--- manual/s_algorithm/text/spatial-discrete.tex	2004/03/23 16:47:04	1.14
+++ manual/s_algorithm/text/spatial-discrete.tex	2006/06/28 16:55:53	1.21
@@ -1,7 +1,10 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.14 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.21 2006/06/28 16:55:53 jmc Exp $
 % $Name:  $
 
 \section{Spatial discretization of the dynamical equations}
+\begin{rawhtml}
+<!-- CMIREDIR:spatial_discretization_of_dyn_eq: -->
+\end{rawhtml}
 
 Spatial discretization is carried out using the finite volume
 method. This amounts to a grid-point method (namely second-order
@@ -10,8 +13,6 @@
 representation of the position of the boundary. We treat the
 horizontal and vertical directions as separable and differently.
 
-\input{part2/notation}
-
 
 \subsection{The finite volume method: finite volumes versus finite difference}
 \begin{rawhtml}
@@ -138,8 +139,8 @@
 grid for all panels. a) The area of a tracer cell, $A_c$, is bordered
 by the lengths $\Delta x_g$ and $\Delta y_g$. b) The area of a
 vorticity cell, $A_\zeta$, is bordered by the lengths $\Delta x_c$ and
-$\Delta y_c$. c) The area of a u cell, $A_c$, is bordered by the
-lengths $\Delta x_v$ and $\Delta y_f$. d) The area of a v cell, $A_c$,
+$\Delta y_c$. c) The area of a u cell, $A_w$, is bordered by the
+lengths $\Delta x_v$ and $\Delta y_f$. d) The area of a v cell, $A_s$,
 is bordered by the lengths $\Delta x_f$ and $\Delta y_u$.}
 \label{fig:hgrid}
 \end{figure}
@@ -147,8 +148,8 @@
 The model domain is decomposed into tiles and within each tile a
 quasi-regular grid is used. A tile is the basic unit of domain
 decomposition for parallelization but may be used whether parallelized
-or not; see section \ref{sect:tiles} for more details. Although the
-tiles may be patched together in an unstructured manner
+or not; see section \ref{sect:domain_decomposition} for more details. 
+Although the tiles may be patched together in an unstructured manner
 (i.e. irregular or non-tessilating pattern), the interior of tiles is
 a structured grid of quadrilateral cells. The horizontal coordinate
 system is orthogonal curvilinear meaning we can not necessarily treat
@@ -366,15 +367,23 @@
 
 The above grid (Fig.~\ref{fig:vgrid}a) 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. An alternative, the
-vertex or interface centered approach, is shown in
+centers are mid-way between the cell interfaces. 
+This discretization is selected when the thickness of the
+levels are provided ({\bf delR}, parameter file {\em data}, 
+namelist {\em PARM04})
+An alternative, the vertex or interface centered approach, is shown in
 Fig.~\ref{fig:vgrid}b. 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 {\em
 INI\_VERTICAL\_GRID} is used to select the interface centered approach
-but no run time option is currently available.
+This form requires to specify $Nr+1$ vertical distances {\bf delRc} 
+(parameter file {\em data}, namelist {\em PARM04}, e.g. 
+{\em verification/ideal\_2D\_oce/input/data})
+corresponding to surface to center, $Nr-1$ center to center, and center to 
+bottom distances.
+%but no run time option is currently available.
 
 \fbox{ \begin{minipage}{4.75in}
 {\em S/R INI\_VERTICAL\_GRID} ({\em
@@ -392,6 +401,9 @@
 
 
 \subsection{Topography: partially filled cells}
+\begin{rawhtml}
+<!-- CMIREDIR:topo_partial_cells: -->
+\end{rawhtml}
 
 \begin{figure}
 \begin{center}
@@ -462,6 +474,10 @@
 
 
 \section{Continuity and horizontal pressure gradient terms}
+\begin{rawhtml}
+<!-- CMIREDIR:continuity_and_horizontal_pressure: -->
+\end{rawhtml}
+
 
 The core algorithm is based on the ``C grid'' discretization of the
 continuity equation which can be summarized as:
@@ -500,6 +516,9 @@
 evaporation and only enters the top-level of the {\em ocean} model.
 
 \section{Hydrostatic balance}
+\begin{rawhtml}
+<!-- CMIREDIR:hydrostatic_balance: -->
+\end{rawhtml}
 
 The vertical momentum equation has the hydrostatic or
 quasi-hydrostatic balance on the right hand side. This discretization