The parametrization of entrainment in cloudy boundary layers

A parametrization for the entrainment rate in shear-free convective cloud-c apped boundary layers is derived. The only information it requires is the e xternal mixed-layer turbulence forcings (the surface buoyancy flux and the net radiative-divergence profile), the inversion jumps of temperature and h umidity, the cloud-top liquid water mixing ratio and the cloud and mixed-la yer depths. Despite this simplicity it is found to compare well against bot h a wide range of large-eddy simulations and observations of stratocumulus. The parametrization is an extension of those derived previously for the ide alised cases of smoke clouds, where turbulence is driven by combinations of surface heating and radiative cooling, and liquid water clouds driven sole ly by buoyancy reversal. The radiative forcing is specified as an indirect forcing, through the buoyant production of turbulence within the boundary l ayer and a direct forcing, which promotes deepening of the boundary layer w hen undulations in the cloud top cause part of the cooling to occur within the horizontally averaged inversion. Condensation of water in saturated air reduces the strength of both these terms but otherwise, for radiatively dr iven liquid water clouds (where evaporative cooling of entrained air does n ot generate buoyancy reversal), the parametrization is unchanged from that for smoke clouds. Where evaporative cooling of entrained air is strong enough to generate buo yancy reversal, and therefore drive convective motions, not only does it pr ovide an additional turbulence source, but it is also found to compensate f or the reduction in strength of the radiative-forcing terms by the presence of saturated air. Allowing for this enhancement, the entrainment rate is p redicted with remarkable accuracy by the sum of previously derived parametr izations for the rates that would have been generated by radiative cooling and buoyancy reversal acting in isolation.