ANALYSIS OF THE MAGNITUDE AND

FREQUENCY OF THE 4-DAY ANNUAL LOW FLOW

AND REGRESSION EQUATIONS FOR

ESTIMATING THE 4-DAY, 3-YEAR LOW-FLOW

FREQUENCY AT UNGAGED SITES ON

UNREGULATED STREAMS IN NEW MEXICO

Prepared in cooperation with the

NEW MEXICO ENVIRONMENT DEPARTMENT

U.S. DEPARTMENT OF THE INTERIOR

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 01-4271
U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 01-4271

ANALYSIS OF THE MAGNITUDE AND

FREQUENCY OF THE 4-DAY ANNUAL LOW FLOW

AND REGRESSION EQUATIONS FOR

ESTIMATING THE 4-DAY, 3-YEAR LOW-FLOW

FREQUENCY AT UNGAGED SITES ON

Prepared in cooperation with the

NEW MEXICO ENVIRONMENT DEPARTMENT

By Scott D. Waltemeyer

Albuquerque, New Mexico

2002

UNREGULATED STREAMS IN NEW MEXICO
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

The use of firm, trade, and brand names in this report is for identification purposes only and does

not constitute endorsement by the U.S. Geological Survey.

For additional information write to: Copies of this report can be purchased

U.S. Geological Survey

Information Services

Box 25286

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District Chief

U.S. Geological Survey

Water Resources Division

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Albuquerque, NM 87109-1311

from:

Information regarding research and data-collection programs of the U.S. Geological Survey is ava

on the Internet via the World Wide Web. You may connect to the home page for the New Mexico D

Office using the URL http://nm.water.usgs.gov.
iii

CONTENTS

P

Abstract.................................................................................................................................................................................. 

Introduction ........................................................................................................................................................................... 

Purpose and scope ....................................................................................................................................................... 

General physiographic and hydrologic setting ............................................................................................................ 

Previous low-flow studies............................................................................................................................................ 

Acknowledgments ....................................................................................................................................................... 

Low-flow frequency characteristics....................................................................................................................................... 

Streamflow data ........................................................................................................................................................... 

Frequency analysis....................................................................................................................................................... 

Development of regression equations to estimate 4-day, 3-year low flow at ungaged sites.................................................. 

Basin and climatic characteristics................................................................................................................................ 

Development of geographical information system............................................................................................ 

Basin characteristics .......................................................................................................................................... 

Climatic characteristics...................................................................................................................................... 

Multiple linear regression............................................................................................................................................ 

Results ............................................................................................................................................................... 

Use and limitations ............................................................................................................................................ 

Summary................................................................................................................................................................................ 

Selected references ................................................................................................................................................................ 

FIGURES

1. Map showing location of streamflow-gaging stations used for 4-day, 3-year low-flow frequency analysis

in New Mexico ................................................................................................................................................... 

2. Graph showing 4-day low-flow frequency curve of Mora River at La Cueva, New Mexico, streamflowgaging station (07215500).................................................................................................................................. 

3. Maps showing geographical information system delineation of basin streams and model-response unit

for Rio Chama near La Puente, New Mexico, streamflow-gaging station (08284100) ..................................... 

TABLES

1. Four-day annual low flows and years of record used for selected streamflow-gaging stations in

New Mexico ....................................................................................................................................................... 

2. Magnitude and frequency of 4-day annual low-flow characteristics and years of record used for selected

streamflow-gaging stations with no flow for the 4-day, 3-year low-flow frequency in New Mexico ................ 

3. Selected basin and climatic characteristics for selected streamflow-gaging stations in New Mexico..................... 

4. Additional basin and climatic characteristics determined using the geographical information system and

drainage areas previously published for selected streamflow-gaging stations in New Mexico ......................... 

5. Ranges of statistically significant basin and climatic characteristics used in the regression analysis ..................... 
iv

CONVERSION FACTORS AND VERTICAL DATUM

Sea level: In this report, "sea level" refers to the National Geodetic Vertical Datum of 1929—a geodetic datum derived from a general adjustment of the first-order level nets of the United States and

Canada, formerly called Sea Level Datum of 1929.

Multiply By To obtain

inch 25.40 millimeter

foot 0.3048 meter

mile 1.609 kilometer

square mile 2.590 square kilometer

cubic foot per second 0.02832 cubic meter per second
1

ABSTRACT

Two regression equations were developed for

estimating the 4-day, 3-year (4Q3) low-flow frequency

at ungaged sites on unregulated streams in New

Mexico. The first, a statewide equation for estimating

the 4Q3 low-flow frequency from drainage area and

average basin mean winter precipitation, was

developed from the data for 50 streamflow-gaging

stations that had non-zero 4Q3 low-flow frequency.

The 4Q3 low-flow frequency for the 50 gaging stations

ranged from 0.08 to 18.7 cubic feet per second. For this

statewide equation, the average standard error of

estimate was 126 percent and the coefficient of

determination was 0.48. The second, an equation for

estimating the 4Q3 low-flow frequency in mountainous

regions from drainage area, average basin mean winter

precipitation, and average basin slope, was developed

from the data for 40 gaging stations located above

7,500 feet in elevation. For this regression equation, the

average standard error of estimate was 94 percent and

the coefficient of determination was 0.66.

A U.S. Geological Survey computer-program

interface for a geographical information system (GIS),

called the GIS Weasel, was used to determine basin and

climatic characteristics for 84 gaging stations that were

not affected by regulation. Mean monthly precipitation

estimates from 1961 to 1990 were used in the GIS

Weasel to compute the climatic characteristics of

average basin winter precipitation and annual mean

precipitation. The U.S. Geological Survey National

Elevation Dataset, which currently consists of the 7.5-

minute, 30-meter digital elevation model for each

State, was used in the GIS Weasel to compute the basin

characteristics of drainage area, average basin slope,

average basin elevation, and average basin aspect.

Basin and climatic characteristics that were statistically

significant in the regression equation with the 4Q3 lowflow frequency were drainage area, which ranged from

1.62 to 5,900 square miles; average basin mean winter

precipitation, which ranged from 3.89 to 19.42 inches;

and average basin slope, which ranged from 0.166 to

0.517 percent.

INTRODUCTION

Estimates of the magnitude and frequency of

annual low flow at ungaged sites on unregulated

streams in New Mexico are necessary for the desig

and administration of water-quality standards. The

New Mexico Water Quality Control Commission

established the 4-day low-flow frequency having a

recurrence interval of 3 years (4Q3) as the daily low

flow for these standards. The 4Q3 low-flow frequen

is the lowest 4-consecutive-day discharge that has 

recurrence interval of 3 years but that does not

necessarily occur every 3 years. The New Mexico

Environment Department (NMED) is required to u

the 4Q3 low flow in the assessment and establishm

of Total Maximum Daily Loads (TMDL’s) for vari

water-quality constituents.

The NMED Surface Water Quality Bureau

certifies permits for the National Pollutant Dischar

Elimination System (NPDES), which is administer

by the U.S. Environmental Protection Agency unde

the Clean Water Act of 1972. The NMED needs

streamflow data for NPDES permitting and

establishment of TMDL’s for both point and nonpo

pollutant sources. The NMED uses the 4Q3 low-flo

frequency, which is statistically derived from U.S.

Geological Survey (USGS) streamflow-gaging stat

data, to (1) determine the assimilation capacities of

receiving water and (2) use as the minimum discha

at which the New Mexico water-quality standards a

applied.

