杭州市极值暴雨的统计建模与频率计算研究
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摘要
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 boththeoretical 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.
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 boththeoretical 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.
引文
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[3]丁瑾佳,许有鹏,潘光波.杭嘉湖地区城市发展对降水影响的分析[J].地理科学,2010,30(6):886-891.DING Jinjia,XU Youpeng,PAN Guangbo.Effect of urbanization on regional precipitation in Hangzhou-Jiaxing-Huzhou area[J].Scientia Geographica Sinica,2010,30(6):886-891.(in Chinese)
[4]廖晓农,魏东,石增云,等.连续少雨背景下北京暴雨的若干特征[J].高原气象,2011,30(3):749-759.LIAO Xiaonong,WEI Dong,SHI Zengyun,et al.Some characteristics of torrential rain events during continuous drought period in Beijing[J].Plateau Meteorology,2011,30(3):749-759.(in Chinese)
[5]王建鹏,孙继松,王式功,等.盆地地形下西安城市热岛效应对周边降水的影响[J].干旱气象,2011,29(2):168-173,181.WANG Jianpeng,SUN Jisong,WANG Shigong,et al.Impact of basin terrain urban heat island effect on precipitation in surrounding region of Xi’an[J].Arid Meteorology,2011,29(2):168-173,181.(in Chinese)
[6]刘睿颖,张俊玉,方舟.超大城市极端天气灾害的统计分析—以广州市为例[J].统计与决策,2012(12):103-105.LIU Ruiying,ZHANG Junyu,FANG Zhou.Statistical analysis of extreme weather disaster in megacity:a case study in Guangzhou[J].Statistics&Decision,2012(12):103-105.(in Chinese)
[7]司波,余锦华,丁裕国.四川盆地短历时强降水极值分布的研究[J].气象科学,2012,32(4):403-410.SI Bo,YU Jinhua,DING Yuguo.Research on extreme value distribution of short-duration heavy precipitation in the Sichuan basin[J].Scientia Meteorologica Sinica,2012,32(4):403-410.(in Chinese)
[8]陈子燊,路剑飞,刘曾美.广东极端降水的三参数概率分布模式对比[J].中山大学学报(自然科学版),2012,51(1):102-106.CHEN Zishen,LU Jianfei,LIU Zengmei.Comparative analysis on three-parameter probability distribution models for extreme precipitation in Guangdong province[J].Editorial Department of Journal of Sun Yatsen University(Natural Science Edition),2012,51(1):102-106.(in Chinese)
[9]苏布达,姜彤,董文杰.长江流域极端强降水分布特征的统计拟合[J].气象科学,2008,28(6):625-629.SU Buda,JIANG Tong,DONG Wenjie.Probabilistic characteristics of precipitation extremes over the Yangtze river basin[J].Journal of the Meteorological Sciences,2008,28(6):625-629.(in Chinese)
[10]LU F,WANG H,YAN D H,et al.Application of profile likelihood function to the uncertainty analysis of hydrometeorological extreme inference[J].Science China Technological Sciences,2013,56(12):3151-3160.