LU Fan, YAN Deng-hua (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China)

Abstract: The generalized extreme value (GEV) distribution has been widely used for modeling the distribution of flood flows. In this paper, the unknown parameters of hydrologic frequency distribution linetype are considered as random variables, and Bayesian Markov chain Monte Carlo (MCMC) method based on Metropolis-Hastings algorithm is used to evaluate the posterior distributions of GEV distribution parameters and flood quantiles. The application example was conducted with flood data from the Han River basin, near the Danjiangkou reservoir, in Hubei, China. The results indicate that MCMC methods based on Metropolis-Hastings algorithm are useful tools for parameter estimation of GEV distribution. Due to effective using of prior information unrelated to asymptotic property of likelihood function, posterior distribution of upper quantile obtained from Bayesian estimation includes more information compared with classical statistical methods in flood frequency analysis. Thus uncertainty of forecasting caused by uncertainty of parameters can be quantificationally expressed. Moreover, the proposed Bayesian method can significantly pass several general goodness-of-fit tests, such as quantile plot, probability plot correlation coefficient method, root mean square error method, and Kolmogrov-Smirnow method. The capabilities and utility of the method in more reliable estimates of extreme floods is illustrated.

Key words: flood frequency analysis, Bayesian statistics, GEV distribution, Metropolis-Hastings algorithm, Goodness-of-fit test

Published in: Journal of Hydraulic Engineering, Vol. 44, No. 8, 2013