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TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
Book VII: Permit Averaging Periods
EPA DOCUMENT NUMBER: EPA-440/4-87.002 DATE: September 1984
ABSTRACT
As part of ongoing efforts to keep EPA's technical guidance readily accessible to water
quality practitioners, selected publications on Water Quality Modeling and TMDL Guidance
available at http://www.epa.gov/waterscience/pc/watqual.html have been enhanced for
easier access.
This document is part of a series of manuals that provides technical information related to
the preparation of technically sound wasteload allocations (WLAs) that ensure that
acceptable water quality conditions are achieved to support designated beneficial uses.
The document presents a rational method for selecting the level of treatment required
based on water quality considerations, and for incorporation of the water quality-based
treatment requirements as permit limits. Conventional procedures for establishing a point
source's effluent limits using a WLA analysis do not quantify the degree to which a given
limit protects against exceedances of acute toxicity water quality criteria. Also, the permit
averaging period can have a substantial influence on the degree and cost of treatment
required and on receiving water quality.
The method presented in this document uses a probabilistic dilution model to evaluate the
extent and frequency of acute criteria violations in the receiving water as computed with
effluent concentrations based on daily, weekly, and monthly average permits. The model
incorporates stream variability to develop probability distributions of daily stream
concentrations for each permit limit, which can then be compared to water quality goals
also expressed in terms of daily concentration frequencies.
In addition to a detailed description of the methodology, the document presents an
annotated example of the method performed first as a hand calculation and then using a
computer program included in the manual. Several representatives applications are
provided along with a discussion of suggested uses of the model. Appendices provide a
review of log-normal distributions, a discussion of technical issues and assumptions, a
listing of typical low flow characteristics for U.S. streams, and computer code for the
model.
KEYWORDS: Wasteload Allocations, Averaging Periods, Permit Limits, Lakes,
Reservoirs, Water Quality Criteria, Water Quality Modeling
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Technical Guidance Manual for
Performing Waste Load Allocations
Book VII: Permit Averaging Periods
September 1984
Final report
for
Office of Water Regulations and Standards
Monitoring and Data Support Division,
Monitoring Branch
U.S. Environmental Protection Agency
401 M Street, S.W. Washington, D.C. 20460
-------
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D C 20460
MEMORANDUM
SUBJECT: Technical Guidance Manual for Performing Waste Load
Allocations Book VII, Permit Averaging Period
TO: Regional Water Management 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 VII, Permit Averaging Periods. We are sending extra copies of
this manual to the Regional Wasteload Allocation Coordinators for
distribution to the States to use in conducting waste load
allocations.
Modifications to the February 1984 draft include:
o The method to calculate the Reductions Factor in
Chapter 2 has been elaborated to include the use of 95%
cut-offs for frequency of permit violations.
o The example calculation in Chapter 3 has been expanded.
Step 7 has been added to the step-procedure to show how
permit limits can be specified using 95% cut-offs for
frequency of permit violations.
o The document recommends that advanced treatment
facilities should be built to meet the long-term
average and the selected effluent variability.
o A flow diagram and an IBM PC-compatible program have
been added to Appendix D.
If you have any questions or comments or desire additional
information please contact Tim S. Stuart, Chief, Monitoring
Branch, Monitoring and Data Support Division (WH-553) on (FTS)
382-7074.
Edwin L. Johnson, Director
Office of Water Regulations
and Standards (WH-551)
Attachment
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TECHNICAL GUIDANCE MANUAL FOR
PERFORMING WASTE LOAD ALLOCATIONS
Book VII
Permit Averaging Periods
Contract Number 58-03-3131-WA9
Project Officer
Hiranmay Biswas
Office of Water Regulations and Standards
Monitoring and Data Support Division
Monitoring Branch
U.S. Environmental Protection Agency
401 M Street, S.W. Washington, D.C. 20460
September 1984
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FOREWORD
This guidance document is a product of several years of
research on many complex water quality issues. Although much
progress has been made, some issues still remain. User
participation will be needed to develop answers to these
unresolved issues and will be key to future revisions of this
document.
Selection of permit averaging periods, as presented in this
manual, is based on an assumed exceedance frequency of an acute
violation in the stream no more than 1 day in 10 years. The EPA is
currently considering the issue of allowable duration and
frequency of exposure to acute as well as chronic toxicity. Based
on this study, the choice of duration and frequency used in this
document as examples may have to be changed.
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CONTENTS
Chapter Page
FOREWORD i
LIST OF TABLES iv
LIST OF FIGURES v
LIST OF ABBREVIATIONS AND SYMBOLS vii
ACKNOWLEDGMENTS ix
EXECUTIVE SUMMARY 1
1 INTRODUCTION 1-1
1.1 Background 1-1
1.2 Objectives 1-2
1. 3 Approach 1-3
1. 4 Organization 1-5
2 METHODOLOGY 2-1
2.1 Description of Probabilistic Dilution Model 2-1
2.2 Choice of the Permit Averaging Period 2-9
3 EXAMPLE COMPUTATION 3-1
3.1 Hypothetical Site-Specific Conditions 3-2
3.2 Example Computation - Hand Calculation 3-8
3.3 Example Computation - Computer Program 3-28
4 RANGE OF EXPECTED VALUES FOR STREAMS IN U.S 4-1
4.1 Analysis for Conservative Substances 4-1
4.2 Use As a Screening Tool 4-10
4.3 Preliminary Analysis for Dissolved Oxygen 4-12
4.4 Analysis for Conservative Substances In Effluent-Dominated
Streams 4-23
5 USES AND LIMITATIONS 5-1
6 REFERENCES 6-1
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CONTENTS (Continued)
Appendix Page
APPENDIX A STATISTICAL PROPERTIES OF LOG-NORMAL DISTRIBUTIONS A-l
A-l. General Considerations A-l
A-2. Probability Distributions A-3
A-3. Relationship Between Distributions A-6
A. 4. Properties of Log-Normal Distributions A-6
A-5. Standard Normal Tables A-10
A-6. References A-12
APPENDIX B FIELD VALIDATION OF LOG-NORMAL DISTRIBUTION AND RELATED
ASSUMPTIONS B-l
B-l. Use of the Log-Normal Distribution B-l
B-2. Verification of the Probabilistic Dilution Model B-3
B-3. Appropriateness of Assumptions B-8
B-4 . References B-ll
APPENDIX C CHARACTERISTIC VALUES FOR INPUT PARAMETERS C-12
C-l. Treatment Plant Effluent Flows C-l
C-2. Treatment Plant Effluent Concentrations C-l
C-3. Stream Flow C-3
C. 4 . References C-6
APPENDIX D COMPUTER PROGRAM FOR THE PROBABILISTIC DILUTION MODEL - POINT
SOURCE (PDM-PS) D-15
D-l. Formulation and Normalization D-l
D-2 . Description of Program Use D-5
111
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LIST OF TABLES
Table Page
2-1 Reduction factors for various coefficients of variation 2-13
4-1 Averaging period selection matrix for conservative substances:
effluent dilution ratio - 1QIO/QE = 50 4-5
4-2 Averaging period selection for conservative substances: effluent
dilution ratio - 1QIQ/QE = b 4-6
4-3 Averaging period selection matrix for conservative substances:
effluent dilution ratio - 1QIO/QE =3 4-7
4-4 Averaging period selection matrix for conservative substances:
effluent dilution ratio - 1QIQ/QE =1 4-9
4-5 Conditional moments for the low flow subpopulation (a = 16.75) .. 4-17
4-6 Permit averaging period selection matrix for MOD/DO: of fluent
dilution ratio - 7Q10/OE = 5 4-20
4-7 Permit averaging period selection matrix for BOD/DO: effluent
dilution ratio - 1QIO/QE =3 4-21
4-8 Permit averaging period selection matrix for BOD/DO: effluent
dilution ratio - 1QIO/QE = 1 4-22
4-9 Averaging period selection matrix for a fluent-dominated
streams 4-26
A-l Probabilities for the standard normal distribution A-ll
B-l Comparison of observed and computed downstream
concentrations (2) B-6
B-2 Approximate overestimation of 10 year return period stream
concentration by ignoring serial correlation B-10
C-l - Coefficient of variation of daily effluent flows, VQE C-2
C-2 - Summary of secondary treatment plant performance - median
coefficients of variation, VCE (from reference 1) C-4
C-3 - Effluent concentration variability for trickling filters (from
reference 4) C-6
C-4 - Summary of stream flow characteristics C-9
IV
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LIST OF FIGURES
Figure Page
1-1 Schematic outline of probabilistic method 1-4
2-1 Simple dilution model 2-2
2-2 Illustration of analysis results: stream concentration versus return
period for three permit averaging periods 2-16
3-1 Step procedure to select optimal permit averaging period 3-1
3-2 Sample stream concentration versus probability plot for 30-day
averaging period 3-15
3-3 Sample stream concentration versus mean recurrence interval for 30-
day averaging period 3-17
3-4 Concentration versus probability plot for 1-, 7-, and 30-day
averaging periods 3-19
3-5 Concentration versus mean recurrence interval plot for 1-, 7-, and
30-day averaging periods 3-19
3-6 Concentration versus probability for PDM-PS computation 3-33
3-7 Concentration versus mean recurrence Interval for POM PS
computation 3-33
4-1 Effect of permit averaging period on stream concentrations for
conservative substances: general analysis 4-4
4-2 Effect of permit averaging period on stream, concentrations for
BOD/DO 4-19
4-3 Effect of permit averaging period on stream concentrations for
conservative substances in effluent-dominated stream 4-25
A-l Probability distribution A-5
A-2 Effect of coefficient of variation on frequency distribution A-7
A-3 Pertinent relationships for log-normal distributor A-8
A-4 Cumulative log-normal distribution A-9
B-l: Evaluations of log-normal distribution for stream flows B-2
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LIST OF FIGURES (continued)
Figure Page
B-2 Probability distribution of treatment plant effluent concentrations -
conventional pollutants B-4
B-3 Probability distribution of treatment plant effluent concentrations
- heavy metals B-5
C-l - Typical low flow characteristics of U.S. streams C-8
D-l CRT - displays D-9
D-2 - Example of printed output D-10
D-3 - Flow chart for PDM-PS program D-ll
D-4 - PDM-PS program listing - HP-85 compatible D-12
D-5 - PDM-PS program listing - IBM-PC and MS-DOS compatible D-15
VI
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LIST OF ABBREVIATIONS AND SYMBOLS
BASIC Computer language
BOD Biochemical oxygen demand
BOD5 The amount of dissolved oxygen consumed in five days by
biological oxidation of organic matter
CE Treatment plant effluent concentration
CFS Cubic feet per second, unit of flow
CL Concentration equal to a water quality standard
CO Downstream concentration, after complete mixing
CRT Cathode ray tube
CSat Saturation concentration of dissolved oxygen
CS Stream concentration upstream of discharge
D Flow ratio, equal to QS/QE
Dc Critical (or maximum) dissolved oxygen deficit
DO Dissolved oxygen
EL Effluent limit. A maximum effluent concentration
determined from a waste load allocation analysis, and
specified by an NPDES permit
FAV Final acute value
FCV Final chronic value
K Stream purification factor
Ka Stream reaeration rate constant
Kd BOD oxidation rate constant
MRI Mean recurrence interval, expressed in years
NPDES National pollutant discharge elimination system
P Pollutant
VII
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PDM-PS
POTW
Pr
7Q10
QE
QS
QT
R
TSS
WLA
WQ
a
P
Hx
a
LIST OF ABBREVIATIONS AND SYMBOLS (Continued)
Probabilistic dilution model: point source
Publicly-owned treatment works
Probability
The lowest 7-day average stream flow with a recurrence
interval of 10 years
Treatment plant effluent flow
Stream flow
Total downstream flow, equal to QS
QE
Vx
Reduction factor, equal to the ratio of the mean CE for
which a treatment plant is designed to the EL
Total suspended solids
Waste load allocation
Water quality
Exceedence probability
Dimensionless unit of concentration equal to CO/CL
Mean value of x
Dilution factor
Standard deviation of x
Coefficient of variation of x
Value of statistical parameter Z for a probability of a
Vlll
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ACKNOWLEDGMENTS
The contents of this section have been removed to comply with
current EPA practice.
IX
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EXECUTIVE SUMMARY
Background
The conventional approach to developing Waste Load
Allocations (WLAs) is based on a steady state analysis of stream
conditions, using a design stream flow (usually the 7Q10) and a
receiving water concentration (usually a water quality standard
based on chronic criteria) for the pollutant to be allocated. An
effluent concentration limit is computed for these conditions, and
is used to establish the NPDES permit conditions.
The water quality based permit conditions apply, in addition
to technology based requirements (e.g., BAT, BCT, and secondary
treatment). This effluent requirement may be incorporated into the
permit as the daily maximum limit, the average limit over a week
(for POTWs) or the average limit over a month (for industrial as
well as municipal source)1. Typical practice for toxic pollutants
is to incorporate the wasteload allocation result as the daily
maximum permit limit. This document provides an innovative
approach to determining which types of permit limits (daily
maximum, weekly, or monthly average) should be specified for the
steady-state model output based on the frequency of acute criteria
violations.
Approach
The method used to evaluate the effect of permit averaging
periods is based on a probabilistic dilution model (PDM) in which
it is assumed that the stream flows, effluent flows and
concentration are log-normally distributed
1 See 40 C&R 122.45 (d)
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and uncorrelated. The log-normal distribution is known to be
representative of effluent behavior and to almost always under-
estimate the lowest stream flows somewhat. Thus, the analysis is
generally conservative (overprotective) to some extent. However, a
verification of the probabilistic dilution model indicates that,
for the cases tested, it correctly estimates observed downstream
concentration probability distributions to within the confidence
limits of the data.
The method applied in using this model to evaluate permit
averaging period choices is based on the following observation. If
chronic criteria and 7-day, 10-year low flow, or any other state-
specified low flow, are used on the WLA analysis to develop the
maximum effluent concentration, the use of monthly or weekly-
permit limits for specifying this effluent requirement presents
the possibility that simultaneous occurrences of high effluent
concentrations and low stream flows may result in stream
concentrations which exceed the acute criteria for a pollutant
without violating maximum average discharge permit conditions.
The analysis consists of computing the level of treatment
required for the three averaging period options for specifying the
WLA results as permit limits. The analysis computes the frequency
at which acute stream criteria concentrations are violated under
each of the permit averaging period options, taking into account
the likely range of stream and effluent variability. Computation
result are normalized so that summary results can be applied to a
variety of pollutants based on their ratio of acute-to-chronic
criteria concentrations.
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Uses
The primary use of this methodology will be specifying the
required level of treatment and deriving permit limits based on
water quality requirements. Care must be taken in the assumptions
related to the permit limits and assumptions used in the
methodology. For example, throughout this document, reference is
made to 7-day and 30-day averages. These averages are equivalent
to weekly and monthly permit limits where the assumption can be
made that the monitoring data is adequate (i.e., that the data
collected in a month adequately reflects the 30-day average).
Where this requirement is not valid, alternative limits may be
calculated which incorporate monitoring frequency, or monitoring
frequency may be adjusted so that these conditions are met.
In addition to the usefulness of this method for permit
writers in selecting the averaging period for discharge permits,
the method has been used to calculate suitable averaging periods
for the range of stream and effluent conditions typified in the
U.S. The results have been summarized in convenient graphic and
tabular displays, and can be used as a "screening tool" that
provides a guide for water quality decisions. These summaries
show, for instance, that for toxic pollutants with acute-to-
chronic ratios of 10 or greater, 30-day permit averages will
virtually always meet the criteria that have been adopted; that
is, that acute criteria violations in the stream will recur with a
frequency that averages less than 1 day in 10 years1.
1 The EPA is presently considering the issue of allowable duration
and frequency of exposure to toxicity. Based upon this work,
duration and frequencies used as the decision criteria may change.
This guidance does not recommend any particular minimum acceptable
duration or frequency.
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For pollutants with acute-to-chronic ratios of between 5 and
10, monthly permit averages will be appropriate in most cases,
although there will be some site-specific conditions that would
call for the use of weekly averages. For pollutants with acute-to-
chronic ratios of less than 5, site specific conditions must be
considered, and no general rule is possible. In these cases, site-
specific analyses of the effects of different permit averaging
periods can be performed using the methods outlined in the text.
Limitations
Several technical refinements to the probabilistic model
would be required to more accurately reflect the deviation of
lowest stream flow from log-normality, and to account for serial
and cross-correlation of stream flows and effluent loads. For
coupled reactions, such as BOD/00, the procedures would have to be
extended to provider seasonal approach and results should be
verified against field data. The analysis method would have to be
extended to incorporate the variability of secondary water quality
parameters such as pH, hardness and temperature, since these
affect the toxicity of a number of pollutants. Finally, the
chronic exposure event, as defined by the state design flow
conditions, was used throughout the document to estimate the
maximum effluent concentration. Further analyses to determine the
possible underprotection or overprotection of chronic criteria
based on the state design flow1 were not done.
1 The EPA is considering studying the Impact of uncertainties
Involving the low flow estimating techniques on the selection of
stream design flow.
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CHAPTER 1
INTRODUCTION
1.1 Background
The conventional procedure for establishing a point source
effluent limit using a waste load allocation (WLA) analysis begins
by specifying a target concentration of the pollutant in the
stream, such as a state water Quality standard based on chronic
criteria. This stream concentration is converted to a maximum
effluent concentration using a mass balance calculation for
conservative substances) or a steady-state analysis (for reactive
substances). The inputs to these analyses are a design stream flow
(representing low stream-flow conditions)1 and a measure of the
effluent flow, typically the mean effluent flow. Although this
technique is presumed to provide adequate protection for receiving
water quality, it fails to account for random and other
fluctuations in the flow rate and concentration that naturally
occur in both the stream and effluent. Thus, the degree to which a
given limit protects against exceedances of acutely toxic
concentrations is not quantified.
Effluent permit limitations are currently specified as
maximum concentrations for one day or averaged over a week or
month. The number of observations from which the average is
computed depends on the frequency of
1 The design stream flow most commonly used is the 7Q10 flow, which
represents the low-flow condition with a recurrence interval of 10
years based on a 7-day averaging period. Other flows, such as the
30Q10 or 30Q5 are occasionally used as the design stream flow.
Wherever the use of stream design flow is called for, these or
other stream design flows can be substituted throughout this
document
1-1
-------
monitoring. Although there is no generally accepted rational
basis for selecting permit averaging periods, the effluent
requirement derived from a WLA is typically expressed as a monthly
average for conventional pollutants and as the daily maximum for
toxic pollutants. A set of conversion factors is then used to
convert these concentrations to other averaging periods. In this
document the maximum daily, weekly, and monthly permit limits are
referred to as 1-day, 7-day, and 30-day permit levels,
respectively.
The permit limit used to incorporate a WLA effluent
requirement can have a substantial influence on the degree (and
cost) of treatment required and on the quality of the receiving
water. It is clear that a permit limit imposed as a daily maximum
requirement is more restrictive than when the same permit limit is
used as a 30-day average requirement, since in the latter case the
effluent concentration can fluctuate above the effluent limit for
days at a time and still meet the 30-day average requirement. Such
fluctuations may or may not be significant in terms of receiving
water quality. The appropriate choice of the averaging period,
then, is one which ensures acceptable receiving water quality
without imposing unnecessarily restrictive treatment requirements.
1.2 Objectives
This guidance document is Intended to achieve the following:
(1) Present a rational method for selecting the level of
treatment required based on considerations of water
quality;
(2) Present a rational method to incorporate the water quality
based treatment requirements as permit limits;
1-2
-------
(3) Provide specific information, including detailed examples,
so that the method can be applied to site-specific cases;
(4) Use the method to provide an overall analysis of a broad
range of conditions likely to be encountered, so as to
provide a screening tool for the rapid assessment of a wide
variety of cases;
(5) Discuss the uses and limitations of the method.
1.3 Approach
The basis of the method is an evaluation of the extent and
frequency of acute criteria violations to be expected in the
stream receiving the Discharge as a result of imposing the
effluent concentration, computed from a steady state wasteload
allocation, as a daily, weekly, or monthly average permit. A
probabilistic framework is adopted to account for the inherent
variability of flows and concentrations. Acute criteria violations
are assumed to be associated with random simultaneous occurrences
of high effluent loadings and low stream flows.1 The analysis is
based on an examination of the probability distributions involved
and how they combine to influence the concentration downstream.
The probabilistic dilution model provides the analysis framework.
The probabilistic dilution model is summarized in Figure 1-1.
The inputs to the model include the flow and concentration
histories (or projections) of both the effluent and the receiving
stream. Each of these is
1 While it is apparent that effluent loadings and stream flows
experience both random and nonrandom (e.g., seasonal) variations,
the problem is analyzed here in purely random terms to limit the
complexity of the analysis.
1-3
-------
OS
OS t OE
CO
EFFLUENT
QE
CE
DILUTION
, ^N&^^BV. *«J&^*u.-*> *t -*S**«
PROBABILITY
FREQUENCY
to
AS
II*
Figure 1.1 - Schematic outline of probabilistic method
1-4
-------
expressed as a probability distribution; that is, in terms of the
probability that a given value is exceeded. Next, the effluent and
stream flows are combined to yield the probability distribution of
the dilution factor; then the dilution factor and concentrations
are combined to provide the probability distribution for the
resulting stream concentration. The stream concentration
probability distribution is then converted to a plot showing the
recurrence interval to be associated with each stream
concentration so that the frequency of occurrence of a given
(high) stream concentration can be compared to water quality
obj ectives.
The probabilistic dilution model is used to guide the choice
of the permit averaging period as follows. Given an effluent
requirement from a WLA analysis, the mean effluent required to
meet that WLA requirement is calculated for each of the three
averaging periods, based on an assumed allowable frequency of
effluent limit violation. This provides three levels of treatment
for the plant in question. Each mean effluent concentration is
then used, together with the parameters that characterize the
stream variability, in the probabilistic dilution model. The
result is a probability distribution of resulting stream
concentration for each of the three treatment plant options, which
can be compared to daily concentration/frequency water quality
goals. The use of daily concentration frequencies allows the use
of acute criteria in establishing water quality goals.
1.4 Organization
This document is organized as follows. Chapter 2 provides a
detailed description of the methodology for finding an optimum
averaging
1-5
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period based on a probabilistic dilution method. Chapter 3
presents an annotated example of the method performed first as a
hand calculation and then using the computer program provided in
Appendix D. Chapter 4 uses the model in several representative
applications, and Chapter 5 discusses the uses of the method.
Several appendices to this document provide detailed additional
material, including a review of relationships for log-normal
distributions (Appendix A) and a discussion of technical issues
and assumptions employed in the analysis (Appendix B).
1-6
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CHAPTER 2
METHOD OF ANALYSIS
This chapter lays the theoretical groundwork for the
application of the probabilistic dilution model to the problem of
permit averaging period selection. This discussion is presented in
two parts. Section 2.1 describes the probabilistic dilution model.
Section 2.2 develops the method whereby the probabilistic dilution
model is employed to predict the water quality effects of the
selection of different averaging periods.
2.1 Description of the Probabilistic Dilution Model
The probabilistic dilution model is based on a simple stream
dilution calculation. The complexity of the model arises from the
probabilistic framework that is superimposed upon the dilution
equation. This section is intended to provide a description of the
derivation of the model, and to reduce it to a manageable set of
equations. While a strict mathematical derivation of the model is
available [I], a rigorous treatment is considered beyond the scope
of this manual.
Figure 2-1 illustrates a treatment plant discharge entering a
stream. The effluent discharge flow (QE), having a concentration
(CE) of the pollutant of interest, mixes with the stream flow
(QS), which may have a background concentration (CS). The
receiving water concentration (CO) is the concentration that
results after complete mixing of the effluent and stream flows. It
is the cross-sectional average concentration downstream of the
discharge, and is given by:
2-1
-------
^-EFFLUENT
\ FLOWsQE
CONCENTRATION aCE
STREAM
7T
UPSTREAM
FLOW-QS
CONCENTRATION » CS
DOWNSTREAM
FLOW-OS-H3E
CONCENTRATION = CC
Figure 2-1 - Simple dilution model
2-2
-------
CO = (QE'CE) + (QS'CS) (2-1)
QE + QS
If the dilution factor, cp, is defined as:
cp = QE = 1 (2-2)
QE + QS 1 + D
The calculated value of CO for a given day could be compared
to a water quality standard (CL) or to any other stream
concentration which relates water quality to water use. This
procedure could be repeated for a large number of days and the
resulting set of values for CO could be subjected to standard
statistical analysis procedures to obtain its probability
distribution. If this were done, the total percentage of days on
which the downstream concentration CO exceeded CL could be
determined.
The ability to perform this direct computation depends upon
the availability of long time series of upstream and treatment
plant flows and concentrations of each pollutant of interest. Such
long data records are usually only available for stream flow, but
estimates based on more limited data sets may be available for the
other elements. An important objective of any modeling framework
is to cast the problem into a manageable form while at the same
time preserving its essential features. Therefore, it is necessary
to characterize the fluctuating behavior of the upstream and
20
-3
-------
effluent flows and concentrations in a concise and realistic
fashion.
The probabilistic dilution calculation procedure used in this
report permits the probability distribution of downstream
concentrations (CO) to be computed directly from the probability
distributions of the flows and concentrations.
