  Isotropic covariance structures can be unreasonable for phenomena in
three-dimensional spaces such as the ocean. In the ocean, the variability of
the 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 using Gaussian
Markov random field approximations.
  The approach is proven in a simulation study where the amount of data
required to estimate these models is explored. Then, the method is applied to
construct a GRF prior on an ocean mass outside Trondheim, Norway, based on
simulations from the complex numerical ocean model SINMOD. This GRF prior is
compared to a stationary anisotropic GRF using in-situ measurements collected
with an autonomous underwater vehicle where our approach outperforms the
stationary anisotropic GRF for real-time prediction of unobserved locations.
