On spatial conditional extremes for ocean storm severity

We describe a model for the conditional dependence of a spatial process measured at one or more remote locations given extreme values of the process at a conditioning location, motivated by the conditional extremes methodology of Heffernan and Tawn. Compared to alternative descriptions in terms of max-stable spatial processes, the model is advantageous because it is conceptually straightforward and admits different forms of extremal dependence (including asymptotic dependence and asymptotic independence). We use the model within a Bayesian framework to estimate the extremal dependence of ocean storm severity (quantified using significant wave height, H ) for locations on spatial transects with approximate east-west (E-W) and north-south (N-S) orientations in the northern North Sea (NNS) and central North Sea (CNS). For H on the standard Laplace marginal scale, the conditional extremes "linear slope" parameter α decays approximately exponentially with distance for all transects. Furthermore, the decay of mean dependence with distance is found to be faster in CNS than NNS. The persistence of mean dependence is greatest for the E-W transect in NNS, potentially because this transect is approximately aligned with the direction of propagation of the most severe storms in the region.