The first step in the use of the probabilistic dilution model
is to develop the statistics of the concentration and flow of both
the stream and effluent.1 These statistics include both the
arithmetic and logarithmic forms of the mean ((j.) , standard
deviation (a), and coefficient of variation (v) . The analysis is
simplified here by specifying an upstream concentration of zero
(CS = 0) so that the results reflect only those effects on the
receiving water due to the effluent discharge, thus highlighting
the comparative differences resulting from choice of permit
averaging period.
The amount of dilution at any time is a variable quantity and
the dilution ratio (D=QS/QE) has a log-normal distribution when
both stream flow (QS) and effluent flow (QE) are log-normal. The
log standard deviation of the flow ratio QS/QE is designated as
CTinD- This can be calculated from the log standard deviations of
stream flow and effluent flow, assuming no cross-correlation
between stream and effluent flows.
= "V o2lnQS + o2lnQE (2-4;
1 Standard statistical procedures are used to compute the mean and
standard deviation using the log transforms of the basic data.
Conversion to the other statistical expressions used in the
analysis is described in Appendix A.
2-4
-------
The probability distribution of the dilution factor, cp =
1/(1+D) is not truly log-normal, even with log-normal runoff and
stream flows. It has an upper bound of 1 and a lower bound of 0,
and where it approaches these values asymptotically, it deviates
appreciably from a log-normal approximation. Deviations at values
of approaching 0 are of no practical significance to the
calculations being performed since they occur at high dilutions.
For smaller streams relative to the size of the discharge,
deviations from a log-normal approximation can be appreciable.
They are large enough to introduce significant error into the
calculated recurrence interval of higher stream concentrations.
The error introduced is almost always conservative; that is, it
projects high concentrations to recur more frequently than they
actually would. The appropriateness of this assumption is
discussed in detail in Appendix B.
A procedure is provided in this report for accurately
calculating the probability distribution of the dilution factor
(
-------
The manual procedure (moments method) estimates the mean
and standard deviation of a log-normal approximation of dilution
by first calculating, and then interpolating, between the 5% and
95% probability values. The value of the dilution factor (
-------
U
-------
50% concentration = CO = exp ((J,inco)
84% concentration = exp ((J,inco + Oinco)
Using this procedure, any concentration of interest can be
identified and its probability of occurrence scaled directly from
the plot.
Alternatively, the concentration that will not be exceeded at
some specific frequency (or probability) can be calculated from:
C0a = exp (Umco + (Za Omco)) (2-13)
where
Za = the value of Z from a standard normal table which
corresponds to the selected percentile a.
To determine the probability of exceedence, (1 = a) is
substituted in Equation 13.
One can also work in the reverse direction; that is, given
some target stream concentration (CL), the probability of CO
exceeding that level can be determined by:
z = ln(CL) - Uinco (2-14;
OlnCO
A standard normal table will provide the probability for the
calculated value of Z.
Because of the way the standard normal table In Appendix A is
organized, the probabilities calculated using this approach
represent the fraction of time the target concentration (CL) is
not exceeded. The
-------
probability that the concentration will be exceeded is obtained
by subtracting the value obtained from 1.0.
2.2 Choice of the Permit Averaging Period
In order to examine the comparative effects of different
choices of permit averaging periods on water quality, it is
necessary to define the relationships between the established
effluent limit (EL) from the steady state WLA, the permit
averaging period, the treatment plant performance that results, in
particular the mean effluent (CE), the downstream concentration
(CO), and a stream target concentration (CL).
The objective of this section is to examine the relationships
among these parameters in order to be able to predict the
probability of an (adverse) water quality outcome based on known
or estimated stream and effluent characteristics and the choice of
permit averaging period. The approach is based on the assumption
that the EL will be violated with a particular frequency. The mean
effluent required to meet this level of compliance with EL is then
calculated for each of the three permit averaging periods, and the
probabilistic dilution model is then used to develop a probability
distribution of the downstream concentration (CO) for the three
cases. A level of acceptable adverse water quality (a decision
expressed in terms of the probability or frequency of experiencing
a selected high value of CO, such as the acute criteria
concentration) is then compared with the probability distributions
to determine the longest permit averaging period that meets the
water quality goals.
2-9
-------
The first step in this sequence is to establish the
relationship between the mean effluent (CE), the effluent limit
(EL), and the permit averaging period. In fact, what is required
is the relationship between the treatment plant performance
necessary to meet the effluent limit as either a daily, weekly, or
monthly maximum permit. The reason for this is that the daily
variation of stream quality is governed, not by the effluent limit
which is a regulatory upper limit, but by the probability
distribution of the daily effluent concentrations which results
from the design of the treatment plant consistent with the
effluent limit and the permit averaging period. For log-normally
distributed random variables, this distribution is specified by
the mean effluent concentration, CE, and its coefficient of
variation, VCE
A particular effluent limit (say 30mg/l) established by
permit as a maximum daily value would require a higher level of
plant performance (a lower mean effluent concentration) to avoid
permit violations than would the same limit specified as a maximum
monthly average. In the latter case, excursions solve the effluent
limit could be tolerated on individual days, without causing a
violation of permit conditions. The reason for this is that a
monthly average of 30 Individual dally effluent concentrations is
less variable than the daily concentrations themselves. Occasional
high daily concentrations are averaged together with lower
concentrations to produce a less variable monthly average. Hence,
treatment plant performance is directly related to the averaging
period specified in the permit.
In order to proceed with the analysis a quantification of
this relationship is required. Daily treatment plant effluent
concentration variations
2-10
-------
are well described by a log-normal distribution parameterized
by a long term average concentration, CE, and a coefficient of
variation, VCE Thus, a relationship between these parameters and
the permit effluent limit and averaging period is required.
A method to be employed is based upon an interpretation of
what is meant, in practice, by specifying permit effluent limits
as maximum values which may never be exceeded for the specified
averaging period without causing a violation. As Haugh, et al. [2]
observe, fixed upper limits, which are never to be exceeded are
conceptually inconsistent with the stochastic nature of wastewater
treatment processes and the effluent concentrations they produce.
Realistically, some exceedence frequency must be acknowledged,
regardless of the averaging period assigned. For the present
analysis, it will be assumed that the effluent limit specified by
a permit is not to be exceeded more frequently than 5 percent or 1
percent of the time. Of course, any other choice is possible.
Once a specific choice is made, say 1 percent, then the
probability of compliance is a = 99 percent and that establishes
the fact that EL is the a-percentile effluent concentration: CEa.
This procedure, then, gives a specific probabilistic
interpretation to the effluent limit. It is the effluent
concentration that Is exceeded with no greater frequency than (l-a)
percent of the time. If the permit is specified as a daily maximum
value, then EL is the a-percentile of dally effluent
concentrations. If the permit is specified as a weekly (or
monthly) maximum value, then EL is the a-percentile of 7-day (or
30-day) average effluent concentrations.
2-11
-------
In order to compute the long term average effluent
concentration, CE, that would insure that CEa = EL as a daily,
weekly, or monthly permit the coefficients of variation are
required for 1-day and 7-day or 30-day averages of effluent
concentrations. Table C-2 presents representative values.
Thus, the requirement that:
CEa = EL (2-15;
and for a coefficient of variation VCE, the average effluent
concentration CE can be computed from
(2-16)
where the reduction factor relating CEa = EL to CE, that is, Ra =
CE/CEa, is
Ra = Vl + vCE2 exp [-Za Vln (1 + vCE2) ] (2-17;
the ratio of the arithmetic average to the a-percentile of a log-
normal random variable with coefficient of variation, VCE Table 2-
1 gives the values of Ra for various coefficients of variation.
The derivation of this formula follows from the expression
for the a-percentile of a log-normal random variable:
CEa = exp (UlnCE + Za OinCE) (2~l'<
and the arithmetic average of a log-normal random variable:
2-12
-------
TABLE 2-1 - Reduction factors for various coefficients of variation
Coefficient of Reduction Factor
Variation Ra
VCE a = 95% a = 99%
0.1 0.853 0.797
0.2 0.736 0.643
0.3 0.644 0.527
0.4 0.571 0.439
0.5 0.514 0.372
0.6 0.468 0.321
0.7 0.432 0.281
0.8 0.403 0.249
0.9 0.379 0.224
1.0 0.360 0.204
1.1 0.344 0.187
1.2 0.330 0.173
1.3 0.319 0.162
1.4 0.310 0.152
1.5 0.302 0.144
2-13
-------
CE = GXP (UlnCE + ^ 02inCE) (2-19)
Thus: Ra = CE/CEa = exp (% a2inCE - Za ainCE) (2-20]
and since exp (^ o2incE) = Vl+v2CE and OincE = Vln (1+ v2CE)
(appendix A, page A-8) equation (2-17) follows.
At this point the effect of the choice of permit averaging
period on treatment plant design can be illustrated. If the permit
averaging period is 1-day, and the daily effluent coefficient of
variation is vCE=0.7 (for example, extended aeration activated
sludges, Table C-2), then for a 1 percent violation frequency a=99
percent, Ra = 0.281, which indicates that the long term average
effluent concentration must be 28.1 percent of the daily maximum
permit limit.
However, if the permit averaging period is 7 days, then the
coefficient of variation of 7-day averages is VCE = 0.6 and Ra =
0.321. Now the treatment plant can be designed to produce a long
term average effluent concentration of 32.1 percent of the weekly
permit limit. For a 30-day average permit limit VCE= 0.45 and Ra =
0.404. Hence, if EL = 10 mg/1, the treatment plant average
effluent concentration must be 2.81, 3.21, or 4.04 mg/1 for a
daily, weekly, or monthly permit specification, respectively.
Hence the selection of the permit averaging period is related
to the CE required for each of the three averaging periods in
order to
2-14
-------
avoid exceeding the EL more often than the selected frequency.
These average values are then used in the probabilistic dilution
model (with other input parameters such as QS and QE) to develop
the probability distribution of CO for each of the three permit
averaging periods.
The value of CO in the probability distribution can be
normalized in terms of a stream target concentration (such as the
chronic criteria concentration, CL) so that the calculation can be
used for a wide variety of pollutants. Stream concentration is
therefore expressed in terms of P = CO/CI, P being a dimensionless
unit of concentration.
A convenient presentation of the resulting probability
distribution makes use of the concept of return period. For daily
stream concentrations the 1 percent exceedence value has an
average recurrence rate of one day every 100 days so that its
average return period is 100 days. Thus the return period for
daily values is defined as:
Return Period (days) = I/Probability of Exceedence (2-28)
The basic assumption in the use of return period as defined above
is that the event whose probability is being examined has a
characteristic time associated with it, in this case, one day for
daily concentrations. Thus, it is assumed that daily stream
concentrations are of concern, and each event corresponds to one
day.
Figure 2-2 illustrates how the results of such an analysis
can be expressed in a plot of concentration versus return period.
2-15
-------
I0
< IT
cr w
o o
z
-------
These snort-term impacts are perhaps most effectively
evaluated with respect to acute criteria concentrations. If the
stream concentration exceeds the acute criteria as a result of ah
occasional high daily effluent loading, the result is presumed to
be an undesirable impact. Hence, there is a direct connection
between the permit averaging period and the probability of acute
criteria violations. Specifying that the WLA requirement be met as
a daily maximum permit limit significantly reduces the possibility
of acute criteria violation since the effluent limit is specified
using the chronic criteria, which is always a smaller
concentration.
The frequency with which daily stream concentrations are
allowed to exceed acute criteria is a regulatory decision1. The
analyses presented herein employ a frequency that corresponds to a
1-day in 10-year recurrence, on average. The choice of 10 years
is, of course, used for example purpose only but it is consistent
with the 10 year return period that is conventionally used for the
design stream flow.
The results of the permit averaging period analysis are
presented in terms of CO/CL which is exceeded with a particular
frequency, such as once in 10 years. This ratio can then be
compared to the acute-to-chronic criteria concentration ratio for
the pollutant of concern. For pollutants with large acute-to-
chronic ratios, occasional large daily fluctuations can be
tolerated; and a 30-day permit averaging period provides
protection from acute criteria violations. Conversely, pollutants
with small acute-to-chronic ratios are more likely to require
shorter day permit averaging periods. Site specific
This is currently under EPA study
2-17
-------
considerations, primarily the ratio of effluent to stream flow and
stream flow variability, become significant in these cases.
The final translation of the selected averaging period option
to permit limits requires consideration of the monitoring
frequency. The method assumes either daily monitoring or other
monitoring adequate to describe the performance of the plant on a
monthly basis. If such conditions are not met, alternate limits
may be calculated which Incorporate monitoring frequency, or
monitoring frequency may be adjusted so that these conditions are
met.
2-18
-------
CHAPTER 3
EXAMPLE COMPUTATION
This chapter presents an example problem, showing step by
step computations using the methodology described in the previous
chapter. A set of hypothetical conditions that apply to a site-
specific situation is assumed, and an analysis is performed to
determine the effect on receiving water quality-resulting from the
assignment of different permit averaging periods to the steady-
state model output. The steps used to conduct this analysis are
summarized below in Figure 3-1. The format used in this chapter
presents data and computations on the left-hand page, and
pertinent commentary and supporting discussion on the facing page
immediately opposite those computations. The manual computation
using the moments approximation is described first, followed by an
analysis using the computer program (PDM-PS) in Appendix D. Both
examples use the same set of hypothetical site-specific
conditions.
GIVEN:
acute and chronic
toxicity
design flows
flow and concentration
variability for
specific averaging
periods
STEP 1:
Compute statistical
parameters of stream and
effluent flow and
concentration
STEP 2:
Compute statistical
parameters of dilution
factor
Figure 3-1 - Step procedure to select optimal permit averaging
period
3-1
-------
3.1 HYPOTHETICAL SITE-SPECIFIC CONDITIONS
This section provides an example of the type and amount of
information required to perform the analysis. It also establishes
the basis for the example computations and assumes that pertinent
site-specific conditions are as follows:
A. Site-Specific Waste Load Allocation (WLA) Results
The pollutant (P) to be allocated has a chronic toxicity
concentration (CL) of 2.5, and an acute toxicity
concentration of 6.25.
WLA policy for the agency performing the analysis is to use
7Q10 as stream assign flow, to use the design capacity of the
treatment plant as the effluent flow, and to compute (e.g.,
using a water quality model) the effluent concentration of
pollutant (P) that will result in a stream concentration
after dilution less than or equal to the chronic value (2.5 =
the stream target concentration, CL). For this example, it
was assumed that:
Design Effluent Flow (QE) = 5 MGD =7.77 cfs
Design Stream Flow (7Q10) = 23.3 cfs
The stream target concentration (CL = 2.5) will be met under
these design flow conditions, when the effluent concentration
Is CE = 10. Therefore based on the WLA analysis, the effluent
limit (EL) for pollutant (P) is specified by the permit as:
EL = 10
3-2
-------
COMMENTARY
from EPA Criteria
State water quality standards do not usually specify both
values; they are usually based on chronic values.
(Any concentration units may be assigned; stream
concentrations will nave to be in the same units.)
77Q10 (the lowest 7-day average stream flow with a recurrence
interval of 10 years) is the most common "design stream
flow". Some states use other values (e.g., 30Q5). This
analysis uses the numerical value of the "design flow".
However, although the. example terminology uses "7Q10", it
should be interpreted as "design stream flow" and the
appropriate value substituted, regardless of the averaging
period or the recurrence interval on which it is based. (For
example, if design flow in a state were 30Q5, assume that
30Q5 =23.3 cfs).
NOTE: The only exception to this is in Figure C-
1, in which the ratio of 7Q10 to average
stream flow is used to estimate the
variability of daily flows in the absence
of a specific local analysis. The use of
this figure is not requisite to either the
analysis methodology or the computations.
CL = (QE * CE) + (QS * CS)
QE + QS
2.5 = (7.77 * CE) + (23.2 * 0]
7.77 + 23.3
CE = 10 = EL
3-3
-------
HYPOTHETICAL SITE-SPECIFIC CONDITIONS
[ continued)
3. Site-Specific Conditions
Stream Flow
Mean Flow
QS = 467 cfs
Coefficient of Variation
= 1.5
Upstream Concentration
Mean (CS ) =0
Coefficient of Variation
(vcs) = 0
Effluent Flow
Mean (QE) = 7.77 cfs
Coefficient of Variation (VQE) = 0.20
3-4
-------
COMMENTARY
Stream flow data are obtained from analysis of flow
gaging records for the stream in question; where the
stream reach is engaged, it is obtained by extrapolation
from an appropriate record.
At present, records are not normally analyzed for the
coefficient of variation, although the computation is
straight forward and can be readily incorporated into a
routine statistical analysis of daily stream flows. In
the absence of specific analysis results, the coefficient
of variation of daily stream flows can be estimated using
the material presented in Figure C-l.
Upstream concentration can be assumed to be zero if the
stream concentration of the pollutant is very low
compared to the discharge, or if the effect of the
discharge only is to be examined. Site-specific values
for upstream concentration statistics would be obtained
from analysis of an appropriate STORET station, or from
local monitoring records. If upstream concentrations are
assigned, enter data here and in the equations when
called for.
The design effluent flow is assumed to be the mean
effluent flow. The variability of daily effluent flows
for a new facility must be estimated on the basis of
available data for existing treatment facilities (such as
Table C-l). For an existing facility being expanded, or
simply re-permitted, variability could be based on an
analysis of past plant records. For many industrial
dischargers, this data will be available in Book VI
(Design Conditions) of the waste load allocation
technical guidance document series (specifically, in
Chapter 4: Effluent Design Conditions).
3-5
-------
HYPOTHETICAL SITE-SPECIFIC CONDITIONS
(continued)
Effluent Concentration
Mean (CE) =
Coefficient of Variation (VCE) = -7
The mean concentration is a function of the permit averaging
period and is that concentration required to avoid exceeding the
effluent limit concentration (EL) more often than the compliance
probability.
The coefficient of variation for the hypothetical treatment plant
is not known because the plant has yet to be constructed. Assuming
that the plant will produce an effluent with a variability similar
to the values given in Table C-2, the following values are used:
Permit Averaging
Period
Daily
7-Day
30-Day
Coeff. of Var,
0.70
0.40
0.20
Equation 2-17 is then used to determine the mean effluent
concentration of (P) which is required to avoid a violation of EL
more often than the compliance probability. For this example,
assume that the exceedence probability is 1 percent. For a = 0.99
percent, Za = 2.327. For VCE= 0.70, Ra= CE /EL is:
Ra = Vl + v2CE exp [-Za
= Vl+ 0.49 exp [-2.327 Vln(l+0.49)]
= 1.221 exp [-2.327 * 0.6315]
=0.281
The reduction factor for 7-day and 30-day averages are computed
similarly with VCE (7-day) = 0.40 and VCE (30-day) = 0.20. The
results are:
Permit
Averaging Period
Daily
7-Day
30-Day
Coeff. Of Var.
of Averaged
Effluent
Concentrations
(VCE)
0.70
0.40
0.20
Reduction Factor
Ra = r^P/EL
0.281
0.439
0.643
Reguired Mean
Effluent Cone.
( CE = Ra EL)
0.281 * 10 = 2.81
0.439 * 10 = 4.39
0.643 * 10 = 6.43
3-6
-------
COMMENTARY
The mean effluent concentration that a treatment
facility is capable of producing is influenced
significantly by process selection. For this example, it
will be assumed that process selection will be made
following the issuance of a permit, and influenced by its
provisions.
The mean effluent concentration that a facility is
required to produce is influenced by the permit averaging
period and the variability of effluent concentrations of
the pollutant in question.
The analysis employed here, which bases permit averaging
period selection on receiving water impacts, is based on
exceedance of the acute criteria on a daily basis.
Therefore, all subsequent stream impact computations
(Step 4) are based on the coefficient of variation of
daily effluent concentrations, or 0.7, as shown.
The mean concentration is shown by (*), because a
different value is used for each permit averaging period.
The recommended exceedence probability for the effluent
limit is either 5 percent or 1 percent. For 5 percent, Za
would be ZQR= 1.645.
Longer averaging periods reduce the variability of
effluent concentrations, and-allow permit exceedance
limits to be mot with higher effluent means. Computation
of the required mean (CE) uses the values of VCE for the
corresponding permit averaging period.
3-7
-------
3.2 EXAMPLE COMPUTATION - HAND CALCULATION
This section illustrates the hand computation using the moments
approximation to evaluate the stream concentration probability
distribution.
STEP 1: Compute statistical parameters (arithmetic and
logarithmic) of inputs using relationships for log-normal
distributions (see notes on page 3-9 or Appendix A for
equations).
o For the mean effluent concentration (CE) for a 30-
day permit averaging period with X = CE, that is
for the variable CE:
ARITHMETIC
Mean
Coef. Var.
Std. Dev.
Median
(ux) =------- (page 3-6)- - -
(vx) =------- (page 3-6)- - -
- - = 6.43
- - = 0.70
ox) = ux * vx = (6.43) * (0.70) ------ = 4.50
= 5.27
(x) = ux/ Vl+ v2x = 6.43/ Vl + (0.7)2
LOGARTHMIC
Log Mean
(u
Inx ,
= In (x) = In (5.27
= 1.662
Log Std. Dev. (oinx) = Vln (I + vxz) = Vln (1 + (0.7) z) = 0.6315
o These computations are repeated for each of the other
input parameters. The results are tabulated below.
Stream
Flow: QS
Effluent
Flow: QE
Upstream
Concentration:
CS
Effluent
Concentration:
CE
467
7.77
Arithmetic
Mean Median Std Dev Coef Var
Ux x °~x vx
259
7.62
6.43 5.27
701
1.55
4.50
1.50
0.20
0.70
Logarithmic
Mean Std Dev
ulnx
°~lnx
5.5570 1.0857
2.0307 0.1980
1.662 0.6315
3-8
-------
COMMENTARY
The following parameters are used subsequently:
Input
Parameter
Stream Flow
Stream Cone.
Effluent Flow
Effluent Cone.
QS
CS
QE
CE
Arithmetic
Median
X
OS
CS
QE
CE
Mean
Ux
UQS
UGS
UQE
UCE
Std.
Dev.
o~x
°~QS
o-cs
0"QE
0~CE
Coef .
Var.
vx
VQS
VGS
VQE
VCE
Logarithmic
Log
Mean
Uln X
UlnQS
ulnCS
ulnQE
UlnCE
Log
S.D.
Pin X
0~lnQS
°"lnCS
°"lnQE
0"lnCE
The following definitions and equations summarize the
relationships among the statistical parameters of log-normal
random variables.
Arithmetic
x
Terms
Random Variable
Mean
Variance
Standard Deviation
Coefficient of Variation
Median
Logarithmic
In x
0"ln X
(not used)
(not used)
Ux = exp
+
= In
1 + vx
x = exp [u
Inx .
vx = Vexp
- 1
= Vln (l-vx
ox = uxvx
3-9
-------
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
STEP 2: (a) Compute the log standard deviation of the flow ratio
QS/QE = 0.
O inQE + 2p O~inQS ' O~inQE
The first two terms are taken from the table in Step I
(and squared). Since, for this example, flows are not
correlated (p=0), the third term drops out. Therefore,
= V(1.0857)2 + (0.1980)2 = 1.1036
(b) Compute the 5th and 95th percentiles of the actual
distribution of the dilution factor (
-------
COMMENTARY
This equation accounts for any correlation that may exist
between stream flow and effluent flow; e.g., where higher
effluent flows tend to occur during periods of high stream
flow.
Ordinarily, there is no reason to expect any such
correlation; therefore p = 0, and the computation in step (a!
is simplified as shown.
cp95 = QE
(QE + Q~S)exp (ZaOinD)
7.62
(7.62 + 259) exp [(1.645) (1.1036) ]
7.62
7.62 +1591
= 0.004766
3-11
-------
EXAMPLE COMPUTATION - HAND CALCULATION (continued)
(d) Compute arithmetic statistical parameters (using equations
on Page 3-9 and tabulate for convenience.
Arithmetic Logarithmic
Mean Median Std Dev Coef Var Mean Std Dev
Dilution (9) 0.0471 0.0270 0.0673 1.43 -3.6115 1.0546
Factor
STEP 3: Compute the statistical parameters of the resulting in-
stream concentration (CO) .
(a) Compute the arithmetic mean concentration using
previously tabulated values, using Equation 2-8.
Uco ~~ [UCE ' Up ] + [Ucs ' (1
= [5.43 0.0471] + [0] = 0.303
(b) Compute the standard deviation, using Equation 2-9.
+ c/cs (
-------
COMMENTARY
The equations are as follows:
Ucp = exp [Ulncp + 1^02incp]
= exp [-3.6115 + ^ (1.0546)2]
= 0.0471
= "Vexp (a incp) - 1
= Vexp [ (1.0546)2]-!
= 1.429
= (0.0471) (1.429)
=0.06729
When the manual ("moments" approximation) analysis presented
here is used, the stream concentrations computed are assumed
to be log-normally distributed. That is, the log-normal
distribution computed is an approximate representation of the
actual distribution that results. The degree of approximation
is examined subsequently.
The equations are:
VGO = aco/Uco = 0.569/0.303
= 1.88
inco = In (UGO)
(Vl + vco2)
= In (0.303)
V(l + (1.88)2
= -1.95
= Vln (1 + v2co)
= Vln [1 + (1.88)2]
= 1.23
3-13
-------
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
STEP 4: use the statistical parameters of stream concentration
computed in the previous step to construct graphical OP
tabular displays summarizing the frequency distribution.
(a) To construct a probability plot using log-
probability graph paper:
The median concentration is plotted at the
50th percentile position.
