Stratospheric Temperature Adjustment Damps the State Dependence of CO2 Radiative Forcing

The radiative forcing of CO₂, which measures its impact on surface warming, is found to vary with background climate state, a phenomenon known as state dependence. Recent studies have suggested the state dependence of radiative forcing in explaining the changes in equilibrium climate sensitivity, primarily due to enhancement of instantaneous forcing in climate states of higher CO₂ concentrations. However, the role of atmospheric adjustment in shaping the overall forcing and its state dependence remains vague. Here we focus on stratospheric temperature adjustment, a dominant component of atmospheric adjustment affecting the magnitude of CO₂ radiative forcing. Using CMIP6 data and a radiative transfer model, we find that forcing associated with stratospheric temperature adjustment decreases in higher CO₂ climate states, offsetting the increase in instantaneous forcing and leading to a smaller overall forcing change with the climate state. To elucidate the mechanisms underlying this decrease, we decompose the forcing adjustment into three multiplicative components of TOA radiative kernel, layerwise temperature Jacobian and instantaneous heating rate perturbation. We find that changes in the kernel and Jacobian contribute weakly, whereas the instantaneous heating rate response dominates the reduction in adjustment. Using a cooling-to-space approximation, we further demonstrate that the combined effects of reduced emission and increased optical depth in a higher CO₂ climate state lead to weaker stratospheric temperature adjustment and thus forcing adjustment.