Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction between these two dependencies that is the focus of Genton and Kleiber’s paper under discussion. We see the problem of ensuring that any multivariate spatial covariance matrix is nonnegative definite as important, but we also see it as a means to an end. That “end” is solving the scientific problem of predicting a multivariate field.
"Capturing Multivariate Spatial Dependence: Model, Estimate and then Predict." Statist. Sci. 30 (2) 170 - 175, May 2015. https://doi.org/10.1214/15-STS517