The impact of fluctuations and correlations in droplet growth by collision-coalescence revisited. Part I: Numerical calculation of post-gel droplet size distribution
Lester Alfonso1 and Graciela B. Raga21Universidad Autónoma de la Ciudad de México, México City, 09790 México 2Centro de Ciencias de la Atmósfera, UNAM, México City, 04510 México
Received: 16 Oct 2016 – Accepted for review: 25 Nov 2016 – Discussion started: 29 Nov 2016
Abstract. The impact of stochastic fluctuations in cloud droplet growth is a matter of broad interest, since stochastic effects are one of the possible explanations of how cloud droplets cross the size-gap and form the raindrop embryos that trigger warm rain development in cumulus clouds. Most theoretical studies in this topic rely on the use of the kinetic collection equation, or the stochastic simulation algorithm (Gillespie 1975). However, the kinetic collection equation is a deterministic equation with no stochastic fluctuations. Moreover, the traditional calculations using the kinetic collection equation are not valid when the system undergoes a transition from a continuous distribution to a distribution plus a runaway raindrop embryo (known as the sol-gel transition). On the other hand, the stochastic simulation algorithm, although intrinsically stochastic, fails to reproduce adequately the large end of the droplet size distribution due to the huge number of realizations required. Therefore, the full stochastic description of cloud droplet growth must be obtained from the solution of the master equation for stochastic coalescence.
In this study the master equation is used to calculate the evolution of the droplet size distribution after the sol-gel transition. These calculations show that after the formation of the raindrop embryo, the expected droplet mass distribution strongly differs from the results obtained with the kinetic collection equation. Furthermore, the low mass bins and bins from the gel fraction are strongly anti-correlated in the vicinity of the critical time, this being one of the possible explanations for the differences between the kinetic and stochastic approaches after the sol-gel transition. Calculations performed within the stochastic framework provide insight into the inability of explicit microphysics cloud models to explain the droplet spectral broadening observed in small, warm clouds.
Alfonso, L. and Raga, G. B.: The impact of fluctuations and correlations in droplet growth by collision-coalescence revisited. Part I: Numerical calculation of post-gel droplet size distribution, Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-922, in review, 2016.