In cooperation with the 

Lower Colorado River Authority

Peak-Flow Frequency for Tributaries 

of the Colorado River Downstream 

of Austin, Texas 

Water-Resources Investigations Report 98–4015

U.S. Department of the Interior

U.S. Geological Survey
Peak-Flow Frequency for Tributaries 

of the Colorado River Downstream 

of Austin, Texas

By William H. Asquith 

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 98–4015

In cooperation with the 

Lower Colorado River Authority

Austin, Texas

1998
ii

U.S. DEPARTMENT OF THE INTERIOR

Bruce Babbitt, Secretary

U.S. GEOLOGICAL SURVEY

Thomas J. Casadevall, Acting Director

Any use of trade, product, or firm names is for 

descriptive purposes only and does not imply 

endorsement by the U.S. Government.

For additional information write to: 

District Chief

U.S. Geological Survey

8011 Cameron Rd.

Austin, TX 78754–3898

Copies of this report can be purchased from:

U.S. Geological Survey

Branch of Information Services

Box 25286

Denver, CO 80225–0286
CONTENTS iii

CONTENTS

Abstract ................................................................................................................................................................................ 1

Introduction .......................................................................................................................................................................... 1

Purpose and Scope .................................................................................................................................................... 4

Peak-Flow Frequency for Streamflow-Gaging Stations ........................................................................................... 4

Basin Characteristics for Streamflow-Gaging Stations ............................................................................................ 5

Large Recorded Floods ............................................................................................................................................. 5

Peak-Flow Frequency Estimation ........................................................................................................................................ 5

Multiple-Regression Equations to Estimate Peak-Flow Frequency ......................................................................... 5

Discussion of Regression Equations ......................................................................................................................... 7

Prediction Intervals ................................................................................................................................................... 9

Application of Regression Equations ....................................................................................................................... 10

Summary .............................................................................................................................................................................. 13

References Cited .................................................................................................................................................................. 13

Appendix—Example of Calculations .................................................................................................................................. I–1

FIGURES

1. Map showing location of streamflow-gaging stations and sites with substantial peak discharges in the 

vicinity of the Colorado River Basin downstream of Austin, Texas .................................................................... 2

2–4. Graphs showing: 

2. Large floods recorded in the Colorado River Basin downstream of Austin, Texas ................................... 6

3. Relation between 100-year peak discharge and (a) contributing drainage area, (b) stream slope,

and (c) basin shape factor for streamflow-gaging stations in the vicinity of the Colorado River 

Basin downstream of Austin, Texas ........................................................................................................... 8

4. Relation between (a) stream slope and contributing drainage area, (b) basin shape factor and 

contributing drainage area, and (c) basin shape factor and stream slope for streamflow-gaging 

stations in the vicinity of the Colorado River Basin downstream of Austin, Texas .................................. 12

TABLES

1. Selected basin characteristics and peak-flow frequency for streamflow-gaging stations in the vicinity of 

the Colorado River Basin downstream of Austin, Texas ...................................................................................... 15

2. Substantial peak discharges for sites without streamflow-gaging stations in the vicinity of the Colorado 

River Basin downstream of Austin, Texas ............................................................................................................ 18

3. Weighted least-squares regression equations for estimation of peak-flow frequency for the Colorado 

River Basin downstream of Austin, Texas ............................................................................................................ 18

4. Covariance matrices and critical values of the t-distribution for regression equations ........................................ 19
Abstract 1

Peak-Flow Frequency for Tributaries 

of the Colorado River Downstream 

of Austin, Texas

By William H. Asquith

Abstract

A procedure to estimate the peak discharge 

associated with large floods is needed for tributaries of the Colorado River downstream of Austin, 

Texas, so that appropriate peak discharges can be 

used to estimate floodplain boundaries and used 

for the design of bridges and other structures. The 

U.S. Geological Survey, in cooperation with the 

Lower Colorado River Authority, studied flood 

peaks for streams in all or parts of 22 counties in 

that part of the Colorado River Basin extending 

downstream of Town Lake in Austin to the Gulf 

of Mexico. The study area was selected because 

the streams in this area either are tributaries to the 

Colorado River or have flood characteristics similar to those tributaries.

Peak-flow frequency for 38 stations with at 

least 8 years of data in natural (unregulated and 

nonurbanized) basins was estimated on the basis of 

annual peak-streamflow data through water year 

1995. Peak-flow frequency represents the peak 

discharges for recurrence intervals of 2, 5, 10, 

25, 50, 100, 250, and 500 years. The peak-flow 

frequency and drainage basin characteristics for the 

stations were used to develop two sets of regression 

equations to estimate peak-flow frequency for tributaries of the Colorado River in the study area. One 

set of equations was developed for contributing 

drainage areas less than 32 square miles, and 

another set was developed for contributing drainage areas greater than 32 square miles. A procedure 

is presented to estimate the peak discharge at sites 

where both sets of equations are considered applicable. Additionally, procedures are presented to 

compute the 50-, 67-, and 90-percent prediction 

interval for any estimation from the equations. 

INTRODUCTION

The tributaries of the Colorado River downstream 

of Austin, Texas, are in an area subject to continentally 

generated storms and hurricanes. These storms occasionally produce local or widespread flooding, sometimes with little warning. Many storms exceeding 10 

inches (in.) of precipitation have been documented in 

the area, including some exceeding 36 in. (Ellsworth, 

1923). These storms typically produce large peak 

discharges that can threaten lives and property. A procedure to estimate the peak discharge associated with 

large floods is needed for tributaries in this area so that 

appropriate peak discharges can be used to estimate 

floodplain boundaries and used for the design of bridges 

and other structures.

In 1997, the U.S. Geological Survey (USGS), in 

cooperation with the Lower Colorado River Authority, 

studied flood peaks for streams in all or parts of 22 

counties in the Colorado River Basin (watershed) 

extending downstream of Town Lake in Austin to the 

Gulf of Mexico. The study area (fig. 1) was selected 

because the streams either are tributaries to the Colorado River or have flood characteristics similar to those 

tributaries. Another study, conducted simultaneously 

with this one, documents peak-flow frequency along the 

main stem of the Colorado River downstream of Austin 

(Asquith, 1997).

The mean annual precipitation in the study area 

for 1951–80 ranges from about 32 in. in the Austin area 

to about 44 in. near the mouth of the Colorado River in 

the Gulf of Mexico (Riggio and others, 1987, p. 23). 

Recently, storms producing severe flooding have 

occurred in or near the study area (Liscum and East, 

1994; National Oceanic and Atmospheric Administration, 1995; Hejl and others, 1996).
2 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

o 30 30’

o

o 29 30’

o 29

o 30

o 96 30’

o 97

o 97 30’

o 98

28 30’

TOWN

LAKE

HAYS

LEE

FAYETTE

COLORADO

LAVACA

JACKSON

CALHOUN

BURLESON

TRAVIS

GONZALES

WILLIAMSON

DE WITT

VICTORIA

BASTROP

CALDWELL

MILAM

Creek

Re d gate Cr e ek

RIVE

R

R

IVER

M iddle

Yegua

Yegu a

East

Creek

Creek

Plum

NAVIDAD

Garc it as Creek

RIVER SAN MARCOS

RIVER

COLO RADO

RIVER

LAVACA

GUADALUPE

Yegua

Elgin

Caldwell

Lexington

Giddings

Gonzales

Yoakum

Shiner

Edna

Cuero

Inez

Victoria

Port

 O’Connor

Port

 Lavaca

Dripping

 Springs

Round

 Rock

Schulenburg

Buda

Creedmore

Kyle

Lockhart

Somerville

Luling

Hallettsville

Bastrop

Smithville

AUSTIN

La Grange

Columbus

Point

 Comfort

45 39

40

41

44

42

43

1

3 5

17

18

19

26

27

28

31

36

37

38

14

15

16

32

13

34

33

35

2 4

20

21

25

23

24

30

29

0 20 40 60 MILES

Figure 1. Location of streamflow-gaging stations and sites with substantial peak discharges in the vicinity of the 
INTRODUCTION 3

95 30’ o

96o

BRAZORIA

FORT

 BEND

AUSTIN

WASHINGTON

WHARTON

MATAGORDA

Tres Pala cios Riv er

Creek

RIVER

SAN

BERNARD

GULF OF MEXICO

RIVER

COLORADO

MATAGORDA

 BAY

BRAZOS

RIVER

Eagle Lake

El Campo

West Columbia

Palacios

Bellville

East

 Bernard

Brenham

Wharton

Bay City

7

8

9

10

11

12

6

22

Site with substantial peak discharge 

(no gaging station)—Number is site 

number from table 2

Streamflow-gaging station used in 

regression analysis—Number is site 

number from table 1

Streamflow-gaging station not used in 

regression analysis—Number is site 

number from table 1

Boundary of study area

Colorado River Basin

39

13

2

EXPLANATION

LOCATION MAP

Study area

Highland

Lakes

TEXAS

Colorado River Basin downstream of Austin, Texas.
4 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

Purpose and Scope

The purpose of this report is to present equations 

to estimate peak-flow frequency for tributaries of the 

Colorado River in the study area. These tributaries have 

natural drainage basins; a natural drainage basin is 

defined as having less than 10-percent impervious cover 

and less than 10 percent of its drainage area controlled 

by reservoirs. Peak-flow frequency in this report refers 

to the peak discharges for recurrence intervals of 2, 5, 

10, 25, 50, 100, 250, and 500 years. 

