Mission 12 of the first Aerosol Characterization Experiment was flown by the National Center for Atmospheric Research C-130 research aircraft to observe stratocumulus cloud decks over the remote Southern Ocean. The objective of the flight was the investigation of the impact of clouds on the formation and destruction of aerosol in the boundary layer. The principle focus of this paper is an examination of the thermodynamic structure and a quantification of the entrainment rate. Three methods are presented. The first method uses the thermodynamic budget of the boundary layer to calculate its evolution over time. The second uses turbulence flux observations near the inversion, while the third uses estimates of the subsidence rate together with direct observations of the rate of change of cloud top height. All three methods suffer from serious errors. Our best estimate for the entrainment rate is 4 mm s-1 with an uncertainty of at least 50%. Based on an analysis of the boundary layer evolution in a mixing diagram, entrainment rates larger than about 8 mm s-1 can probably excluded because these larger entrainment rates would impose an unrealistic thinning of the cloud layer. Similarly, entrainment rates smaller than 2 mm s-1 can be excluded as well on the basis that this would impose unrealistic thickening of the cloud layer. The boundary layer is mostly buoyancy-driven, with shear-generated turbulence at most only half of the buoyancy-generated turbulence. ¿ 1998 American Geophysical Union