Some considerations of climate feedback

Abstract: The entry for feedback (and, by extension, for climate feedback) in the Glossary of Meteorology (AMS, 2000) reads as follows: "A sequence of interactions that determines the response of a system to an initial perturbation. Feedbacks may either amplify (positive feedback) or reduce (negative feedback) the ultimate state of the system." The first sentence, in referring to an initial perturbation, is concerned with the stability of the system (a positive feedback in this sense amplifies an initial perturbation, tending to cause instability). The second sentence, in referring to the ultimate state, is concerned with the sensitivity of the system (its equilibrium response to a forcing). Implicit in the Glossary definition is the assumption that a process that acts as a positive feedback in a stability sense also acts as a positive feedback in a sensitivity sense. This assumption appears to be general in the climate literature. The above assumption is examined using two versions of a simple two-zone climate model, the first (of the Budyko-Sellers type) based on top-of-the-atmosphere energy balance considerations, the second based on surface energy balance considerations. The feedbacks due to dynamical processes in both models are examined. In both cases, it is shown that the dynamical feedback may have one sign in a stability (sensitivity) sense without having that sign in a sensitivity(stability) sense. Thus, the common assumption regarding the equivalence in sign of feedback in the two senses is incorrect. This points to a need for greater precision and explicitness in the definition and use of the term climate feedback. Unambiguous definitions will be proposed.