A Case for a Reassessment of the Risks of Extreme Hydrological Hazards in the Caribbean

There is an urgent need for the development and implementation of modern statistical methodology for long-term risk assessment of extreme hydrological hazards in the Caribbean. Notwithstanding the inevitable scarcity of data relating to extreme events, recent results and approaches call into question standard methods of estimation of the risks of environmental catastrophes that are currently adopted. Estimation of extreme hazards is often based on the Gumbel model and on crude methods for estimating predictive probabilities. In both cases the result is often a remarkable underestimation of the predicted probabilities for disasters of large magnitude. Simplifications do not stop here: assumptions of data homogeneity and temporal independence are usually made regardless of potential inconsistencies with genuine process behaviour and the fact that results may be sensitive to such mis-specifications. These issues are of particular relevance for the Caribbean, given its exposure to diverse meteorological climate conditions.In this article we present an examination of predictive methodologies for the assessment of long-term risks of hydrological hazards, with particular focus on applications to rainfall and flooding, motivated by three data sets from the Caribbean region. Consideration is given to classical and Bayesian methods of inference for annual maxima and daily peaks-over-threshold models. We also examine situations where data non-homogeneity is compromised by an unknown seasonal structure, and the situation in which the process under examination has a physical upper limit. We highlight the fact that standard Gumbel analyses routinely assign near-zero probability to subsequently observed disasters, and that for San Juan, Puerto Rico, standard 100-year predicted rainfall estimates may be routinely underestimated by a factor of two.