Gray Zone Partitioning Functions and Parameterization of Turbulence Fluxes in the Convective Atmospheric Boundary Layer

Here, we present the first attempt to fully represent three-dimensional turbulence fluxes in the "Terra Incognita" or the gray zone in other words. In order to derive partitioning functions, representing the partitioning between subgrid and total fluxes, we make use of high-resolution large-eddy simulations (LES), which are performed with the Weather Research and Forecasting (WRF) model. LES computations are performed for various levels of convective instability, ranging from pure buoyant to strongly sheared convection. Then, the resulting reference-LES fields are successively coarse grained from its original microscale grid spacing ( Delta=50 m) up to typical mesoscale grid spacings ( Delta=3 km). The given process is applied by means of an advanced filter, that is, the Butterworth filter. It enables a clear scale-specific filtering that results in a more controlled energy transition from lower to higher wavenumbers, unlike the drawbacks of current filters in use. Finally, we parameterize the subgrid scale (SGS) partitioning functions of 10 SGS turbulence quantities: momentum fluxes (tau(ij), six terms), heat fluxes (q(j), three terms), and turbulence kinetic energy (k). Turbulence partitioning relations are parameterized in a scale-aware, stability-dependent, and height-dependent form, using the sigmoidal Gompertz function. Thus, the new gray zone model provides a framework that bridges the mesoscale and microscale limits and that is suitable for the development of next generation three-dimensional, multiscale turbulence parameterization methods or planetary boundary layer schemes.