We developed a new framework for quantifying time-dependent, multidimensional risk in a nonstationary climate and applied this framework to quantify the influence of global warming on the joint probability of warm and dry conditions over the past several decades and in future climate forcing trajectories. Our framework (which is summarized below and described in detail in the Supplementary Materials) is based on the canonical vine (C-vine) copula, which we applied to varying severities of annual-scale temperature and precipitation anomalies to calculate the time-varying joint probability that warm and dry conditions occur simultaneously in pairs of regions. The result is a generalized, fully dynamic multidimensional risk framework that models the time-varying temporal and spatial dependence structure between multiple extremes.

While the application of bivariate copulas is now common, applications of four-dimensional copulas are rare (28). To the best of our knowledge, this is the first introduction of a dynamic four-dimensional vine copula (with a dynamic graphical structure) that evolves through time and quantifies the time-varying dependence structure for multiple climate variables in multiple locations. This methodology allows us to account for nonstationarity in the dependence structure between correlated heavy-tailed multiple extremes, including for thresholds that fall in the extreme tail of the historical distribution. In addition, the application of the Bayesian Markov Chain Monte Carlo (MCMC) allowed us to quantify the uncertainty in estimating time-varying statistical moments and subsequently the joint probability of compound extremes through time. Although in this initial study we analyzed the joint probability of varying severities of warm and dry conditions in multiple locations, our framework is generalizable to other climate variables and to other nonclimatic multidimensional risks.

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