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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”, 
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, SteadyState, Models, Water Quality Criteria, Acute, Chronic, Biological, 

Hydrologic 
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 SteadyState 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. 
ii

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-1
iii

APPENDIX B. AN EXAMPLE USE OF DFLOW FOR AMMONIA DISCHARGES FROM 

POTWs ............................................................ B-1 

APPENDIX C. CALCULATION OF BIOLOGICALLY-BASED DESIGN FLOWS ....... C-1

APPENDIX D. DFLOW 2.0 USER'S GUIDE (OMITTED) 

APPENDIX E. QUESTIONS AND ANSWERS CONCERNING THE BIOLOGICALLY-BASED 

METHOD ........................................................... E-1
iv

GLOSSARY 

1B3 - 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 lasts2

 

1

 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. 
v

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

 

3

 EPA. “Terms of Environment: Glossary, Abbreviations, and Acronyms” 

http://www.epa.gov/OCEPAterms/. March 8,2006. 4 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.

4

 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. 5 The American Heritage® Dictionary of the English Language,4th Ed. “Percentile.” Accessed 

at www.Dictionary.com July 3, 2006. 
vi

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.8

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).

 6 EPA. “Terms of Environment: Glossary, Abbreviations, and Acronyms”. 

http://www.epa.gov/OCEPAterms/pterms.html March 8, 2006. 6

 EPA. “Terms of Environment: Glossary, Abbreviations, and Acronyms”. 

http://www.epa.gov/OCEPAterms/tterms.html March 8, 2006. 7 EPA. “Terms of Environment: Glossary, Abbreviations, and Acronyms” 

http://www.epa.gov/OCEPAterms/wterms.html March 8, 2006. 8 EPA. “Terms of Environment: Glossary, Abbreviations, and Acronyms” 

http://www.epa.gov/OCEPAterms/wterms.html March 8, 2006.
1

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 
2

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).
3

concern in each effluent because the CCC and CMC are pollutantspecific, 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. 

1.3 Scope

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. 
4

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.
2-1

SECTION 2. Hydrologically-Based Design Flow 

2.1 Introduction

The purpose of this section is to describe the hydrologicallybased 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 
2-2

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. 
2-3

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 logPearson 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-l indicate that 

the mean of the ratios of 7Ql0 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 

Design flow (ft 3/sec)

Station ID River Name State

Period of 

Record 

CV* 

1Q10 7Q10

7Q10

1Q10

01657000 Bull Run VA 1951-82 4.48 0.3 0.4 1.33 

02092500 Trent NC 1951-82 1.77 1.4 1.6 1.14 

06026000 Birch Cr MT 1946-77 1.32 1.7 2.4 1.41 

12449600 Beaver Cr WA 1960-78 1.77 2.4 3.2 1.22 

05522000 Iroquois IN 1949-78 1.33 3.4 3.9 1.15 

09490800 N Fk White AZ 1966-78 1.24 4.8 5.3 1.10 

14372500 E FK Illinois OR 1942-03 2.03 6.4 6.7 1.05 

05381000 Black WI 1905-83 2.51 5.5 6.7 1.22 

10291500 Buckeye CA 1911-78 1.30 7.1 7.7 1.08 

05585000 LaMoine IL 1921-83 1.99 9.3 9.9 1.06 

12321500 Boundary Cr ID 1928-84 1.65 11.7 13.1 1.12 

01111500 Branch RI 1940-82 1.16 8.8 13.3 1.51 
2-1

Table 2-1 (continued) 

Design flow (ft 3/sec)

