1Universidad Autónoma de la Ciudad de México, México City, 09790 México
2Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, México City, 04510 México
Received: 19 Jan 2010 – Published in Atmos. Chem. Phys. Discuss.: 05 Mar 2010
Abstract. The kinetic collection equation (KCE) has been widely used to describe the evolution of the average droplet spectrum due to the collection process that leads to the development of precipitation in warm clouds. This deterministic, integro-differential equation only has analytic solution for very simple kernels. For more realistic kernels, the KCE needs to be integrated numerically. In this study, the validity time of the KCE for the hydrodynamic kernel is estimated by a direct comparison of Monte Carlo simulations with numerical solutions of the KCE. The simulation results show that when the largest droplet becomes separated from the smooth spectrum, the total mass calculated from the numerical solution of the KCE is not conserved and, thus, the KCE is no longer valid. This result confirms the fact that for kernels appropriate for precipitation development within warm clouds, the KCE can only be applied to the continuous portion of the mass distribution.
Revised: 07 Jul 2010 – Accepted: 07 Jul 2010 – Published: 05 Aug 2010
Alfonso, L., Raga, G. B., and Baumgardner, D.: The validity of the kinetic collection equation revisited – Part 2: Simulations for the hydrodynamic kernel, Atmos. Chem. Phys., 10, 7189-7195, doi:10.5194/acp-10-7189-2010, 2010.