Changeset 11263 for NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc

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NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex

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-                      old
+                      new
+*.aux
+*.bbl
+*.blg
+*.dvi
+*.fdb*
+*.fls
+*.idx
+*.ilg
+*.ind
+*.log
+*.maf
+*.mtc*
+*.out
+*.pdf
+*.toc
+_minted-*
+figures

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO

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NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_A.tex

-                      r10442
+                      r11263
+    {
     \begin{array}{*{20}l}
       \nabla \cdot {\rm {\bf U}}
+      \nabla \cdot {\mathrm {\mathbf U}}
       &= \frac{1}{e_1 \,e_2 }  \left[ \left. {\frac{\partial (e_2 \,u)}{\partial i}} \right|_z
         +\left. {\frac{\partial(e_1 \,v)}{\partial j}} \right|_z  \right]
 …
       $, it becomes:}
+    %
       \nabla \cdot {\rm {\bf U}}
+      \nabla \cdot {\mathrm {\mathbf U}}
       & = \frac{1}{e_1 \,e_2 \,e_3 }  \left[
         \left.  \frac{\partial (e_2 \,e_3 \,u)}{\partial i} \right|_s
 …
+    {
     \begin{array}{*{20}l}
       \nabla \cdot {\rm {\bf U}}
+      \nabla \cdot {\mathrm {\mathbf U}}
       &= \frac{1}{e_1 \,e_2 \,e_3 }    \left[
         \left.  \frac{\partial (e_2 \,e_3 \,u)}{\partial i} \right|_s
 …
+  %
     &= \left. {\frac{\partial u }{\partial t}} \right|_s
     &+ \left.  \nabla \cdot \left(   {{\rm {\bf U}}\,u}   \right)    \right|_s
+    &+ \left.  \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,u}   \right)    \right|_s
       + \,u \frac{1}{e_3 } \frac{\partial e_3}{\partial t}
       - \frac{v}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i}
 …
   \label{apdx:A_sco_Dt_flux}
   \left. \frac{D u}{D t} \right|_s   = \frac{1}{e_3}  \left. \frac{\partial ( e_3\,u)}{\partial t} \right|_s
   + \left.  \nabla \cdot \left(   {{\rm {\bf U}}\,u}   \right)    \right|_s
+  + \left.  \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,u}   \right)    \right|_s
   - \frac{v}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i}
     -u  \;\frac{\partial e_1 }{\partial j}            \right)
 …
 As in $z$-coordinate,
 the horizontal pressure gradient can be split in two parts following \citet{Marsaleix_al_OM08}.
+the horizontal pressure gradient can be split in two parts following \citet{marsaleix.auclair.ea_OM08}.
 Let defined a density anomaly, $d$, by $d=(\rho - \rho_o)/ \rho_o$,
 and a hydrostatic pressure anomaly, $p_h'$, by $p_h'= g \; \int_z^\eta d \; e_3 \; dk$.
 …
     \label{apdx:A_PE_dyn_flux_u}
     \frac{1}{e_3} \frac{\partial \left(  e_3\,u  \right) }{\partial t} =
     \nabla \cdot \left(   {{\rm {\bf U}}\,u}   \right)
+    \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,u}   \right)
     +   \left\{ {f + \frac{1}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i}
           -u  \;\frac{\partial e_1 }{\partial j}            \right)} \right\} \,v     \\
 …
     \label{apdx:A_dyn_flux_v}
     \frac{1}{e_3}\frac{\partial \left(  e_3\,v  \right) }{\partial t}=
     -  \nabla \cdot \left(   {{\rm {\bf U}}\,v}   \right)
+    -  \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,v}   \right)
     +   \left\{ {f + \frac{1}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i}
           -u  \;\frac{\partial e_1 }{\partial j}            \right)} \right\} \,u     \\

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_B.tex

-                      r10442
+                      r11263
 the ($i$,$j$,$k$) curvilinear coordinate system in which
 the equations of the ocean circulation model are formulated,
 takes the following form \citep{Redi_JPO82}:
+takes the following form \citep{redi_JPO82}:
 \begin{equation}
 …
 In practice, isopycnal slopes are generally less than $10^{-2}$ in the ocean,
 so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{Cox1987}:
+so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{cox_OM87}:
 \begin{subequations}
   \label{apdx:B4}
 …
+  {
   \begin{array}{*{20}l}
     \nabla T\;.\left( {{\rm {\bf A}}_{\rm {\bf I}} \nabla T}
+    \nabla T\;.\left( {{\mathrm {\mathbf A}}_{\mathrm {\mathbf I}} \nabla T}
     \right)&=A^{lT}\left[ {\left( {\frac{\partial T}{\partial i}} \right)^2-2a_1
              \frac{\partial T}{\partial i}\frac{\partial T}{\partial k}+\left(
 …
   - \nabla _h \times \left( {A^{lm}\;\zeta \;{\textbf{k}}} \right)
   + \frac{1}{e_3 }\frac{\partial }{\partial k}\left( {\frac{A^{vm}\;}{e_3 }
       \frac{\partial {\rm {\bf U}}_h }{\partial k}} \right) \\
+      \frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}} \right) \\
 \end{equation}
 that is, in expanded form:

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_D.tex

r10442	r11263
32	32
33	33	To satisfy part of these aims, \NEMO is written with a coding standard which is close to the ECMWF rules,
34		named DOCTOR \citep{~~Gibson_TR~~86}.
	34	named DOCTOR \citep{gibson_rpt86}.
35	35	These rules present some advantages like:
36	36

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_E.tex

-                      r10442
+                      r11263
 This results in a dissipatively dominant (\ie hyper-diffusive) truncation error
 \citep{Shchepetkin_McWilliams_OM05}.
 The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}.
+\citep{shchepetkin.mcwilliams_OM05}.
+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.
 It is not a \emph{positive} scheme meaning false extrema are permitted but
 …
 the second term which is the diffusive part of the scheme, is evaluated using the \textit{before} velocity
 (forward in time).
 This is discussed by \citet{Webb_al_JAOT98} in the context of the Quick advection scheme.
+This 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.
 Substituting 1/6 with 1/8 in (\autoref{eq:tra_adv_ubs}) leads to the QUICK advection scheme \citep{Webb_al_JAOT98}.
+Substituting 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 \mdl{traadv\_ubs} module and obtain a QUICK scheme.
 …
 $\tau_w^{ubs}$ will be evaluated using either \textit{(a)} a centered $2^{nd}$ order scheme,
 or \textit{(b)} a TVD scheme, or \textit{(c)} an interpolation based on conservative parabolic splines following
 \citet{Shchepetkin_McWilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS.
+\citet{shchepetkin.mcwilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS.
 The $3^{rd}$ case has dispersion properties similar to an eight-order accurate conventional scheme.
 …
 \subsection{Griffies iso-neutral diffusion operator}
 Let try to define a scheme that get its inspiration from the \citet{Griffies_al_JPO98} scheme,
+Let try to define a scheme that get its inspiration from the \citet{griffies.gnanadesikan.ea_JPO98} scheme,
 but is formulated within the \NEMO framework
 (\ie using scale factors rather than grid-size and having a position of $T$-points that
 …
 Nevertheless, this technique works fine for $T$ and $S$ as they are active tracers
 (\ie they enter the computation of density), but it does not work for a passive tracer.
 \citep{Griffies_al_JPO98} introduce a different way to discretise the off-diagonal terms that
+\citep{griffies.gnanadesikan.ea_JPO98} introduce a different way to discretise the off-diagonal terms that
 nicely solve the problem.
 The idea is to get rid of combinations of an averaged in one direction combined with
 …
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[width=0.70\textwidth]{Fig_ISO_triad}
+    \includegraphics[width=\textwidth]{Fig_ISO_triad}
     \caption{
       \protect\label{fig:ISO_triad}
 …
 \]
 \citep{Griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form.
+\citep{griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form.
 It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity.
 For example in the (\textbf{i},\textbf{k}) plane, the tracer advective fluxes can be transformed as follows:
 …
 The horizontal component reduces to the one use for an horizontal laplacian operator and
 the vertical one keeps the same complexity, but not more.
 This property has been used to reduce the computational time \citep{Griffies_JPO98},
+This property has been used to reduce the computational time \citep{griffies_JPO98},
 but it is not of practical use as usually $A \neq A_e$.
 Nevertheless this property can be used to choose a discret form of \autoref{eq:eiv_skew_continuous} which

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_iso.tex

-                      r10442
+                      r11263
 \newcommand{\rML}[1][i]{\ensuremath{_{\mathrm{ML}\,#1}}}
 \newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}}
+\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}}
+%% Move to ../../global/new_cmds.tex to avoid error with \listoffigures
+%\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}
 \newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}}
 \newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}}
 …
   the vertical skew flux is further reduced to ensure no vertical buoyancy flux,
   giving an almost pure horizontal diffusive tracer flux within the mixed layer.
   This is similar to the tapering suggested by \citet{Gerdes1991}. See \autoref{subsec:Gerdes-taper}
+  This is similar to the tapering suggested by \citet{gerdes.koberle.ea_CD91}. See \autoref{subsec:Gerdes-taper}
 \item[\np{ln\_botmix\_triad}]
   See \autoref{sec:iso_bdry}.
 …
 \label{sec:iso}
 We have implemented into \NEMO a scheme inspired by \citet{Griffies_al_JPO98},
+We have implemented into \NEMO a scheme inspired by \citet{griffies.gnanadesikan.ea_JPO98},
 but formulated within the \NEMO framework, using scale factors rather than grid-sizes.
 …
 \subsection{Expression of the skew-flux in terms of triad slopes}
 \citep{Griffies_al_JPO98} introduce a different discretization of the off-diagonal terms that
+\citep{griffies.gnanadesikan.ea_JPO98} introduce a different discretization of the off-diagonal terms that
 nicely solves the problem.
 % Instead of multiplying the mean slope calculated at the $u$-point by
 …
 \begin{figure}[tb]
   \begin{center}
     \includegraphics[width=1.05\textwidth]{Fig_GRIFF_triad_fluxes}
+    \includegraphics[width=\textwidth]{Fig_GRIFF_triad_fluxes}
     \caption{
       \protect\label{fig:ISO_triad}
 …
 \begin{figure}[tb]
   \begin{center}
     \includegraphics[width=0.80\textwidth]{Fig_GRIFF_qcells}
+    \includegraphics[width=\textwidth]{Fig_GRIFF_qcells}
     \caption{
       \protect\label{fig:qcells}
 …
 To complete the discretization we now need only specify the triad volumes $_i^k\mathbb{V}_{i_p}^{k_p}$.
 \citet{Griffies_al_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells,
+\citet{griffies.gnanadesikan.ea_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells,
 defined in terms of the distances between $T$, $u$,$f$ and $w$-points.
 This is the natural discretization of \autoref{eq:cts-var}.
 …
 \begin{figure}[h]
   \begin{center}
     \includegraphics[width=0.60\textwidth]{Fig_GRIFF_bdry_triads}
+    \includegraphics[width=\textwidth]{Fig_GRIFF_bdry_triads}
     \caption{
       \protect\label{fig:bdry_triads}
 …
 As discussed in \autoref{subsec:LDF_slp_iso},
 iso-neutral slopes relative to geopotentials must be bounded everywhere,
 both for consistency with the small-slope approximation and for numerical stability \citep{Cox1987, Griffies_Bk04}.
+both for consistency with the small-slope approximation and for numerical stability \citep{cox_OM87, griffies_bk04}.
 The bound chosen in \NEMO is applied to each component of the slope separately and
 has a value of $1/100$ in the ocean interior.
 …
 \[
   % \label{eq:iso_tensor_ML}
   D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
+  D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
   \mbox{with}\quad \;\;\Re =\left( {{
         \begin{array}{*{20}c}
 …
     (\eg the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.}
   % }
   \includegraphics[width=0.60\textwidth]{Fig_GRIFF_MLB_triads}
+  \includegraphics[width=\textwidth]{Fig_GRIFF_MLB_triads}
 \end{figure}
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 \[
   % \label{eq:iso_tensor_ML2}
   D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
+  D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
   \mbox{with}\quad \;\;\Re =\left( {{
         \begin{array}{*{20}c}
 …
 \footnote{
   To ensure good behaviour where horizontal density gradients are weak,
   we in fact follow \citet{Gerdes1991} and
+  we in fact follow \citet{gerdes.koberle.ea_CD91} and
   set $\rML^*=\mathrm{sgn}(\tilde{r}_i)\min(|\rMLt^2/\tilde{r}_i|,|\tilde{r}_i|)-\sigma_i$.
+}
 …
 This approach is similar to multiplying the iso-neutral diffusion coefficient by
 $\tilde{r}_{\mathrm{max}}^{-2}\tilde{r}_i^{-2}$ for steep slopes,
 as suggested by \citet{Gerdes1991} (see also \citet{Griffies_Bk04}).
+as suggested by \citet{gerdes.koberle.ea_CD91} (see also \citet{griffies_bk04}).
 Again it is applied separately to each triad $_i^k\mathbb{R}_{i_p}^{k_p}$
 …
 However, when \np{ln\_traldf\_triad} is set true,
 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{Griffies_JPO98}.
+\NEMO instead implements eddy induced advection according to the so-called skew form \citep{griffies_JPO98}.
 It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity.
 For example in the (\textbf{i},\textbf{k}) plane,
 …
 it is equivalent to a horizontal eiv (eddy-induced velocity) that is uniform within the mixed layer
 \autoref{eq:eiv_v}.
 This ensures that the eiv velocities do not restratify the mixed layer \citep{Treguier1997,Danabasoglu_al_2008}.
+This ensures that the eiv velocities do not restratify the mixed layer \citep{treguier.held.ea_JPO97,danabasoglu.ferrari.ea_JC08}.
 Equivantly, in terms of the skew-flux formulation we use here,
 the linear slope tapering within the mixed-layer gives a linearly varying vertical flux,
 …
 $uw$ (integer +1/2 $i$, integer $j$, integer +1/2 $k$) and $vw$ (integer $i$, integer +1/2 $j$, integer +1/2 $k$)
 points (see Table \autoref{tab:cell}) respectively.
 We follow \citep{Griffies_Bk04} and calculate the streamfunction at a given $uw$-point from
+We follow \citep{griffies_bk04} and calculate the streamfunction at a given $uw$-point from
 the surrounding four triads according to:
 \[

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_ASM.tex

-                      r10442
+                      r11263
 it may be preferable to introduce the increment gradually into the ocean model in order to
 minimize spurious adjustment processes.
 This technique is referred to as Incremental Analysis Updates (IAU) \citep{Bloom_al_MWR96}.
+This technique is referred to as Incremental Analysis Updates (IAU) \citep{bloom.takacs.ea_MWR96}.
 IAU is a common technique used with 3D assimilation methods such as 3D-Var or OI.
 IAU is used when \np{ln\_asmiau} is set to true.
 With IAU, the model state trajectory ${\bf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$)
+With IAU, the model state trajectory ${\mathbf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$)
 is corrected by adding the analysis increments for temperature, salinity, horizontal velocity and SSH as
 additional tendency terms to the prognostic equations:
 \begin{align*}
   % \label{eq:wa_traj_iau}
   {\bf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\bf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\bf x}^{a}
+  {\mathbf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\mathbf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\mathbf x}^{a}
 \end{align*}
 where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\bf x}^{a}$ defined such that
+where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\mathbf x}^{a}$ defined such that
 $\sum_{i=1}^{N} F_{i}=1$.
 ${\bf x}^b$ denotes the model initial state and ${\bf x}^a$ is the model state after the increments are applied.
+${\mathbf x}^b$ denotes the model initial state and ${\mathbf x}^a$ is the model state after the increments are applied.
 To control the adjustment time of the model to the increment,
 the increment can be applied over an arbitrary sub-window, $t_{m} \leq t_{i} \leq t_{n}$,
 …
   =\left\{
   \begin{array}{ll}
      &    {\rm if} \; \; \; t_{i} < t_{m}                \\
 /M &    {\rm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\
      &    {\rm if} \; \; \; t_{i} > t_{n}
+     &    {\mathrm if} \; \; \; t_{i} < t_{m}                \\
+/M &    {\mathrm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\
+     &    {\mathrm if} \; \; \; t_{i} > t_{n}
   \end{array}
             \right.
 …
   =\left\{
   \begin{array}{ll}
                            &    {\rm if} \; \; \; t_{i}       <     t_{m}                        \\
     \alpha \, i               &    {\rm if} \; \; \; t_{m}    \leq t_{i}    \leq   t_{M/2}   \\
     \alpha \, (M - i +1) &    {\rm if} \; \; \; t_{M/2}  <    t_{i}    \leq   t_{n}       \\
                             &   {\rm if} \; \; \; t_{i}        >    t_{n}
+                           &    {\mathrm if} \; \; \; t_{i}       <     t_{m}                        \\
+    \alpha \, i               &    {\mathrm if} \; \; \; t_{m}    \leq t_{i}    \leq   t_{M/2}   \\
+    \alpha \, (M - i +1) &    {\mathrm if} \; \; \; t_{M/2}  <    t_{i}    \leq   t_{n}       \\
+                            &   {\mathrm if} \; \; \; t_{i}        >    t_{n}
   \end{array}
                                    \right.
 …
 This type of the initialisation reduces the vertical velocity magnitude and
 alleviates the problem of the excessive unphysical vertical mixing in the first steps of the model integration
 \citep{Talagrand_JAS72, Dobricic_al_OS07}.
+\citep{talagrand_JAS72, dobricic.pinardi.ea_OS07}.
 Diffusion coefficients are defined as $A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$.
 The divergence damping is activated by assigning to \np{nn\_divdmp} in the \textit{nam\_asminc} namelist

