Deformed SPDE models with an application to spatial modeling of significant wave height

A non-stationary Gaussian random field model is developed based on a combination of the stochastic partial differential equation (SPDE) approach and classical deformation method. With method, stationary defined domain which deformed so that becomes non-stationary. We show if Matérn as solution to fractional SPDE, resulting can be represented another SPDE domain. By defining in this way, computational advantages combined with method’s more intuitive parameterization non-stationarity. In particular it allows for independent control over practical correlation range variance, has not been possible previously proposed models. The tested spatial data significant wave height, characteristic ocean surface conditions important when estimating wear risks associated planned journey ship. parameters are estimated from north Atlantic using maximum likelihood approach. fitted used compute height exceedance probabilities distribution accumulated fatigue damage ships traveling popular shipping route. results agree well data, indicating could route optimization naval logistics.