Station 

ID River Name State

Period of 

Record 

CV* 1Q10 7Q10

7Q10

1Q10

02138500 Linville NC 1922-84 1.74 13.4 16.4 1.22 

05053000 Sheyenne ND 1951-81 2.10 15.9 13.3 1.15 

02083000 Fishing Cr NC 1927-82 1.48 17.0 19.4 1.14 

01196500 Quinnipiac CT 1931-84 1.02 17.5 32.3 1.85 

02133500 Drowning Cr NC 1940-78 0.80 38.8 43.4 1.12 

06280300 Shoshone WY 1957-84 1.54 41.8 46.8 1.12 

09149500 Uncompahgre CO 1939-80 0.86 35.6 50.8 1.43 

02296750 Peace FL 1931-84 1.54 49.0 155.3 1.13 

07018500 Rig MO 1922-84 2.16 46.4 55.3 1.19 

02217530 Middle Oconee GA 1902-84 1.37 49.4 57.4 1.16 

01481000 Brandywine PA 1912-84 1.17 61.4 67.2 1.09 

09497500 Salt AZ 1925-80 2.05 64.6 68.7 1.06 

01144000 White VT 1915-84 1.43 75.3 85.2 1.13 

01600000 N Br Potomac MD 1939-83 1.42 54.7 61.6 1.13 

09359500 Animas CO 1946-56 1.56 54.8 62.3 1.15 

01403060 Raritan NJ 1904-83 1.64 54.2 67.1 1.24 

02413500 L Tallapoosa AL 1940-51 1.31 72.7 8.3 1.21 

01421000 E B Delaware NY 1915-78 1.41 80.8 89.7 1.11 

07298500 Big Sunflower MS 1936-80 1.42 89.4 91.9 1.03 

07013300 Meramec MO 1923-78 2.41 88.8 92.2 1.05 

01531000 Chemung NY 19l5-78 1.91 89.7 97.5 1.09 

07096000 Arkansas CO 1901-81 1.12 107.9 126.1 1.17 

09070000 Eagle CO 1947-80 1.36 116.9 131.0 1.12 

01011000 Allegash ME 1932-03 1.39 124.5 134.1 1.38 

03528000 Clinch TN 1919-78 1.55 120.7 135.2 1.05 

13023000 Greys WY 1937-83 1.16 122.9 144.5 1.13 

02424000 Cahaba AL 1902-78 2.07 151.9 156.4 1.03 

05515500 Kankakee IN 1926-78 0.48 179.0 184.3 1.33 

02490500 Bouge Chitto MS 1945-81 1.89 188.6 191.6 1.02 

01315500 Hudson NY 1908-78 1.10 207.7 211.0 1.02 

01610000 Potomac WV 1939-83 1.48 209.6 220.7 1.05 

05386000 Root MN 1938-61 1.65 229.7 245.6 1.07 

02369000 Shoal FL 1939-82 0.95 280.1 291.4 1.04 

07378500 Amite LA 1939-83 1.98 298.1 303.4 1.02 

06465500 Niobrara NE 1939-83 0.59 160.9 322.0 2.00 

02135000 Little Pee Dee SC 1942-78 0.94 306.7 322.4 1.09 

08110200 Brazos TX 1966-70 1.48 311.6 344.9 1.11 

02076000 Dan VA 1924-52 1.25 329.6 387.3 1.18 

03455000 French Broad TN 1901-78 0.93 473.6 532.2 1.12 

05333500 St. Croix WI 1914-81 0.61 505.9 536.0 1.06 

06287000 Bighorn MT 1935-79 0.82 327.1 557.0 1.70 

03107500 Beaver PA 1957-83 1.10 571.3 594.2 1.04 
2-2

Table 2-1 (continued). 

Design flow (ft 3/sec)

Station ID River Name State 

Period of 

Record 

CV* 1Q10 7Q10

7Q10

1Q10

13341000 N P Clearwater ID 1927-68 1.16 529.2 648.6 1.23 

07341500 Red AR 1928-81 1.41 691.0 769.2 1.11 

02350500 Flint GA 1930-58 1.00 207.8 799.8 3.85 

01536500 Susquehanna PA 1901-83 1.34 782.0 814.3 1.04 

01100000 Merrimack MA 1924-83 1.01 270.2 929.3 3.44 

14233430 Cowlitz WA 1968-78 0.93 901.5 958.7 1.07 

*CV = Coefficient of Variation 
3-1

SECTION 3. Biologically-Based Design Flow 

3.1 Introduction

The purpose of this section is to describe the biologicallybased 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 steadystate modeling. The two-number WQC are in the intensity-durationfrequency 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 
3-2

