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TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
Book VI: Design Conditions-
Chapter 1: Stream Design Flow for Steady-State Modeling
EPA DOCUMENT NUMBER: EPA440/4/86-014 DATE: 1986
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 manual describes two techniques to estimate the stream design flow at or
above which EPA's two-number aquatic life protection criteria must be met. The
two-number water quality criteria are: (1) a criteria maximum concentration
(CMC), and (2) a continuous criteria concentration (CCC). Generally, EPA's CMC
represents an acute pollutant concentration that should be exceeded no more
than once in an average of three years for a period of an hour. Similarly, the CCC
represents a chronic pollutant concentration that should be exceeded no more
than once in an average of three years for a continuous period of four days.
Historically, a majority of States in the USA have required that EPA's aquatic life
protection criteria must be met at all flows that are equal to or greater than a
critical flow condition of 7-day 10-year low flow (7Q10).
In a steady-state modeling framework, the critical flow conditions can be used to
estimate the maximum amount of any pollutant that can be discharged without
violating water quality criteria (WQC). The critical low flow that is used to define
the maximum amount of any pollutant that can be discharged without violating
ambient water quality standards (WQS) is called the stream design flow. The
design flow represents the required level of treatment or the size of the
wastewater treatment facility.
This manual recommends a biologically-based stream design flow estimating
technique that is strictly consistent with the duration and frequency criteria of
EPA's two-number WQC. The biologically-based stream design flows 1B3 and
4B3 are synonymous with the 1-hour, 3-year and 4-day, 3-year duration and
frequency criteria of CMC and CCC, respectively. The second estimating
technique included in this manual is for a hydrologically-based stream design
flow represented in the xQy format, such as 7Q10, 1Q10, 30Q10, etc.
This hydrologic flow estimation is consistent with the log Pearson Type III
frequency curve approach described in USGS Surface Water Branch Technical
Memorandum NO. 79.06, "PROGRAMS AND PLANS - Low-Flow Programs",
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available online at http://water.usgs.gov/admin/memo/SW/sw79.06.html. These
two estimating techniques are implemented using EPA's DFLOW computer
program, which is available online at http://www.epa.gov/waterscience/dflow/.
Version 3.1 of DFLOW includes a graphical user interface, and directly
incorporates the USGS implementation of the log Pearson Type III frequency
curve approach and EPA's biologically-based stream design flow technique. The
guidance manual includes a comparison of stream design flows of 60 randomly
selected US streams, calculated using both approaches.
KEYWORDS: Wasteload Allocations, Design Conditions, Design Flow, Steady-
State, Models, Water Quality Criteria, Acute, Chronic, Biological,
Hydrologic
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TECHNICAL GUIDANCE MANUAL
FOR
PERFORMING WASTELOAD ALLOCATION
Book VI
Design Conditions
Chapter 1
Stream Design Flow for Steady-State Modeling
September 1986
EPA Publication: 440/4-86-014
-------
Transmittal
OFFICE OF WATER
September 29, 1986
MEMORANDUM
Subject: Technical Guidance Manual for Performing Wasteload
Allocations Book VI, Design Conditions: Chapter 1 - Stream
Design Flow for Steady-State Modeling
From: William 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 (FTS) 382-7074.
Attachment
Addressees:
Regional Water Management Division Directors
Regional Environmental Services Division Directors
Regional Wasteload Allocation Coordinators
-------
ACKNOWLEDGEMENT
The contents of this section have been removed to comply with
current EPA practice.
-------
Table of Contents
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 2-1
2 .1 Introduction 2-1
2 .2 Rationale 2-2
2 . 3 Example Cases 2-2
Table 2-1. Hydrologically-based design flows (ft3/sec) for
60 streams 2-3
SECTION 3. BIOLOGICALLY-BASED DESIGN FLOW 3-1
3 .1 Introduction 3-1
3.1.1 Exceedances and Excursions 3-2
3.1.2 Features of Calculation 3-4
Figure 3-1: Illustration of biologically-based
design flow 3-5
3 . 2 Procedure 3-6
3 .3 Rationale 3-7
3 .4 Example Cases 3-8
Table 3-1. Biologically-based design flows (ft3/sec)
for 63 rivers 3-9
SECTION 4 . COMPARISON OF THE TWO METHODS 4-1
4.1 Design Flows 4-1
Table 4-1. Comparison of 1Q10 and 7Q10 with 1-day 3-yr and
4-day 3-yr low flows (all flows in ft3/sec) 4-2
4 . 2 Excursions 4-3
4.3 Comparison of the Two Methods 4-4
Table 4-2. Comparison of number of excursions of 1Q10 and
7Q10 with number of excursions of 1-day 3-yr and 4-day 3-yr
design flows 4-5
SECTION 5. RECOMMENDATIONS 5-1
SECTION 6 . REFERENCES 6-1
APPENDIX A. CALCULATION OF HYDROLOGICALLY-BASED DESIGN FLOWS ... A-l
-------
APPENDIX B. AN EXAMPLE USE OF DFLOW FOR AMMONIA DISCHARGES FROM
POTWs B-l
APPENDIX C. CALCULATION OF BIOLOGICALLY-BASED DESIGN FLOWS C-l
APPENDIX D. DFLOW 2.0 USER'S GUIDE (OMITTED)
APPENDIX E. QUESTIONS AND ANSWERS CONCERNING THE BIOLOGICALLY-BASED
METHOD E-l
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GLOSSARY
IBS - 1-hour 3-year duration and frequency criteria of Criterion Maximum
Concentration.
4B3 - 4-day 3-year duration and frequency criteria of Criterion
Continuous Concentration.
7Q10 - EPA's aquatic life protection criteria to meet all flows equal to
or greater than critical flow condition of 7-day 10-year low flow.
xQy - Hydrologically-based design flows expressed as x-day average low
flows whose return period is y years. For example, 1Q4 is the daily low
flow that is exceeded once every four years. Other xQy values commonly
encountered are 1Q10, 4Q3, 7Q5, and 7Q10.
xBy - Biological design flow parameter defined in DFLOW 3.
Averaging period - 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 concentrations of
pollutants in receiving waters in order that the averages can be
compared to the CMC and CCC to identify "exceedances" i.e., one-hour
average concentrations that exceed the CMC and four-day average
concentrations that exceed the CCC.
