This research study was carried out to investigate the characteristics of drought based on the joint distribution of two dependent variables, the duration and severity, in the Eastern Cape Province, South Africa. The drought variables were computed from the Standardized Precipitation Index for 6- and 12-month accumulation period (hereafter SPI-6 and SPI-12) time series calculated from the monthly rainfall data spanning the last five decades. In this context, the characteristics of climatological drought duration and severity were based on multivariate copula analysis. Five copula functions (from the Archimedean and Elliptical families) were selected and fitted to the drought duration and severity series in order to assess the dependency measure of the two variables. In addition, Joe and Gaussian copula functions were considered and fitted to the drought duration and severity to assess the joint return periods for the dual and cooperative cases. The results indicate that the dependency measure of drought duration and severity are best described by Tawn copula families. The dependence structure results suggest that the study area exhibited low probability of drought duration and high probability of drought severity. Furthermore, the multivariate return period for the dual case is found to be always longer across all the selected univariate return periods. Based on multivariate analysis, the study area (particularly Buffalo City, OR Tambo and Alfred Zoo regions) is determined to have higher/lower risks in terms of the conjunctive/cooperative multivariate drought risk (copula) probability index. The results of the present study could contribute towards policy and decision making through e.g., formulation of the forward-looking contingent plans for sustainable management of water resources and the consequent applications in the preparedness for and adaptation to the drought risks in the water-linked sectors of the economy.

中文翻译：

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南非东开普省的干旱风险分析：Copula 镜头

本研究旨在根据持续时间和严重程度这两个因变量的联合分布调查南非东开普省的干旱特征。干旱变量是根据 6 个月和 12 个月累积期（以下简称 SPI-6 和 SPI-12）时间序列的标准化降水指数计算得出的，该时间序列是根据过去五年的月降雨数据计算得出的。在此背景下，气候干旱持续时间和严重程度的特征基于多变量 copula 分析。选择了五个 copula 函数（来自阿基米德和椭圆家族）并拟合干旱持续时间和严重程度系列，以评估两个变量的依赖性度量。此外，Joe 和 Gaussian copula 函数被考虑并拟合到干旱持续时间和严重程度，以评估双重和合作案例的联合回归期。结果表明，干旱持续时间和严重程度的相关性度量最好由 Tawn copula 家族描述。依存结构结果表明，研究区干旱持续时间概率较低，干旱严重程度概率较高。此外，发现双重情况的多元回归期在所有选定的单变量回归期中总是更长。根据多变量分析，研究区域（特别是布法罗市、OR Tambo 和 Alfred Zoo 区域）被确定为在联合/合作多变量干旱风险（copula）概率指数方面具有较高/较低的风险。