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

:2530

N = number of discharges in the sample,
S = standard deviation of the logarithms, and
G = skew coefficient of the logarithms.

The LP3 distribution is defined by the general
formula (U.S. Interagency Advisory Committee on
Water Data, 1982, p. 9):

xp = x+Kp.GS

where
xp = discharge or variate value exceeded with
probability P in any year,
Kp,G = the LP3 frequency factor for exceedance
probability P and skewness G, and

x and S = the same as defined in equations I and 2.

Frequency factors for skew coefficients ranging
from -9.0 to 9.0 and for EP's ranging from 0.0001 to
0.9999 are reported by the U.S. Interagency Advisory
Committee on Water Data (1982).

Skew-Coefficient Analysis

Reliability of the sample skew coefficient (sta-
tion skew) decreases as sample size (years of record)
becomes small (fig. 4); the station skew also is sensitive
to extreme events (U.S. Interagency Advisory Commit-
tee on Water Data, 1982, p. 10). To improve reliability
of the station skew, the U.S. Interagency Advisory
Committee on Water Data (1982, p. 10) recommends
that a generalized skew coefficient (generalized skew)
be used in the frequency analysis. The generalized
skew is used to calculate a weighted skew estimate
(weighted average of station and generalized skew)
under the assumption that the generalized skew is unbi-
ased and independent of station skew (U .S. Interagency
Advisory Committee on Water Data, 1982, p. 12).
Methods for estimating generalized skew for an area
are described by the U.S. Interagency Advisory Com-
mittee on Water Data(1982, p. II-IS); however, ifdata
are insufficient, generalized skew can be estimated
from the national generalized-skew-coefficient map
provided in that report (also see Hardison, 1974).
Because the national map of generalized skews
(U.S. Interagency Advisory Committee on Water Data,
1982) was developed from annual instantaneous peak
discharges, station skews for ROM discharges were
analyzed for selected stations in the vicinity of Pueblo
Reservoir to determine if generalized skews from the
national map were applicable to the PRIUP study. For
the frequency analysis of ROM discharges upstream
from Pueblo Reservoir, station skews were analyzed

(4)

for stations at Canon City, at Portland, and near Pueblo
(fig. I; table I). The near-Pueblo station, although'
downstream from Pueblo Reservoir (fig. I), was
included because the period of record (table I) is prior
to construction of Pueblo Dam. The above-Pueblo
station was not included because only 10 years of non-
regulated discharge data were available. The near-
Portland station also was not included because only
9 years of record were available (table I); the record for
this station could not be combined with that for the
near-Portland station because of tributary flow from
Beaver Creek (fig. I).

Station skews and the skews for plus or minus
one root mean square error for logarithms of ROM dis-
charge during April and May for three stations on the
Arkansas River are shown in figure 5. No definite tem-
poral or spatial trend in station skew is evident at the
stations; moreover, the error bars generally are not very
large. Also, the station skews for the annual instanta-
neous peak discharge logarithms for the at-Canon City
station (0.28), for the at-Portland station (0.72), and for
the above-Pueblo station (1.09) were within the range
of station skews for ROM discharge logarithms (fig. 5).
Therefore, the generalized skew from the national map
(U.S. Interagency Advisory Committee on Water Data,
1982) was considered appropriate in the frequency
analysis of ROM discharges upstream from Pueblo
Reservoir.

For the frequency analysis downstream from
Pueblo Reservoir, station skews were analyzed for
Fountain Creek, the 51. Charles River, and the near-
Avondale station (fig. I; table I). Discharge records for
the four 51. Charles River stations (table I) were com-
bined into a single record because the difference in
drainage area is only about 3 percent and the few
ephemeral tributaries between the most upstream and
downstream stations do not contribute substantial dis-
charge. The period of analysis for the near-Avondale
station includes IS years of record after the completion
of Pueblo Dam; however, because (I) Pueblo Reservoir
usually is operated as a flow-through reservoir during
April and May, (2) Fountain Creek and the 51. Charles
River often have substantial effects on the discharge at
this station, and (3) this station would not be used in the
actual frequency analysis; the analysis of skew coeffi-
cient for this station would be helpful in the analysis of
skew coefficients downstream from Pueblo Reservoir.

Station skews and the skews for plus or minus
one root mean square error for logarithms of ROM dis-
charge during April and May for Fountain Creek, the
51. Charles River, and the near-Avondale station are
shown in figure 6. Some increasing and some decreas-
ing trends in station skew with time can be seen in
figure 6; however, most of the station skews are

FREOUENCY ANALYSIS OF HISTORICAL DAilY MEAN DISCHARGES 9