Implementation of a Total Turbulent Energy (TTE)-based Eddy-Diffusivity Mass-Flux (EDMF) Vertical Turbulent Mixing Scheme in the NCEP GFS

A total turbulent energy (TTE)-based eddy-diffusivity mass-flux (EDMF) vertical turbulent mixing scheme is developed for the National Centers for Environmental Prediction's (NCEP) Global Forecast System (GFS). The TTE is the sum of the turbulent kinetic energy (TKE) and turbulent potential energy (TPE) which is proportional to the potential temperature variance. One problem of the TKE-based scheme for the vertical turbulence mixing is the buoyancy destruction term under stable stratification, which causes a critical Richardson number limit beyond which turbulence cannot be sustained. However, observational studies have shown turbulence to be present at very high stabilities. In the TTE scheme under stable stratification, TKE is converted to TPE instead of buoyancy destruction and thus, a critical Richardson number limit vanishes, which is a main advantage of the TTE scheme. The originally developed eddy diffusivities in the TTE scheme under assumption of steady state and down-gradient diffusion are significantly modified because they tend to largely degrade the GFS forecast skills. In this study, we implement and test the new TTE-based EDMF scheme in the NCEP GFS and present its impacts on the GFS forecast skills.