Semi-implicit Scheme for the Dwd Lokal-modell

The fourth generation of numerical weather prediction (NWP) models is currently under development at the Deutscher Wetterdienst (DWD) consisting of a global grid point model (GME) and limited-area Lokal{Modell (LM). The nonhydrostatic fully compressible LM has been designed to meet high-resolution regional forecast requirements at meso-and meso-scales. The initial LM implementation is based on the NCAR/Penn State MM5 with the addition of a novel generalized terrain-following coordinate and rotated lat-lon grid. A fully 3D semi-implicit time-stepping scheme for the LM based on a minimal residual Krylov iterative solver and line relaxation preconditioners has been implemented. The new semi-implicit scheme is compared with a variant of the Klemp{Wilhelmson split-explicit scheme (horizontal explicit, vertical implicit) on the basis of computational eeciency and accuracy at resolutions ranging from 7km to 400m. Both idealized 3D mountain wave ows and real data cases are analyzed. Below the tropopause, the 3D semi-implicit scheme becomes more eecient at resolutions of 2:5km or higher when the number of small time steps t s increases with the sound speed Courant number.