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_CONFIG.tex

-                      r10442
+                      r11263
 \label{sec:CFG_intro}
 The purpose of this part of the manual is to introduce the \NEMO reference configurations.
+The purpose of this part of the manual is to introduce the NEMO reference configurations.
 These configurations are offered as means to explore various numerical and physical options,
 thus allowing the user to verify that the code is performing in a manner consistent with that we are running.
 …
 The reference configurations also provide a sense for some of the options available in the code,
 though by no means are all options exercised in the reference configurations.
+Configuration is defined manually through the \textit{namcfg} namelist variables.
 %------------------------------------------namcfg----------------------------------------------------
 …
 % 1D model configuration
 % ================================================================
+\section{C1D: 1D Water column model (\protect\key{c1d}) }
+\section[C1D: 1D Water column model (\texttt{\textbf{key\_c1d}})]
+{C1D: 1D Water column model (\protect\key{c1d})}
 \label{sec:CFG_c1d}
+BE careful: to be re-written according to suppression of jpizoom and jpjzoom !!!!
+The 1D model option simulates a stand alone water column within the 3D \NEMO system.
+The 1D model option simulates a stand alone water column within the 3D NEMO system.
 It can be applied to the ocean alone or to the ocean-ice system and can include passive tracers or a biogeochemical model.
 It is set up by defining the position of the 1D water column in the grid
 (see \textit{CONFIG/SHARED/namelist\_ref} ).
+(see \textit{cfgs/SHARED/namelist\_ref}).
 The 1D model is a very useful tool
 \textit{(a)} to learn about the physics and numerical treatment of vertical mixing processes;
 …
 \textit{(d)} to produce extra diagnostics, without the large memory requirement of the full 3D model.
+The methodology is based on the use of the zoom functionality over the smallest possible domain:
+a 3x3 domain centered on the grid point of interest, with some extra routines.
+There is no need to define a new mesh, bathymetry, initial state or forcing,
+since the 1D model will use those of the configuration it is a zoom of.
+The chosen grid point is set in \textit{\ngn{namcfg}} namelist by
+setting the \np{jpizoom} and \np{jpjzoom} parameters to the indices of the location of the chosen grid point.
+The methodology is based on the configuration of the smallest possible domain:
+a 3x3 domain with 75 vertical levels.
 The 1D model has some specifies. First, all the horizontal derivatives are assumed to be zero,
 and second, the two components of the velocity are moved on a $T$-point.
 Therefore, defining \key{c1d} changes five main things in the code behaviour:
+Therefore, defining \key{c1d} changes some things in the code behaviour:
 \begin{description}
 \item[(1)]
-  the lateral boundary condition routine (\rou{lbc\_lnk}) set the value of the central column of
-  the 3x3 domain is imposed over the whole domain;
-\item[(3)]
-  a call to \rou{lbc\_lnk} is systematically done when reading input data (\ie in \mdl{iom});
-\item[(3)]
   a simplified \rou{stp} routine is used (\rou{stp\_c1d}, see \mdl{step\_c1d} module) in which
   both lateral tendancy terms and lateral physics are not called;
 \item[(4)]
+\item[(2)]
   the vertical velocity is zero
   (so far, no attempt at introducing a Ekman pumping velocity has been made);
 \item[(5)]
+\item[(3)]
   a simplified treatment of the Coriolis term is performed as $U$- and $V$-points are the same
   (see \mdl{dyncor\_c1d}).
 \end{description}
 All the relevant \textit{\_c1d} modules can be found in the NEMOGCM/NEMO/OPA\_SRC/C1D directory of
 the \NEMO distribution.
+All the relevant \textit{\_c1d} modules can be found in the src/OCE/C1D directory of
+the NEMO distribution.
 % to be added:  a test case on the yearlong Ocean Weather Station (OWS) Papa dataset of Martin (1985)
 …
 The ORCA family is a series of global ocean configurations that are run together with
+the LIM sea-ice model (ORCA-LIM) and possibly with PISCES biogeochemical model (ORCA-LIM-PISCES),
+using various resolutions.
+An appropriate namelist is available in \path{CONFIG/ORCA2_LIM3_PISCES/EXP00/namelist_cfg} for ORCA2.
+the SI3 model (ORCA-ICE) and possibly with PISCES biogeochemical model (ORCA-ICE-PISCES).
+An appropriate namelist is available in \path{cfgs/ORCA2_ICE_PISCES/EXPREF/namelist_cfg} for ORCA2.
 The domain of ORCA2 configuration is defined in \ifile{ORCA\_R2\_zps\_domcfg} file,
+this file is available in tar file in the wiki of NEMO: \\
+https://forge.ipsl.jussieu.fr/nemo/wiki/Users/ReferenceConfigurations/ORCA2\_LIM3\_PISCES \\
+this file is available in tar file on the NEMO community zenodo platform: \\
+https://doi.org/10.5281/zenodo.2640723
 In this namelist\_cfg the name of domain input file is set in \ngn{namcfg} block of namelist.
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.98\textwidth]{Fig_ORCA_NH_mesh}
+    \includegraphics[width=\textwidth]{Fig_ORCA_NH_mesh}
     \caption{
       \protect\label{fig:MISC_ORCA_msh}
 …
       The two "north pole" are the foci of a series of embedded ellipses (blue curves) which
       are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes).
       Then, following \citet{Madec_Imbard_CD96}, the normal to the series of ellipses (red curves) is computed which
+      Then, following \citet{madec.imbard_CD96}, the normal to the series of ellipses (red curves) is computed which
       provides the j-lines of the mesh (pseudo longitudes).
+    }
 …
 \label{subsec:CFG_orca_grid}
 The ORCA grid is a tripolar is based on the semi-analytical method of \citet{Madec_Imbard_CD96}.
+The ORCA grid is a tripolar grid based on the semi-analytical method of \citet{madec.imbard_CD96}.
 It allows to construct a global orthogonal curvilinear ocean mesh which has no singularity point inside
 the computational domain since two north mesh poles are introduced and placed on lands.
 …
 \begin{figure}[!tbp]
   \begin{center}
     \includegraphics[width=1.0\textwidth]{Fig_ORCA_NH_msh05_e1_e2}
     \includegraphics[width=0.80\textwidth]{Fig_ORCA_aniso}
+    \includegraphics[width=\textwidth]{Fig_ORCA_NH_msh05_e1_e2}
+    \includegraphics[width=\textwidth]{Fig_ORCA_aniso}
     \caption {
       \protect\label{fig:MISC_ORCA_e1e2}
 …
 % -------------------------------------------------------------------------------------------------------------
 %       ORCA-LIM(-PISCES) configurations
+%       ORCA-ICE(-PISCES) configurations
 % -------------------------------------------------------------------------------------------------------------
 \subsection{ORCA pre-defined resolution}
 …
 The ORCA\_R2 configuration has the following specificity: starting from a 2\deg~ORCA mesh,
 local mesh refinements were applied to the Mediterranean, Red, Black and Caspian Seas,
 so that the resolution is 1\deg \time 1\deg there.
+so that the resolution is 1\deg~ there.
 A local transformation were also applied with in the Tropics in order to refine the meridional resolution up to
 .5\deg at the Equator.
+.5\deg~ at the Equator.
 The ORCA\_R1 configuration has only a local tropical transformation to refine the meridional resolution up to
 …
 For ORCA\_R1 and R025, setting the configuration key to 75 allows to use 75 vertical levels, otherwise 46 are used.
 In the other ORCA configurations, 31 levels are used
 (see \autoref{tab:orca_zgr} %\sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}).
 Only the ORCA\_R2 is provided with all its input files in the \NEMO distribution.
 It is very similar to that used as part of the climate model developed at IPSL for the 4th IPCC assessment of
 climate change (Marti et al., 2009).
 It is also the basis for the \NEMO contribution to the Coordinate Ocean-ice Reference Experiments (COREs)
 documented in \citet{Griffies_al_OM09}.
+(see \autoref{tab:orca_zgr}). %\sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}).
+Only the ORCA\_R2 is provided with all its input files in the NEMO distribution.
+%It is very similar to that used as part of the climate model developed at IPSL for the 4th IPCC assessment of
+%climate change (Marti et al., 2009).
+%It is also the basis for the \NEMO contribution to the Coordinate Ocean-ice Reference Experiments (COREs)
+%documented in \citet{griffies.biastoch.ea_OM09}.
 This version of ORCA\_R2 has 31 levels in the vertical, with the highest resolution (10m) in the upper 150m
 (see \autoref{tab:orca_zgr} and \autoref{fig:zgr}).
 The bottom topography and the coastlines are derived from the global atlas of Smith and Sandwell (1997).
 The default forcing uses the boundary forcing from \citet{Large_Yeager_Rep04} (see \autoref{subsec:SBC_blk_core}),
+The default forcing uses the boundary forcing from \citet{large.yeager_rpt04} (see \autoref{subsec:SBC_blk_core}),
 which was developed for the purpose of running global coupled ocean-ice simulations without
 an interactive atmosphere.
 This \citet{Large_Yeager_Rep04} dataset is available through
+This \citet{large.yeager_rpt04} dataset is available through
 the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.
 The "normal year" of \citet{Large_Yeager_Rep04} has been chosen of the \NEMO distribution since release v3.3.
 ORCA\_R2 pre-defined configuration can also be run with an AGRIF zoom over the Agulhas current area
+(\key{agrif} defined) and, by setting the appropriate variables, see \path{CONFIG/SHARED/namelist_ref}.
+The "normal year" of \citet{large.yeager_rpt04} has been chosen of the NEMO distribution since release v3.3.
+ORCA\_R2 pre-defined configuration can also be run with multiply online nested zooms (\ie with AGRIF, \key{agrif} defined). This is available as the AGRIF\_DEMO configuration that can be found in the \path{cfgs/AGRIF_DEMO/} directory.
 A regional Arctic or peri-Antarctic configuration is extracted from an ORCA\_R2 or R05 configurations using
 sponge layers at open boundaries.
 …
 %       GYRE family: double gyre basin
 % -------------------------------------------------------------------------------------------------------------
 \section{GYRE family: double gyre basin }
+\section{GYRE family: double gyre basin}
 \label{sec:CFG_gyre}
 The GYRE configuration \citep{Levy_al_OM10} has been built to
+The GYRE configuration \citep{levy.klein.ea_OM10} has been built to
 simulate the seasonal cycle of a double-gyre box model.
 It consists in an idealized domain similar to that used in the studies of \citet{Drijfhout_JPO94} and
 \citet{Hazeleger_Drijfhout_JPO98, Hazeleger_Drijfhout_JPO99, Hazeleger_Drijfhout_JGR00, Hazeleger_Drijfhout_JPO00},
+It consists in an idealized domain similar to that used in the studies of \citet{drijfhout_JPO94} and
+\citet{hazeleger.drijfhout_JPO98, hazeleger.drijfhout_JPO99, hazeleger.drijfhout_JGR00, hazeleger.drijfhout_JPO00},
 over which an analytical seasonal forcing is applied.
 This allows to investigate the spontaneous generation of a large number of interacting, transient mesoscale eddies
 and their contribution to the large scale circulation.
+The GYRE configuration run together with the PISCES biogeochemical model (GYRE-PISCES).
 The domain geometry is a closed rectangular basin on the $\beta$-plane centred at $\sim$ 30\deg{N} and
 rotated by 45\deg, 3180~km long, 2120~km wide and 4~km deep (\autoref{fig:MISC_strait_hand}).
 …
 The configuration is meant to represent an idealized North Atlantic or North Pacific basin.
 The circulation is forced by analytical profiles of wind and buoyancy fluxes.
 The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{Levy_al_OM10}.
+The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{levy.klein.ea_OM10}.
 The wind stress is zonal and its curl changes sign at 22\deg{N} and 36\deg{N}.
 It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain and
 …
 The GYRE configuration is set like an analytical configuration.
 Through \np{ln\_read\_cfg}\forcode{ = .false.} in \textit{namcfg} namelist defined in
 the reference configuration \path{CONFIG/GYRE/EXP00/namelist_cfg}
+the reference configuration \path{cfgs/GYRE_PISCES/EXPREF/namelist_cfg}
 analytical definition of grid in GYRE is done in usrdef\_hrg, usrdef\_zgr routines.
 Its horizontal resolution (and thus the size of the domain) is determined by
 setting \np{nn\_GYRE} in \ngn{namusr\_def}: \\
 \np{jpiglo} $= 30 \times$ \np{nn\_GYRE} + 2   \\
 \np{jpjglo} $= 20 \times$ \np{nn\_GYRE} + 2   \\
 Obviously, the namelist parameters have to be adjusted to the chosen resolution,
 see the Configurations pages on the NEMO web site (Using NEMO\/Configurations).
+see the Configurations pages on the NEMO web site (NEMO Configurations).
 In the vertical, GYRE uses the default 30 ocean levels (\jp{jpk}\forcode{ = 31}) (\autoref{fig:zgr}).
 …
 even though the physical integrity of the solution can be compromised.
 Benchmark is activate via \np{ln\_bench}\forcode{ = .true.} in \ngn{namusr\_def} in
 namelist \path{CONFIG/GYRE/EXP00/namelist_cfg}.
+namelist \path{cfgs/GYRE_PISCES/EXPREF/namelist_cfg}.
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=1.0\textwidth]{Fig_GYRE}
+    \includegraphics[width=\textwidth]{Fig_GYRE}
     \caption{
       \protect\label{fig:GYRE}
       Snapshot of relative vorticity at the surface of the model domain in GYRE R9, R27 and R54.
       From \citet{Levy_al_OM10}.
+      From \citet{levy.klein.ea_OM10}.
+    }
   \end{center}
 …
 The AMM, Atlantic Margins Model, is a regional model covering the Northwest European Shelf domain on
 a regular lat-lon grid at approximately 12km horizontal resolution.
 The appropriate \textit{\&namcfg} namelist  is available in \textit{CONFIG/AMM12/EXP00/namelist\_cfg}.
+The appropriate \textit{\&namcfg} namelist  is available in \textit{cfgs/AMM12/EXPREF/namelist\_cfg}.
 It is used to build the correct dimensions of the AMM domain.
 This configuration tests several features of NEMO functionality specific to the shelf seas.
+In particular, the AMM uses $S$-coordinates in the vertical rather than $z$-coordinates and
+is forced with tidal lateral boundary conditions using a flather boundary condition from the BDY module.
+The AMM configuration uses the GLS (\key{zdfgls}) turbulence scheme,
+the VVL non-linear free surface(\key{vvl}) and time-splitting (\key{dynspg\_ts}).
+In particular, the AMM uses $s$-coordinates in the vertical rather than $z$-coordinates and
+is forced with tidal lateral boundary conditions using a Flather boundary condition from the BDY module.
+Also specific to the AMM configuration is the use of the GLS turbulence scheme (\np{ln\_zdfgls} \forcode{= .true.}).
 In addition to the tidal boundary condition the model may also take open boundary conditions from

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DIA.tex

-                      r10509
+                      r11263
 the same run performed in one step.
 It should be noted that this requires that the restart file contains two consecutive time steps for
+all the prognostic variables, and that it is saved in the same binary format as the one used by the computer that
+is to read it (in particular, 32 bits binary IEEE format must not be used for this file).
+all the prognostic variables.
 The output listing and file(s) are predefined but should be checked and eventually adapted to the user's needs.
 …
 the writing work is distributed over the processors in massively parallel computing.
 A complete description of the use of this I/O server is presented in the next section.
-By default, \key{iomput} is not defined,
-NEMO produces NetCDF with the old IOIPSL library which has been kept for compatibility and its easy installation.
-However, the IOIPSL library is quite inefficient on parallel machines and, since version 3.2,
-many diagnostic options have been added presuming the use of \key{iomput}.
-The usefulness of the default IOIPSL-based option is expected to reduce with each new release.
-If \key{iomput} is not defined, output files and content are defined in the \mdl{diawri} module and
-contain mean (or instantaneous if \key{diainstant} is defined) values over a regular period of
-nn\_write time-steps (namelist parameter).
 %\gmcomment{                    % start of gmcomment
 …
 in a very easy way.
 All details of iomput functionalities are listed in the following subsections.
+Examples of the XML files that control the outputs can be found in: \path{NEMOGCM/CONFIG/ORCA2_LIM/EXP00/iodef.xml},
+\path{NEMOGCM/CONFIG/SHARED/field_def.xml} and \path{NEMOGCM/CONFIG/SHARED/domain_def.xml}. \\
+Examples of the XML files that control the outputs can be found in:
+\path{cfgs/ORCA2_ICE_PISCES/EXPREF/iodef.xml},
+\path{cfgs/SHARED/field_def_nemo-oce.xml},
+\path{cfgs/SHARED/field_def_nemo-pisces.xml},
+\path{cfgs/SHARED/field_def_nemo-ice.xml} and \path{cfgs/SHARED/domain_def_nemo.xml}. \\
 The second functionality targets output performance when running in parallel (\key{mpp\_mpi}).
 …
 In version 3.6, the iom\_put interface depends on
 an external code called \href{https://forge.ipsl.jussieu.fr/ioserver/browser/XIOS/branchs/xios-1.0}{XIOS-1.0}
+an external code called \href{https://forge.ipsl.jussieu.fr/ioserver/browser/XIOS/branchs/xios-2.5}{XIOS-2.5}
 (use of revision 618 or higher is required).
 This new IO server can take advantage of the parallel I/O functionality of NetCDF4 to
 …
 \xmlline|<variable id="using_server" type="bool"></variable>|
 The {\tt using\_server} setting determines whether or not the server will be used in \textit{attached mode}
 (as a library) [{\tt> false <}] or in \textit{detached mode}
 (as an external executable on N additional, dedicated cpus) [{\tt > true <}].
+The {\ttfamily using\_server} setting determines whether or not the server will be used in \textit{attached mode}
+(as a library) [{\ttfamily> false <}] or in \textit{detached mode}
+(as an external executable on N additional, dedicated cpus) [{\ttfamily > true <}].
 The \textit{attached mode} is simpler to use but much less efficient for massively parallel applications.
 The type of each file can be either ''multiple\_file'' or ''one\_file''.
 …
 \subsubsection{Control of XIOS: the context in iodef.xml}
 As well as the {\tt using\_server} flag, other controls on the use of XIOS are set in the XIOS context in iodef.xml.
+As well as the {\ttfamily using\_server} flag, other controls on the use of XIOS are set in the XIOS context in iodef.xml.
 See the XML basics section below for more details on XML syntax and rules.
 …
 See the installation guide on the \href{http://forge.ipsl.jussieu.fr/ioserver/wiki}{XIOS} wiki for help and guidance.
 NEMO will need to link to the compiled XIOS library.
 The \href{https://forge.ipsl.jussieu.fr/nemo/wiki/Users/ModelInterfacing/InputsOutputs#Inputs-OutputsusingXIOS}
 {XIOS with NEMO} guide provides an example illustration of how this can be achieved.
+The \href{https://forge.ipsl.jussieu.fr/nemo/chrome/site/doc/NEMO/guide/html/install.html#extract-and-install-xios}
+{Extract and install XIOS} guide provides an example illustration of how this can be achieved.
 \subsubsection{Add your own outputs}
 …
 \begin{enumerate}
 \item[1.]
   in NEMO code, add a \forcode{CALL iom\_put( 'identifier', array )} where you want to output a 2D or 3D array.
+  in NEMO code, add a \forcode{CALL iom_put( 'identifier', array )} where you want to output a 2D or 3D array.
 \item[2.]
   If necessary, add \forcode{USE iom ! I/O manager library} to the list of used modules in
 …
 \xmlline|<context src="./nemo_def.xml" />|
+\noindent In NEMO, by default, the field and domain definition is done in 2 separate files:
+\path{NEMOGCM/CONFIG/SHARED/field_def.xml} and \path{NEMOGCM/CONFIG/SHARED/domain_def.xml} that
+\noindent In NEMO, by default, the field definition is done in 3 separate files (
+\path{cfgs/SHARED/field_def_nemo-oce.xml},
+\path{cfgs/SHARED/field_def_nemo-pisces.xml} and
+\path{cfgs/SHARED/field_def_nemo-ice.xml} ) and the  domain definition is done in another file ( \path{cfgs/SHARED/domain_def_nemo.xml} )
+that
 are included in the main iodef.xml file through the following commands:
 \begin{xmllines}
+<field_definition src="./field_def.xml" />
+<domain_definition src="./domain_def.xml" />
+<context id="nemo" src="./context_nemo.xml"/>
 \end{xmllines}
 …
 Secondly, the group can be used to replace a list of elements.
+Several examples of groups of fields are proposed at the end of the file \path{CONFIG/SHARED/field_def.xml}.
+Several examples of groups of fields are proposed at the end of the XML field files (
+\path{cfgs/SHARED/field_def_nemo-oce.xml},
+\path{cfgs/SHARED/field_def_nemo-pisces.xml} and
+\path{cfgs/SHARED/field_def_nemo-ice.xml} ) .
 For example, a short list of the usual variables related to the U grid:
 …
 <field_group id="groupU" >
    <field field_ref="uoce"  />
    <field field_ref="suoce" />
+   <field field_ref="ssu" />
    <field field_ref="utau"  />
 </field_group>
 …
 the tag family domain.
 It must therefore be done in the domain part of the XML file.
 For example, in \path{CONFIG/SHARED/domain_def.xml}, we provide the following example of a definition of
+For example, in \path{cfgs/SHARED/domain_def.xml}, we provide the following example of a definition of
 a 5 by 5 box with the bottom left corner at point (10,10).
 \begin{xmllines}
 <domain_group id="grid_T">
    <domain id="myzoom" zoom_ibegin="10" zoom_jbegin="10" zoom_ni="5" zoom_nj="5" />
+<domain id="myzoomT" domain_ref="grid_T">
+   <zoom_domain ibegin="10" jbegin="10" ni="5" nj="5" />
 \end{xmllines}
 …
 \begin{xmllines}
 <file id="myfile_vzoom" output_freq="1d" >
    <field field_ref="toce" domain_ref="myzoom"/>
+   <field field_ref="toce" domain_ref="myzoomT"/>
 </file>
 \end{xmllines}
 …
 \subsubsection{Define vertical zooms}
 Vertical zooms are defined through the attributs zoom\_begin and zoom\_end of the tag family axis.
+Vertical zooms are defined through the attributs zoom\_begin and zoom\_n of the tag family axis.
 It must therefore be done in the axis part of the XML file.
+For example, in \path{NEMOGCM/CONFIG/ORCA2_LIM/iodef_demo.xml}, we provide the following example:
+\begin{xmllines}
+<axis_group id="deptht" long_name="Vertical T levels" unit="m" positive="down" >
+   <axis id="deptht" />
+   <axis id="deptht_myzoom" zoom_begin="1" zoom_end="10" />
+For example, in \path{cfgs/ORCA2_ICE_PISCES/EXPREF/iodef_demo.xml}, we provide the following example:
+\begin{xmllines}
+<axis_definition>
+   <axis id="deptht" long_name="Vertical T levels" unit="m" positive="down" />
+   <axis id="deptht_zoom" azix_ref="deptht" >
+      <zoom_axis zoom_begin="1" zoom_n="10" />
+   </axis>
 \end{xmllines}
 …
 \end{xmllines}
 Note that, then the code is crashing, writting real4 variables forces a numerical convection from
+Note that, then the code is crashing, writting real4 variables forces a numerical conversion from
 real8 to real4 which will create an internal error in NetCDF and will avoid the creation of the output files.
 Forcing double precision outputs with prec="8" (for example in the field\_definition) will avoid this problem.
 …
     \hline
   \end{tabularx}
   \caption{Field tags ("\tt{field\_*}")}
+  \caption{Field tags ("\ttfamily{field\_*}")}
 \end{table}
 …
     \hline
   \end{tabularx}
   \caption{File tags ("\tt{file\_*}")}
+  \caption{File tags ("\ttfamily{file\_*}")}
 \end{table}
 …
     \hline
   \end{tabularx}
   \caption{Axis tags ("\tt{axis\_*}")}
+  \caption{Axis tags ("\ttfamily{axis\_*}")}
 \end{table}
 …
     \hline
   \end{tabularx}
   \caption{Domain tags ("\tt{domain\_*)}"}
+  \caption{Domain tags ("\ttfamily{domain\_*)}"}
 \end{table}
 …
     \hline
   \end{tabularx}
   \caption{Grid tags ("\tt{grid\_*}")}
+  \caption{Grid tags ("\ttfamily{grid\_*}")}
 \end{table}
 …
     \hline
   \end{tabularx}
   \caption{Reference attributes ("\tt{*\_ref}")}
+  \caption{Reference attributes ("\ttfamily{*\_ref}")}
 \end{table}
 …
     \hline
   \end{tabularx}
   \caption{Domain attributes ("\tt{zoom\_*}")}
+  \caption{Domain attributes ("\ttfamily{zoom\_*}")}
 \end{table}
 …
 \subsection{CF metadata standard compliance}
 Output from the XIOS-1.0 IO server is compliant with
+Output from the XIOS IO server is compliant with
 \href{http://cfconventions.org/Data/cf-conventions/cf-conventions-1.5/build/cf-conventions.html}{version 1.5} of
 the CF metadata standard.
 …
 %       NetCDF4 support
 % ================================================================
+\section{NetCDF4 support (\protect\key{netcdf4})}
+\section[NetCDF4 support (\texttt{\textbf{key\_netcdf4}})]
+{NetCDF4 support (\protect\key{netcdf4})}
 \label{sec:DIA_nc4}
 …
 Chunking and compression can lead to significant reductions in file sizes for a small runtime overhead.
 For a fuller discussion on chunking and other performance issues the reader is referred to
 the NetCDF4 documentation found \href{http://www.unidata.ucar.edu/software/netcdf/docs/netcdf.html#Chunking}{here}.
+the NetCDF4 documentation found \href{https://www.unidata.ucar.edu/software/netcdf/docs/netcdf_perf_chunking.html}{here}.
 The new features are only available when the code has been linked with a NetCDF4 library
 …
 \end{forlines}
 \noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\tt 46x38x1} respectively in
 the mono-processor case (\ie global domain of {\small\tt 182x149x31}).
+\noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\ttfamily 46x38x1} respectively in
+the mono-processor case (\ie global domain of {\small\ttfamily 182x149x31}).
 An illustration of the potential space savings that NetCDF4 chunking and compression provides is given in
 table \autoref{tab:NC4} which compares the results of two short runs of the ORCA2\_LIM reference configuration with
 …
 %       Tracer/Dynamics Trends
 % -------------------------------------------------------------------------------------------------------------
+\section{Tracer/Dynamics trends  (\protect\ngn{namtrd})}
+\section[Tracer/Dynamics trends (\texttt{namtrd})]
+{Tracer/Dynamics trends (\protect\ngn{namtrd})}
 \label{sec:DIA_trd}
 …
 (\ie at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines).
 This capability is controlled by options offered in \ngn{namtrd} namelist.
 Note that the output are done with xIOS, and therefore the \key{IOM} is required.
+Note that the output are done with XIOS, and therefore the \key{iomput} is required.
 What is done depends on the \ngn{namtrd} logical set to \forcode{.true.}:
 …
 Note that the mixed layer tendency diagnostic can also be used on biogeochemical models via
 the \key{trdtrc} and \key{trdmld\_trc} CPP keys.
+the \key{trdtrc} and \key{trdmxl\_trc} CPP keys.
 \textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested.
 …
 %       On-line Floats trajectories
 % -------------------------------------------------------------------------------------------------------------
+\section{FLO: On-Line Floats trajectories (\protect\key{floats})}
+\section[FLO: On-Line Floats trajectories (\texttt{\textbf{key\_floats}})]
+{FLO: On-Line Floats trajectories (\protect\key{floats})}
 \label{sec:FLO}
 %--------------------------------------------namflo-------------------------------------------------------
 …
 The on-line computation of floats advected either by the three dimensional velocity field or constraint to
 remain at a given depth ($w = 0$ in the computation) have been introduced in the system during the CLIPPER project.
 Options are defined by \ngn{namflo} namelis variables.
 The algorithm used is based either on the work of \cite{Blanke_Raynaud_JPO97} (default option),
+Options are defined by \ngn{namflo} namelist variables.
+The algorithm used is based either on the work of \cite{blanke.raynaud_JPO97} (default option),
 or on a $4^th$ Runge-Hutta algorithm (\np{ln\_flork4}\forcode{ = .true.}).
 Note that the \cite{Blanke_Raynaud_JPO97} algorithm have the advantage of providing trajectories which
+Note that the \cite{blanke.raynaud_JPO97} algorithm have the advantage of providing trajectories which
 are consistent with the numeric of the code, so that the trajectories never intercept the bathymetry.
 …
 In case of Ariane convention, input filename is \np{init\_float\_ariane}.
 Its format is: \\
 {\scriptsize \texttt{I J K nisobfl itrash itrash}}
+{\scriptsize \texttt{I J K nisobfl itrash}}
 \noindent with:
 …
 In that case, output filename is trajec\_float.
+Another possiblity of writing format is Netcdf (\np{ln\_flo\_ascii}\forcode{ = .false.}).
+There are 2 possibilities:
+- if (\key{iomput}) is used, outputs are selected in  iodef.xml.
+Another possiblity of writing format is Netcdf (\np{ln\_flo\_ascii}\forcode{ = .false.}) with
+\key{iomput} and outputs selected in iodef.xml.
 Here it is an example of specification to put in files description section:
 …
 \end{xmllines}
- -  if (\key{iomput}) is not used, a file called \ifile{trajec\_float} will be created by IOIPSL library.
- See also \href{http://stockage.univ-brest.fr/~grima/Ariane/}{here} the web site describing the off-line use of
- this marvellous diagnostic tool.
 % -------------------------------------------------------------------------------------------------------------
 %       Harmonic analysis of tidal constituents
 % -------------------------------------------------------------------------------------------------------------
+\section{Harmonic analysis of tidal constituents (\protect\key{diaharm}) }
+\section[Harmonic analysis of tidal constituents (\texttt{\textbf{key\_diaharm}})]
+{Harmonic analysis of tidal constituents (\protect\key{diaharm})}
 \label{sec:DIA_diag_harm}
 %------------------------------------------namdia_harm----------------------------------------------------
+%------------------------------------------nam_diaharm----------------------------------------------------
+%
 \nlst{nam_diaharm}
 …
 This on-line Harmonic analysis is actived with \key{diaharm}.
 Some parameters are available in namelist \ngn{namdia\_harm}:
+Some parameters are available in namelist \ngn{nam\_diaharm}:
  - \np{nit000\_han} is the first time step used for harmonic analysis
 …
 %       Sections transports
 % -------------------------------------------------------------------------------------------------------------
+\section{Transports across sections (\protect\key{diadct}) }
+\section[Transports across sections (\texttt{\textbf{key\_diadct}})]
+{Transports across sections (\protect\key{diadct})}
 \label{sec:DIA_diag_dct}
 …
 Each section is defined by the coordinates of its 2 extremities.
 The pathways between them are contructed using tools which can be found in \texttt{NEMOGCM/TOOLS/SECTIONS\_DIADCT}
 and are written in a binary file \texttt{section\_ijglobal.diadct\_ORCA2\_LIM} which is later read in by
+The pathways between them are contructed using tools which can be found in \texttt{tools/SECTIONS\_DIADCT}
+and are written in a binary file \texttt{section\_ijglobal.diadct} which is later read in by
 NEMO to compute on-line transports.
 …
 \subsubsection{Creating a binary file containing the pathway of each section}
 In \texttt{NEMOGCM/TOOLS/SECTIONS\_DIADCT/run},
+In \texttt{tools/SECTIONS\_DIADCT/run},
 the file \textit{ {list\_sections.ascii\_global}} contains a list of all the sections that are to be computed
 (this list of sections is based on MERSEA project metrics).
 …
  The script \texttt{job.ksh} computes the pathway for each section and creates a binary file
  \texttt{section\_ijglobal.diadct\_ORCA2\_LIM} which is read by NEMO. \\
+ \texttt{section\_ijglobal.diadct} which is read by NEMO. \\
  It is possible to use this tools for new configuations: \texttt{job.ksh} has to be updated with
 …
 The steric effect is therefore not explicitely represented.
 This approximation does not represent a serious error with respect to the flow field calculated by the model
 \citep{Greatbatch_JGR94}, but extra attention is required when investigating sea level,
+\citep{greatbatch_JGR94}, but extra attention is required when investigating sea level,
 as steric changes are an important contribution to local changes in sea level on seasonal and climatic time scales.
 This is especially true for investigation into sea level rise due to global warming.
 Fortunately, the steric contribution to the sea level consists of a spatially uniform component that
 can be diagnosed by considering the mass budget of the world ocean \citep{Greatbatch_JGR94}.
+can be diagnosed by considering the mass budget of the world ocean \citep{greatbatch_JGR94}.
 In order to better understand how global mean sea level evolves and thus how the steric sea level can be diagnosed,
 we compare, in the following, the non-Boussinesq and Boussinesq cases.
 …
 the ocean surface, not by changes in mean mass of the ocean: the steric effect is missing in a Boussinesq fluid.
 Nevertheless, following \citep{Greatbatch_JGR94}, the steric effect on the volume can be diagnosed by
+Nevertheless, following \citep{greatbatch_JGR94}, the steric effect on the volume can be diagnosed by
 considering the mass budget of the ocean.
 The apparent changes in $\mathcal{M}$, mass of the ocean, which are not induced by surface mass flux
 must be compensated by a spatially uniform change in the mean sea level due to expansion/contraction of the ocean
 \citep{Greatbatch_JGR94}.
+\citep{greatbatch_JGR94}.
 In others words, the Boussinesq mass, $\mathcal{M}_o$, can be related to $\mathcal{M}$,
 the total mass of the ocean seen by the Boussinesq model, via the steric contribution to the sea level,
 …
 This value is a sensible choice for the reference density used in a Boussinesq ocean climate model since,
 with the exception of only a small percentage of the ocean, density in the World Ocean varies by no more than
 $\%$ from this value (\cite{Gill1982}, page 47).
+$\%$ from this value (\cite{gill_bk82}, page 47).
 Second, we have assumed here that the total ocean surface, $\mathcal{A}$,
 …
 so that there are no associated ocean currents.
 Hence, the dynamically relevant sea level is the effective sea level,
 \ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{Campin_al_OM08}.
+\ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{campin.marshall.ea_OM08}.
 However, in the current version of \NEMO the sea-ice is levitating above the ocean without mass exchanges between
 ice and ocean.
 …
 %       Other Diagnostics
 % -------------------------------------------------------------------------------------------------------------
+\section{Other diagnostics (\protect\key{diahth}, \protect\key{diaar5})}
+\section[Other diagnostics (\texttt{\textbf{key\_diahth}}, \texttt{\textbf{key\_diaar5}})]
+{Other diagnostics (\protect\key{diahth}, \protect\key{diaar5})}
 \label{sec:DIA_diag_others}
 …
 The available ready-to-add diagnostics modules can be found in directory DIA.
+\subsection{Depth of various quantities (\protect\mdl{diahth})}
+\subsection[Depth of various quantities (\textit{diahth.F90})]
+{Depth of various quantities (\protect\mdl{diahth})}
 Among the available diagnostics the following ones are obtained when defining the \key{diahth} CPP key:
 - the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth})
+- the mixed layer depth (based on a density criterion \citep{de-boyer-montegut.madec.ea_JGR04}) (\mdl{diahth})
 - the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth})
 …
 % -----------------------------------------------------------
+\subsection{Poleward heat and salt transports (\protect\mdl{diaptr})}
+\subsection[Poleward heat and salt transports (\textit{diaptr.F90})]
+{Poleward heat and salt transports (\protect\mdl{diaptr})}
 %------------------------------------------namptr-----------------------------------------
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=1.0\textwidth]{Fig_mask_subasins}
+    \includegraphics[width=\textwidth]{Fig_mask_subasins}
     \caption{
       \protect\label{fig:mask_subasins}
 …
 %       CMIP specific diagnostics
 % -----------------------------------------------------------
+\subsection{CMIP specific diagnostics (\protect\mdl{diaar5})}
+\subsection[CMIP specific diagnostics (\textit{diaar5.F90})]
+{CMIP specific diagnostics (\protect\mdl{diaar5})}
 A series of diagnostics has been added in the \mdl{diaar5}.

