Estimating Phase Transition Rates in Shallow Cumulus Clouds from Mass
Flux. Part I: Theory and Numerical Simulations
Abstract
The system of trade wind cumulus clouds observed during the RICO field
project was simulated by an LES model in a domain of the size of a
mesoscale model grid. More than 2000 clouds were analyzed by stratifying
them by their cloud-top heights. The investigation was focused on phase
transition rates (TR), which in warm tropical clouds are represented by
the processes of condensation/evaporation. We previously demonstrated
(Kogan, 2021a), based on LES data, that a nearly perfect correlation (R
= 0.99) exists between upward mass flux (MFP) and condensation rate
(CR), and that the correlation between MFP and evaporation rate (ER) is
only slightly lower (R = 0.98). The strong dependence of TR on MFP and
the linear relationship between them were explained by applying
condensation theory and the concept of “quasi-steady” supersaturation.
The LES-derived slope of the linear TR−MFP relationship agreed with its
theoretical value, with an error of less than 5%. This result implies
that supersaturation in clouds, on average, varies within a few
percentage points of its quasi-steady value. In our analysis we
considered parameters characterizing cloud as a whole; that is,
parameters integrated over the cloud volume. However, condensation
theory and LES data show that the linear fit is applicable to local
variables and therefore may be integrated to obtain relationships for
horizontally averaged variables. Expanding the TR−MFP relationship to
vertically dependent variables may provide the framework for development
of sub-grid scale latent heat release parameterization.