The Role of Entrainment in the Diurnal Cycle of Continental Convection

In continental convective environments, general circulation models typically produce a diurnal cycle of rainfall that peaks close to the noon maximum of insolation, hours earlier than the observed peak. One possible reason is insufficient sensitivity of their cumulus parameterizations to the state of the environment due to weak entrainment. The Weather Research and Forecasting (WRF) model, run at cloud-resolving (600 and 125 m) resolution, is used to study the diurnal transition from shallow to deep convection during the monsoon break period of the Tropical Warm Pool-International Cloud Experiment. The WRF model develops a transition from shallow to deep convection in isolated events by 1430-1500 local time. The inferred entrainment rate weakens with increasing time of day as convection deepens. Several current cumulus parameterizations are tested for their ability to reproduce the WRF behavior. The Gregory parameterization, in which entrainment rate varies directly with parcel buoyancy and inversely as the square of the updraft speed, is the best predictor of the inferred WRF entrainment profiles. The Gregory scheme depends on a free parameter that represents the fraction of buoyant turbulent kinetic energy generation on the cloud scale that is consumed by the turbulent entrainment process at smaller scales. A single vertical profile of this free parameter, increasing with height above the boundary layer but constant with varying convection depth, produces entrainment rate profiles consistent with those inferred from the WRF over the buoyant depth of the convection. Parameterizations in which entrainment varies inversely with altitude or updraft speed or increases with decreasing tropospheric relative humidity do not perform as well. Entrainment rate at cloud base decreases as convection depth increases; this behavior appears to be related to an increase in vertical velocity at downdraft cold pool edges.