水文双变量重现期分析及在干旱中应用  

Understanding of hydrological bivariate return periods and its application to drought analysis

作　　者：周平[1] 周玉良[1,2] 金菊良[1,2] 蒋尚明[3] 吴成国[1,2] ZHOU Ping;ZHOU Yuliang;JIN Juliang;JIANG Shangming;WU Chengguo(School of Civil Engineering,Hefei University of Technology, Hefei 230009,China;Institute of Water Resources and Environmental System Engineering,Hefei University of Technology, Hefei 230009,China;Water Resources Research Institute of Anhui Province and Huaihe River Commision,MWR,Bengbu 233000,China)

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009 [2]合肥工业大学水资源与环境系统工程研究所,安徽合肥230009 [3]安徽省·水利部淮河水利委员会水利科学研究院,安徽蚌埠233000

出　　处：《水科学进展》2019年第3期382-391,共10页Advances in Water Science

基　　金：国家重点研发计划资助项目(2017YFC1502405);国家自然科学基金资助项目(51579060)~~

摘　　要：单变量水文统计中一些广为接受的概念在多变量环境下尚缺乏深入分析,也易被误解,如N年内重现期大于等于T的多变量事件发生的次数与N/T的关系。实践中,多变量联合重现期与其边缘分布变量重现期的一些经验关系被发现并通过了案例验证分析,但缺乏解释和推导。基于GH Copula推导了双变量联合重现期与边缘分布变量重现期的关系以及双变量事件发生次数与其重现期、变量相关程度间的定量关系。以昆明56年的逐月SPI(Standardized Precipitation Index)和SRI(Standardized Runoff Index)识别了干旱事件,采用GH Copula构建了干旱历时和烈度的联合分布函数,验证了双变量联合重现期与边缘分布变量重现期的关系以及多变量事件发生次数与其重现期的定量关系。表明不宜以“and”第1重现期是否接近于比该干旱事件的旱情更重的干旱发生的平均时间间隔来说明干旱特征值重现期分析的合理性。变量的相关性不强时,需谨慎采用边缘分布变量重现期的较大值近似代替“and”事件的第1重现期。Some well-known notions in univariate statistical analysis becomes misleading in the multivariate context,and have not been correctly understood by many researchers. One example is the relationship between the expected number of events with return periods greater than or equal to T year over a N year period with the ratio N/T . Additionally,in some empirical studies,the relationship between the joint return period of a hydrological multivariate event and the corresponding return periods of its marginal distributions were found and applied. However,there lacks a detailed derivation and interpretation of this relationship. In this paper,based on the GH copula,the relationships between the bivariate return period of an event and return periods of its corresponding marginal distributions was derived theoretically,as well as the relationship between the number of occurrences of bivariate events and their primary return periods at different degrees of correlation between the two marginal variables. The theoretically derived relationships in this study were tested with drought events in Kunming identified on SPI and SRI series with 56 years of monthly precipitation and runoff data. The results suggest that the correctness of drought multivariate return period analysis could not be supported by the closeness of the primary return period of an event and the average inter-arrival time of drought events more severe than the studied event. Future researchers also need to avoid using the maximum marginal return period to approximate the primary return period of an ‘and’ event when the two marginal variables only have a weak correlation.

关 键 词：多变量联合重现期 第1重现期 第2重现期 COPULA函数 干旱 昆明 

分 类 号：TV121[水利工程—水文学及水资源]