The value of **A** has to
be deduced by considering the topography gradients as well as the
strength of the nonlinear terms; however, the latter are quite
small except in very shallow waters. For a discussion of the
mesh-box Reynolds number criterion, see section 2.2.2.

We will now write out the finite-difference analogs of equations
(2), (3) and (4).
In the first exercise we will omit the nonlinear
terms, since these are shown not to be important in barotropic
flows of the deep ocean. Furthermore, we will use the linear
bottom friction formulation
(14),
and locate the variables on a
staggered mesh, called the * C-grid* by Arakawa and Mesinger
[45]
(see Figure 14).

In this arrangement the pressure **p** and
height **h** variables are located at the center of the mesh boxes,
and the mass transports **U** and **V** at the center of the box
boundaries facing the **x** and **y** directions, respectively.