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 into the cloud lowers the concentrations by dilution and may cause partial or total droplet evaporation, depending on whether the mixing is homogeneous or extreme inhomogeneous, respectively. Here we describe a methodology to derive Na based on the rate of cloud droplet effective radius (Re) growth with cloud depth and with respect to the cloud mixing with the entrained ambient air. We use the slope of the tight linear relationship between the adiabatic liquid water mixing ratio and Re3 (or Rv3) to derive an upper limit for Na assuming extreme inhomogeneous mixing. Then we tune Na down to find the theoretical relative humidity that the entrained ambient air would have for each horizontal cloud penetration, in case of homogeneous mixing. 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 the derived Na from the entire profile data is highly correlated with the independent CCN measurements from below cloud base. Moreover, it was found that mixing of sub-saturated ambient air into the cloud at scales of ~100 m and above is inclined towards the extreme inhomogeneous limit, i.e. that the time scale of droplet evaporation is significantly smaller than that for turbulent mixing. This means that ambient air that entrains the cloud 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 and larger cloud drops aloft. Quantifying these effects, based on more examples from other projects and high resolution cloud models is essential for improving our understanding of the interactions between the cloud and its environment. These interactions may play an important role in cloud dynamics and microphysics, by affecting cloud depth and droplet size spectra, for example, and may therefore influence the cloud precipitation formation processes.
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