  We develop two new classes of space-time Gaussian process models by
specifying covariance functions using what we call a half-spectral
representation. The half-spectral representation of a covariance function, $K$,
is a special case of standard spectral representations. In addition to the
introduction of two new model classes, we also develop desirable theoretical
properties of certain half-spectral forms. In particular, for a half-spectral
model, $K$, we determine spatial and temporal mean-square differentiability
properties of a Gaussian process governed by $K$, and we determine whether or
not the spectral density of $K$ meets a regularity condition motivated by a
screening effect analysis. We fit models we develop in this paper to a wind
power dataset, and we show our models fit these data better than other
separable and non-separable space-time models.
