Statistics of extremes with application to extreme floods in Kwazulu Natal Province, South Africa

Abstract

Extreme rainfall has become a prevailing natural disaster in the region of Southern Africa. Flooding is one of the natural disasters that pose damage to property, infrastructure, and human lives. This study conducted a comprehensive extreme value analysis of monthly maximum rainfall recorded at five selected meteorological stations in KwaZulu-Natal province, South Africa; namely Mandini, Mount Edgecombe, Richards Bay Airport, Port Edward, and Virginia, using data spanning from 1952 to 2022 as provided by the South African Weather Service (SAWS). The aimed to compare the performance of advanced extreme value theory (EVT) models, specifically the generalised extreme value distribution (GEVD), generalised extreme value distribution for r-largest order statistics (GEVDr) and the blended generalised extreme value distribution (bGEVD), in modelling extreme rainfall events. Stationarity assessments using the Augmented Dickey-Fuller (ADF), Kwiatkowski-Phillips- Schmidt-Shin (KPSS), and Phillips-Perron (PP) tests produced mixed results, while the Mann-Kendall (M-K) trend test indicated a monotonic decreasing trend in rainfall. Parameter estimation for the GEVD was performed using maximum likelihood estimation (MLE) and Bayesian Markov Chain Monte Carlo (MCMC) methods, both yielding positive shape parameters consistent with the Fr´echet class of distributions. Goodness-of-fit evaluations through Anderson-Darling (A-D) and Kolmogorov-Smirnov (K-S) tests, alongside diagnostic plots, confirmed the suitability of the GEVD model for the data. Additionally, the Shapiro-Wilk test demonstrated the non-normality of the rainfall datasets. Optimal block sizes for the r-largest order statistics model varied across stations, with r-values ranging from 2 to 4. Both the standard GEVD and r-largest GEVD models provided consistent return level estimates, suggesting strong model performance. The bGEVD model further revealed a negative time trend in rainfall maxima, resulting in lower return level estimates compared to the other models. Return levels were calculated for return periods ranging from 5 to 250 years, highlighting that extreme rainfall events become increasingly likely with longer return periods. 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.