基于Copula函数的两变量洪水重现期与设计值计算研究

Calculation of return periods and design values of bivariate floods based on Copula function

传统的洪水频率分析未考虑洪水特征变量之间的相依性,存在一定局限性。本文应用Kendall重现期原理,研究两变量洪水重现期与设计值计算。以陕北地区无定河流域赵石窑和绥德站的洪水资料为例,采用二元Frank Copula函数构建洪峰流量与洪量联合分布模型,运用最可能超越法与极大似然法分别推求联合重现期、Kendall重现期及同现重现期三类重现期标准下的洪水设计值组合。结果表明两种方法均可推求洪水设计值,且结果无较大差异;在给定重现期条件下,以联合重现期作为计算标准推求的洪水设计值最大,Kendall重现期次之,同现重现期最小。从重现期定义的角度考虑,联合重现期与同现重现期根据各变量值定义的危险区域,存在一定不合理性,但仍可满足特定的应用需要;Kendall重现期根据联合概率值定义危险区域,避免了对危险区域或大或小地估算。一般情况下,推荐采用Kendall重现期作为两变量重现期计算标准。

The traditional method of flood frequency analysis based on tmivariate distribution is unable to consider the dependence structure between flood characteristics. This paper focuses on the calculation of return periods and design values of bivariate floods using the theory of Kendall return period. We have applied this calculation method to flood analysis for the Zhaoshiyao and Suide stations of the Wudinghe basin in North Shaanxi, using a bivariate Frank Copula to describe the joint distribution of flood peak and flood volume. To find the most appropriate values of design floods, a component-wise excess method and maximum likelihood method are adopted on three definitions of the return period： joint return period, co-occurrence return period, and Kendall return period. The results indicate that the design values calculated using both methods have no considerable difference, and that the design values on these definitions are the largest, intermediate and the smallest respectively. An examination on the three definitions shows that the former two distinguish dangerous regions by variable values. Both have a certain fault, but they can be applied satisfactorily in some specific cases. The latter makes the distinguishment by joint probability, thus avoiding overestimation or underestimation of the dangerous regions. Therefore, Kendall return period is recommended in general cases.