Researchers at the University of Gothenburg have developed a novel approach to modeling significant wave height, a critical factor in naval logistics and route planning. Anders Hildeman, David Bolin, and Igor Rychlik have combined the stochastic partial differential equation (SPDE) approach with the classical deformation method to create a non-stationary Gaussian random field model. This innovation allows for more accurate spatial modeling of ocean wave heights, which can significantly impact shipping routes and vessel maintenance.
The researchers’ model leverages the deformation method to transform a stationary field into a non-stationary one by adjusting the domain. By defining the stationary field as a Matérn field—a type of random field characterized by its smoothness and correlation structure—they demonstrate that the resulting non-stationary model can be represented as the solution to a fractional SPDE on the deformed domain. This approach merges the computational efficiency of the SPDE method with the intuitive parameterization of non-stationarity offered by the deformation method.
A key advantage of this model is its ability to independently control the non-stationary practical correlation range and the variance. Previous non-stationary SPDE models lacked this capability, limiting their flexibility and accuracy. The researchers tested their model using spatial data of significant wave height in the North Atlantic, employing a maximum likelihood approach to estimate the model parameters. The fitted model was then used to compute wave height exceedance probabilities and the distribution of accumulated fatigue damage for ships traveling a popular shipping route.
The results of this study show a strong agreement between the model predictions and actual data, suggesting that the model could be a valuable tool for route optimization in naval logistics. By providing more accurate predictions of wave heights and their impacts on vessel fatigue, this model can help shipping companies plan safer and more efficient routes, ultimately reducing operational costs and enhancing maritime safety. This research highlights the potential of advanced statistical methods in improving maritime operations and underscores the importance of continued innovation in the field of spatial modeling. Read the original research paper here.