年最大洪水两变量联合分布研究

Annual maximum flood occurrence dates and magnitudes frequency analysis based on bivariate joint distribution

采用Von Mises分布拟合年最大洪水发生时间的概率分布,采用皮尔逊III型分布拟合年最大洪水量级的概率分布,选用能够较好反映年最大洪水发生时间和量级之间相关结构的Gumbel Archimedean Copula函数,建立两变量联合分布,并定义和分析条件频率、联合频率和两变量重现期。实例分析表明年最大洪水的两变量分布拟合较好,可挖掘更多信息,为洪水设计分析提供了一条新的途径。

Annual maximum flood occurrence dates and magnitudes both can provide important information for the hydraulic engineering design and the reservoir operation. The existing literatures only consider the distribution of flood magnitudes, but ignors the flood occurrence dates. In this paper, Von Mises distribution and Pearson Type III distribution are used to describe the occurrence dates and magnitudes of annual maximum flood respectively. A bivariate joint distribution with Von Mises distribution and Pearson Type Ⅲ distribution margins is developed based on the Gumbel Archimedean Copula and used to describe the annual maximum flood series. The approaches for calculating conditional probability, joint probability and bivariate return period are presented. Case study shows that the bivariate joint distribution can fit both occurrence dates and magnitudes of annual maximum flood series well. It can mine more flood information and provide a new way for flood frequency analysis.