FINAL
TECHNICAL GUIDANCE MANUAL FOR
PERFORMING WASTE LOAD ALLOCATION
BOOK VI
DESIGN CONDITIONS:
CHAPTER 1
STREAM DESIGN FLOW FOR STEADY-STATE MODELING
August, 1986
Monitoring and Data Support Division
Office of Water Regulations and Standards
Office of Water
and
Environmental Research Laboratory
Office of Research and Development
Culuth, Minnesota
with the assistance of
Water Engineering Research Laboratory
Office of Research and Development
Cincinnati/ Ohio
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UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
OFFICE OF
WATER
MEMORANDUM
Subject: Technical Guidance Manual for Performing Wasteload
Allocations Book VI, Design Conditions: Chapter 1 - Stream
Design Flow for .Steady-State Modeling
From: Twlliani A. Whittington, Director
Office of Water Regulations and Standards (WH-551)
To: Addressees
Attached, for national use, is the final version of the Technical
Guidance Manual for Performing Wasteload Allocations, Book VI, Design
Conditions: Chapter 1 - Stream Design Flow for Steady-State Modeling.
This manual replaces the interim stream design flow recommendations
included in Appendix D of our Technical Support Document for Water
Quality-based Toxics Control, September, 1985. We are sending extra
copies of this manual to the Regional Waste Load Allocation Coordinators
for distribution to the States to use in conducting waste load allocations.
If you have any questions or desire additional information
please contact Tim S. Stuart, Chief, Monitoring Branch, Monitoring and Data
Support Division (WH-553) on (ETS) 382-7074
Attachment
Addressees:
Regional Water Management Division Directors
Regional Environmental Services Division Directors
Regional Wasteload Allocation Coordinators
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ACKNOWLEDGMENT
The preparation of this document was a collaborative effort of the Office
of Water and the Office of Research and Development. Tim S. Stuart and
Mark Morris of the Office of Water Regulations and Standards, and Nelson
Thomas of Environmental Research Laboratory-Duluth provided overall guidance
and direction in preparation of this manual. Program managers of Regions
III, IV, V, VI and VII, and the Headquarters program managers within the
Office of Municipal Pollution Control and the Office of Water Regulations
and Standards actively participated in developing this guidance.
Hiranmay Biswas of the Monitoring and Data Support Division, Lewis A.
Rossman of Water Engineering Research Laboratory-Cincinnati and Charles E.
Stephen of Environmental Research Laboratory-Duluth are the principal
authors of this manual. Sections 1, 2 and 4, and Appendices B and E were
prepared by Hiranmay Biswas. Sections 3 and 5 of the manual were prepared
by Charles E. Stephen with statistical support from Russell E. Erickson of
Environmental Research Laboratory-Duluth. Appendices A, C and D of the
manual were jointly prepared by Lewis A. Rossman and Charles E. Stephan.
Individuals listed below contributed to the preparation of this manual
and their efforts are greatly appreciated.
Garret Bondy, U.S. EPA Waste Load Allocation (WLA) Section Region VI
Rick Brandes, U.S. EPA Permit Division
Miriam Goldberg, U.S. EPA Analysis and Evaluation Division
Joseph Gormley, U.S. EPA Municipal Facilities Division
Robert C. Horn, U.S. EPA Criteria and Standard Division
Norbert Huang, U.S. EPA Municipal Facilities Division
Sally Marquis, U.S. EPA WLA Coordinator Region X
Robert F. McGhee, U.S. WLA Coordinator Region IV
John Maxted, U.S. EPA Criteria and Standard Division
Rosella 0'Conner, U.S. EPA WLA Coordinator Region II
Thomas W. Purcell, U.S. EPA Criteria.and Standard Division
Robert J. Steiert, U.S. EPA Coordinator Region VII
Randall E. Williams, RTI, FTP, NC
Dale Wismer, U.S. EPA WLA Coordinator Region III
Edward H. Woo, U.S. EPA WLA Coordinator Region I
Phil Woods, U.S. EPA WLA Coordinator Region IX
Bruce Zander, U.S. EPA WLA Coordinator Region VIII
ii
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TABLE OF CONTENTS
Page
SECTION 1. INTRODUCTION 1-1
1.1 Purpose 1-1
1.2 Background 1-1
1.3 Scope 1-3
SECTION 2. HYDROLOGICALLY-BASED DESIGN FLOW METHOD 2-1
2.1 Introduction 2-1
2.2 Rationale 2-2
2.3 Example Cases 2-3
SECTION 3. BIOLOGICALLY-BASED DESIGN FLOW METHOD 3-1
3.1 Introduction 3-1
3.2 Procedure 3-6
3.3 Rationale 3-7
3.4 Example Cases 3-7
SECTION 4. COMPARISON OF RESULTS OF THE TWO METHODS 4-1
4.1 Design Flows 4-1
4.1.1 Use of Biologically-Based Design Flows for Ammonia
Discharges from POTWs 4-4
4.2 Excursions 4-5
4.3 Comparison of the Two Methods 4-8
SECTION 5. RECOMMENDATIONS 5-1
SECTION 6. REFERENCES 6-1
iii
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TABLE OF CONTENTS
Rage
APPENDIX A - Calculation of Hydrologically-based Design Flows A-l
APPENDIX B - Design Flows for Ammonia B-l
APPENDIX C - Calculation of Biologically-based Design Flows C-l
APPENDIX D - Description of the Program DFLCW D-l
APPENDIX E - Questions and Answers Concerning the Biologically-based Method E-l
iv
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SECTION 1. INTRODUCTION
1.1 Purpose
The purpose of this guidance is to describe and compare two methods
that can be used to calculate stream design flows for any pollutant or
effluent for which a two-number water quality criterion (WQC) for the
protection of aquatic life is available. The two methods described are:
1. The hydrologically-based design flow method recommended for
interim use in the Technical Support Document for Water Quality-
based Toxics Control (1); and
2. A biologically-based design flow method that was developed by
the Office of Research and Development of the U.S. EPA.
1.2 Background
National water quality criteria for aquatic life (2) are derived on
the basis of the best available biological, ecological and toxicological
information concerning the effects o£ jjollutants on aquatic organis.iv3
and their uses (3,4). To account for local conditions/ site-specific
criteria may be derived whenever adequately justified (4). In addition,
criteria may be derived from the results of toxicity tests on whole
effluents (1). National, site-specific, and effluent toxicity criteria
specify concentrations of pollutants, durations of averaging periods,
and frequencies of allowed exceedences. If these criteria are to achieve
their intended purpose, decisions concerning not only their derivation,
but also their use, must be based on the biological, ecological, and
toxicological characteristics of aquatic organisms and ecosystems, and
their uses, whenever possible.
1-1
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National, site-specific, and effluent toxicity criteria are expressed
as two concentrations, rather than one, so that the criteria can more
accurately reflect toxicological and practical realities (1 - 4):
a. The lower concentration is called the Criterion Continuous
Concentration (CCC). The CCC is the 4-
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One way of using the CCC and the CMC in steady-state modeling requires
calculation of the two design flows (i.e., a CCC design flow and a CMC
design flow). Whether the CCC and its design flow or the CMC and its
design flow is more restrictive, and therefore controlling/ mist be
determined individually for each pollutant of concern in each effluent
because the CCC and CMC are pollutant-specific, whereas the two design
flows are specific to the receiving waters.
Wasteload allocation modeling for streams usually uses flow data
obtained from the United States Geological Survey gaging stations. If
sufficient flow data are not available for a stream of interest/ data
must be extrapolated from other streams having hydrologic characteristics
similar to those of the stream of interest.
1.3
This guidance is limited to (a) describing two methods that can be
used for calculating stream design flows for any pollutant or effluent
for which a two-number aquatic life water quality criterion is available,
and (b) making recommendations concerning the use of these methods in steady-
state modeling.
The water quality criterion for dissolved oxygen was revised very
recently and the assessment of the appropriate design flow for dissolved
oxygen modeling has not yet been completed. Therefore, the state-specified
design flows that traditionally have been used for conventional pollutants
should not be affected by this guidance.
1-3
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State-specified design flows necessarily preempt any design flow
that is recommended in this guidance unless the state chooses to use either
of these two methods. The choice of design flows for the protection of
human health has been discussed in the Technical Support Document for
Water Quality-based Toxics Control (1).
Aquatic life criteria of sane pollutants are affected by environmental
variables such as water temperature, pH, and hardness. In addition to
the design flow, such other stream variables as pH and temperature might
increase or decrease the allowable in-stream concentrations of some
pollutants (e.g./ ammonia). The need to consider other variables when
determining the design flow for those pollutants should be emphasized.
This document will provide guidance for the calculation of design flow;
pH, temperature, and hardness will likely be addressed later.
1-4
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SECTION 2. HYDRQDDGICALLY-BASED DESIGN FLOW METHOD
2.1 Introduction
The purpose of tills section is to describe the hydrologically-based
design flow calculation method and provide some examples of its use. The
Technical Support Document for Water Quality-based Toxics Control (1)
provides Agency guidance on control of both generic and pollutant-specific
toxicity and recomnended interim use of the hydrologically-based method.
In addition, the Agency also recomnended (1/2) that the frequencies of
allowed exceedences and the durations of the averaging periods specified in
aquatic life criteria should not be used directly to calculate steady-
state design flows using an extreme value analysis. For example, if a
criterion specifies that the four-day average concentration should not
exceed a particular value more than once every three years on the average,
this should not be interpreted as implying that the 4Q3 low flow is
appropriate for use as the design flow.
Because a procedure had not been developed for calculating design
flow based on the durations and frequencies specified in aquatic life
criteria, the U.S. EPA recommended interim use of the 1Q5 and 1010 low
flows as the CMC design flow and the 7Q5 and 7Q10 low flows as the CCC
design flow for unstressed and stressed systems, respectively (1).
Further consideration of stress placed on aquatic ecosystems resulting
from exceedences of water quality criteria indicates that there is little
justification for different design flows for unstressed and stressed
systems. All ecosystems have been changed as a result of man's activities.
These changes have resulted in stress being placed on the ecosystem
before a pollutant stress. In addition/ it is not possible to predict
2-1
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the degree of pollutant stress when one considers both the timing and
variability of flows, effluent discharges, and ecosystem sensitivity and
resilience.
2.2 Rationale
The following provides a rationale for the hydrologically-based
design flow calculation method:
0 About half of the states in the nation use 7Q10 as the design low
flow.
0 The log-Pearson Type III flow estimating technique or other extreme
value analytical techniques that are used to calculate flow
statistics from daily flow data are consistent with past engineering
and statistical practice.
0 Host users are familiar with the log-Pearson Type III flow estimating
procedure and the USGS provides technical support for this technique.
0 Analyses of 60 rivers indicate that, on the average, the biologically-
based CMC and CCC design flows are nearly equal to the 1Q10 and the
7Q10 low flows.
2.3 Example Cases
In order to illustrate the calculation of hydrologically-based
design flows, sixty rivers with flows of various magnitudes and variabilities
were chosen from around the country. The 1Q10 and 7Q10 low flows of the
sixty rivers are presented in Table 2-1. The list of rivers in this table
is arranged in increasing magnitude of the 7Q10 low flows. The
estimates of the 1Q10 and 7Q10 low flows were made using the USGS
daily flow database and the FLDSTAT program (6) which employs the
log-Pearson Type III technique.
