Changeset 11954 for NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/README.rst

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+                      r11954
+**************************
+Building the documentation
+**************************
+.. todo::
+:file:`latex`    : LaTeX sources and Latexmk configuration to build reference manuals with :file:`manual_build.sh`
+:file:`namelists`: Namelist blocks included in the documentation
+:file:`rst`      : |RST man|_ sources and Sphinx configuration to build this guide hereby with :file:`guide_build.sh`
+.. |RST man| replace:: reStructuredText (rst)
 .. warning::

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/main/bibliography.bib

-                      r11336
+                      r11954
+}
+@article{         kraus.turner_tellus67,
+  author = {Kraus, E.B. and Turner, J.},
+  journal = {Tellus},
+  pages = {98--106},
+  title = {A one dimensional model of the seasonal thermocline {II}. {T}he general theory and its consequences},
+  volume = {19},
+  year = {1967}
+}
+@article{        large.ea_RG97,
+  author        = "Large, W. G. and McWilliams, J. C. and Doney, S. C.",
+  doi           = "10.1029/94RG01872",
+  journal       = "Reviews of Geophysics",
+  number        = {4},
+  pages         = {363--403},
+  publisher     = {AGU},
+  title         = "Oceanic vertical mixing: {A} review and a model with a nonlocal boundary layer parameterization",
+  year          = "1994"
+}
 @techreport{      large.yeager_rpt04,
   title         = "Diurnal to decadal global forcing for ocean and sea-ice
 …
+}
+@article{mcwilliams.ea_JFM97,
+   author = {McWilliams, James C. and Sullivan, Peter P. and Moeng, Chin-Hoh},
+   doi = {10.1017/S0022112096004375},
+   journal = {Journal of Fluid Mechanics},
+   pages = {1--30},
+   title = {Langmuir turbulence in the ocean},
+   volume = {334},
+   year = {1997},
+}
 @article{         mellor.blumberg_JPO04,
   title         = "Wave Breaking and Ocean Surface Layer Thermal Response",

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/apdx_DOMAINcfg.tex

-                      r11599
+                      r11954
 \begin{figure}[!tb]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_zgr}
+  \includegraphics[width=0.66\textwidth]{DOMCFG_zgr}
   \caption[DOMAINcfg: default vertical mesh for ORCA2]{
     Default vertical mesh for ORCA2: 30 ocean levels (L30).
 …
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_sco_function}
+  \includegraphics[width=0.66\textwidth]{DOMCFG_sco_function}
   \caption[DOMAINcfg: examples of the stretching function applied to a seamount]{
     Examples of the stretching function applied to a seamount;
 …
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_DOM_compare_coordinates_surface}
+  \includegraphics[width=0.66\textwidth]{DOMCFG_compare_coordinates_surface}
   \caption[DOMAINcfg: comparison of $s$- and $z$-coordinate]{
     A comparison of the \citet{song.haidvogel_JCP94} $S$-coordinate (solid lines),
 …
 This option is described in the Report by Levier \textit{et al.} (2007), available on the \NEMO\ web site.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/apdx_algos.tex

-                      r11598
+                      r11954
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ISO_triad}
+  %\includegraphics[width=0.66\textwidth]{ALGOS_ISO_triad}
   \caption[Triads used in the Griffies's like iso-neutral diffision scheme for
     $u$- and $w$-components)]{
 …
 where $A_{e}$ is the eddy induced velocity coefficient,
 and $r_i$ and $r_j$ the slopes between the iso-neutral and the geopotential surfaces.
+%%gm wrong: to be modified with 2 2D streamfunctions
+\cmtgm{Wrong: to be modified with 2 2D streamfunctions}
 In other words, the eddy induced velocity can be derived from a vector streamfuntion, $\phi$,
 which is given by $\phi = A_e\,\textbf{r}$ as $\textbf{U}^*  = \textbf{k} \times \nabla \phi$.
-%%end gm
 A traditional way to implement this additional advection is to add it to the eulerian velocity prior to
 …
 \ie\ the variance of the tracer is preserved by the discretisation of the skew fluxes.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/apdx_diff_opers.tex

r11598	r11954
421	421	that is a Laplacian diffusion is applied on momentum along the coordinate directions.
422	422
423		\~~onlyinsubfile~~{\input{../../global/epilogue}}
	423	\subinc{\input{../../global/epilogue}}
424	424
425	425	\end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/apdx_invariants.tex

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+                      r11954
 \clearpage
 %%%  Appendix put in gmcomment as it has not been updated for \zstar and s coordinate
+%%%  Appendix put in cmtgm 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
 %\gmcomment{
+%\cmtgm{
 %% =================================================================================================
 …
 %gm comment
 \gmcomment{
+\cmtgm{
 The last equality comes from the following equation,
 \begin{flalign*}
 …
 \label{subsec:INVARIANTS_2.6}
 \gmcomment{
+\cmtgm{
   A pressure gradient has no contribution to the evolution of the vorticity as the curl of a gradient is zero.
   In the $z$-coordinate, this property is satisfied locally on a C-grid with 2nd order finite differences
 …
 %gm comment
 \gmcomment{
+\cmtgm{
   \begin{flalign*}
     \sum\limits_{i,j,k} \biggl\{   p_t\;\partial_t b_t   \biggr\}                                &&&\\
 …
 %}
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/apdx_s_coord.tex

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584	584	the expression of the 3D divergence in the $s-$coordinates established above.
585	585
586		\~~onlyinsubfile~~{\input{../../global/epilogue}}
	586	\subinc{\input{../../global/epilogue}}
587	587
588	588	\end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/apdx_triads.tex

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+                      r11954
 \begin{figure}[tb]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_GRIFF_triad_fluxes}
+  \includegraphics[width=0.66\textwidth]{TRIADS_GRIFF_triad_fluxes}
   \caption[Triads arrangement and tracer gradients to give lateral and vertical tracer fluxes]{
     (a) Arrangement of triads $S_i$ and tracer gradients to
 …
 \begin{figure}[tb]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_GRIFF_qcells}
+  \includegraphics[width=0.66\textwidth]{TRIADS_GRIFF_qcells}
   \caption[Triad notation for quarter cells]{
     Triad notation for quarter cells.
 …
 \begin{figure}[h]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_GRIFF_bdry_triads}
+  \includegraphics[width=0.66\textwidth]{TRIADS_GRIFF_bdry_triads}
   \caption[Boundary triads]{
     (a) Uppermost model layer $k=1$ with $i,1$ and $i+1,1$ tracer points (black dots),
 …
 \begin{figure}[h]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_GRIFF_MLB_triads}
+  \includegraphics[width=0.66\textwidth]{TRIADS_GRIFF_MLB_triads}
   \caption[Definition of mixed-layer depth and calculation of linearly tapered triads]{
     Definition of mixed-layer depth and calculation of linearly tapered triads.
 …
 \]
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_ASM.tex

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194	194	\end{clines}
195	195
196		\~~onlyinsubfile~~{\input{../../global/epilogue}}
	196	\subinc{\input{../../global/epilogue}}
197	197
198	198	\end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_DIA.tex

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+                      r11954
 A complete description of the use of this I/O server is presented in the next section.
 %\gmcomment{                    % start of gmcomment
+%\cmtgm{                    % start of gmcomment
 %% =================================================================================================
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_mask_subasins}
+  \includegraphics[width=0.66\textwidth]{DIA_mask_subasins}
   \caption[Decomposition of the World Ocean to compute transports as well as
   the meridional stream-function]{
 …
 The maximum values from the run are also copied to the ocean.output file.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_DIU.tex

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160	160	\]
161	161
162		\~~onlyinsubfile~~{\input{../../global/epilogue}}
	162	\subinc{\input{../../global/epilogue}}
163	163
164	164	\end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_DOM.tex

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+                      r11954
 \label{chap:DOM}
+% Missing things:
+%  - istate: description of the initial state   ==> this has to be put elsewhere..
+%                  perhaps in MISC ?  By the way the initialisation of T S and dynamics
+%                  should be put outside of DOM routine (better with TRC staff and off-line
+%                  tracers)
+%  -geo2ocean:  how to switch from geographic to mesh coordinate
+%     - domclo:  closed sea and lakes.... management of closea sea area : specific to global configuration, both forced and coupled
+%    {\em 4.0} & {\em Simon M\"{u}ller \& Andrew Coward} &
+%    {\em
+%      Compatibility changes Major simplification has moved many of the options to external domain configuration tools.
+%      (see \autoref{apdx:DOMCFG})
+%    }                                                                                            \\
+%    {\em 3.x} & {\em Rachid Benshila, Gurvan Madec \& S\'{e}bastien Masson} &
+%    {\em First version}                                                                          \\
+% Missing things
+% -    istate: description of the initial state   ==> this has to be put elsewhere..
+%              perhaps in MISC ?  By the way the initialisation of T S and dynamics
+%              should be put outside of DOM routine (better with TRC staff and off-line
+%              tracers)
+% - geo2ocean: how to switch from geographic to mesh coordinate
+% -    domclo: closed sea and lakes....
+%              management of closea sea area: specific to global cfg, both forced and coupled
 \thispagestyle{plain}
 …
 {\footnotesize
+  \begin{tabularx}{\textwidth}{l||X|X}
+    Release & Author(s) & Modifications \\
+    \hline
+    {\em   4.0} & {\em ...} & {\em ...} \\
+    {\em   3.6} & {\em ...} & {\em ...} \\
+    {\em   3.4} & {\em ...} & {\em ...} \\
+    {\em <=3.4} & {\em ...} & {\em ...}
+  \begin{tabularx}{0.8\textwidth}{l||X|X}
+    Release                                                                                 &
+    Author(s)                                                                               &
+    Modifications                                                                           \\
+    \hline
+    {\em 4.0                                                                              } &
+    {\em Simon M\"{u}ller \& Andrew Coward \newline \newline
+      Simona Flavoni and Tim Graham                                                       } &
+    {\em Compatibility changes: many options moved to external domain configuration tools
+      (see \autoref{apdx:DOMCFG}). \newline
+      Updates                                                                             } \\
+    {\em 3.6                                                                              } &
+    {\em Rachid Benshila, Christian \'{E}th\'{e}, Pierre Mathiot and Gurvan Madec         } &
+    {\em Updates                                                                          } \\
+    {\em $\leq$ 3.4                                                                       } &
+    {\em Gurvan Madec and S\'{e}bastien Masson                                            } &
+    {\em First version                                                                    }
   \end{tabularx}
+}
 …
 \clearpage
+Having defined the continuous equations in \autoref{chap:MB} and chosen a time discretisation \autoref{chap:TD},
+Having defined the continuous equations in \autoref{chap:MB} and
+chosen a time discretisation \autoref{chap:TD},
 we need to choose a grid for spatial discretisation and related numerical algorithms.
 In the present chapter, we provide a general description of the staggered grid used in \NEMO,
 …
 \label{subsec:DOM_cell}
 \begin{figure}[!tb]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_cell}
+  \includegraphics[width=0.33\textwidth]{DOM_cell}
   \caption[Arrangement of variables in the unit cell of space domain]{
     Arrangement of variables in the unit cell of space domain.
     $t$ indicates scalar points where
     temperature, salinity, density, pressure and horizontal divergence are defined.
+    $(u,v,w)$ indicates vector points,
+    and $f$ indicates vorticity points where
+    $(u,v,w)$ indicates vector points, and $f$ indicates vorticity points where
     both relative and planetary vorticities are defined.}
   \label{fig:DOM_cell}
 \end{figure}
 The numerical techniques used to solve the Primitive Equations in this model are based on the traditional,
 centred second-order finite difference approximation.
+The numerical techniques used to solve the Primitive Equations in this model are based on
+the traditional, centred second-order finite difference approximation.
 Special attention has been given to the homogeneity of the solution in the three spatial directions.
 The arrangement of variables is the same in all directions.
+It consists of cells centred on scalar points ($t$, $S$, $p$, $\rho$) with vector points $(u, v, w)$ defined in
+the centre of each face of the cells (\autoref{fig:DOM_cell}).
+This is the generalisation to three dimensions of the well-known ``C'' grid in Arakawa's classification
+\citep{mesinger.arakawa_bk76}.
+The relative and planetary vorticity, $\zeta$ and $f$, are defined in the centre of each vertical edge and
+the barotropic stream function $\psi$ is defined at horizontal points overlying the $\zeta$ and $f$-points.
+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:DOM_cell}.
+In all the following, subscripts $u$, $v$, $w$, $f$, $uw$, $vw$ or $fw$ indicate the position of
+the grid-point where the scale factors are defined.
+It consists of cells centred on scalar points ($t$, $S$, $p$, $\rho$) with
+vector points $(u, v, w)$ defined in the centre of each face of the cells (\autoref{fig:DOM_cell}).
+This is the generalisation to three dimensions of the well-known ``C'' grid in
+Arakawa's classification \citep{mesinger.arakawa_bk76}.
+The relative and planetary vorticity, $\zeta$ and $f$, are defined in the centre of each
+vertical edge and the barotropic stream function $\psi$ is defined at horizontal points overlying
+the $\zeta$ and $f$-points.
+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:DOM_cell}.
+In all the following,
+subscripts $u$, $v$, $w$, $f$, $uw$, $vw$ or $fw$ indicate the position of the grid-point where
+the scale factors are defined.
 Each scale factor is defined as the local analytical value provided by \autoref{eq:MB_scale_factors}.
 As a result, the mesh on which partial derivatives $\pd[]{\lambda}$, $\pd[]{\varphi}$ and
 $\pd[]{z}$ are evaluated is a uniform mesh with a grid size of unity.
+Discrete partial derivatives are formulated by the traditional, centred second order finite difference approximation
+while the scale factors are chosen equal to their local analytical value.
+Discrete partial derivatives are formulated by
+the traditional, centred second order finite difference approximation while
+the scale factors are chosen equal to their local analytical value.
 An important point here is that the partial derivative of the scale factors must be evaluated by
 centred finite difference approximation, not from their analytical expression.
 This preserves the symmetry of the discrete set of equations and therefore satisfies many of
 the continuous properties (see \autoref{apdx:INVARIANTS}).
+This preserves the symmetry of the discrete set of equations and
+therefore satisfies many of the continuous properties (see \autoref{apdx:INVARIANTS}).
 A similar, related remark can be made about the domain size:
 when needed, an area, volume, or the total ocean depth must be evaluated as the product or sum of the relevant scale factors
 (see \autoref{eq:DOM_bar} in the next section).
 \begin{table}[!tb]
+when needed, an area, volume, or the total ocean depth must be evaluated as
+the product or sum of the relevant scale factors (see \autoref{eq:DOM_bar} in the next section).
+\begin{table}
   \centering
   \begin{tabular}{|p{46pt}|p{56pt}|p{56pt}|p{56pt}|}
     \hline
     t & $i      $ & $j      $ & $k      $ \\
     \hline
     u & $i + 1/2$ & $j      $ & $k      $ \\
     \hline
     v & $i      $ & $j + 1/2$ & $k      $ \\
     \hline
     w & $i      $ & $j      $ & $k + 1/2$ \\
     \hline
     f & $i + 1/2$ & $j + 1/2$ & $k      $ \\
     \hline
     uw   & $i + 1/2$ & $j      $ & $k + 1/2$ \\
     \hline
     vw   & $i      $ & $j + 1/2$ & $k + 1/2$ \\
     \hline
     fw   & $i + 1/2$ & $j + 1/2$ & $k + 1/2$ \\
+  \begin{tabular}{|l|l|l|l|}
+    \hline
+    t   & $i      $ & $j      $ & $k      $ \\
+    \hline
+    u   & $i + 1/2$ & $j      $ & $k      $ \\
+    \hline
+    v   & $i      $ & $j + 1/2$ & $k      $ \\
+    \hline
+    w   & $i      $ & $j      $ & $k + 1/2$ \\
+    \hline
+    f   & $i + 1/2$ & $j + 1/2$ & $k      $ \\
+    \hline
+    uw  & $i + 1/2$ & $j      $ & $k + 1/2$ \\
+    \hline
+    vw  & $i      $ & $j + 1/2$ & $k + 1/2$ \\
+    \hline
+    fw  & $i + 1/2$ & $j + 1/2$ & $k + 1/2$ \\
     \hline
   \end{tabular}
 …
     Location of grid-points as a function of integer or
     integer and a half value of the column, line or level.
     This indexing is only used for the writing of the semi -discrete equations.
+    This indexing is only used for the writing of the semi-discrete equations.
     In the code, the indexing uses integer values only and
     is positive downwards in the vertical with $k=1$ at the surface.
 …
 firstly, there is no ambiguity in the scale factors appearing in the discrete equations,
 since they are first introduced in the continuous equations;
+secondly, analytical transformations encourage good practice by the definition of smoothly varying grids
+(rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{treguier.dukowicz.ea_JGR96}.
+secondly, analytical transformations encourage good practice by
+the definition of smoothly varying grids
+(rather than allowing the user to set arbitrary jumps in thickness between adjacent layers)
+\citep{treguier.dukowicz.ea_JGR96}.
 An example of the effect of such a choice is shown in \autoref{fig:DOM_zgr_e3}.
 \begin{figure}[!t]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_zgr_e3}
+  \includegraphics[width=0.5\textwidth]{DOM_zgr_e3}
   \caption[Comparison of grid-point position, vertical grid-size and scale factors]{
     Comparison of (a) traditional definitions of grid-point position and grid-size in the vertical,
 …
 \label{subsec:DOM_operators}
 Given the values of a variable $q$ at adjacent points, the differencing and averaging operators at
 the midpoint between them are:
+Given the values of a variable $q$ at adjacent points,
+the differencing and averaging operators at the midpoint between them are:
 \begin{alignat*}{2}
   % \label{eq:DOM_di_mi}
 …
 Similar operators are defined with respect to $i + 1/2$, $j$, $j + 1/2$, $k$, and $k + 1/2$.
+Following \autoref{eq:MB_grad} and \autoref{eq:MB_lap}, the gradient of a variable $q$ defined at a $t$-point has
+its three components defined at $u$-, $v$- and $w$-points while its Laplacian is defined at the $t$-point.
+Following \autoref{eq:MB_grad} and \autoref{eq:MB_lap},
+the gradient of a variable $q$ defined at a $t$-point has
+its three components defined at $u$-, $v$- and $w$-points while
+its Laplacian is defined at the $t$-point.
 These operators have the following discrete forms in the curvilinear $s$-coordinates system:
 \[
+\begin{gather*}
   % \label{eq:DOM_grad}
   \nabla q \equiv   \frac{1}{e_{1u}} \delta_{i + 1/2} [q] \; \, \vect i
                   + \frac{1}{e_{2v}} \delta_{j + 1/2} [q] \; \, \vect j
+                  + \frac{1}{e_{3w}} \delta_{k + 1/2} [q] \; \, \vect k
+\]
+\begin{multline*}
+                  + \frac{1}{e_{3w}} \delta_{k + 1/2} [q] \; \, \vect k \\
   % \label{eq:DOM_lap}
   \Delta q \equiv   \frac{1}{e_{1t} \, e_{2t} \, e_{3t}}
                     \; \lt[   \delta_i \lt( \frac{e_{2u} \, e_{3u}}{e_{1u}} \; \delta_{i + 1/2} [q] \rt)
                             + \delta_j \lt( \frac{e_{1v} \, e_{3v}}{e_{2v}} \; \delta_{j + 1/2} [q] \rt) \; \rt] \\
+                            + \delta_j \lt( \frac{e_{1v} \, e_{3v}}{e_{2v}} \; \delta_{j + 1/2} [q] \rt) \; \rt]
                   + \frac{1}{e_{3t}}
                               \delta_k \lt[ \frac{1              }{e_{3w}} \; \delta_{k + 1/2} [q] \rt]
+\end{multline*}
+Following \autoref{eq:MB_curl} and \autoref{eq:MB_div}, a vector $\vect A = (a_1,a_2,a_3)$ defined at
+vector points $(u,v,w)$ has its three curl components defined at $vw$-, $uw$, and $f$-points, and
+\end{gather*}
+Following \autoref{eq:MB_curl} and \autoref{eq:MB_div},
+a vector $\vect A = (a_1,a_2,a_3)$ defined at vector points $(u,v,w)$ has
+its three curl components defined at $vw$-, $uw$, and $f$-points, and
 its divergence defined at $t$-points:
 \begin{multline}
+\begin{multline*}
 % \label{eq:DOM_curl}
   \nabla \times \vect A \equiv   \frac{1}{e_{2v} \, e_{3vw}}
 …
                                  \Big[   \delta_{i + 1/2} (e_{2v} \, a_2)
                                        - \delta_{j + 1/2} (e_{1u} \, a_1) \Big] \vect k
 \end{multline}
 \begin{equation}
+\end{multline*}
+\[
 % \label{eq:DOM_div}
   \nabla \cdot \vect A \equiv   \frac{1}{e_{1t} \, e_{2t} \, e_{3t}}
                                 \Big[ \delta_i (e_{2u} \, e_{3u} \, a_1) + \delta_j (e_{1v} \, e_{3v} \, a_2) \Big]
                               + \frac{1}{e_{3t}} \delta_k (a_3)
 \end{equation}
 The vertical average over the whole water column is denoted by an overbar and is for
 a masked field $q$ (\ie\ a quantity that is equal to zero inside solid areas):
+\]
+The vertical average over the whole water column is denoted by an overbar and
+is for a masked field $q$ (\ie\ a quantity that is equal to zero inside solid areas):
 \begin{equation}
   \label{eq:DOM_bar}
 …
 \end{equation}
 where $H_q$  is the ocean depth, which is the masked sum of the vertical scale factors at $q$ points,
+$k^b$ and $k^o$ are the bottom and surface $k$-indices, and the symbol $\sum \limits_k$ refers to a summation over
+all grid points of the same type in the direction indicated by the subscript (here $k$).
+$k^b$ and $k^o$ are the bottom and surface $k$-indices,
+and the symbol $\sum \limits_k$ refers to a summation over all grid points of the same type in
+the direction indicated by the subscript (here $k$).
 In continuous form, the following properties are satisfied:
 …
 \end{gather}
 It is straightforward to demonstrate that these properties are verified locally in discrete form as soon as
 the scalar $q$ is taken at $t$-points and the vector $\vect A$ has its components defined at
+It is straightforward to demonstrate that these properties are verified locally in discrete form as
+soon as the scalar $q$ is taken at $t$-points and the vector $\vect A$ has its components defined at
 vector points $(u,v,w)$.
 Let $a$ and $b$ be two fields defined on the mesh, with a value of zero inside continental areas.
+It can be shown that the differencing operators ($\delta_i$, $\delta_j$ and $\delta_k$)
+are skew-symmetric linear operators, and further that the averaging operators $\overline{\cdots}^{\, i}$,
+$\overline{\cdots}^{\, j}$ and $\overline{\cdots}^{\, k}$) are symmetric linear operators, \ie
+\begin{alignat}{4}
+It can be shown that the differencing operators ($\delta_i$, $\delta_j$ and
+$\delta_k$) are skew-symmetric linear operators,
+and further that the averaging operators ($\overline{\cdots}^{\, i}$, $\overline{\cdots}^{\, j}$ and
+$\overline{\cdots}^{\, k}$) are symmetric linear operators, \ie
+\begin{alignat}{5}
   \label{eq:DOM_di_adj}
   &\sum \limits_i a_i \; \delta_i [b]      &\equiv &- &&\sum \limits_i \delta      _{   i + 1/2} [a] &b_{i + 1/2} \\
 …
 \end{alignat}
+In other words, the adjoint of the differencing and averaging operators are $\delta_i^* = \delta_{i + 1/2}$ and
+In other words,
+the adjoint of the differencing and averaging operators are $\delta_i^* = \delta_{i + 1/2}$ and
 $(\overline{\cdots}^{\, i})^* = \overline{\cdots}^{\, i + 1/2}$, respectively.
 These two properties will be used extensively in the \autoref{apdx:INVARIANTS} to
 …
 \label{subsec:DOM_Num_Index}
 \begin{figure}[!tb]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_index_hor}
+  \includegraphics[width=0.33\textwidth]{DOM_index_hor}
   \caption[Horizontal integer indexing]{
     Horizontal integer indexing used in the \fortran\ code.
 …
 The array representation used in the \fortran\ code requires an integer indexing.
+However, the analytical definition of the mesh (see \autoref{subsec:DOM_cell}) is associated with the use of
+integer values for $t$-points only while all the other points involve integer and a half values.
+However, the analytical definition of the mesh (see \autoref{subsec:DOM_cell}) is associated with
+the use of integer values for $t$-points only while
+all the other points involve integer and a half values.
 Therefore, a specific integer indexing has been defined for points other than $t$-points
 (\ie\ velocity and vorticity grid-points).
+Furthermore, the direction of the vertical indexing has been reversed and the surface level set at $k = 1$.
+Furthermore, the direction of the vertical indexing has been reversed and
+the surface level set at $k = 1$.
 %% =================================================================================================
 …
 \label{subsec:DOM_Num_Index_vertical}
 In the vertical, the chosen indexing requires special attention since the direction of the $k$-axis in
 the \fortran\ code is the reverse of that 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 the $t$-level just below
 (\autoref{fig:DOM_index_vert}).
+In the vertical, the chosen indexing requires special attention since
+the direction of the $k$-axis in the \fortran\ code is the reverse of
+that 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 the $t$-level just below (\autoref{fig:DOM_index_vert}).
 The last $w$-level ($k = jpk$) either corresponds to or is below the ocean floor while
 the last $t$-level is always outside the ocean domain (\autoref{fig:DOM_index_vert}).
 Note that a $w$-point and the directly underlaying $t$-point have a common $k$ index
 (\ie\ $t$-points and their nearest $w$-point neighbour in negative index direction),
+in contrast to the indexing on the horizontal plane where the $t$-point has the same index as
+the nearest velocity points in the positive direction of the respective horizontal axis index
+in contrast to the indexing on the horizontal plane where
+the $t$-point has the same index as the nearest velocity points in
+the positive direction of the respective horizontal axis index
 (compare the dashed area in \autoref{fig:DOM_index_hor} and \autoref{fig:DOM_index_vert}).
 Since the scale factors are chosen to be strictly positive,
 …
 accommodate the opposing vertical index directions in implementation and documentation.
 \begin{figure}[!pt]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_index_vert}
+  \includegraphics[width=0.33\textwidth]{DOM_index_vert}
   \caption[Vertical integer indexing]{
     Vertical integer indexing used in the \fortran\ code.
 …
 Two typical methods are available to specify the spatial domain configuration;
+they can be selected using parameter \np{ln_read_cfg}{ln\_read\_cfg} parameter in namelist \nam{cfg}{cfg}.
+they can be selected using parameter \np{ln_read_cfg}{ln\_read\_cfg} parameter in
+namelist \nam{cfg}{cfg}.
 If \np{ln_read_cfg}{ln\_read\_cfg} is set to \forcode{.true.},
+the domain-specific parameters and fields are read from a netCDF input file,
+whose name (without its .nc suffix) can be specified as the value of the \np{cn_domcfg}{cn\_domcfg} parameter in namelist \nam{cfg}{cfg}.
+the domain-specific parameters and fields are read from a NetCDF input file,
+whose name (without its .nc suffix) can be specified as
+the value of the \np{cn_domcfg}{cn\_domcfg} parameter in namelist \nam{cfg}{cfg}.
 If \np{ln_read_cfg}{ln\_read\_cfg} is set to \forcode{.false.},
 …
 subroutines \mdl{usrdef\_hgr} and \mdl{usrdef\_zgr}.
 These subroutines can be supplied in the \path{MY_SRC} directory of the configuration,
 and default versions that configure the spatial domain for the GYRE reference configuration are present in
 the \path{./src/OCE/USR} directory.
+and default versions that configure the spatial domain for the GYRE reference configuration are
+present in the \path{./src/OCE/USR} directory.
 In version 4.0 there are no longer any options for reading complex bathymetries and
 …
 to run similar models with and without partial bottom boxes and/or sigma-coordinates,
 supporting such choices leads to overly complex code.
+Worse still is the difficulty of ensuring the model configurations intended to be identical are indeed so when
+the model domain itself can be altered by runtime selections.
+The code previously used to perform vertical discretisation has been incorporated into an external tool
+(\path{./tools/DOMAINcfg}) which is briefly described in \autoref{apdx:DOMCFG}.
+The next subsections summarise the parameter and fields related to the configuration of the whole model domain.
+These represent the minimum information that must be provided either via the \np{cn_domcfg}{cn\_domcfg} file or set by code
+inserted into user-supplied versions of the \texttt{usrdef\_*} subroutines.
+Worse still is the difficulty of ensuring the model configurations intended to be identical are
+indeed so when the model domain itself can be altered by runtime selections.
+The code previously used to perform vertical discretisation has been incorporated into
+an external tool (\path{./tools/DOMAINcfg}) which is briefly described in \autoref{apdx:DOMCFG}.
+The next subsections summarise the parameter and fields related to
+the configuration of the whole model domain.
+These represent the minimum information that must be provided either via
+the \np{cn_domcfg}{cn\_domcfg} file or
+set by code inserted into user-supplied versions of the \texttt{usrdef\_*} subroutines.
 The requirements are presented in three sections:
 the domain size (\autoref{subsec:DOM_size}), the horizontal mesh (\autoref{subsec:DOM_hgr}),
 …
 \label{subsec:DOM_size}
 The total size of the computational domain is set by the parameters \jp{jpiglo}, \jp{jpjglo} and \jp{jpkglo} for
 the $i$, $j$ and $k$ directions, respectively.
 Note, that the variables \texttt{jpi} and \texttt{jpj} refer to the size of each processor subdomain when
 the code is run in parallel using domain decomposition (\key{mpp\_mpi} defined,
 see \autoref{sec:LBC_mpp}).
+The total size of the computational domain is set by the parameters \jp{jpiglo}, \jp{jpjglo} and
+\jp{jpkglo} for the $i$, $j$ and $k$ directions, respectively.
+Note, that the variables \texttt{jpi} and \texttt{jpj} refer to
+the size of each processor subdomain when the code is run in parallel using domain decomposition
+(\key{mpp\_mpi} defined, see \autoref{sec:LBC_mpp}).
 The name of the configuration is set through parameter \np{cn_cfg}{cn\_cfg},
 …
 The global lateral boundary condition type is selected from 8 options using parameter \jp{jperio}.
+See \autoref{sec:LBC_jperio} for details on the available options and the corresponding values for \jp{jperio}.
+See \autoref{sec:LBC_jperio} for details on the available options and
+the corresponding values for \jp{jperio}.
 %% =================================================================================================
 …
 \label{sec:DOM_hgr_fields}
+The explicit specification of a range of mesh-related fields are required for the definition of a configuration.
+The explicit specification of a range of mesh-related fields are required for
+the definition of a configuration.
 These include:
 \begin{clines}
 int    jpiglo, jpjglo, jpkglo            /* global domain sizes                                          */
 int    jperio                            /* lateral global domain b.c.                                   */
 double glamt, glamu, glamv, glamf        /* geographic longitude (t,u,v and f points respectively)       */
 double gphit, gphiu, gphiv, gphif        /* geographic latitude                                          */
 double e1t, e1u, e1v, e1f                /* horizontal scale factors                                     */
 double e2t, e2u, e2v, e2f                /* horizontal scale factors                                     */
+int    jpiglo, jpjglo, jpkglo     /* global domain sizes                                    */
+int    jperio                     /* lateral global domain b.c.                             */
+double glamt, glamu, glamv, glamf /* geographic longitude (t,u,v and f points respectively) */
+double gphit, gphiu, gphiv, gphif /* geographic latitude                                    */
+double e1t, e1u, e1v, e1f         /* horizontal scale factors                               */
+double e2t, e2u, e2v, e2f         /* horizontal scale factors                               */
 \end{clines}
 …
 \begin{clines}
                                          /* Optional:                                                    */
 int    ORCA, ORCA_index                  /* configuration name, configuration resolution                 */
 double e1e2u, e1e2v                      /* U and V surfaces (if grid size reduction in some straits)    */
 double ff_f, ff_t                        /* Coriolis parameter (if not on the sphere)                    */
+                        /* Optional:                                                 */
+int    ORCA, ORCA_index /* configuration name, configuration resolution              */
+double e1e2u, e1e2v     /* U and V surfaces (if grid size reduction in some straits) */
+double ff_f, ff_t       /* Coriolis parameter (if not on the sphere)                 */
 \end{clines}
 …
 This is particularly useful for locations such as Gibraltar or Indonesian Throughflow pinch-points
 (see \autoref{sec:MISC_strait} for illustrated examples).
+The key is to reduce the faces of $T$-cell (\ie\ change the value of the horizontal scale factors at $u$- or $v$-point) but
+The key is to reduce the faces of $T$-cell
+(\ie\ change the value of the horizontal scale factors at $u$- or $v$-point) but
 not the volume of the cells.
 Doing otherwise can lead to numerical instability issues.
 In normal operation the surface areas are computed from $e1u * e2u$ and $e1v * e2v$ but
 in cases where a gridsize reduction is required,
+the unaltered surface areas at $u$ and $v$ grid points (\texttt{e1e2u} and \texttt{e1e2v}, respectively) must be read or
+pre-computed in \mdl{usrdef\_hgr}.
+If these arrays are present in the \np{cn_domcfg}{cn\_domcfg} file they are read and the internal computation is suppressed.
+Versions of \mdl{usrdef\_hgr} which set their own values of \texttt{e1e2u} and \texttt{e1e2v} should set
+the surface-area computation flag:
+the unaltered surface areas at $u$ and $v$ grid points
+(\texttt{e1e2u} and \texttt{e1e2v}, respectively) must be read or pre-computed in \mdl{usrdef\_hgr}.
+If these arrays are present in the \np{cn_domcfg}{cn\_domcfg} file they are read and
+the internal computation is suppressed.
+Versions of \mdl{usrdef\_hgr} which set their own values of \texttt{e1e2u} and \texttt{e1e2v} should
+set the surface-area computation flag:
 \texttt{ie1e2u\_v} to a non-zero value to suppress their re-computation.
 \smallskip
 Similar logic applies to the other optional fields:
+\texttt{ff\_f} and \texttt{ff\_t} which can be used to provide the Coriolis parameter at F- and T-points respectively if
+the mesh is not on a sphere.
+If present these fields will be read and used and the normal calculation ($2 * \Omega * \sin(\varphi)$) suppressed.
+Versions of \mdl{usrdef\_hgr} which set their own values of \texttt{ff\_f} and \texttt{ff\_t} should set
+the Coriolis computation flag:
+\texttt{ff\_f} and \texttt{ff\_t} which can be used to
+provide the Coriolis parameter at F- and T-points respectively if the mesh is not on a sphere.
+If present these fields will be read and used and
+the normal calculation ($2 * \Omega * \sin(\varphi)$) suppressed.
+Versions of \mdl{usrdef\_hgr} which set their own values of \texttt{ff\_f} and \texttt{ff\_t} should
+set the Coriolis computation flag:
 \texttt{iff} to a non-zero value to suppress their re-computation.
 Note that longitudes, latitudes, and scale factors at $w$ points are exactly equal to those of $t$ points,
 thus no specific arrays are defined at $w$ points.
+Note that longitudes, latitudes, and scale factors at $w$ points are exactly equal to
+those of $t$ points, thus no specific arrays are defined at $w$ points.
 %% =================================================================================================
 \subsection[Vertical grid (\textit{domzgr.F90})]{Vertical grid (\protect\mdl{domzgr})}
 \label{subsec:DOM_zgr}
 \begin{listing}
   \nlst{namdom}
 …
 In the vertical, the model mesh is determined by four things:
 \begin{enumerate}
+  \item the bathymetry given in meters;
+  \item the number of levels of the model (\jp{jpk});
+  \item the analytical transformation $z(i,j,k)$ and the vertical scale factors (derivatives of the transformation); and
+  \item the masking system, \ie\ the number of wet model levels at each
+$(i,j)$ location of the horizontal grid.
+\item the bathymetry given in meters;
+\item the number of levels of the model (\jp{jpk});
+\item the analytical transformation $z(i,j,k)$ and the vertical scale factors
+  (derivatives of the transformation); and
+\item the masking system,
+  \ie\ the number of wet model levels at each $(i,j)$ location of the horizontal grid.
 \end{enumerate}
 \begin{figure}[!tb]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_z_zps_s_sps}
+  \includegraphics[width=0.5\textwidth]{DOM_z_zps_s_sps}
   \caption[Ocean bottom regarding coordinate systems ($z$, $s$ and hybrid $s-z$)]{
     The ocean bottom as seen by the model:
+    (a) $z$-coordinate with full step,
+    (b) $z$-coordinate with partial step,
+    (c) $s$-coordinate: terrain following representation,
+    (d) hybrid $s-z$ coordinate,
+    (e) hybrid $s-z$ coordinate with partial step, and
+    (f) same as (e) but in the non-linear free surface (\protect\np[=.false.]{ln_linssh}{ln\_linssh}).
+    Note that the non-linear free surface can be used with any of the 5 coordinates (a) to (e).}
+    \begin{enumerate*}[label=(\textit{\alph*})]
+    \item $z$-coordinate with full step,
+    \item $z$-coordinate with partial step,
+    \item $s$-coordinate: terrain following representation,
+    \item hybrid $s-z$ coordinate,
+    \item hybrid $s-z$ coordinate with partial step, and
+    \item same as (e) but in the non-linear free surface
+      (\protect\np[=.false.]{ln_linssh}{ln\_linssh}).
+  \end{enumerate*}
+  Note that the non-linear free surface can be used with any of the 5 coordinates (a) to (e).}
   \label{fig:DOM_z_zps_s_sps}
 \end{figure}
 …
 it is not intended to be an option which can be changed in the middle of an experiment.
 The one exception to this statement being the choice of linear or non-linear free surface.
+In v4.0 the linear free surface option is implemented as a special case of the non-linear free surface.
+In v4.0 the linear free surface option is implemented as
+a special case of the non-linear free surface.
 This is computationally wasteful since it uses the structures for time-varying 3D metrics
 for fields that (in the linear free surface case) are fixed.
+However, the linear free-surface is rarely used and implementing it this way means
+a single configuration file can support both options.
+By default a non-linear free surface is used (\np{ln_linssh}{ln\_linssh} set to \forcode{=.false.} in \nam{dom}{dom}):
+the coordinate follow the time-variation of the free surface so that the transformation is time dependent:
+$z(i,j,k,t)$ (\eg\ \autoref{fig:DOM_z_zps_s_sps}f).
+When a linear free surface is assumed (\np{ln_linssh}{ln\_linssh} set to \forcode{=.true.} in \nam{dom}{dom}),
+the vertical coordinates are fixed in time, but the seawater can move up and down across the $z_0$ surface
+However, the linear free-surface is rarely used and
+implementing it this way means a single configuration file can support both options.
+By default a non-linear free surface is used
+(\np{ln_linssh}{ln\_linssh} set to \forcode{=.false.} in \nam{dom}{dom}):
+the coordinate follow the time-variation of the free surface so that
+the transformation is time dependent: $z(i,j,k,t)$ (\eg\ \autoref{fig:DOM_z_zps_s_sps}f).
+When a linear free surface is assumed
+(\np{ln_linssh}{ln\_linssh} set to \forcode{=.true.} in \nam{dom}{dom}),
+the vertical coordinates are fixed in time, but
+the seawater can move up and down across the $z_0$ surface
 (in other words, the top of the ocean in not a rigid lid).
 Note that settings:
+\np{ln_zco}{ln\_zco}, \np{ln_zps}{ln\_zps}, \np{ln_sco}{ln\_sco} and \np{ln_isfcav}{ln\_isfcav} mentioned in the following sections
+appear to be namelist options but they are no longer truly namelist options for \NEMO.
+\np{ln_zco}{ln\_zco}, \np{ln_zps}{ln\_zps}, \np{ln_sco}{ln\_sco} and \np{ln_isfcav}{ln\_isfcav}
+mentioned in the following sections appear to be namelist options but
+they are no longer truly namelist options for \NEMO.
 Their value is written to and read from the domain configuration file and
 they should be treated as fixed parameters for a particular configuration.
 They are namelist options for the \texttt{DOMAINcfg} tool that can be used to build the configuration file and
+serve both to provide a record of the choices made whilst building the configuration and
 to trigger appropriate code blocks within \NEMO.
+They are namelist options for the \texttt{DOMAINcfg} tool that can be used to
+build the configuration file and serve both to provide a record of the choices made whilst
+building the configuration and to trigger appropriate code blocks within \NEMO.
 These values should not be altered in the \np{cn_domcfg}{cn\_domcfg} file.
 …
 A further choice related to vertical coordinate concerns
 the presence (or not) of ocean cavities beneath ice shelves within the model domain.
+A setting of \np{ln_isfcav}{ln\_isfcav} as \forcode{.true.} indicates that the domain contains ocean cavities,
+A setting of \np{ln_isfcav}{ln\_isfcav} as \forcode{.true.} indicates that
+the domain contains ocean cavities,
 otherwise the top, wet layer of the ocean will always be at the ocean surface.
 This option is currently only available for $z$- or $zps$-coordinates.
 In the latter case, partial steps are also applied at the ocean/ice shelf interface.
+Within the model, the arrays describing the grid point depths and vertical scale factors are three set of
+three dimensional arrays $(i,j,k)$ defined at \textit{before}, \textit{now} and \textit{after} time step.
+Within the model,
+the arrays describing the grid point depths and vertical scale factors are
+three set of three dimensional arrays $(i,j,k)$ defined at
+\textit{before}, \textit{now} and \textit{after} time step.
 The time at which they are defined is indicated by a suffix: $\_b$, $\_n$, or $\_a$, respectively.
 They are updated at each model time step.
 …
 \end{clines}
 This set of vertical metrics is sufficient to describe the initial depth and thickness of every gridcell in
 the model regardless of the choice of vertical coordinate.
+This set of vertical metrics is sufficient to describe the initial depth and thickness of
+every gridcell in the model regardless of the choice of vertical coordinate.
 With constant z-levels, e3 metrics will be uniform across each horizontal level.
 In the partial step case each e3 at the \jp{bottom\_level}
 …
 may vary from its horizontal neighbours.
 And, in s-coordinates, variations can occur throughout the water column.
 With the non-linear free-surface, all the coordinates behave more like the s-coordinate in
 that variations occur throughout the water column with displacements related to the sea surface height.
+With the non-linear free-surface, all the coordinates behave more like the s-coordinate in that
+variations occur throughout the water column with displacements related to the sea surface height.
 These variations are typically much smaller than those arising from bottom fitted coordinates.
 The values for vertical metrics supplied in the domain configuration file can be considered as
 those arising from a flat sea surface with zero elevation.
+The \jp{bottom\_level} and \jp{top\_level} 2D arrays define the \jp{bottom\_level} and top wet levels in each grid column.
+The \jp{bottom\_level} and \jp{top\_level} 2D arrays define
+the \jp{bottom\_level} and top wet levels in each grid column.
 Without ice cavities, \jp{top\_level} is essentially a land mask (0 on land; 1 everywhere else).
 With ice cavities, \jp{top\_level} determines the first wet point below the overlying ice shelf.
 …
 From \jp{top\_level} and \jp{bottom\_level} fields, the mask fields are defined as follows:
+\begin{alignat*}{2}
+  tmask(i,j,k) &= &  &
+    \begin{cases}
+&\text{if $                  k  <    top\_level(i,j)$} \\
+&\text{if $bottom\_level(i,j) \leq k \leq   top\_level(i,j)$} \\
+&\text{if $                  k  >     bottom\_level(i,j)$}
+    \end{cases}
+  \\
+  umask(i,j,k) &= &  &tmask(i,j,k) * tmask(i + 1,j,    k) \\
+  vmask(i,j,k) &= &  &tmask(i,j,k) * tmask(i    ,j + 1,k) \\
+  fmask(i,j,k) &= &  &tmask(i,j,k) * tmask(i + 1,j,    k) \\
+               &  &* &tmask(i,j,k) * tmask(i + 1,j,    k) \\
+  wmask(i,j,k) &= &  &tmask(i,j,k) * tmask(i    ,j,k - 1) \\
+  \text{with~} wmask(i,j,1) &= & &tmask(i,j,1)
+\end{alignat*}
+\begin{align*}
+  tmask(i,j,k) &=
+  \begin{cases}
+&\text{if $                             k <    top\_level(i,j)$} \\
+&\text{if $     bottom\_level(i,j) \leq k \leq top\_level(i,j)$} \\
+&\text{if $k >  bottom\_level(i,j)                            $}
+  \end{cases} \\
+  umask(i,j,k) &= tmask(i,j,k) * tmask(i + 1,j,    k) \\
+  vmask(i,j,k) &= tmask(i,j,k) * tmask(i    ,j + 1,k) \\
+  fmask(i,j,k) &= tmask(i,j,k) * tmask(i + 1,j,    k) * tmask(i,j,k) * tmask(i + 1,j,    k) \\
+  wmask(i,j,k) &= tmask(i,j,k) * tmask(i    ,j,k - 1) \\
+  \text{with~} wmask(i,j,1) &= tmask(i,j,1)
+\end{align*}
 Note that, without ice shelves cavities,
+masks at $t-$ and $w-$points are identical with the numerical indexing used (\autoref{subsec:DOM_Num_Index}).
+Nevertheless, $wmask$ are required with ocean cavities to deal with the top boundary (ice shelf/ocean interface)
+masks at $t-$ and $w-$points are identical with the numerical indexing used
+(\autoref{subsec:DOM_Num_Index}).
+Nevertheless,
+$wmask$ are required with ocean cavities to deal with the top boundary (ice shelf/ocean interface)
 exactly in the same way as for the bottom boundary.
 …
 \label{subsec:DOM_closea}
 When a global ocean is coupled to an atmospheric model it is better to represent all large water bodies
+(\eg\ Great Lakes, Caspian sea \dots) even if the model resolution does not allow their communication with
 the rest of the ocean.
+When a global ocean is coupled to an atmospheric model it is better to
+represent all large water bodies (\eg\ Great Lakes, Caspian sea, \dots) even if
+the model resolution does not allow their communication with the rest of the ocean.
 This is unnecessary when the ocean is forced by fixed atmospheric conditions,
 so these seas can be removed from the ocean domain.
+The user has the option to set the bathymetry in closed seas to zero (see \autoref{sec:MISC_closea}) and
+to optionally decide on the fate of any freshwater imbalance over the area.
+The options are explained in \autoref{sec:MISC_closea} but it should be noted here that
+a successful use of these options requires appropriate mask fields to be present in the domain configuration file.
+The user has the option to
+set the bathymetry in closed seas to zero (see \autoref{sec:MISC_closea}) and to
+optionally decide on the fate of any freshwater imbalance over the area.
+The options are explained in \autoref{sec:MISC_closea} but
+it should be noted here that a successful use of these options requires
+appropriate mask fields to be present in the domain configuration file.
 Among the possibilities are:
 \begin{clines}
 int    closea_mask          /* non-zero values in closed sea areas for optional masking                  */
 int    closea_mask_rnf      /* non-zero values in closed sea areas with runoff locations (precip only)   */
 int    closea_mask_emp      /* non-zero values in closed sea areas with runoff locations (total emp)     */
+int closea_mask     /* non-zero values in closed sea areas for optional masking                */
+int closea_mask_rnf /* non-zero values in closed sea areas with runoff locations (precip only) */
+int closea_mask_emp /* non-zero values in closed sea areas with runoff locations (total emp)   */
 \end{clines}
 …
 Most of the arrays relating to a particular ocean model configuration discussed in this chapter
 (grid-point position, scale factors)
+can be saved in a file if
 namelist parameter \np{ln_write_cfg}{ln\_write\_cfg} (namelist \nam{cfg}{cfg}) is set to \forcode{.true.};
+(grid-point position, scale factors) can be saved in a file if
+namelist parameter \np{ln_write_cfg}{ln\_write\_cfg} (namelist \nam{cfg}{cfg}) is set to
+\forcode{.true.};
 the output filename is set through parameter \np{cn_domcfg_out}{cn\_domcfg\_out}.
 This is only really useful if
 …
 Alternatively, all the arrays relating to a particular ocean model configuration
+(grid-point position, scale factors, depths and masks)
+can be saved in a file called \texttt{mesh\_mask} if
+namelist parameter \np{ln_meshmask}{ln\_meshmask} (namelist \nam{dom}{dom}) is set to \forcode{.true.}.
+(grid-point position, scale factors, depths and masks) can be saved in
+a file called \texttt{mesh\_mask} if
+namelist parameter \np{ln_meshmask}{ln\_meshmask} (namelist \nam{dom}{dom}) is set to
+\forcode{.true.}.
 This file contains additional fields that can be useful for post-processing applications.
 …
 \section[Initial state (\textit{istate.F90} and \textit{dtatsd.F90})]{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})}
 \label{sec:DOM_DTA_tsd}
 \begin{listing}
   \nlst{namtsd}
 …
 \begin{description}
+\item [{\np[=.true.]{ln_tsd_init}{ln\_tsd\_init}}] Use T and S input files that can be given on the model grid itself or on their native input data grids.
+  In the latter case, the data will be interpolated on-the-fly both in the horizontal and the vertical to the model grid
+\item [{\np[=.true.]{ln_tsd_init}{ln\_tsd\_init}}] Use T and S input files that can be given on
+  the model grid itself or on their native input data grids.
+  In the latter case,
+  the data will be interpolated on-the-fly both in the horizontal and the vertical to the model grid
   (see \autoref{subsec:SBC_iof}).
+  The information relating to the input files are specified in the \np{sn_tem}{sn\_tem} and \np{sn_sal}{sn\_sal} structures.
+  The information relating to the input files are specified in
+  the \np{sn_tem}{sn\_tem} and \np{sn_sal}{sn\_sal} structures.
   The computation is done in the \mdl{dtatsd} module.
+\item [{\np[=.false.]{ln_tsd_init}{ln\_tsd\_init}}] Initial values for T and S are set via a user supplied \rou{usr\_def\_istate} routine contained in \mdl{userdef\_istate}.
+\item [{\np[=.false.]{ln_tsd_init}{ln\_tsd\_init}}] Initial values for T and S are set via
+  a user supplied \rou{usr\_def\_istate} routine contained in \mdl{userdef\_istate}.
   The default version sets horizontally uniform T and profiles as used in the GYRE configuration
   (see \autoref{sec:CFGS_gyre}).
 \end{description}
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_DYN.tex

