U.S. Department of the Interior

U.S. Geological Survey

Figure 1. Hydrologic regions of South Carolina.

Base from U Geological Sur ey

1:2,000,000 scale Digital Line Graphs

33°

32°

34°

35°

83° 81° 79°

Blue

Ridge

Hydrologic region boundar

Hydrologic region 

EXPLANATION

Approximate area where

regional equations do not apply

0 40

0 40

80 MILES

80 KILOMETERS

TLANTIC OCEAN A

Lower Coastal 

Plains Upper Coastal 

Plains

Piedmont

Blue 

Ridge

y

.S. v

The National Flood-Frequency Program—Methods for Estimating 

Flood Magnitude and Frequency in Rural and Urban Areas in 

South Carolina, 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 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 equations into a computer 

program, titled “The National Flood-Frequency (NFF) Program” (Jennings and 

others, 1994). 

Since 1993, new or updated 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 and urban areas in 

South Carolina. 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

Guimaraes and Bohman (1992) 

developed regression equations for estimating peak discharges (QT), in cubic feet 

per second, that have recurrence intervals 

(T) that range from 2 to 500 years for 

unregulated, nontidal, rural streams in 

South Carolina. Separate sets of equations 

USGS Fact Sheet 001–00

January, 2000

were developed for each of four hydrologic regions (fig. 1), which were determined on the basis of physiography, 

geology, soil characteristics, and analysis 

of geographic patterns in the differences 

between observed and estimated peak discharges for the stations used in the regression analyses. The regression equations 

were developed from peak-discharge 

records available through 1988 at 174 

stream-gaging stations in South Carolina 

(52 stations) and adjacent areas of North 

Carolina (69 stations) and Georgia (53 stations). Guimaraes and Bohman (1992) 

summarized stream-gaging-station information, peak-discharge records, and peakdischarge estimates derived from the peakdischarge records for these 174 stations, 

and for selected sites on regulated streams 

in South Carolina.

The regression equations do not 

apply to some areas of the Upper Coastal 

Plain and Piedmont provinces because of 

distinctly different physiographic characteristics and insufficient streamflow data, 

respectively (fig. 1).

Bohman (1992) developed regression 

equations for estimating peak discharges 

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

recurrence intervals (T) that range from 2 

to 500 years for small, urban watersheds in 

South Carolina. The regression equations 

were based on generalized least-squares 

regression techniques. Synthetic peak-discharge data that resulted from calibrated 
Table 1. Flood-peak discharge regression equations and associated statistics for streams 

that drain rural areas in South Carolina (modified from Guimaraes and Bohman, 1992)

[QT, rural peak discharge for recurrence interval T, 2 to 500 years; A, drainage area; Do., ditto]

Average standard error Applicable range of

of prediction, Equivalent drainage area,

Regression equation in percent years of record in square miles

Blue Ridge

Q2 = 103A0.79 32 3 0.6–945

Q5 = 196A0.76 31 5 Do.

Q10 = 286A0.73 30 8 Do.

Q25 = 429A0.70 31 11 Do.

Q50 = 558A0.69 33 12 Do.

Q100 = 705A0.67 35 13 Do.

Q500 = 1,150A0.63 40 15 Do.

Piedmont

Q2 = 127A0.66 53 1 0.1–1,430

Q5 = 211A0.64 38 4 Do.

Q10 = 267A0.64 31 7 Do.

Q25 = 347A0.63 29 12 Do.

Q50 = 410A0.63 28 15 Do.

Q100 = 474A0.63 28 18 Do.

Q500 = 615A0.63 30 22 Do.

Upper Coastal Plain

Q2 = 25A0.74 23 5 4.4–1,720

Q5 = 44A0.72 25 8 Do.

Q10 = 59A0.71 26 10 Do.

Q25 = 80A0.70 29 12 Do.

Q50 = 97A0.70 31 13 Do.

Q100 = 116A0.69 33 14 Do.

Q500 = 179A0.66 39 15 Do.

