The characteristics of extreme waves in hurricane dominated regions vary systematically with a number of covariates, including location and storm direction. Reliable estimation of design criteria requires incorporation of covariate effects within extreme value models. We present a spatiodirectional model for extreme waves in the Gulf of Mexico motivated by the nonhomogeneous Poisson model for peaks over threshold. The model is applied to storm peak significant wave height for arbitrary geographic areas from the proprietary Gulf of Mexico Oceanographic Study (GOMOS) hindcast for the US region of the Gulf of Mexico for the period of 1900–2005. At each location, directional variability is modeled using a nonparametric directional location and scale; data are standardized (or “whitened”) with respect to local directional location and scale to remove directional effects. For a suitable choice of threshold, the rate of occurrence of threshold exceedences of whitened storm peak with direction per location is modeled as a Poisson process. The size of threshold exceedences is modeled using a generalized Pareto form, the parameters of which vary smoothly in space, and are estimated within a roughness-penalized likelihood framework using natural thin plate spline forms in two spatial dimensions. By reparameterizing the generalized Pareto model in terms of asymptotically independent parameters, an efficient back-fitting algorithm to estimate the natural thin plate spline model is achieved. The algorithm is motivated in an appendix. Design criteria, estimated by simulation, are illustrated for a typical neighborhood of grid locations. Applications to large areas consisting of more than 2500 grid locations are outlined.
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February 2011
Safety And Reliability
A Spatiodirectional Model for Extreme Waves in the Gulf of Mexico
Kevin Ewans
e-mail: kevin.ewans@shell.com
Kevin Ewans
Shell International Exploration and Production
, P.O. Box 60, 2280 AB Rijswijk, The Netherlands
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Philip Jonathan
Kevin Ewans
Shell International Exploration and Production
, P.O. Box 60, 2280 AB Rijswijk, The Netherlandse-mail: kevin.ewans@shell.com
J. Offshore Mech. Arct. Eng. Feb 2011, 133(1): 011601 (9 pages)
Published Online: November 4, 2010
Article history
Received:
February 26, 2009
Revised:
June 11, 2010
Online:
November 4, 2010
Published:
November 4, 2010
Citation
Jonathan, P., and Ewans, K. (November 4, 2010). "A Spatiodirectional Model for Extreme Waves in the Gulf of Mexico." ASME. J. Offshore Mech. Arct. Eng. February 2011; 133(1): 011601. https://doi.org/10.1115/1.4001949
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