Estimating Phase Transition Rates in Shallow Cumulus Clouds from Mass Flux. Part II: Vertically Dependent Formulation

Abstract This work continued the investigation of the relationship between phase transition rates and mass flux in trade wind cumulus clouds. The latter was simulated by an LES model initialized with soundings from the Rain in Cumulus over the Ocean (RICO) field project. In Part I, we demonstrated that a very high correlation exists between integral phase transition rates and upward mass flux. In this study, we focused on the vertically dependent variables and showed that a similar high correlation exists between the condensation rate and the upward mass flux . Based on condensation theory, we showed that under quasi-steady approximation condensation rates can be calculated by a linear function of with the slope coefficient dependent only on temperature and pressure. The model data showed that the error of such approximation is less than a few tenths of a percent. The parameterization of the evaporation process is more complex, mostly because of the slow evaporation of raindrops as they fall through the cloud’s unsaturated areas. Nevertheless, it was possible to define the fraction of the evaporation to condensation rate as a function of vertical coordinate z and cloud thickness H . This function can be quite accurately approximated by the third-order polynomials of z and H . It is suggested that the proposed formulation of evaporation together with the quasi-steady formulation of condensation can serve as a parameterization of water phase transition rates in shallow cumulus clouds. 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. It was found that the vertical distribution of this energy source can be expressed as a linear function of cloud updrafts. This finding suggests a new approach to calculate cloud energy transformations in numerical weather prediction models.