Comparative Study on the Selection Criteria for Fitting Flood Frequency Distribution Models with Emphasis on Upper-Tail Behavior

Abstract:

Many probability distributions have been proposed for flood frequency analysis and several criteria have been used for selecting a best fitted distribution to an observed or generated data set by some random process. The upper tail of flood frequency distribution should be specifically concerned for flood control. However, different model selection criteria often result in different optimal distributions when focus on upper tail of flood frequency distribution. In this study, with emphasis on the upper-tail behavior, 5 distribution selection criteria including 2 hypothesis tests and 3 information-based criteria are evaluated in selecting the best fitted distribution from 8 widely used distributions (Pearson 3, Log-Pearson 3, two-parameter lognormal, three-parameter lognormal, Gumbel, Weibull, Generalized extreme value and Generalized logistic distributions) by using datasets from Thames River (UK), Wabash River (USA), Beijiang River and Huai River (China), which are all within latitude of 23.5-66.5 degrees north. The performance of the 5 selection criteria is verified by using a composite criterion focus on upper tail events defined in this study. This paper shows the approach for the optimal selection of suitable flood frequency distributions for different river basins. Results illustrate that (1) Different distributions are selected by using hypothesis tests and information-based criteria for each river. (2) The information-based criteria perform better than hypothesis tests in most cases when the focus is on the goodness of predictions of the extreme upper tail events. (3) In order to decide on a particular distribution to fit the high flow, it would be better to use the combination criteria, in which the information-based criteria can be used first to rank the models and the results are inspected by hypothesis testing methods. In addition, if the information-based criteria and hypothesis tests provide different results, the composite criterion will be taken for final decision.