  We propose computationally efficient methods for estimating stationary
multivariate spatial and spatial-temporal spectra from incomplete gridded data.
The methods are iterative and rely on successive imputation of data and
updating of model estimates. Imputations are done according to a periodic model
on an expanded domain. The periodicity of the imputations is a key feature that
reduces edge effects in the periodogram and is facilitated by efficient
circulant embedding techniques. In addition, we describe efficient methods for
decomposing the estimated cross spectral density function into a linear model
of coregionalization plus a residual process. The methods are applied to two
storm datasets, one of which is from Hurricane Florence, which struck the
souteastern United States in September 2018. The application demonstrates how
fitted models from different datasets can be compared, and how the methods are
computationally feasible on datasets with more than 200,000 total observations.
