Estimation of anthropogenic signals in atmospheric GCMs using the General Linear Model and an efficient experimental design

A set of atmosphere-only General Circulation Model (AGCM) integrations forced by the observed record of sea surface temperatures and sea-ice extents and a set of anthropogenic forcings are analysed to understand the direct effect of humanity on the atmosphere since 1870.

A General Linear Model (GLM) is used to statistically model the data from these AGCM integrations, assuming the direct anthropogenic effects to be linearly proportional to the time profile of their global mean radiative forcing. Tests are presented that show that the assumptions of the GLM are satisfied for several climate variables at several spatial scales from global to grid-point. This statistical technique is shown to be more efficient than the pairwise comparison of ensemble means that is typically used to estimate anthropogenic effects.

Experimental design theory is applied to this GLM to determine the experimental design that allows the statistical model to most efficiently estimate anthropogenic effects, which are highly correlated with each other in time, given a limited number of integrations. The full factorial design is found to be optimal, where the integrations are distributed evenly across all possible combinations of anthropogenic forcings, so that it is better to have more ensembles, keeping the ensemble size small. This is shown to be more efficient than the experimental designs typically used in climate change studies, which use few ensembles with more members in each.

The factorial design also allows the GLM to provide a general statistical framework for investigating whether anthropogenic effects combined additively. Although a few nonlinear interactions are detected, these are very small.