Abstract
Physical considerations and previous studies suggest that extremal dependence between ocean storm severity at two locations exhibits near asymptotic dependence at short inter-location distances, leading to asymptotic independence and perfect independence with increasing distance. We present a spatial conditional extremes (SCE) model for storm severity, characterising extremal spatial dependence of severe storms by distance and direction. The model is an extension of Shooter et al. 2019 (Environmetrics 30, e2562, 2019) and Wadsworth and Tawn (2019), incorporating piecewise linear representations for SCE model parameters with distance and direction; model variants including parametric representations of some SCE model parameters are also considered. The SCE residual process is assumed to follow the delta-Laplace form marginally, with distance-dependent parameter. Residual dependence of remote locations given conditioning location is characterised by a conditional Gaussian covariance dependent on the distances between remote locations, and distances of remote locations to the conditioning location. We apply the model using Bayesian inference to estimates extremal spatial dependence of storm peak significant wave height on a neighbourhood of 150 locations covering over 200,000 km2 in the North Sea.
Highlights
A key issue in modelling spatial extremes is assessing the nature of dependence between extreme events
In practice we find that allowing directional variation of spatial conditional extremes (SCE) residual parameters μ, σ and δ cannot be justified given data examined to date
For the sample of storm peak significant wave height data transformed to standard Laplace margins, the SCE model was estimated as follows
Summary
A key issue in modelling spatial extremes is assessing the nature of dependence between extreme events. Careful parameterisation of distance and directional effects enables the spatial extremes problem to be described parsimoniously, even when the number of measurement locations is large This reduces computational burden when fitting across hundreds of sampling locations compared to broadly equivalent max-stable proceses, Pareto processes are less computationally expensive than max-stable processes. Shooter et al (2019) found that assuming a simple two-parameter for the decay of SCE slope parameter, α with distance was adequate to capture parameter behaviour adequately whilst reducing computational time for parameter estimation, since α would otherwise need to be estimated separately for pair of conditioning and remote locations. An outline of the Markov chain Monte Carlo (MCMC) scheme used for inference, and the conditional quantile constraints of Keef et al (2013), is given in the Appendix
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
