Cover.  Photographs of an exposed streambed on the Ipswich River upstream of Rt. 28 in North Reading, Massachusetts, taken

June 17, 1999 by David W. Armstrong, MA-RI Water Science Center, and flooding in Evansville, Indiana, January 2005. Flood photograph

(by Vincent Pugliese, copyright The Evansville Courier and Press) shows U.S. Geological Survey hydrographers preparing to make a

streamflow measurement at the White River at Petersburg streamflow-gaging station.
The National Streamflow Statistics 

Program: A Computer Program for 

Estimating Streamflow Statistics for 

Ungaged Sites

Compiled by Kernell G. Ries III

With sections by J.B. Atkins1, P.R. Hummel, M. Gray2, R. Dusenbury2, 

M.E. Jennings1, W.H. Kirby1, H.C. Riggs1, V.B. Sauer1, and W.O. Thomas, Jr.1

Chapter 6 of 

Book 4, Hydrologic Analysis and Interpretation

Section A, Statistical Analysis



 U.S. Geological Survey.



 Aqua Terra Consultants, Inc.

Techniques and Methods 4-A6

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2007

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment:

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Ries III, K.G., 2007, The national streamflow statistics program: A computer program for estimating streamflow 

statistics for ungaged sites: U.S. Geological Survey Techniques and Methods 4-A6, 37 p.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction

 By K.G. Ries III, W.O. Thomas, Jr., and M.E. Jennings...........................................................................1

Purpose...................................................................................................................................................2

Report Format........................................................................................................................................2

How to Obtain the NSS Software and Documentation ..................................................................2

History and Overview of Methods for Regionalization of Streamflow Statistics

 By K.G. Ries III, and W.O. Thomas, Jr. .....................................................................................................3

Introduction............................................................................................................................................3

Index-Flood Procedures ......................................................................................................................3

Ordinary-Least-Squares Regression.................................................................................................3

Weighted- and Generalized-Least-Squares Regression ...............................................................4

Region-Of-Influence Regression........................................................................................................4

Estimating Techniques for Rural Areas

 By K.G. Ries III, W.O. Thomas, Jr., and J.B. Atkins.................................................................................5

Introduction............................................................................................................................................5

Watershed and Climatic Characteristics..........................................................................................5

Hydrologic Regions...............................................................................................................................6

Measures of Accuracy ........................................................................................................................6

Techniques for Watersheds that Span Regional/State Boundaries ............................................8

Weighting of Independent Estimates of Rural Flood Frequency...................................................8

Weighting for Streamgaging Stations ......................................................................................9

Weighting for Ungaged Sites on Gaged Streams...................................................................9

Urban Flood-Frequency Estimating Techniques

 By V.B. Sauer..............................................................................................................................................10

Introduction..........................................................................................................................................10

Nationwide Urban Flood-Frequency Equations.............................................................................10

Local Urban Flood-Frequency Equations........................................................................................11

Flood Hydrograph Estimation

 By V.B. Sauer..............................................................................................................................................13

Estimation of Extreme Floods

 By W.O. Thomas, Jr., and W.H. Kirby......................................................................................................14

Measures of Extreme Floods ............................................................................................................14

Extrapolation for the 500-Year Flood................................................................................................14

Testing and Validation of Techniques

 By K.G. Ries III............................................................................................................................................16

Applicability and Limitations

 By J.B. Atkins, and K.G. Ries III...............................................................................................................17

Summary of Estimating Techniques

 By K.G. Ries III, H.C. Riggs, and W.O. Thomas, Jr. ...............................................................................18

StreamStats

 By K.G. Ries III............................................................................................................................................18
iv

Acknowledgments.......................................................................................................................................19

References Cited..........................................................................................................................................19

Appendix A. National Streamflow Statistics Program Users’ Manual

By P.R. Hummel, M. Gray, R. Dusenbury, and K.G. Ries III................................................................22

Downloading and Installing the Program .......................................................................................22

Starting the Program..........................................................................................................................23

Main Window ......................................................................................................................................23

Menu Items.................................................................................................................................26

File Menu.....................................................................................................................................26

Graph Menu................................................................................................................................26

Help Menu...................................................................................................................................27

Manual................................................................................................................................27

Web Site .............................................................................................................................27

About...................................................................................................................................27

Edit Scenario Window .......................................................................................................................27

Frequency Window.............................................................................................................................31

Hydrograph Window ..........................................................................................................................32

Weight Window...................................................................................................................................33

Appendix B. Summary of Equations for Estimating Basin Lagtime ....................................................36

Figures

1. Schematic of typical drainage basin shapes and subdivision into basin thirds ..............12

2. Graph showing regional flood-frequency curve for the Fenholloway River at 

Foley, Florida................................................................................................................................15

3. Map of the conterminous United States showing flood-region boundaries ....................16

A-1–24. Screenshots showing—

A-1. View of the National Streamflow Statistics Program start-up window, 

which allows selection of the system of units for input and output, 

specification of a user name, and selection of a project status file ......................23

A-2. The main window of the National Streamflow Statistics Program at start-up.....24

A-3. The main window of the National Streamflow Statistics Program showing 

the State selection scroll-down list.............................................................................25

A-4. The main window of the National Streamflow Statistics Program showing 

results of rural and urban peak-flow computations for an example site in 

Tennessee ........................................................................................................................25

A-5. The Open Status File window of the National Streamflow Statistics Program....26

A-6. The Save Status File window of the National Streamflow Statistics Program ....26

A-7. The Save Report File window of the National Streamflow Statistics Program....26

A-8. Example report file output .............................................................................................27

A-9. The National Streamflow Statistics Program Users’ Manual window showing 

navigation by hierarchical structure ...........................................................................28

A-10. The National Streamflow Statistics Program Users’ Manual window showing 

navigation by use of the index of help topics.............................................................28
Tables

1. Flood-frequency computations for Sucarnoochee River at Livingston, Alabama.............8

A-11. The National Streamflow Statistics Program Users’ Manual window showing 

navigation by use of the search facility ......................................................................29

A-12. The National Streamflow Statistics Program About NSS window.........................29

A-13. The National Streamflow Statistics Program Edit Scenario window showing 

the variables that need to be entered to solve the equation for the selected 

Region 1 ............................................................................................................................29

A-14. The National Streamflow Statistics Program Edit Scenario window showing 

the variables that need to be entered to solve the equations for a site with 

drainage area in both selected Regions 1 and 2 .......................................................30

A-15. The National Streamflow Statistics Program Edit Scenario window showing 

the variables that need to be entered to solve the national urban equations......30

A-16. The National Streamflow Statistics Program Frequency window with a rural 

and an urban scenario selected for plotting ..............................................................31

A-17. The National Streamflow Statistics Program Frequency Plot window showing 

rural and urban frequency plots for a sample site ....................................................31

A-18. The National Streamflow Statistics Program Graph Edit window showing 

the Axes tab on top.........................................................................................................32

A-19. The National Streamflow Statistics Program Font window.....................................33

A-20. The National Streamflow Statistics Program Hydrograph window with a 

recurrence interval of 10 years and rural and urban scenarios selected for 

plotting ..............................................................................................................................33

A-21. The National Streamflow Statistics Program Hydrograph Plot window 

showing rural and urban hydrograph plots for a sample site, with a lagtime 

set a 5 hours for the rural hydrograph and at 4 hours for the urban 

hydrograph.......................................................................................................................34

A-22. The National Streamflow Statistics Program Hydrograph List window 

showing rural and urban hydrograph lists for a sample site...................................34

A-23. The National Streamflow Statistics Program Weight window showing 

weighting for a streamgaging station..........................................................................35

A-24. The National Streamflow Statistics Program Weight window showing 

weighting for an ungaged site ......................................................................................35

Abstract

The National Streamflow Statistics (NSS) Program 

is a computer program that should be useful to engineers, 

hydrologists, and others for planning, management, and design 

applications. NSS compiles all current U.S. Geological Survey 

(USGS) regional regression equations for estimating streamflow statistics at ungaged sites in an easy-to-use interface that 

operates on computers with Microsoft Windows operating systems. NSS expands on the functionality of the USGS National 

Flood Frequency Program, and replaces it.

The regression equations included in NSS are used to 

transfer streamflow statistics from gaged to ungaged sites 

through the use of watershed and climatic characteristics as 

explanatory or predictor variables. Generally, the equations 

were developed on a statewide or metropolitan-area basis as 

part of cooperative study programs. Equations are available 

for estimating rural and urban flood-frequency statistics, such 

as the 100-year flood, for every state, for Puerto Rico, and for 

the island of Tutuila, American Samoa. Equations are available for estimating other statistics, such as the mean annual 

flow, monthly mean flows, flow-duration percentiles, and 

low-flow frequencies (such as the 7-day, 10-year low flow) for 

less than half of the states. All equations available for estimating streamflow statistics other than flood-frequency statistics 

assume rural (non-regulated, non-urbanized) conditions.

The NSS output provides indicators of the accuracy of 

the estimated streamflow statistics. The indicators may include 

any combination of the standard error of estimate, the standard 

error of prediction, the equivalent years of record, or 90-percent prediction intervals, depending on what was provided by 

the authors of the equations.

The program includes several other features that can be 

used only for flood-frequency estimation. These include the 

ability to generate flood-frequency plots, and plots of typical 

flood hydrographs for selected recurrence intervals, estimates 

of the probable maximum flood, extrapolation of the 500-year 

flood when an equation for estimating it is not available, and 

weighting techniques to improve flood-frequency estimates for 

gaging stations and ungaged sites on gaged streams.

This report describes the regionalization techniques used 

to develop the equations in NSS and provides guidance on the 

applicability and limitations of the techniques. The report also 

includes a users’ manual and a summary of equations available 

for estimating basin lagtime, which is needed by the program 

to generate flood hydrographs. The NSS software and accompanying database, and the documentation for the regression 

equations included in NSS, are available on the Web at

http://water.usgs.gov/software/.

Introduction

By K.G. Ries III, W.O. Thomas, Jr., and M.E. Jennings 

Estimates of streamflow statistics, such as the mean flow, 

the 100-year flood, and the 7-day, 10-year low flow, are used 

for a variety of design, planning, and management purposes. 

These estimates are often needed at ungaged sites where no 

observed data are available to calculate the statistics. Regression equations are commonly used for estimating streamflow 

statistics at ungaged sites. Regression equations are developed 

by statistically relating the computed streamflow statistics to 

the physical and climatic characteristics of the watersheds for 

a group of gaging stations that have virtually natural streamflow conditions within a region. Regression equations enable 

the transfer of streamflow statistics from gaging stations to 

ungaged sites simply by determining the watershed and climatic characteristics needed for the ungaged site and solving 

the regression equations based on these input values.

The U.S. Geological Survey (USGS) has been developing regression equations for estimating streamflow statistics 

at ungaged sites since at least the early 1960s. Support and justification for the applicability of these equations for estimating 

flood-peak discharges and frequencies for rural watersheds is 

given in reports by the U.S. Water Resources Council (1981) 

and by Newton and Herrin (1982). These reports summarize 

a test of nine different statistical and deterministic procedures 

The National Streamflow Statistics Program: 

A Computer Program for Estimating Streamflow 

Statistics for Ungaged Sites

Compiled by Kernell G. Ries III
for estimating flood frequencies for rural watersheds. The 

results of this test indicate that USGS-developed regression 

equations are unbiased, reproducible, and easy to apply.

By 1993, reports that contained regression equations 

for estimating flood frequencies for rural, unregulated watersheds had been published by the USGS, at least once, for 

every state and for the Commonwealth of Puerto Rico, and 

reports that contained equations for estimating urban flood 

frequencies were available for metropolitan areas in at least 

13 States. These reports were prepared generally in cooperation with individual state Departments of Transportation, and 

were published either by the USGS or the state Departments 

of Transportation. In addition, a report that contained national 

regression equations for estimating urban flood frequencies 

had been prepared in cooperation with the Federal Highway 

Administration by this time (Sauer and others, 1983).

The USGS, in cooperation with the Federal Highway 

Administration and the Federal Emergency Management 

Agency, compiled all USGS-developed flood-frequency 

regional regression equations available as of September 1993 

in the National Flood Frequency (NFF) Program, version 1.0 

(Jennings and others, 1994). NFF was a MS-DOS computer 

program that provided engineers and hydrologists a practical tool for computing estimates of flood-peak discharges at 

selected recurrence intervals used for planning and design 

applications. NFF also provided the ability to generate floodfrequency and flood hydrograph plots for rural and (or) urban 

peak discharges. Version 2.0 of NFF was released in 1996 by 

the U.S. Forest Service, and added conversion between English and metric units of measure.

In 2002, the USGS released version 3.0 of NFF with a 

user-friendly Microsoft Windows user interface and updated 

flood-peak equations for all or parts of 36 states (Ries and 

Crouse, 2002). Version 3.0 of NFF also added weighting 

techniques to improve flood-frequency estimates for gaging 

stations and ungaged sites on gaged streams.

In addition to developing regression equations for estimating flood-frequency statistics, the USGS has developed 

numerous regression equations for estimating other streamflow statistics. For instance, Ries and Friesz (2000) developed 

equations for estimating flow-duration and low-flow frequency 

statistics for ungaged sites in Massachusetts. In addition, Hortness and Berenbrock (2001) developed equations for estimating monthly and annual mean flow and flow-duration statistics for ungaged sites in Idaho. As with the flood-frequency 

equations, equations for estimating other streamflow statistics 

usually are developed on a state-by-state basis through cooperative agreements between the USGS and local agencies. 

Regression equations for non-flood frequency statistics are 

available for fewer than half of the states.