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DIU.tex

-                      r10442
+                      r11263
 (\ie from the temperature of the top few model levels) or from some other source.
 It must be noted that both the cool skin and warm layer models produce estimates of the change in temperature
 ($\Delta T_{\rm{cs}}$ and $\Delta T_{\rm{wl}}$) and
+($\Delta T_{\mathrm{cs}}$ and $\Delta T_{\mathrm{wl}}$) and
 both must be added to a foundation SST to obtain the true skin temperature.
 …
 %===============================================================
 The warm layer is calculated using the model of \citet{Takaya_al_JGR10} (TAKAYA10 model hereafter).
+The warm layer is calculated using the model of \citet{takaya.bidlot.ea_JGR10} (TAKAYA10 model hereafter).
 This is a simple flux based model that is defined by the equations
 \begin{align}
 \frac{\partial{\Delta T_{\rm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p
+\frac{\partial{\Delta T_{\mathrm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p
 \nu}-\frac{(\nu+1)ku^*_{w}f(L_a)\Delta T}{D_T\Phi\!\left(\frac{D_T}{L}\right)} \mbox{,}
 \label{eq:ecmwf1} \\
 L&=&\frac{\rho_w c_p u^{*^3}_{w}}{\kappa g \alpha_w Q }\mbox{,}\label{eq:ecmwf2}
 \end{align}
 where $\Delta T_{\rm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal.
+where $\Delta T_{\mathrm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal.
 In equation (\autoref{eq:ecmwf1}) $\alpha_w=2\times10^{-4}$ is the thermal expansion coefficient of water,
 $\kappa=0.4$ is von K\'{a}rm\'{a}n's constant, $c_p$ is the heat capacity at constant pressure of sea water,
 $\rho_w$ is the water density, and $L$ is the Monin-Obukhov length.
 The tunable variable $\nu$ is a shape parameter that defines the expected subskin temperature profile via
 $T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\rm{wl}}$,
+$T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\mathrm{wl}}$,
 where $T$ is the absolute temperature and $z\le D_T$ is the depth below the top of the warm layer.
 The influence of wind on TAKAYA10 comes through the magnitude of the friction velocity of the water $u^*_{w}$,
 …
 the diurnal layer, \ie
 \[
   Q = Q_{\rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,}
+  Q = Q_{\mathrm{sol}} + Q_{\mathrm{lw}} + Q_{\mathrm{h}}\mbox{,}
   % \label{eq:e_flux_eqn}
 \]
 where $Q_{\rm{h}}$ is the sensible and latent heat flux, $Q_{\rm{lw}}$ is the long wave flux,
 and $Q_{\rm{sol}}$ is the solar flux absorbed within the diurnal warm layer.
 For $Q_{\rm{sol}}$ the 9 term representation of \citet{Gentemann_al_JGR09} is used.
+where $Q_{\mathrm{h}}$ is the sensible and latent heat flux, $Q_{\mathrm{lw}}$ is the long wave flux,
+and $Q_{\mathrm{sol}}$ is the solar flux absorbed within the diurnal warm layer.
+For $Q_{\mathrm{sol}}$ the 9 term representation of \citet{gentemann.minnett.ea_JGR09} is used.
 In equation \autoref{eq:ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$,
 where $L_a=0.3$\footnote{
 …
 %===============================================================
 The cool skin is modelled using the framework of \citet{Saunders_JAS82} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$.
 As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\rm{cs}}$ becomes
+The cool skin is modelled using the framework of \citet{saunders_JAS67} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$.
+As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\mathrm{cs}}$ becomes
 \[
   % \label{eq:sunders_eqn}
   \Delta T_{\rm{cs}}=\frac{Q_{\rm{ns}}\delta}{k_t} \mbox{,}
+  \Delta T_{\mathrm{cs}}=\frac{Q_{\mathrm{ns}}\delta}{k_t} \mbox{,}
 \]
 where $Q_{\rm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and
+where $Q_{\mathrm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and
 $k_t$ is the thermal conductivity of sea water.
 $\delta$ is the thickness of the skin layer and is given by
 …
 \end{equation}
 where $\mu$ is the kinematic viscosity of sea water and $\lambda$ is a constant of proportionality which
 \citet{Saunders_JAS82} suggested varied between 5 and 10.
+\citet{saunders_JAS67} suggested varied between 5 and 10.
 The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{Artale_al_JGR02},
 which is shown in \citet{Tu_Tsuang_GRL05} to outperform a number of other parametrisations at
+The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{artale.iudicone.ea_JGR02},
+which is shown in \citet{tu.tsuang_GRL05} to outperform a number of other parametrisations at
 both low and high wind speeds.
 Specifically,

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DOM.tex

-                      r10502
+                      r11263
 \begin{figure}[!tb]
   \begin{center}
     \includegraphics[]{Fig_cell}
+    \includegraphics[width=\textwidth]{Fig_cell}
     \caption{
       \protect\label{fig:cell}
 …
 the centre of each face of the cells (\autoref{fig:cell}).
 This is the generalisation to three dimensions of the well-known ``C'' grid in Arakawa's classification
 \citep{Mesinger_Arakawa_Bk76}.
+\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.
 …
 \begin{figure}[!tb]
   \begin{center}
     \includegraphics[]{Fig_index_hor}
+    \includegraphics[width=\textwidth]{Fig_index_hor}
     \caption{
       \protect\label{fig:index_hor}
 …
 \begin{figure}[!pt]
   \begin{center}
     \includegraphics[]{Fig_index_vert}
+    \includegraphics[width=\textwidth]{Fig_index_vert}
     \caption{
       \protect\label{fig:index_vert}
 …
 % Domain: Horizontal Grid (mesh)
 % ================================================================
+\section{Horizontal grid mesh (\protect\mdl{domhgr})}
+\section[Horizontal grid mesh (\textit{domhgr.F90})]
+{Horizontal grid mesh (\protect\mdl{domhgr})}
 \label{sec:DOM_hgr}
 …
 (\ie as the analytical first derivative of the transformation that
 gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$)
 is specific to the \NEMO model \citep{Marti_al_JGR92}.
+is specific to the \NEMO model \citep{marti.madec.ea_JGR92}.
 As an example, $e_{1t}$ is defined locally at a $t$-point,
 whereas many other models on a C grid choose to define such a scale factor as
 …
 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{Treguier1996}.
+(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:zgr_e3}.
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[]{Fig_zgr_e3}
+    \includegraphics[width=\textwidth]{Fig_zgr_e3}
     \caption{
       \protect\label{fig:zgr_e3}
 …
 % Domain: Vertical Grid (domzgr)
 % ================================================================
+\section{Vertical grid (\protect\mdl{domzgr})}
+\section[Vertical grid (\textit{domzgr.F90})]
+{Vertical grid (\protect\mdl{domzgr})}
 \label{sec:DOM_zgr}
 %-----------------------------------------nam_zgr & namdom-------------------------------------------
 …
 \begin{figure}[!tb]
   \begin{center}
     \includegraphics[]{Fig_z_zps_s_sps}
+    \includegraphics[width=\textwidth]{Fig_z_zps_s_sps}
     \caption{
       \protect\label{fig:z_zps_s_sps}
 …
       (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{ln\_linssh}~\forcode{= .false.}).
+      (f) same as (e) but in the non-linear free surface (\protect\np{ln\_linssh}\forcode{ = .false.}).
       Note that the non-linear free surface can be used with any of the 5 coordinates (a) to (e).
+    }
 …
 It is not intended as an option which can be enabled or disabled in the middle of an experiment.
 Three main choices are offered (\autoref{fig:z_zps_s_sps}):
 $z$-coordinate with full step bathymetry (\np{ln\_zco}~\forcode{= .true.}),
 $z$-coordinate with partial step bathymetry (\np{ln\_zps}~\forcode{= .true.}),
 or generalized, $s$-coordinate (\np{ln\_sco}~\forcode{= .true.}).
+$z$-coordinate with full step bathymetry (\np{ln\_zco}\forcode{ = .true.}),
+$z$-coordinate with partial step bathymetry (\np{ln\_zps}\forcode{ = .true.}),
+or generalized, $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}).
 Hybridation of the three main coordinates are available:
 $s-z$ or $s-zps$ coordinate (\autoref{fig:z_zps_s_sps} and \autoref{fig:z_zps_s_sps}).
 By default a non-linear free surface is used: the coordinate follow the time-variation of the free surface so that
 the transformation is time dependent: $z(i,j,k,t)$ (\autoref{fig:z_zps_s_sps}).
 When a linear free surface is assumed (\np{ln\_linssh}~\forcode{= .true.}),
+When a linear free surface is assumed (\np{ln\_linssh}\forcode{ = .true.}),
 the vertical coordinate 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).
 …
   N.B. in full step $z$-coordinate, a \ifile{bathy\_level} file can replace the \ifile{bathy\_meter} file,
   so that the computation of the number of wet ocean point in each water column is by-passed}.
 If \np{ln\_isfcav}~\forcode{= .true.}, an extra file input file (\ifile{isf\_draft\_meter}) describing
+If \np{ln\_isfcav}\forcode{ = .true.}, an extra file input file (\ifile{isf\_draft\_meter}) describing
 the ice shelf draft (in meters) is needed.
 …
 %%%
 Unless a linear free surface is used (\np{ln\_linssh}~\forcode{= .false.}),
+Unless a linear free surface is used (\np{ln\_linssh}\forcode{ = .false.}),
 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.
 …
 They are updated at each model time step using a fixed reference coordinate system which
 computer names have a $\_0$ suffix.
 When the linear free surface option is used (\np{ln\_linssh}~\forcode{= .true.}), \textit{before},
+When the linear free surface option is used (\np{ln\_linssh}\forcode{ = .true.}), \textit{before},
 \textit{now} and \textit{after} arrays are simply set one for all to their reference counterpart.
 …
 (found in \ngn{namdom} namelist):
 \begin{description}
 \item[\np{nn\_bathy}~\forcode{= 0}]:
+\item[\np{nn\_bathy}\forcode{ = 0}]:
   a flat-bottom domain is defined.
   The total depth $z_w (jpk)$ is given by the coordinate transformation.
   The domain can either be a closed basin or a periodic channel depending on the parameter \np{jperio}.
 \item[\np{nn\_bathy}~\forcode{= -1}]:
+\item[\np{nn\_bathy}\forcode{ = -1}]:
   a domain with a bump of topography one third of the domain width at the central latitude.
   This is meant for the "EEL-R5" configuration, a periodic or open boundary channel with a seamount.
 \item[\np{nn\_bathy}~\forcode{= 1}]:
+\item[\np{nn\_bathy}\forcode{ = 1}]:
   read a bathymetry and ice shelf draft (if needed).
   The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) at
 …
   The \ifile{isfdraft\_meter} file (Netcdf format) provides the ice shelf draft (positive, in meters) at
   each grid point of the model grid.
   This file is only needed if \np{ln\_isfcav}~\forcode{= .true.}.
+  This file is only needed if \np{ln\_isfcav}\forcode{ = .true.}.
   Defining the ice shelf draft will also define the ice shelf edge and the grounding line position.
 \end{description}
 …
 %        z-coordinate  and reference coordinate transformation
 % -------------------------------------------------------------------------------------------------------------
 \subsection[$Z$-coordinate (\protect\np{ln\_zco}~\forcode{= .true.}) and ref. coordinate]
             {$Z$-coordinate (\protect\np{ln\_zco}~\forcode{= .true.}) and reference coordinate}
+\subsection[$Z$-coordinate (\forcode{ln_zco = .true.}) and ref. coordinate]
+{$Z$-coordinate (\protect\np{ln\_zco}\forcode{ = .true.}) and reference coordinate}
 \label{subsec:DOM_zco}
 …
 \begin{figure}[!tb]
   \begin{center}
     \includegraphics[]{Fig_zgr}
+    \includegraphics[width=\textwidth]{Fig_zgr}
     \caption{
       \protect\label{fig:zgr}
 …
 using parameters provided in the \ngn{namcfg} namelist.
 It is possible to define a simple regular vertical grid by giving zero stretching (\np{ppacr}~\forcode{= 0}).
+It is possible to define a simple regular vertical grid by giving zero stretching (\np{ppacr}\forcode{ = 0}).
 In that case, the parameters \jp{jpk} (number of $w$-levels) and
 \np{pphmax} (total ocean depth in meters) fully define the grid.
 …
 a smooth hyperbolic tangent transition in between (\autoref{fig:zgr}).
 If the ice shelf cavities are opened (\np{ln\_isfcav}~\forcode{= .true.}), the definition of $z_0$ is the same.
+If the ice shelf cavities are opened (\np{ln\_isfcav}\forcode{ = .true.}), the definition of $z_0$ is the same.
 However, definition of $e_3^0$ at $t$- and $w$-points is respectively changed to:
 \begin{equation}
 …
 %        z-coordinate with partial step
 % -------------------------------------------------------------------------------------------------------------
+\subsection{$Z$-coordinate with partial step (\protect\np{ln\_zps}~\forcode{= .true.})}
+\subsection[$Z$-coordinate with partial step (\forcode{ln_zps = .true.})]
+{$Z$-coordinate with partial step (\protect\np{ln\_zps}\forcode{ = .true.})}
 \label{subsec:DOM_zps}
 %--------------------------------------------namdom-------------------------------------------------------
 …
 %        s-coordinate
 % -------------------------------------------------------------------------------------------------------------
+\subsection{$S$-coordinate (\protect\np{ln\_sco}~\forcode{= .true.})}
+\subsection[$S$-coordinate (\forcode{ln_sco = .true.})]
+{$S$-coordinate (\protect\np{ln\_sco}\forcode{ = .true.})}
 \label{subsec:DOM_sco}
 %------------------------------------------nam_zgr_sco---------------------------------------------------
 …
 %--------------------------------------------------------------------------------------------------------------
 Options are defined in \ngn{namzgr\_sco}.
 In $s$-coordinate (\np{ln\_sco}~\forcode{= .true.}), the depth and thickness of the model levels are defined from
+In $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}), the depth and thickness of the model levels are defined from
 the product of a depth field and either a stretching function or its derivative, respectively:
 …
 The original default NEMO s-coordinate stretching is available if neither of the other options are specified as true
 (\np{ln\_s\_SH94}~\forcode{= .false.} and \np{ln\_s\_SF12}~\forcode{= .false.}).
 This uses a depth independent $\tanh$ function for the stretching \citep{Madec_al_JPO96}:
+(\np{ln\_s\_SH94}\forcode{ = .false.} and \np{ln\_s\_SF12}\forcode{ = .false.}).
+This uses a depth independent $\tanh$ function for the stretching \citep{madec.delecluse.ea_JPO96}:
 \[
 …
 A stretching function,
 modified from the commonly used \citet{Song_Haidvogel_JCP94} stretching (\np{ln\_s\_SH94}~\forcode{= .true.}),
+modified from the commonly used \citet{song.haidvogel_JCP94} stretching (\np{ln\_s\_SH94}\forcode{ = .true.}),
 is also available and is more commonly used for shelf seas modelling:
 …
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[]{Fig_sco_function}
+    \includegraphics[width=\textwidth]{Fig_sco_function}
     \caption{
       \protect\label{fig:sco_function}
 …
 Another example has been provided at version 3.5 (\np{ln\_s\_SF12}) that allows a fixed surface resolution in
 an analytical terrain-following stretching \citet{Siddorn_Furner_OM12}.
+an analytical terrain-following stretching \citet{siddorn.furner_OM13}.
 In this case the a stretching function $\gamma$ is defined such that:
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!ht]
   \includegraphics[]{Fig_DOM_compare_coordinates_surface}
+  \includegraphics[width=\textwidth]{Fig_DOM_compare_coordinates_surface}
   \caption{
     A comparison of the \citet{Song_Haidvogel_JCP94} $S$-coordinate (solid lines),
+    A comparison of the \citet{song.haidvogel_JCP94} $S$-coordinate (solid lines),
     a 50 level $Z$-coordinate (contoured surfaces) and
     the \citet{Siddorn_Furner_OM12} $S$-coordinate (dashed lines) in the surface $100~m$ for
+    the \citet{siddorn.furner_OM13} $S$-coordinate (dashed lines) in the surface $100~m$ for
     a idealised bathymetry that goes from $50~m$ to $5500~m$ depth.
     For clarity every third coordinate surface is shown.
 …
 creating a non-analytical vertical coordinate that
 therefore may suffer from large gradients in the vertical resolutions.
 This stretching is less straightforward to implement than the \citet{Song_Haidvogel_JCP94} stretching,
+This stretching is less straightforward to implement than the \citet{song.haidvogel_JCP94} stretching,
 but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes.
 As with the \citet{Song_Haidvogel_JCP94} stretching the stretch is only applied at depths greater than
+As with the \citet{song.haidvogel_JCP94} stretching the stretch is only applied at depths greater than
 the critical depth $h_c$.
 In this example two options are available in depths shallower than $h_c$,
 …
 Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as
 large slopes lead to hydrostatic consistency.
 A hydrostatic consistency parameter diagnostic following \citet{Haney1991} has been implemented,
+A hydrostatic consistency parameter diagnostic following \citet{haney_JPO91} has been implemented,
 and is output as part of the model mesh file at the start of the run.
 …
 %        z*- or s*-coordinate
 % -------------------------------------------------------------------------------------------------------------
+\subsection{\zstar- or \sstar-coordinate (\protect\np{ln\_linssh}~\forcode{= .false.})}
+\subsection[\zstar- or \sstar-coordinate (\forcode{ln_linssh = .false.})]
+{\zstar- or \sstar-coordinate (\protect\np{ln\_linssh}\forcode{ = .false.})}
 \label{subsec:DOM_zgr_star}
 …
 Whatever the vertical coordinate used, the model offers the possibility of representing the bottom topography with
 steps that follow the face of the model cells (step like topography) \citep{Madec_al_JPO96}.
+steps that follow the face of the model cells (step like topography) \citep{madec.delecluse.ea_JPO96}.
 The distribution of the steps in the horizontal is defined in a 2D integer array, mbathy, which
 gives the number of ocean levels (\ie those that are not masked) at each $t$-point.
 …
 % Domain: Initial State (dtatsd & istate)
 % ================================================================
+\section{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})}
+\section[Initial state (\textit{istate.F90} and \textit{dtatsd.F90})]
+{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})}
 \label{sec:DTA_tsd}
 %-----------------------------------------namtsd-------------------------------------------
 …
 salinity fields is controlled through the \np{ln\_tsd\_ini} namelist parameter.
 \begin{description}
 \item[\np{ln\_tsd\_init}~\forcode{= .true.}]
+\item[\np{ln\_tsd\_init}\forcode{ = .true.}]
   use a T and S input files that can be given on the model grid itself or on their native input data grid.
   In the latter case,
 …
   The information relative to the input files are given in the \np{sn\_tem} and \np{sn\_sal} structures.
   The computation is done in the \mdl{dtatsd} module.
 \item[\np{ln\_tsd\_init}~\forcode{= .false.}]
+\item[\np{ln\_tsd\_init}\forcode{ = .false.}]
   use constant salinity value of $35.5~psu$ and an analytical profile of temperature
   (typical of the tropical ocean), see \rou{istate\_t\_s} subroutine called from \mdl{istate} module.

