基于Copula函数的黑河流域干旱频率分析

Frequency analysis of drought in Heihe river basin using Copula function

【目的】构建二、三维干旱特征变量重现期的联合分布模型,对实际的干旱变量重现期范围进行估计,为旱情预报提供参考。【方法】采用4种对称和5种非对称的Archimedean Copula函数,构建黑河流域上游莺落峡、梨园站和正义峡3个水文站干旱历时、干旱烈度和干旱烈度峰值的二、三维联合分布模型;通过拟合度评价,选取Frank和Clayton Copula函数,对黑河流域的联合重现期和同现重现期进行计算,分析黑河流域重现期的空间演变规律。【结果】单变量的重现期理论值介于二、三维变量联合重现期与同现重现期之间;当单变量重现期理论值为5年时,采用干旱历时与干旱烈度的二维联合分布模型,推求的莺落峡、梨园站以及正义峡3个水文站的实际单变量重现期分别为4～7,2～6及4～7年。【结论】Copula函数能够较好地用于构建黑河流域干旱特征变量的重现期分布模型。

[Objective] The joint distribution model based on two- and three-dimensional drought varia- bles was built to estimate intervals of return periods of actual drought variables, which benefits drought forecast. [Method] The joint distribution model of two- and three-dimensional drought variables, drought durations,drought severities and peak intensities, was structured based on 4 symmetric and 5 asymmetric Archimedean Copulas for Yingluoxia, Liyuan and Zhengyixia hydrological stations at upstream of Heihe river. Fitting degrees were evaluated to select Frank and Clayton Copulas and the joint return period and co-occurrence return period were calculated to ascertain the intervals of return period in Heihe river basin. [Result] The return period of single variable ranged between the joint return period and co-occurrence re- turn period by two- and three-dimensional variables. When the theoretical return period of single variable was 5 years,the return periods of Yingluoxia,Liyuan and Zhengyixia calculated by the two-dimension joint distribution model using drought duration and drought severity were 4--7,2--6 and 4--7 years, respective- ly. [Conclusion] This study showed that Copulas functions can describe the return period of multivariate joint distributions of drought variables in Heihe river basin.