Power Distribution for Low Streamflows

Abstract

The power distribution is a special case of the Weibull distribution. It can be derived as the distribution function of the low flows of a stream, when the recession curve is assumed to be exponential, using a theoretical result for the probabilities of maximum dry period lengths. The power distribution is found to have a better fit to the minimum flows of some streams than other two-parameter distributions, such as the Weibull and lognormal. In many streams, the distribution of the smaller low flows is different from that of the remaining data. This part can be fitted by a power distribution function whose parameters are estimated by LL-moments, which are L-moments computed with greater weights for smaller observations. Plotting positions and LL-moments are derived for the power distribution and are applied to data from nine sites. Analyses of data from a number of streams in Turkey and the United Kingdom have shown that the probability plot correlation coefficient test accepts the goodness of fit at very high significance levels when parameters are estimated using LL-moments.