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DYN.tex

-                      r10499
+                      r11263
 %           Horizontal divergence and relative vorticity
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Horizontal divergence and relative vorticity (\protect\mdl{divcur})}
+\subsection[Horizontal divergence and relative vorticity (\textit{divcur.F90})]
+{Horizontal divergence and relative vorticity (\protect\mdl{divcur})}
 \label{subsec:DYN_divcur}
 …
 %           Sea Surface Height evolution
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})}
+\subsection[Horizontal divergence and relative vorticity (\textit{sshwzv.F90})]
+{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})}
 \label{subsec:DYN_sshwzv}
 …
 Replacing $T$ by the number $1$ in the tracer equation and summing over the water column must lead to
 the sea surface height equation otherwise tracer content will not be conserved
 \citep{Griffies_al_MWR01, Leclair_Madec_OM09}.
+\citep{griffies.pacanowski.ea_MWR01, leclair.madec_OM09}.
 The vertical velocity is computed by an upward integration of the horizontal divergence starting at the bottom,
 …
 %        Vorticity term
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Vorticity term (\protect\mdl{dynvor})}
+\subsection[Vorticity term (\textit{dynvor.F90})]
+{Vorticity term (\protect\mdl{dynvor})}
 \label{subsec:DYN_vor}
 %------------------------------------------nam_dynvor----------------------------------------------------
 …
 %                 enstrophy conserving scheme
 %-------------------------------------------------------------
+\subsubsection{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})}
+\subsubsection[Enstrophy conserving scheme (\forcode{ln_dynvor_ens = .true.})]
+{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})}
 \label{subsec:DYN_vor_ens}
 …
 %                 energy conserving scheme
 %-------------------------------------------------------------
+\subsubsection{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})}
+\subsubsection[Energy conserving scheme (\forcode{ln_dynvor_ene = .true.})]
+{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})}
 \label{subsec:DYN_vor_ene}
 …
 %                 mix energy/enstrophy conserving scheme
 %-------------------------------------------------------------
+\subsubsection{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.}) }
+\subsubsection[Mixed energy/enstrophy conserving scheme (\forcode{ln_dynvor_mix = .true.})]
+{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.})}
 \label{subsec:DYN_vor_mix}
 …
 %                 energy and enstrophy conserving scheme
 %-------------------------------------------------------------
+\subsubsection{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.}) }
+\subsubsection[Energy and enstrophy conserving scheme (\forcode{ln_dynvor_een = .true.})]
+{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.})}
 \label{subsec:DYN_vor_een}
 …
 Nevertheless, this technique strongly distort the phase and group velocity of Rossby waves....}
 A very nice solution to the problem of double averaging was proposed by \citet{Arakawa_Hsu_MWR90}.
+A very nice solution to the problem of double averaging was proposed by \citet{arakawa.hsu_MWR90}.
 The idea is to get rid of the double averaging by considering triad combinations of vorticity.
 It is noteworthy that this solution is conceptually quite similar to the one proposed by
 \citep{Griffies_al_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}).
 The \citet{Arakawa_Hsu_MWR90} vorticity advection scheme for a single layer is modified
 for spherical coordinates as described by \citet{Arakawa_Lamb_MWR81} to obtain the EEN scheme.
+\citep{griffies.gnanadesikan.ea_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}).
+The \citet{arakawa.hsu_MWR90} vorticity advection scheme for a single layer is modified
+for spherical coordinates as described by \citet{arakawa.lamb_MWR81} to obtain the EEN scheme.
 First consider the discrete expression of the potential vorticity, $q$, defined at an $f$-point:
 \[
 …
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[width=0.70\textwidth]{Fig_DYN_een_triad}
+    \includegraphics[width=\textwidth]{Fig_DYN_een_triad}
     \caption{
       \protect\label{fig:DYN_een_triad}
 …
 (with a systematic reduction of $e_{3f}$ when a model level intercept the bathymetry)
 that tends to reinforce the topostrophy of the flow
 (\ie the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.
+(\ie the tendency of the flow to follow the isobaths) \citep{penduff.le-sommer.ea_OS07}.
 Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as
 …
 (\ie $\chi$=$0$) (see \autoref{subsec:C_vorEEN}).
 Applied to a realistic ocean configuration, it has been shown that it leads to a significant reduction of
 the noise in the vertical velocity field \citep{Le_Sommer_al_OM09}.
+the noise in the vertical velocity field \citep{le-sommer.penduff.ea_OM09}.
 Furthermore, used in combination with a partial steps representation of bottom topography,
 it improves the interaction between current and topography,
 leading to a larger topostrophy of the flow \citep{Barnier_al_OD06, Penduff_al_OS07}.
+leading to a larger topostrophy of the flow \citep{barnier.madec.ea_OD06, penduff.le-sommer.ea_OS07}.
 %--------------------------------------------------------------------------------------------------------------
 %           Kinetic Energy Gradient term
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Kinetic energy gradient term (\protect\mdl{dynkeg})}
+\subsection[Kinetic energy gradient term (\textit{dynkeg.F90})]
+{Kinetic energy gradient term (\protect\mdl{dynkeg})}
 \label{subsec:DYN_keg}
 …
 %           Vertical advection term
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Vertical advection term (\protect\mdl{dynzad}) }
+\subsection[Vertical advection term (\textit{dynzad.F90})]
+{Vertical advection term (\protect\mdl{dynzad})}
 \label{subsec:DYN_zad}
 …
 When \np{ln\_dynzad\_zts}\forcode{ = .true.},
 a split-explicit time stepping with 5 sub-timesteps is used on the vertical advection term.
 This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}.
+This option can be useful when the value of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}.
 Note that in this case,
 a similar split-explicit time stepping should be used on vertical advection of tracer to ensure a better stability,
 …
 %           Coriolis plus curvature metric terms
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Coriolis plus curvature metric terms (\protect\mdl{dynvor}) }
+\subsection[Coriolis plus curvature metric terms (\textit{dynvor.F90})]
+{Coriolis plus curvature metric terms (\protect\mdl{dynvor})}
 \label{subsec:DYN_cor_flux}
 …
 %           Flux form Advection term
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Flux form advection term (\protect\mdl{dynadv}) }
+\subsection[Flux form advection term (\textit{dynadv.F90})]
+{Flux form advection term (\protect\mdl{dynadv})}
 \label{subsec:DYN_adv_flux}
 …
 a $2^{nd}$ order centered finite difference scheme, CEN2,
 or a $3^{rd}$ order upstream biased scheme, UBS.
 The latter is described in \citet{Shchepetkin_McWilliams_OM05}.
+The latter is described in \citet{shchepetkin.mcwilliams_OM05}.
 The schemes are selected using the namelist logicals \np{ln\_dynadv\_cen2} and \np{ln\_dynadv\_ubs}.
 In flux form, the schemes differ by the choice of a space and time interpolation to define the value of
 …
 %                 2nd order centred scheme
 %-------------------------------------------------------------
+\subsubsection{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})}
+\subsubsection[CEN2: $2^{nd}$ order centred scheme (\forcode{ln_dynadv_cen2 = .true.})]
+{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})}
 \label{subsec:DYN_adv_cen2}
 …
 %                 UBS scheme
 %-------------------------------------------------------------
+\subsubsection{UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})}
+\subsubsection[UBS: Upstream Biased Scheme (\forcode{ln_dynadv_ubs = .true.})]
+{UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})}
 \label{subsec:DYN_adv_ubs}
 …
 where $u"_{i+1/2} =\delta_{i+1/2} \left[ {\delta_i \left[ u \right]} \right]$.
 This results in a dissipatively dominant (\ie hyper-diffusive) truncation error
 \citep{Shchepetkin_McWilliams_OM05}.
 The overall performance of the advection scheme is similar to that reported in \citet{Farrow1995}.
+\citep{shchepetkin.mcwilliams_OM05}.
+The overall performance of the advection scheme is similar to that reported in \citet{farrow.stevens_JPO95}.
 It is a relatively good compromise between accuracy and smoothness.
 It is not a \emph{positive} scheme, meaning that false extrema are permitted.
 …
 while the second term, which is the diffusion part of the scheme,
 is evaluated using the \textit{before} velocity (forward in time).
 This is discussed by \citet{Webb_al_JAOT98} in the context of the Quick advection scheme.
+This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme.
 Note that the UBS and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes only differ by
 one coefficient.
 Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{Webb_al_JAOT98}.
+Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_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{dynadv\_ubs} module and obtain a QUICK scheme.
 …
 %           Hydrostatic pressure gradient term
 % ================================================================
+\section{Hydrostatic pressure gradient (\protect\mdl{dynhpg})}
+\section[Hydrostatic pressure gradient (\textit{dynhpg.F90})]
+{Hydrostatic pressure gradient (\protect\mdl{dynhpg})}
 \label{sec:DYN_hpg}
 %------------------------------------------nam_dynhpg---------------------------------------------------
 …
 %           z-coordinate with full step
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})}
+\subsection[Full step $Z$-coordinate (\forcode{ln_dynhpg_zco = .true.})]
+{Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})}
 \label{subsec:DYN_hpg_zco}
 …
 %           z-coordinate with partial step
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})}
+\subsection[Partial step $Z$-coordinate (\forcode{ln_dynhpg_zps = .true.})]
+{Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})}
 \label{subsec:DYN_hpg_zps}
 …
 Pressure gradient formulations in an $s$-coordinate have been the subject of a vast number of papers
 (\eg, \citet{Song1998, Shchepetkin_McWilliams_OM05}).
+(\eg, \citet{song_MWR98, shchepetkin.mcwilliams_OM05}).
 A number of different pressure gradient options are coded but the ROMS-like,
 density Jacobian with cubic polynomial method is currently disabled whilst known bugs are under investigation.
 $\bullet$ Traditional coding (see for example \citet{Madec_al_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.})
+$\bullet$ Traditional coding (see for example \citet{madec.delecluse.ea_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.})
 \begin{equation}
   \label{eq:dynhpg_sco}
 …
 $\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}\forcode{ = .true.})
 $\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{Shchepetkin_McWilliams_OM05}
+$\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{shchepetkin.mcwilliams_OM05}
 (\np{ln\_dynhpg\_djc}\forcode{ = .true.}) (currently disabled; under development)
 Note that expression \autoref{eq:dynhpg_sco} is commonly used when the variable volume formulation is activated
 (\key{vvl}) because in that case, even with a flat bottom,
 the coordinate surfaces are not horizontal but follow the free surface \citep{Levier2007}.
+the coordinate surfaces are not horizontal but follow the free surface \citep{levier.treguier.ea_rpt07}.
 The pressure jacobian scheme (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) is available as
 an improved option to \np{ln\_dynhpg\_sco}\forcode{ = .true.} when \key{vvl} is active.
 …
 corresponds to the water replaced by the ice shelf.
 This top pressure is constant over time.
 A detailed description of this method is described in \citet{Losch2008}.\\
+A detailed description of this method is described in \citet{losch_JGR08}.\\
 The pressure gradient due to ocean load is computed using the expression \autoref{eq:dynhpg_sco} described in
 …
 %           Time-scheme
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .true./.false.})}
+\subsection[Time-scheme (\forcode{ln_dynhpg_imp = .{true,false}.})]
+{Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .\{true,false\}}.)}
 \label{subsec:DYN_hpg_imp}
 …
 the physical phenomenon that controls the time-step is internal gravity waves (IGWs).
 A semi-implicit scheme for doubling the stability limit associated with IGWs can be used
 \citep{Brown_Campana_MWR78, Maltrud1998}.
+\citep{brown.campana_MWR78, maltrud.smith.ea_JGR98}.
 It involves the evaluation of the hydrostatic pressure gradient as
 an average over the three time levels $t-\rdt$, $t$, and $t+\rdt$
 …
 % Surface Pressure Gradient
 % ================================================================
+\section{Surface pressure gradient (\protect\mdl{dynspg})}
+\section[Surface pressure gradient (\textit{dynspg.F90})]
+{Surface pressure gradient (\protect\mdl{dynspg})}
 \label{sec:DYN_spg}
 %-----------------------------------------nam_dynspg----------------------------------------------------
 …
 which imposes a very small time step when an explicit time stepping is used.
 Two methods are proposed to allow a longer time step for the three-dimensional equations:
 the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt}),
+the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt?}),
 and the split-explicit free surface described below.
 The extra term introduced in the filtered method is calculated implicitly,
 …
 % Explicit free surface formulation
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Explicit free surface (\protect\key{dynspg\_exp})}
+\subsection[Explicit free surface (\texttt{\textbf{key\_dynspg\_exp}})]
+{Explicit free surface (\protect\key{dynspg\_exp})}
 \label{subsec:DYN_spg_exp}
 …
 % Split-explict free surface formulation
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Split-explicit free surface (\protect\key{dynspg\_ts})}
+\subsection[Split-explicit free surface (\texttt{\textbf{key\_dynspg\_ts}})]
+{Split-explicit free surface (\protect\key{dynspg\_ts})}
 \label{subsec:DYN_spg_ts}
 %------------------------------------------namsplit-----------------------------------------------------------
 …
 The split-explicit free surface formulation used in \NEMO (\key{dynspg\_ts} defined),
 also called the time-splitting formulation, follows the one proposed by \citet{Shchepetkin_McWilliams_OM05}.
+also called the time-splitting formulation, follows the one proposed by \citet{shchepetkin.mcwilliams_OM05}.
 The general idea is to solve the free surface equation and the associated barotropic velocity equations with
 a smaller time step than $\rdt$, the time step used for the three dimensional prognostic variables
 …
 \begin{equation}
   \label{eq:BT_dyn}
   \frac{\partial {\rm \overline{{\bf U}}_h} }{\partial t}=
   -f\;{\rm {\bf k}}\times {\rm \overline{{\bf U}}_h}
   -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \rm {\overline{{\bf U}}_h} + \rm {\overline{\bf G}}
+  \frac{\partial {\mathrm \overline{{\mathbf U}}_h} }{\partial t}=
+  -f\;{\mathrm {\mathbf k}}\times {\mathrm \overline{{\mathbf U}}_h}
+  -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \mathrm {\overline{{\mathbf U}}_h} + \mathrm {\overline{\mathbf G}}
 \end{equation}
 \[
   % \label{eq:BT_ssh}
   \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\rm{\bf \overline{U}}}_h \,} \right]+P-E
+  \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\mathrm{\mathbf \overline{U}}}_h \,} \right]+P-E
 \]
 % \end{subequations}
 where $\rm {\overline{\bf G}}$ is a forcing term held constant, containing coupling term between modes,
+where $\mathrm {\overline{\mathbf G}}$ is a forcing term held constant, containing coupling term between modes,
 surface atmospheric forcing as well as slowly varying barotropic terms not explicitly computed to gain efficiency.
 The third term on the right hand side of \autoref{eq:BT_dyn} represents the bottom stress
 (see section \autoref{sec:ZDF_bfr}), explicitly accounted for at each barotropic iteration.
 Temporal discretization of the system above follows a three-time step Generalized Forward Backward algorithm
 detailed in \citet{Shchepetkin_McWilliams_OM05}.
+detailed in \citet{shchepetkin.mcwilliams_OM05}.
 AB3-AM4 coefficients used in \NEMO follow the second-order accurate,
 "multi-purpose" stability compromise as defined in \citet{Shchepetkin_McWilliams_Bk08}
+"multi-purpose" stability compromise as defined in \citet{shchepetkin.mcwilliams_ibk09}
 (see their figure 12, lower left).
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.7\textwidth]{Fig_DYN_dynspg_ts}
+    \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts}
     \caption{
       \protect\label{fig:DYN_dynspg_ts}
 …
 and time splitting not compatible.
 Advective barotropic velocities are obtained by using a secondary set of filtering weights,
 uniquely defined from the filter coefficients used for the time averaging (\citet{Shchepetkin_McWilliams_OM05}).
+uniquely defined from the filter coefficients used for the time averaging (\citet{shchepetkin.mcwilliams_OM05}).
 Consistency between the time averaged continuity equation and the time stepping of tracers is here the key to
 obtain exact conservation.
 …
 external gravity waves in idealized or weakly non-linear cases.
 Although the damping is lower than for the filtered free surface,
 it is still significant as shown by \citet{Levier2007} in the case of an analytical barotropic Kelvin wave.
+it is still significant as shown by \citet{levier.treguier.ea_rpt07} in the case of an analytical barotropic Kelvin wave.
 %>>>>>===============
 …
 the leap-frog splitting mode in equation \autoref{eq:DYN_spg_ts_ssh}.
 We have tried various forms of such filtering,
 with the following method discussed in \cite{Griffies_al_MWR01} chosen due to
+with the following method discussed in \cite{griffies.pacanowski.ea_MWR01} chosen due to
 its stability and reasonably good maintenance of tracer conservation properties (see ??).
 …
 % Filtered free surface formulation
 %--------------------------------------------------------------------------------------------------------------
+\subsection{Filtered free surface (\protect\key{dynspg\_flt})}
+\subsection[Filtered free surface (\texttt{\textbf{key\_dynspg\_flt}})]
+{Filtered free surface (\protect\key{dynspg\_flt})}
 \label{subsec:DYN_spg_fltp}
 The filtered formulation follows the \citet{Roullet_Madec_JGR00} implementation.
+The filtered formulation follows the \citet{roullet.madec_JGR00} implementation.
 The extra term introduced in the equations (see \autoref{subsec:PE_free_surface}) is solved implicitly.
 The elliptic solvers available in the code are documented in \autoref{chap:MISC}.
 …
   \[
     % \label{eq:spg_flt}
     \frac{\partial {\rm {\bf U}}_h }{\partial t}= {\rm {\bf M}}
+    \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= {\mathrm {\mathbf M}}
     - g \nabla \left( \tilde{\rho} \ \eta \right)
     - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right)
 …
   where $T_c$, is a parameter with dimensions of time which characterizes the force,
   $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density,
   and $\rm {\bf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient,
+  and $\mathrm {\mathbf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient,
   non-linear and viscous terms in \autoref{eq:PE_dyn}.
 }   %end gmcomment
 …
 % Lateral diffusion term
 % ================================================================
+\section{Lateral diffusion term and operators (\protect\mdl{dynldf})}
+\section[Lateral diffusion term and operators (\textit{dynldf.F90})]
+{Lateral diffusion term and operators (\protect\mdl{dynldf})}
 \label{sec:DYN_ldf}
 %------------------------------------------nam_dynldf----------------------------------------------------
 …
 % ================================================================
 \subsection[Iso-level laplacian (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})]
             {Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})}
+\subsection[Iso-level laplacian (\forcode{ln_dynldf_lap = .true.})]
+{Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})}
 \label{subsec:DYN_ldf_lap}
 …
   \left\{
     \begin{aligned}
       D_u^{l{\rm {\bf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm}
+      D_u^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm}
           \;\chi } \right]-\frac{1}{e_{2u} {\kern 1pt}e_{3u} }\delta_j \left[
         {A_f^{lm} \;e_{3f} \zeta } \right] \\ \\
       D_v^{l{\rm {\bf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm}
+      D_v^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm}
           \;\chi } \right]+\frac{1}{e_{1v} {\kern 1pt}e_{3v} }\delta_i \left[
         {A_f^{lm} \;e_{3f} \zeta } \right]
 …
 %           Rotated laplacian operator
 %--------------------------------------------------------------------------------------------------------------
 \subsection[Rotated laplacian (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})]
             {Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})}
+\subsection[Rotated laplacian (\forcode{ln_dynldf_iso = .true.})]
+{Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})}
 \label{subsec:DYN_ldf_iso}
 …
 %           Iso-level bilaplacian operator
 %--------------------------------------------------------------------------------------------------------------
 \subsection[Iso-level bilaplacian (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})]
             {Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})}
+\subsection[Iso-level bilaplacian (\forcode{ln_dynldf_bilap = .true.})]
+{Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})}
 \label{subsec:DYN_ldf_bilap}
 …
 %           Vertical diffusion term
 % ================================================================
+\section{Vertical diffusion term (\protect\mdl{dynzdf})}
+\section[Vertical diffusion term (\textit{dynzdf.F90})]
+{Vertical diffusion term (\protect\mdl{dynzdf})}
 \label{sec:DYN_zdf}
 %----------------------------------------------namzdf------------------------------------------------------
 …
 There are two main options for wetting and drying code (wd):
 (a) an iterative limiter (il) and (b) a directional limiter (dl).
 The directional limiter is based on the scheme developed by \cite{WarnerEtal13} for RO
+The directional limiter is based on the scheme developed by \cite{warner.defne.ea_CG13} for RO
 MS
 which was in turn based on ideas developed for POM by \cite{Oey06}. The iterative
+which was in turn based on ideas developed for POM by \cite{oey_OM06}. The iterative
 limiter is a new scheme.  The iterative limiter is activated by setting $\mathrm{ln\_wd\_il} = \mathrm{.true.}$
 and $\mathrm{ln\_wd\_dl} = \mathrm{.false.}$. The directional limiter is activated
 …
 %   Iterative limiters
 %-----------------------------------------------------------------------------------------
 \subsection   [Directional limiter (\textit{wet\_dry})]
          {Directional limiter (\mdl{wet\_dry})}
+\subsection[Directional limiter (\textit{wet\_dry.F90})]
+{Directional limiter (\mdl{wet\_dry})}
 \label{subsec:DYN_wd_directional_limiter}
 The principal idea of the directional limiter is that
 …
 \cite{WarnerEtal13} state that in their scheme the velocity masks at the cell faces for the baroclinic
+\cite{warner.defne.ea_CG13} state that in their scheme the velocity masks at the cell faces for the baroclinic
 timesteps are set to 0 or 1 depending on whether the average of the masks over the barotropic sub-steps is respectively less than
 or greater than 0.5. That scheme does not conserve tracers in integrations started from constant tracer
 …
 %-----------------------------------------------------------------------------------------
 \subsection   [Iterative limiter (\textit{wet\_dry})]
          {Iterative limiter (\mdl{wet\_dry})}
+\subsection[Iterative limiter (\textit{wet\_dry.F90})]
+{Iterative limiter (\mdl{wet\_dry})}
 \label{subsec:DYN_wd_iterative_limiter}
 \subsubsection [Iterative flux limiter (\textit{wet\_dry})]
          {Iterative flux limiter (\mdl{wet\_dry})}
+\subsubsection[Iterative flux limiter (\textit{wet\_dry.F90})]
+{Iterative flux limiter (\mdl{wet\_dry})}
 \label{subsubsec:DYN_wd_il_spg_limiter}
 …
 \end{equation}
 Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\it [Q: Why is
+Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\itshape [Q: Why is
 this necessary/desirable?]}. Substituting from (\ref{dyn_wd_continuity_coef}) gives an
 expression for the coefficient needed to multiply the outward flux at this cell in order
 …
 %      Surface pressure gradients
 %----------------------------------------------------------------------------------------
 \subsubsection   [Modification of surface pressure gradients (\textit{dynhpg})]
          {Modification of surface pressure gradients (\mdl{dynhpg})}
+\subsubsection[Modification of surface pressure gradients (\textit{dynhpg.F90})]
+{Modification of surface pressure gradients (\mdl{dynhpg})}
 \label{subsubsec:DYN_wd_il_spg}
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!ht] \begin{center}
 \includegraphics[width=0.8\textwidth]{Fig_WAD_dynhpg}
+\includegraphics[width=\textwidth]{Fig_WAD_dynhpg}
 \caption{ \label{Fig_WAD_dynhpg}
 Illustrations of the three possible combinations of the logical variables controlling the
 …
 conditions.
 \subsubsection   [Additional considerations (\textit{usrdef\_zgr})]
          {Additional considerations (\mdl{usrdef\_zgr})}
+\subsubsection[Additional considerations (\textit{usrdef\_zgr.F90})]
+{Additional considerations (\mdl{usrdef\_zgr})}
 \label{subsubsec:WAD_additional}
 …
 %      The WAD test cases
 %----------------------------------------------------------------------------------------
 \subsection   [The WAD test cases (\textit{usrdef\_zgr})]
          {The WAD test cases (\mdl{usrdef\_zgr})}
+\subsection[The WAD test cases (\textit{usrdef\_zgr.F90})]
+{The WAD test cases (\mdl{usrdef\_zgr})}
 \label{WAD_test_cases}
 …
 % Time evolution term
 % ================================================================
+\section{Time evolution term (\protect\mdl{dynnxt})}
+\section[Time evolution term (\textit{dynnxt.F90})]
+{Time evolution term (\protect\mdl{dynnxt})}
 \label{sec:DYN_nxt}

