On the entrainment rate of a stratocumulus‐topped mixed layer

Abstract The forced entrainment rate at the top of a stratocumulus deck is derived from the assumption that the negative buoyancy flux there is a particular fraction (1/2) of the average buoyancy flux within the entire mixed layer. A portion of the cloudtop radiative cooling is allowed to occur below the inversion base, thus contributing to the maintenance of the mixed‐layer turbulence. The derived equation clearly shows the dependence of the forced entrainment rate upon the surface heat and moisture fluxes, cloudtop radiative cooling rate, temperature and humidity jumps across the capping inversion, solar absorption rate within the mixed layer, and percentage of the mixed layer occupied by stratocumulus. The forced entrainment rate becomes inapplicable when the thermal jump at cloudtop becomes very small; then either encroachment or free entrainment occurs, and expressions are proposed for each. A useful criterion is that the entrainment rate is the minimum of the calculated rates for forced entrainment, encroachment, and free entrainment. The equation is tested satisfactorily against observations of coastal stratus off California and stratocumulus development over Lake Michigan.