
When two or more sources are subject to application of controls, considera-
tions become more complicated. Two types of situations can be identified to
define the required details of the waste load allocation analysis.
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In the first instance, removals of load from any source yields a
comparable water quality response. A comparable load response may be
encountered when:
All sources are geographically close to each other as
defined by the receiving water response.
Reaction rates for different sources vary so that maximum
impacts (such as maximum dissolved oxygen deficits) occur
at the same location.
The contaminant controlling water quality is conservative
or slowly reactive so that impacts accumulate downstream.
An illustration of this latter situation might be nutrients
that are not used by phytoplankton until stream geometry
changes downstream, or NHj discharges that do not nitrify
until a suitable downstream environment is reached.
The second situation is characterized by spatial or temporal variations
in the water quality response from various sources. Variable load response
may be encountered when:
• Sources are displaced geographically so that the contributions
of each load at a critical location are different and not the
maximum response to the load.
• The timing of loading inputs is different for each load so that
water quality is controlled by different sources depending on
time. Illustrations of this situation are associated with the
short-term impacts of wet weather loads from CSO and urban run-
off in contrast to point source loads.
Variable load response can lead to considerations such as: probability
of simultaneous peak loadings and treatment of a group of dischargers as a
"cluster". Cluster analyses are the subject of future guidance documents. It
is hoped individual allocations can be coordinated so that loading restrictions'
impact, on the dischargers, is less than if considered individually, without
compromising the water quality objectives.
The following discussion addresses the comparable load response and vari-
able load response allocation procedures. The waste load allocation analysis
must define which situation exists for a site-specific project.
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RevH ion Mo. 0
^•M^H
Unit response curves developed in the calibration and verification analysis
will provide the necessary information if one or more calibration calculations
were obtained near critical conditions. If not, a series of unit responses at
critical design conditions will be required. If all controllable loads have
essentially parallel deficit responses at critical conditions, then the compara-
ble load response analysis procedure can be employed. If all controllable load
responses are not essentially parallel at critical conditions, then the variable
load response analysis procedure must be used.
The following example is presented to illustrate a comparable load response
situation. The variation in procedure for variable load response situations is
discussed following this example.
Figure 3-9 contains a numerical example of the details of the calculation
procedure for the allocatable waste load. It is assumed that the critical con-
ditions are 200 cfs and 25*C, the loads and responses are shown, and that both
the point source and the load from the upstream source are controllable. The
critical location for dissolved oxygen is in the region of mile point 12, and
the allocatable dissolved oxygen deficit is 1.07 tng/1, with the associated allo-
catable load equal to 1808 Ibs/day.
A formal method of defining comparable load response and variable load
response situations is to compare the ratios of the mass discharge required to
produce one mg/1 of dissolved oxygen deficit response for each source at the
critical location. For the example problem, these load ratios are 1667 and
1738 Ibs/day/mg/1 for the point and nonpoint sources respectively. Therefore,
removal of one pound of BOD from each source yields essentially the same water
quality improvement.
In the foregoing situation, removal of a pound of contaminant, such as
BODc, from any source yields a comparable water quality response. In the
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Revision No.
8 •
% 6 •
1
o «•
O
2 •
0
(
I».
o 1.0 •
uT
LU _ _
0 0.5 •
O
0 o
c
Il5-
h-
5 1.0 •
tL
S0.5-
O
o a
Flow = 200 cfs & Temperature = 25°C
critical conditions)
i Critical Location
Total
) 4 8 12 16 20 24
1.2 mg/8
@ 2000 Ib/day
/ From point load
) 4 8 12 16 20 24
0.62 mg/8
@ 1078 Ib/day
f From upstream load ^""""•••^
Saturation Concentration
Total Deficit Available
DO Standard
Deficit Available
w/o Violation
Deficit Due to
Uncontrollable Load
(Sediment 02 Demand)
Deficit Which Can
Be Allocated
Less Reserve for Uncertainty
in Projection of Waste Load
Impacts (from statistical
analysis of differences of
calculation vs observation)
Deficit to be Allocated
Among Controllable Sources
(point source and
upstream load)
i n i.u/ iinnn * 1 r
>A (1.2 + 0.62) X(2000'1C
LA- 1808 Ib/day
(allocatabte waste load)
mg/S DO
8.24
8.24
-5.00
3.24
-1.77
1.47
-0.40
1.07
178)
u 1.0 •
iZ
O 0.51
O
O n
8 12 16 20 24
1.77mg/e
From bottom demand
04 8 12 16 20 24
DISTANCE (miles)
Figure 3-9. Example of the calculation procedure for allocatable load.
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example the allocatable load is 1808 Ibs/day, which requires a total removal of
(3078 Ibs/day - 1808 Ibs/day) 1270 Ibs per day.
The next issue is that of allocating this load between the sources subject
to control—in this case the point source and the source that is contributing
to what is identified in this example as a residual load entering from upstream
of the specific study area. Various rationales have been considered for resol-
ving such issues, and state or local policy determinations will play a dominant
role in decisions regarding distribution of allocations among separate sources.
Potential approaches to this issue are discussed elsewhere in the series of
guidance manuals on waste load allocations.
Recognizing that solutions that consider only technical issues will not
apply in many cases, an approach to allocation of several loads, based on the
above example, is presented as one possible approach.
The allocation procedure consists of defining the allocatable load as
illustrated and the site-specific cost curves for treatment of each individual
loading source. These curves can then be combined to define a minimum cost.
