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.