Reinterpretation of cloud-topped mixed-layer entrainment closure

Mixed-layer models of convective boundary layers in the atmosphere and oceans are powerful and useful tools for including important physical processes in general-circulation models of the two media as well as for diagnostic and prognostic studies of air-sea interaction and pollution dispersion. Recently, the appropriate physical and mathematical interpretation of the entrainment closure in such models has come under discussion. In mixed-layer ocean models and models of the dry convective atmospheric mixed layer, the discussion is essentially moot because, when the closure is implemented, its mathematics are independent of the physical interpretation. However, in mixed-layer models of the cloud-topped boundary layer, different physical interpretations lead to quite different mathematical formulations of the closure that yield widely differing results.

In this paper, a new interpretation of the turbulence energetics for the cloud-topped case is discussed. It retains the mathematical simplicity of an earlier approach while allowing consistency with recent numerical results concerning asymmetric diffusivities. Although the definitive study of the problem, by either theoretical, observational or numerical methods, remains for the future, the interpretation of turbulence energetics presented here is sufficiently flexible to be adaptable to new results.