Model Grid

 

The grid-scale variables in the QTCM are located on a staggered C-grid [19]. A schematic of the grid is given in figure 3.1.

  
Figure 3.1: QTCM staggered C-grid

The pair (i,j) denotes a grid point. There are NX=64 grid points in the zonal (longitudinal) direction, and NY=33 grid points in the meridional (latitudinal) direction. 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 diagnostic, 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.

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 QTCM code. For example:

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

Besides the prognostic and diagnostic permanent grid variables, the model also uses some temporary local variables in its computations. Below is an explanation of the names of some of these temporary variables:

vatu

Located at the same position as u. Variable vatu represents ``v calculated at the u position,'' and is computed as the mean of the meridional velocity v at the ``four corners'' surrounding the u point location.

fu

Located at the same j position as u. Variable fu represents the Coriolis parameter evaluated at the latitudinal circle u is located at.

fv

Located at the same j position as v. Variable fv represents the Coriolis parameter evaluated at the latitudinal circle v is located at.

Most variables are dimensioned (NX,NY). However, because of the treatment of the boundaries, some of the model variables are dimensioned a bit differently (see discussion in Section 3.2.3). 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)