2.11.5 Vertical grid

Figure 2.11: Two versions of the vertical grid. a) The cell centered approach where the interface depths are specified and the tracer points centered in between the interfaces. b) The interface centered approach where tracer levels are specified and the w-interfaces are centered in between.

a) $\resizebox{!}{4in}{ \includegraphics{s_algorithm/figs/vgrid-cellcentered.eps}}$

b) $\resizebox{!}{4in}{ \includegraphics{s_algorithm/figs/vgrid-accurate.eps}}$

As for the horizontal grid, we use the suffixes ``c'' and ``f'' to indicates faces and centers. Fig. 2.11a shows the default vertical grid used by the model. $\Delta r_f$ is the difference in

(vertical coordinate) between the faces (i.e. $\Delta r_f \equiv - \delta_k r$ where the minus sign appears due to the convention that the surface layer has index

.).

The vertical grid is calculated in subroutine INI_VERTICAL_GRID and specified via the vector DELR in namelist PARM04. The units of ``r'' are either meters or Pascals depending on the isomorphism being used which in turn is dependent only on the choice of equation of state.

There are alternative namelist vectors DELZ and DELP which dictate whether z- or p- coordinates are to be used but we intend to phase this out since they are redundant.

The reciprocals $\Delta r_f^{-1}$ and $\Delta r_c^{-1}$ are pre-calculated (also in subroutine INI_VERTICAL_GRID). All vertical grid descriptors are stored in common blocks in GRID.h.

The above grid (Fig. 2.11a) is known as the cell centered approach because the tracer points are at cell centers; the cell centers are mid-way between the cell interfaces. This discretization is selected when the thickness of the levels are provided (delR, parameter file data, namelist PARM04) An alternative, the vertex or interface centered approach, is shown in Fig. 2.11b. Here, the interior interfaces are positioned mid-way between the tracer nodes (no longer cell centers). This approach is formally more accurate for evaluation of hydrostatic pressure and vertical advection but historically the cell centered approach has been used. An alternative form of subroutine INI_VERTICAL_GRID is used to select the interface centered approach This form requires to specify

vertical distances delRc (parameter file data, namelist PARM04, e.g. verification/ideal_2D_oce/input/data) corresponding to surface to center,

center to center, and center to bottom distances.

$\fbox{ \begin{minipage}{4.75in} {\em S/R INI\_VERTICAL\_GRID} ({\em model/src/in... ...}) \par $\Delta r_c^{-1}$: {\bf RECIP\_DRc} ({\em GRID.h}) \par \end{minipage} }$