Figure 3-10 presents an illustration for the conditions examined on Figure
3-9 in the example. The cost curve for the point source is shown as a continu-
ous function. In practice, this might well be piecewise and discontinuous. As
an example, additional BOD removals from a secondary plant of approximately 500
Ibs/day might be associated with gravity filtration; removals of 1000 Ibs/day
would probably require chemical coagulation and gravity filtration, while remov-
als of approximately 1500 Ibs/day might require these unit operations plus acti-
vated carbon. Similar considerations would be appropriate for the nonpoint source
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POINT SOURCE
COST CURVE
0.6-
£0.5-
8 0.3-
f 0.2H
< 0.1-
0
S.15x10*/yr
0 50010001500
B005 REMOVED (Ibs)
NONPOINT SOURCE
COST CURVE
0.6-
£0.5-
8 0.3-
3 0.2-
Z
< 0.1-
0 500 1000
BOD5 REMOVED (Ibs)
IA 0.5-
8
I- 0.4-
f.3H
SOJH
-Minimum Cost
30 50 70
100
REMOVED LOAD
FROM POINT SOURCE (%)
(load requiring removal • 1270Ib/day)
VALUE AT
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curve. This curve might also have a higher degree of uncertainty associated with
both annual costs and performance in terms of BOD removal.
The specific calculation procedure is illustrated for the value at
"A" where the load requiring removal is defined by:
LR - Lp - LA (3-7)
1270 Ibs/day - 3078 - 1808
Where: L^ ° load requiring removal (Ibs/day)
LA » allocatable load (Ibs/day)
Lp • projected load from controllable sources
The value at "A" is for 635 Ibs/day removal from both the point source and non-
point source as shown. Removals and costs are then summed for both loads. A
comparable procedure can be used for more than two loads; the minimum cost region
is shown. This region should be checked to confirm that treatment design is
feasible at the removals required. The allocated load to each source is the
projected load of the sources minus the required removal.
Allocation Procedure for Variable Load Response
The case of a variable load response is characterized by unequal effects
from removal of a pound of BOD, considering two or more sources. Figure 3-11
presents an illustration of the types of unit responses that could be found.
The critical location is shown. Load Wj, which is 4500 Ibs/day, contributes a
deficit of 4 mg/1 at this location. The deficit caused by W2, which is 3000
Ibs/day, is also 4 mg/1 at this location. Therefore, one mg/1 of dissolved oxygen
deficit at the critical location could be obtained by removal of 1125 Ibs/day
of load from source "Wj or 750 Ibs/day of load from source W^. The relative
effectiveness of load removals in terms of load V is:
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Revision No,
10-
ID
X
O-
750^-
mg/2
•£1- Relative Effect -r?H= 1.5^1=-for Same Effect
750 n^lOS
If 00 must be increased by 2.0mg/E there is a need
to remove 2250 Ibs from Wi or 1500 Ibs from W2.
Figure 3-11. Example of variable load response system.
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Relative Effectiveness (W2) °
1125 Ibs/day (W,)
me/1 B 1.5 Ibs/day (W.)
750 Ibs/day (W,)Ibs/day (U-)
mg/1 "
Thus, to obtain the same improvement in water quality, fifty percent more
load must be removed at load Wj as compared to load W2. Cost curves are presen-
ted in Figure 3-12 for each source. Calculations are also presented on this
figure for the total cost curve. In particular, for point (c) on the curve, an
illustration is presented for removal of 1000 Ibs/day of W2 with 500 Ibs/day of
W2 equivalent load requiring removal from Wj. Since the relative effectiveness
is 1.5, the actual removal of Wj load must be 750 Ibs/day as indicated.
It is necessary to determine if treatment at the lowest cost point is fea-
sible from the technical, engineering, and economic standpoint. With a cost
curve shape as flat as that shown in the figure, there is a wide latitude in
selection of the actual design.
If the waste load allocation procedures stop short of the cost evaluation
step, the relative effective ratio can be employed to define allocations between
sources. In particular, take as an example the calculations for point (c) with-
out regard to costs:
1500 Ibs/day of load W2 equivalent removal is required
overall as shown by the assumptions on Figure 3-11.
Assume 1000 Ibs/day of W2 removal is to be provided.
The WJ load that must be removed is (1500 - 1000) Ibs/day - 500 Ibs/day
as equivalent (W2) load. Since the effectiveness ratio is 1.5, the W^
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0.6-
0.6-
1000 2000 3000
B005 REMOVED
FROM W2(lbs)
1000 2000
BODS REMOVED
PROM W, (lb$)
i
0.6-
0.5-
0.4-
0.3-
0.1-
30 50 70
100
LOAD REDUCTION REQUIRED
FROM LOAD SOURCE W2 (%)
POINT0 1500lbs removed from W2
Zero removed from Wi
POINT(§) Zero removed from W2
2250 IDS removed from W,
POINT© 1000lbs removed from W2
750 IbsMl removed from W,
(I)NOTE. 1500 lb» required (W2)
- 1000 Ita remoMed (W2)
500 Ita (W2I
Equivalent Wi Ibs
(W Ihs \
wilbT)
750 Ibs requiring removal
Figure 3-12. Example of allocations for variable load response system.
