Modelling Extreme Rainfall in KwaZulu-Natal Province of South Africa Using Extreme Value Theory

This study reviews advanced extreme value theory techniques and applies them to extreme rainfall events recorded at two meteorological stations, Port Edward and Virginia, in the KwaZulu-Natal province of South Africa. The study aims to provide a comparative analysis of the performance of three extreme value theory models—the generalised extreme value distribution (GEVD), the generalised extreme value distribution for r-largest order statistics (GEVDr), and the blended generalised extreme value distribution (bGEVD)—in modelling extreme rainfall events. The monthly maximum rainfall data used in the study was obtained from the South African Weather Service. The Shapiro–Wilk test demonstrated the non-normality of the rainfall datasets. Parameter estimation was performed using maximum likelihood estimation and Bayesian estimation methods, both yielding positive shape parameters consistent with the Fréchet class of distributions. The goodness-of-fit tests confirmed the suitability of the GEVD model for the data. The results of both the standard GEVD and GEVDr models provided consistent return level estimates, suggesting strong model performance. The bGEVD model produced lower return level estimates compared to the GEVD and GEVDr models. Overall, the findings of the study offer valuable insights into the behaviour of extreme rainfall in KwaZulu-Natal province, with significant implications for risk management, infrastructure planning, and disaster preparedness. This study will add value to the literature and knowledge of statistics.