The NFF Program has been modified to enable estimation 

of any streamflow statistics for which the USGS has developed 

compatible regression equations. Additional modifications to 

the program include the ability to provide region-of-influence 

regression estimates and to calculate prediction intervals for 

the estimated statistics. The software has been renamed the 

National Streamflow Statistics (NSS) Program to better reflect 

its new abilities. The version number, however, has been 

increased from 3.0 for the previous version of NFF to 4.0 for 

this initial release of NSS because NSS is considered to be an 

evolution of NFF.

Purpose

The purpose of this report is to document and describe 

the techniques used to develop the regional regression equations and the other functionality included in the NSS Program. 

The report provides guidance on the applicability and limitations of the techniques, and describes how to obtain and use 

the program. The report also describes how to obtain information needed to solve the regression equations available for 

each of the individual states.

Report Format

The main body of this report provides an overview of 

regionalization methods, summarizes the characteristics of the 

estimating techniques, and describes their applicability and 

limitations. Much of the material was taken verbatim from 

the previous NFF Program reports (Ries and Crouse, 2002; 

Jennings and others, 1994). Additions and revisions have been 

made to the report to describe additions to the capabilities of 

the software and changes in regionalization methods. In addition, a section that summarizes the documentation for state 

flood-frequency techniques is included.

This report contains two appendixes. Appendix A is a 

Users’ Manual that explains in detail how to install and use the 

program. Appendix B is a summary of methods for estimating 

basin lagtime.

Many people contributed to the development of the computer program and this associated documentation. Authors are 

listed for each section of the report.

How to Obtain the NSS Software and 

Documentation

USGS hydrologic analysis software is available for 

electronic retrieval through the World Wide Web (Web) at 

http://water.usgs.gov/software/. This Web page has links to all 

USGS software available for use in hydrologic analysis.

The specific Web page from which the NSS software 

and documentation can be retrieved is http://water.usgs.

gov/software/nss.html. The documentation includes a digital 

copy of this report and information for each State, the Commonwealth of Puerto Rico, and American Samoa that contains 

the applicable regression equations and much of the reference 

information needed to solve them. This information is provided through Web links to Fact Sheets, online reports, and 

pages from the first NFF report (Jennings and others, 1994). 

A help facility also is included with the software.

 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
New equations are developed for several areas of the 

Nation each year. As new equations become available, it is 

planned that the NSS software and documentation will be 

updated to include them. NSS users should check the Web site 

often for updates.

History and Overview of 

Methods for Regionalization 

of Streamflow Statistics

By K.G. Ries III, and W.O. Thomas, Jr.

Introduction

The USGS has been involved in the development of 

regionalization procedures for over 50 years. These regionalization procedures are used to transfer flood statistics, such as 

the 100-year flood-peak discharge, and other statistics, such as 

the mean flow and the 7-day, 10-year low flow, from gaged to 

ungaged sites. The USGS has traditionally used regionalization procedures that relate streamflow statistics to watershed 

and climatic characteristics through the use of correlation or 

regression techniques. Because streamflow statistics may vary 

substantially between regions due to differences in climate, 

topography, and geology, tests of regional homogeneity form 

an integral part of streamflow regionalization procedures.

The evolution of regionalization techniques within 

USGS is described by discussing the following six techniques: 

(1) the index-flood procedure used from the late 1940s to the 

1960s, (2) the ordinary-least-squares regression procedure 

used in the 1970s and 1980s, (3) the weighted- and (4) generalized-least-squares regression procedures, first used in the 

late 1980s and still used today (2005), (5) the region-of-influence procedure, first used in the 1990s, and (6) StreamStats, 

an emerging automated procedure for estimating streamflow 

statistics.

Index-Flood Procedures

The index-flood procedure consisted of two major parts: 

(1) the development of basic, dimensionless frequency curves 

representing the ratio of flood discharges at selected recurrence intervals to an index flood—the mean annual flood, 

and (2) the development of a relation between watershed and 

climatic characteristics and the mean annual flood to enable 

the mean annual flood to be predicted at any point in the 

region. The combination of the mean annual flood with the 

basic frequency curve, expressed as a ratio of the mean annual 

flood, provided a frequency curve for any location (Dalrymple, 

1960).

The determination of the dimensionless frequency curve 

involved: (1) graphical determination of the frequency curve 

for each station using the Weibull plotting position, (2) determination of homogeneous regions using a homogeneity test 

on the slopes of the frequency curves, and (3) computation 

of the regional dimensionless frequency curve based on the 

median flood ratios for each recurrence interval for each station in the region. The homogeneity test used the ratio of the 

10-year flood to the mean annual flood to determine whether 

the differences in slopes of frequency curves for all stations in 

a given region are greater than those attributed to chance. The 

10-year flood discharge was first estimated from the regional 

dimensionless frequency curve. The 95-percent confidence 

interval for the recurrence interval of this discharge, as 

determined from the individual station frequency curves, was 

then determined as a function of record length. If the recurrence interval for a given station was within the 95-percent 

confidence bands, then the station was considered part of the 

homogeneous region. Otherwise, the station was assumed to 

be in another region.

The mean annual flood, as used in the index-flood procedure, was determined from the graphical frequency curve 

to have a recurrence interval of 2.33 years. The mean annual 

flood for an ungaged location was estimated from a relation 

that was determined by relating the mean annual flood at gaging stations to measurable watershed characteristics, such as 

drainage area, area of lakes and swamps, and mean altitude.

The index-flood procedure described above was used to 

develop a nationwide series of flood-frequency reports entitled 

“Magnitude and Frequency of Floods in the United States.” 

Each report provided techniques for estimating flood magnitude and frequency for a major drainage basin or subbasin, 

such as the Lower Mississippi River Basin. These reports were 

published as USGS Water-Supply Papers 1671–1689 during 

the period 1964–68.

Ordinary-Least-Squares Regression

Studies by Benson (1962a, 1962b, 1964) indicated that 

T-year flood-peak discharges could be estimated directly using 

watershed and climatic characteristics based on multipleregression techniques. As noted by Benson (1962a), the 

direct estimation of T-year flood-peak discharges avoided 

the following deficiencies in the index-flood procedure: 

(1) the flood ratios for comparable streams may differ because 

of large differences in the index flood; (2) homogeneity of 

frequency-curve slope can be established at the 10-year level, 

but individual frequency curves commonly show wide and 

sometimes systematic differences at the higher recurrence 

levels; and (3) the slopes of the frequency curves generally 

vary inversely with drainage area. Benson (1962b, 1964) also 

showed that the flood ratios vary not only with drainage area 

but also with main-channel slope and climatic characteristics. 

History and Overview of Methods for Regionalization of Streamflow Statistics 
On the basis of this early work of Benson and later work by 

Thomas and Benson (1970), direct regression on the T-year 

flood using ordinary-least-squares (OLS) techniques became 

the standard approach of the USGS for regionalizing flood 

characteristics in the 1970s. OLS techniques also began to 

be used to estimate low-flow and other streamflow statistics 

beginning in the early 1970s (Lystrom, 1970; Yamanaga, 

1972). In OLS regression, equal weight is given to all stations 

in the analysis, regardless of record length and the possible 

correlation of flood estimates among stations.

The flood-frequency statistics for gaging stations 

included in regional studies generally were computed using 

the guidelines described in Bulletin 15 (U.S. Water Resources 

Council, 1967) or some version of Bulletin 17 of the Hydrology Committee of the U.S. Water Resources Council or the 

U.S. Interagency Advisory Committee on Water Data (U.S. 

Water Resources Council, 1976, 1977, 1981; Interagency 

Advisory Committee on Water Data, 1982). These Bulletins 

prescribe estimating the T-year flood-peak discharges for gaging stations by fitting the Pearson Type III distribution to the 

logarithms of the annual peak discharges. The USGS computer program PEAKFQ applies the Bulletin 17B methods to 

estimate the flood statistics for gaging stations. The program 

and documentation can be downloaded from the Web at 

http://water.usgs.gov/software/peakfq.html.

Low-flow frequency statistics for gaging stations 

included in regional studies generally were estimated by 

fitting the Pearson Type III distribution to the logarithms of 

annual series of n-day mean flows. For instance, the 7-day, 

10-year flow is estimated by fitting annual series of 7-day 

mean flows to the distribution and determining the 7-day mean 

flow that corresponds to the 10-year recurrence interval. The 

USGS computer program SWSTAT can be used to estimate 

low-flow frequency statistics, flow-duration statistics, means, 

minimums, maximums, medians, standard deviations, and 

other statistics for user-selected time periods. The SWSTAT 

Program and documentation can be downloaded from the Web 

at http://water.usgs.gov/software/swstat.html.

Weighted- and Generalized-Least-Squares 

Regression

Research on regionalization of flow characteristics 

beginning in the 1980s centered on accounting for deficiencies 

in the assumptions of OLS regression and on developing 

more accurate and objective tests of regional homogeneity. 

OLS regression procedures do not account for variable errors 

in flow characteristics caused by unequal record lengths at 

gaging stations. Tasker (1980) proposed the use of weightedleast-squares (WLS) regression for flood characteristics 

where the variance of the observed flood characteristics was 

estimated as an inverse function of record length. Tasker and 

Stedinger (1986) used WLS regression to estimate regional 

skew of annual peak discharges with greater accuracy than 

results obtained using OLS regression.

Both OLS and WLS regression do not account for the 

possible correlation of concurrent annual peak-flow records 

between sites. This cross correlation of streamflows causes 

bias in the estimated coefficients of the parameters and in the 

estimated variance of the regression equations. The problem 

may be particularly significant where streamgages are located 

on the same stream, on similar and adjacent watersheds, or 

where streamflow statistics have been determined from a rainfall-runoff model using the same long-term rainfall record.

Generalized-least-squares (GLS) regression was 

proposed by Stedinger and Tasker (1985, 1986) to account 

for both the unequal reliability and the correlation of flood 

characteristics between sites. In a Monte Carlo simulation, 

Stedinger and Tasker (1985) showed that GLS regression 

procedures provided more accurate estimates of regression 

coefficients, better estimates of the accuracy of the regression 

coefficients, and better estimates of the model error than did 

OLS procedures. In addition, Tasker and others (1986) showed 

that GLS procedures provided a smaller average variance of 

prediction than OLS procedures for the regional 100-year 

flood for streams in Pima County, Arizona. Stedinger and 

Tasker (1985) found that the WLS procedure, which accounts 

for differences in record length but neglects cross correlations 

among concurrent flows, performs nearly as well as the 

GLS procedure when the cross correlations are modest (less 

than about 0.3) and (or) when model errors are high (model 

standard errors greater than about 70 percent). Equations 

included in the NSS Program for several of the states are based 

on WLS or GLS regression, although the GLS procedure is 

the more popular of the two techniques. A program named 

GLSNET that implements GLS regression is available on the 

Web at http://water.usgs.gov/software/glsnet.html.

The GLSNET program, and SWSTAT and PEAKFQ 

programs described above, require input data to be in a direct 

access file called a Watershed Data Management (WDM) file. 

Additional software programs are needed to import and export 

(IOWDM) and to manage (ANNIE) data in the WDM format. 

The IOWDM program and documentation can be downloaded 

from the Web at http://water.usgs.gov/software/iowdm.html. 

The ANNIE program and documentation can be downloaded 

from the Web at http://water.usgs.gov/software/annie.html.

Region-Of-Influence Regression

The region-of-influence (ROI) regression procedure was 

first suggested by Acreman and Wiltshire (1987) and was subsequently evaluated by Burn (1990a, 1990b). The procedure 

was first used within the USGS by Tasker and Slade (1994). 

ROI regression determines a new equation each time an 

estimate is desired for a new ungaged site. The new equation 

is determined from a unique subset of streamgaging stations, 

referred to as the region of influence, and comprised of the set 

of stations nearest to the ungaged site, with nearness determined by the similarity of climatic and physical characteristics 

rather than the physical distance between the sites. Once the 

   National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
region of influence is determined for the ungaged site, the 

GLS regression procedure is used to develop the unique set of 

flood-frequency equations for the site. Predictions obtained by 

use of the ROI regression method generally are closer to the 

center of the data used to develop the equation than predictions 

obtained by use of more traditional regression methods. Thus, 

extrapolation errors and problems resulting from assumption 

of linearity are reduced (Ensminger, 1998).

ROI regression is still considered somewhat experimental. Results from studies that have used the procedure (Hodge 

and Tasker (1995) for Arkansas; Lorenz and others (1997) 

for Minnesota; Ensminger (1998) for Louisiana; Asquith and 

Slade (1999) for Texas; Pope and Tasker (1999) for North 

Carolina; Eash (2000) for Iowa; Feaster and Tasker (2002) 

for South Carolina, and Berenbrock (2002) for Idaho) indicate that errors obtained by use of the procedure usually (but 

not always) are lower than errors obtained by use of the GLS 

regression procedure. None of the authors of the studies has 

recommended exclusive use of the ROI regression procedure 

in preference to the GLS regression procedure. Berenbrock 

(2002) recommended that the ROI procedure not be used for 

Idaho because errors for the ROI are larger than those for the 

GLS method in Idaho.

Because ROI computations are mathematically complex, 

computer programs are required to solve the equations. NSS 

contains the algorithms needed to perform the ROI procedure 

for states where the ROI method was developed; however, 

because of the special data requirements for the procedure, 

downloading a special database and separate binary files 

is required for each state. Information for downloading the 

needed files is provided at the NSS Web site at http://water.

usgs.gov/software/nss.html. Alternately, users may choose to 

download custom programs that accompany the reports for 

each of the ROI studies. These reports generally can be located 

through “Publications” links from the individual Web pages 

operated by each USGS Water Science Center. Typically, these 

Web pages have the format http://xx.water.usgs.gov, where xx 

is the 2-letter postal state code. Eash (2000) did not provide a 

computer program to apply the ROI method for Iowa because 

the GLS method usually provided better results and was easier 

for users to apply.