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removal required is:
Wj removed ° 500 Ibs/day as equivalent (W2) load X
1.5 Ibs/day (W,) - 750 Ibs/day (W,)
Ibs/day (W2)
and Che allocations for Wj and W2 are:
3750 Ibs/day (W,) = 4500 Ibs/day (W,) - 750 Ibs/day (W,)
2000 Ibs/day (W2) - 3000 Ibs/day (W^ - 1000 Ibs/day (W2)
The procedures indicated above would have to be applied for all loads
and at any critical locations or times as required in a site-specific
analysis.
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SECTION 4.0
TECHNICAL CONSIDERATIONS
4.1 WATER QUALITY PROBLEM DEFINITION
General
A discussion of the water quality problem to be addressed by the WLA
will serve a number of useful purposes. For officials or agencies responsible
for reviewing the WLA study and with making or approving decisions, the problem
discussion can provide a clear summary of the nature, extent, and significance
of the problem, and thereby provide a basis for comparing the changes to be
achieved by adopting the WLA. An effective problem definition can also help
the technical staff performing the WLA study to keep the important issues in
focus during the progress of the effort, to determine the most appropriate
modeling approach and data needs, and to evaluate the significance of uncer-
tainties in the modeling analysis.
In this discussion, it is assumed that the broader aspects of the problem
identification tasks (discussed in Book I) have resulted in a determination
that BOD/DO impacts will be the focus of the WLA. The additional detail neces-
sary to define the pertinent aspects of such problems is discussed here.
"Problem definition" is a task that persists throughout the WLA effort and
is refined and updated at different points during the program. This orientation
will help to maintain focus on the underlying objective: to develop a sufficient
understanding of the receiving water system and its responses to waste loads,
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which will permit sound decisions on WLAs and appropriate levels of treatment.
The early tasks In a phased problem definition effort will help to direct sub-
sequent work elements. The final product of this task becomes: (1) a clear
description of the "problem"—its nature, magnitude, and spatial and temporal
characteristics; (2) an indication of how the waste load being allocated is
related to the problem; and (3) a description of how the allocation selected
will modify the problem.
Problem Definition Phases
Several phases will be involved in problem definition at increasing
levels of refinement and detail, each involving attention at different stages
of the WLA effort and drawing on information developed during prior tasks.
Four phases are outlined below. The number of phases may vary depending
on the local situation; therefore, the summary should be considered illustra-
tive of several stages in a single process. Results from each of the phases
will be aggregated and consolidated for the final output of the problem defini-
tion task.
Initial Phase. The principal purpose is to direct and focus the WLA
study. Principal tasks involved in initial problem definition include the
acquisition and analysis of historical data, i.e., water quality, stream flow,
and waste loads, and possibly some simple impact analysis or dilution calcula-
tions. Any "qualitative" expressions of a problem (other than through numeri-
cal water quality data) would also be recorded.
The initial problem statement should also identify those factors other
than water quality that will enter into the WLA process. Projected changes in
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population, and in development of the area, which would result in increases
in raw waste loads or the introduction of new sources of load, should be
identified and the level of uncertainty associated with such projections
discussed. Also, any policy or policy alternatives relating to reserve
allocations should be identified. A preliminary indication of the future
date when waste loads are proposed to be allocated should be made.
The product of this effort would be the identification of the type of
water quality problem to be addressed by the WLA (for purposes of this
chapter, BOD/DO problems are selected). Tabulations or plots of data and
other pertinent descriptions would be furnished in support of the deter-
mination. Population or industrial growth projections, and existing or
potential policies on reserve allocations would be discussed.
Preliminary Phase. The purpose of this phase is to define important
details that will influence certain aspects of the monitoring and modeling
effort. The principal tasks would include a preliminary impact assessment
similar to that described in the Areawide Assessment Procedures Manual,
Chapter 2 (29) and waste load projections. Available data and estimates
or assumptions would be used where necessary, as would the results and
observations from a reconnaissance survey.
The preliminary assessment should also examine the sensitivity to
uncertainties in population growth, allowances for introducing new load
sources to the area, or to alternate decisions on the amount of allocatable
loads that Vill be held in reserve.
The product would include the following types of information. The spatial
scale of the impacts would be defined, so that monitoring station selection
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will provide adequate coverage. The relative significance of impacts under
different flow or temperature regimes and the relation of current flows to
future drought flows to be selected as a design basis will provide information
on most appropriate times for conducting monitoring surveys. Other factors of
potential importance should be identified, for example, other significant load
sources, benthal deposits, algal activity, etc.
Problem definition at this stage should provide confirmation or modifica-
tion of the initial assessment and furnish additional detail. Results should
be used to help ensure that the monitoring program is structured effectively
and that the model selected can address all the load sources and influences
of importance. Results would also be used to determine the need for refined
growth projections or discussions relating to reserve allocation policies.
Interim Phase. During this phase, problem definition becomes a refinement
of previously developed problem statements. It would draw on data developed
from monitoring efforts performed to that point, and principally on any
insights or understanding of the system and responses derived from model
calibration efforts. Examples of the type of refinement that might be
developed at this stage would be a modified evaluation of the relative
significance of a point source load in relation to sediment oxygen demands,
upstream boundary loads, or the significance of diurnal DO fluctuations due
to algae on violations of DO standards.
Where appropriate, the results would include a clearer appreciation of
the relative significance of the load to be controlled on the water quality
problem, and possibly the identification of specific monitoring tasks to
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provide information on important other sources (e.g., diurnal DO measurements
or benthal Q£ uptake).