The most recent statistical analysis of

streamflow data for New Mexico (Waltemeyer, 198

provides low-flow frequency characteristics for gag

stations using data through 1985; however, that

analysis does not provide regression equations to

estimate the 4Q3 low flow at ungaged sites. Curren

(2001), the NMED estimates the 4Q3 low-flow

frequency for ungaged sites using the methods in

Borland (1970). Because of the availability of mor

streamflow and precipitation data the USGS, in

cooperation with the NMED, conducted a study to

update the regression equations to estimate the 4Q3

low-flow frequency for ungaged sites on unregulate

streams in New Mexico.

ANALYSIS OF THE MAGNITUDE AND FREQUENCY OF THE 4-DAY

ANNUAL LOW FLOW AND REGRESSION EQUATIONS FOR

ESTIMATING THE 4-DAY, 3-YEAR LOW-FLOW FREQUENCY AT

UNGAGED SITES ON UNREGULATED STREAMS IN NEW MEXICO

By Scott D. Waltemeyer
2

Purpose and Scope

This report presents the results of a study to

characterize the magnitude and frequency of the 4-day

annual low flow for selected streamflow-gaging

stations and to develop regional regression equations to

estimate the 4Q3 low-flow frequency at ungaged sites

on unregulated streams in New Mexico. Two

regression equations are presented. For comparison to

the 1970 equation, a statewide equation estimates

regional 4Q3 low-flow frequency derived from 50

gaging stations that had non-zero flow in all

physiographic regions in New Mexico. One equation

estimates 4Q3 low-flow frequency for 40 gaging

stations in mountainous regions that had non-zero flow.

The magnitude and frequency of 4-day annual lowflow characteristics for gaging stations in New Mexico

and selected basin, climatic, and low-flow

characteristics are presented in tables.

General Physiographic and Hydrologic

Setting

The physiography of New Mexico is varied and

complex; it includes mountains, plains, plateaus,

valleys, and deserts. Precipitation characteristics are

the result of physiography, and the corresponding

streamflow response in the unregulated reaches of

streams is influenced by the precipitation. The State is

divided into eight physiographic regions (fig. 1).

The Rocky Mountains (physiographic region 5)

create a marked climatological division in the northcentral part of the State. Storms that originate in the

Pacific Ocean travel over the mountains and

progressively intensify in the plains of eastern New

Mexico (physiographic regions 1 and 4). Isopluvial

contours of annual maximum precipitation intensity

indicate a pattern of greater intensity in an easterly

direction in the eastern plains (Miller and others,

1973). Storms that originate in the Gulf of Mexico

during summer primarily affect the eastern half of New

Mexico. Regional thunderstorms typically develop

over the mountains during early and late summer. The

greatest monthly precipitation, although mostly of

irregular regional extent, typically occurs in July and

August. For mountainous areas, winter precipitation

(October - April) contributes a significant part of the

total annual precipitation, which predominately occurs

as snowfall.

Intense, convective midsummer storm

result in severe flooding, particularly in the e

of the State. Most floods in the northern, sou

and southwestern mountainous regions gener

from snowmelt, sometimes from rainfall, an

occasionally from rainfall on snowpack. Flo

plains, plateaus, valleys, and deserts almost 

result from rainfall.

Previous Low-Flow Studies

Reiland and Haynes (1963) presented 

duration of daily mean discharge and selecte

sequences of low-mean and high-mean disch

122 gaging stations in New Mexico. Their r

provided techniques for determining flow-du

data and low- and high-flow frequency data. 

(1970) presented statewide regression equati

on records for 64 gaging stations. Statewide 

were derived for selected sequences of low- 

flow frequencies in relation to basin and clim

characteristics. Mean monthly and mean ann

discharge relations also were derived. Reilan

presented flow-duration data for 156 gaging 

Waltemeyer (1989) presented statistical sum

mean monthly and mean annual flow univar

statistics and low-flow and high-flow freque

flow-duration information for 169 gaging st

New Mexico. Records for 17 gaging station

separated into periods of before, during, and 

changes in upstream regulation. The report

(Waltemeyer, 1989) had no regional equation

basin and climatic characteristics.

Low-flow magnitude and frequency a

to basin and climatic characteristics. Low-fl

frequency equations have been developed fo

States, especially in the Eastern United State

and Mason, 1993); however, streamflow can 

variable in the Western United States than in 

because of the dramatic variations in vegeta

climate. Because of this variability in stream

regional equations of low-flow frequency

characteristics in relation to basin and clima

characteristics for some physiographic regio

Western United States have more dispersion 

relations. In some physiographic regions, es

a statistically significant equation with basin 

climatic characteristics can be difficult.
O

C

K Y

M

O

U

N

T A I N

S

R

0

0

10

10

20 MILES

20 KILOMETERS

1

2

4 3

5

6

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8

9 10

11

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18 19

20

22 21

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40

41

84

42

43

44

45

46

47 48

49

50

82

36°

35°

34°

33°

32°

109° 108° 107° 106° 105° 104° 103°

37°

SAN JUAN

McKINLEY

CIBOLA

CATRON

GRANT

HIDALGO

RIO ARRIBA

SANDOVAL

BERNALILLO

VALENCIA

SOCORRO

SIERRA

LUNA

DOÑA

ANA

LOS

ALAMOS

SANTA

FE

TORRANCE

LINCOLN

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TAOS

COLFAX

MORA

SAN MIGUEL

GUADALUPE

DE BACA

CHAVES

EDDY

UNION

HARDING

QUAY

CURRY

ROOSEVELT

LEA

REGION 5

REGION 2

REGION 1

REGION 4

REGION 6

REGION 7

REGION 8

REGION 3

07

08

09

25

10

25

40

40

51

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71 70

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EXPLANATION

09 MAJOR RIVER BASIN BOUNDARY AND NUMBER

07 Lower Mississippi River Basin

08 Western Gulf of Mexico Basin

09 Colorado River Basin

52

1 Northeast plains region

2 Northwest plateau region

3 Southeast mountain region

4 Southeast plains region

5 Northern mountain region

6 Central mountain valley region

7 Southwest desert region

8 Southwest mountain region

Streamflow-gaging station with zero discharge for the 4-day, 3-year low flow frequency

Streamflow-gaging station with non-zero discharge for the 4-day, 3-year low flow frequency

3 PHYSIOGRAPHIC REGION BOUNDARY AND NUMBER

83

Figure 1. Location of streamflow-gaging stations used for low-flow frequency anaylsis in New Mexico.

285

285

I R

O

N

GRA

DE

a

Can

dian

River Pecos

Pecos

River

River

San

uan J River

io R

u

r

P

e co

Rio

eñasco P

Animas ve Ri r

3
4

A statewide network analysis prepared for New

Mexico gaging stations (Borland, 1970) indicated that

the 7-day, 2-year low-flow frequency was significantly

related to drainage area and mean winter precipitation

(1931-60). However, the standard error of estimate

(SEE) in Borland’s (1970) study was 101 percent. The

accuracy of simple- or multiple-regression equations

usually is measured by the SEE. The SEE is expressed

as a percentage in this report, and it is the standard

deviation of the distribution (normal) of residuals about

the regression line. For a given regression, about 67

percent of the estimated values will be within one

standard deviation of the actual values, and about 95

percent of the estimated values will be within two

standard deviations of the actual values. For example,

if the SEE of a regression equation is 38 percent, about

67 percent of all values used to develop the regression

equations will be within 38 percent of the estimated

values and about 95 percent of all values will be within

76 percent of the estimated values or two SEE’s.

Acknowledgments

Oregon State University and the Oregon

Climatic Service were helpful in providing the

precipitation data. Roland Viger, USGS Branch of

Regional Research, provided additional programming

to the GIS Weasel for determining average basin

precipitation.

