Transient Climate Response in a Two-Layer Energy-Balance Model. Part I: Analytical Solution and Parameter Calibration Using CMIP5 AOGCM Experiments

This is the first part of a series of two articles analyzing the global thermal properties of atmosphere-ocean coupled general circulation models (AOGCMs) within the framework of a two-layer energy-balance model (EBM). In this part, the general analytical solution of the system is given and two idealized climate change scenarios, one with a step forcing and one with a linear forcing, are discussed. These solutions give a didactic description of the contributions from the equilibrium response and of the fast and slow transient responses during a climate transition. Based on these analytical solutions, a simple and physically based procedure to calibrate the two-layer model parameters using an AOGCM step-forcing experiment is introduced. Using this procedure, the global thermal properties of 16 AOGCMs participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) are determined. It is shown that, for a given AOGCM, the EBM tuned with only the abrupt 4xCO(2) experiment is able to reproduce with a very good accuracy the temperature evolution in both a step-forcing and a linear-forcing experiment. The role of the upper-ocean and deep-ocean heat uptakes in the fast and slow responses is also discussed. One of the main weaknesses of the simple EBM discussed in this part is its ability to represent the evolution of the top-of-the-atmosphere radiative imbalance in the transient regime. This issue is addressed in Part II by taking into account the efficacy factor of deep-ocean heat uptake.