Peak-flow frequency for 38 streamflow-gaging 

stations (stations) with at least 8 years of data in natural 

(unregulated and nonurbanized) basins in the study area 

(fig. 1, table 1 at end of report) was estimated on the 

basis of annual peak-streamflow data through water 

year 1995. The peak-flow frequency was estimated 

following guidelines established by the Interagency 

Advisory Committee on Water Data (IACWD, 1982). 

One station, East Pecan Branch near Gonzales (site 32), 

lies just outside the study area, but was included in the 

data base. This station represents a small basin (defined 

in the “Peak-Flow Frequency Estimation” section), and 

its addition to the data base was considered necessary to 

increase data availability.

Equations to estimate peak-flow frequency were 

developed for streams with natural drainage basins in 

the study area. These equations were developed from 

selected stations based on the relation between peakflow frequency and basin characteristics for each 

station. The entire period of systematic record (through 

1995) was used in the frequency analysis for each 

qualified station except for stations with regulated 

streamflow during part of the record. These stations are 

Yegua Creek near Somerville (site 4) and Plum Creek 

near Luling (site 35). One or more reservoirs were constructed in the basins upstream of each of these stations 

during the period of systematic record, resulting in regulated annual peak discharges. The regulated data were 

excluded from the analysis.

Peak-Flow Frequency for Streamflow-Gaging 

Stations

Peak discharges are or have been monitored at 

each of the stations in the study area. These stations 

have various periods of systematic record (table 1). The 

peak discharges used in this study include the largest 

peak discharge for each year of systematic record 

(annual peak discharge) and all known historical peak 

discharges through 1995. A historical peak discharge—

documented by newspaper articles, personal recollections, or other historical sources—represents the largest 

peak discharge since a known date preceding the 

beginning of the systematic record. Historical peak 

discharges can occur before or within the systematic 

record. The historical record is the number of years represented by the historical peaks. For example, 33 years 

of systematic record (1963–95) exist for the station 

Davidson Creek near Lyons (site 5). However, the October 1994 peak discharge is the highest since at least 

1902; thus, the 1994 peak is the largest in at least 94 

years (1902–95).

The annual and historical peak discharges for 

each station were used, together with the USGS 

computer program PEAKFQ (Slade and Asquith, 

1996), to estimate peak discharges for the 2-, 5-, 

10-, 25-, 50-, 100-, 250-, and 500-year recurrence intervals (table 1). The computer program for peak-flow 

frequency analysis follows the guidelines established by 

the Interagency Advisory Committee on Water 

Data (1982) and uses the log-Pearson Type III (LPIII) 

frequency distribution.

The skew in the distribution of annual peaks is 

characterized by a skew coefficient. A reliable skew 

coefficient is difficult to estimate for stations having 

short records. Therefore, the IACWD recommends 

using a weighted skew coefficient with the LPIII 

distribution. This weighted skew coefficient is computed by weighting the skew coefficient calculated 

for a station (station skew coefficient) with a generalized skew coefficient representative of the surrounding 

area. The weighted skew coefficient is based on the 

inverse of the respective mean square errors for the station and on generalized skew coefficients. Generalized 

skew coefficients were determined in a previous study 

for stations in the study area (Judd and others, 1996). 

A weighted skew coefficient then was used in the calculation of the peak-flow frequency for each station except 

Dry Creek near Rosenberg (site 11). For this 

station, only the station skew coefficient was used 

because, compared to the weighted skew coefficient, it 

produces a better fit of the LPIII frequency curve to the 

data.

Additionally, the IACWD provides a procedure 

for estimating low-outlier thresholds; annual peak 
PEAK-FLOW FREQUENCY ESTIMATION 5

discharges less than this threshold are excluded from the 

fitting of the LPIII frequency curve. The estimation of 

low-outlier thresholds is critical in the calculation of 

peak-flow frequencies. The IACWD procedure for estimating low-outlier thresholds is not always suitable for 

all stations in Texas because of the large variability and 

skewness of annual peaks at a single station. An equation to estimate low-outlier thresholds for Texas stations 

with natural basins was developed by Asquith and 

others (1995) and was used to estimate most low-outlier 

thresholds for the present investigation. The equation 

estimates low-outlier thresholds by using the mean, 

standard deviation, and skew of the logarithms for the 

systematic annual peak discharges. At one station—

Mill Creek near Bellville (site 7)—the low-outlier 

threshold differed from the threshold from the equation. 

This alternative low-outlier threshold was identified by 

visually fitting the LPIII frequency curve to the peakflow data.

Basin Characteristics for Streamflow-Gaging 

Stations

Selected basin characteristics were aggregated for 

each station (table 1). The characteristics selected for 

estimation of peak-flow frequency are from 

previous investigations of peak-flow frequency in 

Texas (Schroeder and Massey, 1977; Slade and 

others, 1995; Asquith and others, 1996). The 2-year 

24-hour precipitation comes from Hershfield (1962). 

The mean annual precipitation comes from U.S. 

Geological Survey (1986, p. 432) and is for the period 

1951–80. The contributing drainage area (CDA) 

represents the areal extent of the drainage basin. The 

stream length represents the length, in miles, of the 

longest mapped channel from the station to the drainage 

divide at the headwaters, based on USGS quadrangle 

maps (scale, 1:100,000). The basin shape factor is the 

ratio of the square of the stream length to the CDA; 

the shape factor represents the ratio of the longest 

stream length to the mean width of the basin. The 

stream slope is the ratio of the change in elevation of the 

longest mapped channel (from the station upstream to 

the drainage divide at the headwaters) to the stream 

length in feet per mile.

Large Recorded Floods

The USGS routinely has documented substantial 

peak discharges at stream sites without stations. Such 

sites in the Colorado River Basin downstream of 

Austin (from Asquith and Slade, 1995) are identified 

in figure 1 (sites 39–45), and ancillary information is 

listed in table 2 (at end of report). The relation to CDA 

of maximum peak discharge for the stations and substantial peak discharge at stream sites without stations 

is shown in figure 2. The relation provides an informative description of large recorded floods in the study 

area. 

PEAK-FLOW FREQUENCY ESTIMATION

Development of equations for estimation of peakflow frequency is a multistep process requiring investigation of the relation between peak discharge and 

selected basin characteristics. The following sections 

discuss multiple regression, the relation between the 

100-year peak discharge and selected basin characteristics, prediction interval calculation, and application of 

the equations. A detailed example of peak-discharge 

estimation is available in the appendix.

Multiple-Regression Equations to Estimate 

Peak-Flow Frequency

Multiple-regression analysis was used to establish statistical relations between one dependent and one 

or more independent variables. The 2-, 5-, 10-, 25-, 

50-, 100-, 250-, and 500-year peak discharges were used 

as dependent variables, and the selected basin characteristics were used as independent variables. Logarithmic 

transformations of the dependent and independent variables were used to increase linearity between variables. 

Logarithmic transformations traditionally have been 

used for hydrologic regression. In this report, logarithmic transformations are base 10 and are represented as 

“log.”

A forward-stepwise weighted least-squares 

(WLS) regression procedure was used for the development of the equations to estimate peak-flow frequency. 

In WLS regression, each data point can be assigned a 

weighting factor. The weights generally are representative of the relative accuracy of each value for the dependent variable; greater weights are assigned to values 

having greater accuracy.
6 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

Empirical equations (G.D. Tasker, U.S. Geological Survey, written commun., 1994) based on Monte 

Carlo simulations (Tasker and Thomas, 1978; Stedinger 

and Cohn, 1986) were used to calculate a regression 

weight factor. The regression weight factor represents 

an equivalent “years of record” for each station with historical information. This factor is based on the length of 

systematic record, length of historical record, and number of high outliers; the regression weight factor for 

each station is listed in table 1. These factors were used 

as the weights for the WLS regression procedure in this 

report.