LOW-FLOW FREQUENCY

CHARACTERISTICS

Gaging stations affected by regulation were not

considered for this low-flow frequency analysis. The

database initially used consisted of streamflow records

for 84 continuous-record gaging stations on

unregulated streams. The subsequent analysis yielded

50 gaging stations that had non-zero flow for 4

consecutive days in each year of record. Unregulated

specifically means that a gaging station is not affected

by known regulation such as dams for water storage or

flood control. Some gaging stations may have unknown

upstream diversions of streamflow.

Streamflow Data

The climatic year was used for this lo

frequency analysis. In New Mexico, streamfl

typically is at its lowest just prior to annual 

runoff. The 1998 climatic year (April 1, 199

March 31, 1998) was the last year considere

analysis in this report.

Annual low-flow data characteristics w

determined by analyzing the minimum 4-da

consecutive low flow of each climatic year fo

stations with 10 or more years of record, wi

exception of two gaging stations with 6 and 

record. The period of record varies from gag

to gaging station, but the average length of r

51 years.

The 50 gaging stations for which the 4

flow was non-zero (0.08 to 18.7 cubic feet p

(ft3/s) are listed in table 1, and the 34 gaging 

that had zero discharge for the 4Q3 low flow 

in table 2.

Frequency Analysis

The 4-day annual low flows for each s

ranked from smallest to largest for frequenc

using the log-Pearson type III distribution; a

description of the log-Pearson type III distri

presented in Kite (1977). Other n-day annual 

commonly used for low-flow frequency ana

include the 1-, 3-, 7-, 14-, 30-, 60-, 90-, 120

day flows. The USGS computer program SW

ANNIE (Lumb and others, 1990) was used f

frequency analysis. SWSTAT is available fo

downloading at http://water.usgs.gov/softwa

surface_water.html, accessed December 14, 

program was used to generate estimated 4-d

flows for selected recurrence intervals rangi

1.11 to 50 years (tables 1 and 2). An examp

frequency curve is shown in figure 2, which 

estimated 4Q3 low-flow discharge to be 1 ft

Basically, the non-exceedance probability is 

lowest 4-day annual low flow in a given yea

generally not be less than 1 ft3

/s at least ever

The 4Q3 low flow ranged from 0.08 to 18.7 f

gaging stations (table 3). The 4Q3 low flow 

exceedance probability that the discharge wi

to but not be less than the value shown in tabl
5

Table 1. Four-day annual low flows and years of record used for selected streamflow-gaging station

___________________________________________________________________________________________

U.S. Discharge, in cubic feet per second, for indGeological recurrence interval, in years, and annu

Site Survey exceedance probability, in percentnum- gaging- ___________________________________________ber station 1.11 1.25 2 3 5 10 (fig. 1) number Station name 90% 80% 50% 33% 20% 10% ___________________________________________________________________________________________

1 07153500 Dry Cimarron River near Guy, N. Mex. 2.14 1.31 0.38 0.14 0.00 0.00 02 07203000 Vermejo River near Dawson, N. Mex. 4.56 3.01 1.26 .77 .44 .22 3 07203525 Vermejo River near Maxwell, N. Mex. 1.33 .92 .28 .10 .02 .00 4 07205000 Sixmile Creek near Eagle Nest, N. Mex. 1.00 .62 .26 .17 .12 .08 5 07207500 Ponil Creek near Cimarron, N. Mex. 2.43 1.52 .37 .10 .00 .00 6 07208500 Rayado Creek at Sauble Ranch near Cimarron, N. Mex. 3.62 3.10 2.20 1.80 1.47 1.16 7 07211500 Canadian River near Taylor Springs, N. Mex. 9.80 6.46 1.92 .64 .01 .00 8 07214500 Mora River near Holman, N. Mex. 4.26 3.09 1.55 1.04 .69 .44 9 07214800 Rio La Casa near Cleveland, N. Mex. 3.29 2.85 2.06 1.68 1.37 1.07 10 07215500 Mora River at La Cueva, N. Mex. 5.39 3.68 1.57 .94 .52 .24 11 07216500 Mora River near Golondrinas, N. Mex. 6.12 4.08 1.67 .99 .53 .24 12 07217100 Coyote Creek above Guadalupita, N. Mex. 2.77 2.10 1.22 .91 .70 .52 13 07218000 Coyote Creek near Golondrinas, N. Mex. 2.83 1.87 .80 .50 .32 .19 14 07220000 Sapello River at Sapello, N. Mex. 4.14 2.35 .75 .38 .17 .00 15 07221000 Mora River near Shoemaker, N. Mex. 6.88 4.54 1.72 .92 .43 .13 16 07221500 Canadian River near Sanchez, N. Mex. 18.4 10.1 1.84 .29 .00 .00 17 08263000 Latir Creek near Cerro, N. Mex. 2.07 2.00 1.68 1.41 1.13 .82 18 08264000 Red River near Red River, N. Mex. 4.22 3.92 3.29 2.94 2.62 2.27 19 08265000 Red River near Questa, N. Mex. 16.3 13.7 9.37 7.45 5.91 4.50 20 08266000 Cabresto Creek near Questa, N. Mex. 4.68 4.01 2.92 2.46 2.08 1.72 
6

Table 1. Four-day annual low flows and years of record used for selected streamflow-gaging 

in New Mexico--Continued

___________________________________________________________________________________________

U.S. Discharge, in cubic feet per second, for indGeological recurrence interval, in years, and annu

Site Survey exceedance probability, in percentnum- gaging- ___________________________________________ber station 1.11 1.25 2 3 5 10 (fig. 1) number Station name 90% 80% 50% 33% 20% 10% ___________________________________________________________________________________________

21 08267500 Rio Hondo near Valdez, N. Mex. 11.3 10.4 8.73 7.90 7.15 6.38 22 08268500 Arroyo Hondo at Arroyo Hondo, N. Mex. 8.95 7.95 6.46 5.86 5.38 4.93 23 08269000 Rio Pueblo de Taos near Taos, N. Mex. 7.71 6.84 5.27 4.54 3.90 3.27 24 08271000 Rio Lucero near Arroyo Seco, N. Mex. 6.43 5.98 5.02 4.49 4.00 3.48 25 08275000 Rio Fernando de Taos near Taos, N. Mex. 1.22 .67 .22 .12 .07 .04 26 08275300 Rio Pueblo de Taos near Ranchito, N. Mex. 9.86 7.06 3.49 2.34 1.58 1.01 27 08275500 Rio Grande del Rancho near Talpa, N. Mex. 5.66 5.02 3.74 3.10 2.54 2.00 28 08275600 Rio Chiquito near Talpa, N. Mex. 2.55 2.18 1.54 1.26 1.03 .81 29 08276300 Rio Pueblo de Taos below Los Cordovas, N. Mex. 20.4 16.0 9.66 7.33 5.60 4.14 30 08284100 Rio Chama near La Puente, N. Mex. 57.4 44.5 25.7 18.7 13.6 9.36 31 08289000 Rio Ojo Caliente at La Madera, N. Mex. 6.87 5.82 4.01 3.21 2.56 1.96 32 08291000 Santa Cruz River at Cundiyo, N. Mex. 10.1 8.66 6.45 5.52 4.75 4.03 33 08292000 Santa Clara Creek near Española, N. Mex. 2.73 2.52 1.61 1.00 .54 .22 34 08302200 North Fork Tesuque Creek near Santa Fe, N. Mex. .46 .44 .39 .37 .35 .33 35 08302500 Tesuque Creek above Diversions near Santa Fe, N. Mex. .99 .87 .60 .46 .34 .24 36 08313350 Rito de los Frijoles in Bandelier National Monument,

