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

Abstract

The upper tail of a flood frequency distribution is always specifically concerned with flood control. However, different model selection criteria often give different optimal distributions when the focus is on the upper tail of distribution. With emphasis on the upper-tail behavior, five distribution selection criteria including two hypothesis tests and three information-based criteria are evaluated in selecting the best fitted distribution from eight widely used distributions by using datasets from Thames River, Wabash River, Beijiang River and Huai River. The performance of the five selection criteria is verified by using a composite criterion with focus on upper tail events. This paper demonstrated an approach for optimally selecting suitable flood frequency distributions. Results illustrate that (1) there are different selections of frequency distributions in the four rivers by using hypothesis tests and information-based criteria approaches. Hypothesis tests are more likely to choose complex, parametric models, and information-based criteria prefer to choose simple, effective models. Different selection criteria have no particular tendency toward the tail of the distribution; (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. The distributions selected by information-based criteria are more likely to be close to true values than the distributions selected by hypothesis test methods in the upper tail of the frequency curve; (3) The proposed composite criterion not only can select the optimal distribution, but also can evaluate the error of estimated value, which often plays an important role in the risk assessment and engineering design. In order to decide on a particular distribution to fit the high flow, it would be better to use the composite criterion.