2-2
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The estimates of 1Q10 and 7Q10 low flows could have been made using
EPA-ORD's DFLOW program, which uses a simplified version of the log-Pearson
Type III method. The simplified version of the log-Pearson Type III
estimating technique for any xQy design flow is presented in Appendix A.
Although the Log-Pearson Type III is in general use, it should be recognized
that there are other distributions that may be more appropriate to use on a
case-by-case basis. The hydrologically-based design flow for ammonia
is discussed in Appendix B.
Analyses 'of the 1Q10 and 7Q10 lew flows in Table 2-1 indicate that
the mean of the ratios of 7010 to 1010 is 1.3. The median of the ratios
is 1.1, whereas the range of the ratios is 1.0 to 3.85. Thus, 7010 low
flows are generally 10 to 30% greater than the corresponding 1010 low
flows, although in one case the 7Q10 is 3.85 times greater than the
corresponding 1010.
Table 2-1. Hydrologically-based design flows (ftVsec) for 60 streams
Station ID River name
Period of
State Record CV*
Design flow (ftVsec)
1010 7Q10
7Q10
TOUT
01657000
02092500
06026000
12449600
05522000
09490800
14372500
05381000
10291500
05585000
12321500
01111500
Bull Run
Trent
Birch Cr
Beaver Cr
Iroguois
N Fk White
E Fk Illinois
Black
Buckeye
La Moine
Boundary Cr
Branch
TO
NC
MT
WA
IN
AZ
OR
WI
CA
IL
ID
RI
1951-82
1951-82
1946-77
1960-78
1949-78
1966-78
1942-83
1905-83
1911-78
1921-83
1928-84
1940-82
4.48
1.77
1.32
1.77
1.33
1.24
2.03
2.51
1.30
1.99
1.65
1.16
0.3
1.4
1.7
2.4
3.4
4.8
6.4
5.5
7.1
9.3
11.7
8.8
0.4
1.6
2.4
3.2
3.9
5.3
6.7
6.7
7.7
9.9
13.1
13.3
1.33
1.14
1.41
1.22
1.15
1.10
1.05
1.22
1.08
1.06
1.12
1.51
2-3
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Table 2-1 (continued).
Station ID River name
Period of
State Record CV*
Design flow (ft3/sec)
1Q10 7Q10
7010
lunr
02138500
05059000
02083000
01196500
02133500
06280300
09149500
02296750
07018500
02217500
01481000
09497500
01144000
01600000
09359500
01403060
02413500
01421000
07288500
07013000
01531000
07096000
09070000
01011000
03528000
13023000
02424000
05515500
02490500
01315500
01610000
05386000
02369000
07378500
06465500
02135000
08110200
02076000
03455000
05333500
06287000
03107500
Linville
Sheyenne
Fishing Cr
Quinnipiac
Drowning Cr
Shoshone
Unconpahgre
Peace
Big
Middle Oconee
Brandywine
Salt
White
N Br Potomac
Animas
Raritan
L Tallapcosa
E B Delaware
Big Sunflower
Meramec
Chenung
Arkansas
Eagle
Allegash
Clinch
Greys
Cahaba
Kankakee
Bouge Chitto
Hudson
Potomac
Root
Shoal
Amite
Niobrara
Little Pee Dee
Brazos
Dan
French Broad
St. Croix
Bighorn
Beaver
NC
ND
NC
CT
NC
WY
CO
PL
MO
GA
PA
AZ
VT
MD
CO
NJ
AL
NY
MS
MO
NY
CO
CO
ME
TN
WY
AL
IN
MS
NY
WV
MN
PL
LA
ME
SC
TX
\&
TN
WI
MT
PA
1922-84
1951-81
1927-82
1931-84
1940-78
1957-84
1939-80
1931-84
1922-84
1902-84
1912-84
1925-80
1915-84
1939-83
1946-56
1904-83
1940-51
1915-78
1936-80
1923-78
1915-78
1901-81
1947-80
1932-83
1919-78
1937-83
1902-78
1926-78
1945-81
1908-78
1939-83
1938-61
1939-82
1939-83
1939-83
1942-78
1966-78
1924-52
1901-78
1914-81
1935-79
1957-83
1.74
2.10
1.48
1.02
0.80
1.54
0.86
1.54
2.16
1.37
1.17
2.05
1.43
1.42
1.56
1.64
1.33
1.41
1.42
2.41
1.91
1.12
1.36
1.39
1.55
1.16
2.07
0.48
1.89
1.10
1.48
1.65
0.95
1.98
0.59
0.94
1.48
1.25
0.93
0.61
0.82
1.10
13.4
15.9
17.0
17.5
38.8
41.8
35.6
49.0
46.4
49.4
61.4
64.6
75.3
54.7
54.8
54.2
72.7
80.8
89.4
88.8
89.7
107.9
116.9
124.5
128.7
122.9
151.9
179.0
188.6
207.7
209.6
229.7
280.1
298.1
160.9
306.7
311.6
329.6
473.6
505.9
327.1
571.3
16.4
18.3
19.4
32.3
43.4
46.8
50.8
55.3
55.3
57.4
67.2
68.7
85.2
61.6
62.3
67.1
88.3
89.7
91.9
92.2
97.5
126.1
131.0
134.1
135.2
144.5
156.4
184.3
191.6
211.0
220.7
245.6
291.4
303.4
322.0
322.4
344.9
387.3
532.2
536.0
557.0
594.2
1.22
1.15
1.14
1.85
1.12
1.12
1.43
1.13
1.19
1.16
1.09
1.06
1.13
1.13
1.15
1.24
1.21
1.11
1.03i
1.0*
1.09
1.17
1.12
1.08
1.05
1.18
1.03
1.03
1.02
1.02
1.05
1.07
1.04
1.02
2.00
1.05
1.11
1.18
1.12
1.06
1.70
1.04
2-4
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Table 2-1 (continued).
Station ID River name
Period of
State Record CV*
Design flow (ft3/sec)
1Q10 7Q10
7Q10
TOUT
13341000
07341500
02350500
01536500
01100000
14233400
N F Qearwater
ted
Flint
Susquehanna
Merrinack
Gbwlitz
ID
AR
GA
PA
MA
WA
1927-68
1928-81
1930-58
1901-83
1924-83
1968-78
1.16
1.41
1.00
1.34
1.01
0.93
529.2
691.0
207.8
782.0
270.2
901.5
648.6
769.2
799.8
814.3
929.3
968.7
1.23
1.11
3.85
1.04
3.44
1.07
*CV o Coefficient of Variation
2-5
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SECTION 3. BIOLOGICALLY-BASED DESIGN FLOW METHOD
3.1 Introduction
The purpose of this section is to describe the biologically-based
design flow calculation method and provide some examples of its use.
This method was developed by the Office of Research and Development of
the U.S. EPA in order to provide a way of directly using EPA's two-number
aquatic life water quality criteria (WQC) for individual pollutants and
whole effluents to calculate the design flow for performing a wasteload
allocation using steady-state modeling. The two-number WQC are in the
intensity-duration-freouency format, in that they specify intensity as
criteria concentrations, duration as averaging periods, and frequency as
average frequency of allowed excursions. Because the flow of, and
concentrations of pollutants in, effluents and streams are easily considered
in terms of intensity, duration, and frequency, use of this format for
expressing WQC allows a direct application to effluents and streams.
Because steady-state modeling assumes that the composition and flow
of the effluent of concern is constant, the ambient (instream) concentration
of a pollutant can be considered to be inversely proportional to stream flow.
Thus by applying a specified averaging period and frequency to a record
of the historical flow of the stream of concern, the design flow can be
calculated as the highest flow that will not cause exceedences to occur
more often than allowed by the specified average frequency, based on
historical data. The allowed exceedences are intended to be small enough
and far enough apart, on the average, that the resulting small stresses
on aquatic organisms will not cause unacceptable effects, except in
those cases when a drought itself would cause unacceptable effects.
3-1
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The averaging periods specified in national water quality criteria
are one hour for the CMC and four days for the CCC. The primary use of
the averaging periods in criteria is for averaging ambient concen-
trations of pollutants in receiving waters in order that the averages
can be compared to the CMC and CCC to identify "exceedences", i.e.,
one-hour average concentrations that exceed the CMC and four-day average
concentrations that exceed the CCC. However, in steady-state modeling,
flow is averaged over a given period to identify "non-exceedences",
i.e., average flows that are below a specified flow.
Use of the terms "exceedence" and "non-exceedence", neither of
which are in the dictionary, can be a cause of confusion. Water quality
criteria are usually expressed as upper limits on concentrations in
ambient water and the periods of concern are when the ambient concentration
exceeds a criterion concentration, i.e., when there is an exceedence.
In steady-state modeling, the averaging is of flows, not concentrations.
Because a low flow results in a high pollutant concentration, the period
of concern for flow is when the flew is less than the design flow, i.e.,
when there is a non-exceedence of a given flow. A non-exceedence of a
design flow corresponds to an exceedence of a criterion. Use of the
non-directional term "excursion", which is in the dictionary, avoids
this confusion. Use of the terra "excursion" also avoids the problem
%
that some water quality criteria, such as those for dissolved oxygen
and low pH, must be stated as lower limits, not upper limits. An
exceedence of a dissolved oxygen criterion is favorable, not unfavorable.
"Excursion", in this guidance manual, will henceforth be used to imply
3-2
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an unfavorable condition/ e.g., a low flow or a pollutant concentration
above an upper limit or below a lower limit.
The national water quality criteria specify that, if R is the
calculated number of excursions occurring in a period of S years, then
S/R should be equal to or greater than 3 years. Most excursions will be
small and most aquatic ecosystems will probably recover from the
resulting minor stress in less than three years. However, the three
years is meant to be longer than the average recovery period so that
ecosystems cannot be in a constant state of recovery even if excursions
are evenly spaced over time.
Although 3 years appears to be appropriate for small excursions
that are somewhat isolated, it appears to be excessively long when many
excursions occur in a short period of time, such as would be caused by a
drought. Droughts are rare events, characterized by long periods of low
flow and should not be allowed to unnecessarily lower design flows.
Although droughts do severely stress aquatic ecosystems, both directly,
because of low flow, and indirectly, because of the resulting high
concentrations of. pollutants, many ecosystems apparently recover from
severe stresses in more than 5, but less than 10 years (1). Because it
is not adequately protective to keep ecosystems in a constant state of
recovery, 15 years seems like an appropriate stress-free period of
time, on the average, to allow after a severe stress caused by a drought
situation. Because three years are allowed for each excursion on the
average, counting no more than 5 excursions for any low flow period will
3-3
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provide no more than 15 years, on the average, for severe stresses caused
by droughts. Thus, for each low flow period, the number of excursions
cannot be less than 1.0 or greater than 5.0. The maximum duration of a
low-flow period was set at 120 days because it is not too uncommon for
excursions to occur within 120 days of each other, whereas it is very
rare for excursions to occur during days 121 to 240 after the beginning
of a low-flow period.
