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5.6 Discretization

Numerical solutions require the domain to be discretized and the governing equations reduced to their finite difference equivalents. Figure 19 shows the numerical grid employed for spatial discretization. The grid is the so-called Arakawa C grid, which belongs to a class of staggered grids. In a C grid, quantities such as and H are defined at the center of the grid, while the east--west component of velocity is displaced half a grid to the west of the center and the north--south component displaced half a grid to the south of the center. Contrast this to the B grid used in Bryan--Cox--Semtner type ocean models where , are at the same location but displaced by half a grid from H and . Which scheme is preferable depends very much on the size of the numerical grid relative to the Rossby radius. For a coarse grid, such as in ocean models used for climate modeling and global ocean modeling purposes, the B grid was once preferable, because of the favorable wave propagation characteristics of such a grid. However, as available computational power has increased dramatically in recent years, it has now become possible to model even the global oceans at a fine resolution. Under these circumstances the C grid appears to be a much better choice for discretization. Besides, for application to shallow coastal waters around ocean basins, high spatial resolution is rather imperative so that the shorter spatial scales typical of the processes in such regions be can resolved. Once again a staggered C grid is better suited to this application.