Time varying axially symmetric vector random fields on the sphere

TL;DR

This paper develops simplified covariance matrix structures and series representations for axially symmetric vector random fields on the sphere, enhancing modeling and simulation capabilities for such fields in spatial and spatio-temporal contexts.

Contribution

It introduces a new, simpler form of covariance matrix structure and series representation for axially symmetric vector random fields on the sphere, including spatio-temporal cases.

Findings

Simpler covariance matrix forms using Legendre functions

Series representations for longitudinally reversible fields

Applicable to modeling and simulation of spatial data

Abstract

This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The series representation is somehow an imitator of the covariance matrix function, and both of them have simpler forms than those proposed in the literature in terms of the associated Legendre functions and are useful for modeling and simulation. Also, a general form of the covariance matrix structure is derived for a spatio-temporal vector random field that is axially symmetric and mean square continuous over the sphere, and a series representation is given for a longitudinally reversible one.