A mass flux scheme view of a high-resolution simulation of a transition from shallow to deep cumulus convection

In this paper, an idealized, high-resolution simulation of a gradually forced transition from shallow, nonprecipitating to deep, precipitating cumulus convection is described; how the cloud and transport statistics evolve as the convection deepens is explored; and the collected statistics are used to evaluate assumptions in current cumulus schemes. The statistical analysis methodologies that are used do not require tracing the history of individual clouds or air parcels; instead they rely on probing the ensemble characteristics of cumulus convection in the large model dataset. They appear to be an attractive way for analyzing outputs from cloud-resolving numerical experiments. Throughout the simulation, it is found that 1) the initial thermodynamic properties of the updrafts at the cloud base have rather tight distributions; 2) contrary to the assumption made in many cumulus schemes, nearly undiluted air parcels are too infrequent to be relevant to any stage of the simulated convection; and 3) a simple model with a spectrum of entraining plumes appears to reproduce most features of the cloudy updrafts, but significantly overpredicts the mass flux as the updrafts approach their levels of zero buoyancy. A buoyancy-sorting model was suggested as a potential remedy. The organized circulations of cold pools seem to create clouds with larger-sized bases and may correspondingly contribute to their smaller lateral entrainment rates. Our results do not support a mass-flux closure based solely on convective available potential energy (CAPE), and are in general agreement with a convective inhibition (CIN)-based closure. The general similarity in the ensemble characteristics of shallow and deep convection and the continuous evolution of the thermodynamic structure during the transition provide justification for developing a single unified cumulus parameterization that encompasses both shallow and deep convection.