CO = C050%
=exp (uinco)
= exp (-1.95)
=0.142
Any other plotting position is determined as
follows:
(1) From Table A-l, select a probability (a) and
determine the corresponding value of Za. For
example,
Probability = 0.841 (84%) Z84.i%=1.00
Probability = 0.159 (16%) Z15.9% = -1.00
(2) Compute the concentration at probability (a)
from the log mean and log standard deviation of
stream concentration (CO).
C0a = exp (U
84% plotting position
C084% = exp (-1.95 + 1.00 1.23) = 0.487
16% plotting position
C016% = exp (-1.95 -1.00 1.23) = 0.0416
[3) Plot these concentrations on log-normal
probability paper and connect with a straight
line.
3-14
-------
COMMENTARY
16% 150% |84%
1 2 5 10 30 50 70
% EQUAL OR LESS THAN
99
99.99
Figure 3-2 - Sample stream concentration versus probability plot
for 30-day averaging period
The probability plot indicates, for example, that the stream
concentration of pollutant (P) will exceed a concentration of 1.0,
at a frequency (probability) of about 5%. Since the analysis is
based on daily values, this is interpreted as: 55 of all days will
have stream concentrations greater than 1.
3-15
-------
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
STEP 4 (continued)
(b) To construct a recurrence interval (return period)
plot using log-log graph paper:
o the formula used in the previous Step
C0a = EXP (UlnCO + Za Oinco)
can be rearranged:
Za = In(COa) - Uinco
O~lnCO
The log mean and log standard deviation were determined
in Step 3:
UlnCO = 'I .95
OinCO = 1.23
o Plotting positions are determined as follows:
(1) Select a series of values for stream
concentration (CO) covering a range of interest,
take the natural log (In) and compute the value
of 2.
(2) From Table A-l identify the probability (Pr)
associated with each 2.
(3) Compute the mean recurrence Interval (MRI) for
each of the selected concentrations:
MRI (years) = 1 1
Pr 365 day/yr
For example:
Stream Probability Mean Recurrence
Concentration CO Z Greater Than Interval (years)
15 3.787 7.626 x 10'5 35.9
10 3.457 2.732 x 10"4 10.0
5 2.894 1.902 x 10"3 1.44
1 1.585 5.648 x 10"2 0.0485
Plot results. If necessary, compute additional values to
assist in drawing a smooth curve.
3-16
-------
COMMENTARY
Probability results can be misleading for the water quality
issues being considered here, unless interpreted very
carefully. For example, a 1% probability of exceeding a
significant stream concentration means that this occurs
nearly 4, times in 1 year, and for more than a month of
individual days over a 10 year period. Expressing results as
recurrence intervals is believed to provide a more useful
expression of analysis results.
100
10 YEAR
RECURRENCE INTERVAL
ACUTE TOXICITY CONC. * S.2S
.02 .05 .1 .2 .5 I 2 5 10 20
MEAN RECURRENCE INTERVAL - YEARS
50
Figure 3-3 Sample stream concentration versus mean recurrence
interval for 30-day averaging period
Note that the acute concentration assumed for the
pollutant (6.25) is exceeded an average of once every
2.6 years. If the exceedance criteria to be met Is an
average of 1 acute toxicity exceedance every 10 years,
then the assignment of a 30-day permit averaging period
is insufficient; shorter averaging periods must be
examined.
However, if the pollutant had an acute concentration of
12.5 (or an acute-to-chronic ratio of 5), the recurrence
interval of 20 years would be sufficiently protective
for acute events.
3-17
-------
STEP 5:
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
Compute the receiving water quality impact that would
result from assigning other permit averaging periods.
Repeat Steps 1-4 using the values for CE that have been
calculated for weekly and daily permit assignment.
7-day permit average CE
Daily maximum permit average
4.39
CE= 2.81
All other inputs remain unchanged.
When the computations are repeated using these values,
the statistical parameters for stream concentration
(Step 3) that are developed are as follows:
STREAM CONCENTRATION (CO) STATISTICS
Permit
Averaging
Period
30-Day
7-Day
1-Day
Mean
Pco
0.303
0.207
0.132
Median
CO
0.142
0.0971
0. 0622
Std. Dev.
0"CO
0.570
0.389
0.248
Coef. Var.
VGO
1.88
1.88
1.88
Mean
PlnCO
-1.95
-2.33
-2.78
Std. Dev.
0~lnCO
1.23
1.23
1.23
Probability and recurrence Interval plots are then
constructed as described in Step 4 to provide a
graphical comparison of the influence of alternative
choices for averaging period on the frequency of
exceeding acutely toxic concentrations of pollutant (P)
in the receiving system.
3-18
-------
COMMENTARY
10
LU
U
O
U
LU
-------
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
STEP 6: Select the appropriate permit averaging period.
The appropriate permit averaging period is chosen to
provide an acceptable level of receiving water quality.
The decision is based on the assumption that an
unacceptable exceedence of the acute criteria in the
receiving stream is more than once every 10 years, on
average.
Therefore, the permit averaging period selected is the
highest one that does not result in a mean recurrence
interval for acute criteria violations that Is less than
10 years. For this example, recurrence intervals for a
stream concentration of 6.25 are approximately
30-day Avg. Period = 2.6 years
7-Day Avg. Period = 7.7 years
1-Day Avg. Period = 31 years
For the site specific conditions assumed for this
example, a 1-day permit averaging period could be
assigned to the effluent limit of 10. However, as shown
below using more exact calculations, a 7-day permit
averaging period Is sufficiently protective for acute
events. Thus a 7-day permit averaging period is assigned
to the effluent limit of 10.
3-20
-------
COMMENTARY
For marginal cases, it should be recognized that the
projections made using the moments approximation tend to be
conservative. As shown below the more exact recurrence
intervals are 6.4, 32, and 280 years".
The acceptable frequency of acute criteria violation is, of
course, a policy decision. Alternate levels are evaluated
directly from Figures 3-3 and 3-4.
The moments approximation used for the foregoing computations
(because it approximates the distribution of dilution factor
(q>) with a log-normal distribution) provides an approximation
of the probability distribution and recurrence interval of
the stream concentrations.
An exact computation that avoids the necessity of this
approximation, is provided by use of the computer program
detailed in the next section and in Appendix D. In this case,
its use is warranted since a 7-day permit averaging period is
sufficiently protective.
Based on the selection of the 7-day permit averaging period,
the maximum 7-day average permit limits = EL = 10 mg/1. This
permit limit is equivalent to a long-term average effluent
concentration CE = Ra EL = (0.439) (10) = 4.39, with
coefficient of variation daily effluent concentration (VCE) =
0.7. Thus, the design of the treatment facility and the
selection of treatment process should be made to meet these
specifications of CE = 4.39 mg/1 with coefficient of
variation of daily effluent concentrations VCE= 0.7.
3-21
-------
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
STEP 7: Compute permit limits for other averaging periods (daily
maximum and monthly) and exceedence percentiles (1
percent and 5 percent) that are consistent with the
treatment performance level established in Step 6.
At this point in the analysis, it has been determined
that assigning the effluent limit of EL = 10 as a weekly
permit, applicable to 7 day averages of the daily
concentrations, is sufficiently protective. This choice
is based upon an effluent limit violation frequency of
one percent. The mean effluent concentration for these
choices is CE = 4.39.
If it is assumed that the same violation frequencies
apply to the other permit concentrations, then they can
be computed directly:
Permit Limit = CE/Ra
Since Ra = CE/CEa and the permit limits are assumed to
be the a-percentile concentrations for each averaging
period.
If other violation frequencies are desired, for example,
5 percent, then permit limits of this frequency can also
be calculated using the appropriate Ra for l-a = 5
percent. The table below presents the results for the
example considered above.
Coeff. of Var. of Reduction Factors'3
Avg.'ed Effluent D p _,.: 4- THTTlH1_ac
Permit a Ra Permit Limits
, . Concentration
Averaging -^ ^ -^ 5%
Period VCE
0.70
0.40
0.20
0.281
0.439
0.643
0.432
0.571
0.736
15.6
10.0
6.83
10.2
7.69
5.96
1-day
7-day
30-day
It should be pointed out that any or all of these
permits are equivalent in the sense that a treatment
plant meeting any of these requirements will also meet
the desired water quality goal. Of course, this Is true
only If the actual coefficients of variation for daily
values and 7 and 30 day average plant effluent
concentrations are as specified.
aThese are assumed to be representative of the treatment plant
effluent behavior.
bTable 2-1, equation 2-17.
GPermit limit = C£/Ra; CE=4.39.
3-22
-------
COMMENTARY
Permit Limits Daily Maximum Weekly Monthly
Reduction factors (see p. 3-6) 0.281 0.439 0.643
Choice of averaging period (from
. ,, no yes no
step 6) -*
Value for the selected averaging
period (from step 6 - steady state - 10
model output)
Permit limits using reduction 10 (0.439) =15.6 10(0.439) = 6.
factors, Ra 0.281 0.643
Long-term average effluent 4 3g 4 3g 4 3g
concentration, CE (see p. 3-6)
Coefficient of variation of daily,
weekly, and monthly permit limits 0.7 0.4 0.2
(see p. 3-6)
The long term average effluent concentration for the
required level of treatment is equal to 4.39 mg/1 with
the coefficient of variation of daily effluent
concentrations equal to 0.7. To meet the water quality
standard at the state specified design flow and to meet
the acute criteria at all times except for 1 day once in
10 years, the treatment facilities need to be built to
meet the long term average concentration of 4.39 mg/1
with coefficient of variation of daily effluent
concentration VCE = 0.7. The permit limits derived above
are based on daily, weekly, and monthly reporting
procedures. If less than adequate monitoring is
required, the appropriate permit limits must be derived
using the long term average and equivalent coefficient
of variation.
3-23
-------
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
Recapitulation
In order to aid in the understanding of the suggested procedure,
the sequence is reviewed below in outline form.
1. Establish streamflow characteristics.
QS VQS
2. Establish effluent flow characteristics.
QE VQE
3. Establish effluent concentration variability characteristics
(VCE) daily values and 7 and 30 day averages.
Coefficient of Variation
Averaging Period VCE
1-day 0.7
7-day 0.4
30-day 0.2
4. Establish effluent limit from steady state wasteload
allocation.
EL = 10
5. Establish violation frequency of EL.
1-a = 1%
a = 99%
and assume CEa = EL
3-24
-------
COMMENTARY
1. These should be site specific since the computation is
usually sensitive to the values.
2. Mean effluent flow is important, but the coefficient of
variation, since it is usually small, is usually not
significant if VQE = VQS
3. These coefficients of variations specify the behavior of
the daily values and temporal averages of effluent
concentrations. More detailed evaluations for industry
specific or pollutant specific situations are required
to be more definitive. The values used are not suggested
as universal.
4. The analysis presented in this manual does not evaluate
the degree of protection afforded by this choice. That
is, the probability of violation of the chronic criteria
is not calculated. It is assumed to be sufficiently
protective.
5. The choice of violation frequency is necessary in order
to give a specific probabilistic meaning to EL.
Reasonable values appear to be one or five percent.
However, a problem may arise if too frequent a violation
frequency is chosen. It may turn put that even
specifying the permit as a daily maximum does not insure
that acute criteria violations are sufficiently rare. In
this case, a lower probability of violation must be
specified.
3-25
-------
EXAMPLE COMPUTATION - HAND CALCULATION
(continued)
6. For a (step 5) and coefficients of variation (step 3) compute
ratio of mean effluent to effluent limit, Ra = CE/CEa and the
resulting mean effluent concentration CE for each averaging
period.
Reduction Factor
Averaging Period Mean Effluent Concentration
Ra CE
1-day 0.281 2.81
7-day 0.439 4.39
30-day 0.643 6.43
7. Evaluate each mean effluent concentration using POM to
compute me return period of acute criteria violation. Choose
the appropriate averaging period.
Return Period (years) for
CO = 6.25
Averaging Moments Quadrature
Period CE Approximation Method
1-day2.8131 281
7-day 4.39 7.7 31.8 > 10 years
30-day 6.43 2.6 6.44
Establish appropriate permit limits for other averaging
periods. CE = 4.39, l-a = 1%.
Averaging Period VCE Ra Permit Limit3
1-day0.700.28115.6
7-day 0.40 0.439 10.0
30-day 0.20 0.643 6.83
^Permit Limit = CE/Ra; 1% violation frequency.
3-26
-------
COMMENTARY
5. This calculation makes the connection between the
effluent limit and the mean effluent concentration
required to meet the effluent limit if it is assigned to
daily values or 7 or 30 day averages. A treatment plant
designed to produce CE and whose variability is as
specified in (3) will meet the effluent limit with one
percent violation frequency.
7. The three treatment plant designs (the three mean
effluent concentrations) and the daily effluent
variability are used in PDM to compute the return period
of an acute criteria violation. The moments approximation
is sufficient if the return periods are significantly
less than or greater than the 10 year criteria violation
frequency being examined. In this case, the 7-day
averaging period result is close to 10 years and the more
accurate computer method is used to improve the accuracy
of the calculation. The calculation indicates that a mean
effluent concentration of CE = 4.39 and a daily VCE = 0.7
is sufficiently protective for acute criteria violations.
This, then, is the basis for the treatment plant design.
The permit limits for the other averaging periods are now
calculated to be consistent with the treatment plant
design. That is, these permit limits are consistent with
effluent mean and coefficients of variation as indicated,
and specify the same performance. Thus, they are
equivalent requirements.
3-27
-------
3.3 EXAMPLE COMPUTATION - COMPUTER PROGRAM
This section illustrates the use of the POM-PS computer program
(included and described in Appendix D) to the solution of the
example presented in the previous section. The site-specific
conditions used to define input values in the previous section are
used in this section as well.
The PDM-PS is structured to accept inputs in the form of
statistical parameters and ratios, determined readily from the
data. The following ratios are entered for this example
computation:
Stream Flow Ratio 1QIO/QS = 23.3/467 = 0.05
Effluent Dilution Ratio 1QIO/QE = 23.3/7.77 = 3.0
Effluent Concentration CE/EL = (*)
Reduction Factor
(*) Reduction factor assigned depends on permit averaging period.
As determined earlier.
30 Day - - - - R = 0.643
CE/EL 7 Day - - - - R = 0.439
1 Day - - - R = 0.281
The only other inputs called for are the coefficients of variation
of stream flow, effluent flow, and effluent concentration, which
have already been determined.
The facing page illustrates the Input prompts that are displayed
when the program is run, and the values entered in response to the
prompts, in this case for evaluating the 30-day permit averaging
period.
3-28
-------
COMMENTARY
DISPLAY AND PROMPTS
POINT SOURCE - RECEIVING WATER
CONCENTRATION ANALYSIS
RESPONSE ENTRIES
INPUTS: COEF VAR OF QS,QE,CE
RATIO...7Q10/avgQS
RATIO...7Q10/avgQE
RATIO... avgCE/EL
BACKGROUND STREAM CONC (CS)
IS ASSUMED TO BE ZERO
ENTER COEF VAR OF QS,QE,CE?
ENTER FOLLOWING RATIOS:
7Q10/avg QS?
7Q10/avg QE?
avgCE/EL?
1.5, 0.2, 0.7
NOTE:
0.05
3.0
0.643
This prompt repeats after the
selected range of values has
been computed and displayed. It
allows the user to be guided by
output In selecting values and
ranges for subsequent
computations.
0.01, 0.06, 0.01
0.08, 0.36, 0.04
0.40, 4.0, 0.2
The manual analysis presented earlier, computed the
ENTER LOWEST, HIGHEST, AND
INCREMENT OF MULT OF TARGET FOR
WHICH% EXCEED IS DESIRED
ENTER LOWEST, HIGHEST, AND
INCREMENT OF MULT OF TARGET FOR
WHICH% EXCEED IS DESIRED
exceedance probability and recurrence interval for specific stream
concentration values. The computerized computation generates these
results for stream concentrations expressed as multiples of the
target concentration (CL) that is explicitly assumed to result
when
Effluent Concentration
CE = EL (the effluent limit;
Effluent Flow
Stream Flow
QE = QE (average QE
QS = 7Q10 (the design stream flow)
3-29
-------
EXAMPLE COMPUTATION - COMPUTER PROGRAM
(continued)
PROGRAM OUTPUT
RECEIVING WATER CONG (CO)
PROBABILITY DISTRIBUTION
AND RETURN PERIOD
FOR MULTIPLES OF TARGET CONG
DUE TO POINT SOURCE LOADS
COEF VAR QS = 1.50
COEF VAR QE = 0.20
COEF VAR CE = 0.70
7Q10/ave QS = 0.05
7Q10/ave QE = 3.00
ave CE/EL = 0.64
STREAM CONCENTRATION (CO)
MULT OF
TARGET
0.02
0.03
0.04
0.05
PERCENT
OF TIME
EXCEEDED
..............
80.916
71.039
62.788
55.862
RETURN
PERIOD
(YEARS)
0.003
0.003
0.004
0.004
0.005
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
40.808
28.659
21.170
16.201
12.728
10.206
8.320
6.875
0.007
0.010
0.013
0.017
0.022
0.027
0.033
0.040
0.40
0.60
0.80
.00
.20
.40
.60
.80
2.00
5.746
2.650
1.399
0.804
0.490
0.312
0.206
0.140
0.097
0.048
0.103
0.190
0.341
0.559
0.878
1.331
1.961
2.821
3-30
-------
COMMENTARY
This output is for a 30-day permit average period (Ra = 0.643)
The range of values selected here is broad enough to
facilitate construction of probability and recurrence
interval plots.
Stream concentrations listed are in terms of a ratio to the
target concentration (CL). In this example, the target stream
concentration is:
CL = 2.5
Actual stream concentration is this value multiplied by the
listed value: e.g., the multiple of Target (CO/CL) = 0.4
Corresponding stream concentration is:
0.4 X 2.5=1.0
Since the acute-to-chronic ratio for pollutant (P) is
6.25/2.50 = 2.5, acute exceedences are reflected by multiple
2.5.
Probability or recurrence interval plots can be constructed,
simply by plotting the values listed in the computer
printout.
Note that the probability distribution of stream
concentrations deviates from-log-normal (a straight line) at
the higher exceedance percentiles.
3-31
-------
EXAMPLE COMPUTATION - COMPUTER PROGRAM
(continued}
STREAM CONCENTRATION (CO) (cont.
MULT OF
TARGET
(CO/CL)
PERCENT
OF TIME
EXCEEDED
oTo'el"""
0.050
0.036
0.027
0.020
0.016
0.012
0.009
0.007
0.006
RETURN
PERIOD
(YEARS)_
-37977
5.507
7.509
10.098
13.411
17.612
22.894
29.482
37.640
47.674
2.20
2.40
2.60
2.80
00
20
40
60
80
4.00
3-32
-------
COMMENTARY
10.!
o
u
u
Z
O
-
z
tu
U
o
u
UJ
cr
. OI
I i i
.01 .1
2 5 10 30 50 70
90
99 99.9 99.99
% EQUAL OR LESS THAN
Figure 3-6 - Concentration versus probability for PDM-PS
computation
I0c
3
Z
U
U
o
u
UJ
-------
EXAMPLE COMPUTATION - COMPUTER PROGRAM
(continued)
To examine stream concentration effects for other permit averaging
periods, repeat the analysis, substituting the appropriate value
for the reduction factor (R = CE/EL)
The return period curves provide a useful summary and perspective;
however, the evaluation can be performed without constructing the
graph. In this case, the range of concentrations specified might
(as shown below) simply bracket those of principal interest. In
this case, a range of CO/CL from 0.5 to 3 is selected, because the
chronic limit (CL= 1), and the acute limit to be exceeded no more
than once every 10 years Is CO/CL = 2.5.
The relevant portions of the output for the three permit averaging
periods are shown below:
STREAM CONCENTRATION (CO)
30-Day Average
CE/EL = 0.643
7-Day Average
CE/EL = 0.439
1-Day Average
CE/EL = 0.281
MULT OF
TARGET
(CO/CL)
oTso"
1.00
1.50
00
50
3.00
0.50
1.00
1.50
2.00
2.50
3.00
0.50
1.00
1.50
2.00
2.50
3.00
PERCENT
OF TIME
EXCEEDED
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
.818
.804
.252
.097
.043
.020
.717
.272
.069
.023
.009
.004
.560
.060
.011
.003
.001
.000
RETURN
PERIOD
( YEARS )
0
0
1
2
6
13
0
1
3
12
31
74
0
4
23
90
281
756
.072
.341
.085
.821
.443
.411
.160
.008
.957
.149
.819
.364
.489
.601
.866
.571
.076
.249
3-34
-------
COMMENTARY
In this case a different averaging period would be selected than
that based upon the manual computation. Acute criteria exceedences
have a mean recurrence interval shorter than 10 years for a 30-day
permit average, so it would be rejected in favor of a 7-day
average, which meets the guideline.
Note that the exact computation using the computer program
indicates a 5.4 year return period for acute violations, compared
with a 2.6 year return period estimated by the manual
approximation. The manual approximation tends to give conservative
projections for the longer return periods that are of interest,
though differences vary depending on specific input conditions.
Hence, there will be marginal cases where the approximate
computation may reject a 30-day average inappropriately.
On the other hand, wherever the manual approximation accepts a 30-
day permit average as appropriate, it is safe to assume that the
more exact computation will not modify the choice.
For the site specific conditions assumed for the example analysis:
Any pollutant with an acute-to-chronic
ratio of 9.5 or greater would, based on the
manual approximation, always be assigned a
30-day permit average.
The POM-PS computation extends this to
pollutants with acute-to-chronic ratios of
3 or more.
NOTE: EPA interprets any return period greater than 25 years as
being highly improbable
3-36
-------
CHAPTER 4
RANGE OF EXPECTED VALUES FOR STREAMS IN U.S.
As illustrated in Chapter 3, the method can be applied to any
site specific evaluation for which the relevant statistical
parameters are available or can be estimated. The purpose of this
section is to present a concise summary of the results of such
computations for the range of site conditions that are likely to
be encountered in practice. This chapter provides such a
compilation along three lines. Section 4.1 describes the basis for
the input values selected to provide a representative range of
site conditions, and presents the results of an analysis using
these typical ranges in the methodology described previously. The
stream flow characteristics were determined from an analysis of
180 streams and rivers; treatment plant effluent characteristics
are based on analysis of data from over 400 POTWs. The results in
this section apply for conservative (nonreacting) pollutants.
Section 4.2 describes how the information provided by such an
analysis can be used as a screening tool for selecting permit
averaging periods. Section 4.3 presents results of a similar
analysis, except that it is specific to oxygen depletion by
biochemical oxygen demand (BOO) loadings. Section 4.4 extends the
analysis for conservative pollutants to the special case of
streams that are highly effluent dominated, including those with
significant zero-flow Periods.
4.1 Analysis for Conservative Substances
The review of stream flow and effluent statistics presented
in Appendix 8 indicates that the following ranges are reasonable.
Effluent
4-1
-------
concentration variability, (VCE) i is in the range of VCE = 0.3 -
1.1. Effluent flow variability, (VQE) , is generally small relative
to stream flow variability and, therefore, does not greatly
influence the computation. VQE = 0.2 is consistently used. Stream
flow variability follows from the empirical relationship of VQS and
1QIO/QS . For a specified ratio, the range of VQS, as indicated by
the data discussed in Appendix B, is used. The ratio 1Q1Q/QS
varies considerably. A representative range is 1Q1Q/QS = 0.01 -
0.25. Finally, the magnitude of the effluent flow relative to the
stream flow is specified by the effluent dilution ratio: 1QIO/QE.
A range from 1QIO/QE= 1 - 50 is chosen to represent effluent
dominated streams and large streams with small discharges. A 10
year return period has been selected as the acute criteria
violation frequency.
In order to compute the ratio of the mean effluent
concentration to the effluent limit Ra = CE/EL, it is assumed that
the permit violation frequency is one percent. The final
specification required is the relationship of 7 and 30 day average
effluent concentrations to the daily effluent concentration
coefficient of variation, VCE Based upon the data presented in
Table C-2, it appears reasonable to expect that the 7-day averages
have a coefficient of variation that Is 0.8 of the dally values,
and that 30 day averages have a coefficient of variation of 0.6 of
the daily values. Thus, the reduction factors used are:
Coefficient of Variation Reduction Factor, Ra
of Daily Values a = 99 percent
VCE 1-day 7-day 30-day
0.3 0.527 0.593 0.671
0.7 0.281 0.340 0.425
1.1 0.187 0.229 0.296
4-2
-------
The results of these computations are summarized in Figure
4-1 and given in detail in Tables 4-1 to 4-4. The three choices
for permit average are shown. Each group of bars represents the
range in effluent concentration variability, VCE Each individual
bar represents a particular effluent dilution, 1QIO/QE. Finally,
the length of each bar represents the range that results from the
range of stream flow variability (1QIO/QS = 0.01 - 0.25) and the
associated coefficient of variation, VQS . The ordinate is the
downstream concentration (in multiples of the chronic criteria)
which has a 10 year return period.
A number of features are immediately apparent. For pollutants
with an acute to chronic ratio of greater than 10, no acute
criteria violations are projected over the ranges Investigated,
and 30-day average permit specifications appear to be sufficiently
protective. For acute-to-chronic ratios of less than 10, site
specific considerations are important.
