9 Walshaw D.Modelling extreme wind speeds in regions prone to hurricanes[J].J.R.Stat.Soc.Ser.C..2000, 49(1):51-62. 10 Huang W,Xu S.Nnaji S.Evaluation of GEV model for frequency analysis of annual maximum water levels in the coast of United States[J].Ocean Eng.2008.35(11-12):1132-1147. [11 Prescott P,Walden A T.Maximum likelihood estimation of the parameters of the generalized extreme-value distri- bution[J].Biometrika,1980,67(3):723-724. 12 Madsen H.Rasmussen PF.Rosbjerg D.Comparison of annual maximum series and partial duration series meth- ods for modeling extreme hydrologic events,1.At-site modeling[J].Water Resour.Res .1997.33(4): 746-757. 13 Coles S.An introduction to statistical modeling of extreme values[Z].Springer,London.2001. [14 Katz R W,Parlange M B,Naveau P.Statistics of extremes in hydrology [J].Adv.Water.Resour.,2002,25 (8-12):1287-1304. 15 Martins E S,Stedinger J R.Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data[J].Water Resour.Res.,2000,36(3):737-744. [16]刘次华，随机过程[M].武汉：华中科技大学出版社，2001. [17]邢贞相，芮孝芳，崔海燕，等.基于AM-MCMC算法的贝叶斯概率洪水预报模型[J].水利学报，2007,38 (12):1500-1506. [18]李向阳，程春田，林剑艺，等，基于BP神经网络的贝叶斯概率水文预报模型[J].水利学报，2006,37(3)： 354-359. [19 Dirceu S,Reis Jr.Jery R.Stedinger.Bayesian MCMC flood frequency analysis with historical information[]]. Joural of Hydrology,2005,313(1-2):97-116. 20 LiangZ M.Li B Q.YuZ B.et al.Application of Bayesian approach to hydrological frequency analysis[J].Sei- ence China Technological Sciences,2011,54(5):1183-1192. Bayesian MCMC flood frequency analysis based on generalized extreme value distribution and Metropolis-Hastings algorithm 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 distri- bution of flood flows.In this paper,the unknown parameters of hydrologic frequeney 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 quantificationally 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. Key words:flood frequency analysis;Bayesian statistics:GEV distribution;Metropolis-Hastings algorithm; Goodness-of-fit test (责任编辑：王成丽) -949-［ 9 ］ Walshaw D . Modelling extreme wind speeds in regions prone to hurricanes［J］. J . R . Stat . Soc . Ser . C . ，2000， 49（1）：51-62 . ［ 10］ Huang W，Xu S，Nnaji S . Evaluation of GEV model for frequency analysis of annual maximum water levels in the coast of United States［J］. Ocean Eng . ，2008，35（11-12）：1132-1147 . ［ 11］ Prescott P，Walden A T . Maximum likelihood estimation of the parameters of the generalized extreme-value distri⁃ bution［J］. Biometrika，1980，67（3）：723-724 . ［ 12］ Madsen H，Rasmussen P F，Rosbjerg D . Comparison of annual maximum series and partial duration series meth⁃ ods for modeling extreme hydrologic events，1，At-site modeling［J］. Water Resour . Res . ，1997，33（4）： 746-757 . ［ 13］ Coles S . An introduction to statistical modeling of extreme values［Z］. Springer，London，2001 . ［ 14］ Katz R W，Parlange M B，Naveau P . Statistics of extremes in hydrology［J］. Adv . Water . Resour . ，2002，25 （8-12）：1287-1304 . ［ 15］ Martins E S，Stedinger J R . Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data［J］. Water Resour . Res . ，2000，36（3）：737-744 . ［ 16］ 刘次华 . 随机过程［M］. 武汉：华中科技大学出版社，2001 . ［ 17］ 邢贞相，芮孝芳，崔海燕，等 . 基于 AM-MCMC 算法的贝叶斯概率洪水预报模型［J］. 水利学报，2007，38 （12）：1500-1506 ． ［ 18］ 李向阳，程春田，林剑艺，等 . 基于 BP 神经网络的贝叶斯概率水文预报模型［J］. 水利学报，2006，37（3）： 354-359 ． ［ 19］ Dirceu S，Reis Jr，Jery R，Stedinger . Bayesian MCMC flood frequency analysis with historical information［J］. Journal of Hydrology，2005，313（1-2）：97-116 . ［ 20］ Liang Z M，Li B Q，Yu Z B，et al . Application of Bayesian approach to hydrological frequency analysis［J］. Sci⁃ ence China Technological Sciences，2011，54（5）：1183-1192 . Bayesian MCMC flood frequency analysis based on generalized extreme value distribution and Metropolis-Hastings algorithm 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 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 quantificationally 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. Key words：flood frequency analysis；Bayesian statistics；GEV distribution；Metropolis-Hastings algorithm； Goodness-of-fit test （责任编辑：王成丽） — 949 —