基于Copula函数的柘林水库设计洪水频率分析

Design Flood Frequency Analysis of Zhelin Reservoir Based on Copula Functions

针对传统设计洪水频率分析采用单变量方法且不考虑变量间相关关系的问题,以江西省柘林水库坝址洪水为研究对象,采用Frank Copula函数构建洪峰与5d洪量的二元联合分布,并引入联合重现期的概念。结果表明,柘林水库坝址洪水主要受洪峰和洪量控制,峰量间存在良好的相关性;两变量方法推求的峰量联合设计值均大于单变量方法,各特征量的重现期均高于设计标准。可见Copula函数拟合度较高,计算所得频率设计值更符合洪水事件的内在规律以及工程实际要求,且同时可得不同情况下的峰量设计值组合,在水文领域具有广阔的应用前景。

Univariate frequency analysis method is commonly used in traditional design flood frequency analysis. This paper takes dam-site flood of Zhelin reservoir in Jiangxi province as research object. According to the deficiency of ignoring the relationship between variables, a new method deriving flood frequency design values is proposed. The fundamental theory and key technologies in application of Copulas are introduced. In the method, Frank Copula is adopted to construct the bivariate joint distribution of flood peak and volume and the concept of bivariate return period is defined. The result shows that the dam-site flood of Zhelin reservoir is commonly controlled by flood peak and volume and the two values are greatly related; the fitting degree of Frank Copula in the study area is high by inspection; the frequency design values based on the new method are larger than the ones based on traditional method; so are the return periods; taking bivariate return period into consideration, the new method is more feasible and accords with the inherent rules of hydrological events as well as the practical engineering; combination of design values in different cases can be obtained. As an effective tool constructing multivariate joint distribution, it has wide application prospect in hydrology.