Changeset 10442

NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.sty

-                      r10146
+                      r10442
 %% ==============================================================================
 %% NEMO_manual.sty: all customizations (packages, )
+%% NEMO_manual.sty: all customizations (packages, styles, cmds)
 %% ==============================================================================
 …
 \usepackage{caption}          %% caption
 \usepackage{xcolor}           %% color
-\usepackage{silence}          %% compilation
 \usepackage{times}            %% font
 \usepackage{hyperref}         %% hyper
 …
 %% Extensions in bundle package
 \usepackage{amssymb, graphicx, makeidx, tabularx, xspace}
+\usepackage{amssymb, graphicx, makeidx, tabularx}
 …
 \graphicspath{{../../../figures/}}
 \hypersetup{
    pdftitle={NEMO ocean engine}, pdfauthor={Gurvan Madec, and the NEMO team},
+   pdftitle={NEMO ocean engine}, pdfauthor={Gurvan Madec, and NEMO System Team},
    colorlinks
+}
 …
 \pagestyle{fancy}
 \bibliographystyle{../main/ametsoc}
 %% Additionnal fonts
 …
+%% Macros (to check)
+%% Global custom commands: \newcommand{<name>}[<args>][<first argument value>]{<code>}
+%% ==============================================================================
+\def\deg{$^{\circ}$}
+\def\degC{$^{\circ}C$}
+\def\degK{$^{\circ}K$}
+\def\degN{$^{\circ}N$}
+\def\degS{$^{\circ}S$}
+%% NEMO and Fortran in small capitals
+\newcommand{\NEMO}{\textsc{nemo}}
+\newcommand{\fortran}{\textsc{Fortran}}
+\newcommand{\fninety}{\textsc{Fortran 90}}
+\def\half{\textstyle\frac{1}{2}}
+\def\hhalf{\scriptstyle\frac{1}{2}}
+%% Common aliases
+\renewcommand{\deg}[1][]{\ensuremath{^{\circ}#1}}
+\newcommand{\zstar }{\ensuremath{z^\star}}
+\newcommand{\sstar }{\ensuremath{s^\star}}
+\newcommand{\ztilde}{\ensuremath{\tilde z}}
+\newcommand{\stilde}{\ensuremath{\tilde s}}
+\newcommand{\ie}{\ensuremath{i.e.}}
+\newcommand{\eg}{\ensuremath{e.g.}}
+\def\quarter{\textstyle\frac{1}{4}}
+\def\qquarter{\scriptstyle\frac{1}{4}}
+\def\squarter{\sfrac{1}{4}}
+\def\stwelfth{\sfrac{1}{12}}
+\def\sthirtysixth{\sfrac{1}{36}}
+%% Inline maths
+\newcommand{\fractext}[2]{\textstyle \frac{#1}{#2}}
+\newcommand{\rdt}{\Delta t}
+\def\bgamma\boldsymbol{\gamma}
+\def\rdt{\Delta t}
+%% Text env. for Gurvan
+\newcommand{\gmcomment}[1]{}
+%% Index (italic font for files, preformat for code)
+\newcommand{\ifile}[1]{\textit{#1.nc}          \index{Input NetCDF files!#1.nc}}
+\newcommand{\mdl}[1]{\textit{#1.F90}           \index{Modules!#1}}
+\newcommand{\jp}[1]{\texttt{#1}                \index{Model parameters!#1}}
+\newcommand{\key}[1]{\texttt{\textbf{key\_#1}} \index{CPP keys!key\_#1}}
+\newcommand{\ngn}[1]{\texttt{#1}               \index{Namelist Group Name!#1}}
+\newcommand{\np}[1]{\texttt{#1}                \index{Namelist variables!#1}}
+\newcommand{\rou}[1]{\texttt{#1}               \index{Routines!#1}}
+%% Maths
+\newcommand{\vect}[1]{\ensuremath{\mathbf{#1}}}
+\newcommand{\pd}[2][]{\ensuremath{\frac{\partial #1}{\partial #2}}}
+%% Shortened DOI in bibliography
+\newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{doi:#1}}
+%% Namelists inclusion
+\newcommand{\nlst}[1]{\forfile{../../../namelists/#1}}
+%% New commands
+%% Minted package: syntax highlighting configuration
+%% ==============================================================================
+\newcommand{\gmcomment}[1]{}
 \newcommand{\sfcomment}[1]{}
 \newcommand{\sgacomment}[1]{}
+%% Global highlighting style
+\setminted{style=emacs, fontsize=\scriptsize, breaklines, frame=leftline}
+\setminted[xml]{style=borland} %% Specific per language
+\newcommand{\nl}[1]{\texttt{\small{\textcolor{blue}{#1}}}}
+\newcommand{\NEMO}{\textit{NEMO}\xspace}
+%% Oneliner
+\newmint[forline]{fortran}{}   % \forline|...|
+\newmint[xmlline]{xml}{}       % \xmlline|...|
+\newmint[cmd]{console}{}       % \cmd|...|
+\newcommand{\hf}[1]{\textit{#1.h90}\index{h90 file!#1}}
+\newcommand{\ifile}[1]{\textit{#1.nc}\index{Input NetCDF files!#1.nc}}
+\newcommand{\jp}[1]{\textit{#1}\index{Model parameters!#1}}
+\newcommand{\key}[1]{\textbf{key\_#1}\index{CPP keys!key\_#1}}
+\newcommand{\mdl}[1]{\textit{#1.F90}\index{Modules!#1}}
+\newcommand{\ngn}[1]{\textit{#1}\index{Namelist Group Name!#1}}
+\newcommand{\np}[1]{\textit{#1}\index{Namelist variables!#1}}
+\newcommand{\rou}[1]{\textit{#1}\index{Routines!#1}}
+%% Multi-lines
+\newminted[forlines]{fortran}{}   % \begin{forlines}
+\newminted[xmllines]{xml}{}       % \begin{xmllines}
+\newminted[cmds]{console}{}       % \begin{cmds}
+\newminted[clines]{c}{}           % \begin{clines}
+\newcommand{\grad}{\nabla}
 \newcommand{\gradh}{\nabla_h}
+%% File
+\newmintedfile[forfile]{fortran}{}   % \forfile{../namelists/nam...}
+\newcommand{\ew}[3]{{e_{3#1}}_{\,#2}^{\,#3} }
+\newcommand{\vect}[1]{\ensuremath{\mathbf{#1}}}
+\newcommand{\Div}{\grad\cdot}
+\newcommand{\curl}{\nabla \times}
+\newcommand{\pd}[2][]{\frac{\partial #1}{\partial #2}}
+\newcommand{\alpbet} {\left(\alpha / \beta \right)}
+\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}}
+\newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}}
+\newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}}
+\newcommand{\rtriad}[2][]{\ensuremath{\triad[#1]{i}{k}{#2}{i_p}{k_p}}}
+\newcommand{\rtriadt}[1]{\ensuremath{\triadt{i}{k}{#1}{i_p}{k_p}}}
+\newcommand{\Alts}{{A}}
+\newcommand{\Alt}{{A^{lT}}}
+\newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}}
+\newcommand{\rML}[1][i]{r_{\mathrm{ML}\,#1}}
+\newcommand{\mygstrut}[2]{\rule[#1 em]{0pt}{#2 em}}
+\newcommand{\mystrut}{\rule[-.9 em]{0pt}{1.79 em}}
+\newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{full-text}}
+\newcommand{\nlst}[1]{\forfile{../../../namelists/#1}}
+%% Inline
+\newmintinline[forcode]{fortran}{fontsize=auto, frame=lines}   % \forcode{...}
+\newmintinline[xmlcode]{xml}{    fontsize=auto, frame=lines}   % \xmlcode{...}
+\newmintinline[snippet]{console}{fontsize=auto, frame=lines}   % \snippet{...}

NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.tex

-                      r10414
+                      r10442
 %% Custom style
 \usepackage{../main/NEMO_manual}
-\usepackage{../main/NEMO_minted}
 \makeindex
 …
 %% ==============================================================================
+%% Trick to include biblio in subfile compilation
+\newcommand{\biblio}{
+  \bibliographystyle{../main/ametsoc}
+  \bibliography{../main/NEMO_manual}
+}
+%% Include references and index for single subfile compilation
+\newcommand{\biblio}{\bibliography{../main/NEMO_manual}}
+\newcommand{\pindex}{\printindex}
 \begin{document}
+%% Trick to include biblio in subfile compilation
+\def\biblio{}
+%% Override custom cmds for full manual compilation
+\renewcommand{\biblio}{}
+\renewcommand{\pindex}{}
 …
 \author{
+\Large Gurvan Madec, and the NEMO team                                                          \\
+\texttt{\small\href{mailto:gurvan.madec@locean-ipsl.umpc.fr}{gurvan.madec@locean-ipsl.umpc.fr}} \\
+  \Large Gurvan Madec and NEMO System Team
+  \thanks{
+    Yevgeny Aksenov, Mireck Andrejczuk, Mike Bell, Romain Bourdalle-Badie, Cl\'{e}ment Bricaud,
+    J\'{e}r\^{o}me Chanut, Stefania Ciliberti, Emanuela Clementi, Andrew Coward, Damiano Delrosso,
+    Massimiliano Drudi, Christian Eth\'{e}, Simona Flavoni, Doroteaciro Iovino, Claire L\'{e}vy, Tomas Lovato,
+    Nicolas Martin, S\'{e}bastien Masson, Pierre Mathiot, Gelsomina Mattia, Francesca Mele, Silvia Mocavero,
+    George Nurser, Enda O'Dea, Julien Paul, Cl\'{e}ment Rousset, Dave Storkey, Martin Vancoppenolle
+  }                                                        \\
+                                                           \\
+  \textit{Issue 27, Notes du P\^{o}le de mod\'{e}lisation} \\
+  \textit{Institut Pierre-Simon Laplace (IPSL)}            \\
+  \textit{ISSN 1288-1619}
+}
+\date{
+Decembre 2017                                                                                \\
+{\small  -- version 4.0 alpha --}                                                            \\
+~                                                                                            \\
+\textit{\small Note du P\^ole de mod\'{e}lisation de l'Institut Pierre-Simon Laplace No 27 } \\
+\vspace{0.45cm}{ ISSN No 1288-1619.}
+}
+\date{Version 4.0 -- January 2019}
 %\date{\today}

NEMO/trunk/doc/latex/NEMO/subfiles/annex_A.tex

-                      r10414
+                      r10442
 In order to establish the set of Primitive Equation in curvilinear $s$-coordinates
 ($i.e.$ an orthogonal curvilinear coordinate in the horizontal and
+(\ie an orthogonal curvilinear coordinate in the horizontal and
 an Arbitrary Lagrangian Eulerian (ALE) coordinate in the vertical),
 we start from the set of equations established in \autoref{subsec:PE_zco_Eq} for
 …
 \]
 leads to the $s-$coordinate formulation of the total $z-$coordinate time derivative,
 $i.e.$ the total $s-$coordinate time derivative :
+\ie the total $s-$coordinate time derivative :
 \begin{align}
   \label{apdx:A_sco_Dt_vect}
 …
+%
 Introducing the vertical scale factor inside the horizontal derivative of the first two terms
 ($i.e.$ the horizontal divergence), it becomes :
+(\ie the horizontal divergence), it becomes :
 \begin{align*}
+  {
 …
 \end{align*}
 which leads to the $s-$coordinate flux formulation of the total $s-$coordinate time derivative,
 $i.e.$ the total $s-$coordinate time derivative in flux form:
+\ie the total $s-$coordinate time derivative in flux form:
 \begin{flalign}
   \label{apdx:A_sco_Dt_flux}
 …
 in particular the pressure gradient.
 By contrast, $\omega$ is not $w$, the third component of the velocity, but the dia-surface velocity component,
 $i.e.$ the volume flux across the moving $s$-surfaces per unit horizontal area.
+\ie the volume flux across the moving $s$-surfaces per unit horizontal area.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/annex_B.tex

r10414	r10442
402	402	\biblio
403	403
	404	\pindex
	405
404	406	\end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/annex_C.tex

-                      r10414
+                      r10442
 \minitoc
 %%%  Appendix put in gmcomment as it has not been updated for z* and s coordinate
+%%%  Appendix put in gmcomment as it has not been updated for \zstar and s coordinate
 %I'm writting this appendix. It will be available in a forthcoming release of the documentation
 …
 $dv=e_1\,e_2\,e_3 \,di\,dj\,dk$  is the volume element, with only $e_3$ that depends on time.
 $D$ and $S$ are the ocean domain volume and surface, respectively.
 No wetting/drying is allow ($i.e.$ $\frac{\partial S}{\partial t} = 0$).
+No wetting/drying is allow (\ie $\frac{\partial S}{\partial t} = 0$).
 Let $k_s$ and $k_b$ be the ocean surface and bottom, resp.
 ($i.e.$ $s(k_s) = \eta$ and $s(k_b)=-H$, where $H$ is the bottom depth).
+(\ie $s(k_s) = \eta$ and $s(k_b)=-H$, where $H$ is the bottom depth).
 \begin{flalign*}
   z(k) = \eta - \int\limits_{\tilde{k}=k}^{\tilde{k}=k_s}  e_3(\tilde{k}) \;d\tilde{k}
 …
 \label{sec:C.1}
 The discretization of pimitive equation in $s$-coordinate ($i.e.$ time and space varying vertical coordinate)
+The discretization of pimitive equation in $s$-coordinate (\ie time and space varying vertical coordinate)
 must be chosen so that the discrete equation of the model satisfy integral constrains on energy and enstrophy.
 Let us first establish those constraint in the continuous world.
 The total energy ($i.e.$ kinetic plus potential energies) is conserved:
+The total energy (\ie kinetic plus potential energies) is conserved:
 \begin{flalign}
   \label{eq:Tot_Energy}
 …
   +   \frac{1}{2} \int_D {  \frac{{\textbf{U}_h}^2}{e_3} \partial_t ( e_3) \;dv }
 \]
 Indeed, using successively \autoref{eq:DOM_di_adj} ($i.e.$ the skew symmetry property of the $\delta$ operator)
+Indeed, using successively \autoref{eq:DOM_di_adj} (\ie the skew symmetry property of the $\delta$ operator)
 and the continuity equation, then \autoref{eq:DOM_di_adj} again,
 then the commutativity of operators $\overline {\,\cdot \,}$ and $\delta$, and finally \autoref{eq:DOM_mi_adj}
 ($i.e.$ the symmetry property of the $\overline {\,\cdot \,}$ operator)
+(\ie the symmetry property of the $\overline {\,\cdot \,}$ operator)
 applied in the horizontal and vertical directions, it becomes:
 \begin{flalign*}
 …
 When the equation of state is linear
 ($i.e.$ when an advection-diffusion equation for density can be derived from those of temperature and salinity)
+(\ie when an advection-diffusion equation for density can be derived from those of temperature and salinity)
 the change of KE due to the work of pressure forces is balanced by
 the change of potential energy due to buoyancy forces:
 …
+  %
   \allowdisplaybreaks
   \intertext{Using successively \autoref{eq:DOM_di_adj}, $i.e.$ the skew symmetry property of
+  \intertext{Using successively \autoref{eq:DOM_di_adj}, \ie the skew symmetry property of
     the $\delta$ operator, \autoref{eq:wzv}, the continuity equation, \autoref{eq:dynhpg_sco},
     the hydrostatic equation in the $s$-coordinate, and $\delta_{k+1/2} \left[ z_t \right] \equiv e_{3w} $,
 …
 Let us first consider the first term of the scalar product
 ($i.e.$ just the the terms associated with the i-component of the advection):
+(\ie just the the terms associated with the i-component of the advection):
 \begin{flalign*}
   &  - \int_D u \cdot \nabla \cdot \left(   \textbf{U}\,u   \right) \; dv   \\
 …
 When the UBS scheme is used to evaluate the flux form momentum advection,
 the discrete operator does not contribute to the global budget of linear momentum (flux form).
 The horizontal kinetic energy is not conserved, but forced to decay ($i.e.$ the scheme is diffusive).
+The horizontal kinetic energy is not conserved, but forced to decay (\ie the scheme is diffusive).
 % ================================================================
 …
 The scheme does not allow but the conservation of the total kinetic energy but the conservation of $q^2$,
 the potential enstrophy for a horizontally non-divergent flow ($i.e.$ when $\chi$=$0$).
+the potential enstrophy for a horizontally non-divergent flow (\ie when $\chi$=$0$).
 Indeed, using the symmetry or skew symmetry properties of the operators
 ( \autoref{eq:DOM_mi_adj} and \autoref{eq:DOM_di_adj}),
 …
+  }
 \end{flalign*}
 The later equality is obtain only when the flow is horizontally non-divergent, $i.e.$ $\chi$=$0$.
+The later equality is obtain only when the flow is horizontally non-divergent, \ie $\chi$=$0$.
 % -------------------------------------------------------------------------------------------------------------
 …
 \end{equation}
 This formulation does conserve the potential enstrophy for a horizontally non-divergent flow ($i.e.$ $\chi=0$).
+This formulation does conserve the potential enstrophy for a horizontally non-divergent flow (\ie $\chi=0$).
 Let consider one of the vorticity triad, for example ${^{i}_j}\mathbb{Q}^{+1/2}_{+1/2} $,
 …
 the internal dynamics and physics (equations in flux form).
 For advection,
 only the CEN2 scheme ($i.e.$ $2^{nd}$ order finite different scheme) conserves the global variance of tracer.
+only the CEN2 scheme (\ie $2^{nd}$ order finite different scheme) conserves the global variance of tracer.
 Nevertheless the other schemes ensure that the global variance decreases
 ($i.e.$ they are at least slightly diffusive).
+(\ie they are at least slightly diffusive).
 For diffusion, all the schemes ensure the decrease of the total tracer variance, except the iso-neutral operator.
 There is generally no strict conservation of mass,
 …
 The conservation of the variance of tracer due to the advection tendency can be achieved only with the CEN2 scheme,
 $i.e.$ when $\tau_u= \overline T^{\,i+1/2}$, $\tau_v= \overline T^{\,j+1/2}$, and $\tau_w= \overline T^{\,k+1/2}$.
+\ie when $\tau_u= \overline T^{\,i+1/2}$, $\tau_v= \overline T^{\,j+1/2}$, and $\tau_w= \overline T^{\,k+1/2}$.
 It can be demonstarted as follows:
 \begin{flalign*}
 …
 the conservation of potential vorticity and the horizontal divergence,
 and the dissipation of the square of these quantities
 ($i.e.$ enstrophy and the variance of the horizontal divergence) as well as
+(\ie enstrophy and the variance of the horizontal divergence) as well as
 the dissipation of the horizontal kinetic energy.
 In particular, when the eddy coefficients are horizontally uniform,
 …
 \end{flalign*}
 If the vertical diffusion coefficient is uniform over the whole domain, the enstrophy is dissipated, $i.e.$
+If the vertical diffusion coefficient is uniform over the whole domain, the enstrophy is dissipated, \ie
 \begin{flalign*}
   \int\limits_D \zeta \, \textbf{k} \cdot \nabla \times
 …
     \left( \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k} \right) \right)\; dv = 0    &&&
 \end{flalign*}
 and the square of the horizontal divergence decreases ($i.e.$ the horizontal divergence is dissipated) if
+and the square of the horizontal divergence decreases (\ie the horizontal divergence is dissipated) if
 the vertical diffusion coefficient is uniform over the whole domain:
 …
 the heat and salt contents are conserved (equations in flux form).
 Since a flux form is used to compute the temperature and salinity,
 the quadratic form of these quantities ($i.e.$ their variance) globally tends to diminish.
+the quadratic form of these quantities (\ie their variance) globally tends to diminish.
 As for the advection term, there is conservation of mass only if the Equation Of Seawater is linear.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/annex_D.tex