N. Mex. .88 .76 .53 .43 .34 .26 

37 08317850 Galisteo Creek above Galisteo Reservoir, N. Mex. .22 .18 .11 .08 .05 .03 38 08321500 Jemez River below East Fork near Jemez Springs,

N. Mex. 13.6 11.9 9.35 8.29 7.44 6.63 

39 08323000 Rio Guadalupe at Box Canyon near Jemez, N. Mex. 11.2 9.58 7.06 5.98 5.09 4.25 40 08324000 Jemez River near Jemez, N. Mex. 22.7 19.6 14.5 12.2 10.4 8.59 
7

Table 1. Four-day annual low flows and years of record used for selected steamflow-gaging 

in New Mexico--Concluded

___________________________________________________________________________________________

U.S. Discharge, in cubic feet per second, for indGeological recurrence interval, in years, and annu

Site Survey exceedance probability, in percentnum- gaging- ___________________________________________ber station 1.11 1.25 2 3 5 10 (fig. 1) number Station name 90% 80% 50% 33% 20% 10% ___________________________________________________________________________________________41 08360000 Alamosa Creek near Monticello, N. Mex. 6.49 6.28 5.90 5.72 5.57 5.41 42 08377900 Rio Mora near Terrero, N. Mex. 6.72 5.91 4.41 3.68 3.06 2.45 43 08378500 Pecos River near Pecos, N. Mex. 28.2 24.7 18.7 15.9 13.6 11.3 44 08379500 Pecos River near Anton Chico, N. Mex. 16.9 8.89 2.17 .91 .32 .05 45 08380500 Gallinas Creek near Montezuma, N. Mex. 4.92 4.02 2.52 1.89 1.41 .99 46 08387000 Rio Ruidoso at Hollywood, N. Mex. 10.0 7.36 3.78 2.57 1.75 1.12 47 08387600 Eagle Creek below South Fork near Alto, N. Mex. .46 .38 .19 .10 .04 .00 48 08388000 Rio Ruidoso at Hondo, N. Mex. 3.21 1.44 .46 .31 .23 .18 49 08396000 Cottonwood Creek near Lake Arthur, N. Mex. .88 .57 .25 .16 .11 .07 50 08405500 Black River above Malaga, N. Mex. 6.34 4.92 3.06 2.40 1.92 1.51 ___________________________________________________________________________________________
8

Table 2. Magnitude and frequency of 4-day low-flow characteristics and years of record use

for selected streamflow-gaging stations with no flow for the 4-day, 3-year low-flow frequency in New 

___________________________________________________________________________________________

U.S. Discharge, in cubic feet per second, for indGeological recurrence interval, in years, and annu

Site Survey exceedance probability, in percentnum- gaging- __________________________________________ber station 1.11 1.25 2 3 5 10 (fig. 1) number Station name 90% 80% 50% 33% 20% 10% ___________________________________________________________________________________________

51 07199000 Canadian River near Hebron, N. Mex. 0.03 0.01 0.00 0.00 0.00 0.00 0.52 07204000 Moreno Creek at Eagle Nest, N. Mex. .00 .00 .00 .00 .00 .00 .53 07204500 Cieneguilla Creek near Eagle Nest, N. Mex. .00 .00 .00 .00 .00 .00 .54 07214000 Canadian River near Roy, N. Mex. 8.25 3.12 .00 .00 .00 .00 .55 07222500 Conchas River at Variadero, N. Mex. .00 .00 .00 .00 .00 .00 .56 07226500 Ute Creek near Logan, N. Mex. .00 .00 .00 .00 .00 .00 .57 07227100 Revuelto Creek near Logan, N. Mex. .17 .08 .00 .00 .00 .00 .58 08252500 Costilla Creek above Costilla Dam, N. Mex. .00 .00 .00 .00 .00 .00 .59 08253000 Casias Creek near Costilla, N. Mex. .00 .00 .00 .00 .00 .00 .60 08253500 Santistevan Creek near Costilla, N. Mex. .00 .00 .00 .00 .00 .00 .61 08284500 Willow Creek near Park View, N. Mex. .17 .00 .00 .00 .00 .00 .62 08284300 Horse Lake Creek above Heron Reservoir near

Los Ojos, N. Mex. .00 .00 .00 .00 .00 .00 .

63 08340500 Arroyo Chico near Guadalupe, N. Mex. .00 .00 .00 .00 .00 .00 .64 08341300 Bluewater Creek above Bluewater Dam near

Bluewater, N. Mex. .20 .12 .04 .00 .00 .00 .

65 08343500 Rio San Jose near Grants, N. Mex. .00 .00 .00 .00 .00 .00 .66 08343100 Grants Canyon at Grants, N. Mex. .00 .00 .00 .00 .00 .00 .67 08382500 Gallinas River near Colonias, N. Mex. .25 .00 .00 .00 .00 .00 .68 08382730 Los Esteros Creek above Santa Rosa Lake, N. Mex. .00 .00 .00 .00 .00 .00 .69 08382760 Los Esteros Creek tributary above Santa Rosa Lake,

N. Mex. .00 .0.0 .00 .00 .00 .00 .

70 08382800 Pecos River above Los Esteros Damsite near

Santa Rosa, N. Mex. .00 .00 .00 .00 .00 .00 .
9

Table 2. Magnitude and frequency of 4-day low-flow characteristics and years of record use

for selected streamflow-gaging stations with no flow for the 4-day, 3-year low-flow frequency in New Mex

___________________________________________________________________________________________

U.S. Discharge, in cubic feet per second, for indGeological recurrence interval, in years, and annu

Site Survey exceedance probability, in percentnum- gaging- __________________________________________ber station 1.11 1.25 2 3 5 10 (fig. 1) number Station name 90% 80% 50% 33% 20% 10% ___________________________________________________________________________________________

71 08334000 Rio Puerco above Arroyo Chico near Guadalupe,

N. Mex. 0.00 0.00 0.00 0.00 0.00 0.00 0.

72 08351500 Rio San Jose at Correo, N. Mex. .00 .00 .00 .00 .00 .00 .73 08387800 Eagle Creek near Alto, N. Mex. .00 .00 .00 .00 .00 .00 .74 08390500 Rio Hondo at Diamond A Ranch near Roswell,

N. Mex. .00 .00 .00 .00 .00 .00 .

75 08393200 Rocky Arroyo above Two Rivers Reservoir near

Roswell, N. Mex. .00 .00 .00 .00 .00 .00 .

76 08393600 North Spring River at Roswell, N. Mex. .00 .00 .00 .00 .00 .00 .77 08394500 Rio Felix at Old Highway Bridge near Hagerman,

N. Mex. .53 .10 .00 .00 .00 .00 .

78 08398500 Rio Peñasco at Dayton, N. Mex. .00 .00 .00 .00 .00 .00 .79 08400000 Fourmile Draw near Lakewood, N. Mex. .00 .00 .00 .00 .00 .00 .80 08401900 Rocky Arroyo at Highway Bridge near Carlsbad,

N. Mex. .00 .00 .00 .00 .00 .00 .

81 08405150 Dark Canyon Draw at Carlsbad, N. Mex. .00 .00 .00 .00 .00 .00 .82 08408500 Delaware River near Red Bluff, N. Mex. .52 .03 .00 .00 .00 .00 .83 09386950 Zuni River above Black Rock Reservoir, N. Mex. .00 .00 .00 .00 .00 .00 .84 09430600 Mogollon Creek near Cliff, N. Mex. .39 .11 .00 .00 .00 .00 .___________________________________________________________________________________________
Figure 2. Four-day low-flow frequency curve for Mora River at