-                      r11599
+                      r11954
 Furthermore, the tendency terms associated with the 2D barotropic vorticity balance (when \texttt{trdvor?} is defined)
 can be derived from the 3D terms.
 \gmcomment{STEVEN: not quite sure I've got the sense of the last sentence. does
 MISC correspond to "extracting tendency terms" or "vorticity balance"?}
+\cmtgm{STEVEN: not quite sure I've got the sense of the last sentence.
+  Does MISC correspond to "extracting tendency terms" or "vorticity balance"?}
 %% =================================================================================================
 …
 as changes in the divergence of the barotropic transport are absorbed into the change of the level thicknesses,
 re-orientated downward.
 \gmcomment{not sure of this...  to be modified with the change in emp setting}
+\cmtgm{not sure of this...  to be modified with the change in emp setting}
 In the case of a linear free surface, the time derivative in \autoref{eq:DYN_wzv} disappears.
 The upper boundary condition applies at a fixed level $z=0$.
 …
 $u$ and $v$ are located at different grid points,
 a price worth paying to avoid a double averaging in the pressure gradient term as in the $B$-grid.
 \gmcomment{ To circumvent this, Adcroft (ADD REF HERE)
+\cmtgm{ To circumvent this, Adcroft (ADD REF HERE)
 Nevertheless, this technique strongly distort the phase and group velocity of Rossby waves....}
 …
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_DYN_een_triad}
+  \includegraphics[width=0.66\textwidth]{DYN_een_triad}
   \caption[Triads used in the energy and enstrophy conserving scheme (EEN)]{
     Triads used in the energy and enstrophy conserving scheme (EEN) for
 …
 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:DYN_adv_cen2} are used.
 UBS is diffusive and is associated with vertical mixing of momentum. \gmcomment{ gm  pursue the
+UBS is diffusive and is associated with vertical mixing of momentum. \cmtgm{ gm  pursue the
 sentence:Since vertical mixing of momentum is a source term of the TKE equation...  }
 …
 there is also the possibility of using a $4^{th}$ order evaluation of the advective velocity as in ROMS.
 This is an error and should be suppressed soon.
 \gmcomment{action :  this have to be done}
+\cmtgm{action :  this have to be done}
 %% =================================================================================================
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_DYN_dynspg_ts}
+  \includegraphics[width=0.66\textwidth]{DYN_dynspg_ts}
   \caption[Split-explicit time stepping scheme for the external and internal modes]{
     Schematic of the split-explicit time stepping scheme for the external and internal modes.
 …
 it is still significant as shown by \citet{levier.treguier.ea_rpt07} in the case of an analytical barotropic Kelvin wave.
 \gmcomment{               %%% copy from griffies Book
+\cmtgm{               %%% copy from griffies Book
 \textbf{title: Time stepping the barotropic system }
 …
 %% gm %%======>>>>   given here the discrete eqs provided to the solver
 \gmcomment{               %%% copy from chap-model basics
+\cmtgm{               %%% copy from chap-model basics
   \[
     % \label{eq:DYN_spg_flt}
 …
   and $\mathrm {\mathbf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient,
   non-linear and viscous terms in \autoref{eq:MB_dyn}.
 }   %end gmcomment
+}   %end cmtgm
 Note that in the linear free surface formulation (\texttt{vvl?} not defined),
 …
 no slip or partial slip boundary conditions are applied according to the user's choice (see \autoref{chap:LBC}).
 \gmcomment{
+\cmtgm{
   Hyperviscous operators are frequently used in the simulation of turbulent flows to
   control the dissipation of unresolved small scale features.
 …
 the first derivative term normal to the coast depends on the free or no-slip lateral boundary conditions chosen,
 while the third derivative terms normal to the coast are set to zero (see \autoref{chap:LBC}).
 \gmcomment{add a remark on the the change in the position of the coefficient}
+\cmtgm{add a remark on the the change in the position of the coefficient}
 %% =================================================================================================
 …
 the snow-ice mass is taken into account when computing the surface pressure gradient.
 \gmcomment{ missing : the lateral boundary condition !!!   another external forcing
+\cmtgm{ missing : the lateral boundary condition !!!   another external forcing
+ }
 …
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_WAD_dynhpg}
+  \includegraphics[width=0.66\textwidth]{DYN_WAD_dynhpg}
   \caption[Combinations controlling the limiting of the horizontal pressure gradient in
   wetting and drying regimes]{
 …
 and only array swapping and Asselin filtering is done in \mdl{dynnxt}.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_LBC.tex

-                      r11598
+                      r11954
 \clearpage
+%gm% add here introduction to this chapter
+\cmtgm{Add here introduction to this chapter}
 %% =================================================================================================
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_LBC_uv}
+  \includegraphics[width=0.66\textwidth]{LBC_uv}
   \caption[Lateral boundary at $T$-level]{
     Lateral boundary (thick line) at T-level.
 …
 \begin{figure}[!p]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_LBC_shlat}
+  \includegraphics[width=0.66\textwidth]{LBC_shlat}
   \caption[Lateral boundary conditions]{
     Lateral boundary conditions
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_LBC_jperio}
+  \includegraphics[width=0.66\textwidth]{LBC_jperio}
   \caption[Setting of east-west cyclic and symmetric across the Equator boundary conditions]{
     Setting of (a) east-west cyclic (b) symmetric across the Equator boundary conditions}
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_North_Fold_T}
+  \includegraphics[width=0.66\textwidth]{LBC_North_Fold_T}
   \caption[North fold boundary in ORCA 2\deg, 1/4\deg and 1/12\deg]{
     North fold boundary with a $T$-point pivot and cyclic east-west boundary condition ($jperio=4$),
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_mpp}
+  \includegraphics[width=0.66\textwidth]{LBC_mpp}
   \caption{Positioning of a sub-domain when massively parallel processing is used}
   \label{fig:LBC_mpp}
 …
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_mppini2}
+  \includegraphics[width=0.66\textwidth]{LBC_mppini2}
   \caption[Atlantic domain defined for the CLIPPER projet]{
     Example of Atlantic domain defined for the CLIPPER projet.
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_LBC_bdy_geom}
+  \includegraphics[width=0.66\textwidth]{LBC_bdy_geom}
   \caption[Geometry of unstructured open boundary]{Example of geometry of unstructured open boundary}
   \label{fig:LBC_bdy_geom}
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_LBC_nc_header}
+  \includegraphics[width=0.66\textwidth]{LBC_nc_header}
   \caption[Header for a \protect\ifile{coordinates.bdy} file]{
     Example of the header for a \protect\ifile{coordinates.bdy} file}
 …
 direction of rotation). %, e.g. anticlockwise or clockwise.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_LDF.tex

-                      r11599
+                      r11954
 \label{sec:LDF_slp}
 \gmcomment{
+\cmtgm{
   we should emphasize here that the implementation is a rather old one.
   Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} iso-neutral scheme.
 …
 $r_{1f}$, $r_{1vw}$, $r_{2t}$, $r_{2vw}$ for $v$.
+%gm% add here afigure of the slope in i-direction
+\cmtgm{Add here afigure of the slope in i-direction}
 %% =================================================================================================
 …
 the diffusive fluxes in the three directions are set to zero and $T$ is assumed to be horizontally uniform,
 \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}
+\cmtgm{Steven : My version is obviously wrong since
+  I'm left with an arbitrary constant which is the local vertical temperature gradient}
 \begin{equation}
 …
 \end{equation}
+%gm%  caution I'm not sure the simplification was a good idea!
+\cmtgm{Caution I'm not sure the simplification was a good idea!}
 These slopes are computed once in \rou{ldf\_slp\_init} when \np[=.true.]{ln_sco}{ln\_sco},
 …
 \end{equation}
+%gm% rewrite this as the explanation is not very clear !!!
+\cmtgm{rewrite this as the explanation is not very clear !!!}
 %In practice, \autoref{eq:LDF_slp_iso} is of little help in evaluating the neutral surface slopes. Indeed, for an unsimplified equation of state, the density has a strong dependancy on pressure (here approximated as the depth), therefore applying \autoref{eq:LDF_slp_iso} using the $in situ$ density, $\rho$, computed at T-points leads to a flattening of slopes as the depth increases. This is due to the strong increase of the $in situ$ density with depth.
 …
   will include a pressure dependent part, leading to the wrong evaluation of the neutral slopes.
-%gm%
   Note: The solution for $s$-coordinate passes trough the use of different (and better) expression for
   the constraint on iso-neutral fluxes.
 …
     \alpha \ \textbf{F}(T) = \beta \ \textbf{F}(S)
   \]
   % gm{  where vector F is ....}
+  \cmtgm{where vector F is ....}
 This constraint leads to the following definition for the slopes:
 …
 This allows an iso-neutral diffusion scheme without additional background horizontal mixing.
 This technique can be viewed as a diffusion operator that acts along large-scale
 (2~$\Delta$x) \gmcomment{2deltax doesnt seem very large scale} iso-neutral surfaces.
+(2~$\Delta$x) \cmtgm{2deltax doesnt seem very large scale} iso-neutral surfaces.
 The diapycnal diffusion required for numerical stability is thus minimized and its net effect on the flow is quite small when compared to the effect of an horizontal background mixing.
 …
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_LDF_ZDF1}
+  \includegraphics[width=0.66\textwidth]{LDF_ZDF1}
   \caption{Averaging procedure for isopycnal slope computation}
   \label{fig:LDF_ZDF1}
 …
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_eiv_slp}
+  \includegraphics[width=0.66\textwidth]{LDF_eiv_slp}
   \caption[Vertical profile of the slope used for lateral mixing in the mixed layer]{
     Vertical profile of the slope used for lateral mixing in the mixed layer:
 …
 %%gm  from Triad appendix  : to be incorporated....
 \gmcomment{
+\cmtgm{
   Values of iso-neutral diffusivity and GM coefficient are set as described in \autoref{sec:LDF_coef}.
   If none of the keys \key{traldf\_cNd}, N=1,2,3 is set (the default), spatially constant iso-neutral $A_l$ and
 …
 \colorbox{yellow}{TBC}
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_OBS.tex

-                      r11598
+                      r11954
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_OBS_avg_rec}
+  \includegraphics[width=0.66\textwidth]{OBS_avg_rec}
   \caption[Observational weights with a rectangular footprint]{
     Weights associated with each model grid box (blue lines and numbers)
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_OBS_avg_rad}
+  \includegraphics[width=0.66\textwidth]{OBS_avg_rad}
   \caption[Observational weights with a radial footprint]{
     Weights associated with each model grid box (blue lines and numbers)
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ASM_obsdist_local}
+  \includegraphics[width=0.66\textwidth]{OBS_obsdist_local}
   \caption[Observations with the geographical distribution]{
     Example of the distribution of observations with
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ASM_obsdist_global}
+  \includegraphics[width=0.66\textwidth]{OBS_obsdist_global}
   \caption[Observations with the round-robin distribution]{
     Example of the distribution of observations with
 …
 %% =================================================================================================
 \section{Standalone observation operator}
+\section{Standalone observation operator (\texttt{SAO})}
 \label{sec:OBS_sao}
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_OBS_dataplot_main}
+  \includegraphics[width=0.66\textwidth]{OBS_dataplot_main}
   \caption{Main window of dataplot}
   \label{fig:OBS_dataplotmain}
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_OBS_dataplot_prof}
+  \includegraphics[width=0.66\textwidth]{OBS_dataplot_prof}
   \caption[Profile plot from dataplot]{
     Profile plot from dataplot produced by right clicking on a point in the main window}
 …
 \end{figure}
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_SBC.tex

-                      r11599
+                      r11954
 %ENDIF
+%\gmcomment{  word doc of runoffs:
+%In the current \NEMO\ setup river runoff is added to emp fluxes, these are then applied at just the sea surface as a volume change (in the variable volume case this is a literal volume change, and in the linear free surface case the free surface is moved) and a salt flux due to the concentration/dilution effect.  There is also an option to increase vertical mixing near river mouths; this gives the effect of having a 3d river.  All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.
+%Our aim was to code the option to specify the temperature and salinity of river runoff, (as well as the amount), along with the depth that the river water will affect.  This would make it possible to model low salinity outflow, such as the Baltic, and would allow the ocean temperature to be affected by river runoff.
+%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
+%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the tra_sbc module.  We decided to separate them throughout the code, so that the variable emp represented solely evaporation minus precipitation fluxes, and a new 2d variable rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use emp or emps and the changes made are below:
+\cmtgm{  word doc of runoffs:
+In the current \NEMO\ setup river runoff is added to emp fluxes,
+these are then applied at just the sea surface as a volume change (in the variable volume case
+this is a literal volume change, and in the linear free surface case the free surface is moved)
+and a salt flux due to the concentration/dilution effect.
+There is also an option to increase vertical mixing near river mouths;
+this gives the effect of having a 3d river.
+All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
+at the same temperature as the sea surface.
+Our aim was to code the option to specify the temperature and salinity of river runoff,
+(as well as the amount), along with the depth that the river water will affect.
+This would make it possible to model low salinity outflow, such as the Baltic,
+and would allow the ocean temperature to be affected by river runoff.
+The depth option makes it possible to have the river water affecting just the surface layer,
+throughout depth, or some specified point in between.
+To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
+the \mdl{tra_sbc} module.
+We decided to separate them throughout the code,
+so that the variable emp represented solely evaporation minus precipitation fluxes,
+and a new 2d variable rnf was added which represents the volume flux of river runoff
+(in $kg/m^2s$ to remain consistent with $emp$).
+This meant many uses of emp and emps needed to be changed,
+a list of all modules which use $emp$ or $emps$ and the changes made are below:}
 %% =================================================================================================
 …
   Two different bulk formulae are available:
    \begin{description}
    \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
      the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
    \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
      (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
      A complete description is available in \citet{jenkins_JGR91}.
    \end{description}
      Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
      Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
      The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m.
      Then, the fluxes are spread over the same thickness (ie over one or several cells).
      If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature.
      This can lead to super-cool temperature in the top cell under melting condition.
      If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
      Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
      There are 3 different ways to compute the exchange coeficient:
    \begin{description}
         \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}.
      \begin{gather*}
+  \begin{description}
+  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
+    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
+  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
+    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
+    A complete description is available in \citet{jenkins_JGR91}.
+  \end{description}
+  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
+  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
+  The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m.
+  Then, the fluxes are spread over the same thickness (ie over one or several cells).
+  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature.
+  This can lead to super-cool temperature in the top cell under melting condition.
+  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
+  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
+  There are 3 different ways to compute the exchange coeficient:
+  \begin{description}
+  \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}.
+    \begin{gather*}
        % \label{eq:SBC_isf_gamma_iso}
        \gamma^{T} = rn\_gammat0 \\
        \gamma^{S} = rn\_gammas0
      \end{gather*}
      This is the recommended formulation for ISOMIP.
    \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
      \begin{gather*}
        \gamma^{T} = rn\_gammat0 \times u_{*} \\
        \gamma^{S} = rn\_gammas0 \times u_{*}
      \end{gather*}
      where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
      See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
    \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
 \[
 \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
 \]
      where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
      $\Gamma_{Turb}$ the contribution of the ocean stability and
      $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
      See \citet{holland.jenkins_JPO99} for all the details on this formulation.
      This formulation has not been extensively tested in \NEMO\ (not recommended).
    \end{description}
   \item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
    The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
    The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
    (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
    (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
    The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
   \item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
    The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
    the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
    the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
    The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
   \item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
    However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
    The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
    As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl})\\
+      \gamma^{T} = rn\_gammat0 \\
+      \gamma^{S} = rn\_gammas0
+    \end{gather*}
+    This is the recommended formulation for ISOMIP.
+  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
+    \begin{gather*}
+      \gamma^{T} = rn\_gammat0 \times u_{*} \\
+      \gamma^{S} = rn\_gammas0 \times u_{*}
+    \end{gather*}
+    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
+    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
+  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
+    \[
+      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
+    \]
+    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
+    $\Gamma_{Turb}$ the contribution of the ocean stability and
+    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
+    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
+    This formulation has not been extensively tested in \NEMO\ (not recommended).
+  \end{description}
+\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
+  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
+  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
+  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
+  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
+  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
+\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
+  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
+  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
+  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
+  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
+\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
+  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
+  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
+  As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl})
 \end{description}
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_SBC_isf}
+  \includegraphics[width=0.66\textwidth]{SBC_isf}
   \caption[Ice shelf location and fresh water flux definition]{
     Illustration of the location where the fwf is injected and
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_SBC_diurnal}
+  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
   \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
     Example of reconstruction of the diurnal cycle variation of short wave flux from
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_SBC_dcy}
+  \includegraphics[width=0.66\textwidth]{SBC_dcy}
   \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
     Example of reconstruction of the diurnal cycle variation of short wave flux from
 …
 % in ocean-ice models.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_STO.tex

r11598	r11954
205	205	The first four parameters define the stochastic part of equation of state.
206	206
207		\~~onlyinsubfile~~{\input{../../global/epilogue}}
	207	\subinc{\input{../../global/epilogue}}
208	208
209	209	\end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_TRA.tex