Final Phase. The final product of this series of tasks would be a
description of the "problem," supported by the pertinent data and analysis
results developed from historical records and WLA efforts. It should describe
the conditions (present and future) under which specified impacts can be
expected to occur, quantify the range of uncertainty based on calibration/
verification of the model, and identify the changes in water quality impacts
to be expected by the recommended WLA. It should further describe the effect
of alternative growth levels, and/or reserve allocation policies on the
recommended WLA.
Specific Steps in Problem Definition
The following tasks should be included in the development of a defini-
tion of the problem being addressed by the WLA and the detailed characteriza-
tion of its important aspects. Several iterations, following the phases
approach described, should be performed.
Beneficial Use. Identify the beneficial use or uses designated for the
affected stream segments. This is often associated in a general way with the
stream segments' formal "classification;" however, for the purposes of a WLA
study, a more specific description of stream use, either existing or intended,
should be made to the extent possible. Examples of such additional detail
would include actual use by the public, location of recreational or water
intake sites, etc.
It is important to go beyond a simple recitation of a list of "uses"
associated with a particular stream classification because decisions that
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have some uncertainty must address the associated risk. The nature of the
actual use, the local importance assigned to it, and the effect (permanent
or temporary) all affect the risk and the decisions regarding load alloca-
tion. The value of such beneficial uses may often be qualified (if not
quantified), for example, by the revenues generated to a local economy from
sport fishing and support activities.
Water Quality Standards. Identify the water quality standards (in this
case DO concentrations) that have been established to protect the assigned
beneficial uses. Describe the standards in enough detail to permit subsequent
evaluation of violations. For example, DO standards may be expressed as any
one or all of the following:
• mean concentration
• minimum concentration
• % saturation
• statistical—e.g., % time a specific concentration may occur
Analyze Historical Data. Review, summarize, and interpret available
i
historical data, and compare with water quality standards. The data of
importance include stream flow records or estimates for the segments of
concern derived from nearby gages; stream temperature records; waste load
levels for the discharge in question and for other relevant sources; and
operational procedures for regulated streams.
Water quality data should be secured from STORET, from reports or studies,
or other available sources. It is generally best to sort the record in ways
that will assist interpretation, for example:
• Spatially. Stations upstream and downstream of the discharge point,
with adequate station coverage for the spatial scale of BOD/DO
reactions. In preliminary evaluations, consolidation of records
from nearby stations may assist and simplify initial screening.
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• By flow regime. Where record can be sorted between periods of
high and low flows, interpretation will be aided.
• By temperature, wet vs. dry periods, etc. to the extent possible
by the nature of the available data.
Where data are in STORE!, the use of several retrievals, rather than a single
one, can assist in performing the above type sorting.
Preliminary Impact Analysis. Perform preliminary screening analysis
using information on loads, flows, temperature, etc. developed from historical
data review, and preliminary estimates using a range of coefficients for
sensitivity tests. Compare preliminary projections under existing conditions
with historical data to identify the extent to which the waste load in
question is likely to account for the observed water quality impacts.
Using population and growth projections, and critical stream flow/
temperature condition(s) being considered for use in WLA decisions, make
preliminary projections of impacts expected under such conditions.
Reconnaissance Survey. During a reconnaissance survey of site sampling
stations for the intensive survey program, look for evidence of other influ-
ences that could be potentially significant in a DO analysis. For example,
is there evidence or reason to believe that sediment oxygen demand might be
significant in some reaches? Are there any obvious NFS loads or significant
tributary inflows that might affect water quality during dry weather or wet
weather, when such conditions cannot be sorted from the historical data set?
Define Problem. From the analysis of historical data, the preliminary
impact analysis, the reconnaissance survey and other available evidence, develop
as detailed a description of the "problem" as is. possible at that stage of the
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study. In addition, identify the factors that should be addressed or refined
further in subsequent program tasks. These could include refined estimates
of future load projections, other pertinent load sources to be covered by the
monitoring program (e.g., sediment oxygen demand), tributary flow and quality
data, etc.
Several levels of problem description should be incorporated in the pro-
blem definition because the distinctions may be important in subsequent judg-
ments regarding the VILA. They may further assist in prioritizing future
actions among a number of separate WLAs.
• Public perception and concern. Is there a general public recogni-
tion of a problem, and an active interest in its resolution (fish
kills, closed beaches, etc.).
• Actual use impaired. An active current use assigned to the stream
is being denied, impaired or threatened (recreational fishery being
degraded, restricted use of beaches, etc.).
• Violations of standards. Water quality standards associated with
the water segment classification are violated, or projected to be
violated. Violations may be indicated by historical data, projected
to occur based on preliminary screening, or projected co be possible
by preliminary screening and confirmed by model calibration/verifica-
tion.
The problem should be described in as much detail as possible, including
discussion of the magnitude, location and frequency, and, to the extent pos-
sible, the conditions under which the problem will occur.
4.2 DATA REQUIREMENTS
Introduction
The type and amount of data available for performing a waste load
allocation will determine the confidence that can be placed in projections
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of the effects of different decision alternatives. Depending on the adequacy
of available historical data and the risk (environmental and economic)
associated with uncertainty in projected impacts due to limitations in histor-
ical data, one or more intensive surveys may be required. It is preferable to
consider which type of model will be used in the WLA ar the earliest stage of
the data collection effort, since the choice of model will affect data needs.
The objective of data acquisition in a WLA study, whether from a search
of historical records or from additional field surveys, is twofold.
• To provide a sound basis for assigning rate coefficients
and other critical input values, such as stream geometry,
loads, etc., which relate to the specific site being
examined.
