Non-stationary Spatio-Temporal Modeling Using the Stochastic Advection-Diffusion Equation

TL;DR

This paper introduces a flexible non-separable spatio-temporal model based on stochastic PDEs with spatially varying diffusion and advection, improving prediction accuracy over separable models in simulations and real-world ocean data.

Contribution

It develops a novel non-separable SPDE-based model with Gaussian Markov random field approximation, enhancing spatio-temporal predictions in complex non-stationary environments.

Findings

Non-separable model outperforms separable model in simulations.

Non-separable model yields better real-time predictions for ocean data.

Model effectively emulates ocean model outputs and underwater vehicle observations.

Abstract

We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation of the solution of the SPDE, which is constructed through a finite volume method. The new flexible non-separable model is compared to a flexible separable model both for reconstruction and forecasting, and evaluated in terms of root mean square errors and continuous rank probability scores. A simulation study demonstrates that the non-separable model performs better when the data is simulated from a non-separable model with diffusion and advection. Further, we estimate surrogate models for emulating the output of a ocean model in Trondheimsfjorden, Norway, and simulate observations of autonomous underwater vehicles. The results show that the flexible non-separable model outperforms the flexible separable model for real-time prediction of unobserved locations.