WSP11570

• File Number: 8111.807
• Description: Arkansas River Compact Administration - Stream Gage Evaluation
• Basin: Arkansas
• Date: 1/1/1980
• Author: USGS
• Title: Cost-Effective Stream Gaging Strategies for the Lower Colorado River
• Water Supply Pro - Doc Type: Publication

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The third step is to define the uncertainty in annual mean discharge

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as a function of the number of visits for each of the stream gage1. This

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step is discussed in detail in a subsequent section of this report.

The final step is to use all of the above to determine the number of

times, N., that each of the NR routes is used during a year such that (1)
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the budget for the network is not exceeded, (2) the minimum number of

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visits to each station is made, and (3) the total uncertainty in the network

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is minimum. Figure 2 presents this step in the form of a mathematical

program.

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In its simplest form the function relating uncertainty at a stream gage

to the number of visits to the gage is

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2
cr.
$ .(M.) ~ dl-1 (1)
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where cr.2 is the variance of an independent series of streamflows that
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comprise the annual streamflow record and M. is the number of visits. In
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the real world streamflows are not independent in time; the streamflow at

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one instant gives a good indication of what streamflow will be one minute

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later and maybe even a day or a week hence. Accounting for the temporal

dependence of streamflow results in a form of~.(M.) that is more complex
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than equation 1, but uncertainty is still inversely related to the number of

visits to the station. This inverse relation, which is nonlinear, precludes

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the use of classical operations research techniques such as integer programming

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(Wagner, 1969) to solve for the best set of decisions, N*, on how often to use

each of the stream gaging routes. Therefore, a direct-search technique was

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used to specify the values of N* that met all of the criteria described in

figure 2.

Figure 3 presents) a tabular layout of the problem.
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Each of the

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