-                      r11599
+                      r11954
 {\footnotesize
   \begin{tabularx}{\textwidth}{l||X|X}
     Release & Author(s) & Modifications \\
+    Release          & Author(s)                                   & Modifications       \\
     \hline
+    {\em   4.0} & {\em ...} & {\em ...} \\
+    {\em   3.6} & {\em ...} & {\em ...} \\
+    {\em   3.4} & {\em ...} & {\em ...} \\
+    {\em <=3.4} & {\em ...} & {\em ...}
+    {\em        4.0} & {\em Christian \'{E}th\'{e}               } & {\em Review       } \\
+    {\em        3.6} & {\em Gurvan Madec                         } & {\em Update       } \\
+    {\em $\leq$ 3.4} & {\em Gurvan Madec and S\'{e}bastien Masson} & {\em First version} \\
   \end{tabularx}
+}
 …
 the tracer equations are available depending on the vertical coordinate used and on the physics used.
 In all the equations presented here, the masking has been omitted for simplicity.
 One must be aware that all the quantities are masked fields and that each time a mean or
 difference operator is used, the resulting field is multiplied by a mask.
+One must be aware that all the quantities are masked fields and that
+each time a mean or difference operator is used, the resulting field is multiplied by a mask.
 The two active tracers are potential temperature and salinity.
 …
 NXT stands for next, referring to the time-stepping.
 From left to right, the terms on the rhs of the tracer equations are the advection (ADV),
+the lateral diffusion (LDF), the vertical diffusion (ZDF), the contributions from the external forcings
+(SBC: Surface Boundary Condition, QSR: penetrative Solar Radiation, and BBC: Bottom Boundary Condition),
+the contribution from the bottom boundary Layer (BBL) parametrisation, and an internal damping (DMP) term.
+the lateral diffusion (LDF), the vertical diffusion (ZDF),
+the contributions from the external forcings (SBC: Surface Boundary Condition,
+QSR: penetrative Solar Radiation, and BBC: Bottom Boundary Condition),
+the contribution from the bottom boundary Layer (BBL) parametrisation,
+and an internal damping (DMP) term.
 The terms QSR, BBC, BBL and DMP are optional.
 The external forcings and parameterisations require complex inputs and complex calculations
 …
 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 \path{./src/OCE/TRA} directory as it directly modifies the tracer fields,
+Note that \mdl{tranpc}, the non-penetrative convection module,
+although located in the \path{./src/OCE/TRA} directory as it directly modifies the tracer fields,
 is described with the model vertical physics (ZDF) together with
 other available parameterization of convection.
 In the present chapter we also describe the diagnostic equations used to compute the sea-water properties
+(density, Brunt-V\"{a}is\"{a}l\"{a} frequency, specific heat and freezing point with
 associated modules \mdl{eosbn2} and \mdl{phycst}).
+In the present chapter we also describe the diagnostic equations used to
+compute the sea-water properties (density, Brunt-V\"{a}is\"{a}l\"{a} frequency, specific heat and
+freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}).
 The different options available to the user are managed by namelist logicals.
 …
 The user has the option of extracting each tendency term on the RHS of the tracer equation for output
+(\np{ln_tra_trd}{ln\_tra\_trd} or \np[=.true.]{ln_tra_mxl}{ln\_tra\_mxl}), as described in \autoref{chap:DIA}.
+(\np{ln_tra_trd}{ln\_tra\_trd} or \np[=.true.]{ln_tra_mxl}{ln\_tra\_mxl}),
+as described in \autoref{chap:DIA}.
 %% =================================================================================================
 …
 the advection tendency of a tracer is expressed in flux form,
 \ie\ as the divergence of the advective fluxes.
 Its discrete expression is given by :
+Its discrete expression is given by:
 \begin{equation}
   \label{eq:TRA_adv}
 …
 where $\tau$ is either T or S, and $b_t = e_{1t} \, e_{2t} \, e_{3t}$ is the volume of $T$-cells.
 The flux form in \autoref{eq:TRA_adv} implicitly requires the use of the continuity equation.
+Indeed, it is obtained by using the following equality: $\nabla \cdot (\vect U \, T) = \vect U \cdot \nabla T$ 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, \ie\ \np[=.true.]{ln_linssh}{ln\_linssh}).
+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
+the continuous equations.
+In other words, by setting $\tau = 1$ in (\autoref{eq:TRA_adv}) we recover the discrete form of
+the continuity equation which is used to calculate the vertical velocity.
+\begin{figure}[!t]
+Indeed, it is obtained by using the following equality:
+$\nabla \cdot (\vect U \, T) = \vect U \cdot \nabla T$ 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,
+\ie\ \np[=.true.]{ln_linssh}{ln\_linssh}).
+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 the continuous equations.
+In other words, by setting $\tau = 1$ in (\autoref{eq:TRA_adv}) we recover
+the discrete form of the continuity equation which is used to calculate the vertical velocity.
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_adv_scheme}
+  \includegraphics[width=0.66\textwidth]{TRA_adv_scheme}
   \caption[Ways to evaluate the tracer value and the amount of tracer exchanged]{
     Schematic representation of some ways used to evaluate the tracer value at $u$-point and
 …
 \end{figure}
 The key difference between the advection schemes available in \NEMO\ is the choice made in space and
 time interpolation to define the value of the tracer at the velocity points
+The key difference between the advection schemes available in \NEMO\ is the choice made in
+space and time interpolation to define the value of the tracer at the velocity points
 (\autoref{fig:TRA_adv_scheme}).
 …
 \begin{description}
 \item [linear free surface:] (\np[=.true.]{ln_linssh}{ln\_linssh})
+\item [linear free surface] (\np[=.true.]{ln_linssh}{ln\_linssh})
   the first level thickness is constant in time:
   the vertical boundary condition is applied at the fixed surface $z = 0$ rather than on
   the moving surface $z = \eta$.
   There is a non-zero advective flux which is set for all advection schemes as
   $\tau_w|_{k = 1/2} = T_{k = 1}$, \ie\ the product of surface velocity (at $z = 0$) by
   the first level tracer value.
 \item [non-linear free surface:] (\np[=.false.]{ln_linssh}{ln\_linssh})
+  the vertical boundary condition is applied at the fixed surface $z = 0$ rather than
+  on the moving surface $z = \eta$.
+  There is a non-zero advective flux which is set for
+  all advection schemes as $\tau_w|_{k = 1/2} = T_{k = 1}$,
+  \ie\ the product of surface velocity (at $z = 0$) by the first level tracer value.
+\item [non-linear free surface] (\np[=.false.]{ln_linssh}{ln\_linssh})
   convergence/divergence in the first ocean level moves the free surface up/down.
+  There is no tracer advection through it so that the advective fluxes through the surface are also zero.
+  There is no tracer advection through it so that
+  the advective fluxes through the surface are also zero.
 \end{description}
 In all cases, this boundary condition retains local conservation of tracer.
+Global conservation is obtained in non-linear free surface case, but \textit{not} in the linear free surface case.
+Nevertheless, in the latter case, it is achieved to a good approximation since
+the non-conservative term is the product of the time derivative of the tracer and the free surface height,
+two quantities that are not correlated \citep{roullet.madec_JGR00, griffies.pacanowski.ea_MWR01, campin.adcroft.ea_OM04}.
+Global conservation is obtained in non-linear free surface case,
+but \textit{not} in the linear free surface case.
+Nevertheless, in the latter case,
+it is achieved to a good approximation since the non-conservative term is
+the product of the time derivative of the tracer and the free surface height,
+two quantities that are not correlated
+\citep{roullet.madec_JGR00, griffies.pacanowski.ea_MWR01, campin.adcroft.ea_OM04}.
 The velocity field that appears in (\autoref{eq:TRA_adv} is
 …
 (see \autoref{chap:LDF}).
+Several tracer advection scheme are proposed, namely a $2^{nd}$ or $4^{th}$ order centred schemes (CEN),
+a $2^{nd}$ or $4^{th}$ order Flux Corrected Transport scheme (FCT), a Monotone Upstream Scheme for
+Conservative Laws scheme (MUSCL), a $3^{rd}$ Upstream Biased Scheme (UBS, also often called UP3),
+and a Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms scheme (QUICKEST).
+The choice is made in the \nam{tra_adv}{tra\_adv} namelist, by setting to \forcode{.true.} one of
+the logicals \textit{ln\_traadv\_xxx}.
+The corresponding code can be found in the \textit{traadv\_xxx.F90} module, where
+\textit{xxx} is a 3 or 4 letter acronym corresponding to each scheme.
+By default (\ie\ in the reference namelist, \textit{namelist\_ref}), all the logicals are set to \forcode{.false.}.
+If the user does not select an advection scheme in the configuration namelist (\textit{namelist\_cfg}),
+the tracers will \textit{not} be advected!
+Several tracer advection scheme are proposed,
+namely a $2^{nd}$ or $4^{th}$ order \textbf{CEN}tred schemes (CEN),
+a $2^{nd}$ or $4^{th}$ order \textbf{F}lux \textbf{C}orrected \textbf{T}ransport scheme (FCT),
+a \textbf{M}onotone \textbf{U}pstream \textbf{S}cheme for
+\textbf{C}onservative \textbf{L}aws scheme (MUSCL),
+a $3^{rd}$ \textbf{U}pstream \textbf{B}iased \textbf{S}cheme (UBS, also often called UP3),
+and a \textbf{Q}uadratic \textbf{U}pstream \textbf{I}nterpolation for
+\textbf{C}onvective \textbf{K}inematics with
+\textbf{E}stimated \textbf{S}treaming \textbf{T}erms scheme (QUICKEST).
+The choice is made in the \nam{tra_adv}{tra\_adv} namelist,
+by setting to \forcode{.true.} one of the logicals \textit{ln\_traadv\_xxx}.
+The corresponding code can be found in the \textit{traadv\_xxx.F90} module,
+where \textit{xxx} is a 3 or 4 letter acronym corresponding to each scheme.
+By default (\ie\ in the reference namelist, \textit{namelist\_ref}),
+all the logicals are set to \forcode{.false.}.
+If the user does not select an advection scheme in the configuration namelist
+(\textit{namelist\_cfg}), the tracers will \textit{not} be advected!
 Details of the advection schemes are given below.
+The choosing an advection scheme is a complex matter which depends on the model physics, model resolution,
+type of tracer, as well as the issue of numerical cost. In particular, we note that
+The choosing an advection scheme is a complex matter which depends on the
+model physics, model resolution, type of tracer, as well as the issue of numerical cost.
+In particular, we note that
 \begin{enumerate}
 \item CEN and FCT schemes require an explicit diffusion operator while the other schemes are diffusive enough so that
   they do not necessarily need additional diffusion;
 \item CEN and UBS are not \textit{positive} schemes
   \footnote{negative values can appear in an initially strictly positive tracer field which is advected},
+\item CEN and FCT schemes require an explicit diffusion operator while
+  the other schemes are diffusive enough so that they do not necessarily need additional diffusion;
+\item CEN and UBS are not \textit{positive} schemes \footnote{negative values can appear in
+    an initially strictly positive tracer field which is advected},
   implying that false extrema are permitted.
   Their use is not recommended on passive tracers;
+\item It is recommended that the same advection-diffusion scheme is used on both active and passive tracers.
+\item It is recommended that the same advection-diffusion scheme is used on
+  both active and passive tracers.
 \end{enumerate}
+Indeed, if a source or sink of a passive tracer depends on an active one, the difference of treatment of active and
+passive tracers can create very nice-looking frontal structures that are pure numerical artefacts.
+Indeed, if a source or sink of a passive tracer depends on an active one,
+the difference of treatment of active and passive tracers can create
+very nice-looking frontal structures that are pure numerical artefacts.
 Nevertheless, most of our users set a different treatment on passive and active tracers,
 that's the reason why this possibility is offered.
 We strongly suggest them to perform a sensitivity experiment using a same treatment to assess the robustness of
 their results.
+We strongly suggest them to perform a sensitivity experiment using a same treatment to
+assess the robustness of their results.
 %% =================================================================================================
 …
 %        2nd order centred scheme
+The centred advection scheme (CEN) is used when \np[=.true.]{ln_traadv_cen}{ln\_traadv\_cen}.
+Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by
+The \textbf{CEN}tred advection scheme (CEN) is used when \np[=.true.]{ln_traadv_cen}{ln\_traadv\_cen}.
+Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on
+horizontal (iso-level) and vertical direction by
 setting \np{nn_cen_h}{nn\_cen\_h} and \np{nn_cen_v}{nn\_cen\_v} to $2$ or $4$.
 CEN implementation can be found in the \mdl{traadv\_cen} module.
 In the $2^{nd}$ order centred formulation (CEN2), the tracer at velocity points is evaluated as the mean of
 the two neighbouring $T$-point values.
+In the $2^{nd}$ order centred formulation (CEN2), the tracer at velocity points is evaluated as
+the mean of the two neighbouring $T$-point values.
 For example, in the $i$-direction :
 \begin{equation}
 …
 \end{equation}
+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.
+The associated time-stepping is performed using a leapfrog scheme in conjunction with an Asselin time-filter,
+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.
+The associated time-stepping is performed using
+a leapfrog scheme in conjunction with an Asselin time-filter,
 so $T$ in (\autoref{eq:TRA_adv_cen2}) is the \textit{now} tracer value.
 …
 %        4nd order centred scheme
+In the $4^{th}$ order formulation (CEN4), tracer values are evaluated at u- and v-points as
+a $4^{th}$ order interpolation, and thus depend on the four neighbouring $T$-points.
+In the $4^{th}$ order formulation (CEN4),
+tracer values are evaluated at u- and v-points as a $4^{th}$ order interpolation,
+and thus depend on the four neighbouring $T$-points.
 For example, in the $i$-direction:
 \begin{equation}
 …
 In the vertical direction (\np[=4]{nn_cen_v}{nn\_cen\_v}),
 a $4^{th}$ COMPACT interpolation has been prefered \citep{demange_phd14}.
+In the COMPACT scheme, both the field and its derivative are interpolated, which leads, after a matrix inversion,
+spectral characteristics similar to schemes of higher order \citep{lele_JCP92}.
+In the COMPACT scheme, both the field and its derivative are interpolated,
+which leads, after a matrix inversion, spectral characteristics similar to schemes of higher order
+\citep{lele_JCP92}.
 Strictly speaking, the CEN4 scheme is not a $4^{th}$ order advection scheme but
 a $4^{th}$ order evaluation of advective fluxes,
 since the divergence of advective fluxes \autoref{eq:TRA_adv} is kept at $2^{nd}$ order.
 The expression \textit{$4^{th}$ order scheme} used in oceanographic literature is usually associated with
 the scheme presented here.
 Introducing a \forcode{.true.} $4^{th}$ order advection scheme is feasible but, for consistency reasons,
 it requires changes in the discretisation of the tracer advection together with changes in the continuity equation,
 and the momentum advection and pressure terms.
+The expression \textit{$4^{th}$ order scheme} used in oceanographic literature is
+usually associated with the scheme presented here.
+Introducing a ``true'' $4^{th}$ order advection scheme is feasible but, for consistency reasons,
+it requires changes in the discretisation of the tracer advection together with
+changes in the continuity equation, and the momentum advection and pressure terms.
 A direct consequence of the pseudo-fourth order nature of the scheme is that it is not non-diffusive,
 \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,
+so $T$ in (\autoref{eq:TRA_adv_cen4}) is the \textit{now} tracer.
+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, so $T$ in (\autoref{eq:TRA_adv_cen4}) is the \textit{now} tracer.
 At a $T$-grid cell adjacent to a boundary (coastline, bottom and surface),
 …
 This hypothesis usually reduces the order of the scheme.
 Here we choose to set the gradient of $T$ across the boundary to zero.
 Alternative conditions can be specified, such as a reduction to a second order scheme for
 these near boundary grid points.
+Alternative conditions can be specified,
+such as a reduction to a second order scheme for these near boundary grid points.
 %% =================================================================================================
 …
 \label{subsec:TRA_adv_tvd}
+The Flux Corrected Transport schemes (FCT) is used when \np[=.true.]{ln_traadv_fct}{ln\_traadv\_fct}.
+Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by
+The \textbf{F}lux \textbf{C}orrected \textbf{T}ransport schemes (FCT) is used when
+\np[=.true.]{ln_traadv_fct}{ln\_traadv\_fct}.
+Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on
+horizontal (iso-level) and vertical direction by
 setting \np{nn_fct_h}{nn\_fct\_h} and \np{nn_fct_v}{nn\_fct\_v} to $2$ or $4$.
 FCT implementation can be found in the \mdl{traadv\_fct} module.
 In FCT formulation, the tracer at velocity points is evaluated using a combination of an upstream and
 a centred scheme.
+In FCT formulation, the tracer at velocity points is evaluated using
+a combination of an upstream and a centred scheme.
 For example, in the $i$-direction :
 \begin{equation}
 …
                      T_{i + 1} & \text{if~} u_{i + 1/2} <    0 \\
                      T_i       & \text{if~} u_{i + 1/2} \geq 0 \\
+    \end{cases}
+    \\
+    \end{cases} \\
     \tau_u^{fct} &= \tau_u^{ups} + c_u \, \big( \tau_u^{cen} - \tau_u^{ups} \big)
   \end{split}
 …
 $\tau_u^{cen}$ is evaluated in (\autoref{eq:TRA_adv_fct}) using the \textit{now} tracer while
 $\tau_u^{ups}$ is evaluated using the \textit{before} tracer.
 In other words, the advective part of the scheme is time stepped with a leap-frog scheme
 while a forward scheme is used for the diffusive part.
+In other words, the advective part of the scheme is time stepped with a leap-frog scheme while
+a forward scheme is used for the diffusive part.
 %% =================================================================================================
 …
 \label{subsec:TRA_adv_mus}
+The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np[=.true.]{ln_traadv_mus}{ln\_traadv\_mus}.
+The \textbf{M}onotone \textbf{U}pstream \textbf{S}cheme for \textbf{C}onservative \textbf{L}aws
+(MUSCL) is used when \np[=.true.]{ln_traadv_mus}{ln\_traadv\_mus}.
 MUSCL implementation can be found in the \mdl{traadv\_mus} module.
 MUSCL has been first implemented in \NEMO\ by \citet{levy.estublier.ea_GRL01}.
 In its formulation, the tracer at velocity points is evaluated assuming a linear tracer variation between
 two $T$-points (\autoref{fig:TRA_adv_scheme}).
+In its formulation, the tracer at velocity points is evaluated assuming
+a linear tracer variation between two $T$-points (\autoref{fig:TRA_adv_scheme}).
 For example, in the $i$-direction :
 \begin{equation}
+\[
   % \label{eq:TRA_adv_mus}
   \tau_u^{mus} = \lt\{
   \begin{split}
                        \tau_i         &+ \frac{1}{2} \lt( 1 - \frac{u_{i + 1/2} \, \rdt}{e_{1u}} \rt)
                        \widetilde{\partial_i         \tau} & \text{if~} u_{i + 1/2} \geqslant 0 \\
                        \tau_{i + 1/2} &+ \frac{1}{2} \lt( 1 + \frac{u_{i + 1/2} \, \rdt}{e_{1u}} \rt)
                        \widetilde{\partial_{i + 1/2} \tau} & \text{if~} u_{i + 1/2} <         0
+    \tau_i        &+ \frac{1}{2} \lt( 1 - \frac{u_{i + 1/2} \, \rdt}{e_{1u}} \rt)
+    \widetilde{\partial_i        \tau} & \text{if~} u_{i + 1/2} \geqslant 0 \\
+    \tau_{i + 1/2} &+ \frac{1}{2} \lt( 1 + \frac{u_{i + 1/2} \, \rdt}{e_{1u}} \rt)
+    \widetilde{\partial_{i + 1/2} \tau} & \text{if~} u_{i + 1/2} <         0
   \end{split}
                                                                                                       \rt.
 \end{equation}
 where $\widetilde{\partial_i \tau}$ is the slope of the tracer on which a limitation is imposed to
 ensure the \textit{positive} character of the scheme.
 The time stepping is performed using a forward scheme, that is the \textit{before} tracer field is used to
 evaluate $\tau_u^{mus}$.
+\]
+where $\widetilde{\partial_i \tau}$ is the slope of the tracer on which
+a limitation is imposed to ensure the \textit{positive} character of the scheme.
+The time stepping is performed using a forward scheme,
+that is the \textit{before} tracer field is used to evaluate $\tau_u^{mus}$.
 For an ocean grid point adjacent to land and where the ocean velocity is directed toward land,
 an upstream flux is used.
 This choice ensure the \textit{positive} character of the scheme.
 In addition, fluxes round a grid-point where a runoff is applied can optionally be computed using upstream fluxes
 (\np[=.true.]{ln_mus_ups}{ln\_mus\_ups}).
+In addition, fluxes round a grid-point where a runoff is applied can optionally be computed using
+upstream fluxes (\np[=.true.]{ln_mus_ups}{ln\_mus\_ups}).
 %% =================================================================================================
 …
 \label{subsec:TRA_adv_ubs}
+The Upstream-Biased Scheme (UBS) is used when \np[=.true.]{ln_traadv_ubs}{ln\_traadv\_ubs}.
+The \textbf{U}pstream-\textbf{B}iased \textbf{S}cheme (UBS) is used when
+\np[=.true.]{ln_traadv_ubs}{ln\_traadv\_ubs}.
 UBS implementation can be found in the \mdl{traadv\_mus} module.
 The UBS scheme, often called UP3, is also known as the Cell Averaged QUICK scheme
+(Quadratic Upstream Interpolation for Convective Kinematics).
+(\textbf{Q}uadratic \textbf{U}pstream \textbf{I}nterpolation for
+\textbf{C}onvective \textbf{K}inematics).
 It is an upstream-biased third order scheme based on an upstream-biased parabolic interpolation.
 For example, in the $i$-direction:
 …
   \tau_u^{ubs} = \overline T ^{i + 1/2} - \frac{1}{6}
     \begin{cases}
                                                       \tau"_i       & \text{if~} u_{i + 1/2} \geqslant 0 \\
                                                       \tau"_{i + 1} & \text{if~} u_{i + 1/2} <         0
+      \tau"_i       & \text{if~} u_{i + 1/2} \geqslant 0 \\
+      \tau"_{i + 1} & \text{if~} u_{i + 1/2} <         0
     \end{cases}
+  \quad
+  \text{where~} \tau"_i = \delta_i \lt[ \delta_{i + 1/2} [\tau] \rt]
+  \quad \text{where~} \tau"_i = \delta_i \lt[ \delta_{i + 1/2} [\tau] \rt]
 \end{equation}
 This results in a dissipatively dominant (i.e. hyper-diffusive) truncation error
 \citep{shchepetkin.mcwilliams_OM05}.
+The overall performance of the advection scheme is similar to that reported in \cite{farrow.stevens_JPO95}.
+The overall performance of the advection scheme is similar to that reported in
+\cite{farrow.stevens_JPO95}.
 It is a relatively good compromise between accuracy and smoothness.
 Nevertheless the scheme is not \textit{positive}, meaning that false extrema are permitted,
 but the amplitude of such are significantly reduced over the centred second or fourth order method.
+Therefore it is not recommended that it should be applied to a passive tracer that requires positivity.
+Therefore it is not recommended that it should be applied to
+a passive tracer that requires positivity.
 The intrinsic diffusion of UBS makes its use risky in the vertical direction where
 the control of artificial diapycnal fluxes is of paramount importance
 \citep{shchepetkin.mcwilliams_OM05, demange_phd14}.
 Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme or a $4^th$ order COMPACT scheme
 (\np[=2 or 4]{nn_ubs_v}{nn\_ubs\_v}).
 For stability reasons (see \autoref{chap:TD}), the first term  in \autoref{eq:TRA_adv_ubs}
 (which corresponds to a second order centred scheme)
 is evaluated using the \textit{now} tracer (centred in time) while the second term
 (which is the diffusive part of the scheme),
+Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme or
+a $4^th$ order COMPACT scheme (\np[=2 or 4]{nn_ubs_v}{nn\_ubs\_v}).
+For stability reasons (see \autoref{chap:TD}),
+the first term  in \autoref{eq:TRA_adv_ubs} (which corresponds to a second order centred scheme)
+is evaluated using the \textit{now}    tracer (centred in time) while
+the second term (which is the diffusive part of the scheme),
 is evaluated using the \textit{before} tracer (forward in time).
+This choice is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the QUICK advection scheme.
+This choice is discussed by \citet{webb.de-cuevas.ea_JAOT98} in
+the context of the QUICK advection scheme.
 UBS and QUICK schemes only differ by one coefficient.
+Replacing 1/6 with 1/8 in \autoref{eq:TRA_adv_ubs} leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}.
+Replacing 1/6 with 1/8 in \autoref{eq:TRA_adv_ubs} leads to the QUICK advection scheme
+\citep{webb.de-cuevas.ea_JAOT98}.
 This option is not available through a namelist parameter, since the 1/6 coefficient is hard coded.
+Nevertheless it is quite easy to make the substitution in the \mdl{traadv\_ubs} module and obtain a QUICK scheme.
+Nevertheless it is quite easy to make the substitution in the \mdl{traadv\_ubs} module and
+obtain a QUICK scheme.
 Note that it is straightforward to rewrite \autoref{eq:TRA_adv_ubs} as follows:
 …
 Firstly, it clearly reveals that the UBS scheme is based on the fourth order scheme to which
 an upstream-biased diffusion term is added.
+Secondly, this emphasises that the $4^{th}$ order part (as well as the $2^{nd}$ order part as stated above) has to
+be evaluated at the \textit{now} time step using \autoref{eq:TRA_adv_ubs}.
+Thirdly, the diffusion term is in fact a biharmonic operator with an eddy coefficient which
+is simply proportional to the velocity: $A_u^{lm} = \frac{1}{12} \, {e_{1u}}^3 \, |u|$.
+Note the current version of \NEMO\ uses the computationally more efficient formulation \autoref{eq:TRA_adv_ubs}.
+Secondly,
+this emphasises that the $4^{th}$ order part (as well as the $2^{nd}$ order part as stated above) has to be evaluated at the \textit{now} time step using \autoref{eq:TRA_adv_ubs}.
+Thirdly, the diffusion term is in fact a biharmonic operator with
+an eddy coefficient which is simply proportional to the velocity:
+$A_u^{lm} = \frac{1}{12} \, {e_{1u}}^3 \, |u|$.
+Note the current version of \NEMO\ uses the computationally more efficient formulation
+\autoref{eq:TRA_adv_ubs}.
 %% =================================================================================================
 …
 \label{subsec:TRA_adv_qck}
+The Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms (QUICKEST) scheme
+proposed by \citet{leonard_CMAME79} is used when \np[=.true.]{ln_traadv_qck}{ln\_traadv\_qck}.
+The \textbf{Q}uadratic \textbf{U}pstream \textbf{I}nterpolation for
+\textbf{C}onvective \textbf{K}inematics with \textbf{E}stimated \textbf{S}treaming \textbf{T}erms
+(QUICKEST) scheme proposed by \citet{leonard_CMAME79} is used when
+\np[=.true.]{ln_traadv_qck}{ln\_traadv\_qck}.
 QUICKEST implementation can be found in the \mdl{traadv\_qck} module.
 QUICKEST is the third order Godunov scheme which is associated with the ULTIMATE QUICKEST limiter
 \citep{leonard_CMAME91}.
+It has been implemented in \NEMO\ by G. Reffray (MERCATOR-ocean) and can be found in the \mdl{traadv\_qck} module.
+It has been implemented in \NEMO\ by G. Reffray (Mercator Ocean) and
+can be found in the \mdl{traadv\_qck} module.
 The resulting scheme is quite expensive but \textit{positive}.
 It can be used on both active and passive tracers.
 …
 Therefore the vertical flux is evaluated using the CEN2 scheme.
 This no longer guarantees the positivity of the scheme.
+The use of FCT in the vertical direction (as for the UBS case) should be implemented to restore this property.
+%%%gmcomment   :  Cross term are missing in the current implementation....
+The use of FCT in the vertical direction (as for the UBS case) should be implemented to
+restore this property.
+\cmtgm{Cross term are missing in the current implementation....}
 %% =================================================================================================
 …
 Options are defined through the \nam{tra_ldf}{tra\_ldf} namelist variables.
 They are regrouped in four items, allowing to specify
+$(i)$   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 (\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}.
+\begin{enumerate*}[label=(\textit{\roman*})]
+\item the type of operator used (none, laplacian, bilaplacian),
+\item the direction along which the operator acts (iso-level, horizontal, iso-neutral),
+\item some specific options related to the rotated operators (\ie\ non-iso-level operator), and
+\item the specification of eddy diffusivity coefficient
+  (either constant or variable in space and time).
+\end{enumerate*}
+Item (iv) will be described in \autoref{chap:LDF}.
 The direction along which the operators act is defined through the slope between
 this direction and the iso-level surfaces.
 …
 \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:TD}).
+When \np[=.true.]{ln_traldf_msc}{ln\_traldf\_msc}, a Method of Stabilizing Correction is used in which
+the pure vertical component is split into an explicit and an implicit part \citep{lemarie.debreu.ea_OM12}.
+This latter component is solved implicitly together with the vertical diffusion term
+(see \autoref{chap:TD}).
+When \np[=.true.]{ln_traldf_msc}{ln\_traldf\_msc},
+a Method of Stabilizing Correction is used in which the pure vertical component is split into
+an explicit and an implicit part \citep{lemarie.debreu.ea_OM12}.
 %% =================================================================================================
 …
 \begin{description}
+\item [{\np[=.true.]{ln_traldf_OFF}{ln\_traldf\_OFF}}] no operator selected, the lateral diffusive tendency will not be applied to the tracer equation.
+  This option can be used when the selected advection scheme is diffusive enough (MUSCL scheme for example).
+\item [{\np[=.true.]{ln_traldf_OFF}{ln\_traldf\_OFF}}] no operator selected,
+  the lateral diffusive tendency will not be applied to the tracer equation.
+  This option can be used when the selected advection scheme is diffusive enough
+  (MUSCL scheme for example).
 \item [{\np[=.true.]{ln_traldf_lap}{ln\_traldf\_lap}}] a laplacian operator is selected.
+  This harmonic operator takes the following expression:  $\mathcal{L}(T) = \nabla \cdot A_{ht} \; \nabla T $,
+  This harmonic operator takes the following expression:
+  $\mathcal{L}(T) = \nabla \cdot A_{ht} \; \nabla T $,
   where the gradient operates along the selected direction (see \autoref{subsec:TRA_ldf_dir}),
   and $A_{ht}$ is the eddy diffusivity coefficient expressed in $m^2/s$ (see \autoref{chap:LDF}).
 …
   $\mathcal{B} = - \mathcal{L}(\mathcal{L}(T)) = - \nabla \cdot b \nabla (\nabla \cdot b \nabla T)$
   where the gradient operats along the selected direction,
+  and $b^2 = B_{ht}$ is the eddy diffusivity coefficient expressed in $m^4/s$ (see \autoref{chap:LDF}).
+  and $b^2 = B_{ht}$ is the eddy diffusivity coefficient expressed in $m^4/s$
+  (see \autoref{chap:LDF}).
   In the code, the bilaplacian operator is obtained by calling the laplacian twice.
 \end{description}
 …
 minimizing the impact on the larger scale features.
 The main difference between the two operators is the scale selectiveness.
+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),
+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 choice of a direction of action determines the form of operator used.
 The operator is a simple (re-entrant) laplacian acting in the (\textbf{i},\textbf{j}) plane when
 iso-level option is used (\np[=.true.]{ln_traldf_lev}{ln\_traldf\_lev}) or
 when a horizontal (\ie\ geopotential) operator is demanded in \textit{z}-coordinate
+iso-level option is used (\np[=.true.]{ln_traldf_lev}{ln\_traldf\_lev}) or when
+a horizontal (\ie\ geopotential) operator is demanded in \textit{z}-coordinate
 (\np{ln_traldf_hor}{ln\_traldf\_hor} and \np[=.true.]{ln_zco}{ln\_zco}).
 The associated code can be found in the \mdl{traldf\_lap\_blp} module.
 …
 see \mdl{traldf\_iso} or \mdl{traldf\_triad} module, resp.), or
 when a horizontal (\ie\ geopotential) operator is demanded in \textit{s}-coordinate
 (\np{ln_traldf_hor}{ln\_traldf\_hor} and \np{ln_sco}{ln\_sco} = \forcode{.true.})
 \footnote{In this case, the standard iso-neutral operator will be automatically selected}.
+(\np{ln_traldf_hor}{ln\_traldf\_hor} and \np{ln_sco}{ln\_sco} = \forcode{.true.}) \footnote{
+  In this case, the standard iso-neutral operator will be automatically selected}.
 In that case, a rotation is applied to the gradient(s) that appears in the operator so that
 diffusive fluxes acts on the three spatial direction.
 …
 first (and third in bilaplacian case) horizontal tracer derivative are masked.
 It is implemented in the \rou{tra\_ldf\_lap} subroutine found in the \mdl{traldf\_lap\_blp} module.
+The module also contains \rou{tra\_ldf\_blp}, the subroutine calling twice \rou{tra\_ldf\_lap} in order to
+The module also contains \rou{tra\_ldf\_blp},
+the subroutine calling twice \rou{tra\_ldf\_lap} in order to
 compute the iso-level bilaplacian operator.
 It is a \textit{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}{ln\_traldf\_lap} or \np[=.true.]{ln_traldf_blp}{ln\_traldf\_blp},
+we have \np[=.true.]{ln_traldf_lev}{ln\_traldf\_lev} or \np{ln_traldf_hor}{ln\_traldf\_hor}~=~\np[=.true.]{ln_zco}{ln\_zco}.
+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}{ln\_traldf\_lap} or \np[=.true.]{ln_traldf_blp}{ln\_traldf\_blp},
+we have \np[=.true.]{ln_traldf_lev}{ln\_traldf\_lev} or
+\np[=]{ln_traldf_hor}{ln\_traldf\_hor}\np[=.true.]{ln_zco}{ln\_zco}.
 In both cases, it significantly contributes to diapycnal mixing.
 It is therefore never recommended, even when using it in the bilaplacian case.
 …
 Note that in the partial step $z$-coordinate (\np[=.true.]{ln_zps}{ln\_zps}),
 tracers in horizontally adjacent cells are located at different depths in the vicinity of the bottom.
+In this case, horizontal derivatives in (\autoref{eq:TRA_ldf_lap}) at the bottom level require a specific treatment.
+In this case,
+horizontal derivatives in (\autoref{eq:TRA_ldf_lap}) at the bottom level require a specific treatment.
 They are calculated in the \mdl{zpshde} module, described in \autoref{sec:TRA_zpshde}.
 …
 \subsubsection[Standard rotated (bi-)laplacian operator (\textit{traldf\_iso.F90})]{Standard rotated (bi-)laplacian operator (\protect\mdl{traldf\_iso})}
 \label{subsec:TRA_ldf_iso}
 The general form of the second order lateral tracer subgrid scale physics (\autoref{eq:MB_zdf})
 takes the following semi -discrete space form in $z$- and $s$-coordinates:
+takes the following semi-discrete space form in $z$- and $s$-coordinates:
 \begin{equation}
   \label{eq:TRA_ldf_iso}
 …
 or both \np[=.true.]{ln_traldf_hor}{ln\_traldf\_hor} and \np[=.true.]{ln_zco}{ln\_zco}.
 The way these slopes are evaluated is given in \autoref{sec:LDF_slp}.
+At the surface, bottom and lateral boundaries, the turbulent fluxes of heat and salt are set to zero using
+the mask technique (see \autoref{sec:LBC_coast}).
+At the surface, bottom and lateral boundaries,
+the turbulent fluxes of heat and salt are set to zero using the mask technique
+(see \autoref{sec:LBC_coast}).
 The operator in \autoref{eq:TRA_ldf_iso} involves both lateral and vertical derivatives.
 For numerical stability, the vertical second derivative must be solved using the same implicit time scheme as that
 used in the vertical physics (see \autoref{sec:TRA_zdf}).
+For numerical stability, the vertical second derivative must be solved using
+the same implicit time scheme as that used in the vertical physics (see \autoref{sec:TRA_zdf}).
 For computer efficiency reasons, this term is not computed in the \mdl{traldf\_iso} module,
 but in the \mdl{trazdf} module where, if iso-neutral mixing is used,
+the vertical mixing coefficient is simply increased by $\frac{e_{1w} e_{2w}}{e_{3w}}(r_{1w}^2 + r_{2w}^2)$.
+the vertical mixing coefficient is simply increased by
+$\frac{e_{1w} e_{2w}}{e_{3w}}(r_{1w}^2 + r_{2w}^2)$.
 This formulation conserves the tracer but does not ensure the decrease of the tracer variance.
 Nevertheless the treatment performed on the slopes (see \autoref{chap:LDF}) allows the model to run safely without
 any additional background horizontal diffusion \citep{guilyardi.madec.ea_CD01}.
+Nevertheless the treatment performed on the slopes (see \autoref{chap:LDF}) allows the model to
+run safely without any additional background horizontal diffusion \citep{guilyardi.madec.ea_CD01}.
 Note that in the partial step $z$-coordinate (\np[=.true.]{ln_zps}{ln\_zps}),
+the horizontal derivatives at the bottom level in \autoref{eq:TRA_ldf_iso} require a specific treatment.
+the horizontal derivatives at the bottom level in \autoref{eq:TRA_ldf_iso} require
+a specific treatment.
 They are calculated in module zpshde, described in \autoref{sec:TRA_zpshde}.
 …
 \label{subsec:TRA_ldf_triad}
+An alternative scheme developed by \cite{griffies.gnanadesikan.ea_JPO98} which ensures tracer variance decreases
+is also available in \NEMO\ (\np[=.true.]{ln_traldf_triad}{ln\_traldf\_triad}).
+An alternative scheme developed by \cite{griffies.gnanadesikan.ea_JPO98} which
+ensures tracer variance decreases is also available in \NEMO\
+(\np[=.true.]{ln_traldf_triad}{ln\_traldf\_triad}).
 A complete description of the algorithm is given in \autoref{apdx:TRIADS}.
+The lateral fourth order bilaplacian operator on tracers is obtained by applying (\autoref{eq:TRA_ldf_lap}) twice.
+The lateral fourth order bilaplacian operator on tracers is obtained by
+applying (\autoref{eq:TRA_ldf_lap}) twice.
 The operator requires an additional assumption on boundary conditions:
 both first and third derivative terms normal to the coast are set to zero.
+The lateral fourth order operator formulation on tracers is obtained by applying (\autoref{eq:TRA_ldf_iso}) twice.
+The lateral fourth order operator formulation on tracers is obtained by
+applying (\autoref{eq:TRA_ldf_iso}) twice.
 It requires an additional assumption on boundary conditions:
 first and third derivative terms normal to the coast,
 …
 \label{subsec:TRA_ldf_options}
+\begin{itemize}
+\item \np{ln_traldf_msc}{ln\_traldf\_msc} = Method of Stabilizing Correction (both operators)
+\item \np{rn_slpmax}{rn\_slpmax} = slope limit (both operators)
+\item \np{ln_triad_iso}{ln\_triad\_iso} = pure horizontal mixing in ML (triad only)
+\item \np{rn_sw_triad}{rn\_sw\_triad} $= 1$ switching triad; $= 0$ all 4 triads used (triad only)
+\item \np{ln_botmix_triad}{ln\_botmix\_triad} = lateral mixing on bottom (triad only)
+\end{itemize}
+\begin{labeling}{{\np{ln_botmix_triad}{ln\_botmix\_triad}}}
+\item [{\np{ln_traldf_msc}{ln\_traldf\_msc}    }] Method of Stabilizing Correction (both operators)
+\item [{\np{rn_slpmax}{rn\_slpmax}             }] Slope limit (both operators)
+\item [{\np{ln_triad_iso}{ln\_triad\_iso}      }] Pure horizontal mixing in ML (triad only)
+\item [{\np{rn_sw_triad}{rn\_sw\_triad}        }] \forcode{=1} switching triad;
+  \forcode{= 0} all 4 triads used (triad only)
+\item [{\np{ln_botmix_triad}{ln\_botmix\_triad}}] Lateral mixing on bottom (triad only)
+\end{labeling}
 %% =================================================================================================
 …
 Options are defined through the \nam{zdf}{zdf} namelist variables.
+The formulation of the vertical subgrid scale tracer physics is the same for all the vertical coordinates,
+and is based on a laplacian operator.
+The vertical diffusion operator given by (\autoref{eq:MB_zdf}) takes the following semi -discrete space form:
+\begin{gather*}
+The formulation of the vertical subgrid scale tracer physics is the same for
+all the vertical coordinates, and is based on a laplacian operator.
+The vertical diffusion operator given by (\autoref{eq:MB_zdf}) takes
+the following semi-discrete space form:
+\[
   % \label{eq:TRA_zdf}
     D^{vT}_T = \frac{1}{e_{3t}} \, \delta_k \lt[ \, \frac{A^{vT}_w}{e_{3w}} \delta_{k + 1/2}[T] \, \rt] \\
     D^{vS}_T = \frac{1}{e_{3t}} \; \delta_k \lt[ \, \frac{A^{vS}_w}{e_{3w}} \delta_{k + 1/2}[S] \, \rt]
 \end{gather*}
 where $A_w^{vT}$ and $A_w^{vS}$ are the vertical eddy diffusivity coefficients on temperature and salinity,
 respectively.
+  D^{vT}_T = \frac{1}{e_{3t}} \, \delta_k \lt[ \, \frac{A^{vT}_w}{e_{3w}} \delta_{k + 1/2}[T] \, \rt] \quad
+  D^{vS}_T = \frac{1}{e_{3t}} \; \delta_k \lt[ \, \frac{A^{vS}_w}{e_{3w}} \delta_{k + 1/2}[S] \, \rt]
+\]
+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
 (\ie\ \np[=.true.]{ln_zdfddm}{ln\_zdfddm},).
 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
+$\frac{e_{1w} e_{2w}}{e_{3w} }({r_{1w}^2 + r_{2w}^2})$ to account for the vertical second derivative of
 \autoref{eq:TRA_ldf_iso}.
+Furthermore, when iso-neutral mixing is used,
+both mixing coefficients are increased by $\frac{e_{1w} e_{2w}}{e_{3w} }({r_{1w}^2 + r_{2w}^2})$ to
+account for the vertical second derivative of \autoref{eq:TRA_ldf_iso}.
 At the surface and bottom boundaries, the turbulent fluxes of heat and salt must be specified.
 …
 a geothermal flux forcing is prescribed as a bottom boundary condition (see \autoref{subsec:TRA_bbc}).
 The large eddy coefficient found in the mixed layer together with high vertical resolution implies that
 there would be too restrictive constraint on the time step if we use explicit time stepping.
+The large eddy coefficient found in the mixed layer together with high vertical resolution implies
+that there would be too restrictive constraint on the time step if we use explicit time stepping.
 Therefore an implicit time stepping is preferred for the vertical diffusion since
 it overcomes the stability constraint.
 …
 Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components
+(\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
+(\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.
 They are both included directly in $Q_{ns}$, the surface heat flux,
 and $F_{salt}$, the surface salt flux (see \autoref{chap:SBC} for further details).
+By doing this, the forcing formulation is the same for any tracer (including temperature and salinity).
+The surface module (\mdl{sbcmod}, see \autoref{chap:SBC}) provides the following forcing fields (used on tracers):
+\begin{itemize}
+\item $Q_{ns}$, the non-solar part of the net surface heat flux that crosses the sea surface
+  (\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})
+By doing this, the forcing formulation is the same for any tracer
+(including temperature and salinity).
+The surface module (\mdl{sbcmod}, see \autoref{chap:SBC}) provides the following forcing fields
+(used on tracers):
+\begin{labeling}{\textit{fwfisf}}
+\item [$Q_{ns}$] The non-solar part of the net surface heat flux that crosses the sea surface
+  (\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.
+\item $\textit{sfx}$, the salt flux resulting from ice-ocean mass exchange (freezing, melting, ridging...)
+\item \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
+\item [\textit{sfx}] The salt flux resulting from ice-ocean mass exchange
+  (freezing, melting, ridging...)
+\item [\textit{emp}] The mass flux exchanged with the atmosphere (evaporation minus precipitation) and
   possibly with the sea-ice and ice-shelves.
 \item \textit{rnf}, the mass flux associated with runoff
+\item [\textit{rnf}] The mass flux associated with runoff
   (see \autoref{sec:SBC_rnf} for further detail of how it acts on temperature and salinity tendencies)
 \item \textit{fwfisf}, the mass flux associated with ice shelf melt,
+\item [\textit{fwfisf}] The mass flux associated with ice shelf melt,
   (see \autoref{sec:SBC_isf} for further details on how the ice shelf melt is computed and applied).
 \end{itemize}
+\end{labeling}
 The surface boundary condition on temperature and salinity is applied as follows:
 \begin{equation}
   \label{eq:TRA_sbc}
+  \begin{alignedat}{2}
+    F^T &= \frac{1}{C_p} &\frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}} &\overline{Q_{ns}      }^t \\
+    F^S &=               &\frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}} &\overline{\textit{sfx}}^t
+  \end{alignedat}
+    F^T = \frac{1}{C_p} \frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}} \overline{Q_{ns}      }^t \qquad
+    F^S =               \frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}} \overline{\textit{sfx}}^t
 \end{equation}
 where $\overline x^t$ means that $x$ is averaged over two consecutive time steps
 …
 Such time averaging prevents the divergence of odd and even time step (see \autoref{chap:TD}).
+In the linear free surface case (\np[=.true.]{ln_linssh}{ln\_linssh}), an additional term has to be added on
+both temperature and salinity.
+On temperature, this term remove the heat content associated with mass exchange that has been added to $Q_{ns}$.
+On salinity, this term mimics the concentration/dilution effect that would have resulted from a change in
+the volume of the first level.
+In the linear free surface case (\np[=.true.]{ln_linssh}{ln\_linssh}),
+an additional term has to be added on both temperature and salinity.
+On temperature, this term remove the heat content associated with
+mass exchange that has been added to $Q_{ns}$.
+On salinity, this term mimics the concentration/dilution effect that would have resulted from
+a change in the volume of the first level.
 The resulting surface boundary condition is applied as follows:
 \begin{equation}
   \label{eq:TRA_sbc_lin}
+  \begin{alignedat}{2}
+    F^T &= \frac{1}{C_p} &\frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}}
+          &\overline{(Q_{ns}       - C_p \, \textit{emp} \lt. T \rt|_{k = 1})}^t \\
+    F^S &=               &\frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}}
+          &\overline{(\textit{sfx} -        \textit{emp} \lt. S \rt|_{k = 1})}^t
+  \end{alignedat}
+\end{equation}
+Note that an exact conservation of heat and salt content is only achieved with non-linear free surface.
+    F^T = \frac{1}{C_p} \frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}}
+          \overline{(Q_{ns}       - C_p \, \textit{emp} \lt. T \rt|_{k = 1})}^t \qquad
+    F^S =               \frac{1}{\rho_o \lt. e_{3t} \rt|_{k = 1}}
+          \overline{(\textit{sfx} -        \textit{emp} \lt. S \rt|_{k = 1})}^t
+\end{equation}
+Note that an exact conservation of heat and salt content is only achieved with
+non-linear free surface.
 In the linear free surface case, there is a small imbalance.
+The imbalance is larger than the imbalance associated with the Asselin time filter \citep{leclair.madec_OM09}.
+This is the reason why the modified filter is not applied in the linear free surface case (see \autoref{chap:TD}).
+The imbalance is larger than the imbalance associated with the Asselin time filter
+\citep{leclair.madec_OM09}.
+This is the reason why the modified filter is not applied in the linear free surface case
+(see \autoref{chap:TD}).
 %% =================================================================================================
 …
 When the penetrative solar radiation option is used (\np[=.true.]{ln_traqsr}{ln\_traqsr}),
 the solar radiation penetrates the top few tens of meters of the ocean.
+If it is not used (\np[=.false.]{ln_traqsr}{ln\_traqsr}) all the heat flux is absorbed in the first ocean level.
