Model Grid

 

The grid-scale variables in the QTCM1 are located on a staggered C-grid [28] of dimensions , where the x (zonal, longitudinal) coordinate indexes from 1 to NX, and the y (meridional, latitudinal) coordinate indexes from 1 to NY. (there are certain exceptions to this description of the dimensioning, which are noted in Section 3.3.1). A schematic of the grid is given in Figure 3.1.

  
Figure: QTCM1 staggered C-grid. Note that j=0 only exists for v and variables dependent on v. See text in Section 3.3.1 for details.

The pair (i,j) denotes a grid point. For the standard version, and . Figure 3.1 abbreviates variables as follows:

These variables are all prognostic.

Thus, temperature is located at grid point (i,j), while zonal velocity is located at ( ), meridional velocity is located at ( ), and is located at ( ). Recall that the subscript ``0'' refers to the barotropic mode, while the subscript ``1'' refers to the baroclinic mode.

Other variables are also defined at the above locations. These include:

Located at the same position as T. Variable is the surface temperature, and is received from the ocean, except over land where it is prognostic.

Located at the same position as T. Variable is the humidity, and is prognostic.

Located at the same position as vort0. Variable is the barotropic streamfunction, and is diagnostic from vort0.

All other model variables are diagnostic, and are centered at (i,j) on the grid.

Although the C-grid has half-step variable indices, array indices in FORTRAN do not. Thus, we have adopted the convention that all half-indices are truncated when referred to in the QTCM1 code. For example:

In all other sections of this document, array indice naming follows the FORTRAN model code convention.