La Cueva, New Mexico. Location of gaging station shown as number 10 in figure 1.

streamflow-gaging station 07215500

4-DAY LOW FLOW

DISCHARGE FOR 3-YEAR RECURRENCE INTERVAL OR 0.33 NON-EXCEEDANCE

PROBABILITY

6

5

4

3

2

1

0

DIS

C

H

A

R

G

E, NI C

U

BIC FE

E

T

P

E

R

S

E

C

O

N

D

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

NON-EXCEEDANCE PROBABILITY

1.0 1.11 1.25 1.43 1.67 2 2.5 3.33 5 10

RECURRENCE INTERVAL, IN YEARS

10
11

Table 3. Selected basin and climatic characteristics for selected streamflow-gaging stations in N

[mi2, square miles; ft3/s, cubic feet per second; 4Q3, 4-day, 3-year low-flow frequency; Pw, mean winter 

(October - April 1961-90); basin and climatic characteristics determined with GIS Weasel]

___________________________________________________________________________________________

U.S.Geological

Site Survey Average Averagenum- gaging- Drainage basin basinber station area 4Q3 Pw slope(fig. 1) number Station name (mi2) (ft3/s) (inches) (percent)

___________________________________________________________________________________________

1 07153500 Dry Cimarron River near Guy, N. Mex. 611 0.14 5.25 0.1132 07203000 Vermejo River near Dawson, N. Mex. 342 .77 7.80 1.2253 07203525 Vermejo River near Maxwell, N. Mex. 548 .10 6.72 1.1954 07205000 Sixmile Creek near Eagle Nest, N. Mex. 9.5 .17 7.97 1.2695 07207500 Ponil Creek near Cimarron, N. Mex. 183 .10 8.04 1.2506 07208500 Rayado Creek at Sauble Ranch near Cimarron, N. Mex. 59.1 1.80 9.68 1.2247 07211500 Canadian River near Taylor Springs, N. Mex. 2,760 .64 6.07 .1578 07214500 Mora River near Holman, N. Mex. 62.7 1.04 11.77 1.2659 07214800 Rio la Casa near Cleveland, N. Mex. 22.9 1.68 16.03 1.30910 07215500 Mora River at La Cueva, N. Mex. 179 .94 10.17 1.25011 07216500 Mora River near Golondrinas, N. Mex. 267 .99 9.10 1.22212 07217100 Coyote Creek above Guadalupita, N. Mex. 75.2 .91 8.95 1.17813 07218000 Coyote Creek near Golondrinas, N. Mex. 237 .50 6.66 1.16614 07220000 Sapello River at Sapello, N. Mex. 132 .38 8.86 1.21815 07221000 Mora River near Shoemaker, N. Mex. 1,070 .92 6.69 .14016 07221500 Canadian River near Sanchez, N. Mex. 5,900 .29 5.58 .12717 08263000 Latir Creek near Cerro, N. Mex. 10.5 1.41 15.20 1.39618 08264000 Red River near Red River, N. Mex. 19.1 2.94 16.83 1.36219 08265000 Red River near Questa, N. Mex. 111 7.45 13.85 1.39820 08266000 Cabresto Creek near Questa, N. Mex. 35.6 2.46 13.99 1.408
12

Table 3. Selected basin and climatic characteristics for selected streamflow-gaging stations in New M

___________________________________________________________________________________________

U.S.Geological

Site Survey Average Averagenum- gaging- Drainage basin basinber station area 4Q3 Pw slope(fig. 1) number Station name (mi2) (ft3/s) (inches) (percent)

___________________________________________________________________________________________

21 08267500 Rio Hondo near Valdez, N. Mex. 36.7 7.90 13.90 10.51722 08268500 Arroyo Hondo at Arroyo Hondo, N. Mex. 66.2 5.86 10.77 1.39623 08269000 Rio Pueblo de Taos near Taos, N. Mex. 57.5 4.54 12.02 1.35524 08271000 Rio Lucero near Arroyo Seco, N. Mex. 16.7 4.49 14.83 1.50625 08275000 Rio Fernando de Taos near Taos, N. Mex. 60.3 .12 9.68 1.28326 08275300 Rio Pueblo de Taos near Ranchito, N. Mex. 187 2.34 10.20 1.30427 08275500 Rio Grande del Rancho near Talpa, N. Mex. 76.2 3.10 15.80 1.30428 08275600 Rio Chiquito near Talpa, N. Mex. 37.6 1.26 13.31 1.31229 08276300 Rio Pueblo de Taos below Los Cordovas, N. Mex. 384 7.33 10.87 1.26830 08284100 Rio Chama near La Puente, N. Mex. 467 18.7 16.96 1.18631 08289000 Rio Ojo Caliente at La Madera, N. Mex. 409 3.21 11.22 1.18032 08291000 Santa Cruz River at Cundiyo, N. Mex. 91.5 5.52 11.32 1.35933 08292000 Santa Clara Creek near Española, N. Mex. 36.5 1.00 11.20 1.32934 08302200 North Fork Tesuque Creek near Santa Fe, N. Mex. 1.62 .37 15.26 1.36035 08302500 Tesuque Creek above Diversions near Santa Fe, N. Mex. 11.6 .46 9.29 1.38036 08313350 Rito de los Frijoles in Bandelier National Monument, N. Mex. 18.3 .43 8.05 1.27937 08317850 Galisteo Creek above Galisteo Reservoir, N. Mex. 562 .08 5.31 .09738 08321500 Jemez River below East Fork near Jemez Springs, N. Mex. 172 8.29 12.76 1.22739 08323000 Rio Guadalupe at Box Canyon near Jemez, N. Mex. 233 5.98 13.37 1.22540 08324000 Jemez River near Jemez, N. Mex. 467 12.2 12.44 1.234
13

Table 3. Selected basin and climatic characteristics for selected streamflow-gaging stations in New M

___________________________________________________________________________________________

U.S.Geological

Site Survey Average Averagenum- gaging- Drainage basin basinber station area 4Q3 Pw slope(fig. 1) number Station name (mi2) (ft3/s) (inches) (percent)

___________________________________________________________________________________________

41 08360000 Alamosa Creek near Monticello, N. Mex. 401 5.72 5.16 0.19042 08377900 Rio Mora near Terrero, N. Mex. 53.2 3.68 19.42 1.28043 08378500 Pecos River near Pecos, N. Mex. 170 15.9 17.23 1.30444 08379500 Pecos River near Anton Chico, N. Mex. 1,040 .91 7.59 .18445 08380500 Gallinas Creek near Montezuma, N. Mex. 75.9 1.89 10.89 1.30546 08387000 Rio Ruidoso at Hollywood, N. Mex. 120 2.57 8.06 1.25247 08387600 Eagle Creek below South Fork near Alto, N. Mex. 8.19 .10 9.15 1.41848 08388000 Rio Ruidoso at Hondo, N. Mex. 289 .31 6.63 .24549 08396000 Cottonwood Creek near Lake Arthur, N. Mex. 201 .16 3.89 .02550 08405500 Black River above Malaga, N. Mex. 373 2.40 4.21 .162___________________________________________________________________________________________1Mean basin elevation greater than 7,500 feet.
14

DEVELOPMENT OF REGRESSION

EQUATIONS TO ESTIMATE 4-DAY, 3-YEAR

LOW FLOW AT UNGAGED SITES

Basin and Climatic Characteristics

Development of Geographical Information System

Basin and climatic characteristics were

computed using an ARC/INFO geographical

information system (GIS) (ESRI, 1999) and algorithms

developed by the USGS. The GIS Weasel (U.S.

