Combining Non-local Scalings with a TKE Closure for Mixing in Boundary-layer Clouds

A new approach to the parametrization of the cumulus-capped boundary layer is described. It combines a traditional higher-order turbulence closure, appropriate for boundary layers where the skewness of thermodynamic variable probability distributions is low (typically stratocumulus-capped), with non-local scaled similarity functions. These are introduced in order to represent explicitly that part of the distribution arising from skewed cumulus elements and the scalings are found to work very well against equilibrium shallow cumulus large-eddy simulations. Results from a wide range of single column model simulations, from stratocumulus to shallow cumulus to cumulus rising into stratocumulus, are presented that demonstrate the validity of the approach as a means of parametrizing the cloudy boundary layer. Sensitivity tests show that enhancement of the turbulence length scales and the buoyancy production of TKE are especially important.