Low-flow frequency analysis using probability-plot correlation coefficients

Although a vast amount of literature exists on the selection of an appropriate probability distribution for annual maximum floodflows, few studies have examined which probability distributions are most suitable to fit to sequences of annual minimum streamflows. Probability plots have been used widely in hydrology as a graphical aid to assess the goodness of fit of alternative distributions. Recently, probability-plot correlation-coefficient (PPCC) tests were introduced to test the normal, two-parameter lognormal and Gumbel hypotheses. Those procedures are extended here to include both regional and at-site tests for the two-parameter Weibull and lognormal distributional hypotheses. In theory, PPCC-hypothesis tests can only be developed for two-parameter distributions that exhibit a fixed shape. Nevertheless, the PPCC is a useful goodness-of-fit statistic for comparing three-parameter distributions. The PPCC derived from fitting the two- and three-parameter lognormal, two- and three-parameter Weibull, and log-Pearson type III distributions to sequences of annual minimum seven-day low flows at 23 sites in Massachusetts are compared. How the PPCC can be used to discriminate among both competing distributional hypotheses for the distributions of fixed shape and competing parameter-estimation procedures for the distributions with variable shape is described. An approximate regional PPCC test is developed and used to show that there is almost no evidence to contradict the hypothesis that annual minimum seven-day low flows in Massachusetts are two-parameter lognormal.