Lower Coastal Plain

Q2 = 56A0.63 30 5 0.6–1,252

Q5 = 111A0.61 31 7 Do.

Q10 = 157A0.59 34 8 Do.

Q25 = 221A0.59 40 9 Do.

Q50 = 275A0.58 44 9 Do.

Q100 = 335A0.58 47 10 Do.

Q500 = 569A0.52 47 14 Do.

rainfall-runoff model simulations using 

long-term rainfall and evaporation data 

were used for 30 sites in South Carolina 

and Georgia, and observed peak-discharge 

data were used at 4 sites in Charlotte, 

North Carolina to develop the equations.

 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 

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 for Rural Areas

The equations for both the rural and 

urban areas are based on the inch-pound 

system of units, but the NFF Program will 

accept and report either the inch-pound or 

metric system of units. Drainage area (A), 

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 equations, the average standard 

errors of prediction, the equivalent years of 

record, and the range of drainage area for 

which the equations are applicable in rural 

areas are shown in table 1. The average 

standard error of prediction is a measure of 

the accuracy of a regression equation when 

used to estimate peak discharges for 

ungaged watersheds similar to those used 

to derive the regression equation. Errors in 

the QT estimates for about two-thirds of 

the ungaged sites will be within the given 

standard errors. Errors increase appreciably when the drainage area is near or 

beyond the range limits 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 regression equation.

Procedure for Urban Areas

The explanatory watershed variables 

used in the regression equations for estimating UT for urban areas are as follow:

Drainage area (A), in square miles, is the 

total area that contributes runoff upstream 

of the location of the stream site of interest. In urban areas runoff from subwatersheds may be diverted out of or into the 

drainage area of interest by stormwater 

sewers. The areas of such subwatersheds 

should be subtracted or added, as appropriate, to the drainage area of the stream site 

of interest to compute the effective drainage area.

Impervious Area (IA) is the percentage of 

the drainage area, A, that is covered by 

impervious surfaces and can be estimated 

from maps or aerial photos by use of the 

grid-sampling method or a planimeter, and 

from field reconnaissance of the basin.

Rural peak discharge (QT), in cubic feet 

per second, is generated by using the equations of Guimaraes and Bohman (1992) for 
the equivalent recurrence interval (T), 

shown in table 1.

The regression equations, the standard errors of prediction, and the ranges 

over which the explanatory watershed 

variables are applicable are shown in table 

2. The standard error of prediction 

increases appreciably when any explanatory watershed variable is near or beyond 

the range limits.

The equations in table 2 are not 

intended for use with basins that have 

impervious areas less than 10 percent or 

more than 50 percent, and they are not 

applicable to basins with significant inchannel detention or basin storage. Urbanization (imperviousness) should be 

roughly homogeneous over the entire 

basin. If the computed urban peak discharge is less than the computed rural peak 

discharge, hydrologic judgement is 

required to determine which peak-discharge estimate should be used or if a 

weighted estimate should be developed.

Improving Estimates With 

Gaged Data

Guimaraes and Bohman (1992) 

developed weighting techniques to 

improve estimates of peak discharge at 

rural gaged locations by combining the 

estimates derived from analysis of gage 

records with estimates derived from the 

regression equations. The weights of these 

two independent estimates are based on the 

length of the gage record in years (N) and 

the equivalent years of records (EQ) of the 

applicable regression equation. The 

weighted estimate of peak discharge for 

the gaged site is computed as:

where

QT(G)w is the weighted estimate of discharge Q for recurrence interval 

T at the gage location,

QT(G)s is the estimate of QT derived 

from analysis of the systematic 

gage records,

QT(G)r is the estimate of QT derived 

from application of the appropriate regression equation in 

table 1,

N is the number of years in the 

gage record used to compute 

QT(G)s, and

EQ is the equivalent years of record 

(table 1).

The accuracy of the weighted discharge 

estimate, in equivalent years of record, is 

equal to N + EQ. The NFF Program performs these computations. 

