Spatially varying anisotropy for Gaussian random fields in three-dimensional space
Journal article, Peer reviewed
Published version
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https://hdl.handle.net/11250/3111446Utgivelsesdato
2023Metadata
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- Institutt for matematiske fag [2354]
- Publikasjoner fra CRIStin - NTNU [37253]
Sammendrag
Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces. In the ocean, the variability of a response may vary with depth, and ocean currents may lead to spatially varying anisotropy. We construct a class of non-stationary anisotropic Gaussian random fields (GRFs) in three dimensions through stochastic partial differential equations (SPDEs), where computations are done efficiently using Gaussian Markov random field approximations. A key novelty is the parametrization of the spatially varying anisotropy through vector fields.
In a simulation study, we find that simple stationary models obtain reasonable parameter estimates with a moderate number of observations and a single realization, whereas the most complex non-stationary anisotropic model requires dense observations and multiple realizations. Further, we construct a stationary and a non-stationary GRF prior for salinity in an ocean mass outside Trondheim, Norway, based on simulations from the complex numerical ocean model SINMOD. These GRF priors are then evaluated using in-situ measurements collected with an autonomous underwater vehicle. We find that the new model outperforms the stationary anisotropic GRF prior for real-time prediction of unobserved locations both in terms of root mean square error and continuous rank probability score.