U.S. Department of the Interior

U.S. Geological Survey

Figure 1. Hydrologic regions of New Mexico.

0 50

50

100 MILES

0 100 KILOMETERS

109° 106° 103°

32°

34°

36°

Northwest 

Plateau

Northwest 

Plateau

Northern 

Mountain

Northeast Plains

Central 

Mountain-Valley

SouthWest

Southwest 

Desert

EXPLANATION

Hydrologic region boundary

Hydrologic region 

Southeast 

Mountain

Southeast Plains

Mountain

Digital base from U.S. Geological Survey

1:2,000,000, 1970

The National Flood-Frequency Program—Methods for Estimating Flood 

Magnitude and Frequency in Rural Areas in New Mexico, 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 FloodFrequency (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 New Mexico. 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

New Mexico is divided into eight 

hydrologic regions (fig. 1) on the basis of 

physiography, elevation, and precipitation. 

Waltemeyer (1996) 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, 

rural streams in each of these regions. A 

ninth set of equations were developed for 

small watersheds that drain less than 

10 square miles and that are less than 

7,500 feet in mean basin elevation. 

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. 

Waltemeyer (1996) provided the 

peak-discharge estimates (QT) and explanatory watershed variables for the 201 

streamflow-gaging stations used to 

develop the regression equations. The 

peak-discharge estimates were determined 

from available records through 1993. An 

envelope curve of the relation between 

maximum observed peak discharge and 

drainage area was also provided for each 

region.

USGS Fact Sheet 055-00

October, 2000

Pecos River

Sandia

Mountains
Procedure

The equations are based on the inchpound system of units, but the NFF Program will accept or report either the inchpound or metric system of units. The 

explanatory watershed variables used in 

the regression equations shown in table 1 

are as follow:

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

total area that contributes runoff upstream 

of the stream site of interest, measured by 

planimeter using the largest scale topographic map available.

Average channel elevation (Ec), in feet 

above sea level [National Geodetic Vertical Datum of 1929 (NGVD of 1929)], is 

the average of the elevations at points 10 

and 85 percent of the distance along the 

main channel from the location of the 

desired peak discharge to the drainage 

divide.

Mean basin elevation (E), in feet above sea 

level (NGVD of 1929), is the mean elevation of the drainage basin determined by 

the grid-sampling method. A transparent 

grid is placed over a topographic map on 

which the basin boundary is drawn. The 

mean elevation is determined as the average of the elevations at each grid intersection.

Maximum precipitation intensity, 24-hour 

duration storm, 10-year recurrence interval 

(I24,10), in inches, is the depth of rainfall 

from a 24-hour duration storm with a 

10 percent chance of being exceeded in 

any given year at the stream site of interest, as determined by interpolation 

between lines of equal intensity from the 

National Oceanic and Atmospheric 

Administration (NOAA) Atlas 2 precipitation frequency map (Miller and others, 

1973).

Maximum precipitation intensity, 24-hour 

duration storm, 25-year recurrence interval 

(I24,25), in inches, is the depth of rainfall 

from a 24-hour duration storm with a 

4 percent chance of occurring in any given 

year at the stream site of interest, as determined by interpolation between lines of 

equal intensity from the NOAA Atlas 2 

precipitation frequency map (Miller and 

others, 1973).

The regression equations and the standard errors of prediction are shown in table 

1. The standard error of prediction is a 

measure of the accuracy of a regression 

equation when estimating peak-discharges 

for ungaged watersheds similar to those 

that were used to derive the regression 

equations. Errors in the QT estimates for 

about two thirds of the ungaged watersheds 

will be less than or equal to the given standard errors of prediction. The standard 

error of prediction increases appreciably 

when any explanatory watershed variable is 

near or beyond the range limits shown in 

table 2, or when the location of the desired 

peak discharge is east of the Pecos River in 

the Southeast Plains region or in the Sandia 

Mountains in the Central Mountain Valley 

region, where limited peak-discharge data 

are available.

Improving Estimates With 

Gaged Data

Waltemeyer (1996) developed weighting techniques to improve estimates of 

peak discharge at gaged locations by combining the estimates derived from analysis 

of systematic 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 for the gaged site is computed as:

,

where

QT(G)w is the weighted estimate of peak 

discharge, QT, for recurrence 

interval T at the gaged 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.

The accuracy of the weighted discharge 

estimate, in equivalent years of record, is 

QT G( )w log

N QT G( )s ⋅ log EQ QT G( )r + ⋅ log

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

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

Ungaged Sites Near Gaged 

Sites on the Same Stream

Waltemeyer (1996) also showed how 

the weighted estimate for peak discharge at 

a gaged site can be used to improve estimates of peak discharge of an 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 regression 

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 U( )w

2∆A

A

g

----------QT U( )r 1 2∆A

A

g

– ----------     QT U( )g = +

QT U( )g

Au

A

g

------

      b

QT G( )w = ⋅
Table 1. Flood-peak discharge regression equations and associated statistics for streams that drain rural areas in New Mexico 

(modified from Waltemeyer, 1996)

[QT, peak discharge for recurrence interval T, 2 to 500 years, in cubic feet per second; A, drainage area, in square miles; E, mean basin elevation, in

feet above sea level; Ec, average channel elevation, in feet above sea level; I24,10, maximum precipitation intensity, 24-hour duration storm, 10-year

recurrence interval, in inches; I24,25, maximum precipitation intensity, 24-hour duration storm, 25-year recurrence interval, in inches]