"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 
3-3

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 
3-4

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-l 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 
3-5

Figure 3-1: Illustration of biologically-based design flow 
3-7

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 oneday 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. 
3-8

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 B1 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-l 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 l-day 3year low flow. 
3-9

Table 3-1. Biologically-based design flows (ft3

/sec) for 63 rivers 

CCC

01657000 Bull Run VA 1951-82 4.48 0.20 0.40 2.00

02092500 Trent NC 1951-82 1.77 1.40 1.60 1.14

06026000 Birch Cr MT 1946-77 1.32 1.70 2.40 1.41

12449600 Beaver Cr WA 1960-78 1.77 2.80 3.40 1.21

05522000 Iroquois IN 1949-78 1.33 2.40 3.00 1.25

09490800 N Fk White AZ 1966-78 1.24 4.80 5.30 1.10

14372500 E FK Illinois OR 1942-03 2.03 5.80 6.90 1.19

05381000 Black WI 1905-83 2.51 5.00 6.10 1.22

10291500 Buckeye CA 1911-78 1.30 7.00 7.20 1.03

05585000 LaMoine IL 1921-83 1.99 8.90 9.40 1.06

12321500 Boundary Cr ID 1928-84 1.65 12.00 13.00 1.08

01111500 Branch RI 1940-82 1.16 10.00 13.20 1.32

02138500 Linville NC 1922-84 1.74 13.00 15.00 1.15

05053000 or 

03059000

Sheyenne ND 1951-81 2.10 15.40 17.60 1.14

02083000 Fishing Cr NC 1927-82 1.48 12.00 13.50 1.13

01196500 Quinnipiac CT 1931-84 1.02 14.90 34.00 2.25

02133500 Drowning Cr NC 1940-78 0.80 33.90 36.20 1.07

06280300 Shoshone WY 1957-84 1.54 42.90 45.80 1.07

09149500 Uncompahgre CO 1939-80 0.86 29.90 49.00 1.26

02296750 Peace FL 1931-84 1.54 48.00 55.20 1.15

07018500 Big MO 1922-84 2.16 45.00 51.50 1.14

02217530 Middle Oconee GA 1902-84 1.37 33.00 45.70 1.38

01600000 N Br Potomac MD 1939-83 1.42 42.90 49.00 1.17

09359500 Animas CO 1946-56 1.56 60.00 61.10 1.02

01403060 Raritan NJ 1904-83 1.64 46.90 53.60 1.14

01481000 Brandywine PA 1912-84 1.17 55.80 59.30 1.06

09497500 Salt AZ 1925-80 2.05 63.00 59.50 1.10

01144000 White VT 1915-84 1.43 75.90 86.00 1.13

02413500 L Tallapoosa AL 1940-51 1.33 57.90 70.20 1.21

01421000 E B Delaware NY 1915-78 1.41 82.00 91.40 1.11

07288500 Big Sunflower MS 1936-80 1.42 82.70 85.40 1.03

07013300 Meramec MO 1923-78 2.41 89.90 92.70 1.03

01531000 Chemung NY 19l5-78 1.91 85.70 92.50 1.08

07096000 Arkansas CO 1901-81 1.12 89.90 114.00 1.27

09070000 Eagle CO 1947-80 1.36 120.00 126.00 1.05

01011000 Allegash ME 1932-03 1.39 134.00 138.40 1.03

03528000 Clinch TN 1919-78 1.55 127.70 132.20 1.04

13023000 Greys WY 1937-83 1.16 124.80 135.80 1.09

02424000 Cahaba AL 1902-78 2.07 122.80 149.80 1.22

Station ID River Name State CV*

Period of 

Record 1-day 3-year 4-day 3-year

Design flow (ft3

/sec)

CMC08
3-10

Table 3-1 (continued). 

