The validity of the kinetic collection equation revisited L. Alfonso1, G. B. Raga2, and D. Baumgardner2 1Universidad Autónoma de la Ciudad de México, México City, 09790, México 2Centro de Ciencias de la Atmósfera, Universidad Nacional Autonoma de Mexico, Mexico City, 04510, México
Abstract. The kinetic collection equation (KCE) describes the evolution of the average
droplet spectrum due to successive events of collision and coalescence.
Fluctuations and non-zero correlations present in the stochastic coalescence
process would imply that the size distributions may not be correctly modeled
by the KCE.
In this study we expand the known analytical studies of the coalescence
equation with some numerical tools such as Monte Carlo simulations of the
coalescence process. The validity time of the KCE was estimated by
calculating the maximum of the ratio of the standard deviation for the
largest droplet mass over all the realizations to the averaged value. A good
correspondence between the analytical and the numerical approaches was found
for all the kernels. The expected values from analytical solutions of the
KCE, were compared with true expected values of the stochastic collection
equation (SCE) estimated with Gillespie's Monte Carlo algorithm and
analytical solutions of the SCE, after and before the breakdown time.
The possible implications for cloud physics are discussed, in particular the
possibility of application of these results to kernels modified by
turbulence and electrical processes.
Citation: Alfonso, L., Raga, G. B., and Baumgardner, D.: The validity of the kinetic collection equation revisited, Atmos. Chem. Phys., 8, 969-982, doi:10.5194/acp-8-969-2008, 2008.