Spectral Simulation of Gaussian Vector Random Fields on the Sphere

Abstract

Isotropic Gaussian random fields on the sphere are used in astronomy, geophysics, oceanography, climatology and remote sensing applications. However, to date, there is a lack of simulation algorithms that reproduce the spatial covariance structure without any approximation and, at the same time, are parsimonious in terms of computation time and memory storage requirements. This work presents two such algorithms that rely on the spectral representation of isotropic covariances on the sphere. Both algorithms are illustrated with synthetic examples.