Fast-slow climate dynamics and peak global warming.

The dynamics of a linear two-box energy balance climate model is analyzed as a fast-slow system, where the atmosphere, land, and near-surface ocean taken together respond within few years to external forcing whereas the deep-ocean responds much more slowly. Solutions to this system are approximated by estimating the system's time-constants using a first-order expansion of the system's eigenvalue problem in a perturbation parameter, which is the ratio of heat capacities of upper and lower boxes. The solution naturally admits an interpretation in terms of a fast response that depends approximately on radiative forcing and a slow response depending on integrals of radiative forcing with respect to time. The slow response is inversely proportional to the 'damping-timescale', the timescale with which deep-ocean warming influences global warming. Applications of approximate solutions are discussed: conditions for a warming peak, effects of an individual pulse emission of carbon dioxide (CO $$_{\mathrm{2}}$$ ), and metrics for estimating and comparing contributions of different climate forcers to maximum global warming. [ABSTRACT FROM AUTHOR]