The system of trade wind cumulus clouds observed during the RICO field project was simulated by an LES model over a domain size of a mesoscale model grid. More than 2000 clouds were analyzed by stratifying them by their size/stage of maturity. The investigation was focused on phase transition rates, which in warm tropical clouds are represented by the processes of condensation/evaporation. Data from LES simulations of shallow cumulus clouds demonstrated a nearly perfect correlation between condensation rate (CR) and upward (positive) mass flux (MFP). This strong correlation is explained using the condensation theory. The strong CR-MFP correlation implies that supersaturation in clouds varies within a few percent of its quasi-steady value. Calculating the slope of the CR-MFP linear fit from concurrent measurements of temperature and vertical velocity, and comparing it with the corresponding slope based on the quasi-steady supersaturation assumption, may provide a method for estimating the supersaturation in clouds. The strong dependence of condensation rates on vertical velocity may indicate the direction for development of SGS latent heat release parameterization.