A turbulence closure for the convective boundary layer based on a two-scale mass-flux approach

The closure problem for the convective turbulence of the shear-free and low to moderate wind atmospheric boundary layer is considered. Non-Gaussian parameterizations are developed for fourth-order moments based on a two-scale mass-flux approach. With this approach the ballistic stirring of fluid by coherent structures is taken into account and the differences in the horizontal scales and spacing of the velocity and temperature fields are recognized. The fractional coverage of positive temperature variations is introduced, as well as the fractional coverage of positive vertical velocity fluctuations. The parameterizations are compared to those of the traditional mass-flux scheme and of the classical eddy-damped quasi-normal approach, and the principal similarities and dissimilarities are outlined. The results of testing the parameterizations against aircraft measurements at moderate wind and against large eddy simulation data of free convective conditions show good agreement between model predictions and data.