A Formal Analysis of the Feedback Concept in Climate Models. Part I: Exclusive and Inclusive Feedback Analyses*

Abstract

Abstract Climate sensitivity and feedback are key concepts if the complex behavior of climate response to perturbation is to be interpreted in a simple way. They have also become an essential tool for comparing global circulation models and assessing the reason for the spread in their results. The authors introduce a formal basic model to analyze the practical methods used to infer climate feedbacks and sensitivity from GCMs. The tangent linear model is used first to critically review the standard methods of feedback analyses that have been used in the GCM community for 40 years now. This leads the authors to distinguish between exclusive feedback analyses as in the partial radiative perturbation approach and inclusive analyses as in the “feedback suppression” methods. This review explains the hypotheses needed to apply these methods with confidence. Attention is paid to the more recent regression technique applied to the abrupt 2×CO2 experiment. A numerical evaluation of it is given, related to the Lyapunov analysis of the dynamical feature of the regression. It is applied to the Planck response, determined in its most strict definition within the GCM. In this approach, the Planck feedback becomes a dynamical feedback among others and, as such, also has a fast response differing from its steady-state profile.