FLOOD00005

• County: Statewide
• Title: Precipitation Records and Flood-Producing Storms in Cheyenne Wyoming
• Date: 10/23/2003
• Prepared For: Cheyenne
• Floodplain - Doc Type: Educational/Technical/Reference Information

PRECIPITATION-FREQUENCY CURVES

Precipitation data for 5-, 10-, 15-, and 30-minute, and 1-, 2-, and 24-
hour duratIons were used in this study. Amount of precipitation for each
duration is plotted against "recurrence interval "--the length of time in
which the given amount of precipitation can be expected to be equalled or
exceeded once. The resultin,g graph is called a precipitation-frequency
curve. ,The analytical procedure is based on the assumption that the data
are described by one of several possible data distributions. Three
different distributions were examined in this report to determine which one
seemed to best fit the Cheyenne data.

Method of Analysis

Annual maximum precipitation data for 5-, 10-, 15-, and 30-minute, and
1-, 2-, and 24-hour durations were analyzed three times, based on the
assumption that: (1) The data were described by a Gumbel distribution, (2)
the logarithms of the data were described by a Gumbel distribution (referred
to as "log-Gumbel distribution" in this report), or (3) the logarithms of
'the data were described by a Pearson Type III distribution (referred to as
"log-Pearson Type III distribution" in this report). Data for each duration
and assumed distribution were examined twice. The first analysis, using
only data, collected before 1985, created the frequency curves defined before
the storm of August 1, 1985, (subsequently referred to as "previously
defined curves"). Precipitation-frequency curves were then updated by
including all data collected through 1986 in order to assess the effects of
the August 1 storm on predicted storm magnitudes.

The initial analysis was carried out assuming that the data were
described by a Gumbel distribution because the Gumbel distribution is used
by the National Weather Service for analyzing precipitation data. The
method used in this report for fitting a straight line to the precipitation
data is identical to the method used by the National Weather Service (Frank
Richards, National Weather Service, oral commun., 1987, and Robert Lichty,
U.S. Geological Survey, written commun., 1987). Morel-Seytoux (1986, p. 75)
cites a previous study that demonstrated the legitimacy of using the
assumption of a Gumbel distribution to extrapolate precipitation data up to
a l,OOO-year recurrence interval based on 25 years of data. However, Chow
(1964, p. 8-35) cites studies that indicate the Gumbel approximation
underpredicts the maximum values of rainfall for long recurrence intervals.

The Gumbel distribution is based on only two parameters, the mean and
the standard deviation, and assumes a constant skewness of 1.14. Skewness
was calculated for all the rainfall durations of interest for all data
available through 1986 and ranged from 0.984 to 3.41 (table 2). For a
given mean and standard deviation, the higher the skewness, the higher the
estimation of the magnitude of the 100-year event will be. Particularly for
the 1-, 2-, and 24-hour arithmetic data, the actual value of skewness is
substantially higher than the value assumed in the Gumbel distribution.
Therefore, a straight line based on the Gumbel distribution fitted to this
data may underpredict the magnitude of the 100-year storm.

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