How Much Sunlight Reflection is Necessary to Compensate for a Given Increase in CO2?

In Experiment G1 of the Geoengineering Model Intercomparison Project, CO₂ concentrations are abruptly quadrupled while the solar constant is reduced in order to maintain preindustrial temperatures. The required solar constant reduction varies between 3.2% and 5.0%, depending on the model. This quantity, which has implications for the scope of possible solar geoengineering deployments, is uncorrelated with the models' equilibrium climate sensitivity, while a formula from the experiment specifications based on the models' effective CO₂ forcing and planetary albedo is well-correlated with but consistently underpredicts the required solar reduction. We propose a formula for the required solar reduction based on instantaneous CO₂ forcing and the sum of radiative adjustments to the combined CO₂ and solar forcings. These adjustments, which we quantify using established methods, include the effects of changes in clouds, atmospheric temperature, and specific humidity on the top of atmosphere radiation budget. Low cloud fraction decreases in all models in G1, an effect that is robust and widespread across ocean and vegetated land areas. While the surface exhibits cooling in the tropics and warming in high latitudes, the upper troposphere is dominated by cooling which exceeds that at the surface, and the stratosphere cools more than anywhere else. Tropospheric specific humidity decreases due to the cooler temperatures there. The low cloud fraction reduction and atmospheric temperature decrease have strong warming effects on the planet, due to reduced reflection of shortwave radiation and reduced emission of longwave radiation. About 50% to 75% of the temperature effect is caused by the stratospheric cooling, while the reduction in atmospheric humidity results in increased outgoing longwave radiation that roughly offsets the tropospheric temperature effect. The longwave effect of the cloud changes is small in the global mean, despite an increase in high cloud fraction. The sum of the diagnosed radiative adjustments and the CO₂ instantaneous forcing explains the required solar forcing in G1 to within about 6%. Understanding the relative contributions of the two forcings to these adjustments will require analyzing a solar-forcing-only experiment in a multi-model framework.