Analysis of Grid Imprinting on the Cubed-Sphere

The quasi-uniform grids solve the problem of scalability of the grid-point models of the atmosphere, and represent the clear choice for future applications at high global resolutions running on machines with tens of thousands of processors.   One of the remaining important problems to be addressed within the framework of models that use quasi-uniform grids is the effect that grid topology has on the solution, so-called ‘grid imprinting’, that on the quasi-uniform grids may take form of a small-scale noise around singular points and in the long-term integrations reveals itself as a forcing of a specific wave-number that is characteristic for the grid.  The problem has been to some extend analyzed for the geodesic spherical grid (e.g., Peixoto and Barros 2013), but not yet sufficiently for the cubed-sphere.  We perform analysis using the novel cubed-sphere derived under assumption of uniform Jacobians that maximizes the grid homogeneity with a smooth transition over the cube edges, and consider a solution as a correction of numerical approximations based on discretization of vector operators in the integral from that correctly takes into account the grid geometry.  The general relevance of the derived results will be estimated and a pathway for the best implementation of the solution within the framework of other models that use geometry of the cubed-sphere, particularly, FV3 will be established.