Climate energy balance models (EBMs) – simple energy-balance-based models of climate change – are widely used. The simplest “linear” EBM is deficient in capturing the behavior of complex climate models, so a “two-layer” model with an additional degree of complexity, i.e. two vertical layers, is typically used. Other additional degrees of complexity are equally plausible as well, however, and different approaches to add a degree complexity have not been compared quantitatively. Here we compare four types of EBMs - two-layer, order-two (temperature-dependent feedback), two-region (in space), and two-timescale (fast and slow climate responses) - specifically, their ability to capture historical temperature change and simulated temperature changes in abrupt (4x) and gradual (1%-ramp) forcing scenarios. The two-region model outperforms the others. The two-region model’s best-fit parameters to historical temperatures are also more physically plausible than the next-best-fitting model, the two-layer model. We therefore conclude that the two-region model is the preferred climate EBM.

The atmospheric Green’s function method is a technique for modeling the response of the atmosphere to changes in the spatial field of surface temperature. While early studies applied this method to changes in atmospheric circulation, it has also become an important tool to understand changes in radiative feedbacks due to evolving patterns of warming, a phenomenon called the "pattern effect." To better study this method, this paper presents a protocol for creating atmospheric Green’s functions to serve as the basis for a model intercomparison project, GFMIP. The protocol has been developed using a series of sensitivity tests performed with the HadAM3 atmosphere-only general circulation model, along with existing and new simulations from other models. Our preliminary results have uncovered nonlinearities in the response of the atmosphere to surface temperature changes, including an asymmetrical response to warming vs. cooling patch perturbations, and a change in the dependence of the response on the magnitude and size of the patches. These nonlinearities suggest that the pattern effect may depend on the heterogeneity of warming as well as its location. These experiments have also revealed tradeoffs in experimental design between patch size, perturbation strength, and the length of control and patch simulations. The protocol chosen on the basis of these experiments balances scientific utility with the simulation time and setup required by the Green’s function approach. Running these simulations will further our understanding of many aspects of atmospheric response, from the pattern effect and radiative feedbacks to changes in circulation, cloudiness, and precipitation.

Using model simulations, we demonstrate that the response of top-of-atmosphere radiative fluxes to localized tropical sea surface temperature (SST) perturbations exhibits numerous non-linearities. Most pronounced is an ‘asymmetry’ in the response to positive and negative SST perturbations. Additionally, we identify a ‘magnitude-dependence’ of response on the size of the SST perturbation. We then explain how these non-linearities arise as a robust consequence of convective quasi-equilibrium and weak (but non-zero) temperature gradients in the tropical free-troposphere, which we encapsulate in a ‘circus tent’ model of the tropical atmosphere. These results demonstrate that the climate response to SST perturbations is fundamentally non-linear, and highlight potential deficiencies in work which has assumed linearity in the response.