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 CO2 $\mathrm{C}{\mathrm{O}}_{\mathrm{2}}$ 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 W/m2 $\mathrm{W}/{\mathrm{m}}^{\mathrm{2}}$ and 1.2–10.1 W/m2 $\mathrm{W}/{\mathrm{m}}^{\mathrm{2}}$ 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 CO2 $\mathrm{C}{\mathrm{O}}_{\mathrm{2}}$ dependence by showing our model largely captures the change in atmospheric emissivity purely due to CO2 $\mathrm{C}{\mathrm{O}}_{\mathrm{2}}$ (i.e., the instantaneous radiative forcing) in CMIP6 models. Plain Language Summary The downwelling longwave radiation (DLR) at the surface is a key component of the energy balance at the Earth's surface. Understanding how the DLR will change under future climate conditions is vital. For the first time, we explicitly write a set of equations to calculate the DLR that sufficiently account for the impact of CO2 $\mathrm{C}{\mathrm{O}}_{\mathrm{2}}$ and clouds simultaneously. Our model is more accurate than existing methods, and provides a much stronger physical basis for the estimation of the downwelling longwave from near‐surface information. In this paper, we extend an existing method for estimating the DLR under clear‐sky conditions (i.e., no clouds) to operate under all sky conditions. This method can be used to inform models where the DLR is needed, but only basic observations are available. Key Points Downwelling longwave radiation (DLR) is a poorly estimated element of the surface energy budget by existing analytical models Explicitly accounting for temperature inversions and cloud emissivities improves the accuracy of DLR estimation Considering the radiative forcing from increasing CO2 $\mathrm{C}{\mathrm{O}}_{\mathrm{2}}$ is necessary to produce unbiased future estimates of DLR