U.S. Department of the Interior

U.S. Geological Survey

1

2

3

PEARL

CITY

HONOLULU

WAIANAE RANGE

KOOLAU RANGE

158° 157°40'

21°40'

21°20'

Base modified from U.S. Geological Survey

digital data, 1:24,000, 1983, Albers equal area 

projection, standard parallels 21°15' and 21°45', 

central meridian 157°59'

PAC IF IC OCEAN

Kauai

Niihau Oahu

Lanai

Kahoolawe

Hawaii

LOCATION MAP

22°

20°

160°

Maui

Molokai

HAWAII

156°

Figure 1. Hydrologic regions for the Island of Oahu, Hawaii.

EXPLANATION

Hydrologic region boundary

2 Hydrologic region number

0

0

8 MILES

8 KILOMETERS

4

4

2 6

2 6

The National Flood-Frequency Program—Methods for Estimating Flood 

Magnitude and Frequency in Rural Areas in Hawaii, Island of Oahu, 

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 in Hawaii, 

island of Oahu. 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 (1994) developed regression 

equations for estimating peak discharges 

(QT), in cubic feet per second, having 

recurrence intervals (T) ranging from 2 to 

100 years, for the island of Oahu, Hawaii. 

Separate sets of equations were developed 

for each of three hydrologic regions: (1) 

leeward, (2) windward, and (3) north 

(fig. 1).

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. 

The regression equations shown in 

table 1 were developed from peak-discharge records available through 1988 and 

basin and climatic characteristics for 79 

continuous and crest-stage stations on 

Oahu. These peak-discharge records and 

characteristics were presented for the 79 

stations in tabular form by Wong (1994). 

The mean record length for the stations 

was 30 years, and ranged from 11 to 72 

years. Generalized-least-squares regression techniques were used to develop the 

equations (Tasker, 1982). 

The regression equations are not 

applicable to sites subject to diversion, regulation, or some proportion of urbanization. For Oahu, urbanization is considered 

substantial when the urban cover, defined 

below, is greater than 36 percent (Wong, 

1994).

USGS Fact Sheet 004–00

October, 2000
Procedure

The equations in table 1 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. 

The explanatory watershed and climatic 

variables used in the regression equations 

are as follow:

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

total area that contributes runoff upstream 

of the stream site of interest. Drainage area 

is determined from 1:24,000-scale USGS 

topographic maps by planimeter.

Median annual precipitation (P), in inches, 

is the average median precipitation for the 

drainage basin and is determined by the 

grid-sampling method from an equal-precipitation map developed by the Division 

of Water and Land Development (1982).

2-year, 24-hour precipitation (P224), in 

inches, is the average of the 2-year recurrence interval, 24-hour duration storm 

conservative median value of the estimated 

peak discharge. Users of the NFF Program 

do not need to enter the BCF values 

because they have been incorporated into 

the equations.

The regression equations, the bias 

correction factors, the average standard 

errors of prediction, and the equivalent 

years of record 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 any explanatory 

variable is near or beyond the range limits 

shown in table 2. The equivalent years of 

record is the number of years of streamflow records needed to achieve the same 

accuracy as the regression equation.

Improving Estimates With 

Gaged Data

Wong (1994) 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) and the 

equivalent years of record of the applicable 

regression equation. The weighted estimate of peak discharge is computed as:

where

QT(G)w is the weighted estimate of peak 

discharge, QT, 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

QT( ) G w log

N QT G( )s ⋅log EQ QT( ) G r + ⋅log

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

determined for the drainage basin from a 

map by Giambelluca and others (1984) by 

use of the grid-sampling method.

Urban cover (UC), in percent, is not 

included as an explanatory variable in the 

regression equations, but it should be measured because the equations do not apply 

for basins with greater than the percentages of urban area shown in table 2. UC 

can be determined by measuring urban 

areas within the basin of interest, shown in 

pink on 1:24,000-scale USGS topographic 

maps, and dividing the sum of the areas by 

the drainage area of the basin, and multiplying the result by 100.

