基于极值理论的北京市极端降水概率分布研究

Probability distribution of extreme precipitation in Beijing based on extreme value theory

以北京市作为研究区域,基于极值理论分析北京市降水极值的概率统计特征,探索不同极值分布在北京市降水极值研究中的适用性.选择北京市45个雨量站的1960~2012年汛期逐日降水数据,基于年最大值法和超门限阈值法(百分位法)筛选降水极值样本序列(AM和POT序列).利用广义极值分布(GEV)和广义Pareto分布(GPD)拟合两组样本序列,采用L矩法估计两种分布函数的拟合参数.基于Kolmogorov-Smirnov检验结果确定最优拟合分布函数,并根据最优拟合分布函数推求不同重现期水平下的降水量.结果表明:(1)除半壁店和沿河城外,AM序列的均值大于POT序列,所有站点AM序列的最小值小于POT序列;(2)GEV分布在AM序列的最优拟合分布函数中占优(40个站点,占全部站点的88.9%),而GEV和GPD分布均可用于POT序列降水极值的拟合,其中GPD分布的拟合结果较好(38个站点,占比为84.4%);(3)两种序列得到的不同重现期水平的降水量空间分布基本相似,总体上利用AM序列推求不同重现期水平下的降水量略大于POT序列,即基于AM序列推算一定重现期水平下的降水极值更有利于规避风险.

In this study, the statistical characteristics of the probability distribution in precipitation extremes in Beijing were explored and discussed based on the extreme value theory. The extreme precipitation series were filtered from the daily precipitation data （45 rain gauge stations） in the warm season during 1960-2012 based on the annual maximum （AM） and peak-over-threshold （POT） method. The generalized extreme distribution （GEV） and generalized Pareto distribution （GPD） were used to fit the two precipitation series and to investigate their statistic characteristics. The parameters of GEV and GPD distribution were estimated by the L-moment method. The best distribution was determined by the Kolmogorov-Smirnov test and then the best distribution was used to estimate the precipitation extremes in different return periods. The results showed that the mean values of AM series for all the rain gauges apart from Banbidian and Yanhecheng were larger than that of POT series, whereas the minimum values of AM series were lower than that of POT series. Furthermore, the optimal distribution of 40 sites for the AM series were GEV distribution, and the best distribution 38 sites for the POT series were GPD distribution, based on the results of the Kolmogorov-Smirnov test. Finally, the distributions of precipitation extremes in different return periods for this two series were similar, with the high value in the south and east and the low value in the north and west. Overall, the estimated precipitation amounts by the AM series were larger than that of POT series in the different return periods, which means the precipitation extremes based on the AM series will be relatively safer when it was used in the engineering design.