+Thus, in the former case a term is added to the time evolution equation of temperature \autoref{eq:MB_PE_tra_T} and
+the surface boundary condition is modified to take into account only the non-penetrative part of the surface
+heat flux:
+If it is not used (\np[=.false.]{ln_traqsr}{ln\_traqsr}) all the heat flux is absorbed in
+the first ocean level.
+Thus, in the former case a term is added to the time evolution equation of temperature
+\autoref{eq:MB_PE_tra_T} and the surface boundary condition is modified to
+take into account only the non-penetrative part of the surface heat flux:
 \begin{equation}
   \label{eq:TRA_PE_qsr}
 …
 The shortwave radiation, $Q_{sr}$, consists of energy distributed across a wide spectral range.
 The ocean is strongly absorbing for wavelengths longer than 700~nm and these wavelengths contribute to
 heating the upper few tens of centimetres.
 The fraction of $Q_{sr}$ that resides in these almost non-penetrative wavebands, $R$, is $\sim 58\%$
+The ocean is strongly absorbing for wavelengths longer than 700 $nm$ and
+these wavelengths contribute to heat the upper few tens of centimetres.
+The fraction of $Q_{sr}$ that resides in these almost non-penetrative wavebands, $R$, is $\sim$ 58\%
 (specified through namelist parameter \np{rn_abs}{rn\_abs}).
+It is assumed to penetrate the ocean with a decreasing exponential profile, with an e-folding depth scale, $\xi_0$,
+of a few tens of centimetres (typically $\xi_0 = 0.35~m$ set as \np{rn_si0}{rn\_si0} in the \nam{tra_qsr}{tra\_qsr} namelist).
+For shorter wavelengths (400-700~nm), the ocean is more transparent, and solar energy propagates to
+larger depths where it contributes to local heating.
+The way this second part of the solar energy penetrates into the ocean depends on which formulation is chosen.
+It is assumed to penetrate the ocean with a decreasing exponential profile,
+with an e-folding depth scale, $\xi_0$, of a few tens of centimetres
+(typically $\xi_0 = 0.35~m$ set as \np{rn_si0}{rn\_si0} in the \nam{tra_qsr}{tra\_qsr} namelist).
+For shorter wavelengths (400-700 $nm$), the ocean is more transparent,
+and solar energy propagates to larger depths where it contributes to local heating.
+The way this second part of the solar energy penetrates into
+the ocean depends on which formulation is chosen.
 In the simple 2-waveband light penetration scheme (\np[=.true.]{ln_qsr_2bd}{ln\_qsr\_2bd})
 a chlorophyll-independent monochromatic formulation is chosen for the shorter wavelengths,
 …
 where $\xi_1$ is the second extinction length scale associated with the shorter wavelengths.
 It is usually chosen to be 23~m by setting the \np{rn_si0}{rn\_si0} namelist parameter.
 The set of default values ($\xi_0, \xi_1, R$) corresponds to a Type I water in Jerlov's (1968) classification
 (oligotrophic waters).
+The set of default values ($\xi_0, \xi_1, R$) corresponds to
+a Type I water in Jerlov's (1968) classification (oligotrophic waters).
 Such assumptions have been shown to provide a very crude and simplistic representation of
 …
 a 61 waveband formulation.
 Unfortunately, such a model is very computationally expensive.
+Thus, \cite{lengaigne.menkes.ea_CD07} have constructed a simplified version of this formulation in which
+visible light is split into three wavebands: blue (400-500 nm), green (500-600 nm) and red (600-700nm).
+For each wave-band, the chlorophyll-dependent attenuation coefficient is fitted to the coefficients computed from
+the full spectral model of \cite{morel_JGR88} (as modified by \cite{morel.maritorena_JGR01}),
+assuming the same power-law relationship.
+As shown in \autoref{fig:TRA_qsr_irradiance}, this formulation, called RGB (Red-Green-Blue),
+Thus, \cite{lengaigne.menkes.ea_CD07} have constructed a simplified version of
+this formulation in which visible light is split into three wavebands:
+blue (400-500 $nm$), green (500-600 $nm$) and red (600-700 $nm$).
+For each wave-band, the chlorophyll-dependent attenuation coefficient is fitted to
+the coefficients computed from the full spectral model of \cite{morel_JGR88}
+(as modified by \cite{morel.maritorena_JGR01}), assuming the same power-law relationship.
+As shown in \autoref{fig:TRA_qsr_irradiance}, this formulation,
+called RGB (\textbf{R}ed-\textbf{G}reen-\textbf{B}lue),
 reproduces quite closely the light penetration profiles predicted by the full spectal model,
 but with much greater computational efficiency.
 …
 The RGB formulation is used when \np[=.true.]{ln_qsr_rgb}{ln\_qsr\_rgb}.
 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
+The RGB attenuation coefficients (\ie\ the inverses of the extinction length scales) are
+tabulated over 61 nonuniform chlorophyll classes ranging from 0.01 to 10 $g.Chl/L$
 (see the routine \rou{trc\_oce\_rgb} in \mdl{trc\_oce} module).
 Four types of chlorophyll can be chosen in the RGB formulation:
 \begin{description}
+\item [{\np[=0]{nn_chldta}{nn\_chldta}}] a constant 0.05 g.Chl/L value everywhere ;
+\item [{\np[=1]{nn_chldta}{nn\_chldta}}] an observed time varying chlorophyll deduced from satellite surface ocean color measurement spread uniformly in the vertical direction;
+\item [{\np[=2]{nn_chldta}{nn\_chldta}}] same as previous case except that a vertical profile of chlorophyl is used.
+  Following \cite{morel.berthon_LO89}, the profile is computed from the local surface chlorophyll value;
+\item [{\np[=.true.]{ln_qsr_bio}{ln\_qsr\_bio}}] simulated time varying chlorophyll by TOP biogeochemical model.
+  In this case, the RGB formulation is used to calculate both the phytoplankton light limitation in
+  PISCES and the oceanic heating rate.
+\item [{\np[=0]{nn_chldta}{nn\_chldta}}] a constant 0.05 $g.Chl/L$ value everywhere;
+\item [{\np[=1]{nn_chldta}{nn\_chldta}}] an observed time varying chlorophyll deduced from
+  satellite surface ocean color measurement spread uniformly in the vertical direction;
+\item [{\np[=2]{nn_chldta}{nn\_chldta}}] same as previous case except that
+  a vertical profile of chlorophyl is used.
+  Following \cite{morel.berthon_LO89},
+  the profile is computed from the local surface chlorophyll value;
+\item [{\np[=.true.]{ln_qsr_bio}{ln\_qsr\_bio}}] simulated time varying chlorophyll by
+  \TOP\ biogeochemical model.
+  In this case, the RGB formulation is used to calculate both
+  the phytoplankton light limitation in \PISCES\ and the oceanic heating rate.
 \end{description}
 …
 (\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.
+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
 (\ie\ $I$ is masked).
 \begin{figure}[!t]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_TRA_Irradiance}
+  \includegraphics[width=0.66\textwidth]{TRA_Irradiance}
   \caption[Penetration profile of the downward solar irradiance calculated by four models]{
     Penetration profile of the downward solar irradiance calculated by four models.
 …
 waveband RGB formulation (red),
 waveband Morel (1988) formulation (black) for a chlorophyll concentration of
     (a) Chl=0.05 mg/m$^3$ and (b) Chl=0.5 mg/m$^3$.
+    (a) Chl=0.05 $mg/m^3$ and (b) Chl=0.5 $mg/m^3$.
     From \citet{lengaigne.menkes.ea_CD07}.}
   \label{fig:TRA_qsr_irradiance}
 …
   \label{lst:nambbc}
 \end{listing}
+\begin{figure}[!t]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_TRA_geoth}
+  \includegraphics[width=0.66\textwidth]{TRA_geoth}
   \caption[Geothermal heat flux]{
     Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{emile-geay.madec_OS09}.
 …
 \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.
+This flux is weak compared to surface fluxes (a mean global value of $\sim 0.1 \, W/m^2$ \citep{stein.stein_N92}),
+However, there is a non-zero heat flux across the seafloor that
+is associated with solid earth cooling.
+This flux is weak compared to surface fluxes
+(a mean global value of $\sim 0.1 \, W/m^2$ \citep{stein.stein_N92}),
 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
+(\ie\ 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 \nam{bbc}{bbc} namelist variables.
+The presence of geothermal heating is controlled by setting the namelist parameter \np{ln_trabbc}{ln\_trabbc} to true.
+Then, when \np{nn_geoflx}{nn\_geoflx} is set to 1, a constant geothermal heating is introduced whose value is given by
+the \np{rn_geoflx_cst}{rn\_geoflx\_cst}, which is also a namelist parameter.
+When \np{nn_geoflx}{nn\_geoflx} is set to 2, a spatially varying geothermal heat flux is introduced which is provided in
+the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:TRA_geothermal}) \citep{emile-geay.madec_OS09}.
+The presence of geothermal heating is controlled by
+setting the namelist parameter \np{ln_trabbc}{ln\_trabbc} to true.
+Then, when \np{nn_geoflx}{nn\_geoflx} is set to 1, a constant geothermal heating is introduced whose
+value is given by the \np{rn_geoflx_cst}{rn\_geoflx\_cst}, which is also a namelist parameter.
+When \np{nn_geoflx}{nn\_geoflx} is set to 2,
+a spatially varying geothermal heat flux is introduced which is provided in
+the \ifile{geothermal\_heating} NetCDF file
+(\autoref{fig:TRA_geothermal}) \citep{emile-geay.madec_OS09}.
 %% =================================================================================================
 …
 where dense water formed in marginal seas flows into a basin filled with less dense water,
 or along the continental slope when dense water masses are formed on a continental shelf.
+The amount of entrainment that occurs in these gravity plumes is critical in determining the density and
+volume flux of the densest waters of the ocean, such as Antarctic Bottom Water, or North Atlantic Deep Water.
+The amount of entrainment that occurs in these gravity plumes is critical in
+determining the density and volume flux of the densest waters of the ocean,
+such as Antarctic Bottom Water, or North Atlantic Deep Water.
 $z$-coordinate models tend to overestimate the entrainment,
+because the gravity flow is mixed vertically by convection as it goes ''downstairs'' following the step topography,
+because the gravity flow is mixed vertically by convection as
+it goes ''downstairs'' following the step topography,
 sometimes over a thickness much larger than the thickness of the observed gravity plume.
+A similar problem occurs in the $s$-coordinate when the thickness of the bottom level varies rapidly downstream of
+a sill \citep{willebrand.barnier.ea_PO01}, and the thickness of the plume is not resolved.
+The idea of the bottom boundary layer (BBL) parameterisation, first introduced by \citet{beckmann.doscher_JPO97},
+A similar problem occurs in the $s$-coordinate when
+the thickness of the bottom level varies rapidly downstream of a sill
+\citep{willebrand.barnier.ea_PO01}, and the thickness of the plume is not resolved.
+The idea of the bottom boundary layer (BBL) parameterisation, first introduced by
+\citet{beckmann.doscher_JPO97},
 is to allow a direct communication between two adjacent bottom cells at different levels,
 whenever the densest water is located above the less dense water.
+The communication can be by a diffusive flux (diffusive BBL), an advective flux (advective BBL), or both.
+The communication can be by a diffusive flux (diffusive BBL),
+an advective flux (advective BBL), or both.
 In the current implementation of the BBL, only the tracers are modified, not the velocities.
 Furthermore, it only connects ocean bottom cells, and therefore does not include all the improvements introduced by
 \citet{campin.goosse_T99}.
+Furthermore, it only connects ocean bottom cells,
+and therefore does not include all the improvements introduced by \citet{campin.goosse_T99}.
 %% =================================================================================================
 …
 \label{subsec:TRA_bbl_diff}
+When applying sigma-diffusion (\np[=.true.]{ln_trabbl}{ln\_trabbl} and \np{nn_bbl_ldf}{nn\_bbl\_ldf} set to 1),
+When applying sigma-diffusion
+(\np[=.true.]{ln_trabbl}{ln\_trabbl} and \np{nn_bbl_ldf}{nn\_bbl\_ldf} set to 1),
 the diffusive flux between two adjacent cells at the ocean floor is given by
 \[
 …
   \vect F_\sigma = A_l^\sigma \, \nabla_\sigma T
 \]
 with $\nabla_\sigma$ the lateral gradient operator taken between bottom cells, and
 $A_l^\sigma$ the lateral diffusivity in the BBL.
+with $\nabla_\sigma$ the lateral gradient operator taken between bottom cells,
+and $A_l^\sigma$ the lateral diffusivity in the BBL.
 Following \citet{beckmann.doscher_JPO97}, the latter is prescribed with a spatial dependence,
 \ie\ in the conditional form
 …
       \begin{cases}
         A_{bbl} & \text{if~} \nabla_\sigma \rho \cdot \nabla H < 0 \\
+        \\
+      & \text{otherwise} \\
+      & \text{otherwise}
       \end{cases}
 \end{equation}
+where $A_{bbl}$ is the BBL diffusivity coefficient, given by the namelist parameter \np{rn_ahtbbl}{rn\_ahtbbl} and
+where $A_{bbl}$ is the BBL diffusivity coefficient,
+given by the namelist parameter \np{rn_ahtbbl}{rn\_ahtbbl} and
 usually set to a value much larger than the one used for lateral mixing in the open ocean.
 The constraint in \autoref{eq:TRA_bbl_coef} implies that sigma-like diffusion only occurs when
 …
   \nabla_\sigma \rho / \rho = \alpha \, \nabla_\sigma T + \beta \, \nabla_\sigma S
 \]
+where $\rho$, $\alpha$ and $\beta$ are functions of $\overline T^\sigma$, $\overline S^\sigma$ and
+$\overline H^\sigma$, the along bottom mean temperature, salinity and depth, respectively.
+where $\rho$, $\alpha$ and $\beta$ are functions of
+$\overline T^\sigma$, $\overline S^\sigma$ and $\overline H^\sigma$,
+the along bottom mean temperature, salinity and depth, respectively.
 %% =================================================================================================
 …
 %}
 \begin{figure}[!t]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_BBL_adv}
+  \includegraphics[width=0.33\textwidth]{TRA_BBL_adv}
   \caption[Advective/diffusive bottom boundary layer]{
     Advective/diffusive Bottom Boundary Layer.
 …
 %!!        i.e. transport proportional to the along-slope density gradient
+%%%gmcomment   :  this section has to be really written
+When applying an advective BBL (\np[=1..2]{nn_bbl_adv}{nn\_bbl\_adv}), an overturning circulation is added which
+connects two adjacent bottom grid-points only if dense water overlies less dense water on the slope.
+\cmtgm{This section has to be really written}
+When applying an advective BBL (\np[=1..2]{nn_bbl_adv}{nn\_bbl\_adv}),
+an overturning circulation is added which connects two adjacent bottom grid-points only if
+dense water overlies less dense water on the slope.
 The density difference causes dense water to move down the slope.
+\np[=1]{nn_bbl_adv}{nn\_bbl\_adv}:
+the downslope velocity is chosen to be the Eulerian ocean velocity just above the topographic step
+(see black arrow in \autoref{fig:TRA_bbl}) \citep{beckmann.doscher_JPO97}.
+It is a \textit{conditional advection}, that is, advection is allowed only
+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[=2]{nn_bbl_adv}{nn\_bbl\_adv}:
+the downslope velocity is chosen to be proportional to $\Delta \rho$,
+the density difference between the higher cell and lower cell densities \citep{campin.goosse_T99}.
+The advection is allowed only  if dense water overlies less dense water on the slope
+(\ie\ $\nabla_\sigma \rho \cdot \nabla H < 0$).
+For example, the resulting transport of the downslope flow, here in the $i$-direction (\autoref{fig:TRA_bbl}),
+is simply given by the following expression:
+\[
+  % \label{eq:TRA_bbl_Utr}
+  u^{tr}_{bbl} = \gamma g \frac{\Delta \rho}{\rho_o} e_{1u} \, min ({e_{3u}}_{kup},{e_{3u}}_{kdwn})
+\]
+where $\gamma$, expressed in seconds, is the coefficient of proportionality provided as \np{rn_gambbl}{rn\_gambbl},
+a namelist parameter, and \textit{kup} and \textit{kdwn} are the vertical index of the higher and lower cells,
+respectively.
+The parameter $\gamma$ should take a different value for each bathymetric step, but for simplicity,
+and because no direct estimation of this parameter is available, a uniform value has been assumed.
+The possible values for $\gamma$ range between 1 and $10~s$ \citep{campin.goosse_T99}.
+Scalar properties are advected by this additional transport $(u^{tr}_{bbl},v^{tr}_{bbl})$ using the upwind scheme.
+Such a diffusive advective scheme has been chosen to mimic the entrainment between the downslope plume and
+the surrounding water at intermediate depths.
+\begin{description}
+\item [{\np[=1]{nn_bbl_adv}{nn\_bbl\_adv}}] the downslope velocity is chosen to
+  be the Eulerian ocean velocity just above the topographic step
+  (see black arrow in \autoref{fig:TRA_bbl}) \citep{beckmann.doscher_JPO97}.
+  It is a \textit{conditional advection}, that is,
+  advection is allowed only 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\ $\vect U \cdot \nabla H > 0$).
+\item [{\np[=2]{nn_bbl_adv}{nn\_bbl\_adv}}] the downslope velocity is chosen to be proportional to
+  $\Delta \rho$, the density difference between the higher cell and lower cell densities
+  \citep{campin.goosse_T99}.
+  The advection is allowed only  if dense water overlies less dense water on the slope
+  (\ie\ $\nabla_\sigma \rho \cdot \nabla H < 0$).
+  For example, the resulting transport of the downslope flow, here in the $i$-direction
+  (\autoref{fig:TRA_bbl}), is simply given by the following expression:
+  \[
+    % \label{eq:TRA_bbl_Utr}
+    u^{tr}_{bbl} = \gamma g \frac{\Delta \rho}{\rho_o} e_{1u} \, min ({e_{3u}}_{kup},{e_{3u}}_{kdwn})
+  \]
+  where $\gamma$, expressed in seconds, is the coefficient of proportionality provided as
+  \np{rn_gambbl}{rn\_gambbl}, a namelist parameter, and
+  \textit{kup} and \textit{kdwn} are the vertical index of the higher and lower cells, respectively.
+  The parameter $\gamma$ should take a different value for each bathymetric step, but for simplicity,
+  and because no direct estimation of this parameter is available, a uniform value has been assumed.
+  The possible values for $\gamma$ range between 1 and $10~s$ \citep{campin.goosse_T99}.
+\end{description}
+Scalar properties are advected by this additional transport $(u^{tr}_{bbl},v^{tr}_{bbl})$ using
+the upwind scheme.
+Such a diffusive advective scheme has been chosen to mimic the entrainment between
+the downslope plume and the surrounding water at intermediate depths.
 The entrainment is replaced by the vertical mixing implicit in the advection scheme.
 Let us consider as an example the case displayed in \autoref{fig:TRA_bbl} where
 the density at level $(i,kup)$ is larger than the one at level $(i,kdwn)$.
 The advective BBL scheme modifies the tracer time tendency of the ocean cells near the topographic step by
 the downslope flow \autoref{eq:TRA_bbl_dw}, the horizontal \autoref{eq:TRA_bbl_hor} and
 the upward \autoref{eq:TRA_bbl_up} return flows as follows:
 \begin{alignat}{3}
+The advective BBL scheme modifies the tracer time tendency of
+the ocean cells near the topographic step by the downslope flow \autoref{eq:TRA_bbl_dw},
+the horizontal \autoref{eq:TRA_bbl_hor} and the upward \autoref{eq:TRA_bbl_up} return flows as follows:
+\begin{alignat}{5}
   \label{eq:TRA_bbl_dw}
+  \partial_t T^{do}_{kdw} &\equiv \partial_t T^{do}_{kdw}
+                                &&+ \frac{u^{tr}_{bbl}}{{b_t}^{do}_{kdw}} &&\lt( T^{sh}_{kup} - T^{do}_{kdw} \rt) \\
+  \partial_t T^{do}_{kdw} &\equiv \partial_t T^{do}_{kdw} &&+ \frac{u^{tr}_{bbl}}{{b_t}^{do}_{kdw}} &&\lt( T^{sh}_{kup} - T^{do}_{kdw} \rt) \\
   \label{eq:TRA_bbl_hor}
+  \partial_t T^{sh}_{kup} &\equiv \partial_t T^{sh}_{kup}
+                                &&+ \frac{u^{tr}_{bbl}}{{b_t}^{sh}_{kup}} &&\lt( T^{do}_{kup} - T^{sh}_{kup} \rt) \\
+  %
+  \intertext{and for $k =kdw-1,\;..., \; kup$ :}
+  %
+  \partial_t T^{sh}_{kup} &\equiv \partial_t T^{sh}_{kup} &&+ \frac{u^{tr}_{bbl}}{{b_t}^{sh}_{kup}} &&\lt( T^{do}_{kup} - T^{sh}_{kup} \rt) \\
+  \shortintertext{and for $k =kdw-1,\;..., \; kup$ :}
   \label{eq:TRA_bbl_up}
+  \partial_t T^{do}_{k} &\equiv \partial_t S^{do}_{k}
+                                &&+ \frac{u^{tr}_{bbl}}{{b_t}^{do}_{k}}   &&\lt( T^{do}_{k +1} - T^{sh}_{k}   \rt)
+  \partial_t T^{do}_{k}   &\equiv \partial_t S^{do}_{k}   &&+ \frac{u^{tr}_{bbl}}{{b_t}^{do}_{k}}   &&\lt( T^{do}_{k +1} - T^{sh}_{k}   \rt)
 \end{alignat}
 where $b_t$ is the $T$-cell volume.
 …
 \end{listing}
+In some applications it can be useful to add a Newtonian damping term into the temperature and salinity equations:
+In some applications it can be useful to add a Newtonian damping term into
+the temperature and salinity equations:
 \begin{equation}
   \label{eq:TRA_dmp}
+  \begin{gathered}
+    \pd[T]{t} = \cdots - \gamma (T - T_o) \\
+    \pd[S]{t} = \cdots - \gamma (S - S_o)
+  \end{gathered}
+\end{equation}
+where $\gamma$ is the inverse of a time scale, and $T_o$ and $S_o$ are given temperature and salinity fields
+(usually a climatology).
+Options are defined through the  \nam{tra_dmp}{tra\_dmp} namelist variables.
+    \pd[T]{t} = \cdots - \gamma (T - T_o) \qquad \pd[S]{t} = \cdots - \gamma (S - S_o)
+\end{equation}
+where $\gamma$ is the inverse of a time scale,
+and $T_o$ and $S_o$ are given temperature and salinity fields (usually a climatology).
+Options are defined through the \nam{tra_dmp}{tra\_dmp} namelist variables.
 The restoring term is added when the namelist parameter \np{ln_tradmp}{ln\_tradmp} is set to true.
+It also requires that both \np{ln_tsd_init}{ln\_tsd\_init} and \np{ln_tsd_dmp}{ln\_tsd\_dmp} are set to true in
+\nam{tsd}{tsd} namelist as well as \np{sn_tem}{sn\_tem} and \np{sn_sal}{sn\_sal} structures are correctly set
+It also requires that both \np{ln_tsd_init}{ln\_tsd\_init} and
+\np{ln_tsd_dmp}{ln\_tsd\_dmp} are set to true in \nam{tsd}{tsd} namelist as well as
+\np{sn_tem}{sn\_tem} and \np{sn_sal}{sn\_sal} structures are correctly set
 (\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.
+The restoring coefficient $\gamma$ is a three-dimensional array read in during
+the \rou{tra\_dmp\_init} routine.
 The file name is specified by the namelist variable \np{cn_resto}{cn\_resto}.
 The DMP\_TOOLS tool is provided to allow users to generate the netcdf file.
+The \texttt{DMP\_TOOLS} are provided to allow users to generate the netcdf file.
 The two main cases in which \autoref{eq:TRA_dmp} is used are
+\textit{(a)} the specification of the boundary conditions along artificial walls of a limited domain basin and
+\textit{(b)} the computation of the velocity field associated with a given $T$-$S$ field
+(for example to build the initial state of a prognostic simulation,
+or to use the resulting velocity field for a passive tracer study).
+\begin{enumerate*}[label=(\textit{\alph*})]
+\item the specification of the boundary conditions along
+  artificial walls of a limited domain basin and
+\item the computation of the velocity field associated with a given $T$-$S$ field
+  (for example to build the initial state of a prognostic simulation,
+  or to use the resulting velocity field for a passive tracer study).
+\end{enumerate*}
 The first case applies to regional models that have artificial walls instead of open boundaries.
 In the vicinity of these walls, $\gamma$ takes large values (equivalent to a time scale of a few days) whereas
 it is zero in the interior of the model domain.
+In the vicinity of these walls, $\gamma$ takes large values (equivalent to a time scale of a few days)
+whereas it is zero in the interior of the model domain.
 The second case corresponds to the use of the robust diagnostic method \citep{sarmiento.bryan_JGR82}.
 It allows us to find the velocity field consistent with the model dynamics whilst
 having a $T$, $S$ field close to a given climatological field ($T_o$, $S_o$).
 The robust diagnostic method is very efficient in preventing temperature drift in intermediate waters but
 it produces artificial sources of heat and salt within the ocean.
+The robust diagnostic method is very efficient in preventing temperature drift in
+intermediate waters but it produces artificial sources of heat and salt within the ocean.
 It also has undesirable effects on the ocean convection.
+It tends to prevent deep convection and subsequent deep-water formation, by stabilising the water column too much.
+The namelist parameter \np{nn_zdmp}{nn\_zdmp} sets whether the damping should be applied in the whole water column or
+only below the mixed layer (defined either on a density or $S_o$ criterion).
+It tends to prevent deep convection and subsequent deep-water formation,
+by stabilising the water column too much.
+The namelist parameter \np{nn_zdmp}{nn\_zdmp} sets whether the damping should be applied in
+the whole water column or only below the mixed layer (defined either on a density or $S_o$ criterion).
 It is common to set the damping to zero in the mixed layer as the adjustment time scale is short here
 \citep{madec.delecluse.ea_JPO96}.
 For generating \ifile{resto}, see the documentation for the DMP tool provided with the source code under
 \path{./tools/DMP_TOOLS}.
+For generating \ifile{resto},
+see the documentation for the DMP tools provided with the source code under \path{./tools/DMP_TOOLS}.
 %% =================================================================================================
 …
 Options are defined through the \nam{dom}{dom} namelist variables.
+The general framework for tracer time stepping is a modified leap-frog scheme \citep{leclair.madec_OM09},
+\ie\ a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:TD_mLF}):
+The general framework for tracer time stepping is a modified leap-frog scheme
+\citep{leclair.madec_OM09}, \ie\ a three level centred time scheme associated with
+a Asselin time filter (cf. \autoref{sec:TD_mLF}):
 \begin{equation}
   \label{eq:TRA_nxt}
   \begin{alignedat}{3}
+  \begin{alignedat}{5}
     &(e_{3t}T)^{t + \rdt} &&= (e_{3t}T)_f^{t - \rdt} &&+ 2 \, \rdt \,e_{3t}^t \ \text{RHS}^t \\
     &(e_{3t}T)_f^t        &&= (e_{3t}T)^t            &&+ \, \gamma \, \lt[ (e_{3t}T)_f^{t - \rdt} - 2(e_{3t}T)^t + (e_{3t}T)^{t + \rdt} \rt] \\
 …
   \end{alignedat}
 \end{equation}
+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 $T$
+(\ie\ fluxes plus content in mass exchanges).
+$\gamma$ is initialized as \np{rn_atfp}{rn\_atfp} (\textbf{namelist} parameter).
+Its default value is \np[=10.e-3]{rn_atfp}{rn\_atfp}.
+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 $T$ (\ie\ fluxes plus content in mass exchanges).
+$\gamma$ is initialized as \np{rn_atfp}{rn\_atfp}, its default value is \forcode{10.e-3}.
 Note that the forcing correction term in the filter is not applied in linear free surface
 (\jp{ln\_linssh}\forcode{=.true.}) (see \autoref{subsec:TRA_sbc}).
+Not also that in constant volume case, the time stepping is performed on $T$, not on its content, $e_{3t}T$.
+When the vertical mixing is solved implicitly, the update of the \textit{next} tracer fields is done in
+\mdl{trazdf} module.
+Not also that in constant volume case, the time stepping is performed on $T$,
+not on its content, $e_{3t}T$.
+When the vertical mixing is solved implicitly,
+the update of the \textit{next} tracer fields is done in \mdl{trazdf} module.
 In this case only the swapping of arrays and the Asselin filtering is done in the \mdl{tranxt} module.
 In order to prepare for the computation of the \textit{next} time step, a swap of tracer arrays is performed:
 $T^{t - \rdt} = T^t$ and $T^t = T_f$.
+In order to prepare for the computation of the \textit{next} time step,
+a swap of tracer arrays is performed: $T^{t - \rdt} = T^t$ and $T^t = T_f$.
 %% =================================================================================================
 …
 \label{subsec:TRA_eos}
+The Equation Of Seawater (EOS) is an empirical nonlinear thermodynamic relationship linking seawater density,
+$\rho$, to a number of state variables, most typically temperature, salinity and pressure.
+The \textbf{E}quation \textbf{O}f \textbf{S}eawater (EOS) is
+an empirical nonlinear thermodynamic relationship linking
+seawater density, $\rho$, to a number of state variables,
+most typically temperature, salinity and pressure.
 Because density gradients control the pressure gradient force through the hydrostatic balance,
 the equation of state provides a fundamental bridge between the distribution of active tracers and
 the fluid dynamics.
+the equation of state provides a fundamental bridge between
+the distribution of active tracers and the fluid dynamics.
 Nonlinearities of the EOS are of major importance, in particular influencing the circulation through
 determination of the static stability below the mixed layer,
+thus controlling rates of exchange between the atmosphere and the ocean interior \citep{roquet.madec.ea_JPO15}.
+Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{fofonoff.millard_bk83}) or
+TEOS-10 \citep{ioc.iapso_bk10} standards should be used anytime a simulation of the real ocean circulation is attempted
+thus controlling rates of exchange between the atmosphere and the ocean interior
 \citep{roquet.madec.ea_JPO15}.
+Therefore an accurate EOS based on either the 1980 equation of state
+(EOS-80, \cite{fofonoff.millard_bk83}) or TEOS-10 \citep{ioc.iapso_bk10} standards should
+be used anytime a simulation of the real ocean circulation is attempted \citep{roquet.madec.ea_JPO15}.
 The use of TEOS-10 is highly recommended because
+\textit{(i)}   it is the new official EOS,
+\textit{(ii)}  it is more accurate, being based on an updated database of laboratory measurements, and
+\textit{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature and
+practical salinity for EOS-80, both variables being more suitable for use as model variables
+\citep{ioc.iapso_bk10, graham.mcdougall_JPO13}.
+\begin{enumerate*}[label=(\textit{\roman*})]
+\item it is the new official EOS,
+\item it is more accurate, being based on an updated database of laboratory measurements, and
+\item it uses Conservative Temperature and Absolute Salinity
+  (instead of potential temperature and practical salinity for EOS-80),
+  both variables being more suitable for use as model variables
+  \citep{ioc.iapso_bk10, graham.mcdougall_JPO13}.
+\end{enumerate*}
 EOS-80 is an obsolescent feature of the \NEMO\ system, kept only for backward compatibility.
 For process studies, it is often convenient to use an approximation of the EOS.
 To that purposed, a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is also available.
+In the computer code, a density anomaly, $d_a = \rho / \rho_o - 1$, is computed, with $\rho_o$ a reference density.
+Called \textit{rau0} in the code, $\rho_o$ is set in \mdl{phycst} to a value of $1,026~Kg/m^3$.
+This is a sensible choice for the reference density used in a Boussinesq ocean climate model, as,
+with the exception of only a small percentage of the ocean,
+density in the World Ocean varies by no more than 2$\%$ from that value \citep{gill_bk82}.
+In the computer code, a density anomaly, $d_a = \rho / \rho_o - 1$, is computed,
+with $\rho_o$ a reference density.
+Called \textit{rau0} in the code,
+$\rho_o$ is set in \mdl{phycst} to a value of \texttt{1,026} $Kg/m^3$.
+This is a sensible choice for the reference density used in a Boussinesq ocean climate model,
+as, with the exception of only a small percentage of the ocean,
+density in the World Ocean varies by no more than 2\% from that value \citep{gill_bk82}.
 Options which control the EOS used are defined through the \nam{eos}{eos} namelist variables.
 \begin{description}
+\item [{\np[=.true.]{ln_teos10}{ln\_teos10}}] the polyTEOS10-bsq equation of seawater \citep{roquet.madec.ea_OM15} is used.
+\item [{\np[=.true.]{ln_teos10}{ln\_teos10}}] the polyTEOS10-bsq equation of seawater
+  \citep{roquet.madec.ea_OM15} is used.
   The accuracy of this approximation is comparable to the TEOS-10 rational function approximation,
+  but it is optimized for a boussinesq fluid and the polynomial expressions have simpler and
+  more computationally efficient expressions for their derived quantities which make them more adapted for
+  use in ocean models.
+  Note that a slightly higher precision polynomial form is now used replacement of
+  the TEOS-10 rational function approximation for hydrographic data analysis \citep{ioc.iapso_bk10}.
+  but it is optimized for a Boussinesq fluid and
+  the polynomial expressions have simpler and more computationally efficient expressions for
+  their derived quantities which make them more adapted for use in ocean models.
+  Note that a slightly higher precision polynomial form is now used
+  replacement of the TEOS-10 rational function approximation for hydrographic data analysis
+  \citep{ioc.iapso_bk10}.
   A key point is that conservative state variables are used:
+  Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \deg{C}, 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.
+  It is set to $C_p = 3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{ioc.iapso_bk10}.
+  It is set to $C_p$ = 3991.86795711963 $J.Kg^{-1}.\deg{K}^{-1}$,
+  according to \citet{ioc.iapso_bk10}.
   Choosing polyTEOS10-bsq implies that the state variables used by the model are $\Theta$ and $S_A$.
   In particular, the initial state deined by the user have to be given as \textit{Conservative} Temperature and
   \textit{Absolute} Salinity.
+  In particular, the initial state defined by the user have to be given as
+  \textit{Conservative} Temperature and \textit{Absolute} Salinity.
   In addition, when using TEOS10, the Conservative SST is converted to potential SST prior to
   either computing the air-sea and ice-sea fluxes (forced mode) or
   sending the SST field to the atmosphere (coupled mode).
 \item [{\np[=.true.]{ln_eos80}{ln\_eos80}}] the polyEOS80-bsq equation of seawater is used.
   It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized to
   accurately fit EOS80 (Roquet, personal comm.).
+  It takes the same polynomial form as the polyTEOS10,
+  but the coefficients have been optimized to accurately fit EOS80 (Roquet, personal comm.).
   The state variables used in both the EOS80 and the ocean model are:
   the Practical Salinity ((unit: psu, notation: $S_p$)) and
   Potential Temperature (unit: $^{\circ}C$, notation: $\theta$).
+  the Practical Salinity (unit: $psu$, notation: $S_p$) and
+  Potential Temperature (unit: $\deg{C}$, notation: $\theta$).
   The pressure in decibars is approximated by the depth in meters.
   With thsi EOS, the specific heat capacity of sea water, $C_p$, is a function of temperature, salinity and
   pressure \citep{fofonoff.millard_bk83}.
+  With EOS, the specific heat capacity of sea water, $C_p$, is a function of
+  temperature, salinity and pressure \citep{fofonoff.millard_bk83}.
   Nevertheless, a severe assumption is made in order to have a heat content ($C_p T_p$) which
   is conserved by the model: $C_p$ is set to a constant value, the TEOS10 value.
+\item [{\np[=.true.]{ln_seos}{ln\_seos}}] a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is chosen,
+  the coefficients of which has been optimized to fit the behavior of TEOS10
+  (Roquet, personal comm.) (see also \citet{roquet.madec.ea_JPO15}).
+\item [{\np[=.true.]{ln_seos}{ln\_seos}}] a simplified EOS (S-EOS) inspired by
+  \citet{vallis_bk06} is chosen,
+  the coefficients of which has been optimized to fit the behavior of TEOS10 (Roquet, personal comm.)
+  (see also \citet{roquet.madec.ea_JPO15}).
   It provides a simplistic linear representation of both cabbeling and thermobaricity effects which
   is enough for a proper treatment of the EOS in theoretical studies \citep{roquet.madec.ea_JPO15}.
   With such an equation of state there is no longer a distinction between
   \textit{conservative} and \textit{potential} temperature,
   as well as between \textit{absolute} and \textit{practical} salinity.
+  With such an equation of state there is no longer a distinction between \textit{conservative} and
+  \textit{potential} temperature, as well as between \textit{absolute} and
+  \textit{practical} salinity.
   S-EOS takes the following expression:
   \begin{gather*}
     % \label{eq:TRA_S-EOS}
+    \begin{alignedat}{2}
+    &d_a(T,S,z) = \frac{1}{\rho_o} \big[ &- a_0 \; ( 1 + 0.5 \; \lambda_1 \; T_a + \mu_1 \; z ) * &T_a \big. \\
+    &                                    &+ b_0 \; ( 1 - 0.5 \; \lambda_2 \; S_a - \mu_2 \; z ) * &S_a       \\
+    &                              \big. &- \nu \;                           T_a                  &S_a \big] \\
+    \end{alignedat}
+    \\
+    d_a(T,S,z) = \frac{1}{\rho_o} \big[ - a_0 \; ( 1 + 0.5 \; \lambda_1 \; T_a + \mu_1 \; z ) * T_a \big.
+                                        + b_0 \; ( 1 - 0.5 \; \lambda_2 \; S_a - \mu_2 \; z ) * S_a
+                                  \big. - \nu \;                           T_a                  S_a \big] \\
     \text{with~} T_a = T - 10 \, ; \, S_a = S - 35 \, ; \, \rho_o = 1026~Kg/m^3
   \end{gather*}
+  where the computer name of the coefficients as well as their standard value are given in \autoref{tab:TRA_SEOS}.
+  where the computer name of the coefficients as well as their standard value are given in
+  \autoref{tab:TRA_SEOS}.
   In fact, when choosing S-EOS, various approximation of EOS can be specified simply by
   changing the associated coefficients.
+  Setting to zero the two thermobaric coefficients $(\mu_1,\mu_2)$ remove thermobaric effect from S-EOS.
+  setting to zero the three cabbeling coefficients $(\lambda_1,\lambda_2,\nu)$ remove cabbeling effect from
+  S-EOS.
+  Setting to zero the two thermobaric coefficients $(\mu_1,\mu_2)$
+  remove thermobaric effect from S-EOS.
+  Setting to zero the three cabbeling coefficients $(\lambda_1,\lambda_2,\nu)$
+  remove   cabbeling effect from S-EOS.
   Keeping non-zero value to $a_0$ and $b_0$ provide a linear EOS function of T and S.
 \end{description}
 \begin{table}[!tb]
+\begin{table}
   \centering
   \begin{tabular}{|l|l|l|l|}
     \hline
     coeff.     & computer name   & S-EOS           & description                      \\
+    coeff.      & computer name                & S-EOS            & description                     \\
     \hline
     $a_0$       & \np{rn_a0}{rn\_a0}     & $1.6550~10^{-1}$ & linear thermal expansion coeff. \\
+    $a_0      $ & \np{rn_a0}{rn\_a0}           & $1.6550~10^{-1}$ & linear thermal expansion coeff. \\
     \hline
     $b_0$         & \np{rn_b0}{rn\_b0}       & $7.6554~10^{-1}$ & linear haline  expansion coeff. \\
+    $b_0      $ & \np{rn_b0}{rn\_b0}           & $7.6554~10^{-1}$ & linear haline  expansion coeff. \\
     \hline
     $\lambda_1$   & \np{rn_lambda1}{rn\_lambda1}& $5.9520~10^{-2}$ & cabbeling coeff. in $T^2$       \\
+    $\lambda_1$ & \np{rn_lambda1}{rn\_lambda1} & $5.9520~10^{-2}$ & cabbeling coeff. in $T^2$       \\
     \hline
     $\lambda_2$   & \np{rn_lambda2}{rn\_lambda2}& $5.4914~10^{-4}$ & cabbeling coeff. in $S^2$       \\
+    $\lambda_2$ & \np{rn_lambda2}{rn\_lambda2} & $5.4914~10^{-4}$ & cabbeling coeff. in $S^2$       \\
     \hline
     $\nu$       & \np{rn_nu}{rn\_nu}     & $2.4341~10^{-3}$ & cabbeling coeff. in $T \, S$     \\
+    $\nu      $ & \np{rn_nu}{rn\_nu}           & $2.4341~10^{-3}$ & cabbeling coeff. in $T \, S$    \\
     \hline
     $\mu_1$     & \np{rn_mu1}{rn\_mu1}    & $1.4970~10^{-4}$ & thermobaric coeff. in T         \\
+    $\mu_1    $ & \np{rn_mu1}{rn\_mu1}         & $1.4970~10^{-4}$ & thermobaric coeff. in T         \\
     \hline
     $\mu_2$     & \np{rn_mu2}{rn\_mu2}    & $1.1090~10^{-5}$ & thermobaric coeff. in S         \\
+    $\mu_2    $ & \np{rn_mu2}{rn\_mu2}         & $1.1090~10^{-5}$ & thermobaric coeff. in S         \\
     \hline
   \end{tabular}
 …
 \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
 paramount importance as determine the ocean stratification and is used in several ocean parameterisations
+An accurate computation of the ocean stability (i.e. 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,
 non-penetrative convection, tidal mixing  parameterisation, iso-neutral diffusion).
 …
 where $(T,S) = (\Theta,S_A)$ for TEOS10, $(\theta,S_p)$ for TEOS-80, or $(T,S)$ for S-EOS, and,
 $\alpha$ and $\beta$ are the thermal and haline expansion coefficients.
 The coefficients are a polynomial function of temperature, salinity and depth which expression depends on
 the chosen EOS.
+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 \fortran\ function that can be found in \mdl{eosbn2}.
 …
 \begin{equation}
   \label{eq:TRA_eos_fzp}
+  \begin{split}
+    &T_f (S,p) = \lt( a + b \, \sqrt{S} + c \, S \rt) \, S + d \, p \\
+    &\text{where~} a = -0.0575, \, b = 1.710523~10^{-3}, \, c = -2.154996~10^{-4} \\
+    &\text{and~} d = -7.53~10^{-3}
+    \end{split}
+  \begin{gathered}
+    T_f (S,p) = \lt( a + b \, \sqrt{S} + c \, S \rt) \, S + d \, p \\
+    \text{where~} a = -0.0575, \, b = 1.710523~10^{-3}, \, c = -2.154996~10^{-4} \text{and~} d = -7.53~10^{-3}
+    \end{gathered}
 \end{equation}
 …
 \label{sec:TRA_zpshde}
 \gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators,
+\cmtgm{STEVEN: to be consistent with earlier discussion of differencing and averaging operators,
 I've changed "derivative" to "difference" and "mean" to "average"}
+With partial cells (\np[=.true.]{ln_zps}{ln\_zps}) at bottom and top (\np[=.true.]{ln_isfcav}{ln\_isfcav}),
+With partial cells (\np[=.true.]{ln_zps}{ln\_zps}) at bottom and top
+(\np[=.true.]{ln_isfcav}{ln\_isfcav}),
 in general, tracers in horizontally adjacent cells live at different depths.
 Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} module) and
 the hydrostatic pressure gradient calculations (\mdl{dynhpg} module).
 The partial cell properties at the top (\np[=.true.]{ln_isfcav}{ln\_isfcav}) are computed in the same way as
 for the bottom.
+Horizontal gradients of tracers are needed for horizontal diffusion
+(\mdl{traldf} module) and the hydrostatic pressure gradient calculations (\mdl{dynhpg} module).
+The partial cell properties at the top (\np[=.true.]{ln_isfcav}{ln\_isfcav}) are computed in
+the same way as for the bottom.
 So, only the bottom interpolation is explained below.
 …
 a linear interpolation in the vertical is used to approximate the deeper tracer as if
 it actually lived at the depth of the shallower tracer point (\autoref{fig:TRA_Partial_step_scheme}).
+For example, for temperature in the $i$-direction the needed interpolated temperature, $\widetilde T$, is:
+\begin{figure}[!p]
+For example, for temperature in the $i$-direction the needed interpolated temperature,
+$\widetilde T$, is:
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_partial_step_scheme}
+  \includegraphics[width=0.33\textwidth]{TRA_partial_step_scheme}
   \caption[Discretisation of the horizontal difference and average of tracers in
   the $z$-partial step coordinate]{
 …
     the case $(e3w_k^{i + 1} - e3w_k^i) > 0$.
     A linear interpolation is used to estimate $\widetilde T_k^{i + 1}$,
+    the tracer value at the depth of the shallower tracer point of
+    the two adjacent bottom $T$-points.
+    the tracer value at the depth of the shallower tracer point of the two adjacent bottom $T$-points.
     The horizontal difference is then given by:
+    $\delta_{i + 1/2} T_k = \widetilde T_k^{\, i + 1} -T_k^{\, i}$ and
+    the average by:
+    $\delta_{i + 1/2} T_k = \widetilde T_k^{\, i + 1} -T_k^{\, i}$ and the average by:
     $\overline T_k^{\, i + 1/2} = (\widetilde T_k^{\, i + 1/2} - T_k^{\, i}) / 2$.}
   \label{fig:TRA_Partial_step_scheme}
 \end{figure}
 \[
   \widetilde T = \lt\{
     \begin{alignedat}{2}
       &T^{\, i + 1} &-\frac{ \lt( e_{3w}^{i + 1} -e_{3w}^i \rt) }{ e_{3w}^{i + 1} } \; \delta_k T^{i + 1}
       & \quad \text{if $e_{3w}^{i + 1} \geq e_{3w}^i$} \\ \\
+      & \quad \text{if $e_{3w}^{i + 1} \geq e_{3w}^i$} \\
       &T^{\, i}     &+\frac{ \lt( e_{3w}^{i + 1} -e_{3w}^i \rt )}{e_{3w}^i       } \; \delta_k T^{i + 1}
       & \quad \text{if $e_{3w}^{i + 1} <    e_{3w}^i$}
 …
   \rt.
 \]
+and the resulting forms for the horizontal difference and the horizontal average value of $T$ at a $U$-point are:
+and the resulting forms for the horizontal difference and the horizontal average value of
+$T$ at a $U$-point are:
 \begin{equation}
   \label{eq:TRA_zps_hde}
 …
     \delta_{i + 1/2} T       &=
     \begin{cases}
+                                \widetilde T - T^i          & \text{if~} e_{3w}^{i + 1} \geq e_{3w}^i \\
+                                \\
+                                T^{\, i + 1} - \widetilde T & \text{if~} e_{3w}^{i + 1} <    e_{3w}^i
+    \end{cases}
+    \\
+      \widetilde T - T^i          & \text{if~} e_{3w}^{i + 1} \geq e_{3w}^i \\
+      T^{\, i + 1} - \widetilde T & \text{if~} e_{3w}^{i + 1} <    e_{3w}^i
+    \end{cases} \\
     \overline T^{\, i + 1/2} &=
     \begin{cases}
+                                (\widetilde T - T^{\, i}   ) / 2 & \text{if~} e_{3w}^{i + 1} \geq e_{3w}^i \\
+                                \\
+                                (T^{\, i + 1} - \widetilde T) / 2 & \text{if~} e_{3w}^{i + 1} <   e_{3w}^i
+      (\widetilde T - T^{\, i}    ) / 2 & \text{if~} e_{3w}^{i + 1} \geq e_{3w}^i \\
+      (T^{\, i + 1} - \widetilde T) / 2 & \text{if~} e_{3w}^{i + 1} <   e_{3w}^i
     \end{cases}
   \end{split}
 …
 The computation of horizontal derivative of tracers as well as of density is performed once for all at
 each time step in \mdl{zpshde} module and stored in shared arrays to be used when needed.
+It has to be emphasized that the procedure used to compute the interpolated density, $\widetilde \rho$,
+is not the same as that used for $T$ and $S$.
+Instead of forming a linear approximation of density, we compute $\widetilde \rho$ from the interpolated values of
+$T$ and $S$, and the pressure at a $u$-point
+It has to be emphasized that the procedure used to compute the interpolated density,
+$\widetilde \rho$, is not the same as that used for $T$ and $S$.
+Instead of forming a linear approximation of density,
+we compute $\widetilde \rho$ from the interpolated values of $T$ and $S$,
+and the pressure at a $u$-point
 (in the equation of state pressure is approximated by depth, see \autoref{subsec:TRA_eos}):
 \[
 …
 This is a much better approximation as the variation of $\rho$ with depth (and thus pressure)
+is highly non-linear with a true equation of state and thus is badly approximated with a linear interpolation.
+This approximation is used to compute both the horizontal pressure gradient (\autoref{sec:DYN_hpg}) and
+the slopes of neutral surfaces (\autoref{sec:LDF_slp}).
+Note that in almost all the advection schemes presented in this Chapter,
+is highly non-linear with a true equation of state and thus is badly approximated with
+a linear interpolation.
+This approximation is used to compute both the horizontal pressure gradient (\autoref{sec:DYN_hpg})
+and the slopes of neutral surfaces (\autoref{sec:LDF_slp}).
+Note that in almost all the advection schemes presented in this chapter,
 both averaging and differencing operators appear.
 Yet \autoref{eq:TRA_zps_hde} has not been used in these schemes:
 …
 The main motivation is to preserve the domain averaged mean variance of the advected field when
 using the $2^{nd}$ order centred scheme.
 Sensitivity of the advection schemes to the way horizontal averages are performed in the vicinity of
 partial cells should be further investigated in the near future.
 \gmcomment{gm :   this last remark has to be done}
 \onlyinsubfile{\input{../../global/epilogue}}
+Sensitivity of the advection schemes to the way horizontal averages are performed in
+the vicinity of partial cells should be further investigated in the near future.
+\cmtgm{gm :   this last remark has to be done}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_ZDF.tex

