A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: Comparison of hexagonal-icosahedral and cubed-sphere grids
Geoscientific Model Development
European Geosciences Union (EGU)
© Author(s) 2014. CC Attribution 3.0 License.
A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly. © Author(s) 2014.
We are grateful to Almut Gaßmann, Paul Ullrich, and an anonymous referee for valuable comments that helped improve the manuscript. We are especially grateful to Hilary Weller for valuable discussions and for drawing our attention to the inconsistency of the W operator. The contributions of J. Thuburn and C. J. Cotter were funded by the Natural Environment Research Council (grants NE/I021136/1 and NE/I02013X/1) under the Next Generation Weather and Climate Prediction project, informally known as “Gung Ho”. Part of the work presented here was carried out during the programme “Multiscale Numerics for the Atmosphere and Ocean” that took place at the Isaac Newton Institute for Mathematical Sciences, Cambridge, during Autumn 2012.
This is the final version of the article. Available from the publisher via the DOI in this record.
Published by Copernicus Publications on behalf of the European Geosciences Union.
Vol. 7, pp. 909 - 929