基于Copulas函数的多维干旱变量联合分布

通过构建多变量联合分布进行干旱分析,可揭示干旱的演变规律.根据新疆乌鲁木齐和石河子气象站的长系列月降水资料,提取干旱历时、干旱烈度和烈度峰值3个干旱特征变量,基于4种对称的Archimedean Copulas函数分别构建二维、三维干旱变量的联合分布;基于5种非对称的Archimedean Copulas函数构建三维干旱变量的联合分布,以进一步推求各自的重现期.经拟合优度检验,Frank Copula 函数对干旱历时和干旱烈度、干旱历时和烈度峰值的二维联合分布的拟合度最好;Clayton Copula 函数对于干旱烈度和烈度峰值的二维联合分布以及干旱历时、干旱烈度和烈度峰值的三维联合分布拟合效果最佳.单变量的重现期介于二维、三维变量联合重现期与同现重现期之间.表明Copulas函数能描述多维干旱特征变量的联合分布.

Multivariate Joint Distributions of Drought Variables Based on Copulas Function

Drought analysis through multivariate joint distributions can determine the evolution rules of drought. Three drought variables, i.e., drought duration, drought severity and drought peak, were selected from long sequence of monthly rainfall data for Urumqi and Shihezi weather stations in Xinjiang, China. Two-dimension and three-dimension joint distributions of drought variables were analyzed based on four kinds of symmetric Archimedean Copulas functions. And three-dimension joint distributions of drought variables were analyzed using five kinds of asymmetric Archimedean Copulas functions. Furthermore their return periods were determined. Test of goodness of fit showed that, Frank Copula function was the best when it was applied to two-dimension joint distribution for drought duration-drought severity, and drought duration-drought peak.Clayton Copula function was the best when it was applied to two-dimension joint distributions of drought severity-drought peak and three-dimension joint distribution of the three drought variables. The return period of single variable ranged between return periods of the two-dimension, three-dimension and co-occurrence. This study showed that Copulas function can describe multivariate joint distributions of drought variables well.