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

Francis X. Giraldo

Naval Research Laboratory Monterey, CA 93943

Abstract:
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.