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_LBC.tex

-                      r10614
+                      r11263
 % Boundary Condition at the Coast
 % ================================================================
+\section{Boundary condition at the coast (\protect\np{rn\_shlat})}
+\section[Boundary condition at the coast (\texttt{rn\_shlat})]
+{Boundary condition at the coast (\protect\np{rn\_shlat})}
 \label{sec:LBC_coast}
 %--------------------------------------------nam_lbc-------------------------------------------------------
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_LBC_uv}
+    \includegraphics[width=\textwidth]{Fig_LBC_uv}
     \caption{
       \protect\label{fig:LBC_uv}
 …
 \begin{figure}[!p]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_LBC_shlat}
+    \includegraphics[width=\textwidth]{Fig_LBC_shlat}
     \caption{
       \protect\label{fig:LBC_shlat}
 …
 % Boundary Condition around the Model Domain
 % ================================================================
+\section{Model domain boundary condition (\protect\np{jperio})}
+\section[Model domain boundary condition (\texttt{jperio})]
+{Model domain boundary condition (\protect\np{jperio})}
 \label{sec:LBC_jperio}
 …
 %        Closed, cyclic (\np{jperio}\forcode{ = 0..2})
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Closed, cyclic (\protect\np{jperio}\forcode{= [0127]})}
+\subsection[Closed, cyclic (\forcode{jperio = [0127]})]
+{Closed, cyclic (\protect\np{jperio}\forcode{ = [0127]})}
 \label{subsec:LBC_jperio012}
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=1.0\textwidth]{Fig_LBC_jperio}
+    \includegraphics[width=\textwidth]{Fig_LBC_jperio}
     \caption{
       \protect\label{fig:LBC_jperio}
 …
 %        North fold (\textit{jperio = 3 }to $6)$
 % -------------------------------------------------------------------------------------------------------------
+\subsection{North-fold (\protect\np{jperio}\forcode{ = 3..6})}
+\subsection[North-fold (\forcode{jperio = [3-6]})]
+{North-fold (\protect\np{jperio}\forcode{ = [3-6]})}
 \label{subsec:LBC_north_fold}
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_North_Fold_T}
+    \includegraphics[width=\textwidth]{Fig_North_Fold_T}
     \caption{
       \protect\label{fig:North_Fold_T}
 …
 % Exchange with neighbouring processors
 % ====================================================================
+\section{Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})}
+\section[Exchange with neighbouring processors (\textit{lbclnk.F90}, \textit{lib\_mpp.F90})]
+{Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})}
 \label{sec:LBC_mpp}
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_mpp}
+    \includegraphics[width=\textwidth]{Fig_mpp}
     \caption{
       \protect\label{fig:mpp}
 …
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_mppini2}
+    \includegraphics[width=\textwidth]{Fig_mppini2}
     \caption {
       \protect\label{fig:mppini2}
 …
 The BDY module was modelled on the OBC module (see NEMO 3.4) and shares many features and
 a similar coding structure \citep{Chanut2005}.
+a similar coding structure \citep{chanut_rpt05}.
 The specification of the location of the open boundary is completely flexible and
 allows for example the open boundary to follow an isobath or other irregular contour.
 …
 \label{subsec:BDY_FRS_scheme}
 The Flow Relaxation Scheme (FRS) \citep{Davies_QJRMS76,Engerdahl_Tel95},
+The Flow Relaxation Scheme (FRS) \citep{davies_QJRMS76,engedahl_T95},
 applies a simple relaxation of the model fields to externally-specified values over
 a zone next to the edge of the model domain.
 …
 \label{subsec:BDY_flather_scheme}
 The \citet{Flather_JPO94} scheme is a radiation condition on the normal,
+The \citet{flather_JPO94} scheme is a radiation condition on the normal,
 depth-mean transport across the open boundary.
 It takes the form
 …
 \label{subsec:BDY_orlanski_scheme}
 The Orlanski scheme is based on the algorithm described by \citep{Marchesiello2001}, hereafter MMS.
+The Orlanski scheme is based on the algorithm described by \citep{marchesiello.mcwilliams.ea_OM01}, hereafter MMS.
 The adaptive Orlanski condition solves a wave plus relaxation equation at the boundary:
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=1.0\textwidth]{Fig_LBC_bdy_geom}
+    \includegraphics[width=\textwidth]{Fig_LBC_bdy_geom}
     \caption {
       \protect\label{fig:LBC_bdy_geom}
 …
 These restrictions mean that data files used with versions of the
 model prior to Version 3.4 may not work with Version 3.4 onwards.
 A \fortran utility {\it bdy\_reorder} exists in the TOOLS directory which
+A \fortran utility {\itshape bdy\_reorder} exists in the TOOLS directory which
 will re-order the data in old BDY data files.
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=1.0\textwidth]{Fig_LBC_nc_header}
+    \includegraphics[width=\textwidth]{Fig_LBC_nc_header}
     \caption {
       \protect\label{fig:LBC_nc_header}

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_LDF.tex

-                      r10442
+                      r11263
 % Direction of lateral Mixing
 % ================================================================
+\section{Direction of lateral mixing (\protect\mdl{ldfslp})}
+\section[Direction of lateral mixing (\textit{ldfslp.F90})]
+{Direction of lateral mixing (\protect\mdl{ldfslp})}
 \label{sec:LDF_slp}
 …
 \gmcomment{
   we should emphasize here that the implementation is a rather old one.
   Better work can be achieved by using \citet{Griffies_al_JPO98, Griffies_Bk04} iso-neutral scheme.
+  Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} iso-neutral scheme.
+}
 …
 %In practice, \autoref{eq:ldfslp_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:ldfslp_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.
 %By definition, neutral surfaces are tangent to the local $in situ$ density \citep{McDougall1987}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters).
+%By definition, neutral surfaces are tangent to the local $in situ$ density \citep{mcdougall_JPO87}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters).
 %In the $z$-coordinate, the derivative of the  \autoref{eq:ldfslp_iso} numerator is evaluated at the same depth \nocite{as what?} ($T$-level, which is the same as the $u$- and $v$-levels), so  the $in situ$ density can be used for its evaluation.
 …
   thus the $in situ$ density can be used.
   This is not the case for the vertical derivatives: $\delta_{k+1/2}[\rho]$ is replaced by $-\rho N^2/g$,
   where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{McDougall1987}
+  where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{mcdougall_JPO87}
   (see \autoref{subsec:TRA_bn2}).
 …
   Note: The solution for $s$-coordinate passes trough the use of different (and better) expression for
   the constraint on iso-neutral fluxes.
   Following \citet{Griffies_Bk04}, instead of specifying directly that there is a zero neutral diffusive flux of
+  Following \citet{griffies_bk04}, instead of specifying directly that there is a zero neutral diffusive flux of
   locally referenced potential density, we stay in the $T$-$S$ plane and consider the balance between
   the neutral direction diffusive fluxes of potential temperature and salinity:
 …
 a minimum background horizontal diffusion for numerical stability reasons.
 To overcome this problem, several techniques have been proposed in which the numerical schemes of
 the ocean model are modified \citep{Weaver_Eby_JPO97, Griffies_al_JPO98}.
+the ocean model are modified \citep{weaver.eby_JPO97, griffies.gnanadesikan.ea_JPO98}.
 Griffies's scheme is now available in \NEMO if \np{traldf\_grif\_iso} is set true; see Appdx \autoref{apdx:triad}.
 Here, another strategy is presented \citep{Lazar_PhD97}:
+Here, another strategy is presented \citep{lazar_phd97}:
 a local filtering of the iso-neutral slopes (made on 9 grid-points) prevents the development of
 grid point noise generated by the iso-neutral diffusion operator (\autoref{fig:LDF_ZDF1}).
 …
 Nevertheless, this iso-neutral operator does not ensure that variance cannot increase,
 contrary to the \citet{Griffies_al_JPO98} operator which has that property.
+contrary to the \citet{griffies.gnanadesikan.ea_JPO98} operator which has that property.
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[width=0.70\textwidth]{Fig_LDF_ZDF1}
+    \includegraphics[width=\textwidth]{Fig_LDF_ZDF1}
     \caption {
       \protect\label{fig:LDF_ZDF1}
 …
 % In addition and also for numerical stability reasons \citep{Cox1987, Griffies_Bk04},
+% In addition and also for numerical stability reasons \citep{cox_OM87, griffies_bk04},
 % the slopes are bounded by $1/100$ everywhere. This limit is decreasing linearly
 % to zero fom $70$ meters depth and the surface (the fact that the eddies "feel" the
 % surface motivates this flattening of isopycnals near the surface).
 For numerical stability reasons \citep{Cox1987, Griffies_Bk04}, the slopes must also be bounded by
+For numerical stability reasons \citep{cox_OM87, griffies_bk04}, the slopes must also be bounded by
 $1/100$ everywhere.
 This constraint is applied in a piecewise linear fashion, increasing from zero at the surface to
 …
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[width=0.70\textwidth]{Fig_eiv_slp}
+    \includegraphics[width=\textwidth]{Fig_eiv_slp}
     \caption{
       \protect\label{fig:eiv_slp}
 …
 % Lateral Mixing Operator
 % ================================================================
+\section{Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf}) }
+\section[Lateral mixing operators (\textit{traldf.F90})]
+{Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf})}
 \label{sec:LDF_op}
 …
 % Lateral Mixing Coefficients
 % ================================================================
+\section{Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn}) }
+\section[Lateral mixing coefficient (\textit{ldftra.F90}, \textit{ldfdyn.F90})]
+{Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn})}
 \label{sec:LDF_coef}
 …
 which is specified through the \np{rn\_ahm0} and \np{rn\_aht0} namelist parameters.
+\subsubsection{Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})}
+\subsubsection[Vertically varying mixing coefficients (\texttt{\textbf{key\_traldf\_c1d}} and \texttt{\textbf{key\_dynldf\_c1d}})]
+{Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})}
 The 1D option is only available when using the $z$-coordinate with full step.
 Indeed in all the other types of vertical coordinate,
 …
 This profile is hard coded in file \textit{traldf\_c1d.h90}, but can be easily modified by users.
+\subsubsection{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})}
+\subsubsection[Horizontally varying mixing coefficients (\texttt{\textbf{key\_traldf\_c2d}} and \texttt{\textbf{key\_dynldf\_c2d}})]
+{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})}
 By default the horizontal variation of the eddy coefficient depends on the local mesh size and
 the type of operator used:
 …
 This variation is intended to reflect the lesser need for subgrid scale eddy mixing where
 the grid size is smaller in the domain.
 It was introduced in the context of the DYNAMO modelling project \citep{Willebrand_al_PO01}.
+It was introduced in the context of the DYNAMO modelling project \citep{willebrand.barnier.ea_PO01}.
 Note that such a grid scale dependance of mixing coefficients significantly increase the range of stability of
 model configurations presenting large changes in grid pacing such as global ocean models.
 …
 For example, in the ORCA2 global ocean model (see Configurations),
 the laplacian viscosity operator uses \np{rn\_ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$ north and south and
 decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{Madec_al_JPO96, Delecluse_Madec_Bk00}.
+decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{madec.delecluse.ea_JPO96, delecluse.madec_icol99}.
 This modification can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}.
 Similar modified horizontal variations can be found with the Antarctic or Arctic sub-domain options of
 ORCA2 and ORCA05 (see \&namcfg namelist).
+\subsubsection{Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})}
+\subsubsection[Space varying mixing coefficients (\texttt{\textbf{key\_traldf\_c3d}} and \texttt{\textbf{key\_dynldf\_c3d}})]
+{Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})}
 The 3D space variation of the mixing coefficient is simply the combination of the 1D and 2D cases,
 …
 % Eddy Induced Mixing
 % ================================================================
+\section{Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})}
+\section[Eddy induced velocity (\textit{traadv\_eiv.F90}, \textit{ldfeiv.F90})]
+{Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})}
 \label{sec:LDF_eiv}
 …
 since it allows us to take advantage of all the advection schemes offered for the tracers
 (see \autoref{sec:TRA_adv}) and not just the $2^{nd}$ order advection scheme as in
 previous releases of OPA \citep{Madec1998}.
+previous releases of OPA \citep{madec.delecluse.ea_NPM98}.
 This is particularly useful for passive tracers where \emph{positivity} of the advection scheme is of
 paramount importance.

