A Mixed-Layer Model Of The Well-Mixed Stratocumulus-Topped Boundary Layer

Recently a range of sophisticated large-eddy simulations of thecloud-topped boundary layer have been intercompared and furthercompared with observations and single column models. Here we comparethese results with perhaps the simplest model of the cloud-toppedboundary layer, namely a mixed-layer model. Results from the model aredescribed with two aims in mind. Firstly, the good results act as areminder of the success of simple models, and, secondly, we suggestthat a simple mixed-layer model could be used as a baseline for futuremodel intercomparisons.The mixed-layer model is based on two assumptions that follow previousstudies. Firstly, the liquid-water potential temperature and the total waterspecific humidity are assumed to be constant with height in the boundarylayer. Secondly, turbulence entrains air across the inversion into the boundarylayer at a rate that is assumed to be proportional to the jump in radiative flux at the cloud top and inversely proportional to the jump in buoyancy at the inversion. The constant of proportionality is called the entrainment efficiency.Results from the model for the entrainment rate and height evolutionof the boundary layer are compared with the observations and modelsconsidered in a EUCREM intercomparison study. Thepresent mixed-layer model accurately predicts the observed heightevolution of the boundary layer, but over-estimates the entrainmentrate to a similar degree as the large-eddy simulations. We show that,if the subsidence rate is reduced to the value given by observationsrather than the value used in the EUCREM intercomparison study,then the model agrees well with observed value of the entrainment rateif the entrainment efficiency is taken to be 0.6. With this value, themodel also agrees well with a further case study byBechtold et al. An entrainment efficiency of 0.6 is a little higherthan suggested by large eddy simulations, but such simulations do notcurrently resolve the entrainment events explicitly. Hence this pointdeserves further study.