In forward-stepwise regression, the independent 

variable (basin characteristic) having the highest mathematical correlation to the dependent variable (peakflow frequency) is entered into the equation, and 

successively, the remaining independent variables are 

tested for their statistical significance to the dependent 

variable. Each independent variable testing statistically 

significant (F ratio > 1.5) is entered into the equation. 

Thus, each independent variable in the final equation 

is considered statistically significant, and a basin 

characteristic’s inclusion into the equation contributes 

to the explanation of the variance in the dependent 

variable.

Before the final equations were developed, 

an investigation of the relation between the 100-year 

peak discharge (Q100) and the principal physical basin 

0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 1,000 2,000

CONTRIBUTING DRAINAGE AREA, IN SQUARE MILES

100

500,000

200

300

400

500

700

1,000

2,000

3,000

4,000

5,000

7,000

10,000

20,000

30,000

40,000

50,000

70,000

100,000

200,000

300,000

400,000

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

EXPLANATION

Maximum peak discharge for streamflow-gaging station

Substantial peak discharge for site without streamflow-gaging station

Figure 2. Large floods recorded in the Colorado River Basin downstream of Austin, Texas.
PEAK-FLOW FREQUENCY ESTIMATION 7

characteristics (CDA, stream slope, and basin shape factor) was conducted. The 100-year peak discharge was 

selected because this discharge information most often 

is needed by water managers and planners. Similar 

results, as described below, were recorded for the other 

recurrence intervals. The relation between Q100 and 

CDA, stream slope, and basin shape factor is presented 

in figure 3. Additionally, 16 stations (including Fox 

Branch near Oak Hill, site 16) with a CDA less than 32 

square miles (mi2), and 22 stations (including Onion 

Creek near Driftwood, site 13) with a CDA greater than 

32 mi2

 are shown in figure 3. Hereafter, in this report, 

stations with a CDA less than 32 mi2

 are referred to as 

“small basin” stations, and stations with a CDA greater 

than 32 mi2

 are referred to as “large basin” stations. A 

study of peak-flow frequency conducted by Asquith and 

Slade (1997) indicates that a change in flood characteristics for many parts of the State occurs at CDA of about 

32 mi2

 or 1.5 log-mi2.

The relation between Q100 and the basin characteristics indicates that a slight curvilinear relation exists 

between Q100 and CDA. By developing separate regression equations for the small and large basin stations, 

improved estimates of Q100 are calculated because of 

increased linearity (Asquith and Slade, 1997). Also, 

classifying the stations as “small” and “large” produces 

a change in the slope of the relation between Q100 and 

CDA. The slope (fig. 3b) is better correlated to Q100 for 

the large basins than for the small basins. The apparent 

change in the relation of stream slope between the large 

and small basins indicates that separate regression equations would improve Q100 estimation.

Also in figure 3b the relation between stream 

slope and Q100 is proportional for each CDA class 

(small and large basin stations)—larger slopes are 

associated with larger values of Q100. However, if all the 

stations are considered together, then the apparent relation between Q100 and stream slope becomes inversely 

proportional—larger slopes are associated with smaller 

values of Q100. Asquith and Slade (1997) found slope to 

be proportional to Q100. It is thought 

that steep slopes produce more rapid runoff and therefore larger peak discharges. Thus, the classification 

of stations as small and large produces a stream slope 

and Q100 relation with some conceptualized physical 

basis.

Two stations were excluded from the regression 

analysis; Onion Creek near Driftwood (site 13) and one 

of its tributaries, Fox Branch near Oak Hill (site 16). 

The watershed for each of these stations (fig. 1) lies 

entirely within the Texas Hill Country where topography and soil characteristics are significantly different 

than for the remaining stations in the study area. Both 

Onion Creek near Driftwood and Fox Branch near Oak 

Hill have stream slopes that are substantially different 

in comparison to other stations in their respective CDA 

classes (fig. 3b). Excluding these two stations reduces 

the number of stations available for the regression 

analysis to 15 small basin stations and 21 large basin 

stations.

Two sets of equations were developed using the 

15 small basin and 21 large basin stations to estimate 

2-, 5-, 10-, 25-, 50-, 100-, 250-, and 500-year peak discharges (table 3 at end of report). Of the six independent 

variables considered, stream length was excluded from 

the regression analysis because it correlates highly with 

the CDA. Many equations were developed for each 

recurrence interval using various combinations of the 

five remaining independent variables (2-year 24-hour 

precipitation, mean annual precipitation, CDA, basin 

shape factor, and stream slope) in the forward-stepwise 

regression procedure. CDA and stream slope consistently were the most significant independent variables. 

Additional basin characteristics were significant for 

some recurrence intervals but were not retained in the 

final equations. Testing of equations showed that if 

the independent variables were not consistent among 

the equations, some combinations of variable values can 

produce inconsistent peak discharges between recurrence intervals. For example, an inconsistent 

peak discharge would occur if the peak discharge for 

a given recurrence interval is less than the peak discharge for a smaller recurrence interval. Thus, only 

CDA and stream slope appear in the equations listed in 

table 3.

Discussion of Regression Equations

CDA proved to be the most significant variable 

in all the regression equations (table 3); whereas, stream 

slope proved to be the second most significant variable. 

Also, the exponents on CDA and stream slope are 

positive, which indicates that peak discharge is directly 

proportional to each of these characteristics. Additionally, the exponents on CDA and stream slope increase 

with increasing recurrence interval, a characteristic 
8 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 1,000 2,000

CONTRIBUTING DRAINAGE AREA, IN SQUARE MILES

200

400,000

500

1,000

2,000

5,000

10,000

20,000

50,000

100,000

200,000

2 3 4 5 7 10 20 30 40 50 70 100 200

STREAM SLOPE, IN FEET PER MILE

200

400,000

500

1,000

2,000

5,000

10,000

20,000

50,000

100,000

200,000

100-YEAR PEAK DISCHARGE, IN CUBIC FEET PER SECOND

0.2 0.3 0.4 0.5 0.7 1 2 3 4 5 7 10 20

BASIN SHAPE FACTOR, DIMENSIONLESS

200

400,000

500

1,000

2,000

5,000

10,000

20,000

50,000

100,000

200,000

EXPLANATION

Basin characteristic for station with contributing drainage area less than 32 square miles

Basin characteristic for station with contributing drainage area greater than 32 square miles

Basin characteristic for station not included in regression analysis

Fox Branch

Fox Branch

Fox Branch

Onion Creek

Onion Creek

Onion Creek

near Oak Hill

near Oak Hill

near Oak Hill

near Driftwood

near Driftwood

near Driftwood

(a)

(b)

(c)

Figure 3. Relation between 100-year peak discharge and (a) contributing drainage area, (b) stream slope, and 

(c) basin shape factor for streamflow-gaging stations in the vicinity of the Colorado River Basin downstream of 

Austin, Texas.
PEAK-FLOW FREQUENCY ESTIMATION 9

frequently seen in peak-flow frequency equations 

(Schroeder and Massey, 1977; Slade and others, 1995; 

Asquith and others, 1996; and Asquith and Slade, 

1997). The regression constants for each of the two sets 

of equations are similar as recurrence interval increases, 

which indicates that CDA and stream slope produce 

increasing peak discharge for increasing recurrence 

interval. The exponent on stream slope for each 2-year 

equation is considerably smaller than the analogous 

value for larger recurrence intervals (table 3). The influence of slope—as represented by large exponents—

increases with increasing recurrence interval.

The (weighted) standard errors of estimate (standard deviation of residuals) for small basins generally 

are greater than the standard errors of estimate for large 

basins. The greater error is attributed to availability of 

short record (less than 20 years) for 13 of 15 small 

basin stations. Consequently, the peak-flow frequency 

for the short record stations shows greater variability. 

The mean record length for the small basin stations is 

about 14 years, whereas the mean record length for the 

large basin stations is about 33 years. Thus, the peakflow frequency for the small basin stations has more 

potential error. 

Finally, the standard error of estimate dramatically increases as the recurrence interval increases for 

the small basin stations (table 3), whereas the standard 

error remains relatively constant for the large basin 

stations. The increasing standard errors with recurrence 

interval for the small basins are also partially attributed 

to the short record availability, which results in 

increased extrapolation errors of the LPIII distribution 

for the larger recurrence intervals.

Prediction Intervals

The regression equations of table 3 list individual 

estimates of peak discharge, and the adjusted R-squared 

and (weighted) standard errors of estimate provide overall measures of equation accuracy. However, frequently 

the accuracy (error) of individual estimates from the 

equation is desired. As estimates are made 

for basin characteristics (independent variables) further 

“away” from the basin characteristics of the stations 

on which the regression is based, the accuracy of the 

estimate decreases. The means for evaluating the 

accuracy of any estimate from the equations is the calculation of the prediction intervals (Helsel and Hirsch, 

1992, p. 241–242, 300).

