Modeling average monthly rainfall for South Africa using extreme value theory

Abstract

The main purpose of modelling rare events such as heavy rainfall, heat waves, wind speed, interest rate and many other rare events is to try and mitigate the risk that might arise from these events. Heavy rainfall and floods are still troubling many countries. Almost every incident of heavy rainfall or floods might result in loss of lives, damages to infrastructure and roads, and also financial losses. In this dissertation, the interest was in modelling average monthly rainfall for South Africa using extreme value theory (EVT). EVT is made up mainly of two approaches: the block maxima and peaks-over thresh old (POT). This leads to the generalised extreme value and the generalised Pareto distributions, respectively. The unknown parameters of these distri butions were estimated using the method of maximum likelihood estimators in this dissertation. According to goodness-of-fit test, the distribution in the Weibull domain of attraction, Gumbel domain and generalised Pareto distri butions were appropriate distributions to model the average monthly rainfall for South Africa. When modelling using the POT approach, the point process model suggested that some areas within South Africa might experience high rainfall in the coming years, whereas the GPD model suggested otherwise. The block maxima approach using the GEVD and GEVD for r-largest order statistics also revealed similar findings to that of the GPD. The study recommend that for future research on average monthly rainfall for South Africa the findings might be improved if we can invite the Bayesian approach and multivariate extremes. Furthermore, on the POT approach, time-varying covariates and thresholds are also recommended.