U.S. Department of the Interior

U.S. Geological Survey

The National Flood-Frequency Program—Methods for Estimating 

Flood Magnitude and Frequency in Rural and Urban Areas in Georgia

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.

Fact sheets that describe application 

of the updated NFF Program to various 

areas of the Nation are available. This fact 

sheet describes the application of the 

updated NFF Program to streams that drain 

rural and urban areas in Georgia.

Rural Basins

Georgia is divided into four hydrologic regions (fig. 1) on the basis of previous flood-frequency studies, geology, 

soils, physiography, and analysis of floodfrequency regression residuals. Stamey 

and Hess (1993) 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 ungaged, unregulated, 

USGS Fact Sheet 169-98

August, 1999

Region 1

Region 2

Region 3

Region 4

Undefined

0 20 40 60 KILOMETERS

0 20 40 60 MILES

35 °

34 °

33 °

32 °

31°

84° 82°

Figure 1. Hydrologic regions for Georgia.

Rome 

 City location

Chattaho oche e Rive r

Flint 

 Rive r

Ocmulge e

Rive r

Altamaha

Ri

v

e

r

O

c

o

n

e

e

River

Savannah

Rive r

Alapaha River

O

c

hloc

k

n

e

e

R

i

v

e

r

Base from U.S. Geological Survey digital files

EXPLANATION 

River

Oge

ech

e

e

non-tidal rural streams. The regression 

equations are not applicable to the 

Okefenokee Swamp in southeast Georgia. 

The regression equations also are not 

applicable to urban, channelized, or large 

main-stem streams or to streams where 

large sinkholes or depressions can affect 

the flood-frequency relation. These features can be identified by the study of geologic and topographic maps or by the 

reconnaissance of the basin.

Drainage area (A) was found to be 

the most statistically significant explanatory watershed variable and is the only 

variable that is used in the regression 

equations. The drainage area is the total 

area that contributes runoff upstream of 

the stream site of interest. Drainage areas 

were measured in square miles for the 
Table 1. Flood-peak discharge regression equations and associated statistics for streams 

that drain rural areas in Georgia (modified from Stamey and Hess, 1993)

[QT, peak discharge for recurrence interval T, 2 to 500 years, in cubic feet per second; A, drainage area; Do., ditto]

Regression equation

Average standard 

error of prediction,

in percent

Equivalent

years of record

Applicable range of 

drainage area,

in square miles

Region 1

Q2 = 207A0.654 31 3 0.17–730

Q5 = 357A0.632 29 4 Do.

Q10 = 482A0.619 29 5 Do.

Q25 = 666A0.605 29 12 Do.

Q50 = 827A0.595 30 14 Do.

Q100 = 1,010A0.584 31 16 Do.

Q200 = 1,220A0.575 33 17 Do.

Q500 = 1,530A0.563 36 18 Do.

Region 2

Q2 = 182A0.622 33 4 0.10–3,000

Q5 = 311A0.616 28 7 Do.

Q10 = 411A0.613 27 10 Do.

Q25 = 552A0.610 28 14 Do.

Q50 = 669A0.607 30 16 Do.

Q100 = 794A0.605 33 17 Do.

Q200 = 931A0.603 36 19 Do.

Q500 = 1,130A0.601 40 21 Do.

Region 3

Q2 = 76A0.620 36 3 0.14–3,000

Q5 = 133A0.620 35 6 Do.

Q10 = 176A0.621 35 10 Do.

Q25 = 237A0.623 37 15 Do.

Q50 = 287A0.625 38 18 Do.

Q100 = 340A0.627 38 19 Do.

Q200 = 396A0.629 40 19 Do.

Q500 = 474A0.632 43 20 Do.

Region 4

Q2 = 142A0.591 25 8 0.25–2,000

Q5 = 288A0.589 19 27 Do.

Q10 = 410A0.591 19 37 Do.

Q25 = 591A0.595 21 43 Do.

Q50 = 748A0.599 24 40 Do.

Q100 = 926A0.602 28 37 Do.

Q200 = 1,120A0.606 32 35 Do.

Q500 = 1,420A0.611 37 32 Do.

equations determined by Stamey and Hess 

(1993), but the NFF Program will accept 

input and report results in either the inchpound or metric system of units.