Figure 3-1 illustrates the features of the biologically-based design
flow calculation method. Intervals a-b and c-d are excursion periods and
each day in these intervals is part of an average flow that is below the
design flow. The number of excursions in an excursion period is calculated
as the number of days in the excursion period divided by the duration (in
days) of the averaging period (e.g., 1 day for the CMC and 4 days for the
CCC). A low-flow period is defined as one or more excursion periods
occurring within a 120-day interval. As discussed above, if the calculated
number of excursions that occur in a 120-day low-flow period is greater
than 5, the number is set at 5 for the purposes of calculating the design
flew.
Because biologically-based design flows are based on the averagiag
periods and frequencies specified in water quality criteria for individual
pollutants and whole effluents, they can be based on the available biological,
ecological, and toxicological information concerning the stresses that
aquatic organisms, ecosystems, and their uses can tolerate. The
biologically-based calculation method is flexible enough to make full use
3-4
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F
L
0
W
DESIGN FLOW
EXCURSION
PERIOD
EXCURSION
PERIOD
a
b c
TIME, (DAYS)
Figure 3-1: Illustration of biologically-based design flow
3-5
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of special averaging periods and frequencies that might be selected for
specific pollutants (e.g., ammonia) or in site-specific criteria. This
method is enpirical, not statistical, because it deals with the actual
flow record itself, not with a statistical distribution that is intended
to describe the flow record.
In addition, this method provides an understanding of how many excursions
of the CCC or CMC are likely to occur, and during what time of the year,
based on actual historical flow data. Thus, it is possible to examine the
pattern and magnitudes of what would have been historical excursions.
This method makes it clear that criteria concentrations should not be
interpreted as values that are never to be exceeded "at any time or place"
in the receiving waters. An understanding of what level of protection
actually is provided should aid in the use of criteria.
3.2 Procedure
Although the calculation procedure described in Appendix C might
look complicated, it merely consists of a sequence of steps that are
quite simple. Because flew records usually consist of daily flows for
20 to 80 years, manual calculation of design flow is very time-consuming.
The DFLCW computer program (Appendix D) will calculate biologically-based
design flows and display the dates, durations, and magnitudes of the
excursions within each low flow period.
3-6
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The CMC and CCC design flows are calculated in almost the same manner.
The differences result fron the fact that the CMC is expressed as a one-
hour average, whereas the CCC is expressed as a four-day average. However,
the flow records that are available consist of one-day average flows.
For streams with naturally occurring low flows, calculation of the CMC design
flow from one-day averages, rather than one-hour averages, should be
reasonably acceptable because naturally occurring low flows of receiving
streams are usually very similar from one hour to the next. In regulated
streams, such as those affected by hydroelectric or irrigation projects,
hour-to-hour variation of low flows could be significant and in those
situations, use of hourly values, when available, is appropriate. Both
the pollutant concentrations and the flows of most effluents are expected
to change much more from one hour to the next than the naturally occurring
flows of streams.
3.3 Rationale
The following provides a rationale for the biologically-based
design flow calculation method:
0 It allows the use of the new two-nunber WQC for aquatic life in the
calculation of design flow. If water quality criteria for aquatic
life are to achieve their intended purpose, decisions concerning their
derivation and use should be based on the biological, ecological,
and toxicological characteristics of aquatic organisms and ecosystems
and their uses whenever possible.
0 It takes into account all excursions in the flow record.
0 It provides the necessary design flow directly without requiring any
design flow statistics in the xCy format.
0 It is flexible enough so that any averaging period and frequency
selected for particular pollutants, effluents, or site-specific
criteria can be used directly in design flow calculations.
3-7
-------
3.4 Example Cases
The sixty flow records that were analyzed using the hydrologically-
based method (see Table 2-1) were also analyzed using the biologically-
based design flow method. The CMC design flow was calculated for a
1-day averaging period and the CCC design flow was calculated using the
4-day averaging period. Both were calculated using a frequency of once
every three years on the average. Table 3-1 presents biologically-based
design flows for these sixty rivers.
In addition to the hydrologically-based design flows, Table B-l
in Appendix B also includes biologically-based CMC and CCC design
flows for 13 streams for 30-day averaging periods and a frequency of
once every three years on the average. The purpose of the biologically-
based design flows for ammonia (5) in Appendix B is to illustrate how
this method might be used for site-specific and pollutant-specific
situations where the durations and frequencies in aquatic life criteria
might be different from those specified in national two-number aouatic
life criteria.
Analyses of the 1-day 3-year and the 4-<1ay 3-year low flows in Table
3-1 indicate that the mean ratio of the 4-day 3-year low flows to
the corresponding 1-day .3-year low flows is 1.23. The median of the
ratios is 1.11, whereas the range of the ratios is 1.0 to 2.81. Thus,
4-day 3-year low flows are generally 11 to 23% greater than the corresponding
1-day 3-year low flows, although in one case, the 4-day 3-year low flow
is 2.81 times greater than the corresponding 1-day 3-year low flow.
3-8
-------
Table 3-1. Biologically-based design flows fft3/sec) for 60 rivers
Station ID River name
Period of
State record CV*
Design flows (ft3/sec)
1-day 3-year 4-day 3 -year
/"TIC*
m~**
^••^
\-i 1«-
01657000
02092500
06026000
12449600
05522000
09490800
14372500
05381000
10291500
05585000
12321500
01111500
02138500
05059000
02083000
01196500
02133500
06280300
09149500
02296750
07018500
02217500
01600000
09359500
01403060
01481000
09497500
01144000
02413500
01421000
07288500
07013000
01531000
07096000
09070000
01011000
03528000
13023000
02424000
Bull Run
Trent
Birch Cr
Beaver Cr
Iroquois
N Fk White
E Fk Illinois
Black
Buckeye
la Moine
Boundary Cr
Brancli
Linville
Sheyenne
Fishing Cr
Quinnipiac
Drowning Cr
Shoshone
Unccnpangre
Peace
Big
Middle Oconee
N Br Potomac
Animas
Raritan
Brandywine
Salt
White
L lallapoosa
E B Delaware
Big Sunflower
Meramec
Chenung
Arkansas
Eagle
Allegash
Qinch
Greys
Cahaba
VA
NC
MT
WA
IN
AZ
OR
WI
CA
IL
ID
RI
NC
ND
NC
CT
NC
WY
CO
FL
MO
GA
MD
CO
NJ
PA
AZ
VT
AL
NY
MS
MO
NY
CO
CO
ME
TN
WY
AL
1951-82
1951-82
1946-77
1960-78
1949-78
1966-78
1942-83
1905-83
1911-78
1921-83
1928-84
1940-82
1922-84
1951-81
1927-82
1931-84
1940-78
1957-84
1939-80
1931-84
1922-84
1902-84
1939-83
1946-56
1904-83
1912-84
1925-80
1915-84
1940-51
1915-73
1936-80
1923-78
1915-78
1901-81
1947-80
1932-83
1919-78
1937-83
1902-78
4.48
1.77
1.32
1.77
1.33
1.24
2.03
2.51
1.30
1.99
1.65
1.16
1.74
2.10
1.48
1.02
0.80
1.54
0.86
1.54
2.16
1.37
1.42
1.56
1.64
1.17
2.05
1.43
1.33
1.41
1.42
2.41
1.91
1.12
1.36
1.39
1.55
1.J6
2.07
0.2
1.4
1.7 .
2.8
2.4
4.8
5.8
5.0
7.0
8.9
12.0
10.0
13.0
15.4
12.0
14.9
33.9
42.9
39.9
48.0
45.0
33.0
42.9
60.0
46.9
55.8
63.0
75.9
57.9
82.0
82.7
89.9
85.7
89.9
120.0
134.0
127.7
124. R
122.8
0.4
1.6
2.4
3.4
3.0
5.3
6.9
6.1
7.2
9.4
13.0
13.2
15.0
17.6
13.5
34.0
36.2
45.8
49.0
55.2
51.5
45.7
49.0
61.1
53.6
59.3
69.5
86.0
70.2
91.4
85.4
92.7
92.5
114.0
126.0
138.4
132.2
135. a
149.8
2.00
1.14
1.41
1.
1,
1.
1.
,21
.25
,10
,19
1.22
1.03
06
08
32
1.15
1.14
1.13
2.28
1.07
1.07
1.26
1.15
14
38
1.17
02
14
06
10
13
21
1.11
1,
1.
1.
.03
.03
.03
1.27
1.05
1.03
1.04
1.09
1.22
3-9
-------
Table 3-1 (Continued)
Station ID River name
Period of
State record CV*
Design flows (ft3/sec)
1-day 3-year 4-day 3-year
rw*
^v*%»
CMC
05515500
02490500
01315500
01610000
05386000
02369000
07378500
06465500
02135000
08110200
02076000
03455000
05333500
06287000
03107500
13341000
07341500
02350500
01100000
14233400
Kankakee
Bouge Chitto
Hudson
Potomac
Root
Shoal
Amite
Niobrara
Little Pee Dee
Brazos
Dan
French Broad
St. Croix
Bighorn
Beaver
N F Clearwater
Red
Flint
Merriinack
Gowlitz
IN
MS
NY
W
MN
PL
LA
NE
SC
TX
VA
TN
WI
WT
PA
ID
AR
GA
MA
VA
1926-78
1945-81
1908-78
1939-83
1938-61
1939-82
1939-83
1939-83
1942-78
1966-78
1924-52
1901-78
1914-81
1935-79
1957-83
1927-68
1928-81
1930-58
1924-83
1968-78
0.48
1.89
1.10
1.48
1.65
0.95
1.98
0.59
0.94
1.48
1.25
0.93
0.61
0.82
1.10
1.16
1.41
1.00
1.01
0.93
167.6
187.5
170.0
202.2
239.3
270.5
282.1
199.7
298.7
277.7
321.6
494.3
477.5
364.0
539.9
469.6
537.4
262.5
284.0
934.7
174.2
189.6
191.9
219.6
239.7
286.0
295.5
304.3
298.9
305.3
380.4
535.5
508.5
520.2
557.5
613.0
603.3
731.0
797.3
959.9
1.04
1.01
1.13
1.09
1.00
1.06
1.05
1.52
1.00
1.10
1.18
1.08
1.06
1.43
1.07
1.31
1.12
2.78
2.81
1.03
*CV = Coefficient of Variation
3-10
-------
For further clarification of the biologically-based method, refer to
Appendix E, Questions and Answers.
3-11
-------
SECTION 4. COMPARISON OF THE TWO METHODS
4.1 Design Flews
Table 4-1 shews hew the biologically-based 1-day 3-year low flows
and the hydrologically-based 1Q10 low flows for the sixty example rivers.
The table also presents the difference between 4-day 3-year low flows and
the 7Q10 low flows.
For 39 of the 60 streams, the 1-day 3-year low flows are
less than the 1010 low flows. For 18 streams, the 1-day 3-year low
flows are greater than the 1Q10 low flows, and for the remaining
3 streams the differences are less than 0.1%. Thus, for the majority of:
the streams the 1-day 3-year low flow is lower than the 1Q10 low flow.
For all sixty streams, the difference between 1-day 3-year low flows
and 1Q10 low flows ((1-day 3-year)-(lQ10))/(l-day 3-year) ranges from
-50.0% to 20.8%, with the mean and median equal to -4.9% and -3.1%,
respectively.
