Why is climate sensitivity so unpredictable? Supplementary material

Feedback terminology In this section we derive the parameters we use in discussing feedbacks. We employ the standard terminology of feedback analysis from electronics (e.g., S1-S5). It is, however, different from the terminology found in much of the climate literature, which reverses the definition of a feedback factor and a gain (e.g., S6). Consider the net radiation balance at the top of the atmosphere, R, to be the sum of the outgoing longwave radiation, F, and the net absorbed solar radiation, S (all fluxes are defined as positive downwards). If the climate is in equilibrium then R = 0, so F = −S, and the global mean temperature has its equilibrium value. Now let∆Rf be some specified, constant, radiative forcing (here, due to anthropogenic emissions of CO2). ∆Rf is assumed small compared with F and S so that the changes it introduces in system dynamics are all small and linear in the forcing. In order to attain a new equilibrium state, the radiative balance must change by an amount∆R that is equal and opposite to the forcing. That is, ∆R = −∆Rf. In other words, in the new equilibrium state the longwave and shortwave radiation must adjust: ∆R = ∆F +∆S, and the temperature reaches a new equilibrium value, displaced from the old by an amoun