杭州市极值暴雨的统计建模与频率计算研究

Study on statistical modeling and frequency calculation of extremum rainstorm in Hangzhou City

以杭州市1951—2012年的逐日降水资料为基础,通过极值统计理论中的广义极值分布和广义帕累托分布分别模拟城市暴雨的年最大值序列和超阈值序列,采用极大似然估计法估计模型参数,采用分位数图和Kolmogorov-Smirnov方法对拟合结果进行拟合优度检验,并借助轮廓似然函数估计方法估计模型关键参数及设计暴雨的置信区间。研究结果表明:虽然广义极值分布和广义帕累托分布的分布类型和样本序列存在一定差异,但两种分布关于杭州市暴雨极值的统计推断结果比较相近。在样本资料长度有限的条件下,应重视暴雨极值不确定性的分析研究。轮廓似然函数法可以反映重现期长短对设计暴雨置信区间的影响,有助于定量估计设计暴雨的置信区间。此方法和研究成果对于评估杭州市暴雨极值及其不确定性具有理论与实际意义,可为城市洪涝规划与工程设计提供技术支撑。

The daily rainfall data from 1951 to 2012 of Hangzhou City are used to simulate annual maximum series and above-threshold series of urban storms respectively by generalized extreme value distribution and generalized Pareto distribution of extreme value statistics theory, and model parameters are estimated by the method of maximum likelihood estimation. Goodness-of-fit of Fitting Result is tested by the method of quantile plot and Kolmogorov-Smirnov and profile likelihood function estimation method is used to estimate the key parameters and the confidence intervals of design storms. The results show that even though generalized extreme value distribution and generalized Pareto distribution have different distribution types and sample series, their statistical results of the extremum rainstorms of Hangzhou City are consistent with each other. Under the conditions of limited sample series, uncertainty analysis of extremum rainstorms should be considered. Profile likelihood function estimation method is used to analyze the influence of the length of recurrence on the confidence interval of design storms and it helps in the quantitative estimation of the confidence interval of design storms. The proposed methods and results have both theoretical and practical significance for the evaluations of extreme value and uncertainty of rainstorms of Hangzhou City, and give technical support for urban flood control plan and project design.