The German Weather Service (Deutscher Wetterdienst) has recently developed a new operational global numerical weather prediction model, named GME, based on an almost uniform icosahedral-hexagonal grid. The GME gridpoint approach avoids the disadvantages of spectral techniques as well as the pole problem in latitudelongitude grids and provides a data structure extremely well suited to high efficiency on distributed memory parallel computers. The formulation of the discrete operators for this grid is described and evaluations that demonstrate their second-order accuracy are provided. These operators are derived for local basis functions that are orthogonal and conform perfectly to the spherical surface. The local basis functions, unique for each grid point, are the latitude and longitude of a spherical coordinate system whose equator and zero meridian intersect at the grid point. The prognostic equations for horizontal velocities, temperature, and surface pressure are solved using a semi-implicit Eulerian approach and for two moisture fields using a semi-Lagrangian scheme to ensure monotonicity and positivity. In the vertical direction, finite differences are applied in a hybrid (sigma pressure) coordinate system to all prognostic variables. The semi-implicit treatment of gravity waves presented here leads to a 3D Helmholtz equation that is diagonalized into a set of 2D Helmholtz equations that are solved by successive relaxation. Most of the same physical parameterizations used in the authors' previous operational regional model, named EM, are employed in GME. Some results from the verification process for GME are provided and GME performance statistics on a Cray T3E1200 as well as on the ECMWF Fujitsu VPP5000 systems are summarized. For the case of the severe Christmas 1999 storm over France and Germany the pronounced sensitivity of the model with respect to the initial state is discussed. Finally, a test case is shown where it is currently possible, though not yet operationally practical, to run GME at 15-km resolution on the VPP5000.

Computer models of mantle convection constrained by the history of Cenozoic and Mesozoic plate motions explain some deep-mantle structural heterogeneity imaged by seismic tomography, especially those related to subduction. They also reveal a 150-million-year time scale for generating thermal heterogeneity in the mantle, comparable to the record of plate motion reconstructions, so that the problem of unknown initial conditions can be overcome. The pattern of lowermost mantle structure at the core-mantle boundary is controlled by subduction history, although seismic tomography reveals intense large-scale hot (low-velocity) upwelling features not explicitly predicted by the models.