Evaporative cooling amplification of the entrainment velocity in radiatively driven stratocumulus

Evaporative cooling monotonically increases as the thermodynamical properties of the inversion allow for more evaporation in shear-free radiatively driven stratocumulus. However, the entrainment velocity can deviate from the evaporative cooling trend and even become insensitive to variations in the inversion properties. Here the efficiency of evaporative cooling at amplifying the entrainment velocity is quantified by means of direct numerical simulations of a cloud top mixing layer. We demonstrate that variations in the efficiency modulate the effect of evaporative cooling on entrainment, explaining the different trends. These variations are associated with the evaporation of droplets in cloud holes below the inversion point. The parametrization of the efficiency provides the evaporative amplification of the entrainment velocity as a function of a single parameter that characterizes the inversion. The resulting entrainment velocities match our experiments and previous measurements to within +/- 25%. The parametrization also predicts the transition to a broken-cloud field consistently with observations.