An Improved Double-Gaussian Closure for the Subgrid Vertical VelocityProbability Distribution Function

The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the loweratmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallowcumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent awide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence toshallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of themodel closures are found to perform well in the former case, the latter presents a considerable challenge.A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloudlayers. The well-established parabolic relationship between skewness and kurtosis is examined, with results inagreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified re-lationship is necessary to improve performance. The new closure significantly improves the estimation of thevertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. Inparticular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remainowing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.