--- manual/s_overview/text/manual.tex	2001/10/25 12:06:56	1.7
+++ manual/s_overview/text/manual.tex	2001/11/21 14:13:17	1.14
@@ -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 1.14 2001/11/21 14:13:17 cnh 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 1.14 2001/11/21 14:13:17 cnh Exp $
 % $Name:  $
 
 \section{Introduction}
@@ -83,13 +83,58 @@
 computational platforms.
 \end{itemize}
 
-Key publications reporting on and charting the development of the model are
-listed in an Appendix.
+Key publications reporting on and charting the development of the model are:
+
+\begin{verbatim}
+
+Hill, C. and J. Marshall, (1995)
+Application of a Parallel Navier-Stokes Model to Ocean Circulation in 
+Parallel Computational Fluid Dynamics
+In Proceedings of Parallel Computational Fluid Dynamics: Implementations 
+and Results Using Parallel Computers, 545-552.
+Elsevier Science B.V.: New York
+
+Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997)
+Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling,
+J. Geophysical Res., 102(C3), 5733-5752.
+
+Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, (1997)
+A finite-volume, incompressible Navier Stokes model for studies of the ocean
+on parallel computers,
+J. Geophysical Res., 102(C3), 5753-5766.
+
+Adcroft, A.J., Hill, C.N. and J. Marshall, (1997)
+Representation of topography by shaved cells in a height coordinate ocean
+model
+Mon Wea Rev, vol 125, 2293-2315
+
+Marshall, J., Jones, H. and C. Hill, (1998)
+Efficient ocean modeling using non-hydrostatic algorithms
+Journal of Marine Systems, 18, 115-134
+
+Adcroft, A., Hill C. and J. Marshall: (1999)
+A new treatment of the Coriolis terms in C-grid models at both high and low
+resolutions,
+Mon. Wea. Rev. Vol 127, pages 1928-1936
+
+Hill, C, Adcroft,A., Jamous,D., and J. Marshall, (1999)
+A Strategy for Terascale Climate Modeling.
+In Proceedings of the Eighth ECMWF Workshop on the Use of Parallel Processors
+in Meteorology, pages 406-425
+World Scientific Publishing Co: UK
+
+Marotzke, J, Giering,R., Zhang, K.Q., Stammer,D., Hill,C., and T.Lee, (1999)
+Construction of the adjoint MIT ocean general circulation model and 
+application to Atlantic heat transport variability
+J. Geophysical Res., 104(C12), 29,529-29,547.
+
+
+\end{verbatim}
 
 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 1.14 2001/11/21 14:13:17 cnh Exp $
 % $Name:  $
 
 \section{Illustrations of the model in action}
@@ -102,7 +147,7 @@
 numerical algorithm and implementation that lie behind these calculations is
 given later. Indeed many of the illustrative examples shown below can be
 easily reproduced: simply download the model (the minimum you need is a PC
-running linux, together with a FORTRAN\ 77 compiler) and follow the examples
+running Linux, together with a FORTRAN\ 77 compiler) and follow the examples
 described in detail in the documentation.
 
 \subsection{Global atmosphere: `Held-Suarez' benchmark}
@@ -126,7 +171,7 @@
 %% CNHend
 
 As described in Adcroft (2001), a `cubed sphere' is used to discretize the
-globe permitting a uniform gridding and obviated the need to Fourier filter.
+globe permitting a uniform griding and obviated the need to Fourier filter.
 The `vector-invariant' form of MITgcm supports any orthogonal curvilinear
 grid, of which the cubed sphere is just one of many choices.
 
@@ -163,7 +208,7 @@
 visible.
 
 %% CNHbegin
-\input{part1/ocean_gyres_figure}
+\input{part1/atl6_figure}
 %% CNHend
 
 
@@ -191,7 +236,7 @@
 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
@@ -231,7 +276,7 @@
 
 As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity}
 maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude
-of the overturning streamfunction shown in figure \ref{fig:large-scale-circ}
+of the overturning stream-function shown in figure \ref{fig:large-scale-circ}
 at 60$^{\circ }$N and $
 \mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over
 a 100 year period. We see that $J$ is
@@ -248,7 +293,7 @@
 An important application of MITgcm is in state estimation of the global
 ocean circulation. An appropriately defined `cost function', which measures
 the departure of the model from observations (both remotely sensed and
-insitu) over an interval of time, is minimized by adjusting `control
+in-situ) over an interval of time, is minimized by adjusting `control
 parameters' such as air-sea fluxes, the wind field, the initial conditions
 etc. Figure \ref{fig:assimilated-globes} shows an estimate of the time-mean
 surface elevation of the ocean obtained by bringing the model in to
@@ -256,7 +301,7 @@
 1992-1997. {\bf CHANGE THIS TEXT - FIG FROM PATRICK/CARL/DETLEF}
 
 %% CNHbegin
-\input{part1/globes_figure}
+\input{part1/assim_figure}
 %% CNHend
 
 \subsection{Ocean biogeochemical cycles}
@@ -277,7 +322,7 @@
 \subsection{Simulations of laboratory experiments}
 
 Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a 
-laboratory experiment enquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An
+laboratory experiment inquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An
 initially homogeneous tank of water ($1m$ in diameter) is driven from its
 free surface by a rotating heated disk. The combined action of mechanical
 and thermal forcing creates a lens of fluid which becomes baroclinically
@@ -289,7 +334,7 @@
 \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 1.14 2001/11/21 14:13:17 cnh Exp $
 % $Name:  $
 
 \section{Continuous equations in `r' coordinates}
@@ -326,31 +371,33 @@
 \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:
 
@@ -430,7 +477,7 @@
 
 \begin{equation}
 \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \
-(oceansurface,bottomoftheatmosphere)}  \label{eq:movingbc}
+(ocean surface,bottom of the atmosphere)}  \label{eq:movingbc}
 \end{equation}
 
 Here
@@ -523,8 +570,8 @@
 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 +607,8 @@
 \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 +621,7 @@
 \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 +714,6 @@
 
 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 +776,7 @@
 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 +825,8 @@
 \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 +883,8 @@
 
 \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 +909,7 @@
 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 +917,16 @@
 \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 +956,7 @@
 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 +996,7 @@
 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 +1004,7 @@
 \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 +1052,7 @@
 \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 +1070,10 @@
 
 \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 1.14 2001/11/21 14:13:17 cnh Exp $
 % $Name:  $
 
 \section{Appendix ATMOSPHERE}
@@ -1147,15 +1192,15 @@
 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 1.14 2001/11/21 14:13:17 cnh Exp $
 % $Name:  $
 
 \section{Appendix OCEAN}
@@ -1171,13 +1216,14 @@
 \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
+non-hydrostatic motions, a geostrophic (Rossby) mode and a thermohaline
 mode. As written, they cannot be integrated forward consistently - if we
 step $\rho $ forward in (\ref{eq-zns-cont}), the answer will not be
 consistent with that obtained by stepping (\ref{eq-zns-heat}) and (\ref
@@ -1193,8 +1239,7 @@
 \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 +1416,7 @@
 _{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 1.14 2001/11/21 14:13:17 cnh Exp $
 % $Name:  $
 
 \section{Appendix:OPERATORS}