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+                      r10442
 \label{sec:D_coding}
 - Use of the universal language \textsc{Fortran} 90, and try to avoid obsolescent features like statement functions,
+- Use of the universal language \fninety, and try to avoid obsolescent features like statement functions,
 do not use GO TO and EQUIVALENCE statements.
 …
 %--------------------------------------------------------------------------------------------------------------
 N.B. Parameter here, in not only parameter in the \textsc{Fortran} acceptation,
+N.B. Parameter here, in not only parameter in the \fortran acceptation,
 it is also used for code variables that are read in namelist and should never been modified during a simulation.
 It is the case, for example, for the size of a domain (jpi,jpj,jpk).
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/annex_E.tex

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+                      r10442
 $\tau "_i =\frac{e_{1T}}{e_{2T}\,e_{3T}}\delta_i \left[ \frac{e_{2u} e_{3u} }{e_{1u} }\delta_{i+1/2}[\tau] \right]$.
 This results in a dissipatively dominant (i.e. hyper-diffusive) truncation error
+This results in a dissipatively dominant (\ie hyper-diffusive) truncation error
 \citep{Shchepetkin_McWilliams_OM05}.
 The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}.
 …
 \end{equation}
 with ${A_u^{lT}}^2 = \frac{1}{12} {e_{1u}}^3\ |u|$,
 $i.e.$ $A_u^{lT} = \frac{1}{\sqrt{12}} \,e_{1u}\ \sqrt{ e_{1u}\,|u|\,}$
+\ie $A_u^{lT} = \frac{1}{\sqrt{12}} \,e_{1u}\ \sqrt{ e_{1u}\,|u|\,}$
 it comes:
 \begin{equation}
 …
   \end{split}
 \end{equation}
 if the velocity is uniform ($i.e.$ $|u|=cst$) then the diffusive flux is
+if the velocity is uniform (\ie $|u|=cst$) then the diffusive flux is
 \begin{equation}
   \label{eq:tra_ldf_lap}
 …
   \end{split}
 \end{equation}
 if the velocity is uniform ($i.e.$ $|u|=cst$) and
+if the velocity is uniform (\ie $|u|=cst$) and
 choosing $\tau "_i =\frac{e_{1T}}{e_{2T}\,e_{3T}}\delta_i \left[ \frac{e_{2u} e_{3u} }{e_{1u} } \delta_{i+1/2}[\tau] \right]$
 …
 not $2\rdt$ as it can be found sometimes in literature.
 The leap-Frog time stepping is a second order centered scheme.
 As such it respects the quadratic invariant in integral forms, $i.e.$ the following continuous property,
+As such it respects the quadratic invariant in integral forms, \ie the following continuous property,
 \[
   % \label{eq:Energy}
 …
 Let try to define a scheme that get its inspiration from the \citet{Griffies_al_JPO98} scheme,
 but is formulated within the \NEMO framework
 ($i.e.$ using scale factors rather than grid-size and having a position of $T$-points that
+(\ie using scale factors rather than grid-size and having a position of $T$-points that
 is not necessary in the middle of vertical velocity points, see \autoref{fig:zgr_e3}).
 …
 (see \autoref{chap:LDF}).
 Nevertheless, this technique works fine for $T$ and $S$ as they are active tracers
 ($i.e.$ they enter the computation of density), but it does not work for a passive tracer.
+(\ie they enter the computation of density), but it does not work for a passive tracer.
 \citep{Griffies_al_JPO98} introduce a different way to discretise the off-diagonal terms that
 nicely solve the problem.
 …
 \item[$\bullet$ implicit treatment in the vertical]
   In the diagonal term associated with the vertical divergence of the iso-neutral fluxes
   (i.e. the term associated with a second order vertical derivative)
+  \ie the term associated with a second order vertical derivative)
   appears only tracer values associated with a single water column.
   This is of paramount importance since it means that
 …
 \item[$\bullet$ pure iso-neutral operator]
   The iso-neutral flux of locally referenced potential density is zero, $i.e.$
+  The iso-neutral flux of locally referenced potential density is zero, \ie
   \begin{align*}
     % \label{eq:Gf_property2}
 …
 \item[$\bullet$ conservation of tracer]
   The iso-neutral diffusion term conserve the total tracer content, $i.e.$
+  The iso-neutral diffusion term conserve the total tracer content, \ie
   \[
     % \label{eq:Gf_property1}
 …
 \item[$\bullet$ decrease of tracer variance]
   The iso-neutral diffusion term does not increase the total tracer variance, $i.e.$
+  The iso-neutral diffusion term does not increase the total tracer variance, \ie
   \[
     % \label{eq:Gf_property1}
 …
 It is a key property for a diffusion term.
 It means that the operator is also a dissipation term,
 $i.e.$ it is a sink term for the square of the quantity on which it is applied.
+\ie it is a sink term for the square of the quantity on which it is applied.
 It therfore ensures that, when the diffusivity coefficient is large enough,
 the field on which it is applied become free of grid-point noise.
 \item[$\bullet$ self-adjoint operator]
   The iso-neutral diffusion operator is self-adjoint, $i.e.$
+  The iso-neutral diffusion operator is self-adjoint, \ie
   \[
     % \label{eq:Gf_property1}
 …
 the formulation of which depends on the slopes of iso-neutral surfaces.
 Contrary to the case of iso-neutral mixing, the slopes used here are referenced to the geopotential surfaces,
 $i.e.$ \autoref{eq:ldfslp_geo} is used in $z$-coordinate,
+\ie \autoref{eq:ldfslp_geo} is used in $z$-coordinate,
 and the sum \autoref{eq:ldfslp_geo} + \autoref{eq:ldfslp_iso} in $z^*$ or $s$-coordinates.
 …
 Nevertheless this property can be used to choose a discret form of \autoref{eq:eiv_skew_continuous} which
 is consistent with the iso-neutral operator \autoref{eq:Gf_operator}.
 Using the slopes \autoref{eq:Gf_slopes} and defining $A_e$ at $T$-point($i.e.$ as $A$,
+Using the slopes \autoref{eq:Gf_slopes} and defining $A_e$ at $T$-point(\ie as $A$,
 the eddy diffusivity coefficient), the resulting discret form is given by:
 \begin{equation}
 …
 it uses the same definition for the slopes.
 It also ensures the conservation of the tracer variance (see Appendix \autoref{apdx:eiv_skew}),
 $i.e.$ it does not include a diffusive component but is a "pure" advection term.
+\ie it does not include a diffusive component but is a "pure" advection term.
 $\ $\newpage      %force an empty line
 …
 Exactly the same thing occurs for the triad ${_i^k \mathbb{R}_{-1/2}^{+1/2}}$ in the $i$ direction.
 Therefore the sum over the domain is zero,
 $i.e.$ the variance of the tracer is preserved by the discretisation of the skew fluxes.
+\ie the variance of the tracer is preserved by the discretisation of the skew fluxes.
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/annex_iso.tex

