Matérn cross-covariance functions for multivariate random fields

We introduce a flexible parametric family of matrix-valued covariance functions for multivariate spatial random fields, where each constituent component is a Matern process. The model parameters are interpretable in terms of process variance, smoothness, correlation length, and co-located correlation coefficients, which can be positive or negative. Both the marginal and the cross covariance functions are of the Matern type. In a data example on error fields for numerical predictions of temperature and pressure over the Pacific Northwest, we compare the Matern model to the traditional linear model of coregionalization