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2.4.1 Explicit Time Integration     continued...

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.