-                      r11599
+                      r11954
 \clearpage
+%gm% Add here a small introduction to ZDF and naming of the different physics (similar to what have been written for TRA and DYN.
+\cmtgm{ Add here a small introduction to ZDF and naming of the different physics
+(similar to what have been written for TRA and DYN).}
 %% =================================================================================================
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_mixing_length}
+  \includegraphics[width=0.66\textwidth]{ZDF_mixing_length}
   \caption[Mixing length computation]{Illustration of the mixing length computation}
   \label{fig:ZDF_mixing_length}
 …
  in \citet{reffray.guillaume.ea_GMD15} for the \NEMO\ model.
+%% =================================================================================================
+\subsection[OSM: OSMosis boundary layer scheme (\forcode{ln_zdfosm})]{OSM: OSMosis boundary layer scheme (\protect\np{ln_zdfosm}{ln\_zdfosm})}
+% -------------------------------------------------------------------------------------------------------------
+%        OSM OSMOSIS BL Scheme
+% -------------------------------------------------------------------------------------------------------------
+\subsection[OSM: OSMOSIS boundary layer scheme (\forcode{ln_zdfosm = .true.})]
+{OSM: OSMOSIS boundary layer scheme (\protect\np{ln_zdfosm}{ln\_zdfosm})}
 \label{subsec:ZDF_osm}
 …
 \end{listing}
+The OSMOSIS turbulent closure scheme is based on......   TBC
+%--------------------------------------------------------------------------------------------------------------
+\paragraph{Namelist choices}
+Most of the namelist options refer to how to specify the Stokes
+surface drift and penetration depth. There are three options:
+\begin{description}
+  \item \protect\np[=0]{nn_osm_wave}{nn\_osm\_wave} Default value in \texttt{namelist\_ref}. In this case the Stokes drift is
+      assumed to be parallel to the surface wind stress, with
+      magnitude consistent with a constant turbulent Langmuir number
+    $\mathrm{La}_t=$ \protect\np{rn_m_la} {rn\_m\_la} i.e.\
+    $u_{s0}=\tau/(\mathrm{La}_t^2\rho_0)$.  Default value of
+    \protect\np{rn_m_la}{rn\_m\_la} is 0.3. The Stokes penetration
+      depth $\delta = $ \protect\np{rn_osm_dstokes}{rn\_osm\_dstokes}; this has default value
+      of 5~m.
+  \item \protect\np[=1]{nn_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is
+      assumed to be parallel to the surface wind stress, with
+      magnitude as in the classical Pierson-Moskowitz wind-sea
+      spectrum.  Significant wave height and
+      wave-mean period taken from this spectrum are used to calculate the Stokes penetration
+      depth, following the approach set out in  \citet{breivik.janssen.ea_JPO14}.
+    \item \protect\np[=2]{nn_osm_wave}{nn\_osm\_wave} In this case the Stokes drift is
+      taken from  ECMWF wave model output, though only the component parallel
+      to the wind stress is retained. Significant wave height and
+      wave-mean period from ECMWF wave model output are used to calculate the Stokes penetration
+      depth, again following \citet{breivik.janssen.ea_JPO14}.
+    \end{description}
+    Others refer to the treatment of diffusion and viscosity beneath
+    the surface boundary layer:
+\begin{description}
+   \item \protect\np{ln_kpprimix} {ln\_kpprimix}  Default is \np{.true.}. Switches on KPP-style Ri \#-dependent
+     mixing below the surface boundary layer. If this is set
+     \texttt{.true.}  the following variable settings are honoured:
+    \item \protect\np{rn_riinfty}{rn\_riinfty} Critical value of local Ri \# below which
+      shear instability increases vertical mixing from background value.
+    \item \protect\np{rn_difri} {rn\_difri} Maximum value of Ri \#-dependent mixing at $\mathrm{Ri}=0$.
+    \item \protect\np{ln_convmix}{ln\_convmix} If \texttt{.true.} then, where water column is unstable, specify
+       diffusivity equal to \protect\np{rn_dif_conv}{rn\_dif\_conv} (default value is 1 m~s$^{-2}$).
+ \end{description}
+ Diagnostic output is controlled by:
+  \begin{description}
+    \item \protect\np{ln_dia_osm}{ln\_dia\_osm} Default is \np{.false.}; allows XIOS output of OSMOSIS internal fields.
+  \end{description}
+Obsolete namelist parameters include:
+\begin{description}
+   \item \protect\np{ln_use_osm_la}\np{ln\_use\_osm\_la} With \protect\np[=0]{nn_osm_wave}{nn\_osm\_wave},
+      \protect\np{rn_osm_dstokes} {rn\_osm\_dstokes} is always used to specify the Stokes
+      penetration depth.
+   \item \protect\np{nn_ave} {nn\_ave} Choice of averaging method for KPP-style Ri \#
+      mixing. Not taken account of.
+   \item \protect\np{rn_osm_hbl0} {rn\_osm\_hbl0} Depth of initial boundary layer is now set
+     by a density criterion similar to that used in calculating \emph{hmlp} (output as \texttt{mldr10\_1}) in \mdl{zdfmxl}.
+\end{description}
+\subsubsection{Summary}
+Much of the time the turbulent motions in the ocean surface boundary
+layer (OSBL) are not given by
+classical shear turbulence. Instead they are in a regime known as
+`Langmuir turbulence',  dominated by an
+interaction between the currents and the Stokes drift of the surface waves \citep[e.g.][]{mcwilliams.ea_JFM97}.
+This regime is characterised by strong vertical turbulent motion, and appears when the surface Stokes drift $u_{s0}$ is much greater than the friction velocity $u_{\ast}$. More specifically Langmuir turbulence is thought to be crucial where the turbulent Langmuir number $\mathrm{La}_{t}=(u_{\ast}/u_{s0}) > 0.4$.
+The OSMOSIS model is fundamentally based on results of Large Eddy
+Simulations (LES) of Langmuir turbulence and aims to fully describe
+this Langmuir regime. The description in this section is of necessity incomplete and further details are available in Grant. A (2019); in prep.
+The OSMOSIS turbulent closure scheme is a similarity-scale scheme in
+the same spirit as the K-profile
+parameterization (KPP) scheme of \citet{large.ea_RG97}.
+A specified shape of diffusivity, scaled by the (OSBL) depth
+$h_{\mathrm{BL}}$ and a turbulent velocity scale, is imposed throughout the
+boundary layer
+$-h_{\mathrm{BL}}<z<\eta$. The turbulent closure model
+also includes fluxes of tracers and momentum that are``non-local'' (independent of the local property gradient).
+Rather than the OSBL
+depth being diagnosed in terms of a bulk Richardson number criterion,
+as in KPP, it is set by a prognostic equation that is informed by
+energy budget considerations reminiscent of the classical mixed layer
+models of \citet{kraus.turner_tellus67}.
+The model also includes an explicit parametrization of the structure
+of the pycnocline (the stratified region at the bottom of the OSBL).
+Presently, mixing below the OSBL is handled by the Richardson
+number-dependent mixing scheme used in \citet{large.ea_RG97}.
+Convective parameterizations such as described in \ref{sec:ZDF_conv}
+below should not be used with the OSMOSIS-OBL model: instabilities
+within the OSBL are part of the model, while instabilities below the
+ML are handled by the Ri \# dependent scheme.
+\subsubsection{Depth and velocity scales}
+The model supposes a boundary layer of thickness $h_{\mathrm{bl}}$ enclosing a well-mixed layer of thickness $h_{\mathrm{ml}}$ and a relatively thin pycnocline at the base of thickness $\Delta h$; Fig.~\ref{fig: OSBL_structure} shows typical (a) buoyancy structure and (b) turbulent buoyancy flux profile for the unstable boundary layer (losing buoyancy at the surface; e.g.\ cooling).
+\begin{figure}[!t]
+  \begin{center}
+    %\includegraphics[width=0.7\textwidth]{ZDF_OSM_structure_of_OSBL}
+    \caption{
+      \protect\label{fig: OSBL_structure}
+     The structure of the entraining  boundary layer. (a) Mean buoyancy profile. (b) Profile of the buoyancy flux.
+    }
+  \end{center}
+\end{figure}
+The pycnocline in the OSMOSIS scheme is assumed to have a finite thickness, and may include a number of model levels. This means that the OSMOSIS scheme must parametrize both the thickness of the pycnocline, and the turbulent fluxes within the pycnocline.
+Consideration of the power input by wind acting on the Stokes drift suggests that the Langmuir turbulence has velocity scale:
+\begin{equation}\label{eq:w_La}
+w_{*L}= \left(u_*^2 u_{s\,0}\right)^{1/3};
+\end{equation}
+but at times the Stokes drift may be weak due to e.g.\ ice cover, short fetch, misalignment with the surface stress, etc.\ so  a composite velocity scale is assumed for the stable (warming) boundary layer:
+\begin{equation}\label{eq:composite-nu}
+  \nu_{\ast}= \left\{ u_*^3 \left[1-\exp(-.5 \mathrm{La}_t^2)\right]+w_{*L}^3\right\}^{1/3}.
+\end{equation}
+For the unstable boundary layer this is merged with the standard convective velocity scale $w_{*C}=\left(\overline{w^\prime b^\prime}_0 \,h_\mathrm{ml}\right)^{1/3}$, where $\overline{w^\prime b^\prime}_0$ is the upwards surface buoyancy flux, to give:
+\begin{equation}\label{eq:vel-scale-unstable}
+\omega_* = \left(\nu_*^3 + 0.5 w_{*C}^3\right)^{1/3}.
+\end{equation}
+\subsubsection{The flux gradient model}
+The flux-gradient relationships used in the OSMOSIS scheme take the form:
+%
+\begin{equation}\label{eq:flux-grad-gen}
+\overline{w^\prime\chi^\prime}=-K\frac{\partial\overline{\chi}}{\partial z} + N_{\chi,s} +N_{\chi,b} +N_{\chi,t},
+\end{equation}
+%
+where $\chi$ is a general variable and $N_{\chi,s}, N_{\chi,b} \mathrm{and} N_{\chi,t}$  are the non-gradient terms, and represent the effects of the different terms in the turbulent flux-budget on the transport of $\chi$. $N_{\chi,s}$ represents the effects that the Stokes shear has on the transport of $\chi$, $N_{\chi,b}$  the effect of buoyancy, and $N_{\chi,t}$ the effect of the turbulent transport.  The same general form for the flux-gradient relationship is used to parametrize the transports of momentum, heat and salinity.
+In terms of the non-dimensionalized depth variables
+%
+\begin{equation}\label{eq:sigma}
+\sigma_{\mathrm{ml}}= -z/h_{\mathrm{ml}}; \;\sigma_{\mathrm{bl}}= -z/h_{\mathrm{bl}},
+\end{equation}
+%
+in unstable conditions the eddy diffusivity ($K_d$) and eddy viscosity ($K_\nu$) profiles are parametrized as:
+%
+\begin{align}\label{eq:diff-unstable}
+K_d=&0.8\, \omega_*\, h_{\mathrm{ml}} \, \sigma_{\mathrm{ml}} \left(1-\beta_d \sigma_{\mathrm{ml}}\right)^{3/2}
+\\\label{eq:visc-unstable}
+K_\nu =& 0.3\, \omega_* \,h_{\mathrm{ml}}\, \sigma_{\mathrm{ml}} \left(1-\beta_\nu \sigma_{\mathrm{ml}}\right)\left(1-\tfrac{1}{2}\sigma_{\mathrm{ml}}^2\right)
+\end{align}
+%
+where $\beta_d$ and $\beta_\nu$ are parameters that are determined by matching Eqs \ref{eq:diff-unstable} and \ref{eq:visc-unstable} to the eddy diffusivity and viscosity at the base of the well-mixed layer, given by
+%
+\begin{equation}\label{eq:diff-wml-base}
+K_{d,\mathrm{ml}}=K_{\nu,\mathrm{ml}}=\,0.16\,\omega_* \Delta h.
+\end{equation}
+%
+For stable conditions the eddy diffusivity/viscosity profiles are given by:
+%
+\begin{align}\label{diff-stable}
+K_d= & 0.75\,\, \nu_*\, h_{\mathrm{ml}}\,\,  \exp\left[-2.8 \left(h_{\mathrm{bl}}/L_L\right)^2\right]\sigma_{\mathrm{ml}} \left(1-\sigma_{\mathrm{ml}}\right)^{3/2} \\\label{eq:visc-stable}
+K_\nu = & 0.375\,\,  \nu_*\, h_{\mathrm{ml}} \,\, \exp\left[-2.8 \left(h_{\mathrm{bl}}/L_L\right)^2\right] \sigma_{\mathrm{ml}} \left(1-\sigma_{\mathrm{ml}}\right)\left(1-\tfrac{1}{2}\sigma_{\mathrm{ml}}^2\right).
+\end{align}
+%
+The shape of the eddy viscosity and diffusivity profiles is the same as the shape in the unstable OSBL. The eddy diffusivity/viscosity depends on the stability parameter $h_{\mathrm{bl}}/{L_L}$ where $ L_L$ is analogous to the Obukhov length, but for Langmuir turbulence:
+\begin{equation}\label{eq:L_L}
+  L_L=-w_{*L}^3/\left<\overline{w^\prime b^\prime}\right>_L,
+\end{equation}
+with the mean turbulent buoyancy flux averaged over the boundary layer given in terms of its surface value $\overline{w^\prime b^\prime}_0$ and (downwards) )solar irradiance $I(z)$ by
+\begin{equation} \label{eq:stable-av-buoy-flux}
+\left<\overline{w^\prime b^\prime}\right>_L = \tfrac{1}{2} {\overline{w^\prime b^\prime}}_0-g\alpha_E\left[\tfrac{1}{2}(I(0)+I(-h))-\left<I\right>\right].
+\end{equation}
+%
+In unstable conditions the eddy diffusivity and viscosity depend on stability through the velocity scale $\omega_*$, which depends on the two velocity scales $\nu_*$ and $w_{*C}$.
+Details of the non-gradient terms in \eqref{eq:flux-grad-gen} and of the fluxes within the pycnocline $-h_{\mathrm{bl}}<z<h_{\mathrm{ml}}$ can be found in Grant (2019).
+\subsubsection{Evolution of the boundary layer depth}
+The prognostic equation for the depth of the neutral/unstable boundary layer is given by \citep{grant+etal18},
+\begin{equation} \label{eq:dhdt-unstable}
+%\frac{\partial h_\mathrm{bl}}{\partial t} + \mathbf{U}_b\cdot\nabla h_\mathrm{bl}= W_b - \frac{{\overline{w^\prime b^\prime}}_\mathrm{ent}}{\Delta B_\mathrm{bl}}
+\frac{\partial h_\mathrm{bl}}{\partial t} = W_b - \frac{{\overline{w^\prime b^\prime}}_\mathrm{ent}}{\Delta B_\mathrm{bl}}
+\end{equation}
+where $h_\mathrm{bl}$ is the horizontally-varying depth of the OSBL,
+$\mathbf{U}_b$ and $W_b$ are the mean horizontal and vertical
+velocities at the base of the OSBL, ${\overline{w^\prime
+    b^\prime}}_\mathrm{ent}$ is the buoyancy flux due to entrainment
+and $\Delta B_\mathrm{bl}$ is the difference between the buoyancy
+averaged over the depth of the OSBL (i.e.\ including the ML and
+pycnocline) and the buoyancy just below the base of the OSBL. This
+equation for the case when the pycnocline has a finite thickness,
+based on the potential energy budget of the OSBL, is the leading term
+\citep{grant+etal18} of a generalization of that used in mixed-layer
+models e.g.\ \citet{kraus.turner_tellus67}, in which the thickness of the pycnocline is taken to be zero.
+The entrainment flux for the combination of convective and Langmuir turbulence is given by
+\begin{equation} \label{eq:entrain-flux}
+  {\overline{w^\prime b^\prime}}_\mathrm{ent} = -\alpha_{\mathrm{B}} {\overline{w^\prime b^\prime}}_0 - \alpha_{\mathrm{S}} \frac{u_*^3}{h_{\mathrm{ml}}}
+  + G\left(\delta/h_{\mathrm{ml}} \right)\left[\alpha_{\mathrm{S}}e^{-1.5\, \mathrm{La}_t}-\alpha_{\mathrm{L}} \frac{w_{\mathrm{*L}}^3}{h_{\mathrm{ml}}}\right]
+\end{equation}
+where the factor $G\equiv 1 - \mathrm{e}^ {-25\delta/h_{\mathrm{bl}}}(1-4\delta/h_{\mathrm{bl}})$ models the lesser efficiency of Langmuir mixing when the boundary-layer depth is much greater than the Stokes depth, and $\alpha_{\mathrm{B}}$, $\alpha_{S}$  and $\alpha_{\mathrm{L}}$ depend on the ratio of the appropriate eddy turnover time to the inertial timescale $f^{-1}$. Results from the LES suggest $\alpha_{\mathrm{B}}=0.18 F(fh_{\mathrm{bl}}/w_{*C})$, $\alpha_{S}=0.15 F(fh_{\mathrm{bl}}/u_*$  and $\alpha_{\mathrm{L}}=0.035 F(fh_{\mathrm{bl}}/u_{*L})$, where $F(x)\equiv\tanh(x^{-1})^{0.69}$.
+For the stable boundary layer, the equation for the depth of the OSBL is:
+\begin{equation}\label{eq:dhdt-stable}
+\max\left(\Delta B_{bl},\frac{w_{*L}^2}{h_\mathrm{bl}}\right)\frac{\partial h_\mathrm{bl}}{\partial t} = \left(0.06 + 0.52\,\frac{ h_\mathrm{bl}}{L_L}\right) \frac{w_{*L}^3}{h_\mathrm{bl}} +\left<\overline{w^\prime b^\prime}\right>_L.
+\end{equation}
+Equation. \ref{eq:dhdt-unstable} always leads to the depth of the entraining OSBL increasing (ignoring the effect of the mean vertical motion), but the change in the thickness of the stable OSBL given by Eq. \ref{eq:dhdt-stable} can be positive or negative, depending on the magnitudes of $\left<\overline{w^\prime b^\prime}\right>_L$ and $h_\mathrm{bl}/L_L$. The rate at which the depth of the OSBL can decrease is limited by choosing an effective buoyancy $w_{*L}^2/h_\mathrm{bl}$, in place of $\Delta B_{bl}$ which will be $\approx 0$ for the collapsing OSBL.
 %% =================================================================================================
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ZDF_TKE_time_scheme}
+  \includegraphics[width=0.66\textwidth]{ZDF_TKE_time_scheme}
   \caption[Subgrid kinetic energy integration in GLS and TKE schemes]{
     Illustration of the subgrid kinetic energy integration in GLS and TKE schemes and
 …
 \begin{figure}[!htb]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_npc}
+  \includegraphics[width=0.66\textwidth]{ZDF_npc}
   \caption[Unstable density profile treated by the non penetrative convective adjustment algorithm]{
     Example of an unstable density profile treated by
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_zdfddm}
+  \includegraphics[width=0.66\textwidth]{ZDF_ddm}
   \caption[Diapycnal diffusivities for temperature and salt in regions of salt fingering and
   diffusive convection]{
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_coeff}
+  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_coeff}
   \caption[Partitioning coefficient used to partition vertical velocities into parts]{
     The value of the partitioning coefficient (\cf) used to partition vertical velocities into
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_overflow_frames}
+  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_overflow_frames}
   \caption[OVERFLOW: time-series of temperature vertical cross-sections]{
     A time-series of temperature vertical cross-sections for the OVERFLOW test case.
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_overflow_all_rdt}
+  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_overflow_all_rdt}
   \caption[OVERFLOW: sample temperature vertical cross-sections from mid- and end-run]{
     Sample temperature vertical cross-sections from mid- and end-run using
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_maxCf}
+  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_maxCf}
   \caption[OVERFLOW: maximum partitioning coefficient during a series of test runs]{
     The maximum partitioning coefficient during a series of test runs with
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ZDF_zad_Aimp_maxCf_loc}
+  \includegraphics[width=0.66\textwidth]{ZDF_zad_Aimp_maxCf_loc}
   \caption[OVERFLOW: maximum partitioning coefficient for the case overlaid]{
     The maximum partitioning coefficient for the \forcode{nn_rdt=10.0} case overlaid with
 …
 \end{figure}
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_cfgs.tex

