The Importance of the Shape of Cloud Droplet Size Distributions in Shallow Cumulus Clouds. Part I: Bin Microphysics Simulations

In this two-part study, the relationships between the width of the cloud droplet size distribution and the microphysical processes and cloud characteristics of nonprecipitating shallow cumulus clouds are investigated using large-eddy simulations. In Part I, simulations are run with a bin microphysics scheme and the relative widths (standard deviation divided by mean diameter) of the simulated cloud droplet size distributions are calculated. They reveal that the value of the relative width is higher and less variable in the subsaturated regions of the cloud than in the supersaturated regions owing to both the evaporation process itself and enhancedmixing and entrainment of environmental air. Unlike in some previous studies, the relative width is not found to depend strongly on the initial aerosol concentration ormean droplet concentration. Nonetheless, local values of the relative width are found to positively correlate with local values of the droplet concentrations, particularly in the supersaturated regions of clouds. In general, the distributions become narrower as the local droplet concentration increases, which is consistent with the difference in relative width between the supersaturated and subsaturated cloud regions and with physically based expectations. Traditional parameterizations for the relative width (or shape parameter, a related quantity) of cloud droplet size distributions in bulk microphysics schemes are based on cloud mean values, but the bin simulation results shown here demonstrate that more appropriate parameterizations should be based on the relationship between the local values of the relative width and the cloud droplet concentration.