基于Copulas函数的多维干旱变量联合分布

doi:10.11849/zrzyxb.2013.02.012

自然资源学报 ›› 2013, Vol. 28 ›› Issue (2): 312-320.doi: 10.11849/zrzyxb.2013.02.012

基于Copulas函数的多维干旱变量联合分布

李计, 李毅, 宋松柏, 崔晨风

西北农林科技大学水利与建筑工程学院,陕西杨凌 712100

收稿日期:2011-07-07 修回日期:2012-06-11 出版日期:2013-02-20 发布日期:2013-01-30
通讯作者: 李毅(1974- ),女,陕西武功人,博士,副教授,主要从事农业水资源利用研究.
作者简介:李计(1986- ),男,陕西礼泉人,硕士,从事水资源利用与保护研究.
基金资助:
国家自然科学基金新疆联合基金(U1203182);陕西省国际科技合作重点项目(2012KW-24-01).

Multivariate Joint Distributions of Drought Variables Based on Copulas Function

LI Ji, LI Yi, SONG Song-bai, CUI Chen-feng

College of Water Resources and Architecture Engineering, Northwest Agriculture and Forestry University, Yangling 712100, China

Received:2011-07-07 Revised:2012-06-11 Online:2013-02-20 Published:2013-01-30

摘要/Abstract

摘要：

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.

关键词: 水文学及水资源, 联合分布, Copulas 函数, 重现期, 拟合优度

Abstract:

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.

Key words: hydrology and water resources, joint distribution, Copulas function, return period, goodness of fit

中图分类号:

P333.3

李计, 李毅, 宋松柏, 崔晨风. 基于Copulas函数的多维干旱变量联合分布[J]. 自然资源学报, 2013, 28(2): 312-320.

LI Ji, LI Yi, SONG Song-bai, CUI Chen-feng. Multivariate Joint Distributions of Drought Variables Based on Copulas Function[J]. JOURNAL OF NATURAL RESOURCES, 2013, 28(2): 312-320.

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基于Copulas函数的多维干旱变量联合分布

Multivariate Joint Distributions of Drought Variables Based on Copulas Function

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