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A simple method is proposed to extend a low-order turbulence scheme including a subgrid-scale cloudiness scheme to represent not only nonconvective (stratiform) cloudiness and turbulence but also shallow, nonprecipitating cumulus convection by utilizing an appropriate subgrid-scale distribution function. A simple approach is chosen that avoids the knowledge of the skewness parameter. All cloud water-related variables (cloud water content, partial cloudiness, liquid water flux) are computed by interpolating linearly as a function of the saturation deficit between two limit cases: the stratocumulus case, which can be well represented by a Gaussian distribution function, and the trade wind cumulus case, characterized by a positively skewed distribution function with a skewness of 2. Comparisons of the scheme with a third-order turbulence scheme and large-eddy simulations (LES) for the Puerto Rico Field Experiment show satisfying results. It is shown that the liquid water flux term, which is strongly dependent on the distribution chosen, is the crucial parameter of the scheme.
Bechtold et al. (Wed,) studied this question.