-                      r10414
+                      r10442
 \documentclass[../main/NEMO_manual]{subfiles}
+%% Local cmds
+\newcommand{\rML}[1][i]{\ensuremath{_{\mathrm{ML}\,#1}}}
+\newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}}
+\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}}
+\newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}}
+\newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}}
+\newcommand{\rtriad}[2][]{\ensuremath{\triad[#1]{i}{k}{#2}{i_p}{k_p}}}
+\newcommand{\rtriadt}[1]{\ensuremath{\triadt{i}{k}{#1}{i_p}{k_p}}}
 \begin{document}
 …
 % Iso-neutral diffusion :
 % ================================================================
+\chapter[Iso-Neutral Diffusion and Eddy Advection using Triads]
+         {\texorpdfstring{Iso-Neutral Diffusion and\\ Eddy Advection using Triads}{Iso-Neutral Diffusion and Eddy Advection using Triads}}
+\chapter{Iso-Neutral Diffusion and Eddy Advection using Triads}
 \label{apdx:triad}
 …
 even though the eddy advection is accomplished by means of the skew fluxes.
 The options specific to the Griffies scheme include:
 \begin{description}[font=\normalfont]
+\begin{description}
 \item[\np{ln\_triad\_iso}]
   See \autoref{sec:taper}.
 …
 \end{description}
 The options shared with the Standard scheme include:
 \begin{description}[font=\normalfont]
+\begin{description}
 \item[\np{ln\_traldf\_msc}]   blah blah to be added
 \item[\np{rn\_slpmax}]  blah blah to be added
 …
   \label{eq:iso_tensor_1}
   \begin{equation}
     D^{lT}=-\Div\vect{f}^{lT}\equiv
+    D^{lT}=-\nabla \cdot\vect{f}^{lT}\equiv
     -\frac{1}{e_1e_2e_3}\left[\pd{i}\left (f_1^{lT}e_2e_3\right) +
       \pd{j}\left (f_2^{lT}e_2e_3\right) + \pd{k}\left (f_3^{lT}e_1e_2\right)\right],
 …
   where the diffusive flux per unit area of physical space
   \begin{equation}
     \vect{f}^{lT}=-\Alt\Re\cdot\grad T,
+    \vect{f}^{lT}=-{A^{lT}}\Re\cdot\nabla T,
   \end{equation}
   \begin{equation}
 …
     \mbox{with}\quad \;\;\Re =
     \begin{pmatrix}
    &  0   & -r_1           \mystrut \\
    &  1   & -r_2           \mystrut \\
       -r_1 & -r_2 &  r_1 ^2+r_2 ^2 \mystrut
+   &  0   & -r_1           \rule[-.9 em]{0pt}{1.79 em} \\
+   &  1   & -r_2           \rule[-.9 em]{0pt}{1.79 em} \\
+      -r_1 & -r_2 &  r_1 ^2+r_2 ^2 \rule[-.9 em]{0pt}{1.79 em}
     \end{pmatrix}
     \quad \text{and} \quad\grad T=
+    \quad \text{and} \quad\nabla T=
     \begin{pmatrix}
       \frac{1}{e_1} \pd[T]{i} \mystrut \\
       \frac{1}{e_2} \pd[T]{j} \mystrut \\
       \frac{1}{e_3} \pd[T]{k} \mystrut
+      \frac{1}{e_1} \pd[T]{i} \rule[-.9 em]{0pt}{1.79 em} \\
+      \frac{1}{e_2} \pd[T]{j} \rule[-.9 em]{0pt}{1.79 em} \\
+      \frac{1}{e_3} \pd[T]{k} \rule[-.9 em]{0pt}{1.79 em}
     \end{pmatrix}
+    .
 …
 \begin{align}
   \label{eq:i13c}
   f_{13}=&+\Alt r_1\frac{1}{e_3}\frac{\partial T}{\partial k},\qquad f_{23}=+\Alt r_2\frac{1}{e_3}\frac{\partial T}{\partial k}\\
+  f_{13}=&+{A^{lT}} r_1\frac{1}{e_3}\frac{\partial T}{\partial k},\qquad f_{23}=+{A^{lT}} r_2\frac{1}{e_3}\frac{\partial T}{\partial k}\\
   \intertext{and in the k-direction resulting from the lateral tracer gradients}
   \label{eq:i31c}
   f_{31}+f_{32}=& \Alt r_1\frac{1}{e_1}\frac{\partial T}{\partial i}+\Alt r_2\frac{1}{e_1}\frac{\partial T}{\partial i}
+  f_{31}+f_{32}=& {A^{lT}} r_1\frac{1}{e_1}\frac{\partial T}{\partial i}+{A^{lT}} r_2\frac{1}{e_1}\frac{\partial T}{\partial i}
 \end{align}
 …
 \begin{equation}
   \label{eq:i33c}
   f_{33}=-\Alt(r_1^2 +r_2^2) \frac{1}{e_3}\frac{\partial T}{\partial k}.
+  f_{33}=-{A^{lT}}(r_1^2 +r_2^2) \frac{1}{e_3}\frac{\partial T}{\partial k}.
 \end{equation}
 …
 the $1/{e_{3}}_{i+1/2}^k$ associated with the vertical tracer gradient, is then \autoref{eq:tra_ldf_iso}
 \[
   \left(F_u^{13} \right)_{i+\hhalf}^k = \Alts_{i+\hhalf}^k
+  \left(F_u^{13} \right)_{i+\frac{1}{2}}^k = {A}_{i+\frac{1}{2}}^k
   {e_{2}}_{i+1/2}^k \overline{\overline
     r_1} ^{\,i,k}\,\overline{\overline{\delta_k T}}^{\,i,k},
 …
   \frac{\delta_{i+1/2} [\rho]}{\overline{\overline{\delta_k \rho}}^{\,i,k}},
 \]
 and here and in the following we drop the $^{lT}$ superscript from $\Alt$ for simplicity.
+and here and in the following we drop the $^{lT}$ superscript from ${A^{lT}}$ for simplicity.
 Unfortunately the resulting combination $\overline{\overline{\delta_k\bullet}}^{\,i,k}$ of a $k$ average and
 a $k$ difference of the tracer reduces to $\bullet_{k+1}-\bullet_{k-1}$,
 …
 To correct this, we introduced a smoothing of the slopes of the iso-neutral surfaces (see \autoref{chap:LDF}).
 This technique works for $T$ and $S$ in so far as they are active tracers
 ($i.e.$ they enter the computation of density), but it does not work for a passive tracer.
+(\ie they enter the computation of density), but it does not work for a passive tracer.
 \subsection{Expression of the skew-flux in terms of triad slopes}
 …
 \begin{multline}
   \label{eq:i13}
   \left( F_u^{13}  \right)_{i+\frac{1}{2}}^k = \Alts_{i+1}^k a_1 s_1
+  \left( F_u^{13}  \right)_{i+\frac{1}{2}}^k = {A}_{i+1}^k a_1 s_1
   \delta_{k+\frac{1}{2}} \left[ T^{i+1}
   \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  + \Alts _i^k a_2 s_2 \delta
+  \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  + {A} _i^k a_2 s_2 \delta
   _{k+\frac{1}{2}} \left[ T^i
   \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}} \\
   +\Alts _{i+1}^k a_3 s_3 \delta_{k-\frac{1}{2}} \left[ T^{i+1}
   \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  +\Alts _i^k a_4 s_4 \delta
+  +{A} _{i+1}^k a_3 s_3 \delta_{k-\frac{1}{2}} \left[ T^{i+1}
+  \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  +{A} _i^k a_4 s_4 \delta
   _{k-\frac{1}{2}} \left[ T^i \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}},
 \end{multline}
 where the contributions of the triad fluxes are weighted by areas $a_1, \dotsc a_4$,
 and $\Alts$ is now defined at the tracer points rather than the $u$-points.
+and ${A}$ is now defined at the tracer points rather than the $u$-points.
 This discretization gives a much closer stencil, and disallows the two-point computational modes.
 The vertical skew flux \autoref{eq:i31c} from tracer cell $i,k$ to $i,k+1$ at
 the $w$-point $i,k+\hhalf$ is constructed similarly (\autoref{fig:ISO_triad}b) by
+the $w$-point $i,k+\frac{1}{2}$ is constructed similarly (\autoref{fig:ISO_triad}b) by
 multiplying lateral tracer gradients from each of the four surrounding $u$-points by the appropriate triad slope:
 \begin{multline}
   \label{eq:i31}
   \left( F_w^{31} \right) _i ^{k+\frac{1}{2}} =  \Alts_i^{k+1} a_{1}'
+  \left( F_w^{31} \right) _i ^{k+\frac{1}{2}} =  {A}_i^{k+1} a_{1}'
   s_{1}' \delta_{i-\frac{1}{2}} \left[ T^{k+1} \right]/{e_{3u}}_{i-\frac{1}{2}}^{k+1}
   +\Alts_i^{k+1} a_{2}' s_{2}' \delta_{i+\frac{1}{2}} \left[ T^{k+1} \right]/{e_{3u}}_{i+\frac{1}{2}}^{k+1} \\
   + \Alts_i^k a_{3}' s_{3}' \delta_{i-\frac{1}{2}} \left[ T^k\right]/{e_{3u}}_{i-\frac{1}{2}}^k
   +\Alts_i^k a_{4}' s_{4}' \delta_{i+\frac{1}{2}} \left[ T^k \right]/{e_{3u}}_{i+\frac{1}{2}}^k.
+  +{A}_i^{k+1} a_{2}' s_{2}' \delta_{i+\frac{1}{2}} \left[ T^{k+1} \right]/{e_{3u}}_{i+\frac{1}{2}}^{k+1} \\
+  + {A}_i^k a_{3}' s_{3}' \delta_{i-\frac{1}{2}} \left[ T^k\right]/{e_{3u}}_{i-\frac{1}{2}}^k
+  +{A}_i^k a_{4}' s_{4}' \delta_{i+\frac{1}{2}} \left[ T^k \right]/{e_{3u}}_{i+\frac{1}{2}}^k.
 \end{multline}
 …
       \protect\label{fig:qcells}
       Triad notation for quarter cells. $T$-cells are inside boxes,
       while the  $i+\half,k$ $u$-cell is shaded in green and
       the $i,k+\half$ $w$-cell is shaded in pink.
+      while the  $i+\fractext{1}{2},k$ $u$-cell is shaded in green and
+      the $i,k+\fractext{1}{2}$ $w$-cell is shaded in pink.
+    }
   \end{center}
 …
 the intersection of the $i,k$ $T$-cell, the $i+i_p,k$ $u$-cell and the $i,k+k_p$ $w$-cell.
 Expressing the slopes $s_i$ and $s'_i$ in \autoref{eq:i13} and \autoref{eq:i31} in this notation,
 we have $e.g.$ \ $s_1=s'_1={\:}_i^k \mathbb{R}_{1/2}^{1/2}$.
+we have \eg \ $s_1=s'_1={\:}_i^k \mathbb{R}_{1/2}^{1/2}$.
 Each triad slope $_i^k\mathbb{R}_{i_p}^{k_p}$ is used once (as an $s$) to
 calculate the lateral flux along its $u$-arm, at $(i+i_p,k)$,
 …
 and we notate these areas, similarly to the triad slopes,
 as $_i^k{\mathbb{A}_u}_{i_p}^{k_p}$, $_i^k{\mathbb{A}_w}_{i_p}^{k_p}$,
 where $e.g.$ in \autoref{eq:i13} $a_{1}={\:}_i^k{\mathbb{A}_u}_{1/2}^{1/2}$,
+where \eg in \autoref{eq:i13} $a_{1}={\:}_i^k{\mathbb{A}_u}_{1/2}^{1/2}$,
 and in \autoref{eq:i31} $a'_{1}={\:}_i^k{\mathbb{A}_w}_{1/2}^{1/2}$.
 …
   \label{eq:i11}
   \left( F_u^{11} \right) _{i+\frac{1}{2}} ^{k} =
   - \left( \Alts_i^{k+1} a_{1} + \Alts_i^{k+1} a_{2} + \Alts_i^k
     a_{3} + \Alts_i^k a_{4} \right)
+  - \left( {A}_i^{k+1} a_{1} + {A}_i^{k+1} a_{2} + {A}_i^k
+    a_{3} + {A}_i^k a_{4} \right)
   \frac{\delta_{i+1/2} \left[ T^k\right]}{{e_{1u}}_{\,i+1/2}^{\,k}},
 \end{equation}
 …
 \begin{equation}
   \label{eq:latflux-triad}
   _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) = - \Alts_i^k{ \:}_i^k{\mathbb{A}_u}_{i_p}^{k_p}
+  _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) = - {A}_i^k{ \:}_i^k{\mathbb{A}_u}_{i_p}^{k_p}
   \left(
     \frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} }
 …
   \label{eq:i33}
   \left( F_w^{33} \right) _i^{k+\frac{1}{2}} =
   - \left( \Alts_i^{k+1} a_{1}' s_{1}'^2
     + \Alts_i^{k+1} a_{2}' s_{2}'^2
     + \Alts_i^k a_{3}' s_{3}'^2
     + \Alts_i^k a_{4}' s_{4}'^2 \right)\delta_{k+\frac{1}{2}} \left[ T^{i+1} \right],
+  - \left( {A}_i^{k+1} a_{1}' s_{1}'^2
+    + {A}_i^{k+1} a_{2}' s_{2}'^2
+    + {A}_i^k a_{3}' s_{3}'^2
+    + {A}_i^k a_{4}' s_{4}'^2 \right)\delta_{k+\frac{1}{2}} \left[ T^{i+1} \right],
 \end{equation}
 where the areas $a'$ and slopes $s'$ are the same as in \autoref{eq:i31}.
 …
   \label{eq:vertflux-triad}
   _i^k {\mathbb{F}_w}_{i_p}^{k_p} (T)
   &= \Alts_i^k{\: }_i^k{\mathbb{A}_w}_{i_p}^{k_p}
+  &= {A}_i^k{\: }_i^k{\mathbb{A}_w}_{i_p}^{k_p}
     \left(
     {_i^k\mathbb{R}_{i_p}^{k_p}}\frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} }
 …
 the $u$-point $i+i_p,k$ and a vertical flux $_i^k{\mathbb{F}_w}_{i_p}^{k_p} (T)$ across the $w$-point $i,k+k_p$.
 The lateral flux drives a net rate of change of variance,
 summed over the two $T$-points $i+i_p-\half,k$ and $i+i_p+\half,k$, of
+summed over the two $T$-points $i+i_p-\fractext{1}{2},k$ and $i+i_p+\fractext{1}{2},k$, of
 \begin{multline}
   {b_T}_{i+i_p-1/2}^k\left(\frac{\partial T}{\partial t}T\right)_{i+i_p-1/2}^k+
 …
 \end{multline}
 while the vertical flux similarly drives a net rate of change of variance summed over
 the $T$-points $i,k+k_p-\half$ (above) and $i,k+k_p+\half$ (below) of
+the $T$-points $i,k+k_p-\fractext{1}{2}$ (above) and $i,k+k_p+\fractext{1}{2}$ (below) of
 \begin{equation}
   \label{eq:dvar_iso_k}
 …
 \autoref{eq:latflux-triad} and \autoref{eq:vertflux-triad}, it is
 \begin{multline*}
   -\Alts_i^k\left \{
+  -{A}_i^k\left \{
     { } _i^k{\mathbb{A}_u}_{i_p}^{k_p}
     \left(
 …
 \begin{equation}
   \label{eq:perfect-square}
   -\Alts_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p}
+  -{A}_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p}
   \left(
     \frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} }
 …
 \begin{equation}
   \label{eq:cts-var}
   \frac{\partial}{\partial t}\int\!\half T^2\, dV =
+  \frac{\partial}{\partial t}\int\!\fractext{1}{2} T^2\, dV =
   \int\!\mathbf{F}\cdot\nabla T\, dV,
 \end{equation}
 …
 \begin{equation}
   \label{eq:V-NEMO}
   _i^k\mathbb{V}_{i_p}^{k_p}=\quarter {b_u}_{i+i_p}^k,
+  _i^k\mathbb{V}_{i_p}^{k_p}=\fractext{1}{4} {b_u}_{i+i_p}^k,
 \end{equation}
 as a quarter of the volume of the $u$-cell inside which the triad quarter-cell lies.
 …
 \begin{equation}
   \label{eq:lat-normal}
   -\overline\Alts_{\,i+1/2}^k\;
+  -\overline{A}_{\,i+1/2}^k\;
   \frac{{b_u}_{i+1/2}^k}{{e_{1u}}_{\,i + i_p}^{\,k}}
   \;\frac{\delta_{i+ 1/2}[T^k] }{{e_{1u}}_{\,i + i_p}^{\,k}}
   = -\overline\Alts_{\,i+1/2}^k\;\frac{{e_{1w}}_{\,i + 1/2}^{\,k}\:{e_{1v}}_{\,i + 1/2}^{\,k}\;\delta_{i+ 1/2}[T^k]}{{e_{1u}}_{\,i + 1/2}^{\,k}}.
+  = -\overline{A}_{\,i+1/2}^k\;\frac{{e_{1w}}_{\,i + 1/2}^{\,k}\:{e_{1v}}_{\,i + 1/2}^{\,k}\;\delta_{i+ 1/2}[T^k]}{{e_{1u}}_{\,i + 1/2}^{\,k}}.
 \end{equation}
 In fact if the diffusive coefficient is defined at $u$-points,
 so that we employ $\Alts_{i+i_p}^k$ instead of  $\Alts_i^k$ in the definitions of the triad fluxes
+so that we employ ${A}_{i+i_p}^k$ instead of  ${A}_i^k$ in the definitions of the triad fluxes
 \autoref{eq:latflux-triad} and \autoref{eq:vertflux-triad},
 we can replace $\overline{A}_{\,i+1/2}^k$ by $A_{i+1/2}^k$ in the above.
 …
   \begin{align}
     \label{eq:triadfluxu}
     _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) &= - \Alts_i^k{
+    _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) &= - {A}_i^k{
                                           \:}\frac{{{}_i^k\mathbb{V}}_{i_p}^{k_p}}{{e_{1u}}_{\,i + i_p}^{\,k}}
                                           \left(
 …
     \intertext{and}
     _i^k {\mathbb{F}_w}_{i_p}^{k_p} (T)
                                         &= \Alts_i^k{\: }\frac{{{}_i^k\mathbb{V}}_{i_p}^{k_p}}{{e_{3w}}_{\,i}^{\,k+k_p}}
+                                        &= {A}_i^k{\: }\frac{{{}_i^k\mathbb{V}}_{i_p}^{k_p}}{{e_{3w}}_{\,i}^{\,k+k_p}}
                                           \left(
                                           {_i^k\mathbb{R}_{i_p}^{k_p}}\frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} }
 …
   \[
     % \label{eq:V-NEMO2}
     _i^k{\mathbb{V}}_{i_p}^{k_p}=\quarter {b_u}_{i+i_p}^k.
+    _i^k{\mathbb{V}}_{i_p}^{k_p}=\fractext{1}{4} {b_u}_{i+i_p}^k.
   \]
 \end{subequations}
 …
     D_l^T = \frac{1}{b_T} \
     \delta_{i} \left[ \frac{e_{2u}\,e_{3u}}{e_{1u}} \;
       \overline\Alts^{\,i} \; \delta_{i+1/2}[T] \right] \qquad
+      \overline{A}^{\,i} \; \delta_{i+1/2}[T] \right] \qquad
     \text{when} \quad { _i^k \mathbb{R}_{i_p}^{k_p} }=0
   \]
 …
   \[
     \frac{1}{b_w}\sum_{\substack{i_p, \,k_p}} \left\{
       {\:}_i^k\mathbb{V}_{i_p}^{k_p} \: \Alts_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2
+      {\:}_i^k\mathbb{V}_{i_p}^{k_p} \: {A}_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2
     \right\}  =
     \frac{1}{4b_w}\sum_{\substack{i_p, \,k_p}} \left\{
       {b_u}_{i+i_p}^k\: \Alts_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2
+      {b_u}_{i+i_p}^k\: {A}_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2
     \right\},
   \]
 …
 \item[$\bullet$ conservation of tracer]
   The iso-neutral diffusion conserves tracer content, $i.e.$
+  The iso-neutral diffusion conserves tracer content, \ie
   \[
     % \label{eq:iso_property1}
 …
 \item[$\bullet$ no increase of tracer variance]
   The iso-neutral diffusion does not increase the tracer variance, $i.e.$
+  The iso-neutral diffusion does not increase the tracer variance, \ie
   \[
     % \label{eq:iso_property2}
 …
   It is a key property for a diffusion term.
   It means that it is also a dissipation term,
   $i.e.$ it dissipates the square of the quantity on which it is applied.
+  \ie it dissipates the square of the quantity on which it is applied.
   It therefore ensures that, when the diffusivity coefficient is large enough,
   the field on which it is applied becomes free of grid-point noise.
 \item[$\bullet$ self-adjoint operator]
   The iso-neutral diffusion operator is self-adjoint, $i.e.$
+  The iso-neutral diffusion operator is self-adjoint, \ie
   \begin{equation}
     \label{eq:iso_property3}
 …
   \[
     % \label{eq:TScovar}
     - \Alts_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p}
+    - {A}_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p}
     \left(
       \frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} }
 …
 or down into the ocean floor, must be masked out.
 See \autoref{fig:bdry_triads}.
 Surface layer triads $\triad{i}{1}{R}{1/2}{-1/2}$ (magenta) and $\triad{i+1}{1}{R}{-1/2}{-1/2}$ (blue) that
+Surface layer triads \triad{i}{1}{R}{1/2}{-1/2} (magenta) and \triad{i+1}{1}{R}{-1/2}{-1/2} (blue) that
 require density to be specified above the ocean surface are masked (\autoref{fig:bdry_triads}a):
 this ensures that lateral tracer gradients produce no flux through the ocean surface.
 However, to prevent surface noise, it is customary to retain the $_{11}$ contributions towards
 the lateral triad fluxes $\triad[u]{i}{1}{F}{1/2}{-1/2}$ and $\triad[u]{i+1}{1}{F}{-1/2}{-1/2}$;
+the lateral triad fluxes \triad[u]{i}{1}{F}{1/2}{-1/2} and \triad[u]{i+1}{1}{F}{-1/2}{-1/2};
 this drives diapycnal tracer fluxes.
 Similar comments apply to triads that would intersect the ocean floor (\autoref{fig:bdry_triads}b).
+Note that both near bottom triad slopes $\triad{i}{k}{R}{1/2}{1/2}$ and
+$\triad{i+1}{k}{R}{-1/2}{1/2}$ are masked when either of the $i,k+1$ or $i+1,k+1$ tracer points is masked,
+i.e.\ the $i,k+1$ $u$-point is masked.
+Note that both near bottom triad slopes \triad{i}{k}{R}{1/2}{1/2} and \triad{i+1}{k}{R}{-1/2}{1/2} are masked when
+either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, \ie the $i,k+1$ $u$-point is masked.
 The associated lateral fluxes (grey-black dashed line) are masked if \np{ln\_botmix\_triad}\forcode{ = .false.},
 but left unmasked, giving bottom mixing, if \np{ln\_botmix\_triad}\forcode{ = .true.}.
 …
       (a) Uppermost model layer $k=1$ with $i,1$ and $i+1,1$ tracer points (black dots),
       and $i+1/2,1$ $u$-point (blue square).
       Triad slopes $\triad{i}{1}{R}{1/2}{-1/2}$ (magenta) and $\triad{i+1}{1}{R}{-1/2}{-1/2}$ (blue) poking through
+      Triad slopes \triad{i}{1}{R}{1/2}{-1/2} (magenta) and \triad{i+1}{1}{R}{-1/2}{-1/2} (blue) poking through
       the ocean surface are masked (faded in figure).
       However, the lateral $_{11}$ contributions towards $\triad[u]{i}{1}{F}{1/2}{-1/2}$ and
       $\triad[u]{i+1}{1}{F}{-1/2}{-1/2}$ (yellow line) are still applied,
+      However, the lateral $_{11}$ contributions towards \triad[u]{i}{1}{F}{1/2}{-1/2} and
+      \triad[u]{i+1}{1}{F}{-1/2}{-1/2} (yellow line) are still applied,
       giving diapycnal diffusive fluxes.
       \newline
       (b) Both near bottom triad slopes $\triad{i}{k}{R}{1/2}{1/2}$ and
       $\triad{i+1}{k}{R}{-1/2}{1/2}$ are masked when either of the $i,k+1$ or $i+1,k+1$ tracer points is masked,
       i.e.\ the $i,k+1$ $u$-point is masked.
+      (b) Both near bottom triad slopes \triad{i}{k}{R}{1/2}{1/2} and
+      \triad{i+1}{k}{R}{-1/2}{1/2} are masked when either of the $i,k+1$ or $i+1,k+1$ tracer points is masked,
+      \ie the $i,k+1$ $u$-point is masked.
       The associated lateral fluxes (grey-black dashed line) are masked if
       \protect\np{botmix\_triad}\forcode{ = .false.}, but left unmasked,
 …
   where $i,k_{10}$ is the tracer gridbox within which the depth reaches 10~m.
   See the left side of \autoref{fig:MLB_triad}.
   We use the $k_{10}$-gridbox instead of the surface gridbox to avoid problems e.g.\ with thin daytime mixed-layers.
+  We use the $k_{10}$-gridbox instead of the surface gridbox to avoid problems \eg with thin daytime mixed-layers.
   Currently we use the same $\Delta\rho_c=0.01\;\mathrm{kg\:m^{-3}}$ for ML triad tapering as is used to
   output the diagnosed mixed-layer depth $h_{\mathrm{ML}}=|z_{W}|_{k_{\mathrm{ML}}+1/2}$,
 …
                                                        % \label{eq:Rbase}
     \\
     \intertext{with e.g.\ the green triad}
+    \intertext{with \eg the green triad}
     {\:}_i{\mathbb{R}_{\mathrm{base}}}_{1/2}^{-1/2}&=
                                                      {\:}^{k_{\mathrm{ML}}}_i{\mathbb{R}_{\mathrm{base}}}_{\,1/2}^{-1/2}.
 …
     ${\:}_i{\mathbb{R}_{\mathrm{base}}}_{\,i_p}^{k_p}$.
     Triads with different $i_p,k_p$, denoted by different colours,
     (e.g. the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.}
+    (\eg the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.}
   % }
   \includegraphics[width=0.60\textwidth]{Fig_GRIFF_MLB_triads}
 …
 the formulation of which depends on the slopes of iso-neutral surfaces.
 Contrary to the case of iso-neutral mixing, the slopes used here are referenced to the geopotential surfaces,
 $i.e.$ \autoref{eq:ldfslp_geo} is used in $z$-coordinate,
+\ie \autoref{eq:ldfslp_geo} is used in $z$-coordinate,
 and the sum \autoref{eq:ldfslp_geo} + \autoref{eq:ldfslp_iso} in $z^*$ or $s$-coordinates.
 …
   \begin{align}
     \label{eq:skewfluxu}
     _i^k {\mathbb{S}_u}_{i_p}^{k_p} (T) &= + \quarter {A_e}_i^k{
+    _i^k {\mathbb{S}_u}_{i_p}^{k_p} (T) &= + \fractext{1}{4} {A_e}_i^k{
                                           \:}\frac{{b_u}_{i+i_p}^k}{{e_{1u}}_{\,i + i_p}^{\,k}}
                                           \ {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}} \
 …
+    }
     _i^k {\mathbb{S}_w}_{i_p}^{k_p} (T)
                                         &= -\quarter {A_e}_i^k{\: }\frac{{b_u}_{i+i_p}^k}{{e_{3w}}_{\,i}^{\,k+k_p}}
+                                        &= -\fractext{1}{4} {A_e}_i^k{\: }\frac{{b_u}_{i+i_p}^k}{{e_{3w}}_{\,i}^{\,k+k_p}}
                                           {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}}\frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} }.\label{eq:skewfluxw}
   \end{align}
 …
 \subsubsection{No change in tracer variance}
 The discretization conserves tracer variance, $i.e.$ it does not include a diffusive component but is a `pure' advection term.
+The discretization conserves tracer variance, \ie it does not include a diffusive component but is a `pure' advection term.
 This can be seen %either from Appendix \autoref{apdx:eiv_skew} or
 by considering the fluxes associated with a given triad slope $_i^k{\mathbb{R}}_{i_p}^{k_p} (T)$.
 For, following \autoref{subsec:variance} and \autoref{eq:dvar_iso_i},
 the associated horizontal skew-flux $_i^k{\mathbb{S}_u}_{i_p}^{k_p} (T)$ drives a net rate of change of variance,
 summed over the two $T$-points $i+i_p-\half,k$ and $i+i_p+\half,k$, of
+summed over the two $T$-points $i+i_p-\fractext{1}{2},k$ and $i+i_p+\fractext{1}{2},k$, of
 \begin{equation}
   \label{eq:dvar_eiv_i}
 …
 \end{equation}
 while the associated vertical skew-flux gives a variance change summed over
 the $T$-points $i,k+k_p-\half$ (above) and $i,k+k_p+\half$ (below) of
+the $T$-points $i,k+k_p-\fractext{1}{2}$ (above) and $i,k+k_p+\fractext{1}{2}$ (below) of
 \begin{equation}
   \label{eq:dvar_eiv_k}
 …
   % gives two terms. The
   % first $\rtriad{R}$ term (the only term for $z$-coordinates) is:
   &=-\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}}
+  &=-\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}}
     \frac{ -\alpha _i^k\delta_{i+ i_p}[T^k]+ \beta_i^k\delta_{i+ i_p}[S^k]} { {e_{1u}}_{\,i + i_p}^{\,k} } \notag \\
   &=+\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k
+  &=+\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k
     \left({_i^k\mathbb{R}_{i_p}^{k_p}}+\frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}}\right) {_i^k\mathbb{R}_{i_p}^{k_p}}
     \frac{-\alpha_i^k \delta_{k+ k_p}[T^i]+ \beta_i^k\delta_{k+ k_p}[S^i]} {{e_{3w}}_{\,i}^{\,k+k_p}},
 …
     -\alpha _i^k {\:}_i^k {\mathbb{S}_u}_{i_p}^{k_p} (T) + \beta_i^k {\:}_i^k {\mathbb{S}_u}_{i_p}^{k_p} (S)
   \right] \\
   = +\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k
+  = +\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k
   \frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}}
   \left({_i^k\mathbb{R}_{i_p}^{k_p}}+\frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}}\right)
 …
   g{e_{3w}}_{\,i}^{\,k+k_p}{\mathbb{S}_w}_{i_p}^{k_p} (\rho) +
   g\delta_{i+i_p}[z_T^k] {\:}_i^k {\mathbb{S}_u}_{i_p}^{k_p} (\rho) \\
   = +\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k
+  = +\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k
   \left({_i^k\mathbb{R}_{i_p}^{k_p}}+\frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}}\right)^2
   \frac{-\alpha_i^k \delta_{k+ k_p}[T^i]+ \beta_i^k\delta_{k+ k_p}[S^i]} {{e_{3w}}_{\,i}^{\,k+k_p}}.
 …
 Thus surface layer triads $\triadt{i}{1}{R}{1/2}{-1/2}$ and $\triadt{i+1}{1}{R}{-1/2}{-1/2}$ are masked,
 and both near bottom triad slopes $\triadt{i}{k}{R}{1/2}{1/2}$ and $\triadt{i+1}{k}{R}{-1/2}{1/2}$ are masked when
 either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$ $u$-point is masked.
+either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, \ie the $i,k+1$ $u$-point is masked.
 The namelist parameter \np{ln\_botmix\_triad} has no effect on the eddy-induced skew-fluxes.
 …
 \[
   % \label{eq:sfdiagi}
   {\psi_1}_{i+1/2}^{k+1/2}={\quarter}\sum_{\substack{i_p,\,k_p}}
+  {\psi_1}_{i+1/2}^{k+1/2}={\fractext{1}{4}}\sum_{\substack{i_p,\,k_p}}
   {A_e}_{i+1/2-i_p}^{k+1/2-k_p}\:\triadd{i+1/2-i_p}{k+1/2-k_p}{R}{i_p}{k_p}.
 \]
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex

r10414	r10442
179	179	\biblio
180	180
	181	\pindex
	182
181	183	\end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_CONFIG.tex

