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 ). A schematic of the grid is given in Figure .
Figure: QTCM1 staggered C-grid. Note that j=0 only exists
for v and variables dependent on v. See text in
Section for details.
The pair (i,j) denotes a grid point. For the standard version, and . Figure 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:
T
.
Variable is the surface temperature, and is received
from the ocean, except over land where it is prognostic.
T
.
Variable is the humidity, and is prognostic.
vort0
. Variable
is the barotropic streamfunction, and is diagnostic from
vort0
.
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.
Below is a portion of the file qtcm.h which contains the array declarations for the main prognostic grid variables:
c baroclinic mode real*8 u1(NX,NY),v1(NX,0:NY),T1(NX,NY),q1(NX,NY) c barotropic mode V0; note only vort0 and u0bar are prognostic real*8 u0bar,u0(NX,NY),v0(NX,0:NY),vort0(NX,NY),psi0(NX,0:NY) c- Boundary inputs and derived; exception: Ts overland is prognostic real*8 Ts(NX,NY),qs(NX,NY),Ts0(NX,NY)