基于三维Copula函数的沙颍河流域水文干旱频率分析

为进一步研究水文干旱特征及其演变规律,选取沙颍河流域2个水文站1951—2008年逐月径流资料,采用游程理论提取水文干旱特征变量,选取4种对称Archimedean Copula函数和对应的非对称Archimedean Copula函数拟合干旱特征变量的联合分布并计算联合重现期和同现重现期。经拟合检验,Frank Copula对干旱特征变量二维联合分布的拟合效果最优,M3 Copula函数对三维干旱变量的联合分布拟合效果最优。干旱特征的单变量重现期值大于二、三维变量的联合重现期,小于二、三维变量的同现重现期。因此,Copula函数能够较好地拟合沙颍河流域水文干旱特征变量间的联合分布。

Analyzing the Drought Frequency in Shaying River Basin Using the Three-dimensional Copula Function

This paper analyzed the drought characteristics based on data measured in 1951-2008 from two hydrological stations in the Shaying River Basin.We took standardized runoff index as an indicator of the hydrological drought,calculating the hydrological drought characteristics including drought duration,drought severity,and peak of the drought severity,using the theory of run test.The joint distributions of the drought characteristic variables were analyzed using four types of symmetric and asymmetric Archimedean Copulas functions;the goodness of the fitting of the functions was evaluated using the Kolmogorov-Smimov test method.The results showed that the Frank Copula function gave the best fitting for two-dimensional joint distributions of two characteristic drought variables,while the M3 copula function worked better for fitting three-dimensional joint distributions of three characteristic drought variables.It was also found that the return period calculated from single variable was greater than that calculated from the two-and three-dimensional distribution for the joint return periods,but less than that from the two-and three-dimensional distributions for the co-occurrence return periods.Thus,the Copula functions are able to describe the multivariate joint distributions of hydrological drought variables in the Shaying River Basin.