Potential for bias in effective climate sensitivity from state-dependent energetic imbalance

Abstract. To estimate equilibrium climate sensitivity from a simulation where a step change in carbon dioxide concentrations is imposed, a common approach is to linearly extrapolate temperatures as a function of top-of-atmosphere energetic imbalance to estimate the equilibrium state (“effective climate sensitivity”). In this study, we find that this estimate may be biased in some models due to state-dependent energetic leaks. Using an ensemble of multi-millennial simulations of climate model response to a constant forcing, we estimate equilibrium climate sensitivity through Bayesian calibration of simple climate models which allow for responses from subdecadal to multi-millennial timescales. Results suggest potential biases in effective climate sensitivity in the case of particular models where radiative tendencies imply energetic imbalances which differ between pre-industrial and quadrupled CO2 states, whereas for other models even multi-thousand-year experiments are insufficient to predict the equilibrium state. These biases draw into question the utility of effective climate sensitivity as a metric of warming response to greenhouse gases and underline the requirement for operational climate sensitivity experiments on millennial timescales to better understand committed warming following a stabilization of greenhouse gases.