Linear eddy modeling of droplet spectral evolution during entrainment and mixing in cumulus clouds

The explicit mixing parcel model (EMPM) of Krueger et al. [Krueger, S.K., Su, C.-W., McMurtry, P.A., 1997. Modeling entrainment and fine-scale mixing in cumulus clouds. J. Atmos. Sci. 54, 2697–2712.] is extended to explicitly account for individual droplet growth. The model provides a 1D representation of physical properties within a cloud parcel and incorporates the rising of the cloud parcel, entrainment of environmental air into the parcel, finite-rate turbulent mixing parameterized by Kolmogorov inertial range scalings, and droplet growth. Because the simulation is performed in a 1D domain, all relevant length scales of the mixing process can be resolved. For the typical domain size used (20 m) in this study, the growth of approximately 2000 droplets is explicitly calculated based on their local environments. Comparisons of computed droplet spectra with spectra obtained from airplane penetration exhibit good agreement. Further results showing effects of entrained CCN, droplet sedimentation and mixing rates on droplet spectral evolution are provided.