Investigation of the Gamma Distribution Shape Parameter in Shallow Cumulus Clouds

Many bulk microphysics parameterizations assume that the droplet size distribution (DSD) of hydrometeor species such as cloud water and rain water conform to a gamma probability distribution function (PDF). Such an assumption is necessary in order to simplify the description of microphysical processes in such bulk parameterizations. The gamma PDF has a parameter that influences the width of the distribution that is commonly referred to as the shape parameter. In one- and two-moment bulk microphysics schemes, this parameter is often arbitrarily set to a fixed value throughout the simulation. This is in part due to limited observations of the shape parameter. While many studies have sought to understand this parameter for rain, few studies examine this parameter for cloud droplets.

In this study, we use high-resolution simulations of shallow cumulus clouds with a spectral bin representation of the hydrometeor species to find best-fit parameters of the gamma PDF to the predicted cloud DSDs. These simulations reveal that the cloud shape parameter is high in the supersaturated regions of the cloud and low in regions where the cloud water is evaporating. Values many times higher than the standard values of 1-4 are not uncommon in the bin simulations. The results of this analysis are used to suggest appropriate values of the cloud shape parameter in simulations employing a bulk microphysics scheme. The sensitivity of cloud properties, dynamics, and rainfall to the cloud shape parameter are investigated in simulations in which the parameter is fixed. Conclusions about the importance of choosing an appropriate cloud shape parameter for simulating cumulus clouds in climate or weather models are drawn.