-                      r11598
+                      r11954
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ORCA_NH_mesh}
+  \includegraphics[width=0.66\textwidth]{CFGS_ORCA_NH_mesh}
   \caption[ORCA mesh conception]{
     ORCA mesh conception.
 …
 \begin{figure}[!tbp]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_ORCA_NH_msh05_e1_e2}
   \includegraphics[width=0.66\textwidth]{Fig_ORCA_aniso}
+  \includegraphics[width=0.66\textwidth]{CFGS_ORCA_NH_msh05_e1_e2}
+  \includegraphics[width=0.66\textwidth]{CFGS_ORCA_aniso}
   \caption[Horizontal scale factors and ratio of anisotropy for ORCA 0.5\deg\ mesh]{
     \textit{Top}: Horizontal scale factors ($e_1$, $e_2$) and
 …
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_GYRE}
+  \includegraphics[width=0.66\textwidth]{CFGS_GYRE}
   \caption[Snapshot of relative vorticity at the surface of the model domain in GYRE R9, R27 and R54]{
     Snapshot of relative vorticity at the surface of the model domain in GYRE R9, R27 and R54.
 …
 Unlike ordinary river points the Baltic inputs also include salinity and temperature data.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_conservation.tex

r11598	r11954
334	334	It has not been implemented.
335	335
336		\~~onlyinsubfile~~{\input{../../global/epilogue}}
	336	\subinc{\input{../../global/epilogue}}
337	337
338	338	\end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_misc.tex

-                      r11598
+                      r11954
 \begin{figure}[!tbp]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_Gibraltar}
   \includegraphics[width=0.66\textwidth]{Fig_Gibraltar2}
+  \includegraphics[width=0.66\textwidth]{MISC_Gibraltar}
+  \includegraphics[width=0.66\textwidth]{MISC_Gibraltar2}
   \caption[Two methods to defined the Gibraltar strait]{
     Example of the Gibraltar strait defined in a 1\deg\ $\times$ 1\deg\ mesh.
 …
 \begin{figure}[!tbp]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_closea_mask_example}
+  \includegraphics[width=0.66\textwidth]{MISC_closea_mask_example}
   \caption[Mask fields for the \protect\mdl{closea} module]{
     Example of mask fields for the \protect\mdl{closea} module.
 …
 increment also applies to the time.step file which is otherwise updated every timestep.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_model_basics.tex

-                      r11608
+                      r11954
 {\footnotesize
   \begin{tabularx}{\textwidth}{l||X|X}
     Release & Author(s) & Modifications \\
+  \begin{tabular}{l||l|l}
+    Release          & Author(s)                                   & Modifications       \\
     \hline
     {\em   4.0} & {\em Mike Bell                       } & {\em Update       } \\
     {\em   3.6} & {\em Gurvan Madec                    } & {\em Minor changes} \\
     {\em <=3.4} & {\em Gurvan Madec and Steven Alderson} & {\em First version} \\
   \end{tabularx}
+    {\em        4.0} & {\em Mike Bell                            } & {\em Review       } \\
+    {\em        3.6} & {\em Tim Graham and Gurvan Madec          } & {\em Updates      } \\
+    {\em $\leq$ 3.4} & {\em Gurvan Madec and S\'{e}bastien Masson} & {\em First version} \\
+  \end{tabular}
+}
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_I_ocean_bc}
+  \includegraphics[width=0.66\textwidth]{MB_ocean_bc}
   \caption[Ocean boundary conditions]{
     The ocean is bounded by two surfaces, $z = - H(i,j)$ and $z = \eta(i,j,t)$,
 …
 \]
 Two strategies can be considered for the surface pressure term:
 \begin{enumerate*}[label={(\alph*)}]
+\begin{enumerate*}[label=(\textit{\alph*})]
 \item introduce of a new variable $\eta$, the free-surface elevation,
 for which a prognostic equation can be established and solved;
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.33\textwidth]{Fig_I_earth_referential}
+  \includegraphics[width=0.33\textwidth]{MB_earth_referential}
   \caption[Geographical and curvilinear coordinate systems]{
     the geographical coordinate system $(\lambda,\varphi,z)$ and the curvilinear
 …
 \item [Flux form of the momentum equations]
   % \label{eq:MB_dyn_flux}
   \begin{multline*}
+  \begin{alignat*}{2}
     % \label{eq:MB_dyn_flux_u}
     \pd[u]{t} = + \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, v - \frac{1}{e_1 \; e_2} \lt( \pd[(e_2 \, u \, u)]{i} + \pd[(e_1 \, v \, u)]{j} \rt) \\
     - \frac{1}{e_3} \pd[(w \, u)]{k} - \frac{1}{e_1} \pd[]{i} \lt( \frac{p_s + p_h}{\rho_o} \rt) + D_u^{\vect U} + F_u^{\vect U}
   \end{multline*}
   \begin{multline*}
+    \pd[u]{t} = &+ \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, v - \frac{1}{e_1 \; e_2} \lt( \pd[(e_2 \, u \, u)]{i} + \pd[(e_1 \, v \, u)]{j} \rt) - \frac{1}{e_3} \pd[(w \, u)]{k} \\
+    &- \frac{1}{e_1} \pd[]{i} \lt( \frac{p_s + p_h}{\rho_o} \rt) + D_u^{\vect U} + F_u^{\vect U}
+  \end{alignat*}
+  \begin{alignat*}{2}
     % \label{eq:MB_dyn_flux_v}
     \pd[v]{t} = - \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, u - \frac{1}{e_1 \; e_2} \lt( \pd[(e_2 \, u \, v)]{i} + \pd[(e_1 \, v \, v)]{j} \rt) \\
     - \frac{1}{e_3} \pd[(w \, v)]{k} - \frac{1}{e_2} \pd[]{j} \lt( \frac{p_s + p_h}{\rho_o} \rt) + D_v^{\vect U} + F_v^{\vect U}
   \end{multline*}
+    \pd[v]{t} = &- \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, u - \frac{1}{e_1 \; e_2} \lt( \pd[(e_2 \, u \, v)]{i} + \pd[(e_1 \, v \, v)]{j} \rt) - \frac{1}{e_3} \pd[(w \, v)]{k} \\
+    &- \frac{1}{e_2} \pd[]{j} \lt( \frac{p_s + p_h}{\rho_o} \rt) + D_v^{\vect U} + F_v^{\vect U}
+  \end{alignat*}
   where $\zeta$, the relative vorticity, is given by \autoref{eq:MB_curl_Uh} and
   $p_s$, the surface pressure, is given by:
 …
 an explicit computation of vertical advection relative to the moving s-surfaces.
+%\gmcomment{
+%A key point here is that the $s$-coordinate depends on $(i,j)$ ==> horizontal pressure gradient...
+\cmtgm{A key point here is that the $s$-coordinate depends on $(i,j)$
+  ==> horizontal pressure gradient...}
 The generalized vertical coordinates used in ocean modelling are not orthogonal,
 which contrasts with many other applications in mathematical physics.
 …
   \end{gather*}
 \item [Flux form of the momentum equation]
   \begin{multline*}
+  \begin{alignat*}{2}
     % \label{eq:MB_sco_u_flux}
     \frac{1}{e_3} \pd[(e_3 \, u)]{t} = + \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, v - \frac{1}{e_1 \; e_2 \; e_3} \lt( \pd[(e_2 \, e_3 \, u \, u)]{i} + \pd[(e_1 \, e_3 \, v \, u)]{j} \rt) \\
     - \frac{1}{e_3} \pd[(\omega \, u)]{k} - \frac{1}{e_1} \pd[]{i} \lt( \frac{p_s + p_h}{\rho_o} \rt) - g \frac{\rho}{\rho_o} \sigma_1 + D_u^{\vect U} + F_u^{\vect U}
   \end{multline*}
   \begin{multline*}
+    \frac{1}{e_3} \pd[(e_3 \, u)]{t} = &+ \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, v - \frac{1}{e_1 \; e_2 \; e_3} \lt( \pd[(e_2 \, e_3 \, u \, u)]{i} + \pd[(e_1 \, e_3 \, v \, u)]{j} \rt) - \frac{1}{e_3} \pd[(\omega \, u)]{k} \\
+    &- \frac{1}{e_1} \pd[]{i} \lt( \frac{p_s + p_h}{\rho_o} \rt) - g \frac{\rho}{\rho_o} \sigma_1 + D_u^{\vect U} + F_u^{\vect U}
+  \end{alignat*}
+  \begin{alignat*}{2}
   % \label{eq:MB_sco_v_flux}
     \frac{1}{e_3} \pd[(e_3 \, v)]{t} = - \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, u - \frac{1}{e_1 \; e_2 \; e_3} \lt( \pd[( e_2 \; e_3 \, u \, v)]{i} + \pd[(e_1 \; e_3 \, v \, v)]{j} \rt) \\
     - \frac{1}{e_3} \pd[(\omega \, v)]{k} - \frac{1}{e_2} \pd[]{j} \lt( \frac{p_s + p_h}{\rho_o} \rt) - g \frac{\rho}{\rho_o}\sigma_2 + D_v^{\vect U} + F_v^{\vect U}
   \end{multline*}
+    \frac{1}{e_3} \pd[(e_3 \, v)]{t} = &- \lt[ f + \frac{1}{e_1 \; e_2} \lt( v \pd[e_2]{i} - u \pd[e_1]{j} \rt) \rt] \, u - \frac{1}{e_1 \; e_2 \; e_3} \lt( \pd[( e_2 \; e_3 \, u \, v)]{i} + \pd[(e_1 \; e_3 \, v \, v)]{j} \rt) - \frac{1}{e_3} \pd[(\omega \, v)]{k} \\
+    &- \frac{1}{e_2} \pd[]{j} \lt( \frac{p_s + p_h}{\rho_o} \rt) - g \frac{\rho}{\rho_o}\sigma_2 + D_v^{\vect U} + F_v^{\vect U}
+  \end{alignat*}
   where the relative vorticity, $\zeta$, the surface pressure gradient,
   and the hydrostatic pressure have the same expressions as in $z$-coordinates although
 …
 and similar expressions are used for mixing and forcing terms.
 \gmcomment{
+\cmtgm{
   \colorbox{yellow}{ to be updated $= = >$}
   Add a few works on z and zps and s and underlies the differences between all of them
 …
 \begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_z_zstar}
+  \includegraphics[width=0.66\textwidth]{MB_z_zstar}
   \caption[Curvilinear z-coordinate systems (\{non-\}linear free-surface cases and re-scaled \zstar)]{
     \begin{enumerate*}[label={(\alph*)}]
+    \begin{enumerate*}[label=(\textit{\alph*})]
     \item $z$-coordinate in linear free-surface case;
     \item $z$-coordinate in non-linear free surface case;
 …
 \begin{equation}
   \label{eq:MB_iso_slopes}
   r_1 = \frac{e_3}{e_1} \lt( \pd[\rho]{i} \rt) \lt( \pd[\rho]{k} \rt)^{-1} \quad
   r_2 = \frac{e_3}{e_2} \lt( \pd[\rho]{j} \rt) \lt( \pd[\rho]{k} \rt)^{-1}
+  r_1 = \frac{e_3}{e_1} \lt( \pd[\rho]{i} \rt) \lt( \pd[\rho]{k} \rt)^{-1} \quad
+  r_2 = \frac{e_3}{e_2} \lt( \pd[\rho]{j} \rt) \lt( \pd[\rho]{k} \rt)^{-1}
 \end{equation}
 while in $s$-coordinates $\pd[]{k}$ is replaced by $\pd[]{s}$.
 …
 where $ \vect U^\ast = \lt( u^\ast,v^\ast,w^\ast \rt)$ is a non-divergent,
 eddy-induced transport velocity. This velocity field is defined by:
 \begin{gather*}
+\[
   % \label{eq:MB_eiv}
   u^\ast =   \frac{1}{e_3}            \pd[]{k} \lt( A^{eiv} \;        \tilde{r}_1 \rt) \quad
   v^\ast =   \frac{1}{e_3}            \pd[]{k} \lt( A^{eiv} \;        \tilde{r}_2 \rt) \\
+  v^\ast =   \frac{1}{e_3}            \pd[]{k} \lt( A^{eiv} \;        \tilde{r}_2 \rt) \quad
   w^\ast = - \frac{1}{e_1 e_2} \lt[   \pd[]{i} \lt( A^{eiv} \; e_2 \, \tilde{r}_1 \rt)
                                      + \pd[]{j} \lt( A^{eiv} \; e_1 \, \tilde{r}_2 \rt) \rt]
 \end{gather*}
+\]
 where $A^{eiv}$ is the eddy induced velocity coefficient
 (or equivalently the isoneutral thickness diffusivity coefficient),
 …
 the $u$ and $v$-fields are considered as independent scalar fields,
 so that the diffusive operator is given by:
 \begin{gather*}
+\[
   % \label{eq:MB_lapU_iso}
     D_u^{l \vect U} = \nabla . \lt( A^{lm} \; \Re \; \nabla u \rt) \\
+    D_u^{l \vect U} = \nabla . \lt( A^{lm} \; \Re \; \nabla u \rt) \quad
     D_v^{l \vect U} = \nabla . \lt( A^{lm} \; \Re \; \nabla v \rt)
 \end{gather*}
+\]
 where $\Re$ is given by \autoref{eq:MB_iso_tensor}.
 It is the same expression as those used for diffusive operator on tracers.
 …
 Nevertheless it is currently not available in the iso-neutral case.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

-                      r11599
+                      r11954
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_DYN_dynspg_ts}
+  %\includegraphics[width=0.66\textwidth]{MBZ_DYN_dynspg_ts}
   \caption[Schematic of the split-explicit time stepping scheme for
   the barotropic and baroclinic modes, after \citet{Griffies2004?}]{
 …
 In particular, this means that in filtered case, the matrix to be inverted has to be recomputed at each time-step.
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/NEMO/subfiles/chap_time_domain.tex

