A probabilistic bulk model of coupled mixed layer and convection. Part II: Shallow convection case

The probabilistic bulk convection model (PBCM) developed in a companion paper is here extended to shallow nonprecipitating convection. The PBCM unifies the clear-sky and shallow convection boundary layer regimes by obtaining mixed-layer growth, cloud fraction, and convective inhibition from a single parameterization based on physical principles. The evolution of the shallow convection PBCM is based on the statistical distribution of the surface thermodynamic state of convective plumes. The entrainment velocity of the mixed layer is related to the mass flux of the updrafts overshooting the dry inversion capping the mixed layer. The updrafts overcoming the convective inhibition generate active cloudbase mass flux, which is the boundary condition for the shallow cumulus scheme. The subcloud-layer entrainment velocity is directly coupled to the cloud-base mass flux through the distribution of vertical velocity and fractional cover of the updrafts. Comparisons of the PBCM against large-eddy simulations from the Barbados Oceanographic and Meteorological Experiment (BOMEX) and from the Southern Great Plains Atmospheric Radiation Measurement Program (ARM) facility demonstrate good agreement in terms of thermodynamic structure, cloud-base mass flux, and cloud top. The equilibrium between the cloud-base mass flux and rate of growth of the mixed layer determines the equilibrium convective inhibition and cloud cover. This process is an important new insight on the coupling between the mixed-layer and cumulus dynamics. Given its relative simplicity and transparency, the PBCM represents a powerful tool for developing process-based understanding and intuition about the physical processes involved in boundary layer-convection interactions, as well as a test bed for diagnosing and validating shallow convection parameterizations.