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_OBS.tex

-                      r10442
+                      r11263
 \subsubsection{Horizontal interpolation}
 Consider an observation point ${\rm P}$ with with longitude and latitude $({\lambda_{}}_{\rm P}, \phi_{\rm P})$ and
 the four nearest neighbouring model grid points ${\rm A}$, ${\rm B}$, ${\rm C}$ and ${\rm D}$ with
 longitude and latitude ($\lambda_{\rm A}$, $\phi_{\rm A}$),($\lambda_{\rm B}$, $\phi_{\rm B}$) etc.
+Consider an observation point ${\mathrm P}$ with with longitude and latitude $({\lambda_{}}_{\mathrm P}, \phi_{\mathrm P})$ and
+the four nearest neighbouring model grid points ${\mathrm A}$, ${\mathrm B}$, ${\mathrm C}$ and ${\mathrm D}$ with
+longitude and latitude ($\lambda_{\mathrm A}$, $\phi_{\mathrm A}$),($\lambda_{\mathrm B}$, $\phi_{\mathrm B}$) etc.
 All horizontal interpolation methods implemented in NEMO estimate the value of a model variable $x$ at point $P$ as
 a weighted linear combination of the values of the model variables at the grid points ${\rm A}$, ${\rm B}$ etc.:
+a weighted linear combination of the values of the model variables at the grid points ${\mathrm A}$, ${\mathrm B}$ etc.:
 \begin{align*}
   {x_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} &
                                                    \frac{1}{w} \left( {w_{}}_{\rm A} {x_{}}_{\rm A} +
                                                    {w_{}}_{\rm B} {x_{}}_{\rm B} +
                                                    {w_{}}_{\rm C} {x_{}}_{\rm C} +
                                                    {w_{}}_{\rm D} {x_{}}_{\rm D} \right)
+  {x_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} &
+                                                   \frac{1}{w} \left( {w_{}}_{\mathrm A} {x_{}}_{\mathrm A} +
+                                                   {w_{}}_{\mathrm B} {x_{}}_{\mathrm B} +
+                                                   {w_{}}_{\mathrm C} {x_{}}_{\mathrm C} +
+                                                   {w_{}}_{\mathrm D} {x_{}}_{\mathrm D} \right)
 \end{align*}
 where ${w_{}}_{\rm A}$, ${w_{}}_{\rm B}$ etc. are the respective weights for the model field at
 points ${\rm A}$, ${\rm B}$ etc., and $w = {w_{}}_{\rm A} + {w_{}}_{\rm B} + {w_{}}_{\rm C} + {w_{}}_{\rm D}$.
+where ${w_{}}_{\mathrm A}$, ${w_{}}_{\mathrm B}$ etc. are the respective weights for the model field at
+points ${\mathrm A}$, ${\mathrm B}$ etc., and $w = {w_{}}_{\mathrm A} + {w_{}}_{\mathrm B} + {w_{}}_{\mathrm C} + {w_{}}_{\mathrm D}$.
 Four different possibilities are available for computing the weights.
 …
 \begin{enumerate}
 \item[1.] {\bf Great-Circle distance-weighted interpolation.}
+\item[1.] {\bfseries Great-Circle distance-weighted interpolation.}
   The weights are computed as a function of the great-circle distance $s(P, \cdot)$ between $P$ and
   the model grid points $A$, $B$ etc.
   For example, the weight given to the field ${x_{}}_{\rm A}$ is specified as the product of the distances
   from ${\rm P}$ to the other points:
+  For example, the weight given to the field ${x_{}}_{\mathrm A}$ is specified as the product of the distances
+  from ${\mathrm P}$ to the other points:
   \begin{align*}
     {w_{}}_{\rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D})
+    {w_{}}_{\mathrm A} = s({\mathrm P}, {\mathrm B}) \, s({\mathrm P}, {\mathrm C}) \, s({\mathrm P}, {\mathrm D})
   \end{align*}
   where
   \begin{align*}
     s\left ({\rm P}, {\rm M} \right )
+    s\left ({\mathrm P}, {\mathrm M} \right )
      & \hspace{-2mm} = \hspace{-2mm} &
       \cos^{-1} \! \left\{
                \sin {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm M}
              + \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm M}
                \cos ({\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P})
+               \sin {\phi_{}}_{\mathrm P} \sin {\phi_{}}_{\mathrm M}
+             + \cos {\phi_{}}_{\mathrm P} \cos {\phi_{}}_{\mathrm M}
+               \cos ({\lambda_{}}_{\mathrm M} - {\lambda_{}}_{\mathrm P})
                    \right\}
    \end{align*}
    and $M$ corresponds to $B$, $C$ or $D$.
    A more stable form of the great-circle distance formula for small distances ($x$ near 1)
    involves the arcsine function (\eg see p.~101 of \citet{Daley_Barker_Bk01}:
+   involves the arcsine function (\eg see p.~101 of \citet{daley.barker_bk01}:
    \begin{align*}
      s\left( {\rm P}, {\rm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\}
+     s\left( {\mathrm P}, {\mathrm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\}
    \end{align*}
    where
    \begin{align*}
      x & \hspace{-2mm} = \hspace{-2mm} &
                                          {a_{}}_{\rm M} {a_{}}_{\rm P} + {b_{}}_{\rm M} {b_{}}_{\rm P} + {c_{}}_{\rm M} {c_{}}_{\rm P}
+                                         {a_{}}_{\mathrm M} {a_{}}_{\mathrm P} + {b_{}}_{\mathrm M} {b_{}}_{\mathrm P} + {c_{}}_{\mathrm M} {c_{}}_{\mathrm P}
    \end{align*}
    and
    \begin{align*}
       {a_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, \\
       {a_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm P}, \\
       {b_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \cos {\phi_{}}_{\rm M}, \\
       {b_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm P}, \\
       {c_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \sin {\phi_{}}_{\rm M}, \\
       {c_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm P}.
+      {a_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\mathrm M}, \\
+      {a_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\mathrm P}, \\
+      {b_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm M} \cos {\phi_{}}_{\mathrm M}, \\
+      {b_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm P} \cos {\phi_{}}_{\mathrm P}, \\
+      {c_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm M} \sin {\phi_{}}_{\mathrm M}, \\
+      {c_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm P} \sin {\phi_{}}_{\mathrm P}.
   \end{align*}
 \item[2.] {\bf Great-Circle distance-weighted interpolation with small angle approximation.}
+\item[2.] {\bfseries Great-Circle distance-weighted interpolation with small angle approximation.}
   Similar to the previous interpolation but with the distance $s$ computed as
   \begin{align*}
     s\left( {\rm P}, {\rm M} \right)
+    s\left( {\mathrm P}, {\mathrm M} \right)
     & \hspace{-2mm} = \hspace{-2mm} &
                                       \sqrt{ \left( {\phi_{}}_{\rm M} - {\phi_{}}_{\rm P} \right)^{2}
                                       + \left( {\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P} \right)^{2}
                                       \cos^{2} {\phi_{}}_{\rm M} }
+                                      \sqrt{ \left( {\phi_{}}_{\mathrm M} - {\phi_{}}_{\mathrm P} \right)^{2}
+                                      + \left( {\lambda_{}}_{\mathrm M} - {\lambda_{}}_{\mathrm P} \right)^{2}
+                                      \cos^{2} {\phi_{}}_{\mathrm M} }
   \end{align*}
   where $M$ corresponds to $A$, $B$, $C$ or $D$.
 \item[3.] {\bf Bilinear interpolation for a regular spaced grid.}
+\item[3.] {\bfseries Bilinear interpolation for a regular spaced grid.}
   The interpolation is split into two 1D interpolations in the longitude and latitude directions, respectively.
 \item[4.] {\bf Bilinear remapping interpolation for a general grid.}
+\item[4.] {\bfseries Bilinear remapping interpolation for a general grid.}
   An iterative scheme that involves first mapping a quadrilateral cell into
   a cell with coordinates (0,0), (1,0), (0,1) and (1,1).
   This method is based on the SCRIP interpolation package \citep{Jones_1998}.
+  This method is based on the \href{https://github.com/SCRIP-Project/SCRIP}{SCRIP interpolation package}.
 \end{enumerate}
 …
 \begin{figure}
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rec}
+    \includegraphics[width=\textwidth]{Fig_OBS_avg_rec}
     \caption{
       \protect\label{fig:obsavgrec}
 …
 \begin{figure}
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rad}
+    \includegraphics[width=\textwidth]{Fig_OBS_avg_rad}
     \caption{
       \protect\label{fig:obsavgrad}
 …
 This is the most difficult and time consuming part of the 2D interpolation procedure.
 A robust test for determining if an observation falls within a given quadrilateral cell is as follows.
 Let ${\rm P}({\lambda_{}}_{\rm P} ,{\phi_{}}_{\rm P} )$ denote the observation point,
 and let ${\rm A}({\lambda_{}}_{\rm A} ,{\phi_{}}_{\rm A} )$, ${\rm B}({\lambda_{}}_{\rm B} ,{\phi_{}}_{\rm B} )$,
 ${\rm C}({\lambda_{}}_{\rm C} ,{\phi_{}}_{\rm C} )$ and ${\rm D}({\lambda_{}}_{\rm D} ,{\phi_{}}_{\rm D} )$
+Let ${\mathrm P}({\lambda_{}}_{\mathrm P} ,{\phi_{}}_{\mathrm P} )$ denote the observation point,
+and let ${\mathrm A}({\lambda_{}}_{\mathrm A} ,{\phi_{}}_{\mathrm A} )$, ${\mathrm B}({\lambda_{}}_{\mathrm B} ,{\phi_{}}_{\mathrm B} )$,
+${\mathrm C}({\lambda_{}}_{\mathrm C} ,{\phi_{}}_{\mathrm C} )$ and ${\mathrm D}({\lambda_{}}_{\mathrm D} ,{\phi_{}}_{\mathrm D} )$
 denote the bottom left, bottom right, top left and top right corner points of the cell, respectively.
 To determine if P is inside the cell, we verify that the cross-products
 \begin{align*}
   \begin{array}{lllll}
     {{\bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC}
     & = & [({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} )
           - ({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
     {{\bf r}_{}}_{\rm PB} \times {{\bf r}_{}}_{\rm PA}
     & = & [({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} )
           - ({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
     {{\bf r}_{}}_{\rm PC} \times {{\bf r}_{}}_{\rm PD}
     & = & [({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm D}   \; -\; {\phi_{}}_{\rm P} )
           - ({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
     {{\bf r}_{}}_{\rm PD} \times {{\bf r}_{}}_{\rm PB}
     & = & [({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} )
           - ({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} )
           ({\phi_{}}_{\rm D}  \;  - \; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
+    {{\mathbf r}_{}}_{\mathrm PA} \times {{\mathbf r}_{}}_{\mathrm PC}
+    & = & [({\lambda_{}}_{\mathrm A}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm C}   \; -\; {\phi_{}}_{\mathrm P} )
+          - ({\lambda_{}}_{\mathrm C}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm A}   \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\
+    {{\mathbf r}_{}}_{\mathrm PB} \times {{\mathbf r}_{}}_{\mathrm PA}
+    & = & [({\lambda_{}}_{\mathrm B}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm A}   \; -\; {\phi_{}}_{\mathrm P} )
+          - ({\lambda_{}}_{\mathrm A}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm B}   \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\
+    {{\mathbf r}_{}}_{\mathrm PC} \times {{\mathbf r}_{}}_{\mathrm PD}
+    & = & [({\lambda_{}}_{\mathrm C}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm D}   \; -\; {\phi_{}}_{\mathrm P} )
+          - ({\lambda_{}}_{\mathrm D}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm C}   \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\
+    {{\mathbf r}_{}}_{\mathrm PD} \times {{\mathbf r}_{}}_{\mathrm PB}
+    & = & [({\lambda_{}}_{\mathrm D}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm B}   \; -\; {\phi_{}}_{\mathrm P} )
+          - ({\lambda_{}}_{\mathrm B}\; -\; {\lambda_{}}_{\mathrm P} )
+          ({\phi_{}}_{\mathrm D}  \;  - \; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\
   \end{array}
   % \label{eq:cross}
 \end{align*}
 point in the opposite direction to the unit normal $\widehat{\bf k}$
 (\ie that the coefficients of $\widehat{\bf k}$ are negative),
 where ${{\bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, etc. correspond to
+point in the opposite direction to the unit normal $\widehat{\mathbf k}$
+(\ie that the coefficients of $\widehat{\mathbf k}$ are negative),
+where ${{\mathbf r}_{}}_{\mathrm PA}$, ${{\mathbf r}_{}}_{\mathrm PB}$, etc. correspond to
 the vectors between points P and A, P and B, etc..
 The method used is similar to the method used in the SCRIP interpolation package \citep{Jones_1998}.
+The method used is similar to the method used in the \href{https://github.com/SCRIP-Project/SCRIP}{SCRIP interpolation package}.
 In order to speed up the grid search, there is the possibility to construct a lookup table for a user specified resolution.
 …
 \begin{figure}
   \begin{center}
     \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_local}
+    \includegraphics[width=\textwidth]{Fig_ASM_obsdist_local}
     \caption{
       \protect\label{fig:obslocal}
 …
 \begin{figure}
   \begin{center}
     \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_global}
+    \includegraphics[width=\textwidth]{Fig_ASM_obsdist_global}
     \caption{
       \protect\label{fig:obsglobal}
 …
 \begin{figure}
   \begin{center}
     % \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_main}
     \includegraphics[width=9cm,angle=-90.]{Fig_OBS_dataplot_main}
+    % \includegraphics[width=\textwidth]{Fig_OBS_dataplot_main}
+    \includegraphics[width=\textwidth]{Fig_OBS_dataplot_main}
     \caption{
       \protect\label{fig:obsdataplotmain}
 …
 \begin{figure}
   \begin{center}
     % \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_prof}
     \includegraphics[width=7cm,angle=-90.]{Fig_OBS_dataplot_prof}
+    % \includegraphics[width=\textwidth]{Fig_OBS_dataplot_prof}
+    \includegraphics[width=\textwidth]{Fig_OBS_dataplot_prof}
     \caption{
       \protect\label{fig:obsdataplotprofile}

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_SBC.tex

-                      r10614
+                      r11263
 % Chapter —— Surface Boundary Condition (SBC, ISF, ICB)
 % ================================================================
 \chapter{Surface Boundary Condition (SBC, ISF, ICB) }
+\chapter{Surface Boundary Condition (SBC, ISF, ICB)}
 \label{chap:SBC}
 \minitoc
 …
 % Input Data specification (\mdl{fldread})
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Input data specification (\protect\mdl{fldread})}
+\subsection[Input data specification (\textit{fldread.F90})]
+{Input data specification (\protect\mdl{fldread})}
 \label{subsec:SBC_fldread}
 …
 The only tricky point is therefore to specify the date at which we need to do the interpolation and
 the date of the records read in the input files.
 Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the time step.
+Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
 For example, for an experiment starting at 0h00'00" with a one hour time-step,
 a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
 …
 % Analytical formulation (sbcana module)
 % ================================================================
+\section{Analytical formulation (\protect\mdl{sbcana})}
+\section[Analytical formulation (\textit{sbcana.F90})]
+{Analytical formulation (\protect\mdl{sbcana})}
 \label{sec:SBC_ana}
 …
 % Flux formulation
 % ================================================================
+\section{Flux formulation (\protect\mdl{sbcflx})}
+\section[Flux formulation (\textit{sbcflx.F90})]
+{Flux formulation (\protect\mdl{sbcflx})}
 \label{sec:SBC_flx}
 %------------------------------------------namsbc_flx----------------------------------------------------
 …
 % ================================================================
 \section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}]
                         {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}}
+{Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}}
 \label{sec:SBC_blk}
 …
 %        CORE Bulk formulea
 % -------------------------------------------------------------------------------------------------------------
+\subsection{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})}
+\subsection[CORE formulea (\textit{sbcblk\_core.F90}, \forcode{ln_core = .true.})]
+{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})}
 \label{subsec:SBC_blk_core}
 %------------------------------------------namsbc_core----------------------------------------------------
 …
 %-------------------------------------------------------------------------------------------------------------
 The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
+The CORE bulk formulae have been developed by \citet{large.yeager_rpt04}.
 They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data.
 They use an inertial dissipative method to compute the turbulent transfer coefficients
 (momentum, sensible heat and evaporation) from the 10 metre wind speed, air temperature and specific humidity.
 This \citet{Large_Yeager_Rep04} dataset is available through
+This \citet{large.yeager_rpt04} dataset is available through
 the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.
 Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
 This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
+This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
 Options are defined through the  \ngn{namsbc\_core} namelist variables.
 …
 %        CLIO Bulk formulea
 % -------------------------------------------------------------------------------------------------------------
+\subsection{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})}
+\subsection[CLIO formulea (\textit{sbcblk\_clio.F90}, \forcode{ln_clio = .true.})]
+{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})}
 \label{subsec:SBC_blk_clio}
 %------------------------------------------namsbc_clio----------------------------------------------------
 …
 The CLIO bulk formulae were developed several years ago for the Louvain-la-neuve coupled ice-ocean model
 (CLIO, \cite{Goosse_al_JGR99}).
+(CLIO, \cite{goosse.deleersnijder.ea_JGR99}).
 They are simpler bulk formulae.
 They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover.
 …
 % Coupled formulation
 % ================================================================
+\section{Coupled formulation (\protect\mdl{sbccpl})}
+\section[Coupled formulation (\textit{sbccpl.F90})]
+{Coupled formulation (\protect\mdl{sbccpl})}
 \label{sec:SBC_cpl}
 %------------------------------------------namsbc_cpl----------------------------------------------------
 …
 %        Atmospheric pressure
 % ================================================================
+\section{Atmospheric pressure (\protect\mdl{sbcapr})}
+\section[Atmospheric pressure (\textit{sbcapr.F90})]
+{Atmospheric pressure (\protect\mdl{sbcapr})}
 \label{sec:SBC_apr}
 %------------------------------------------namsbc_apr----------------------------------------------------
 …
 %        Surface Tides Forcing
 % ================================================================
+\section{Surface tides (\protect\mdl{sbctide})}
+\section[Surface tides (\textit{sbctide.F90})]
+{Surface tides (\protect\mdl{sbctide})}
 \label{sec:SBC_tide}
 …
 \[
   % \label{eq:PE_dyn_tides}
   \frac{\partial {\rm {\bf U}}_h }{\partial t}= ...
+  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
   +g\nabla (\Pi_{eq} + \Pi_{sal})
 \]
 …
 The SAL term should in principle be computed online as it depends on
 the model tidal prediction itself (see \citet{Arbic2004} for a
+the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
 discussion about the practical implementation of this term).
 Nevertheless, the complex calculations involved would make this
 …
 %        River runoffs
 % ================================================================
+\section{River runoffs (\protect\mdl{sbcrnf})}
+\section[River runoffs (\textit{sbcrnf.F90})]
+{River runoffs (\protect\mdl{sbcrnf})}
 \label{sec:SBC_rnf}
 %------------------------------------------namsbc_rnf----------------------------------------------------
 …
 %coastal modelling and becomes more and more often open ocean and climate modelling
 %\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
 %required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}.
+%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
 …
 \footnote{
   At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
   properly represent the diurnal cycle \citep{Bernie_al_JC05}.
+  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
   see also \autoref{fig:SBC_dcy}.}.
 …
 %        Ice shelf melting
 % ================================================================
+\section{Ice shelf melting (\protect\mdl{sbcisf})}
+\section[Ice shelf melting (\textit{sbcisf.F90})]
+{Ice shelf melting (\protect\mdl{sbcisf})}
 \label{sec:SBC_isf}
 %------------------------------------------namsbc_isf----------------------------------------------------
 …
 %--------------------------------------------------------------------------------------------------------
 The namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation.
 Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{Mathiot2017}.
+Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
 The different options are illustrated in \autoref{fig:SBC_isf}.
 …
    \item[\np{nn\_isfblk}\forcode{ = 1}]:
      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{Hunter2006}.
+     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
    \item[\np{nn\_isfblk}\forcode{ = 2}]:
      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{Jenkins1991}.
+     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{Losch2008}.
+     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}.
      The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m.
 …
 \]
      where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
      See \citet{Jenkins2010} for all the details on this formulation. It is the recommended formulation for realistic application.
+     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
    \item[\np{nn\_gammablk}\forcode{ = 2}]:
      The salt and heat exchange coefficients are velocity and stability dependent and defined as:
 …
      $\Gamma_{Turb}$ the contribution of the ocean stability and
      $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
      See \citet{Holland1999} for all the details on this formulation.
+     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{nn\_isf}\forcode{ = 2}]:
    The ice shelf cavity is not represented.
    The fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting.
+   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}) and the base of the ice shelf along the calving front
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.8\textwidth]{Fig_SBC_isf}
+    \includegraphics[width=\textwidth]{Fig_SBC_isf}
     \caption{
       \protect\label{fig:SBC_isf}
 …
 %-------------------------------------------------------------------------------------------------------------
 Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}.
 Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ).
+Icebergs are modelled as lagrangian particles in NEMO \citep{marsh.ivchenko.ea_GMD15}.
+Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
 (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO).
 Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
 …
 %        Interactions with waves (sbcwave.F90, ln_wave)
 % -------------------------------------------------------------------------------------------------------------
+\section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
+\section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})]
+{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
 \label{sec:SBC_wave}
 %------------------------------------------namsbc_wave--------------------------------------------------------
 …
 % ================================================================
+\subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
+\subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})]
+{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
 \label{subsec:SBC_wave_cdgw}
 …
 Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,
 the drag coefficient is computed according to the stable/unstable conditions of the
 air-sea interface following \citet{Large_Yeager_Rep04}.
+air-sea interface following \citet{large.yeager_rpt04}.
 …
 % 3D Stokes Drift (ln_sdw, nn_sdrift)
 % ================================================================
+\subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
+\subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})]
+{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
 \label{subsec:SBC_wave_sdw}
 The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}.
+The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
 It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
 and the current measured at a fixed point (Eulerian velocity).
 …
 \begin{description}
 \item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by
 \citet{Breivik_al_JPO2014}:
+\citet{breivik.janssen.ea_JPO14}:
 \[
 …
 \item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a
 reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface
 \citep{Breivik_al_OM2016}:
+\citep{breivik.bidlot.ea_OM16}:
 \[
 …
 % Stokes-Coriolis term (ln_stcor)
 % ================================================================
+\subsection{Stokes-Coriolis term (\protect\np{ln\_stcor})}
+\subsection[Stokes-Coriolis term (\texttt{ln\_stcor})]
+{Stokes-Coriolis term (\protect\np{ln\_stcor})}
 \label{subsec:SBC_wave_stcor}
 …
 % Waves modified stress (ln_tauwoc, ln_tauw)
 % ================================================================
+\subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}
+\subsection[Wave modified sress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})]
+{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}
 \label{subsec:SBC_wave_tauw}
 The surface stress felt by the ocean is the atmospheric stress minus the net stress going
 into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not
+into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
 available for forcing the mean circulation, while in the opposite case of a decaying sea
 state more momentum is available for forcing the ocean.
 …
 %        Diurnal cycle
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Diurnal cycle (\protect\mdl{sbcdcy})}
+\subsection[Diurnal cycle (\textit{sbcdcy.F90})]
+{Diurnal cycle (\protect\mdl{sbcdcy})}
 \label{subsec:SBC_dcy}
 %------------------------------------------namsbc_rnf----------------------------------------------------
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal}
+    \includegraphics[width=\textwidth]{Fig_SBC_diurnal}
     \caption{
       \protect\label{fig:SBC_diurnal}
 …
       the mean value of the analytical cycle (blue line) over a time step,
       not as the mid time step value of the analytically cycle (red square).
       From \citet{Bernie_al_CD07}.
+      From \citet{bernie.guilyardi.ea_CD07}.
+    }
   \end{center}
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less.
+\cite{bernie.woolnough.ea_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less.
 Unfortunately high frequency forcing fields are rare, not to say inexistent.
 Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at
 high frequency \citep{Bernie_al_CD07}.
+high frequency \citep{bernie.guilyardi.ea_CD07}.
 Furthermore, only the knowledge of daily mean value of SWF is needed,
 as higher frequency variations can be reconstructed from them,
 assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
 The \cite{Bernie_al_CD07} reconstruction algorithm is available in \NEMO by
+The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO by
 setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when
 using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or
 the flux formulation (\np{ln\_flx}\forcode{ = .true.}).
 The reconstruction is performed in the \mdl{sbcdcy} module.
 The detail of the algoritm used can be found in the appendix~A of \cite{Bernie_al_CD07}.
+The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
 The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at
 a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.7\textwidth]{Fig_SBC_dcy}
+    \includegraphics[width=\textwidth]{Fig_SBC_dcy}
     \caption{
       \protect\label{fig:SBC_dcy}
 …
 %        Surface restoring to observed SST and/or SSS
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
+\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]
+{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
 \label{subsec:SBC_ssr}
 %------------------------------------------namsbc_ssr----------------------------------------------------
 …
 (observed, climatological or an atmospheric model product),
 \textit{SSS}$_{Obs}$ is a sea surface salinity
 (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
+(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
 $\left.S\right|_{k=1}$ is the model surface layer salinity and
 $\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
 Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as
 the atmosphere does not care about ocean surface salinity \citep{Madec1997}.
+the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
 The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
 reduce the uncertainties we have on the observed freshwater budget.
 …
 % {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
+\subsection{Interface to CICE (\protect\mdl{sbcice\_cice})}
+\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]
+{Interface to CICE (\protect\mdl{sbcice\_cice})}
 \label{subsec:SBC_cice}
 …
 %        Freshwater budget control
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Freshwater budget control (\protect\mdl{sbcfwb})}
+\subsection[Freshwater budget control (\textit{sbcfwb.F90})]
+{Freshwater budget control (\protect\mdl{sbcfwb})}
 \label{subsec:SBC_fwb}

