Spectral Element Eulerian and Semi-Lagrangian Methods for Numerical Weather Prediction Models

Francis X. Giraldo

Naval Research Laboratory Monterey, CA 93943

Two new dynamical cores for NWP based on the spectral element method (SEM) and the spectral element semi-Lagrangian method (SESL) are presented. In this work, the 3D primitive hydrostatic atmospheric equations are written, discretized, and solved in 3D Cartesian space. The advantages of this approach are: the pole singularity which plagues all gridpoint methods disappears, the horizontal operators can be approximated by local high-order elements, and any grid can be used including lat-lon, icosahedral, hexahedral, and adaptive unstructured grids. The locality property of spectral elements means that the method will scale efficiently on distributed-memory computers. The Lagrangian formulation of SESL allows for very large time-steps to be used without losing accuracy. Both models currently use finite differences in the vertical but results for fully spectral element (in all three-dimensions) will be presented. In order to validate our 3D atmospheric models, we have run three test cases: Rossby-Haurwitz waves 1 and 4, and the Held-Suarez test case. Comparisons with the Navy's operational NWP model (NOGAPS) using the Rossby-Haurwitz waves demonstrate the high-order accuracy of the solutions obtained with the new models. The Eulerian model is shown to scale linearly on distributed-memory computers; it is hoped that the semi-Lagrangian model will scale at a similar rate. Plans for implementing physics and realistic terrain into the models will be discussed.