Comparing Numerical Accuracy of Icosahedral A-grid and C-grid Schemes for the Shallow-Water Model
Abstract
Numerical accuracy and long-time integration stability (tested without explicit numerical damping) are important for model development in weather prediction and climatology. We have implemented in a single software framework the A-grid (NICAM, Tomita et al. (2001)) and C-grid (MPAS, Ringler et al. (2010)) shallow-water model solvers on icosahedral grids, allowing for a fair, side-by-side comparison on computational accuracy. Simulation on five out of the seven Williamson test cases indicates that the C-grid staggering scheme excels in numerical noise control and total energy conservation, which result in exceptional long-time integration stability without explicit numerical damping. However, three of the five test cases reveal the failure of the C-grid scheme to reduce the maximum error (L∞ norm) with increasing grid resolution. We find this correlates with the velocity interpolation and the Coriolis force term formulation in the current C-grid scheme. Results from the A-grid scheme show good behavior in potential enstrophy conservation and the linear reduction of error norms with respect to the number of grid points. However, the grid point noise is an issue for the A-grid, which is less obvious on the C-grid. Our work suggests further improvement is needed in the current C-grid scheme for MPAS.
Reference: Tomita, H., M. Tsugawa, M. Satoh, and K. Goto, 2001: Shallow water model on a modified icosahedral geodesic grid by using spring dynamics. J. Comput. Phys., 174, 579-613. Ringler, T. D., J. Thuburn, J. B. Klemp, and W. C. Skamarock, 2010: A unified approach to en- ergy conservation and potential vorticity dynamics for arbitrarily-structured C-grids. J. Comput. Phys., 229, 3065-3090.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.A13H3024Y
- Keywords:
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- 3336 Numerical approximations and analyses;
- ATMOSPHERIC PROCESSES;
- 3337 Global climate models;
- ATMOSPHERIC PROCESSES