# Evaluating explanatory models of the spatial pattern of surface climate trends using model selection and bayesian averaging methods

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## Abstract

We evaluate three categories of variables for explaining the spatial pattern of warming and cooling trends over land: predictions of general circulation models (GCMs) in response to observed forcings; geographical factors like latitude and pressure; and socioeconomic influences on the land surface and data quality. Spatial autocorrelation (SAC) in the observed trend pattern is removed from the residuals by a well-specified explanatory model. Encompassing tests show that none of the three classes of variables account for the contributions of the other two, though 20 of 22 GCMs individually contribute either no significant explanatory power or yield a trend pattern negatively correlated with observations. Non-nested testing rejects the null hypothesis that socioeconomic variables have no explanatory power. We apply a Bayesian Model Averaging (BMA) method to search over all possible linear combinations of explanatory variables and generate posterior coefficient distributions robust to model selection. These results, confirmed by classical encompassing tests, indicate that the geographical variables plus three of the 22 GCMs and three socioeconomic variables provide all the explanatory power in the data set. We conclude that the most valid model of the spatial pattern of trends in land surface temperature records over 1979–2002 requires a combination of the processes represented in some GCMs and certain socioeconomic measures that capture data quality variations and changes to the land surface.

## Keywords

GCM testing Spatial trend patterns Climate data contamination, spatial autocorrelation Non-nested tests Encompassing tests Bayesian model averaging## References

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