The prediction interval of any discharge estimate 

for a site from the regression equations in table 3 is computed from the relation (Helsel and Hirsch, 1992, 

p. 300, sec. 11.4.4):

, (1)

where

= the logarithm of T-year recurrence 

interval peak discharge for a site from 

a regression equation, in log-cubic feet 

per second,

= the critical value of t-distribution for a 

100 • (1-α)-percent confidence 

interval,

= the number of stations in a regression 

equation, 

= the number of independent variables 

(basin characteristics) plus one (for 

regression constant),

= the square of standard error of estimate, 

and

= the leverage of the site.

The leverage of a site is an expression of the distance of the site’s basin characteristics from the center 

of the multidimensional space defined by the independent variables in the regression. The prediction interval 

is related directly to the square root of the magnitude of 

the leverage. The leverage of a site is computed by the 

following equation (Helsel and Hirsch, 1992, p. 300):

, (2)

where

= a row vector of the log basin 

characteristics for the site, 

= the covariance matrix of the 

regression equation, and 

= a column vector of the log basin 

characteristics of the site. 

QT log t

(, ) α ⁄ 2 n p – s

2 1 ho – ( ) + QT ≤ log

logQT t

(, ) α ⁄ 2 n p – s

2 1 ho ≤ + ( ) +

QT log

t

(, ) α ⁄ 2 n p –

n

p

s

2

ho

ho x

o

XTW–1 { } X –1x

o

T =

x

o

XT

W–1 { } X –1

x

o

T
10 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

The covariance matrices for the regression equations 

are listed in table 4 (at end of report); the covariance 

matrices are in log-space. Critical values for the 

t-distribution for selected prediction intervals pertinent 

to the regression equations are also listed in table 4. 

Application of the above equations for prediction interval calculation is presented later.

Application of Regression Equations

The equations are designed to be used only for 

sites on the Colorado River tributaries in the study area. 

The equations are less applicable as the distance from 

the center of the study area increases. However, quantification of the diminishing applicability with increasing 

distance from the center of the study area is difficult. 

Also, the applicability of the equations for sites outside 

the study area is questionable.

In order to provide a smooth transition in determining peak discharge between small and large basins 

(separated at a CDA of 32 mi2

), a weighted peakdischarge estimate is used for sites within a CDA interval of 10 to 100 mi2

 (Asquith and Slade, 1997, p. 12). 

The logarithmically-weighted peak discharge (eq. 3) is 

based on estimates from both the equation for CDA 

less than 32 mi2

 and the equation for CDA greater than 

32 mi2

. 

, (3)

where

= the weighted peak discharge associated with 

the T-year recurrence interval, in cubic feet 

per second,

= the peak discharge associated with the equation 

for sites with CDAs less than 

32 mi2

, in cubic feet per second,

= the peak discharge associated with the equation 

for sites with CDAs greater than 

32 mi2

, in cubic feet per second, and

= the CDA of the site, in square miles.

Since a weighted peak discharge is used for sites 

within the CDA range of 10 to 100 mi2

, a weighted prediction interval is needed as well. The prediction interval (see “Prediction Intervals” section) of a weighted 

peak discharge for a site within the 10- to 100-mi2 CDA 

range is estimated by the following equations, which are 

constructed similar to equation 3:

, and (4)

, (5)

where

= the upper prediction interval of the 

(eq. 3), in cubic feet per second, 

= the upper prediction interval of the 

(eq. 3), in cubic feet per second,

= the upper prediction interval of the 

(eq. 3), in cubic feet per second,

= the lower prediction interval of the 

(eq. 3), in cubic feet per second, 

= the lower prediction interval of the 

(eq. 3), in cubic feet per second, and 

= the lower prediction interval of the 

(eq. 3), in cubic feet per second.

For sites at or near the stations included in the 

regression analyses, the peak discharge for such sites 

can be calculated from the regression equations ( ). 

However, the regression equations might provide estimates that conflict with those from the LPIII frequency 

analysis of the station data ( ). Thus, a weighted 

discharge ( ) calculated from and can be 

used. The weighted discharge is calculated from equation 6 in which the relative weights assigned to and 

 are inversely related for the error variances (squared 

standard errors of estimate in log units) for the values of 

 and .

, (6)

where:

= the weighted peak-discharge estimate for 

recurrence interval , in cubic feet per 

second,

= the peak-discharge estimate from regression, in 

cubic feet per second,

= the peak-discharge estimate from the LPIII 

frequency analysis, in cubic feet per second,

= the square standard error of the LPIII distribution, in log-cubic feet per second, and

QTW ( ) 2 – logA QT1 ( ) log 1 A – QT2 = +

QTW

QT1

QT2

A

QTW UP – ( ) 2 – logA QT1–UP =

( ) log 1 A – QT2–UP +

QTW LOW – ( ) 2 – logA QT1–LOW =

( ) log 1 A – QT2–LOW +

QTW UP – QTW

QT1–UP QT1

QT2–UP QT2

QTW LOW – QTW

QT1–LOW QT1

QT2–LOW QT2

QT

r

QT

f

QT

w QTr QTf

Qr

Qf

QT

r QTf

QT

w QT

r

(SET

f

)

2

QT

f

(SET

r

)

2

+

(SET

f

)

2 (SET

r

)

2

+

= ----------------------------------------------------------

QT

w

T

QT

r

QT

f

SET

f
PEAK-FLOW FREQUENCY ESTIMATION 11

= the square standard error from the regression, 

in log-cubic feet per second.

The standard error from the regression ( ) in 

the above equation is estimated from one-half the difference of the logarithmic 67-percent prediction interval, 

 . 

The standard error from the LPIII distribution is 

estimated as one-half the difference of the logarithmic 

67-percent confidence limits, which can be determined 

from program PEAKFQ (confidence limits set at 83.5 

percent1 documented by Slade and Asquith (1996)). 

Equation 6 provides a simple and convenient 

means of combining and ; however, the development of an always appropriate weighting procedure is 

difficult. The difficulties include: (1) the consideration 

of the number of years of record available at a station; 

peak discharges calculated from the regression equations are preferred in cases of very short record (about 

15 years or less); (2) the consideration of the fit of the 

LPIII distribution to the station data; and (3) the knowledge that the presence of low and high outliers in the 

data can greatly affect the resulting LPIII distribution. 

Another difficulty in developing an always appropriate 

weighting procedure is how to quantify what is meant 

by “near” a station. The , derived from annual 

peak data, is increasingly less applicable for sites 

increasingly farther away (upstream or downstream) 

from the station. 

A final consideration when using a specific equation for a specific site concerns the range in basin characteristics for which the equations are applicable. If a 

regression equation is used to estimate peak discharge 

for a site having a combination of basin characteristics 

substantially different from the stations on which the 

equation is based, erroneous estimates could result. Two 

techniques are available for evaluation of equation 

applicability. Each of these techniques involves analysis 

of the differences between the basin characteristics of 

the site and the basin characteristics involved in the 

regression. The first technique is to graphically compare 

the basin characteristics of the site with the characteristics involved in the regression. The second technique is 

to compare the leverage of the site with the maximum or 

mean leverage of the stations in the regression.

The graphical technique for evaluating the applicability of an equation is done by using the relation 

among the basin characteristics involved in the regression equations; the internal relation among the basin 

characteristics (CDA, stream slope, and basin shape factor) is shown in figure 4. If the basin characteristics for 

a site plot near or outside the approximate region 

defined by the basin characteristics (indicated by the 

shaded area), the resulting peak discharge could be erroneous. Consequently, the equations become less applicable when the site basin characteristics plot farther 

away from the shaded areas. Although, basin shape factor does not appear in the equations, the shape factor is 

intrinsically involved because it was considered in the 

regression analysis. For example, if stations with substantially different shape factors were available in the 

study area, then shape factor could have proven statistically significant. Therefore, the applicability of the 

equations is reduced for sites having basin shape factors 

substantially different from those in the data base.

The second technique for evaluation of equation 

applicability uses the leverage statistic, ho (eq. 2). 

