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

A two time-level, two-dimensional semi-Lagrangian and semiimplicit (SLSI) scheme based on an unstaggered horizontal grid is presented for limited-area grid-point models of the atmosphere. A Lorenz grid is used for the vertical discretisation. An isothermal reference atmosphere with surface topography is used for the semi-implicit linearisation of the governing moist, diabatic, hydrostatic primitive equations. The momentum equation is discretised in vector form. Semi-implicit treatment of the gravity wave terms and linear part of the Coriolis force terms followed by a vertical decoupling transformation, lead to a set of two-dimensional separable elliptic equations that are solved by an efficient iterative solver. The main original contribution of this paper is in the use of the unstaggered horizontal A grid to develop the 2D SLSI scheme. The scheme is implemented in the regional NWP model LAPS (Limited Area Prediction System) of the Australian Bureau of Meteorology. The currently operational LAPS is an Eulerian model with 19 σ-levels in the vertical and a uniform horizontal resolution of 0.75°. While the fully explicit Eulerian 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 stable, accurate, and computationally efficient alternative to the Eulerian model.