CO₂ Dependence in Global Estimation of All-Sky Downwelling Longwave: Parameterization and Model Comparison

The downwelling longwave radiation at the surface (DLR) is a key component of the Earth's surface energy budget. We present a novel set of equations that explicitly account for both clouds and the (Formula presented.) effect to calculate the all-sky DLR. This paper first extends the clear-sky DLR model of Shakespeare and Roderick (2021, https://doi.org/10.1002/qj.4176) to include temperature inversions and clouds. We parameterize relevant cloud properties through theoretical and empirical considerations to formulate an all-sky model. Our model is more accurate than existing methods (reduces Root Mean Squared Error by 2.1–8.7 (Formula presented.) and 1.2–10.1 (Formula presented.) compared to ERA5 reanalysis and in-situ data respectively), and provides a strong physical basis for the estimation of the downwelling longwave from near-surface information. We highlight the important role of (Formula presented.) dependence by showing our model largely captures the change in atmospheric emissivity purely due to (Formula presented.) (i.e., the instantaneous radiative forcing) in CMIP6 models.