• To contribute to the development of an understanding of
how the receiving water system responds to various load
Levels and sources. This is achieved through the use of
data in the calibration and verification of water quality
models.
The methodology described in this manual recommends that an initial
or preliminary impact assessment be performed using available historical
data. Among the benefits of such a calculation is the information it will
provide to assist in structuring intensive surveys or other data acquisition
activities for the WLA study. The collection of new data should emphasize
those areas where the greatest uncertainty exists, and where WLA decisions
are sensitive to the values selected. Examples of such information include
the following:
• waste loads (sources) that should be monitored
• the flow regimes at which transport studies are required
• the most appropriate conditions under which intensive stream
surveys should be performed (waste loads, stream flow,
temperature)
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• the spatial coverage that should be considered for station A
• special studies that may be required
Methodologies for performing such initial assessments are described in
some depth in both the Areawide Assessment Procedures Manual (AAFM, 29), and
in Water Quality Assessment: A Screening Method for Non Designated 208 Areas
(38). In addition to providing a preliminary screening to aid in the design
of an effective monitoring program, these methodologies can also be used to
provide estimates for Category II loads, which will not be monitored.
In addition, Chapter 2 of the AAPM provides information on sources of
historical data that should be searched, as well as Instructions for access
to some sources. Appendix D of this document presents general guidelines on
station location (Part I). It also includes a Parameter Handbook (Part II)
that presents a concise summary of enough salient information about each
water parameter to aid in decisions concerning the likelihood of the constitu-
ent's presence in a particular stream or discharge and its effects on water
quality or use. It discusses factors pertaining to sampling and analysis of
the constituent that should be considered in determining the ramifications
of including the parameter in a water quality monitoring program. It also
presents information on analytical methodology, including sample quantity
and preservation and handling considerations.
The material that follows in this section presents more specific
guidance and recommendations pertaining to data requirements for WLA that
address BOD/DO problems in rivers and streams. It should be evaluated in
conjunction with the broader information and guidance referenced above.
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Sample Station Location
Spatial plots of historical or calculated water quality should be
developed by the initial assessment for a set of flow regimes of interest.
One of the conditions analyzed in this manner should be current loading
conditions and "typical" stream flows (i.e., those flows expected to pre-
vail during proposed intensive surveys). These plots, together with
observations made during a reconnaissance survey, should provide the basis
for establishing the location of field sampling stations. The number and
location of sampling stations will be controlled by site-specific factors,
including access to the stream and other logistic issues as well as the
cost of sampling. Normally, a minimum of four sample stations should be
considered with maximum distance between stations on the order of one-half
to one day's travel of water time. This represents a minimum requirement,
applying to the simplest of WLA stations; for example, a single discharge
to a perennial flowing stream, where the ^QjQ flow is greater than the
discharge flow, and there are no significant tributaries downstream.
Figure 4-1 illustrates three situations that contain typical issues
encountered when defining the location of sampling stations.
In illustration I, there is a single waste discharge station with no
tributaries. This is a typical situation when the minimum of four sampling
stations is usually adequate. Sampling station A is employed to define
upstream water quality while stations B and C define the dissolved oxygen
response to the load. Station D provides information in the recovery
zone, which is dominated by reaeration, and may be examined for nitrifi-
cation and/or increased diurnal dissolved oxygen variations.
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DISTANCE
DISTANCE
III
DISTANCE
Figure 4-1. Sampling station locations.
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In Illustration II, several tributaries are shown to enter :he system
downstream of the discharge. Sampling stations A through D serve the same
functions as indicated in illustration I. One additional sanpLing station
is located on the major tributary. Minor tributaries need not be sampled.
In this instance, minor tributaries are defined in a manner similar to
category II load sources, i.e., they have a small influence on water
quality; and errors in assigning the quality in the tributary will not
influence the waste load allocation. A sensitivity calculation conducted
in the initial assessment analysis could provide the information necessary
to distinguish between major and minor tributaries. The category I source
"Wj" and major tributaries should be sampled before and during each survey
in both illustrations I and II.
Significant sources of waste load (i.e., category I loads) are sampled
one or more days in advance of the instream monitoring during an intensive
survey in order to ensure that, given the time of travel to the most down-
stream station, an accurate estimate of the waste load that affects the
stream sample is available. In a true steady-state condition (i.e., constant
waste loading rate and constant stream flow), this would not be important
since any single measurement would represent all conditions during a steady-
state period. Normally, however, the conditions selected will not reflect
a true steady-state condition, but rather an acceptable approximation of
one. The greater the likelihood of appreciable fluctuations, either in
waste loading or more probably in stream flow, the greater the attention
that should be given to lagging monitoring of waste loads and stream
samples. In addition, where the likelihood of such fluctuations is high,
increases in both the duration of an intensive survey and the number of
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samples collected per day for averaging, in excess of those recommended
later in this section, should be considered.
Illustration III presents the added complexity of multiple waste
sources entering the system. In this instance, sources "Wj" and "t^" are
category I sources and should be sampled, while "Wj" is assumed to be a
category II source and need not be sampled during each survey. It should
also be noted that sampling stations B through E are located to provide data
on the overall water quality response of the stream or river and are not
located adjacent to and immediately downstream of individual inputs, such as
sources or major tributaries. The objective of the water sampling program
is to define overall system response to waste loads. Apart from the fact
that a significantly larger number of sampling stations would be called for
.in such a case, it is a very unique situation when upstream and downstream
measurements around a load or tributary can provide meaningful data on the
overall dissolved oxygen response of their system. This results from the
time and space scale over which dissolved oxygen changes tend to occur.
