State Dependence of CO₂ Effective Radiative Forcing from 1/163 to 163CO₂

Most research on the state dependence of climate sensitivity has focused on radiative feedbacks, with less attention given to radiative forcing. However, recent studies show that the carbon dioxide (CO₂) radiative forcing depends not only on the CO₂ concentration but also on the base state, particularly the stratospheric temperature profile. Hence, we here carry out atmosphere-only experiments with prescribed sea surface temperatures using Community Earth System Model, version 1, Large Ensemble (CESM1-LE), broadband radiative transfer calculations, and a one-dimensional radiative–convective equilibrium model to thoroughly investigate the dependence of effective radiative forcing (ERF) on varying levels of CO₂ forcing and base-state stratospheric temperatures from 1/16× to 16×CO₂. Using both the CESM1-LE and a radiative–convective equilibrium model, we demonstrate that ERF strongly depends on the CO₂ value of the underlying base state, deviating significantly from a simple logarithmic relationship with CO₂ concentration. Specifically, doubling CO₂ from a base state of 8×CO₂ results in an ERF value that is 50% higher than doubling CO₂ from a 1/16×CO₂ state. By decomposing ERF into instantaneous radiative forcing (IRF) and radiative adjustments, we show that the IRF is largely responsible for the state dependence of ERF. We attribute the increase in IRF with CO₂ concentrations to the stratospheric cooling at 10 hPa. Furthermore, we find that the radiative adjustments are not constant with each CO₂ doubling and halving, and their magnitude depends on the method used to compute them, be it via radiative kernels or via offline radiative transfer calculations. A significant implication of our findings is that the state dependence of ERF needs to be taken into account when studying climate sensitivity under large CO₂ perturbations within the feedback-forcing framework.