Estimating Techniques for 

Rural Areas

By K.G. Ries III, W.O. Thomas, Jr., and J.B. Atkins

Introduction

The NSS Program provides equations for estimating the 

magnitude and frequency of flood characteristics for rural, 

unregulated watersheds in the 50 states, the Commonwealth 

of Puerto Rico, and American Samoa. NSS also provides 

equations for estimating other streamflow statistics for rural, 

unregulated watersheds in many states. These equations are 

taken from USGS reports that were published between 1973 

and 2005.

The purpose of this section is to provide a brief overview 

of the rural regression equations that are presented in NSS. A 

summary of information needed to solve the regression equations for each state is provided in the section “Summary of 

State Estimating Techniques.”

Watershed and Climatic Characteristics

The rural equations in NSS are based on watershed and 

climatic characteristics that can be obtained from topographic 

maps, aerial photographs, rainfall reports and atlases, or digital 

map data derived from those sources. Drainage area or contributing drainage area appears in nearly all of the statewide rural 

regression equations given in NSS. The other most frequently 

used watershed and climatic characteristics are main-channel 

slope and mean annual precipitation. The regression equations 

are generally reported in the following form:

The dependent and independent variables usually are 

transformed to logarithms before regression analysis is done to 

assure that regression residuals (differences between regression and station (observed) estimates of streamflow statistics) 

are normally distributed. In instances where a variable could 

equal zero (such as percentage of drainage area covered by 

Estimating Techniques for Rural Areas 
lakes and ponds), a constant is added to the variable before 

taking the logarithms. Drainage area is the only explanatory 

variable in the peak-flow regression equations for several 

states, but it is more common to have up to four explanatory 

variables in the equations. The USGS has published peakflow regression equations in many states based on channelgeometry characteristics, such as channel width; however, 

these equations are not provided in NSS because a site visit is 

required to obtain the explanatory variables.

Different names and symbols are often given to the same 

basin and climatic characteristics in reports that describe the 

regression equations for different states. For example, there are 

10 different names in NSS for one of the most commonly used 

characteristics—the precipitation amount that occurs during 

24 hours, on average, once in 2 years. In addition, main-channel slope is also referred to as channel slope or streambed 

slope, and is identified by symbols such as S, SL, Sc, Sb, 

and Sm. All of these symbols represent the slope between 

two points on the main channel, 85 percent and 10 percent of 

the channel length upstream from the streamgaging station 

or outlet of the watershed. NSS uses the names given to the 

characteristics in the original state reports to avoid differences 

between the program and the state documentation.

Source data (maps, aerial photographs, atlases, 

Geographic Information System (GIS) data layers, and 

graphical relations) used to measure the characteristics may 

vary from state to state, although the name used may be 

the same. It is important to use the same source data and 

methods to measure the characteristics for input to NSS as 

those that were used to develop the regression equations. Use 

of different source data and methods will result in estimates 

of streamflow statistics with unknown errors. In most cases, 

the data sources were the best available topographic maps or 

digital representations of the features on those maps. In some 

cases, digital map data used in the studies are available from 

the authors of the state reports.

Percentages, such as the percentage of the watershed 

in forests or lakes and ponds (when not determined by use 

of a GIS) are generally determined by a grid-sampling 

method using 20–80 points in the watershed. A transparent 

grid is overlain on the outline of the watershed on the most 

appropriate topographic map. The grid should have from 

20–80 nodes within the respective watershed boundary, the 

number of nodes overlying green (forest) or blue (lakes and 

ponds) is determined, and the percentage of forest or lakes and 

ponds is computed as the number of node intersections (with 

green or blue) divided by the total nodes within the watershed. 

Mean basin elevation is also generally determined by the same 

grid-sampling method averaging elevations for 20–80 points 

in the watershed. The documentation for the individual states 

commonly contains maps of variables, such as mean annual 

precipitation, the 2-year 24-hour rainfall, average annual 

snowfall, and minimum mean January temperature.

Hydrologic Regions

Most reports that contain regression equations for 

estimating streamflow statistics have a statewide geographic 

extent. For most of the studies described in these reports, the 

analysts divided their states into multiple hydrologic regions 

that represent areas of relatively homogeneous streamflow 

characteristics. The regions were usually determined by 

using major watershed boundaries and an analysis of the 

areal distribution of the regression residuals (differences 

between regression estimates of the streamflow statistics for 

the streamgaging stations used in the analysis and estimates 

determined from the available data for the stations). Analysis 

of the residuals is done to identify regions of residuals whose 

magnitude and algebraic sign were similar within and dissimilar between regions. Hydrologic regions were also defined 

by the mean elevation of the watershed in some states. These 

procedures for determining hydrologic region boundaries 

generally improve the accuracy of the estimating technique, 

but they are somewhat subjective. Statistical tests, such as the 

Wilcoxon signed-rank test, usually were used to determine 

if the streamflow statistics were statistically different among 

regions. More objective procedures for defining regions are 

beginning to be used, such as kriging, cluster analysis, and 

discriminant analysis.

On average, there are about four hydrologic regions per 

state; however, some states have inadequate data to define 

streamflow relations in some regions. For example, Florida, 

Georgia, and South Carolina have regions of undefined flood 

frequency, and regression equations are provided only for the 

island of Oahu, Hawaii. Regression equations for estimating 

flood-peak discharges for the other islands were computed as 

part of a nationwide network analysis (Yamanaga, 1972), but 

those equations are not included in NSS because that study did 

not focus specifically on flood-frequency analysis. Flood-peak 

regression equations are provided only for the island of Tutuila, American Samoa. Idaho and Massachusetts have regions 

where both floods and low flows are undefined. Hydrologic 

regions for floods and low flows are the same in some states 

but different in others.

Measures of Accuracy

Estimates obtained from regression equations have a 

related degree of uncertainty that can be described by various measures of accuracy. Every USGS report that contains 

regional regression equations provides some measure of the 

accuracy of the equations.

Accuracy varies from site to site depending on the values 

of the explanatory variables (basin and climatic characteristics) for the sites. Estimates for sites with values of explanatory variables that are closer to the average values for the 

stations used in the regression analyses have greater accuracy 

than estimates for sites with values of explanatory variables 

that are far from the average values.

 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
The average standard error of estimate, usually in percent, was used as the primary measure of accuracy in many of 

the reports that are more than about 15 years old. The average 

standard error of estimate is a measure of the average variation 

between the regression estimates and estimates derived from 

the station data for those stations used to develop the regression equations. About two-thirds of the regression estimates 

for the gaging stations used in the regression analyses have 

errors less than the average standard error of estimate. About 

one-third of the estimates have errors larger than the average 

standard error of estimate.

The average standard error of prediction, usually in 

percent, is used as the primary measure of accuracy in many 

recent reports. It is preferred over use of the average standard error of estimate because the average standard error of 

prediction is a measure of the average accuracy of the regression equations when predicting values for ungaged sites—the 

condition under which regression equations are most often 

applied. The average standard error of prediction is usually a 

few percent larger than the average standard error of estimate. 

About two-thirds of the regression estimates for ungaged sites 

will have errors less than the average standard errors of prediction given for the equations. NSS provides standard errors of 

estimate only when the standard errors of prediction were not 

provided in the individual statewide reports.

The average standard errors of estimate or prediction 

range from 30–60 percent for most of the flood-peak equations, though some equations have average standard errors 

near 15 percent, and some equations have standard errors 

greater than 100 percent. The smallest flood-peak standard 

errors generally are for equations developed for the eastern 

part of the Nation, whereas the largest standard errors generally are for flood-peak equations developed for the western 

and southwestern parts of the Nation. Errors generally are 

largest in the west and southwest because at-site variability of 

the flood records is greater, the network of unregulated gaging stations is less dense, and the flood records are generally 

shorter there than in other areas. In addition, regionalization 

generally is more difficult in the west and southwest than 

elsewhere because local climate and hydrology are sensitive to 

the larger variations in relief and aspect that are present in the 

west and southwest. In addition, the relation between natural 

streamflow and drainage area changes seasonally in much of 

this area, where streamflow often decreases with increasing 

drainage area as a result of high losses to evaporation, transpiration, and infiltration of water from streams to the ground.

No other streamflow statistics have equations that are 

available nationally, as is the case for flood-peak statistics. 

Because of this, errors associated with other streamflow 

statistics are difficult to analyze from a national perspective; 

however, regional conditions that favor or inhibit the accuracy 

of flood-peak estimates typically have similar effects on other 

streamflow statistics.

Previous versions of NFF did not distinguish between 

standard errors of estimation and prediction in the output, where they were given under a single heading named 

“Standard error, %.” When possible, NSS now distinguishes 

between standard errors of estimation and prediction in the 

output. Standard errors of estimation are given under a heading named “Estimation error, %,” and prediction errors are 

given under a heading named “Prediction error, %.” When 

the type of error was not specified in the report, the “Standard 

error, %” heading is given.

The equivalent years of record is another measure of 

accuracy that is available in NSS for many flood-frequency 

regression equations. Equivalent years of record is defined 

as the number of years of actual streamflow record needed to 

achieve the same accuracy as the regional regression equations. This accuracy measure is related to the average standard 

error of prediction of the regression equations, the recurrence 

interval, and the average variance and skew of the annual peak 

flows at the gaging stations used in the analysis (Hardison, 

1971).

Several reports published since the late 1980s for regional 

regression studies have contained information needed to calculate prediction intervals for estimates of streamflow statistics 

for individual sites. Prediction intervals indicate the probability that the true flow for a site is within the given bounds 

of flow. For example, the 90-percent prediction interval for a 

flow estimate at a site indicates that there is 90 percent confidence that the true flow for the site is between the given 

flow values.

Calculation of prediction intervals is complex. Authors of 

individual reports that describe methods for computing prediction intervals usually provide computer programs that can be 

used to compute the intervals. For example, Hodgkins (1999) 

describes methods for computing prediction intervals for 

flood-frequency estimates for ungaged sites in Maine, and he 

provides a computer program that can be used to compute the 

estimates and prediction intervals. NSS contains an algorithm 

described by Tasker and Driver (1988) that can be used to 

compute 90-percent prediction intervals for sites when report 

authors have provided documentation for computing them.

When estimates of streamflow statistics are determined 

from regression equations for an ungaged site with basin 

characteristics that are outside the ranges of the basin 

characteristics for the gaging stations used to develop the 

equations, the estimates are said to be extrapolated. The 

accuracies of extrapolated estimates are unknown. NSS 

allows extrapolations to be done, but users should carefully 

consider the possible consequences for using such estimates 

for planning and design purposes. The applicable ranges of 

basin characteristics used to develop the equations are listed 

in the reports from which the equations are taken, and they are 

also shown in the NSS user interface. NSS warns users when 

they have entered an explanatory variable that is outside an 

applicable range and asks them if they want to proceed. NSS 

also provides a warning in the output for these cases. Measures 

of accuracy are not provided for extrapolated estimates.

Estimating Techniques for Rural Areas 
Techniques for Watersheds that Span 

Regional/State Boundaries

NSS can estimate streamflow statistics for basins that 

span more than one hydrologic region within the same state. 

This is accomplished on the basis of percentage of drainage 

area in each region. The user should verify that the resultant 

estimates reflect the streamflow characteristics of the regions 

by consulting the respective state report, and in the case of 

flood-frequency statistics, by examining plots of the computed 

frequency curves.

When an ungaged site has drainage area in two or 

more regions, the NSS report shows the estimates from each 

individual region as well as the final area-weighted averaged 

estimates. The error measures provided for the area-weighted 

averaged estimates are calculated by area weighting of the 

error measures for the individual regions. If the estimates for 

any region are extrapolated, the error measures are not shown 

in the output for the averaged estimates. In these cases, users 

should consider whether to use the non-extrapolated regional 

estimates in preference to the averaged estimates.

Regional estimates for watersheds that span state 

boundaries may give different results depending on which 

state’s equations are used. NSS is not able to weight the 

computations by drainage area for basins that cross state 

boundaries. Because of this limitation, the user must perform 

this procedure manually, which can be accomplished by 

applying NSS for each state using the basin’s full drainage 

area. Next, the user must manually weight the estimates based 

on the percentage of the basin’s drainage area in each state. 

For example, two sets of flood-frequency computations were 

obtained for the Sucarnoochee River at Livingston, Alabama; 

320 square miles of the basin’s total area of 606 square miles 

are in Mississippi, and 286 square miles of the basin are in 

Alabama. Table 1 shows the frequency computations using the 

full drainage area in the application of each state’s equation 

and the weighted frequency computations.

The weighted flood-frequency computations were 

obtained by using the following equation:

where

QT(MS) and QT(AL) are the computed T-year peak discharges, 

in cubic feet per second, using the 

Mississippi and Alabama regression 

equations, respectively; and

QT(w) is the weighted T-year peak discharge, in 

cubic feet per second.

Differences between the Mississippi and the Alabama 

estimates are substantial. For example, the 100-year flood 

discharge for the Sucarnoochee River would be about 

63,800 cubic feet per second if the basin was entirely within 

Mississippi, but only about 43,400 cubic feet per second if the 

basin was entirely within Alabama. The weighted estimate for 

the site, obtained from the equation above, is 55,200 cubic feet 

per second.

