. Comparing Numerical Accuracy of Icosahedral A-grid and C-grid Schemes for the Shallow Water Model

Abstract
We have implemented in a single software framework the A-grid and C-grid shallow water model solvers on icosahedral grids. Five out of the seven Williamson test cases have been performed to compare the numerical accuracy of the two schemes, enriching the previous case studies by Tomita et al. (2001) (NICAM) and Ringler et al. (2010) (MPAS). The C-grid staggering scheme excels in numerical noise control and total energy conservation, which results in exceptional long-time integration stability without numerical damping. However, three of the five test cases reveal the failure of the C-grid scheme to reduce the maximum error (L_infty norm) with increasing grid resolution. Surprisingly, we find this is due to the velocity interpolation and the Coriolis force term formulation in the current C-grid scheme on sphere. Results from the A-grid staggering scheme show good behavior in potential enstrophy conservation and the linear reduction of error norms with the number of grid points. We verify that the finite volume method has only the first order accuracy for the quasi-uniform grid on sphere. The grid point noise is an issue for A-grid. This is manifest from the noisy iso-surface shapes of geopotential after relatively long time integration, as well as from the large standard deviation in the time evolution of numerical error norms. Our work suggests further improvement is needed in the current C-grid scheme.