The quantification and understanding of direct aerosol forcing is essential in the study of climate. One of the main issues that makes its quantification difficult is the lack of a complete understanding of the role of the vertical distribution of aerosols and clouds. This work aims at reducing the uncertainty of aerosol top-of-the-atmosphere (TOA) forcing due to the vertical superposition of several short-lived atmospheric components, in particular different aerosol species and clouds. We propose a method to quantify the contribution of different parts of the atmospheric column to the TOA forcing as well as to evaluate the contribution to model differences that is exclusively due to different spatial distributions of aerosols and clouds. We investigate the contribution of aerosol above, below and in clouds by using added diagnostics in the aerosol–climate model LMDz. We also compute the difference between the TOA forcing of the ensemble of the aerosols and the sum of the forcings from individual species in clear sky. This difference is found to be moderate for the global average (14%) but can reach high values regionally (up to 100%). Nonlinear effects are even more important when superposing aerosols and clouds. Four forcing computations are performed: one where the full aerosol 3-D distribution is used, and then three where aerosols are confined to regions above, inside and below clouds, respectively. We find that the TOA forcing of aerosols depends crucially on the presence of clouds and on their position relative to that of the aerosol, in particular for black carbon (BC). We observe a strong enhancement of the TOA forcing of BC above clouds, attenuation for BC below clouds, and a moderate enhancement when BC is found within clouds. BC above clouds accounts for only about 30% of the total BC optical depth but for 55% of the forcing, while forcing efficiency increases by a factor of 7.5 when passing from below to above clouds. The different behaviour of forcing nonlinearities for these three components of the atmospheric column encouraged us to develop the method for application to inter-model variability studies by reading 3-D aerosol and cloud fields from different general circulation models (GCMs) into the same model. We apply the method to the comparison of forcing due to the aerosols and clouds distributions of the general circulation models LMDz and SPRINTARS. The different amount of BC above but also within clouds is revealed to play a major role on the differences of cloudy-sky forcings between the two models, which can exceed 100% regionally.
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