Statistical Modeling of Spatial Extremes through Max-Stable Process Models: Application to Extreme Rainfall Events in South Africa

Abstract

A quantification of the spatial dependence among extremes of rainfall events is important for investigating the properties of intense, extreme weather-related hazards. Extreme value theory has been widely applied to weather variables, and rigorous approaches have also been employed to investigate dependence structures among extreme values in space. To investigate the joint dependence of extreme rainfall events in space, spatial dependence modeling through max-stable process models has been considered to analyze extreme rainfall data across selected weather stations in South Africa. The analysis was also used to illustrate how the geographic and temporal covariates can affect the extreme rainfall field and subsequently the distribution of spatial random variables. The results revealed significant trends in the time-heterogeneous spatially fitted generalised extreme value (GEV) distribution. In addition, the max-stable process model predicted the probability of annual maximum rainfall and spatial contrasts of extreme rainfall characteristics across selected weather stations in South Africa. The results indicated that the annual extreme rainfall across selected weather stations in South Africa exhibits noticeable spatial variability. This study also depicted the significance of spatial max-stable process models over the univariate modeling and how models of spatial extremes with dependence can be used to better understand the probability of extreme rainfall events and to account for the influence of temporal covariates. Results obtained in this study have essential scientific and practical applications in monitoring hydrological-related risks for mitigation and adaptation strategies.