4-1
-------
Table 4-1. Ccnparison of 1Q10 and 7Q10 with 1-day 3-yr and 4-day 3-yr low flows
{all flows in ft3/sec.)
River Name State
Bull Run VA
Trent NC
Birch Cr MT
Beaver Cr WA
Iroquois IN
N Fk Wiite AZ
E Fk Illinois OR
Blade WI
Buckeye CA
La Moine IL
Boundary Cr ID
Branch RI
Linvillle NC
Sheyenne ND
Fishing Cr .NC
Quinnipiac CT
Drowning Cr NC
Shoshone WY
Uncortpahgre CO
Peace FL
Big MO
Middke Oconee GA
N Br Potomac MD
Aniroas CO
Raritan NJ
Brandywine PA
Salt AZ
White VT
L Tallapoosa AL
E B Delaware NY
Big Sunflower MS
Meramec MO
Chemung NY
Arkansas CO
Eagle CO
Allegash ME
Clinch TN
Greys WY
Cahaba AL
Conparison of CMC Design Flows
1Q10
0.3
1.4
1.7
2.4
3.4
4.8
6.4
5.5
7.1
9.3
11.7
8.8
13.4
15.9
17.0
17.5
38.8
41.8
35.6
49.0
46.4
49.4
54.7
54.8
54.2
61.4
64.6
75.3
72.7
80.8
89.4
88.8
89.7
99.9
116.9
124.5
128.7
122.9
151.9
1-day
0.2
1.4
1.7
2.8
2.4
4.8
5.8
5.0
7.0
8.9
12.0
10.0
13.0
15.4
12.0
14.9
33.9
42.9
39.9
48.0
45.0
33.0
42.9
60.0
46.9
55.8
63.0
75.9
57.9
82.0
82.7
89.9
85.7
89.9
120.0
134.0
127.7
124.8
122.8
3-yr %DIFF*
-50.0
0.0
0.0
14.3
-41.7
0.0
-10.3
-10.0
-1.4
-4.5
2.5
12.0
-3.1
-3.2
-41.7
-17.4
-14.4
2.6
10.8
-2.1
-3.1
-49.7
-27.5
8.7
-15.6
-10.0
-2.5
0.8
-25.6
1.5
-8.1
1.2
-4.7
-11.1
2.6
7.1
-0.8
1.5
-23.7
Conparison
of CCC
Dssign Flow0
7Q10 4-day 3-yr %DIFF**
0.4
1.6
2.4
3.2
3.9
5.3
6.7
6.7
7.7
9.9
13.1
13.3
16.4
18.3
19.4
32.3
43.4
46.8
50.8
55.3
55.3
57.4
61.6
62.3
67.1
67.2
68.7
85.2
88.3
89.7
91.9
92.2
97.5
120.1
131.0
134.1
135.2
144.5
156.4
0.4
1.6
2.4
3.4
3.0
5.3
6.9
6.1
7.2
9.4
13.0
13.2
15.0
17.6
13.5
34.0
36.2
45.8
49.0
55.2
51.5
45.7
49.0
61.1
53.6
59.3
69.5
86.0
70.2
91.4
85.4
92.7
92.5
114.0
126.0
138.4
132.2
135.8
149.8
0.0
0.0
0.0
5.9
-30.0
0.0
2.9
-9.8
-6.9
-5.3
-0.8
-0.8
-9.3
-4.0
-43.7
5.0
-19.9
-2.2
-3.7
-0.2
-7
-25
-25. /
-2.6
-25.2
-13.3
1.2
0.9
-25.8
1.9
-7.6
0.5
-5.4
-9.3
-4.0
3.1
-2.3
-6.4
-4.4
* %Difference = ((1-day 3-year flow) - (1Q10)) * 100 / (1-day 3-year flow)
**%Difference = ((4-day 3-year flow) - (7Q10)) * 100 / (4-day 3-year flow)
4-2
-------
Table 4-1. (Continued)
River Name State
Comparison of CMC Design Flows
1010 1-day 3-yr %DIFF*
Conparison of CCC Design Flows
7Q10 4-day 3-yr %DIFF**
Kankakee
Bouge Chitto
Hudson
Potomac
Root
Shoal
Mite
Niobrara
Little Fee Dee
Brazos
Dan
French Broad
St. Croix
Bighorn
Beaver
N F Qearwater
Red
Flint
Merrimack
Cowlitz
IN
MS
NY
W
MN
FL
IA
NE
SC
•DC
VA
TN
WI
WT
PA
ID
AR
G&
MA
VA
179.0
188.6
207.7
209.6
229.7
280.1
298.1
160.9
306.7
311.6
329.6
473.6
505.9
327.1
571.3
529.2
691.0
207.8
270.2
901.5
167.6
187.5
170.0
202.2
239.3
270.5
282.1
199.7
298.7
277.7
321.6
494.3
477.5
364.0
539.9
469.6
537.4
262.5
284.0
934.7
-6.8
-0.6
-22.2
-3.7
4.0
-3.5
-5.7
19.4
-2.7
-12.2
-2.5
4.2
-5.9
10.1
-5.8
-12.7
-28.6
20.8
3.6
4.9
184.3
191.6
211.0
220.7
245.6
291.4
303.4
322.0
322.4
344.9
387.3
532.2
536.0
557.0
594.2
648.6
769.2
799.8
929.3
968.7
174.2
189.6
191.9
219.6
239.7
286.0
295.5
304.3
298.9
305.3
380.4
535.5
508.5
520.2
557.5
613.0
603.3
731.0
797.3
959.9
-5.8
-1.1
-10.0
-0.5
-2.5
-1.9
-2.7
-5.8
-7.9
-13.0
-1.8
0.6
-5.4
-7.1
-6.6
-5.8
-27.5
-9.4
-16.6
-0.9
* %Difference = ((1-day 3-year flow) - (1010)) * 100 / (1-day 3-year flow)
**%Difference = ((4-day 3-year flow) - (7Q10)) * 100 / (4-day 3-year flow)
Similar conparisons can be made between the 4-day 3-year low flows
and the 7010 low flows based on Table 4-1. For 46 of the 60 streams,
the 4-day 3-year low flows are less than the 7Q10 low flows. For nine
streams, 4-day 3-year low flows are greater than the 7Q10 low flows,
and for the remaining four streams, the differences are less than 0.1%.
Thus, the 4-day 3-year low flow is usually lower than the 7Q10 low flow.
For all sixty streams, the difference between the 4-day 3-year low flows
and 7Q10 low flows ((4-day 3-year) - (7Q10))/(4-day 3-year) ranges from
-44% to 6%, with the mean and median equal to - 7.0% and - 4.4%, respectively.
4-3
-------
4.2 Excursions
Table 4-2 presents the calculated number of excursions that occurred
in the 60 streams for the low flows calculated using the hydrologically-
and biologically-based methods. The table demonstrates the impact of
the choice of one design flow method over the other in terms of number
of excursions. For any stream, a higher flow will always result in the
same or a greater number of excursions than a lower flow. Occasionally,
the difference in the number of excursions of the two design flows
is quite dramatic even if the difference between the two design flows is
quite small. For example, the 1Q10 and the 1-day 3-year design flow of
the Quinnipiac River in Connecticut are 17.5 ft3/sec and 14.9 ft3/sec,
respectively, but the corresponding number of excursions were 39 and 13.
Similar observations could be made for many other streams in Table 4-2.
A small difference in design flow may not have a significant impact in
wasteload allocations for these streams but may result in a larger number
of excursions than desired during the period of flow record.
4.3 Ccniparison_of_the Two Methods
The comparisons of the design flows show that the magnitudes of the
1-day 3-year and 1Q10 low flows, and the 4-day 3-year and 7Q10 low flows
are, on an average basis, similar in magnitude. Although these flows are
similar on the average, there may be large differences in the values of
these flows for individual streams. More importantly, there can be a
significant difference in the number of excursions that result, even if the
magnitudes of the flows calculated by the two methods are nearly equal.
4-4
-------
Table 4-2. Conparison of number of excursions of 1010 and 7Q10 with
number of excursions of 1-day 3-yr and 4-day 3-yr design flows.
River Name
Jull Run
Crent
3irch Cr
Jeaver Cr
Croguois
* Fk White
S Fk Illinois
Jlack
Juckeye
:* Moine
Joundary Cr
Jranch
-inville
Sheyenne
pishing Cr
Juinnipiac
Drowning Cr
»hoshone
Jnccnpahgre
5eace
Jig
liddle Oconee
fl Br Potomac
\nimas
feritan
Jrandywine
Salt
flute
., Tallapoosa
2 B Delaware
Jig Sunflower
leramec
Ihemung
State
TO
NC
MT
WA
IN
AZ
OR
m
CA
IL
ID
RI
NC
ND
NC
CT
NC
WY
CO
FL
MO
GA
MD
CO
NJ
PA
AZ
VT
AL
NY
MS
MO
NY
Conparison of CMC Design
1010
0.3
1.4
1.7
2.4
3.4
4.8
6.4
5.5
7.1
9.3
11.7
8.8
13.4
15.9
17.0
17.5
38.8
41.8
35.6
49.0
46.4
49.4
54.7
54.8
54.2
61.4
64.6
75.3
72.7
80.8
89.4
88.8
89.7
IBxcur
19
9
8
1
18
2
13
27
13
33
15
10
21
11
17
39
26
3
7
17
23
25
29
0
25
30
21
20
6
17
31
17
26
1-day 3-yr
0.2
1.4
1.7
2.8
2.4
4.8
5.8
5.0
7.0
8.9
12.0
10.0
13.0
15.4
12.0
14.9
33.9
42.9
39.9
48.0
45.0
33.0
42.9
60.0
46.9
55.8
63.0
75.9
57.9
82.0
82.7
89.9
85.7
Flows
fExcur
10
9
8
6
9
2
12
21
7
20
15
13
15
6
15
13
12
6
13
16
15
11
14
_. 2
13
14
18
20
3
20
8
18
18
Comparison of CCC Design Flo-
7Q10
0.4
1.6
2.4
3.2
3.9
5.3
6.7
6.7
7.7
9.9
13.1
13.3
16.4
18.3
19.4
32.3
43.4
46.8
50.8
55.3
55.3
57.4
61.6
62.3
67.1
67.2
68.7
85.2
88.3
89.7
91.9
92.2
97.5
lExcur
8.50
9.25
9.25
4.00
16.75
4.00
11.25
26.00
10.00
24.50
15.75
18.25
25.00
14.50
29.25
11.25
27.75
9.25
17.50
17.25
27.75
23.25
28.00
6.75
24.25
33.00
17.25
20.75
7.00
19.00
30.25
16.50
25.00
4-day 3-yr
0.4
1.6
2.4
3.4
3.0
5.3
6.9
6.1
7.2
9.4
13.0
13.2
15.0
17.6
13.5
34.0
36.2
45.8
49.0
55.2
51.5
45.7
49.0
61.1
53.6
59.3
69.5
86.0
70.2
91.4
85.4
92.7
92.5
#Excu
8.5C
9. ">.'.
9.25
6.0C
9.7!
