Equilibrium global warming – a scaling perspective

Abstract. In the field of climate-change research a lot of effort is devoted to the ‘narrowing down’ of uncertainties in the estimation of the (fast-feedback) Equilibrium climate sensitivity (ECS), the mean global warming as a result of a doubling of the CO₂ concentration in the atmosphere, in order to improve the predictability of the Earth climate system to determine required future greenhouse-gas mitigation targets. A recent update of this quantity was provided by Hansen et al. (2023), reporting a value of 4.8 °C ± 1.2 °C for doubled CO₂. This outcome is based on a variety of paleo-climate information to overcome limitations of the present, mainly model-based, “best estimate” of 3 °C (IPCC AR6, 2021). Applying the formal framework of feedback analysis, originating in electrical engineering and control systems, the present study sets out to explore possible consequences of this high-end ECS update for the long-term Earth system sensitivity (ESS), taking into account ‘slow’ feedbacks by ice sheets and trace gases in a warming world (according to the recent Hansen study for today’s GHGs concentrations in the atmosphere likely leading to 10 °C equilibrium global warming). As a result, principal scaling relations between variations in the fast-feedback ECS and slow-feedback ESS are derived, primarily focusing on a better mechanistic understanding of interactions in (besides merely improving the predictability of) the Earth climate system. These scaling relations may be applied to determine the equilibrium global warming eventually to be expected for a specified CO₂ amount in the atmosphere. As an illustration, implications for the current geopolitical approach, aiming at 1.5 or at most 2 degrees Celsius of global warming as required by the Paris agreement—while we already seem to be on a 10 degrees track because of warming in the pipeline—are analyzed. In total, the analysis leads to a 4°C future warming in the pipeline on top of the 2°C ‘Paris’ setpoint, resulting in a committed warming of about 6°C. However, as demonstrated in the paper, this estimate is accompanied by considerable fundamental uncertainties in projected changes, caused by cascading feedbacks from the at present more or less still stable Holocene glacial boundary conditions in a rapidly warming world.