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.
翻译:对于海洋等三维空间的现象来说,共振结构可能是不合理的。在海洋中,反应的变异性会随深度而变化,而洋流则可能导致空间上的差异性异质。我们通过使用Gausian Markov随机场近似值进行计算时的随机偏差方程式(SPDEs),在三个维度上建造了一组非静止的异质高斯罗洲随机场(GRFs ) 。这个方法在模拟研究中得到了证明,在模拟研究中探讨了估计这些模型所需的数据数量。然后,根据复杂的数字海洋模型SINMOD的模拟,在挪威特隆海姆以外海洋质量上先建一个GRFs。这个GRF在使用与自主水下飞行器收集的静态反位测量方法进行对比后,我们的方法超越了用于实时预测未观测地点的静止异质GRF。