A long-standing problem in cloud microphysics is the difference in width of observed and modeled droplet size distributions from condensation. One hypothesis for the difference, explored here, is that the droplets can experience largely different supersaturation histories depending upon their individual trajectories through the cloud, and these differences result in a variety of different droplet sizes at a given location in the cloud. Classical calculations of droplet growth by condensation ignore such variations in supersaturation and result in a narrower drop size distribution than those commonly observed.

The study presented here is an exploration of supersaturation variations in a cloud using numerical modeling. A numerical simulation of a warm cumulus in two dimensions with high spatial resolution (<50 m) provides the backdrop for the calculations. Novel approaches for parameterizing the sub-grid scale turbulence are explored, because of the large gap between the droplet size scale and the smallest grid spacing in the 2D model. At various points in the simulated cloud, droplet trajectories are run backward, using a first guess of the droplet sizes, and shrinking the droplets accordingly along the trajectories. The trajectories are then run forward, growing the droplets according to a condensation model that incorporates the bulk microphysical properties from the simulated cloud. This process is repeated until the results have converged. The resulting computed droplet size distributions are compared in a general sense with those observed during the Small Cumulus Microphysics Study, which have been corrected for artificial broadening by the measurement probe. The results of this study will demonstrate if variations in supersaturation histories can result in droplet size variations large enough to explain the width of the droplet size distributions commonly observed.