Probability Distribution of Low Streamflow Series in the United States

Abstract

Estimates of low streamflow statistics are required for a variety of water resource applications. At gauged river sites, the estimation of low streamflow statistics requires estimation of annual n-day minimum streamflows, selection of a probability distribution to describe annual minimums, and estimation of the distribution’s parameters. Using L-moment diagrams, the ability of various probability distributions to describe low streamflow series was examined at 1,505 gauged river sites in the United States. A weighted distance statistic was developed to compare the goodness-of-fit of different probability distributions for describing low streamflow series. Compared to perennial streamflow sites, a shift of L-moments ratios was observed at intermittent river sites where discharge is sometimes reported as zero. An analytical experiment compared the observed shifts in L-moment ratios at intermittent sites with theoretical L-moment ratio shifts for a number of real- and log-spaced probability distributions. Results of these experiments indicate that Pearson Type III and the 3-parameter lognormal distributions should be the recommended distributions for describing low streamflow statistics in the United States at intermittent and nonintermittent (perennial) sites, respectively.