An Analytical Model for CO₂ Radiative Forcing

CO₂ radiative forcing is a central quantity in climate science and is accurately modeled by state-of-the-art radiative transfer codes. But, the combined intricacies of molecular spectroscopy as well as radiative transfer have rendered a chalkboard understanding of this quantity elusive. Here, building on the work of Gea-Banacloche and Wilson, we construct an analytical model for CO₂ forcing which accounts for spectral variations in absorption and reproduces the results from comprehensive radiative transfer codes with surprising accuracy. Moreover, the analytical model allows for a fairly accurate back-of-the-envelope estimate of CO₂ forcing via evaluation of the Planck function, provides insight into how and why CO2 forcing varies over the globe (strongest in the tropics and weakest at the poles), and shows how the presence of water vapor weakens CO2 forcing, particularly in the tropics.