ABSTRACT

ABSTRACT

Simple analytical equations for aerosol radiative forcing are useful to quickly see how global aerosol forcing changes with key atmosphere, surface and aerosol parameters. Until now, the coefficients in these analytical equations have been estimated from simplified observations under untested assumptions.  In the present study, I first derive a simple analytical equation by combining Charlson’s for purely scattering aerosols with the extensions of Chy ́lek and Wong to scattering and absorbing aerosols.  Then I determine the coefficients of this equation using the output from the global MACR (Monte-Carlo Aerosol Cloud Radiation) model. The MACR model provides realistic radiation simulations.  In the coefficient determination, I also check the validity of the equation.

The analytical equation assumes globally uniform parameters that consist of AOD (Aerosol Optical Depth), SSA (Single Scattering Albedo), ASY (Asymmetric parameter) and Upscatter fraction.  The MACR model was run with the same globally uniform parameters but with realistically varying values in space and season for the other parameters that the model requires and the equation does not require.  These parameters include surface albedo, cloud optical depth, Ångström exponent, ocean albedo, stratosphere column ozone and represent observations for the 2001-2010 period.  The MACR model was run for both cloudy and cloud-free conditions.  In one set of experiment, the asymmetry parameter (ASY) was allowed to change from 0.69 to 0.82 while keeping uniform SSA at 0.80 and 1. For each of these SSA value, 23 MACR simulations were conducted for each of the cloudy or cloud-free condition. In another set of experiment, the single scattering albedo (SSA) was allowed to change from 0.75 to 1.0 while keeping uniform ASY at 0.63 and 0.7. For each of these ASY values, 26 simulations were conducted for each of the cloudy and cloud-free condition.

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.  Furthermore, I have found that the global atmospheric transmittance, the fraction of radiation passing through the atmosphere, is around 0.74 in case of cloud-free conditions. However, in case of cloudy-sky conditions, the fraction is highly unrealistic, around 1.03. On the other hand, surface albedo calculated from the analytical equation is around 0.18 and 0.28 in case of cloud-free and cloudy-sky conditions respectively. Because the cloud included result yields unrealistic parameter values, I conclude that the equation is more adequate for cloud-free conditions.