Coefficients of an analytical aerosol forcing equation determined with a Monte-Carlo radiation model

- We test a simple analytical equation for direct aerosol radiative forcing.
- We find that the equation works well in terms of the functional relationship.
- The parameters in the equation need to be unrealistic, especially for all-sky cases.

Simple analytical equations for global-average direct aerosol radiative forcing are useful to quickly estimate aerosol forcing changes as function of key atmosphere, surface and aerosol parameters. The surface and atmosphere parameters in these analytical equations are the globally uniform atmospheric transmittance and surface albedo, and have so far been estimated from simplified observations under untested assumptions. In the present study, we take the state-of-the-art analytical equation and write the aerosol forcing as a linear function of the single scattering albedo (SSA) and replace the average upscatter fraction with the asymmetry parameter (ASY). Then we determine the surface and atmosphere parameter values of this equation using the output from the global MACR (Monte-Carlo Aerosol Cloud Radiation) model, as well as testing the validity of the equation. The MACR model incorporated spatio-temporally varying observations for surface albedo, cloud optical depth, water vapor, stratosphere column ozone, etc., instead of assuming as in the analytical equation that the atmosphere and surface parameters are globally uniform, and should thus be viewed as providing realistic radiation simulations.The modified analytical equation needs globally uniform aerosol parameters that consist of AOD (Aerosol Optical Depth), SSA, and ASY. The MACR model is run here with the same globally uniform aerosol parameters. The MACR model is also run without cloud to test the cloud effect. In both cloudy and cloud-free runs, the equation fits in the model output well whether SSA or ASY varies. This means the equation is an excellent approximation for the atmospheric radiation. On the other hand, the determined parameter values are somewhat realistic for the cloud-free runs but unrealistic for the cloudy runs. The global atmospheric transmittance, one of the determined parameters, is found to be around 0.74 in case of the cloud-free conditions and around 1.03 with cloud. The surface albedo, another determined parameter, is found to be around 0.18 and 0.28 in case of cloud-free and cloudy-sky conditions respectively. Because the cloudy-sky runs yield unrealistic parameter values, we conclude that the equation is more adequate for cloud-free conditions.