A new framework for isolating individual feedback processes in coupled general circulation climate models. Part I: formulation

This paper proposes a coupled atmosphere-surface climate feedback-response analysis method (CFRAM) as a new framework for estimating climate feedbacks in coupled general circulation models with a full set of physical parameterization packages. The formulation of the CFRAM is based on the energy balance in an atmosphere-surface column. In the CFRAM, the isolation of partial temperature changes due to an external forcing or an individual feedback is achieved by solving the linearized infrared radiation transfer model subject to individual energy flux perturbations (external or due to feedbacks). The partial temperature changes are addable and their sum is equal to the (total) temperature change (in the linear sense). The decomposition of feedbacks is based on the thermodynamic and dynamical processes that directly affect individual energy flux terms. Therefore, not only those feedbacks that directly affect the TOA radiative fluxes, such as water vapor, clouds, and ice-albedo feedbacks, but also those feedbacks that do not directly affect the TOA radiation, such as evaporation, convections, and convergence of horizontal sensible and latent heat fluxes, are explicitly included in the CFRAM. In the CFRAM, the feedback gain matrices measure the strength of individual feedbacks. The feedback gain matrices can be estimated from the energy flux perturbations inferred from individual parameterization packages and dynamical modules. The inter-model spread of a feedback gain matrix would help us to detect the origins of the uncertainty of future climate projections in climate model simulations.