Effects of Variable Droplet Growth Histories on Droplet Size Distributions. Part I: Theory

Abstract

A theoretical framework is developed that permits estimation of the effects of fluctuating supersaturation on the development of cloud droplet size spectra. The studies focus on the role of turbulent fluctuations in vertical wind and in the microphysical environments in which droplets grow, and represent the effects of droplets mixing together that have encountered different trajectories through the cloud. It is contended that the effects can be analyzed in terms of two contributions to the variance in supersaturation history, one dependent on the average microphysical environment (specifically, integral radius) of the near environment in which a droplet grows, and the other dependent on the correlation between the integral radius and the updraft along the droplet trajectory. Variations in the possible trajectories that all end at a given point (and so form the droplet spectrum there) are used to estimate the possible widths of droplet spectra, and methods of testing these predictions using experimental data are also proposed. Possible broadening effects due to fluctuations in the updraft at cloud base are also analyzed. It is suggested that simple turbulent motions in a stochastically varying cloud may provide significant broadening of the cloud droplet spectrum if those motions are accompanied by a variable microphysical structure produced by dry-air entrainment.