Weighting of Independent Estimates of 

Rural Flood Frequency

Tasker (1975) demonstrated that if two independent 

estimates of a streamflow statistic are available, a properly 

weighted average of the independent estimates will 

provide an estimate that is more accurate than either of the 

independent estimates. NSS includes weighting algorithms 

that can produce improved flood-frequency estimates for 

streamgaging stations and ungaged sites. Improved floodfrequency estimates are determined for streamgaging stations 

by weighting regression-derived estimates with estimates 

determined from the systematic peak-flow record at the 

station. Improved estimates are determined for ungaged 

sites by weighting the regression-derived flood-frequency 

estimates for an ungaged site with estimates determined 

based on the flow per unit area of an upstream or downstream 

streamgaging station. The weighting equations provided in the 

following sections could, in theory, be used for many types 

of streamflow statistics, but weighting can only be done for 

flood-frequency statistics in NSS.

Some researchers have recommended different weighting 

methods in reports that describe the flood-frequency regression equations for individual states. Before using the weighting algorithms in NSS, users should refer to the state reports to 

determine if different weighting methods are recommended.

Table 1. Flood-frequency computations for Sucarnoochee River 

at Livingston, Alabama.

[Q, discharge; (ft3/s), cubic feet per second]

Recurrence 

interval

(years)

Computed 

peak Q in 

Mississippi

(ft3/s)

Computed 

peak Q in 

Alabama

(ft3/s)

Weighted 

frequency 

estimates

(ft3/s)

2 16,000 8,750 12,600

5 27,900 15,400 22,000

10 36,100 20,700 28,800

25 47,400 28,800 38,600

50 58,200 35,700 47,600

100 63,800 43,400 55,200

200 74500 51,500 63,600

500 85,700 64,100 75,500

 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Weighting for Streamgaging Stations

NSS includes the weighting procedure for streamgaging 

stations presented by the Interagency Advisory Committee on 

Water Data (1982), which combines flood-frequency estimates 

determined from log-Pearson type III analysis of the systematic annual peaks for a streamgaging station with estimates 

obtained for the station from regression equations. Weighting is based on the years of record for the estimates obtained 

from the station records and on the equivalent years of record 

for the regression estimates. If the two different estimates are 

assumed to be independent, weighted flood-frequency estimates can be computed as:

The accuracy of the weighted estimate, in equivalent 

years of record, is equal to the N + EQ. No other indicators 

of accuracy are available for these weighted estimates. 

NSS cannot compute weighted estimates for streamgaging 

stations if the equivalent years of record are not available for 

the regression equations. In these cases, if NSS is used to 

calculate weighted estimates, the results will be identical to 

the estimates from the systematic flood peaks.

Weighting for Ungaged Sites on Gaged Streams

NSS includes the weighting procedure presented by 

Guimaraes and Bohman (1992) and Stamey and Hess (1993) 

to improve flood-frequency estimates for a rural ungaged 

site with a drainage area that is between 0.5 and 1.5 times 

the drainage area of a streamgaging station that is on the 

same stream. To obtain a weighted peak-flow estimate QT for 

recurrence interval T at the ungaged site (QT(U)w), the NSS 

program must first be used to create a scenario of weighted 

flow estimates for an upstream or downstream gaging station. 

The weighted gaging station estimate (QT(G)w) is then used 

to obtain an estimate for the ungaged site that is based on the 

flow per unit area at the gaging station (QT(U)g) by use of the 

equation:

NSS applies the appropriate b values automatically. The 

weighted estimate for the ungaged site (QT(U)w) is then computed as:

The weighting algorithm gives full weight to the regression estimates when the drainage area for the gaging station is 

less than 0.5 or greater than 1.5 times the drainage area for the 

ungaged site and increasing weight to the gaging station-based 

estimates as the drainage area ratio approaches 1. The weighting procedure should not be applied when the drainage area is 

less than 0.5 or greater than 1.5.

NSS computes the equivalent years of record for the 

weighted estimates for an ungaged site, EQT(U)w. It first computes the equivalent years of record for the weighted estimate 

of peak discharge at the streamgaging station, EQT(U)g by substituting the weighted equivalent years of record computed by 

NFF for QT(G)w into the equation above. It then inserts EQT(U)g

for QT(U)g and the equivalent years of record from the regression equations, EQT(U)g, for QT(U)g into the first equation in 

this section to compute EQT(U)w. No other indicators of accuracy are available for these estimates. In theory, the standard 

errors for these estimates should be at least as small as those 

for the estimates derived from the regression equations alone.

Estimating Techniques for Rural Areas 
Urban Flood-Frequency 

Estimating Techniques

By V.B. Sauer

Introduction

The NSS Program provides equations for estimating the 

magnitude and recurrence intervals for floods in urbanized 

areas throughout the conterminous United States and Hawaii. 

The seven-parameter nationwide equations described in USGS 

Water-Supply Paper (WSP) 2207 (Sauer and others, 1983), 

are based on urban runoff data from 199 basins in 56 cities 

and 31 states. These equations have been thoroughly tested 

and proven to give reasonable estimates for floods having 

recurrence intervals between 2 and 500 years. A later study by 

Sauer (1985) of urban data at 78 additional sites in the southeastern United States verified the seven-parameter equations 

as unbiased and having standard errors equal to or better than 

those reported in WSP 2207.

Additional equations for urban areas in some states have 

been included in the NSS program as optional methods to 

estimate and compare urban flood frequency. These equations 

were developed for local use within their designated urban 

area and should not be used for other urban areas.

Nationwide Urban Flood-Frequency Equations

The following seven-parameter equations and definitions 

are excerpted from Sauer and others (1983). The equations are 

based on multiple regression analysis of urban flood-frequency 

data from 199 urbanized basins,

UQ2 = 2.35 A.41 SL.17 (RI2+3)2.04 (ST+8)-.65

(13-BDF)-.32 IA.15 RQ2.47

standard error of estimate is 38 percent

UQ5 = 2.70 A.35 SL.16 (RI2+3)1.86 (ST+8)-.59

(13-BDF)-.31 IA.11 RQ5.54

standard error of estimate is 37 percent

UQ10 = 2.99 A.32 SL.15 (RI2+3)1.75 (ST+8)-.57

(13-BDF)-.30 IA.09 RQ10.58

standard error of estimate is 38 percent

UQ25 = 2.78 A.31 SL.15 (RI2+3)1.76 (ST+8)-.55

(13-BDF)-.29 IA.07 RQ25.60

standard error of estimate is 40 percent

UQ50 = 2.67 A.29 SL.15 (RI2+3)1.74 (ST+8)-.53

(13-BDF)-.28 IA.06 RQ50.62

standard error of estimate is 42 percent

UQ100 = 2.50 A.29 SL.15 (RI2+3)1.76 (ST+8)-.52

(13-BDF)-.28 IA.06 RQ100.63

standard error of estimate is 44 percent

UQ500 = 2.27 A.29 SL.16 (RI2+3)1.86 (ST+8)-.54

(13-BDF)-.27 IA.05 RQ500.63

standard error of estimate is 49 percent

where

UQ2, UQ5,...UQ500 are the urban peak discharges, in cubic 

feet per second, for the 2-, 5-, ... 500-year recurrence intervals;

A is the contributing drainage area, in square 

miles, as determined from the best available 

topographic maps; in urban areas, drainage systems sometimes cross topographic divides. Such 

drainage changes should be accounted for when 

computing A;

SL is the main channel slope, in feet per mile 

(ft/mi), measured between points that are 

10 percent and 85 percent of the main channel 

length upstream from the study site (for sites 

where SL is greater than 70 ft/mi, 70 ft/mi is 

used in the equations);

RI2 is the rainfall, in inches, for the 2-hour, 2-year 

recurrence interval, determined from U.S. 

Weather Bureau Technical Paper 40 (1961) 

(eastern United States), or from National 

Oceanic and Atmospheric Administration Atlas 

2 (Miller and others, 1973) (western United 

States);

ST is basin storage, the percentage of the drainage 

basin occupied by lakes, reservoirs, swamps, 

and wetlands; in-channel storage of a temporary nature, resulting from detention ponds or 

roadway embankments, should not be included 

in the computation of ST;

BDF is the basin development factor, an index of the 

prevalence of the urban drainage improvements;

IA is the percentage of the drainage basin occupied 

by impervious surfaces, such as houses, buildings, streets, and parking lots; and

RQT are the peak discharges, in cubic feet per second, for an equivalent rural drainage basin in the 

same hydrologic area as the urban basin, for a 

recurrence interval of T years; equivalent rural 

peak discharges are computed from the rural 

equations for the appropriate state, in the NSS 

program, and are automatically transferred to 

the urban computations.

10 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
The basin development factor (BDF) is a highly 

significant variable in the equations, and provides a measure 

of the efficiency of the drainage basin. It can easily be 

determined from drainage maps and field inspections of the 

drainage basin. The basin is first divided into upper, middle, 

and lower thirds on a drainage map, as shown in figures 1A–C. 

Each third should contain about one-third of the contributing 

drainage area, and stream lengths of two or more streams 

should be approximately the same in each third. Stream 

lengths of different thirds, however, can be different. For 

instance, in figure 1C, the stream distances of the lower third 

are all about equal, but are longer than those in the middle 

third. Precise definition of the basin thirds is not considered 

necessary because it will not have much effect on the final 

value of BDF. Therefore, the boundaries between basin thirds 

can be drawn by eye without precise measurements.

Within each third of the basin, four characteristics of the 

drainage system must be evaluated and assigned a code of 0 

or 1. Summation of the 12 codes (four codes in each third of 

the basin) yields the BDF. The following guidelines should not 

be considered as requiring precise measurements. A certain 

amount of subjectivity will necessarily be involved, and field 

checking should be performed to obtain the best estimates.

Channel improvements.—If channel improvements 

such as straightening, enlarging, deepening, and 

clearing are prevalent for the main drainage channels 

and principal tributaries (those that drain directly 

into the main channel), then a code of 1 is assigned. 

To be considered prevalent, at least 50 percent of 

the main drainage channels and principal tributaries 

must be improved to some degree over natural conditions. If channel improvements are not prevalent, 

then a code of 0 is assigned.

Channel linings.—If more than 50 percent of the 

length of the main channels and principal tributaries has been lined with an impervious surface, such 

as concrete, then a code of 1 is assigned to this 

characteristic; otherwise, a code of 0 is assigned. 

The presence of channel linings would obviously 

indicate the presence of channel improvements as 

well. Therefore, this is an added factor and indicates 

a more highly developed drainage system.

Storm drains or storm sewers.—Storm drains are 

defined as those enclosed drainage structures (usually pipes), commonly used on the secondary tributaries where the drainage is received directly from 

streets or parking lots. Many of these drains empty 

into open channels; however, in some basins they 

empty into channels enclosed as box and pipe culverts. Where more than 50 percent of the secondary 

tributaries within a subarea (third) consists of storm 

drains, then a code of 1 is assigned to this aspect; 

otherwise, a code of 0 is assigned.

.

.

3.

Curb-and-gutter streets.—If more than 50 percent 

of the subarea (third) is urbanized (covered with 

residential, commercial, and/or industrial development), and if more than 50 percent of the streets 

and highways in the subarea are constructed with 

curbs and gutters, then a code of 1 is assigned to this 

aspect; otherwise, a code of 0 is assigned. Drainage 

from curb- and-gutter streets commonly empties into 

storm drains.

Estimates of urban flood-frequency values should not 

be made using the seven-parameter equations under certain 

conditions. For instance, the equations should not be used for 

basins where flow is controlled by reservoirs, or where detention storage is used to reduce flood peaks. The equations also 

should not be used if the rural equations for the region of interest contain independent variables, such as basin development 

factor, percentage of impervious area, percentage of urban 

development, or an urbanization index. Though classified in 

NSS as rural equations, estimates obtained from equations that 

contain these types of variables already reflect the effects of 

urbanization.

The urban equations should not be used if any of the 

values of the seven parameters are outside the range of values 

used in the original regression study (except for SL, which 

is limited to 70 ft/mi). These ranges are provided in the NSS 

Program, and the user is warned by the program anytime a 

variable value exceeds the range. The program will compute 

urban estimates even though a parameter may be outside the 

range; however, the standard error of estimate may be greater 

than the value given for each equation.

Local Urban Flood-Frequency Equations

The NSS Program includes additional equations for some 

cities and metropolitan areas that were developed for local 

use in those designated areas only. These local urban equations can be used in lieu of the nationwide urban equations, 

or they can be used for comparative purposes. It would be 

highly coincidental for the local equations and the nationwide 

equations to give identical results. Therefore, the user should 

compare results of the two (or more) sets of urban equations, 

and compare the urban results to the equivalent rural results. 

Ultimately, it is the user’s decision as to which urban results 

to use.

The local urban equations are described in the individual 

summaries of state flood-frequency techniques for states that 

use the same equations as those that appeared in the previous version of NSS. The local urban equations are described 

in Fact Sheets for states that have updated either their rural 

or urban equations since the previous version of NSS was 

released (Jennings and others, 1994). In addition, some of 

the rural reports contain estimation techniques for urban 

watersheds. Several of the rural reports suggest the use of the 

nationwide equations given by Sauer and others (1983) and 

described above.

4.

Urban Flood-Frequency Estimating Techniques 11
Figure 1. Schematic of typical drainage basin shapes and subdivision into basin thirds. (Note that streamchannel distances within any given third of a basin in the examples are approximately equal, but between basin 

thirds the distances are not equal, to compensate for the relative basin width of the thirds.) (from Jennings and 

others, 1994).

12  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Flood Hydrograph Estimation

By V.B. Sauer

The NSS Program contains a procedure for computing 

a typical hydrograph that represents average runoff for a 

specified peak discharge. It should be emphasized that this is 

an average hydrograph, and is not necessarily representative 

of any particular rainfall distribution. The average, or typical, 

hydrograph could be considered a design hydrograph for some 

applications.