*CV = coefficient of variation

CCC

05515500 Kankakee IN 1926-78 0.48 167.60 174.20 1.04

02490500 Bouge Chitto MS 1945-81 1.89 187.50 189.60 1.13

01315500 Hudson NY 1908-78 1.10 170.00 191.90 1.13

01610000 Potomac WV 1939-83 1.48 22.20 219.60 1.09

05386000 Root MN 1938-61 1.65 239.30 23937.00 1.00

02369000 Shoal FL 1939-82 0.95 270.50 2860.00 1.06

07378500 Amite LA 1939-83 1.98 282.10 295.50 1.05

06465500 Nebraska NE 1939-83 0.59 199.70 304.30 1.52

02135000 Little Pee Dee SC 1942-78 0.94 298.70 298.90 1.00

08110200 Brazos TX 1966-70 1.48 277.70 305.30 1.10

02076000 Dan VA 1924-52 1.25 321.60 380.40 1.18

03455000 French Broad TN 1901-78 0.93 494.30 535.50 1.08

05333500 St. Croix WI 1914-81 0.61 477.50 508.50 1.06

06287000 Bighorn MT 1935-79 0.82 364.00 520.20 1.43

03107500 Beaver PA 1957-83 1.10 539.90 557.50 1.07

13341000 N P Clearwater ID 1927-68 1.16 429.60 613.00 1.31

07341500 Red AR 1928-81 1.41 537.40 603.30 1.12

02350500 Flint GA 1930-58 1.00 262.50 731.00 2.78

01100000 Merrimack MA 1924-83 1.01 284.00 797.30 2.81

14233430 Cowlitz WA 1968-78 0.93 934.70 959.90 1.03

Design flow (ft3

/sec)

1-day 3-year 4-day 3-year CMC08

Station ID River Name State

Period of 

Record CV*
3-11

For further clarification of the biologically-based method, refer to 

Appendix E, Questions and Answers.
3-6

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. 
4-1

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 l-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.
4-2

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) 

