3/26/2023 0 Comments Sphere grids![]() Such robustness comes at a cost in computational time, but the weights only need be computed once for each grid pair and stored in a file for later use. Throughout the descriptions above, the most general algorithms have been presented that are robust enough to work for any grid on a sphere. ![]() Remapping from a fine grid to a coarse grid consists of averaging over cells on the fine grid the gradient components in (5) will average to zero when averaging over an entire cell. It should also be noted that (5) implies that little increase in accuracy is gained using the second-order remappings to remap from a fine grid to a coarse grid. When gradient limiters are employed, formal second-order accuracy is lost, but the remappings can be made monotone. Avoiding such oscillations requires limiting the gradient, and sample methods for limiting the gradient are discussed in Dukowicz and Kodis (1987). In such cases, (5) may overshoot the expected value of the field, resulting in spurious oscillations in the resulting remapped field. If a field to be remapped has strong gradients, numerical approximations to the gradient may be too steep. Methods for computing gradients can vary depending on the grid and numerical algorithm employed, and the remapping method above requires only that the gradient be at least first-order accurate. The third section will describe practical considerations and problems encountered in spherical coordinates.įor a second-order remapping, a gradient must be supplied. The method was originally introduced by Dukowicz and Kodis (1987) but will be derived for spherical coordinates in the next section. We present here a method for computing remapping weights that will work for any general grid and will provide weights for both first- and second-order accurate remappings. Also, it has been primarily applied to situations where both grids are latitude–longitude rectangular grids. Such a scheme is automatically conservative, but is only first-order accurate. Currently, many coupled models utilize an area-weighted remapping where the interpolation weights are based on the fractional area-overlap of the source and destination grid cells ( Bryan et al. Fluxes in particular must be remapped in a conservative manner in order to maintain the energy and water budgets of the coupled climate system. In a fully coupled climate model, state variables and heat and water fluxes must be transferred between models periodically, and such fields must be remapped from one component grid to another. Similarly, atmosphere models have begun to use icosahedral grids or triangular tesselations for horizontal discretizations ( Schättler and Krenzien 1997 Heikes and Randall 1995). 1995) or that can utilize local mesh refinement ( Levin et al. For example, ocean circulation models have begun to utilize grids that cover the polar regions effectively ( Smith et al. ![]() Component models are often developed as stand-alone models or perhaps as pairs of components (e.g., atmosphere–land or ocean–ice) and utilize grids that work best for that particular component. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.In order to study the earth’s climate system, climate models are often created by coupling individual component models that simulate the atmosphere, land surface, ocean, and sea ice. 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. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. 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. ![]() 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 algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere 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). A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. ![]()
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