An eddy-diffusivity/mass-flux approach to the vertical transport of turbulent kinetic energy in convective boundary layers

In this study a new approach to the vertical transport of the turbulent kinetic energy (TKE) is proposed. The principal idea behind the new parameterization is that organized updrafts or convective plumes play an important role in transferring TKE vertically within convectively driven boundary layers. The parameterization is derived by applying an updraft-environment decomposition to the vertical velocity triple correlation term in the TKE prognostic equation. The additional mass-flux (MF) term that results from this decomposition closely resembles the features of the TKE transport diagnosed from large-eddy simulations (LES), and accounts for 97% of the LES diagnosed transport when the updraft fraction is set to 0.13. Another advantage of the MF term is that it is a function of the updraft vertical velocity, and can be readily calculated using already existing parameterization. The new MF approach, combined with several eddy-diffusivity formulations, is implemented into a simplified 1D TKE prognostic model. The 1D model results, compared against LES simulations of dry convective boundary layers, show substantial improvement in representing the vertical structure of TKE. The new combined eddy-diffusivity/mass-flux parameterization, as well as the MF term alone, surpasses in accuracy the eddy-diffusivity parameterizations. The proposed TKE transport parameterization shows large potential of improving TKE simulations in mesoscale and global circulation models.