Abstract
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.
Highlights
The need to understand factors influencing climate feedback and sensitivity make simple models indispensable as means to investigate the climate response to changes in the Earth’s energy balance
We question the difference between the concept of ocean heat uptake efficacy and a pattern effect due to regional feedbacks weighted by a geographic pattern of surface warming
The analytical solution for each layer, thoroughly described in Geoffroy et al (2013a, b) but presented here independently to highlight important features, consists of the sum of the equilibrium response and two modes which increase exponentially towards zero with their characteristic timescales. These modes are characterized by the fast and slow adjustment timescale f and s, their amplitudes f and s which sum up to the initial ocean heat uptake temperature, and the mode parameters f and s which scale the adjustment of the deep-ocean layer; T(t) = F + − eq fe−t∕ f +
Summary
The need to understand factors influencing climate feedback and sensitivity make simple models indispensable as means to investigate the climate response to changes in the Earth’s energy balance. Hasselmann (1979) already recognized the multiple timescale structure of the climate response, but at this time the global feedback was assumed to depend on the global mean surface temperature only These characteristic adjustment timescales have been explicitly linked to nonconstant global feedback associating them with different state-variables each of which influences the radiative response (e.g. Held et al 2010; Winton et al 2010; Geoffroy et al 2013a, b; Armour et al 2013; Andrews et al 2015; Hedemann et al 2019). To understand the radiative response of the climate system, state-of-the-art climate models such as the Max Planck Institute Earth System Model 1.2 (MPI-ESM1.2), thoroughly described in Mauritsen et al (2018), can be forced by step forcing—usually an abrupt increase in atmospheric CO2 concentration Such experiments reveal changes or common features in the relationship between N and T To compute specific response times, the MPI-ESM1.2 temperature output has been smoothed by running mean with a window of thirty
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