Comparison of CMC Design Flows Comparison of CCC Design Flows

River Name State 1Q10 1-day 

3-yr

%DIFF* 7Q10 4-day 3-

yr

%DIFF*

Bull Run VA 0.3 0.2 -50.0 0.4 0.4 0.0

Trent NC 1.4 1.4 0.0 1.6 1.6 0.0

Birch Cr MT 1.7 1.7 0.0 2.4 2.4 0.0

Beaver Cr WA 2.4 2.8 14.3 3.2 3.4 5.9

Iroquois IN 3.4 2.4 -41.7 3.9 3.0 -30.0

N Fk White AZ 4.8 4.8 0.0 5.3 5.3 0.0

E FK Illinois OR 6.4 5.8 -10.3 6.7 6.9 2.9

Black WI 5.5 5.0 -10.0 6.7 6.1 -9.8

Buckeye CA 7.1 7.0 -1.4 7.7 7.2 -6.9

LaMoine IL 9.3 8.9 -4.5 9.9 9.4 -5.3

Boundary Cr ID 11.7 12.0 2.5 13.1 13.0 -0.8

Branch RI 8.8 10.0 12.0 13.3 13.2 -0.8

Linville NC 13.4 13.0 -3.1 16.4 15.0 -9.3

Sheyenne ND 15.9 15.4 -3.2 18.3 17.6 -4.0

Fishing Cr NC 17.0 12.0 -41.7 19.4 13.5 -43.7

Quinnipiac CT 17.5 14.9 -17.4 32.3 34.0 5.0

Drowning Cr NC 38.8 33.9 -14.4 43.4 36.2 -19.9

Shoshone WY 41.8 42.9 2.6 46.8 45.8 -2.2

Uncompahgre CO 35.6 39.9 10.8 50.8 49.0 -3.7

Peace FL 49.0 48.0 -2.1 55.3 55.2 -0.2

Big MO 46.4 45.0 -3.1 55.3 51.5 -7.4

Middle Oconee GA 49.4 33.0 -49.7 57.4 45.7 -25.6

N Br Potomac MD 54.7 42.9 -27.5 61.6 49.0 -25.7

Animas CO 54.8 60.0 8.7 62.3 61.1 -2.6

Raritan NJ 54.2 46.9 -15.6 67.1 53.6 -25.2

Brandywine PA 61.4 55.8 -10.0 67.2 59.3 -13.3

Salt AZ 64.6 63.0 -2.5 68.7 69.5 1.2

White VT 75.3 75.9 0.8 85.2 86.0 0.9

L Tallapoosa AL 72.7 57.9 -25.6 88.3 70.2 -25.8

E B Delaware NY 80.8 82.0 1.5 89.7 91.4 1.9

Big Sunflower MS 89.4 82.7 -8.1 91.9 85.4 -7.6

Meramec MO 88.8 89.9 1.2 92.2 92.7 0.5

Chemung NY 89.7 85.7 -4.7 97.5 92.5 -5.4

Arkansas CO 99.9 89.9 -11.1 120.1 114.0 -9.3

Eagle CO 116.9 120.0 2.6 131.0 126.0 -4.0

Allegash ME 124.5 134.0 7.1 134.1 138.4 3.1

Clinch TN 128.7 127.7 -0.8 135.2 132.2 -2.3

Greys WY 122.9 124.8 1.5 144.5 135.8 -6.4

Cahaba AL 151.9 122.0 -23.7 156.4 149.8 -5.4

* %Difference - ((4-day 3-year flow) - (1Q10))*100 / (4-day 3-year flow) 

* %Difference - (4-day 3-year flow) - (7Q10))*100 / ((4-day 3-year flow)
4-3

Table 4-1. (continued). 

Comparison of CMC Design 

Flows

Comparison of CCC Design 

Flows

River Name State 1Q10 1-day 3-yr %DIFF* 7Q10 4-day 3-yr %DIFF*

Kankakee IN 179.0 167.6 -6.8 184.3 174.2 -5.8

Bouge Chitto MS 188.6 167.5 -0.6 191.6 189.6 -1.1

Hudson NY 207.7 170.0 -22.2 211.0 191.9 -10.0

Potomac WV 209.6 202.2 -3.7 220.7 219.6 -0.5

Root MN 229.7 239.3 4.0 245.6 239.7 -2.5

Shoal FL 280.1 270.5 -3.5 291.4 286.0 -1.9

Amite LA 298.1 202.1 -5.7 303.4 295.5 -2.7

Niobrara NE 160.9 199.7 19.4 322.0 304.3 -5.8

Little Pee Dee SC 306.7 298.7 -2.7 322.4 298.9 -7.9

Brazos TX 311.6 277.7 -12.2 344.9 305.3 -13.0

Dan VA 329.6 321.6 -2.5 307.3 380.4 -1.8

French Broad TN 473.6 494.3 4.2 532.2 535.5 0.6

St. Croix WI 505.9 477.5 -5.9 536.0 508.5 -5.4

Bighorn MT 327.1 364.0 10.1 557.0 520.2 -7.1

Beaver PA 571.3 539.9 -5.8 594.2 557.5 -6.6

N P Clearwater ID 529.2 469.6 -12.7 648.6 613.0 -5.9

Red AR 691 537.4 -29.6 769.2 603.3 -27.5

Flint GA 207.8 262.5 20.8 799.8 731.3 -9.4

Merrimack MA 270.2 284.0 3.6 929.3 797.3 -16.6

Cowlitz WA 901.5 934.7 4.9 968.7 959.9 -0.9

* %Difference - ((1-day 3-year flow) - (1Q10))*100 / (1-day 3-year flow) 

* %Difference - (4-day 3-year flow) - (7Q10))*100 / ((4-day 3-year flow) 

Similar comparisons can be made between the 4-day 3-year low 

flows and the 7Q10 low flows based on Table 4-l. 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
4-4

Table 4-2 presents the calculated number of excursions that 

occurred in the 60 streams for the low flows calculated using the 

hydrologically- and biologically-based methods. The table 

demonstrates the impact of the choice of one design flow method over 

the other in terms of number of excursions. For any stream, a 

higher flow will always result in the same or a greater number of 

excursions than a lower flow. Occasionally, the difference in the 

number of excursions of the two design flows is quite dramatic even 

if the difference between the two design flows is quite small. For 

example, the 1Q10 and the 1-day 3-year design flow of the Quinnipiac 

River in Connecticut are 17.5 ft3

/sec and 14.9 ft3/sec, respectively, 

but the corresponding 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. 
4-5

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. 

