融合极值分布与MCMC的降水极值模拟研究

Simulations of extreme precipitations based on extreme distributions and MCMC method

模拟降水极值对于城市防洪具有重要意义。根据北京、深圳、济南1952—2012年的日降水资料,采用广义极值分布(GEV)与广义帕累托分布(GPD)分别模拟三个城市的年最大降水与超阈值降水序列,通过马尔科夫链蒙特卡洛方法(MCMC)识别参数,并对模拟结果加以综合分析。研究发现,MCMC方法在GEV与GPD参数的贝叶斯估计中行之有效,所识别最佳模型的相关性系数与确定性系数均普遍高达0.95,降水极值的均方根误差与平均绝对误差分别普遍低于0.6 mm与2.5 mm,且所获得的模拟值置信区间性质优良;采用GEV得到相同重现期的设计暴雨更大,采用GPD得到的模拟值置信区间性质更优;GEV与GPD对于不同地区的适用性不同,在模拟区域降水极值时应综合运用多种分布。

Analysis of the uncertainty of extreme precipitations is essential to urban flood control.In this study,we select the records of daily precipitations in Beijing,Shenzhen and Jinan in the period of 1952 to 2012,and use them to simulate the annual maximum and peak-over-threshold precipitation sequences for each of these cities with the generalized extreme distribution(GEV)and generalized Pareto distribution(GPD).And the parameters are estimated using Markov chain Monte Carlo(MCMC)method.The simulation results show the MCMC method is well applicable to uncertainty analysis of extreme precipitation simulations.The best models it identified are featured with correlation coefficients and determination coefficients both generally as high as 0.95,root-mean-square errors and mean absolute errors of extreme precipitations generally lower than 0.6 mm and 2.5 mm,respectively,and well-behaved confidence intervals of the simulated values.The confidence intervals simulated using GPD perform better;the design rainstorms with the same recurrence interval calculated using GEV are stronger.Considering the difference of GEV and GPD in applicability to different cities,we recommend the method of combining different distributions be used in simulation of extreme precipitations.