P.A. Kagoda and J.G. Ndiritu (South Africa)
Parameter Uncertainty, Bayesian Inference; Generalized Pareto Distribution; Gibbs Sampler; Predictive Distribution.
Using daily rainfall data taken from fifteen gauge stations selected from across South Africa, a Bayesian and an L moments approach to extreme rainfall frequency estimation were compared. The Bayesian approach enables distribution parameter uncertainties to be taken into account unlike the L moments and other probability weighed moment approaches and the comparison therefore helped evaluate the effect of incorporating parameter uncertainty on extreme rainfall estimates. To implement the Bayesian approach, the Generalized Pareto Distribution (GPD) was used to model the exceedances of rainfall data over a threshold that had been chosen from a mean residual life plot of the rainfall data. The joint prior distribution which had been formulated for the shape and scale parameters of the Generalized Pareto Distribution (GPD) was sequentially modified by the rainfall data resulting in a posterior distribution from which a Markov chain was generated using the Gibbs Sampler. This output of the Gibbs sampler was then used to obtain estimates of rainfall magnitudes at various return periods. These estimates were compared to those obtained using the regional storm index method which uses the Generalized Extreme Value (GEV) distribution and L-moments for parameter estimation. Generally, the Bayesian estimates of rainfall magnitudes for all return periods were greater than the corresponding estimates of rainfall magnitudes obtained by the regional storm index methodology. However, the differences between corresponding estimates increased with the length of the return period and for the shorter return periods, the estimates by the two methods were reasonably similar. At the 100 and the 200 year return periods, the Bayesian estimates were greater by 63.2 % and 87.5 % respectively. These differences in extreme rainfall magnitudes are considered to be the result of incorporating parameter uncertainties in the Bayesian approach. Although flood mitigation design is often wrought with many uncertainties, the considerable impact of incorporating parameter uncertainties calls for a comprehensive review of extreme rainfall estimation methods in South Africa and elsewhere.
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