The procedure used in NSS to compute the average 

hydrograph is known as the dimensionless-hydrograph 

method. Stricker and Sauer (1982) developed the method for 

urban basins using theoretical techniques. Inman (1987) used 

actual streamflow data for both urban and rural streams in 

Georgia, and confirmed the theoretical, dimensionless hydrograph developed by Stricker and Sauer. Other investigators 

have since developed similar dimensionless hydrographs for 

numerous other states (Sauer, 1989). Except in some relatively 

flat-topography, slow-runoff areas, the same dimensionless 

hydrograph seems to apply with reasonable accuracy. The 

dimensionless-hydrograph approach, however, is not applicable to snowmelt runoff or for estimating more complex 

double-peaked hydrographs.

The dimensionless-hydrograph method has three essential parts: (1) the peak discharge for which a hydrograph 

is desired, (2) the basin lagtime, and (3) the dimensionlesshydrograph ordinates. In order to compute the average, or 

design hydrograph using the NSS procedures, the user selects 

the peak discharge from the NSS frequency output. The user 

must also provide an estimate of the basin lagtime. The NSS 

Program then computes the hydrograph using the dimensionless ordinates of the hydrograph developed by Inman (1987), 

which are stored in the program.

Basin lagtime (LT) is defined as the elapsed time, in 

hours, from the center of mass of rainfall excess to the center 

of mass of the resultant runoff hydrograph. This is the most 

difficult estimate to make for the hydrograph computations. 

For rural basins, the user must make an estimate of lagtime, 

independent of the NSS Program, because there are no lagtime 

equations currently available in NSS for rural watersheds. 

However, Sauer (1989) summarized basin lagtime equations 

that have been developed for rural and urban watersheds in 

several states. The following statewide equations computed for 

rural Georgia streams by Inman (1987) are an example:

Appendix B provides a summary of equations for estimating basin lagtime as given by Sauer (1989), in addition to a 

few other known studies.

The following generalized equation was developed by 

Sauer and others (1983) for urban basins for use on a nationwide basis:

The standard error for the above lagtime equation is plus 

or minus 61 percent, based on regression analysis for 170 stations on a nationwide basis. For urban basins, the user has a 

choice of using the nationwide lagtime equation given above, 

or inputting an independent estimate of lagtime.

Flood Hydrograph Estimation 13
Estimation of Extreme Floods

By W.O. Thomas, Jr., and W.H. Kirby

Measures of Extreme Floods

Very large or extreme floods can be characterized in several ways. Some examples are the Probable Maximum Flood 

(PMF), envelope curve values based on maximum observed 

floods (Crippen and Bue, 1977; Crippen, 1982), and probabilistic floods, such as the 500-year flood, which has only a 

0.2 percent chance of being exceeded in any given year.

The PMF is defined as the most severe flood that is 

considered reasonably possible at a site as a result of hydrologic and meteorologic conditions (Cudworth, 1989; Hansen 

and others, 1982). The estimation of the PMF involves three 

steps: (1) determination of the Probable Maximum Precipitation (PMP) from reports published by the National Weather 

Service (e.g., Hansen and others, 1982), (2) determination 

of infiltration and other losses, and (3) the conversion of the 

excess precipitation to runoff. In step (2), it is general practice 

to assume that an antecedent storm of sufficient magnitude has 

reduced water losses, such as interception, evaporation, and 

surface depression storage, to negligible levels. In step (3), the 

conversion of precipitation excess to runoff is accomplished 

by one of a number of techniques or models ranging from 

detailed watershed models to a less detailed unit-hydrograph 

approach. Most Federal construction and regulatory agencies 

use the less detailed unit-hydrograph approach that is based on 

the principle of linear superposition of hydrographs as originally described by Sherman (1932).

The words “probable” and “likely” in the definition of 

the PMF and PMP do not refer to any specific quantitative 

measures of probability or likelihood of occurrence. Moreover, 

an interagency work group of the Hydrology Subcommittee 

of the Interagency Advisory Committee on Water Data 

decided “It is not within the state of the art to calculate the 

probability of PMF-scale floods within definable confidence 

or error bounds” (Interagency Advisory Committee on Water 

Data, 1986).

The definition of another type of large or extreme flood is 

based on the maximum observed flood for a given size watershed. Crippen and Bue (1977) and Crippen (1982) developed 

flood-envelope curves by plotting the maximum known flood 

discharges against drainage area for 17 flood regions of the 

conterminous United States. These flood-envelope curves 

approximate the maximum flood-peak discharge that has been 

regionally experienced for a given size watershed. Like the 

PMF, these flood-envelope values do not have an associated 

probability of exceedance.

In general, the largest flood having a defined probability 

of exceedance that is used for planning, management, and 

design is the 500-year flood. This flood discharge has a 

0.2 percent chance of being exceeded in any given year or, 

stated another way, will be exceeded at intervals of time 

averaging 500 years in length. The 500-year flood is the 

most extreme flood discharge computed in flood-frequency 

programs of the USGS (Kirby, 1981) and the U.S. Army 

Corps of Engineers (1982) that implement Federal Interagency 

Bulletin 17B guidelines for flood frequency (Interagency 

Advisory Committee on Water Data, 1982). These two 

computer programs are the ones most frequently used by the 

hydrologic community.

Estimates of 500-year flood discharges are used in 

defining flood plains for the flood insurance studies of the 

Federal Emergency Management Agency (FEMA), as well 

as by the National Park Service for defining flood plains 

in National Parks. Flood-plain boundaries based on the 

500-year flood are used mostly for planning purposes to 

identify areas that would be inundated by an extreme flood. 

Prompted by a number of bridge failures beginning in the 

late 1980s that resulted from excessive scour, the Federal 

Highway Administration (FHWA) has developed procedures 

for evaluating scour at bridges. As part of this program, the 

FHWA advised the state Departments of Transportation 

nationwide to evaluate the risk of their bridges being subjected 

to scour damage during floods on the order of 100- to 500-

year or greater average return periods. Therefore, there is a 

defined need for estimates of flood discharges having return 

periods on the order of 500 years.

Extrapolation for the 500-Year Flood

Before 1989, USGS policy prohibited publication of 

at-site estimates of the 500-year flood and regional regression equations for estimating the 500-year flood at ungaged 

sites. Therefore, only USGS statewide reports published since 

1989 contain regression equations or at-site estimates for the 

500-year flood. A procedure is given in the NSS Program for 

extrapolating the regional regression equations in any state 

to the 500-year flood. The extrapolation procedure basically 

consists of fitting a log-Pearson Type III curve to the 2- to 

100-year flood discharges given by NSS and extrapolating this 

curve to the 500-year flood discharge. The procedure consists 

of the following steps for a given watershed.

Determine the flood-peak discharges for selected 

return periods from the appropriate regional regression equations given in NSS. At least three points are 

needed to define the skew coefficient required in a 

subsequent step. Use of additional points improves 

the definition of the frequency curve that is defined 

by the regional equations, and helps to average 

out any minor irregularities that may exist in the 

relations among the regional equations. The NSS 

program uses all available regional equations for 

selected return periods to define the frequency curve.

.

14 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Fit a quadratic curve to the selected points on logprobability paper using least-squares regression 

computations. The variables used in the regression 

computations are the logarithms of the selected discharges and the standard normal deviates associated 

with the corresponding probabilities. The purpose 

of this quadratic curve is to obtain a smooth curve 

through the selected flood-peak discharges from 

step 1 above. The quadratic curve is an approximation of the log-Pearson Type III curve that will be 

computed.

Determine the skew coefficient of the log-Pearson 

Type III frequency curve that passes through the 2-, 

10-, and 100-year floods defined by the quadratic 

curve. The skew coefficient is defined approximately 

by the formula (Interagency Advisory Committee on 

Water Data, 1982):

Replot (conceptually) the selected discharges and 

return periods using a Pearson Type III probability 

scale defined such that a frequency curve with the 

computed skew plots as a straight line. This scale is 

defined by plotting probability values p at positions 

x on the probability axis, where x is defined by the 

standardized Pearson Type III deviate (K values) for 

the given skew and probability. A Wilson-Hilferty 

approximation (Kirby, 1972) is used to compute the 

K value.

Fit a straight line by least-squares regression to the 

points plotted in step 4, and extrapolate this line to 

the 500-year flood-peak discharge. The variables 

used in the least-squares computation are the logarithms of the selected discharges and the Pearson 

Type III K values associated with the corresponding 

probabilities.

An example of a flood-frequency curve computed by 

this procedure for the Fenholloway River at Foley, Florida is 

shown in figure 2. The solid triangles are the regional floodfrequency values as estimated by the equations given by 

Bridges (1982), which are incorporated in the NSS Program. 

The 500-year value, shown as a solid circle (12,800 cubic feet 

per second), is estimated using the extrapolation procedure 

described above. Note that the extrapolated 500-year value 

is a reasonable extension (see dashed line) of the regional 

frequency curve.

The solid triangle (fig. 2) (11,500 cubic feet per second) 

for the 500-year value is the regional value as obtained directly 

from the 500-year equation given in Bridges (1982). The 500-

year flood for the Fenholloway River can be estimated without 

extrapolation since Florida is one of the states for which 500-

year regression equations have been published. The difference 

.

3.

4.

5.

between the two 500-year values is 11.3 percent. This is 

typical of several comparisons of extrapolated 500-year floods 

to published regional equations made by Jennings and others 

(1994), which mostly agree within plus or minus 15 percent.

For comparison with and evaluation of extrapolated 

500-year flood values, the NSS Program can display the maximum flood-envelope curve values given by Crippen and Bue 

(1977) and Crippen (1982). Because there is no frequency of 

occurrence associated with envelope-curve estimates, the comparison of these values to the extrapolated 500-year floods is 

merely a qualitative evaluation. In general, one would expect 

the extrapolated 500-year flood-peak discharges to be less than 

the envelope-curve values, assuming that several watersheds in 

a given region have experienced at least one flood exceeding 

the 500-year value during the period of data collection. For 

the Fenholloway River at Foley, Florida, estimates of the 500-

year flood range from 11,500 to 12,800 cubic feet per second. 

The envelope-curve value from Crippen and Bue (1977) and 

Crippen (1982) is 101,000 cubic feet per second given that 

the watershed is in Region 3 as defined by Crippen and Bue 

(1977) and Crippen (1982). A map of the conterminous 

United States showing the flood-region boundaries (fig. 3) 

from Crippen and Bue (1977) can be displayed within NSS so 

the user can determine the appropriate flood region for a site 

of interest.

Figure 2. Regional flood-frequency curve for the Fenholloway 

River at Foley, Florida (from Jennings and others, 1994).

Estimation of Extreme Floods 15
Testing and Validation of 

Techniques

By K.G. Ries III

The algorithms in the original version of the NFF 

Program were tested extensively before the initial release of 

the software. Flood-frequency estimates were obtained using 

NFF for three to five gaged sites from each hydrologic region 

in each state, using watershed and climatic data obtained for 

the sites from published flood-frequency reports or provided 

by local USGS Water Science Centers. These estimates were 

compared to the published regional regression-equation estimates for the sites to confirm the reliability of the software. 

Particular emphasis was placed on testing the accuracy of the 

500-year extrapolation procedure described in the previous 

section of this report. The testing process indicated that the 

extrapolation procedure for the 500-year flood was reasonable 

and gave estimates similar to those based on station data and 

regional equations developed by regression analysis. Jennings 

and others (1994) described the tests and results in detail.

Although the operating environment changed from MSDOS for the initial version of the software to MS Windows for 

NFF version 3.0, most of the underlying algorithms did not 

change. There also were few changes to the basic algorithms 

with this new update to NSS version 4.0. As a result, rigorous 

testing before releasing the present version was done only for 

the algorithms that were changed. Emphasis was placed on 

assuring that the equations for each region in each state were 

correct, and that estimates obtained from NSS for tested gaged 

sites agreed with the regional regression-equation estimates for 

the sites that were published in the state reports. At least one 

test was made of the equations for each region in each state. 

These tests were done primarily by personnel from the USGS 

offices in which the state reports originated.

Figure 3. Map of the conterminous United States showing flood-region boundaries (modified from Crippen 

and Bue, 1977).

16  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Applicability and Limitations

By J.B. Atkins, and K.G. Ries III

The regression equations in the NSS Program are 

applicable and representative of the data used to derive them. 

Because the user of NSS is responsible for the assessment 

and interpretation of the computed results, the following 

limitations of NSS should be observed.

Estimates from the regression equations in NSS 

reflect natural flow conditions. The estimates do not 

account for the effects of water diversions, dams, 

flood-detention structures, and other manmade 

works. The equations can be used to obtain estimates 

of natural flow conditions on streams that do not 

have natural flows. The equations should not be used 

to obtain estimates of streamflow statistics under 

existing conditions if the streams do not have natural 

flows. Users should carefully assess the degree to 

which flows may be modified at their selected sites. 

A flood-retention reservoir on a stream may have 

a large effect on peak flows but no effect on low 

flows. Likewise, a diversion of a few million gallons 

per day may have a large effect on low flows but an 

insignificant effect on peak flows.

The rural flood-frequency equations and all equations for estimating other types of streamflow 

statistics in NSS can be used to obtain estimates of 

natural flow conditions on urbanized streams. The 

equations should not be used to obtain estimates of 

existing streamflow statistics on urbanized streams 

unless the equations contain independent variables, 

such as basin development factor, percentage of 

impervious area, percentage of urban development, 

or an urbanization index that accounts for the effects 

of urbanization. NSS users should refer to the reports 

that document the equations to determine the extent 

of regulations, diversions, or urbanization that is 

allowable for use of the rural equations.

