Estimating Phase Transition Rates in Shallow Cumulus Clouds from Mass Flux. Part I: Theory and Numerical Simulations

Abstract

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, 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 subgrid-scale latent heat release parameterization. Significance Statement This study investigated condensation/evaporation processes in tropical cumulus clouds. The energy exchanged during these processes is an important driving force behind a wide range of atmospheric phenomena. We found theoretically, and confirmed in computer simulations, that the rate of condensation/evaporation can be expressed as a linear function of the cloud vertical velocity. This finding suggests a new approach to calculate cloud energy transformations in numerical weather prediction models.