A probabilistic bulk model of coupled mixed layer and convection. Part I: Clear-sky case

A new bulk model of the convective boundary layer, the probabilistic bulk convection model (PBCM), is presented. Unlike prior bulk approaches that have modeled the mixed-layer-top buoyancy flux as a constant fraction of the surface buoyancy flux, PBCM implements a newmixed-layer-top entrainment closure based on the mass flux of updrafts overshooting the inversion. This mass flux is related to the variability of the surface state (potential temperature u and specific humidity q) of an ensemble of updraft plumes. The authors evaluate themodel against observed clear-skyweak and strong inversion cases and show that PBCMperforms well. The height, state, and timing of the boundary layer growth are accurately reproduced. Sensitivity studies are performed highlighting the role of the main parameters (surface variances, lateral entrainment). The model is weakly sensitive to the exact specification of the variability at the surface and is most sensitive to the lateral entrainment of environmental air into the rising plumes. Apart from allowing time-dependent top-ofthe-boundary-layer entrainment rates expressed in terms of surface properties, which can be observed in situ, PBCM naturally takes into account the transition to the shallow convection regime, as described in a companion paper. Thus, PBCM represents an important step toward a unified framework bridging parameterizations of mixed-layer entrainment velocity in both clear-sky and moist convective boundary layers.