Biologically-based stream design flow - Design flow based on the
averaging periods and frequencies specified in water quality criteria
for individual pollutants and whole effluents.
Criteria - Descriptive factors taken into account by EPA in setting
standards for various pollutants. These factors are used to determine
limits on allowable concentration levels, and to limit the number of
violations per year. When issued by EPA, the criteria provide guidance
to the states on how to establish their standards.1
Criterion Continuous Concentration (CCC) - The CCC is the 4-day average
concentration of a pollutant in ambient water that should not be
exceeded more than once every three years on the average.
Criterion Maximum Concentration (CMC) - The one-hour average
concentration in ambient water should not exceed the CMC more than once
every three years on the average.
Design flow - A flow rate resulting from an applied waste load
allocation process, used to ensure ambient water quality compliance.
DFLOW - The DFLOW (Design FLOW) program was originally developed by EPA
to support design flow analysis as described in this manual. At the
time of original publication, Version 2.0 of DFLOW was available to
support this analysis on personal computers. The latest version of
DFLOW at the time of enhancement of this manual was Version 3.1, which
combines a graphical user interface with the USGS implementation of the
Log Pearson Type III calculation. Additional information may be
available at http://www.epa.gov/waterscience/dflow/.
Duration - The time during which something exists or lasts
EPA. "Terms of Environment: Glossary, Abbreviations, and Acronyms"
http://www.epa.gov/OCEPAterms/cterms.html March 8, 2006.
2
Merriam-Webster Online Dictionary, http://www.m-w.com/dictionary/duration Accessed April
14, 2006.
-------
Dynamic models - Preferred for the application of aquatic life criteria
in order to make best use of the specified concentrations, durations,
and frequencies. Use of aquatic life criteria for developing water
quality-based permit limits and for designing waste treatment
facilities requires the selection of an appropriate wasteload
allocation model.
Effluent - Wastewater--treated or untreated--that flows out of a
treatment plant, sewer, or industrial outfall. Generally refers to
wastes discharged into surface waters.3
Exceedance - Violation of the pollutant levels and average
concentration frequencies that are permitted by environmental
protection standards
Excursion - An unfavorable conditions, e.g. low flow or noncompliant
pollutant concentrations
Flow Averaging Period - Monitor of water flow for a specific number of
days, usually 30, to determine pollutant concentrations.
Frequency - The number of repetitions of a particular event in a unit
of time.
Gaging stations - The locations at which measurements are recorded,
generally hydraulic or hydrologic in nature, usually referring to
stream flow gages or rain gages.
Harmonic Mean - Set of numbers that is the reciprocal of the arithmetic
mean of the reciprocals of the numbers.
Hydrologic Flow - The characteristic behaviour and the total quantity
of water involved in a drainage basin, determined by measuring such
quantities as rainfall, surface and subsurface storage and flow, and
evapotranspiration.(Source: BJGEO)4
Hydrologically-based design flow - Design flow calculated solely from
the hydrologic record.
Log Pearson Type III - Statistical analysis, recommended by the US Water
Resources Council Bulletin #17B, used to gage natural flood data.4
Model - Either a steady-state or dynamic simulation that uses hydraulic
and biological criteria to design regulatory compliant waste loads.
Non-exceedance - Relating to steady-state models as flow rates that are
less than design flows.
Percentile - One of a set of points on a scale arrived at by dividing a
group into parts in order of magnitude.5
Pollutant - Generally, any substance introduced into the environment
that adversely affects the usefulness of a resource or the health of
humans, animals, or ecosystems.6
EPA. "Terms of Environment: Glossary, Abbreviations, and Acronyms"
http://www.epa.gov/OCEPAterms/. March 8,2006.
EPA. "Terminology Reference System: Hydrologic Flow"
http://iaspub.epa.gov/trs/trs proc qry.navigate term?p term id=26386&p term cd=TERMDIS
May 2, 2006.
Texas Department of Transportation. "Hydraulic Design Manual, Section 10. Statistical
Analysis of Stream Gauge Data".
http://manuals.dot.state.tx.us/dynaweb/colbridg/hyd/@Generic BookTextView/14106;cs=defau
lt;ts=default;pt=14873 March 2004.
The American Heritage® Dictionary of the English Language,4th Ed. "Percentile." Accessed
at www.Dictionary.com July 3, 2006.
-------
Receiving waters - Bodies of water into which effluents are discharged.
Return Period - Annual x-day average low flow repeated in y-years.
Site-specific criteria - Regulatory concentrations, parameters, or
frequencies that are exclusive to proximity or spatially exclusive.
Steady-state models - Models that assume a constant average flow rate.
Toxicity - The degree to which a substance or mixture of substances can
harm humans or animals. Acute toxicity involves harmful effects in an
organism through a single or short-term exposure. Chronic toxicity is
the ability of a substance or mixture of substances to cause harmful
effects over an extended period, usually upon repeated or continuous
exposure sometimes lasting for the entire life of the exposed organism.6
Two-number water quality criterion - Criterion Continuous and Criterion
Maximum Concentrations (CCC, CMC) that are used as the basis for the
both hydrologically- and biologically-based design flows
Variability - Reference to the consistency of pollutant concentrations
in effluent and ambient waters.
Wasteload allocation - 1.) The maximum load of pollutants each
discharger of waste is allowed to release into a particular waterway.
Discharge limits are usually required for each specific water quality
criterion being, or expected to be, violated. 2.) The portion of a
stream's total assimilative capacity assigned to an individual
discharge.7
Water quality criteria (WQC) - Levels of water quality expected to
render a body of water suitable for its designated use. Criteria are
based on specific levels of pollutants that would make the water
harmful if used for drinking, swimming, farming, fish production, or
industrial processes.
Water quality-based permit - A permit with an effluent limit more
stringent than one based on technology performance. Such limits may be
necessary to protect the designated use of receiving waters (e.g.
recreation, irrigation, industry or water supply).
EPA. "Terms of Environment: Glossary, Abbreviations, and Acronyms".
http://www.epa.gov/OCEPAterms/pterms.html March 8, 2006.
EPA. "Terms of Environment: Glossary, Abbreviations, and Acronyms"
http://www.epa.gov/OCEPAterms/tterms.html March 8, 2006.