A Bias Correction Factor (BCF) is 

used to correct the retransformation bias 

introduced by the logarithmic transformation of the dataset used to develop the 

regression equations. Use of the BCF in 

the regression equation yields the mean 

value of the estimated peak discharge, 

whereas not using the BCF yields the less 

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

that drain rural areas in Hawaii, island of Oahu (modified from Wong, 1994)

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

DA, drainage area, in square miles; P, median annual precipitation, in inches; P224, 2-year, 24-hour 

precipitation intensity, in inches] 

Average

standard error

Bias correction of prediction Equivalent

Regression equation factor in percent years of record

Region 1 (Leeward)

Q2 = 3.26DA0.634P1.08 1.115 43 4.2

Q5 = 25.8DA0.642P0.773 1.069 40 5.8

Q10 = 73.5DA0.646P0.621 1.052 39 8.2

Q25 = 217DA0.646P0.464 1.040 38 11.4

Q50 = 425DA0.645P0.368 1.037 38 13.7

Q100 = 758DA0.643P0.286 1.040 39 15.8

Region 2 (Windward)

Q2 = 525DA0.704 1.165 62 2.5

Q5 = 1,140DA0.748 1.138 58 3.9

Q10 = 1,700DA0.763 1.129 54 5.7

Q25 = 2,580DA0.773 1.124 52 8.6

Q50 = 3,360DA0.776 1.125 51 11.0

Q100 = 4,250DA0.777 1.133 50 13.6

Region 3 (North)

Q2 = 0.00356DA0.870P2245.85 1.036 45 3.6

Q5 = 0.151DA0.836P2244.30 1.000 34 8.3

Q10 = 1.76DA0.805P2243.24 1.000 34 10.2

Q25 = 24.8DA0.777P2242.10 1.000 38 10.7

Q50 = 125DA0.765P2241.39 1.000 43 10.5

Q100 = 500DA0.758P2240.792 1.011 48 10.1
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 Stream

Wong (1994) showed how the 

weighted estimate of 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 150 percent of the 

drainage area of the gaged site. The regression estimate for the ungaged site is multiplied by an adjustment factor, which is 

computed as:

,

where

AF is the adjustment factor,

∆A is the absolute value of difference 

in drainage area between the 

gaged site (Ag) and the ungaged 

site (Au), |Ag -Au|, and

R is the ratio of the weighted peakdischarge estimate to the regression estimate for the gaged site, 

QT(G)w/QT(G)r.

The equations are used without adjustment 

where the drainage area of the ungaged site 

is not within 0.5 to 1.5 times the drainage 

area of the gaged site.

AF R ∆A R( ) – 1

0.5Ag

= – -------------------------

—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

Division of Water and Land Development, 

1982, Median rainfall, State of 

Hawaii: Department of Land and Natural Resources, State of Hawaii, Circular C88, 44 p.

Giambelluca, T.W., and others, 1984, Rainfall frequency study for Oahu: Division of Water and Land Development, 

Department of Natural Resources, 

State of Hawaii, Report R–73, 34 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.

Tasker, G.D., 1982, Hydrologic regression 

with weighted least squares: Water 

Resources Research, v. 16, no. 6., p. 

1107-1113.

Wong, M.F., 1994, Estimation of magnitude and frequency of floods for 

streams on the island of Oahu, Hawaii: 

U.S. Geological Survey WaterResources Investigations Report 94–

4052, 37 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 2. Range of explanatory variables for which regression equations are applicable (modified 

from Wong, 1994)

Median annual 2-year, 24-hour

Drainage area rainfall, rainfall intensity, Urban cover

Hydrologic study region in square miles in inches in inches in percent

Region 1 (Leeward) 0.60–45.7 29–239 4.72–8.78 0–32

Region 2 (Windward) 0.03–5.34 52–146 5.62–9.10 0–36

Region 3 (North) 1.11–13.5 66–197 5.21–9.04 0