Spatially Varying Anisotropy for Gaussian Random Fields in Three-Dimensional Space

Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces. We construct a class of non-stationary anisotropic Gaussian random fields (GRFs) in three dimensions through stochastic partial differential equations allowing for Gaussian Markov random field approximations. The class is proven in a simulation study where we explore the amount of data required to estimate these models. Then, we apply it to an ocean mass outside Trondheim, Norway, based on simulations from a numerical ocean model. And our model outperforms a stationary anisotropic GRF on predictions using in-situ measurements collected with an autonomous underwater vehicle.