Because leverage is a measure of the distance from the 

center of the multidimensional space defined by the 

basin characteristics involved in the regression analysis, 

the error of a peak-discharge estimate is directly proportional to the square root of leverage (eq. 1)—high 

leverage sites have large prediction intervals. The applicability of the equations diminishes as the site leverage 

increases. One guide in considering applicability of the 

equation is whether the site leverage is less than the 

maximum leverage of the regression. The maximum 

leverage for the small basin equations is 0.54, whereas 

the maximum leverage for the large basin equations 

is 0.38. Another guide in considering the equation applicability is whether the site leverage is less than 2 to 3 

times the mean leverage. The mean leverage for the 

small basin equations is 0.24, whereas the mean leverage for the large basin equations is 0.14. More thorough 

discussion pertinent to interpretation of the leverage statistic is available in Helsel and Hirsch (1992, p. 300–

305).

The most reliable peak-discharge estimates from 

the equations are for sites that plot within the shaded 

areas of figure 4 and have sufficiently small leverage 

1Program PEAKFQ uses a different definition of confidence 

limits than used in the current report. The 67-percent confidence 

limits of this report are the {100 - (100 - 67)/2} = 83.5-percent 

confidence limits in PEAKFQ.

SET

r

SET

f

1

2

-- (QT

r QT HIGH –67 percent – ) (QTr QT LOW –67 percent [ ] log – log – )

Qr Qf

QT

f
12 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

Figure 4. Relation between (a) stream slope and contributing drainage area, (b) basin shape factor and 

contributing drainage area, and (c) basin shape factor and stream slope for streamflow-gaging stations in the 

vicinity of the Colorado River Basin downstream of Austin, Texas.

0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 1,000 2,000

CONTRIBUTING DRAINAGE AREA, IN SQUARE MILES

2

200

3

4

5

7

10

20

30

40

50

70

100

STREAM SLOPE,

IN FEET PER MILE

0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 1,000 2,000

CONTRIBUTING DRAINAGE AREA, IN SQUARE MILES

0.2

20

0.3

0.4

0.5

0.7

1

2

3

4

5

7

10

BASIN SHAPE FACTOR,

DIMENSIONLESS

2 3 4 5 7 10 20 30 40 50 70 100 200

STREAM SLOPE, IN FEET PER MILE

0.2

20

0.3

0.4

0.5

0.7

1

2

3

4

5

7

10

BASIN SHAPE FACTOR,

DIMENSIONLESS

EXPLANATION

Basin characteristic for station with contributing drainage area less than 32 square miles

Basin characteristic for station with contributing drainage area greater than 32 square miles

Basin characteristic for station not included in regression analysis

Fox Branch near Oak Hill

Fox Branch

Fox Branch

Onion Creek near Driftwood

Onion Creek near Driftwood

Onion Creek near Driftwood

near Oak Hill

near Oak Hill

APPROXIMATE REGION DEFINED

BY BASIN CHARACTERISTICS

APPROXIMATE REGION DEFINED

BY BASIN CHARACTERISTICS

APPROXIMATE REGION DEFINED

BY BASIN CHARACTERISTICS

(a)

(b)

(c)
SUMMARY 13

statistics. The reliability of peak-discharge estimates is 

questionable for sites that plot near or outside the 

shaded areas in figure 4 or for sites that have large leverage. However, it is difficult to determine for which sites 

the equations become unapplicable.

SUMMARY

Equations estimating peak-flow frequency are 

described for tributaries of the Colorado River in a study 

area encompassing all or parts of 22 counties downstream of Austin, Texas, to the Gulf of Mexico. The 

study area was selected because streams in the area are 

either tributaries to the Colorado River or have characteristics similar to the tributaries.

The peak-flow frequency was estimated for 38 

qualified streamflow-gaging stations (stations) in the 

study area. Peak-flow frequency refers to the peak discharges for recurrence intervals of 2, 5, 10, 25, 100, 250, 

and 500 years. Qualified stations have at least 8 years 

of peak-flow data collected from natural basins. A natural drainage basin has less than 10-percent impervious 

cover and less than 10 percent of its drainage area controlled by reservoirs. The entire period of systematic 

record (through water year 1995) was used in the frequency analysis for each station, except at stations 

where streamflow was regulated during part of the 

record. Regulated data was excluded from the analyses.

Data from 36 of 38 stations were used to develop 

regressions equations to estimate peak-flow frequency. 

Multiple-regression analysis was performed using 

weighted least squares. Two sets of regression equations 

for peak-flow frequency were developed on the basis of 

the relation between peak-flow frequency and the basin 

characteristics of the stations. One set of equations was 

developed for contributing drainage area (CDA) less 

than 32 mi2

, and another set was developed for CDA 

greater than 32 mi2. Procedures to compute the 50-, 67-

, and 90-percent confidence limits for any estimation 

derived from the equations are presented. Additionally, 

a procedure is presented for determining a weighted discharge for sites where both sets of equations are applicable. 

REFERENCES CITED

Asquith, W.H., 1997, Peak-flow frequency along 

the Colorado River downstream of Austin, Texas: 

U.S. Geological Survey Water-Resources Investigations 

Report 97–4265, 19 p.

Asquith, W.H., and Slade, R.M., Jr., 1995, Documented 

and potential extreme peak discharges and relation 

between potential extreme peak discharges and probable 

maximum flood peak discharges in Texas: U.S. 

Geological Survey Water-Resources Investigations 

Report 95–4249, 58 p.

______1997, Regional equations for estimation of peakstreamflow frequency for natural basins in Texas: U.S. 

Geological Survey Water-Resources Investigations 

Report 96–4307, 27 p.

Asquith, W.H., Slade, R.M., Jr., and Judd, L.J., 1995, 

Analysis of low-outlier thresholds for log Pearson Type 

III peak-streamflow frequency analysis in Texas, in

Texas Water '95, A Component Conference of the First 

International Conference on Water Resources Engineering, Water Resources Engineering Division, American 

Society of Civil Engineers, August 16–17, 1995, San 

Antonio, Proceedings: San Antonio, American Society 

of Civil Engineers, p. 379–384.

Asquith, W.H., Slade, R.M., Jr., and Lanning-Rush, Jennifer, 

1996, Peak-flow frequency and extreme flood potential 

for streams in the vicinity of the Highland Lakes, central 

Texas: U.S. Geological Survey Water-Resources 

Investigations Report 96–4072, 1 sheet.

Ellsworth, C.E., 1923, The floods in central Texas in September, 1921: U.S. Geological Survey Water-Supply 

Paper 488, 56 p.

Hejl, H.R., Jr., Slade, R.M., Jr., and Jennings, M.E., 

1996, Floods in central Texas, December 1991: U.S. 

Geological Survey Water-Resources Investigations 

Report 95–4289, 1 sheet.

Helsel, D.R., and Hirsch, R.M., 1992, Studies in environmental science 49—Statistical methods in water resources: 

Amsterdam, Elsevier, 522 p.

Hershfield, D.M., 1962, Rainfall frequency atlas of the 

United States for durations from 30 minutes to 24 hours 

and return periods from 1 to 100 years: U.S. Weather 

Bureau Technical Paper 40, Washington D.C., 61 p.

Interagency Advisory Committee on Water Data, 1982, 

Guidelines for determining flood flow frequency: 

Reston, Va., U.S. Geological Survey, Office of Water 

Data Coordination, Hydrology Subcommittee Bulletin 

17B [variously paged].

Judd, L.J., Asquith, W.H., and Slade, R.M., Jr., 1996, 

Techniques to estimate generalized skew coefficients 

of annual peak streamflow for natural basins in Texas: 

U.S. Geological Survey Water-Resources Investigations 

Report 96–4117, 28 p.

Liscum, Fred, and East, J.W., 1994, Floods in Southeast 

Texas, October 1994: U.S. Geological Survey Fact Sheet 

94–073, 2 p.
14 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

National Oceanic and Atmospheric Administration, 1995, 

Southeast Texas tropical mid-latitude rainfall and flood 

event, October 1994: Natural Disaster Survey Report, 23 

p.

Riggio, R.F., Bomar, G.W., and Larkin, T.J., 1987, Texas 

droughts—its recent history (1931–1985): Texas Water 

Commission Report LP 87–04, 74 p.

Schroeder, E.E., and Massey, B.C., 1977, Technique for 

estimating the magnitude and frequency of floods in 

Texas: U.S. Geological Survey Water-Resources 

Investigations/Open-File Report 77–110, 22 p.

Slade R.M., Jr., and Asquith, W.H., 1996, Peak data for 

U.S. Geological Survey gaging stations, Texas network; 

and computer program to estimate peak-streamflow 

frequency: U.S. Geological Survey Open-File Report 

96–148, 57 p.

Slade R.M., Jr., Asquith, W.H., and Tasker, G.D., 1995, 

Multiple-regression equations to estimate peak-flow 

frequency for streams in Hays County, Texas: U.S. 

Geological Survey Water-Resources Investigations 

Report 95–4019, 1 sheet.

