Parameterizations of deep cumulus convection employ a wide variety of assumptions about how the cumulus cloud ensemble and associated fluxes of heat, moisture and momentum relate to large-scale variables. Frequently, a shallow cumulus parameterization is also used, and often employs another incompatible set of assumptions. We use an idealized simulation of a transition from shallow, nonprecipitating to deep, precipitating cumulus convection to explore how the cloud and transport statistics evolve as the convection deepens. Our simulation starts from the sounding and forcings of a classic and well-studied oceanic trade cumulus boundary layer (BOMEX) then slowly ramps up the surface latent and sensible heat fluxes, forcing the convection to slowly deepen over a period of days. We use the Colorado State University cloud resolving model (courtesy Marat Khairoutdinov) on a 12.8x12.8x28 km domain with 100 m horizontal and 50 m vertical resolution to resolve turbulent mixing processes.

To analyze the statistics of the cloud ensemble at each time, we bin the gridpoints at each vertical level using a roughly conservative variable, moist static energy. Within the cloud layer, high moist static energy corresponds to cloudy air that is less diluted by entrainment and more buoyant. We can segregate the vertical velocity, mass flux, and other properties of cloud ensemble in a similar way, and interpret the results in terms of a family of entraining plumes. We find that most cumulus updrafts lie in a fairly narrow range of effective entrainment rates, and that the mean buoyancy of cloudy updrafts is quite small and far less than the adiabatic value. We suggest that the mean updraft buoyancy may be controlled by the penetrative entrainment induced by overshooting cumuli. We also find that there is no qualitative difference between the statistics of the shallow and deep cumulus layers, and suggest implications for cumulus parameterizations.