4.0'
11. 5(
24. 5f
8.5'
20.51
15. 7'
14.0'
16.71
10.51
17.2'
13.0'
12.7
6.2
13.7
16.0
18.2
14.2
14.7
2. 5
13.2
i>3. n
Itf.Q
21. S
3.7
20. S
13.7
17.0
20.5
4-5
-------
Table 4-2. (Continued)
River Name State
Comparison c
1010 #Excur
}f CMC Design Flows
1-day 3-yr tExcur
Conparison ol
7Q10 lExcur
E CCC Design Flow
4-day 3-yr #Excu
Arkansas
Eaale
Allegash
Clinch
Greys
Cahaba
Kankakee
Bouge Chitto
Hudson
Potomac
Root
Shoal
Amite
Niobrara
Little Pee Dee
Brazos
Dan
French Broad
St. Croix
Bighorn
Beaver
N F Clearwater
Red
Flint
Merrimack
Cowlitz
CO
CO
ME
IN
VK
AL
IN
MS
NY
W
MN
PL
IA
NE
SC
IX
W.
TN
WT
MT
PA
ID
AR
GA
MA
W^
107.9
116.9
124.5
128.7
122.9
151.9
179.0
188.6
207.7
209.6
229.7
280.1
298.1
160.9
306.7
311.6
329.6
473.6
505.9
327.1
571.3
529.2
691.0
207.8
270.2
901.5
23
9
15
23
10
33
34
13
30
19
7
20
19
4
15
11
11
13
34
12
15
20
28
7
13
0
115.8
120.0
134.0
127.7
124.8
122.8
167.6
187.5
170.0
202.2
239.3
270.5
282.1
199.7
298.7
277.7
321.6
494.3
477.5
364.0
539.9
469.6
537.4
262.5
284.0
934.7
26
11
17
17
10
10
14
10
28
14
7
12
14
8
12
4
9
18
22
14
4
13
17
9
18
2
126.1
131.0
134.1
135.2
144.5
156.4
184.3
191.6
211.0
220.7
245.6
291.4
303.4
322.0
322.4
344.9
387.3
532.2
536.0
557.0
594.2
648.6
769.2
799.8
929.3
963.7
28.00
17.50
13.00
25.00
18.75
24.75
29.50
19.25
27.75
15.00
10.75
19.25
14.00
11.25
15.00
6.75
10.25
16.00
34.50
16.50
13.25
14.75
28.75
20.25
41.75
4.50
123.8
126.0
138.4
132.2
135.8
149.8
174.2
189.6
191.9
219.6
239.7
286.0
295.5
304.3
298.9
305.3
380.4
535.5
50R.5
520.2
557.5
613.0
603.3
731.0
797.3
959.9
26.0
11.0
17. ^
18. S
10. E
is.r
14. r
11. (
24.5
14. r
7.f
17.:
14.i
8.
11.
4.
21.
14.
7.
13.
17.
8.
19
3.
4-6
-------
Die hydrologically-based design flows may actually provide a greater
degree of protection of water quality in cases where the value of the
design flows are less than that of the corresponding biologically-based
design flows. Hydrologically-based design flows have been used successfully
in the past in many water quality-based permits. In addition, on an average
basis, the values of hydrologically-based design flows are not greatly
different from the corresponding values of biologically-based design flows.
The biologically-based design flows are not always smaller than the
corresponding hydrologically-based design flows for a given stream. Thus,
it cannot be stated that choosing one method over the other will always
result in the most protective wasteload allocation (and therefore the
fewest nunnber of excursions over the period of record). However, the
biologically-based method will always provide insurance that the design
flow calculated will have resulted in no more than the required number of
excursions.
Based upon the above, both the hydrologically-based and the bio-
logically-based methods for calculating stream design flows are recommended
for use in steady-state modeling.
4-7
-------
SECTION 5. RECOMMENDATIONS
1. If steady-state modeling is used/ the hydrologically-based or the
biologically-based stream design flow method should be used. If the
hydrologically-based method is used, the 1Q10 and 7Q10 low flows should
be used as the CMC and CCC design flows, except that the 30010 low flow
should be used as the CCC design flow for ammonia in situations involving
POTW's designed to remove ammonia where limited variability of effluent
pollutant concentrations and resulting concentrations in the receiving
water can be demonstrated.
2. Other technically defensible methods may also be used.
5-1
-------
SECTION 6. REFERENCES
1. U.S. EPA. 1985. Technical support document for water-quality based
toxics control. Office of Water, Washington, DC. September, 1985.
2. U.S. EPA. Water Quality Criteria. 50 PR 30784 July 29, 1985
3. Stephan, C.E., D.I. Mount, D.J, Hansen, J.H. Gentile, G.A. Chapman and
W.A. Brungs. 1985. Guidelines for deriving numerical national water
quality criterial for the protection of aquatic organisms and their uses.
PB85-227049. National Technical Information Service, Springfield, VA.
4. U.S. EPA. 1984. Water Quality Standards Handbook. Office of Water
Regulations and Standards, Washington, DC.
5. U.S. EPA. 1985. Ambient water quality criteria for ammonia - 1984.
EPA 440/5-85-001. National Tecnical Information Service, Springfield, Vb.
6. U.S. EP^. 1985. STORE! User Handbook, Part FL, Flow Data File.
6-1
-------
APPENDIX A. Calculation of Hydroloqically-based Design Flows
Design flews can be calculated as annual x-day average low flows
whose return period is y years, i.e., the xQy low flow. These flows can
be estimated from a historical flow record of n years using two different
methods. The first is a distribution-free method which makes no assumption
about the true probability distribution of annual low flows. The expression
for xQy is
xQy = (1-e) X(ml) + eX(m2)
where X(m) = the m-th lowest annual low flow of record
ml = [(n+D/Yl
m2 = [(n+D/yl + 1
[z] = the largest integer less than or equal to z
e =
This method is only appropriate when the desired return period is less
than n/5 years (1).
The second method fits the historical low flow data to a specific
probability density function and then computes from this function the
flow whose probability of not being exceeded is 1/y. The log Pearson
Type III distribution is a convenient function to use because it can
accommodate a large variety of distributional shapes and has seen wide-
spread use in streamflcw frequency analysis. However, there is no physically
based rationale for choosing one distribution over another.
The xQy low flow based on the log Pearson Type III method is
= exp( u + K(g,y) s)
where u = mean of the logarithms (base e) of the historical annual
low flows,
s = standard deviation of the logarithms of the historical low flows,
g = skewness coefficient of the logarithms of the historical low
flows,
K a frequency factor for skewness g and return period y.
A- 1
-------
A sample listing of frequency factors is given in Table A-l. These factors can
also be approximated as
K = (2/g)[ (1 + (g z)/6 - g2/36)3 - 1]
for |g| <, 3 where z is the standard normal variate with cumulative probability
1/y (2). Tables of the normal variates are available in most elementary
statistics texts. An approximate value (3) can be found from
z » 4.91 [ (l/y)-14-(l-l/y)'14].
Tb illustrate the use of the two xQy low flow estimation methods, the data
in Table A-2 will be analyzed for the 705. The flow values in this table
represent the lowest 7-day average flow for each year of record. Also shown
are the rankings of these flows from lowest (rank 1) to highest (rank 45).
The mean, standard deviation, and skewness coefficient of the logarithms of
these annual low flows are shewn at the bottom of the table.
For the distribution-free approach, the value of (n+l)yfy is (45+D/5
or 9.2. Therefore, the 705 low flow lies between the 9-th and 10-th
Ah
lowest annual flow. The interpolation factor, e, is 9.2 - 9 - 0.2.
Thus we have
7Q5 = (1. - .20) X(9) + (.20) X(10)
• (.80(335) + (.20)(338)
= 335.6 cfs
A-2
-------
For the log Pearson Type III method, the frequency factor K will be estimated
from Table A-l. For skewness of 0.409 and a 5-year return period interpolation
results in K = -0.856. The 7Q5 low flow is
7Q5 =exp(6.01 + (-.856) (.24))
o 331.8 cfs
For purposes of comparison, K will be estimated using the formulae given above:
z - 4.91 [ (0.2) •14-(1-0.2)-14]
= -0.840
K = (2/.409)[(l + (.409)(-.840)/6 - (.409)/36)3 - 1]
= -.853
7Q5 - exp(6.01 + (-.853) (.24))
= 331.8 cfs
The difference in the three estimates of the 7Q5 low flow is less than 2 percent.
A- 3
-------
Table A-l. Frequency Factors (K) for the log Pearson Type III Distribution
Skewness
Coefficient
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
-1.8
-2.0
-2.2
-2.4
-2.6
-2.8
-3.0
Return Period
5
-0.636
-0.666
-0.696
-0.725
-0.752
-0.777
-0.799
-0.817
-0.832
-0.844
-0.852
-0.856
-0.857
-0.855
-0.850
-0.842
-0.830
-0.816
-0.800
-0.780
-0.758
-0.732
-0.705
-0.675
-0.643
-0.609
-0.574
-0.537
-0.499
-0.460
-0.420
, Years
10
-0.660
-0.702
-0.747
-0.795
-0.844
-0.895
-0.945
-0.994
-1.041
-1.086
-1.128
-1.166
-1.200
-1.231
-1.258
-1.282
-1.301
-1.317
-1.328
-1.336
-1.340
-1.340
-1.337
-1.329
-1.318
-1.302
-1.284
-1.262
-1.238
-1.210
-1.180
A- 4
-------
Table A-2. Annual 7-Day Low Flows (ft3/sec) for the Amite River Near
Denhara Brings, LA
Year
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
Flow
299
338
355
439
371
410
407
508
450
424
574
489
406
291
352
309
322
278
369
483
523
385
474
Rank
5
10
15
30
20
28
27
38
33
29
41
36
26
4
13
7
8
2
19
35
39
21
34
Year
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
Flow
396
275
392
348
385
335
306
280
354
388
357
499
448
650
356
364
648
619
567
445
349
595
Rank
25
1
24
11
22
9
6
3
14
23
17
37
32
45
16
18
44
43
40
31
12
42
n = 45
u = 6.0
s = 0.23
q = 0.385
A- 5
-------
REFERENCES
1. Linsley, R.K., et al., Hydrology for Engineers, 2nd Editionf McGraw-
Hill, New York, NY, 1977.
2. Loucks, D.P., et al., Water Resource Systems Planning and Analysis,
Prentice-Hall, Englewood Cliffs, NJ, 1981.
3. Joiner and Rosenblatt, JASA, 66:394, 1971.
A- 6
-------
APPENDIX B. An Example Use Of DFLCW For Ammonia Discharges Front POIWs
The purpose of this Appendix is to illustrate the use of the DFLCW
program to calculate biologically-based design flows for ammonia and
conpare them with the hydrologically-based design flows of 30Q10 for
the 13 streams with the lowest coefficients of variation shown
in Table 2-1.
B.I Introduction
As stated in the two-nunber WQC for anmonia (1), a CCC averaging
period of as long as 30 days may be used in situations involving POTWs
designed to remove ammonia where low variability of effluent pollutant
concentration and resultant concentrations in receiving waters can be
demonstrated. In cases where low variability can be demonstrated, longer
averaging periods for the anmonia CCC (e.g., a 30-day averaging period)
would be acceptable because the magnitudes and durations of excursions
above the CCC would be sufficiently limited (1).
