Modeling Concurrent Hydroclimatic Extremes With Parametric Multivariate Extreme Value Models

Estimating the dependence structure of concurrent extremes is a fundamental issue for accurate assessment of their occurrence probabilities. Identifying the extremal dependence behavior is also crucial for scientific understanding of interactions between the variables of a multidimensional environmental process. This study investigates the suitability of parametric multivariate extreme value models to correctly represent and estimate the dependence structure of concurrent extremes. Probabilistic aspects of multivariate extreme value theory with point process representation are discussed and illustrated with application to the concurrence of rainfall deficits, soil moisture deficits, and high temperatures. Application is concerned with the investigation of extremal behavior and risk assessment in Marathwada, a drought-prone region of Maharashtra state, India. To characterize the multivariate extremes, marginal distributions are specified first and transformed into unit Frechet margins. Standardized distributions are represented by a Poisson point process and coordinates of data points are transformed to pseudo-polar coordinates to make the dependence form more explicit. The extremal dependence structure is described through angular densities on the unit simplex. Strong dependence is observed between soil moisture deficits and high temperatures, whereas rainfall deficits are mildly dependent on these two variables. Overall, a weak dependence is observed between the variables considered. Estimated extremal dependence is further used to compute probabilities of a few critical extreme combinations. Results demonstrate the ability of parametric multivariate models to characterize the complex dependence structure of concurrent extremes. These models can provide a powerful new perspective for appropriate statistical analysis of dependent hydroclimatic extremes in higher dimensions.