Modelling Drought Risk Using Bivariate Spatial Extremes: Application to the Limpopo Lowveld Region of South Africa

Abstract

Weather and climate extremes such as heat waves, droughts and floods are projected to become more frequent and intense in several regions. There is compelling evidence indicating that changes in climate and its extremes over time influence the living conditions of society and the surrounding environment across the globe. This study applies max-stable models to capture the spatio–temporal extremes with dependence. The objective was to analyse the risk of drought caused by extremely high temperatures and deficient rainfall. Hopkin’s statistic was used to assess the clustering tendency before using the agglomerative method of hierarchical clustering to cluster the study area into n=3 temperature clusters and n=3 precipitation clusters. For the precipitation and temperature data, the values of Hopkin’s statistic were 0.7317 and 0.8446, respectively, which shows that both are significantly clusterable. Various max-stable process models were then fitted to each cluster of each variable, and the Schlather model with several covariance functions was found to be a good fit on both datasets compared to the Smith model with the Gaussian covariance function. The modelling approach presented in this paper could be useful to hydrologists, meteorologists and climatologists, including decision-makers in the agricultural sector, in enhancing their understanding of the behaviour of drought caused by extremely high temperatures and low rainfall. The modelling of these compound extremes could also assist in assessing the impact of climate change. It can be seen from this study that the size, including the topography of the location (cluster/region), provides important information about the strength of the extremal dependence.