Breaking a turbulence parameterization: a comparison of a stochastic eddy diffusivity mass flux scheme to scale dependent statistics from coarse graining of a large eddy simulation

The so-called "gray zone" or "terra incognita" of atmospheric length scales offers a significant challenge to parameterization development. These scales lie between the large scales where ensemble means of turbulent fluctuations are well approximated by spatial means and the small scales where the instantaneous variability becomes relatively unimportant. In this work we describe the scale dependent breakdown within the gray zone of a stochastic Eddy Diffusivity Mass Flux (EDMF) scheme for the dry convective boundary layer. The breakdown is identified by the divergence of stochastic EDMF single column model statistics from the scale dependent conditional statistics computed by coarse graining results from a large eddy simulation that spans the gray zone. Results will be reported for various formulations of the stochastic component of the EDMF scheme and ways to adopt the EDMF framework for scale-aware parameterizations will be discussed.