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A numerical scheme applicable to arbitrarily structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector invariant form of the momentum equation, the relationship between the nonlinear Coriolis force and the potential vorticity flux can be used to guarantee that mass, velocity and potential vorticity evolve in a… (More)

A C-grid staggering, in which the mass variable is stored at cell centers and the normal velocity component is stored at cell faces (or edges in two dimensions) is attractive for atmospheric modeling since it enables a relatively accurate representation of fast wave modes. However, the discretization of the Coriolis terms is non-trivial. For constant… (More)

The rationale for designing atmospheric numerical model dynamical cores with certain conservation properties is reviewed. The conceptual difficulties associated with the multiscale nature of realistic atmospheric flow, and its lack of time-reversibility, are highlighted. A distinction is made between robust invariants, which are conserved or nearly… (More)

Accurate simulation of atmospheric flow in weather and climate prediction models requires the discretization of the governing equations to have a number of desirable properties. Although these properties can be achieved relatively straightforwardly on a latitude-longitude grid, they are much more challenging on the various quasi-uniform spherical grids that… (More)

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