Bayesian analysis of extreme rainfall in Dar es Salaam region using generalized pareto distribution model.

In order to minimize the risks of death tolls and destruction of properties, it is paramount to draw proper inferences about extreme rainfall. This study presents a statistical modelling of extreme rainfall over Dar es Salaam. The study is aimed at determining the best fitting model for the daily extreme rainfall data as well as quantifying extreme rainfall events with high accuracy utilizing small amount of available daily rainfall data for the period of 54 years (i.e. 1961-2014). The results of a visual inspection method of L-moments ratio diagram showed that the Generalized Pareto distribution (GPD) would be a most suitable for modelling the extreme rainfall over Dar es Salaam. Using a Peak Over Threshold (POT) technique, the excesses above the threshold were fitted to GPD model using L-moments(LMOM), Maximum Likelihood (MLE) and adaptive Markov chain Monte Carlo (MCMC). MLE is an efficient approach to provide reliable estimates of a model only when the sample size is large. To circumvent the problem of dealing with scarce data especially in extreme events analysis, L-moments which is able to model small data and adaptive MCMC were used. The comparison between the performance of the LMOM, MLE and adaptive MCMC methods using the root mean square error (RMSE) showed that adaptive MCMC performs better compared with classical approaches. Finally, based on the better approach the return levels for the next 10, 20, 50 and 100 years with their corresponding confidence of the variation.