Impact of entrainment-mixing and turbulent fluctuations on droplet size distributions in a cumulus cloud

The rain formation process in clouds is not fully understood, and its representation in climate models is a significant source of uncertainty. A key variable for rain initiation, the spectral width of the cloud droplet size distributions (DSDs), is critically impacted by entrainment-mixing and turbulent fluctuations in cumulus clouds. This problem is investigated via a new sophisticated modeling framework using the CM1 LES model and a Lagrangian cloud microphysics scheme -- the ``super-droplet method'' (SDM) -- coupled with sub-grid-scale (SGS) schemes for particle transport and supersaturation fluctuations. This modeling framework is used to simulate a cumulus congestus cloud. Average DSDs in different cloud regions show broadening from entrainment and secondary cloud droplet activation (activation above the cloud base). DSD width increases with increasing entrainment-induced dilution as expected from past work, except in the most diluted cloud regions. The new modeling framework with SGS transport and supersaturation fluctuations allows a more sophisticated treatment of secondary activation compared to previous studies. In these simulations, it contributes about 25% of the cloud droplet population and impacts DSDs in two contrasting ways: narrowing in extremely diluted regions and broadening in relatively less diluted. SGS supersaturation fluctuations contribute significantly to an increase in DSD width via condensation growth and evaporation. Mixing of super-droplets from SGS velocity fluctuations also broadens DSDs. SGS supersaturation fluctuations also increases droplet activation near the cloud base by a significant amount. The relative dispersion (ratio of DSD dispersion and mean radius) negatively correlates with grid-scale vertical velocity in updrafts, but is positively correlated in downdrafts. The latter is from droplet activation driven by positive SGS supersaturation fluctuations in grid-mean subsaturated conditions. They have greater influence as the grid length is increased, and they partially compensate for the reduced model resolution.