Population index flood method for regional frequency analysis

Regional frequency analyses based on index flood procedures have been used within the hydrologic community since 1960. It appears that when the index flood method was first suggested, the index flood was taken to be the at-site population mean, which, in turn, in the last two or three decades, has been estimated by the at-site, sample mean. The objectives of this paper are to investigate the consequences of replacing a population characteristic with its sample counterpart and to propose an analytically correct regional model dubbed as the population index flood (PIF) method. In this method the homogeneity of the region is embedded in the structure of the parameter space of the underlying distribution model. Simulation experiments are conducted to test the proposed PIF method based on the generalized extreme value distribution with parameters estimated using the method of maximum likelihood (MLE) and the method of probability-weighted moments (PWM). Furthermore, in the simulation experiments the PIF method is compared with the Hosking and Wallis [1997] regional estimation scheme (HW scheme). Comparing among all index flood methods investigated herein, the PIF method with parameters estimated using MLE provides the best overall results for the 0.95 and the 0.99 quantiles in terms of both bias and root-mean-square error for moderate to sufficiently large sample sizes, but for the 0.995 quantile the HW scheme seems to perform best for the investigated sample sizes.