Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A spatiodirectional model for extreme waves in the Gulf of Mexico
AU - Jonathan, P.
AU - Ewans, K.
PY - 2010
Y1 - 2010
N2 - 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 HS 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 HS 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 17×17 grid locations. Applications to large areas consisting of more than 2500 grid locations are outlined. © 2011 American Society of Mechanical Engineers.
AB - 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 HS 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 HS 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 17×17 grid locations. Applications to large areas consisting of more than 2500 grid locations are outlined. © 2011 American Society of Mechanical Engineers.
KW - Covariates
KW - Design criterion
KW - Directional effects
KW - Extreme value
KW - Extreme waves
KW - Fitting algorithms
KW - Geographic areas
KW - Grid location
KW - Gulf of Mexico
KW - Hindcasts
KW - Independent parameters
KW - Non-parametric
KW - Nonhomogeneous poisson
KW - Oceanographic study
KW - Pareto model
KW - Peaks over threshold
KW - Penalized likelihood
KW - Poisson process
KW - Significant wave height
KW - Spatial dimension
KW - Storm direction
KW - Thin plate spline
KW - Thin-plate spline models
KW - Location
KW - Poisson distribution
KW - Splines
KW - Storms
KW - Parameter estimation
KW - covariance analysis
KW - experimental design
KW - extreme event
KW - geographical distribution
KW - hindcasting
KW - Poisson ratio
KW - roughness
KW - spatiotemporal analysis
KW - storm surge
KW - wave height
KW - Atlantic Ocean
KW - United States
U2 - 10.1115/1.4001949
DO - 10.1115/1.4001949
M3 - Journal article
VL - 133
JO - Journal of Offshore Mechanics and Arctic Engineering
JF - Journal of Offshore Mechanics and Arctic Engineering
SN - 0892-7219
IS - 1
M1 - 011601
ER -