The continuity equation for the stratospheric aerosol and its characteristic curves

A four-dimensional continuity equation for particles undergoing growth proc ess in the atmosphere is introduced. It is applied to the stratospheric aer osol in the simplified case of two dimensions under the assumption of horiz ontal homogeneity. In the radius range beyond which coagulation is importan t, the analytical solution of the equation gives the characteristic curve f or the aerosol in the stratosphere and determines the relation between the growth and the settling distance of the particle. This relation, which incl udes the effect of a background vertical motion, essentially determines the aerosol size distribution The resulting size distribution is too narrow in comparison with observations, but introducing diffusive processes into the governing continuity equation results in a size distribution close to that observed. The approximate analytic results give insight into the relative roles of condensation, particle fail velocity, vertical motion. and diffusi on in determining the aerosol size distribution, which are verified by nume rical calculation.