A Numerical Experiment on Stochastic Condensation Theory

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Abstract
A three-dimensional numerical model is used to study the effect of small-scale supersaturation fluctuations on the evolving droplet distribution in the first 150 m above cloud base. The primary purpose of this research is to determine whether the irreversible coupling between the thermodynamics and dynamics due to finite phase relaxation time scales τs is sufficient to produce significant small-scale horizontal variations in supersaturation. Thus, the paper is concerned only with this internal source for thermodynamic variability. All other source terms, such as the downgradient flux of the variance of thermodynamic fields, have purposely been neglected. Lagrangian particle experiments were run in parallel with the basic Eulerian model. The purpose of these experiments is to relax some of the microphysical parameterization assumptions with respect to assumed distribution shape and as a result add credibility to the results of distribution broadening. Model results of five cases are presented, representing the cloud condensation nuclei characteristics of typical continental and maritime cumulus with mean dissipation rate of −100 cm2 s−3. The results show that for a maritime case of N≈100 cm−3 and w¯=0.5 m s−1 the standard deviation of the supersaturation is as large as its horizontal mean. The horizontal variability of all thermodynamic fields is shown to increase significantly with τs. The droplet broadening response to this irreversible coupling effect is found to be significant for the larger values of τs in the Eulerian experiments. The Lagrangian particle experiments showed a somewhat reduced but still significant effect. Although the experiments do show a broadening effect caused by finite values of τs, in no case were we able to show a continual increase in distribution broadening with height as reported from cumulus observations.

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