We introduce a flexible parametric family of matrix-valued covariance functions for multivariate spatial random fields, where each constituent component is a Mat´ern 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 Mat´ern type. In a data example on error fields for numerical predictions of surface pressure and temperature over the Pacific Northwest, a parsimonious bivariate Mat´ern model compares favorably to the traditional linear model of coregionalization.
Keywords: co-kriging; convolution; cross-correlation; Mat´ern class; Gaussian spatial random field; maximum likelihood; multivariate geostatistics; numerical weather prediction; positive definite