Third-Order Moment Closure Through A Mass-Flux Approach

The parameterization of the third moments, the flux of the heat flux and the flux of the potential temperature variance, is considered. It is shown that present parameterizations of these moments using the mass-flux approach with a `top-hat' profile assumption lead to a significant underestimation, resulting in an inaccurate representation of second moments in the convective boundary layer. It is also shown that the underestimation is a result of the `top-hat' profileassumption in which the sub-plume contributions to the total fluxes are ignored. By including these contributions a new parameterization is proposed, whichsatisfies the physical requirements of symmetry andrealizability, and gives results that are in fair agreement with thelarge-eddy simulation data.