  For a vector random field that is isotropic and mean square continuous on a
sphere and stationary on a temporal domain, this paper derives a general form
of its covariance matrix function and provides a series representation for the
random field, which involve the ultraspherical polynomials. The series
representation is somehow an imitator of the covariance matrix function, but
differs from the the spectral representation in terms of the ordinary spherical
harmonics, and is useful for modeling and simulation. Some semiparametric
models are also illustrated.