Where the appropriate shape of the dissolved oxygen sag curve, indicated by
historical data or calculated in the initial assessment, is such that it
covers an extended stretch of river (as illustrated here), additional
sampling stations should be established along the main stem.
Water Quality Variables and Frequency of Sampling
In general, the water quality variables and the frequency of measurements
obtained during a survey will be defined by site-specific water quality problems
and system responses. The following comments are offered to provide some
assistance in defining the details of water quality sampling programs.
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It is neither necessary nor cost-effective to analyze every variable to
be measured during a water quality survey with the same frequency at every
sampling station. One overall approach to defining the variables to be
monitored and frequency of measurement is to structure the water quality
survey in the context of the following "two key questions":
• How are the measured values of this variable to be used in detail
in the waste load allocation analysis?
• Would the waste load allocation decisipn be expected to change if
this variable were either not measured or measured less frequently
or at fewer stations?
Supplemental questions that assist in this process are:
• What is the specific relationship of this variable to the water
quality problem?
• What is the anticipated variability of this variable?
• What is the anticipated response time of the system to changes in
value of this variable?
There are several contexts in which site-specific dissolved oxygen problems
can be encountered. These are:
• Dissolved oxygen dominated by CBOD oxidation
• Dissolved oxygen dominated by oxidation of both CBOD and NBOD
• Dissolved oxygen dominated by diurnal fluctuations and oxidation
of BOD.
Table 4-1 provides an indication of the minimum survey duration, number
of measurements, and percent of stations that could be sampled as a function
of the water quality variable and dissolved oxygen problem context. The
information in this table is for a minimum effort where relatively low
capital and/or environmental risks are associated with a site-specific
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TABLE 4-1. SUGGESTED MINIMUM SAMPLING REQUIREMENTS
Variable^2*
Dissolved Oxygen
Temperature
pH
BOD5
BOD5
UOD
UOD
Organic-N
NH3
N03
N02
Flow
Time of Travel
Velocity and Depth
Reaeration^ '
Bottom Demand' '
Light & Dark Bottles
Diurnal
Nitrifier Counts<4)
DO Problem
Context
All Problems
All Problems
All Problems
CBOD
CBOD & NBOD
CBOD
CBOD & NBOD
CBOD & NBOD
CBOD & NBOD
CBOD & NBOD
CBOD & NBOD
All Problems
All Problems
All Problems
All Problems
All Problems
Eutrophication
Eutrophication
NBOD
of Survey
2 Days
2 Days
1 Day
2 Days
2 Days
—
—
2 Days
2 Days
2 Days
—
2 Days
—
2 Days
—
—
1 Day
1 Day
~
'' Number of
Measurements m
2 /Day AM/PM
2/Day
I/Day
I/Day
I/Day
Once
Once
I/Day
I/Day
II Day
Once
1-Day
Once
I/Day
Once
Once
—
—
Once
Z of (:
Sampling
Station
100Z
100Z
100Z
50-100Z
50Z
50Z
SOZ
50-100%
100%
100%
25Z
1 Sta.
100Z
100%
100%
100%
50%
50%
50%
Notes: 1. Suggested minimums should be increased for more complex pro-
blem settings.
2. Other variables may be added, SO^, TOC, COD, etc.
3. Source measurements add one day before survey.
4. Contingent on problem setting and available funds.
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allocation. A more normal level of effort would provide twice the minimum
number of measurements per day at all sample stations.
In general, our level of confidence in understanding system responses
and, hence, in decisions on waste load allocations increases with the amount
of data available for analysis. However, more important than the absolute
number of data points are the specific contaminants included, whether they
are measured concurrently, the spatial coverage, and the times and conditions
under which the date were obtained.
It has been suggested that the equivalent of two independent data sets
will normally be required in what has been characterized as the typical or
"base case." A good set of historical data will often satisfy the require-
ment for one of these sets. As discussed in the manual section, which addresses
"Level of Effort" (Section 1), specific circumstances may justify lesser,
or require greater, amounts of data. The criteria to be applied in determin-
ing the number of data sets and the amount of data in any set would include
the capital costs involved, the environmental risk associated with WLA deci-
sions, the adequacy of model calibration and verification, and the sensitivity
of the decisions to be made on the residual uncertainty in the prediction of
water quality responses.
There may be site-specific justification for including measurements of
additional variables such as TOO, COD, suspended solids, toxics, heavy metals,
the phosphorus series, chlorophyll, SO^, Alk, Na, Ca, etc. These can
materially increase the cost of analysis and data handling/reduction. Use of
the "two key questions" approach will provide some insight into the value of
measuring additional variables.
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4.3 QUALITY ASSURANCE FOR WASTE LOAD ALLOCATION STUDIES
As used here, quality Assurance (QA) Is a system of activities
used to provide documented assurance that a data product of known and accept-
able quality is being produced.
The importance of QA should be evident; however, because of the additional
effort it requires in advance planning, management, supervision, and re-
sources, it is often neglected or overlooked. This manual has addressed, at
some length, guidelines for the analysis of data that will lead to the per-
formance of technically sound, defensible WLA studies. It is imperative that
any data secured, on which such analyses are based, be adequate and defensible,
i.e., of proven and acceptable accuracy and precision. This is particularly
important where decisions having serious economic and environmental import
will be based on the results of the WLA study.
