Cloud optical thickness and liquid water path - does the k coefficient vary with droplet concentration?

Cloud radiative transfer calculations in general circulation models involve a link between cloud microphysical and optical properties. Indeed, the liquid water content expresses as a function of the mean volume droplet radius, while the light extinction is a function of their mean surface radius. There is a small difference between these two parameters because of the droplet spectrum width. This issue has been addressed by introducing an empirical multiplying correction factor to the droplet concentration. Analysis of in situ sampled data, however, revealed that the correction factor decreases when the concentration increases, hence partially mitigating the aerosol indirect effect. Five field experiments are reanalyzed here, in which standard and upgraded versions of the droplet spectrometer were used to document shallow cumulus and stratocumulus topped boundary layers. They suggest that the standard probe noticeably underestimates the correction factor compared to the upgraded versions. The analysis is further refined to demonstrate that the value of the correction factor derived by averaging values calculated locally along the flight path overestimates the value derived from liquid water path and optical thickness of a cloudy column, and that there is no detectable relationship between the correction factor and the droplet concentration. It is also shown that the droplet concentration dilution by entrainment-mixing after CCN activation is significantly stronger in shallow cumuli than in stratocumulus layers. These various effects are finally combined to produce the today best estimate of the correction factor to use in general circulation models.