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This paper investigates the cross-correlations across multiple climate modelerrors. We build a Bayesian hierarchical model that accounts for the spatialdependence of individual models as well as cross-covariances across differentclimate models. Our method allows for a nonseparable and nonstationarycross-covariance structure. We also present a covariance approximation approachto facilitate the computation in the modeling and analysis of very largemultivariate spatial data sets. The covariance approximation consists of twoparts: a reduced-rank part to capture the large-scale spatial dependence, and asparse covariance matrix to correct the small-scale dependence error induced bythe reduced rank approximation. We pay special attention to the case that thesecond part of the approximation has a block-diagonal structure. Simulationresults of model fitting and prediction show substantial improvement of theproposed approximation over the predictive process approximation and theindependent blocks analysis. We then apply our computational approach to thejoint statistical modeling of multiple climate model errors.

Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors