--- manual/s_overview/text/manual.tex	2001/10/25 12:06:56	1.7
+++ manual/s_overview/text/manual.tex	2001/11/13 20:13:07	1.9
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.7 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.9 2001/11/13 20:13:07 adcroft Exp $
 % $Name:  $
 
 %tci%\documentclass[12pt]{book}
@@ -34,7 +34,7 @@
 
 % Section: Overview
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.7 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.9 2001/11/13 20:13:07 adcroft Exp $
 % $Name:  $
 
 \section{Introduction}
@@ -89,7 +89,7 @@
 We begin by briefly showing some of the results of the model in action to
 give a feel for the wide range of problems that can be addressed using it.
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.7 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.9 2001/11/13 20:13:07 adcroft Exp $
 % $Name:  $
 
 \section{Illustrations of the model in action}
@@ -191,7 +191,7 @@
 ocean may be influenced by rotation when the deformation radius is smaller
 than the width of the cooling region. Rather than gravity plumes, the
 mechanism for moving dense fluid down the shelf is then through geostrophic
-eddies. The simulation shown in the figure \ref{fig::convect-and-topo}
+eddies. The simulation shown in the figure \ref{fig:convect-and-topo}
 (blue is cold dense fluid, red is
 warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to
 trigger convection by surface cooling. The cold, dense water falls down the
@@ -289,7 +289,7 @@
 \input{part1/lab_figure}
 %%CNHend
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.7 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.9 2001/11/13 20:13:07 adcroft Exp $
 % $Name:  $
 
 \section{Continuous equations in `r' coordinates}
@@ -326,31 +326,33 @@
 \begin{equation*}
 \frac{D\vec{\mathbf{v}_{h}}}{Dt}+\left( 2\vec{\Omega}\times \vec{\mathbf{v}}
 \right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}}
-\text{ horizontal mtm}
+\text{ horizontal mtm} \label{eq:horizontal_mtm}
 \end{equation*}
 
-\begin{equation*}
+\begin{equation}
 \frac{D\dot{r}}{Dt}+\widehat{k}\cdot \left( 2\vec{\Omega}\times \vec{\mathbf{
 v}}\right) +\frac{\partial \phi }{\partial r}+b=\mathcal{F}_{\dot{r}}\text{
-vertical mtm}
-\end{equation*}
+vertical mtm} \label{eq:vertical_mtm}
+\end{equation}
 
 \begin{equation}
 \mathbf{\nabla }_{h}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \dot{r}}{
-\partial r}=0\text{ continuity}  \label{eq:continuous}
+\partial r}=0\text{ continuity}  \label{eq:continuity}
 \end{equation}
 
-\begin{equation*}
-b=b(\theta ,S,r)\text{ equation of state}
-\end{equation*}
+\begin{equation}
+b=b(\theta ,S,r)\text{ equation of state} \label{eq:equation_of_state}
+\end{equation}
 
-\begin{equation*}
+\begin{equation}
 \frac{D\theta }{Dt}=\mathcal{Q}_{\theta }\text{ potential temperature}
-\end{equation*}
+\label{eq:potential_temperature}
+\end{equation}
 
-\begin{equation*}
+\begin{equation}
 \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity}
-\end{equation*}
+\label{eq:humidity_salt}
+\end{equation}
 
 Here:
 
@@ -523,8 +525,8 @@
 atmosphere)}  \label{eq:moving-bc-atmos}
 \end{eqnarray}
 
-Then the (hydrostatic form of) eq(\ref{eq:continuous}) yields a consistent
-set of atmospheric equations which, for convenience, are written out in $p$
+Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) 
+yields a consistent set of atmospheric equations which, for convenience, are written out in $p$
 coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).
 
 \subsection{Ocean}
@@ -560,7 +562,8 @@
 \end{eqnarray}
 where $\eta $ is the elevation of the free surface.
 
-Then eq(\ref{eq:continuous}) yields a consistent set of oceanic equations
+Then equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yield a consistent set 
+of oceanic equations
 which, for convenience, are written out in $z$ coordinates in Appendix Ocean
 - see eqs(\ref{eq:ocean-mom}) to (\ref{eq:ocean-salt}).
 
@@ -573,7 +576,7 @@
 \phi (x,y,r)=\phi _{s}(x,y)+\phi _{hyd}(x,y,r)+\phi _{nh}(x,y,r)
 \label{eq:phi-split}
 \end{equation}
-and write eq(\ref{incompressible}a,b) in the form:
+and write eq(\ref{eq:incompressible}) in the form:
 
 \begin{equation}
 \frac{\partial \vec{\mathbf{v}_{h}}}{\partial t}+\mathbf{\nabla }_{h}\phi
@@ -666,8 +669,6 @@
 
 Grad and div operators in spherical coordinates are defined in appendix
 OPERATORS.
-\marginpar{
-Fig.6 Spherical polar coordinate system.}
 
 %%CNHbegin
 \input{part1/sphere_coord_figure.tex}
@@ -730,7 +731,7 @@
 three dimensional elliptic equation must be solved subject to Neumann
 boundary conditions (see below). It is important to note that use of the
 full \textbf{NH} does not admit any new `fast' waves in to the system - the
-incompressible condition eq(\ref{eq:continuous})c has already filtered out
+incompressible condition eq(\ref{eq:continuity}) has already filtered out
 acoustic modes. It does, however, ensure that the gravity waves are treated
 accurately with an exact dispersion relation. The \textbf{NH} set has a
 complete angular momentum principle and consistent energetics - see White
@@ -779,9 +780,8 @@
 \subsection{Solution strategy}
 
 The method of solution employed in the \textbf{HPE}, \textbf{QH} and \textbf{
-NH} models is summarized in Fig.7.
-\marginpar{
-Fig.7 Solution strategy} Under all dynamics, a 2-d elliptic equation is
+NH} models is summarized in Figure \ref{fig:solution-strategy}.
+Under all dynamics, a 2-d elliptic equation is
 first solved to find the surface pressure and the hydrostatic pressure at
 any level computed from the weight of fluid above. Under \textbf{HPE} and 
 \textbf{QH} dynamics, the horizontal momentum equations are then stepped
@@ -838,8 +838,8 @@
 
 \subsubsection{Surface pressure}
 
-The surface pressure equation can be obtained by integrating continuity, (
-\ref{eq:continuous})c, vertically from $r=R_{fixed}$ to $r=R_{moving}$
+The surface pressure equation can be obtained by integrating continuity,
+(\ref{eq:continuity}), vertically from $r=R_{fixed}$ to $r=R_{moving}$
 
 \begin{equation*}
 \int_{R_{fixed}}^{R_{moving}}\left( \mathbf{\nabla }_{h}\cdot \vec{\mathbf{v}
@@ -864,7 +864,7 @@
 where we have incorporated a source term.
 
 Whether $\phi $ is pressure (ocean model, $p/\rho _{c}$) or geopotential
-(atmospheric model), in (\ref{mtm-split}), the horizontal gradient term can
+(atmospheric model), in (\ref{eq:mom-h}), the horizontal gradient term can
 be written 
 \begin{equation}
 \mathbf{\nabla }_{h}\phi _{s}=\mathbf{\nabla }_{h}\left( b_{s}\eta \right)
@@ -872,16 +872,16 @@
 \end{equation}
 where $b_{s}$ is the buoyancy at the surface.
 
-In the hydrostatic limit ($\epsilon _{nh}=0$), Eqs(\ref{eq:mom-h}), (\ref
+In the hydrostatic limit ($\epsilon _{nh}=0$), equations (\ref{eq:mom-h}), (\ref
 {eq:free-surface}) and (\ref{eq:phi-surf}) can be solved by inverting a 2-d
 elliptic equation for $\phi _{s}$ as described in Chapter 2. Both `free
 surface' and `rigid lid' approaches are available.
 
 \subsubsection{Non-hydrostatic pressure}
 
-Taking the horizontal divergence of (\ref{hor-mtm}) and adding $\frac{
-\partial }{\partial r}$ of (\ref{vertmtm}), invoking the continuity equation
-(\ref{incompressible}), we deduce that:
+Taking the horizontal divergence of (\ref{eq:mom-h}) and adding 
+$\frac{\partial }{\partial r}$ of (\ref{eq:mom-w}), invoking the continuity equation
+(\ref{eq:continuity}), we deduce that:
 
 \begin{equation}
 \nabla _{3}^{2}\phi _{nh}=\nabla .\vec{\mathbf{G}}_{\vec{v}}-\left( \mathbf{
@@ -911,7 +911,7 @@
 depending on the form chosen for the dissipative terms in the momentum
 equations - see below.
 
-Eq.(\ref{nonormalflow}) implies, making use of (\ref{mtm-split}), that:
+Eq.(\ref{nonormalflow}) implies, making use of (\ref{eq:mom-h}), that:
 
 \begin{equation}
 \widehat{n}.\nabla \phi _{nh}=\widehat{n}.\vec{\mathbf{F}}
@@ -951,7 +951,7 @@
 converges rapidly because $\phi _{nh}\ $is then only a small correction to
 the hydrostatic pressure field (see the discussion in Marshall et al, a,b).
 
-The solution $\phi _{nh}\ $to (\ref{eq:3d-invert}) and (\ref{homneuman})
+The solution $\phi _{nh}\ $to (\ref{eq:3d-invert}) and (\ref{eq:inhom-neumann-nh})
 does not vanish at $r=R_{moving}$, and so refines the pressure there.
 
 \subsection{Forcing/dissipation}
@@ -959,7 +959,7 @@
 \subsubsection{Forcing}
 
 The forcing terms $\mathcal{F}$ on the rhs of the equations are provided by
-`physics packages' described in detail in chapter ??.
+`physics packages' and forcing packages. These are described later on.
 
 \subsubsection{Dissipation}
 
@@ -1007,7 +1007,7 @@
 \subsection{Vector invariant form}
 
 For some purposes it is advantageous to write momentum advection in eq(\ref
-{hor-mtm}) and (\ref{vertmtm}) in the (so-called) `vector invariant' form:
+{eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the (so-called) `vector invariant' form:
 
 \begin{equation}
 \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t}
@@ -1025,10 +1025,10 @@
 
 \subsection{Adjoint}
 
-Tangent linear and adjoint counterparts of the forward model and described
+Tangent linear and adjoint counterparts of the forward model are described
 in Chapter 5.
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.7 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.9 2001/11/13 20:13:07 adcroft Exp $
 % $Name:  $
 
 \section{Appendix ATMOSPHERE}
@@ -1147,15 +1147,15 @@
 The final form of the HPE's in p coordinates is then: 
 \begin{eqnarray}
 \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}
-_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \\
+_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \label{eq:atmos-prime} \\
 \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\
 \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{
 \partial p} &=&0 \\
 \frac{\partial \Pi }{\partial p}\theta ^{\prime } &=&\alpha ^{\prime } \\
-\frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi }  \label{eq:atmos-prime}
+\frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } 
 \end{eqnarray}
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.7 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.9 2001/11/13 20:13:07 adcroft Exp $
 % $Name:  $
 
 \section{Appendix OCEAN}
@@ -1171,10 +1171,11 @@
 \epsilon _{nh}\frac{Dw}{Dt}+g+\frac{1}{\rho }\frac{\partial p}{\partial z}
 &=&\epsilon _{nh}\mathcal{F}_{w} \\
 \frac{1}{\rho }\frac{D\rho }{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{v}}
-_{h}+\frac{\partial w}{\partial z} &=&0 \\
-\rho &=&\rho (\theta ,S,p) \\
-\frac{D\theta }{Dt} &=&\mathcal{Q}_{\theta } \\
-\frac{DS}{Dt} &=&\mathcal{Q}_{s}  \label{eq:non-boussinesq}
+_{h}+\frac{\partial w}{\partial z} &=&0 \label{eq-zns-cont}\\
+\rho &=&\rho (\theta ,S,p) \label{eq-zns-eos}\\
+\frac{D\theta }{Dt} &=&\mathcal{Q}_{\theta } \label{eq-zns-heat}\\
+\frac{DS}{Dt} &=&\mathcal{Q}_{s}  \label{eq-zns-salt}
+\label{eq:non-boussinesq}
 \end{eqnarray}
 These equations permit acoustics modes, inertia-gravity waves,
 non-hydrostatic motions, a geostrophic (Rossby) mode and a thermo-haline
@@ -1193,8 +1194,7 @@
 \end{equation}
 
 Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is the
-reciprocal of the sound speed ($c_{s}$) squared. Substituting into \ref
-{eq-zns-cont} gives: 
+reciprocal of the sound speed ($c_{s}$) squared. Substituting into \ref{eq-zns-cont} gives: 
 \begin{equation}
 \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{
 v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}
@@ -1371,7 +1371,7 @@
 _{nh}=0$ form of these equations that are used throughout the ocean modeling
 community and referred to as the primitive equations (HPE).
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.7 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.9 2001/11/13 20:13:07 adcroft Exp $
 % $Name:  $
 
 \section{Appendix:OPERATORS}
