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

TL;DR

This paper introduces a Bayesian hierarchical model with a novel covariance approximation method for large multivariate spatial datasets, specifically applied to analyze errors across multiple climate models, improving computational efficiency and accuracy.

Contribution

It develops a nonseparable, nonstationary cross-covariance model with a covariance approximation combining reduced-rank and sparse structures for large climate data sets.

Findings

Significant improvement over existing covariance approximations.

Effective modeling of cross-correlations among climate model errors.

Enhanced computational feasibility for large spatial datasets.

Abstract

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors.