Estimating nucleation rates from apparent particle formation rates and vice versa: Revised formulation of the Kerminen–Kulmala equation

Connections between observed particle formation rates (typically at diameter 3 nm or larger) and the actual nucleation rates have important applications in atmospheric science. First, nucleation theories can be evaluated and second, semi-empirical particle formation rates can be developed for large scale models that neglect the cumbersome initial steps of formation and growth. Kerminen and Kulmala, by estimating the particle formation rate, nucleation mode growth rate and scavenging rate onto background particles (coagulation sink) from measured size distribution evolution, derived a simple yet rather accurate formula for this purpose [Kerminen V.-M., Kulmala, M. (2002). Analytical formulae connecting the “real” and the “apparent” 25 nucleation rate and the nuclei number concentration for atmospheric nucleation events, Journal of Aerosol Science 33, 609–622]. The present work reformulates the original theory in a way that two drawbacks are eliminated: (1) the original expression was derived using a slightly inaccurate coagulation sink dependence on particle size and (2) was based on knowing the condensation sink which requires knowledge of the condensing vapors.