A parameterization of cloud droplet nucleation part I: single aerosol type

A critical link between clouds and aerosols is the nucleation process, in which supersaturation activates some fraction of the aerosols to form cloud droplets. Under conditions of strong updraft velocity or low aerosol number concentration, high supersaturations are achieved and most of the aerosols are activated. At weaker updraft velocities or higher aerosol number concentrations, supersaturations remain low and only a small fraction of the aerosols are activated. These limiting cases are represented in the parameterization, N = N(a)w/(w + dN(a)) derived from Kohler theory, where N is the number of droplets nucleated, N. is the total aerosol number concentration and w is the updraft velocity. The coefficient d depends on the geometric standard deviation of the log-normal aerosol size distribution, the mode radius and the aerosol composition. The parameterization is compared with detailed simulations by a size-resolving Lagrangian parcel model. Differences are found to be less than 50% for realistic aerosol size distributions with aerosol number concentration ranging from 50 to 5000 cm(-3) and updraft velocity ranging from 1 to 500 cm s(-1). Errors in the sensitivity of N to changes in N-a are typically only 10%. Errors are comparable to those of the Twomey parameterization. The simplicity of the parameterization permits its application to three-dimensional atmospheric circulation models that cannot afford a size-resolving treatment of the nucleation process.