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.
