Gaussian random fields on the product of spheres: Theory and applications

We consider Gaussian random fields on the product of spheres. We study the regularity and the Hölder continuity of such random fields via their covariance function. Moreover, we approximate the Gaussian random fields using truncations of the Karhunen-Loéve expansion and conduct simulation experiments to illustrate our approximation results. Using hourly wind speed and global space-time cloud cover datasets, we discuss mod-elling data in a Bayesian framework using Gaussian random fields over the product of spheres with covariance approximations through truncated series expansions.