EPA. "Terms of Environment: Glossary, Abbreviations, and Acronyms"
http://www.epa.gov/OCEPAterms/wterms.html March 8, 2006.
EPA. "Terms of Environment: Glossary, Abbreviations, and Acronyms"
http://www.epa.gov/OCEPAterms/wterms.html March 8, 2006.
-------
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
(WOC) 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 of pollutants on
aquatic organisms and their uses (3,4). To account for local
conditions, site-specific criteria may he 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 exceedances. 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.
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-day average*
concentration of a pollutant in ambient water that should
not be exceeded more than once every three years on the
average.
b. The higher concentration is called the Criterion Maximum
Concentration (CMC). The one-hour average concentration in
ambient water should not exceed the CMC more than once
every three years on the average.
Use of aquatic life criteria for developing water quality-based
permit limits and for designing waste treatment facilities requires
the selection of an appropriate wasteload allocation model.
Dynamic models are preferred for the application of aquatic life
criteria in order to make best use of the specified concentrations,
durations, and frequencies (2). If none of the dynamic models can
be used, then an alternative is steady-state modeling. Because
steady-state modeling is based on various simplifying assumptions,
it is less complex, and may be less realistic, than dynamic
modeling. An important step in the application of steady-state
modeling to stream is the selection of the design flow.
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, must be determined individually for each pollutant of
Although a 4-day averaging period should be used for the CCC in
most situations, an averaging period as long as 30 days may be used
in situations involving POTWs designed to remove ammonia when 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 ammonia 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 (5).
-------
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 stream 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.
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.
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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 some 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.
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SECTION 2. Hydrologically-Based Design Flow
2 .1 Introduction
The purpose of this 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 recommended interim use of the
hydrologically-based method. In addition, the Agency also recommended
(1, 2) that the frequencies of allowed exceedances 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 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 1Q10 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 exceedances of water quality criteria indicates that there is
little justification for different design flows for unstressed and
stressed system. 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:
• About half of the states in the nation use 7Q10 as the design
low flow.
• The log-Pearson Type III flow estimating technique of other
extreme value analytical techniques that are used to calculate
flow statistics from daily flow data are consistent with past
engineering and statistical practice.
• Most users are familiar with the log-Pearson Type III flow
estimating procedure and the USGS provides technical support for
this technique.
• 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 flow 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 FLOSTAT 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 low flow in Table 2-1 indicate that
the mean of the ratios of 7Q10 to 1Q10 is 1.3. The median of the
ratios is 1.1, whereas the range of the ratios is 1.0 to 3.85. Thus,
7Q10 low flows are generally 10 to 30% greater than the corresponding
1Q10 low flows, although in one case the 7Q10 is 3.85 tines greater
than the corresponding 1Q10.
Table 2-1. Hydrologically-based design flows (ft3/sec) for 60 streams
Station ID
01657000
02092500
06026000
12449600
05522000
09490800
14372500
05381000
10291500
05585000
12321500
01111500
River Name
Bull Run
Trent
Birch Cr
Beaver Cr
Iroquois
N Fk White
E FK Illinois
Black
Buckeye
LaMoine
Boundary Cr
Branch
State
VA
NC
MT
WA
IN
AZ
OR
WI
CA
IL
ID
RI
Period of
Record
1951-82
1951-82
1946-77
1960-78
1949-78
1966-78
1942-03
1905-83
1911-78
1921-83
1928-84
1940-82
CV*
4 .48
1.77
1.32
1.77
1.33
1.24
2 .03
2 .51
1.30
1.99
1.65
1.16
Design flow (ft 3/sec)
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
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
7Q10
1Q10
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 QV*
State Record
Design flow (ft 3/sec)
1Q10 7Q10
7Q10
1Q10
02138500
05053000
02083000
01196500
02133500
06280300
09149500
02296750
07018500
02217530
01481000
09497500
01144000
01600000
09359500
01403060
02413500
01421000
07298500
07013300
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
S ho shone
Uncompahgre
Peace
Rig
Middle Oconee
Brandywine
Salt
White
N Br Potomac
Animas
Raritan
L Tallapoosa
E B Delaware
Big Sunflower
Meramec
Chemung
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
FL
MO
GA
PA
AZ
VT
MD
CO
NJ
AL
NY
MS
MO
NY
CO
CO
ME
TN
WY
AL
IN
MS
NY
WV
MN
FL
LA
NE
SC
TX
VA
TN
WI
MT
PA
1922-
1951-
1927-
1931-
1940-
1957-
1939-
1931-
1922-
1902-
1912-
1925-
1915-
1939-
1946-
1904-
1940-
1915-
1936-
1923-
1915-
1901-
1947-
1932-
1919-
1937-
1902-
1926-
1945-
1908-
1939-
1938-
1939-
1939-
1939-
1942-
1966-
1924-
1901-
1914-
1935-
1957-
84
81
82
84
78
84
80
84
84
84
84
80
84
83
56
83
51
78
80
78
78
81
80
03
78
83
78
78
81
78
83
61
82
83
83
78
70
52
78
81
79
83
1 .
2 .
1.
1.
0.
1 .
0.
1.
2 .
1 .
1.
2 .
1 .
1 .
1.
1.
1 .
1 .
1.
2 .
1 .
1 .
1.
1.
1 .
1 .
2 .
0.
1 .
1 .
1.
1.
0.
1 .
0.
0.
1 .
1 .
0.
0.
0.
1.
.74
.10
.48
.02
.80
.54
.86
.54
.16
.37
.17
.05
.43
.42
.56
.64
.31
.41
.42
.41
.91
.12
.36
.39
.55
.16
.07
.48
.89
.10
.48
.65
.95
.98
.59
.94
.48
.25
.93
.61
.82
.10
13 .
15.
17.
17.
38 .
41.
35.
49.
46 .
49.
61.
64 .
75.
54 .
54 .
54 .
72 .
80.
89.
88 .
89.
107
116
124
120
122
151
179
188
207
209
229
280
298
160
306
311
329
473
505
327
571
4
9
0
5
8
8
6
0
4
4
4
6
3
7
8
2
7
8
4
8
7
.9
.9
.5
.7
.9
.9
.0
.6
.7
.6
.7
.1
.1
.9
.7
.6
.6
.6
.9
.1
.3
16
13
19
32
43
46
50
155
55
57
67
68
85
61
62
67
8 .
