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The ocean wave distribution in a specific region of space and time isdescribed by its sea state. Knowledge about the sea states a ship encounters ona journey can be used to assess various parameters of risk and wear associatedwith the journey.  Two important characteristics of the sea state are the significant waveheight and mean wave period. We propose a joint spatial model of these twoquantities on the north Atlantic ocean. The model describes the distribution ofthe logarithm of the two quantities as a bivariate Gaussian random field. Thisrandom field is modeled as a solution to a system of coupled stochastic partialdifferential equations. The bivariate random field can model a wide variety ofnon-stationary anisotropy and allows for arbitrary, and different,differentiability for the two marginal fields.  The parameters of the model are estimated on data of the north Atlantic usinga stepwise maximum likelihood method. The fitted model is used to derive thedistribution of accumulated fatigue damage for a ship sailing a transatlanticroute. Also, a method for estimating the risk of capsizing due to broaching-to,based on the joint distribution of the two sea state characteristics, isinvestigated. The risks are calculated for a transatlantic route betweenAmerica and Europe using both data and the fitted model.  The results show that the model compares well with observed data. Also, itshows that the bivariate model is needed and cannot simply be approximated by amodel of significant wave height alone.

Joint spatial modeling of significant wave height and wave period using the SPDE approach