How to think about the shortwave water vapor feedback

Recent studies have provided analytical descriptions of Earth’s longwave feedback λ_LW; to expand on this, we propose an analytical model for the shortwave water vapor feedback λ_SW. In this model, λ_SW is proportional to the change in the square of atmopsheric transmissivity t_atm with temperature T and thus mainly originates from spectral regions that ”transition” from optically thin to optically thick. Following Jeevanjee (2023, DOI: 10.1119/5.0135727), we approximate t_atm based on the column water vapor M_H2O and the water vapor mass absorption cross-section κ_H2O. We show that in order to capture the weak T dependence of λ_SW, it is crucial to account for spectral variations in κ_H2O, which can already be achieved by a simple exponential fit.

We further demonstrate that the T dependence of λ_SW can be explained by the opposing effects of two main processes: At low T, more optically thin parts of the spectrum ”start” their transition than optically thick parts ”complete” their transition, leading to an increase in λ_SW with T. At high T, the inverse T dependence of the Clausius-Clapeyron relation leads to a decrease in λ_SW.

We can also extend our model to incorporate second-order effects such as spectral variations in solar irradiance and deviations of κ_H2O from the idealized exponential fit. This version of the model is in good agreement with full radiative transfer simulations. The remaining discrepancies can be attributed to non-linear absorption by the water vapor continuum, deviations in M_H2O from the approximated Clausius-Clapeyron scaling, and the effects of molecular Rayleigh scattering.

In conclusion, we demonstrate that the shortwave water vapor feedback λ_SW can be understood using a simple analytical model. This model also demonstrates the merits of a spectral approach to understand λ_SW and illuminates the two key processes that drive its T dependence.