-                      r10414
+                      r10442
   the 3x3 domain is imposed over the whole domain;
 \item[(3)]
   a call to \rou{lbc\_lnk} is systematically done when reading input data ($i.e.$ in \mdl{iom});
+  a call to \rou{lbc\_lnk} is systematically done when reading input data (\ie in \mdl{iom});
 \item[(3)]
   a simplified \rou{stp} routine is used (\rou{stp\_c1d}, see \mdl{step\_c1d} module) in which
 …
       \protect\label{fig:MISC_ORCA_msh}
       ORCA mesh conception.
       The departure from an isotropic Mercator grid start poleward of 20\degN.
+      The departure from an isotropic Mercator grid start poleward of 20\deg{N}.
       The two "north pole" are the foci of a series of embedded ellipses (blue curves) which
       are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes).
 …
       \textit{Bottom}: ratio of anisotropy ($e_1 / e_2$)
       for ORCA 0.5\deg ~mesh.
       South of 20\degN a Mercator grid is used ($e_1 = e_2$) so that the anisotropy ratio is 1.
       Poleward of 20\degN, the two "north pole" introduce a weak anisotropy over the ocean areas ($< 1.2$) except in
+      South of 20\deg{N} a Mercator grid is used ($e_1 = e_2$) so that the anisotropy ratio is 1.
+      Poleward of 20\deg{N}, the two "north pole" introduce a weak anisotropy over the ocean areas ($< 1.2$) except in
       vicinity of Victoria Island (Canadian Arctic Archipelago).
+    }
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 The method is applied to Mercator grid ($i.e.$ same zonal and meridional grid spacing) poleward of 20\degN,
+The method is applied to Mercator grid (\ie same zonal and meridional grid spacing) poleward of 20\deg{N},
 so that the Equator is a mesh line, which provides a better numerical solution for equatorial dynamics.
 The choice of the series of embedded ellipses (position of the foci and variation of the ellipses)
 …
 For ORCA\_R1 and R025, setting the configuration key to 75 allows to use 75 vertical levels, otherwise 46 are used.
 In the other ORCA configurations, 31 levels are used
 (see \autoref{tab:orca_zgr} \sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}).
+(see \autoref{tab:orca_zgr} %\sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}).
 Only the ORCA\_R2 is provided with all its input files in the \NEMO distribution.
 …
 and their contribution to the large scale circulation.
 The domain geometry is a closed rectangular basin on the $\beta$-plane centred at $\sim$ 30\degN and
+The domain geometry is a closed rectangular basin on the $\beta$-plane centred at $\sim$ 30\deg{N} and
 rotated by 45\deg, 3180~km long, 2120~km wide and 4~km deep (\autoref{fig:MISC_strait_hand}).
 The domain is bounded by vertical walls and by a flat bottom.
 …
 The circulation is forced by analytical profiles of wind and buoyancy fluxes.
 The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{Levy_al_OM10}.
 The wind stress is zonal and its curl changes sign at 22\degN and 36\degN.
+The wind stress is zonal and its curl changes sign at 22\deg{N} and 36\deg{N}.
 It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain and
 a small recirculation gyre in the southern corner.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIA.tex

-                      r10414
+                      r10442
   The possibility to extract a vertical or an horizontal subdomain.
 \item
   The choice of the temporal operation to perform, $e.g.$: average, accumulate, instantaneous, min, max and once.
+  The choice of the temporal operation to perform, \eg: average, accumulate, instantaneous, min, max and once.
 \item
   Control over metadata via a large XML "database" of possible output fields.
 …
 create a single output file and therefore to bypass the rebuilding phase.
 Note that writing in parallel into the same NetCDF files requires that your NetCDF4 library is linked to
 an HDF5 library that has been correctly compiled ($i.e.$ with the configure option $--$enable-parallel).
+an HDF5 library that has been correctly compiled (\ie with the configure option $--$enable-parallel).
 Note that the files created by iomput through XIOS are incompatible with NetCDF3.
 All post-processsing and visualization tools must therefore be compatible with NetCDF4 and not only NetCDF3.
 …
 It is very easy to add your own outputs with iomput.
 Many standard fields and diagnostics are already prepared ($i.e.$, steps 1 to 3 below have been done) and
+Many standard fields and diagnostics are already prepared (\ie, steps 1 to 3 below have been done) and
 simply need to be activated by including the required output in a file definition in iodef.xml (step 4).
 To add new output variables, all 4 of the following steps must be taken.
 …
 reference grids and axes either defined in the code
 (iom\_set\_domain\_attr and iom\_set\_axis\_attr in \mdl{iom}) or defined in the domain\_def.xml file.
 $e.g.$:
+\eg:
 \begin{xmllines}
 …
 \noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\tt 46x38x1} respectively in
 the mono-processor case (i.e. global domain of {\small\tt 182x149x31}).
+the mono-processor case (\ie global domain of {\small\tt 182x149x31}).
 An illustration of the potential space savings that NetCDF4 chunking and compression provides is given in
 table \autoref{tab:NC4} which compares the results of two short runs of the ORCA2\_LIM reference configuration with
 …
 Each trend of the dynamics and/or temperature and salinity time evolution equations can be send to
 \mdl{trddyn} and/or \mdl{trdtra} modules (see TRD directory) just after their computation
 ($i.e.$ at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines).
+(\ie at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines).
 This capability is controlled by options offered in \ngn{namtrd} namelist.
 Note that the output are done with xIOS, and therefore the \key{IOM} is required.
 …
 \textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested.
 In particular, options associated with \np{ln\_dyn\_mxl}, \np{ln\_vor\_trd}, and \np{ln\_tra\_mxl} are not working,
 and none of the options have been tested with variable volume ($i.e.$ \key{vvl} defined).
+and none of the options have been tested with variable volume (\ie \key{vvl} defined).
 % -------------------------------------------------------------------------------------------------------------
 …
  - \texttt{long2 lat2}, coordinates of the second extremity of the section;
  - \texttt{nclass}    the number of bounds of your classes (e.g. 3 bounds for 2 classes);
+ - \texttt{nclass}    the number of bounds of your classes (\eg bounds for 2 classes);
  - \texttt{okstrpond} to compute    heat and       salt transports, \texttt{nostrpond} if no;
 …
 The first term in equation \autoref{eq:ssh_nBq} alters sea level by adding or subtracting mass from the ocean.
 The second term arises from temporal changes in the global mean density; $i.e.$ from steric effects.
+The second term arises from temporal changes in the global mean density; \ie from steric effects.
 In a Boussinesq fluid, $\rho$ is replaced by $\rho_o$ in all the equation except when $\rho$ appears multiplied by
 the gravity ($i.e.$ in the hydrostatic balance of the primitive Equations).
+the gravity (\ie in the hydrostatic balance of the primitive Equations).
 In particular, the mass conservation equation, \autoref{eq:Co_nBq}, degenerates into the incompressibility equation:
 …
 The above formulation of the steric height of a Boussinesq ocean requires four remarks.
 First, one can be tempted to define $\rho_o$ as the initial value of $\mathcal{M}/\mathcal{V}$,
 $i.e.$ set $\mathcal{D}_{t=0}=0$, so that the initial steric height is zero.
+\ie set $\mathcal{D}_{t=0}=0$, so that the initial steric height is zero.
 We do not recommend that.
 Indeed, in this case $\rho_o$ depends on the initial state of the ocean.
 …
 Third, the discretisation of \autoref{eq:steric_Bq} depends on the type of free surface which is considered.
 In the non linear free surface case, $i.e.$ \key{vvl} defined, it is given by
+In the non linear free surface case, \ie \key{vvl} defined, it is given by
 \[
 …
 so that there are no associated ocean currents.
 Hence, the dynamically relevant sea level is the effective sea level,
 $i.e.$ the sea level as if sea ice (and snow) were converted to liquid seawater \citep{Campin_al_OM08}.
+\ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{Campin_al_OM08}.
 However, in the current version of \NEMO the sea-ice is levitating above the ocean without mass exchanges between
 ice and ocean.
 …
 - the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth})
 - the depth of the 20\deg C isotherm (\mdl{diahth})
+- the depth of the 20\deg{C} isotherm (\mdl{diahth})
 - the depth of the thermocline (maximum of the vertical temperature gradient) (\mdl{diahth})
 …
 (see the \textit{\ngn{namptr} } namelist below).
 When \np{ln\_subbas}\forcode{ = .true.}, transports and stream function are computed for the Atlantic, Indian,
 Pacific and Indo-Pacific Oceans (defined north of 30\deg S) as well as for the World Ocean.
+Pacific and Indo-Pacific Oceans (defined north of 30\deg{S}) as well as for the World Ocean.
 The sub-basin decomposition requires an input file (\ifile{subbasins}) which contains three 2D mask arrays,
 the Indo-Pacific mask been deduced from the sum of the Indian and Pacific mask (\autoref{fig:mask_subasins}).
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIU.tex

-                      r10414
+                      r10442
 Models are provided for both the warm layer, \mdl{diurnal\_bulk}, and the cool skin, \mdl{cool\_skin}.
 Foundation SST is not considered as it can be obtained either from the main NEMO model
 ($i.e.$ from the temperature of the top few model levels) or from some other source.
+(\ie from the temperature of the top few model levels) or from some other source.
 It must be noted that both the cool skin and warm layer models produce estimates of the change in temperature
 ($\Delta T_{\rm{cs}}$ and $\Delta T_{\rm{wl}}$) and
 …
 and $\rho_a$ is the density of air.
 The symbol $Q$ in equation (\autoref{eq:ecmwf1}) is the instantaneous total thermal energy flux into
 the diurnal layer, $i.e.$
+the diurnal layer, \ie
 \[
   Q = Q_{\rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,}
 …
 \end{equation}
 where $\zeta=\frac{D_T}{L}$.  It is clear that the first derivative of (\autoref{eq:stab_func_eqn}),
 and thus of (\autoref{eq:ecmwf1}), is discontinuous at $\zeta=0$ ($i.e.$ $Q\rightarrow0$ in
+and thus of (\autoref{eq:ecmwf1}), is discontinuous at $\zeta=0$ (\ie $Q\rightarrow0$ in
 equation (\autoref{eq:ecmwf2})).
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_DOM.tex

-                      r10414
+                      r10442
 the barotropic stream function $\psi$ is defined at horizontal points overlying the $\zeta$ and $f$-points.
 The ocean mesh ($i.e.$ the position of all the scalar and vector points) is defined by
+The ocean mesh (\ie the position of all the scalar and vector points) is defined by
 the transformation that gives ($\lambda$ ,$\varphi$ ,$z$) as a function of $(i,j,k)$.
 The grid-points are located at integer or integer and a half value of $(i,j,k)$ as indicated on \autoref{tab:cell}.
 …
 The vertical average over the whole water column denoted by an overbar becomes for a quantity $q$ which
 is a masked field (i.e. equal to zero inside solid area):
+is a masked field (\ie equal to zero inside solid area):
 \begin{equation}
   \label{eq:DOM_bar}
 …
 the differencing operators ($\delta_i$, $\delta_j$ and $\delta_k$) are skew-symmetric linear operators,
 and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$, $\overline{\,\cdot\,}^{\,k}$ and
+$\overline{\,\cdot\,}^{\,k}$) are symmetric linear operators,
+$i.e.$
+$\overline{\,\cdot\,}^{\,k}$) are symmetric linear operators, \ie
 \begin{align}
   \label{eq:DOM_di_adj}
 …
     \caption{
       \protect\label{fig:index_hor}
       Horizontal integer indexing used in the \textsc{Fortran} code.
+      Horizontal integer indexing used in the \fortran code.
       The dashed area indicates the cell in which variables contained in arrays have the same $i$- and $j$-indices
+    }
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 The array representation used in the \textsc{Fortran} code requires an integer indexing while
+The array representation used in the \fortran code requires an integer indexing while
 the analytical definition of the mesh (see \autoref{subsec:DOM_cell}) is associated with the use of
 integer values for $t$-points and both integer and integer and a half values for all the other points.
 Therefore a specific integer indexing must be defined for points other than $t$-points
 ($i.e.$ velocity and vorticity grid-points).
+(\ie velocity and vorticity grid-points).
 Furthermore, the direction of the vertical indexing has been changed so that the surface level is at $k=1$.
 …
 In the vertical, the chosen indexing requires special attention since
 the $k$-axis is re-orientated downward in the \textsc{Fortran} code compared to
+the $k$-axis is re-orientated downward in the \fortran code compared to
 the indexing used in the semi-discrete equations and given in \autoref{subsec:DOM_cell}.
 The sea surface corresponds to the $w$-level $k=1$ which is the same index as $t$-level just below
 …
 have the same $i$ or $j$ index
 (compare the dashed area in \autoref{fig:index_hor} and \autoref{fig:index_vert}).
 Since the scale factors are chosen to be strictly positive, a \emph{minus sign} appears in the \textsc{Fortran}
+Since the scale factors are chosen to be strictly positive, a \emph{minus sign} appears in the \fortran
 code \emph{before all the vertical derivatives} of the discrete equations given in this documentation.
 …
     \caption{
       \protect\label{fig:index_vert}
       Vertical integer indexing used in the \textsc{Fortran } code.
+      Vertical integer indexing used in the \fortran code.
       Note that the $k$-axis is orientated downward.
       The dashed area indicates the cell in which variables contained in arrays have the same $k$-index.
 …
 \section{Needed fields}
 \label{sec:DOM_fields}
 The ocean mesh ($i.e.$ the position of all the scalar and vector points) is defined by the transformation that gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$.
+The ocean mesh (\ie the position of all the scalar and vector points) is defined by the transformation that gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$.
 The grid-points are located at integer or integer and a half values of as indicated in \autoref{tab:cell}.
 The associated scale factors are defined using the analytical first derivative of the transformation
 …
 \label{subsec:DOM_hgr_coord_e}
 The ocean mesh ($i.e.$ the position of all the scalar and vector points) is defined by
+The ocean mesh (\ie the position of all the scalar and vector points) is defined by
 the transformation that gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$.
 The grid-points are located at integer or integer and a half values of as indicated in \autoref{tab:cell}.
 …
 Note that the definition of the scale factors
 ($i.e.$ as the analytical first derivative of the transformation that
+(\ie as the analytical first derivative of the transformation that
 gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$)
 is specific to the \NEMO model \citep{Marti_al_JGR92}.
 …
 (2) the number of levels of the model (\jp{jpk});
 (3) the analytical transformation $z(i,j,k)$ and the vertical scale factors (derivatives of the transformation); and
 (4) the masking system, $i.e.$ the number of wet model levels at each
+(4) the masking system, \ie the number of wet model levels at each
 $(i,j)$ column of points.
 …
   The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) at
   each grid point of the model grid.
   The bathymetry is usually built by interpolating a standard bathymetry product ($e.g.$ ETOPO2) onto
+  The bathymetry is usually built by interpolating a standard bathymetry product (\eg ETOPO2) onto
   the horizontal ocean mesh.
   Defining the bathymetry also defines the coastline: where the bathymetry is zero,
 …
 % -------------------------------------------------------------------------------------------------------------
 %        z*- or s*-coordinate
+%        \zstar- or \sstar-coordinate
 % -------------------------------------------------------------------------------------------------------------
 \subsection{$Z^*$- or $S^*$-coordinate (\protect\np{ln\_linssh}\forcode{ = .false.}) }
 …
 follow the face of the model cells (step like topography) \citep{Madec_al_JPO96}.
 The distribution of the steps in the horizontal is defined in a 2D integer array, mbathy,
 which gives the number of ocean levels ($i.e.$ those that are not masked) at each $t$-point.
+which gives the number of ocean levels (\ie those that are not masked) at each $t$-point.
 mbathy is computed from the meter bathymetry using the definiton of gdept as
 the number of $t$-points which gdept $\leq$ bathy.
 …
 the cavities are performed in the \textit{zgr\_isf} routine.
 The compatibility between ice shelf draft and bathymetry is checked.
 All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked).
+All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded (\ie masked).
 If only one cell on the water column is opened at $t$-, $u$- or $v$-points,
 the bathymetry or the ice shelf draft is dug to fit this constrain.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_DYN.tex

