Analytical formulae connecting the “real” and the “apparent” nucleation rate and the nuclei number concentration for atmospheric nucleation events

A simple yet relatively accurate analytical formula has been derived between the “real” atmospheric nucleation rate and the rate at which the resulting clusters, or nuclei, appear at some larger size (the “apparent” nucleation rate) as a result of their growth by condensation. In addition, another analytical formula was derived that connects the nucleation rate and the total nuclei concentration in a desired size range. The derived formulae are applicable to situations in which there are no major fluctuations in the pre-existing particle size distribution or in the concentration of vapours responsible for the nuclei growth, and in which the total nuclei number concentration remains sufficiently low (<105–106 nuclei cm−3) to prevent effective self-coagulation between the nuclei. With the help of these formulae, an explicit nucleation scheme can be included into an atmospheric model without the requirement that the modelled particle diameter range must be extended down to one nanometer. In field measurements only the “apparent” nucleation rate can currently be determined. The derived formulae provide a means to convert this rate to a “real” nucleation rate, making it possible to test more rigorously the viability of different nucleation theories under atmospheric conditions.