Geological Survey, 2000) was used to derive basin and

climatic characteristics from raster data. GIS Weasel

uses a GRID subsystem of ARC/INFO to discretize

coverages (vector data) into grids of cells with specific

dimensions (for example, 85 feet by 85 feet) and to

assign a data value to each grid cell. The grid of data

values represents some aspect of the discretized

coverage, such as elevation or precipitation. The data

values can be manipulated by applying mathematical

operations to individual cells, to the whole grid, or by

combining two or more grids. GIS Weasel currently

(2001) runs on a Unix or Windows NT platform and is

available for downloading at http://

wwwbrr.cr.usgs.gov/weasel/, accessed July 10, 2000.

Coverages of vector data were converted to raster

data by discretizing coverages into a regularly spaced

grid. The rasterization of the vector data or the use of

raster data is herein referred to as “raster modeling.”

Grid cells were assigned data values representing

geospatial characteristics.

Basin Characteristics

The following basin and climatic characteristics

were determined with raster modeling using GIS

Weasel (tables 3 and 4): drainage area, average basin

slope, basin aspect, average basin elevation, average

basin mean annual precipitation (1961-90), and

average basin mean winter precipitation (1961-90).

Existing basin and climatic characteristics also were

available from the USGS Water-Data Storage and

Retrieval System (WATSTORE) computerized data

system (Dempster, 1981; 1983). Existing data values

for the following basin and climatic characteristics

were obtained from WATSTORE: drainage area, mean

annual precipitation (1931-60), basin slope, latitude of

gaging station, and channel elevation at 10 and 85

percent of the stream length, in feet (above sea level).

These data values were used for preliminary analysis

and are not listed in this report.

The National Elevation Dataset (NED

USGS raster product (U.S. Geological Surv

designed to provide national elevation data i

seamless form with a consistent datum, elev

and cartographic projection. Seamless mean

7.5-minute quadrangles for New Mexico can 

compiled into a single coverage or layer. Da

corrections were made in the NED assembly 

minimize artifacts, permit edge matching, an

areas of missing data. The NED has a resolu

arc-second (approximately 30 meters or 91 fe

conterminous United States. The New Mexi

minute, 30-meter NED actual cell size is 28 m

feet). In the NED assembly process, the elev

values were converted to decimal meters as a 

unit of measure, the North American Datum 

was consistently used as a horizontal datum

data were recast in a geographic projection o

degrees. The web page describing the NED i

(2001) available at http://edcnts12.cr.usgs.g

default.htm, accessed July 10, 2000.

The GIS Weasel (U.S. Geological Sur

was developed to aid in the preparation of sp

information for input to lumped and distribu

parameter physical-process models. GIS We

provides tools to delineate, characterize, mo

parameterize “model response units” (MRU’

geographical area; in this report the area is t

watershed. An MRU in a watershed is typica

represent an area that is characterized or attr

predict a uniform physical hydrologic proce

Selected basin and climatic characteristics w

computed for each watershed (drainage area

basin slope, average basin elevation, average 

aspect, average basin mean annual precipita

average basin mean winter precipitation) usin

MRU for each watershed as shown by the ex

figure 3. The 7.5-minute digital elevation m

(DEM’s) of the NED were used for New Me

parts of Colorado. The mean annual and win

precipitation grids were composed for New 

and parts of basins that originate in Colorad

coverage (latitude and longitude) was develo

streamflow-gaging station locations listed in 

Drainage area (DA), in square miles, i

determined by planimetering the delineated a

largest scale topographic maps available (gen

7.5-minute quadrangles). In this investigatio

determined by raster modeling using 7.5-mi

meter DEM’s. Average basin mean winter pr
15

Table 4. Additional basin and climatic characteristics determined using the geographical information sy

areas previously published for selected streamflow-gaging stations in New Mexico

[Basin and climatic characteristics determined with GIS Weasel; drainage area, in square miles, determined prio___________________________________________________________________________________________

U.S.Geological Primary Average 

Site Survey basin basin num- gaging- Drainage aspect elevation pber station area (degrees (feet above (fig. 1) number Station name (mi2) from north) sea level) 

___________________________________________________________________________________________

1 07153500 Dry Cimarron River near Guy, N. Mex. 545 90 6,340 2 07203000 Vermejo River near Dawson, N. Mex. 301 90 8,100 3 07203525 Vermejo River near Maxwell, N. Mex. 486 90 7,620 4 07205000 Sixmile Creek near Eagle Nest, N. Mex. 10.5 135 9,320 5 07207500 Ponil Creek near Cimarron, N. Mex. 171 90 8,310 6 07208500 Rayado Creek at Sauble Ranch near Cimarron, N. Mex. 65.0 45 9,630 7 07211500 Canadian River near Taylor Springs, N. Mex. 2,850 135 7,220 8 07214500 Mora River near Holman, N. Mex. 57.0 90 9,360 9 07214800 Rio la Casa near Cleveland, N. Mex. 23.0 45 10,300 10 07215500 Mora River at La Cueva, N. Mex. 173 90 8,620 11 07216500 Mora River near Golondrinas, N. Mex. 267 90 8,180 12 07217100 Coyote Creek above Guadalupita, N. Mex. 71.0 90 9,040 13 07218000 Coyote Creek near Golondrinas, N. Mex. 215 90 8,060 14 07220000 Sapello River at Sapello, N. Mex. 132 135 7,800 15 07221000 Mora River near Shoemaker, N. Mex. 1,100 135 7,380 16 07221500 Canadian River near Sanchez, N. Mex. 6,020 135 6,780 17 08263000 Latir Creek near Cerro, N. Mex. 10.5 0 11,100 18 08264000 Red River near Red River, N. Mex. 19.1 90 11,000 19 08265000 Red River near Questa, N. Mex. 113 90 10,100 20 08266000 Cabresto Creek near Questa, N. Mex. 36.7 180 10,300 
16

Table 4. Additional basin and climatic characteristics determined using the geographical informat

drainage areas previously published for selected streamflow-gaging stations in New Mexico--

___________________________________________________________________________________________

U.S.Geological Primary Average 

Site Survey basin basin num- gaging- Drainage aspect elevation pber station area (degrees (feet above (fig. 1) number Station name (mi2) from north) sea level) 

___________________________________________________________________________________________

21 08267500 Rio Hondo near Valdez, N. Mex. 36.2 225 10,500 22 08268500 Arroyo Hondo at Arroyo Hondo, N. Mex. 65.6 225 9,530 23 08269000 Rio Pueblo de Taos near Taos, N. Mex. 66.6 180 9,520 24 08271000 Rio Lucero near Arroyo Seco, N. Mex. 16.6 180 10,900 25 08275000 Rio Fernando de Taos near Taos, N. Mex. 71.7 315 9,070 26 08275300 Rio Pueblo de Taos near Ranchito, N. Mex. 199 225 9,080 27 08275500 Rio Grande del Rancho near Talpa, N. Mex. 83.0 315 9,410 28 08275600 Rio Chiquito near Talpa, N. Mex. 37.0 0 9,460 29 08276300 Rio Pueblo de Taos below Los Cordovas, N. Mex. 380 225 8,870 30 08284100 Rio Chama near La Puente, N. Mex. 480 225 9,570 31 08289000 Rio Ojo Caliente at La Madera, N. Mex. 419 90 8,520 32 08291000 Santa Cruz River at Cundiyo, N. Mex. 86.0 270 9,140 33 08292000 Santa Clara Creek near Española, N. Mex. 34.5 180 8,830 34 08302200 North Fork Tesuque Creek near Santa Fe, N. Mex. 1.60 270 10,900 35 08302500 Tesuque Creek above Diversions near Santa Fe, N. Mex. 11.7 270 8,830 36 08313350 Rito de los Frijoles in Bandelier National Monument, N. Mex. 17.5 180 7,690 37 08317850 Galisteo Creek above Galisteo Reservoir, N. Mex. 567 270 6,580 38 08321500 Jemez River below East Fork near Jemez Springs, N. Mex. 173 270 8,850 39 08323000 Rio Guadalupe at Box Canyon near Jemez, N. Mex. 235 135 8,520 40 08324000 Jemez River near Jemez, N. Mex. 470 135 8,570 
17