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_STO.tex

-                      r10442
+                      r11263
 The stochastic parametrization module aims to explicitly simulate uncertainties in the model.
 More particularly, \cite{Brankart_OM2013} has shown that,
+More particularly, \cite{brankart_OM13} has shown that,
 because of the nonlinearity of the seawater equation of state, unresolved scales represent a major source of
 uncertainties in the computation of the large scale horizontal density gradient (from T/S large scale fields),
 …
 A generic approach is thus to add one single new module in NEMO,
 generating processes with appropriate statistics to simulate each kind of uncertainty in the model
 (see \cite{Brankart_al_GMD2015} for more details).
+(see \cite{brankart.candille.ea_GMD15} for more details).
 In practice, at every model grid point,

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_TRA.tex

-                      r10544
+                      r11263
 The user has the option of extracting each tendency term on the RHS of the tracer equation for output
 (\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}~\forcode{= .true.}), as described in \autoref{chap:DIA}.
+(\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}\forcode{ = .true.}), as described in \autoref{chap:DIA}.
 % ================================================================
 % Tracer Advection
 % ================================================================
+\section{Tracer advection (\protect\mdl{traadv})}
+\section[Tracer advection (\textit{traadv.F90})]
+{Tracer advection (\protect\mdl{traadv})}
 \label{sec:TRA_adv}
 %------------------------------------------namtra_adv-----------------------------------------------------
 …
 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{ln\_linssh}~\forcode{= .true.}).
+(which reduces to $\nabla \cdot \vect U = 0$ in linear free surface, \ie \np{ln\_linssh}\forcode{ = .true.}).
 Therefore it is of paramount importance to design the discrete analogue of the advection tendency so that
 it is consistent with the continuity equation in order to enforce the conservation properties of
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[]{Fig_adv_scheme}
+    \includegraphics[width=\textwidth]{Fig_adv_scheme}
     \caption{
       \protect\label{fig:adv_scheme}
 …
 \begin{description}
 \item[linear free surface:]
   (\np{ln\_linssh}~\forcode{= .true.})
+  (\np{ln\_linssh}\forcode{ = .true.})
   the first level thickness is constant in time:
   the vertical boundary condition is applied at the fixed surface $z = 0$ rather than on
 …
   the first level tracer value.
 \item[non-linear free surface:]
   (\np{ln\_linssh}~\forcode{= .false.})
+  (\np{ln\_linssh}\forcode{ = .false.})
   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.
 …
 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_al_MWR01, Campin2004}.
 The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco}) is
+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} and \autoref{eq:tra_adv_zco?}) is
 the centred (\textit{now}) \textit{effective} ocean velocity, \ie the \textit{eulerian} velocity
 (see \autoref{chap:DYN}) plus the eddy induced velocity (\textit{eiv}) and/or
 …
 %        2nd and 4th order centred schemes
 % -------------------------------------------------------------------------------------------------------------
+\subsection{CEN: Centred scheme (\protect\np{ln\_traadv\_cen}~\forcode{= .true.})}
+\subsection[CEN: Centred scheme (\forcode{ln_traadv_cen = .true.})]
+{CEN: Centred scheme (\protect\np{ln\_traadv\_cen}\forcode{ = .true.})}
 \label{subsec:TRA_adv_cen}
 %        2nd order centred scheme
 The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}~\forcode{= .true.}.
+The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}\forcode{ = .true.}.
 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by
 setting \np{nn\_cen\_h} and \np{nn\_cen\_v} to $2$ or $4$.
 …
   \tau_u^{cen4} = \overline{T - \frac{1}{6} \, \delta_i \Big[ \delta_{i + 1/2}[T] \, \Big]}^{\,i + 1/2}
 \end{equation}
 In the vertical direction (\np{nn\_cen\_v}~\forcode{= 4}),
 a $4^{th}$ COMPACT interpolation has been prefered \citep{Demange_PhD2014}.
+In the vertical direction (\np{nn\_cen\_v}\forcode{ = 4}),
+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_JCP1992}.
+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
 …
 %        FCT scheme
 % -------------------------------------------------------------------------------------------------------------
+\subsection{FCT: Flux Corrected Transport scheme (\protect\np{ln\_traadv\_fct}~\forcode{= .true.})}
+\subsection[FCT: Flux Corrected Transport scheme (\forcode{ln_traadv_fct = .true.})]
+{FCT: Flux Corrected Transport scheme (\protect\np{ln\_traadv\_fct}\forcode{ = .true.})}
 \label{subsec:TRA_adv_tvd}
 The Flux Corrected Transport schemes (FCT) is used when \np{ln\_traadv\_fct}~\forcode{= .true.}.
+The Flux Corrected Transport schemes (FCT) is used when \np{ln\_traadv\_fct}\forcode{ = .true.}.
 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by
 setting \np{nn\_fct\_h} and \np{nn\_fct\_v} to $2$ or $4$.
 …
 (\ie it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}).
 There exist many ways to define $c_u$, each corresponding to a different FCT scheme.
 The one chosen in \NEMO is described in \citet{Zalesak_JCP79}.
+The one chosen in \NEMO is described in \citet{zalesak_JCP79}.
 $c_u$ only departs from $1$ when the advective term produces a local extremum in the tracer field.
 The resulting scheme is quite expensive but \textit{positive}.
 It can be used on both active and passive tracers.
 A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{Levy_al_GRL01}.
+A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{levy.estublier.ea_GRL01}.
 An additional option has been added controlled by \np{nn\_fct\_zts}.
 …
 a $2^{nd}$ order FCT scheme is used on both horizontal and vertical direction, but on the latter,
 a split-explicit time stepping is used, with a number of sub-timestep equals to \np{nn\_fct\_zts}.
 This option can be useful when the size of the timestep is limited by vertical advection \citep{Lemarie_OM2015}.
+This option can be useful when the size of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}.
 Note that in this case, a similar split-explicit time stepping should be used on vertical advection of momentum to
 insure a better stability (see \autoref{subsec:DYN_zad}).
 …
 %        MUSCL scheme
 % -------------------------------------------------------------------------------------------------------------
+\subsection{MUSCL: Monotone Upstream Scheme for Conservative Laws (\protect\np{ln\_traadv\_mus}~\forcode{= .true.})}
+\subsection[MUSCL: Monotone Upstream Scheme for Conservative Laws (\forcode{ln_traadv_mus = .true.})]
+{MUSCL: Monotone Upstream Scheme for Conservative Laws (\protect\np{ln\_traadv\_mus}\forcode{ = .true.})}
 \label{subsec:TRA_adv_mus}
 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln\_traadv\_mus}~\forcode{= .true.}.
+The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln\_traadv\_mus}\forcode{ = .true.}.
 MUSCL implementation can be found in the \mdl{traadv\_mus} module.
 MUSCL has been first implemented in \NEMO by \citet{Levy_al_GRL01}.
+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:adv_scheme}).
 …
 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{ln\_mus\_ups}~\forcode{= .true.}).
+(\np{ln\_mus\_ups}\forcode{ = .true.}).
 % -------------------------------------------------------------------------------------------------------------
 %        UBS scheme
 % -------------------------------------------------------------------------------------------------------------
+\subsection{UBS a.k.a. UP3: Upstream-Biased Scheme (\protect\np{ln\_traadv\_ubs}~\forcode{= .true.})}
+\subsection[UBS a.k.a. UP3: Upstream-Biased Scheme (\forcode{ln_traadv_ubs = .true.})]
+{UBS a.k.a. UP3: Upstream-Biased Scheme (\protect\np{ln\_traadv\_ubs}\forcode{ = .true.})}
 \label{subsec:TRA_adv_ubs}
 The Upstream-Biased Scheme (UBS) is used when \np{ln\_traadv\_ubs}~\forcode{= .true.}.
+The Upstream-Biased Scheme (UBS) is used when \np{ln\_traadv\_ubs}\forcode{ = .true.}.
 UBS implementation can be found in the \mdl{traadv\_mus} module.
 …
 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{Farrow1995}.
+\citep{shchepetkin.mcwilliams_OM05}.
+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,
 …
 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_PhD2014}.
+\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{nn\_cen\_v}~\forcode{= 2 or 4}).
+(\np{nn\_cen\_v}\forcode{ = 2 or 4}).
 For stability reasons (see \autoref{chap:STP}), the first term  in \autoref{eq:tra_adv_ubs}
 …
 (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_al_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_al_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.
 …
 %        QCK scheme
 % -------------------------------------------------------------------------------------------------------------
+\subsection{QCK: QuiCKest scheme (\protect\np{ln\_traadv\_qck}~\forcode{= .true.})}
+\subsection[QCK: QuiCKest scheme (\forcode{ln_traadv_qck = .true.})]
+{QCK: QuiCKest scheme (\protect\np{ln\_traadv\_qck}\forcode{ = .true.})}
 \label{subsec:TRA_adv_qck}
 The Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms (QUICKEST) scheme
 proposed by \citet{Leonard1979} is used when \np{ln\_traadv\_qck}~\forcode{= .true.}.
+proposed by \citet{leonard_CMAME79} is used when \np{ln\_traadv\_qck}\forcode{ = .true.}.
 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{Leonard1991}.
+\citep{leonard_CMAME91}.
 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}.
 …
 % Tracer Lateral Diffusion
 % ================================================================
+\section{Tracer lateral diffusion (\protect\mdl{traldf})}
+\section[Tracer lateral diffusion (\textit{traldf.F90})]
+{Tracer lateral diffusion (\protect\mdl{traldf})}
 \label{sec:TRA_ldf}
 %-----------------------------------------nam_traldf------------------------------------------------------
 …
 except for the pure vertical component that appears when a rotation tensor is used.
 This latter component is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}).
 When \np{ln\_traldf\_msc}~\forcode{= .true.}, a Method of Stabilizing Correction is used in which
 the pure vertical component is split into an explicit and an implicit part \citep{Lemarie_OM2012}.
+When \np{ln\_traldf\_msc}\forcode{ = .true.}, 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}.
 % -------------------------------------------------------------------------------------------------------------
 %        Type of operator
 % -------------------------------------------------------------------------------------------------------------
+\subsection[Type of operator (\protect\np{ln\_traldf}\{\_NONE,\_lap,\_blp\}\})]{Type of operator (\protect\np{ln\_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp}) }
+\subsection[Type of operator (\texttt{ln\_traldf}\{\texttt{\_NONE,\_lap,\_blp}\})]
+{Type of operator (\protect\np{ln\_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp}) }
 \label{subsec:TRA_ldf_op}
 …
 \begin{description}
 \item[\np{ln\_traldf\_NONE}~\forcode{= .true.}:]
+\item[\np{ln\_traldf\_NONE}\forcode{ = .true.}:]
   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{ln\_traldf\_lap}~\forcode{= .true.}:]
+\item[\np{ln\_traldf\_lap}\forcode{ = .true.}:]
   a laplacian operator is selected.
   This harmonic operator takes the following expression:  $\mathpzc{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}).
 \item[\np{ln\_traldf\_blp}~\forcode{= .true.}]:
+\item[\np{ln\_traldf\_blp}\forcode{ = .true.}]:
   a bilaplacian operator is selected.
   This biharmonic operator takes the following expression:
 …
 %        Direction of action
 % -------------------------------------------------------------------------------------------------------------
+\subsection[Action direction (\protect\np{ln\_traldf}\{\_lev,\_hor,\_iso,\_triad\})]{Direction of action (\protect\np{ln\_traldf\_lev}, \protect\np{ln\_traldf\_hor}, \protect\np{ln\_traldf\_iso}, or \protect\np{ln\_traldf\_triad}) }
+\subsection[Action direction (\texttt{ln\_traldf}\{\texttt{\_lev,\_hor,\_iso,\_triad}\})]
+{Direction of action (\protect\np{ln\_traldf\_lev}, \protect\np{ln\_traldf\_hor}, \protect\np{ln\_traldf\_iso}, or \protect\np{ln\_traldf\_triad}) }
 \label{subsec:TRA_ldf_dir}
 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{ln\_traldf\_lev}~\forcode{= .true.}) or
+iso-level option is used (\np{ln\_traldf\_lev}\forcode{ = .true.}) or
 when a horizontal (\ie geopotential) operator is demanded in \textit{z}-coordinate
 (\np{ln\_traldf\_hor} and \np{ln\_zco} equal \forcode{.true.}).
 …
 %       iso-level operator
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Iso-level (bi -)laplacian operator ( \protect\np{ln\_traldf\_iso}) }
+\subsection[Iso-level (bi-)laplacian operator (\texttt{ln\_traldf\_iso})]
+{Iso-level (bi-)laplacian operator ( \protect\np{ln\_traldf\_iso})}
 \label{subsec:TRA_ldf_lev}
 …
 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} or \np{ln\_traldf\_blp}~\forcode{= .true.},
 we have \np{ln\_traldf\_lev}~\forcode{= .true.} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}~\forcode{= .true.}.
+It is thus used when, in addition to \np{ln\_traldf\_lap} or \np{ln\_traldf\_blp}\forcode{ = .true.},
+we have \np{ln\_traldf\_lev}\forcode{ = .true.} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}\forcode{ = .true.}.
 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{ln\_zps}~\forcode{= .true.}),
+Note that in the partial step $z$-coordinate (\np{ln\_zps}\forcode{ = .true.}),
 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.
 …
 %         Rotated laplacian operator
 % -------------------------------------------------------------------------------------------------------------
 \subsection{Standard and triad (bi -)laplacian operator}
+\subsection{Standard and triad (bi-)laplacian operator}
 \label{subsec:TRA_ldf_iso_triad}
 %&&    Standard rotated (bi -)laplacian operator
+%&&    Standard rotated (bi-)laplacian operator
 %&& ----------------------------------------------
+\subsubsection{Standard rotated (bi -)laplacian operator (\protect\mdl{traldf\_iso})}
+\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:PE_zdf})
 …
 $r_1$ and $r_2$ are the slopes between the surface of computation ($z$- or $s$-surfaces) and
 the surface along which the diffusion operator acts (\ie horizontal or iso-neutral surfaces).
 It is thus used when, in addition to \np{ln\_traldf\_lap}~\forcode{= .true.},
 we have \np{ln\_traldf\_iso}~\forcode{= .true.},
 or both \np{ln\_traldf\_hor}~\forcode{= .true.} and \np{ln\_zco}~\forcode{= .true.}.
+It is thus used when, in addition to \np{ln\_traldf\_lap}\forcode{ = .true.},
+we have \np{ln\_traldf\_iso}\forcode{ = .true.},
+or both \np{ln\_traldf\_hor}\forcode{ = .true.} and \np{ln\_zco}\forcode{ = .true.}.
 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
 …
 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_al_CD01}.
 Note that in the partial step $z$-coordinate (\np{ln\_zps}~\forcode{= .true.}),
+any additional background horizontal diffusion \citep{guilyardi.madec.ea_CD01}.
+Note that in the partial step $z$-coordinate (\np{ln\_zps}\forcode{ = .true.}),
 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}.
 %&&     Triad rotated (bi -)laplacian operator
+%&&     Triad rotated (bi-)laplacian operator
 %&&  -------------------------------------------
+\subsubsection{Triad rotated (bi -)laplacian operator (\protect\np{ln\_traldf\_triad})}
+\subsubsection[Triad rotated (bi-)laplacian operator (\textit{ln\_traldf\_triad})]
+{Triad rotated (bi-)laplacian operator (\protect\np{ln\_traldf\_triad})}
 \label{subsec:TRA_ldf_triad}
 If the Griffies triad scheme is employed (\np{ln\_traldf\_triad}~\forcode{= .true.}; see \autoref{apdx:triad})
 An alternative scheme developed by \cite{Griffies_al_JPO98} which ensures tracer variance decreases
 is also available in \NEMO (\np{ln\_traldf\_grif}~\forcode{= .true.}).
+If the Griffies triad scheme is employed (\np{ln\_traldf\_triad}\forcode{ = .true.}; see \autoref{apdx:triad})
+An alternative scheme developed by \cite{griffies.gnanadesikan.ea_JPO98} which ensures tracer variance decreases
+is also available in \NEMO (\np{ln\_traldf\_grif}\forcode{ = .true.}).
 A complete description of the algorithm is given in \autoref{apdx:triad}.
 …
 % Tracer Vertical Diffusion
 % ================================================================
+\section{Tracer vertical diffusion (\protect\mdl{trazdf})}
+\section[Tracer vertical diffusion (\textit{trazdf.F90})]
+{Tracer vertical diffusion (\protect\mdl{trazdf})}
 \label{sec:TRA_zdf}
 %--------------------------------------------namzdf---------------------------------------------------------
 …
 The large eddy coefficient found in the mixed layer together with high vertical resolution implies that
 in the case of explicit time stepping (\np{ln\_zdfexp}~\forcode{= .true.})
+in the case of explicit time stepping (\np{ln\_zdfexp}\forcode{ = .true.})
 there would be too restrictive a constraint on the time step.
 Therefore, the default implicit time stepping is preferred for the vertical diffusion since
 it overcomes the stability constraint.
 A forward time differencing scheme (\np{ln\_zdfexp}~\forcode{= .true.}) using
+A forward time differencing scheme (\np{ln\_zdfexp}\forcode{ = .true.}) using
 a time splitting technique (\np{nn\_zdfexp} $> 1$) is provided as an alternative.
 Namelist variables \np{ln\_zdfexp} and \np{nn\_zdfexp} apply to both tracers and dynamics.
 …
 %        surface boundary condition
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Surface boundary condition (\protect\mdl{trasbc})}
+\subsection[Surface boundary condition (\textit{trasbc.F90})]
+{Surface boundary condition (\protect\mdl{trasbc})}
 \label{subsec:TRA_sbc}
 …
 Such time averaging prevents the divergence of odd and even time step (see \autoref{chap:STP}).
 In the linear free surface case (\np{ln\_linssh}~\forcode{= .true.}), an additional term has to be added on
+In the linear free surface case (\np{ln\_linssh}\forcode{ = .true.}), 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 $Q_{ns}$.
 …
 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}.
+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:STP}).
 …
 %        Solar Radiation Penetration
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Solar radiation penetration (\protect\mdl{traqsr})}
+\subsection[Solar radiation penetration (\textit{traqsr.F90})]
+{Solar radiation penetration (\protect\mdl{traqsr})}
 \label{subsec:TRA_qsr}
 %--------------------------------------------namqsr--------------------------------------------------------
 …
 Options are defined through the \ngn{namtra\_qsr} namelist variables.
 When the penetrative solar radiation option is used (\np{ln\_flxqsr}~\forcode{= .true.}),
+When the penetrative solar radiation option is used (\np{ln\_flxqsr}\forcode{ = .true.}),
 the solar radiation penetrates the top few tens of meters of the ocean.
 If it is not used (\np{ln\_flxqsr}~\forcode{= .false.}) all the heat flux is absorbed in the first ocean level.
+If it is not used (\np{ln\_flxqsr}\forcode{ = .false.}) 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:PE_tra_T} and
 the surface boundary condition is modified to take into account only the non-penetrative part of the surface
 …
 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{ln\_qsr\_2bd}~\forcode{= .true.})
+In the simple 2-waveband light penetration scheme (\np{ln\_qsr\_2bd}\forcode{ = .true.})
 a chlorophyll-independent monochromatic formulation is chosen for the shorter wavelengths,
 leading to the following expression \citep{Paulson1977}:
+leading to the following expression \citep{paulson.simpson_JPO77}:
 \[
   % \label{eq:traqsr_iradiance}
 …
 Such assumptions have been shown to provide a very crude and simplistic representation of
 observed light penetration profiles (\cite{Morel_JGR88}, see also \autoref{fig:traqsr_irradiance}).
+observed light penetration profiles (\cite{morel_JGR88}, see also \autoref{fig:traqsr_irradiance}).
 Light absorption in the ocean depends on particle concentration and is spectrally selective.
 \cite{Morel_JGR88} has shown that an accurate representation of light penetration can be provided by
+\cite{morel_JGR88} has shown that an accurate representation of light penetration can be provided by
 a 61 waveband formulation.
 Unfortunately, such a model is very computationally expensive.
 Thus, \cite{Lengaigne_al_CD07} have constructed a simplified version of this formulation in which
+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}),
+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:traqsr_irradiance}, this formulation, called RGB (Red-Green-Blue),
 …
 The 2-bands formulation does not reproduce the full model very well.
 The RGB formulation is used when \np{ln\_qsr\_rgb}~\forcode{= .true.}.
+The RGB formulation is used when \np{ln\_qsr\_rgb}\forcode{ = .true.}.
 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
 …
 \begin{description}
 \item[\np{nn\_chdta}~\forcode{= 0}]
+\item[\np{nn\_chdta}\forcode{ = 0}]
   a constant 0.05 g.Chl/L value everywhere ;
 \item[\np{nn\_chdta}~\forcode{= 1}]
+\item[\np{nn\_chdta}\forcode{ = 1}]
   an observed time varying chlorophyll deduced from satellite surface ocean color measurement spread uniformly in
   the vertical direction;
 \item[\np{nn\_chdta}~\forcode{= 2}]
+\item[\np{nn\_chdta}\forcode{ = 2}]
   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{ln\_qsr\_bio}~\forcode{= .true.}]
+  Following \cite{morel.berthon_LO89}, the profile is computed from the local surface chlorophyll value;
+\item[\np{ln\_qsr\_bio}\forcode{ = .true.}]
   simulated time varying chlorophyll by TOP biogeochemical model.
   In this case, the RGB formulation is used to calculate both the phytoplankton light limitation in
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[]{Fig_TRA_Irradiance}
+    \includegraphics[width=\textwidth]{Fig_TRA_Irradiance}
     \caption{
       \protect\label{fig:traqsr_irradiance}
 …
 waveband Morel (1988) formulation (black) for a chlorophyll concentration of
       (a) Chl=0.05 mg/m$^3$ and (b) Chl=0.5 mg/m$^3$.
       From \citet{Lengaigne_al_CD07}.
+      From \citet{lengaigne.menkes.ea_CD07}.
+    }
   \end{center}
 …
 %        Bottom Boundary Condition
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Bottom boundary condition (\protect\mdl{trabbc})}
+\subsection[Bottom boundary condition (\textit{trabbc.F90})]
+{Bottom boundary condition (\protect\mdl{trabbc})}
 \label{subsec:TRA_bbc}
 %--------------------------------------------nambbc--------------------------------------------------------
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[]{Fig_TRA_geoth}
+    \includegraphics[width=\textwidth]{Fig_TRA_geoth}
     \caption{
       \protect\label{fig:geothermal}
       Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{Emile-Geay_Madec_OS09}.
       It is inferred from the age of the sea floor and the formulae of \citet{Stein_Stein_Nat92}.
+      Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{emile-geay.madec_OS09}.
+      It is inferred from the age of the sea floor and the formulae of \citet{stein.stein_N92}.
+    }
   \end{center}
 …
 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_Nat92}),
+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  \ngn{namtra\_bbc} namelist variables.
 …
 the \np{nn\_geoflx\_cst}, which is also a namelist parameter.
 When \np{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:geothermal}) \citep{Emile-Geay_Madec_OS09}.
+the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:geothermal}) \citep{emile-geay.madec_OS09}.
 % ================================================================
 % Bottom Boundary Layer
 % ================================================================
+\section{Bottom boundary layer (\protect\mdl{trabbl} - \protect\key{trabbl})}
+\section[Bottom boundary layer (\textit{trabbl.F90} - \texttt{\textbf{key\_trabbl}})]
+{Bottom boundary layer (\protect\mdl{trabbl} - \protect\key{trabbl})}
 \label{sec:TRA_bbl}
 %--------------------------------------------nambbl---------------------------------------------------------
 …
 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_al_PO01}, and the thickness of the plume is not resolved.
 The idea of the bottom boundary layer (BBL) parameterisation, first introduced by \citet{Beckmann_Doscher1997},
+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.
 …
 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_Tel99}.
+\citet{campin.goosse_T99}.
 % -------------------------------------------------------------------------------------------------------------
 %        Diffusive BBL
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Diffusive bottom boundary layer (\protect\np{nn\_bbl\_ldf}~\forcode{= 1})}
+\subsection[Diffusive bottom boundary layer (\forcode{nn_bbl_ldf = 1})]
+{Diffusive bottom boundary layer (\protect\np{nn\_bbl\_ldf}\forcode{ = 1})}
 \label{subsec:TRA_bbl_diff}
 …
 with $\nabla_\sigma$ the lateral gradient operator taken between bottom cells, and
 $A_l^\sigma$ the lateral diffusivity in the BBL.
 Following \citet{Beckmann_Doscher1997}, the latter is prescribed with a spatial dependence,
+Following \citet{beckmann.doscher_JPO97}, the latter is prescribed with a spatial dependence,
 \ie in the conditional form
 \begin{equation}
 …
 %        Advective BBL
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Advective bottom boundary layer  (\protect\np{nn\_bbl\_adv}~\forcode{= 1..2})}
+\subsection[Advective bottom boundary layer (\forcode{nn_bbl_adv = [12]})]
+{Advective bottom boundary layer (\protect\np{nn\_bbl\_adv}\forcode{ = [12]})}
 \label{subsec:TRA_bbl_adv}
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[]{Fig_BBL_adv}
+    \includegraphics[width=\textwidth]{Fig_BBL_adv}
     \caption{
       \protect\label{fig:bbl}
 …
 %%%gmcomment   :  this section has to be really written
 When applying an advective BBL (\np{nn\_bbl\_adv}~\forcode{= 1..2}), an overturning circulation is added which
+When applying an advective BBL (\np{nn\_bbl\_adv}\forcode{ = 1..2}), 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{nn\_bbl\_adv}~\forcode{= 1}:
+\np{nn\_bbl\_adv}\forcode{ = 1}:
 the downslope velocity is chosen to be the Eulerian ocean velocity just above the topographic step
 (see black arrow in \autoref{fig:bbl}) \citep{Beckmann_Doscher1997}.
+(see black arrow in \autoref{fig: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{nn\_bbl\_adv}~\forcode{= 2}:
+\np{nn\_bbl\_adv}\forcode{ = 2}:
 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_Tel99}.
+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 $\nabla_\sigma \rho \cdot \nabla H < 0$).
 …
 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_Tel99}.
+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.
 …
 % Tracer damping
 % ================================================================
+\section{Tracer damping (\protect\mdl{tradmp})}
+\section[Tracer damping (\textit{tradmp.F90})]
+{Tracer damping (\protect\mdl{tradmp})}
 \label{sec:TRA_dmp}
 %--------------------------------------------namtra_dmp-------------------------------------------------
 …
 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{Sarmiento1982}.
+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 ($T_o$, $S_o$).
 …
 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_al_JPO96}.
+\citep{madec.delecluse.ea_JPO96}.
 For generating \ifile{resto}, see the documentation for the DMP tool provided with the source code under
 …
 % Tracer time evolution
 % ================================================================
+\section{Tracer time evolution (\protect\mdl{tranxt})}
+\section[Tracer time evolution (\textit{tranxt.F90})]
+{Tracer time evolution (\protect\mdl{tranxt})}
 \label{sec:TRA_nxt}
 %--------------------------------------------namdom-----------------------------------------------------
 …
 Options are defined through the \ngn{namdom} namelist variables.
 The general framework for tracer time stepping is a modified leap-frog scheme \citep{Leclair_Madec_OM09},
+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:STP_mLF}):
 \begin{equation}
 …
 (\ie fluxes plus content in mass exchanges).
 $\gamma$ is initialized as \np{rn\_atfp} (\textbf{namelist} parameter).
 Its default value is \np{rn\_atfp}~\forcode{= 10.e-3}.
+Its default value is \np{rn\_atfp}\forcode{ = 10.e-3}.
 Note that the forcing correction term in the filter is not applied in linear free surface
 (\jp{lk\_vvl}~\forcode{= .false.}) (see \autoref{subsec:TRA_sbc}).
+(\jp{lk\_vvl}\forcode{ = .false.}) (see \autoref{subsec:TRA_sbc}).
 Not also that in constant volume case, the time stepping is performed on $T$, not on its content, $e_{3t}T$.
 …
 % Equation of State (eosbn2)
 % ================================================================
+\section{Equation of state (\protect\mdl{eosbn2}) }
+\section[Equation of state (\textit{eosbn2.F90})]
+{Equation of state (\protect\mdl{eosbn2})}
 \label{sec:TRA_eosbn2}
 %--------------------------------------------nameos-----------------------------------------------------
 …
 %        Equation of State
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Equation of seawater (\protect\np{nn\_eos}~\forcode{= -1..1})}
+\subsection[Equation of seawater (\forcode{nn_eos = {-1,1}})]
+{Equation of seawater (\protect\np{nn\_eos}\forcode{ = {-1,1}})}
 \label{subsec:TRA_eos}
 …
 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_JPO2015}.
 Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{UNESCO1983}) or
 TEOS-10 \citep{TEOS10} standards should be used anytime a simulation of the real ocean circulation is attempted
 \citep{Roquet_JPO2015}.
+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{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature and
 practical salinity for EOS-980, both variables being more suitable for use as model variables
 \citep{TEOS10, Graham_McDougall_JPO13}.
+\citep{ioc.iapso_bk10, graham.mcdougall_JPO13}.
 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{Vallis06} is also available.
+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.
 …
 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{Gill1982}.
+density in the World Ocean varies by no more than 2$\%$ from that value \citep{gill_bk82}.
 Options are defined through the \ngn{nameos} namelist variables, and in particular \np{nn\_eos} which
 …
 \begin{description}
 \item[\np{nn\_eos}~\forcode{= -1}]
   the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used.
+\item[\np{nn\_eos}\forcode{ = -1}]
+  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
 …
   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{TEOS10}.
+  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: $\Theta$).
   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{TEOS10}.
+  It is set to $C_p = 3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, 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
 …
   either computing the air-sea and ice-sea fluxes (forced mode) or
   sending the SST field to the atmosphere (coupled mode).
 \item[\np{nn\_eos}~\forcode{= 0}]
+\item[\np{nn\_eos}\forcode{ = 0}]
   the polyEOS80-bsq equation of seawater is used.
   It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized to
 …
   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{UNESCO1983}.
+  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{nn\_eos}~\forcode{= 1}]
   a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen,
+\item[\np{nn\_eos}\forcode{ = 1}]
+  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_JPO2015}).
+  (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_JPO2015}.
+  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,
 …
 %        Brunt-V\"{a}is\"{a}l\"{a} Frequency
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Brunt-V\"{a}is\"{a}l\"{a} frequency (\protect\np{nn\_eos}~\forcode{= 0..2})}
+\subsection[Brunt-V\"{a}is\"{a}l\"{a} frequency (\forcode{nn_eos = [0-2]})]
+{Brunt-V\"{a}is\"{a}l\"{a} frequency (\protect\np{nn\_eos}\forcode{ = [0-2]})}
 \label{subsec:TRA_bn2}
 …
 \label{subsec:TRA_fzp}
 The freezing point of seawater is a function of salinity and pressure \citep{UNESCO1983}:
+The freezing point of seawater is a function of salinity and pressure \citep{fofonoff.millard_bk83}:
 \begin{equation}
   \label{eq:tra_eos_fzp}
 …
 % Horizontal Derivative in zps-coordinate
 % ================================================================
+\section{Horizontal derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})}
+\section[Horizontal derivative in \textit{zps}-coordinate (\textit{zpshde.F90})]
+{Horizontal derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})}
 \label{sec:TRA_zpshde}
 …
 I've changed "derivative" to "difference" and "mean" to "average"}
 With partial cells (\np{ln\_zps}~\forcode{= .true.}) at bottom and top (\np{ln\_isfcav}~\forcode{= .true.}),
+With partial cells (\np{ln\_zps}\forcode{ = .true.}) at bottom and top (\np{ln\_isfcav}\forcode{ = .true.}),
 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{ln\_isfcav}~\forcode{= .true.}) are computed in the same way as
+The partial cell properties at the top (\np{ln\_isfcav}\forcode{ = .true.}) are computed in the same way as
 for the bottom.
 So, only the bottom interpolation is explained below.
 …
 \begin{figure}[!p]
   \begin{center}
     \includegraphics[]{Fig_partial_step_scheme}
+    \includegraphics[width=\textwidth]{Fig_partial_step_scheme}
     \caption{
       \protect\label{fig:Partial_step_scheme}
       Discretisation of the horizontal difference and average of tracers in the $z$-partial step coordinate
       (\protect\np{ln\_zps}~\forcode{= .true.}) in the case $(e3w_k^{i + 1} - e3w_k^i) > 0$.
+      (\protect\np{ln\_zps}\forcode{ = .true.}) in 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.

