Basin-wide spatial conditional extremes for severe ocean storms
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Basin-wide spatial conditional extremes for severe ocean storms Rob Shooter1,2
· Jonathan Tawn3 · Emma Ross4 · Philip Jonathan3,5
Received: 14 June 2019 / Revised: 18 May 2020 / Accepted: 30 July 2020 / © The Author(s) 2020
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.
R. Shooter would like to acknowledge financial support from Engineering and Physical Sciences Research Council grant EP/L015692/1 (STOR-i Centre for Doctoral Training) and Shell Research Ltd. Rob Shooter
[email protected] 1
Met Office Hadley Centre, FitzRoy Road, Exeter, EX1 3PB, UK
2
STOR-i Centre for Doctoral Training, Department of Mathematics and Statistics, Lancaster University, Lancashire LA1 4YR, UK
3
Department of Mathematics and Statistics, Lancaster University, Lancashire LA1 4YW, UK
4
Shell Global Solutions International BV, Amsterdam, The Netherlands
5
Shell Research Ltd., London SE1 7NA, UK
R. Shooter et al.
Keywords Spatial conditional extremes · Extremal dependence · Covariate effects · Ocean storms Mathematics Subject Classification 2010 60G70 (primary) · 62F15 · 62G20 · 62G32 · 62H11 · 62M30 · 62P12 · 62P30 · 62P35.
1 Introduction A key issue in modelling spatial extremes is assessing the nature of dependence between extreme events. If we observe an extreme event at a location, we are interested in the information provided by this event about the probability of observing extreme events simultaneously at other locations. We expect that over short distances, an extreme event being observed at one location may be related to an extreme observation at another. However extremes observed at distant locations are likely to be less related to each other. To describe extremal dependence, Coles et al. (1999) introduce the measures χ and χ, most easily calcul
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