89
91
92
97
126
131
134
135
144
156
184
191
211
220
245
291
303
322
322
344
387
532
536
557
594
.4
.3
.4
.3
.4
.8
.8
.3
.3
.4
.2
.7
.2
.6
.3
.1
3
.7
.9
.2
.5
.1
.0
.1
.2
.5
.4
.3
.6
.0
.7
.6
.4
.4
.0
.4
.9
.3
.2
.0
.0
.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
1.03
1.05
1.09
1.17
1.12
1.38
1.05
1.13
1.03
1.33
1.02
1.02
1.05
1.07
1.04
1.02
2 .00
1.09
1 .11
1.18
1.12
1.06
1.70
1.04
2-1
-------
Table 2-1 (continued).
Station ID
13341000
07341500
02350500
01536500
01100000
14233430
River Name
N P Clearwater
Red
Flint
Susquehanna
Merrimack
Cowlitz
State
ID
AR
GA
PA
MA
WA
Period of
Record
1927-68
1928-81
1930-58
1901-83
1924-83
1968-78
CV*
1.16
1.41
1.00
1.34
1.01
0.93
Design flow (ft 3/sec)
1Q10
529.2
691.0
207.8
782 .0
270.2
901.5
7Q10
648 .6
769.2
799.8
814 .3
929.3
958 .7
7Q10
1Q10
1.23
1.11
3 .85
1.04
3 .44
1.07
*CV = Coefficient of Variation
2-2
-------
SECTION 3. Biologically-Based Design Flow
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-
frequency 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 stream 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 exceedances to occur more often
than allowed by the specified average frequency, based on
historical data. The allowed exceedances 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.
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 concentrations of pollutants in receiving waters in order
that the averages can be compared to the CMC and CCC to identify
3-1
-------
"exceedances" 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-exceedances", i.e., average flows that are
below a specified flow.
3.1.1 Exceedances and Excursions
Use of the term "exceedance" and "non-exceedance" 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 exceedance. 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 flow is less than the design flow, i.e., when
there is non-exceedance of a given flow. A non-exceedance of a
design flow corresponds to an exceedance of a criterion. Use of
the non-directional term "excursion", which is in the dictionary,
avoids this confusion. Use of the term "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 exceedance of a dissolved oxygen criterion is
favorable, not unfavorable. "Excursions", in this guidance manual,
will henceforth be used to imply
3-2
-------
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 or
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 seem 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
-------
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.
3.1.2 Features of Calculation
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 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 flow.
Because biologically-based design flows are based on the
averaging 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
-------
Exclusion
Time
Figure 3-1: Illustration of biologically-based design flow
3-5
-------
The CMC and CCC design flows are calculated in almost the same
manner. The differences result from 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:
* It allows the use of the new two-number 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.
* It takes into account all excursions in the flow record.
* It provides the necessary design flow directly without requiring
any design flow statistics in the xQy format.
* 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-
1 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 aquatic life criteria.
Analyses of the 1-day 3-year and the 4-day 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 2.91 times greater than the
corresponding 1-day 3year low flow.
-------
Table 3-1. Biologically-based design flows (ft3/sec) for 63 rivers
Station ID
01657000
02092500
06026000
12449600
05522000
09490800
14372500
05381000
10291500
05585000
12321500
01111500
02138500
05053000 or
03059000
02083000
01196500
02133500
06280300
09149500
02296750
07018500
02217530
01600000
09359500
01403060
01481000
09497500
01144000
02413500
01421000
07288500
07013300
01531000
07096000
09070000
01011000
03528000
13023000
02424000
River Name
Bull Run
Trent
Birch Cr
Beaver Cr
Iroquois
N Fk White
E FK Illinois
Black
Buckeye
LaMoine
Boundary Cr
Branch
Linville
Sheyenne
Fishing Cr
Quinnipiac
Drowning Cr
S ho shone
Uncompahgre
Peace
Big
Middle Oconee
N Br Potomac
Animas
Raritan
Brandy wine
Salt
White
L Tallapoosa
E B Delaware
Big Sunflower
Meramec
Chemung
Arkansas
Eagle
Allegash
Clinch
Greys
Cahaba
State
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
Period of
Record
1951-82
1951-82
1946-77
1960-78
1949-78
1966-78
1942-03
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
1915-78
1936-80
1923-78
1915-78
1901-81
1947-80
1932-03
1919-78
1937-83
1902-78
CV*
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
1.16
2 .07
Design flow (itybsec)
1-day 3 -year
0.20
1.40
1. 70
2.80
2.40
4 . 80
5. 80
5.00
7.00
8 . 90
12 .00
10.00
13 .00
15.40
12 .00
14 .90
33 .90
42 .90
29.90
48 .00
45 .00
33 .00
42 .90
60.00
46 .90
55 .80
63 .00
75.90
57.90
82 .00
82 .70
89 .90
85.70
89.90
120.00
134 .00
127.70
124 .80
122 .80
4 -day 3 -year
0.40
1. 60
2 .40
3.40
3.00
5.30
6 . 90
6.10
7.20
9.40
13 . 00
13.20
15.00
17.60
13.50
34 . 00
36 .20
45.80
49.00
55.20
51. 50
45. 70
49.00
61.10
53.60
59.30
59. 50
86.00
70.20
91.40
85.40
92 . 70
92.50
114.00
126.00
138 .40
132.20
135.80
149. 80
ccc
CMC 08
2 .00
1 .14
1 .41
1.21
1.25
1 .10
1 .19
1.22
1.03
1 .06
1 .08
1.32
1.15
1.14
1.13
2 .25
1 .07
1.07
1.26
1 .15
1 .14
1 .38
1.17
1.02
1.14
1 .06
1 .10
1.13
1.21
1.11
1 .03
1 .03
1.08
1.27
1.05
1 .03
1.04
1.09
1 .22
-------
Table 3-1 (continued).
