A fully probabilistic approach to extreme rainfall modeling

Abstract It is an embarrassingly frequent experience that statistical practice fails to foresee historical disasters. It is all too easy to blame global trends or some sort of external intervention, but in this article we argue that statistical methods that do not take comprehensive account of the uncertainties involved in both model and predictions, are bound to produce an over-optimistic appraisal of future extremes that is often contradicted by observed hydrological events. Based on the annual and daily rainfall data on the central coast of Venezuela, different modeling strategies and inference approaches show that the 1999 rainfall which caused the worst environmentally related tragedy in Venezuelan history was extreme, but not implausible given the historical evidence. We follow in turn a classical likelihood and Bayesian approach, arguing that the latter is the most natural approach for taking into account all uncertainties. In each case we emphasize the importance of making inference on predicted levels of the process rather than model parameters. Our most detailed model comprises of seasons with unknown starting points and durations for the extremes of daily rainfall whose behavior is described using a standard threshold model. Based on a Bayesian analysis of this model, so that both prediction uncertainty and process heterogeneity are properly modeled, we find that the 1999 event has a sizeable probability which implies that such an occurrence within a reasonably short time horizon could have been anticipated. Finally, since accumulation of extreme rainfall over several days is an additional difficulty—and indeed, the catastrophe of 1999 was exaggerated by heavy rainfall on successive days—we examine the effect of timescale on our broad conclusions, finding results to be broadly similar across different choices.