Table 4. Additional basin and climatic characteristics determined using the geographical information sy

areas previously published for selected streamflow-gaging stations in New Mexico--Conc

___________________________________________________________________________________________

U.S.Geological Primary Average 

Site Survey basin basin num- gaging- Drainage aspect elevation pber station area (degrees (feet above (fig. 1) number Station name (mi2) from north) sea level) 

___________________________________________________________________________________________

41 08360000 Alamosa Creek near Monticello, N. Mex. 403 135 7,320 42 08377900 Rio Mora near Terrero, N. Mex. 53.2 315 10,400 43 08378500 Pecos River near Pecos, N. Mex. 189 270 10,100 44 08379500 Pecos River near Anton Chico, N. Mex. 1,050 135 7,030 45 08380500 Gallinas Creek near Montezuma, N. Mex. 84.0 45 8,640 46 08387000 Rio Ruidoso at Hollywood, N. Mex. 120 45 7,640 47 08387600 Eagle Creek below South Fork near Alto, N. Mex. 8.14 135 8,560 48 08388000 Rio Ruidoso at Hondo, N. Mex. 290 45 7,150 49 08396000 Cottonwood Creek near Lake Arthur, N. Mex. 199 45 3,730 50 08405500 Black River above Malaga, N. Mex. 343 135 4,080 ___________________________________________________________________________________________
Figure 3. Geographical information system delineation of basin streams and model-response units for

Rio Chama near La Puente, New Mexico, streamflow-gaging station (08284100).

Basin streams Model-response unit

Mora River

at La Cueva

streamflowgaging station

(07215500)

18
19

(Pw) and average basin mean annual precipitation (Pa)

(1961-90, in inches) were averaged for each basin by

raster modeling using a 4-kilometer (2.5-mile) grid

developed by Daly and others (1998). Average basin

slope (S), in percent, was averaged for each basin by

raster modeling using the grid cells of the 7.5-minute,

30-meter DEM’s. Average basin aspect (A), in degrees

from north, was averaged for each basin by raster

modeling using the grid cells of the 7.5-minute, 30-

meter DEM’s. Average basin elevation (E), in feet, was

averaged for each basin by raster modeling using the

grid cells of the 7.5-minute, 30-meter DEM’s.

Climatic Characteristics

Estimates of mean monthly and mean annual

precipitation for 1961-90 have been developed for 4-

kilometer (2.5-mile) grid cells by Daly and others

(1998) using the Parameter-Elevation Regressions on

Independent Slopes Model (PRISM) as presented by

Daly and others (1994). PRISM estimates are based on

all available point data, including the high-elevation

precipitation data from Natural Resources

Conservation Service data collection, and a DEM to

account for the effects of topography through station

weighting and simple linear regression of precipitation

and elevation. The mean monthly precipitation raster

datasets are available at http://www.ocs.orst.edu/prism/

prism_new.html, accessed November 15, 1999. The

raster precipitation data units are in millimeters

multiplied by 100, and the geographical coordinates of

the grid cells are in decimal degrees.

The mean monthly precipitation (1961-90) raster

data were available only by month. By using the 12

monthly values of 30-year mean precipitation for each

grid cell, the GRID subsystem of ARC/INFO was used

to compute mean values for the annual 12-month

period and for the 7-month winter period (October -

April). GIS Weasel was then used to compute an

average, areally weighted value for each basin from the

values for the 4-kilometer (2.5-mile) grid cells within

each basin. Finally, total values of precipitation for

each period were computed and converted from

millimeters to inches by multiplying by the number of

months in the period (7 for the winter and 12 for the

annual) and dividing by 2,540.

The software system uses a graphical user

interface (GUI) based on the ARC/INFO, arc macro

language (AML) scripts, and C++ programming

language. The operation of the software does not

require GIS expertise, but knowledge of ARC/INFO is

helpful in changing the geographical projections fr

decimal degrees to other projections and in mergin

grids.

Multiple Linear Regression

Multiple-linear regression equations were us

to estimate 4Q3 low-flow frequency characteristics 

ungaged sites on unregulated streams. An assumpt

was made that by using separate regression equatio

for each of the eight physiographic regions in New

Mexico (fig. 1), the SEE would decrease in compari

to using one regression equation for the entire State

This assumption was based on prior regression

equations developed for physiographic regions in N

Mexico (Waltemeyer, 1996). In areas where the 10

year peak discharge was improved by regionalizing, 

SEE ranged from 41 to 96 percent for the eight

physiographic regions (a decrease from 157 percen

using one statewide regression equation) (Waltemey

1996). The greatest decrease in the SEE was expec

to be in mountainous regions. Streamflow from the

mountainous regions generally is derived from

snowmelt runoff where the duration of flow is long

and, thus, low flows are more sustainable. In additi

a more current value for the precipitation variable w

desired and used for the regression equations. The

mean annual and mean winter precipitation (1961-

for New Mexico was developed by Daly and others

(1998), and these data were used to obtain average

basin mean winter precipitation and mean annual

precipitation for the 50 gaging stations.

As stated earlier, analysis of the initial 84 gag

stations available for this study indicated that 50 ha

non-zero 4Q3 low-flow frequencies (table 1) and 3

had 4Q3 low-flow frequency of zero (table 2).

Consequently, the gaging station network was

insufficient to develop regression equations for low

flow frequency for all physiographic regions in Ne

Mexico. Therefore, development of regression

equations was limited to mountainous regions of N

Mexico and to the other regions in New Mexico wh

gaging stations had zero 4Q3 low-flow frequencies

Results

Regional-regression equations commonly ar

used to estimate streamflow characteristics at locati

where streamflow data are not available. For this stu

two equations were developed that relate the 4Q3 l
20

flow frequency determined at gaging stations to basin

and climatic characteristics. Basin and climatic

characteristics, derived from GIS Weasel, determined

to be significant for inclusion as independent variables

in the regression equations were:

DA = drainage area, in square miles;

Pw = average basin mean winter

precipitation, in inches; and

S = average basin slope, in percent.

Average basin aspect was not statistically

significant in the regression equations, average basin

elevation was highly cross correlated with

precipitation, and basin mean annual precipitation was

cross correlated with basin mean winter precipitation.

Average basin mean winter precipitation was used in

the regression equations because of its higher

correlation coefficient and statistical significance with

4Q3 low-flow frequency. The published drainage area

was compared to the drainage area determined in this

investigation by GIS Weasel, and the GIS Weasel

drainage area had a slightly improved statistical

significance and improved overall accuracy in the

regression equations. Existing basin and climatic

characteristics also were evaluated for statistical

significance. Characteristics from the USGS

streamflow/basin characteristics file (Dempster, 1981;

1983) (drainage area, average basin elevation, average

basin mean annual precipitation, main channel slope,

latitude at gaging station, and elevation at 10 and 85

percent of the stream length) were analyzed in the

regression equation. Characteristics from the USGS

streamflow/basin characteristics file were not used in

the final regression equation because of cross

correlation or lesser statistical significance.