The regression equations, the average 

standard errors of prediction, the equivalent years of record, and the range of the 

drainage area that is applicable for use in 

the equations are shown in table 1. The 

average standard error of prediction is a 

measure of the average accuracy of the 

regression equations when estimating 

peak-discharge values for ungaged watersheds similar to those that were used to 

derive the regression equations. The equivalent years of record is the number of years 

of streamflow record needed to achieve the 

same accuracy as the regression equation. 

The standard error of prediction increases 

appreciably when drainage-area values that 

are outside the quoted range of data used to 

develop the equations are applied in the 

equation.

The regression equations were developed by using peak-discharge data for 

streamflow-gaging stations with at least 10 

years of record collected through September 1990 at 357 locations in Georgia and 

69 locations in Alabama, Florida, North 

Carolina, South Carolina, and Tennessee.

Stamey and Hess (1993) developed 

weighting techniques to improve estimates 

of peak discharge at 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 is computed as:

where

QT(W) is the weighted estimate for recurrence interval T at the gage location,

QT(S) is the estimate of QT derived from 

analysis of the gage records,

QT(R) is the estimate of QT derived from 

application of the regression 

equation,

N is the number of years in the gage 

record, and

EQ is the equivalent years of record 

(table 1).

Q log( ) T( ) W

N QT ⋅log( ) ( ) S EQ QT + ⋅log( ) ( ) R

N EQ + = ------------------------------------------------------------------------------ QT(W)u is the weighted estimate for recurrence interval T at the ungaged 

site,

∆A is the difference in drainage area 

between the gaged site (Ag) and 

the ungaged site, (Ag-Aungaged),

QT(R)u is the peak flow estimate for 

recurrence interval T at the 

ungaged site derived from the 

applicable regional equation 

(table 1),

QTu is the weighted estimate of peak 

discharge at the gaged site, 

QT(W), adjusted for the effect of 

the difference in drainage area 

The accuracy of the weighted discharge 

estimate, in equivalent years of record, is 

equal to N + EQ.

Stamey and Hess (1993) also showed 

how the weighted estimate for peak discharge at a gaged site can be used to 

improve estimates of peak discharge for an 

ungaged site on the same stream that has a 

drainage that is between 50 and 200 percent of the drainage area of the gaged site. 

The weighted estimate is computed as:

where

QT( ) W u 2∆A

Ag

---------- QT ⋅ ( ) R u 1 2∆A

Ag

– ----------     QT = + ⋅ u
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 

some 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 interest to compute the effective drainage area.

Total impervious area (TIA) is the 

percentage of the drainage area, A, that is 

covered by impervious surfaces and can be 

estimated by examination of maps or 

aerial photos and the use of the grid-sampling method or planimeters and field 

reconnaissance of the basin.

The regression equations and average 

standard errors of prediction are shown in 

table 2. The applicable range of basin variables used to develop the equations are 

shown in table 3. The regression equations 

were based on generalized least-squares 

(GLS) regression techniques used on synthetic peak-discharge data that resulted 

from calibrated rainfall-runoff model simulations using long-term rainfall and evaporation data for 65 sites in urban areas of 

Georgia. If the estimate of peak discharge 

using the rural equations (Stamey and 

Hess, 1993) exceeds the estimates derived 

from the application of the urban equations, use the rural peak-discharge estimates.

Inman (1995) presented rainfall-runoff model parameters, explanatory watershed variables, and peak-discharge 

estimates (QT) for the 65 streamflow-gaging stations used to develop the equations, 

and analyses of the sensitivity of the equation to errors in estimates of watershed 

variables.

Prepared by Robert R. Mason, Jr., of the 

U.S. Geological Survey; Lordian P. 

Turner, Jeffrey N. King, and Wilbert O. 

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

References

Inman, E.J., 1995, Flood-frequency relations for urban streams in Georgia–

1994 update: U.S. Geological Survey 

Water-Resources Investigations 

Report 95-4017, 27 p.

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

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

Survey regional regression equations 

between the gaged site and the 

ungaged site and computed as:

,

where

b is the exponent of drainage area in 

the appropriate regression equation (table 1).

