WSP05071

• File Number: 8146.400
• Description: Pueblo Dam - Reports
• State: CO
• Basin: Arkansas
• Water Division: 2
• Date: 10/1/1994
• Author: US Geological Survey
• Title: Use of Frequency Analysis and the Extended Streamflow Prediction Procedure to Estimate Evacuation Dates for the Joint-Use Pool of Pueblo Reservoir Colorado
• Water Supply Pro - Doc Type: Report/Study

2959

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Sta'lon 07109500 AI'dnsaa Rtver near Avonc:ime

Water Year 1942
Water Year 1944

12.000

9,000

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'" 6,000
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is
Z 3,000
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o 0

......

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

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:-...........: .
...:.

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....

Figure 3. Recorded daily mean discharge for selected stations in the vicinity of Pueblo Reservoir
--Continued.

FREQUENCY ANALYSIS OF HISTORICAL
DAILY MEAN DISCHARGES

Frequency analysis (or development of a fre-
quency curve) is a method in which the magnitude of a
variable can be related to its probability (or frequency)
of occurrence (Riggs, 1968, p. 1). In the PRJUP study,
the variable considered is daily mean discharge and the
probability level is 0.01. In the frequency analysis
described in this report, the probabilities refer to
exceedances based on random samples consisting of
one trial per year (one daily discharge on a given day or
one discharge volume for a number of days). Thus, the
statement that "the 0.01 exceedance probability (EP)
discharge on April I is 333 ft3/s" is equivalent to the
statement that ''there is a I-percent chance in any year
for the discharge on April I to exceed 333 ft3/s."

Frequency curves can be titted to a number of
mathematical distributions; the normal, log-normal,
type I extreme value (Gumbel), and log-Pearson type-
III (log-gamma) (hereinafter referred to as LP3) distri-
butions often are used in hydrologic analysis. The LP3
distribution commonly is used in flood-frequency
analysis and is the distribution recommended by the
U.S. Interagency Advisory Committee on Water Data
(1982) for nationwide flood-frequency analysis; the

LP3 distribution was used for frequency analysis in the
PRJUP study.

Log-Pearson Type-III Distribution

The LP3 distribution has three parameters, which
are computed by the following equations (U.S. Inter-
agency Advisory Committee on Water Data, 1982,
p.IO):

1:%
x=
N

(I)

[ 2 0.5
= I:(X-X)]
S (N-l)

(2)

G=

- 3
NI:(x-x)
(N-I) (N-2)s3

(3)

where

x = mean of the logarithms,
x = logarithm of each discharge in the sample,

8 UI8 of Frequ.ncy Ansly.'. end tho Extended St....mflow Prediction Procodu... to E.t1mote Ev.eu.t1on O.t.. lor tho
Jolnt~UIe Pool ot Pueblo ReselVolr, Colorado