Spatial modeling of significant wave height using stochastic partial differential equations
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The general condition of the ocean surface at a certain location in space and time is described by the sea state. Knowing the distribution of the sea state is, for example, important when estimating the wear and risks associated with a planned journey of a ship. One important characteristic of the sea state is the significant wave height. We propose a spatial model for the logarithm of significant wave height based on a continuously indexed Gaussian random field defined as a solution to a stochastic partial differential equation (SPDE). The SPDE is obtained by combining the SPDE representation of a stationary Gaussian Matérn field with the deformation approach by sampson and Guttorp (1992). The resulting model can capture both non-stationarity and anisotropy, has beneficial computational properties, and easily interpretable parameters. We also show that the introduction of non-stationarity through the deformation approach allow us to derive theoretical bounds for exceedance probabilities of the field. Such bounds are of importance when modelling extreme loads on ships. The parameters of the model are estimated on data of the north Atlantic taken from the ERA-Interim data set. The fitted model is used to compute wave height exceedance probabilities and the distribution of accumulated fatigue damage for ships traveling a popular shipping route. The computed distributions of fatigue damage and exceedence probability is shown to agree well with data.
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