Estimating the Pattern Effect Using Regularized Linear Regression

How the spatially varying temperature field affects global radiation (the “pattern effect”) is crucial to understanding how sensitive Earth’s temperature is to anthropogenic forcing. Here we estimate this phenomenon by forming temperature sensitivity maps using the regularized linear regression methods ridge, LASSO, and elastic net. When trained on internal variability from 1,000 years of climate model control output, the resulting sensitivity maps across four models explain between 78% and 84% of the variance in net top-of-atmosphere radiation in out-of-sample, internal variability tests. When trained on only 24 years of output (to mimic the length of the CERES record), the median explained variance is reduced to 56%, with a 95% range of [40%, 69%]. Results trained on internal variability from 1,000 years of control output reproduce ~75% of the forced radiative response magnitude in RCP 8.5 climate change simulations. However, results trained on only 24 years of internal variability are unreliable for projecting the forced radiative response. We use the methods to develop physically interpretable radiative feedback sensitivity maps based on observations.