The number concentration of activated CCN (Na) is the most fundamental microphysical property of a convective cloud. It determines the rate of droplet growth with cloud depth and conversion into precipitation sized particles and affects the radiative properties of the clouds. However, measuring Na is not always possible, even in the cores of the convective clouds, because entrainment of sub-saturated ambient air deeper and deeper into the cloud lowers the concentrations by dilution and may cause partial or total droplet evaporation, depending whether the mixing is homogeneous or extreme inhomogeneous, respectively.
Here we describe a technique to derive Na based on the rate of cloud droplet effective radius (Re) growth with cloud depth and with respect to the cloud mixing. We use the slope of the strong linear relationship between the adiabatic water and Re3 to derive an upper limit for Na. Then we tune it down by looking for the minimum residuals in the mixing diagram for the entire profile. This allows us to evaluate both the entrainment and mixing process in the vertical dimension in addition to getting a better estimation for Na.
We found that Na is comparable with the independent CCN measurements. It was also evident that clouds with higher Na needed to grow deeper for the cloud droplets reaching the size that allows fast coalescence into precipitation-sized particles, as expected. This technique was applied successfully to data from different campaigns with only slight quantitative differences. In addition it was found that mixing of sub-saturated ambient air into the cloud is inclined towards the extreme inhomogeneous limit, i.e. that the time scale of droplet evaporation is much smaller than that for turbulent mixing. This means that entrained ambient air is pre-moistened by total evaporation of cloud droplets before it mixes deeper into the clouds where it can hardly change the droplet size distribution, hence Re remains close to its adiabatic value at any given cloud depth. However the tendency towards the extreme inhomogeneous mixing appeared to slightly decrease with altitude, possibly due to enhanced turbulence aloft.
Quantifying these effects, based on more examples from other projects and cloud models is essential. The derived parameterizations can be readily included in non-cloud resolving models in order to take into account the important effects of aerosols on precipitation formation processes.