1Q10 % Excur 1-day 3-yr % Excur 7Q10 % Excur 1-day 3-yr % Excur

Bull Run VA 0.3 19 0.2 10 0.4 8.5 0.4 8.5

Trent NC 1.4 9 1.4 9 1.6 9.3 1.6 9.2

Birch Cr MT 1.7 8 1.7 8 2.4 9.3 2.4 9.2

Beaver Cr WA 2.4 1 2.8 6 3.2 4.0 3.4 6.0

Iroquois IN 3.4 18 2.4 9 3.9 16.8 3.0 9.7

N Fk White AZ 4.8 2 4.8 2 5.3 4.0 5.3 4.0

E FK Illinois OR 6.4 13 5.8 12 6.7 11.3 6.9 11.5

Black WI 5.5 27 5.0 21 6.7 26.0 6.1 24.5

Buckeye CA 7.1 13 7.0 7 7.7 10.0 7.2 8.5

LaMoine IL 9.3 33 8.9 20 9.9 24.5 9.4 20.5

Boundary Cr ID 11.7 15 12.0 15 13.1 15.8 13.0 15.7

Branch RI 8.8 10 10.0 13 13.3 18.3 13.2 14.0

Linville NC 13.4 21 13.0 15 16.4 25.0 15.0

Sheyenne ND 15.9 11 15.4 6 18.3 14.5 17.6

Fishing Cr NC 17.0 17 12.0 15 19.4 29.3 13.5 17.2

Quinnipiac CT 17.5 39 14.9 13 32.3 11.3 34.0 13.0

Drowning Cr NC 38.8 26 33.9 12 43.4 27.8 36.2 12.7

Shoshone WY 41.8 3 42.9 6 46.8 9.3 45.8 6.3

Uncompahgre CO 35.6 7 39.9 13 50.8 17.5 49.0

Peace FL 49.0 17 48.0 16 55.3 17.3 55.2

Big MO 46.4 23 45.0 15 55.3 27.8 51.5

Middle Oconee GA 49.4 25 33.0 11 57.4 23.3 45.7 14.3

N Br Potomac MD 54.7 29 42.9 14 61.6 28.0 49.0 14.8

Animas CO 54.8 0 60.0 2 62.3 6.8 61.1 2.5

Raritan NJ 54.2 25 46.9 13 67.1 24.3 53.6 13.3

Brandywine PA 61.4 30 55.8 14 67.2 33.0 59.3

Salt AZ 64.6 21 63.0 18 68.7 17.3 6935.0

White VT 75.3 20 75.9 20 85.2 20.8 86.0 21.5

L Tallapoosa AL 72.7 6 57.9 3 88.3 7.0 70.2 3.8

E B Delaware NY 80.8 17 82.0 20 89.7 19.0 91.4 20.5

Big Sunflower MS 89.4 31 82.7 8 91.9 30.3 85.4 13.8

Meramec MO 88.8 17 89.9 18 92.2 16.5 92.7 17.0

Chemung NY 89.7 26 85.7 18 97.5 25.0 92.5 20.5

River Name State

Comparison of CMC Design Flows Comparison of CCC Design Flows
4-6

Table 4-2. (Continued) 

1Q10 % Excur 1-day 3-yr % Excur 7Q10 % Excur 1-day 3-yr % Excur Arkansas CO 107.9 23 115.8 26 126.1 28.0 123.8 26.0

