Abstract
A Bayesian hierarchical framework is used to model extreme sea states, incorporating a latent spatial process to more effectively capture the spatial variation of the extremes. The model is applied to a 34-year hindcast of significant wave height off the west coast of Ireland. The generalised Pareto distribution is fitted to declustered peaks over a threshold given by the 99.8th percentile of the data. Return levels of significant wave height are computed and compared against those from a model based on the commonly-used maximum likelihood inference method. The Bayesian spatial model produces smoother maps of return levels. Furthermore, this approach greatly reduces the uncertainty in the estimates, thus providing information on extremes which is more useful for practical applications.
Highlights
A detailed knowledge of the extreme sea states affecting a region is essential for any marine activity
We have applied a Bayesian hierarchical model (BHM) to a hindcast dataset in order to study the extremes of significant wave height off the west coast of Ireland
Exceedances of Hs over a high threshold are modelled with the generalised Pareto distribution
Summary
A detailed knowledge of the extreme sea states affecting a region is essential for any marine activity. Extreme value theory provides statistical tools for such an analysis (Coles, 2001) and the methods have been widely applied in 10 studies of ocean waves; reviews may be found in Vanem (2011) and Jonathan and Ewans (2013). Bayesian inference allows for a more detailed analysis of this uncertainty, by providing complete probability distributions for the parameters given the data (Gelman et al, 2013). We follow the approach of Cooley et al (2007), who include a latent spatial process within a Bayesian hierarchical framework to capture the spatial dependence of precipitation extremes.
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