考虑历史洪水不确定性的多维联合洪水频率分析  

Multi-dimensional Joint Flood Frequency Analysis Considering the Uncertainty of Historical Flood Events

作　　者：尚晓三[1,2] 王栋 SHANG Xiaosan;WANG Dong(Department of Hydrosciences,School of Earth Sciences and Engineering,Nanjing University,Nanjing 210093,China;Anhui Survey and Design Institute of Water Conservancy&Hydropower Company Limited,Hefei 230088,China)

机构地区：[1]南京大学地球科学与工程学院水科学系,江苏南京210093 [2]安徽省水利水电勘测设计研究总院有限公司,安徽合肥230088

出　　处：《地球科学进展》2022年第4期407-416,共10页Advances in Earth Science

基　　金：第二次青藏高原综合科学考察研究项目“青藏高原河流尼克带水系纵剖面变化分析”(编号:2019QZKK0203-03)资助.

摘　　要：洪水过程由多个特征变量组成,各变量之间存在正相关性,应进行多变量联合分析。但随着变量的增多,在相同样本条件下,多维联合分布具有更大的抽样不确定性。将历史洪水纳入多维联合频率分析,以提升各特征变量边缘分布和Copula函数相关性参数的准确性。以分层Archimedean Copulas函数为基础,构建了考虑历史洪水不确定性的多维联合洪水频率分析层次模型,将多维联合分布分解成为若干个二维Copula函数的多级层叠形式,并结合极大似然法,选用遗传算法求解特征变量边缘分布及各层Copula函数的相关性参数。长江流域宜昌站的应用结果表明,考虑历史洪水不确定性的多维联合洪水频率分析层次模型能够完整地描述整个洪水过程,考虑洪水过程特征变量之间的相关性,也能够有效利用历史洪水,改善样本的代表性,Copula函数的相关性参数符合实测序列峰量之间的相关关系。The entire flood process consists of multiple characteristic variables,including the flood peak and flood volume,for different durations.There is a positive correlation between these variables,and multivariate joint analysis should be performed for flood frequency analysis.However,the multi-dimensional joint distribution has greater sampling uncertainty with increasing variables using limited measurable samples.This could improve the accuracy of the marginal distribution of each characteristic variable and the correlation parameters of the Copula function using historical flood information that predated the period of systematic gauging for extending observation records in the multi-dimensional joint frequency analysis.Based on the hierarchical Archimedean Copulas function,a multi-dimensional joint flood frequency analysis hierarchical model,considering the uncertainty of historical flood events,was constructed and decomposed into several cascaded multi-level forms of two-dimensional Copula functions.Combined with the maximum likelihood method,the parameters of the nested multi-level Copula function and the marginal distribution of the characteristic variables are effectively estimated using a genetic algorithm.The Yichang hydrological station,located in the main stream of the Yangtze River,was selected as a case study,including systematic gauge records and historical flood data.The results show that it can completely describe the entire flood process and consider the correlation between the characteristic variables of the flood process with the multi-dimensional joint flood frequency analysis hierarchical model.This could improve the representativeness of the values of the marginal distribution parameters.Meanwhile,it could effectively use historical floods and improve the representativeness of the samples,and the correlation parameters of the Copula function were more consistent with the correlation between the measured data.

关 键 词：历史洪水 不确定性 多维分层Copula函数 洪水频率分析 

分 类 号：P331.2[天文地球—水文科学]