Estimating the probability of simultaneous rainfall extremes within a region: a spatial approach

In this paper we investigate the impact of model mis-specification, in terms of the dependence structure in the extremes of a spatial process, on the estimation of key quantities that are of interest to hydrologists and engineers. For example, it is often the case that severe flooding occurs as a result of the observation of rainfall extremes at several locations in a region simultaneously. Thus, practitioners might be interested in estimates of the joint exceedance probability of some high levels across these locations. It is likely that there will be spatial dependence present between the extremes, and this should be properly accounted for when estimating such probabilities. We compare the use of standard models from the geostatistics literature with max-stables models from extreme value theory. We find that, in some situations, using an incorrect spatial model for our extremes results in a significant under-estimation of these probabilities which -- in flood defence terms -- could lead to substantial under-protection.