Ungaged Sites Near Gaged 

Sites on the Same Streams

Guimaraes and Bohman (1992) also 

showed how the weighted estimate for 

peak discharge at a rural gaged site can be 

used to improve estimates of peak discharge at a rural ungaged site on the same 

stream that has a drainage area that is 

between 50 and 150 percent of the drainage area of the gaged site. The weighted 

estimate for the ungaged site is computed 

as:

,

where

QT(U)w is the weighted estimate of discharge QT for recurrence interval 

T at the ungaged site,

∆A is the absolute value of the difference between the drainage 

areas of the gaged site, (Ag), and 

the ungaged site, (Au), |Ag - Au|,

QT(U)r is the peak-flow estimate for 

recurrence interval T at the 

ungaged site derived from the 

applicable regional equation 

(table 1),

QT(U)g is the peak-flow estimate for 

recurrence interval T at the 

ungaged site derived from the 

weighted estimate of peak discharge at the gaged site, QT(G)w, 

by adjusting for the effect of the 

difference in drainage area 

between the gaged site and the 

ungaged site. QT(U)g is computed 

as:

,

where b is the exponent of drainage area 

from the appropriate regression 

equation (table 1).

This weighting method can be used to 

improve the estimate at the ungaged site 

when the drainage area at the ungaged site 

is within 50–150 percent of the drainage 

area of the gaged site. Otherwise, the estimate at the ungaged site should be based 

only on the appropriate regression equation from table 1.

QT( ) G w log

N QT G( )s ⋅log EQ QT( ) G r + ⋅log

N EQ + = ----------------------------------------------------------------------------

QT U( )w

2∆A

Ag

----------QT U( )r 1 2∆A

Ag

– ----------     QT U( )g = +

QT U( )g

Au

Ag

-----     b

QT G( )w = ⋅

Table 2. Flood-peak discharge regression equations and associated statistics for streams that 

drain urban basins in South Carolina (modified from Bohman, 1992)

[UT, urban peak discharge for recurrence interval T, 2 to 500 years, in cubic feet per second; A, drainage area; 

IA, impervious area; QT, rural equivalent peak discharge in cubic feet per second; Do., ditto]

Average Applicable

standard Applicable range of

error of range of impervious

prediction, drainage area, area,

Regression equations in percent in square miles in percent

U2 = 1.36A0.554IA1.241Q2

0.323 34.3 0.18–41 10–50

U5 = 2.58A0.544IA1.170Q5

0.299 31.2 Do. Do.

U10 = 3.77A0.536IA1.115Q10

0.291 29.1 Do. Do.

U25 = 5.84A0.524IA1.041Q25

0.284 26.8 Do. Do.

U50 = 7.76A0.514IA0.987Q50

0.283 25.8 Do. Do.

U100 = 10.4A0.506IA0.932Q100

0.28 25.6 Do. Do.

U500 = 18.8A0.484IA0.800Q500

0.281 28.5 Do. Do.
Sites in Transition Zones

When the drainage area of the site of 

interest is in more than one region, a 

weighted estimate of the peak discharge 

should be computed. The equations for the 

appropriate regions should be applied to 

the total drainage area for the site, as if the 

entire basin was in each region. The 

weighted estimate is then computed by 

multiplying each regional estimate against 

the fraction of the drainage area in that 

region and summing the products. The 

NFF Program provides an algorithm for 

this computation.

—Prepared by Robert R. Mason, Jr., and 

Luis A. Fuste, of the U.S. Geological Survey; and Jeffrey N. King, and Wilbert O. 

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

References

Bohman, L.R., 1992, Determination of 

flood hydrographs for streams in 

South Carolina: Volume 2. Estimation 

of peak-discharge frequency, runoff 

volumes, and flood hydrographs for 

urban watersheds: U.S. Geological 

Survey Water-Resources Investigations Report 92-4040, 79 p.

Guimaraes, W.B., and Bohman, L.R., 1992, 

Techniques for estimating magnitude 

and frequency of floods in South 

Carolina, 1988: U.S. Geological Survey Water-Resources Investigations 

Report 91-4157, 174 p.

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.

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.