The Step-Mountain Coordinate: Physical Package

Abstract

A comprehensive physical package has been developed for a regional eta coordinate model with the steplike mountain representation. This paper describes the basic problems, concepts and numerical techniques developed, and reviews primarily those aspects of the performance of the model which reflect the effects of the parameterized physical processes. The Level 2.5 turbulence closure model in the Mellor-Yamada hierarchy was chosen to represent the turbulence above the surface layer. A severe instability encountered in the early experiments in the turbulent kinetic energy (TKF) equation was found to be of a numerical origin. The instability was removed by a suitably designed time-differencing scheme. As implemented in the eta-coordinate model, the Level 2.5 turbulence closure model is computationally remarkably inexpensive. An unconditionally stable, trivially implicit, time-differencing scheme is proposed for the vertical diffusion. The Mellor-Yamada Level 2 turbulence closure scheme is used for the surface layer. For additional flexibility, a shallow logarithmic, dynamical turbulence layer, is introduced at the bottom of the Level 2 surface layer. A rather conventional formulation has been chosen for the ground surface processes and surface hydrology. The nonlinear fourth order lateral diffusion scheme was implemented in the model. The diffusion coefficient depends on deformation and TKE. The ratio of the horizontal turbulent coefficients for momentum and heat was estimated. The divergence damping is used as another mechanism for maintaining the smoothness of prognostic fields and/or accelerating the geostrophic adjustment. The Betts and Miller approach has been adopted for deep and shallow cumulus convection. The formulation of the large-scale condensation is rather conventional, and includes the evaporation of precipitating water in the unsaturated layers below the condensation level. A review of the available results of numerical experiments suggests that the eta model is competitive with other sophisticated models using similar resolutions, and requiring similar computational effort. Thus, it is believed that the viability of the eta coordinate step-mountain approach in grid point models has been finally demonstrated.