A Comparison of Several Regional Climate Model Outputs Using an Extended Model for Large Spatio-Temporal Lattices

For the purpose of statistically analyzing regional climate model outputs such as in the NARCCAP program, I propose an extension of the usual CAR (conditional spatial auto regression) model for spatial lattice data. The extension incorporates a second spatial parameter that governs smoothness of the underlying spatial field. The advantage of using this model is that the inverse of the spatial covariance matrix (the precision matrix) is modeled directly and that it is sparse. Further this model is defined via the spectral decomposition of the precision matrix which also serves as a prewhitening transformation. For regular rectangular lattices, assuming a circulant structure, the spectral decomposition is the Fast Fourier transform (FFT) and thus provides a computationally feasible method for very large data. In transformed space after prewhitening the estimation problem is reduced to that of a heteroscedastic regression model with a structured variance matrix, but no spatial dependence, which is trivial from the computational point of view.
We consider strategies to applying this method to a variety of space - time regression and functional ANOVA type models for precipitation and temperature NARCCAP model outputs.