B.2 Hydrologically-based Design Flow
The 30Q10 low flows of the 13 streams with the lowest coefficients
of variation (CV) are presented in Table B-l.
B - 1
-------
Table B-l. Design flows and resulting number of excursions using a 30-day averaging
period (all flows in ft3/sec).
Iti-vsr Name State
Quinnipiac CT
Drowning Cr NC
Unccnpahgre CO
Greys W
Kankakee IN
Hudson NY
Shoal PL
Little Pee Dee SC
St. Croix WI
Niobrara NE
French Broad IN
Bighorn WT
Flint GA
Coeff
of
Variation
1.02
0.80
0.86
1.16
0.48
1.10
0.95
0.94
0.61
0.59
0.93
0.82
1.00
30Q10
Flow ^Excursions
42.3 7.8
54.7 8.5
71.0 6.9
160.7 5.7
201.8 10.0
288.0 13.4
323.5 10.2
366.3 7.4
571.8 16.2
613.2 6.4
636.2 11.9
913.6 8.1
1000.0 6.4
30-day 3-year
Flow # Excursions
46.5 15.0
65.5 15.0
77.3 14.6
166.9 9.9
213.6 16.7
340.7 24.3
339.0 12.1
450.0 11.8
598.6 21.9
673.6 8.1
715.7 20.3
1103. n 14.3
1097.0 9.6
**0i^
9.0
16.5
8.2
3.7
5.5
15.5
4.6
18.6
4.5
9.0
11.1
17.2
8.8
*%Difference = ((30-day 3-year flow) - (30Q10)) * 100 / (30-day 3-year flow)
B.3 Biologically-based Design Flow
The 30-day 3-year low flows for 13 streams are presents in Table B-l.
To obtain the biologically-based design flow for these streams, an averaging
period of 30 days instead of 4 days was entered into the DFLOW program (see
Table D-3, page D-6). Table B-l also includes toe number of excursions that
occurred in each of 13 flow records for the hydrologically and biologically-
based design flows.
B.4 Comparison of Design Flows
Table B-l shows that for all 13 streams the 30Q10 low flow is always
less than the 30-day 3-year low flow. The difference between the low flows
((30-^lay 3-year - 30O10)/ 30-day 3-year)) 3.7% to 18.6% with the mean
equal to 10.2%. Because the 30Q10 low flow is always lower, it results
in fewer excursions than the 30-day 3-year low flow.
B - 2
-------
B.5 Use of Biologically-Based Design Flows for Ammonia Discharges
from POTWs
As stated earlier, an averaging period of 4 days and a frequency of
occurrence of once every three years is used for the CCC. However, for
ammonia discharges from POIWs, a longer averaging period may be used in
certain cases. According to the national WQC for ammonia, an averaging
period as long as 30 days may be used in situations involving POIWs
designed to remove ammonia where low variability of effluent concentrations
and the resulting concentrations in the receiving waters can be demonstrated.
In cases where low variability can be demonstrated, longer averaging
periods for the amnonia CCC (e.g., a 30-tfay averaging period) would t«
acceptable because the magnitudes and durations of excursions above the
CCC would be sufficiently limited.
In Section 4.1, the hydrologically-based design flows have been
compared with the biologically-based design flows for the 4-day avsracjioj
period for all pollutants. Appendix B shows a comparison between the
biologically-based 30-day 3-year low flows and the hydrologically-based
30Q10 low flows Cor 13 streams for aimonia. For these 13 stream, the
30Q10 flow was always less than the 30-day 3-year flew, by an average of
10.2%. Thus, the use of the 30Q10 as the design flow is relatively more
protective for these streams.
REFERENCE
1. U.S. EPA. 1985d. Ambient water quality criteria for ammonia - 1934.
EPA 440/5-85-001. National Technical Information Service, Springfield,
VA.
B - 3
-------
APPENDIX C. Calculation of a Biologically-based Design Flows
The biologically-based design flow calculation method is an iterative
convergence procedure consisting of five parts. In Part I, z (the allowed
number of excursions) is calculated. In Part II, the set of X-day running
averages is calculated from the record of daily flows. Because the ambient
(instream) concentration of a pollutant can be considered to be inversely
proportional to stream flow, the appropriate "running averages" of stream
flow are actually "running harmonic means." (The harmonic mean of a set
of numbers is the reciprocal of the arithmetic mean of the reciprocals
of the numbers.) Thus, "X-day running averages" should be calculated
as X/z (1/F), not as (RF)/X» where F is the flow for an individual day.
Throughout this Appendix C, the term "running average" will mean "running
harmonic mean."
Part III describes the calculation of N (the total number of excursions
of a specified flow in the flow record). The calculations described in
Part III will be performed for a number of different flows that are
specified in Parts IV and V. In Part IV, initial lower and upper limits
on the design flow are calculated, the number of excursions at each
limit are calculated using Part III, and an initial trial flow is calculated
by interpolation between the lower and upper limits. In Part V, successive
iterations are performed using the method of false position (1) to calculate
the design flow as the hiqhest flow that results in no more than the
number of allowed excursions calculated in Part I.
Part I. Calculation of allowed number of excursions.
1-1. Calculate Z = D/[(Y)(365.25 days/year)]
C - 1
-------
where D = the nunber of days in the flow record;
Y = the average number of years specified in
the frequency; and
Z = the allowed nunber of excursions.
Part II. Calculation of X-day running averages, i.e./ x-day running
harmonic means.
II-l. Where X = the specified duration (in days) of the averaging period,
calculate the set of X-day running averages for the entire flow
record, i.e., calculate an X-day average starting with day 1,
day 2, day 3, etc. Each average will have X-l days in cannon
with the next average, and the nunber of X-day averages
calculated from the flow record will be (Dfl-X).
Part III. Determination of the nunber of excursions of a specified
flow in a set of running averages, i.e., running harmonic means.
III-l. Obtain a specified flow of interest from either Part IV or Part V.
II1-2. In the set of X-day running averages for the entire flow
record, record the date for which the first average is below the
specified flow and record the number of consecutive days that are
part of at least one or more of the X-day averages that are
below the specified flow. (Note that whether a day is counted
as an excursion day does not depend exclusively on whether
the X-day average for that day is below the specified flow of
interest. Instead, it depends entirely on whether that day
is part of any X-day average that is below the specified flow.
Table C-l provides examples of the counting of excursion days.)
C - 2
-------
Table C-l. ODuntlng excursion days for a specified flow of 100 ft3/sec using 4-day averages
o
Date
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Daily
flow
130
120
110
90
90
100
130
150
70
60
130
90
80
110
100
100
200
500
4-day
avg
flow
112.5
102.5
97.5
102.5
117.5
112.5
102.5
102.5
87.5
90.0
102.5
95.0
97.5
127.5
225.0
>100
>100
>100
Is the
4-day
average
below 100?
No
No
Yes
NO
No
No
No
No
Yes
Yes
No
Yes
Yes
No
No
No
No
NO
Is this date
part of any 4-day
average that is
below 100?
NO
No
Yes
Yes
Yes
Yes
NO
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
NO
No
Date of Number of Date of Number of Number of
start of days in start of excursion excursions
excursion excursion low flow days in low in low
period period period flow period flow period
3 4 3 12 3
9 8
The daily flows and four-day average flows for days 19 to 200 are all above 100
-------
Thus the starting date and the duration (in days) of the
first excursion period will be recorded. By definition, the
minimum duration is X days.
II1-3, Determine the starting dates of, and number of days in, each
succeeding excursion period in the flow record.
II1-4. Identify all of the excursion periods that begin within 120 days
after the beginning of the first excursion period. (Although
the first excursion period is often the only one in the 120-
day period, two or three sometimes occur within the 120 days.
Rarely do any excursion periods occur during days 121 to
240.) All of these excursion periods are considered to be in
the first low flow period. Add up the total number of excursion
days in the first low flow period and divide the sum by X to
obtain the number of excursions in the first low flow period.
If the nunber of excursions is calculated to be greater than
5.0, set it equal to 5.0
III-5. Identify the first excursion period that begins after the end
of the first low flow period, and start the beginning of the
second 120-day low flow period on the first day of this
excursion period. Determine the number of excursion days and
excursions in the second low flow period.
III-6. Determine the starting dates of, and the nunber of excursions in,
each succeeding 120-day low flow period.
II1-7. Sum the nunber of excursions in all the low-flow periods to
C - 4
-------
determine S = the total number of excursions of the specified
flow of interest.
Part IV. Calculation of initial limits of the design flow and initial
trial flow.
IV-1. Use L - 0 as the initial lower limit.
IV-2. Use U - the XQY low flow as the initial upper limit.
IV-3. Use NL.O as the number of excursions (see Part III) of the
initial lower limit.
IV-4. Calculate V\j = the nunber of excursions (See Part III) of the
initial upper limit.
(Z-Nr.HU-L)
IV-5. Calculate T = the initial trial flow as T = L + (Nu-NL)
Part V. Iterative convergence to the design flow.
V-l. Calculate Np = the nunber of excursions (see Part III) of the
trial flow.
V-2. If -0.005 £ ((Np-ZJ/Z) <_ +0.005, use T as the design flow and stop.
If NT >Z, set U = T and NU = NT.
If NT
-------
APPENDIX D. Description of the DFLCW Computer Program
DFLOW is a computer program that can perform a variety of calculations
related to design flow for any stream for which daily flow data are in
STORE!. The program is installed on the U.S. EPA's NCC-IBM conputer
and is run under the TSO operating environment. DFLOW consists of two
procedures: the first retrieves the daily flow record for the U.S.
Geological Survey (USGS) gaging station of interest from the U.S. EPA's
STORET system/ whereas the second allows selection of one or more calculations.
After logging on to TSO, the user invokes the program by entering
the command: exec 'mrfursr.dflow.clist1.
The following menu will appear:
ENTER THE NUMBER OF THE PROCEDURE YOU WISH TO EXECUTE:
1 RETRIEVE FLOW DATA FROM STORET
2 PERFORM CALCULATIONS USING RETRIEVED FLOW DATA
3 EXIT THE PROGRAM
If procedure 1 is selected, the user will be asked for the 8-digit USGS
station number for the flow gage of interest and a 2-digit state code
(see Table D-l). Gaging station numbers can be obtained from local USGS
offices or through a separate retrieval from the STORET system. After
this information is entered, a batch job is automatically submitted to
the IBM system to carry out the STORET retrieval. The user may log off
the system at this point because the retrieval might take several hours.
An example flow retrieval session is shown in Table D-2.
After a period of time, the user can invoke the DFLOW program again
and select procedure 2. If the flow data have not been successfully
retrieved, the message "FILE NOT AVAILABLE" will appear. If the retrieval
D-l
-------
is not successful within about six hours, a new retrieval can be attempted.
After a successful retrieval, procedure 2 will allow one or more of the
following to be calculated:
1. A biologically-based CMC design flow using a 1-day averaging period
and a frequency of allowed excursions of once every three years on
the average. After the CMC design flow has been calculated and the
excursion table printed for that flow, any flows can be entered
in order to obtain CMC excursion tables for those flows.
