Deformed SPDE models with an application to spatial modeling of significant wave height
Journal article, 2020

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

Significant wave height

Rice's method

Non-stationary

SPDE-approach

Gaussian random field

Deformation

Author

Anders Hildeman

King Abdullah University of Science and Technology (KAUST)

University of Gothenburg

Chalmers, Space, Earth and Environment, Microwave and Optical Remote Sensing

Chalmers, Mathematical Sciences

David Bolin

King Abdullah University of Science and Technology (KAUST)

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Chalmers, Space, Earth and Environment, Microwave and Optical Remote Sensing

Igor Rychlik

University of Gothenburg

King Abdullah University of Science and Technology (KAUST)

Chalmers, Mathematical Sciences

Chalmers, Space, Earth and Environment, Microwave and Optical Remote Sensing

Spatial Statistics

2211-6753 (ISSN)

Vol. In press 100449

Subject Categories

Applied Mechanics

Computational Mathematics

Probability Theory and Statistics

DOI

10.1016/j.spasta.2020.100449

More information

Latest update

9/15/2020