Bayes统计模型在出山月均径流极小值研究中的应用  

A Bayesian Analysis of Monthly Average Runoff Minima in Mountain Areas

作　　者：刘友存[1] 霍雪丽 郝永红[1] 崔玉环[3] 韩添丁[4] 沈永平[4] 王建[4] 

机构地区：[1]天津师范大学天津市水资源与水环境重点实验室,天津300387 [2]天津师范大学城市与环境科学学院,天津300387 [3]安徽农业大学理学院,安徽合肥230036 [4]中国科学院寒区旱区环境与工程研究所,甘肃兰州730000

出　　处：《山地学报》2015年第4期425-433,共9页Mountain Research

基　　金：国家自然科学基金(41471001;41272245;41401022;41001006);中国博士后科学基金项目(20100480444)~~

摘　　要：数理统计方法在解决全球气候变化引起的洪水、干旱等极端水文事件中获得了越来越广泛的应用。选取乌鲁木齐河1958—2006年枯水期的月平均出山径流资料,采用广义Pareto极值分布(GPD)模型,并运用Bayes统计模型估计GPD的参数,最后对乌鲁木齐河枯水期月均出山径流极小值变化进行了估算。研究表明:1.参数的初始值、先验分布的均值分别取其极大似然估计值,先验分布的标准差取较小值,随机游走项分布的标准差取较大值,这种方法能使Markov链快速收敛;2.基于Bayes参数估计值的GPD在拟合月均径流量的极小值时具有很高的精确度,与传统的极大似然估计方法相比,Bayes统计模型的推断效果较好;3.乌鲁木齐河重现期为10 a、25 a、50 a和100 a的枯水期月均径流极小值分别约为0.60 m3/s、0.44 m3/s、0.32 m3/s和0.20 m3/s;4.100 a重现水平的95%置信区间的下限为-0.238 m3/s,说明当乌鲁木齐河在枯水期遇上百年一遇的极小值时,有可能出现断流的情况。Global warming has intensified hydrological extreme events and resulted in disasters around the world.For disaster management and adaption of extreme events,it is essential to improve the accuracy of extreme value statistical models. In this study,Bayes＇ Theorem is introduced to estimate parameters in the Generalized Pareto Distribution（ GPD） model which is applied to simulate the distribution of monthly average runoff minima during dry periods in mountain areas of rümqi River. Bayes＇ Theorem treats parameters as random variables and provides machinery way to convert the prior distribution of parameters into a posterior distribution. Statistical inferences based on posterior distribution can provide a more comprehensive representation of the parameters. An improved Markov Chain Monte Carlo（ MCMC） method,which can solve high-dimensional integral computation in the Bayes equation,is used to generate parameter simulations from the posterior distribution. Model diagnosis plots are made to guarantee the fitted GPD model is appropriate. Then based on the GPD model with Bayesian parameter estimates,monthly average minima corresponding to different return periods can be calculated. The results show that the improved MCMC method is able to make Markov chains converge at a high speed. Compared with the GPD model based on maximum likelihood parameter estimates,the GPD model based on Bayesian parameter estimates obtain more accurate estimations of minimum monthly average runoff. Moreover,the monthly average runoff minima in dry periods corresponding to 10 a,25 a,50 a and 100 a return periods are 0. 60 m^3/ s,0. 44 m^3/ s,0. 32 m^3/s and 0. 20 m^3/ s respectively. The lower boundary of 95% confidence interval of 100 a return level is- 0. 238 m^3/s,which implies that rümqi River is likely to cease when 100 a return level occurs in dry periods.

关 键 词：径流极小值 广义PARETO分布 MARKOV Chain MONTE Carlo(MCMC)方法 乌鲁木齐河 

分 类 号：P333.3[天文地球—水文科学]