The user is cautioned that the magnitude of the true 

standard errors of estimates for ungaged sites will be 

larger than the reported average standard errors if the 

equations in NSS are used to estimate flood magnitudes for streams with explanatory variables near 

the ranges identified in NSS. The errors for ungaged 

sites with explanatory variables beyond the ranges 

identified in NSS are unknown.

Drainage area must always be determined because 

NSS requires a value. Although a hydrologic region 

may not include drainage area as a variable in the 

prediction equation to compute a frequency curve, 

.

.

3.

4.

NSS requires the use of a watershed’s drainage area 

for other computations, such as determining the 

maximum flood-envelope discharge from Crippen 

and Bue (1977) and (or) Crippen (1982), and weighting of flood-frequency curves for watersheds in more 

than one region. 

Flood-frequency curves for watersheds contained 

in more than one region cannot be computed if the 

regions involved do not have corresponding T-year 

equations. Failure to observe this limitation of NSS 

will lead to erroneous results. Frequency curves are 

weighted by the percentage of drainage area in each 

region within a given state. No provision is provided 

in the software for weighting frequency curves for 

watersheds in different states.

In some instances, the maximum flood-envelope 

value might be less than some T-year computed peak 

discharges for a given watershed. The T-year peak 

discharge is the discharge that will be exceeded as 

an annual maximum peak discharge, on average, 

every T years. The user should carefully determine 

which maximum flood region contains the watershed 

being analyzed (fig. 3), and is encouraged to consult 

Crippen and Bue (1977) and (or) Crippen (1982) for 

guidance and interpretation.

The NSS Program allows the weighting of the logarithms of the estimated and observed peak discharges 

for streamgaging stations using the equivalent years 

of record of the regression estimate and the number 

of years of observed record as the weighting factors. 

If NSS has determined the 500-year flood for the site 

of interest by extrapolation, then the equivalent years 

of record of the 100-year regression equation and the 

extrapolated 500-year flood are used in the weighting calculation. If the equivalent years of record are 

not available for the 2- through 200-year floods, NSS 

cannot compute weighted estimates, and it uses the 

observed peak discharges as the final estimates.

The NSS Program allows the weighting of regression estimates for ungaged sites with estimates based 

on the flow per unit area of an upstream or downstream streamgaging station to determine improved 

estimates for the ungaged site. The drainage area for 

the ungaged site should be within 0.5 and 1.5 times 

the drainage area for the streamgaging station; otherwise, only the regression estimates should be used.

Some hydrologic regions do not have prediction 

equations for peak discharges as large as or larger 

than the 100-year peak discharge. The user is 

responsible for the assessment and interpretation 

of any interpolated or any extrapolated T-year peak 

discharges. Examination of plots of the frequency 

curves computed by NSS is highly desirable.

5.

6.

7.

8.

9.

Applicability and Limitations 17
Hydrographs of flood flows, computed by procedures in NSS, are not applicable to watersheds 

where flood hydrographs are typically derived from 

snowmelt runoff, or to watersheds that typically 

exhibit double-peaked hydrographs. Furthermore, 

the flood-hydrograph estimation procedure might 

not be applicable to watersheds in the semi-arid/arid 

regions of the Nation because the procedure is based 

on data from Georgia (Inman, 1987).

Summary of Estimating 

Techniques

By K.G. Ries III, H.C. Riggs, and W.O. Thomas, Jr.

Full documentation of the equations and information necessary to solve them is provided in the individual reports for 

each state. Many of the state reports are available for download from the Web. In addition, USGS Fact Sheets are available that summarize the flood-frequency reports for 20 states 

with new or corrected equations developed since the release of 

NFF version 1.0. Summaries of the equations for estimating 

flood flows from the original NFF report (Jennings and others, 

1994) are available online for the states that have not developed new equations since the release of NFF version 1.0. 

The NSS Web site (http://water.usgs.gov/software/nss.

html) provides links to the online reports, the Fact Sheets, 

and the state summaries that document the equations in NSS. 

These sites will be updated as new equations become available. Specific documentation on the state equations is not 

provided in this report because several new sets of equations 

are developed each year, and the documentation would quickly 

become obsolete. It is recommended that users check the NSS 

Web site periodically to determine if new equations have been 

developed for areas of interest to them. Users should obtain an 

updated version of the database and new documentation when 

new equations are available.

Figures and maps needed to determine the input variables 

are included in the Fact Sheets and state summaries when they 

could be easily digitized, though often they are of smaller 

scale than the maps provided in the statewide flood-frequency 

reports. In some cases, the user will need to consult the 

original reports to obtain some of the input variables for the 

regression equations. StreamStats should be used to measure 

the input variables and solve the regression equations for areas 

where it is implemented.

The regression equations are provided in the same format 

in the Fact Sheets and summaries as in the original reports. 

In the application of these equations, it is often necessary to 

add constants to input variables that might equal zero. These 

constants are not always shown in the equations. The user 

0. should enter the actual value of the variable and the necessary 

constants will be applied in the computer program.

Brief descriptions of each variable used in the regression 

equations are provided in the documentation. It is assumed 

that the user is knowledgeable with regard to determination of 

many of the routine watershed characteristics, such as drainage 

area and channel length, from topographic maps. The applicable range of all variables is given in the NSS Program so the 

user will know if estimates are being made outside the range 

of data used in developing the regression equations. Users 

should exercise caution when extrapolating the flood estimates 

beyond the data used to develop the equations.

StreamStats

By K.G. Ries III

The USGS has developed a Web application named 

StreamStats that automates the process of computing streamflow statistics for ungaged sites and provides previously 

computed streamflow statistics for USGS data-collection 

stations. StreamStats provides a map-based user interface that 

appears in a Web-browser window. Users can obtain estimates 

of streamflow statistics for ungaged sites by clicking on site 

locations in the interface. A GIS program determines boundaries of the drainage basins for the ungaged sites, measures the 

physical characteristics of the drainage basins, and inserts the 

characteristics into the NSS program to solve the regression 

equations that estimate the streamflow statistics for the sites, 

which appear in a pop-up Web browser window. This process 

for measuring the basin characteristics is much faster, more 

accurate, and more consistent than previous manual methods. 

Users also can obtain previously published streamflow statistics and other information for USGS data-collection stations 

by clicking on station locations in the user interface.

Because of the ease of use and accuracy of the results, 

StreamStats should be used to obtain estimates for sites 

located in areas where the application is available. A map 

on the StreamStats Web page at http://streamstats.usgs.

gov/ shows the states where the application is available and 

provides a link to the application and documentation of the 

regression equations for each state. The StreamStats Web site 

also provides a description of the application, user instructions, definitions of terms, answers to frequently asked questions, a description of limitations, links to presentations, and 

contact information. A Fact Sheet on StreamStats (Ries and 

others, 2004) is available on the Web at http://md.water.usgs.

gov/publications/fs-2004-3115/.

StreamStats currently does not incorporate all of the 

functionality of NSS, such as the ability to generate floodfrequency plots and flood hydrographs, and to analyze the 

sensitivity of the estimates to changes in basin characteristics. 

18  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Users can insert the basin characteristics measured by StreamStats into the NSS Program to take advantage of its additional 

functionality. It also should be noted that StreamStats cannot 

be used to obtain flood-peak estimates for urban streams using 

the national urban equations described previously in this report 

because the basin development factor used as an independent 

variable in those equations cannot be measured by a GIS.

It is a goal of the USGS to eventually have StreamStats 

implemented throughout the Nation. Implementation for individual states usually requires cooperative funding agreements 

between the USGS and one or more Federal, State, or local 

agencies, whereby the other agency or agencies pay for at least 

half of the implementation cost. Because of this reliance on 

funding from other agencies, full national implementation may 

take several years.

Acknowledgments

NSS was developed by Aqua Terra Consultants, Inc., 

through a contract with the USGS. Craig Perl, previously 

of the USGS, populated much of the NSS database. Robert 

Mason, of the USGS Office of Surface Water, and several 

hydrologists from the USGS Washington Water Science Center coauthored many of the USGS Fact Sheets that describe 

the regression equations. Scientists from the Mississippi and 

Washington USGS Water Science Centers created many of the 

graphics used in this report and in the supporting Fact Sheets. 

Hydrologists from each Water Science Center verified results 

from NSS for their respective states. The Publication Staff 

at the Maryland-Delaware-D.C. and New Hampshire USGS 

Water Science Centers provided illustrations, layout, and editorial review for this report.

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Sauer, V.B., 1989, Dimensionless hydrograph method of 

simulating flood hydrographs: National Research Council, 

Transportation Research Board, Transportation Research 

Record 1224, p. 67–78.

Sauer, V.B., Thomas, W.O., Jr., Stricker, V.A., and Wilson, 

K.V., 1983, Flood characteristics of urban watersheds in the 

United States: U.S. Geological Survey Water-Supply Paper 

2207, 63 p.

Sherman, L.K., 1932, The relation of hydrographs of runoff to 

size and character of drainage basins: Transactions of the 

American Geophysical Union, p. 332–339.

20 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Stamey, T.C., and Hess, G.W., 1993, Techniques for estimating magnitude and frequency of floods in rural basins of 

Georgia: U.S. Geological Survey Water-Resources Investigations Report 93–4002, 75 p.

Stedinger, J.R., and Tasker, G.D., 1985, Regional hydrologic analysis—ordinary, weighted, and generalized least 

squares compared: Water Resources Research, v. 21, no. 9, 

p. 1,421–1,432.

Stedinger, J.R., and Tasker, G.D., 1986, Regional hydrologic 

analysis 2, model-error estimators, estimation of sigma 

and log-Pearson type 3 distributions: Water Resources 

Research, v. 22, no. 10, p. 1,487–1,499.

Stricker, V.A., and Sauer, V.B., 1982, Techniques for estimating flood hydrographs for ungaged urban watersheds: U.S. 

Geological Survey Open-File Report 82–365, 24 p.

Tasker, G.D., 1975, Combining estimates of low-flow characteristics of streams in Massachusetts and Rhode Island: 

U.S. Geological Survey Journal of Research, vol. 3, no. 1, 

January–February 1975, p. 107–112.

Tasker, G.D., 1980, Hydrologic regression with weighted 

least squares: Water Resources Research, v. 16, no. 6, 

p. 1,107–1,113.

Tasker, G.D., and Driver, N.E., 1988, Nationwide regression 

models for predicting urban runoff water quality at unmonitored sites: Water Resources Bulletin, v. 24, no. 5, 

p. 1,091–1,101.

Tasker, G.D., Eychaner, J.H., and Stedinger, J.R., 1986, Application of generalized least squares in regional hydrologic 

regression analysis, in Selected Papers in the Hydrologic 

Sciences 1986, U.S. Geological Survey Water-Supply Paper 

2310, p. 107–115.

Tasker, G.D., and Slade, R.M., 1994, An interactive regional 

regression approach to estimating flood quantiles: in

Fontane, D.G., and Tuvel, H.N., Water policy and management: solving problems: American Society of Civil 

Engineers, Proceedings of the 21st Annual Conference of 

the Water Resources Planning and Management Division, 

p. 782–785.

Tasker, G.D., and Stedinger, J.R., 1986, Regional skew with 

weighted LS regression: American Society of Civil Engineers Journal of Water Resources Planning and Management, v. 112, no. 2, p. 225–237.

Thomas, D.M., and Benson, M.A., 1970, Generalization 

of streamflow characteristics from drain­age-basin characteristics: U.S. Geological Survey Water-Supply Paper 1975, 

55 p.

U.S. Army Corps of Engineers, 1982, Generalized computer 

program 723-X6-L7550 flood flow frequency analysis, 

user’s manual: Davis, California, The Hydrologic Engineering Center.

U.S. Water Resources Council, 1967, A uniform technique for 

determining flood flow frequencies: U.S. Water Resources 

Council, Hydrology Committee, Bulletin 15, [variously 

paged].

U.S. Water Resources Council, 1976, Guidelines for determining flood flow frequency: U.S. Water Resources Council, 

Hydrology Committee, Bulletin 17A, [variously paged].

U.S. Water Resources Council, 1977, Guidelines for determining flood flow frequency: U.S. Water Resources Council, 

Hydrology Committee, Bulletin 17A, [variously paged].

U.S. Water Resources Council, 1981, Guidelines for determining flood flow frequency: U.S. Water Resources Council, 

Hydrology Committee, Bulletin 17B, [variously paged].

U.S. Weather Bureau, 1961, Rainfall frequency atlas of the 

United States: U.S. Department of Commerce Technical 

Paper no. 40, 61 p.

Yamanaga, G., 1972, Evaluation of the streamflow-data program in Hawaii: U.S. Geological Survey Open-File Report 

72–0453, 37 p., 5 sheets.

References Cited  21
Version 4.0 of the National Streamflow Statistics (NSS) 

computer program solves regression equations for estimating 

T-year flood-peak discharges for rural and urban watersheds 

throughout the United States, and it solves regression equations for other types of streamflow statistics that are available 

in many areas of the Nation. The program also provides methods for (1) plotting flood-frequency curves, (2) estimating a 

typical flood hydrograph corresponding to a given T-year peak 

discharge, (3) weighting flood-peak estimates obtained from 

regression equations for streamgaging stations with estimates 

computed from the annual peak flows at the stations, and 

(4) weighting flood-peak estimates obtained from regression 

equations for ungaged sites with estimates obtained by applying the peak flow per unit area for an upstream or downstream 

gaging station to the ungaged site.

The NSS computer program has four components—

a user interface, a calculation routine, a Microsoft Access 

database, and a help facility. The NSS user interface allows 

users to control the operation of the software and presents 

results. The calculation routine calculates streamflow statistics 

using basin and climatic characteristics entered by the user 

and provides tabling and graphing capabilities. The Access 

database contains the regression coefficients, standard errors, 

and other information, for more than 2,000 multiple regression 

equations. The help facility contains an electronic copy of this 

report, a link to the NSS Web page, and version information. 