A properly planned and implemented QA program will enable the substanti-
ation of data accuracy and precision by an outside impartial review, and fore-
stall any attempts to discredit or impeach the data that are produced. This
section is intended to outline the minimum QA effort that will be required
to ensure a reliable WLA study. Thus, its aim is to assist the user in de-
veloping a reliable and effective Quality Assurance program that will meet
data user requirements for completeness, precision, accuracy and comparability
of data. The Quality Assurance requirements are minimum and are not to be
viewed as complete. They are presented rather as a foundation upon which the
user can build a viable QA program.
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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 reproducibility (repeatability) of the
measurement, when repeated on a homogenous, time-stationary measurand, re-
gardless 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, mode, etc) 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 observations, 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 with an establishable relationship between the magnitude 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 re-
spect to the particular condition that is suspect. In the method of substi-
tution, the object of measurement is replaced by one of known magnitude (a
calibration standard); an instrument with a known calibration curve is sub-
stituted for the measuring instrument in question, and so on. Thus, system-
atic errors bear heavily on the accuracy of the measurement.
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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 their chief characteristics is that they 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 assur-
ance 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 mea-
sure of the confidence placed in this determination.
Elements of a QA Program
The basic elements of any quality assurance program include the
following:
• Management's commitment to provide resources necessary to
implement quality assurance activities (approximately ten to
twenty percent of total water monitoring resources)
• Designation of a quality assurance coordinator responsible
for coordinating and implementing 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 4-2. The wheel arrangement illustrates the'nature
of a quality assurance system that will address all elements and at the same
time allow program managers the flexibility to emphasize those elements
that are most applicable to their particular program. Quality assurance
elements are grouped on the wheel according to the organizational level to
which responsibility is normally assigned. These organizational levels are
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Statistical Analysis
of Data
Procurement
Quality Control
'otic
Figure 4-2. Quality assurance elements and responsibilities
(the quality assurance wheel).
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Che quality assurance 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 are achieving the desired program objectives.
The following specific elements are suggested to be minimal require-
ments for structuring a QA program for a WLA 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
responsible for the quality assurance program, and specify proper
sample collection, use of approved measurement techniques, cali-
bration standards and their verification, internal quality control
practices, and appropriate data management controls.
• An estimate of costs associated with the quality assurance program
in terms of percentage of overall project cost should be developed.
Normally, a minimum of 10 percent of the estimated sample collec-
tion and analyses costs will be necessary for adequate quality
control.
• A program for demonstration of acceptable performance through the
use of audit samples should be established and utilized throughout
the duration of the study.
• Provision should be made for performing on-site field and labora-
tory audits at the option of and on a schedule established by the
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 performance should be submitted
with the final report and otherwise as directed by the Project
Officer.
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 categories: water chemistry (laboratory), field data
collection, and data handling and reporting.
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Minimum QA Requirements for Water Chemistry;
• Quality control management manual
- Outline of Quality Assurance program objectives
- Outline of the administrative structure of the laboratory (in-
cluding an organizational chart)
- Clear identification of the responsibilities for implementing
the specific quality control activities
- Commitment of resources by management to implement the necessary
quality control activities
- Description of laboratory training program
- Designation of a laboratory quality assurance coordinator, In-
cluding a statement addressing coordination responsibilities and
duties
• Laboratory operations manual
- Description of analytical methodologies and procedures
- Description of laboratory quality control activities
- Description of the laboratory's internal chain-of-custody
procedures
- Description of general laboratory requirements
- 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
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Revision NO. u
Minimum QA Requirements for Field Data Collection;
• 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 procedures:
chain-of-custody
• Collection of samples/field investigations
Minimum QA Requirements for Data Handling and Reporting:
• 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
4-27
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ii m
Revision No. 0
REFERENCES
1. Hunter, J.S. 1979. Accounting for the Effects of Water Temperature in
Aerator Test Procedures, Proceedings: Workshop Toward an Oxygen
Transfer Standard, EPA 600/9-78-021.
2. Tetra Tech., Inc. 1978. "Rates, Constants and Kinetic Formulations in
Surface Water Quality Modeling," EPA - 600/3-78-105.
3. Leopold, L.B., and T.G. Maddock. 1953. The Hydraulic Geometry of
Stream Channels and Some Physiographic Implications, USGS
Professional Paper 252.
4. Willingham, William T., Ammonia Toxicity. 1976. EPA 908/3-76-001.
5. Manhattan College. 1980. "Mathematical Modeling of Natural Systems,"
Manhattan College Summer Institute Notes.
6. Fischer, H.B. et al. 1979. Mixing in Inland and Coastal Waters,
Academic Press.
7. 0'Conner, D.J., and Hydroscience, Inc. 1971. "Simplified Mathematical
Modeling of Water Quality," Water Programs, EPA, U.S. Government
Printing Office, 1971, 444-368/392.
8. "Effects of Polluting Discharge on the Thames Estuary." 1964. HMSO,
Water Pollution Res. Tech., Paper No. 11.
9. O'Connor, D.J., and Hydroscience, Inc. 1968. "Water Quality Analysis
of the Mohawk River - Barge Canal."
10. Thomann, R.V. 1971. Systems Analysis and Water Quality Management,
Environmental Research and Application, Inc.
11. U.S. Environmental Protection Agency, Office of Air, Land,.and Water
Use and Office of Research and Development. 1976. Evaluation of
Water Quality Models: A Management Guide for Planners, EPA-
600/5-76-004.
