A.4  Spatial Discretization on the A-Grid

The current version of CANDIE uses the Arakawa A grid formulation. It was developed by Dan Wright. The main reason for choosing the A grid CANDIE as our standard model code is based on the finding that the C-grid model does not reproduce well the bottom trapped baroclinic topographic Rossby waves in a periodic channel with a uniformly slopping bottom. The governing equations and time discretization used on the A grid CANDIE are identical to the C grid (see Sections A.1 and A.2). The main differences between the A-grid and C-grid formations are solely associated with the spatial discretization of horizontal velocity components u and v. On the A grid u and v are defined at the center of each cell (i.e., the p points, see Figure 1). On the C grid, on the other hand, u and v are defined on the cell faces normal to the x and y directions, respectively.

The A grid formulation overcomes the difficulty of the C-grid in estimating the Coriolis terms since the state variables u and v are defined at the same location. The conservation equations for heat, salt and momentum, however, each require knowledge of the velocity components on the cell faces, i.e. on the C grid. Thus interpolations of the horizontal velocity components on the A grid onto the C grid are still required. The trial velocity components on the C grid page56_1.gif can be calculated from the A-grid velocity components. Using two-point averaging, for example, we have:


The surface pressure correction page56_3.gif can then be calculated from the depth integrated horizontal divergence of page56_4.gif over each water column. The barotropic velocity corrections page56_5.gif can readily be calculated from page56_3.gif through (33) and (34). Interpolations of page56_5.gif back to the p-points yield the total horizontal velocity components on the A grid page56_6.gif at the end of the time step:


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