The characterization of droughts and their impacts is very dependent on the time scale that is involved. In order to obtain an overall drought assessment, the cumulative effects of water deficits over different times need to be examined together. For example, the recently developed joint deficit index (JDI) is based on multivariate probabilities of precipitation over various time scales from 1- to 12-months, and was constructed from empirical copulas. In this paper, we examine the Gaussian copula model for the JDI. We model the covariance across the temporal scales with a two-parameter function that is commonly used in the specific context of spatial statistics or geostatistics. The validity of the covariance models is demonstrated with long-term precipitation series. Bootstrap experiments indicate that the Gaussian copula model has advantages over the empirical copula method in the context of drought severity assessment: (i) it is able to quantify droughts outside the range of the empirical copula, (ii) provides adequate drought quantification, and (iii) provides a better understanding of the uncertainty in the estimation.

干旱及其影响的特征非常取决于所涉及的时间范围。为了获得全面的干旱评估，需要一起研究不同时期缺水的累积影响。例如，最近开发的联合赤字指数（JDI）是基于1到12个月不同时间尺度上降水的多变量概率，并且是根据经验copulas构造的。在本文中，我们研究了用于JDI的高斯copula模型。我们使用通常在空间统计或地统计学的特定上下文中使用的两参数函数对时间尺度上的协方差建模。长期降水序列证明了协方差模型的有效性。