A Two Time-Level, Three-Dimensional, Semi-Lagrangian, Semi-implicit, Limited-Area Gridpoint Model of the Primitive Equations. Part II: Extension to Hybrid Vertical Coordinates

Abstract

A two time-level, three-dimensional, semi-Lagrangian semi-implicit primitive equation gridpoint model that incorporates a sophisticated physics package and uses hybrid coordinates in the vertical is derived. A simple filter, which is needed to stabilize large time-step forecasts, is introduced. Using it, the model is shown to give accurate 24-h forecasts when integrated over a limited area using a 1.5°?1.5° Arakawa C grid in the horizontal and 16 levels in the vertical for time steps up to 2 h. Also, it is shown to give accurate forecasts on a 0.5°?0.5° horizontal grid, again using 16 vertical levels, for time steps up to 40 min, and to be as accurate as, and approximately twice as efficient as, a three time-level semi-Lagrangian scheme.