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

ODJ237

Peak discharges for selected recurrence intervals
were detennined for each gaging station from a fiood-
frequency curve based on a Log-Pearson Type III
probability distribution as recommended by the
Interagency Advisory Committee on Water Data
(lACWD) (1982), These peak discharges are listed in
table 3 (in the "Supplement~1 Data" section at the back
of the ieport). TllI"t:t: parameters required for fitting a
Log-Pearson Type III probability distribution to a
series of annual peak discharges are the mean, stan-
dard deviation, and skew coefficient of the logarithms
of the peak discharges. The skew of a frequency distri-
bution has a large effect on the resulting shape of the
distribution. The skew coefficient of the station record
is sensitive to extreme events, making it difficult to
obtain an estimate of an accurate skew coefficient
from a small sample. The accuracy of the estimated
skew coefficient can be improved by weighting the
gaging-station skew with a generalized skew coeffi-
cient estimated by pooling infonnation from nearby
sites. Generalized skew coefficients of logarithms
of annual maximum streamfiow from a generalized
skew map developed by the IACWD (1982) (fig. 2)
were weighted with gaging-station skew to determine
a weighted skew coefficient, Using the assumption
that the generalized skew coefficient is unbiased
and independent of the gaging-station skew, the
mean square error of the weighted estimate is mini-
mized by weighting the gaging-station and the
generalized skew coefficients in inverse proportion
to their individual mean square errors (Tasker,
1978).
Historical adjustments to the recorded gaging-
station data were used where applicable, and low
outliers were deleted using the low-outlier test
recommended by the IACWD (1982). Low outliers
are small peak discharges (less than a given base) that
depart from the low end of a fitted flood-frequency
curve. Low outliers can have an adverse effect on
computed flood-frequency curves for gaged sites by
causing a large negative skew coefficient that can
distort the upper end of the fiood-frequency curve,
Flood-frequency curves for gaging statiolls within
about 50 miles of the Colorado State line that were
developed by other investigators ill neighboring States
may differ from the flood-frequency curves developed
for this analysis because of the use of a different skew-
coefficient map or the deletion of different low
outliers.

4 Analysis of the Magnitude and Frequency at Floods in Colorado

A flood-frequency curve (fig. 3) graphically
depicts the relation of annual peak discharge to annual
exceedance probability as determined from the Log-
Pearson probability distribution. Annual exceedance
probability is the probability, in percent, that a given
fiood magnitude would be exceeded in any 1 year,
A recurrence interval is the reciprocal of the annual
exceedance probability multiplied by 100 and is
the average time interval, in years, between exceed-
ances of a given fiood. For example, a fiood having
a I-percent exceedance probability has a recurrence
interval of 100 years. Because recurrence intervals
are long-tenn averages, fiood magnitudes greater
than those of a specific recurrence interval may have
occurred more or less frequently than indicated by
the recurrence interval. For example. to-year floods
may occur in successive years at some sites and may
not occur for more than 10 years at other sites. In
this report, the term "recurrence interval" is used to
describe the exceedance probability of a fiood magni-
tude. Flood-frequency curves were developed for
328 gaging stations on unregulated streams having a
minimum of 10 years of record. The fiood magnitudes
that were determined from the fiood-frequency curves
for each gaging station are listed in table 3 (in the
"Supplemental Data" section at the back of the report).
Included are data for recurrence intervals of 2, 5, to,
25, 50. 100, 200. and 500 years.

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Regional Flood-Frequency Analysis

The regional regression equations discussed in
this report relate flood magnitude, the dependent vari-
able, to easily measured drainage-basin and climatic
characteristics, the independent variable. The study
area was divided into five distinct hydrologic regions;
each region representing an area of similar basin phys-
iographic and climatic characteristics. The hydrologic
regional boundaries were defined by McCain and
Jarrett (1976) and Kircher and others (1985). These
boundaries were detennined by plotting the regression
residuals (the difference between the discharge
predicted from the regression equation and the
discharge determined from the station flood-frequency
curve) on a map and drawing boundaries around phys-
iographic regions in which the regression residuals
were similar. Examination of regression residuals for
the cUrrent study did not indicate any need to change
the previously defined regional boundaries.