基于广义极值分布和Metropolis-Hastings抽样算法的贝叶斯MCMC洪水频率分析方法  

Bayesian MCMC flood frequency analysis based on generalized extreme value distribution and Metropolis-Hastings algorithm

作　　者：鲁帆[1] 严登华[1] 

机构地区：[1]中国水利水电科学研究院流域水循环模拟与调控国家重点实验室,北京100038

出　　处：《水利学报》2013年第8期942-949,共8页Journal of Hydraulic Engineering

基　　金：国家自然科学基金项目(51109224);国家重点基础研究发展计划课题(2013CB036406;2010CB951102)

摘　　要：广义极值(GEV)分布是国内外洪水频率分析建模中广泛应用的一种概率分布。本文将水文频率分布线型的未知参数看作随机变量,通过基于Metropolis-Hastings抽样算法的贝叶斯MCMC方法估计GEV分布参数和设计洪水的后验分布,并据此进行极值洪水的频率分析。汉江流域丹江口水库年最大1日(3日、5日、7日)洪量和年最大洪峰流量频率分析结果表明,基于Metropolis-Hastings抽样的MCMC模拟在GEV分布参数的贝叶斯估计计算中行之有效;由于利用了与似然函数渐近性质无关的先验信息,贝叶斯估计方法得到的高分位数设计洪量的后验分布比经典统计方法得到的设计洪量能包含更多的信息,从而能表达由于参数不确定性而引起的预测不确定性。该方法能显著地通过分位数图、PPCC法、均方根误差法、K-S法等多种拟合优度检验方法,拟合效果不亚于矩法、极大似然估计法等常用的经典统计方法。The generalized extreme value （GEV） distribution has been widely used for modeling the distri- bution 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 Me- tropolis-Hastings algorithm are useful tools for parameter estimation of GEV distribution. Due to effective us- ing of prior information unrelated to asymptotic property of likelihood function, posterior distribution of up- per 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 quantifieationally expressed. Moreover, the proposed Bayesian method can significantly pass several gener- al 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 re- liable estimates of extreme floods is illustrated.

关 键 词：洪水频率分析 贝叶斯估计 广义极值分布 Metropolis—Hastings抽样 拟合优化度检验 

分 类 号：P333[天文地球—水文科学]