-                      r10414
+                      r10442
 \label{subsec:DYN_divcur}
 The vorticity is defined at an $f$-point ($i.e.$ corner point) as follows:
+The vorticity is defined at an $f$-point (\ie corner point) as follows:
 \begin{equation}
   \label{eq:divcur_cur}
 …
 the tracer equation \autoref{eq:tra_nxt}:
 a leapfrog scheme in combination with an Asselin time filter,
 $i.e.$ the velocity appearing in \autoref{eq:dynspg_ssh} is centred in time (\textit{now} velocity).
+\ie the velocity appearing in \autoref{eq:dynspg_ssh} is centred in time (\textit{now} velocity).
 This is of paramount importance.
 Replacing $T$ by the number $1$ in the tracer equation and summing over the water column must lead to
 …
 The upper boundary condition applies at a fixed level $z=0$.
 The top vertical velocity is thus equal to the divergence of the barotropic transport
 ($i.e.$ the first term in the right-hand-side of \autoref{eq:dynspg_ssh}).
+(\ie the first term in the right-hand-side of \autoref{eq:dynspg_ssh}).
 Note also that whereas the vertical velocity has the same discrete expression in $z$- and $s$-coordinates,
 its physical meaning is not the same:
 in the second case, $w$ is the velocity normal to the $s$-surfaces.
 Note also that the $k$-axis is re-orientated downwards in the \textsc{fortran} code compared to
+Note also that the $k$-axis is re-orientated downwards in the \fortran code compared to
 the indexing used in the semi-discrete equations such as \autoref{eq:wzv}
 (see \autoref{subsec:DOM_Num_Index_vertical}).
 …
 Options are defined through the \ngn{namdyn\_adv} namelist variables Coriolis and
 momentum advection terms are evaluated using a leapfrog scheme,
 $i.e.$ the velocity appearing in these expressions is centred in time (\textit{now} velocity).
+\ie the velocity appearing in these expressions is centred in time (\textit{now} velocity).
 At the lateral boundaries either free slip, no slip or partial slip boundary conditions are applied following
 \autoref{chap:LBC}.
 …
 In the enstrophy conserving case (ENS scheme),
 the discrete formulation of the vorticity term provides a global conservation of the enstrophy
 ($ [ (\zeta +f ) / e_{3f} ]^2 $ in $s$-coordinates) for a horizontally non-divergent flow ($i.e.$ $\chi$=$0$),
+($ [ (\zeta +f ) / e_{3f} ]^2 $ in $s$-coordinates) for a horizontally non-divergent flow (\ie $\chi$=$0$),
 but does not conserve the total kinetic energy.
 It is given by:
 …
 the presence of grid point oscillation structures that will be invisible to the operator.
 These structures are \textit{computational modes} that will be at least partly damped by
 the momentum diffusion operator ($i.e.$ the subgrid-scale advection), but not by the resolved advection term.
+the momentum diffusion operator (\ie the subgrid-scale advection), but not by the resolved advection term.
 The ENS and ENE schemes therefore do not contribute to dump any grid point noise in the horizontal velocity field.
 Such noise would result in more noise in the vertical velocity field, an undesirable feature.
 …
 (with a systematic reduction of $e_{3f}$ when a model level intercept the bathymetry)
 that tends to reinforce the topostrophy of the flow
 ($i.e.$ the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.
+(\ie the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.
 Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as
 …
 This EEN scheme in fact combines the conservation properties of the ENS and ENE schemes.
 It conserves both total energy and potential enstrophy in the limit of horizontally nondivergent flow
 ($i.e.$ $\chi$=$0$) (see \autoref{subsec:C_vorEEN}).
+(\ie $\chi$=$0$) (see \autoref{subsec:C_vorEEN}).
 Applied to a realistic ocean configuration, it has been shown that it leads to a significant reduction of
 the noise in the vertical velocity field \citep{Le_Sommer_al_OM09}.
 …
 In the flux form (as in the vector invariant form),
 the Coriolis and momentum advection terms are evaluated using a leapfrog scheme,
 $i.e.$ the velocity appearing in their expressions is centred in time (\textit{now} velocity).
+\ie the velocity appearing in their expressions is centred in time (\textit{now} velocity).
 At the lateral boundaries either free slip,
 no slip or partial slip boundary conditions are applied following \autoref{chap:LBC}.
 …
 compute the product of the Coriolis parameter and the vorticity.
 However, the energy-conserving scheme (\autoref{eq:dynvor_een}) has exclusively been used to date.
 This term is evaluated using a leapfrog scheme, $i.e.$ the velocity is centred in time (\textit{now} velocity).
+This term is evaluated using a leapfrog scheme, \ie the velocity is centred in time (\textit{now} velocity).
 %--------------------------------------------------------------------------------------------------------------
 …
 The schemes are selected using the namelist logicals \np{ln\_dynadv\_cen2} and \np{ln\_dynadv\_ubs}.
 In flux form, the schemes differ by the choice of a space and time interpolation to define the value of
 $u$ and $v$ at the centre of each face of $u$- and $v$-cells, $i.e.$ at the $T$-, $f$-,
+$u$ and $v$ at the centre of each face of $u$- and $v$-cells, \ie at the $T$-, $f$-,
 and $uw$-points for $u$ and at the $f$-, $T$- and $vw$-points for $v$.
 …
 \end{equation}
 The scheme is non diffusive (i.e. conserves the kinetic energy) but dispersive ($i.e.$ it may create false extrema).
+The scheme is non diffusive (\ie conserves the kinetic energy) but dispersive (\ie it may create false extrema).
 It is therefore notoriously noisy and must be used in conjunction with an explicit diffusion operator to
 produce a sensible solution.
 …
 \end{equation}
 where $u"_{i+1/2} =\delta_{i+1/2} \left[ {\delta_i \left[ u \right]} \right]$.
 This results in a dissipatively dominant ($i.e.$ hyper-diffusive) truncation error
+This results in a dissipatively dominant (\ie hyper-diffusive) truncation error
 \citep{Shchepetkin_McWilliams_OM05}.
 The overall performance of the advection scheme is similar to that reported in \citet{Farrow1995}.
 …
 But the amplitudes of the false extrema are significantly reduced over those in the centred second order method.
 As the scheme already includes a diffusion component, it can be used without explicit lateral diffusion on momentum
 ($i.e.$ \np{ln\_dynldf\_lap}\forcode{ = }\np{ln\_dynldf\_bilap}\forcode{ = .false.}),
+(\ie \np{ln\_dynldf\_lap}\forcode{ = }\np{ln\_dynldf\_bilap}\forcode{ = .false.}),
 and it is recommended to do so.
 The UBS scheme is not used in all directions.
 In the vertical, the centred $2^{nd}$ order evaluation of the advection is preferred, $i.e.$ $u_{uw}^{ubs}$ and
+In the vertical, the centred $2^{nd}$ order evaluation of the advection is preferred, \ie $u_{uw}^{ubs}$ and
 $u_{vw}^{ubs}$ in \autoref{eq:dynadv_cen2} are used.
 UBS is diffusive and is associated with vertical mixing of momentum. \gmcomment{ gm  pursue the
 …
 The key distinction between the different algorithms used for
 the hydrostatic pressure gradient is the vertical coordinate used,
 since HPG is a \emph{horizontal} pressure gradient, $i.e.$ computed along geopotential surfaces.
+since HPG is a \emph{horizontal} pressure gradient, \ie computed along geopotential surfaces.
 As a result, any tilt of the surface of the computational levels will require a specific treatment to
 compute the hydrostatic pressure gradient.
 The hydrostatic pressure gradient term is evaluated either using a leapfrog scheme,
 $i.e.$ the density appearing in its expression is centred in time (\emph{now} $\rho$),
+\ie the density appearing in its expression is centred in time (\emph{now} $\rho$),
 or a semi-implcit scheme.
 At the lateral boundaries either free slip, no slip or partial slip boundary conditions are applied.
 …
 Pressure gradient formulations in an $s$-coordinate have been the subject of a vast number of papers
 ($e.g.$, \citet{Song1998, Shchepetkin_McWilliams_OM05}).
+(\eg, \citet{Song1998, Shchepetkin_McWilliams_OM05}).
 A number of different pressure gradient options are coded but the ROMS-like,
 density Jacobian with cubic polynomial method is currently disabled whilst known bugs are under investigation.
 …
 $\bullet$ The main hypothesis to compute the ice shelf load is that the ice shelf is in an isostatic equilibrium.
 The top pressure is computed integrating from surface to the base of the ice shelf a reference density profile
 (prescribed as density of a water at 34.4 PSU and -1.9\degC) and
+(prescribed as density of a water at 34.4 PSU and -1.9\deg{C}) and
 corresponds to the water replaced by the ice shelf.
 This top pressure is constant over time.
 …
 It involves the evaluation of the hydrostatic pressure gradient as
 an average over the three time levels $t-\rdt$, $t$, and $t+\rdt$
 ($i.e.$  \textit{before},  \textit{now} and  \textit{after} time-steps),
+(\ie \textit{before}, \textit{now} and  \textit{after} time-steps),
 rather than at the central time level $t$ only, as in the standard leapfrog scheme.
 …
 the model time step is chosen to be small enough to resolve the external gravity waves
 (typically a few tens of seconds).
 The surface pressure gradient, evaluated using a leap-frog scheme ($i.e.$ centered in time),
+The surface pressure gradient, evaluated using a leap-frog scheme (\ie centered in time),
 is thus simply given by :
 \begin{equation}
 …
 \end{equation}
 Note that in the non-linear free surface case ($i.e.$ \key{vvl} defined),
+Note that in the non-linear free surface case (\ie \key{vvl} defined),
 the surface pressure gradient is already included in the momentum tendency through
 the level thickness variation allowed in the computation of the hydrostatic pressure gradient.
 …
 (\np{ln\_bt\_av}\forcode{ = .false.}).
 In that case, external mode equations are continuous in time,
 $i.e.$ they are not re-initialized when starting a new sub-stepping sequence.
+\ie they are not re-initialized when starting a new sub-stepping sequence.
 This is the method used so far in the POM model, the stability being maintained by
 refreshing at (almost) each barotropic time step advection and horizontal diffusion terms.
 …
 the description of the coefficients is found in the chapter on lateral physics (\autoref{chap:LDF}).
 The lateral diffusion of momentum is evaluated using a forward scheme,
 $i.e.$ the velocity appearing in its expression is the \textit{before} velocity in time,
+\ie the velocity appearing in its expression is the \textit{before} velocity in time,
 except for the pure vertical component that appears when a tensor of rotation is used.
 This latter term is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}).
 …
   In finite difference methods,
   the biharmonic operator is frequently the method of choice to achieve this scale selective dissipation since
   its damping time ($i.e.$ its spin down time) scale like $\lambda^{-4}$ for disturbances of wavelength $\lambda$
+  its damping time (\ie its spin down time) scale like $\lambda^{-4}$ for disturbances of wavelength $\lambda$
   (so that short waves damped more rapidelly than long ones),
   whereas the Laplace operator damping time scales only like $\lambda^{-2}$.
 …
 (3) When \np{nn\_ice\_embd}\forcode{ = 2} and LIM or CICE is used
 ($i.e.$ when the sea-ice is embedded in the ocean),
+(\ie when the sea-ice is embedded in the ocean),
 the snow-ice mass is taken into account when computing the surface pressure gradient.
 …
 Options are defined through the \ngn{namdom} namelist variables.
 The general framework for dynamics time stepping is a leap-frog scheme,
 $i.e.$ a three level centred time scheme associated with an Asselin time filter (cf. \autoref{chap:STP}).
+\ie a three level centred time scheme associated with an Asselin time filter (cf. \autoref{chap:STP}).
 The scheme is applied to the velocity, except when
 using the flux form of momentum advection (cf. \autoref{sec:DYN_adv_cor_flux})
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_LBC.tex

-                      r10414
+                      r10442
 %The lateral ocean boundary conditions contiguous to coastlines are Neumann conditions for heat and salt (no flux across boundaries) and Dirichlet conditions for momentum (ranging from free-slip to "strong" no-slip). They are handled automatically by the mask system (see \autoref{subsec:DOM_msk}).
 %OPA allows land and topography grid points in the computational domain due to the presence of continents or islands, and includes the use of a full or partial step representation of bottom topography. The computation is performed over the whole domain, i.e. we do not try to restrict the computation to ocean-only points. This choice has two motivations. Firstly, working on ocean only grid points overloads the code and harms the code readability. Secondly, and more importantly, it drastically reduces the vector portion of the computation, leading to a dramatic increase of CPU time requirement on vector computers.  The current section describes how the masking affects the computation of the various terms of the equations with respect to the boundary condition at solid walls. The process of defining which areas are to be masked is described in \autoref{subsec:DOM_msk}.
+%OPA allows land and topography grid points in the computational domain due to the presence of continents or islands, and includes the use of a full or partial step representation of bottom topography. The computation is performed over the whole domain, \ie we do not try to restrict the computation to ocean-only points. This choice has two motivations. Firstly, working on ocean only grid points overloads the code and harms the code readability. Secondly, and more importantly, it drastically reduces the vector portion of the computation, leading to a dramatic increase of CPU time requirement on vector computers.  The current section describes how the masking affects the computation of the various terms of the equations with respect to the boundary condition at solid walls. The process of defining which areas are to be masked is described in \autoref{subsec:DOM_msk}.
 Options are defined through the \ngn{namlbc} namelist variables.
 …
 Since most of the boundary conditions consist of a zero flux across the solid boundaries,
 they can be simply applied by multiplying variables by the correct mask arrays,
 $i.e.$ the mask array of the grid point where the flux is evaluated.
+\ie the mask array of the grid point where the flux is evaluated.
 For example, the heat flux in the \textbf{i}-direction is evaluated at $u$-points.
 Evaluating this quantity as,
 …
 \item[free-slip boundary condition (\np{rn\_shlat}\forcode{ = 0}):] the tangential velocity at
   the coastline is equal to the offshore velocity,
   $i.e.$ the normal derivative of the tangential velocity is zero at the coast,
+  \ie the normal derivative of the tangential velocity is zero at the coast,
   so the vorticity: mask$_{f}$ array is set to zero inside the land and just at the coast
   (\autoref{fig:LBC_shlat}-a).
 …
 \item["partial" free-slip boundary condition (0$<$\np{rn\_shlat}$<$2):] the tangential velocity at
   the coastline is smaller than the offshore velocity, $i.e.$ there is a lateral friction but
+  the coastline is smaller than the offshore velocity, \ie there is a lateral friction but
   not strong enough to make the tangential velocity at the coast vanish (\autoref{fig:LBC_shlat}-c).
   This can be selected by providing a value of mask$_{f}$ strictly inbetween $0$ and $2$.
 …
 Each time such a boundary condition is needed, it is set by a call to routine \mdl{lbclnk}.
 The computation of momentum and tracer trends proceeds from $i=2$ to $i=jpi-1$ and from $j=2$ to $j=jpj-1$,
 $i.e.$ in the model interior.
+\ie in the model interior.
 To choose a lateral model boundary condition is to specify the first and last rows and columns of
 the model variables.
 …
 are organized by explicit statements (message passing method).
 A big advantage is that the method does not need many modifications of the initial FORTRAN code.
+A big advantage is that the method does not need many modifications of the initial \fortran code.
 From the modeller's point of view, each sub domain running on a processor is identical to the "mono-domain" code.
 In addition, the programmer manages the communications between subdomains,
 …
 After a computation, a communication phase starts:
 each processor sends to its neighbouring processors the update values of the points corresponding to
 the interior overlapping area to its neighbouring sub-domain ($i.e.$ the innermost of the two overlapping rows).
+the interior overlapping area to its neighbouring sub-domain (\ie the innermost of the two overlapping rows).
 The communication is done through the Message Passing Interface (MPI).
 The data exchanges between processors are required at the very place where
 lateral domain boundary conditions are set in the mono-domain computation:
 the \rou{lbc\_lnk} routine (found in \mdl{lbclnk} module) which manages such conditions is interfaced with
 routines found in \mdl{lib\_mpp} module when running on an MPP computer ($i.e.$ when \key{mpp\_mpi} defined).
+routines found in \mdl{lib\_mpp} module when running on an MPP computer (\ie when \key{mpp\_mpi} defined).
 It has to be pointed out that when using the MPP version of the model,
 the east-west cyclic boundary condition is done implicitly,
 …
 Note that this is a problem for the meshmask file which requires to be defined over the whole domain.
 Therefore, user should not eliminate land processors when creating a meshmask file
 ($i.e.$ when setting a non-zero value to \np{nn\_msh}).
+(\ie when setting a non-zero value to \np{nn\_msh}).
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 Note that the sea-surface height gradient in \autoref{eq:bdy_fla1} is a spatial gradient across the model boundary,
 so that $\eta_{e}$ is defined on the $T$ points with $nbr=1$ and $\eta$ is defined on the $T$ points with $nbr=2$.
 $U$ and $U_{e}$ are defined on the $U$ or $V$ points with $nbr=1$, $i.e.$ between the two $T$ grid points.
+$U$ and $U_{e}$ are defined on the $U$ or $V$ points with $nbr=1$, \ie between the two $T$ grid points.
 %----------------------------------------------
 …
 These restrictions mean that data files used with previous versions of the model may not work with version 3.4.
 A fortran utility {\it bdy\_reorder} exists in the TOOLS directory which
+A\fortran utility {\it bdy\_reorder} exists in the TOOLS directory which
 will re-order the data in old BDY data files.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_LDF.tex

-                      r10414
+                      r10442
 (3) the space and time variations of the eddy coefficients.
 These three aspects of the lateral diffusion are set through namelist parameters
 (see the \textit{\ngn{nam\_traldf}} and \textit{\ngn{nam\_dynldf}} below).
+(see the \ngn{nam\_traldf} and \ngn{nam\_dynldf} below).
 Note that this chapter describes the standard implementation of iso-neutral tracer mixing,
 and Griffies's implementation, which is used if \np{traldf\_grif}\forcode{ = .true.},
 …
 \subsection{Slopes for tracer geopotential mixing in the $s$-coordinate}
 In $s$-coordinates, geopotential mixing ($i.e.$ horizontal mixing) $r_1$ and $r_2$ are the slopes between
+In $s$-coordinates, geopotential mixing (\ie horizontal mixing) $r_1$ and $r_2$ are the slopes between
 the geopotential and computational surfaces.
 Their discrete formulation is found by locally solving \autoref{eq:tra_ldf_iso} when
 the diffusive fluxes in the three directions are set to zero and $T$ is assumed to be horizontally uniform,
 $i.e.$ a linear function of $z_T$, the depth of a $T$-point.
+\ie a linear function of $z_T$, the depth of a $T$-point.
 %gm { Steven : My version is obviously wrong since I'm left with an arbitrary constant which is the local vertical temperature gradient}
 …
 Their formulation does not depend on the vertical coordinate used.
 Their discrete formulation is found using the fact that the diffusive fluxes of
 locally referenced potential density ($i.e.$ $in situ$ density) vanish.
+locally referenced potential density (\ie $in situ$ density) vanish.
 So, substituting $T$ by $\rho$ in \autoref{eq:tra_ldf_iso} and setting the diffusive fluxes in
 the three directions to zero leads to the following definition for the neutral slopes:
 …
       \textit{(a)} in the real ocean the slope is the iso-neutral slope in the ocean interior,
       which has to be adjusted at the surface boundary
       (i.e. it must tend to zero at the surface since there is no mixing across the air-sea interface:
+      \ie it must tend to zero at the surface since there is no mixing across the air-sea interface:
       wall boundary condition).
       Nevertheless, the profile between the surface zero value and the interior iso-neutral one is unknown,
 …
 \textit{vw}- points for the $v$-component.
 They are computed from the slopes used for tracer diffusion,
 $i.e.$ \autoref{eq:ldfslp_geo} and \autoref{eq:ldfslp_iso} :
+\ie \autoref{eq:ldfslp_geo} and \autoref{eq:ldfslp_iso}:
 \[
 …
 The major issue remaining is in the specification of the boundary conditions.
 The same boundary conditions are chosen as those used for lateral diffusion along model level surfaces,
 $i.e.$ using the shear computed along the model levels and with no additional friction at the ocean bottom
+\ie using the shear computed along the model levels and with no additional friction at the ocean bottom
 (see \autoref{sec:LBC_coast}).
 …
 Changes in the computer code when switching from one option to another have been minimized by
 introducing the eddy coefficients as statement functions
 (include file \hf{ldftra\_substitute} and \hf{ldfdyn\_substitute}).
+(include file \textit{ldftra\_substitute.h90} and \textit{ldfdyn\_substitute.h90}).
 The functions are replaced by their actual meaning during the preprocessing step (CPP).
 The specification of the space variation of the coefficient is made in \mdl{ldftra} and \mdl{ldfdyn},
 or more precisely in include files \hf{traldf\_cNd} and \hf{dynldf\_cNd}, with N=1, 2 or 3.
+or more precisely in include files \textit{traldf\_cNd.h90} and \textit{dynldf\_cNd.h90}, with N=1, 2 or 3.
 The user can modify these include files as he/she wishes.
 The way the mixing coefficient are set in the reference version can be briefly described as follows:
 …
 the surface value is \np{rn\_aht0} (\np{rn\_ahm0}), the bottom value is 1/4 of the surface value,
 and the transition takes place around z=300~m with a width of 300~m
 ($i.e.$ both the depth and the width of the inflection point are set to 300~m).
 This profile is hard coded in file \hf{traldf\_c1d}, but can be easily modified by users.
+(\ie both the depth and the width of the inflection point are set to 300~m).
+This profile is hard coded in file \textit{traldf\_c1d.h90}, but can be easily modified by users.
 \subsubsection{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})}
 …
 The 3D space variation of the mixing coefficient is simply the combination of the 1D and 2D cases,
 $i.e.$ a hyperbolic tangent variation with depth associated with a grid size dependence of
+\ie a hyperbolic tangent variation with depth associated with a grid size dependence of
 the magnitude of the coefficient.
 …
 $A^{eiv}$, the eddy induced coefficient has to be defined.
 Its space variations are controlled by the same CPP variable as for the eddy diffusivity coefficient
 ($i.e.$ \key{traldf\_cNd}).
+(\ie \key{traldf\_cNd}).
 (5) the eddy coefficient associated with a biharmonic operator must be set to a \emph{negative} value.
 …
 the formulation of which depends on the slopes of iso-neutral surfaces.
 Contrary to the case of iso-neutral mixing, the slopes used here are referenced to the geopotential surfaces,
 $i.e.$ \autoref{eq:ldfslp_geo} is used in $z$-coordinates,
+\ie \autoref{eq:ldfslp_geo} is used in $z$-coordinates,
 and the sum \autoref{eq:ldfslp_geo} + \autoref{eq:ldfslp_iso} in $s$-coordinates.
 The eddy induced velocity is given by:
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_OBS.tex