-                      r11599
+                      r11954
 {\footnotesize
+  \begin{tabularx}{\textwidth}{l||X|X}
+    Release & Author(s) & Modifications \\
+  \begin{tabularx}{0.5\textwidth}{l||X|X}
+    Release          & Author(s)                                       &
+    Modifications                                                      \\
     \hline
+    {\em   4.0} & {\em ...} & {\em ...} \\
+    {\em   3.6} & {\em ...} & {\em ...} \\
+    {\em   3.4} & {\em ...} & {\em ...} \\
+    {\em <=3.4} & {\em ...} & {\em ...}
+    {\em        4.0} & {\em J\'{e}r\^{o}me Chanut \newline Tim Graham} &
+    {\em Review \newline Update                                      } \\
+    {\em        3.6} & {\em Christian \'{E}th\'{e}                   } &
+    {\em Update                                                      } \\
+    {\em $\leq$ 3.4} & {\em Gurvan Madec                             } &
+    {\em First version                                               } \\
   \end{tabularx}
+}
 …
 % Missing things:
+%  - daymod: definition of the time domain (nit000, nitend and the calendar)
+\gmcomment{STEVEN :maybe a picture of the directory structure in the introduction which could be referred to here,
+  would help  ==> to be added}
+Having defined the continuous equations in \autoref{chap:MB}, we need now to choose a time discretization,
+% - daymod: definition of the time domain (nit000, nitend and the calendar)
+\cmtgm{STEVEN :maybe a picture of the directory structure in the introduction which
+could be referred to here, would help  ==> to be added}
+Having defined the continuous equations in \autoref{chap:MB},
+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
 (\ie\ on its flowchart).
 In the present chapter, we provide a general description of the \NEMO\  time stepping strategy and
+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.
 …
 \end{equation}
 where $x$ stands for $u$, $v$, $T$ or $S$;
 RHS is the Right-Hand-Side of the corresponding time evolution equation;
+RHS is the \textbf{R}ight-\textbf{H}and-\textbf{S}ide of the corresponding time evolution equation;
 $\rdt$ is the time step;
 and the superscripts indicate the time at which a quantity is evaluated.
+Each term of the RHS is evaluated at a specific time stepping depending on the physics with which it is associated.
+Each term of the RHS is evaluated at a specific time stepping depending on
+the physics with which it is associated.
 The choice of the time stepping used for this evaluation is discussed below as well as
 the implications for starting or restarting a model simulation.
 Note that the time stepping calculation is generally performed in a single operation.
 With such a complex and nonlinear system of equations it would be dangerous to let a prognostic variable evolve in
 time for each term separately.
+With such a complex and nonlinear system of equations it would be dangerous to
+let a prognostic variable evolve in time for each term separately.
 The three level scheme requires three arrays for each prognostic variable.
 …
 The third array, although referred to as $x_a$ (after) in the code,
 is usually not the variable at the after time step;
+but rather it is used to store the time derivative (RHS in \autoref{eq:TD}) prior to time-stepping the equation.
+The time stepping itself is performed once at each time step where implicit vertical diffusion is computed, \ie\ in the \mdl{trazdf} and \mdl{dynzdf} modules.
+but rather it is used to store the time derivative (RHS in \autoref{eq:TD})
+prior to time-stepping the equation.
+The time stepping itself is performed once at each time step where
+implicit vertical diffusion is computed,
+\ie\ in the \mdl{trazdf} and \mdl{dynzdf} modules.
 %% =================================================================================================
 …
 \label{sec:TD_leap_frog}
 The time stepping used for processes other than diffusion is the well-known leapfrog scheme
 \citep{mesinger.arakawa_bk76}.
+The time stepping used for processes other than diffusion is
+the well-known \textbf{L}eap\textbf{F}rog (LF) scheme \citep{mesinger.arakawa_bk76}.
 This scheme is widely used for advection processes in low-viscosity fluids.
+It is a time centred scheme, \ie\ the RHS in \autoref{eq:TD} is evaluated at time step $t$, the now time step.
+It is a time centred scheme, \ie\ the RHS in \autoref{eq:TD} 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.
 It is an efficient method that achieves second-order accuracy with
 just one right hand side evaluation per time step.
 Moreover, it does not artificially damp linear oscillatory motion nor does it produce instability by
 amplifying the oscillations.
+Moreover, it does not artificially damp linear oscillatory motion
+nor does it produce instability by amplifying the oscillations.
 These advantages are somewhat diminished by the large phase-speed error of the leapfrog scheme,
+and the unsuitability of leapfrog differencing for the representation of diffusion and Rayleigh damping processes.
+and the unsuitability of leapfrog differencing for the representation of diffusion and
+Rayleigh damping processes.
 However, the scheme allows the coexistence of a numerical and a physical mode due to
 its leading third order dispersive error.
 In other words a divergence of odd and even time steps may occur.
+To prevent it, the leapfrog scheme is often used in association with a Robert-Asselin time filter
+(hereafter the LF-RA scheme).
+This filter, first designed by \citet{robert_JMSJ66} and more comprehensively studied by \citet{asselin_MWR72},
+To prevent it, the leapfrog scheme is often used in association with
+a \textbf{R}obert-\textbf{A}sselin time filter (hereafter the LF-RA scheme).
+This filter,
+first designed by \citet{robert_JMSJ66} and more comprehensively studied by \citet{asselin_MWR72},
 is a kind of laplacian diffusion in time that mixes odd and even time steps:
 \begin{equation}
 …
 However, the second order truncation error is proportional to $\gamma$, which is small compared to 1.
 Therefore, the LF-RA is a quasi second order accurate scheme.
+The LF-RA scheme is preferred to other time differencing schemes such as predictor corrector or trapezoidal schemes,
+because the user has an explicit and simple control of the magnitude of the time diffusion of the scheme.
+When used with the 2nd order space centred discretisation of the advection terms in
+The LF-RA scheme is preferred to other time differencing schemes such as
+predictor corrector or trapezoidal schemes, because the user has an explicit and simple control of
+the magnitude of the time diffusion of the scheme.
+When used with the 2$^nd$ order space centred discretisation of the advection terms in
 the momentum and tracer equations, LF-RA avoids implicit numerical diffusion:
 diffusion is set explicitly by the user through the Robert-Asselin
 filter parameter and the viscosity and diffusion coefficients.
+diffusion is set explicitly by the user through the Robert-Asselin filter parameter and
+the viscosity and diffusion coefficients.
 %% =================================================================================================
 …
 \label{sec:TD_forward_imp}
+The leapfrog differencing scheme is unsuitable for the representation of diffusion and damping processes.
+The leapfrog differencing scheme is unsuitable for
+the representation of diffusion and damping processes.
 For a tendency $D_x$, representing a diffusion term or a restoring term to a tracer climatology
 (when present, see \autoref{sec:TRA_dmp}), a forward time differencing scheme is used :
 …
 This is diffusive in time and conditionally stable.
+The conditions for stability of second and fourth order horizontal diffusion schemes are \citep{griffies_bk04}:
+The conditions for stability of second and fourth order horizontal diffusion schemes are
+\citep{griffies_bk04}:
 \begin{equation}
   \label{eq:TD_euler_stability}
 …
   \end{cases}
 \end{equation}
+where $e$ is the smallest grid size in the two horizontal directions and $A^h$ is the mixing coefficient.
+where $e$ is the smallest grid size in the two horizontal directions and
+$A^h$ is the mixing coefficient.
 The linear constraint \autoref{eq:TD_euler_stability} is a necessary condition, but not sufficient.
 If it is not satisfied, even mildly, then the model soon becomes wildly unstable.
+The instability can be removed by either reducing the length of the time steps or reducing the mixing coefficient.
+The instability can be removed by either reducing the length of the time steps or
+reducing the mixing coefficient.
 For the vertical diffusion terms, a forward time differencing scheme can be used,
+but usually the numerical stability condition imposes a strong constraint on the time step. To overcome the stability constraint, a
+backward (or implicit) time differencing scheme is used. This scheme is unconditionally stable but diffusive and can be written as follows:
+but usually the numerical stability condition imposes a strong constraint on the time step.
+To overcome the stability constraint, a backward (or implicit) time differencing scheme is used.
+This scheme is unconditionally stable but diffusive and can be written as follows:
 \begin{equation}
   \label{eq:TD_imp}
 …
 \end{equation}
+%%gm
+%%gm   UPDATE the next paragraphs with time varying thickness ...
+%%gm
+This scheme is rather time consuming since it requires a matrix inversion. For example, the finite difference approximation of the temperature equation is:
+\cmtgm{UPDATE the next paragraphs with time varying thickness ...}
+This scheme is rather time consuming since it requires a matrix inversion.
+For example, the finite difference approximation of the temperature equation is:
 \[
   % \label{eq:TD_imp_zdf}
 …
 \end{equation}
 where
+\begin{align*}
+  c(k) &= A_w^{vT} (k) \, / \, e_{3w} (k)     \\
+  d(k) &= e_{3t}   (k)       \, / \, (2 \rdt) + c_k + c_{k + 1}    \\
+  b(k) &= e_{3t}   (k) \; \lt( T^{t - 1}(k) \, / \, (2 \rdt) + \text{RHS} \rt)
+\end{align*}
+\autoref{eq:TD_imp_mat} is a linear system of equations with an associated matrix which is tridiagonal.
+Moreover,
+$c(k)$ and $d(k)$ are positive and the diagonal term is greater than the sum of the two extra-diagonal terms,
+\[
+  c(k) = A_w^{vT} (k) \, / \, e_{3w} (k) \text{,} \quad
+  d(k) = e_{3t}   (k)       \, / \, (2 \rdt) + c_k + c_{k + 1} \quad \text{and} \quad
+  b(k) = e_{3t}   (k) \; \lt( T^{t - 1}(k) \, / \, (2 \rdt) + \text{RHS} \rt)
+\]
+\autoref{eq:TD_imp_mat} is a linear system of equations with
+an associated matrix which is tridiagonal.
+Moreover, $c(k)$ and $d(k)$ are positive and
+the diagonal term is greater than the sum of the two extra-diagonal terms,
 therefore a special adaptation of the Gauss elimination procedure is used to find the solution
 (see for example \citet{richtmyer.morton_bk67}).
 …
 \label{sec:TD_spg_ts}
+The leapfrog environment supports a centred in time computation of the surface pressure, \ie\ evaluated
+at \textit{now} time step. This refers to as the explicit free surface case in the code (\np[=.true.]{ln_dynspg_exp}{ln\_dynspg\_exp}).
+This choice however imposes a strong constraint on the time step which should be small enough to resolve the propagation
+of external gravity waves. As a matter of fact, one rather use in a realistic setup, a split-explicit free surface
+(\np[=.true.]{ln_dynspg_ts}{ln\_dynspg\_ts}) in which barotropic and baroclinic dynamical equations are solved separately with ad-hoc
+time steps. The use of the time-splitting (in combination with non-linear free surface) imposes some constraints on the design of
+the overall flowchart, in particular to ensure exact tracer conservation (see \autoref{fig:TD_TimeStep_flowchart}).
+Compared to the former use of the filtered free surface in \NEMO\ v3.6 (\citet{roullet.madec_JGR00}), the use of a split-explicit free surface is advantageous
+on massively parallel computers. Indeed, no global computations are anymore required by the elliptic solver which saves a substantial amount of communication
+time. Fast barotropic motions (such as tides) are also simulated with a better accuracy.
+%\gmcomment{
+\begin{figure}[!t]
+The leapfrog environment supports a centred in time computation of the surface pressure,
+\ie\ evaluated at \textit{now} time step.
+This refers to as the explicit free surface case in the code
+(\np[=.true.]{ln_dynspg_exp}{ln\_dynspg\_exp}).
+This choice however imposes a strong constraint on the time step which
+should be small enough to resolve the propagation of external gravity waves.
+As a matter of fact, one rather use in a realistic setup,
+a split-explicit free surface (\np[=.true.]{ln_dynspg_ts}{ln\_dynspg\_ts}) in which
+barotropic and baroclinic dynamical equations are solved separately with ad-hoc time steps.
+The use of the time-splitting (in combination with non-linear free surface) imposes
+some constraints on the design of the overall flowchart,
+in particular to ensure exact tracer conservation (see \autoref{fig:TD_TimeStep_flowchart}).
+Compared to the former use of the filtered free surface in \NEMO\ v3.6 (\citet{roullet.madec_JGR00}),
+the use of a split-explicit free surface is advantageous on massively parallel computers.
+Indeed, no global computations are anymore required by the elliptic solver which
+saves a substantial amount of communication time.
+Fast barotropic motions (such as tides) are also simulated with a better accuracy.
+%\cmtgm{
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_TimeStepping_flowchart_v4}
+  \includegraphics[width=0.66\textwidth]{TD_TimeStepping_flowchart_v4}
   \caption[Leapfrog time stepping sequence with split-explicit free surface]{
     Sketch of the leapfrog time stepping sequence in \NEMO\ with split-explicit free surface.
     The latter combined with non-linear free surface requires the dynamical tendency being
     updated prior tracers tendency to ensure conservation.
+    The latter combined with non-linear free surface requires
+    the dynamical tendency being updated prior tracers tendency to ensure conservation.
     Note the use of time integrated fluxes issued from the barotropic loop in
     subsequent calculations of tracer advection and in the continuity equation.
 …
 %% =================================================================================================
 \section{Modified Leapfrog -- Asselin filter scheme}
+\section{Modified LeapFrog -- Robert Asselin filter scheme (LF-RA)}
 \label{sec:TD_mLF}
+Significant changes have been introduced by \cite{leclair.madec_OM09} in the LF-RA scheme in order to
+ensure tracer conservation and to allow the use of a much smaller value of the Asselin filter parameter.
+Significant changes have been introduced by \cite{leclair.madec_OM09} in
+the LF-RA scheme in order to ensure tracer conservation and to
+allow the use of a much smaller value of the Asselin filter parameter.
 The modifications affect both the forcing and filtering treatments in the LF-RA scheme.
 In a classical LF-RA environment, the forcing term is centred in time,
 \ie\ it is time-stepped over a $2 \rdt$ period:
+In a classical LF-RA environment,
+the forcing term is centred in time, \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:TD_asselin} so that $Q$ is redistributed over several time step.
+and the time filter is given by \autoref{eq:TD_asselin} so that
+$Q$ is redistributed over several time step.
 In the modified LF-RA environment, these two formulations have been replaced by:
 \begin{gather}
 …
                     - \gamma \, \rdt \, \lt( Q^{t + \rdt / 2} - Q^{t - \rdt / 2} \rt)
 \end{gather}
+The change in the forcing formulation given by \autoref{eq:TD_forcing} (see \autoref{fig:TD_MLF_forcing})
+has a significant effect:
+the forcing term no longer excites the divergence of odd and even time steps \citep{leclair.madec_OM09}.
+The change in the forcing formulation given by \autoref{eq:TD_forcing}
+(see \autoref{fig:TD_MLF_forcing}) has a significant effect:
+the forcing term no longer excites the divergence of odd and even time steps
+\citep{leclair.madec_OM09}.
 % forcing seen by the model....
 This property improves the LF-RA scheme in two aspects.
 First, the LF-RA can now ensure the local and global conservation of tracers.
 Indeed, time filtering is no longer required on the forcing part.
 The influence of the Asselin filter on the forcing is explicitly removed by adding a new term in the filter
 (last term in \autoref{eq:TD_RA} compared to \autoref{eq:TD_asselin}).
+The influence of the Asselin filter on the forcing is explicitly removed by
+adding a new term in the filter (last term in \autoref{eq:TD_RA} compared to \autoref{eq:TD_asselin}).
 Since the filtering of the forcing was the source of non-conservation in the classical LF-RA scheme,
 the modified formulation becomes conservative \citep{leclair.madec_OM09}.
 Second, the LF-RA becomes a truly quasi -second order scheme.
+Second, the LF-RA becomes a truly quasi-second order scheme.
 Indeed, \autoref{eq:TD_forcing} used in combination with a careful treatment of static instability
 (\autoref{subsec:ZDF_evd}) and of the TKE physics (\autoref{subsec:ZDF_tke_ene})
 …
 even if separated by only $\rdt$ since the time filter is no longer applied to the forcing term.
 \begin{figure}[!t]
+\begin{figure}
   \centering
   \includegraphics[width=0.66\textwidth]{Fig_MLF_forcing}
+  \includegraphics[width=0.66\textwidth]{TD_MLF_forcing}
   \caption[Forcing integration methods for modified leapfrog (top and bottom)]{
     Illustration of forcing integration methods.
 …
 \end{listing}
 The first time step of this three level scheme when starting from initial conditions is a forward step
 (Euler time integration):
+The first time step of this three level scheme when starting from initial conditions is
+a forward step (Euler time integration):
 \[
   % \label{eq:TD_DOM_euler}
   x^1 = x^0 + \rdt \ \text{RHS}^0
 \]
+This is done simply by keeping the leapfrog environment (\ie\ the \autoref{eq:TD} three level time stepping) but
+This is done simply by keeping the leapfrog environment
+(\ie\ the \autoref{eq:TD} 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 a leapfrog time step ($2 \rdt$).
 …
 running the model for $2N$ time steps in one go,
 or by performing two consecutive experiments of $N$ steps with a restart.
+This requires saving two time levels and many auxiliary data in the restart files in machine precision.
+This requires saving two time levels and many auxiliary data in
+the restart files in machine precision.
 Note that the time step $\rdt$, is also saved in the restart file.
+When restarting, if the time step has been changed, or one of the prognostic variables at \textit{before} time step
+is missing, an Euler time stepping scheme is imposed. A forward initial step can still be enforced by the user by setting
+the namelist variable \np[=0]{nn_euler}{nn\_euler}. Other options to control the time integration of the model
+are defined through the  \nam{run}{run} namelist variables.
+\gmcomment{
+When restarting, if the time step has been changed, or
+one of the prognostic variables at \textit{before} time step is missing,
+an Euler time stepping scheme is imposed.
+A forward initial step can still be enforced by the user by
+setting the namelist variable \np[=0]{nn_euler}{nn\_euler}.
+Other options to control the time integration of the model are defined through
+the \nam{run}{run} namelist variables.
+\cmtgm{
 add here how to force the restart to contain only one time step for operational purposes
 add also the idea of writing several restart for seasonal forecast : how is it done ?
 verify that all namelist pararmeters are truly described
+verify that all namelist parameters are truly described
 a word on the check of restart  .....
+}
 \gmcomment{       % add a subsection here
+\cmtgm{       % add a subsection here
 %% =================================================================================================
 …
 \label{subsec:TD_time}
 Options are defined through the  \nam{dom}{dom} namelist variables.
+Options are defined through the\nam{dom}{dom} namelist variables.
  \colorbox{yellow}{add here a few word on nit000 and nitend}
  \colorbox{yellow}{Write documentation on the calendar and the key variable adatrj}
 add a description of daymod, and the model calandar (leap-year and co)
 }        %% end add
 \gmcomment{       % add implicit in vvl case  and Crant-Nicholson scheme
+add a description of daymod, and the model calendar (leap-year and co)
+}     %% end add
+\cmtgm{       % add implicit in vvl case  and Crant-Nicholson scheme
 Implicit time stepping in case of variable volume thickness.
 …
+}
 \onlyinsubfile{\input{../../global/epilogue}}
+\subinc{\input{../../global/epilogue}}
 \end{document}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/SI3/namelists/namdyn_adv

-                      r11026
+                      r11954
 &namdyn_adv     !   Ice advection
 !------------------------------------------------------------------------------
    ln_adv_Pra       = .false.         !  Advection scheme (Prather)
    ln_adv_UMx       = .true.          !  Advection scheme (Ultimate-Macho)
+   ln_adv_Pra       = .true.         !  Advection scheme (Prather)
+   ln_adv_UMx       = .false.          !  Advection scheme (Ultimate-Macho)
       nn_UMx        =   5             !     order of the scheme for UMx (1-5 ; 20=centered 2nd order)
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/TOP/subfiles/model_description.tex

-                      r11591
+                      r11954
 \chapter{Model Description}
 \label{chap:ModDes}
 \minitoc
+\chaptertoc
 \section{Basics}
 …
 \nlst{namtrc_ldf}
 %-------------------------------------------------------------------------------------------------------------
 In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set  in the \ngn{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{nemo_manual}.
+In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set  in the \nam{namtra_ldf}{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{nemo_manual}.
 …
 The use of newtonian damping  to climatological fields or observations is also coded, sharing the same routine dans active tracers. Boolean variables are defined in the namelist\_top\_ref to select the tracers on which restoring is applied
 Options are defined through the  \ngn{namtrc\_dmp} namelist variables. The restoring term is added when the namelist parameter \np{ln\_trcdmp} is set to true. The restoring coefficient is a three-dimensional array read in a file, which name is specified by the namelist variable \np{cn\_resto\_tr}. This netcdf file can be generated using the DMP\_TOOLS tool.
+Options are defined through the \nam{namtrc_dmp}{namtrc\_dmp} namelist variables. The restoring term is added when the namelist parameter \np{ln\_trcdmp} is set to true. The restoring coefficient is a three-dimensional array read in a file, which name is specified by the namelist variable \np{cn\_resto\_tr}. This netcdf file can be generated using the DMP\_TOOLS tool.
  \subsection{ Tracer positivity}
 …
 Sometimes, numerical scheme can generates negative values of passive tracers concentration that must be positive. For exemple,  isopycnal diffusion can created extrema. The trcrad routine artificially corrects negative concentrations with a very crude solution that either sets negative concentration to zero without adjusting the tracer budget, or by removing negative concentration and keeping mass conservation.
 The treatment of negative concentrations is an option and can be selected in the namelist \ngn{namtrc\_rad} by setting the parameter \np{ln\_trcrad}  to true.
+The treatment of negative concentrations is an option and can be selected in the namelist \nam{namtrc_rad}{namtrc\_rad} by setting the parameter \np{ln\_trcrad}  to true.
 \section{The SMS modules}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/global/document.tex

-                      r11591
+                      r11954
 %% End of common preamble between main and sub-files
 %% Override custom cmds for full manual compilation
 \newcommand{\onlyinsubfile}[1]{#1}
 \newcommand{\notinsubfile}[1]{}
+\newcommand{\subinc}[1]{#1}
+\newcommand{\subexc}[1]{}
 \begin{document}
 \renewcommand{\onlyinsubfile}[1]{}
 \renewcommand{\notinsubfile}[1]{#1}
+\renewcommand{\subinc}[1]{}
+\renewcommand{\subexc}[1]{#1}

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/global/frontpage.tex

r11591	r11954
33	33	\LARGE Version \version\ -\ \today \\
34	34	\medskip
35		\href{http://doi.org/10.5281/zenodo.\zid}{ \includegraphics{~~{badges/zenodo.\zid}.pdf~~} }
	35	\href{http://doi.org/10.5281/zenodo.\zid}{ \includegraphics{badges/zenodo.\zid} }
36	36	\end{center}
37	37

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/global/new_cmds.tex

r11584	r11954
34	34
35	35	%% Gurvan's comments
36		\newcommand{\~~gmcomment~~}[1]{}
	36	\newcommand{\cmtgm}[1]{}
37	37
38	38	%% Maths

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/global/packages.tex

-                      r11595
+                      r11954
 %% Issue with fontawesome pkg: path to FontAwesome.otf has to be hard-coded
 \defaultfontfeatures{
     Path = /home/ntmlod/.local/texlive2019/texmf-dist/fonts/opentype/public/fontawesome/
+    Path = /usr/local/texlive/2019/texmf-dist/fonts/opentype/public/fontawesome/
+}
 \usepackage{academicons, fontawesome, newtxtext}
 %% Formatting
+\usepackage[inline]{enumitem}
 \usepackage{etoc, tabularx, xcolor}
 %% Graphics
 \usepackage{caption, graphicx}
+\usepackage{caption, graphicx, grffile}
 %% Labels
 …
 %% Mathematics
 \usepackage{amsmath, amssymb}
+\usepackage{amsmath, amssymb, mathtools}
 %% Versatility

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/latex/global/styles.tex

-                      r11572
+                      r11954
+}
+%% Temporary fix
+\def\set@curr@file#1{%
+  \begingroup
+    \escapechar\m@ne
+    \xdef\@curr@file{\expandafter\string\csname #1\endcsname}%
+  \endgroup
+}
+\def\quote@name#1{"\quote@@name#1\@gobble""}
+\def\quote@@name#1"{#1\quote@@name}
+\def\unquote@name#1{\quote@@name#1\@gobble"}
 \makeatother

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nam_diadct

r11536	r11954
1	1	!-----------------------------------------------------------------------
2		&nam_diadct ~~! transports through some sections~~ (default: OFF)
	2	&nam_diadct ! transports through some sections (default: OFF)
3	3	!-----------------------------------------------------------------------
4	4	ln_diadct = .false. ! Calculate transport thru sections or not

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nam_diaharm

r11536	r11954
7	7	nstep_han = 15 ! Time step frequency for harmonic analysis
8	8	tname(1) = 'M2' ! Name of tidal constituents
9		tname(2) = 'K1'
	9	tname(2) = 'K1' ! ---
10	10	/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nambdy

r11536	r11954
26	26	ln_dyn3d_dmp =.false. ! open boundary condition for baroclinic velocities
27	27	rn_time_dmp = 1. ! Damping time scale in days
28		rn_time_dmp_out = 1. ! Outflow damping time scale
	28	rn_time_dmp_out = 1. ! Outflow damping time scale
29	29	nn_rimwidth = 10 ! width of the relaxation zone
30	30	ln_vol = .false. ! total volume correction (see nn_volctl parameter)

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nambdy_dta

-                      r11536
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    bn_ssh      = 'amm12_bdyT_u2d'        ,         24        , 'sossheig',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
    bn_u2d      = 'amm12_bdyU_u2d'        ,         24        , 'vobtcrtx',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
    bn_v2d      = 'amm12_bdyV_u2d'        ,         24        , 'vobtcrty',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
    bn_u3d      = 'amm12_bdyU_u3d'        ,         24        , 'vozocrtx',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
    bn_v3d      = 'amm12_bdyV_u3d'        ,         24        , 'vomecrty',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
    bn_tem      = 'amm12_bdyT_tra'        ,         24        , 'votemper',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
    bn_sal      = 'amm12_bdyT_tra'        ,         24        , 'vosaline',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
+   bn_ssh      = 'amm12_bdyT_u2d'        ,         24.       , 'sossheig',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
+   bn_u2d      = 'amm12_bdyU_u2d'        ,         24.       , 'vobtcrtx',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
+   bn_v2d      = 'amm12_bdyV_u2d'        ,         24.       , 'vobtcrty',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
+   bn_u3d      = 'amm12_bdyU_u3d'        ,         24.       , 'vozocrtx',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
+   bn_v3d      = 'amm12_bdyV_u3d'        ,         24.       , 'vomecrty',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
+   bn_tem      = 'amm12_bdyT_tra'        ,         24.       , 'votemper',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
+   bn_sal      = 'amm12_bdyT_tra'        ,         24.       , 'vosaline',    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''
 !* for si3
    bn_a_i      = 'amm12_bdyT_ice'        ,         24.       , 'siconc'  ,    .true.   , .false.,  'daily'  ,    ''            ,   ''     ,     ''

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namberg

r11005	r11954
37	37	! ! file name ! frequency (hours) ! variable ! time interp.! clim ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
38	38	! ! ! (if <0 months) ! name ! (logical) ! (T/F) ! 'monthly' ! ! pairing ! filename !
39		sn_icb = 'calving' , -1 ,'calvingmask', .true. , .true. , 'yearly' , '' , '' , ''
	39	sn_icb = 'calving' , -1. ,'calvingmask', .true. , .true. , 'yearly' , '' , '' , ''
40	40	/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namc1d_uvd

-                      r10075
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_ucur     = 'ucurrent'              ,         -1        ,'u_current',   .false.   , .true. , 'monthly' ,  ''              ,  'Ume'   , ''
    sn_vcur     = 'vcurrent'              ,         -1        ,'v_current',   .false.   , .true. , 'monthly' ,  ''              ,  'Vme'   , ''
+   sn_ucur     = 'ucurrent'              ,         -1.       ,'u_current',   .false.   , .true. , 'monthly' ,  ''              ,  'Ume'   , ''
+   sn_vcur     = 'vcurrent'              ,         -1.       ,'v_current',   .false.   , .true. , 'monthly' ,  ''              ,  'Vme'   , ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namdia

-                      r11536
+                      r11954
 &namdia         !   Diagnostics
 !------------------------------------------------------------------------------
    ln_icediachk     = .false.         !  check online the heat, mass & salt budgets at each time step
       !                               !     rate of ice spuriously gained/lost. For ex., rn_icechk=1. <=> 1mm/year, rn_icechk=0.1 <=> 1mm/10years
       rn_icechk_cel =  1.             !     check at any gridcell           => stops the code if violated (and writes a file)
       rn_icechk_glo =  0.1            !     check over the entire ice cover => only prints warnings
+   ln_icediachk     = .false.         !  check online heat, mass & salt budgets
+      !                               !   rate of ice spuriously gained/lost at each time step => rn_icechk=1 <=> 1.e-6 m/hour
+      rn_icechk_cel =  100.           !     check at each gridcell          (1.e-4m/h)=> stops the code if violated (and writes a file)
+      rn_icechk_glo =  1.             !     check over the entire ice cover (1.e-6m/h)=> only prints warnings
    ln_icediahsb     = .false.         !  output the heat, mass & salt budgets (T) or not (F)
    ln_icectl        = .false.         !  ice points output for debug (T or F)

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namdta_dyn

-                      r11025
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_tem      = 'dyna_grid_T'           ,       120         , 'votemper'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_sal      = 'dyna_grid_T'           ,       120         , 'vosaline'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_mld      = 'dyna_grid_T'           ,       120         , 'somixhgt'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_emp      = 'dyna_grid_T'           ,       120         , 'sowaflup'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_fmf      = 'dyna_grid_T'           ,       120         , 'iowaflup'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_ice      = 'dyna_grid_T'           ,       120         , 'soicecov'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_qsr      = 'dyna_grid_T'           ,       120         , 'soshfldo'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_wnd      = 'dyna_grid_T'           ,       120         , 'sowindsp'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_uwd      = 'dyna_grid_U'           ,       120         , 'uocetr_eff',  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_vwd      = 'dyna_grid_V'           ,       120         , 'vocetr_eff',  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_wwd      = 'dyna_grid_W'           ,       120         , 'wocetr_eff',  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_avt      = 'dyna_grid_W'           ,       120         , 'voddmavs'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_ubl      = 'dyna_grid_U'           ,       120         , 'sobblcox'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_vbl      = 'dyna_grid_V'           ,       120         , 'sobblcoy'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_tem      = 'dyna_grid_T'           ,       120.        , 'votemper'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_sal      = 'dyna_grid_T'           ,       120.        , 'vosaline'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_mld      = 'dyna_grid_T'           ,       120.        , 'somixhgt'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_emp      = 'dyna_grid_T'           ,       120.        , 'sowaflup'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_fmf      = 'dyna_grid_T'           ,       120.        , 'iowaflup'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_ice      = 'dyna_grid_T'           ,       120.        , 'soicecov'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_qsr      = 'dyna_grid_T'           ,       120.        , 'soshfldo'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_wnd      = 'dyna_grid_T'           ,       120.        , 'sowindsp'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_uwd      = 'dyna_grid_U'           ,       120.        , 'uocetr_eff',  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_vwd      = 'dyna_grid_V'           ,       120.        , 'vocetr_eff',  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_wwd      = 'dyna_grid_W'           ,       120.        , 'wocetr_eff',  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_avt      = 'dyna_grid_W'           ,       120.        , 'voddmavs'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_ubl      = 'dyna_grid_U'           ,       120.        , 'sobblcox'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_vbl      = 'dyna_grid_V'           ,       120.        , 'sobblcoy'  ,  .true.   , .true. , 'yearly'  , ''               , ''       , ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namdyn

-                      r11025
+                      r11954
    rn_ishlat        =   2.            !  lbc : free slip (0) ; partial slip (0-2) ; no slip (2) ; strong slip (>2)
    ln_landfast_L16  = .false.         !  landfast: parameterization from Lemieux 2016
-   ln_landfast_home = .false.         !  landfast: parameterization from "home made"
       rn_depfra     =   0.125         !        fraction of ocean depth that ice must reach to initiate landfast
+                                      !          recommended range: [0.1 ; 0.25] - L16=0.125 - home=0.15
+      rn_icebfr     =  15.            !        ln_landfast_L16:  maximum bottom stress per unit volume [N/m3]
+                                      !        ln_landfast_home: maximum bottom stress per unit area of contact [N/m2]
+                                      !          recommended range: ?? L16=15 - home=10
+                                      !          recommended range: [0.1 ; 0.25]
+      rn_icebfr     =  15.            !        maximum bottom stress per unit volume [N/m3]
       rn_lfrelax    =   1.e-5         !        relaxation time scale to reach static friction [s-1]
       rn_tensile    =   0.2           !        ln_landfast_L16: isotropic tensile strength
+      rn_tensile    =   0.05          !        isotropic tensile strength [0-0.5??]
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namini

r11536	r11954
23	23	rn_hpd_ini_n = 0.05 ! initial pond depth (m), North
24	24	rn_hpd_ini_s = 0.05 ! " " South
25		! ~~! if ln_iceini_file=~~T
	25	! -- for ln_iceini_file = T
26	26	sn_hti = 'Ice_initialization' , -12 ,'hti' , .false. , .true., 'yearly' , '' , '', ''
27	27	sn_hts = 'Ice_initialization' , -12 ,'hts' , .false. , .true., 'yearly' , '' , '', ''

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nammpp

-                      r11536
+                      r11954
 &nammpp        !   Massively Parallel Processing                        ("key_mpp_mpi")
 !-----------------------------------------------------------------------
+   ln_listonly =  .false.  !  do nothing else than listing the best domain decompositions (with land domains suppression)
+   !                       !  if T: the largest number of cores tested is defined by max(mppsize, jpni*jpnj)
    ln_nnogather =  .true.  !  activate code to avoid mpi_allgather use at the northfold
    jpni        =   0       !  jpni   number of processors following i (set automatically if < 1)
    jpnj        =   0       !  jpnj   number of processors following j (set automatically if < 1)
+   jpni        =   0       !  number of processors following i (set automatically if < 1), see also ln_listonly = T
+   jpnj        =   0       !  number of processors following j (set automatically if < 1), see also ln_listonly = T
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namobs

r11316	r11954
8	8	ln_sla = .false. ! Logical switch for SLA observations
9	9	ln_sst = .false. ! Logical switch for SST observations
10		ln_sss = .false. ! Logical switch for SSS observations
	10	ln_sss = .false. ! Logical swithc for SSS observations
11	11	ln_sic = .false. ! Logical switch for Sea Ice observations
12	12	ln_vel3d = .false. ! Logical switch for velocity observations

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nampisatm

-                      r11025
+                      r11954
 !              !  file name   ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
 !              !              !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
    sn_patm     = 'presatm'    ,     -1            , 'patm'    ,  .true.      , .true. , 'yearly'  , ''       , ''       , ''
    sn_atmco2   = 'presatmco2' ,     -1            , 'xco2'    ,  .true.      , .true. , 'yearly'  , ''       , ''       , ''
+   sn_patm     = 'presatm'    ,     -1.           , 'patm'    ,  .true.      , .true. , 'yearly'  , ''       , ''       , ''
+   sn_atmco2   = 'presatmco2' ,     -1.           , 'xco2'    ,  .true.      , .true. , 'yearly'  , ''       , ''       , ''
    cn_dir      = './'     !  root directory for the location of the dynamical files
+!

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nampisopt

r11025	r11954
4	4	! ! file name ! frequency (hours) ! variable ! time interp. ! clim ! 'yearly'/ ! weights ! rotation ! land/sea mask !
5	5	! ! ! (if <0 months) ! name ! (logical) ! (T/F) ! 'monthly' ! filename ! pairing ! filename !
6		sn_par = 'par.orca' , 24 , 'fr_par' , .true. , .true. , 'yearly' , '' , '' , ''
	6	sn_par = 'par.orca' , 24. , 'fr_par' , .true. , .true. , 'yearly' , '' , '' , ''
7	7	cn_dir = './' ! root directory for the location of the dynamical files
8	8	ln_varpar = .true. ! boolean for PAR variable

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/nampissbc

-                      r11025
+                      r11954
 !              !  file name        ! frequency (hours) ! variable      ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
 !              !                   !  (if <0  months)  !   name        !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
    sn_dust     = 'dust.orca'       ,     -1            , 'dust'        ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_solub    = 'solubility.orca' ,    -12            , 'solubility1' ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
    sn_riverdic = 'river.orca'      ,    120            , 'riverdic'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_riverdoc = 'river.orca'      ,    120            , 'riverdoc'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_riverdin = 'river.orca'      ,    120            , 'riverdin'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_riverdon = 'river.orca'      ,    120            , 'riverdon'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_riverdip = 'river.orca'      ,    120            , 'riverdip'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_riverdop = 'river.orca'      ,    120            , 'riverdop'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_riverdsi = 'river.orca'      ,    120            , 'riverdsi'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
    sn_ndepo    = 'ndeposition.orca',    -12            , 'ndep'        ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
    sn_ironsed  = 'bathy.orca'      ,    -12            , 'bathy'       ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
    sn_hydrofe  = 'hydrofe.orca'    ,    -12            , 'epsdb'       ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
+   sn_dust     = 'dust.orca'       ,     -1.           , 'dust'        ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_solub    = 'solubility.orca' ,    -12.           , 'solubility1' ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
+   sn_riverdic = 'river.orca'      ,    120.           , 'riverdic'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_riverdoc = 'river.orca'      ,    120.           , 'riverdoc'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_riverdin = 'river.orca'      ,    120.           , 'riverdin'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_riverdon = 'river.orca'      ,    120.           , 'riverdon'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_riverdip = 'river.orca'      ,    120.           , 'riverdip'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_riverdop = 'river.orca'      ,    120.           , 'riverdop'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_riverdsi = 'river.orca'      ,    120.           , 'riverdsi'    ,  .true.      , .true. , 'yearly'  , ''       , ''    , ''
+   sn_ndepo    = 'ndeposition.orca',    -12.           , 'ndep'        ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
+   sn_ironsed  = 'bathy.orca'      ,    -12.           , 'bathy'       ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
+   sn_hydrofe  = 'hydrofe.orca'    ,    -12.           , 'epsdb'       ,  .false.     , .true. , 'yearly'  , ''       , ''    , ''
+!
    cn_dir      = './'      !  root directory for the location of the dynamical files

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namrun

-                      r11005
+                      r11954
       cn_ocerst_indir = "."         !  directory from which to read input ocean restarts
       cn_ocerst_out   = "restart"   !  suffix of ocean restart name (output)
       cn_ocerst_outdir = "."         !  directory in which to write output ocean restarts
+      cn_ocerst_outdir = "."        !  directory in which to write output ocean restarts
    ln_iscpl    = .false.   !  cavity evolution forcing or coupling to ice sheet model
    nn_istate   =       0   !  output the initial state (1) or not (0)
    ln_rst_list = .false.   !  output restarts at list of times using nn_stocklist (T) or at set frequency with nn_stock (F)
+   nn_stock    =    5840   !  frequency of creation of a restart file (modulo referenced to 1)
+   nn_stock    =       0   !  used only if ln_rst_list = F: output restart freqeuncy (modulo referenced to 1)
+      !                          !    =  0 force to write restart files only at the end of the run
+      !                          !    = -1 do not do any restart
    nn_stocklist = 0,0,0,0,0,0,0,0,0,0 ! List of timesteps when a restart file is to be written
+   nn_write    =    5840   !  frequency of write in the output file   (modulo referenced to nn_it000)
+   ln_mskland  = .false.   !  mask land points in NetCDF outputs (costly: + ~15%)
+   nn_write    =       0   !  used only if key_iomput is not defined: output frequency (modulo referenced to nn_it000)
+      !                          !    =  0 force to write output files only at the end of the run
+      !                          !    = -1 do not do any output file
+   ln_mskland  = .false.   !  mask land points in NetCDF outputs
    ln_cfmeta   = .false.   !  output additional data to netCDF files required for compliance with the CF metadata standard
    ln_clobber  = .true.    !  clobber (overwrite) an existing file

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_apr

r10075	r11954
10	10	! ! file name ! frequency (hours) ! variable ! time interp.! clim ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
11	11	! ! ! (if <0 months) ! name ! (logical) ! (T/F) ! 'monthly' ! ! pairing ! filename !
12		sn_apr = 'patm' , -1 ,'somslpre' , .true. , .true. , 'yearly' , '' , '' , ''
	12	sn_apr = 'patm' , -1. ,'somslpre' , .true. , .true. , 'yearly' , '' , '' , ''
13	13	/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_blk

