WSP11333

• File Number: 8273.100
• Description: Colorado River Basin Salinity Control - Federal Agency Reports - BOR
• Basin: Colorado Mainstem
• Water Division: 5
• Date: 5/1/1975
• Title: Application of Stochastic Hydrology to Simulate Streamflow and Salinity in the Colorado River
• Water Supply Pro - Doc Type: Report/Study

4.4.3 Monthly Properties

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In addition to mllintsining the .correct total flow in a ballin, the
data generation procedure must also preserve the annual periodicity
reflecting the seasonal runoff pattern. Since it would require an
enormous volume to compare the periodic patterns of all stations, two
major ones will be illustrated here. The present modified values were
taken from Appendix 1 and the synthetic monthly parameters from an
analysis of the generated traces. Figures.9 and 10 of the July 1974
report show monthly means and standard deviations, respectively, for
the flow of the Gunnison River at Blue Hesa Reservoir. This station
was chosen to illustrate the behavior of synthetic traces at an
upstream or "rim" station. The population values, indicated by solid
lines connecting them, are generally in the center of the synthetic
trace values. This indicates the streamflow generation me~hanism
creates values which might be expected if the flow were sampled for
the given periods. The good agreement in the standard deviation plot
further indicates that the monthly variation is well preserved .in the
synthetic traces.

Figures 11 and 12 of the July 1974 report show the same properties
for the Lees Ferry station. This station is especially significant
since it represents the SUDI of many flow increments and "rim stations"
from above. The good comparison between properties of the synthetic
traces and those of the present modified flows clearly illustratesthe
efficacy of the generating procedure as well as the adequacy of the
coefficients used in the model.

4.4.4 Probability Distributions

The final comparison was made in the July 1974 report to illustrate
the validity of synthetic flows is a series of plots containing the
probability distributions of flows. To construct long sequences of
data, 30-year traces were used together to provide five 60-year traces.
These data were then averaged for three periods (3, 5, and 9 years)
by a moving mean process.11 Plotting positions were calculated by
the equation

m
P(x) . N+f . 100

(15)

In the equation P(x) is the probability of the random variable being less than
or equal to x, m is the ordered sequence of a particular x value and
N is the sample size. P(x) is in percentage units. These probabili-
ties were calculated for the annual as well as 3-, 5-, and 9-year

11 Calculations and results produced by the computer program "SUTl"
described in the unpublished user I s guide, "Simulation Util ity
Program I," by R. W. Ribbens, Division of Planning Coordination, USBR.

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