Bayesian Modelling of Extreme Rainfall Data: Construction of Priors Using WRF Model Outputs, A Case of Dar es Salaam Tanzania

A 54 years dataset (1961 -2014) of recordings of the maximum daily (24 h) rainfall in the Dar Es Salaam area, Tanzania is analyzed using Extreme Value Theory with Bayesian framework. Prior distributions are constructed using quantiles approach. Experts in the field are normally used to elicit distribution of quantiles. With scarcity of data, these experts may not exist. In this paper a different approach in eliciting prior distribution is proposed. In this proposal the quantiles for prior construction are obtained from the Weather Research Forecasting (WRF) model. For the case of Dar es Salaam, WRF outputs are generated based on the physical conditions around 20th December 2011, a day when Dar es Salaam experienced the extreme rainfall which has never been experienced for more than 50 years. A combination of these two data sets, through Bayesian framework, has improved the reliability of forecasting of extreme events. The point estimates for both Maximum Likelihood and Bayesian estimation methods are almost the same, but the associated 95 % confidence intervals for Bayesian method are narrower highlighting the reliability of the estimator. It is demonstrated in this paper that WRF outputs can be used to construct prior distributions, and hence improve reliability of extreme rainfall forecasting.