Simulating space-time random fields with nonseparable Gneiting-type covariance functions

TL;DR

This paper introduces two scalable algorithms for simulating space-time Gaussian random fields with nonseparable Gneiting-type covariance functions, useful for modeling complex spatiotemporal phenomena.

Contribution

The paper presents novel algorithms for simulating nonseparable space-time Gaussian fields using Gneiting-type covariance functions, with scalable computational complexity.

Findings

Algorithms are scalable and efficient for unevenly spaced data.

Simulations accurately reproduce specified covariance structures.

Validated through synthetic examples demonstrating effectiveness.

Abstract

Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial structure and a conditionally negative definite function associated with the temporal structure. In both cases, the simulated random field is constructed as a weighted sum of cosine waves, with a Gaussian spatial frequency vector and a uniform phase. The difference lies in the way to handle the temporal component. The first algorithm relies on a spectral decomposition in order to simulate a temporal frequency conditional upon the spatial one, while in the second algorithm the temporal frequency is replaced by an intrinsic random field whose variogram is proportional to the conditionally negative definite function associated with the temporal structure. Both algorithms are scalable as their computational cost is proportional to the number of space-time locations, which may be unevenly spaced in space and/or in time. They are illustrated and validated through synthetic examples.