Flood frequency analysis using generalized distributions and entropy-based model selection method

Abstract

Flood frequency analysis (FFA) is used for estimating the return period of a design flood. Fundamental to FFA is the selection of a frequency distribution fitted to the data set, where an inappropriate choice of a distribution can lead to significant error and bias in the design flood estimate. The usual criteria for selecting a distribution are Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE), although these criteria have limitations. This paper performed FFA using three main steps. First, five generalized distributions were considered as candidate distributions for FFA; second, the principle of maximum entropy (POME) and the method of maximum likelihood (MLE) were used for parameter estimation; and third a new model selection criterion based on the value of entropy was proposed to choose the best-fitted distribution. Monte Carlo simulation was carried out to test this entropy-based method for four sample sizes equal to 50, 200, 1000, and 10000, and simulation was repeated 1000 times for each sample size. Then, the probability that a given method identified the correct distribution was determined. The probabilities affected by the sample size, skewness, and shape of the probability density function (PDF) were assessed. Using Qing River basin, China, as a case study, the design flood values were calculated and compared. Results of simulation showed that the proposed method was better than other methods for the following cases: (a) the sample size of data set X is small; (b) the skewness coefficient CS>0; and (c) the shape of PDFs is bell-shaped.