The results are most sensitive to the stream flow parameter
1QIO/QS, as can be seen from the range covered by each bar. For
example, the last bar in the figure, 30-day permit averaging
period, 1QIO/QE = 50, vCE=l-l/ covers the range from |3= 0.9 to 4.6,
corresponding to 1QIO/QS = 0.01 and VQS = 2-4.
Following, in order of decreasing sensitivity, is the
effluent dilution ratio: 1QIO/QE. A significant distinction can be
found between
1The EPA is presently considering the issue of allowable duration
and frequency of exposure to toxicity. Based upon this word,
duration and frequencies used as the decision criteria may change.
This guidance does not recommend any particular minimum acceptable
duration or frequency.
4-3
-------
-i 5
S
o
u
T
I 38 SO
EFFLUENT
DILUTION
(TOIO/AVO.OE)
u
NOTE'-
MEICMT OF BAN INDICATES STREAM
> FLOW VARIABILITY (7010/OS)
EFFLUENT LIMIT FROM WLA
SPECIFIED AS DAY AW.
CFFUJENT UNIT FROM WLA
SPECIFIED AS 7 . DAY AV*.
EFFLUENT LIMIT FROM WLA
AS 30 WT Ava.
^INDICATES THE STREAM CONCENTRATION (co) WHICH WILL BE EXCEEDED WITH A
FREQUENCY OF ONCE IN TEN YEARS, EXPRESSED AS A MULTIPLE OF THE CHRONIC
CRITERIA (CL)
Figure 4-1 - Effect of permit averaging period on stream
concentrations for conservative substances:
general analysis
4-4
-------
TABLE 4-1 - Averaging period selection matrix for conservative substances: effluent dilution ratio
- 1QIQ/QE = 50
Stream
Flow
7Q10/QS
Avg. Q
0.01
0.05
0.10
0.15
0.25
Estimate
of
Variability
Range VQS
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
2.00
3.00
4.00
1.00
1.50
2.00
0.75
1.00
1.50
0.60
0.90
1.25
0.50
0.75
1.00
Effluent VCE :
30- 7-
Day Day
Avg . Avg .
1.0
3.0
6.1
0.9
2.3
4.7
1.0
1.7
4.4
1.0
2.0
4.1
1.3
2.4
4.1
0.9
2.7
5.4
0.8
2.0
4.2
0.9
1.5
3.9
0.9
1.8
3.7
1.1
2.1
3.6
= 0.3
1-
Daily
Max.
0.8
2.4
4.8
0.7
1.8
3.7
0.8
1.4
3.4
0.8
1.6
3.3
1.0
1.0
3.2
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.9
2.5
4.9
0.9
2.2
4.2
1.1
1.8
4.2
1.2
2.2
4.1
1.6
2.6
4.2
0.7
2.0
3.9
0.7
1.7
3.4
0.8
1.4
3.3
0.9
1.7
3.3
1.3
2.1
3.4
= 0.7
1-
Daily
Max.
0.6
1.7
3.2
0.6
1.4
2.8
0.7
1.2
2.7
0.8
1.4
2.7
1.0
1.7
2.8
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.9
2.3
4.4
1.0
2.2
4.1
1.2
1.9
4.2
1.4
2.4
4.3
1.9
2.9
4.6
0.7
1.8
3.4
0.7
1.7
3.2
0.9
1.5
3.2
1.0
1.8
3.3
1.5
2.3
3.5
= 1.1
1-
Daily
Max.
0.5
1.5
2.8
0.6
1.4
2.6
0.8
1.2
2.7
0.9
1.5
2.7
1.2
1.9
2.9
4-5
-------
TABLE 4-2 - Averaging period selection for conservative substances: effluent dilution ratio - 1QIO/QE
= b
Stream
Flow
7Q10/
Avg. Q
0.01
0.05
0.10
0.15
0.25
Estimate
of
Variability
Range VQS
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
2.00
3.00
4.00
1.00
1.50
2.00
0.75
1.00
1.50
0.60
0.90
1.25
0.50
0.75
1.00
Effluent VCE :
30- 7-
Day Day
Avg . Avg .
1.0
2.2
3.1
0.9
1.9
2.9
1.0
1.5
2.8
1.0
1.8
2.8
1.3
2.0
2.8
0.9
1.9
2.8
0.8
1.7
2.6
0.9
1.4
2.5
0.9
1.6
2.5
1.1
1.8
2.5
= 0.3
1-
Daily
Max.
0.8
1.7
2.5
0.7
1.5
2.3
0.8
1.2
2.2
0.8
1.4
2.2
1.0
1.6
2.2
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.9
2.0
3.1
0.9
1.9
3.0
1.1
1.7
3.1
1.2
2.0
3.2
1.6
2.4
3.4
0.7
1.6
2.5
0.8
1.5
2.4
0.9
1.4
2.5
1.0
1.6
2.5
1.3
1.9
2.7
= 0.7
1-
Daily
Max.
0.6
1.3
2.1
0.6
1.3
2.0
0.7
1.1
2.1
0.8
1.3
2.1
1.1
1.6
2.2
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.9
2.0
3.1
1.0
2.0
3.2
1.3
1.9
3.4
1.5
2.3
3.5
2.0
2.8
3.9
0.7
1.5
2.4
0.8
1.6
2.5
1.0
1.5
2.6
1.1
1.8
2.7
1.5
2.2
3.0
= 1.1
1-
Daily
Max.
0.6
1.3
2.0
0.7
1.3
2.0
0.8
1.2
2.2
0.9
1.5
2.2
1.3
1.8
2.4
4-6
-------
TABLE 4-3 - Averaging period selection matrix for conservative substances: effluent dilution ratio -
1QIQ/QE = 3
Stream
Flow
7Q10/
Avg. Q
0.01
0.05
0.10
0.15
0.25
Estimate
of
Variability
Range VQS
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
2.00
3.00
4.00
1.00
1.50
2.00
0.75
1.00
1.50
0.60
0.90
1.25
0.50
0.75
1.00
Effluent VCE :
30- 7-
Day Day
Avg . Avg .
1.0
1.9
2.6
0.9
1.7
2.5
1.0
1.5
2.4
1.0
1.7
2.4
1.3
1.9
2.5
0.9
1.7
2.3
0.8
1.5
2.2
0.9
1.3
2.2
0.9
1.5
2.2
1.1
1.6
2.2
= 0.3
1-
Daily
Max .
0.8
1.5
2.0
0.7
1.3
1.9
0.8
1.2
1.9
0.8
1.3
1.9
1.0
1.5
1.9
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.9
1.9
2.7
1.0
1.8
2.7
1.2
1.7
2.8
1.3
2.0
2.9
1.6
2.3
3.1
0.7
1.5
2.2
0.8
1.5
2.2
0.9
1.3
2.3
1.0
1.6
2.3
1.3
1.9
2.5
= 0.7
1-
Daily
Max .
0.6
1.2
1.8
0.6
1.2
1.8
0.8
1.1
1.9
0.8
1.3
1.9
1.1
1.5
2.0
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.9
1.9
2.8
1.1
2.0
3.0
1.3
1.9
3.2
1.5
2.3
3.3
2.1
2.8
3.7
0.7
1.5
2.2
0.8
1.5
2.3
1.0
1.5
2.5
1.2
1.8
2.6
1.6
2.2
2.8
= 1.1
1-
Daily
Max .
0.6
1.2
1.8
0.7
1.3
1.9
0.9
1.2
2.0
1.0
1.5
2.1
1.3
1.8
2.3
4-7
-------
4-8
-------
TABLE 4-4 - Averaging period selection matrix for conservative substances: effluent dilution ratio
- 1QIQ/QE = I
Stream
Flow
7Q10/
Avg. Q
0.01
0.05
0.10
0.15
0.25
Estimate
of
Variability
Range VQS
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
2.00
3.00
4.00
1.00
1.50
2.00
0.75
1.00
1.50
0.60
0.90
1.25
0.50
0.75
1.00
Effluent VCE :
30- 7-
Day Day
Avg . Avg .
1.0
1.5
1.8
0.9
1.4
1.8
1.0
1.3
1.8
1.1
1.5
1.8
1.3
1.6
1.9
0.8
1.3
1.6
0.8
1.3
1.6
0.9
1.2
1.6
1.0
1.3
1.6
1.1
1.4
1.7
= 0.3
1-
Daily
Max.
0.8
1.2
1.4
0.7
1.1
1.4
0.8
1.1
1.4
0.8
1.2
1.4
1.0
1.3
1.5
Effluent VCE
30- 7-
Day Day
Avg . Avg .
1.0
1.7
2.1
1.1
1.7
2.2
1.3
1.7
2.4
1.4
1.9
2.5
1.8
2.2
2.6
0.8
1.3
1.7
0.9
1.4
1.8
1.0
1.4
1.9
1.2
1.6
2.0
1.4
1.8
2.1
= 0.7
1-
Daily
Max.
0.7
1.1
1.4
0.7
1.2
1.5
0.9
1.1
1.6
1.0
1.3
1.6
1.2
1.5
1.7
Effluent VCE
30- 7-
Day Day
Avg . Avg .
1.1
1.8
2.4
1.3
2.0
2.6
1.6
2.0
2.9
1.8
2.4
3.0
2.3
2.9
3.3
0.8
1.4
1.8
1.0
1.6
2.0
1.2
1.6
2.2
1.4
1.9
2.3
1.8
2.2
2.6
= 1.1
1-
Daily
Max.
0.7
1.1
1.5
0.8
1.3
1.7
1.0
1.3
1.8
1.2
1.5
1.9
1.5
1.8
2.1
4-9
-------
the effluent nominated streams, 1QIO/QE < 5, and the large stream
case, QE = 50 for the latter cases, the stream flow variability is
a more important determinant of the normalized downstream
concentration. Finally, the effluent variability, VCE= affects the
results by approximately a factor of 2, all other things being
equal.
4.2 Use As a Screening Tool
It is suggested that Figure 4-1 may be used as a screening
tool to separate the cases which can be dealt with immediately
from those for which more site specific information is required.
For the latter cases, the flow ratios, 1QIQ/QE and 1QIO/QS can
usually be found quite easily so that a more specific answer can
be found in Tables 4-1 to 4-4. The final determinant, VQS, requires
a log-normal analysis of the stream flow record. Since this is
reasonably straightforward, a more refined analysis is not
excessively burdensome and would serve to reduce the range of
possible values of P, from which the permit averaging decision can
be made.
As an example of such a screening analysis, consider the
hypothetical case of a state establishing permit averaging periods
for phenol. Phenol has an acute-to-chronic ratio of 4, so that
stream concentrations which exceed a multiple of 4 times the
chronic concentration will not be accepted (assuming that the
acute criteria is not to be exceeded on a daily basis more often
than once every 10 years).
Comparing the bars on Figure 4-1 with the multiple of P = 4, the
following conclusions relative to the permit averaging period can
be
4-10
-------
drawn. For situations with an effluent dilution ratio of 5 or
less (1QIO/QE < 5) :
a. A 30-day permit averaging period will be selected whenever
the VCE is 0.7 or less.
b. Where VCE =1.1 a 7-day permit averaging period will meet
requirements under all reasonable possibilities of stream
flow variability (VQS) . (The upper ends of the bars correspond
to high values of VQS . )
c. Even for effluent variability as high as VCE = !!/ there will
be many streams where it would be appropriate to select a 30-
day permit average, since only the upper end of the bars
exceeds a multiple of 4.
For an effluent dilution ratio 1QIQ/QE = 5, the third column from
the right (VCE =1.1; 30-day permit average) in Table 4-2 indicates
that only the highly variable stream flows approach violations
using a 30-day permit average. State records could be examined to
determine if the set of streams under consideration (or a
representative set from Appendix C) experiences VQS in this range.
A conservative decision, then, would be to select a 7-day
permit averaging period, although a site-specific assessment of
stream flow variability or a restriction of vQS values could be
expected (in most cases) to support selection of a 30-day permit
averaging period.
4-11
-------
4.3 Preliminary Analysis for Dissolved Oxygen
The choice, of permit averaging periods for effluent limits
of oxygen-consuming pollutants, such as BOD or ammonia, is a more
complex problem than that addressed in the previous sections. The
variations of the minimum or critical DO are caused not only by
effluent concentration and dilution fluctuations, which are
addressed by the probabilistic dilution model, but also by
fluctuations in reaction rates and other sources and sinks of DO,
such as algal production, respiration, and sediment oxygen demand.
Stream flow and temperature variations affect these parameters,
the latter also determining the DO saturation. A comprehensive
probabilistic analysis that would include these effects as well is
beyond the scope of this report.
It is desirable, however, to provide at least a preliminary
analysis for suitably restricted cases that are amenable to
analysis using the probabilistic dilution model. The method to be
employed makes use of the similarity of the formula for critical
DO deficit for those streams for which the simple Streeter-Phelps
formulation is adequate, and the dilution equation. The principal
assumptions are (1) a single point source of BOD is the only DO
sink; (2) the stream flow, geometry and reaction rates are
spatially constant; and (3) the reaction rates are temporally
constant. For this restrictive situation, the critical or maximum
dissolved oxygen deficit (Dc) is a function of the reaeration rate
(Ka), the BOD oxidation rate (Kd) and the ultimate-to-5-day BOD
ratio.
4-12
-------
The Streeter-Phelps equation can be solved for the
critical or dissolved oxygen deficit (Dc) :
Dc « CE F 9 . p (4-1
where:
CE = treatment plant effluent BOD5 concentration.
F = ratio of ultimate/5-day BOD. Stream calculations are
based on ultimate BOD; effluent criteria on 5-day BOD.
cp = stream dilution factor QE/(QS = QE) .
P = stream purification factor; for a BOD oxidation rate (Ka
and stream reaeration rate (Ka)
P « ( A )1-A ; where A -
(Note that if the purification factor were constant then Equation
4-1 would be formally equivalent to the dilution equation analyzed
previously.) One remaining difficulty is that it is not the
critical DO deficit (Dc) that is of concern but rather the critical
dissolved oxygen (DOc) itself:
D°c CSat - D
(4-2)
which is a function of stream temperature through the DO
saturation concentration, Csat. Hence, the applicability of
probabilistic dilution to the dissolved oxygen problem requires
that the analysis be restricted to periods for which temperatures
are essentially constant and fluctuations in the purification
factor (P) are small.
4-13
-------
An evaluation of this latter effect can be made as
follows. A relationship between P and stream depth, H, which
follows from Ka and K] and total stream flow are
negatively correlated would further reduce the effect.
Hence, the key observation is that If it were possible to
restrict consideration to those flows for which VQS = VCE, then
purification factor fluctuations would not be very significant and
probabilistic dilution can be applied. If these flows also
correspond to periods of
4-14
-------
approximately constant temperature, then the two requirements
for applying probabilistic dilution to critical dissolved oxygen
have been met. For a site-specific analysis, the obvious solution
is to seasonally analyze the stream flow and temperature data and
apply probabilistic dilution, making any necessary corrections for
purification factor variations. However, for the general case
considered here, an alternate approach is required.
Consider, instead, restricting consideration to that period
of the year during, which flows are low. This period corresponds,
presumably, to the period of time during which 7Q10 occurs, and
includes the conditions for which the WLA was performed.
Considering this period alone significantly reduces the
variability of the stream flows to be considered. If, in addition,
it can be argued that these low flows tend to occur during the
same season each year, then the temperature variation is less than
the annual variability and will be less significant as well.
Hence, for these low flow periods, the assumption of constant P is
much more realistic.
The technical problem to be solved is to compute the
reduction in the average stream flow and coefficient of variation
when flows are restricted to the low values for this restricted
period. We restrict consideration to the lowest one-sixth of the
total population. This corresponds to an average of 2 out of 12
months in each year, and the presumption is that this period
recurs during the same months each year so that the temperature-
variation during this restricted period is small. This
simplification also assumes that the lower one-sixth of the daily
stream flows occur only in the two month period when temperature
and reaction rates are assumed to be approximately constant.
4-15
-------
As indicated earlier, a statistical analysis of actual stream
data, stratified by month or critical season, could be performed
to provide actual results and avoid the need for this type of
estimate. However, data of this type are not presently available.
The estimation described There is performed in order to allow a
preliminary analysis for BOO/DO to be made.
The computation of the required statistical parameters, the
stream flow average and coefficient of variation for flows
restricted to the lower a-quantil e of the total population, is
straightforward! For log-normal random variables, it can be shown
that these conditional moments, denoted by primes, are:
= Q(olnQS + Za)/Q(Za) (4-6)
os
v2QS = exp(o2lnQS) Q(2o2lnQS + Za) Q(Za) - 1 (4-7)
Qz(oinQS + Za)
where Q(Z*) = Pr Z > Z* for Z, a standard normal random variable,
and Za are the Z scores for the a-quantile which is the upper bound
for the flows being considered. For a = 1/6, Za = 0.967. Table 4-5
presents the results. These corrections, when applied to 1Q1Q/QS
and VQS in the first two columns of Tables 4-1 to 4-4 adjust these
parameters to represent the low flow periods. For highly variable
streams, VQS and therefore ainQs are large and the corrections are
quite substantial.
Reduction factors for the mean range from 0.45 to 0.024 for
the highly variable streams. The range in coefficient of variation
is sharply
4-16
-------
TABLE 4-5 - Conditional moments for the low flow subpopulation
(a = 16.75)
Coefficient of Variation
for
EntiiTG ^ ^""^ ^
rxc o^ j_ ^
Reduction
in
Mean
QS' /QS
Reduced
Coefficient of
variation
VQS VQS'
0,
0,
0,
0,
1,
1,
1,
2,
3,
4,
.50
.60
.75
.90
.00
.25
.50
.00
.00
.00
0
0
0
0
0
0
0
0.
0.
0.
.450
.384
.306
.247
.216
.158
.120
0761
0389
0241
0
0
0
0
0
0
0
0
0
0
.188
.216
.254
.287
.306
.348
.381
.431
.500
.547
This table provides a basis for a preliminary estimate of the
average stream flow and flow variability during critical low flow
periods, relative to overall long-term characteristics. For site-
specific cases, the actual values can be determined readily from a
statistical analysis of stream flows during the selected critical
period of the year.
4-17
-------
compressed from VQS = 0.5 - 4.0 to VQS = 0.19 - 0.55, so that the
sub-population of low flows fluctuates much less violently than
the entire population, which includes the annual cyclical
variation as well.
A 10 year return period was selected for consistency with the
general analysis, but since only one-sixth of the flow population
is being considered, and we assume that no DO acute criteria
violations occur during the remaining higher flows, the exceedence
probability to be applied in the probabilistic dilution
calculation is a 10/6 = 1.67 year return period. Figure 4-2 and
Tables 4-6 to 4-8 present the results.
In order to properly evaluate the computations, it is
necessary to realize that they apply to 10 year return period
critical deficit ratios. To convert critical DO concentrations to
the deficit ratio (p) shown by the tables, the DO standard (CL)
the DO saturation (Csat) used in the WLA, and the DO concentration
taken to represent an acute criteria value are required. For most
reasonable combinations of these values, the ratio will be between
approximately 2.0 and 2.5. For example, if CS =3, CL = 5, and
acute DO = 2, then |3=2.0. Alternatively, if these concentrations
are CS = 9.0, CL = 6.0, acute DO = 1.5, then (the acute-to-chronic
deficit ratio) |3 =2.5.
Appropriate permit averaging periods are seen in Tables 4-6
to 4-8 to be strongly influenced by local conditions of effluent
load and stream flow variability. Because of this, a general
statement on permit averaging period for effluent BOD/DO is not
possible; it must be selected on the basis of site conditions.
4-18
-------
8
o
o
o
z
o
LfSfMO-
Hi NOTE:
HEIGHT OF BAA INDICATES STREAM
FLOW VARIABILITY (7010/03)
I 95
EFFLUENT
DILUTION
(7010/AVQ.OE)
EFFLUENT LIMIT FftOM WLA
SPECIFIED AS DAY AV«.
EFFLUENT LIMIT FMM WLA
SFCOF1ED AS f DAY AVO.
EFFLUENT LIMIT FROM WLA
SPECIFIES AS 30 OAYAVG.
^INDICATES THE STREAK CONCENTRATION (co) WHICH WILL IE EXCEEDED
WITH A FREQUENCY Of ONCE IN TEN YEARS, EXPRESSED AS A MULTIPLE OF
THE CHRONIC CRITERIA (CL).
Figure 4-2 - Effect of permit averaging period on stream,
concentrations for BOD/DO
4-19
-------
TABLE 4-6 - Permit averaging period selection matrix for MOD/DO: of fluent dilution ratio -
7Q10/OE = 5
Stream Flow Characteristics
All Periods Low Flow
7Q10/QS
0.01
0.05
0.10
0.15
0.25
VQS 7Q10/QS'
2
3
4
1
1
2
0
1
1
0
0
1
0
0
1
.00
.00
.00
.00
.50
.00
.75
.00
.50
.60
.90
.25
.50
.75
.00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
.13
.26
.41
.23
.42
. 66
.33
.46
.83
.39
. 61
. 95
.55
.82
.16
Periods
VQS'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.43
.50
.55
.31
.38
.43
.25
.31
.38
.22
.29
.35
.19
.25
.31
Effluent VCE = 0.3
30- 7- 1-
Day Day Day
Avg . Avg . Avg .
0.
1.
1.
0.
1.
1.
0.
1.
2.
0.
1.
2.
1.
1.
2.
5
0
6
6
2
9
8
2
0
9
4
2
2
7
4
0
0
1
0
1
1
0
1
1
0
1
1
1
1
2
.4
.9
.4
.6
.1
.7
.7
.0
.8
.8
.3
. 9
.0
.5
.1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
.4
.8
.3
.5
.0
.5
. 6
.9
.6
.7
.1
.7
. 9
.3
. 9
Effluent VCE = 0.7
30- 7- 1-
Day Day Day
Avg . Avg . Avg .
0
1
1
0
1
2
1
1
2
1
1
2
1
2
3
.5
.1
.8
.8
.4
.2
.0
.4
.5
.1
.8
.7
.5
.2
.0
0
0
1
0
1
1
0
1
2
0
1
2
1
1
2
.4
.9
.4
.6
.2
.8
.8
.2
.0
.9
.4
.2
.2
.8
.4
0
0
1
0
1
1
0
1
1
0
1
1
1
1
2
.4
.7
.2
.5
.0
.5
.7
.0
.7
.8
.2
.8
.0
.5
.0
Effluent VCE = 1
30-Day 7~
7 Day
Avg. 7
^ Avg.
0.
1.
1.
0.
1.
2.
1.
1.
2.
1.
2.
3.
1.
2.
3.
6
2
9
9
6
5
2
7
9
3
1
1
8
6
5
0
1
1
0
1
1
0
1
2
1
1
2
1
2
2
.5
.0
.5
.7
.3
.9
.9
.3
.2
.0
.6
.4
.4
.0
.7
.1
1-
Day
Avg.
0
0
1
0
1
1
0
1
1
0
1
2
1
1
2
.4
.8
.2
.6
.0
.6
.7
.0
.8
.8
.3
.0
.1
.6
.2
Critical DO deficit exceeded one day In 10 years as a multiple target deficit used in WLA.
4-20
-------
TABLE 4-7 - Permit averaging period selection matrix for BOD/DO: effluent dilution ratio -
1QIQ/QE = 3
Stream Flow Characteristics
All Periods Low Flow
7Q10/QS
0.01
0.05
0.10
0.15
0.25
VQS 7Q10/QS'
2
3
4
1
1
2
0
1
1
0
0
1
0
0
1
.00
.00
.00
.00
.50
.00
.75
.00
.50
.60
.90
.25
.50
.75
.00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
.13
.26
.41
.23
.42
. 66
.33
.46
.83
.39
. 61
. 95
.55
.82
.16
Periods
VQS'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.43
.50
.55
.31
.38
.43
.25
.31
.38
.22
.29
.35
.19
.25
.31
Effluent VCE = 0.3
30- 7- 1-
Day Day Day
Avg . Avg . Avg .
0.
1.
1.
0.
1.
1.
0.
1.
1.
0.
1.
2.
1.
1.
2.
5
0
5
7
2
8
8
2
9
9
4
0
2
7
2
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
.4
.9
.3
.6
.1
.5
.7
.0
.7
.8
.2
.8
.0
.5
. 9
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
.4
.8
.2
.5
.0
.4
.7
.9
.5
.7
.1
. 6
. 9
.3
.7
Effluent VCE = 0.7
30- 7- 1-
Day Day Day
Avg . Avg . Avg .
0
1
1
0
1
2
1
1
2
1
1
2
1
2
2
.6
.2
.7
.8
.5
.2
.0
.5
.4
.2
.8
. 6
.5
.2
. 9
0
0
1
0
1
1
0
1
1
0
1
2
1
1
2
.5
.9
.4
.7
.2
.7
.8
.2
.9
.9
.4
.1
.2
.7
.3
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
.4
.8
.2
.5
.0
.4
.7
.0
.6
.8
.2
.7
.0
.4
.9
Effluent VCE = 1
30-Day 7~
7 Day
Avg. 7
^ Avg.
0.
1.
1.
0.
1.
2.
1.
1.
2.
1.
2.
3.
1.
2.
3.
6
3
9
9
7
5
2
7
8
4
1
0
8
6
4
0
1
1
0
1
1
1
1
2
1
1
2
1
2
2
.5
.0
.5
.7
.3
.9
.0
.3
.2
.1
.6
.3
.4
.0
.6
.1
1-
Day
Avg.