2. A biologically-based CCC design flow using a 4-day averaging period
and a frequency of allowed excursions of once every three years on
the average. After the CCC design flow has been calculated and the
excursion table printed for that flow, any flows can be entered in
order to obtain CCC excursion tables for those flows.
3. One or more user-defined design flows. If a biologically-based
design flow is selected, the user will be asked to input six variables
so that the desired design flow and excursion table can be printed.
If a hydrologically-based design flow is selected, the user will be
asked to input four variables so that the desired xCy low flow can
be calculated.
Table D-3 demonstrates the use of DFLOW for the Amite River in
Louisiana. Ihe allowed number of excursions and the CCC design flow are
calculated, and the excursion table is printed. DFLOW is then used to
calculate the 30-day 3-year biologically-based user-defined design flow.
Finally, procedure 2 is used to calculate the 7Q10 low flow for the Amite
River.
D- 2
-------
A copy of the FORTRAN source code for DFDOW can be obtained from
Lewis A. ftossnan, WERL, U.S. EPA. 26 West St. CLair Street, Cincinnati,
OH 45268 (-telephone 513-684-7603 or FTS - 684-7603).
Table 0-1. STORE! State Codes
01 Alabi
02 Alaska
04 Arizona
OS Arkansas
06 California
08 Colorado
09 Connecticut
10 Delaware
11 District of Columbia
12 Florida
13 Georgia
IS Hawaii
16 Idaho
17 Illinois
18 Indiana
19 Iowa
20 Kansas
21 Kentucky
22 Louisiana
23 Maine
24 Maryland
25 Massachusetts
26 Michigan
27 Minnesota
28 Mississippi
29 Missouri
30 Montana
31 Nebraska
32 Nevada
33 Hew Hampshire
34 New Jersey
35 Hew Mexico
36 Hew York
37 Horth Carolina
38 North Dakota
39 Ohio
40 Oklahoma
41 Oregon
42 Pennsylvania
44 Rhode Island
45 South Carolina
46 South Dakota
47 Tennessee
48 Texas
49 Utah
50 Vermont
51 Virginia
S3 Washington
54 West Virginia
SS Wisconsin
56 Wyoming
0-3
-------
Table D-2. Example Flow Data Retrieval Using DFLOW (User input is underlined)
exec 'mrfursr.dflow.clist'
ENTER THE NUMBER OF THE PROCEDURE YOU WISH TO EXECUTE:
1 RETRIEVE FLOW DATA FROM STORET
2 PERFORM CALCULATIONS USING RETRIEVED FLOW DATA
3 EXIT THE PROGRAM
ENTER 8-DIGIT USGS STATION NUMBER ---- 07378500
ENTER 2-DIGIT STORET STATE CODE ...... 22
SAVED
JOB ABC(JOB12345) SUBMITTED
AFTER JOB IS COMPLETED. FLOW DATA WILL RESIDE IN FILE DFLOW. DATA
D-4
-------
Table D-3. Use~of DFLOW for the Amite River.
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D - 5
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P-fe
-------
QUESTIONS AND ANSWERS CONCERNING THE BIOLOGICALLY-BASED METHOD*
Q. I 1: New aquatic life protection criteria specify that the acute criteria
(CMC) and the chronic criteria (CCC) may be exceeded no more than
once every three years on the average by 1-hour and 4-day averages,
respectively. They also state that extreme value analyses may not be
appropriate for estimating the ambient exposure condition. What is
an extreme value analysis?
A. This is a very broad question. There are many types of extreme value
analyses. But all extreme value analytical techniques have something
in ccnmon. Let's consider a time-series of daily flow data in order
to explain extreme value techniques.
A lew-flow water year starts on April 1 of each year and ends on
March 30 of the following year. If we perform an extreme value
analysis for a 4-day average condition, we should estimate 4-day
running averages for each water year, then determine which running
average is the lowest (extreme) for each water year. Finally, we
rank the extreme value of each year for frequency analyses.
Q. f 2: Would you explain how running averages are estimated?
A. Starting with April 1, our first running average will be the arithmetic
mean of flow data for April 1, 2, 3 and 4; the second running average
will be the arithmetic mean of April 2, 3, 4 and 5; and the third
running average will be the 3,4, etc. Thus, there will be 362 4-day
running averages for each water year of 365 days.
Q. # 3: By extreme value, do you mean lowest running average of the water year?
A. In low-flow analyses, the extreme value for a water year is the lowest
running average for that year.
0. # 4: So, do I have 30 extreme values from 30 years' flow record considering
one extreme value for each water year?
A. Exactly.
* The biologically-based design flow method has been supported by an overwhelming
majority of water quality coordinators at Regional and Headquarter levels.
But the method, being totally new, tends to raise a lot of questions which
we have heard over time from many reviewers. Some of these questions and
related answers are listed here for additional clarification to Appendices
C and D of the Guidance. If this paper becomes too long, in a way it defeats
its purpose. So we chose questions based on their importance. We encourage
our readers to be critical about our answers and raise other questions which
they may consider important. This will help us to improve both the method
itself and its presentation. In this context, readers may contact Hiranmay
Biswas (FTS-382-7012) or Nelson Thomas (ETS-780-5702)
E - 1
-------
Q. I 5: You said something about ranking the extreme values. How do you rank
them and why do you rank them?
A. For low flow analyses, ranking can be done from lowest to highest.
For a low-flow analysis of a 30-year flow record, we have 30 extreme
values. If we rank them from the lowest to the highest value, and no
two extreme values are equal, then we have one value for each of 30
ranks, and the return period of the first ranked flow is approximately
30 years, and that of the 10th ranked flow is approximately 3 years.
Q. f 6: The frequency analysis using the ranked extreme values seems to be
quite straight forward. Why are various kinds of distributions used
for frequency analyses?
A. If we are concerned with a prediction of low flow for a return period
that is equal or less than the flow record, then we will not have to
use any distribution at all. The distribution-free, or non-parametric
technique, is the best for frequency analyses. But, suppose you need
100-, 200- or 500-year flood and drought forecasts for the design of
a dam (for use power production and irrigation) and we do not have a
flow record of such a long period; then, we need to use some form of
distribution to extrapolate to 100, 200 or 500 years. There are many
well known distributions which can be chosen on a case-by-case basis.
Q. # 7: The new WQC also make some reference to the Log-Pearson Type III
distribution as an example of the extreme value analysis. While we
are on the subject of distribution, is it the only distribution that
is currently in use in the water quality analytical field?
A. The United States Geological Survey uses the Log-Pearson Type III
distribution in low-flow as well as flood-flow analyses. Tr;y -na^e thi-
choice after conducting a study of flood flow analyses using various
other techniques. The choice of techniques should be based on the
nature of the distribution of extreme values. But, for national
consistency of estimates, the USGS chose this technique.
0. # 3: Extreme value analytical techniques are often used in the hydrologic
field, and seem to be quite reasonable. "Is there any biological/
ecological reason why extreme value analyses are not appropriate
for estimating desLjn flow using the anibient duration anl Cos-n^v:/
of the new WQC?
A. Yes, a direct use of extreme value analyses is not appropriate
because biological effects are cumulative.
Q. # 9: Would you elaborate how the cumulative nature of biological effects
is related to extreme value analyses?
A. In extreme value analytical techniques, only the most extreme drought
exposure event is considered, but other, less severe within-year
exposure events are totally ignored, although their cumulative effects
could be severe. The severity of those smaller within-year exposure
E - 2
-------
events of extreme drought conditions that are ignored may outrank in
severity the extreme exposure events of other less-than-most severe
drought conditions. Since the biological effects are cumulative, we
rtust find a way to account for all within-year exposures in addition
to the most extreme exposure event of each year.
Q. I 10: Your answer is difficult to follow; would you give an example?
A. Hydrologists know that we had, in various parts of the USA, extreme
drought events during the water years 1925-1932, 1955-1956, and during
a few years in the late seventies. In other years, drought was not
as severe. Suppose that in water year 1925, there were 4 very low 4-day
running averages of which only one was accepted as the extreme value
of that year; the 2nd, 3rd, and the 4th values were ignored. Similarly,
one extreme value was estimated for each of the other Water years.
But, sane of the extreme values of other water years are less severe
than 2nd, 3rd or the 4th running averages of the year 1925. Thus, by
ignoring these 3 running averages of the water year 1925, the extreme
value method has ignored potential severe effects that may result
frcra those exposure events. In addition, the inclusion of other
extreme values that are less severe than the 2nd, 3rd and the 4th
running averages of the year 1925, and exclusion of more severe
excursion events (2nd, 3rd and 4th excursions of water-year 1925)
result in a skewed estimate of low flow.
Q. I 11: The method described to implement the two-number aquatic life criteria
is called a biologically-based method. What is biological about it?
A. Almost every parameter that is used in this method is derived on tv?
basis of either biological, toxicological or ecological considerations,
whereas the parameters used in the extreme value analyses are unrelaco.1
to biological, toxicological or ecological considerations.
Q. # 12: Would you name the things that you think are biological, toxicological
or ecolgoical in nature?
- durations of acceptable exposure conditions: 1 hour for OK and 4
days for CCC are biologically derived.
- 3 years on tlw average is the allowed ecological recovery period
after a single excursion (see Table D - 2 of Appendix D of the
Technical Support Document for Water Quality-based Toxics Control
(TSD)).
- 15 years is selected for ecological recovery after a total of 5 or
more excursions within a low flow period (see reference Table
D-2 in Appendix D of TSD).
Q. #13: I see neither 15 years nor 5 exposure events in the referenced
Table D-2. Could you explain the discrepency?
E - 3
-------
It is true that neither 15 years nor 5 excursions are found in the
reference Table. But what is available is that rivers and streams
are fully recovered between 5 to 10 years after a severe exposure
event. Aquatic biologists consider that repeated within-year
exposures can result in catastrophic effects. In their judgement/
10 years' exposure interval is inadequate because under that situation
the ecology of the receiving system will be under constant stress
and recovery. By the same token, a 20-year interval was considered
to be unnecessarily stringent for attaining healthy biota. After
these considerations and debates among biologists and wasteload
allocation coordinators, we decided to use 15 years as an acceptable
interval after a severe exposure event consisting of several within-year
exposures.
Q. f 14: Have you anything to say about how you decided to allow 5 excursions
in an interval of 15 years?
A. WQC allow an excursion once every three years on the average.
Since the effects of excursions are cumulative, ecological recovery
from a severe exposure event recr-iires about 15 years and the
recovery period fron a single exposure event, according to the
national WQC, is 3 years. Therefore, 15/3 or 5 excursions are
accepted as the upper limit of within-year excursion counts.
0. f 15: Why did you not choose a 12-year interval for 4 within-year exposure
events? Or could you not choose an 18-year interval for 6 within-yeai:
exposure events (based on the info available in Table D-2 of TSD)?
A. One could make various other choices based on site-specific knowled.jp
but we made our choice for average conditions.
Q. I 16: If 12- or 18-year intervals are chosen for 4 or 6 within-year exposure
conditions, would the design flow be different from that of die 15-year
interval choice? Do we have any idea about how different the CCC
or CMC flew will be for the choices of 12- or 18-year interval?
A. No, we did not perform such analyses or comparisons but our guess is
that the difference will not be substantial.