Station ID
05515500
02490500
01315500
01610000
05386000
02369000
07378500
06465500
02135000
08110200
02076000
03455000
05333500
06287000
03107500
13341000
07341500
02350500
01100000
14233430
River Name
Kankakee
Bouge Chitto
Hudson
Potomac
Root
Shoal
Amite
Nebraska
Little Pee Dee
Brazos
Dan
French Broad
St . Croix
Bighorn
Beaver
N P Clearwater
Red
Flint
Merrimack
Cowl it z
State
IN
MS
NY
WV
MN
FL
LA
NE
SC
TX
VA
TN
WI
MT
PA
ID
AR
GA
MA
WA
Period of
Record
1926-78
1945-81
1908-78
1939-83
1938-61
1939-82
1939-83
1939-83
1942-78
1966-70
1924-52
1901-78
1914-81
1935-79
1957-83
1927-68
1928-81
1930-58
1924-83
1968-78
CV*
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
Design flow (ft /sec)
1-day 3-year
167.60
187.50
170.00
22.20
239.30
270.50
282.10
199.70
298.70
277.70
321.60
494 .30
477.50
364 .00
539.90
429.60
537.40
262 .50
284.00
934 .70
4-day 3-year
174.20
189.60
191.90
219.60
23937.00
2860.00
295.50
304.30
298.90
305.30
380.40
535.50
508.50
520.20
557.50
613.00
603 .30
731.00
797.30
959.90
ccc
CMC08
1.04
1.13
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
= coefficient of variation
3-10
-------
For further clarification of the biologically-based method, refer to
Appendix E, Questions and Answers.
3-11
-------
of special averaging periods and frequencies that might be selected
for specific pollutants (e.g., ammonia) or in site-specific
criteria. This method is empirical, 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 flow records usually consist of
daily flows for 20 to 80 years, manual calculation of design flow
is very time-consuming. The DFLOW computer program (Appendix D
(OMITTED) - DFLOW 2.0 has been superseded by newer versions. The
current versions of DFLOW and its documentation are available
online at http://www.epa.gov/waterscience/dflow.) will calculate
biologically-based design flows and display the dates, durations,
and magnitudes of the excursions within each low flow period.
3-6
-------
SECTION 4. COMPARISON OF THE TWO METHODS
4 .1 Design Flows
Table 4-1 shows 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 1Q10 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)-(1Q10))/(1-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. Comparison 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 White AZ
E FK Illinois OR
Black WI
Buckeye CA
LaMoine IL
Boundary Cr ID
Branch RI
Linville NC
Sheyenne ND
Fishing Cr NC
Quinnipiac CT
Drowning Cr NC
Shoshone WY
Uncompahgre CO
Peace FL
Big MO
Middle Oconee GA
N Br Potomac MD
Animas 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
Comparison of CMC Design Flows
1Q10 1-day %DIFF*
3-yr
0.3 0.2 -50.0
1.4 1.4 0.0
1.7 1.7 0.0
2.4 2.8 14 .3
3.4 2.4 -41.7
4.8 4.8 0.0
6.4 5.8 -10.3
5.5 5.0 -10.0
7.1 7.0 -1.4
9.3 8.9 -4.5
11.7 12 .0 2.5
8.8 10.0 12 .0
13 .4 13 .0 -3.1
15.9 15.4 -3.2
17.0 12.0 -41.7
17.5 14.9 -17.4
38.8 33.9 -14.4
41.8 42 .9 2.6
35.6 39.9 10.8
49.0 48 .0 -2.1
46 .4 45.0 -3.1
49.4 33 .0 -49.7
54.7 42.9 -27.5
54 .8 60.0 8.7
54.2 46.9 -15.6
61.4 55.8 -10.0
64 .6 63 .0 -2.5
75.3 75.9 0.8
72.7 57.9 -25.6
80.8 82 .0 1.5
89.4 82 .7 -8.1
88 .8 89.9 1.2
89.7 85.7 -4.7
99.9 89.9 -11.1
116.9 120.0 2.6
124.5 134.0 7.1
128.7 127.7 -0.8
122.9 124.8 1.5
151.9 122.0 -23.7
Comparison of CCC Design Flows
7Q10 4 -day 3- %DIFF*
yr
0.4 0.4 0.0
1.6 1.6 0.0
2.4 2.4 0.0
3.2 3.4 5.9
3.9 3.0 -30.0
5.3 5.3 0.0
6.7 6.9 2.9
6.7 6.1 -9.8
7.7 7.2 -6.9
9.9 9.4 -5.3
13 .1 13 .0 -0.8
13 .3 13 .2 -0.8
16 .4 15.0 -9.3
18 .3 17.6 -4.0
19.4 13.5 -43.7
32 .3 34 .0 5.0
43.4 36.2 -19.9
46 .8 45.8 -2.2
50.8 49.0 -3.7
55.3 55.2 -0.2
55.3 51.5 -7.4
57.4 45.7 -25.6
61.6 49.0 -25.7
62 .3 61.1 -2.6
67.1 53.6 -25.2
67.2 59.3 -13.3
68 .7 69.5 1.2
85.2 86 .0 0.9
88.3 70.2 -25.8
89.7 91.4 1.9
91.9 85.4 -7.6
92.2 92.7 0.5
97.5 92.5 -5.4
120.1 114.0 -9.3
131.0 126.0 -4.0
134.1 138.4 3.1
135.2 132.2 -2.3
144.5 135.8 -6.4
156.4 149.8 -5.4
* %Difference
* %Difference
-day 3-year flow)
day 3-year flow)
(1Q10)),100 / (4-day
(7Q10)),100 / ((4-day
3-year flow)
3-year flow)
4-2
-------
Table 4-1. (continued).
