PROJ00441

• Contract/PO #: C153459
• Contractor Name: Loveland, City of
• Water District: 0
• County: Larimer
• Bill Number: XB 99-999
• Loan Projects - Doc Type: Feasibility Study

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disperse the data. A standard deviation of 0.0 would only occur for data
that are all equal. The skewness coefficient is a measure of symmetry.
Data with positive skewness consists of values which are mostly less than
the mean value, while data with negative skewness exhibit the opposite
tendency. The average annual streamflow in the augmented record is
slightly less that that of the historic data. This is due to inclusion of
the 1930's drought in the augmented record as compared to the lack of that
same data in the historic data (the streamflow gauge is not continuous from
1929 to 1938). The augmented record thus provides a more realistic repre-
sentation of the range of drought conditions that may be encountered in the
Big Thompson River.

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4.4 GENERATION OF SYNTHETIC STREAMFLOW RECORD FOR THE BIG THOMPSON RIVER

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The augmented historical records of Big Thompson native flows were used to
generate a synthetic record of values which is statistically identical to
the input record(s). This procedure is based on the "Markov model" (a
statistical theory) which generates flow values using an equation which has
both a direct and a random component:

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qi = d. + e.
1 1

where:

q. = Big Thompson monthly average flow for month i;
1
d. direct component for month i; and
1
ei = random component for month 1.
i = 1, 2, . . . 12 to represent Jan., Feb. , . . Dec.

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The direct component, d., is based on the mean for month i and the flow for
1
the previous months. Prior flows are considered since it has been shown
that most streamflows show a dependence on flows in preceding months
(Fiering and Jackson 1971). The influence of prior flows is represented by
the serial correlation coefficient. This value will be in the range from
-1.0 to 1.0, with a value of -1.0 or 1.0 representing an exact correlation

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