Stedinger, J.R., and Cohn, T.A., 1986, Flood frequency analysis with historical and paleoflood information: Water 

Resources Research, v. 22, no. 5, p. 785–793.

Tasker, G.D., and Thomas, W.O., 1978, Flood frequency 

analysis with pre-record information: Journal of the 

Hydraulics Division, American Society of Civil 

Engineers, v. 104, no. 2, p. 249–259.

U.S. Geological Survey, 1986, National water summary 

1985: Water-Supply Paper 2300, 506 p.
Table 1 15

Table 1

Table 1. Selected basin characteristics and peak-flow frequency for streamflow-gaging stations in the vicinity of the Colorado 

River Basin downstream of Austin, Texas

[in., inches; FM, Farm Road; mi2, square miles; mi, miles; ft/mi, feet per mile; yr, years; ft3/s, cubic feet per second; Q500, 500-year peak 

discharge; Q100, 100-year peak discharge] 

1

 Stations with available record ending 1995 were active as of 1996.

2

 Somerville Lake completed in 1967. Only peak discharges for 1925–66 used in analysis.

3

 Station not used in regression analysis.

4

 Many small reservoirs completed in 1964. Only peak discharges for 1930–63 used in analysis.

Site

no.

(fig. 1)

Station

no. Station name Latitude Longitude

Available

period of

systematic

record1

2-year

24-hour

precipitation

(in.)

Mean

annual

precipitation

1951–80

(in.)

1 08105900 Avery Branch near Taylor 30°29'11" 97°27'27" 1967–74 4.19 33.0

2 08109700 Middle Yegua Creek near Dime Box 30°20'21" 96°54'16" 1963–95 4.32 35.0

3 08109800 East Yegua Creek near Dime Box 30°24'26" 96°49'02" 1963–95 4.35 36.0

4 08110000 Yegua Creek near Somerville 30°19'18" 96°30'26" 1925–662 4.39 36.0

5 08110100 Davidson Creek near Lyons 30°25'10" 96°32'24" 1963–95 4.42 36.0

6 08111100 Winkleman Creek near Brenham 30°15'19" 96°15'44" 1966–74 4.62 39.0

7 08111700 Mill Creek near Bellville 29°52'51" 96°12'18" 1964–93 4.60 40.0

8 08114900 Seabourne Creek near Rosenberg 29°31'27" 95°48'28" 1967–74 4.90 43.0

9 08115000 Big Creek near Needville 29°28'35" 95°48'45" 1947–95 4.88 43.0

10 08115500 Fairchild Creek near Needville 29°26'45" 95°45'41" 1945–54 4.92 43.0

11 08116400 Dry Creek near Rosenberg 29°30'42" 95°44'48" 1959–79 4.93 43.0

12 08117500 San Bernard River near Boling 29°18'48" 95°53'37" 1955–95 4.75 42.0

13 08158700 Onion Creek near Driftwood3 30°04'59" 98°00'29" 1980–95 4.01 32.5

14 08158810 Bear Creek below FM 1826 near Driftwood 30°09'19" 97°56'23" 1979–95 4.06 33.0

15 08158840 Slaughter Creek at FM 1826 near Austin 30°12'32" 97°54'11" 1978–95 4.07 32.5

16 08158900 Fox Branch near Oak Hill3 30°14'01" 97°52'29" 1966–74 4.08 32.0

17 08159150 Wilbarger Creek near Pflugerville 30°27'16" 97°36'02" 1964–80 4.15 32.0

18 08159450 Reeds Creek near Bastrop 30°00'26" 97°15'03" 1965–74 4.32 36.0

19 08160000 Dry Creek at Buescher Lake near Smithville 30°02'32" 97°09'34" 1940–66 4.35 36.5

20 08160800 Redgate Creek near Columbus 29°47'56" 96°31'55" 1962–95 4.60 40.5

21 08161580 Dry Branch tributary near Altair 29°34'39" 96°28'16" 1967–74 4.65 41.0

22 08162600 Tres Palacios River near Midfield 28°55'40" 96°10'15" 1971–95 4.79 42.0

23 08163500 Lavaca River at Hallettsville 29°26'35" 96°56'39" 1940–95 4.43 38.0

24 08164000 Lavaca River near Edna 28°57'35" 96°41'10" 1939–95 4.47 37.5

25 08164300 Navidad River near Hallettsville 29°28'00" 96°48'45" 1962–95 4.47 38.5

26 08164350 Navidad River near Speaks 29°19'18" 96°42'32" 1982–89 4.48 39.0

27 08164450 Sandy Creek near Louise 29°09'34" 96°32'47" 1980–95 4.60 41.0

28 08164500 Navidad River near Ganado 29°01'32" 96°33'08" 1939–80 4.57 40.0

29 08164503 West Mustang Creek near Ganado 29°04'17" 96°28'01" 1980–95 4.70 41.0

30 08164600 Garcitas Creek near Inez 28°53'28" 96°49'08" 1971–95 4.51 37.0

31 08164800 Placedo Creek near Placedo 28°43'30" 96°46'07" 1971–95 4.53 38.0

32 08169850 East Pecan Branch near Gonzales 29°29'58" 97°31'36" 1966–74 4.28 34.5

33 08172000 San Marcos River at Luling 29°39'54" 97°38'59" 1940–95 4.03 33.0

34 08172100 West Elm Creek near Niederwald 29°59'04" 97°44'39" 1966–74 4.16 34.0

35 08173000 Plum Creek near Luling 29°41'58" 97°36'12" 1930–634 4.19 35.0

36 08173500 San Marcos River at Ottine 29°35'36" 97°35'22" 1916–43 4.10 33.5

37 08174600 Peach Creek below Dilworth 29°28'26" 97°18'59" 1960–79 4.32 36.5

38 08176200 Irish Creek near Cuero 29°08'02" 97°12'10" 1967–74 4.41 35.0

Table continued on next two pages.
16 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

Table 1. Selected basin characteristics and peak-flow frequency for streamflow-gaging stations in the vicinity of the Colorado 

Site no.

(fig. 1)

Contributing

drainage

area

(mi2)

Stream

length

(mi)

Basin

shape

factor

(dimensionless)

Stream

slope

(ft/mi)

Available

unregulated

systematic

record

(yr)

No.

of

historical

peaks

Historical

record

(yr)

Equivalent

years of record

(regression

weight factor)