River Name State
Kankakee IN
Bouge Chitto MS
Hudson NY
Potomac WV
Root MN
Shoal FL
Amite LA
Niobrara NE
Little Pee Dee SC
Brazos TX
Dan VA
French Broad TN
St. Croix WI
Bighorn MT
Beaver PA
N P Clearwater ID
Red AR
Flint GA
Merrimack MA
Cowlitz WA
Comparison of CMC Design
Flows
1Q10 1-day 3-yr %DIFF*
179.0 167.6 -6.8
188.6 167.5 -0.6
207.7 170.0 -22.2
209.6 202.2 -3.7
229.7 239.3 4 .0
280.1 270.5 -3.5
298.1 202.1 -5.7
160.9 199.7 19.4
306.7 298.7 -2.7
311.6 277.7 -12.2
329.6 321.6 -2.5
473.6 494.3 4.2
505.9 477.5 -5.9
327.1 364.0 10.1
571.3 539.9 -5.8
529.2 469.6 -12.7
691 537.4 -29.6
207.8 262.5 20.8
270.2 284.0 3.6
901.5 934.7 4.9
Comparison of CCC Design
Flows
7Q10 4 -day 3-yr %DIFF*
184.3 174.2 -5.8
191 .6 189 .6 -1.1
211 . 0 191 . 9 -10 . 0
220.7 219.6 -0.5
245.6 239.7 -2.5
291.4 286.0 -1.9
303.4 295.5 -2.7
322.0 304.3 -5.8
322.4 298.9 -7.9
344.9 305.3 -13.0
307.3 380.4 -1.8
532.2 535.5 0.6
536.0 508.5 -5.4
557.0 520.2 -7.1
594.2 557.5 -6.6
648.6 613.0 -5.9
769.2 603.3 -27.5
799.8 731.3 -9.4
929.3 797.3 -16.6
968.7 959.9 -0.9
* %Difference - ((1
* %Difference - (4-
-day 3-year flow)
day 3-year flow)
(1Q10)),100 / (1
(7Q10)),100 / ((4
-day 3-year flow)
-day 3-year flow)
Similar comparisons can be made between the 4-day 3-year low
flows and the 7Q10 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.
4.2 Excursions
4-3
-------
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 ft2/sec, respectively,
but the corresponding numbers 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 that desired during the period of flow record.
4.3 Comparison 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. Comparison of number of excursions of 1Q10 and 7Q10 with
number of excursions of 1-day 3-yr and 4-day 3-yr design
flows.
River Name
Bull Run
Trent
Birch Cr
Beaver Cr
Iroquois
N Fk White
E FK Illinois
Black
Buckeye
LaMoine
Boundary Cr
Branch
Linville
Sheyenne
Fishing Cr
Quinnipiac
Drowning Cr
Shoshone
Uncompahgre
Peace
Big
Middle Oconee
N Br Potomac
Animas
Raritan
Brandywine
Salt
White
L Tallapoosa
E B Delaware
Big Sunflower
Meramec
Chemung
State
VA
NC
MT
WA
IN
AZ
OR
WI
CA
IL
ID
RI
NC
ND
NC
CT
NC
WY
CO
PL
MO
GA
MD
CO
NJ
PA
AZ
VT
AL
NY
MS
MO
NY
Comparison of CMC Design Flows Comparison of CCC Design Flows
1Q10 % Excur 1-day 3-yr % Excur 7Q10 % Excur 1-day 3-yr % Excur
0.3 19 0.2 10 0.4 8.5 0.4 8.5
1.4 9 1.4 9 1.6 9.3 1.6 9.2
1.7 8 1.7 8 2.4 9.3 2.4 9.2
2.4 1 2.8 6 3.2 4.0 3.4 6.0
3.4 18 2.4 9 3.9 16.8 3.0 9.7
4.8 2 4.8 2 5.3 4.0 5.3 4.0
6.4 13 5.8 12 6.7 11.3 6.9 11.5
5.5 27 5.0 21 6.7 26.0 6.1 24.5
7.1 13 7.0 7 7.7 10.0 7.2 8.5
9.3 33 8.9 20 9.9 24.5 9.4 20.5
11.7 15 12.0 15 13.1 15.8 13.0 15.7
8.8 10 10.0 13 13.3 18.3 13.2 14.0
13.4 21 13.0 15 16.4 25.0 15.0
15.9 11 15.4 6 18.3 14.5 17.6
17.0 17 12.0 15 19.4 29.3 13.5 17.2
17.5 39 14.9 13 32.3 11.3 34.0 13.0
38.8 26 33.9 12 43.4 27.8 36.2 12.7
41.8 3 42.9 6 46.8 9.3 45.8 6.3
35.6 7 39.9 13 50.8 17.5 49.0
49.0 17 48.0 16 55.3 17.3 55.2
46.4 23 45.0 15 55.3 27.8 51.5
49.4 25 33.0 11 57.4 23.3 45.7 14.3
54.7 29 42.9 14 61.6 28.0 49.0 14.8
54.8 0 60.0 2 62.3 6.8 61.1 2.5
54.2 25 46.9 13 67.1 24.3 53.6 13.3
61.4 30 55.8 14 67.2 33.0 59.3
64.6 21 63.0 18 68.7 17.3 6935.0
75.3 20 75.9 20 85.2 20.8 86.0 21.5
72.7 6 57.9 3 88.3 7.0 70.2 3.8
80.8 17 82.0 20 89.7 19.0 91.4 20.5
89.4 31 82.7 8 91.9 30.3 85.4 13.8
88.8 17 89.9 18 92.2 16.5 92.7 17.0
89.7 26 85.7 18 97.5 25.0 92.5 20.5
4-5
-------
Table 4-2. (Continued)
River Name
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
N P Clearwater
Red
Flint
Merrimack
Cowlitz
State
CO
CO
ME
TN
WY
AL
IN
MS
NY
WV
MN
FL
LA
NE
SC
TX
VA
TN
WI
MT
PA
ID
AR
GA
MA
WA
Comparison of CMC Design
1Q10
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
% Excur
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
1-day
115
120
134
127
1234
122
167
187
170
202
239
270
282
199
299
277
321
494
477
364
539
469
537
2625
284
934
3-yr
8
0
0
7
.8
8
6
5
0
2
3
5
1
7
7
7
6
3
5
0
9
6
4
.0
0
7
Flows
% Excur
26
11
17
17
10
10
14
10
29
14
7
12
14
8
12
4
9
18
2 2
14
4
13
17
9
18
2
Comparison of CCC Design
7Q10
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
643.6
769.2
799.8
929.3
963.7
% Excur
28.0
17.5
13.0
25.0
18.8
24.8
29.5
19.3
27.8
15.0
10.8
19.3
14.0
11.3
15.0
6.8
10.3
16.0
34.5
16.5
13.3
14.8
28.8
20.3
41.8
4.5
1-day
123
126
138
132
135
149
174
189
191
219
239
286
295
304
298
305
380
535
508
520
557
613
603
731
797
959
3-yr
8
0
4
2
8
8
2
6
9
6
7
0
5
3
9
3
4
5
5
2
5
0
3
0
3
3
Flows
% Excur
26.0
11.0
12.0
10.0
16.0
14.0
11.0
24.0
14.0
7.0
17.0
4.0
8.0
19.0
3.0
4-6
-------
The 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 number 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
biologically-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 flow,
except that the 30Q10 low flow should be used as the CCC design
flow for ammonia is situations involving POTWs designed to
remove ammonia where limited variability of effluent pollutant
concentrations and resulting concentrations 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 D.C.