-                      r10414
+                      r10442
 This now works in a generalised vertical coordinate system.
 Some profile observation types (e.g. tropical moored buoys) are made available as daily averaged quantities.
+Some profile observation types (\eg tropical moored buoys) are made available as daily averaged quantities.
 The observation operator code can be set-up to calculate the equivalent daily average model temperature fields using
 the \np{nn\_profdavtypes} namelist array.
 …
 the model equivalent of the observation is calculated by interpolating from
 the four surrounding grid points to the observation location.
 Some satellite observations (e.g. microwave satellite SST data, or satellite SSS data) have a footprint which
+Some satellite observations (\eg microwave satellite SST data, or satellite SSS data) have a footprint which
 is similar in size or larger than the model grid size (particularly when the grid size is small).
 In those cases the model counterpart should be calculated by averaging the model grid points over
 …
    and $M$ corresponds to $B$, $C$ or $D$.
    A more stable form of the great-circle distance formula for small distances ($x$ near 1)
    involves the arcsine function ($e.g.$ see p.~101 of \citet{Daley_Barker_Bk01}:
+   involves the arcsine function (\eg see p.~101 of \citet{Daley_Barker_Bk01}:
    \begin{align*}
      s\left( {\rm P}, {\rm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\}
 …
       \protect\label{fig:obsavgrec}
       Weights associated with each model grid box (blue lines and numbers)
       for an observation at -170.5E, 56.0N with a rectangular footprint of 1\deg x 1\deg.
+      for an observation at -170.5\deg{E}, 56.0\deg{N} with a rectangular footprint of 1\deg x 1\deg.
+    }
   \end{center}
 …
       \protect\label{fig:obsavgrad}
       Weights associated with each model grid box (blue lines and numbers)
       for an observation at -170.5E, 56.0N with a radial footprint with diameter 1\deg.
+      for an observation at -170.5\deg{E}, 56.0\deg{N} with a radial footprint with diameter 1\deg.
+    }
   \end{center}
 …
 \end{align*}
 point in the opposite direction to the unit normal $\widehat{\bf k}$
 (i.e., that the coefficients of $\widehat{\bf k}$ are negative),
+(\ie that the coefficients of $\widehat{\bf k}$ are negative),
 where ${{\bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, etc. correspond to
 the vectors between points P and A, P and B, etc..
 …
 any MPP communication.
 Of course, this is under the assumption that we are only using a $2 \times 2$ grid-point stencil for
 the interpolation (e.g., bilinear interpolation).
+the interpolation (\eg bilinear interpolation).
 For higher order interpolation schemes this is no longer valid.
 A disadvantage with the above scheme is that the number of observations on each processor can be very different.
 …
 \begin{description}
 \item[cl4\_prefix]
   Prefix for class 4 files e.g. class4
+  Prefix for class 4 files \eg class4
 \item[cl4\_date]
   YYYYMMDD validity date
 \item[cl4\_sys]
   The name of the class 4 model system e.g. FOAM
+  The name of the class 4 model system \eg FOAM
 \item[cl4\_cfg]
   The name of the class 4 model configuration e.g. orca025
+  The name of the class 4 model configuration \eg orca025
 \item[cl4\_vn]
   The name of the class 4 model version e.g. 12.0
+  The name of the class 4 model version \eg 12.0
 \end{description}
 …
   The name of the producers institution.
 \item[cl4\_cfg]
   The name of the class 4 model configuration e.g. orca025
+  The name of the class 4 model configuration \eg orca025
 \item[cl4\_vn]
   The name of the class 4 model version e.g. 12.0
+  The name of the class 4 model version \eg 12.0
 \end{description}
 …
 Some tools for viewing and processing of observation and feedback files are provided in
 the NEMO repository for convenience.
 These include OBSTOOLS which are a collection of Fortran programs which are helpful to deal with feedback files.
+These include OBSTOOLS which are a collection of \fortran programs which are helpful to deal with feedback files.
 They do such tasks as observation file conversion, printing of file contents,
 some basic statistical analysis of feedback files.
 …
 \subsection{Obstools}
 A series of Fortran utilities is provided with NEMO called OBSTOOLS.
+A series of \fortran utilities is provided with NEMO called OBSTOOLS.
 This are helpful in handling observation files and the feedback file output from the NEMO observation operator.
 The utilities are as follows
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex

-                      r10414
+                      r10442
 a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler)
 (\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}).
 When used ($i.e.$ \np{ln\_apr\_dyn}\forcode{ = .true.}),
+When used (\ie \np{ln\_apr\_dyn}\forcode{ = .true.}),
 the atmospheric pressure forces both ocean and ice dynamics.
 …
 the momentum vertical mixing trend (see \autoref{eq:dynzdf_sbc} in \autoref{sec:DYN_zdf}).
 As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
 $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
+\ie resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
 The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
 $Q_{ns}$ and $Q_{sr}$, respectively.
 The former is the non penetrative part of the heat flux
 ($i.e.$ the sum of sensible, latent and long wave heat fluxes plus
+(\ie the sum of sensible, latent and long wave heat fluxes plus
 the heat content of the mass exchange with the atmosphere and sea-ice).
 It is applied in \mdl{trasbc} module as a surface boundary condition trend of
 …
+%
 %Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
 %ssv) i.e. information required by flux computation or sea-ice
+%ssv) \ie information required by flux computation or sea-ice
+%
 %\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
 …
       Ocean variables provided by the ocean to the surface module (SBC).
       The variable are averaged over nn{\_}fsbc time step,
       $i.e.$ the frequency of computation of surface fluxes.
+      \ie the frequency of computation of surface fluxes.
+    }
   \end{center}
 …
       The stem name is assumed to be 'fn'.
       For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
       ($i.e.$ 'sun','sat','fri','thu','wed','tue','mon').
+      (\ie 'sun','sat','fri','thu','wed','tue','mon').
       The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits.
       Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc',
 …
   This has been cut down and now only calculates surface forcing and the ice model required.
   New surface modules that can function when only the surface level of the ocean state is defined can also be added
   (e.g. icebergs).
+  (\eg icebergs).
 \item
   \mdl{daymod}:
 …
 A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true.
 In this case $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
 $i.e.$ the mean value of $\eta_{ib}$ is kept to zero at all time step.
+\ie the mean value of $\eta_{ib}$ is kept to zero at all time step.
 The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
 …
 The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
 the bottom of the lowest box the river water is being added to
 (i.e. the total depth that river water is being added to in the model).
+(\ie the total depth that river water is being added to in the model).
 The mass/volume addition due to the river runoff is, at each relevant depth level, added to
 …
 It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
 i.e. modelling the Baltic flow in and out of the North Sea.
+\ie modelling the Baltic flow in and out of the North Sea.
 When the flow is out of the domain there is no change in temperature and salinity,
 regardless of the namelist options used,
 …
   At each time step, a test is performed to see if there is enough ice mass to
   calve an iceberg of each class in order (1 to 10).
   Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling).
+  Note that this is the initial mass multiplied by the number each particle represents (\ie the scaling).
   If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
 \end{description}
 …
 \label{subsec:SBC_wave_cdgw}
 The neutral surface drag coefficient provided from an external data source ($i.e.$ a wave model),
+The neutral surface drag coefficient provided from an external data source (\ie a wave model),
 can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist.
 Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,
 …
 a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
 The use of diurnal cycle reconstruction requires the input SWF to be daily
 ($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
+(\ie a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
 Furthermore, it is recommended to have a least 8 surface module time step per day,
 that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
 …
   Note that the activation of a sea-ice model is is done by defining a CPP key (\key{lim3} or \key{cice}).
   The activation automatically overwrites the read value of nn{\_}ice to its appropriate value
   ($i.e.$ $2$ for LIM-3 or $3$ for CICE).
+  (\ie $2$ for LIM-3 or $3$ for CICE).
 \end{description}
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_STO.tex

-                      r10414
+                      r10442
 The simulation will continue exactly as if it was not interrupted only
 when \np{ln\_rstseed} is set to \forcode{.true.},
 $i.e.$ when the state of the random number generator is read in the restart file.
+\ie when the state of the random number generator is read in the restart file.
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_TRA.tex

-                      r10414
+                      r10442
 The terms QSR, BBC, BBL and DMP are optional.
 The external forcings and parameterisations require complex inputs and complex calculations
 ($e.g.$ bulk formulae, estimation of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and
+(\eg bulk formulae, estimation of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and
 described in \autoref{chap:SBC}, \autoref{chap:LDF} and \autoref{chap:ZDF}, respectively.
 Note that \mdl{tranpc}, the non-penetrative convection module, although located in the NEMO/OPA/TRA directory as
 …
 %-------------------------------------------------------------------------------------------------------------
 When considered ($i.e.$ when \np{ln\_traadv\_NONE} is not set to \forcode{.true.}),
+When considered (\ie when \np{ln\_traadv\_NONE} is not set to \forcode{.true.}),
 the advection tendency of a tracer is expressed in flux form,
 $i.e.$ as the divergence of the advective fluxes.
+\ie as the divergence of the advective fluxes.
 Its discrete expression is given by :
 \begin{equation}
 …
 $\nabla \cdot \left( \vect{U}\,T \right)=\vect{U} \cdot \nabla T$ which
 results from the use of the continuity equation,  $\partial _t e_3 + e_3\;\nabla \cdot \vect{U}=0$
 (which reduces to $\nabla \cdot \vect{U}=0$ in linear free surface, $i.e.$ \np{ln\_linssh}\forcode{ = .true.}).
+(which reduces to $\nabla \cdot \vect{U}=0$ in linear free surface, \ie \np{ln\_linssh}\forcode{ = .true.}).
 Therefore it is of paramount importance to design the discrete analogue of the advection tendency so that
 it is consistent with the continuity equation in order to enforce the conservation properties of
 …
   There is a non-zero advective flux which is set for all advection schemes as
   $\left. {\tau_w } \right|_{k=1/2} =T_{k=1} $,
   $i.e.$ the product of surface velocity (at $z=0$) by the first level tracer value.
+  \ie the product of surface velocity (at $z=0$) by the first level tracer value.
 \item[non-linear free surface:]
   (\np{ln\_linssh}\forcode{ = .false.})
 …
 The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco})
 is the centred (\textit{now}) \textit{effective} ocean velocity,
 $i.e.$ the \textit{eulerian} velocity (see \autoref{chap:DYN}) plus
+\ie the \textit{eulerian} velocity (see \autoref{chap:DYN}) plus
 the eddy induced velocity (\textit{eiv}) and/or
 the mixed layer eddy induced velocity (\textit{eiv}) when
 …
 The corresponding code can be found in the \mdl{traadv\_xxx} module,
 where \textit{xxx} is a 3 or 4 letter acronym corresponding to each scheme.
 By default ($i.e.$ in the reference namelist, \ngn{namelist\_ref}), all the logicals are set to \forcode{.false.}.
+By default (\ie in the reference namelist, \ngn{namelist\_ref}), all the logicals are set to \forcode{.false.}.
 If the user does not select an advection scheme in the configuration namelist (\ngn{namelist\_cfg}),
 the tracers will \textit{not} be advected!
 …
 \end{equation}
 CEN2 is non diffusive ($i.e.$ it conserves the tracer variance, $\tau^2)$ but dispersive
 ($i.e.$ it may create false extrema).
+CEN2 is non diffusive (\ie it conserves the tracer variance, $\tau^2)$ but dispersive
+(\ie it may create false extrema).
 It is therefore notoriously noisy and must be used in conjunction with an explicit diffusion operator to
 produce a sensible solution.
 …
 A direct consequence of the pseudo-fourth order nature of the scheme is that it is not non-diffusive,
 $i.e.$ the global variance of a tracer is not preserved using CEN4.
+\ie the global variance of a tracer is not preserved using CEN4.
 Furthermore, it must be used in conjunction with an explicit diffusion operator to produce a sensible solution.
 As in CEN2 case, the time-stepping is performed using a leapfrog scheme in conjunction with an Asselin time-filter,
 …
 where $c_u$ is a flux limiter function taking values between 0 and 1.
 The FCT order is the one of the centred scheme used
 ($i.e.$ it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}).
+(\ie it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}).
 There exist many ways to define $c_u$, each corresponding to a different FCT scheme.
 The one chosen in \NEMO is described in \citet{Zalesak_JCP79}.
 …
 where $\tau "_i =\delta_i \left[ {\delta_{i+1/2} \left[ \tau \right]} \right]$.
 This results in a dissipatively dominant (i.e. hyper-diffusive) truncation error
+This results in a dissipatively dominant (\ie hyper-diffusive) truncation error
 \citep{Shchepetkin_McWilliams_OM05}.
 The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}.
 …
 $(i)$   the type of operator used (none, laplacian, bilaplacian),
 $(ii)$  the direction along which the operator acts (iso-level, horizontal, iso-neutral),
 $(iii)$ some specific options related to the rotated operators ($i.e.$ non-iso-level operator), and
+$(iii)$ some specific options related to the rotated operators (\ie non-iso-level operator), and
 $(iv)$  the specification of eddy diffusivity coefficient (either constant or variable in space and time).
 Item $(iv)$ will be described in \autoref{chap:LDF}.
 …
 The lateral diffusion of tracers is evaluated using a forward scheme,
 $i.e.$ the tracers appearing in its expression are the \textit{before} tracers in time,
+\ie the tracers appearing in its expression are the \textit{before} tracers in time,
 except for the pure vertical component that appears when a rotation tensor is used.
 This latter component is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}).
 …
 minimizing the impact on the larger scale features.
 The main difference between the two operators is the scale selectiveness.
 The bilaplacian damping time ($i.e.$ its spin down time) scales like $\lambda^{-4}$ for
+The bilaplacian damping time (\ie its spin down time) scales like $\lambda^{-4}$ for
 disturbances of wavelength $\lambda$ (so that short waves damped more rapidelly than long ones),
 whereas the laplacian damping time scales only like $\lambda^{-2}$.
 …
 The operator is a simple (re-entrant) laplacian acting in the (\textbf{i},\textbf{j}) plane when
 iso-level option is used (\np{ln\_traldf\_lev}\forcode{ = .true.}) or
 when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{z}-coordinate
+when a horizontal (\ie geopotential) operator is demanded in \zstar-coordinate
 (\np{ln\_traldf\_hor} and \np{ln\_zco} equal \forcode{.true.}).
 The associated code can be found in the \mdl{traldf\_lap\_blp} module.
 …
 (\np{ln\_traldf\_iso} or \np{ln\_traldf\_triad} equals \forcode{.true.},
 see \mdl{traldf\_iso} or \mdl{traldf\_triad} module, resp.), or
 when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{s}-coordinate
+when a horizontal (\ie geopotential) operator is demanded in \textit{s}-coordinate
 (\np{ln\_traldf\_hor} and \np{ln\_sco} equal \forcode{.true.})
 \footnote{In this case, the standard iso-neutral operator will be automatically selected}.
 …
 compute the iso-level bilaplacian operator.
 It is a \emph{horizontal} operator ($i.e.$ acting along geopotential surfaces) in
+It is a \emph{horizontal} operator (\ie acting along geopotential surfaces) in
 the $z$-coordinate with or without partial steps, but is simply an iso-level operator in the $s$-coordinate.
 It is thus used when, in addition to \np{ln\_traldf\_lap} or \np{ln\_traldf\_blp}\forcode{ = .true.},
 …
 where $b_t$=$e_{1t}\,e_{2t}\,e_{3t}$  is the volume of $T$-cells,
 $r_1$ and $r_2$ are the slopes between the surface of computation ($z$- or $s$-surfaces) and
 the surface along which the diffusion operator acts ($i.e.$ horizontal or iso-neutral surfaces).
+the surface along which the diffusion operator acts (\ie horizontal or iso-neutral surfaces).
 It is thus used when, in addition to \np{ln\_traldf\_lap}\forcode{ = .true.},
 we have \np{ln\_traldf\_iso}\forcode{ = .true.},
 …
 where $A_w^{vT}$ and $A_w^{vS}$ are the vertical eddy diffusivity coefficients on temperature and salinity,
 respectively.
 Generally, $A_w^{vT}=A_w^{vS}$ except when double diffusive mixing is parameterised ($i.e.$ \key{zdfddm} is defined).
+Generally, $A_w^{vT}=A_w^{vS}$ except when double diffusive mixing is parameterised (\ie \key{zdfddm} is defined).
 The way these coefficients are evaluated is given in \autoref{chap:ZDF} (ZDF).
 Furthermore, when iso-neutral mixing is used, both mixing coefficients are increased by
 …
 Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components
 ($i.e.$ atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer of the ocean is due
+(\ie atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer of the ocean is due
 both to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$) and
 to the heat and salt content of the mass exchange.
 …
 $\bullet$ $Q_{ns}$, the non-solar part of the net surface heat flux that crosses the sea surface
 (i.e. the difference between the total surface heat flux and the fraction of the short wave flux that
+(\ie the difference between the total surface heat flux and the fraction of the short wave flux that
 penetrates into the water column, see \autoref{subsec:TRA_qsr})
 plus the heat content associated with of the mass exchange with the atmosphere and lands.
 …
   \end{split}
 \end{equation}
 where $Q_{sr}$ is the penetrative part of the surface heat flux ($i.e.$ the shortwave radiation) and
+where $Q_{sr}$ is the penetrative part of the surface heat flux (\ie the shortwave radiation) and
 $I$ is the downward irradiance ($\left. I \right|_{z=\eta}=Q_{sr}$).
 The additional term in \autoref{eq:PE_qsr} is discretized as follows:
 …
 The RGB formulation is used when \np{ln\_qsr\_rgb}\forcode{ = .true.}.
 The RGB attenuation coefficients ($i.e.$ the inverses of the extinction length scales) are tabulated over
+The RGB attenuation coefficients (\ie the inverses of the extinction length scales) are tabulated over
 nonuniform chlorophyll classes ranging from 0.01 to 10 g.Chl/L
 (see the routine \rou{trc\_oce\_rgb} in \mdl{trc\_oce} module).
 …
 the depth of $w-$levels does not significantly vary with location.
 The level at which the light has been totally absorbed
 ($i.e.$ it is less than the computer precision) is computed once,
+(\ie it is less than the computer precision) is computed once,
 and the trend associated with the penetration of the solar radiation is only added down to that level.
 Finally, note that when the ocean is shallow ($<$ 200~m), part of the solar radiation can reach the ocean floor.
 In this case, we have chosen that all remaining radiation is absorbed in the last ocean level
 ($i.e.$ $I$ is masked).
+(\ie $I$ is masked).
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 Usually it is assumed that there is no exchange of heat or salt through the ocean bottom,
 $i.e.$ a no flux boundary condition is applied on active tracers at the bottom.
+\ie a no flux boundary condition is applied on active tracers at the bottom.
 This is the default option in \NEMO, and it is implemented using the masking technique.
 However, there is a non-zero heat flux across the seafloor that is associated with solid earth cooling.
 …
 but it warms systematically the ocean and acts on the densest water masses.
 Taking this flux into account in a global ocean model increases the deepest overturning cell
 ($i.e.$ the one associated with the Antarctic Bottom Water) by a few Sverdrups  \citep{Emile-Geay_Madec_OS09}.
+(\ie the one associated with the Antarctic Bottom Water) by a few Sverdrups  \citep{Emile-Geay_Madec_OS09}.
 Options are defined through the  \ngn{namtra\_bbc} namelist variables.
 …
 and  $A_l^\sigma$ the lateral diffusivity in the BBL.
 Following \citet{Beckmann_Doscher1997}, the latter is prescribed with a spatial dependence,
 $i.e.$ in the conditional form
+\ie in the conditional form
 \begin{equation}
   \label{eq:tra_bbl_coef}
 …
 \label{subsec:TRA_bbl_adv}
 \sgacomment{"downsloping flow" has been replaced by "downslope flow" in the following
 if this is not what is meant then "downwards sloping flow" is also a possibility"}
+%\sgacomment{"downsloping flow" has been replaced by "downslope flow" in the following
+%if this is not what is meant then "downwards sloping flow" is also a possibility"}
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 %!!      nn_bbl_adv = 1   use of the ocean velocity as bbl velocity
 %!!      nn_bbl_adv = 2   follow Campin and Goosse (1999) implentation
 %!!        i.e. transport proportional to the along-slope density gradient
+%!!        \ie transport proportional to the along-slope density gradient
 %%%gmcomment   :  this section has to be really written
 …
 (see black arrow in \autoref{fig:bbl}) \citep{Beckmann_Doscher1997}.
 It is a \textit{conditional advection}, that is, advection is allowed only
 if dense water overlies less dense water on the slope ($i.e.$ $\nabla_\sigma \rho  \cdot  \nabla H<0$) and
 if the velocity is directed towards greater depth ($i.e.$ $\vect{U}  \cdot  \nabla H>0$).
+if dense water overlies less dense water on the slope (\ie $\nabla_\sigma \rho  \cdot  \nabla H<0$) and
+if the velocity is directed towards greater depth (\ie $\vect{U}  \cdot  \nabla H>0$).
 \np{nn\_bbl\_adv}\forcode{ = 2}:
 …
 the density difference between the higher cell and lower cell densities \citep{Campin_Goosse_Tel99}.
 The advection is allowed only  if dense water overlies less dense water on the slope
 ($i.e.$ $\nabla_\sigma \rho  \cdot  \nabla H<0$).
+(\ie $\nabla_\sigma \rho  \cdot  \nabla H<0$).
 For example, the resulting transport of the downslope flow, here in the $i$-direction (\autoref{fig:bbl}),
 is simply given by the following expression:
 …
 It also requires that both \np{ln\_tsd\_init} and \np{ln\_tsd\_tradmp} are set to true in
 \textit{namtsd} namelist as well as \np{sn\_tem} and \np{sn\_sal} structures are correctly set
 ($i.e.$ that $T_o$ and $S_o$ are provided in input files and read using \mdl{fldread},
+(\ie that $T_o$ and $S_o$ are provided in input files and read using \mdl{fldread},
 see \autoref{subsec:SBC_fldread}).
 The restoring coefficient $\gamma$ is a three-dimensional array read in during the \rou{tra\_dmp\_init} routine.
 …
 This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1.
 The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work.
 The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for
+The \ngn{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for
 the restoration coefficient.
 …
 \np{cp\_cfg}, \np{cp\_cpz}, \np{jp\_cfg} and \np{jperio} specify the model configuration being used and
 should be the same as specified in \nl{namcfg}.
 The variable \nl{lzoom} is used to specify that the damping is being used as in case \textit{a} above to
+should be the same as specified in \ngn{namcfg}.
+The variable \np{lzoom} is used to specify that the damping is being used as in case \textit{a} above to
 provide boundary conditions to a zoom configuration.
 In the case of the arctic or antarctic zoom configurations this includes some specific treatment.
 Otherwise damping is applied to the 6 grid points along the ocean boundaries.
 The open boundaries are specified by the variables \np{lzoom\_n}, \np{lzoom\_e}, \np{lzoom\_s}, \np{lzoom\_w} in
 the \nl{nam\_zoom\_dmp} name list.
+the \ngn{nam\_zoom\_dmp} name list.
 The remaining switch namelist variables determine the spatial variation of the restoration coefficient in
 …
 Options are defined through the  \ngn{namdom} namelist variables.
 The general framework for tracer time stepping is a modified leap-frog scheme \citep{Leclair_Madec_OM09},
 $i.e.$ a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:STP_mLF}):
+\ie a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:STP_mLF}):
 \begin{equation}
   \label{eq:tra_nxt}
 …
 where RHS is the right hand side of the temperature equation, the subscript $f$ denotes filtered values,
 $\gamma$ is the Asselin coefficient, and $S$ is the total forcing applied on $T$
 ($i.e.$ fluxes plus content in mass exchanges).
+(\ie fluxes plus content in mass exchanges).
 $\gamma$ is initialized as \np{rn\_atfp} (\textbf{namelist} parameter).
 Its default value is \np{rn\_atfp}\forcode{ = 10.e-3}.
 …
   the TEOS-10 rational function approximation for hydrographic data analysis \citep{TEOS10}.
   A key point is that conservative state variables are used:
   Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \degC, notation: $\Theta$).
+  Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \deg{C}, notation: $\Theta$).
   The pressure in decibars is approximated by the depth in meters.
   With TEOS10, the specific heat capacity of sea water, $C_p$, is a constant.
 …
 \label{subsec:TRA_bn2}
 An accurate computation of the ocean stability (i.e. of $N$, the brunt-V\"{a}is\"{a}l\"{a} frequency) is of
+An accurate computation of the ocean stability (\ie of $N$, the brunt-V\"{a}is\"{a}l\"{a} frequency) is of
 paramount importance as determine the ocean stratification and is used in several ocean parameterisations
 (namely TKE, GLS, Richardson number dependent vertical diffusion, enhanced vertical diffusion,
 …
 The coefficients are a polynomial function of temperature, salinity and depth which
 expression depends on the chosen EOS.
 They are computed through \textit{eos\_rab}, a \textsc{Fortran} function that can be found in \mdl{eosbn2}.
+They are computed through \textit{eos\_rab}, a \fortran function that can be found in \mdl{eosbn2}.
 % -------------------------------------------------------------------------------------------------------------
 …
 \autoref{eq:tra_eos_fzp} is only used to compute the potential freezing point of sea water
 ($i.e.$ referenced to the surface $p=0$),
+(\ie referenced to the surface $p=0$),
 thus the pressure dependent terms in \autoref{eq:tra_eos_fzp} (last term) have been dropped.
 The freezing point is computed through \textit{eos\_fzp},
 a \textsc{Fortran} function that can be found in \mdl{eosbn2}.
+a \fortran function that can be found in \mdl{eosbn2}.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex

