The advantages of using Betts' (1973) liquid-water potential temperature (θl) and also a total moisture variable (qw) within a shallow-cloud numerical model are enumerated. The saturation condition is parameterized as a function of these two variables and pressure, and the subgrid-scale buoyancy flux is expressed in terms of the subgrid-scale vertical fluxes of θl and qw.
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J. W. Deardorff (1976) studied this question.