Analytic and numerical calculations of the formation of a sulphuric acid aerosol in the upper troposphere

Analytic and numerical calculations are performed on the production of sulphuric acid aerosol in conditions of a very large nucleation event observed in the upper troposphere. The numerical results feature a growing peak in the size distribution whose magnitude is reproduced well analytically, and are consistent with the observed particle number concentration at sizes greater than 25 nm (measured dry diameter), but suggest that most of the aerosol was at unobserved smaller sizes. Because of growth and coagulation, number concentrations of the aerosol rapidly become independent of the number initially nucleated, so that conclusions as to the nucleation process, either homogeneous or ion-induced nucleation, cannot easily be drawn from existing atmospheric observations. The final concentration is very insensitive to the magnitude of the SO₂ source, but, if condensation on, and coagulation with, a remnant background aerosol occurs, such nucleation events will be cut off for source magnitudes less than a specific value. Anthropogenic emissions of SO₂ which exceed this value can produce higher aerosol number concentrations in the atmosphere with consequences for the indirect effect of aerosols on the climate.