The Step-Mountain Eta Coordinate Model: Further Developments of the Convection, Viscous Sublayer, and Turbulence Closure Schemes

The step-mountain eta model has shown a surprising skill in forecasting severe storms. Much of the credit for this should be given to the Betts and Miller (hereafter referred to as BM) convection scheme and the Mellor-Yamada (hereafter referred to as MY) planetary boundary layer (PBL) formulation. However, the eta model was occasionally producing heavy spurious precipitation over warm water, as well as widely spread light precipitation over oceans. In addition, the convective forcing, particularly the shallow one, could lead to negative entropy changes. As the possible causes of the problems, the convection scheme, the processes at the air-water interface, and the MY level 2 and level 2.5 PBL schemes were reexamined. A major revision of the BM scheme was made, a new marine viscous sublayer scheme was designed, and the MY schemes were retuned. The deep convective regimes are postulated to be characterized by a parameter called “cloud efficiency.” The relaxation time is extended for low cloud efficiencies and vice versa. It is also postulated that there is a range of reference equilibrium states. The specific reference state is chosen depending on the cloud efficiency. The treatment of the shallow cloud tops was modified, and the shallow reference humidity profiles are specified requiring that the entropy change be nonnegative. Over the oceans there are two layers: (a) a viscous sublayer with the vertical transports determined by the molecular diffusion, and (b) a layer above it with the vertical transports determined by the turbulence. The viscous sublayer operates in different regimes depending on the roughness Reynolds number. The MY level 2.5 turbulent kinetic energy (TKE) is initialized from above in the PBL, so that excessive TKE is dissipated at most places during the PBL spinup. The method for calculating the MY level 2.5 master length scale was rectified. To demonstrate the effects of the new schemes for the deep convection and the viscous sublayer, tests were made using two summer cases: one with heavy spurious precipitation, and another with a successful 36-h forecast of a tropical storm. The new schemes had dramatic positive impacts on the case with the spurious precipitation. The results were also favorable in the tropical storm case. The developments presented here were incorporated into the eta model in 1990. The details of further research will be reported elsewhere. The eta model became operational at the National Meteorological Center, Washington, D.C., in June 1993.