Abstract: Multivariate spatial modeling is a rapidly growing field; however, most extant models are infeasible for use with massive spatial processes. In this work, we introduce a highly flexible, interpretable, and scalable multiresolution approach to multivariate spatial modeling. Compactly supported basis functions and Gaussian Markov random field specifications for the coefficients yield efficient and scalable calculation routines for likelihood evaluations and co-kriging. We analytically show that special parameterizations approximate popular existing models. Moreover, the multiresolution approach allows for an arbitrary specification of scale dependence between processes. We use Monte Carlo studies to illustrate the implied stochastic behavior of our approach and to test our ability to recover scale dependence. Moreover, we examine a complex large bivariate observational minimum and maximum temperature data set for the western United States.

Key words and phrases: Coherence, multiresolution, scale dependence, sparse, Wendland.