0
0
1
0
1
1
0
1
1
0
1
1
1
1
2
.4
.8
.2
.6
.1
.6
.8
.1
.8
.9
.3
.9
.2
.6
.1
Critical DO deficit exceeded one day In 10 years as a Multiple target deficit used in WLA.
4-21
-------
TABLE 4-8 - Permit averaging period selection matrix for BOD/DO: effluent dilution ratio -
1QIQ/QE = I
Stream Flow Characteristics
All Periods Low Flow
7Q10/QS
0.01
0.05
0.10
0.15
0.25
VQS 7Q10/QS'
2
3
4
1
1
2
0
1
1
0
0
1
0
0
1
.00
.00
.00
.00
.50
.00
.75
.00
.50
.60
.90
.25
.50
.75
.00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
.13
.26
.41
.23
.42
. 66
.33
.46
.83
.39
. 61
. 95
.55
.82
.16
Periods
VQS'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.43
.50
.55
.31
.38
.43
.25
.31
.38
.22
.29
.35
.19
.25
.31
Effluent VCE = 0.3
30- 7- 1-
Day Day Day
Avg . Avg . Avg .
0.
1.
1.
0.
1.
1.
0.
1.
1.
1.
1.
1.
1.
1.
1.
6
0
4
8
2
5
9
2
6
0
4
7
2
5
8
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
.5
.9
.2
.7
.1
.4
.8
.1
.5
.9
.2
.5
.1
.4
. 6
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
.5
.8
.1
.6
.0
.2
.7
.9
.3
.8
.1
.3
.0
.2
.4
Effluent VCE = 0.7
30- 7- 1-
Day Day Day
Avg . Avg . Avg .
0
1
1
1
1
2
1
1
2
1
1
2
1
2
2
.7
.3
.7
.0
. 6
.1
.2
.6
.2
.4
.8
.3
.7
.1
.5
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
.6
.0
.4
.8
.3
.6
.0
.3
.8
.1
.5
.9
.3
.7
.0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
.5
.8
.1
.7
.0
.4
.8
.0
.5
.9
.2
.5
.1
.4
.7
Effluent VCE = 1
30-Day 7~
7 Day
Avg. 7
^ Avg.
0.
1.
2.
1.
1.
2.
1.
1.
2.
1.
2.
2.
2.
2.
3.
8
5
0
2
8
4
5
9
7
6
2
8
0
6
0
0
1
1
0
1
1
1
1
2
1
1
2
1
2
2
.6
.1
.5
.9
.4
.9
.1
.5
.1
.3
.7
.2
.6
.0
.4
.1
1-
Day
Avg.
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
.5
.9
.3
.7
.2
.5
.9
.2
.7
.0
.4
.8
.3
.6
.9
Critical DO deficit exceeded one day in 10 years as a multiple target deficit used in WLA.
4-22
-------
A table for the effluent dilution ratio (1QIO/QE) equal to
50 has not been prepared for BOD/DO. For small discharges entering
larger streams, it is likely that an effluent BOD limit determined
from a steady -state WLA analysis would be greater than the
technology-based limit which would be used in the permit. The use
of the standard matrix table* which would show a higher pattern of
violations, would tend to be misleading, since the computations
and the tables assume that the allowable effluent concentration
determined from a WLA becomes the effluent limit (EL) specified by
the permit.
It should be emphasized at this point that the dissolved
oxygen analysis presented in this section is meant only as a
preliminary application. There are, as yet, no verification
examples that support the applicability of a probabilistic
dilution/critical deficit analysis, It has not been shown that
actual stream 00 data conform to the probabilistic assumptions and
simplifications used in this preliminary analysis. Further, it is
well known that the DO distribution in streams cannot always be
described by the simplest (Streeter-Phelps) model. Upstream
sources of BOO and deficit are common, as are nitrification, algal
effects, and sediment oxygen demand. A more comprehensive analysis
would be required to Incorporate these effects into a calculation
of the effect of selecting a permit averaging period.
4.4 Analysis for Conservative Substances In Effluent-Dominated
Streams
An effluent -dominated stream Is defined, for the purpose of
this analysis, as one in which the effluent flow exceeds the
design stream flow
4-23
-------
(e.g., the 7Q10). There are then two bounds to this analysis.
The upper sound is the effluent dilution ratio 7Q10/avg QE = 1,
which was the lowest dilution ratio examined in Section 4.1. The
lower bound is provided by the case where the design stream flow
is zero (7Q10 = 0).
It should be recognized that as the degree of dilution
decreases, a WLA-based EL becomes increasingly restrictive. When
the design stream flow is zero, the effluent limit must equal the
stream target concentration (CL) .
While the degree of effluent domination has a subsequent
influence on the magnitude of an EL assigned in a permit, the
screening analysis results presented below suggest that in most
situations, a 30-day permit averaging period will be adequate for
effluent dominated streams.
The results of a broad hypothetical analysis of affluent
dominated streams are summarized in Figure 4-3 and Table 4-9,
using the format used earlier to illustrate the influence of
permit averaging period, effluent variability and dilution ratio.
o The bars on the provide the upper bound; i.e., the
condition where 7Q10/avg QE = 1 (these results were also shown in
Figure 4-1).
o The bars on the left represent an effluent dilution ratio
of 7Q10/avg QE = 0.1, that is, where effluent How is ten times
greater than design stream flow. High variability of daily flow is
expected for such streams, together with a very small ratio of
stream design flow to average stream flow. The screening analysis
assumes that the coefficient of variation ranges between VQS =
4-24
-------
u
o
? 5
§3-
2 -
I -
LffffMO?
NOTE:
HEIGHT OF BAH INDICATES STREAM
FLOW VARIABILITY (7010/08)
I a* I LO
OJ O.S
EFFLUENT
DILUTION
(7010/AVQ. OC)
Vet* 0.3 l/eg«Q.T Vct*U
EFFLUENT LIMIT PftOM WLA
SPECIFIED AS DAY AVO.
EFFLUENT LIMIT FKOM WLA
SFECJF1ED AS DAY AV9.
EFFLUENT LIMIT FROM WLA
SFECIFIEO AS 3Q DAY AV«.
^INDICATES THE STREAM CONCENTRATION (co) WHICH WILL BE EXCEEDED
WITH A FREQUENCY OF ONCE IN TEN YEARS, EXPRESSED AS A MULTIPLE OF
THE CHRONIC CRITERIA (CL).
Figure 4-3 - Effect of permit averaging period on stream
concentrations for conservative substances in
effluent-dominated stream
4-25
-------
TABLE 4-9 - Averaging period selection matrix for a fluent-dominated streams
Stream
Flow
7Q10/
Avg. Q
1.0
0.5
0.2
0.1
Estimate
of
Variability
Range VQS
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
LO
PROB
HI
2.00
4.00
5.00
2.00
4.00
5.00
2.00
4.00
5.00
2.00
4.00
5.00
Effluent VCE :
30- 7-
Day Day
Avg . Avg .
0.6
1.1
1.5
0.7
1.1
1.3
0.9
1.1
1.3
1.0
1.2
1.3
0.6
1.0
1.3
0.6
1.0
1.2
0.8
1.0
1.1
0.9
1.1
1.2
= 0.3
1-
Daily
Max .
0.5
0.9
1.2
0.6
0.9
1.1
0.7
0.9
1.0
0.8
0.9
1.0
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.6
1.2
1.6
0.8
1.2
1.6
1.0
1.4
1.7
1.2
1.6
1.8
0.5
0.9
1.3
0.6
1.0
1.3
0.8
1.1
1.3
1.0
1.3
1.5
= 0.7
1-
Daily
Max .
0.4
0.8
1.1
0.5
0.8
1.0
0.7
0.9
1.1
0.8
1.1
1.2
Effluent VCE
30- 7-
Day Day
Avg . Avg .
0.6
1.2
1.7
0.8
1.3
1.8
1.1
1.6
2.0
1.4
1.9
2.2
0.5
0.9
1.3
0.6
1.0
1.4
0.9
1.3
1.5
1.1
1.5
1.7
= 1.1
1-
Daily
Max .
0.4
0.8
1.1
0.5
0.9
1.1
0.7
1.0
1.3
0.9
1.2
1.4
4-26
-------
2 and VQS = 5, and estimates a stream flow ratio 7Q10/avg QS =
0.005, for this condition near the lower bound for effluent-
dominated streams.
The conditions under which the design stream flow is greater
than zero are listed in more detail in Table 4-9. Results for
several additional intermediate effluent dilution ratios
(1Q1Q/QE = 0.2 and 0.5) are also presented. A comparison of
results for an effluent ratio of 1.0 presented here as an
upper bound, and previously (Table 4-4 and Figure 4-1) as a
lower bound will indicate that results are similar but not
exactly the same. The differences are due to different
assumed values for 7Q10/QS and the range of coefficients of
variations used as inputs for the POM-PS model.
For the case where-the design stream flow is zero, 7Q10 is
zero and there appears to be a problem since 1Q1Q/QS and
1QIQ/QE are both zero, what actually matters is QS and QE
Thus, in order to evaluate these cases, the use of the actual
QS, QE and a small 7Q10 suffices since the computation
depends only on QS/ QE and 7Q10 cancels out (Equation D-14) .
Finally, the use of a small 1QIO/QE correctly indicates that
the WLA is done with QS = 0 (Equation D-15). Thus, no
problems arise.
Screening analysis results Indicate that In the case of
effluent-dominated streams, a 30=day permit averaging period
provides adequate protection for pollutants with the acute-
to-chronic ratios summarized below:
4-27
-------
When
30-Day Permit Average
Acute-to-Chronic Is Adequate for
Ratio Acute Protection
3 or more Always
Effluent variability is
2 to 3 relatively high, but
less than VCE = 1.1
4-28
-------
CHAPTER 5
USES AND LIMITATIONS
The probabilistic dilution model has been demonstrated to be
useful in selecting the appropriate averaging period for discharge
permits. The method is easily adaptable to situations which vary
widely in terms of stream and effluent characteristics, data
availability, and policy-level assumptions used in the analysis.
Although the example in Chapter 3 of how to use the method is
based on the typical WLA assumptions of 7Q10 as the design flow
and chronic criteria as the effluent limit, the method is easily
adjusted to accommodate other assumptions.
The method is intended to apply to pollutants for which the
regulatory concern is at the point of complete mixing and for
which the toxicity can be evaluated in terms of the total
pollutant concentration. The method has been applied to a range of
stream and effluent characteristics which typify the
characteristics of streams and effluents in the United States. The
results of this application are useful as a screening tool, by
which the appropriate averaging period for many field situations
can be readily; identified. However, pollutants whose toxicity is
a function of pH, temperature, and harness require site-specific
evaluations incorporating these parameters.
There are also several limitations on the use of the method.
One of the technical limitations is that the level of chronic
protection is based on state-specified design flow, e.g., 7Q10,
7Q2, etc., which may be overprotective or underprotective for many
site-specific conditions. The EPA is presently considering the
issue of allowable duration and frequency of
5-1
-------
exposure to acute as well as chronic toxicity. Users of this
manual are advised to refer to Part A, Stream Design Flow, of Book
VI, Selecting Design Conditions, when considering the choice of an
appropriate chronic exposure event. Book VI is currently under
peer review and will be issued by the Office of water Regulations
and Standards once the peer review process is completed.
Modifications are required to compute the probability
distribution of 30-day average concentrations, as required for
chronic criteria compliance; these would have to be investigated
and verified in the field.
The major shortcoming of the log-normal probabilistic
dilution model is its misrepresentation of the lowest stream
flows, thus tending to overestimate the probability of high stream
concentrations. The use of a seasonally segmented approach could
be investigated.
The effect of serial correlation on the return period
specification would also need to be investigated, particularly
with regard to the duration . of criteria violations. For example,
a knowledge of the return period for n-day successive violations
could be compared to the time scales of the criteria themselves.
This would provide a direct link to the toxicity data. At a less
sophisticated level of analysis, the tendency of criteria
violations to cluster on successive days could be investigated to
provide a basis for modifications to the method.
For pollutants whose toxicity is a function of such secondary
variables as pH, temperature and hardness, probabilistic methods
are essential in that it is not possible to rationally choose
"critical" or "sufficiently
5-2
-------
protective" values for these variables. Arbitrary choices cannot
be defended in terms of the probability of criteria violations.
Methods for analyzing these situations could be developed,
following the logic of probabilistic dilution and incorporating
the additional random variations of the variable.
The application of this method to dissolved oxygen has
indicated that the probabilistic method provides a useful approach
to the problem of DO deficit. However this work has only been a
first" step. Probabilistic methods can be further developed to
assess the effects of DO fluctuations on resources and to provide
a more rational approach to advanced waste treatment decisions.
5-3
-------
CHAPTER 6
REFERENCES
1. DiToro, D. M., Probability Model of Stream Quality Due to
Runoff. J. Environmental Engineering, American Society of Chemical
Engineers, Vol. 110, No. 3, June 1984, p. 607-628.
2. DiToro, 0. M. and Fitzpatriclc, J. J., Verification Analysis of
the Probabilistic Dilution Model, report prepared for EPA Contract
No. 68-01-6275, U. S. Environmental Protection Agency, Washington,
B.C., 1982.
3. Driscoll & Associates, Combined Sewer Overflow Analysis
Handbook for Use in 201 Facility Planning, report prepared for EPA
Contract No. 68-01-6148, U. S. Environmental Protection Agency,
Washington, B.C. (1981)
4. Hazen and Sawyer, Review of Performance of Secondary Municipal
Treatment Works, Draft Final Report for Contract 68-01-6275, Work
Assignment No. 5, U. S. Environmental Protection Agency,
Washington, O.C., December 1982.
5. Niku, Shroeder, and Samaniego, Performance of Activated Sludge
Process and Reliability Related Design. JWPCF, Vol. 51, No. 12,
December 1979.
6. Niku, et al., Performance of Activated Sludge Processes;
Reliability, Stability and Variability. EPA 600/52-81-227,
December 1981.
6-1
-------
7. Haugn, et al., Performance of Trickling Filter Plants:.
Reliability Stability and Variability. EPA 600/52-81-228, December
1981.
8. Hydroscience, Inc., Simplified Mathematical Modeling of Water
Quality, for u. S. Environmental Protection Agency, March 1971.
6-2
-------
APPENDIX A
Statistical Properties of Log-Normal Distributions
-------
This appendix is intended to present a brief, simplified
review of the statistical properties of log-normal distributions
which characterize the important variables in the water quality
analysis procedures used for this report. It is designed to help
the user without a formal background in statistics to appreciate
the physical significance of the statistical properties employed.
It is not the intent of this appendix to present a theoretical
discussion or to provide technical support for developing
relationships or equations used in the development of the methods
employed.
A-l. General Considerations
The factors which influence the concentration of a pollutant
in a receiving water body are subject to a significant degree of
variability. This variability results in fluctuations in the
resulting stream concentration, which is compared with target
concentrations such as criteria or standards, and which provides a
basis for decisions on treatment requirements. The approach
adopted in this report for examining the effects of different
averaging periods on treatment plant discharges uses the concept
"how much how often" as a basis for such decisions. It is,
therefore, essential that statistical aspects be Incorporated into
the methodology even though they may add complexity.
The standard statistical parameters of a population of values
for a random variable which are used as a concise means of
describing central tendency and spread are:
Mean: (p,x or x) the arithmetic average, x defines the average of
the available (usually limited) data set;
A-l
-------
H,x denotes the true mean of the total population of variable x. x
will be an increasingly better approximation of p,x as the size of
the sample (the number of data points) Increases.
Variance: (a2x) by definition, the average of the square of the
differences between individual values of x and the mean (x) . The
greater the variation in the data, the higher the variance:
o2x = (XI-K) - + (x2-x) - + (XN-x) -
N
Standard
Deviation: (ox) another measure of the spread of a population of
random variables; by definition, the square root of the variance;
Coefficient of
Variation: (vx) is defined as the ratio of the standard deviation
(ox) to the mean ((j,x) :
vx = ox/ux
It is the principal measure of variation used in the
analyses described in this report. The coefficient of
variation is a dimensionless quantity and Is thus freed
from any dependence on
A-2
-------
the specific dimensions used to describe the variable
(e.g., flow rate, concentrations, etc.). High
coefficients of variation reflect greater variability in
the random variable x.
Median: (x) This is the value in a data set for which half the
values are greater and half are lesser.
Mode: The "most probable value" -- more of the individual data
points are at this value (or are within this interval)
than at other values or ranges. On a frequency histogram,
this is the highest point on the graph. The mode has no
real significance in the calculations in the methodology
employed.
Comparing the statistical properties of different data sets
provides a convenient, concise way of recognizing similarities and
differences. This could not be accomplished simply by "looking at
the data" where reasonably large data sets are involved. These
statistical properties convey no information concerning frequency,
or the probability at which any particular value or range of
values in the total population will occur. This essential item of
information is provided by a knowledge of the type of
distribution, technically, the probability distribution function
(PDF) .
A-2. Probability Distributions
There are several different patterns which characterize the
distribution of individual values in a large population of
variable events.
A-3
-------
Most analysts are familiar with the normal distribution, in which
a histogram of the frequency of occurrence of various values
describes the familiar bell-shaped curve (Figure A-l(a)). When the
cumulative frequency is plotted on probability paper, a straight
line is generated as in Figure A-l(b) .
Many variables, particularly those which are important in
water quality applications, have been shown by a rapidly
accumulating body of data to be represented by or adequately
approximated by a log-normal distribution. A log-normal
distribution has a skewed frequency histogram (Figure A-l(c))
which indicates an asymmetrical distribution of values about an
axis defining the central tendency of the data set. There is a
constraining limit to lower values (sometimes zero) and a
relatively small number of rather large values but no upper
constraint. Point source effluent concentrations [1,2]= and
pollutant concentrations in combined sewer overflows and separate
storm runoff [3,4], are parameters which are usually well
characterized by log-normal distributions. In general, daily
stream flows are satisfactorily approximated by log-normal
distributions [5,6]. Scattered data from a number of unpublished
sources suggest that receiving water concentrations are also log-
normally distributed. Stream flows and concentrations are
currently being examined from this perspective. A log-normal
distribution appears as a straight line on log/probability paper
(using cumulative frequency) as shown in Figure A-l(d). In this
report natural (base "e") logs are used throughout.
Cumulative frequency is the relative frequency (or probability) of
values being less than or equal to a specific value.
A-4
-------
CD
O
u_
O
o
Z
(a)
Crt
O)
o
u.
O
o
MAGNITUDE OF VALUE (X)
MAGNITUDE OF VALUE (X)
NORMAL
LOG-NORMAL
X
UJ
u_
O
UJ
Q
10 50 90 99
PROBABILITY
% LESS THAN OR EQUAL
O"
UJ
a
I 10 50 90 '59
PROBABILITY
% LESS THAN OR EQUAL
Figure A-l- Probability distribution
A-5
-------
A-3. Relationship Between Distributions
There are circumstances when two different types of
distribution can begin to look similar -- so that either one will
provide a reasonably good approximation of the probability
distribution of a particular data set. For example, as the
coefficient of variation becomes smaller and smaller, approaching
zero, log-normal distributions begin to look more and more like a
normal distribution. Figure A-2 shows a series of histograms for
log-normally distributed populations, all having (arithmetic)
population means of 100, but with different coefficients of
variation (v) as shown. As discussed above, smaller values of v
approach a normal distribution.
A. 4. Properties of Log-Normal Distributions
Figure A-3 summarizes the pertinent statistical relationships
for log-normal probability distributions. The mathematical
formulas shown are based on statistical theory, and permit back-
and-forth conversions between arithmetic properties (in which
concentrations, flows, and loads are reported) and the log of the
variable (in which probability and frequency characteristics are
defined).
Normalized plots of probability versus the magnitude of a
variable expressed as a multiple of the mean are presented In
Figure A-4 for log-normal distributions. These plots present a
family of curves reflecting the effect of coefficient of variation
on probability of occurrence of events of specific magnitude.
These plots can be used directly in the
A-6
-------
u
z
LJ
3
O
z
uJ
O
UJ
*
U
z
O
UJ
IT
COEFFICIENT
VARIATION
MEDIAN, x
MEAN
COEFFICIENT OF
VARIATION
,s 1.0
COEFFICIENT OF
VARIATION
RANDOM VARIABLE
Figure A-2 - Effect of coefficient of variation on frequency
distribution
A-7
-------
Arithmetic Soace
log Soace
Natural Logs (base e!
Frequency
in x
x is a random variable
x
Ux
a2,
Ox
Vx
X
Definition of Terms
Random Variable
In x
Pr
Mean Uin x
Variance o2in x
Standard Deviation Oin x
Coefficient of Variation... (not used)
Median
Relationships Between Statistical Properties
In Arithmetic and Log Space
Ux = exp [Uinx + ^ 0inx]
X = exp [Uinx]
vx = Vexp (o2inx) - 1
Ox = UXVX
Oinx =
(1 + Vx
Figure A-3 - Pertinent relationships for log-normal distributor
A-8
-------
UJ
2
UJ
O
UJ
_j
Q.
UJ
2
UJ
UJ
-I
a.
COEFFICIENT
OF
VARI ATION.
C.I 0.512 5 1020 50 70 90 98 99.8 S9.99
COEFFICIENT OF
VARIATION,
01 051 2 5 10 20 50 70 9O 99 99.8 99.99
PERCENT LESS THAN OR EQUAL TO
Figure A-4 - Cumulative log-normal distribution
A-9
-------
analysis methodology and permit direct determination of frequency
for events of any" specified magnitude with a known OP estimated
coefficient of variation.
A-5. Standard Normal Tables
FOP normal (or log-normal) distributions, probabilities can
be defined in terms of the magnitude of a value, normalized by the
standard deviation. This technique is used in the calculations of
the probability of exceeding specified receiving water
concentrations in this analysis. Standard normal tables can be
obtained from any statistics textbook [8,9]. Table A-l presents
the standard normal table to provide a convenient source for the
analyses used in this report. Table A-l lists the probability fop
the interval between 0 and the value of Z listed. Thus, it
represents the probability that a value will be less than or equal
to the selected value of Z.
A-10
-------
TABLE A-l - Probabilities for the standard normal distribution
Each entry in the table Indicates the proportion of the total area
under the normal curve to the left of a perpendicular raised at a
distance of Z standard deviation units.
Example: 88.69 percent of the area under a normal curve Ile$ to
the left of a point 1.21 standard deviation units to the right of
the mean.
z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
0.0
0.5000
0.5398
0.5793
0.6179
0.6554
0.6915
0.7258
0.7580
0.7881
0.8159
0.8413
0.8643
0.8849
0.9032
0.9192
0.9332
0.9452
0.9554
0.9641
0.9713
0.9773
0.9821
0.9861
0.9893
0.9918
0.9938
0.9953
0.9965
0.9974
0.9981
0.9987
0.9990
0.9993
0.9995
0.9997
0.9998
0.9998
0.9999
0.9999
1 .0000
0.01
0.5040
0.5438
0.5832
0.6217
0.6591
0.6950
0.7291
0.7612
0.7910
0.8186
0.8438
0.8665
0.8869
0.9049
0.9207
0.9345
0.9463
0.9564
0.9649
0.9719
0.9778
0.9826
0.9865
0.9896
0.9920
0.9940
0.9955
0.9966
0.9975
0.9982
0.9987
0.9991
0.9993
0.9995
0.9997
0.9998
0.9999
0.9999
0.9999
1 .0000
0.02
0.5080
0.5478
0.5871
0.6255
0.6628
0.6985
0.7324
0.7642
0.7939
0.8212
0.8461
0.8686
0.8888
0.9066
0.9222
0.9357
0.9474
0.9573
0.9656
0.9726
0.9783
0.9830
0.9868
0.9898
0.9922
0.9941
0.9956
0.9967
0.9976
0.9983
0.9987
0.9991
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1 .0000
0.03
0.5120
0.5517
0.5910
0.6293
0.6664
0.7019
0.7357
0.7673
0.7967
0.8238
0.8485
0.8708
0.8907
0.9082
0.9236
0.9370
0.9485
0.9582
0.9664
0.9732
0.9788
0.9834
0.9871
0.9901
0.9925
0.9943
0.9957
0.9968
0.9977
0.9983
0.9988
0.9991
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1 .0000
0.04
0.5160
0.5557
0.5948
0.6331
0.6700
0.7054
0.7389
0.7704
0.7996
0.8264
0.8508
0.8729
0.8925
0.9099
0.9251
0.9382
0.9495
0.9591
0.9671
0.9738
0.9793
0.9838
0.9875
0.9904
0.9927
0.9945
0.9959
0.9969
0.9977
0.9984
0.9988
0.9992
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1 .0000
0.05
0.5199
0.5596
0.5987
0.6368
0.6736
0.7088
0.7422
0.7734
0.8023
0.8289
0.8531
0.8749
0.8944
0.9115
0.9265
0.9394
0.9505
0.9599
0.9678
0.9744
0.9798
0.9842
0.9878
0.9906
0.9929
0.9946
0.9960
0.9970
0.9978
0.9984
0.9989
0.9992
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1 .0000
0.06
0.5239
0.5636
0.6026
0.6406
0.6772
0.7123
0.7454
0.7764
0.8051
0.8315
0.8554
0.8770
0.8962
0.9131
0.9279
0.9406
0.9515
0.9608
0.9686
0.9750
0.9803
0.9846
0.9881
0.9909
0.9931
0.9948
0.9961
0.9971
0.9979
0.9985
0.9989
0.9992
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1 .0000
0.07
0.5279
0.5675
0.6064
0.6443
0.6808
0.7157
0.7486
0.7794
0.8079
0.8340
0.8577
0.8790
0.8980
0.9147
0.9292
0.9418
0.9525
0.9616
0.9693
0.9756
0.9808
0.9850
0.9884
0.9911
0.9932
0.9949
0.9962
0.9972
0.9980
0.9985
0.9989
0.9992
0.9995
0.9996
0.9997
0.9998
0.9999
0.9999
1 .0000
1 .0000
0.08
0.5319
0.5714
0.6103
0.6480
0.6844
0.7190
0.7518
0.7823
0.8106
0.8365
0.8599
0.8810
0.8997
0.9162
0.9306
0.9430
0.9535
0.9625
0.9700
0.9762
0.9812
0.9854
0.9887
0.9913
0.9934
0.9951
0.9963
0.9973
0.9980
0.9986
0.9990
0.9993
0.9995
0.9996
0.9998
0.9998
0.9999
0.9999
1 .0000
1 .0000
0.09
0.5359
0.5754
0.6141
0.6517
0.6879
0.7224
0.7549
0.7852
0.8133
0.8389
0.8621
0.8830
0.9015
0.9177
0.9319
0.9441
0.9545
0.9633
0.9706
0.9767
0.9817
0.9857
0.9890
0.9916
0.9936
0.9952
0.9964
0.9974
0.9981
0.9986
0.9990
0.9993
0.9995
0.9997
0.9998
0.9998
0.9999
0.9999
1 .0000
1 .0000
A-ll
-------
A-6. References
1. Niku, et al., "Performance of Activated Sludge Processes and
Reliability Based Design." Journal WPCF, Vol. 51, No. 12,
(December, 1979).
