Modelling extreme rainfall with Block Maxima and Peak-Over Threshold methods in Rwanda

Abstract In this study two fundamental approaches of extreme value theory (EVT) were applied on the extreme precipitation incidents over twelve synoptic stations of Rwanda: the Block Maxima (BM) and the Peak-Over Threshold (POT). Annual maximum rainfall series (AMS) and partial duration rainfall series (PDS) higher than a selected threshold were fitted respectively to the Generalized Extreme Value (GEV) distribution and the Generalized Pareto (GP) distribution at each station. Four methods were used for the estimation of the parameters of the GEV and the GP distributions: the Maximum Likelihood Estimation (MLE) method, the L-Moments Estimation (LME) method, the Bayesian Estimation (BAYE) method and the Generalized Maximum Likelihood Estimation (GMLE) method. The performances of those methods were analyzed and compared for best fitting the data based on goodness-of-fit tests. It was found that in general, those methods are suitable for the two distributions at the sites considered in Rwanda with slight differences in estimated return levels and their confidence intervals. However, the MLE and LME methods perform better than the other methods for the GEV distributions whereas for the GP distribution it is the BAYE method. Return levels of extreme rainfalls with their 95% confidence intervals were computed for return periods of 10, 20, 50, 75, 100, 150 and 200 years. It was found that using the selected parameterization methods, the GP distribution presents higher return levels than GEV distribution for all stations Those methods can therefore be recommended as best parametric methods for estimating extreme rainfall in Rwanda using EVT.