Eagle CO 116.9 9 120.0 11 131.0 17.5 126.0 11.0

Allegash ME 124.5 15 134.0 17 134.1 13.0 138.4

Clinch TN 128.7 23 127.7 17 135.2 25.0 132.2 12.0

Greys WY 122.9 10 1234.8 10 144.5 18.8 135.8 10.0

Cahaba AL 151.9 33 122.8 10 156.4 24.8 149.8 16.0

Kankakee IN 179.0 34 167.6 14 184.3 29.5 174.2 14.0

Bouge Chitto MS 188.6 13 187.5 10 191.6 19.3 189.6 11.0

Hudson NY 207.7 30 170.0 29 211.0 27.8 191.9 24.0

Potomac WV 209.6 19 202.2 14 220.7 15.0 219.6 14.0

Root MN 229.7 7 239.3 7 245.6 10.8 239.7 7.0

Shoal FL 280.1 20 270.5 12 291.4 19.3 286.0 17.0

Amite LA 298.1 19 282.1 14 303.4 14.0 295.5 4.0

Niobrara NE 160.9 4 199.7 8 322.0 11.3 304.3 8.0

Little Pee Dee SC 306.7 15 299.7 12 322.4 15.0 298.9

Brazos TX 311.6 11 277.7 4 344.9 6.8 305.3

Dan VA 329.6 11 321.6 9 387.3 10.3 380.4

French Broad TN 473.6 13 494.3 18 532.2 16.0 535.5

St. Croix WI 505.9 34 477.5 22 536.0 34.5 508.5

Bighorn MT 327.1 12 364.0 14 557.0 16.5 520.2

Beaver PA 571.3 15 539.9 4 594.2 13.3 557.5

N P Clearwater ID 529.2 20 469.6 13 643.6 14.8 613.0

Red AR 691.0 28 537.4 17 769.2 28.8 603.3

Flint GA 207.8 7 2625.0 9 799.8 20.3 731.0

Merrimack MA 270.2 13 284.0 18 929.3 41.8 797.3 19.0

Cowlitz WA 901.5 0 934.7 2 963.7 4.5 959.3 3.0

River Name State

Comparison of CMC Design Flows Comparison of CCC Design Flows
4-7

 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.
5-1

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.
6-1

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.
A-1

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+1)/y] 

m2 = [(n+l)/y] + 1 

 [z] = the largest integer less than or equal to z 

e = (n+l)/y - [(n+l)/y] 

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-2

A sample listing of frequency factors is given in Table A-1. 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+1)/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-3

For the log Pearson Type III method, the frequency factor K 

will be estimated from Table A-1. 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)[1+(.409)(-.840)/5-

(.409)/36)3

-1] 

= -.853 

7Q5 = exp(6.01+(-.853)(.24)) 

