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 -