2. McCarty, et al ., "Reliability of Advanced Wastewater
Treatment."
2. EPA Water Planning Division, "Preliminary Results of the
Nationwide Uroan Runoff Program," (March 1982).
4. Mancini, J. L., "Methods for Developing Wet Weather Water
Quality Criteria." Progress Report, June 1981; EPA ORO Grant No.
R8068280H Cincinnati.
5. Chow, V.T. "Handbook of Applied Hydrology." Mc-Graw Hill, New
York (1964).
6. Linsley, et al., "Hydrology for Engineers." Mc-Graw Hill, 2nd
Edition, (1975).
7. Hydroscience, In., "A Statistical Method for the Assessment of
Urban Stormwater." USEPA, EPA 440/3-79-023, (May 1979).
8. Benjamin, J. R. and C. A. Cornell, "Probability, Statistics and
Decision for Civil Engineers." McGraw-Hill, New York, (1970).
9. Johnson, R. R., "Elementary Statistics." Duxbury Press, North
Scituate, Massachusetts, (1980).
A-12
-------
APPENDIX B
Field validation of Log-Normal Distribution and Related
Assumptions
-------
This appendix presents a discussion of several technical
issues and assumptions which are necessary to the use of the
probabilistic dilution model to guide selection of permit
averaging periods. This discussion is organized in two sections:
the first provides- a justification for the use of the
probabilistic dilution model in the method; the second provides a
discussion of several key assumptions.
B-l. Use of the Log-Normal Distribution
A relatively simple and straightforward analysis is made
possible by the assumption that each of the input variables is
log-normally distributed and independent. The appropriateness of
these assumptions and their implications are discussed below.
A basic feature of any random time series of numerical values
is its probability distribution function, which specifies the
distribution of values and their frequency of occurrence. More
detailed characterizations which account for seasonal trends and
day-to-day correlations are also possible, but at minimum the
univariate probability density function is required. An
examination of flow data from a number of streams indicates that
the data can be reasonably well represented by a log-normal
distribution. Figure B-l summarizes an examination of the adequacy
of a log-normal distribution for dally flows of 60 streams with
long periods of record. The actually observed 10th and 1st
percent, ie low flows are compared with the flow estimated by a
log-normal distribution. The major important discrepancy occurs at
the lowest flows where the predicted distribution is lower than
that actually observed. The most likely cause
B-l
-------
tft
LU
CJ
or
LU
Q.
LU
_(
^
Z
LU
o:
LU
a.
P 10 ?£RC£NT!LE
s * I
' * » I I I » t f Lf f f I I t « E f4 I t t t i t »J i i . .
:0 ' 'Ow 10' .10*
LOG NORMAL APPROXIMATION (cf$)
.0'
10"
10"
ttlllltt t llftl 1 1 Itltf lit
I j t t i t t»<
10" 10° 10' I02 I0:
LOG NORMAL APPROXIMATION (cfs)
Figure B-l: Evaluations of log-normal distribution for stream
flows
B-2
-------
is the presence of a base stream flow which does not vary
appreciably. THUS, the log-normal representation is generally a
lower bound characterization of this distribution of the very
lowest flows, which will tend to provide upper bound estimates of
stream concentrations if these misrepresented-low flows are
important. For the analysis results in this report, therefore, the
calculations may be overprotective in some cases.
Log probability plots of treatment plant effluent flows and
concentrations are illustrated in Figure B-2 for conventional
pollutants and figure B-3 for heavy metals. Essentially, all data
examined to date indicate that a log-normal characterization is
representative.
B-2. Verification of the Probabilistic Dilution Model
The probabilistic dilution model itself has been subjected to
a number of tests in order to check its validity and realism.
Detailed simulation studies using Monte Carlo methods [1] have
verified the calculated downstream concentration probability
distribution when the upstream and effluent flows and
concentrations are exactly log-normal.
In addition, detailed analysis of actual discharges into
streams, (11 data sets for 5 streams) has been performed [2].
Observed data were available for upstream and effluent flows and
concentrations, as well as for downstream concentrations. The log-
normal probability dilution model was used to predict the
probability distribution of downstream concentrations. Table 8-1
compares the observed and computed median and 95tn percentiles
values for selected water quality parameters. The 95% confidence
limits of these observed quantities, computed from the known
sampling
B-3
-------
»o
«n
[F
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tit 3 .
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PQ
CL>
tn
-H
B-4
-------
Si
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B-5
-------
TABLE B-l - Comparison of observed and computed downstream
concentrations (2)
Median
Location
(50th Percentile) Concentrations
Variable
Model Observed
Prediction Quantile
Confidence
Limit of
Observed
Quantile
North Buffalo Creek, NC
Jackson River, VA
Haw River, NC
Pigeon River, NC
Mississippi River, MN
BOD
COD
TSS
BOD
TSS
Color
BOD
COD
BOD
COD
NH3
(mg/1)
(mg/1)
(mg/1)
(mg/1)
(mg/1)
(PCU)
(mg/1)
(mg/1)
(mg/1)
(mg/1)
(mg/1)
95^ Percentile
North Buffalo Creek, NC
Jackson River, VA
Haw River, NC
Pigeon River, NC
BOD
COD
TSS
BOD
TSS
Color
BOD
COD
BOD
COD
(mg/1)
(mg/1)
(mg/1)
(mg/1)
(mg/1)
(PCU)
(mg/1)
(mg/1)
(mg/1)
(mg/1)
9.
51.
16.
6.
15.
110.
2.
23.
3.
85.
1.
7
0
0
0
8
0
0
8
7
0
0
10.
59.
15.
5.
13.
100.
1.
22.
3.
78.
1.
0
0
0
3
6
0
7
0
8
0
1
8
47
12
10
90.
19
65
.5 - 11.
.0 - 66.
.0 - 22.
4.2 - 6.
.0 - 17.
0 - 130.
1.5 - 1.
.0 - 26.
3.0 - 5.
.0 - 87.
1.0 - 1.
0
0
0
0
0
0
7
0
1
0
2
Concentrations
31.
120.
15.
18.
41.
324.
4.
43.
8.
186.
0
0
8
1
6
0
5
0
7
0
22.
97.
13.
15.
32.
330.
4.
46.
7.
229.
0
0
6
6
0
0
7
0
6
0
20
82.
10
13
30
300.
33.
188.
.0 - 33.
0 - 129.
.0 - 17.
.0 - 20.
.0 - 40.
0 - 410.
3.2 - 5.
0 - 53.
6.4 - 9.
0 - 233.
0
0
0
0
0
0
6
0
4
0
Mississippi River, MN
NH3 (mg/i;
3.5
43
3.2 - 5.0
B-6
-------
distribution of quantiles, are also listed. In all but one case,
the computed quantiles are within the confidence limits.
Thus, there is no statistical evidence, to reject the
computed quantiles as not being the true quantiles of the observed
concentration distribution. This is strong statistical evidence
that indeed the log-normal probabilistic dilution model is
representative of actually observed downstream concentration
distributions for the 95th percentile at least.
The 11 data sets used in the verification analysis were
examined for cress correlations between effluent flows and
concentrations. The observed ranges in correlation coefficients
have no significant impact on the computation. Correlations
between stream flow and effluent load for a point source are not
expected. Upstream concentrations are not employee in the
comparison of permit averaging period effects, so that any
correlation between stream flow and concentration is not relevant
to this analysis. Modifications to the probabilistic dilution
model computations are available for use in situations where cross
correlations must be considered [1].
The influence of. possible deviations from the assumed log-
normality of the upstream and effluent flows and concentrations
upon more extreme quantiles is unknown at present due to lack of
larger data sets that encompass these extreme quantiles. However,
the quality of the alternatives to and the simplicity of this
model argue strongly for Its use in the present context of
describing comparative differences in water quality impacts.
B-7
-------
B-3. Appropriateness of Assumptions
We have chosen to ignore the seasonal and day-to-day
correlation structure of both stream flow and effluent behavior in
order to simplify the characterization of each variable. The
consequences of this simplification are discussed below in more
detail, but it should be pointed out that trends and correlations
do not invalidate the use of the log-normal probability
distribution function to characterize the frequency of occurrence
of flows and concentrations. Trends and day-to-day correlations
affect the time sequences with which certain values occur, but not
their long term frequency of occurrence. This is judged to be an
acceptable penalty to be endured when compared to the
simplification achieved. If a more refined, site specific analysis
is required, then a seasonal breakdown of the data, with the
appropriate means and standard deviations for each time period,
can be generated and the analysis performed as described below.
The consequence of a possible serial correlation can be
approximately quantified as follows. If, in fact, the serial
correlation is such that 10 consecutive daily violations always
occur when one violation occurs, then the proper percentile to
consider Is not 0.0274 (10 years) but rather 0.274 (1 year return
period). The degree to which the 10 year return period
concentration is overestimated can be estimated by comparing the
ratio of the 10 year to the 1 year stream concentrations which are
compiled without regard to serial correlation.
The ratio of the 10 year return period concentration to that
for
B-8
-------
some other return period can be computed for log-normally
distribute random concentrations by:
Cio yr = EXP [ (Zio yr ~ Zx yr) OinC]
cxyr
Where
Oinc = log standard deviation of stream concentrations (C)
ZIQ yr, Cio yr = Z score and concentration corresponding to a 10 year
return period
Zx yr, Cx Yr = I score and concentration corresponding to an x year
return period
Table 3-2 summarizes results for a range of values for
coefficient of variation of stream concentrations. Clustering
tendencies of 5 and 10 are examined as approximations of the
degree of serial correlation which might exist. If clusters of 10
occur, the comparison is between 10 and 1 year return periods as
discussed above; for clusters of 5, the comparison is between 10
and 2 year return periods. On the basis of this analysis, the
water quality effects presented in Chapter 4 for various permit
averaging periods may overstate the 10 year stream concentrations
by approximately a factor of 1.5 to 2.0.
Until stream and effluent data can be analyzed to define the
serial correlation structure and the methodology modified to
incorporate it, the results presented in Table B-2 should be
interpreted to indicate with the following possibilities:
B-9
-------
TABLE B-2 - Approximate overestimation of 10 year return period
stream concentration by ignoring serial correlation
Variability of
Stream Concentration
Ratio of Stream Concentration
At Indicated Average Return Periods
Coefficient
of
Variation
(vc)
.5
1.0
1.5
2.0
Log
Sigma
(CTlnc)
.4724
.8326
1.0857
1.2686
10 Year
to 1 Year
(Cio/Ci)
1.4
1.8
2.1
2.4
10 Year
to 2 Year
(Cio/C2)
1.25
1.50
1.65
1.80
= EXP[
- Zi
(10 year Return Period) = 3.456
(1 year Return Period) = 2.778
(2 year Return Period) = 2.778
B-10
-------
o Stream concentrations indicated by the methodology used
in the report to recur on average for 1 day every 10
years would, if they actually never occur except in
clusters of 5 to 10 days, have return periods of 50 to
100 years.
o Conversely, for the same clustering assumptions, the
stream concentrations that occur at 10-year intervals
should be 50 to 70% (1/2 to 1/1.5) of the 10-year
concentrations projected by the report methodology.
B-4. References
1. DiToro, D.M., "Probability Model of Stream Quality Due to
Runoff." J. Environmental Engr. ASCE, Vol. 110., #3, June 1984 p.
607-628.
2. DiToro, D.M. and Fitzpatrick, J.J., "Verification Analysis of
the Probabilistic Dilution Model" Report prepared for EPA Contract
No. 68-01-6275, U.S. Environmental Protection Agency, Washington,
D.C., (1982).
B-ll
-------
APPENDIX C
Characteristic Values for Input Parameters
-------
The results reported here represent an attempt to develop
characteristic values and ranges for stream flow and effluent
variability. These values and ranges have been extracted from the
results of published analyses, and are used in Chapter 4 to
evaluate the influence of the permit averaging period on typical
receiving water conditions. These values are provided for effluent
flows (Section 1), effluent concentrations (Section 2), and stream
flow (Section 3).
C-l. Treatment Plant Effluent Flows
A recent study [1] analyzed several years of performance data
from approximately 400 secondary treatment plants in 8 different
process categories. Average plant effluent flows ranged from 0.002
to 82 MGD. Table C-l summarizes the coefficient of variation of
treatment plant effluent flows.
C-2. Treatment Plant Effluent Concentrations
Data on the variability of effluent BOD5 and total suspended
solids (TSS) from municipal biological treatment plants are
available from several sources. Niku, et al . [2] provide analysis
results for 37 activated sludge plants which show the coefficient
of variation of effluent 8005 concentrations to range between 0.34
and 1.11 for individual plants. The median of the individual
plant- values was 0.635. The EPA research report [3] on which the
foregoing was basedl reported a mean coefficient of variation for
43 activated sludge plants using a variety of processes. Daily
effluent concentrations were found to be well represented
C-l
-------
TABLE C-l - Coefficient of variation of daily effluent flows, v
QE
Process Category
Number of Range For Median of
Plants Individual Plants All Plants
Trickling Filter
Rock
Trickling Filter
Plastic
Conventional Activated
Sludge
Contact Stabilization
Activated Sludge
Extended Aeration
Activated Sludge
Rotating Biological
Contact
Oxidation Ditch
Stabilization Pond
64
17
66
57
28
27
28
37
0.06 - 0.97
0.16 - 0.88
0.04 - 1.04
0.06 - 1.35
0.11 - 1.32
0.12 - 1.19
0.09 - 1.16
0.00 - 0.83
0.27
0.38
0.24
0.34
0.34
0.31
0.31
0.31
C-2
-------
by a log-normal distribution. The mean of all plants analyzed had
coefficients of variation of 0.7 for BOD5 and 0.84 for TSS.
Two recent studies have extended the analysis of effluent
concentration variability, and report coefficients of variation of
BOD5 and TSS for 7- and 30-day averages as well as for daily
values. Results reported by Hazen and Sawyer [1] provide the basis
for the summary presented in Table C-2 as well as the two other
sources cited in the table. An analysis of the performance of 11
trickling filter plants by Haugh, et al. [4] produced me results
summarized by Table C-3.
Based on available data, a single representative value for
coefficient of variation of effluent concentrations cannot be
defined. The most appropriate characteristic value will be
influenced by process category, effluent concentration averaging
period, and the pollutant in question (e.g., BOD, TSS, etc.), as
well as individual plant differences. The computations in this
report are performed using a range of values estimated to
encompass most of the conditions of interest.
C-3. Stream Flow
Figure C-l provides a basis for estimating the coefficient of
variation of daily stream flows on the basis of the ratio of 7Q10
to average (QS) stream flow. These flow values are usually readily
available. The relationship shown is derived from a set of flow
measurements and statistics which has been developed for a sample
of 130 streams in various areas of the country [5] and is
summarized in Table C-4, along with additional details on the
location of the stream gages used. The ranges
C-3
-------
TABLE C-2 - Summary of secondary treatment plant performance - median coefficients of variation, VCE
(from reference 1)
Number Effluent BOD (mg/1)
Process Category
of
Plants Mean
Coefficient of
Variation*
Daily
Values
Trickling Filter Rock 64
Trickling Filter Plastic 17
Conventional Activated 66
Sludge
Contact Stabilization
Activated Sludge
Extended Aeration
Activated Sludge
Rotating Biological
Contacter
Oxidation Ditch
Stabilization Pond
57
28
27
28
37
26.0
19.0
14.8
12.6
7.2
17.0
8.4
22.7
Values shown are
*Basis: VCE =
Standard
Deviation of
0
0
0
0
0
0
0
0
.40
.50
.65
.60
.70
.60
.60
.50
rounded
Median
7-day
Avgs .
0
0
0
0
0
0
0
0
to
.30
.35
.55
.50
. 60
.45
.55
Effluent TSS (mg/1)
Coefficient of
Mean Variation*
30-Day Daily
Avgs Values
0
0
0
0
0
0
0
.45 0
nearest
.25 25.3 0.50
.30 19.4 0.65
.40 14.3 0.85
.40 13.8 0.70
.45 9.8 0.65
.35 15.2 0.70
.40 12.3 0.70
.40 39.5 0.65
0.05 for V(CE)
7-day 30-Day
Avgs . Avgs
0.30 0
0.55 0
0. 60 0
0. 65 0
0.45 0
0.50 0
0
0.55 0
.25
.40
.45
.50
.30
.35
.50
.45
Plant
Mean of Median Plant
C-4
-------
Pollutant
Cr
Cu
Fe
Mn
Ni
Zn
Tss
Chemical Precipitation/Settling1
Coefficient of Variation
.99
.60
.57
.34
.81
.84
.66
Pharmaceutical Industry2
Coefficient of Variation
Plant Number
12015
12072
12026
12036
12097
12098
12117
12160
12161
12186
12187
12136
12248
12257
12294
12307
BOD
1.01
.97
.95
.74
1.08
1.37
.70
.92
.55
.71
.21
1.02
.58
.64
.93
1.55
(n)
46
392
44
366
222
24
39
34
249
54
12
110
50
56
56
39
1
1
1
1
1
1
1
TSS
.85
.63
.49
.12
.21
.52
.81
.11
.99
.50
.26
.16
.55
.92
.25
.34
(n)
195
395
53
364
249
25
51
32
355
54
12
111
52
56
50
38
From Table 3, page 14 of 10-18-83 memorandum from H. Kahn to E,
Hall titled, "Revisions to Data and Analysis of the Combined
Metals Data Base."
2From preliminary descriptive statistics generated on
pharmaceutical data by SRI International, 11-12-82.
C-5
-------
TABLE C-3 - Effluent concentration variability for trickling
filters (from reference 4)
BOD5 TSS
Mean for 11 plants (mg/1) 29.6 29.3
Coefficient of Variation (median of
Individual plant values):
Daily Values 0.39 0.55
7-Day Averages 0.35 0.31
30-Day Averages 0.31 0.26
shown reflect the bulk of the data in the sample of stream records
which were used. However, a relatively small percentage of streams
will have coefficients of variation which fall outside the
indicated ranges. The statistical analysis was performed for the
entire period of record. Results in some cases may be distorted,
if flow regulation works were installed on the stream sometime
during the period of record.
C.4. References
1. Hazen and Sawyer, "Review of Performance of Secondary Municipal
Treatment Works." Draft Final Report for Contract 68-01-6275, Work
Assignment No. 5, U.S. Environmental Protection Agency,
Washington, D.C., (December 1982).
2. Niku, Shroeder, and Samaniego, "Performance of Activated Sludge
Process and Reliability Related Design." JWPCF, Vol. 51, No. 12,
(December 1979).
3. Niku, et al., "Performance of Activated Sludge Processes:
Reliability, Stability and Availability." EPA 600/52-81-227,
(December 1981).
4. Haugh, et al. "Performance of Trickling Filter Plants:
Reliability, Stability and Variability." EPA 600/52-81-228.
(December 1981).
5. Driscoll & Associates, "Combined Sewer Overflow Analysis
Handbook for Use in 201 Facility Planning." Report prepared for
C-6
-------
EPA Contract No. 68-01-6148, U.S. Environmental Protection Agency,
Washington, B.C. (1981).
C-7
-------
5
o
UJ
or
O
<
.10
o
o
r»
O
H-
<
.001
O.I
RANGE
COEFFICIENT OF VARIATION
OF STREAM FLOWS
10
Figure C-l - Typical low flow characteristics of U.S. streams
C-8
-------
TABLE C-4 - Summary of stream flow characteristics
USGS
Gage No.
91 01 1000
03 6500
02 1500
07 3000
09 1000
09 4500
16 2500
17 6000
IB 1000
11 1500
12 4000
12 7500
33 4500
36 1500
37 7000
39 8500
42 0500
43 5000
44 9500
48 1500
State
HE
HE
HE
HE
Nil
HA
HA
HA
HA
Rl
CT
CT
NV
NV
NJ
NJ
NV
NV
I*A
1*
Gage Location1
River
V
Alagash River
Kenduskeag Streaw
Hachtas River
Oyster River
S. Br. Plscataquag River
N. Nashua River
Priest Brook
Quaboag River
y. Br. Westfield River
Branch River
Qulnebaug River
Vantic River
IfcDsIc River
Cat ski II Creek
llarfcensack River
N. Br. Raritan River
Beaver Kill
fevers ink River
Wild Creek
Brandywlne Creek
t Jl A. M I
(At or Near)
Alagash, HE
Kenduskeag, HE
Whttneyville. HE
Durham. NH
Goffstown, Nil
leant nster. HA
Winchendon, HA
U. Brtwfleld. HA
Hunt Ing ton. HA
Forestdale. Rl
.... CT
.... CT
Eagle Bridge, NY
Oak Hill. NY
Rivervale, NJ
Far Hills. NJ
Cook Falls. NV
Claryvllle. NY
Hatchery. PA
Wilmington. DE
Or a i n
Area
(HI?)
1250
178
457
12
104
110
19
151
94
91
156
90
510
98
5U
2<> 1
241 2
66 2
17 2
314 1
0
.49
.72
>.oo
.49
.58
.75
.60
.58
.90
.82
.77
.69
.75
.27
.55
.72
'.26
'.68
.02
.38
Stream Flow
(cfs/H|2)
~
Q 7QIO
0.84 .102
.62 .Oil
1.30 .130
.66 0
.73 .029
1.19 .300
.77 0
1.01 .093
.96 .053
1.14 .132
1.04 .103
.91 .044
1.15 .186
.35 0
1.07 .121
.20 .076
.34 .133
.74 .152
.49 .119
.11 .217
1Q2
.034
.008
.081
.016
.017
.086
.021
.060
.030
,061
.050
.042
.076
.003
.079
.095
.068
.102
.149 I
.175 (1
"Q
1.46
?.58
1.17
?.02
1.91
.07
.81
.19
.70
.24
.37
.56
.14
.51
.05
.03
.35
.17
1.91
1.74
70,10
U
.0611
.006
.064
0
.018
.172
0
.06
.03
.07
.06
.03
.11
0
.08
.04
.06
.06
.06
.16
AJIO
IQ2
2.95
1.33
1.59
0
1.67
3.47
U
1.56
2.2
2.1
2.1
I.I
2.4
0
1.5
.8
1.9
1.5
.8
1.2
C-9
-------
TABLE C-4 (Cont.)
uses
Gage No. State
01 SO 0500
51 1500
52 9500
54 3000
55 5500
58 6000
59 1000
59 7000
61 7000
61 5000
64 5000
65 7000
66 3500
02 01 2500
03 4000
06 2500
05 3500
10 6500
09 9500
11 1000
13 Q500
15 2500
NY
NV
NY
PA
PA
HO
HD
HI)
UV
VA
HO
VA
VA
VA
VA
VA
1C
1C
NC
NC
NC
NC
Gage Location
River
» \ .
