文章摘要
宋松柏,王小军.基于Copula函数的水文随机变量和概率分布计算[J].水利学报,2018,49(6):687-693
基于Copula函数的水文随机变量和概率分布计算
Probability distribution calculation of the sum of hydrological random variables based on Copula function approach
投稿时间:2017-11-02  
DOI:10.13243/j.cnki.slxb.20171063
中文关键词: 相依性  随机变量和  概率分布  Copula函数  清江流域
英文关键词: dependent  sum of random variables  probability calculation  Copula function  Qingjiang water-shed
基金项目:国家自然科学基金项目(51479171,51579059,51179160);国家重点研发计划项目(2017YFC0403506)
作者单位E-mail
宋松柏 西北农林科技大学 水利与建筑工程学院, 旱区农业水土工程教育部重点实验室, 陕西 杨凌 712100  
王小军 南京水利科学研究院 水文水资源与水利工程科学国家重点实验室, 江苏 南京 210029 xjwang@nhri.cn 
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中文摘要:
      水文随机变量和分布计算是推求设计洪水地区组成、梯级水库下游设计洪水等的重要内容,对于水库下游水利水电工程规划设计与管理、城市防洪风险评估等至关重要。传统的水文随机变量和分布是根据二维变量函数分布推导而来,边际分布必须为同一类型分布,其应用受到限制。本文根据二维随机变量和概率分布定义,运用条件Copula函数和积分变换原理,严格地推导了二维相依随机变量和概率分布计算公式,以及Gamma分布、P-Ⅲ分布两类常用边际分布下变量和的分布概率计算公式,该计算公式仅为条件Copula函数的一维积分,避免了概率组合离散求和法数据转换的信息失真,克服了传统多变量分布要求边际分布为同一类型分布。以清江流域水布垭水库至隔河岩水库3h洪量组成为例,给出了水文随机变量和分布的计算方法。文中模型与计算方法以期为我国设计洪水地区组成和梯级水库下游设计洪水计算提供理论支撑。
英文摘要:
      The distribution probability calculation of the sum of hydrological random variables is a key content for the design flood in regional composition and the design flood in downstream area of cascade reservoirs.It is also important for planning,designing and management of water resources projects in downstream area of cascade reservoirs,and evaluating urban flood risk.But probability distribution of the sum of random is derived by two dimensional random function distribution,its marginal distributions must have the same type probability distribution,and the applications are limited in practical.In this study,based on the probability distribution definition of the sum of two dimensional random variables,a probability distribution calculation model of the sum of two dimensional dependent random variables was proposed by using of Copula function and mathematical transformation.This model was also extended to calculate probability distribution for the sum of two dimensional dependent random variables with Gamma and P-Ⅲ marginal distribution,respectively.The proposed model,which expressed as an integral of one dimensional conditional Copula,can overcome shortcomings of information distortion in data transformation process of probability combination discrete summation method,and the same type marginal distributions.Taking the 3h flood volumes of downstream area of the Qingjiang cascade reservoirs as an example,the proposed model calculation method and procedures were given.It also indicates that the model in this paper can provide some basic theories for the design flood region composition and design flood of downstream area of cascade reservoirs.
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