Shallow water model
Shallow water models (SWMs) solve the
dynamical equations for one layer of fluid on the rotating sphere.
These models allow to test a number of properties of the numerical
solution of the shallow water equation. A set of standard tests has been proposed by Williamson et al. (1992).
- Williamson, D. L. , J. B. Drake, J. J. Hack, R. Jakob, and
R. N. Swarztrauber.
A standard test set for numerical approximations to the shallow water
equations in spherical geometry.
J. Comput. Phys., 102, 211-224, 1992.
For the development of the icosahedral shallow water prototype model (ICOSWP) we use the spectral transform
shallow water model (STSWM) , derived from the NCAR STSWM, as a reference model.
The reference solutions of the STSWM are compared with the solutions of the existing GME SWM of DWD that uses hexagonal and pentagonal cells, and the new ICOSWP with triangular cells.
Normalized errors are used as a guideline and documentation of the
improvements in the development of the ICON SWM. The figure below shows
for example a comparison of normalized L2 errors in the geopotential of
test case 6 at day 15 for two ICON SWM versions, the GME SWM and the
NCAR STSWM for a range of resolutions in comparison to the solution of
the NCAR STSWM at truncation T511.
(mag, 30.11.2005)