12. Texas Water Development Board. 1970. DOSAG-I Simulation of Water
Quality in Streams & Canals. Program Documentation & Users Manual.
EPA OWP TEX-DOSAG-1, 58 p., PB 202 974.
13. Braster, Robert E., S.C. Chaptra, G.A. Nossa. 1975. SNSIM-1/2 A
Computer Program for the Steady State Water Quality Simulation of
a Stream Network. 4th Edition, 56 p., PB 241 923.
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Revision No. 0
14. Roesner, L.A., J.R. Monser, D.E. Evenson. 1973. Computer Program
Documentation for the Stream Water Quality Model, QUAL-II, Water
Resources Engineers, Inc.
15. Roesner, L.A, P.R. Giguere, D.E. Evenson. 1977. "Computer Program
Documentation for the Stream Quality Model QUAL-II, prepared
for the Southeast Michigan Council of Governments by WRE.
16. Texas Water Development Board. 1971. Simulation of Water Quality in
Streams & Canals. Theory & Description of the QUAL-I Mathematical
Modeling System. Report No. 118, EPA OWP Tex 128, 62 p., PB
202 975.
17. Texas Water Development Board. 1970. QUAL-I Simulation of Water
Quality in Streams and Canals. Program Documentation and User's
Manual. EPA OWP Tex-QUAL-1. 102 p., PB 202 973.
18. Raytheon Company. 1974. New England River Basins Modeling Project,
V. Ill - Documentation Report, Part 1 - RECEIV II, Water Quantity
and Quality Model.
19. U.S. Environmental Protection Agency, Office of Research and Develop-
ment. 1975. Storm Water Management Model Users Manual, Version
II, EPA-670/2-75-017.
20. Armstrong, N.E. 1977. Development & Documentation of Mathematical
Models for the Paraiba River Basin Study, Vol. II - DOSAGM:
Simulation of Water Quality in Streams & Estuaries, Univ. of
Texas, Austin.
21. Duke, J.H. Jr., and F.D. Masch. 1973. Computer Program Documentation
for the Stream Quality Model DOSAG3, by WRE for Systems Develop-
ment Branch, EPA, Contract No. 68-01-0708.
22. Johanson, R.C., J.C. Imhoff, and H.H. Davis. 1980. Users Manual for
Hydrological Simulation Program—FORTRAN (HSPF), EPA-600/9-80-015.
Environmental Research Laboratory, Athens, GA 30605.
23. Wu, Jy. S. & R.C. Ahler. 1979. Application of a Steady-State One-
Dimensional Water Quality Model, Water Resources Bulletin. AWRA,
pp. 660-670, V. 15, No. 3.
24. Lin, S.H., L.T. Fan, and L.E. Erickson. 1973. Transient Temperature
Effects on BOD and DO Concentrations Along a Stream, Water
Research, pp. 1861-1873, V. 7.
25. Novotny, V. and P.A. Krenkel. 1975. A Waste Assimilative Capacity
Model for a Shallow Turbulent Stream, Water Research, pp. 233-241,
V. 9.
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II (1)
Revision No. 0
26. Sparr, T.M. 1979. A Verification of the QUAL-I Water Quality Model
for the Lower Mississippi, Water Resources Bulletin. AWRA,
pp. 853-860, V. 15, No. 3.
27. U.S. Environmental Protection Agency. 1979. Environmental Modeling
Catalogue, Abstracts of Environmental Models, Management
Information and Data Systems Division, EPA Contract 68-01-4723.
28. Hinson, M.O. and D.J. Basta. 1979. Analyzing Receiving Water
Systems, in D.J. Basta, B.T. Bower, Eds., Analysis for
Residuals—Environmental Quality Management: Analyzing Natural
Systems, prepared by Resources for the Future for ORD, EPA.
29. Areawide Assessment Procedures Manual, Vol. I, EPA, 600/9-76-014.
30. Hydroscience,. Inc. 1975. "Time Variable Water Quality Analysis and
Related Studies, Upper Delaware River.
31. Hydroscience, Inc. 1968. "Water Quality Analysis of the Mohawk River -
Barge Canal."
32. Metcalf and Eddy, Inc. 1977. "Urban Stormwater Management and Technology,
EPA - 600/8-77-014.
33. Omernik, J.M. 1976. "The Influence of Land Use on Stream Nutrient Levels.'
EPA-- 403079-73-014.
34. Elmore, H.L. and Hayes, T.W. 1960. "Solubility of Atmospheric Oxygen
in Water," Twenty-ninth Progress Report of the Committee on
Sanitary Engineer Research, SED Journal. ASCE 86. SA4, 41.
35. Rathbun, R.E. "Comparison of Radioactive and Modified Tracer Techniques
for Measurements of Stream Reaeration Coefficients," USGS Water
Resources Investigation, 78-68.
36. Wright and McDonnell. 1979. In Stream Deoxygenation Rate Prediction,
Journal of Environmental Engineering Division, ASCE.
37. Thomann, R.V., Segna, J.S. 1979. "Dynamic Phytoplankton - Phosphorus
Model of Lake Ontario - Ten Year Verification and Simulation,"
presented at Phosphorus Management Strategic Conference, Rochester,
New York.
38. Tetra Tech., Inc. 1978. Water Quality Assessments: A Screening
Method for Non Designated 208 Areas for EPA/Athens, GA. EPA
600/9-78-105.
39. (Personal Communication with D.J. O1Conner, March 1980.)
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