Semi-implicit scheme for the DWD Lokal-Modell

The fourth generation of numerical weather prediction (NWP) models is curre ntly under development at the Deutscher Wetterdienst (DWD) consisting of a global grid point model (GME) and limited-area Lokal-Modell (LM). The nonhy drostatic fully compressible LM has been designed to meet high-resolution r egional fore-cast requirements at meso-beta and meso-gamma scales. The init ial LM implementation is based on the NCAR/Penn State MM5 with the addition of a novel generalized terrain-following coordinate and rotated lat-lon gr id. A fully 3D semiimplicit time-stepping scheme has been implemented by re taining the full buoyancy term instead of the approximate form found in MM5 . In contrast with earlier schemes, mass-lumping is not applied to simplify the elliptic operator on an Arakawa-C/Lorenz grid. The resulting variable- coefficient elliptic problem is solved using a minimal residual Krylov iter ative method with line relaxation preconditioners. The new semi-implicit sc heme is compared with a variant of the Klemp-Wilhelmson split-explicit sche me (horizontal explicit, vertical implicit) on the basis of computational e fficiency and accuracy at resolutions ranging from 7 km to 400 m. Both idea lized 3D mountain wave flows and naturally occuring flows are analyzed. Bel ow the tropopause, the 3D semi-implicit scheme can be more efficient for lo w Mach number M much less than 1 flows when the number of small time steps Delta t(s) of the split-explicit approach increases with the sound-speed Co urant number.