Joint spatial modeling of significant wave height and wave period using the SPDE approach
share
The ocean wave distribution in a specific region of space and time is described by its sea state. Knowledge about the sea states a ship encounters on a journey can be used to assess various parameters of risk and wear associated with the journey. Two important characteristics of the sea state are the significant wave height and mean wave period. We propose a joint spatial model of these two quantities on the north Atlantic ocean. The model describes the distribution of the logarithm of the two quantities as a bivariate Gaussian random field. This random field is modeled as a solution to a system of coupled stochastic partial differential equations. The bivariate random field can model a wide variety of non-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 using a stepwise maximum likelihood method. The fitted model is used to derive the distribution of accumulated fatigue damage for a ship sailing a transatlantic route. Also, a method for estimating the risk of capsizing due to broaching-to, based on the joint distribution of the two sea state characteristics, is investigated. The risks are calculated for a transatlantic route between America and Europe using both data and the fitted model. The results show that the model compares well with observed data. Also, it shows that the bivariate model is needed and cannot simply be approximated by a model of significant wave height alone.
READ FULL TEXT