Susquehanna River
Tionghnioga River
Cohocton River
Driftwood Brook
East Nahantango Creek
N. Br. Patapsco River
Patuxent River
Crabtree Creek
Tuscarora Creek
Opequon Creek
Seneca Creek
Bui 1 Run
Hazel River
Jackson River
Rivanna River
Roanoke (St a union) River
Ahoskle Creek
Black River
Deep River
Ya-Mctn Kiver
Linville River
First Broad River
(At or Near)
Unadtlla. NY
Itaska. NY
Campbell . NY
Sterling. PA
Dal mat la, PA
teda, HD
Unity. HD
Swan ton. HD
Hartlnsburg. UV
Berryville. VA
Dawsonville. HD
Hanassas, VA
Rixeyville. VA
Falling Sprg. VA
Palmyra. VA
Brook ne. VA
Ahoskie. NC
Tomahawk. NC
Randlenar, NC
Patterson, NC
Nebo. NC
Lawndale, NC
Drain
Area
(HI2)
902
730
470
272
162
57
35
17
11
57
101
148
287
411
. 664
2415
57
61)0
124
2'J
6/
l')B
St ream F 1 ow
(cfs/H|2)
Q
1.57
1.66
.93
1.63
1.30
1.04
.98
1.68
.80
.64
.89
.88
1.15
.16
.08
.02
.12
.10
.96
1.59
2.10
1.41
***
Q
.89
.78
.45
.66
.69
.82
.75
.75
.63
.31
.66
.23
.67
.70
.62
.69
.31
.71
.45
1.33
1.52
1.02
7QIO
.081
.077
.045
.011
.025
.124
.086
0
0
.017
.050
0
.014
.151
.036
.142
0
.034
.048
.216
.223
.258
1Q2
.037
.018
.012
.012
.Q25
.106
.086
.018
.071
.009
/
.066
.001
.031
.036
.027
,046
.001
.044
.010
.231
.134
.091
i
*Q
1.45
1.87
1.79
2.26
1.58
0.78
0.80
1.98
.78
1.82
.91
3.67
1.40
1.32
1.42
1.10
3.52
1.19
1.89
.64
.96
.95
7QIO
Q
.05
.05
.05
.01
.02
.12
.09
0
0
.03
.06
0
.01
.13
.03
.14
0
.03
.05
.17
.10
.18
7Q10
igZ
2.2
4.1
3.8
.9
1.0
1.2
1.0
0
0
2.0
.7
0.4
4.1
1.3
3.1
0
.8
4.6
1.2
1.7
2.8
C-10
-------
TABLE C-4 (Cont.
£ t_i
Location.
20 7500
21 6000
23 8000
29 7100
30 2500
32 6900
33 7000
34 3300
36 9000
38 3500
39 2000
41 2000
42 2500
43 4000
45 6000
47 6500
48 0500
48 4000
03 02 5000
05 3500
06 5000
10 950(1
FL
FL
FL
n
PI
HS
MS
Hatnes Creek
Joshua Creek
Black water CreeK
St. Marks River
Sweettfater Creek
Abbie Creek
Shoal River
Coosawattee River
Etowah River
Tallapoesa River
Mulberry Creek
Town Creek
Turkey Creek
So.ashee Creek
luiachanile Creek
Vockanookany
PA
uv
uv
OH
Sugar Creek
Buckhannon River
Ory
L. Beaver Creek
Stream Flow
Drain _______
. Area
(At or Near)
. .
Covington. GA
Towns, GAS
Lisbon. FL
Hoc a tee, FL
Knights. FL
Newport. FL
Austell. GA
Haleburg. AL
Crestvlew. FL
Pine Chapel. GA
9
Canton. GA
Iteflin. AL
Jones. AL
Tupelo. HS
Morris, AL
Meridian. HS
Biloxl. HS
Kosclusko. Hb
Sugar Creek, PA
Mall. MV
llenrlcks. HV
Liperpool. u" ,
(Hl<)
370 1
329
640
132
110
i »u
535
246
144
474
856
605
444
208
110
82
52
92
404
166
277
34 b
A46
1 J*r
*
' '
.13
.80
.45
.89
.93
1.37
1.35
1.39
2.27
1.70
1.89
1.41
1.50
1.53
1.53
1.08
1.98
1.25
1.57
2.12
2.13
1.02
jcis/nili_-
Q 7Q10
__
.76
.20
.20
.93
1.29
.81
1.08
2.20
1.26
1.58
.97
.94
.14
.74
.32
.60
.21
.86
.90
1.05
.48
.061
.006
.154
o
.018
.600
.057
.208
.635
.312
.405
.065
.226
0
.123
.032
.017
ft f\
.10
.007
.023
.04
_
1Q2
.058
.001
.005
0
.458
.011
.125
.156
.116
.299
.149
.120
.003
.020
004
\f\J*
.005
.001
03
V «*
.05
.03
.01
7Q10 70JO
I/Q . Q 1Q2
;
1.06
3.84
2.02
5.17
.36
1.33
.82
.24
.90
.66
1.07
1.25
10.79
I.b3
3.26
3.13
5.74
1.52
2.14
1.77
1.85
.05
.01
.34
0
.44
.04
.15
.28
.18
.21
.05
.15
0
.08
0
.02
.01
.U6
.003
.01
.04
»f\
.0
5.0
33.0
0
11
.3
5.2
1.7
4.1
2.7
1.4
0.4
0
6.25
6f\
.u
20.0
2.9
.8
2.7
C-ll
-------
TABLE C-4 (Cont.
taqe Location
uses
Gage No.
03 14 6500
15 7500
17 0000
18 6500
, 21 3500
22 4500
24 0000
32 4000
35 2500
35 7500
42 1000
42 7500
04 02 7500
04 6000
06 4500
08 6500
11 4500
12 3000
15 5500
15 9500
16 6500
18 0000
State
Oil
Oil
VA
UV
VA
Oil
Oil
IN
IN
IN
TN
TN
Ul
HI
Ul
Ul
HI
HI
HI
HI
HI
IN
River
licking River
IkKking River
Little River
Will 4 MS River
Panther Creek
Whetstone Creek
L. Miami River
Little River
Fall Creek
Big Walnut Creek
Collins River
E. Fork Stones River
White River
Black River
Pine River
Cedar Creek
Looking Glass River
Dig Sa.lle River
Pine River
Ulack River
River Range
Cedar Creek
(At or Near)
. Newark . Oil
Enterprise. OH
Graysonton. VA
Dyer. WV
Panther. UV
Ashley. Oil
Old town, Oil .
Hunt ing ton, IN
Hillersville. IN
Reel sv 1 lie, IN
HcHinnville. TN
Lascass, TN
Ashland. Ul
Garnet. HI
Pine R. Pwrplnt,
Cedarburg. Ul
Eagle, HI
Freesail, HI
Midland, HI
Fargo, HI
Detroit, HI
Cedarvllle. IN
Drain
Area
(HI2)
537
459
300
128
31
99
129
263
298
326
640
262
279
28
Ul 528
121
281
127
390
4HO
107
270
Stream Flow
(cfs/H|2)
U
.99
.95
1.20
2.50
1.17
.89
.74
.84
.78
.98
1.78
1.58
1.04
.93
.79
.51
.56
1.09
.69
.56
.56
.85
Q
.50
.49
.93
1.12
.36
.28
.46
.25
.48
.41
.83
.48
.85
.75
.61
.23
.34
1.05
.51
.14
.29
.42
7QIO
.07
.063
.223
.008
0
6
.05
.01
.04
.01
.096
.01
.47
.21
.13
.008
.05
.67
.08
.01
.02
.07
IQ2
.01
.01
.11
.03
.003
.003
.02
.003
.03
.00,8
.02-
.003
.13
.09
.07
.005
.02
.43
.05
.001
.009
.011
-
"Q
1.71
1.69
.81
1.95
3.09
3.04
1.26
3.20
1.28
2.18
1.91
3.13
.69
.78
.85
2.01
M.34
.30
.93
3.90
1.63
1.7/
7Q10
Q
.07
.07
.19
.003
0
0
.07
.01
.06
.01
.05
.01
.45
.23
.16
.02
.09
.61
.12
.02
.04
.OU
7Q10
1Q2
4.6
4.3
2.0
.3
0
0
2.1
4.3
1.6
1.5
4.8
3.8
3.6
2.4
1.8
1.7
2.8
1.5
1.6
10.0
2.2
6.3
C-12
-------
TABLE C-4 (Cont.
uses
Gage No.
04 19 9000
22 7500
05 29 3000
38 5500
41 3500
41 7700
40 6500
43 2500
44 4000
45 7000
45 5500
48 6000
50 2000
51 5000
52 8000
55 4500
57 8500
12 33 5000
37 0000
32 1500
45 5000
17 7500
State
Oil
NY
HN
HN
Ul
IA
HI
Ul
IL
HN
IA
IA
HO
IN
IL
IL
IL
MT
MF
ID
MA
OK
Gage Location
(liver
Huron River
Genesee River
Yellow Bank River
S. Fork Root River
Grant River
Bear Creek
Black Earth Creek
Pecatonlca River
Elkhorn Creek
Cedar River
English River
North River
Bear Creek
Kankakee River
Des Plalnes River
Ver«lll ion River
Salt Creek
Black foot River
Swan River
boundary Creek
Menatchce River
Stetdttle Creek
(At or Near)
Milan. Oil
Jones Bridge. NY
Odessa. MN
Howton. MN
Burton. Ul
Monmouth. IA
Black Earth, Ul
Oar liny ton, Ul
Penrose. IL
Austin. MN
Kalona. IA
Norwalk. IA
Hannibal. MO
North Liberty. IN
Gurnee, IL
Pont lac. IL
Ho well, IL
Itelmville, MT
Uiyfork. MT
Por thill, ||)
Uontch. L.. WA
Nowhalan. WA
Drain
Area
(Ml?)
371
1417
390
275
269
61
46
273
146
425
573
349
31
174
23?
5/9
335
4HI
671
9/
273
22
Stream Flow
(cfs/MI?)
U
.72
1.12
.14
.45
.59
.64
.61
.66
.56
.41
.57
.49
.48
.81
.52
.58
.64
.73
1.70
1.98
4.82
8.40
or
.24
.58
.025
.40
.42
.34
.60
.44
.38
.23
.16
.09
.11
.76
.14
.15
.24
.45
1.21
.82
2.97
5.82
71)10
.008
.05
0
.196
.138
.03
.26
.117
.10
.05
.003
0
0
.30
0
0
.006
.146
.31)0
.124
.54
.82
1Q2
.003
.019
0
.098
.035
.011
,.330
.030
.030
.010
.001
.006
.001
.260
.001
.001
.003
.025
.109
.015
.147
.445
"0
2.79
1.66
5.45
0.49
.99
1.59
.19
l.ll
1.07
1.50
3.29
»5.54
4.43
.37
3.64
3.80
2.43
1.28
.98
2.19
1.28
1.05
/QiU
Q
.Ul
.05
0
.44
.23
.US
.43
.18
.17
.12
.01
0
U
.38
U
U
.01
.?U
.22
.06
.11
.10
7QIU
IQ2
2.7
2.7
0
2.0
3.9
2.9
.8
3.9
3.4
5.1
2.2
0
0
1.2
0
0
1.7
5.7
3.5
8.0
3.7
1.8
C-13
-------
TABLE C-4 (Cont.
uses
Gage No.
12 13 3000
14 8000
. 10 4500
08 2500
04 8000
01 3500
02 4000
13 04 7500
18 5000
29 2000
31 3000
35 1000
14 01 7000
05 7500
14 5500
22 2500
22 6500
17 1000
18 2500
20 3500
31 2000
34 1500
37 2500
- : *~
State
WA
UA
WA
UA
UA
UA
UA
ID
ID
OK
ID
UA
UA
OR
Oil
UA
UA
OK
OK
Oil
OK
UK
OK
Gage Location
River
S. Fork Skyromish River
S. Fork To It River
Gr en River
Nl squally River
Dungeness River
Uillapa River
S. Fork Newaukum River
Falls River
Boise River
Imnaha River
Johnson Creek
Pa louse River
Tonchet River
Fall River
H. Fork Willamette River
E. Fork Lewis River
Cowl It z River
Mary's River
Little N. Sant lam River
Tualatin River
S. Unpqua River
S. Fork Little Butte Cr.
E. Fork Illinois River
(At or Near)
Index, UA
Carnation, UA
Lester, UA
National . UA
Sequim. UA
Uillapa. UA
Onal.... UA
Squirrel, ID
Twin Springs, ID
Imnaha, OR
Yellow Pine. ID
Hooper. UA
Holies, UA
LaPine, OR
above Salt Cr.. OR
lie Is son, UA
Packwuod. UA
Philomath, Or s
Men..., OK
DM ley. OK
Brockway, OK
Lakec , OK
Taklhna, OK
lira iu
Area
(Ml?)
355
20
96
133
156
130
42
326
830
622
213
2500
361
45
392
125
287
159
112
12!)
16/0
1 )H
42
Stream Flow >
(cfs/MI?)
Q
6.90
10.00
4.27
5.92
2.45
5.04
4.74
2.44
1.41
.80
1.61
.24
.65
3.41
2.90
6.12
5.75
2.97
6.85
3.111
1.74
0.78
4.38
*-w»
Q
4.71
4.97
2.41
4.90
1.94
2.02
2.88
1.87
.87
.49
.75
.07
.35
3.27
1.97
3.08
4.12
.86
3.18
1.08
0.56
.39
1.62
7Q10
.80
.76
.29
1.25
.56
.138
.49
.80
.25
.10
.206
.001
.033
2.18
.45
.30
.832
.03
.18
.016
.036
.050
.142
1Q2
.344
.152
.094
.83
.26
.038
.142
.205
.048
.024
.019
.001
.014
1.33
.14
.09
.38
.006
.08
.013
.006
.011
.02
"u
1.07
1.75
1.46
.68
.77
2.29
1.30
.83
1.28
1.30
1.90
3.03
1.55
.31
1.09
1.72
.97
3.31
1.91
2.78
2.96
1.70
2.52
7Q1U
Q
.12
.08
.07
.21
.23
.03
.11
.33
.18
.13
.13
.01
.05
.64
.16
.05
.14
.01
.03
.01
.02
.07
.03
7QIU
1Q2
2.3
5.0
3.1
1.5
2.2
3.6
3.5
3.9
5.3
4.3
10.7
1.5
2.4
1.6
3.3
3.1
2.2
5.6
2.2
1.25
6.1
4.4
6.0
C-14
-------
APPENDIX D
Computer Program for the
Probabilistic Dilution Model - Point Source
(PDM-PS)
-------
This appendix describes a computer program (PDM-PS) which
performs the computations of the Probabilistic Dilution Model for
Point Source discharges using numerical methods based on
quadratures. The program is written In BASIC for the HP-85 and the
IBM-PC, and should be readily applicable to other personal
computers with perhaps minor modifications to reflect individual
machine characteristics.
The program is structured around slightly different Input
format than that used for the manual calculation using the moments
approximation. A series of normalizations (ratios) of certain of
the input data items is used to provide a computation framework
that provides a more generalized perspective
The appendix is organized as follows. Section 1 describes the
basis for the formulation and normalization of the input data, as
used in program. Section 2 provides an annotated description of
the CRT and functions, as well as the nature of the user's
response. Figures and D-2 provide the results of running the PDM-
PS through the example described in Section 3.2 of this report.
Finally, Figure D-3 provides a of the POM-PS program for entry
into a personal computer.
D-l. Formulation and Normalization
The analysis can be made more useful in a general way if the
normalization described below is applied to reduce certain of the
inputs recognized ratios, and to express-results (stream
concentration as a multiple or fraction of the target stream
concentration (CL).
D-l
-------
The explicit assumptions in the normalization scheme that is
used are that:
- The stream target concentration (CL) is produced when the
discharge flow is the mean effluent flow (QE}, the discharge
pollutant concentration is equal to the permit effluent limit
(EL), and the stream flow is equal to the design value (here
designated 7Q10 - though any other basis may be used for
designating the numerical value of stream design flow, e.g.,
30Q5, 30Q10, etc.).
- The reduction factor (R = CE/EL) determines the mean effluent
concentration of the pollutant being evaluated. It, could be
selected arbitrarily; however, as applied in this manual for
evaluating the permit averaging period, the value selected
will be dictated by the variability of effluent
concentrations and the permit averaging period.
In the usual case, where the stream target concentration (CL) is
set at the chronic toxicity level, the multiples of the target -
in which stream concentrations are expressed (CO/CL) - correspond
with the acute toxicity level. The basis for the normalization
scheme adopted is as follows.
The downstream concentration, CO, is given by the dilution
equation:
CO = CE QE = (|)CE
QS + QE
(D-l)
For a chronic criteria concentration, CL, the effluent limit
concentration,
D-2
-------
EL, is computed using QS * 7Q10 and an average effluent flow, QE :
CL = EL QE = EL(|)STD
7Q10 + QE
(D-2;
where pCL] = PR [CO > p^STD CE/R]
(D-5)
where Equation D-4 has been substituted for CL. Dividing both
sides of the inequality by CE provides the first normalization
site
CO/CE = (CE/CE) QE
QS + QE
(D-6)
D-3
-------
and CE/ CE is the normalized effluent concentration. The
probability distribution of this random variable no longer depends
upon the mean effluent concentration, but only on the coefficient
of variation, VCE This is easily seen from the following
representation of a log-normal random variable:
InCE = InCE + ZainCE
(D-7;
where CE is the median,
-------
Note mat QS/QE is log-normally distributed since both QS and QE
are assumed to be log-normal. Thus, only the ratio of the average
flows, QS/QE, is required. A convenient normalization using ratios
that are more readily available results if the average effluent
and stream flows are standardized relative to design stream flow
(here designated by 7Q10). Defining
Fl = 7Q10/QS
(D-12;
F2 = 7Q10/QE
(D-13;
Then
(D-14;
QS/QE = F2/F1
And
F2
(D-15)
These ratios, Fl and F2, together with the coefficients of
variation, VQS, VQE, and VCE, completely specify the characteristics
of the random variables in the normalized dilution Equation D-ll.
R specifies the effect of permit averaging period and |3, the acute
to chronic criteria ratio, specifies the toxicity behavior of the
substance being considered. This completes the normalization.
D-2. Description of Program Use
The program is easy to use. The values of the input variables
are sequentially requested on the CRT. Once the input values are
entered, a summary of the input data is printed out, as is a
tabular listing of the
D-5
-------
results of the calculations. The user should be thoroughly
familiar with the theoretical and practical bases for the PDM-PS
as described in Chapters 2 and 3 before attempting to use the PDM-
PS.
USER: Initiates program execution.
PRINTER: Writes title.
CRT: Displays title and general descriptive material shown in
Figure D-l.
CRT: Question #1 is displayed: "Enter coefficient of variation
of QS, QE, and CE.
USER: Enters the values of VQS, VQS and VCE= separated by commas.
CRT: Question #2 is displayed: "7Q10/avg QS?"
USER: Enters the ratio of the 7Q10 flow to the average stream
flow (QS) .
CRT: Question #3 Is displayed: "7Q10/avg QE?"
USER: Enters the design dilution ratio, i.e., the ratio of 7Q10
flow rate to the average effluent flow rate (QE) .
CRT: Question #4 Is displayed: "avg CE/EL?"
USER: Enters the ratio of the average effluent concentration
which the treatment plant will be designed to produce
(avg CE), to the effluent concentration derived from the
D-6
-------
WLA analysis (EL). This latter value is that concentration in
the effluent which will result in the stream target
concentration being met, when the following flow conditions
prevail:
Stream flow (QS) is at the 7Q10 flow rate.
Effluent flow (QE) is at the average discharge rate of flow.
PRINTER: Prints a tabular summary of the input data selected.
CR: Question #5 is displayed: "Enter lowest, highest and
increment of multiple of target for which % exceedence is
desired."
USER: Decides on a range of stream concentrations (expressed as
multiples of the target concentration, CL) for which the
probability of occurrence and the recurrence interval are
desired. The user enters (1) the lowest value, (2) the
highest value and (3) the incremental step desired for
values between the highest and lowest.
PRINTER: Prints tabular listing of results. For each multiple of
CL, the exceedence frequency and return period are
listed. When the printing is completed, a tone sounds and
Question 5 is repeated.
USER: Enters a new set of values for multiples of CL, if
D-7
-------
desired. This allows the user to conveniently search out
the ranges of interest and select the most appropriate
levels of incremental detail. When the desired amount of
output has been obtained, the program is interrupted, and
begun again at Question #1 to examine another set of
conditions. The user can formally "end" the program by
entering 0,0,0 in response to Question 5.
D-8
-------
POINT SOURCE - RECEIVING WATER
CONCENTRATION ANALYSIS
INPUTS: COEF. VAR OF QS, QE, CE
RATIO. . .7Q10/avgQS
RATIO. . .7Q10/avgQE
RATIO. . .avg CE/EL
BACKGROUND STREAM CONC (CS)
IS ASSUMED TO BE ZERO
GENERAL DESCRIPTIVE MATERIAL
ENTER COEF VAR OF QS, QE, CE?
1.6, .2, .7
QUESTION #1
ENTER FOLLOWING RATIOS:
...... 7Q10avg/ QS ?
.05
...... 7Q10avg/ QE ?
QUESION #2
QUESTION #3
avg CE/ EL ?
.57
ENTER LOWEST, HIGHEST, AND INCREM-
ENT OF MULT OF TARGET FOR WHICH
% EXCEED IS DESIRED
9
QUESTION #4
QUESTION #5(CONTINUES TO
REPEAT AS
NEEDED)
ENTER LOWEST, HIGHEST, AND INCREM-
ENT OF MULT OF TARGET FOR WHICH
% EXCEED IS DESIRED
9
2.5, 3, .05
Figure D-l CRT - displays
D-9
-------
RECEIVING WATER CONG (CO)
PROBABILITY DISTRIBUTION
AND RETURN PERIOD
FOR MULTIPLES OF TARGET CONG
DUE TO POINT SOURCE LOADS
******************************
TITLE
VIOLATION
MULT OF
TARGET
1.00
2.00
3.00
4.00
5.00
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
COEF VAR QS = 1.50
COEF VAR QE = 0.20
COEF VAR CE = 0.70
7Q10/avg QS = 0.05
7Q10/avg QE = 3.00
avg CE/ EL = 0. 05
PERCENT RETURN
OF TIME PERIOD
EXCEEDED (YEARS)
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
894
112
024
007
002
050
046
043
040
037
034
032
030
028
026
024
0
2
11
39
114
5
5
6
6
7
8
8
9
9
10
11
.3
.4
.3
.4
.4
.5
.9
.4
.9
.4
.0
.6
.2
.9
.6
.3
SUMMARY OF INPUT DATA
CALCULATED RESULTS
Figure D-2 - Example of printed output
D-10
-------
Start
Clear screen
Print header
messages
Prompt for and
input coef. of
variations for
QS, QE, CE
Prompt for and
input ratios
of 7Q10/QS,
7Q10/QE,
and avg. CE/CL
Compute normal
and reverse normal
coefficients
All
CO/CL values
= 6?
Prompt for and input
lowest, highest, and
delta increment of
multiples of CO/CL
To use
Print input values
and table header
.Iterate on CO/CL values
Evaluate Q(x)
Compute return
period
Print CO/CL, % of time
exceeded, and
return period
Next CO/CL
Figure D-3 - Flow chart for PDM-PS program
D-ll
-------
FvR
ION MODEL
SOURCE DISCHASut
DEFINITION - INPUT
CE
FLOW
EFFLUENT FLOW
EFFLUENT CONCENTS
RATIO
l i*
:i3
i~e
.1**
156
1*0
17*
i*e
1J1*
16*
1*
'2£
7 5
4 A
* DIM R3
* DIM R.
* DIM P--
0 PRINT
xxxxxxxxxxx'
34$ PP.IMT - RECEIVING UATEP CO
NC ''CO PROBABILITY D
SPECIFIED STREAM
7Gl*'»vfi.:.£ DESIGN
EFFLUENT DILUTION P*T 10
*v«C£ 'EL .* .P.ftTIC OP
THE SPECIFIED *'.'EPftGE
PLP"NT EFFLUENT CONCENTK;
-TCf THE EFFLUENT LllIT
£-> CONCENTRiSTlON
EL Ii THE EFFL
CC'HC "H«T PPOO'JCE? THE
STPESM TAPPET CONC UHEM
.373
730
3?0
4*0
4i*
a 2©
4~0
4-0
430
100".
P*INT " FOP MULTIPLES OF TAR
GET CONC DUE TO POINT SO
UP.CE LOADS-
PRINT -xxxxxxxxxxxxxxxxxxx**
xxxxxxxxxxx-
DISP "POINT SOURCE - RECIEVI
NG WATER"
OISP ' CONCENTRATION
I i "
DISP
OISP
OISP -INPUTS
/QE CE-
OISP '
COEF VAR OF Q«
DISP
OISP
''EL
RATIO.
RATIO
DISP
DISP BACKPOUNO
ep
39
$99
DISP »
OISP
OISP CENTER COEF VAR OF 0$
INPUT'U: ,'..'2. '..'3
OISP -ENTER FOLLOWING P.ATI.
OISP .
INPUT Fl
OISP " 7Qiu« or
INPUT F2
DISP " . ..*v* CE' EL"
INPUT F3
PRINT
IMAGE 21 A..201 ic
PRINT USING 60* ; " CQEr
Aft Q *^ ** 'J1
PRINT USING «&** crifft
A.R. .QE » " -J2.
PRINT U?IN«; *yi9 , » rr.rp
AR CE » *;VT
PRINT
PRINT USING *** , ' -,
*x»w^ QS « -', pj
PRINT USING «** ; "
*'»v* QE ",F>
PRINT USING 6*9 " i-
CE/ EL « ",F3
PRINT
PRINT
STPgAW-
739
749
739
. TAB-: 1 7
PRINT
PRINT
I ON <. CO .<
PRINT
PRINT MULT OF
ERCENT ; TAB < 25 > ;
PRINT TARGET.
TIME" ; TAB. 25 >; "PER 100"
PRINT CCO-'CL) ";TAgri35
CEEOED";TAB<25); -r YEARS:-
PRINT --------
OF-
£,v
W 1 «SQft < LOG <1+V1~2
»
U3-SQP C LOG< 1 *W3A2 > >
< U 1 »2
779
789
799
899
819
S29 U3"LOG/>SQP<1*V3-. ..