Standard Standard

error of error or

prediction, prediction,

Regression equation in percent Regression equation in percent

Northeast Plains Northern Mountain

Q2 = 1.14 x 102A0.53 96 Q2 = 8.54 x 102A0.83(E/1,000)-2.22I24,250.31 92

Q5 = 3.07 x 102

A0.50 78 Q5 = 7.39 x 103A0.81(E/1,000)-3.01I24,250.63 82

Q10 = 5.08 x 102

A0.49 75 Q10 = 2.19 x 104A0.81(E/1,000)-3.41I24,250.81 78

Q25 = 8.53 x 102A0.48 72 Q25 = 6.90 x 104A0.80(E/1,000)-3.85I24,251.03 75

Q50 = 1.18 x 103

A0.48 72 Q50 = 1.44 x 105A0.80(E/1,000)-4.13I24,251.18 78

Q100 = 1.58 x 103A0.48 75 Q100 = 2.80 x 105A0.80(E/1,000)-4.40I24,251.33 82

Q500 = 2.80 x 103

A0.48 82 Q500 = 1.10 x 106A0.80(E/1,000)-4.95I24,251.64 92

Northwest Plateau Central Mountain Valley

Q2 = 8.47 x 101A0.47 111 Q2 = 7.47 x 105A0.50(Ec/1,000)-5.28I24,101.18 103

Q5 = 1.97 x 102

A0.46 82 Q5 = 2.57 x 105A0.47(Ec/1,000)-4.49I24,101.76 69

Q10 = 3.06 x 102

A0.46 72 Q10 = 1.53 x 105A0.46(Ec/1,000)-4.09I24,102.06 57

Q25 = 4.86 x 102

A0.45 66 Q25 = 8.89 x 104A0.44(Ec/1,000)-3.67I24,102.37 46

Q50 = 6.54 x 102

A0.45 63 Q50 = 6.11 x 104A0.43(Ec/1,000)-3.38I24,102.57 43

Q100 = 8.53 x 102

A0.45 63 Q100 = 4.18 x 104A0.42(Ec/1,000)-3.09I24,102.74 41

Q500 = 1.45 x 103A0.45 66 Q500 = 1.78 x 104A0.40(Ec/1,000)-2.45I24,103.03 43

Southeast Mountain Southwest Desert

Q2 = 8.54 x 106A0.60(E/1,000)-5.96 36 Q2 = 1.28 x 102A0.46 57

Q5 = 7.14 x 107

A0.67(E/1,000)-6.69 38 Q5 = 2.46 x 102A0.48 51

Q10 = 1.60 x 108A0.70(E/1,000)-6.94 41 Q10 = 3.45 x 102A0.49 51

Q25 = 3.04 x 108A0.75(E/1,000)-7.10 43 Q25 = 4.91 x 102A0.50 54

Q50 = 4.15 x 108A0.78(E/1,000)-7.16 46 Q50 = 6.15 x 102A0.51 57

Q100 = 5.21 x 108A0.81(E/1,000)-7.19 49 Q100 = 7.51 x 102A0.52 60

Q500 = 7.11 x 108

A0.87(E/1,000)-7.20 60 Q500 = 1.12 x 103A0.55 72

Southeast Plains Southwest Mountain

Q2 = 8.17 x 101A0.51 192 Q2 = 2.58 x 107A0.19(Ec/1,000)-6.10 88

Q5 = 2.36 x 102

A0.54 124 Q5 = 1.49 x 107A0.23(Ec/1,000)-5.53 85

Q10 = 4.07 x 102A0.55 103 Q10 = 1.03 x 107A0.25(Ec/1,000)-5.19 85

Q25 = 7.21 x 102

A0.57 88 Q25 = 6.53 x 106A0.27(Ec/1,000)-4.80 88

Q50 = 1.04 x 103

A0.58 78 Q50 = 4.69 x 106A0.29(Ec/1,000)-4.52 92

Q100 = 1.43 x 103A0.59 72 Q100 = 3.40 x 106A0.30(Ec/1,000)-4.25 96

Q500 = 2.72 x 103A0.62 66 Q500 = 1.66 x 106A0.32(Ec/1,000)-3.68 116

Statewide small basin, less than 10 square miles and less than 7,500 feet mean basin elevation

Q2 = 1.07 x 102A0.39 120 Q50 = 7.92 x 102A0.45 66

Q5 = 2.43 x 102A0.42 88 Q100 = 1.03 x 103A0.46 63

Q10 = 3.74 x 102A0.43 75 Q500 = 1.73 x 103A0.47 63

Q25 = 5.91 x 102A0.44 69
Sites in Transition Zones

When the drainage area of the site of 

interest is in more than one of the regions, 

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. 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

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.

Miller, J.F., Frederick, R.H., and Tracey, 

R.J., 1973, Precipitation-frequency 

atlas of the western United States, volume IV—New Mexico: National Oceanic and Atmospheric Administration 

NOAA Atlas 2, 43 p.

Waltemeyer, S.D., 1996, Analysis of the 

magnitude and frequency of peak discharge and maximum observed peak 

discharge in New Mexico: U.S. Geological Survey Water-Resources 

Investigations Report 96–4112, 79 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

[--, data not statistically significant]

Maximum 24-hour

Average precipitation intensity

channel Mean basin for indicated

Drainage elevation, elevation, recurrence interval

area, in feet in feet

Hydrologic in square above above 10 years, 25 years,

study region miles sea level1 sea level1 in inches in inches

Northeast plains 0.36–2,060 -- -- -- --

Northwest plateau .17–925 -- -- -- --

Southeast mountain 3.08–947 -- 5,440–9,060 -- --

Southeast plains .16–689 -- -- -- --

Northern mountain .63–2,850 -- 7,810–11,400 -- 2.00–4.45

Central mountain valley .16–3,660 5,310–9,280 -- 2.15–3.00 --

Southwest desert .20–2,830 -- -- -- --

Southwest mountain 2.12–426 6,160–8,980 -- -- --

Small basins statewide .20–10.0 -- -- -- --

1NGVD of 1929.