Cloud scattering impact on thermal radiative transfer and global longwave radiation

The potential importance of longwave (LW) cloud scattering has been recognized but the actual estimate of this effect on thermal radiation varies greatly among different studies. General circulation models (GCMs) generally neglect or simplify the multiple scattering in the LW. In this study, we use a rigorous radiative transfer algorithm to explicitly consider LW multiple-scattering and apply the GCM to quantify the impact of cloud LW scattering on thermal radiation fluxes. Our study shows that the cloud scattering effect on downward thermal radiation at the surface is concentrated in the infrared atmospheric window spectrum (800-1250 cm^-1). The scattering effect on the outgoing longwave radiation (OLR) is also present in the window region over low clouds but it is mainly in the far-infrared spectrum (300-600 cm^-1) over high clouds. For clouds with small to moderate optical depth (τ < 10), the scattering effect on thermal fluxes shows large variation with the cloud τ and has a maximum at an optical depth of ~3. For opaque clouds, the scattering effect approaches an asymptote and is smaller and less important. The 2-stream radiative transfer scheme could have an error over 10% with an RMS error around 3.5%-4.0% in the calculated LW flux. This algorithm error of the 2-stream approximation could readily exceed the no-scattering error in the LW, and thus it is worthless to include the time-consuming computation of multiple scattering in a 2-stream radiative transfer scheme. However, the calculation error rapidly decreases as stream number increases and the RMS error in LW flux using the 4-stream scheme is under 0.3%, an accuracy sufficient for most climate studies. We implement the 4-stream discrete-ordinate algorithm in the GISS GCM and run the GCM for 20 years with and without the LW scattering effect, respectively. When cloud LW scattering is included, we find that the global annual mean OLR is reduced by 2.7 W/m², and the downward surface flux and the net atmospheric absorption are increased by 1.6 W/m² and 1.8 W/m², respectively. Using one year of ISCCP clouds and running the standalone radiative transfer offline, the global annual mean non-scattering errors in OLR, surface LW downward flux and net atmospheric absorption are 3.6W/m², -1.1 W/m², and -2.5 W/m², respectively. The global scattering impact of 2.7 W/m² on the OLR is small when compared to the typical global OLR value of 240W/m², but it is significant when compared to cloud LW radiative forcing (30W/m²) and net cloud forcing (-14W/m²). Overall, the effect of neglecting scattering on the thermal fluxes is comparable to the reported clear sky radiative effect of doubling CO₂.