 1 (Avery Branch-Taylor) 3.52 2.74 2.13 13.17 8 0 0 8

 2 (Middle Yegua Creek-Dime Box) 236 41.08 7.15 6.79 33 1 83 51

 3 (East Yegua Creek-Dime Box) 244 34.84 4.97 7.25 33 0 0 33

 4 (Yegua Creek-Somerville) 1,009 61.83 3.79 4.14 42 0 0 42

 5 (Davidson Creek-Lyons) 195 39.52 8.01 8.30 33 2 94 56

 6 (Winkleman Creek-Brenham) .75 1.08 1.56 39.49 9 0 0 9

 7 (Mill Creek-Bellville) 376 44.62 5.30 8.01 30 0 0 30

 8 (Seabourne Creek-Rosenberg) 5.78 4.06 2.84 3.24 8 0 0 8

 9 (Big Creek-Needville) 42.8 14.47 4.89 2.83 48 0 0 48

10 (Fairchild Creek-Needville) 26.2 6.73 1.73 4.39 8 0 0 8

11(Dry Creek-Rosenberg) 8.65 5.83 3.93 3.38 21 1 48 31

12 (San Bernard River-Boling) 727 83.45 9.58 4.01 41 0 0 41

13 (Onion Creek-Driftwood) 124 31.99 8.25 21.02 16 0 0 16

14 (Bear Creek-Driftwood) 12.2 5.49 2.47 55.55 17 1 81 40

15 (Slaughter Creek-Austin) 8.24 4.20 2.14 52.32 18 0 0 18

16 (Fox Branch-Oak Hill) .18 .40 .87 124.32 9 0 0 9

17 (Wilbarger Creek-Pflugerville) 4.61 2.99 1.94 38.44 17 1 87 42

18 (Reeds Creek-Bastrop) 5.22 4.49 3.86 40.91 10 0 0 10

19 (Dry Creek-Smithville) 1.48 1.78 2.15 69.96 26 1 32 28

20 (Redgate Creek-Columbus) 17.3 7.61 3.35 18.11 34 0 0 34

21 (Dry Branch tributary-Altair) .68 .58 .49 11.31 8 0 0 8

22 (Tres Palacios River-Midfield) 145 30.55 6.44 3.33 25 0 0 25

23 (Lavaca River-Hallettsville) 108 25.23 5.89 12.18 56 2 156 92

24 (Lavaca River-Edna) 817 85.59 8.97 5.44 57 3 116 80

25 (Navidad River-Hallettsville) 332 37.31 4.19 8.35 34 0 0 34

26 (Navidad River-Speaks) 437 53.39 6.52 6.27 8 0 0 8

27 (Sandy Creek-Louise) 289 55.48 10.65 5.97 16 0 0 16

28 (Navidad River-Ganado) 826 92.67 10.40 4.78 42 2 105 66

29 (West Mustang Creek-Ganado) 178 39.05 8.56 2.77 16 0 0 16

30 (Garcitas Creek-Inez) 91.7 24.98 6.81 6.83 25 2 93 51

31 (Placedo Creek-Placedo) 68.3 21.57 6.81 4.72 25 1 29 27

32 (East Pecan Branch-Gonzales) .24 .27 .30 33.33 9 0 0 9

33 (San Marcos River-Luling) 838 124.26 18.43 13.07 56 0 0 56

34 (West Elm Creek-Niederwald) .44 .47 .50 78.72 9 0 0 9

35 (Plum Creek-Luling) 309 42.30 5.79 12.56 34 1 96 56

36 (San Marcos River-Ottine) 1,249 137.12 15.05 12.11 28 0 0 28

37 (Peach Creek-Dilworth) 460 50.28 5.50 7.83 20 1 40 28

38 (Irish Creek-Cuero) 15.5 6.59 2.80 18.43 8 0 0 8

Continued from previous page.
Table 1 17

River Basin downstream of Austin, Texas—Continued 

Date of

maximum

peak

discharge

of record

Maximum

peak

discharge

of record

(ft3/s)

Peak discharge for indicated recurrence interval obtained

from log-Pearson Type III frequency curve

(ft3/s)

2 yr 5 yr 10 yr 25 yr 50 yr 100 yr 250 yr 500 yr

05/01/1972 2,950 691 1,188 1,580 2,147 2,619 3,135 3,697 4,519 1.44

12/22/1991 12,500 1,490 4,650 7,860 13,060 17,640 22,270 28,220 36,080 1.62

05/24/1975 14,000 2,150 5,290 8,129 12,480 16,200 20,280 24,690 31,020 1.53

07/01/1940 56,800 6,790 16,960 26,680 42,460 56,760 73,200 91,890 120,200 1.64

10/17/1994 26,400 3,660 8,160 12,100 18,070 23,180 28,810 34,960 43,890 1.52

03/24/1973 870 302 555 748 1,010 1,220 1,440 1,660 1,970 1.37

06/13/1973 44,400 13,630 22,840 29,890 39,800 47,870 56,510 65,760 79,010 1.40

06/13/1973 480 269 395 479 586 667 747 827 935 1.25

06/26/1960 10,400 2,520 4,200 5,470 7,240 8,660 10,170 11,770 14,050 1.38

05/18/1953 2,560 997 1,680 2,210 2,940 3,530 4,160 4,840 5,800 1.39

10/31/1959 2,410 689 995 1,220 1,530 1,790 2,060 2,350 2,760 1.34

06/28/1960 21,200 7,080 12,350 16,550 22,660 27,780 33,400 39,550 48,570 1.45

06/06/1985 8,990 2,680 7,380 12,120 20,080 27,440 36,030 45,890 60,980 1.69

1939 14,200 793 3,100 6,120 12,370 19,240 28,380 40,250 60,930 2.15

12/20/1991 6,330 718 2,240 3,990 7,280 10,650 14,920 20,230 29,120 1.95

09/04/1967 249 49 99 142 208 267 332 407 518 1.56

1921 2,300 596 980 1,240 1,550 1,780 2,000 2,210 2,480 1.24

05/16/1965 4,000 230 840 1,660 3,450 5,550 8,520 12,640 20,410 2.40

06/30/1940 1,870 226 756 1,390 2,590 3,840 5,440 7,440 10,790 1.90

05/22/1979 5,360 1,790 3,120 4,110 5,460 6,510 7,590 8,710 10,250 1.35

06/13/1973 495 133 283 417 626 811 1,020 1,260 1,620 1.59

10/17/1983 17,000 5,130 8,250 10,590 13,820 16,420 19,180 22,110 26,280 1.37

08/31/1981 99,500 7,720 16,210 24,070 36,880 48,740 62,750 79,220 105,300 1.68

10/19/1994 150,000 11,590 22,910 33,120 49,520 64,540 82,190 102,800 135,400 1.65

09/13/1974 53,500 9,710 19,800 28,370 41,240 52,250 64,420 77,800 97,460 1.51

05/14/1982 19,300 6,480 12,110 16,730 23,540 29,290 35,620 42,560 52,740 1.48

10/19/1994 24,900 5,050 9,410 13,090 18,670 23,530 29,010 35,170 44,480 1.53

1936 94,000 13,620 25,760 36,660 54,240 70,450 89,650 112,300 148,500 1.66

10/19/1994 20,000 3,850 7,540 10,790 15,870 20,410 25,650 31,650 40,920 1.60

06/12/1981 19,700 4,550 8,860 12,540 18,140 23,020 28,510 34,670 43,930 1.54

10/31/1981 18,300 5,930 10,300 13,610 18,170 21,810 25,630 29,650 35,270 1.38

09/13/1974 175 81 141 188 257 314 377 445 545 1.45

09/12/1952 57,000 10,250 23,090 35,250 55,330 74,000 96,100 122,000 163,000 1.70

05/15/1970 700 185 402 599 910 1,190 1,510 1,880 2,440 1.62

07/01/1936 78,500 6,330 15,590 25,370 43,160 61,240 84,260 113,300 162,900 1.93

05/29/1929 202,000 14,800 39,880 68,870 126,100 188,600 273,200 386,000 592,300 2.17

04/20/1977 76,800 7,420 16,040 24,060 37,170 49,280 63,570 80,300 106,700 1.68

05/10/1972 6,000 1,550 5,380 10,250 20,260 31,380 46,410 66,280 101,900 2.20

Q500

Q100

-------------
18 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

Table 3

Table 2

Table 3. Weighted least-squares regression equations for estimation of peak-flow frequency for the Colorado River 

Basin downstream of Austin, Texas—Continued

Recurrence

interval

Weighted least-squares

regression equation for

corresponding recurrence

interval1

(cubic feet per second)

Range of

indicated

independent

variables

(units as noted)

Adjusted

R-squared2

Weighted

standard

error of

estimate

(percent)

Weighted

standard

error of

estimate

(log10 units)

No. of

stations

in

equation

Sites3 with contributing drainage area less than 32 mi2 (small basin stations)

2 yr Q2 = 176.4 CDA0.611 SL0.0460

CDA: 0.24 to 26.2

square miles

0.79 38 0.16 15

5 yr Q5 = 139.3 CDA0.701 SL0.326 .87 31 .13 Do.

10 yr Q10 = 126.8 CDA0.744 SL0.460 .85 38 .16 Do.

25 yr Q25 = 117.5 CDA0.788 SL0.594

SL: 3.24 to 78.72

feet per mile

.79 51 .21 Do.

50 yr Q50 = 113.3 CDA0.814 SL0.676 .75 63 .25 Do.

100 yr Q100 = 110.6 CDA0.836 SL0.746 .71 75 .29 Do.

250 yr Q250 = 108.9 CDA0.856 SL0.807

SH: 0.30 to 3.93

dimensionless

.67 88 .33 Do.

500 yr Q500 = 107.9 CDA0.879 SL0.878 .63 103 .37 Do.

Table 2. Substantial peak discharges for sites without streamflow-gaging stations in the vicinity of the Colorado 

River Basin downstream of Austin, Texas

[mi2, square miles; ft3

/s, cubic feet per second] 

Table 3. Weighted least-squares regression equations for estimation of peak-flow frequency for the Colorado River 

Basin downstream of Austin, Texas

[mi2, square miles; yr, year; CDA, contributing drainage area in square miles; SL, stream slope in feet per mile—ratio of 

change in elevation of (1) the length of the longest mapped channel to (2) the distance from the longest mapped channel of the 

site (or station) to the headwaters; SH, basin shape factor—ratio of length of longest mapped channel (stream length) squared 

to contributing drainage area (dimensionless)] 

Site

no.