Ordinary least-squares (OLS) regression

techniques were used to determine the most

appropriate basin and climatic variables. An OLS

multiple-linear regression procedure (Mathsoft, Inc.,

1999) was used to determine which independent

variables were significant in the two regression

equations for the 4Q3 low-flow frequency. The

dependent and independent variables were transformed

to logarithms (base 10). The general form of the

mathematical equation is:

log Q = log k + a log x1 + b log x2 +...+ n log xn (1)

or by taking antilogarithms, the nonlinear form is:

Q = k x1

a x2b

...xn

n

where Q = dependent variable (4Q3 for this

report);

k = regression constant;

a,b,...n = regression coefficients; an

x1,x2,...xn = basin and climatic variab

(independent variables)

Drainage area determined using GIS W

the 50 gaging stations that had non-zero disc

the 4Q3 low-flow frequency ranged from 1.6

square miles (table 3). Average basin mean 

precipitation in these basins ranged from 3.8

inches (table 3). The regression equation dev

the 50 gaging stations in physiographic regio

Mexico is:

4Q3 = 1.2856 x 10-4 DA0.42 Pw

3.16 

where 4Q3 = 4-day, 3-year low-flow fre

cubic feet per second;

DA = drainage area, in square m

Pw = average basin mean winte

precipitation, 1961-90, i

The average SEE for equation 2 is 12

The coefficient of determination (R2) is the f

proportion of the variance in the 4Q3 low-fl

frequency that is explained by the variation 

independent variables in the regression equa

equation 2, the R2

 is 48 percent. The indepe

variables were evaluated for inclusion in the 

analysis at the 5-percent level of significanc

An assumption was made that the lati

gaging station would help explain the variati

low-flow frequency in the statewide model; 

latitude was not statistically significant. This 

due to the general lack of data statewide and 

reduced database in non-mountainous region

the 4Q3 low-flow frequency was zero; there

range in latitude is not representative or is n

significant.

A regression analysis was conducted 

the 50 streamflow-gaging stations located in

mountainous regions with basin elevations gr

7,500 feet. The assumption was that basins a

locations would be homogenous. The regres

equation developed for the mountainous reg

provides a more accurate estimate of the 4Q3 

frequency than the statewide regression equ

(eq. 2). For the 40 gaging stations that had a 

discharge for the 4Q3 low-flow frequency, d

area determined using GIS Weasel ranged fro

548 square miles (table 3). Average basin me

precipitation in these basins ranged from 6.6
21

inches (table 3). Average basin slope ranged from

0.166 to 0.517 percent (table 3). The regression

equation for the mountainous regions of New Mexico

is:

4Q3 = 7.3287 x 10-5 DA0.70 Pw

3.58 S1.35 (3)

The average SEE for this regression equation is

94 percent and the R2

 is 66 percent. For example, the

average SEE for a 4Q3 low-flow frequency of 10 ft3/s

ranges from 0.6 to 19.4 ft3

/s at the 95-percent

confidence interval.

Use and Limitations

The intended use of regression equations 2 and 3

is to provide reliable estimates of 4Q3 low flow at

ungaged sites on unregulated streams in New Mexico.

The application of regional equations is not intended to

preclude the use of sound hydrologic judgment or any

other hydrologic or engineering method that may

provide a more reliable estimate. In New Mexico, use

of the 4Q3 low-flow frequency regression equations (2

and 3) is limited to perennial streams, mostly in the

mountainous regions. The regression equation (eq. 3)

defines the 4Q3 low-flow frequency for the

mountainous regions and should not be applied

elsewhere. Intermittent and ephemeral streams in other

mountainous regions of the State had zero flow for the

4Q3 low-flow frequency and thus could not be

considered in this analysis. The regression equation for

the mountainous regions is intended for perennial

streams above 7,500 feet in elevation; thus, it is safe to

assume that the 4Q3 for an intermittent or ephemeral

stream is zero in all likelihood.

Major rivers in the State have streamflow data

from gaging stations, but these stations are mostly

regulated; therefore these sites also were not

considered for analysis and these data should be used

only for the pre-regulation conditions. For sites of

interest that are downstream or upstream from a nearby

gaging station, the USGS has developed techniques to

transfer the data to an ungaged site (Riggs, 1972). In

this situation, a partial-record gaging station is

established for a discharge relation; thus, the 4Q3 lowflow frequency can be determined to provide an

estimate at the partial-record site.

Application of the two regression equations in

this report is limited to the range of basin and climatic

characteristics used to develop the equations (table 5);

application of the regression equations beyond the

range of the basin and climatic characteristics listed 

table 5 could result in unreliable estimates of the 4

low flow.

SUMMARY

Estimates of the magnitude and frequency of 

4-day annual low flow at ungaged sites on unregula

streams in New Mexico are necessary for the desig

and administration of water-quality standards. The

New Mexico Water Quality Control Commission

established the 4Q3 low-flow frequency for those

standards. The NMED uses the 4Q3 low-flow

frequency for administration of the NPDES and

currently for establishment of TMDL’s for watersh

in New Mexico, including both point and nonpoint

pollutant sources. Because of the availability of mo

recent streamflow and precipitation data, the USGS

cooperation with the NMED, conducted a study to

update 4Q3 low-flow frequency characteristics for

ungaged sites on unregulated streams in New Mexi

Two equations were developed for estimating 

4Q3 low-flow frequency: one statewide regression

equation estimates 4Q3 low-flow frequency based 

data for 50 gaging stations that had non-zero flow in 

physiographic regions in New Mexico. The averag

SEE was 126 percent, and the R2 was 0.48. The seco

equation estimates 4Q3 low-flow frequency at 40

gaging stations for mountainous regions greater tha

7,500 feet in elevation that had non-zero flow. The

average SEE was 94 percent, and the R2 was 0.66. T

regression equations were developed for estimating 

magnitude of the 4Q3 low-flow frequency at ungag

sites using data from the start of record through 19

Eighty-four gaging stations not affected by regulat

were available for analysis. The 4Q3 low-flow

Table 5. Ranges of statistically significant bas

and climatic characteristics used in the

regression analysis

[Pw, average winter precipitation (1961-90);

--, data not statistically significant]

Area used in

regression

analysis

Drainage

area

(square miles)

Average basin

Pw (inches)

Average ba

slope

(percent

Mountainous

regions

1.62 -548 6.66 -19.42 0.166 -0.5

Statewide 1.62 -5,900 3.89 -19.42 --
22

frequency was zero for 34 gaging stations; thus, 50

gaging stations were used for regression analysis. For

the 50 gaging stations, the 4Q3 low-flow frequency

ranged from 0.08 to 18.7 ft3/s.

Basin and climatic characteristics that were

statistically significant in relation to the 4Q3 low-flow

frequency were drainage area, which ranged from 1.62

to 5,900 square miles; average basin mean winter

precipitation, which ranged from 3.89 to 19.42 inches;

and average basin slope, which ranged from 0.166 to

0.517 percent. The USGS NED was used in a GIS to

determine drainage area and average basin slope.

Average basin mean winter precipitation was

determined by a GIS using mean winter precipitation

for 1961-90.

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S.D. Waltemeyer—ANALYSIS OF THE MAGNITUDE AND FREQUENCY OF THE 4-DAY ANNUAL LOW FLOW AND REGRESSION EQUATIONS

FOR ESTIMATING THE 4-DAY, 3-YEAR LOW-FLOW FREQUENCY AT UNGAGED SITES ON UNREGULATED STREAMS IN NEW MEXICO—

U.S. Geological Survey Water-Resources Investigations Report 01-4271

U.S. Department of the Interior

U.S. Geological Survey, WRD

5338 Montgomery Blvd. NE, Suite 400

Albuquerque, NM 87109-1311

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