The Continuity Equation for the Stratospheric Aerosol and Its Characteristic Curves

A four-dimensional continuity equation for particles undergoing growth process in the atmosphere is introduced. It is applied to the stratospheric aerosol in the simplified case of two dimensions under the assumption of horizontal homogeneity. In the radius range beyond which coagulation is important, the analytical solution of the equation gives the characteristic curve for the aerosol in the stratosphere and determines the relation between the growth and the settling distance of the particle. This relation, which includes 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 fall velocity, vertical motion, and diffusion in determining the aerosol size distribution, which are verified by numerical calculation.