September, 1985.
2. U.S. EPA. Water Quality Criteria. 50 FR 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 criteria 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 D.C.
5. U.S. EPA. 1985. Ambient water quality criteria for ammonia -
1984. EPA 440/5-85-001. National Technical Information Service,
Springfield, VA.
6. U.S. EPA. 1985. STORET User Handbook, Part FL, Flow Data File.
-------
APPENDIX A. Calculation of Hydrologically-Based Design Flows
Design flows 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+l)/y]
m2 = [(n+l)/y] + 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 stream flow 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
xQy = 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 = frequency factor for skewness g and return period y.
A-l
-------
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 appropriate value (3) can be
found from
z = 4.91 [(1/y)-14 -(1-1/y)-14]
To illustrate the use of the two xQy low flow estimation
methods, the data in Table A-2 will be analyzed for the 7Q5. 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 flow are shown at the bottom of the table.
For the distribution-free approach, the value of (n+l)/y is
(45+1)/5 or 9.2. Therefore, the 7Q5 low flow lies between the 9-th
and 10-th 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 = -0.956. The 7Q5 low
flow is:
7Q5 = exp(6.01 + (-.856) ( .24) )
= 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)/5-
(.409)/36)3-l]
= -.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.
2.
2.
2.
2.
2.
1.
1.
1.
1.
1.
0.
0.
0.
0.
0.
-0
-0
-0
-0
-1
-1
-1
-1
-1
-2
-2
-2
-2
-2
-3
0
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
.2
.4
.6
.8
.0
.2
.4
.6
.8
.0
.2
.4
.6
.8
.0
Return
5
-0
-0
-0
-0
-10
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
Period,
.636
.666
.696
.725
.752
.777
.799
.817
.832
.844
.852
.856
.857
.855
.850
.842
.830
.816
.800
.758
.758
.732
.705
.675
.643
.609
.574
.537
.499
.460
.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
Denham Springs, 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
n = 45
u = 6.0
s = 0.23
q = 0.385
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
A-5
-------
References
1. Linsley, R.K., et al. Hydrology for Engineers, 2nd Edition.
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.
-------
Appendix B. An Example Use of DFLOW for Ammonia Discharges From POTWs
The purpose of this Appendix is to illustrate the use of the DFLOW
program to calculate biologically-based design flows for ammonia and compare
them with the hydrologically-based design flows of 30Q10 for the 13 streams
with the lowest coefficients of variations shown in Table 2-1.
B.1 Introduction
As stated in the two-number WQC for ammonia (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
ammonia 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-l
-------
Table B-l. Design flows and resulting number of excursions using 30-day
averaging period (all flows in ft3/sec).
River Name
Quinnipiac
Drowning Cr
Uncompahgre
Greys
Kankakee
Hudson
Shoal
Little Pee Dee
St. Croix
Niobrara
French Broad
Bighorn
Flint
State
CT
NC
CO
WY
IN
NY
FL
SC
WI
NE
TN
MT
GA
Coeff
of
Variation
1.02
0.8
0.86
1.16
0.48
1 . 1
0.95
0.94
0.61
0.59
0.93
0.82
1
30Q10
Flow
42.3
54.7
71
160.7
201.8
288
323.5
366.3
571.8
613.2
636.2
913.6
1000
%Excursions
7.8
8.5
6.9
5.7
10
13.4
10.2
7 .4
16.2
6.4
11.9
8.1
6.4
30 -day 3 -year
Flow
46.5
65.5
77 .3
166.9
213.6
340.7
339
450
598.6
673.6
715.7
1103
1097
%Excursions
15
15
14 .6
9.9
16.7
24.3
12.1
11.8
21.9
8.1
20.3
14.3
9.6
%Diff*
9
16.5
8.2
3.7
5.5
13.5
4.5
18.6
4.5
9
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 flows for 13 streams arc presented 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
(Appendix D (OMITTED). DFLOW 2.0 has been superseded by newer versions. The
current versions of DFLOW and its documentation are available online at
http://www.epa.gov./waterscience/dflow). Table B-l also includes the 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-day 3-year - 30Q10)/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 POTWs, 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 POTWs 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 ammonia 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.
In Section 4.1, the hydrologically-based design flows have been
compared with the biologically-based design flows for the 4-day averaging
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 for 13 streams for ammonia. For these 13 streams, the 30Q10
flow was always less than the 30-day 3-year flow, by an average to 10.2%.
Thus, the use of the 30Q10 as the design flow is relatively more protective
for these streams.
Reference
1. US EPA. 1985d. Ambient water quality criteria for ammonia. 1984. EPA
440/5-85-001. National Technical Information Service, Springfield, VA.
B-3
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APPENDIX C. Calculation of 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/E (1/F), not as (E 5)/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 highest 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)]
where D = the number of days in the flow record;
Y = the average number of years specified in
the frequency and
C-l
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Z = the allowed number 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 average
period, calculate the set of X-day running averages for the
entice 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 common with the next average, and the
number of X-day averages calculated from the flow record
will be (D+l-X).
Part III. Determination of the number 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.
III-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
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Table C-l. Counting excursion days for a specified flow of 100 ft3/sec using 4-day averages
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
112.5
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
Yea
No
Yes
Yes
No
No
No
No
No
Date
Is the date of Number of Number of
part of any Date of Number of start excursion excursions
4 -day avg. start of days in of low days in in low
that is below excursion excursion flow low flow flow
100? period period period period period
No
No
Yes 3 4 3 12 3
Yes
Yes
Yes
No
No
Yes 9 8
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
The daily flows and four-day average flows for days 19 to 200 are all above 100 ft3/sec
C-3
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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.
