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The role of the gamma function shape parameter in determining differences...

Igel, A. L., and S. van den Heever (2017), The role of the gamma function shape parameter in determining differences between condensation rates in bin and bulk microphysics schemes, Atmos. Chem. Phys., 17, 4599-4609, doi:10.5194/acp-17-4599-2017.
Abstract: 

The condensation and evaporation rates predicted by bin and bulk microphysics schemes in the same model framework are compared in a statistical way using simulations of non-precipitating shallow cumulus clouds. Despite other fundamental disparities between the bin and bulk condensation parameterizations, the differences in condensation rates are predominantly explained by accounting for the width of the cloud droplet size distributions simulated by the bin scheme. While the bin scheme does not always predict a cloud droplet size distribution that is well represented by a gamma distribution function (which is assumed by bulk schemes), this fact appears to be of secondary importance for explaining why the two schemes predict different condensation and evaporation rates. The width of the cloud droplet size is not well constrained by observations, and thus it is difficult to know how to appropriately specify it in bulk microphysics schemes. However, this study shows that enhancing our observations of this width and its behavior in clouds is important for accurately predicting condensation and evaporation rates.

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