(fig. 1)

Stream site name and

approximate location Latitude Longitude

Contributing

drainage area

(mi2)

Date of

substantial

peak discharge

Substantial

peak

discharge

(ft3/s)

39 Little Piney Creek near Bastrop 30°01'00" 97°16'38" 7.08 05/12/1969 4,220

40 Rabbs Creek near Warda 30°01'50" 96°54'40" 92.8 06/30/1940 55,000

41 Buckners Creek near La Grange 29°53'07" 96°53'55" 184 06/30/1940 106,000

42 Youngs Branch near Moulton 29°33'50" 97°06'40" 6.8 06/30/1940 8,900

43 Rocky Creek near Hallettsville 29°23'10" 96°59'00" 116 06/30/1940 74,700

44 West Navidad River near Schulenburg 29°38'20" 96°55'00" 106 06/30/1940 124,000

45 Bunton Branch near Kyle 30°01'00" 97°51'00" 4.12 06/30/1936 13,800

Footnotes at end of table.
Table 4 19

Table 4

1 Order of independent variables (basin characteristics) in each equation from left to right indicates the relative statistical 

significance of each independent variable to the dependent variable (peak-flow frequency).

2 Presented so that equations based on different numbers of stations can be compared.

3 For stream sites with CDA within the range 10 to 100 mi2, use equation 3 to calculate weighted discharge and equations 

4 and 5 to calculate weighted prediction interval.

Table 4. Covariance matrices and critical values of the t-distribution for regression equations

[These matrices can be used to compute the prediction interval for any estimation from the regression equations (table 3). 

Qualifications as to which equations a matrix applies to are shown in this table. CDA, contributing drainage area; mi2

, square 

miles] 

Sites3 with contributing drainage area greater than 32 mi2 (large basin stations)

2 yr Q2 = 460.6 CDA0.379 SL0.239

CDA: 42.8 to 1,249

square miles

0.32 57 0.23 21

5 yr Q5 = 571.8 CDA0.414 SL0.407 .54 43 .18 Do.

10 yr Q10 = 617.3 CDA0.437 SL0.499 .63 38 .16 Do.

25 yr Q25 = 650.4 CDA0.466 SL0.598

SL: 2.77 to 13.07

feet per mile

.69 38 .16 Do.

50 yr Q50 = 662.6 CDA0.486 SL0.664 .71 38 .16 Do.

100 yr Q100 = 667.0 CDA0.506 SL0.725 .72 41 .17 Do.

250 yr Q250 = 665.4 CDA0.525 SL0.781

SH: 3.79 to 18.43

dimensionless

.73 41 .17 Do.

500 yr Q500 = 656.6 CDA0.549 SL0.849 .72 43 .18 Do.

Matrix {XTW-1X}-1

Sites with CDA less than 32 mi2 Sites with CDA greater than 32 mi2

Area Slope Constant Area Slope Constant

Area 0.28411 0.10328 -0.34482 Area 0.27877 -0.052138 -0.64721

Slope .10328 .37361 -.59347 Slope -.052138 1.1778 -.85108

Constant -.34482 -.59347 1.1372 Constant -.64721 -.85108 2.3593

Critical values of the t-distribution for selected confidence limits (two-tailed)

Sites with CDA less than 32 mi2

Degrees of freedom = 12

Sites with CDA greater than 32 mi2

Degrees of freedom = 18

50 percent (α = 0.25) 0.69548 0.68836

67 percent (α = 0.165) 1.0153 1.0012

90 percent (α = 0.05) 1.7823 1.7340

Table 3. Weighted least-squares regression equations for estimation of peak-flow frequency for the Colorado River 

Basin downstream of Austin, Texas—Continued

Recurrence

interval

Weighted least-squares

regression equation for

corresponding recurrence

interval1

(cubic feet per second)

Range of

indicated

independent

variables

(units as noted)

Adjusted

R-squared2

Weighted

standard

error of

estimate

(percent)

Weighted

standard

error of

estimate

(log10 units)

No. of

stations

in

equation
Appendix I–1

Peak-Flow Frequency for Tributaries 

of the Colorado River Downstream 

of Austin, Texas

Appendix

Appendix—

Example of Calculations
I–2 Peak-Flow Frequency for Tributaries of the Colorado River Downstream of Austin, Texas 

The following example illustrates the calculation of peak-flow frequency and prediction intervals for a site. 

The example involves the estimation of the 100-year peak discharge for a 50-mi2 site with a stream slope of 10.5 

feet per mile (ft/mi) and a basin shape factor of 5.0; additionally, the 67-percent prediction interval is desired. 

Because the CDA for the site is within the interval 10 to 100 mi2

, estimates are made from equations with CDA both 

less than and greater than 32 mi2. 

The estimate from the equation for CDA < 32 mi2 (small basin estimate) is:

Q100<32 = 110.6 (50)0.836 (10.5)0.746 = 16,800 cubic feet per second (ft3/s).

The estimate from the equation for CDA > 32 mi2

 (large basin estimate) is:

Q100>32 = 667 (50)0.506 (10.5)0.725 = 26,600 ft3/s.

Because the CDA of the site lies within the 10- to 100-mi2

 interval, the weighted estimate is:

Q100W = [2 - log(50)] (16,800) + [log10(50) - 1] (26,600) = 0.30 (16,800) + 0.70 (26,600)

Q100W = 23,700 ft3/s.

A check on the applicability of the equations indicates that this site’s basin characteristics plot in or near the 

shaded regions in figure 4. Notice that the site CDA and stream slope plot closer to the shaded region of the large 

CDA basins than to the shaded region of the small CDA basins; therefore, the large basin estimate has the larger 

weight factor (0.070) in the weighting equation than the small basin estimate (0.30). Thus, the large basin estimate 

is considered slightly more applicable than the small basin estimate. 

The calculation of the 67-percent prediction interval for the large basin equation begins with calculation of the 

leverage, ho, using the covariance matrix for sites with a CDA greater than 32 mi2 from table 4. The vector for 

this site is [log(50) log(10.5) 1] or [1.6990 1.0212 1]. The large basin leverage is: 

.

Now, using equation 1 with s

2

 equal to (0.17)2 or 0.0289 from table 3 and a critical value for the t-distribution of 

1.0012 from table 4, the prediction interval is calculated from equation 1:

logQ100>32-UP = log (26,600) + 1.0012 [0.0289 (1 + 0.27388)]0.5 = 4.6170 log-ft3/s

Q100>32-UP = 41,400 ft3

/s.

logQ100>32-LOW = log (26,600) - 1.0012 [0.0289 (1 + 0.27388)]0.5 = 4.2328 log-ft3

/s

Q100>32-LOW = 17,100 ft3/s.

There is a 67-percent chance that this prediction interval contains the true 100-year peak discharge for this site 

and equation, and the true discharge falls within the interval 17,100 to 41,400 ft3

/s. However, because this site lies 

within the CDA range of 10 to 100 mi2

, and two separate equations are considered applicable; the weighted 

prediction intervals are needed (eqs. 4 and 5). The 67-percent prediction interval for the 100-year peak discharge for 

a site with less than 32 mi2

 are (eq. 1):

logQ100<32-UP = log (16,800) + 1.0153 [0.0841 (1 + 0.32152)]0.5 = 4.5638 log-ft3

/s

Q100<32-UP = 36,600 ft3/s.

logQ100<32-LOW = log (16,800) - 1.0153 [0.0841 (1 + 0.32152)]0.5 = 3.8868 log-ft3/s

Q100<32-LOW = 7,710 ft3

/s.

x

o

ho [ ] 1.6990 1.0212 1

 

= = 0.27388

1.6990

1.0212

1

0.27877 -0.052138 -0.64721

-0.052138 1.1778 -0.85108

-0.64721 -0.85108 2.3593
Appendix I–3

The weighted prediction interval is calculated using the weighting equations 4 and 5:

Q100W-UP = [2 - log (50)] (36,600) + [log (50) -1] (41,400) = 0.30 (36,600) + 0.70 (41,400)

Q100W-UP = 39,960 ft3/s.

Q100W-LOW = [2 - log (50)] (7,710) + [log (50)-1] (17,100) = 0.30 (7,710) + 0.70 (17,100)

Q100W-LOW = 14,300 ft3

/s.

The prediction interval constructed for a prediction from any one regression equation can be statistically 

interpreted. However, the weighted prediction interval is only estimated, and therefore strict statistical interpretation 

of it requires relaxation.

A check on the leverage statistics on the large basin equation indicates that the site leverage (0.27) is less than 

the maximum leverage (0.38) and less than 2 to 3 times the mean leverage (0.28 to 0.42). A check on the leverage 

statistics on the small basin equation indicates that the site leverage (0.32) is less than the maximum leverage (0.54) 

and less than 2 to 3 times the mean leverage (0.48 to 0.72). The two site leverages (0.27 and 0.32) cannot be 

compared to each other to determine which equation is the most applicable for a site. Both sets of equations are 

considered applicable because both site leverages are sufficiently less than the maximum leverage and less than 2 to 

3 times the mean leverage of their respective equations.