Experiments with different discretizations for the shallow‐water equations on a sphere

Three models with different discretizations for the shallow-water equations on a sphere are presented and compared using selected test cases. The first model is based on the global latitude–longitude grid system with a uniform Arakawa C grid and a two-time-level Crank–Nicolson iterative semi-Lagrangian method with an advecting wind interpolated in time. The second model uses the overset Yin–Yang grid, which is singularity-free and has quasi-uniform resolution. The local solver on each of the two component grids is based on the same time and space discretizations as in the first model. The positive-definite Helmholtz problem in the second model is solved using an optimized Schwarz-type domain-decomposition method with specific Robin or higher-order transmission conditions. The first and second models are obtained through the barotropic option incorporated into the Global Environmental Multiscale model used operationally at the Canadian Meteorological Center. The third model is discretized using the finite-volume methodology on a geodesic icosahedral grid. The time integration is performed with a fourth-order Runge–Kutta scheme. The tests employed to compare the three models are passive advection of a cosine bell, steady-state geostrophic flow, flow over an idealized mountain, a Rossby–Haurwitz wave, real-case 500 mb flow and evolution of a growing barotropic wave. When no analytic solution is available for a specific test, we compare the results with a high-resolution solution obtained from the first model in which all horizontal operations are evaluated in spectral space. © 2011 Crown in the right of Canada. Published by JohnWiley & Sons Ltd.