-                      r10445
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ !       weights filename               ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                                      ! pairing  !    filename   !
    sn_wndi     = 'u_10.15JUNE2009_fill'       ,    6         , 'U_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bicubic_noc.nc'  , 'Uwnd'   , ''
    sn_wndj     = 'v_10.15JUNE2009_fill'       ,    6         , 'V_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bicubic_noc.nc'  , 'Vwnd'   , ''
    sn_qsr      = 'ncar_rad.15JUNE2009_fill'   ,   24         , 'SWDN_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
    sn_qlw      = 'ncar_rad.15JUNE2009_fill'   ,   24         , 'LWDN_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
    sn_tair     = 't_10.15JUNE2009_fill'       ,    6         , 'T_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
    sn_humi     = 'q_10.15JUNE2009_fill'       ,    6         , 'Q_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
    sn_prec     = 'ncar_precip.15JUNE2009_fill',   -1         , 'PRC_MOD1',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
    sn_snow     = 'ncar_precip.15JUNE2009_fill',   -1         , 'SNOW'    ,   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
    sn_slp      = 'slp.15JUNE2009_fill'        ,    6         , 'SLP'     ,   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+   sn_wndi     = 'u_10.15JUNE2009_fill'       ,    6.        , 'U_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bicubic_noc.nc'  , 'Uwnd'   , ''
+   sn_wndj     = 'v_10.15JUNE2009_fill'       ,    6.        , 'V_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bicubic_noc.nc'  , 'Vwnd'   , ''
+   sn_qsr      = 'ncar_rad.15JUNE2009_fill'   ,   24.        , 'SWDN_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+   sn_qlw      = 'ncar_rad.15JUNE2009_fill'   ,   24.        , 'LWDN_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+   sn_tair     = 't_10.15JUNE2009_fill'       ,    6.        , 'T_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+   sn_humi     = 'q_10.15JUNE2009_fill'       ,    6.        , 'Q_10_MOD',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+   sn_prec     = 'ncar_precip.15JUNE2009_fill',   -1.        , 'PRC_MOD1',   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+   sn_snow     = 'ncar_precip.15JUNE2009_fill',   -1.        , 'SNOW'    ,   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+   sn_slp      = 'slp.15JUNE2009_fill'        ,    6.        , 'SLP'     ,   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
    sn_tdif     = 'taudif_core'                ,   24         , 'taudif'  ,   .false.   , .true. , 'yearly'  , 'weights_core_orca2_bilinear_noc.nc' , ''       , ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_flx

-                      r10075
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_utau     = 'utau'                  ,        24         , 'utau'    , .false.     , .false., 'yearly'  , ''               , ''       , ''
    sn_vtau     = 'vtau'                  ,        24         , 'vtau'    , .false.     , .false., 'yearly'  , ''               , ''       , ''
    sn_qtot     = 'qtot'                  ,        24         , 'qtot'    , .false.     , .false., 'yearly'  , ''               , ''       , ''
    sn_qsr      = 'qsr'                   ,        24         , 'qsr'     , .false.     , .false., 'yearly'  , ''               , ''       , ''
    sn_emp      = 'emp'                   ,        24         , 'emp'     , .false.     , .false., 'yearly'  , ''               , ''       , ''
+   sn_utau     = 'utau'                  ,        24.        , 'utau'    , .false.     , .false., 'yearly'  , ''               , ''       , ''
+   sn_vtau     = 'vtau'                  ,        24.        , 'vtau'    , .false.     , .false., 'yearly'  , ''               , ''       , ''
+   sn_qtot     = 'qtot'                  ,        24.        , 'qtot'    , .false.     , .false., 'yearly'  , ''               , ''       , ''
+   sn_qsr      = 'qsr'                   ,        24.        , 'qsr'     , .false.     , .false., 'yearly'  , ''               , ''       , ''
+   sn_emp      = 'emp'                   ,        24.        , 'emp'     , .false.     , .false., 'yearly'  , ''               , ''       , ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_isf

-                      r10445
+                      r11954
    !           !             !  (if <0  months)  !   name    !  (logical)  !  (T/F)  ! 'monthly' ! filename ! pairing  ! filename      !
 !* nn_isf = 4 case
    sn_fwfisf   = 'rnfisf'    ,         -12       ,'sowflisf' ,  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
+   sn_fwfisf   = 'rnfisf'    ,         -12.      ,'sowflisf' ,  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
 !* nn_isf = 3 case
    sn_rnfisf   = 'rnfisf'    ,         -12       ,'sofwfisf' ,  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
+   sn_rnfisf   = 'rnfisf'    ,         -12.      ,'sofwfisf' ,  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
 !* nn_isf = 2 and 3 cases
    sn_depmax_isf ='rnfisf'    ,         -12       ,'sozisfmax',  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
    sn_depmin_isf ='rnfisf'    ,         -12       ,'sozisfmin',  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
+   sn_depmax_isf ='rnfisf'   ,         -12.      ,'sozisfmax',  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
+   sn_depmin_isf ='rnfisf'   ,         -12.      ,'sozisfmin',  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
 !* nn_isf = 2 case
    sn_Leff_isf = 'rnfisf'    ,         -12       ,'Leff'     ,  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
+   sn_Leff_isf = 'rnfisf'    ,         -12.      ,'Leff'     ,  .false.    , .true.  , 'yearly'  ,    ''    ,   ''     ,    ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_rnf

-                      r10445
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_rnf      = 'runoff_core_monthly'   ,        -1         , 'sorunoff',   .true.    , .true. , 'yearly'  , ''               , ''       , ''
    sn_cnf      = 'runoff_core_monthly'   ,         0         , 'socoefr0',   .false.   , .true. , 'yearly'  , ''               , ''       , ''
    sn_s_rnf    = 'runoffs'               ,        24         , 'rosaline',   .true.    , .true. , 'yearly'  , ''               , ''       , ''
    sn_t_rnf    = 'runoffs'               ,        24         , 'rotemper',   .true.    , .true. , 'yearly'  , ''               , ''       , ''
    sn_dep_rnf  = 'runoffs'               ,         0         , 'rodepth' ,   .false.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_rnf      = 'runoff_core_monthly'   ,        -1.        , 'sorunoff',   .true.    , .true. , 'yearly'  , ''               , ''       , ''
+   sn_cnf      = 'runoff_core_monthly'   ,         0.        , 'socoefr0',   .false.   , .true. , 'yearly'  , ''               , ''       , ''
+   sn_s_rnf    = 'runoffs'               ,        24.        , 'rosaline',   .true.    , .true. , 'yearly'  , ''               , ''       , ''
+   sn_t_rnf    = 'runoffs'               ,        24.        , 'rotemper',   .true.    , .true. , 'yearly'  , ''               , ''       , ''
+   sn_dep_rnf  = 'runoffs'               ,         0.        , 'rodepth' ,   .false.   , .true. , 'yearly'  , ''               , ''       , ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_sas

-                      r10075
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_usp      = 'sas_grid_U'            ,       120         , 'uos'     ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
    sn_vsp      = 'sas_grid_V'            ,       120         , 'vos'     ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
    sn_tem      = 'sas_grid_T'            ,       120         , 'sosstsst',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
    sn_sal      = 'sas_grid_T'            ,       120         , 'sosaline',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
    sn_ssh      = 'sas_grid_T'            ,       120         , 'sossheig',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
    sn_e3t      = 'sas_grid_T'            ,       120         , 'e3t_m'   ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
    sn_frq      = 'sas_grid_T'            ,       120         , 'frq_m'   ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_usp      = 'sas_grid_U'            ,       120.        , 'uos'     ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_vsp      = 'sas_grid_V'            ,       120.        , 'vos'     ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_tem      = 'sas_grid_T'            ,       120.        , 'sosstsst',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_sal      = 'sas_grid_T'            ,       120.        , 'sosaline',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_ssh      = 'sas_grid_T'            ,       120.        , 'sossheig',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_e3t      = 'sas_grid_T'            ,       120.        , 'e3t_m'   ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_frq      = 'sas_grid_T'            ,       120.        , 'frq_m'   ,   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_ssr

-                      r10075
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_sst      = 'sst_data'              ,        24         ,  'sst'    ,    .false.  , .false., 'yearly'  ,    ''            ,    ''    ,     ''
    sn_sss      = 'sss_data'              ,        -1         ,  'sss'    ,    .true.   , .true. , 'yearly'  ,    ''            ,    ''    ,     ''
+   sn_sst      = 'sst_data'              ,        24.        ,  'sst'    ,    .false.  , .false., 'yearly'  ,    ''            ,    ''    ,     ''
+   sn_sss      = 'sss_data'              ,        -1.        ,  'sss'    ,    .true.   , .true. , 'yearly'  ,    ''            ,    ''    ,     ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namsbc_wave

-                      r10445
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_cdg      =  'sdw_ecwaves_orca2'    ,        6          , 'drag_coeff' ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_usd      =  'sdw_ecwaves_orca2'    ,        6          , 'u_sd2d'     ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_vsd      =  'sdw_ecwaves_orca2'    ,        6          , 'v_sd2d'     ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_hsw      =  'sdw_ecwaves_orca2'    ,        6          , 'hs'         ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_wmp      =  'sdw_ecwaves_orca2'    ,        6          , 'wmp'        ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_wfr      =  'sdw_ecwaves_orca2'    ,        6          , 'wfr'        ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_wnum     =  'sdw_ecwaves_orca2'    ,        6          , 'wave_num'   ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_tauwoc   =  'sdw_ecwaves_orca2'    ,        6          , 'wave_stress',  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_tauwx    =  'sdw_ecwaves_orca2'    ,        6          , 'wave_stress',  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
    sn_tauwy    =  'sdw_ecwaves_orca2'    ,        6          , 'wave_stress',  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_cdg      =  'sdw_ecwaves_orca2'    ,        6.         , 'drag_coeff' ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_usd      =  'sdw_ecwaves_orca2'    ,        6.         , 'u_sd2d'     ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_vsd      =  'sdw_ecwaves_orca2'    ,        6.         , 'v_sd2d'     ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_hsw      =  'sdw_ecwaves_orca2'    ,        6.         , 'hs'         ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_wmp      =  'sdw_ecwaves_orca2'    ,        6.         , 'wmp'        ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_wfr      =  'sdw_ecwaves_orca2'    ,        6.         , 'wfr'        ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_wnum     =  'sdw_ecwaves_orca2'    ,        6.         , 'wave_num'   ,  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_tauwoc   =  'sdw_ecwaves_orca2'    ,        6.         , 'wave_stress',  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_tauwx    =  'sdw_ecwaves_orca2'    ,        6.         , 'wave_stress',  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+   sn_tauwy    =  'sdw_ecwaves_orca2'    ,        6.         , 'wave_stress',  .true.  , .true. , 'yearly'  ,  ''              , ''       , ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namtra_qsr

r10075	r11954
16	16	! ! file name ! frequency (hours) ! variable ! time interp.! clim ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
17	17	! ! ! (if <0 months) ! name ! (logical) ! (T/F) ! 'monthly' ! ! pairing ! filename !
18		sn_chl ='chlorophyll' , -1 , 'CHLA' , .true. , .true. , 'yearly' , '' , '' , ''
	18	sn_chl ='chlorophyll' , -1. , 'CHLA' , .true. , .true. , 'yearly' , '' , '' , ''
19	19	/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namtrc_dta

r11025	r11954
4	4	! ! file name ! frequency (hours) ! variable ! time interp. ! clim ! 'yearly'/ ! weights ! rotation ! land/sea mask !
5	5	! ! ! (if <0 months) ! name ! (logical) ! (T/F) ! 'monthly' ! filename ! pairing ! filename !
6		sn_trcdta(1) = 'data_TRC_nomask' , -12 , 'TRC' , .false. , .true. , 'yearly' , '' , '' , ''
	6	sn_trcdta(1) = 'data_TRC_nomask' , -12. , 'TRC' , .false. , .true. , 'yearly' , '' , '' , ''
7	7	!
8	8	cn_dir = './' ! root directory for the location of the data files

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/namelists/namtsd

-                      r10075
+                      r11954
    !           !  file name              ! frequency (hours) ! variable  ! time interp.!  clim  ! 'yearly'/ ! weights filename ! rotation ! land/sea mask !
    !           !                         !  (if <0  months)  !   name    !   (logical) !  (T/F) ! 'monthly' !                  ! pairing  !    filename   !
    sn_tem = 'data_1m_potential_temperature_nomask',  -1      , 'votemper',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
    sn_sal = 'data_1m_salinity_nomask'             ,  -1      , 'vosaline',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_tem = 'data_1m_potential_temperature_nomask',  -1.     , 'votemper',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+   sn_sal = 'data_1m_salinity_nomask'             ,  -1.     , 'vosaline',   .true.    , .true. , 'yearly'  ,    ''            ,    ''    ,    ''
+/

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/rst/Makefile

-                      r10990
+                      r11954
 # Minimal makefile for Sphinx documentation
+# Makefile for Sphinx documentation
+#
 …
 SPHINXOPTS    =
 SPHINXBUILD   = sphinx-build
+SPHINXPROJ    = NEMO
+SOURCEDIR     = source
+PAPER         =
 BUILDDIR      = build
+# Put it first so that "make" without argument is like "make help".
+# Internal variables.
+PAPEROPT_a4     = -D latex_paper_size=a4
+PAPEROPT_letter = -D latex_paper_size=letter
+ALLSPHINXOPTS   = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source
+# the i18n builder cannot share the environment and doctrees with the others
+I18NSPHINXOPTS  = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source
+.PHONY: help clean html dirhtml drafthtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext
 help:
+   @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+   @echo "Please use \`make <target>' where <target> is one of"
+   @echo "  html       to make standalone HTML files"
+   @echo "  dirhtml    to make HTML files named index.html in directories"
+   @echo "  drafthtml  to make an autoupdate HTML export while editing (todo list included)"
+   @echo "  singlehtml to make a single large HTML file"
+   @echo "  pickle     to make pickle files"
+   @echo "  json       to make JSON files"
+   @echo "  htmlhelp   to make HTML files and a HTML help project"
+   @echo "  qthelp     to make HTML files and a qthelp project"
+   @echo "  devhelp    to make HTML files and a Devhelp project"
+   @echo "  epub       to make an epub"
+   @echo "  latex      to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
+   @echo "  latexpdf   to make LaTeX files and run them through pdflatex"
+   @echo "  text       to make text files"
+   @echo "  man        to make manual pages"
+   @echo "  texinfo    to make Texinfo files"
+   @echo "  info       to make Texinfo files and run them through makeinfo"
+   @echo "  gettext    to make PO message catalogs"
+   @echo "  changes    to make an overview of all changed/added/deprecated items"
+   @echo "  linkcheck  to check all external links for integrity"
+   @echo "  doctest    to run all doctests embedded in the documentation (if enabled)"
+.PHONY: help Makefile
+clean:
+   -rm -rf $(BUILDDIR)/*
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
    @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+html:
+   $(SPHINXBUILD)   -b html          $(ALLSPHINXOPTS) $(BUILDDIR)/html
+   @echo
+   @echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
+# Watch source directory and rebuild the documentation when a change is detected
+# Browse to 127.0.0.1:8000/NEMO_guide.html
+htmllive:
+   sphinx-autobuild $(SPHINXOPTS) $(SOURCEDIR) $(BUILDDIR)/htmllive
+dirhtml:
+   $(SPHINXBUILD)   -b dirhtml       $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
+   @echo
+   @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
+drafthtml:
+   sphinx-autobuild -b html -t draft $(ALLSPHINXOPTS) $(BUILDDIR)/drafthtml
+   @echo
+   @echo "Build finished. The HTML pages are in $(BUILDDIR)/drafthtml."
+singlehtml:
+   $(SPHINXBUILD)   -b singlehtml    $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
+   @echo
+   @echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
+pickle:
+   $(SPHINXBUILD)   -b pickle        $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
+   @echo
+   @echo "Build finished; now you can process the pickle files."
+json:
+   $(SPHINXBUILD)   -b json          $(ALLSPHINXOPTS) $(BUILDDIR)/json
+   @echo
+   @echo "Build finished; now you can process the JSON files."
+htmlhelp:
+   $(SPHINXBUILD)   -b htmlhelp      $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
+   @echo
+   @echo "Build finished; now you can run HTML Help Workshop with the" \
+         ".hhp project file in $(BUILDDIR)/htmlhelp."
+qthelp:
+   $(SPHINXBUILD)   -b qthelp        $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp
+   @echo
+   @echo "Build finished; now you can run "qcollectiongenerator" with the" \
+         ".qhcp project file in $(BUILDDIR)/qthelp, like this:"
+   @echo "# qcollectiongenerator $(BUILDDIR)/qthelp/NEMO.qhcp"
+   @echo "To view the help file:"
+   @echo "# assistant -collectionFile $(BUILDDIR)/qthelp/NEMO.qhc"
+devhelp:
+   $(SPHINXBUILD)   -b devhelp       $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp
+   @echo
+   @echo "Build finished."
+   @echo "To view the help file:"
+   @echo "# mkdir -p $$HOME/.local/share/devhelp/NEMO"
+   @echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/NEMO"
+   @echo "# devhelp"
+epub:
+   $(SPHINXBUILD)   -b epub          $(ALLSPHINXOPTS) $(BUILDDIR)/epub
+   @echo
+   @echo "Build finished. The epub file is in $(BUILDDIR)/epub."
+latex:
+   $(SPHINXBUILD)   -b latex         $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+   @echo
+   @echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex."
+   @echo "Run \`make' in that directory to run these through (pdf)latex" \
+         "(use \`make latexpdf' here to do that automatically)."
+latexpdf:
+   $(SPHINXBUILD)   -b latex         $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+   @echo "Running LaTeX files through pdflatex..."
+   $(MAKE) -C $(BUILDDIR)/latex all-pdf
+   @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
+text:
+   $(SPHINXBUILD)   -b text          $(ALLSPHINXOPTS) $(BUILDDIR)/text
+   @echo
+   @echo "Build finished. The text files are in $(BUILDDIR)/text."
+man:
+   $(SPHINXBUILD)   -b man           $(ALLSPHINXOPTS) $(BUILDDIR)/man
+   @echo
+   @echo "Build finished. The manual pages are in $(BUILDDIR)/man."
+texinfo:
+   $(SPHINXBUILD)   -b texinfo       $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+   @echo
+   @echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo."
+   @echo "Run \`make' in that directory to run these through makeinfo" \
+         "(use \`make info' here to do that automatically)."
+info:
+   $(SPHINXBUILD)   -b texinfo       $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+   @echo "Running Texinfo files through makeinfo..."
+   make -C $(BUILDDIR)/texinfo info
+   @echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo."
+gettext:
+   $(SPHINXBUILD)   -b gettext      $(I18NSPHINXOPTS) $(BUILDDIR)/locale
+   @echo
+   @echo "Build finished. The message catalogs are in $(BUILDDIR)/locale."
+changes:
+   $(SPHINXBUILD)   -b changes       $(ALLSPHINXOPTS) $(BUILDDIR)/changes
+   @echo
+   @echo "The overview file is in $(BUILDDIR)/changes."
+linkcheck:
+   $(SPHINXBUILD)   -b linkcheck     $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
+   @echo
+   @echo "Link check complete; look for any errors in the above output " \
+         "or in $(BUILDDIR)/linkcheck/output.txt."
+doctest:
+   $(SPHINXBUILD)   -b doctest       $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
+   @echo "Testing of doctests in the sources finished, look at the " \
+         "results in $(BUILDDIR)/doctest/output.txt."

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/rst/README.rst

-                      r10991
+                      r11954
 **********************
+| The NEMO guide is made up of several files written in `ReStructuredText <http://docutils.sourceforge.net/rst.html>`_ (`.rst` extension), a WYSIWYG markup language used in the Python community, and scattered all over the NEMO sources.
+| The NEMO guide is made up of several files written in
+  `ReStructuredText <http://docutils.sourceforge.net/rst.html>`_ (`.rst` extension),
+  a WYSIWYG markup language used in the Python community, and scattered all over the NEMO sources.
 | You can view them one by one in plain text from `./source` folder, or export all to a user-friendly guide under `./build` (only HTML format at the moment, PDF expected later).

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/rst/source/_static/style.css

-                      r10279
+                      r11954
 .rstblue               { color: blue    ; }
 .rstgrey , .rstgreysup { color: grey    ; }
 .rstgreen              { color: seagreen; }
+.blue            { color: blue    ; }
+.grey , .greysup { color: grey    ; }
+.green           { color: seagreen; }
 .logo { filter: invert(1) !important; }

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/rst/source/conf.py

-                      r10991
+                      r11954
 # -*- coding: utf-8 -*-
+#
+# Configuration file for the Sphinx documentation builder.
+#
+# This file does only contain a selection of the most common options. For a
+# full list see the documentation:
+# http://www.sphinx-doc.org/en/master/config
+# -- Project information -----------------------------------------------------
+project = 'NEMO'
+author = 'NEMO System Team'
+# The short X.Y version
+version = 'trk'
+# The full version, including alpha/beta/rc tags
+release = 'trunk'
+# -- General configuration ---------------------------------------------------
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = ['sphinx.ext.extlinks', 'sphinxcontrib.bibtex']
+# NEMO documentation build configuration file, created by
+# sphinx-quickstart on Tue Oct 15 20:13:55 2019.
+#
+# This file is execfile()d with the current directory set to its containing dir.
+#
+# Note that not all possible configuration values are present in this
+# autogenerated file.
+#
+# All configuration values have a default; values that are commented out
+# serve to show the default.
+import sys, os
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+#sys.path.insert(0, os.path.abspath('.'))
+# -- General configuration -----------------------------------------------------
+# If your documentation needs a minimal Sphinx version, state it here.
+#needs_sphinx = '1.0'
+# Add any Sphinx extension module names here, as strings. They can be extensions
+# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
+extensions = ['sphinx.ext.extlinks', 'sphinxcontrib.bibtex',
+              'sphinx.ext.todo'    , 'sphinx.ext.autosectionlabel']
 # Add any paths that contain templates here, relative to this directory.
 templates_path = ['_templates']
+# The suffix of source filenames.
+source_suffix = '.rst'
+# The encoding of source files.
+#source_encoding = 'utf-8-sig'
 # The master toctree document.
+master_doc = 'NEMO_guide'
+master_doc = 'guide'
+# General information about the project.
+project = u'NEMO'
+copyright = u'2019, NEMO Consortium'
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+# The short X.Y version.
+version = 'trk'
+# The full version, including alpha/beta/rc tags.
+release = 'trunk'
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+#language = None
+# There are two options for replacing |today|: either, you set today to some
+# non-false value, then it is used:
+#today = ''
+# Else, today_fmt is used as the format for a strftime call.
+#today_fmt = '%B %d, %Y'
 # List of patterns, relative to source directory, that match files and
 # directories to ignore when looking for source files.
+# This pattern also affects html_static_path and html_extra_path .
+exclude_patterns = ['global.rst', 'coarsening.rst']
+exclude_patterns = ['global.rst', 'readme.rst']
+# The reST default role (used for this markup: `text`) to use for all documents.
+#default_role = None
+# If true, '()' will be appended to :func: etc. cross-reference text.
+#add_function_parentheses = True
+# If true, the current module name will be prepended to all description
+# unit titles (such as .. function::).
+#add_module_names = True
+# If true, sectionauthor and moduleauthor directives will be shown in the
+# output. They are ignored by default.
+#show_authors = False
 # The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+# -- Options for HTML output -------------------------------------------------
+pygments_style = 'emacs'
+# A list of ignored prefixes for module index sorting.
+#modindex_common_prefix = []
+# -- Options for HTML output ---------------------------------------------------
 # The theme to use for HTML and HTML Help pages.  See the documentation for
 # a list of builtin themes.
+#
 html_theme = 'sphinx_rtd_theme'
 …
 # further.  For a list of options available for each theme, see the
 # documentation.
+#
+html_theme_options = {}
+#html_theme_options = {}
+# Add any paths that contain custom themes here, relative to this directory.
+#html_theme_path = []
+# The name for this set of Sphinx documents.  If None, it defaults to
+# "<project> v<release> documentation".
+#html_title = None
+# A shorter title for the navigation bar.  Default is the same as html_title.
+#html_short_title = None
+# The name of an image file (relative to this directory) to place at the top
+# of the sidebar.
+#html_logo = None
+# The name of an image file (within the static path) to use as favicon of the
+# docs.  This file should be a Windows icon file (.ico) being 16x16 or 32x32
+# pixels large.
+html_favicon = '_static/ORCA.ico'
 # Add any paths that contain custom static files (such as style sheets) here,
 …
 html_static_path = ['_static']
+html_favicon = '_static/ORCA.ico'
+# -- Options for LaTeX output ------------------------------------------------
+# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
+# using the given strftime format.
+#html_last_updated_fmt = '%b %d, %Y'
+# If true, SmartyPants will be used to convert quotes and dashes to
+# typographically correct entities.
+#html_use_smartypants = True
+# Custom sidebar templates, maps document names to template names.
+#html_sidebars = {}
+# Additional templates that should be rendered to pages, maps page names to
+# template names.
+#html_additional_pages = {}
+# If false, no module index is generated.
+#html_domain_indices = True
+# If false, no index is generated.
+#html_use_index = True
+# If true, the index is split into individual pages for each letter.
+#html_split_index = False
+# If true, links to the reST sources are added to the pages.
+#html_show_sourcelink = True
+# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
+#html_show_sphinx = True
+# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
+#html_show_copyright = True
+# If true, an OpenSearch description file will be output, and all pages will
+# contain a <link> tag referring to it.  The value of this option must be the
+# base URL from which the finished HTML is served.
+#html_use_opensearch = ''
+# This is the file name suffix for HTML files (e.g. ".xhtml").
+#html_file_suffix = None
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'NEMOdoc'
+# -- Options for LaTeX output --------------------------------------------------
 latex_elements = {
+    # The paper size ('letterpaper' or 'a4paper').
+    #
+    # 'papersize': 'letterpaper',
+    # The font size ('10pt', '11pt' or '12pt').
+    #
+    # 'pointsize': '10pt',
+    # Additional stuff for the LaTeX preamble.
+    #
+    # 'preamble': '',
+    # Latex figure (float) alignment
+    #
+    # 'figure_align': 'htbp',
+# The paper size ('letterpaper' or 'a4paper').
+#'papersize': 'letterpaper',
+# The font size ('10pt', '11pt' or '12pt').
+#'pointsize': '10pt',
+# Additional stuff for the LaTeX preamble.
+#'preamble': '',
+}
 # Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title,
+#  author, documentclass [howto, manual, or own class]).
+# (source start file, target name, title, author, documentclass [howto/manual]).
 latex_documents = [
     (master_doc, 'NEMO_guide.tex', 'NEMO Quick Start Guide',
      'NEMO System Team', 'howto'),
+  ('guide', 'guide.tex', u'NEMO Quick Start Guide',
+   u'NEMO Consortium', 'howto'),
+]
+# -- Customisation -----------------------------------------------------------
+# The name of an image file (relative to this directory) to place at the top of
+# the title page.
+#latex_logo = None
+# For "manual" documents, if this is true, then toplevel headings are parts,
+# not chapters.
+#latex_use_parts = False
+# If true, show page references after internal links.
+#latex_show_pagerefs = False
+# If true, show URL addresses after external links.
+#latex_show_urls = False
+# Documents to append as an appendix to all manuals.
+#latex_appendices = []
+# If false, no module index is generated.
+#latex_domain_indices = True
+# -- Options for manual page output --------------------------------------------
+# One entry per manual page. List of tuples
+# (source start file, name, description, authors, manual section).
+man_pages = [
+    ('guide', 'nemo', u'NEMO Documentation',
+     [u'NEMO System Team'], 1)
+]
+# If true, show URL addresses after external links.
+#man_show_urls = False
+# -- Options for Texinfo output ------------------------------------------------
+# Grouping the document tree into Texinfo files. List of tuples
+# (source start file, target name, title, author,
+#  dir menu entry, description, category)
+texinfo_documents = [
+  ('guide', 'NEMO', u'NEMO Documentation',
+   u'NEMO System Team', 'NEMO', 'Community Ocean Model',
+   'Miscellaneous'),
+]
+# Documents to append as an appendix to all manuals.
+#texinfo_appendices = []
+# If false, no module index is generated.
+#texinfo_domain_indices = True
+# How to display URL addresses: 'footnote', 'no', or 'inline'.
+#texinfo_show_urls = 'footnote'
+# -- Customisation -------------------------------------------------------------
 # Timestamping
 …
 # Link aliases
 extlinks = {
+   'doi'    : ('https://doi.org/%s'                       , None),
+   'forge'  : ('https://forge.ipsl.jussieu.fr/nemo/%s'    , None),
+   'github' : ('https://github.com/%s'                    , None),
+   'xios'   : ('https://forge.ipsl.jussieu.fr/ioserver/%s', None),
+   'website': ('https://www.nemo-ocean.eu/%s'             , None),
+   'zenodo' : ('https://zenodo.org/publication/%s'        , None)
+   'doi'    : ('https://doi.org/%s'                                                    , 'doi:'),
+   'manhtml': ('https://forge.ipsl.jussieu.fr/nemo/chrome/site/doc/NEMO/manual/html/%s', None  ),
+   'forge'  : ('https://forge.ipsl.jussieu.fr/nemo/%s'                                 , None  ),
+   'gmd'    : ('https://www.geosci-model-dev.net/%s'                                   , None  ),
+   'github' : ('https://github.com/NEMO-ocean/%s'                                      , None  ),
+   'xios'   : ('https://forge.ipsl.jussieu.fr/ioserver/%s'                             , None  ),
+   'website': ('https://www.nemo-ocean.eu/%s'                                          , None  ),
+   'zenodo' : ('https://zenodo.org/publication/%s'                                     , None  )
+}
 …
 # SVN revision
 import subprocess
+revision = subprocess.check_output("svnversion").decode("utf-8")
+rst_prolog = '.. |revision| replace:: %s' % revision
+rev = subprocess.check_output("svnversion").decode("utf-8")
+rst_prolog = '.. |revision| replace:: %s' % rev
+# 'draft' build tag: DRAFT watermark and TODO list
+if tags.has('draft'):
+   todo_include_todos = True
+   todo_emit_warnings = True
+else:
+   exclude_patterns = ['global.rst', 'readme.rst', 'todos.rst', 'unpub*']
+# Default language to highlight set to fortran
+highlight_language = 'fortran'

NEMO/branches/2019/dev_r11613_ENHANCE-04_namelists_as_internalfiles/doc/rst/source/global.rst

-                      r10605
+                      r11954
 .. Roles (custom styles related to CSS classes in 'source/_static/style.css')
+.. Roles
+.. role:: rstblue
+.. role:: rstgreen
+.. role:: rstgrey
+.. role:: rstgreysup(sup)
+.. role:: underline
+   :class: underline
+.. custom styles related to CSS classes in './_static/style.css'
+.. role:: blue
+.. role:: green
+.. role:: grey
+.. role:: greysup(sup)
+.. inline code snippets
+.. role:: python(code)
+   :language: python
+   :class: highlight
+.. role:: fortran(code)
+   :language: fortran
+   :class: highlight
+.. role:: console(code)
+   :language: console
+   :class: highlight
 .. Substitutions
+.. |OPA| replace:: :rstblue:`NEMO-OPA`
+.. |SI3| replace:: :rstgrey:`NEMO-SI`\ :rstgreysup:`3`
+.. |TOP| replace:: :rstgreen:`NEMO-TOP/PISCES`
+.. |NEMO-OCE| replace::  :blue:`NEMO-OCE (Ocean dynamics)`
+.. |OCE|      replace::  :blue:`NEMO-OCE`
+.. |NEMO-ICE| replace::  :grey:`NEMO-SI`\ :greysup:`3`  :grey:`(Sea Ice)`
+.. |ICE|      replace::  :grey:`NEMO-SI`\ :greysup:`3`
+.. |NEMO-MBG| replace:: :green:`NEMO-TOP/PISCES (Tracers)`
+.. |MBG|      replace:: :green:`NEMO-TOP/PISCES`
 .. Institutes
+.. External links
+.. _CMCC:           https://www.cmcc.it
+.. _CNRS:           https://www.cnrs.fr
+.. _Mercator Ocean: https://www.mercator-ocean.fr
+.. _Met Office:     https://www.metoffice.gov.uk
+.. _MOI:            https://www.mercator-ocean.fr
+.. _NERC:           https://nerc.ukri.org
+   .. Consortium institutes
+.. Models / Softwares
+.. _CMCC:       https://www.cmcc.it
+.. _CNRS:       https://www.cnrs.fr
+.. _Met Office: https://www.metoffice.gov.uk
+.. _MOI:        https://www.mercator-ocean.fr
+.. _NERC:       https://nerc.ukri.org
+   .. Models / Libraries / Dependencies
 .. _AGRIF:  http://agrif.imag.fr
+.. _FCM:    https://metomi.github.io/fcm/doc/
+.. _BFM:    http://www.bfm-community.eu
+.. _FCM:    https://metomi.github.io/fcm
 .. _IOIPSL: https://forge.ipsl.jussieu.fr/igcmg/browser/IOIPSL
+.. _NEMO:   https://www.nemo-ocean.eu
 .. _OASIS:  https://portal.enes.org/oasis
+.. _XIOS:   https://forge.ipsl.jussieu.fr/ioserver
+.. NEMO
+   .. Misc.
+.. _NEMO:          https://www.nemo-ocean.eu
+.. _NEMO strategy: https://doi.org/10.5281/zenodo.1471663
+.. _NEMO guide:    :samp: https://doi.org/10.5281/zenodo.1475325
+.. _NEMO manual:   https://doi.org/10.5281/zenodo.1464816
+.. _SI3 manual:    :samp: https://doi.org/10.5281/zenodo.1471689
+.. _TOP manual:    :samp: https://doi.org/10.5281/zenodo.1471700
+.. _EGU: http://www.egu.eu
+.. _Special Issue: https://www.geosci-model-dev.net/special_issue40.html
+.. _BFM man: https://cmcc-foundation.github.io/www.bfm-community.eu/files/bfm-nemo-manual_r1.0_201508.pdf
+.. _RST man: https://www.sphinx-doc.org/en/master/usage/restructuredtext/index.html
+.. _PAPA station: http://www.pmel.noaa.gov/OCS/Papa/index-Papa.shtml
+.. _ISOMIP: http://staff.acecrc.org.au/~bkgalton/ISOMIP/test_cavities.pdf
+.. DOI
+   .. Publications (`:samp:` to deactivate link for unpublished documents)
+.. _DOI man OCE:          https://doi.org/10.5281/zenodo.1464816
+.. _DOI man ICE:   :samp: https://doi.org/10.5281/zenodo.1471689
+.. _DOI man MBG:   :samp: https://doi.org/10.5281/zenodo.1471700
+.. _DOI qsg:       :samp: https://doi.org/10.5281/zenodo.1475325
+.. _DOI dev  stgy:        https://doi.org/10.5281/zenodo.1471663
+.. _DOI data:             https://doi.org/10.5281/zenodo.1472245
+   .. Badges (same labels as previously, substitution to link images)
+.. |DOI man OCE| image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1464816.svg
+.. |DOI man ICE| image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1471689.svg
+.. |DOI man MBG| image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1471700.svg
+.. |DOI qsg|     image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1475325.svg
+.. |DOI data|    image:: https://zenodo.org/badge/DOI/10.5281/zenodo.1472245.svg

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