Parameterization of cloud droplet activation using a simplified treatment of the aerosol number size distribution

The number-to-volume concentration ratio, R, defined as the number concentration of particles larger than a certain cut-off diameter divided by the total particle volume concentration, can be used for expressing aerosol number size distributions in a simplified way. Earlier studies have shown that R shows less variability than random size distributions would produce. In this article the parameter R was used to develop a new parameterization for estimating the cloud droplet number concentration (CDNC). The parameterization is a function of four input parameters: the total submicron volume concentration (V-tot), number-to-volume concentration ratio with a 0.1-mu m cut-off diameter (R(0.1 mu m)), soluble fraction of the particle volume (epsilon) and air updraft velocity (v(up)). The parameterization was derived by finding the best fit to a series of simulations made with an adiabatic air parcel model simulating cloud droplet activation, and the model input parameters were varied over a range typical for northern European background air. Results from the parameterization were compared with cloud droplet concentrations measured in Northern Finland, and a good agreement was found. The new parameterization demonstrates that if the value of R( 0.1 mm) can be estimated or parameterized without knowing the whole particle number size distribution, cloud droplet number concentrations can be estimated relatively accurately by using only the four parameters mentioned above. This would reduce significantly the computer resources needed for calculating CDNC in large-scale atmospheric models.