基于Copula函数的北京市设计降雨研究

Study on design rainfalls in Beijing based on Copula functions

准确描述不同重现期下的设计降雨,能够为水利工程规划设计和防洪减灾提供重要的科学依据。本文以北京市2005—2018年20个站点逐小时的降水数据为基础,采用超定量法提取各分区不同场次强降雨的降雨历时和降雨量,构建了各个分区降雨历时和降雨量的二元分布,并计算了各个分区在不同重现期下的设计雨量。结果表明:北京市城区的强降雨事件明显多于山区,且降雨历时以服从广义极值(GEV)分布和对数正态分布为主,而降雨量则均服从GEV分布;在大多数分区通过Gumbel Copula函数可以更好地表征降雨历时和降雨量二者的联合分布,而在少部分分区运用Frank Copula函数来表征更佳;运用二元Copula函数可以较好地推求不同重现期下的设计雨量。

An accurate description of design rainfalls with different return periods is an important basis for planning and design of water conservancy structures,flood control,and disaster reduction.Based on the hourly rainfall data of 2005 to 2018 from 20 stations in Beijing,this study uses an over-threshold method to extract the depth and duration of heavy rainfalls over different regions,and estimates their joint distribution functions to calculate the design rainfalls of different return periods in each region.The results show that significantly more heavy rainfall events were observed in the downtown of this city than in the mountainous areas;the duration of most rainfalls follows the generalized extreme value(GEV)or Lognormal distributions,while the rainfall depths follow the GEV distribution.The joint distribution of the depth and duration of rainfalls is better characterized using a Gumbel Copula function for most of the regions in the study area,while a Frank Copula function is better in several other regions.The use of binary Copula functions can improve the estimation of design rainfalls of different return periods.