A semi-Lagrangiam and semi-implicit scheme on an unstaggered horizontal grid

A two time-level, two-dimensional semi-Lagrangian and semiimplicit (SLSI) s cheme based on an unstaggered horizontal grid is presented for limited-area grid-point models of the atmosphere. A Lorenz grid is used for the vertica l discretisation. An isothermal reference atmosphere with surface topograph y is used for the semi-implicit linearisation of the governing moist, diaba tic, hydrostatic primitive equations. The momentum equation is discretised in vector form. Semi-implicit treatment of the gravity wave terms and linea r part of the Coriolis force terms followed by a vertical decoupling transf ormation, lead to a set of two-dimensional separable elliptic equations tha t are solved by an efficient iterative solver. The main original contributi on of this paper is in the use of the unstaggered horizontal A grid to deve lop the 2D SLSI scheme. The scheme is implemented in the regional NWP model LAPS (Limited Area Pred iction System) of the Australian Bureau of Meteorology. The currently opera tional LAPS is an Eulerian model with 19 sigma -levels in the vertical and a uniform horizontal resolution of 0.75 degrees. While the fully explicit E ulerian model employs a time step of 90 s for computational stability, the SLSI model can use a time step up to 30 min. Results from 48 hour forecasts using the two models show that the newly developed SLSI model provides a s table, accurate, and computationally efficient alternative to the Eulerian model.