This paper introduces a method to assess whether two data sets come from the same source. Current methods do not adequately consider spatial and temporal correlations and their annual cycles in a comprehensive test. This method addresses that gap, thereby providing a new and rigorous tool for evaluating the realism of climate simulations and measuring changes in variability over time.

This paper uses the tail pairwise dependence matrix (TPDM) proposed by Cooley and Thibaud (2019), which we extend to the description of common extremes in two variables. We develop an extreme pattern index (EPI), a pattern-based aggregation to describe spatially extended weather extremes. Our results show that the EPI is suitable for describing heat waves.  We extend the EPI to describe extremes in two variables and obtain an index to describe compound precipitation deficits and heat waves.

In hydrology, the probability distributions are used to determine the probability of occurrence of rainfall events. In this study, two different methods for modeling rainfall time characteristics have been applied: a direct method and an indirect method that make it possible to relax the assumptions of the renewal process. The analysis was extended to two additional time variables that may be of great interest for practical hydrological applications: wet chains and dry chains.