On simple representations of the climate response to external radiative forcing

Global warming in response to external radiative forcing is determined by the feedback of the climate system. Recent studies have suggested that simple mathematical models incorporating a radiative response which is related to upper- and deep-ocean disequilibrium (ocean heat uptake efficacy), inhomogeneous patterns of surface warming and radiative feedbacks (pattern effect), or an explicit dependence of the strength of radiative feedbacks on surface temperature change (feedback temperature dependence) may explain the climate response in atmosphere-ocean coupled general circulation models (AOGCMs) or can be useful for interpreting the instrumental record. We analyze a two-layer model with an ocean heat transport efficacy, a two-region model with region specific heat capacities and radiative responses; a one-layer model with a temperature dependent feedback; and a model which combines elements of the two-layer/region models and the state-dependent feedback parameter. We show that, from the perspective of the globally averaged surface temperature and radiative imbalance, the two-region and two-layer models are equivalent. State-dependence of the feedback parameter introduces a nonlinearity in the system which makes the adjustment timescales forcing-dependent. Neither the linear two-region/layer models, nor the state-dependent feedback model adequately describes the behavior of complex climate models. The model which combines elements of both can adequately describe the response of more comprehensive models but may require more experimental input than is available from single forcing realizations.