Cloud optical thickness and liquid water path. Does the k coefficient vary with droplet concentration?

To parameterize cloud radiative properties in regional and global models, a relationship between cloud liquid water path and optical thickness shall first be established. The so-called k coefficient was therefore introduced in the nineties, which relates the mean surface droplet radius (light extinction) in a droplet spectrum to the mean volume radius (liquid water content). With such a formalism, the Twomey, or first indirect effect, can be reinterpreted by expressing that the optical thickness increases like the cubic root of kN, instead of N. Data collected in situ with instrumented aircraft revealed that the k coefficient decreases when the droplet concentration N increases, hence leading to the conclusion that the Twomey effect was attenuated. Diverse data sets have been reanalyzed, with a careful examination of the accuracy of droplet spectra measurements with airborne spectrometers and it is demonstrated that, first, the relationship between k and N is an artefact of the measuring systems and data analysis procedures, second that the k coefficient has been overestimated. Best estimates of the k coefficient to use in climate modelling are thus derived.