Effect of Number Density of CCN on Competitive Growth of Cloud Droplet by Condensation of Atmospheric Water Vapor

Cloud droplets grow on cloud condensation nuclei (CCN) with condensing the ambient water vapor in the atmospheric air parcel. The size of the cloud droplet in the equilibrium state is estimated usually Köhler Equation. However, Köhler Equation is based on the assumption that the cloud droplet grows in an infinitely large reservoir of water vapor at constant pressure, i. e., at constant saturation ratio. This assumption causes some erroneous results in the estimation of real size in the air parcel, although the assumption makes the calculation easy. Thereare two apparent deficiencies in Köhler Equation. One is that the equilibrium size cannot be decided in case of the larger saturation ratio than the critical ratio. The other is that the variation of the size with the number density of CCN, in other words the competitive growth, cannot be considered in the estimation ofthe size. In order to improve these deficiencies, the conventional Köhler Equation has been modified using the mass conservation of the water contained in the air parcel.