摘要：With the advent of wide-spread global and continental-scale spatiotemporal datasets, increased attention has been given to covariance functions on spheres over time. This paper provides results for stationary covariance functions of random fields defined over $d$-dimensional spheres cross time. Specifically, we provide a bridge between the characterization in Berg and Porcu (2017) for covariance functions on spheres cross time and Gneiting’s lemma (Gneiting, 2002) that deals with planar surfaces.
