U.S. Department of the Interior

U.S. Geological Survey

0 1 2 3 MILES

0 1 2 3 KILOMETERS

Base modified from U.S. Geological Survey

Tutuila Island, 1:24,000, 1963

EXPLANATION

North-South Basin divide

Figure 1. The island of Tutuila, American Samoa.

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500 1,000 MILES .

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500 1,000 KILOMETERS INDONESIA AMERICAN

PAPUA SAMOA

 NEW GUINEA

FIJI

AUSTRALIA Tahiti

Tutuila PACIFIC OCEAN

20° S

0°

140° E 160° 180° 160° W

14°

15' 

 S

14°

20' 

 S

170°50' W 170°35' W

The National Flood-Frequency Program—Methods for Estimating Flood 

Magnitude and Frequency in Rural Areas on the Island of Tutuila, 

American Samoa, 2000

Introduction

Estimates of the magnitude and frequency of flood-peak discharges and flood 

hydrographs are used for a variety of purposes, such as for the design of bridges, 

culverts, and flood-control structures; and 

for the management and regulation of 

flood plains. To provide simple methods of 

estimating flood-peak discharges, the U.S. 

Geological Survey (USGS) has developed 

and published regression equations for 

every State, the Commonwealth of Puerto 

Rico, American Samoa, and a number of 

metropolitan areas in the United States. In 

1993, the USGS, in cooperation with the 

Federal Emergency Management Agency 

and the Federal Highway Administration, 

compiled all current USGS statewide and 

metropolitan area regression equations into 

a computer program, titled “The National 

Flood-Frequency (NFF) Program” 

(Jennings and others, 1994). 

Since 1993, new or updated regression equations have been developed by the 

USGS for various areas of the Nation. 

These new equations have been incorporated into an updated version of the NFF 

Program. 

This Fact Sheet describes the application of the updated NFF Program to 

streams that drain rural areas on the island 

of Tutuila, American Samoa. Information 

on obtaining the NFF software and fact 

sheets for other areas of the Nation is provided at the end of this Fact Sheet.

Overview

Wong (1996) developed regression 

equations for estimating peak discharges 

(QT), in cubic feet per second, that have 

recurrence intervals (T) that range from 2 

to 100 years for rural, unregulated streams 

on Tutuila, American Samoa. The equations were developed using ordinary-leastsquares regression techniques. Peak-discharge data from 10 streamflow-gaging 

stations with 9 to 32 years of record collected between 1958 and 1990 were used 

in the analyses. The entire island is represented by a single hydrologic region 

(fig. 1). The equations are not applicable to 

urban areas.

Recurrence interval is the reciprocal 

of the annual exceedance probability and 

represents the average number of years 

between exceedances. For example, a 

flood-peak discharge with an exceedance 

probability of 0.01 has a recurrence interval of 100 years. This does not imply that 

USGS Fact Sheet 008–00

October, 2000
the 100-year flood will be equaled or 

exceeded each 100 years, but that it will be 

equaled or exceeded on the average once 

every 100 years. 

Procedure

The equations presented by Wong 

(1996) are shown in table 1. The equations 

are in the inch-pound system of units; 

however, the NFF Program will accept and 

report either the inch-pound or the metric 

system of units. Drainage area (DA), in 

square miles, is the only explanatory basin 

variable that is used in the regression equations for estimating QT for rural areas. The 

drainage area is the total area that contributes runoff upstream of the stream site of 

interest, and is determined from the largest 

scale topographic map available.

The average standard errors of estimate, and the applicable range of drainage 

area are shown along with the equations in 

table 1. The average standard error of estimate is a measure of the goodness of fit 

between a regression equation and the data 

used to derive the equation. Errors in the 

QT estimates for about two thirds of the 

gaging stations used in the regression analysis were within the given standard errors. 

Errors in the QT estimates for ungaged 

sites are somewhat larger than the standard 

errors of estimate shown in table 1. The 

equivalent years of record is the number of 

years of streamflow record needed to 

achieve the same accuracy as the equation.

The regression equations are valid 

only for drainage areas greater than 0.11 

and less than 0.78 square miles. Use of the 

equations for drainage areas near or 

beyond this range can result in large 

extrapolation errors. In addition, conditions, such as channelization, urbanization, 

and diversions, in some drainage basins on 

Tutuila can be substantially different than 

those for the gaging stations used in the 

regression analysis, and users should evaluate whether equation estimates should be 

used or possibly adjusted in these areas.

Miscellaneous

Wong (1996) summarized watershed 

characteristics, peak-discharge estimates, 

and maximum known discharges for the 10 

streamflow-gaging stations used to 

develop the regression equations. The 

report also includes regionalized regression equations for mean flow, median 

flow, and 7-day low flows for 2- and 10-

year recurrence intervals for ungaged locations. In addition, selected low-flow, flow 

duration, and daily high-flow characteristics for 11 continuous record stations, 78 

low-flow partial record stations, and 49 

miscellaneous stream sites are presented.

—Prepared by Steve S. Sumioka, and Robert R. Mason, Jr., of the U.S. Geological 

Survey; and Jeffrey N. King and Wilbert O. 

Thomas, Jr., of Michael Baker, Jr., Inc.

References

Jennings, M.E., Thomas, W.O., Jr., and 

Riggs, H.C., comps., 1994, Nationwide summary of U.S. Geological 

Survey regional regression equations 

for estimating magnitude and frequency of floods for ungaged sites, 

1993: U.S. Geological Survey WaterResources Investigations Report 

94–4002, 196 p.

Wong, M.F., 1996, Analysis of streamflow 

characteristics for streams on the 

Island of Tutuila, American Samoa: 

U.S. Geological Survey WaterResources Investigations Report 

95–4185, 168 p.

For more information contact:

U.S. Geological Survey

Office of Surface Water

415 National Center

Reston, Virginia 20192

(703) 648-5301

USGS hydrologic analysis software is 

available for electronic retrieval through 

the World Wide Web (WWW) at 

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

and through anonymous File Transfer Protocol (FTP) from water.usgs.gov 

(directory: /pub/software). The WWW 

page and anonymous FTP directory from 

which the National Flood-Frequency software and user documentation can be 

retrieved are 

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

and 

/pub/software/surface_water/nff, 

respectively.

Additional earth science information is 

available from the USGS through the 

WWW at http://www.usgs.gov/ 

or by calling 1-888-ASK-USGS.

Table 1. Flood-peak discharge regression equations and associated statistics for streams that drain 

rural areas of the Island of Tutuila, American Samoa (modified from Wong, 1996)

[QT, peak discharge for recurrence interval T, 2 to 100 years, in cubic feet per second; DA, drainage, in 

square miles]

Average standard Applicable range of

error of estimate, drainage area,

Regression equation in percent in square miles

Q2 = 1,040DA1.13 47.4 0.11–0.78

Q5 = 1,530DA1.10 45.8 .11–.78

Q10 = 1,810DA1.07 45.1 .11–.78

Q25 = 2,110DA1.02 44.4 .11–.78

Q50 = 2,300DA0.981 44.0 .11–.78

Q100 = 2,470DA0.941 44.1 .11–.78