Q. # 17: It is understood that, if a 15-year interval is chosen for ecological
recovery, then 5 within-year exposures inay be allowed because UQC
specify 1 exposure on the average of every 3 years. But some extreme
drought related low flow periods might include less than 5 within-year
exposures, and some more severe low flow periods include more
than 5 within-year exposures. If exposure effects are cunulative,
why not include all exposures within a year; why limit it to 5?
A. The biological method accounts for all within-year excursions when
the number of excursions during a low-flow period is 5 or less.
So, 5 is the upper limit, and the lower limit is 1.
E - 4
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Q. t 18: What if the within-year excursions for a given flow based on the
biological method is naturally greater than 5 during say, a 50-
or 100-year drought? In those years, flow may remain low for a
long time, such as for 40-50 days, not necessarily for just 20
days for 5 excursions. After all, we cannot change nature, can we?
A. No, we cannot change nature. But we can modify our approach to suit
our objective after understanding the consequences of severe events.
We made a number of analyses to find out what happens if we account for
all, not just 5, excursions that one may expect from those most severe
drought years. We found that inclusion of all excursions from thos-?
years results in the following:
- Design flows of all return periods of say, 3, 5, 10, 20, 50 years,
etc. are completely dominated by those most severe drought years; and
- this leads to extremely stringent design flows.
Q. # 19: There is nothing biological in these analyses. Since the exposure
effects are cumulative, should we not count all exposures regardless
of how rarely one may expect them, or how stringent the resulting
design flow is?
A. This is where a little understanding of ecological recovery and
familiarity with the North American aquatic life are necessary to
make a reasonable choice. The upper bounds of the life cycles and
life spans of most North American aquatic species are 2 and 10 years,
respectively. An exposure event of 20- or 50-year interval may
not be meaningful, particularly when one considers other ways, for
exarple recruitment from the surrounding ecosystem, in which recovery
may take place. So, in our judgement, a recovery period of 15 years
is adequate for situations where the number of exposures in a low
flow period is 5 or more.
Q. # 20: What is described here in the biological method is similar to
is done by hydrologists for partial duration series. They address
the problem using traditional statistical approach. Why did you
not use a classical statistical method?
A. First, the statistical science of partial duration series, particularly
in the hydrologic field, is not well developed. Not many people
understand it. Although the biological method lacks statistical
elegance, it is sinple and can be used and understood by field
biologists and engineers, alike. We would not be surprised if a
statistician comes up with a better statistical answer for the
problem that we have in hand. But it would be important for the
regions to understand most aspects of the method if we expected
them to use it.
E - 5
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Q. # 21: Over the last 20-25 years, the majority of the states in the U.S. used
the 7Q10 low flow as the design flow for what we essentially had as
a not-to-be exceeded single number WQC value. It seems that it worked
fine, although a rationale for such a choice is hard to cone by. Why
is it so important now to have a rational biologically-based
method to implement the two-number WQC?
A. It is important to provide a rational method for three major
reasons. First, lack of a biologically-based method in the past
led to the adoption of design flows such as 3Q20, 7Q10, 30Q10,
30Q2, and even the annual average flow for identical water use. A
technically defensible method will bring about technical consistency
for any desired level of protection. Second, the introduction
of tlie two-nunber national WQC, whole effluent toxicity, and the
guidance on site-specific water quality standards have unalterably
changed the environment of toxics control. In these situations, a
biologically-based method is necessary that can be applied not
only to national tvo-numbered WQC, but also to other site- and
use-specific durations and frequencies of pollutants and whole
effluent toxicities. Third, since WQC and their field use have
beconie complex, it is very important that we develop a simple
method that is easily understandable to field biologists and
engineers, alike. In the past, very few understood the relation
between the WQC and the corresponding 7Q10 or other xQy design flow.
Q. # 22: Why is the biologically-based method considered to be more directly
based on the water quality criteria than the hydrologically-based
method?
A. In the biologically-based method, both the averaging period and the
frequency (for example, 4 days and 3 years) are taken directly from
the criterion, whereas? in the hydrologically-based approach, the
two numbers in XQY are not. Most of the other aspects of the
biologically-based approach are also based on biological, ecological,
and toxicological considerations. One.of the major technical
differences between the methods is that the 3 years in the biologic* Uv/
based method is an average frequency, whereas the 10 years in the
hydrologically-based approach is a return period.
Q. # 23: Does it make any difference whether biologists, ecologists, and
toxicologists understand how design flow is calculated?
A. Yes, for three major reasons. First, these are the people who
derive the aquatic life criteria. If the criteria are not used in
a manner that is consistent with their derivation, the intended
level of protection will probably not be achieved. Second, site-
specific frequencies and durations will not correctly affect design
flow if the duration and frequency are not directly used in the
calculation. Third, if they understand what parameters affect
design flow, biologists, ecologists, and toxicologisfcs can gather
data that might allow them to refine their estimates of such values
as one hour, four days, three years, and fifteen years.
E - 6
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Q. # 24: Let us discuss the simplicity of the biologically-based method.
I am not clear how an excursion is counted. Would you explain how
you count excursions and estimate design flows?
A. This is the key to understanding the biologically-based method.
Since the stream flow is inversely proportional to instream
concentration, any consecutive 4-day average of low-flow that is
lower than the design flow is counted as one excursion of the CCC.
The following is the step-by-step explanation of how excursions
are counted in estimating x-day y-year design flow:
1. An excursion period is defined as a sequence of consecutive days
where each day belongs to a x-day average flow that is below the
design flow. For example, if the three running averages of a
consecutive 6-day period are less than the 4-day 3-year design
flow, then those 6 days belong to an excursion period.
2. The number of excursions in an excursion period is the length of
the period divided by the criteria averaging period. For example,
if an excursion period is 6 days long, then the nunber of excursions
for the 4-day averaging period for CCC is 6/4 or 1.5.
3. The total number of excursions is limited to 5 within a low
flow period, usually a low flow period lasts 120 days or less.
In sane rare stream situations, more than one low flow period
within a water year is possible.
4. The allowed total number of excursions over the period of record
is the number of years of record divided by the frequency of
aquatic life criteria (3 years for the CCC of the new national
two-number criteria). For example, if we have a 30-year flow
record, then total nuniwc of excursions that are allowed for
x-day 3-year criteria is equal to 30/3 or 10.
5. The 4^3ay 3-year design flow for the 4-day 3-year CCC based on
a 30-year flow record of a given river is equal that flow which
results in no more than the allowable nunber of excursions.
*br example, the total allowable number of excursions for the
given record is 10. The design flow is the highest flow that
results in no more than 10 excursions calculated as defined in
steps 1 through 4 above.
Q. # 25: Let us take the example printout (from page D-5) for the Amite River
as presented below. Will you explain the procedure using this
example?
A. As shown in the following printout, we have a flow record from 1937
to 1983 which is approximately 42 years. Since we are allowed to
have no more than one excursion in every 3 years on the average,
we have 42/3 or about 14 excursions. In October 1952, we encountered
the first excursion for a continuous period of 6 days. Thus, we
calculate 6/4 or 1.5 excursions for that low flow event. The next
excursion period occurs, starting from October 10, 1956, for
30 consecutive days. Since the upper limit of excursions in a low
flow period (a low flow period is usually 120 days long) is 5, we
E - 7
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obtained a total of 5 e«cursions oaly, altiiough in reality
there were altogether 30/4 or 7.50 excursions in that low flow
period. Similarly/ we found only 5 excursions for total period of
30 days during the low flow period of 1963. In 1969, we had 2.5
excursions foe a low flow period that lasted for 10 days. (
26: It seems like the accuracy of the design flow estimates is totally
dependent on the length of the flow record. Do you agree with this
observation?
Absolutely. This is true about any analysis. More relevant data
are necessary to provide more accurate information.
0. # 27: What rninLnum length of flow record is recommended?
A. The longer the flow record, the more reliable the estimated design
conditions will be. Figure E-l shows how the spread in the 90% confidence
limits on the extreme value-based design load with 10-year return
period decreases with increasing period of record. (This figure w^s
derived on the basis of lognormal statistics, not log Pearson type 3).
Results ace shown for both low variability (CV=0.2) and high variability
(CV=Q.8) situations. Based on the behavior of these curves, it appears
that 20 to 30 years of record is a reasonable minimum requirement for
extreme value analysis at a 10-year return period.
The case for the biologically-based excursion criterion is less
definitive. However, since it considers all days within the period
of record as its sample (not just the worst condition of each year),
its sample size is much larger than that of an extreme value analysis.
Thus, it may be possible to use periods of record less than 20 years
with this criterion and still have a good level of confidence in
the results.
f. - 3
-------
60
? 20
*
- 40
ev . o.e
20
cv • 0.2
10
20 30
YEARS OF RECORD
40
SO
Figure E-l. Spread in 90% Confidence Limits on Estimating a Quantity
with a 10-year Return Period as a Function of the
Record Length (Derived frcm tables in Stedinger (1983))
0. # 28: What would you do for intermittent streenns where low f.l>ya is zero
during low flow periods? Also, how will you use the biologically-
based methoj in situations where flow data are not available?
A. These are problems that are generic to all flow estimating techniques.
For intermittent streams for which the low flow is zero, the design
flows for CMC as well as CCC are equal to zero. In situations
where flow data are not available, field hydrologists and engineers
sonetimes use flow data from hydrologically comparable drainage
basins.
0. ft 29: The table given in Question 23 looks simple. How much time does it
take to conduct a biologically-based analysis for any stream
of interest?
A. The analysis is perforated in two steps. First, daily flow data are
retrieved from the daily flow file in STORET, by submitting a batch job.
This will take A Fev -ninutes of time at the conputer. rl>«»/ec, th-3 job
run might take anywhere from a few minutes to several hours, depending
on how busy the conputer system is -it t'ae time of submittal. Once
the data has been retrieved, the analysis can be performed in five
or ten minutes.
0. ft 30: It seems that die foundation of the information about ecological
recovery periods for the two-number WQC is all that are listed
in Table D-2 of the TSD. But, anybody familiar with these references
will tell you that the recovery periods listed in that table are
related to recovery from catastrophic exposures caused by spills,
not by effluents of malfunctioned advanced treatment facilities.
Would you agree that this is not a satisfactory set of in Coronation
to make such an important decision?
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A. This is the best available information that we could use to estimate
ecological recovery. Considering the complexities involved in the
implementation of the two number WQC, and the site-specific WQC for
pollutants and whole effluent toxicity, we could not leave the
recovery question open to anyone's interpretation. Considering
the potential for misuse of the WQC in their implementation phase,
we had to use our best judgement and the best information available,
although we recognize that our best judgement would be debatable.
Since the information base is not as strong we want to have, in
keeping with the Agency policy and legal background, we had to go
in the direction of protection in the over-all decision making
process.
Q. f 31: What are you doing to improve the information base?
A. QRD is planning to undertake a major effort before the next update
of the WQC. But, this is an area in which success is dependent more
on cooperative efforts in which field biologists, ecologists,
toxicologists, engineers and hydologists share their experience
than doing mere literature reviews and/or gathering laboratory-
generated information.
REFERENCE
1. Stedinger, J.R., "Confidence Intervals for Design Events",
Jour. Hyd. Eng. Div., ASCE, Vol. 109, No. 1, January 1983.
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