-                      r10414
+                      r10442
 At the surface they are prescribed from the surface forcing (see \autoref{chap:SBC}),
 while at the bottom they are set to zero for heat and salt,
 unless a geothermal flux forcing is prescribed as a bottom boundary condition ($i.e.$ \key{trabbl} defined,
+unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \key{trabbl} defined,
 see \autoref{subsec:TRA_bbc}), and specified through a bottom friction parameterisation for momentum
 (see \autoref{sec:ZDF_bfr}).
 …
 The hypothesis of a mixing mainly maintained by the growth of Kelvin-Helmholtz like instabilities leads to
 a dependency between the vertical eddy coefficients and the local Richardson number
 ($i.e.$ the ratio of stratification to vertical shear).
+(\ie the ratio of stratification to vertical shear).
 Following \citet{Pacanowski_Philander_JPO81}, the following formulation has been implemented:
 \[
 …
   \end{aligned}
 \]
 where $l^{(k)}$ is computed using \autoref{eq:tke_mxl0_1}, $i.e.$ $l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$.
+where $l^{(k)}$ is computed using \autoref{eq:tke_mxl0_1}, \ie $l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$.
 In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same value:
 …
 \forcode{.true.} in the namtke namelist.
 By making an analogy with the characteristic convective velocity scale ($e.g.$, \citet{D'Alessio_al_JPO98}),
+By making an analogy with the characteristic convective velocity scale (\eg, \citet{D'Alessio_al_JPO98}),
 $P_{LC}$ is assumed to be :
 \[
 …
 This bias is particularly acute over the Southern Ocean.
 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}.
 The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations,
+The parameterization is an empirical one, \ie not derived from theoretical considerations,
 but rather is meant to account for observed processes that affect the density structure of
 the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme
 ($i.e.$ near-inertial oscillations and ocean swells and waves).
 When using this parameterization ($i.e.$ when \np{nn\_etau}\forcode{ = 1}),
+(\ie near-inertial oscillations and ocean swells and waves).
+When using this parameterization (\ie when \np{nn\_etau}\forcode{ = 1}),
 the TKE input to the ocean ($S$) imposed by the winds in the form of near-inertial oscillations,
 swell and waves is parameterized by \autoref{eq:ZDF_Esbc} the standard TKE surface boundary condition,
 …
 % excluded by the hydrostatic assumption and the model resolution.
 % Thus far, the representation of internal wave mixing in ocean models has been relatively crude
 % (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002).
+% (\eg Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002).
 % -------------------------------------------------------------------------------------------------------------
 …
 %--------------------------------------------------------------------------------------------------------------
 Static instabilities (i.e. light potential densities under heavy ones) may occur at particular ocean grid points.
+Static instabilities (\ie light potential densities under heavy ones) may occur at particular ocean grid points.
 In nature, convective processes quickly re-establish the static stability of the water column.
 These processes have been removed from the model via the hydrostatic assumption so they must be parameterized.
 …
 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously the statically unstable portion of
 the water column, but only until the density structure becomes neutrally stable
 ($i.e.$ until the mixed portion of the water column has \textit{exactly} the density of the water just below)
+(\ie until the mixed portion of the water column has \textit{exactly} the density of the water just below)
 \citep{Madec_al_JPO91}.
 The associated algorithm is an iterative process used in the following way (\autoref{fig:npc}):
 …
 In this case, the vertical eddy mixing coefficients are assigned very large values
 (a typical value is $10\;m^2s^{-1})$ in regions where the stratification is unstable
 ($i.e.$ when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}.
+(\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}.
 This is done either on tracers only (\np{nn\_evdm}\forcode{ = 0}) or
 on both momentum and tracers (\np{nn\_evdm}\forcode{ = 1}).
 …
 momentum in the case of static instabilities.
 It requires the use of an implicit time stepping on vertical diffusion terms
 (i.e. \np{ln\_zdfexp}\forcode{ = .false.}).
+(\ie np{ln\_zdfexp}\forcode{ = .false.}).
 Note that the stability test is performed on both \textit{before} and \textit{now} values of $N^2$.
 …
 because the mixing length scale is bounded by the distance to the sea surface.
 It can thus be useful to combine the enhanced vertical diffusion with the turbulent closure scheme,
 $i.e.$ setting the \np{ln\_zdfnpc} namelist parameter to true and
+\ie setting the \np{ln\_zdfnpc} namelist parameter to true and
 defining the turbulent closure CPP key all together.
 …
 The factor 0.7 in \autoref{eq:zdfddm_f_T} reflects the measured ratio $\alpha F_T /\beta F_S \approx  0.7$ of
 buoyancy flux of heat to buoyancy flux of salt ($e.g.$, \citet{McDougall_Taylor_JMR84}).
+buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{McDougall_Taylor_JMR84}).
 Following  \citet{Merryfield1999}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$.
 …
 The linear bottom friction parameterisation (including the special case of a free-slip condition) assumes that
 the bottom friction is proportional to the interior velocity (i.e. the velocity of the last model level):
+the bottom friction is proportional to the interior velocity (\ie the velocity of the last model level):
 \[
   % \label{eq:zdfbfr_linear}
 …
 For stability, the drag coefficient is bounded such that it is kept greater or equal to
 the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional namelist parameter:
 \np{rn\_bfri2\_max}, i.e.:
+\np{rn\_bfri2\_max}, \ie
 \[
   rn\_bfri2 \leq C_D \leq rn\_bfri2\_max
 …
 and update it with the latest value.
 On the other hand, the bottom friction contributed by the other terms
 (e.g. the advection term, viscosity term) has been included in the 3-D momentum equations and
+(\eg the advection term, viscosity term) has been included in the 3-D momentum equations and
 should not be added in the 2-D barotropic mode.
 …
 while the three dimensional prognostic variables are solved with the longer time step of \np{rn\_rdt} seconds.
 The trend in the barotropic momentum due to bottom friction appropriate to this method is that given by
 the selected parameterisation ($i.e.$ linear or non-linear bottom friction) computed with
+the selected parameterisation (\ie linear or non-linear bottom friction) computed with
 the evolving velocities at each barotropic timestep.
 …
 The associated vertical viscosity is calculated from the vertical diffusivity assuming a Prandtl number of 1,
 $i.e.$ $A^{vm}_{tides}=A^{vT}_{tides}$.
+\ie $A^{vm}_{tides}=A^{vT}_{tides}$.
 In the limit of $N \rightarrow 0$ (or becoming negative), the vertical diffusivity is capped at $300\,cm^2/s$ and
 impose a lower limit on $N^2$ of \np{rn\_n2min} usually set to $10^{-8} s^{-2}$.
 …
 Once generated, internal tides remain confined within this semi-enclosed area and hardly radiate away.
 Therefore all the internal tides energy is consumed within this area.
 So it is assumed that $q = 1$, $i.e.$ all the energy generated is available for mixing.
+So it is assumed that $q = 1$, \ie all the energy generated is available for mixing.
 Note that for test purposed, the ITF tidal dissipation efficiency is a namelist parameter (\np{rn\_tfe\_itf}).
 A value of $1$ or close to is this recommended for this parameter.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex

-                      r10414
+                      r10442
 The alternative is to use diffusive schemes such as upstream or flux corrected schemes.
 This last option was rejected because we prefer a complete handling of the model diffusion,
 i.e. of the model physics rather than letting the advective scheme produces its own implicit diffusion without
+\ie of the model physics rather than letting the advective scheme produces its own implicit diffusion without
 controlling the space and time structure of this implicit diffusion.
 Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required.
 …
 \textbf{* relative, planetary and total vorticity term:}
 Let us define as either the relative, planetary and total potential vorticity, i.e. ?, ?, and ?, respectively.
+Let us define as either the relative, planetary and total potential vorticity, \ie, ?, and ?, respectively.
 The continuous formulation of the vorticity term satisfies following integral constraints:
 \[
 …
 This properties is satisfied locally with the choice of discretization we have made (property (II.1.9)~).
 In addition, when the equation of state is linear
 (i.e. when an advective-diffusive equation for density can be derived from those of temperature and salinity)
+(\ie when an advective-diffusive equation for density can be derived from those of temperature and salinity)
 the change of horizontal kinetic energy due to the work of pressure forces is balanced by the change of
 potential energy due to buoyancy forces:
 …
 In continuous formulation, the advective terms of the tracer equations conserve the tracer content and
 the quadratic form of the tracer, $i.e.$
+the quadratic form of the tracer, \ie
 \[
   % \label{eq:tra_tra2}
 …
 In discrete form, all these properties are satisfied in $z$-coordinate (see Appendix C).
 In $s$-coordinates, only first order properties can be demonstrated,
 $i.e.$ the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence.
+\ie the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence.
 % -------------------------------------------------------------------------------------------------------------
 …
 the heat and salt contents are conserved (equations in flux form, second order centred finite differences).
 As a form flux is used to compute the temperature and salinity,
 the quadratic form of these quantities (i.e. their variance) globally tends to diminish.
+the quadratic form of these quantities (\ie their variance) globally tends to diminish.
 As for the advective term, there is generally no strict conservation of mass even if,
 in practice, the mass is conserved with a very good accuracy.
 …
 \]
 \textbf{* vertical physics: }conservation of tracer, dissipation of tracer variance, $i.e.$
+\textbf{* vertical physics: }conservation of tracer, dissipation of tracer variance, \ie
 \[
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_misc.tex

-                      r10414
+                      r10442
 This technique is sometime called "partially open face" or "partially closed cells".
 The key issue here is only to reduce the faces of $T$-cell
 ($i.e.$ change the value of the horizontal scale factors at $u$- or $v$-point) but not the volume of the $T$-cell.
+(\ie change the value of the horizontal scale factors at $u$- or $v$-point) but not the volume of the $T$-cell.
 Indeed, reducing the volume of strait $T$-cell can easily produce a numerical instability at
 that grid point that would require a reduction of the model time step.
 …
       \textit{Bottom}: using viscous boundary layers.
       The four fmask parameters along the strait coastlines are set to a value larger than 4,
       $i.e.$ "strong" no-slip case (see \autoref{fig:LBC_shlat}) creating a large viscous boundary layer that
+      \ie "strong" no-slip case (see \autoref{fig:LBC_shlat}) creating a large viscous boundary layer that
       allows a reduced transport through the strait.
+    }
 …
 \noindent These files define a horizontal domain of 362x332.
 Assuming the first row with open ocean wet points in the non-isf bathymetry for this set is row 42
 (Fortran indexing) then the formally correct setting for \np{open\_ocean\_jstart} is 41.
+(\fortran indexing) then the formally correct setting for \np{open\_ocean\_jstart} is 41.
 Using this value as the first row to be read will result in a 362x292 domain which is the same size as
 the original ORCA1 domain.
 …
 \label{subsec:MISC_sign}
 The SIGN(A, B) is the \textsc {Fortran} intrinsic function delivers the magnitude of A with the sign of B.
+The SIGN(A, B) is the \fortran intrinsic function delivers the magnitude of A with the sign of B.
 For example, SIGN(-3.0,2.0) has the value 3.0.
 The problematic case is when the second argument is zero, because, on platforms that support IEEE arithmetic,
 …
 There is a positive zero and a negative zero.
 In \textsc{Fortran}~90, the processor was required always to deliver a positive result for SIGN(A, B) if B was zero.
 Nevertheless, in \textsc{Fortran}~95, the processor is allowed to do the correct thing and deliver ABS(A) when
+In \fninety, the processor was required always to deliver a positive result for SIGN(A, B) if B was zero.
+Nevertheless, in \fninety, the processor is allowed to do the correct thing and deliver ABS(A) when
 B is a positive zero and -ABS(A) when B is a negative zero.
 This change in the specification becomes apparent only when B is of type real, and is zero,
 and the processor is capable of distinguishing between positive and negative zero,
 and B is negative real zero.
 Then SIGN delivers a negative result where, under \textsc{Fortran}~90 rules, it used to return a positive result.
+Then SIGN delivers a negative result where, under \fninety rules, it used to return a positive result.
 This change may be especially sensitive for the ice model,
 so we overwrite the intrinsinc function with our own function simply performing :   \\
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics.tex

