The "pattern effect" refers to the dependence of Earth’s net radiative feedback not just on the global-mean temperature anomalies, but on the full pattern of surface temperature change. General Circulation Models (GCMs) show substantial uncertainty in the magnitude of this effect. This uncertainty is so large that a recent World Climate Research Program assessment concluded that the observational record of Earth’s energy budget cannot constrain the upper bound of climate sensitivity. The lack of observational constraints on the pattern effect thus presents one of the largest roadblocks to improved estimates of climate sensitivity.

A primary difficulty lies in the fact that the joint satellite record of radiative imbalance and surface temperature is short (and correlated) relative to the number of degrees of freedom in the sensitivity map of top-of-atmosphere radiation to regional temperature changes – the so-called radiative Green’s function. This leads to a classic under constrained problem.

Here we show how we can overcome this limitation and bring observational constraints on the pattern effect by assimilating GCM simulations and satellite data in a hierarchical Bayesian learning approach. We use GCMs’ output to build a prior distribution for the spatial structure of the Green’s function, a structure formally encoded as a Gaussian process. This prior distribution is then further constrained by using the CERES record of top-of-atmosphere radiation. The predictive skill of this approach is validated by using a perfect model approach, wherein we use prescribed-SST GCM simulations over the CERES interval as synthetic observations and evaluate the skill of the posterior Green’s function in constraining the magnitude of the pattern effect in that model.