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  1. Abstract

    The dynamical core that predicts the three‐dimensional vorticity rather than the momentum, which is called Vector‐Vorticity Model (VVM), is implemented on a cubed sphere. Its horizontal coordinate system is not restricted to orthogonal, while the vertical coordinate is orthogonal to the horizontal surface. Accordingly, all the governing equations of the VVM, which are originally developed with Cartesian coordinates, are rewritten in terms of general curvilinear coordinates. The local coordinates on each cube surface are constructed with the gnomonic equiangular projection. Using global channel domains, the VVM on the cubed sphere has been evaluated by (1) advecting a passive tracer with a bell‐shaped initial perturbation along an east‐west latitude circle and along a north‐south meridional circle and (2) simulating the evolution of barotropic and baroclinic instabilities. The simulated results with the cubed‐sphere grids are compared to analytic solutions or those with the regular longitude‐latitude grids. The convergence with increasing spatial resolution is also quantified using standard error norms. The comparison shows that the solutions with the cubed‐sphere grids are quite reasonable for both linear and nonlinear problems when high resolutions are used. With coarse resolution, degeneracy appears in the solutions of the nonlinear problems such as spurious wave growth; however, it is effectively reduced with increased resolution. Based on the encouraging results in this study, we intend to use this model as the cloud‐resolving component in a global Quasi‐Three‐Dimensional Multiscale Modeling Framework.

     
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