339 GOSU6 1239
649 OISP "ENTER LOWEST/HIGHEST.n
NO INCREM-ENT OF MULT OF TAk
GET FOR WHICH :: EXCEED Ii D
ESIRED-
Figure D-4 - PDM-PS program listing - HP-85 compatible
D-12
-------
.j^y I NP'.'J" B1 B2 ' f 3
£*.* IF
IIS ? - C*n?UTE'PORTION OF
flPGUHENT INOEP OF C*
Din :?'-32>
1C IN'J
* 2 V3 ' £- --
TRflNSFOftnflTION
*T$ p-iBRS' I >
i*y GO?U6 133*
?** IJ< I /»LOG«:
x
S'' >-'.
dniji NEXT I
z-* i - CONCENTRATION LOOP
sift FOP C*-Bl TO B2 STEP B3
?JV?"!-a,j*o LOOP- IVflW*TE OC
X) « F MHO SUM
'6 IF P?<.3 THEN 145*
143* P?«1-P?
1446 S9
1456 P?
147*
1488
14**
15*e
151*
152*
153*
i«:4*
1538
RETURN
! -QUflOftflTURE SUBROUTINE -
COMPUTE ROOTS i=»NO WEIGHTi
! 15 INTEGRAL
! R5'-'N*> N* ROOT* ' *- £r
USSIfl.N ROOTS. % N*-'2 LftG?'? ft
OOTS--
! S3:R
I5rh ORDER C*USSI*N ,
L0*0 ROOTS
1578
158*
15?*
1*1*
163*
1646
1678
1659
179*
1718
1729
173*
1746
1738
1768
1779
1739
1799
1899
1319
1S29
R<2> .*
R< 3 )« **3*3l 2*2:4
P<4;« .75346440*4
R<7)
S8<3>
S8<4>
S8<5>
S3C7? 1826634154
18*45*6185
N6-4XP1
! CONVERT GfiUSSIftN P.OOT-9
WEIGHTS FOR '.*!' INTECP
! ftNO DIVIDE BY TwQ FOP i
POSITE FORMULA '
FOR K2«l TO Rl
.
2*115*355*$
.*?5*125*?*4
*2715245?42
**22S3527?4
8*515551168
. 12462SS713
149555?838
.
3- 5»R
NEXT K9
! -LORD THE LACUERPE POO-TS
ftHD HEIGHTS, PROPEPLV
RTEO
Figure D-4 (cont'd.)
D-13
-------
. LP-CUEPPE
i WEIGHTS
1 ;«3l . 79 I 16933?*:
23 .3135'9S694
1?*S PC7>«15.4413273633
1919 P"S>»12 21422336S9
1*29 P«3 43798663389
1968 PU3>»2. 1292836431
1976 P<14'«i.14183777483
1988 PU5;>«.462696328915
USe P-: 16 ^-S . 76494 184739E-2
*'.l>-4. 16146237E-22
.0 ' 6 '' 1 SS;9i4i34 i E-?
* ' 7 ^»6 82*3 1 9.33 1 E-"
i-'S^'l . 4S445S687E-3
Cf? j«2.e427l*i33E-*
.
Sie Q--12---4 7328J286941E-2
ii* Q-' 13 >«. 136296934296,
13* Q' 14 ^-2637937776*4
14ft Qi :3 /«. 33 183733493 1
139 GM6>« 29*131714933
169 FOP K2«l TO
"9 R'3- <2
=« NEXT K.2*
>H
Figure D-4 (cont'd.)
D-14
-------
- -i:. , ?r.35A2ALISTIC
:-. rt» riLUTIOU . MODEL
-: F.I:: FOR PCI::T scurcz :I-SCHA?.GE
: - =
= r.i:. AUGUST, . .-
'- -T- IBM-PC ATD US-DOS COMPATIBLE VESSIOK
:.:L._rs~-. KORI2CI' SYSTEM C05PCP.ATION
; S' (703) -71-
co :i:-: HS#( 32) ,'25*132) '
:C SIM P*(S),SS#(8)
20 si:-: p*(i6),G#(i6),Z9*(32)
;2T CLS ' .
:-C ?=^'; " SEC'-VIIIG WATER CCt.'C (CO) PFOEAEILITY DISTRI3UTIOI: "
:. LIT,.- n A!.'D RETURN. PERIOD"
:r: i;"'.! FC.R i-iULTIPLIS CF TASGET COMC"
-" 3r':-- - 'EuE TO POIKT SOURCE LOAES"
-..- ::j::: -,, ......... «
:50 ?HI::T "poii-iT SOURCE - RECEIVING WATS?"
:CC PF.IIJT "COKCSTTSATIOU
"
-, j rr.i*.. i i I i i i i iiii i i i it"
20 FHIIIT "***''** " * i i i i i i i - ^
-~C 'SUIT "INPUT COEF OF VAP. OF QS.OE.CE" . -
% sJ5r*r " F.ATI0...7G10/AVCQS" .
-c =-:::T " RATIO.-.TQIO/AVGQE"
.gc 3=-vrr n . RATIO'...AVG CE/CL" . '
^_, p.:,;.'. 5ACXGROUJS STSSAK COMC (CS) IS ASSOMD TO EE ZEP.O"
*" ~** * ** . ^^^ M . ^ . . ^.^^^--^ . . , j_ - ^ - - - I*
-00 ?Rli:T "SilTSB COEF OF VAP. OF QS,QE,C£"
'10' T!«PUT V1 V2 V3
^20 PR HIT "siTSS THE FOLLCWI2IG RATIOS:"
;30 INPUT " 7Q10/AVG CS «;F1
-UC IIJPUT " 7C10/AVG CE ";F2
:=C I!IPUT ." AVG CE/EL^ ";F3
50 PREIT
=65 CLS
57C PSIIIT " COEF CF VAP.../. .CS « »;V1
= £0 PRIKT " COEF OF VAP. GE * ";V2
581 PRIHT " CCEF OF VAP CE s ";V3
9C PRIHT
iOC FRIKT " 7C10/AVG GS s ";F1
;:o PP.I::T." 7Q1 o/AVG CE s ";F2
i 20 ?RL»:T " AVG CE/EL = n;F3
-:3C rHINT
5uo ?RI::T " > *
Figure D-5 - PDM-PS program listing - IBM-PC and MS-DOS compatible
D-15
-------
i~ ':' -sc'n(Lcc( 1-VT2)
:C V;2sSvR(LOG( 1-V2~2)
-C '..:3=3Q?.(LCG( 1~V2"2)
i: c-csus 1 160
?: ??.I::T -EKTER LCV;EST, HIGHEST", -ALT n:c?.a-z::T or IULT or TARGET FOR-
.-5 :::?UT "'..-HICK -'EXCEED IS DESIRES" ; 51 ,E2,B3
?6 ir Z1-E2*33=C THEl! GOTO 11 2C "
-_ r.. r
:; rr.IIT " CCEF OF VAE ..... QS r ";V1
:- ?ni:;T n cosr CF VAF. ..... QS- ";V2
-.5 PRI::T n COEJ- of VA?......C£ * n;73
7C10/AVG CS s ";F1
7C10/AVG CE s ";F2
AVG CE/EL s ";F3
STREAM COtIC (CO"
5 ?K:::T - .VJLT OFW;TAB( i3);I>PEPCc;T";TAB(25) ;"RETORB"
5.?SIi;T.n TAPGE7 " ;TAS( 13) ; "OF TIrEn;TAB( 25)
7 Pr.IIIT "(CO/CL) "j'TABdS.^^EXCEEDED-jTAECZSJ
3 rrll.'T » ------ ";TAS(13);W --- ";TA3(25);"
0 EEI-J - LOAT QUAD-.. -WOTS * ROOTS
C GOSUE 1U10
-C HE-: COIIPUT PORTION OF Q(X) Ar.GUI^BT 2IDBP OF CO
o FOR 1=1 TO ;:o
: HZ:: - EVALUATE USUIG INV PROE
: ?9--':=r-5-v^i}
: GCSUE 1 ? 1 c
C :9fr-(I)sLCC(l*EXP(U9-W9*29))-U3
C 53' - COKC LOOP
3 FOR CO=B1 TO £2 STEP 33
3 15=0 . . .
C H2-; - CCAD LOOP - EVALUATE Q(X) s T Ah-D SUH
C FOR Is1 TO TO '
C X = (LC-G(CO)
G XOsSGlKZ)
0 Z=A2S(X)
C Fs1*X*(D 1*
00 Fs.5*F*(-l6)
TO. IF X0>0 TKEi; GOTO 1030
20 F=1-F
HO Z5«I5»F«Z5#(I)
40 .'SXT I
50 RE2: COtlPUTS RETUPJ: PERIOD
£0 IC«1/365/I5
Figure D-5 (cont'd.)
D-16
-------
C7C I5alOC«i5
:;; ?.= :::T r;s:i:c- "v*$.vv? n;cc,i5,io
:-c-c ::EXT cc ..-.'
:oc ??I::T ci-incc?) . ' . . .
-1C1 i::Fl'T "EI.'TES TO CONTINUE, OR 'STOP' ";AS
: C2 I~ AiO"STO?n. THE!" GOTO 560 -
1C F.ET. GOTO 790 , '
-.20 TCP Lsl TO 7- '
3'C ??.i:!7 ' . - - -
;-'-c" ::EXT L . . - . .
^ r'.EY Of! . '
6: HE:: sui?.cut:i:E TO LOAD ::OP.KAI. ATD -Rtvssss ;:CPJIAL COEFFIC:"::TS
:: :T=. 01198673*57*' ' ' '
',2Z : 2s. 021 H*1 00-1
.
2CC E^=2 .60036E-C5
2^C 11*2.51-5517
I". E2s.sC2:53
Z9C E£s.CC13'0£ ' ' . ' .
'' -"0 ' r.E-TUPi" "
'io ~^' 'u^ROurii-ii TO cot:?uTE nr/ERsE iiOrJ-
"sc iis: POLYI.-C^AL ;JPROX TC DIVERSE TABLE
'.30 :EF F::C(vii)s x^-(E1*E2*X#*E3*X#-2)/(1*E^X^E5»X?-2*E6«X^ 3)
' uc . 59 s 1 .
^-9 IF .?9*<1Z-i8 THE?: P9#.s1E-l8
!:5C IF P9*<.5 THE!-'. GOTO 1380
£: ??/: = : -?9v - ; .
3£C ?9*
;90 X9=F!:C(
-00 P.ETURK -' ' -
-10 REh QUADRATURE SUBROUTIKE - C011PUTE HOOTS AKC WEIGHTS
U20 RS-i ISsIIITSGRAL
-30 HS: 35(KO)= NO ROOTS
-iiC.FlE!-! Z5('lCO)s NO WEIGHTS
iJ50 RS>: LOAD ROOTS AI!D WEIGHTS FOR 32HD ORCER QUADS
a60 FEM FIRST THE GAUSSIAN, TEEN THE LAGUERRE TER1-3
«70 RS-; GOAD ROOTS & WEIGHTS FOR 16TH ORDER GAUSSIAN
-80 R1«8 ' -
"90 R#(D a-. 985*00935* '
=00- R#(2)a-.9**575023*
= 10 ?:tf(3)s-.865631202U# ' '
530 R*(5)a-. 6176762****
5ttO Rtf(6)s-.U5cOl67776#
550 R*(7)a-.28l603550'e*
Figure D-5 (cont'd.)
D-17
-------
= 3 r#(£)s-.095C125C9S40
50 S£#(2)=.062253523940
9C £8
-------
RECEIVING WATER CONG (CO) PROBABILITY DISTRIBUTION
AND RETURN PERIOD
FOR MULTIPLES OF TARGET CONG
DUE TO POINT SOURCE LOADS
POINT SOURCE - RECEIVING WATER
CONCENTRATION ANALYSIS
INPUT COEF OF VAR OF QS,QE,CE
RATIO...7Q10/AVG QS
RATIO...7Q10/AVG QE
RATIO...AVG CE/CL
BACKGROUND STREAM CONG (CS) IS ASSUMED TO BE
ZERO
ENTER COEF OF VAR OF QS, QE, CE
? 1.5, .2, .7
ENTER THE FOLLOWING RATIOS:
7Q10/AVG QS ? .05
7Q10/AVG QE ? 3.0
AVG CE/EL ? . 67
COEF OF VAR QS 1.5
COEF OF VAR QE .2
COEF OF VAR.... CE .7
7Q10/AVG QS = .05
7Q10/AVG QE = 3
AVG CE/EL = . 67
ENTER LOWEST, HIGHEST, AMD INCREMENT OF MULT OF TARGET FOR WHICH %
EXCEED IS DESIRES? 1,5,1
COEF OF VAR QS 1.5
COEF OF VAR QE .2
COEF OF VAR CE .7
7Q10/AVG QS = .05
7Q10/AVG QE = 3
AVG CE/EL = . 67
Figure D-5 (cont'd.)
D-19
-------
STREAM CONG (CO)
MULT OF PERCENT RETURN
TARGET OF TIME PERIOD
(CO/CL) EXCEEDED (YEARS)
1.000
2.000
3.000
4.000
5.000
0.894
0.112
0.024
0.007
0.002
0.306
2.443
11.313
39.429
114.356
ENTER TO CONTINUE, OR 'STOP'?
COEF OF VAR QS = 1.5
COEF OF VAR QE = .2
COEF OF VAR CE = .7
7Q10/AVG QS = .05
7Q10/AVG QE = 3
AVG CE/EL = .67
ENTER LOWEST, HIGHEST, AJJD INCREMENT OF MJLT OF TARGET FOR WHICH
% EXCEED IS DESIRED? 2.5, 3, .1
COEF OF VAR QS = 1.5
COEF OF VAR QE = .2
COEF OF VAP CS = .7
7Q10/AVG QS = .05
7Q10/AVG QE = 3
AVG CE/EL = . 67
STREAM CONG (CO)
MULT OF PERCENT RETURN
TARGET OF TIME PERIOD
(CO/CL) EXCEEDED (YEARS)
2.500
2.600
2.700
2.800
2.900
3.000
0.050
0.043
0.037
0.032
0.028
0.024
5.501
6.395
7.410
8.558
9.854
11.313
ENTER TO CONTINUE, OR STOP? STOP
Figure D-5 (cont'd.
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DISCLAIMER
We have made efforts to ensure that this electronic document is an accurate reproduction
of the original paper document. However, this document does not substitute for EPA
regulations; nor is it a regulation itself. Thus, it does not and cannot impose legally
binding requirements on EPA, the states, tribes or the regulated community, and may not
apply to a particular situation based on the circumstances. If there are any differences
between this web document and the statute or regulations related to this document, or
the original (paper) document, the statute, regulations, and original document govern. We
may change this guidance in the future.
Supplemental material such as this disclaimer, a document abstract and glossary entries
may have been added to the electronic document.
NOTE TO THE BROWSER
These original guidance documents - enhanced for easier access in 2006/2007 - still
contain much of EPA's current thinking with regards to water quality modeling and TMDLs.
However, the reader may discover that some of the referenced tools and materials have
been superseded or are no longer in general use. Information on the latest EPA-supported
and other models is available at the EPA Center for Exposure Assessment Modeling
(CEAM), currently located online at http://www.epa.gov/ceampubl/.
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GLOSSARY
Activated sludge - A secondary wastewater treatment process that removes organic
matter by mixing air and recycled sludge bacteria with sewage to promote decomposition.
Acute toxicity - A chemical stimulus severe enough to rapidly induce an effect; in aquatic
toxicity tests, an effect observed within 96 hours or less is considered acute. When
referring to aquatic toxicology or human health, an acute effect is not always measured in
terms of lethality.
Advanced waste treatment (AWT) - Wastewater treatment process that includes
combinations of physical and chemical operation units designed to remove nutrients, toxic
substances, or other pollutants. Advanced, or tertiary, treatment processes treat effluent
from secondary treatment facilities using processes such as nutrient removal (nitrification,
denitrification), filtration, or carbon adsorption. Tertiary treatment plants typically achieve
about 95% removal of solids and BOD in addition to removal of nutrients or other
materials.
Ammonia - Inorganic form of nitrogen; product of hydrolysis of organic nitrogen and
denitrification. Ammonia is preferentially used by phytoplankton over nitrate for uptake of
inorganic nitrogen.
Biochemical oxygen demand (BOD) - The amount of oxygen per unit volume of water
required to bacterially or chemically oxidize (stabilize) the oxidizable matter in water.
Biochemical oxygen demand measurements are usually conducted over specific time
intervals (5,10,20,30 days). The term BOD generally refers to standard 5 day BOD test.
Chronic Toxicity - Toxicity, marked by a long duration, that produces an adverse effect
on organisms. The end result of chronic toxicity can be death although the usual effects
are sublethal; e.g., inhibits reproduction, reduces growth, etc. These effects are reflected
by changes in the productivity and population structure of the community.
Combined sewer overflows (CSOs) - A combined sewer carries both wastewater and
stormwater runoff. CSOs discharged to receiving water can result in contamination
problems that may prevent the attainment of water quality standards.
Complete mixing - No significant difference in concentration of a pollutant exists across
the transect of the waterbody.
Concentration - Amount of a substance or material in a given unit volume of solution.
Usually measured in milligrams per liter (mg/l) or parts per million (ppm).
Conservative substance - Substance that does not undergo any chemical or biological
transformation or degradation in a given ecosystem.
Conventional pollutants -As specified under the Clean Water Act, conventional
contaminants include suspended solids, coliform bacteria, biochemical oxygen demand,
pH, and oil and grease.
Design stream flow - The stream flow used to conduct steady state wasteload allocation
modeling.
Dilution - Addition of less concentrated liquid (water) that results in a decrease in the
original concentration.
Discharge permits (NPDES) - A permit issued by the U.S. EPA or a State regulatory
agency that sets specific limits on the type and amount of pollutants that a municipality or
industry can discharge to a receiving water; it also includes a compliance schedule for
-------
achieving those limits. It is called the NPDES because the permit process was established
under the National Pollutant Discharge Elimination System, under provisions of the
Federal Clean Water Act.
Dissolved oxygen (DO) - The amount of oxygen that is dissolved in water. It also refers to
a measure of the amount of oxygen available for biochemical activity in water body, and as
indicator of the quality of that water.
Effluent - Municipal sewage or industrial liquid waste (untreated, partially treated, or
completely treated) that flows out of a treatment plant, septic system, pipe, etc.
Heavy Metals - Metals that can be precipitated by hydrogen sulfide in acid solution, for
example, lead, silver, gold, mercury, bismuth, copper.
In situ - In place; in situ measurements consist of measurement of component or
processes in a full scale system or a field rather than in a laboratory.
Load allocation (LA) - The portion of a receiving water's total maximum daily load that is
attributed either to one of its existing or future nonpoint sources of pollution or to natural
background sources.
Low flow (7Q10) - Low flow (7Q10) is the 7 day average low flow occurring once in 10
years; this probability based statistic is used in determining stream design flow conditions
and for evaluating the water quality impact of effluent discharge limits.
Mass balance - An equation that accounts for the flux of mass going into a defined area
and the flux of mass leaving the defined area. The flux in must equal the flux out.
Mathematical model - A system of mathematical expressions that describe the spatial
and temporal distribution of water quality constituents resulting from fluid transport and the
one, or more, individual processes and interactions within some prototype aquatic
ecosystem. A mathematical water quality model is used as the basis for waste load
allocation evaluations.
Modeling - The simulation of some physical or abstract phenomenon or system with
another system believed to obey the same physical laws or abstract rules of logic, in order
to predict the behavior of the former (main system) by experimenting with latter (analogous
system).
Monitoring - Routine observation, sampling and testing of designated locations or
parameters to determine efficiency of treatment or compliance with standards or
requirements.
Nitrification - The oxidation of ammonium salts to nitrites (via Nitrosomonas bacteria) and
the further oxidation of nitrite to nitrate via Nitrobacter bacteria.
Organic - Refers to volatile, combustible, and sometimes biodegradable chemical
compounds containing carbon atoms (carbonaceous) bonded together and with other
elements. The principal groups of organic substances found in wastewater are proteins,
carbohydrates, and fats and oils.
Organic matter - The organic fraction that includes plant and animal residue at various
stages of decomposition, cells and tissues of soil organisms, and substance synthesized
by the soil population. Commonly determined as the amount of organic material contained
in a soil or water sample.
Oxidation - The chemical union of oxygen with metals or organic compounds
accompanied by a removal of hydrogen or another atom. It is an important factor for soil
formation and permits the release of energy from cellular fuels.
-------
Oxygen Deficit - The difference between observed oxygen concentration and the amount
that would theoretically be present at 100% saturation for existing conditions of
temperature and pressure.
Oxygen demand - Measure of the dissolved oxygen used by a system (microorganisms)
in the oxidation of organic matter. See also biochemical oxygen demand.
Oxygen depletion - Deficit of dissolved oxygen in a water system due to oxidation of
organic matter.
Partition coefficients - Chemicals in solution are partitioned into dissolved and particulate
adsorbed phase based on their corresponding sediment to water partitioning coefficient.
Point source - Pollutant loads discharged at a specific location from pipes, outfalls, and
conveyance channels from either municipal wastewater treatment plants or industrial
waste treatment facilities. Point sources can also include pollutant loads contributed by
tributaries to the main receiving water stream or river.
Pollutant - A contaminant in a concentration or amount that adversely alters the physical,
chemical, or biological properties of a natural environment. The term include pathogens,
toxic metals, carcinogens, oxygen demanding substances, or other harmful substances.
Examples of pollutant sources include dredged spoil, solid waste, incinerator residue,
sewage, garbage, sewage sludge, munitions, chemical waste, biological material,
radioactive materials, heat, wrecked or discharged equipment, sediment, cellar dirt,
hydrocarbons, oil, and municipal, industrial, and agricultural waste discharged into surface
water or groundwater.
Quality - A term to describe the composite chemical, physical, and biological
characteristics of a water with respect to it's suitability for a particular use.
Reaeration - The absorption of oxygen into water under conditions of oxygen deficiency.
Respiration - Biochemical process by means of which cellular fuels are oxidized with the
aid of oxygen to permit the release of the energy required to sustain life; during respiration
oxygen is consumed and carbon dioxide is released.
Secondary treatment plant - Waste treatment process where oxygen demanding organic
materials (BOD) are removed by bacterial oxidation of the waste to carbon dioxide and
water. Bacterial synthesis of wastewater is enhanced by injection of oxygen.
Sediment - Particulate organic and inorganic matter that accumulates in a loose,
unconsolidated form on the bottom of natural waters.
Sediment oxygen demand (SOD) - The solids discharged to a receiving water are partly
organics, and upon settling to the bottom, they decompose anaerobically as well as
aerobically, depending on conditions. The oxygen consumed in aerobic decomposition
represents another dissolved oxygen sink for the waterbody.
Simulation - Refers to the use of mathematical models to approximate the observed
behavior of a natural water system in response to a specific known set of input and forcing
conditions. Models that have been validated, or verified, are then used to predict the
response of a natural water system to changes in the input or forcing conditions.
Stabilization pond - Large earthen basins that are used for the treatment of wastewater
by natural processes involving the use of both algae and bacteria.
Steady state model - Mathematical model of fate and transport that uses constant values
of input variables to predict constant values of receiving water quality concentrations.
-------
STORET - U.S. Environmental Protection Agency (EPA) national water quality database
for STORage and RETrieval (STORET). Mainframe water quality database that includes
physical, chemical, and biological data measured in waterbodies throughout the United
States.
Storm runoff - Rainfall that does not evaporate or infiltrate the ground because of
impervious land surfaces or a soil infiltration rate lower than rainfall intensity, but instead
flows onto adjacent land or waterbodies or is routed into a drain or sewer system.
Streamflow - Discharge that occurs in a natural channel. Although the term "discharge"
can be applied to the flow of a canal, the word "streamflow" uniquely describes the
discharge in a surface stream course. The term streamflow is more general than "runoff"
as streamflow may be applied to discharge whether or not it is affected by diversion or
regulation.
Suspended solids or load - Organic and inorganic particles (sediment) suspended in and
carried by a fluid (water). The suspension is governed by the upward components of
turbulence, currents, or colloidal suspension.
Trickling filter - A wastewater treatment process consisting of a bed of highly permeable
medium to which microorganisms are attached and through which wastewater is
percolated or trickled.
Verification (of a model) - Subsequent testing of a precalibrated model to additional field
data usually under different external conditions to further examine model validity (also
called validation).
Waste load allocation (WLA) - The portion of a receiving water's total maximum daily
load that is allocated to one of its existing or future point sources of pollution.
Wastewater - Usually refers to effluent from a sewage treatment plant. See also domestic
wastewater.
Wastewater treatment - Chemical, biological, and mechanical procedures applied to an
industrial or municipal discharge or to any other sources of contaminated water in order to
remove, reduce, or neutralize contaminants.
Water quality criteria (WQC) - Water quality criteria comprised numeric and narrative
criteria. Numeric criteria are scientifically derived ambient concentrations developed by
EPA or States for various pollutants of concern to protect human health and aquatic life.
Narrative criteria are statements that describe the desired water quality goal.
Water quality standard (WQS) - A water quality standard is a law or regulation that
consists of the beneficial designated use or uses of a waterbody, the numeric and
narrative water quality criteria that are necessary to protect the use or uses of that
particular waterbody, and an antidegradation statement.
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