Broadening of droplet size distributions from entrainment and mixing in a cumulus cloud

Quantitative predictions of the relationship between the droplet size-distribution width and entrainment in warm cumulus have been elusive, largely because of the difficulty in representing the extent of the scales involved, A new modelling framework is presented as a first step toward quantitative predictions of droplet size distributions resulting from entrainment, consisting of a three-dimensional cloud model coupled with a Lagrangian microphysical parcel model. The cloud model represents turbulent cloud dynamics but parametrizes microphysical processes such as condensation, and the parcel model complements this approach by performing explicit microphysical calculations within the kinematic and thermodynamic constraints established by the cloud model. The parcel model is run along trajectories all ending at the same point in the cloud, and the individual droplet size distributions are averaged together at this point to represent the turbulent mixing together of the droplets produced by these different parcel trajectories. The results replicate some important features of observed cloud droplet size distributions, including large widths, the continued presence of small droplets high in the clouds, and the bimodal structure. The origin of these features in these calculations is the variability introduced by entrainment, which leads to possibilities for droplets to encounter varying supersaturation histories during their transit through the cloud to the point of observation. Droplet sizes larger than those calculated for adiabatic ascent are also produced, with possible implications for coalescence initiation.