Atmospheric adjustments moderate the state dependence of CO₂ radiative forcing

Previous studies have shown that both the instantaneous radiative forcing (IRF) and effective radiative forcing (ERF) of CO₂ become larger in warmer climates. However, the increase in ERF is much smaller than that in IRF, indicating that atmospheric adjustments partially compensate for the initial IRF enhancement. This paper aims to quantify the processes responsible for this compensation. Using the Community Earth System Model version 1.2, we consistently evaluate how the IRF, stratosphere-adjusted radiative forcing (SARF), and ERF respond when the climate changes from the piControl state to the abrupt-4xCO₂ state. By employing a radiative transfer model, we show that the IRF4xCO₂ increases by 2.27 W m^-2 (41%), the SARF_4xCO2 by 1.64 W m^-2 (20%), and the ERF by 1.26 W m^-2 (17%), indicating that atmospheric adjustments progressively offset the initial IRF enhancement. The weaker SARF enhancement results from reduced stratospheric cooling in the abrupt-4xCO2 state, due to both a colder stratospheric baseline and a higher background CO₂ concentration. The further reduction from SARF to ERF is associated with tropospheric adjustments, particularly stronger tropospheric warming and smaller surface albedo changes, with the latter linked to Arctic snow cover. These findings are supported by an idealized radiative-convective equilibrium (RCE) model and by multi-model comparisons from CMIP6. Overall, this work highlights the critical role of stratospheric temperature adjustment, tropospheric temperature adjustment and surface albedo change in modulating the state dependence of CO2 radiative forcing.