18. Topography and geometry

As described in Chapter 16, the model domain (as defined in module grids) is populated with a horizontally rectangular arrangement of T-cells and U-cells arranged in an Arakawa B-grid fashion and stacked vertically on top of each other. The vertical stacking is such that T-cells overlay T-cells and U-cells overlay U-cells. In general, some of these grid cells will be treated as land cells and others as ocean cells. Geometry and topography determine whether individual cells are treated as land or ocean. This three dimensional land/ocean cell arrangement is encapsulated in a two dimensional array of integers (an example is given in Figure 18.1) which indicate the number of ocean cells stacked vertically between the surface and ocean bottom for each longitude and latitude coordinate xt_i and yt_jrow on the T-grid. For instance, the following settings

kmt_i,jrow = 0 (18.1)

kmt_i+1,jrow = 6 (18.2)

specify that there are no ocean cells^18.1 at coordinate location with index (i,jrow) but the location immediately to the east has 6 ocean T-cells^18.2. On the U grid, there is a corresponding field of integers derived as the minimum of the four surrounding values.

$$\kmu = min(\kmt, kmt_{i+1,jrow}, kmt_{i,jrow+1}, kmt_{i+1,jrow+1})$$ (18.3)

Vertical levels are indexed from the uppermost at k=1 to the bottom of the domain at k=km. Beneath the ocean surface, land cells exist where k > on the T grid and where k > on the U grid. The depth from the ocean surface to the bottom of the ocean is defined at the longitude and latitude of U-cells by

$$\hij = zw_{kbu} \;\;\;\;\; where\;\; kbu = kmu_{i,jrow} \\$$ (18.4)

where zw_k is the depth from the ocean surface to the bottom face of the kth vertical level.