The NSS Program is written in the Visual Basic programming 

language.

This users’ manual provides instructions for downloading, installing, and using NSS. The provided instructions 

assume a general basic knowledge of the Windows operating 

systems. In the discussion that follows, the names of windows 

that appear on the users’ desktop are shown in italics, and the 

names of text boxes, menu items, and command buttons are 

shown in bold.

Downloading and Installing the Program

NSS can be run on a variety of personal computers (PCs). 

It requires a computer running Windows 98/NT version 4.0 or 

higher with service pack 5 or higher. For optimal performance, 

a processor running at 400 megahertz or faster with at least 

64 megabytes (Mb) of memory is recommended. A VGA or 

better color monitor also is recommended.

NSS can be downloaded from the Web at http://water.

usgs.gov/software/nss.html. Users will need to download at 

least two files— NSSv4.exe, which contains the NSS Setup 

Wizard and the NSS computer program (about 8 Mb), and 

NSSv4_YYYY-MM-DD.mdb, which is the database (about 

14 Mb), where YYYY is the year, MM is the month, and DD 

is the day of the most recent release. To download and install 

NSS by either facility, users should follow these steps:

Double click with the left mouse button on the 

file names or icons for the files shown in the Web 

browser window.

Specify a directory and save both files to the localhard drive.

Locate NSSv4.exe on the hard drive using Windows 

Explorer or My Computer.

Double click with the left mouse button on the file 

name (NSSv4.exe) to start the NSS Setup Wizard.

Click on the Next button in the Setup Wizard Welcome window.

At the prompt, specify the directory in which NSS 

will be installed. A default path name, C:\Program 

Files\NSS, will be displayed, and is recommended. 

Alternately, the user can browse to select a different 

directory or type in the path name.

.

.

3.

4.

5.

6.

Appendix A. National Streamflow Statistics Program Users’ 

Manual

By P.R. Hummel2, M. Gray2, R. Dusenbury2, and K.G. Ries III1

1

 U.S. Geological Survey, Baltimore, Maryland.

2

 Aqua Terra Consultants, Inc.

22  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
At the prompt, select the Start menu folder in which 

to place the program’s shortcut. The default folder 

name is USGS. It is suggested that this folder name 

be used if other USGS software is or will be installed 

on the user’s PC. If not, the user may wish to name 

the folder NSS or to select another folder that is 

already available.

Choose whether or not to create a desktop icon for 

the program.

Click on the Install button.

When the Wizard provides notification that the 

installation is complete, click on the Finish button to 

close the Wizard.

Copy the NSSv4_YYYY-MM-DD.mdb file to the 

NSS directory. (The default location is C:\Program 

Files\NSS).

When installation is complete, start NSS to assure 

that the installation was successful and the program 

works.

If NSS works correctly, delete the downloaded file, 

NSSv4.exe, from its original saved location.

For basic installation, the NSS directory should contain 

seven files: (1) current.nss, which is a text file that contains 

instructions provided to NSS by the user during the previous 

and current sessions, (2 and 3) unin000.dat and unins000.

exe, which are used to uninstall the program, (4) NSS.exe, 

which is the executable program file, (5) NSS.chm, which 

is the help facility, (6) NSSv4_YYYY-MM-DD.mdb, which 

is the database, and (7) ATCoRend.mdb, which is an Access 

database of colors used for graphics. To run NSS, double 

click on NSS.exe in Windows Explorer or My Computer. 

Alternately, the program may be started by clicking on the 

NSS entry in the Start menu, or if an icon has been created on 

the computer desktop, by double-clicking on the icon. To run 

the help facility, double click on NSS.chm. The help facility 

may also be started by clicking on the Manual menu item of 

the Help menu in the NSS user interface. To uninstall NSS, 

double click on unins0000.exe.

Region-Of-Influence (ROI) regression is available for 

use in estimating peak-flow statistics for several states. If 

users want to obtain ROI estimates for a state, they must 

download one or two binary files of data needed to run ROI 

for each individual state. These files can be downloaded from 

the above-mentioned Web and FTP sites. The file names 

are formatted as SS.ttt.bin, where SS is the 2-letter postal 

abbreviation for the state; ttt is the data type, rec, or rho; and 

bin indicates the file has a binary format. Most states have 

two binary files, and users must download both files to obtain 

ROI estimates.

7.

8.

9.

0.

.

.

3.

Figure A-1. View of the National Streamflow Statistics 

Program start-up window, which allows selection of the 

system of units for input and output, specification of a 

user name, and selection of a project status file.

Starting the Program

NSS can be started by double-clicking on the desktop 

icon, if one was created during installation, by clicking on the 

NSS listing in the Start menu (by default under USGS), or by 

double-clicking on NSS.exe in the NSS directory. Starting the 

program will cause a small NSS window to appear. Buttons 

in this window allow the user to choose whether English or 

Metric units will be used during the session (fig. A-1). If users 

enter their name in the User text box, their name will be

included in any reports generated during the session.

The Project text box specifies the path and file name to 

a project status file, which saves the selections made during a 

previous session of NSS. The default status file name is current.nss, which is saved in the root directory of the application. 

This file will reset the user selections to those made during the 

most recent session of NSS. Alternatively, the user may type 

in a pathname or click on the Browse button to locate a different status file that was saved during an older session of NSS. 

Once the desired entries have been made in the NSS startup 

window, press the Run button to begin the session. Clicking 

on the Quit button will terminate the session.

Main Window

After the Run button is pressed in the NSS startup 

window, that window will disappear and the National Streamflow Statistics Program (NSS) main window will appear. This 

window (fig. A-2) features pull-down menus, small input text 

boxes, two large frames with large text boxes for display of 

input parameters and output, and several command buttons.

Appendix A  23
Figure A-2. The main window of the National Streamflow Statistics Program at start-up.

The File, Graph, and Help pull-down menus are at the 

top left of the main window. These menus provide additional 

utilities to the user, and are described later. Directly below 

the pull-down menus are a pair of boxes that allow the user 

to select the state in which the site of interest is located, and 

to name the site. A state must be chosen before estimates can 

be obtained. Selection is accomplished by clicking on the 

downward-pointing arrow at the right side of the State box. 

Clicking will cause a list of state names to appear along with 

a scroll bar at the right of the list that allows moving to a state 

of interest (fig. A-3). Clicking on an individual state will cause 

its name to appear in the box. Alternately, users may type the 

first letter of the state name to select their state of interest. 

When more than one state has the same first letter, typing the 

first letter again will advance to the next one in alphabetical 

order. When selecting a new state, any results from the current state will be cleared, so care should be taken to save any 

desired results before selecting a new state.

Use of the Site Name text box is optional. If a name is 

entered in the box, the name will appear in saved reports for 

the site. If no name is entered, the site name “Unnamed” will 

be used by default.

Two large frames, one for rural estimates and the other 

for urban estimates, fill the center of the main window. A box 

at the top left of each frame shows the name of the current scenario (a scenario is a set of input parameters and estimates for 

a site). To the right of the boxes are the New, Edit, and Delete

buttons that allow the user to create, edit, or delete scenarios, 

respectively. When multiple scenarios have been created for a 

selected state, the scenarios can be selected from the scrolldown list for viewing, editing, and deleting.

Below the buttons are a pair of text boxes. The top 

box shows input parameters used to evaluate the regression 

equations for the selected rural or urban scenario (fig. A-4). 

The bottom box shows the output. The first column lists the 

recurrence intervals for peak-flow estimates or the names of 

the statistics for other statistic types. The second column lists 

the estimated flows. Ensuing columns list whatever measures 

of the accuracy of the estimates are available. These always 

include the average standard errors of estimate or prediction, and may include 90-percent prediction intervals or the 

equivalent years of record, or both. When both rural and urban 

estimates have been computed, input and output for both types 

of estimates are shown at the same time.

When a rural or urban scenario has been computed, the 

physical characteristics used as explanatory variables in the 

computation are displayed in the top text box and the computed flow statistics and error indicators associated with the 

24 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Figure A-3. The main window of the National Streamflow Statistics Program showing the State selection scrolldown list.

Figure A-4. The main window of the National Streamflow Statistics Program showing results of rural and urban 

peak-flow computations for an example site in Tennessee.

Appendix A  25
estimates are displayed in the bottom text box. When both 

types of estimates (rural or urban) have been computed, both 

sets of estimates are displayed at the same time.

The Frequency Plot, Hydrograph, and Weight command buttons at the bottom of the main window work only for 

peak-flow scenarios. The Frequency Plot and Hydrograph

buttons can be used to create the indicated types of graphs. 

The Weight button at the bottom of the main window can be 

used to obtain improved estimates for streamgaging stations 

and ungaged sites. The plotting and weighting functions are 

described in separate sections.

Menu Items

The File, Graph, and Help menus at the top left of the 

main window provide additional utilities to the user. The 

menus are accessed by clicking on their titles. The menu items 

that appear can be selected by clicking on them.

File Menu

The File menu has four options: Open, Save As..., 

Report, and Exit. Selecting the Open, Save As..., and 

Report menu items causes a file dialogue form to appear that 

allows users to browse their PC, select, and name files. Clicking on the Open command button in the Open Status File window causes the selected file to be used. Clicking on the Save

command button in the Save Status File or the Save Report

window causes the selected file to be saved. Clicking on the 

Cancel command button in any of these windows causes no 

changes to be made.

The Open option allows users to open an NSS status 

file, which contains information on results of previous work 

(fig. A-5).

The Save As... option allows the user to save work in a 

new status file (fig. A-6).

The Report option is used to create reports that can be 

saved and printed (fig. A-7).

The Exit option lets the user exit the program.

Reports are saved as text files. An example report is 

shown in figure A-8 for an ungaged site in Tennessee for 

which both rural and urban estimates have been obtained.

The Exit option lets the user exit the program. The state 

of the system will be saved to the default status file name, 

current.NSS.

Graph Menu

The Graph menu allows users to create flood-frequency 

plots and flood hydrographs. These functions are duplicated 

by the Frequency Plot and Hydrograph command buttons 

at the bottom of the NSS main window. The functions are 

discussed in the Frequency Plots and Hydrographs sections.

Figure A-5. The Open Status File window of the National 

Streamflow Statistics Program.

Figure A-6. The Save Status File window of the National 

Streamflow Statistics Program.

Figure A-7. The Save Report File window of the National 

Streamflow Statistics Program.

26  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Help Menu

The Help menu contains three items: Manual, Web 

Site, and About. The Manual item is used to bring up a 

window for accessing the NSS help file. The Web Site item 

provides access to the NSS Web site. The About item provides 

information about the NSS program.

Manual

The NSS help file contains all of the information in this 

report. The user can move through the help file by navigating 

the hierarchical structure (fig. A-9), by navigating the index of 

help topics (fig. A-10), or by use of the search facility 

(fig. A-11).

To navigate the help file using the hierarchical structure, 

click on the Contents tab to bring it to the front in the left 

frame of the window. When this is done, the headings from 

this report will appear in the frame. Double-click on a heading 

to make the information for that heading appear in the right 

frame of the window.

To navigate the help file using the index of help topics, 

click on the Index tab to bring it to the front in the left frame 

of the window. When this is done, an alphabetical list of subjects will be displayed in the frame. Double-click on any of the 

subjects to make the information for that subject appear in the 

right frame of the window.

To navigate the Help file using the search facility, click 

on the Search tab to bring it to the front in the left frame of 

the window. When this is done, a text box will appear in which 

the user can type in the keyword to be used for searching. 

After the keyword is typed in, the user should click on the List 

Topics command button directly below the text box. This will 

cause a list of topics to appear in the frame below the button. 

Double-click on a topic to make information for the topic 

appear in the right frame of the window. The keywords will be 

highlighted in blue in the right frame.

Web Site

Clicking on the Web Site item allows users to access the 

NSS Web site, which contains a brief description of NSS, links 

for downloading the software and database, and links to the 

documentation, including documentation for the individual 

states. An Internet connection must be available to connect to 

the Web site. Users should access the Web site often to check 

whether an updated version of the database is available for 

downloading.

About

Clicking on the About item causes a small window to 

open that displays the version information for the program 

(fig. A-12). Clicking the System info... command button 

causes the Microsoft System Information window to appear. 

This window allows users to obtain information on the availability and configuration of hardware and software installed on 

their PCs. Clicking on OK closes the window.

Edit Scenario Window

When a rural or urban New button is pressed in the NSS 

main window, the Edit Scenario window opens (fig. A-13). 

A name for the scenario can be specified in the Scenario text 

box. If a name is not specified, NSS will name the scenario 

“Rural X,” where X is one more than the previous number of 

rural scenarios that have been created.

Available regions are listed in the Regions box on the 

left side of the window. When a region is selected by clicking 

on a region name or number in the Regions box, the variables 

for that region appear in the table to the right. Note that the 

variables in the Edit Scenario window will vary depending on 

the state and region selected.

Values for each variable are entered in the data entry 

boxes to the right of the variable names. Values that are not yet 

entered or are outside the recommended range for a variable 

are highlighted in yellow. When values within the recommended range are entered, the yellow highlighting is removed. 

The recommended range for the current variable is displayed 

beneath the table of values.

Figure A-8. Example report file output.

Appendix A  27
Figure A-9. The National Streamflow Statistics Program Users’ Manual window showing navigation by 

hierarchical structure.

Figure A-10. The National Streamflow Statistics Program Users’ Manual window showing navigation by use of the 

index of help topics.

28  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Figure A-11. The National Streamflow Statistics Program Users’ Manual window showing navigation by 

use of the search facility.