The NFF Program contains algorithms for each of the weighting computations. The equation estimates are used 

without adjustment where the drainage area 

at the ungaged site is not within one-half to 

two times the drainage area of the gaged 

site.

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 independently using basinwide estimates of the 

required explanatory variables 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.

Stamey and Hess (1993) summarized 

peak-discharge estimates derived from the 

peak-discharge records, the years of record, 

and the peak-discharge estimate derived 

from weighting the regression equation and 

station-record estimates for 357 sites 

located in Georgia. They also presented 

graphs of peak discharge as a function of 

drainage area for selected recurrence intervals for portions of the Ocmulgee, the 

Oconee, the Altamaha, and the Flint Rivers.

Urban Basins

Georgia is divided into four urban 

hydrologic regions that correspond to the 

hydrologic regions developed by Stamey 

and Hess (1993). Inman (1995) 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 the four hydrologic 

regions and a separate set of equations for 

the city of Rome, Ga. The equations are not 

applicable to basins with significant surface 

or embankment storage.

QTu Aungaged

Ag

----------------------

     b

Q = ⋅ T( ) W

Table 2. Flood-peak discharge regression 

equations and associated statistics for 

streams draining urban basins in Georgia 

(modified from Inman, 1995)

[QT, peak discharge for recurrence interval T, 2 to 

500 years, in cubic feet per second; A, drainage area, 

in square miles; TIA, area that is impervious to infiltration of rainfall, in percent]

Regression equation

Average

standard

error of

prediction,

in percent

Region 1

Q2 = 167A0.73TIA0.31 34

Q5 = 301A0.71TIA0.26 31

Q10 = 405A0.70TIA0.21 31

Q25 = 527A0.70TIA0.20 29

Q50 = 643A0.69TIA0.18 28

Q100 = 762A0.69TIA0.17 28

Q200 = 892A0.68TIA0.16 28

Q500 = 1,063A0.68TIA0.14 28

Rome

Q2 = 107A0.73TIA0.31 40

Q5 = 183A0.71TIA0.26 36

Q10 = 249A0.70TIA0.21 35

Q25 = 316A0.70TIA0.20 33

Q50 = 379A0.69TIA0.18 33

Q100 = 440A0.69TIA0.17 33

Q200 = 505A0.68TIA0.16 34

Q500 = 589A0.68TIA0.14 34

Region 2

Q2 = 145A0.70TIA0.31 35

Q5 = 258A0.69TIA0.26 31

Q10 = 351A0.70TIA0.21 31

Q25 = 452A0.70TIA0.20 29

Q50 = 548A0.70TIA0.18 29

Q100 = 644A0.70TIA0.17 29

Q200 = 747A0.70TIA0.16 28

Q500 = 888A0.70TIA0.14 28

Region 3

Q2 = 54.6A0.69TIA0.31 34

Q5 = 99.7A0.69TIA0.26 31

Q10 = 164A0.71TIA0.21 32

Q25 = 226A0.71TIA0.20 30

Q50 = 288A0.72TIA0.18 30

Q100 = 355A0.72TIA0.17 30

Q200 = 428A0.72TIA0.16 30

Q500 = 531A0.72TIA0.14 30

Region 4

Q2 = 110A0.66TIA0.31 34

Q5 = 237A0.66TIA0.26 31

Q10 = 350A0.68TIA0.21 30

Q25 = 478A0.69TIA0.20 29

Q50 = 596A0.70TIA0.18 28

Q100 = 717A0.70TIA0.17 28

Q200 = 843A0.70TIA0.16 28

Q500 = 1,017A0.71TIA0.14 28
Table 3. Range of explanatory variables for 

which regression equations are applicable

[do., Do., ditto]

Hydrologic

study

region

Drainage area,

in square miles

Total

impervious

area,

in percent

Region 1 0.04–19.1 1.00–62

Rome do. Do.

Region 2 do. Do.

Region 3 do. Do.

Region 4 do. Do.

for estimating magnitude and frequency of floods for ungaged sites, 

1993: U.S. Geological Survey WaterResources Investigations Report 

94–4002, 196 p.

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 93-4016, 75 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 1-800-426-9000.