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 fore-cast requirements at meso-beta and meso-gamma 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 semiimplicit time-stepping scheme has been implemented by retaining 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 iterative method with line relaxation preconditioners. 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 efficiency and accuracy at resolutions ranging from 7 km to 400 m. Both idealized 3D mountain wave flows and naturally occuring flows are analyzed. Below the tropopause, the 3D semi-implicit scheme can be more efficient for low 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 Courant number.