Figure A-12. The National 

Streamflow Statistics Program 

About NSS window.

Figure A-13. The National 

Streamflow Statistics Program 

Edit Scenario window showing the 

variables that need to be entered 

to solve the equation for the 

selected Region 1.

Appendix A  29
drop-down list near the bottom of the window. Users can view 

the map showing the Crippen and Bue regions (fig. 3 in the 

main body of the report) by clicking on the Map button.

When a set of urban estimates is being computed 

(fig. A-15), only one regional or national set of equations can 

be selected. Some urban equations depend on the results of 

rural calculations. These equations will only be available if a 

rural estimate was computed before the urban New button is 

pressed.

When all of the selections and data entry are complete, 

click the Ok button to calculate the new estimates and display 

the results on the main window. Click the Cancel button at any 

time to close the compute window without calculating a new 

estimate.

For rural computations, it is possible to select more than 

one region for cases where the drainage area for the site of 

interest spans regional boundaries (fig. A-14). Recommended 

value ranges for the same variable are commonly different for 

different regions, so it is important to continually reference 

the suggested values if more than one region is selected. The 

drainage area associated with each individual region is entered 

in the drainage area box for each region, whereas the other 

variables entered in the boxes should reflect the entire drainage area encompassed by all regions. The basin total drainage 

area is shown above the data entry table in a box that is not 

editable.

Probable maximum flood estimates determined by the 

Crippen and Bue (1977) method can be obtained for the current scenario by selecting one of the 17 flood regions from the 

Figure A-14. The National Streamflow Statistics Program Edit Scenario window showing the variables that need 

to be entered to solve the equations for a site with drainage area in both selected Regions 1 and 2.

Figure A-15. The National Streamflow Statistics Program Edit Scenario window showing the variables that need 

to be entered to solve the national urban equations.

30 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Frequency Window

The Frequency window (fig. A-16) is used to create 

graphs showing the relation between flood-peak discharge and 

recurrence interval. The window opens when the Frequency 

Plot command button is clicked or the Frequency item is 

selected from the Graph menu in the main window (fig A-4). 

The Frequency window allows creation of peak-flow frequency plots for any scenarios that have been created. Select 

the scenarios to include on the graph by clicking in the boxes 

that appear to the left of the scenario names, then press the 

Plot button to create a frequency plot (fig. A-17).

The Frequency Plot window (fig. A-17) contains File, 

Edit, and View pull-down menus. The File menu contains 

Print, Save, Open Specification, and Close items. The Print

item allows users to send the plot to a printer. The Save item 

allows users to save the plot as a Windows bitmap (.bmp) 

file and to save selected specifications for the current graph, 

such as curve and axis properties, and legend locations, in a 

Windows metafile (.grf) file. Saving the specifications allows 

users to create a series of graphs with the same specifications. 

The Open Specification item allows users to select a saved 

specifications file for use in the plots. The Close item clears 

the plot from the desktop.

The Edit menu contains the Axes, Titles, Curves, Lines, 

General, Font, and Copy to Clipboard items. Clicking on 

any of the first five items causes the Graph Edit window 

(fig. A-18) to open, with the selected item tab shown in the 

Figure A-16. The National Streamflow Statistics Program Frequency window with a rural and 

an urban scenario selected for plotting.

Figure A-17. The National Streamflow Statistics Program Frequency Plot window showing 

rural and urban frequency plots for a sample site.

Appendix A  31
Figure A-18. The National Streamflow Statistics Program Graph Edit window showing the Axes 

tab on top.

front. The Axes tab allows specifying arithmetic or logarithmic scales, minimum and maximum axis values, and for 

arithmetic scales the number of ticks. The Titles tab allows 

specifying the plot title and the axes titles. The Curves tab 

allows specifying the placement of the scale (left, right, auxiliary, bottom), the curve thickness, the point markers, the curve 

colors, and the name for the curve that appears in the legend. 

The Lines tab is not used. The General tab allows specifying 

the legend location and entry and placement of any additional 

text desired by the user. Clicking the Apply command button 

at the bottom of the Graph Edit window applies any selected 

changes to the plot. Clicking the Ok command button closes 

the window with any applied changes saved. Clicking the 

Cancel command button closes the window without saving 

the changes. The Font menu item opens the Font window 

(fig. A-19), which allows changes to the font type, style, and 

size of the text that appears in the plot. The Copy to Clipboard menu item copies the plot to the Windows clipboard, 

from which the plot can be pasted into other Windows 

applications.

The View menu appears in gray rather than black letters 

in the Frequency Plot window. This menu normally is used 

to list data shown in a plot, but it has been disabled in NSS 

because its listing features are duplicated elsewhere in the 

program.

Hydrograph Window

The Hydrograph window (fig. A-20) is used to create 

graphs showing how discharge changes over time during 

an average flood of specified recurrence interval and basin 

lagtime for the user-selected hydrologic region. The Hydrograph window opens when the Hydrograph command button 

is clicked or when the Hydrograph item is selected from the 

Graph menu in the main window (fig. A-4). The Hydrograph

window allows creation of hydrographs for any scenarios that 

have been created. A recurrence interval must be selected 

from the scroll-down list near the top left of the window. The 

scenarios to include on the graph are selected by clicking in 

the boxes that appear to the left of the scenario names. If the 

national urban equations have been used to create an urban 

scenario, basin lagtime can be computed by NSS if the basin 

length is known. Click on the check box at the top left of the 

Hydrograph window and enter the basin length in the box at 

the top right of the window to automatically calculate lagtime 

for the urban estimates. If the national urban equations were 

not used for the scenarios, lagtimes determined by the user 

must be entered for each scenario in the boxes to the right of 

the scenario names. Appendix B provides a summary of available equations for manually estimating basin lagtime.

32  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
After the scenarios have been selected and the lagtimes 

have been entered, clicking on the Plot command button 

will cause the hydrographs to appear in the Hydrograph Plot

window (fig. A-21). Clicking on the List command button 

will cause the Hydrograph List window to appear (fig. A-22). 

Clicking on the Close command button will cause the window 

to disappear. The Hydrograph Plot window has File, Edit, and

View pull-down menus with exactly the same functions as 

those for the pull-down menus in the Frequency Plot window.

Weight Window

The Weight window allows users to produce improved 

flood-frequency estimates for rural streamgaging stations 

and ungaged sites. Users must compute rural estimates for 

a streamgaging station and have the appropriate scenario 

selected in the NSS main window before weighted estimates 

can be obtained for the station. For an ungaged site, users must 

first compute weighted estimates for an upstream or downstream streamgaging station to be used in the weighting, and 

then they must compute rural estimates for the ungaged site 

before weighted estimates can be obtained for the ungaged 

site. After the required rural scenarios have been computed, 

clicking the Weight command button at the bottom of the 

main NSS window will cause the Weight window to open 

(fig. A-23).

Upon opening the form, the button to Weight for gaged 

site using observed data is selected by default. A text box 

near the top of the form is used for entering the Years of 

observed data, which is used by NSS as the weight for the 

observed flow estimates. The equivalent years of record, which 

Figure A-19. The National Streamflow Statistics Program Font window.

Figure A-20. The National Streamflow Statistics Program Hydrograph window with a 

recurrence interval of 10 years and rural and urban scenarios selected for plotting.

Appendix A  33
are stored in the database, are used by NSS as the weights for 

the regression equation estimates. The user must manually 

enter the Observed Flow for each recurrence interval. As the 

Observed Flow values are entered, the Weighted Flow values 

shown in the right-hand column of the form change automatically from being the same as the Estimated Flow values to values somewhere between the observed and estimated flows. If 

the equivalent years of record are not available for the regression estimates, the weighted estimates will equal the observed 

estimates. Click on the Apply command button to save the 

weighted estimates as a scenario. This scenario will have the 

same name as the original scenario, except that weighted, 

in parentheses, will be appended to the name (i.e. “Rural 1

(weighted)”). Click on the Cancel button to return to the main 

form without creating a new scenario.

To obtain weighted estimates for an ungaged site, click 

on the Weight command button in the main NSS window, 

then click on the radio button in the top right of the form 

to Weight for ungaged site using weighted gaged values

(fig. A-24). Choose the scenario containing the weighted 

gaged values from the Select scenario containing weighted 

gaged values drop-down list beneath the radio button. The 

regression-based estimates for the ungaged site, the weighted 

estimates for the streamgaging station, and the weighted 

estimates for the ungaged site will automatically appear on 

the form. Click on the Apply button to save the weighted 

estimates for the ungaged site as a scenario. This scenario 

will have the same name as the original scenario, except that 

weighted, in parentheses, will be appended to the name 

(i.e. “Rural 2 (weighted)”). Click on the Cancel button to 

return to the main form without creating a new scenario.

Figure A-21. The National Streamflow 

Statistics Program Hydrograph Plot 

window showing rural and urban 

hydrograph plots for a sample site, with 

a lagtime set a 5 hours for the rural 

hydrograph and at 4 hours for the urban 

hydrograph.

Figure A-22. The National Streamflow 

Statistics Program Hydrograph List 

window showing rural and urban 

hydrograph lists for a sample site.

34 National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Figure A-23. The National Streamflow Statistics Program Weight window 

showing weighting for a streamgaging station.

Figure A-24. The National Streamflow Statistics Program Weight window 

showing weighting for an ungaged site.

Appendix A  35
Appendix B. Summary of Equations for Estimating 

Basin Lagtime.

[LT, basin lagtime, in hours]

State/Area/Region Equation Standard error, 

in percent

Alabama

North of Fall Line LT = 2.66A.46 S-.08 32

South of Fall Line LT = 5.06A.50 S-.20 31

Statewide, urban LT = 2.85A.295 S-.183 IA-.122 31

Arkansas

Rural LT = 256A.90 (P-30).61 Q100-.65 Qp

-.16 S-.25 33

Memphis, urban LT = 2.05A.35 C-.87 IA-.22 24

Georgia

North of Fall Line LT = 4.64A.49 S-.21 31

South of Fall Line LT = 13.6A.43 S-.231 25

Atlanta, urban LT = 161A.22 S-.66 IA-.67 19

Regions 1, 2, and 3, urban LT = 7.86A.35 TIA-.22 S-.31 30

Region 3, urban LT = 6.10A.35 TIA-.22 S-.31 30

Missouri, rural

Equation 1 LT = 2.79L.39 S-.195 26

Equation 2 LT = 1.46A.27 26

Missouri, urban

Equation 1 LT = 0.87L.60 S-.30 (13-BDF).45 23

Equation 2 LT = 0.32A.50 (13-BDF).37 22

Montana

Statewide, rural LT = 0.393A.58 40

Nationwide, urban

Equation 1 LT = 0.85L.67 S-.31 (13-BDF).47 76

Equation 2 LT = 0.003L.71 (13-BDF).34 (ST+10)2.53 RI2-.44 IA-.20 S-.14 22

New Mexico

Statewide, rural LT = 0.04L.606 Sh.253 56

Ohio

Small, rural LT = 16.4S-.78 (F+10).38 (ST+1)

.31 35

Small, urban LT = 1.13(L/SL0.5)

.57 (13-BDF).46 53

Oklahoma

Statewide, rural LT = 0.206A.239 S-.280 RI242.54 40

36  National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites
Appendix B. Summary of Equations for Estimating 

Basin Lagtime.—Continued

[LT, basin lagtime, in hours]

State/Area/Region Equation Standard error, 

in percent

South Carolina (average basin LT)

Blue Ridge LT = 3.71A.265 7

Piedmont LT = 2.66A.460 26

Inner Coastal Plain LT = 6.10A.417 34

Lower Coastal Plain

Region 1 LT = 6.62A.341 26

Region 2 LT = 10.88A.341 26

Statewide, urban LT = 20.2(L/S0.5)

.623 TIA-.919 RI21.129 24

South Carolina (Qp adjusted LT)

Blue Ridge LT = 7.21A.322 Qp

-.112 --

Piedmont LT = 3.30A.614 Qp

-.120 --

Inner Coastal Plain LT = 7.03A.375 Qp

-.010 --

Lower Coastal Plain

Region 1 LT = 6.95A.348 Qp

-.022 --

Region 2 LT = 11.7A.348 Qp

-.022 --

Tennessee

East LT = 1.26L.825 47

Central LT = 0.94L.868 39

Central, urban LT = 1.64A.49 IA-.16 16

West LT = 0.707A.73 43

West, urban LT = 2.65A.348 IA-.357 39

A = drainage area, in square miles.

S = main channel slope, in feet per mile.

L = main channel length, in miles.

Qp = peak discharge, in cubic feet per second.

F = percent forest area.

ST = percent of surface storage in basin.

Sh = basin width per stream length, in feet per mile.

P = mean annual precipitation, in inches.

Q100 = 100-year recurrence interval peak discharge, in cubic feet per second.

IA = percent of basin covered by impervious surfaces.

BDF = basin development factor.

RI2 = 2-year 2-hour rainfall intensity.

RI24 = 2-year 24-hour rainfall.

TIA = total percentage of basin covered by impervious area.

C = channel condition (unpaved 1, full paved 2).

SL = main channnel slope, in feet per mile, determined as the difference in elevation between points 10 percent and 85 percent

 along the stream from the site of interest to the basin boundary, divided by the distance between the points.

Appendix B  37

Prepared by Publishing Service Centers 3 and 1.

Edited by Valerie M. Gaine.

Graphics by Timothy W. Auer.

Layout by Ann Marie Squillacci.

For additional information, contact:

Director, MD-DE-DC Water Science Center

U.S. Geological Survey

8987 Yellow Brick Road

Baltimore, MD 21237

or visit our Web site at:

http://md.water.usgs.gov