WSP07730

• File Number: 8062
• Description: Federal Reserved Water Rights
• State: CO
• Basin: Statewide
• Date: 1/1/2000
• Author: USGS
• Title: Analysis of the Magnitude and Frequency of Floods in Colorado - USGS - Water Resources Investigations Report 99-4190
• Water Supply Pro - Doc Type: Report/Study

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Regression coefficients were estimated by
considering the time-sampling error in the streamflow
characteristics and the cross correlation between sites.
The time-sampling error is associated with the length
of record for a gaging station. A gaging station with a
short period of record may have a large time-sampling
error because the record may not be representative of
the actual flood history of the site based on a larger
number of years, A short period of record has the
possibility of falling within a wet or dry climatic cycle
(Thomas and Lindskov, 1983).
Use of the GLS method requires estimates of the
cross correlation between stream flows at every pair of
sites. Sample estimates of cross correlation based on
recorded streamflows from short periods of record are
often imprecise. To overcome this problem, the sample
correlations were smoothed by relating them to
distance between gaging stations using a nonlinear-
regression model (Tasker and Stedinger, 1989),
The regression equations that were developed
using the GLS method related drainage-basin character-
istics to peak discharges by using a weighting matrix to
account for the different time-sampling errors and cross
correlations of concurrent peak-discharge records of the
various gaging stations, The final regression equations
developed for each region using GLS. the standard
errors of estimate, and the average standard error of
prediction are listed in table 1.

Limitations and Accuracy of Regression
Equations

The regression equations provide a means for
II determining flood peaks for selected recurrence inter-
vals for ungaged streams in Colorado. The equations
were developed from gaging-station data on streams
i. with little or no regulation in the basin and where
I
significant urban development or other major basin
changes have not occurred. Thus, the regression equa-
tions may not be valid where regulation is a factor or
where a drainage basin has been altered by urban
development. The regression equations also will not
be valid where unique. ]ocalized geologic features
affect floods. As with any regression analysis, the
regression equations are delined only within the range
of the independent variables used. For this study, the
range of values of the basin characteristics used is
listed in table 2. Extrapolation beyond the range of
basin characteristics given may provide unreliable
results.

8 Analysis of the Magnitude and Frequency of Floods in Colorado

The accuracy of a regression equation generally
is assessed in terms of the standard error of estimate
and the average standard error of prediction. The
standard error of estimate is a measure of how well
the observed peak stream flows agree with the regres-
sion estimate of the peak stream flows, The largest
standard errors of estimate were found in the plains
region. The standard errors ranged from 204 to
306 percent. These large errors may be attributed to
the sparsity of gaging stations within the streamflow-
gaging-station network in this region and the vari-
ability of the magnitude of annual peak streamflows.
The smallest standard errors of estimate were found
in the mountain region where the errors ranged from
4] to 58 percent. Standard errors of estimate and the
average standard error of prediction for the regression
equations in each hydrologic region are listed in
table I.
The average standard error of prediction at an
ungaged site is a measure of the expected accuracy
with which the regression equation can estimate a
flood of a given recurrence interval. The average
standard error of prediction includes errors associated
with the regression equation and any time sampling
error. The largest average standard errors of prediction
were found in the plains region where errors ranged
from 89 to \00 percent. The smallest average standard
errors of prediction were found in the mountain region
where errors ranged from 44 to 52 percent.

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ESTIMATING MAGNITUDE OF PEAK
DISCHARGES

The regression equations developed for this
study are for estimation of peak discharges at ungaged
sites, Peak-discharge estimates also are often required
at or near gaged sites or at an ungaged site on the same
stream as a gaged site. The methods for estimating the
magnitude of peak discharges in general are explained
in this section_

Gaged Sites

Magnitudes of peak discharges for gaged
sites can be estimated using equations defined in this
study. Table 3 (in the "Supplemental Data.section
at the back of the repon) lists the peak discharges
from the flood-frequency curve for each gaging station
for various recurrence intervals. Once the recurrence