 = 331.8 cfs 

The difference in the three estimates of the 7Q5 low flow is less 

than 2 percent. 
A-4

Table A-1. Frequency Factors (K) for the Log Pearson Type III 

Distribution 

Skewness Return Period, Years 

Coefficient 5 10 

3.0 -0.636 -0.660

2.8 -0.666 -0.702

2.6 -0.696 -0.747

2.4 -0.725 -0.795

2.2 -10.752 -0.844

2.0 -0.777 -0.895

1.8 -0.799 -0.945

1.6 -0.817 -0.994

1.4 -0.832 -1.041

1.2 -0.844 -1.086

1.0 -0.852 -1.128

0.8 -0.856 -1.166

0.6 -0.857 -1.200

0.4 -0.855 -1.231

0.2 -0.850 -1.258

0.0 -0.842 -1.282

-0.2 -0.830 -1.301

-0.4 -0.816 -1.317

-0.6 -0.800 -1.328

-0.8 -0.758 -1.336

-1.0 -0.758 -1.340

-1.2 -0.732 -1.340

-1.4 -0.705 -1.337

-1.6 -0.675 -1.329

-1.8 -0.643 -1.318

-2.0 -0.609 -1.302

-2.2 -0.574 -1.284

-2.4 -0.537 -1.262

-2.6 -0.499 -1.238

-2.8 -0.460 -1.210

-3.0 -0.420 -1.180
A-5

Table A-2. Annual 7-Day Low Flows (ft3

/sec) for the Amite River Near 

Denham Springs, LA 

n = 45 

u = 6.0 

s = 0.23 

q = 0.385 

Year Flow Rank Year Flow Rank 

1939 299 5 1962 396 25

1940 338 10 1963 275 1

1941 355 15 1964 392 24

1942 439 30 1965 348 11

1943 371 20 1966 385 22

1944 410 28 1967 335 9

1945 407 27 1968 306 6

1946 508 38 1969 280 3

1947 450 33 1970 354 14

1948 424 29 1971 388 23

1949 574 41 1972 357 17

1950 489 36 1973 499 37

1951 406 26 1974 448 32

1952 291 4 1975 650 45

1953 352 13 1976 356 16

1954 309 7 1977 364 18

1955 322 8 1978 648 44

1956 278 2 1979 619 43

1957 369 19 1980 567 40

1958 483 35 1981 445 31

1959 523 39 1982 349 12

1960 385 21 1983 595 42

1961 474 34
A-6

References 

1. Linsley, R.K., et al. Hydrology for Engineers, 2nd Edition. 

McGraw- Hi11, 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.
B-1

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-1. 
B-2

Table B-1. Design flows and resulting number of excursions using 30-day 

averaging period (all flows in ft3

/sec). 

River Name State Coeff 30Q10 30-day 3-year 

of 

Variation Flow %Excursions Flow %Excursions 

%Diff* 

Quinnipiac CT 1.02 42.3 7.8 46.5 15 9 

Drowning Cr NC 0.8 54.7 8.5 65.5 15 16.5 

Uncompahgre CO 0.86 71 6.9 77.3 14.6 8.2 

Greys WY 1.16 160.7 5.7 166.9 9.9 3.7 

Kankakee IN 0.48 201.8 10 213.6 16.7 5.5 

Hudson NY 1.1 288 13.4 340.7 24.3 13.5 

Shoal FL 0.95 323.5 10.2 339 12.1 4.5 

Little Pee Dee SC 0.94 366.3 7.4 450 11.8 18.6 

St. Croix WI 0.61 571.8 16.2 598.6 21.9 4.5 

Niobrara NE 0.59 613.2 6.4 673.6 8.1 9 

French Broad TN 0.93 636.2 11.9 715.7 20.3 11.1 

Bighorn MT 0.82 913.6 8.1 1103 14.3 17.2 

Flint GA 1 1000 6.4 1097 9.6 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-1. 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-1 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-1 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 

((3O-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-3

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.
C-1

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/Σ (1/F), not as (Σ 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. 

I-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-2

 Z = the allowed number of excursions. 

Part II. Calculation of X-day running averages, i.e., x-day running 

harmonic means. 

II-1. 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+1-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-1. 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-1 provides examples of the counting of excursion days.) 
C-3

Table C-1. Counting excursion days for a specified flow of 100 ft3/sec using 4-day av

Date Daily Flow 4-day 

avg flow 

Is the 4-day average below 100? 

Is the date part of any 4-day avg. that is below 100? 

Date of start of excursion period 

Number of days in excursion period 

Date of start of low flow period 

Numbexcudays low peri

1 130 112.5 No No 2 120 102.5 No No 3 110 97.5 Yes Yes 3 4 3 4 90 102.5 No Yes 5 90 112.5 No Yes 6 100 112.5 No Yes 7 130 102.5 No No 8 150 102.5 No No 9 70 87.5 Yes Yes 9 8 

10 60 90.0 Yea Yes 11 130 102.5 No Yes 12 90 95.0 Yes Yes 13 80 97.5 Yes Yes 14 110 127.5 No Yes 15 100 225.0 No Yes 16 100 >100 No Yes 17 200 >100 No Yes 18 500 >100 No Yes 

The daily flows and four-day average flows for days 19 to 200 are all above 100 ft3/se
C-4

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-5

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 NU = 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)

 (NU-NL) 

Part V. Iterative convergence to the design flow. 

V-1. 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 NU = 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-1, V-2, and V-3 as necessary. 

REFERENCE 

1. Carnahan, B., H.A. Luther, and J.O. Wilkes. 1969. Applied 

numerical methods. Wiley, New York. 

(NU-NL)
D-1

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.
E-1

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 l-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 timeseries 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-2

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-3

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? 
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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 withinyear 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 withinyear 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-5

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-6

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 hydrologicallybased 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 biologicallybased 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-1

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 lowflow 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 
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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-1 (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-3

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-4

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. 
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