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Technical Report

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streamflow, gamma distribution, Weibull distribution, zero storage, reservoir size


Streamflow data from unregulated streams in Arkansas were processed through Moran’s Model for a dam. The process involved calculating a cumulative gamma distribution for each stream as the streamflow values were incremented in units of 0.1 cubic feet per second per square mile of drainage area. This gamma distribution was then used as input for Moran’s Model. The output from Moran's Model includes the probability of the reservoir having zero contents as the size of the reservoir is decreased. The logarithm of the probability of zero contents, 1n PO, versus reservoir size, K, is a straight line of the form 1n PO = -n-sK. The constants in the equation, n and s, are functions of the logarithm of the draft when the draft is expressed as a percentage of mean annual flow. The equations for 1n PO versus K were determined for each stream studied. In addition, a general equation for all streams was determined.

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