III-3. Determine the starting dates of, and number of days in, each
succeeding excursion period in the flow record.
III-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 period and divide the sum by
X to obtain the number of excursions in the first low period.
If the number 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 flow period.
III-6. Determine the starting dates of and the number of excursions
in each succeeding 120-day low flow period.
III-7. Sum the number of excursions in all the low-flow periods to
C-4
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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 = 0 as the number of excursions (see Part III) of the
initial lower limit.
IV-4. Calculate Nn = the number of excursions (See Part III) of the
initial upper limit.
IV-5. Calculate T = the initial trial flow as T = L + (Z - NL) (U-L)
(ND-NL)
Part V. Iterative convergence to the design flow.
V-l. Calculate NT = the number of excursions (see Part III) of the
trial flow.
V-2. If -0.005 <= (NT-Z)/Z) <= +0.005, use T as the design flow and
stop.
If NT > Z, set U = T and Nn = NT.
If NT < Z, set L = T and NL = NT.
V-3. If ((U-L)/U)<0.005, use L as the design flow and stop.
Otherwise, calculate a new trial flow as T = L + (Z - NL) (U-L) ,
and repeat steps V-l, V-2, and V-3 as necessary. (Nu-NL)
REFERENCE
1. Carnahan, B., H.A. Luther, and J.O. Wilkes. 1969. Applied
numerical methods. Wiley, New York.
C-5
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APPENDIX D. DFLOW 2.0 User's Guide (OMITTED)
NOTE: DFLOW 2.0 has been superseded by newer versions. The current
versions of DFLOW and its documentation are available online at
http://www.epa.gov/waterscience/dflow.
D-l
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APPENDIX E. Questions and Answers Concerning the Bi ologically-Based
Method
Q #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 common. Let's consider a time-
series of daily flow data in order to explain extreme value
techniques.
A low-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 #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.
Q #4: So, do I have 30 extreme values from 30 years' flow record
considering one extreme value for each water year?
A. Exactly.
Q #5: You said about ranking the extreme values. How do you rank
them and why do you rank them?
A. For low flow analysis, ranking can be done from lowest to
highest. For a low-flow analysis of a 30-year flow record, we
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
Bisuas (FTS-382-7012) or Nelson Thomas (FTS-780-5702).
E-l
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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 low is approximately 30 years, and that of
the 10th ranked flow is approximately 3 years.
Q #6: The frequency analysis using the ranked extreme values seems
to be quite straight forward. Why are various kinds of
distribution used for frequency analysis?
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.
They made this 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.
Q #8: 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 design flow using the
ambient duration and frequency 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 efforts could be severe. The severity of
those smaller within-year exposure 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
must find a way to account for all within-year exposures in
addition to the most extreme event of each year.
Q #10: Your answer is difficult to follow; would you give an
example?
A. Hydrologists know that we had, in various parts of the US,
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
E-2
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water year 1925, there were 4 very low 4-day running averages
of which only one was acceptable 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, some 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 from 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 #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 the basis of either biological, toxicological or
ecological considerations. Whereas the parameters used in
the extreme value analysis are unrelated to biological,
toxicological or ecological consideration.
Q #12: Would you name the things that you think are biological,
toxicological, or ecological in nature?
- Durations of acceptable exposure conditions: 1 hour
for CMC and 4 days for CCC are biologically derived.
- 3 years on the 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 discrepancy?
E-3
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A. 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 5 to 10 years after a severe
exposure event. Aquatic biologists consider that repeated
within-year exposures can result in catastrophic affects. In
their judgment, 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 #14: Have you anything to say about how you decided to allow 5
excursions in an interval of 15 years?
A. WDC allow an excursion once every three years on the average.
Since the effects of excursions are cumulative, ecological
recovery from a severe exposure event requires about 15 years
and the recovery period from a single exposure event,
according to the national WDC is 3 years. Therefore 15/3 or
5 excursions are accepted as the upper limit of within-year
excursion counts.
Q #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-year exposure events (based on the information
available in Table D-2 of TSD) ?
A. One could make various other choices based on site-specific
knowledge but we made our choice for average conditions.
Q #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 the 15-year interval choice? Do we have any idea
about how different the CCC or CMC flow will be for the
choices of 12- or 13-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 may be
allowed because WQC 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 cumulative, 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.
Q #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, flows may remain
low for a long time, such as for 40-50 days, not necessarily
E-4
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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 those 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 example
recruitment from the surrounding ecosystem, in which recovery
may take place. So, in our judgment, 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
what 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 simple 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.
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 come by. Why is it so important now
to have a rational biolocially-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
E-5
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water use. A technically defensible method will bring about
technical consistency for any desired level of protection.
Second, the introduction of the two-number 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 two-numbered WQC, but also to other
sites-and use-specific durations and frequencies of
pollutants and whole effluent toxicities. Third, since WQC
and their field use have become 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 number 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 biologically-
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 toxicologists
can gather data that might allow them to refine their
estimates of such values as one hours, 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 an 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 number 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 some 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 number of excursions
that are allowed for x-day 3-year criteria is equal to 30/3
or 10.
5. The 4-day 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 number of
excursions. For 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-l
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obtained a total of 5 excursions only, although 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.
Q #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?
A. Absolutely. This is true about any analysis. More relevant
data are necessary to provide more accurate information.
Q #27: What minimum length of flow record is recommended?
A. The longer the flow record, the more reliable the estimated
design conditions will be. Figure E-l (OMITTED) 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 was derived on the
basis of lognormal statistics, not log Pearson type 3).
Results are shown for both low variability (CV=0.2) and high
variability (CV=0.8) 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.
E-2
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Q #28: What would you do for intermittent streams where low flow is
zero during low flow periods? Also, how will you use the
biologically-based method 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 sometimes use flow data from
hydrologically comparable drainage basins.
Q #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 performed 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 few minutes of time
at the computer. However, the job run might take anywhere
from a few minutes to several hours, depending on how busy the
computer system is at the time of submittal. Once the data
has been retrieved, the analysis can be performed in five or
ten minutes.
Q #30: It seems that the 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 information to make such an
important decision?
E-3
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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
judgment and the best information available, although we
recognize that our best judgment 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 #31: What are you doing to improve the information base?
A. ORD 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
hydrologists 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, M. 1, January 1983.
E-4
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