WSP07449

• File Number: 8056
• Description: Drought Preparedness
• State: CO
• Basin: Statewide
• Date: 7/1/1985
• Author: Resource Consultants
• Title: Droughts and Their Effect on the Water Supplies for the City of Fort Collins Colorado
• Water Supply Pro - Doc Type: Report/Study

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Stochastic generation of long-term records

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A stochastic model was used for generating long-term virgin flow

records for each of the five gaging stations. Records were generated for a

total of 50,000 years which is not excessive considering that the data were

generated and stored on computer. The stochastic process consisted basically

of generating a succession of virgin flows for each station that varied

randomly about the known historical means and that varied with the same

overall standard deviation as the historical data. The model was actually

more complex in that it also considered the small lag 1 auto-correlation

for the Poudre and Michigan rivers and preserved the cross-correlations

that exist between all five stations. The statistical model used was a

multivariate type which generated a residual matrix, preserving cross-

correlations, then utilized the residual to generate the flows at each

station. The methods used are presented in Salas et al. (Ref. 2). The

model for the Poudre and Michigan rivers utilized a log-normal and square

root-normal transformation of the data, respectively. Numerous checks were

performed on the generated data, and it was concluded that the long-term

generated records statistically matched the short-term historical records

quite well. A separate report was prepared describing the details of the

stochastic modeling process and is available in the technical addendum.

The generated record is too lengthy to include with this report. Five

traces of the Poudre River annual virgin flows, each spanning 500 years,

were selected from the 50,000-year record. These traces, labeled data sets

1 through 5, are listed as part of the technical addendum. A bar graph of

the Poudre River virgin flows for one of the data sets (data set 2) is

presented in Fig. 5. Generated data for all five of the river stations are

also included with the technical addendum, but only for data set 2.

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Comparisons to tree-ring results

The 50,000 years of record were generated strictly by using a stochas-

tic process. The results for the Poudre River were found to be quite

reasonable when compared to the historic record, however there were no

assurances that the runoff patterns observed over the relatively short

historic record were representative of a longer record, say the runoff

which occurred within the last 500 years. It was decided to use data on

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RE:~OURCE: CON~ULT~NT~ INC

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