-                      r10414
+                      r10442
 The ocean is a fluid that can be described to a good approximation by the primitive equations,
 $i.e.$ the Navier-Stokes equations along with a nonlinear equation of state which
+\ie the Navier-Stokes equations along with a nonlinear equation of state which
 couples the two active tracers (temperature and salinity) to the fluid velocity,
 plus the following additional assumptions made from scale considerations:
 …
 it is useful to choose an orthogonal set of unit vectors (\textbf{i},\textbf{j},\textbf{k}) linked to
 the earth such that \textbf{k} is the local upward vector and (\textbf{i},\textbf{j}) are two vectors orthogonal to
 \textbf{k}, $i.e.$ tangent to the geopotential surfaces.
+\textbf{k}, \ie tangent to the geopotential surfaces.
 Let us define the following variables: \textbf{U} the vector velocity, $\textbf{U}=\textbf{U}_h + w\, \textbf{k}$
 (the subscript $h$ denotes the local horizontal vector, $i.e.$ over the (\textbf{i},\textbf{j}) plane),
+(the subscript $h$ denotes the local horizontal vector, \ie over the (\textbf{i},\textbf{j}) plane),
 $T$ the potential temperature, $S$ the salinity, \textit{$\rho $} the \textit{in situ} density.
 The vector invariant form of the primitive equations in the (\textbf{i},\textbf{j},\textbf{k}) vector system
 …
   \footnote{
     In fact, it has been shown that the heat flux associated with the solid Earth cooling
     ($i.e.$the geothermal heating) is not negligible for the thermohaline circulation of the world ocean
+    (\ie the geothermal heating) is not negligible for the thermohaline circulation of the world ocean
     (see \autoref{subsec:TRA_bbc}).
   }.
   The boundary condition is thus set to no flux of heat and salt across solid boundaries.
   For momentum, the situation is different. There is no flow across solid boundaries,
   $i.e.$ the velocity normal to the ocean bottom and coastlines is zero (in other words,
+  \ie the velocity normal to the ocean bottom and coastlines is zero (in other words,
   the bottom velocity is parallel to solid boundaries). This kinematic boundary condition
   can be expressed as:
 …
 the time step would have to be very short if they were present in the model.
 The latter strategy filters out these waves since the rigid lid approximation implies $\eta=0$,
 $i.e.$ the sea surface is the surface $z=0$.
+\ie the sea surface is the surface $z=0$.
 This well known approximation increases the surface wave speed to infinity and
 modifies certain other longwave dynamics ($e.g.$ barotropic Rossby or planetary waves).
+modifies certain other longwave dynamics (\eg barotropic Rossby or planetary waves).
 The rigid-lid hypothesis is an obsolescent feature in modern OGCMs.
 It has been available until the release 3.1 of  \NEMO, and it has been removed in release 3.2 and followings.
 …
 In many ocean circulation problems, the flow field has regions of enhanced dynamics
 ($i.e.$ surface layers, western boundary currents, equatorial currents, or ocean fronts).
+(\ie surface layers, western boundary currents, equatorial currents, or ocean fronts).
 The representation of such dynamical processes can be improved by
 specifically increasing the model resolution in these regions.
 …
 (\textbf{i},\textbf{j},\textbf{k}) linked to the earth such that
 \textbf{k} is the local upward vector and (\textbf{i},\textbf{j}) are two vectors orthogonal to \textbf{k},
 $i.e.$ along geopotential surfaces (\autoref{fig:referential}).
+\ie along geopotential surfaces (\autoref{fig:referential}).
 Let $(\lambda,\varphi,z)$ be the geographical coordinate system in which a position is defined by
 the latitude $\varphi(i,j)$, the longitude $\lambda(i,j)$ and
 …
 This is the so-called \textit{vector invariant form} of the momentum advection term.
 For some purposes, it can be advantageous to write this term in the so-called flux form,
 $i.e.$ to write it as the divergence of fluxes.
+\ie to write it as the divergence of fluxes.
 For example, the first component of \autoref{eq:PE_vector_form} (the $i$-component) is transformed as follows:
 \begin{flalign*}
 …
 Note that in the case of geographical coordinate,
 $i.e.$ when $(i,j) \to (\lambda ,\varphi )$ and $(e_1 ,e_2) \to (a \,\cos \varphi ,a)$,
+\ie when $(i,j) \to (\lambda ,\varphi )$ and $(e_1 ,e_2) \to (a \,\cos \varphi ,a)$,
 we recover the commonly used modification of the Coriolis parameter $f \to f+(u/a) \tan \varphi$.
 …
 Therefore, in order to represent the ocean with respect to
 the first point a space and time dependent vertical coordinate that follows the variation of the sea surface height
 $e.g.$ an $z$*-coordinate;
+\eg an \zstar-coordinate;
 for the second point, a space variation to fit the change of bottom topography
 $e.g.$ a terrain-following or $\sigma$-coordinate;
+\eg a terrain-following or $\sigma$-coordinate;
 and for the third point, one will be tempted to use a space and time dependent coordinate that
 follows the isopycnal surfaces, $e.g.$ an isopycnic coordinate.
+follows the isopycnal surfaces, \eg an isopycnic coordinate.
 In order to satisfy two or more constrains one can even be tempted to mixed these coordinate systems, as in
 …
 In this section we first establish the PE in the generalised vertical $s$-coordinate,
 then we discuss the particular cases available in \NEMO, namely $z$, $z$*, $s$, and $\tilde z$.
+then we discuss the particular cases available in \NEMO, namely $z$, \zstar, $s$, and \ztilde.
 %}
 …
 Starting from the set of equations established in \autoref{sec:PE_zco} for the special case $k=z$ and thus $e_3=1$,
 we introduce an arbitrary vertical coordinate $s=s(i,j,k,t)$,
 which includes $z$-, \textit{z*}- and $\sigma-$coordinates as special cases
 ($s=z$, $s=\textit{z*}$, and $s=\sigma=z/H$ or $=z/\left(H+\eta \right)$, resp.).
+which includes $z$-, \zstar- and $\sigma-$coordinates as special cases
+($s=z$, $s=\zstar$, and $s=\sigma=z/H$ or $=z/\left(H+\eta \right)$, resp.).
 A formal derivation of the transformed equations is given in \autoref{apdx:A}.
 Let us define the vertical scale factor by $e_3=\partial_s z$  ($e_3$ is now a function of $(i,j,k,t)$ ),
 …
 % -------------------------------------------------------------------------------------------------------------
 % Curvilinear z*-coordinate System
 % -------------------------------------------------------------------------------------------------------------
 \subsection{Curvilinear \textit{z*}--coordinate system}
+% Curvilinear \zstar-coordinate System
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Curvilinear \zstar--coordinate system}
 \label{subsec:PE_zco_star}
 …
       (a) $z$-coordinate in linear free-surface case ;
       (b) $z-$coordinate in non-linear free surface case ;
       (c) re-scaled height coordinate (become popular as the \textit{z*-}coordinate
+      (c) re-scaled height coordinate (become popular as the \zstar-coordinate
       \citep{Adcroft_Campin_OM04} ).
+    }
 …
 %\gmcomment{
 The \textit{z*} coordinate approach is an unapproximated, non-linear free surface implementation which allows one to
+The \zstar coordinate approach is an unapproximated, non-linear free surface implementation which allows one to
 deal with large amplitude free-surface variations relative to the vertical resolution \citep{Adcroft_Campin_OM04}.
 In the \textit{z*} formulation,
+In the \zstar formulation,
 the variation of the column thickness due to sea-surface undulations is not concentrated in the surface level,
 as in the $z$-coordinate formulation, but is equally distributed over the full water column.
 Thus vertical levels naturally follow sea-surface variations, with a linear attenuation with depth,
 as illustrated by figure fig.1c.
 Note that with a flat bottom, such as in fig.1c, the bottom-following $z$ coordinate and \textit{z*} are equivalent.
 The definition and modified oceanic equations for the rescaled vertical coordinate  \textit{z*},
+Note that with a flat bottom, such as in fig.1c, the bottom-following $z$ coordinate and \zstar are equivalent.
+The definition and modified oceanic equations for the rescaled vertical coordinate  \zstar,
 including the treatment of fresh-water flux at the surface, are detailed in Adcroft and Campin (2004).
 The major points are summarized here.
 The position ( \textit{z*}) and vertical discretization (\textit{z*}) are expressed as:
+The position ( \zstar) and vertical discretization (\zstar) are expressed as:
 \[
   % \label{eq:z-star}
   H +  \textit{z*} = (H + z) / r \quad \text{and} \ \delta \textit{z*} = \delta z / r \quad \text{with} \ r = \frac{H+\eta} {H}
+  H +  \zstar = (H + z) / r \quad \text{and} \ \delta \zstar = \delta z / r \quad \text{with} \ r = \frac{H+\eta} {H}
 \]
 Since the vertical displacement of the free surface is incorporated in the vertical coordinate \textit{z*},
 the upper and lower boundaries are at fixed  \textit{z*} position,
 $\textit{z*} = 0$ and  $\textit{z*} = -H$ respectively.
+Since the vertical displacement of the free surface is incorporated in the vertical coordinate \zstar,
+the upper and lower boundaries are at fixed  \zstar position,
+$\zstar = 0$ and  $\zstar = -H$ respectively.
 Also the divergence of the flow field is no longer zero as shown by the continuity equation:
 \[
   \frac{\partial r}{\partial t} = \nabla_{\textit{z*}} \cdot \left( r \; \rm{\bf U}_h \right)
+  \frac{\partial r}{\partial t} = \nabla_{\zstar} \cdot \left( r \; \rm{\bf U}_h \right)
   \left( r \; w\textit{*} \right) = 0
 \]
 …
 The second term in \autoref{eq:PE_p_sco} depends on the tilt of the coordinate surface and
 introduces a truncation error that is not present in a $z$-model.
 In the special case of a $\sigma-$coordinate (i.e. a depth-normalised coordinate system $\sigma = z/H$),
+In the special case of a $\sigma-$coordinate (\ie depth-normalised coordinate system $\sigma = z/H$),
 \citet{Haney1991} and \citet{Beckmann1993} have given estimates of the magnitude of this truncation error.
 It depends on topographic slope, stratification, horizontal and vertical resolution, the equation of state,
 …
 In contrast, the ocean will stay at rest in a $z$-model.
 As for the truncation error, the problem can be reduced by introducing the terrain-following coordinate below
 the strongly stratified portion of the water column ($i.e.$ the main thermocline) \citep{Madec_al_JPO96}.
+the strongly stratified portion of the water column (\ie the main thermocline) \citep{Madec_al_JPO96}.
 An alternate solution consists of rotating the lateral diffusive tensor to geopotential or to isoneutral surfaces
 (see \autoref{subsec:PE_ldf}).
 …
 % Curvilinear z-tilde coordinate System
 % -------------------------------------------------------------------------------------------------------------
 \subsection{\texorpdfstring{Curvilinear $\tilde{z}$--coordinate}{}}
+\subsection{\texorpdfstring{Curvilinear \ztilde--coordinate}{}}
 \label{subsec:PE_zco_tilde}
 The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM11}.
+The \ztilde-coordinate has been developed by \citet{Leclair_Madec_OM11}.
 It is available in \NEMO since the version 3.4.
 Nevertheless, it is currently not robust enough to be used in all possible configurations.
 …
 The effects of smaller scale motions (coming from the advective terms in the Navier-Stokes equations) must be represented entirely in terms of large-scale patterns to close the equations.
 These effects appear in the equations as the divergence of turbulent fluxes
 ($i.e.$ fluxes associated with the mean correlation of small scale perturbations).
+(\ie fluxes associated with the mean correlation of small scale perturbations).
 Assuming a turbulent closure hypothesis is equivalent to choose a formulation for these fluxes.
 It is usually called the subgrid scale physics.
 …
 All the vertical physics is embedded in the specification of the eddy coefficients.
 They can be assumed to be either constant, or function of the local fluid properties
 ($e.g.$ Richardson number, Brunt-Vais\"{a}l\"{a} frequency...),
+(\eg Richardson number, Brunt-Vais\"{a}l\"{a} frequency...),
 or computed from a turbulent closure model.
 The choices available in \NEMO are discussed in \autoref{chap:ZDF}).
 …
 and a sub mesoscale turbulence which is never explicitly solved even partially, but always parameterized.
 The formulation of lateral eddy fluxes depends on whether the mesoscale is below or above the grid-spacing
 ($i.e.$ the model is eddy-resolving or not).
+(\ie the model is eddy-resolving or not).
 In non-eddy-resolving configurations, the closure is similar to that used for the vertical physics.
 …
 (or more precisely neutral surfaces \cite{McDougall1987}) rather than across them.
 As the slope of neutral surfaces is small in the ocean, a common approximation is to assume that
 the `lateral' direction is the horizontal, $i.e.$ the lateral mixing is performed along geopotential surfaces.
+the `lateral' direction is the horizontal, \ie the lateral mixing is performed along geopotential surfaces.
 This leads to a geopotential second order operator for lateral subgrid scale physics.
 This assumption can be relaxed: the eddy-induced turbulent fluxes can be better approached by assuming that
 …
 it has components in the three space directions.
 However,
 both horizontal and isoneutral operators have no effect on mean ($i.e.$ large scale) potential energy whereas
+both horizontal and isoneutral operators have no effect on mean (\ie large scale) potential energy whereas
 potential energy is a main source of turbulence (through baroclinic instabilities).
 \citet{Gent1990} have proposed a parameterisation of mesoscale eddy-induced turbulence which
 …
   \begin{cases}
     r_n            &      \text{in $z$-coordinate}    \\
     r_n + \sigma_n &      \text{in \textit{z*} and $s$-coordinates}
+    r_n + \sigma_n &      \text{in \zstar and $s$-coordinates}
   \end{cases}
                      \quad \text{where } n=1,2
 …
 Unfortunately, it is only available in \textit{iso-level} direction.
 When a rotation is required
 ($i.e.$ geopotential diffusion in $s-$coordinates or isoneutral diffusion in both $z$- and $s$-coordinates),
+(\ie geopotential diffusion in $s-$coordinates or isoneutral diffusion in both $z$- and $s$-coordinates),
 the $u$ and $v-$fields are considered as independent scalar fields, so that the diffusive operator is given by:
 \[
 …
 It is the same expression as those used for diffusive operator on tracers.
 It must be emphasised that such a formulation is only exact in a Cartesian coordinate system,
 $i.e.$ on a $f-$ or $\beta-$plane, not on the sphere.
+\ie on a $f-$ or $\beta-$plane, not on the sphere.
 It is also a very good approximation in vicinity of the Equator in
 a geographical coordinate system \citep{Lengaigne_al_JGR03}.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

-                      r10414
+                      r10442
 % ================================================================
 % ================================================================
 % Curvilinear z*- s*-coordinate System
 % ================================================================
 \chapter{ essai z* s*}
 \section{Curvilinear \textit{z*}- or \textit{s*} coordinate system}
+% Curvilinear \zstar- \sstar-coordinate System
+% ================================================================
+\chapter{ essai \zstar \sstar}
+\section{Curvilinear \zstar- or \sstar coordinate system}
 % -------------------------------------------------------------------------------------------------------------
 …
 and $\rho_w =1,000\,Kg.m^{-3}$ is the volumic mass of pure water.
 The sea-surface height is evaluated using a leapfrog scheme in combination with an Asselin time filter,
 i.e. the velocity appearing in (\autoref{eq:dynspg_ssh}) is centred in time (\textit{now} velocity).
+(\ie the velocity appearing in (\autoref{eq:dynspg_ssh}) is centred in time (\textit{now} velocity).
 The surface pressure gradient, also evaluated using a leap-frog scheme, is then simply given by:
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/chap_time_domain.tex

-                      r10414
+                      r10442
 Having defined the continuous equations in \autoref{chap:PE}, we need now to choose a time discretization,
 a key feature of an ocean model as it exerts a strong influence on the structure of the computer code
 ($i.e.$ on its flowchart).
+(\ie on its flowchart).
 In the present chapter, we provide a general description of the \NEMO time stepping strategy and
 the consequences for the order in which the equations are solved.
 …
 \citep{Mesinger_Arakawa_Bk76}.
 This scheme is widely used for advection processes in low-viscosity fluids.
 It is a time centred scheme, $i.e.$ the RHS in \autoref{eq:STP} is evaluated at time step $t$, the now time step.
+It is a time centred scheme, \ie the RHS in \autoref{eq:STP} is evaluated at time step $t$, the now time step.
 It may be used for momentum and tracer advection, pressure gradient, and Coriolis terms,
 but not for diffusion terms.
 …
 In a classical LF-RA environment, the forcing term is centred in time,
 $i.e.$ it is time-stepped over a $2\rdt$ period:
+\ie it is time-stepped over a $2\rdt$ period:
 $x^t  = x^t + 2\rdt Q^t $ where $Q$ is the forcing applied to $x$,
 and the time filter is given by \autoref{eq:STP_asselin} so that $Q$ is redistributed over several time step.
 …
   x^1 = x^0 + \rdt \ \text{RHS}^0
 \]
 This is done simply by keeping the leapfrog environment ($i.e.$ the \autoref{eq:STP} three level time stepping) but
+This is done simply by keeping the leapfrog environment (\ie the \autoref{eq:STP} three level time stepping) but
 setting all $x^0$ (\textit{before}) and $x^{1}$ (\textit{now}) fields equal at the first time step and
 using half the value of $\rdt$.
 …
 \biblio
+\pindex
 \end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/foreword.tex

r10414	r10442
59	59	\biblio
60	60
	61	\pindex
	62
61	63	\end{document}

NEMO/trunk/doc/latex/NEMO/subfiles/introduction.tex

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+                      r10442
 This manual is organised in as follows.
 \autoref{chap:PE} presents the model basics, $i.e.$ the equations and their assumptions,
+\autoref{chap:PE} presents the model basics, \ie the equations and their assumptions,
 the vertical coordinates used, and the subgrid scale physics.
 This part deals with the continuous equations of the model
 (primitive equations, with temperature, salinity and an equation of seawater).
 The equations are written in a curvilinear coordinate system, with a choice of vertical coordinates
 ($z$, $s$, \textit{z*}, \textit{s*}, $\tilde{z}$, $\tilde{s}$, and a mixture of them).
+($z$, $s$, \zstar, \sstar, \ztilde, \stilde, and a mixture of them).
 Momentum equations are formulated in vector invariant or flux form.
 Dimensional units in the meter, kilogram, second (MKS) international system are used throughout.
 …
 linear free surface (level position are then fixed in time).
 In non-linear free surface,
 the corresponding rescaled height coordinate formulation (\textit{z*} or \textit{s*}) is used
+the corresponding rescaled height coordinate formulation (\zstar or \sstar) is used
 (the level position then vary in time as a function of the sea surface heigh).
 The following two chapters (\autoref{chap:TRA} and \autoref{chap:DYN}) describe the discretisation of
 …
 Interactive coupling to Atmospheric models is possible via the OASIS coupler \citep{OASIS2006}.
 Two-way nesting is also available through an interface to the AGRIF package
 (Adaptative Grid Refinement in \textsc{Fortran}) \citep{Debreu_al_CG2008}.
+(Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008}.
 The interface code for coupling to an alternative sea ice model (CICE, \citet{Hunke2008}) has now been upgraded so
 that it works for both global and regional domains, although AGRIF is still not available.
 …
 \noindent \index{CPP keys} CPP keys \newline
 Some CPP keys are implemented in the FORTRAN code to allow code selection at compiling step.
+Some CPP keys are implemented in the \fortran code to allow code selection at compiling step.
 This selection of code at compilation time reduces the reliability of the whole platform since
 it changes the code from one set of CPP keys to the other.
 …
 \begin{forlines}
 #if defined key_option1
    ! This part of the FORTRAN code will be active
+   ! This part of the \fortran code will be active
    ! only if key_option1 is activated at compiling step
 #endif
 …
 There is one namelist file for each component of NEMO (dynamics, sea-ice, biogeochemistry...)
 containing all the FOTRAN namelists needed.
 The implementation in NEMO uses a two step process. For each FORTRAN namelist, two files are read:
+The implementation in NEMO uses a two step process. For each \fortran namelist, two files are read:
 \begin{enumerate}
 \item
 …
 (water column model, ORCA and GYRE families of configurations).
 The model is implemented in \textsc{Fortran 90}, with preprocessing (C-pre-processor).
+The model is implemented in \fninety, with preprocessing (C-pre-processor).
 It runs under UNIX.
 It is optimized for vector computers and parallelised by domain decomposition with MPI.
 …
 The model is organized with a high internal modularity based on physics.
 For example, each trend ($i.e.$, a term in the RHS of the prognostic equation) for momentum and tracers
+For example, each trend (\ie, a term in the RHS of the prognostic equation) for momentum and tracers
 is computed in a dedicated module.
 To make it easier for the user to find his way around the code, the module names follow a three-letter rule.
 …
 \begin{enumerate}
 \item
   transition to full native \textsc{Fortran} 90, deep code restructuring and drastic reduction of CPP keys;
+  transition to full native \fninety, deep code restructuring and drastic reduction of CPP keys;
 \item
   introduction of partial step representation of bottom topography
 …
   and suppression of the rigid-lid option;
 \item
   non linear free surface associated with the rescaled height coordinate \textit{z*} or \textit{s};
+  non linear free surface associated with the rescaled height coordinate \zstar or \textit{s};
 \item
   additional schemes for vector and flux forms of the momentum advection;
 …
   additional advection schemes for tracers;
 \item
   implementation of the AGRIF package (Adaptative Grid Refinement in \textsc{Fortran}) \citep{Debreu_al_CG2008};
+  implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008};
 \item
   online diagnostics : tracers trend in the mixed layer and vorticity balance;
 …
 \biblio
+\pindex
 \end{document}

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