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_ZDF.tex

-                      r10442
+                      r11263
 At the surface they are prescribed from the surface forcing (see \autoref{chap:SBC}),
 while at the bottom they are set to zero for heat and salt,
 unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \key{trabbl} defined,
+unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \np{ln\_trabbc} defined,
 see \autoref{subsec:TRA_bbc}), and specified through a bottom friction parameterisation for momentum
 (see \autoref{sec:ZDF_bfr}).
+(see \autoref{sec:ZDF_drg}).
 In this section we briefly discuss the various choices offered to compute the vertical eddy viscosity and
 …
 respectively (see \autoref{sec:TRA_zdf} and \autoref{sec:DYN_zdf}).
 These coefficients can be assumed to be either constant, or a function of the local Richardson number,
 or computed from a turbulent closure model (either TKE or GLS formulation).
 The computation of these coefficients is initialized in the \mdl{zdfini} module and performed in
 the \mdl{zdfric}, \mdl{zdftke} or \mdl{zdfgls} modules.
+or computed from a turbulent closure model (either TKE or GLS or OSMOSIS formulation).
+The computation of these coefficients is initialized in the \mdl{zdfphy} module and performed in
+the \mdl{zdfric}, \mdl{zdftke} or \mdl{zdfgls} or \mdl{zdfosm} modules.
 The trends due to the vertical momentum and tracer diffusion, including the surface forcing,
 are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively.
+These trends can be computed using either a forward time stepping scheme
+(namelist parameter \np{ln\_zdfexp}\forcode{ = .true.}) or a backward time stepping scheme
+(\np{ln\_zdfexp}\forcode{ = .false.}) depending on the magnitude of the mixing coefficients,
+and thus of the formulation used (see \autoref{chap:STP}).
+% -------------------------------------------------------------------------------------------------------------
+%        Constant
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Constant (\protect\key{zdfcst})}
+\label{subsec:ZDF_cst}
+%--------------------------------------------namzdf---------------------------------------------------------
+%These trends can be computed using either a forward time stepping scheme
+%(namelist parameter \np{ln\_zdfexp}\forcode{ = .true.}) or a backward time stepping scheme
+%(\np{ln\_zdfexp}\forcode{ = .false.}) depending on the magnitude of the mixing coefficients,
+%and thus of the formulation used (see \autoref{chap:STP}).
+%--------------------------------------------namzdf--------------------------------------------------------
 \nlst{namzdf}
 %--------------------------------------------------------------------------------------------------------------
+% -------------------------------------------------------------------------------------------------------------
+%        Constant
+% -------------------------------------------------------------------------------------------------------------
+\subsection[Constant (\forcode{ln_zdfcst = .true.})]
+{Constant (\protect\np{ln\_zdfcst}\forcode{ = .true.})}
+\label{subsec:ZDF_cst}
 Options are defined through the \ngn{namzdf} namelist variables.
 When \key{zdfcst} is defined, the momentum and tracer vertical eddy coefficients are set to
+When \np{ln\_zdfcst} is defined, the momentum and tracer vertical eddy coefficients are set to
 constant values over the whole ocean.
 This is the crudest way to define the vertical ocean physics.
 It is recommended that this option is only used in process studies, not in basin scale simulations.
+It is recommended to use this option only in process studies, not in basin scale simulations.
 Typical values used in this case are:
 \begin{align*}
 …
 %        Richardson Number Dependent
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Richardson number dependent (\protect\key{zdfric})}
+\subsection[Richardson number dependent (\forcode{ln_zdfric = .true.})]
+{Richardson number dependent (\protect\np{ln\_zdfric}\forcode{ = .true.})}
 \label{subsec:ZDF_ric}
 …
 %--------------------------------------------------------------------------------------------------------------
 When \key{zdfric} is defined, a local Richardson number dependent formulation for the vertical momentum and
+When \np{ln\_zdfric}\forcode{ = .true.}, a local Richardson number dependent formulation for the vertical momentum and
 tracer eddy coefficients is set through the \ngn{namzdf\_ric} namelist variables.
 The vertical mixing coefficients are diagnosed from the large scale variables computed by the model.
 …
 a dependency between the vertical eddy coefficients and the local Richardson number
 (\ie the ratio of stratification to vertical shear).
 Following \citet{Pacanowski_Philander_JPO81}, the following formulation has been implemented:
+Following \citet{pacanowski.philander_JPO81}, the following formulation has been implemented:
 \[
   % \label{eq:zdfric}
 …
 The final $h_{e}$ is further constrained by the adjustable bounds \np{rn\_mldmin} and \np{rn\_mldmax}.
 Once $h_{e}$ is computed, the vertical eddy coefficients within $h_{e}$ are set to
 the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{Lermusiaux2001}.
+the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{lermusiaux_JMS01}.
 % -------------------------------------------------------------------------------------------------------------
 %        TKE Turbulent Closure Scheme
 % -------------------------------------------------------------------------------------------------------------
+\subsection{TKE turbulent closure scheme (\protect\key{zdftke})}
+\subsection[TKE turbulent closure scheme (\forcode{ln_zdftke = .true.})]
+{TKE turbulent closure scheme (\protect\np{ln\_zdftke}\forcode{ = .true.})}
 \label{subsec:ZDF_tke}
 %--------------------------------------------namzdf_tke--------------------------------------------------
 …
 a prognostic equation for $\bar{e}$, the turbulent kinetic energy,
 and a closure assumption for the turbulent length scales.
 This turbulent closure model has been developed by \citet{Bougeault1989} in the atmospheric case,
 adapted by \citet{Gaspar1990} for the oceanic case, and embedded in OPA, the ancestor of NEMO,
 by \citet{Blanke1993} for equatorial Atlantic simulations.
 Since then, significant modifications have been introduced by \citet{Madec1998} in both the implementation and
+This turbulent closure model has been developed by \citet{bougeault.lacarrere_MWR89} in the atmospheric case,
+adapted by \citet{gaspar.gregoris.ea_JGR90} for the oceanic case, and embedded in OPA, the ancestor of NEMO,
+by \citet{blanke.delecluse_JPO93} for equatorial Atlantic simulations.
+Since then, significant modifications have been introduced by \citet{madec.delecluse.ea_NPM98} in both the implementation and
 the formulation of the mixing length scale.
 The time evolution of $\bar{e}$ is the result of the production of $\bar{e}$ through vertical shear,
 its destruction through stratification, its vertical diffusion, and its dissipation of \citet{Kolmogorov1942} type:
+its destruction through stratification, its vertical diffusion, and its dissipation of \citet{kolmogorov_IANS42} type:
 \begin{equation}
   \label{eq:zdftke_e}
 …
 $P_{rt}$ is the Prandtl number, $K_m$ and $K_\rho$ are the vertical eddy viscosity and diffusivity coefficients.
 The constants $C_k =  0.1$ and $C_\epsilon = \sqrt {2} /2$ $\approx 0.7$ are designed to deal with
 vertical mixing at any depth \citep{Gaspar1990}.
+vertical mixing at any depth \citep{gaspar.gregoris.ea_JGR90}.
 They are set through namelist parameters \np{nn\_ediff} and \np{nn\_ediss}.
 $P_{rt}$ can be set to unity or, following \citet{Blanke1993}, be a function of the local Richardson number, $R_i$:
+$P_{rt}$ can be set to unity or, following \citet{blanke.delecluse_JPO93}, be a function of the local Richardson number, $R_i$:
 \begin{align*}
   % \label{eq:prt}
 …
   \end{cases}
 \end{align*}
-Options are defined through the  \ngn{namzdfy\_tke} namelist variables.
 The choice of $P_{rt}$ is controlled by the \np{nn\_pdl} namelist variable.
 At the sea surface, the value of $\bar{e}$ is prescribed from the wind stress field as
 $\bar{e}_o = e_{bb} |\tau| / \rho_o$, with $e_{bb}$ the \np{rn\_ebb} namelist parameter.
 The default value of $e_{bb}$ is 3.75. \citep{Gaspar1990}), however a much larger value can be used when
+The default value of $e_{bb}$ is 3.75. \citep{gaspar.gregoris.ea_JGR90}), however a much larger value can be used when
 taking into account the surface wave breaking (see below Eq. \autoref{eq:ZDF_Esbc}).
 The bottom value of TKE is assumed to be equal to the value of the level just above.
 …
 the numerical scheme does not ensure its positivity.
 To overcome this problem, a cut-off in the minimum value of $\bar{e}$ is used (\np{rn\_emin} namelist parameter).
 Following \citet{Gaspar1990}, the cut-off value is set to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$.
 This allows the subsequent formulations to match that of \citet{Gargett1984} for the diffusion in
+Following \citet{gaspar.gregoris.ea_JGR90}, the cut-off value is set to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$.
+This allows the subsequent formulations to match that of \citet{gargett_JMR84} for the diffusion in
 the thermocline and deep ocean :  $K_\rho = 10^{-3} / N$.
 In addition, a cut-off is applied on $K_m$ and $K_\rho$ to avoid numerical instabilities associated with
 too weak vertical diffusion.
 They must be specified at least larger than the molecular values, and are set through \np{rn\_avm0} and
 \np{rn\_avt0} (namzdf namelist, see \autoref{subsec:ZDF_cst}).
+\np{rn\_avt0} (\ngn{namzdf} namelist, see \autoref{subsec:ZDF_cst}).
 \subsubsection{Turbulent length scale}
 For computational efficiency, the original formulation of the turbulent length scales proposed by
 \citet{Gaspar1990} has been simplified.
+\citet{gaspar.gregoris.ea_JGR90} has been simplified.
 Four formulations are proposed, the choice of which is controlled by the \np{nn\_mxl} namelist parameter.
 The first two are based on the following first order approximation \citep{Blanke1993}:
+The first two are based on the following first order approximation \citep{blanke.delecluse_JPO93}:
 \begin{equation}
   \label{eq:tke_mxl0_1}
 …
 The resulting length scale is bounded by the distance to the surface or to the bottom
 (\np{nn\_mxl}\forcode{ = 0}) or by the local vertical scale factor (\np{nn\_mxl}\forcode{ = 1}).
 \citet{Blanke1993} notice that this simplification has two major drawbacks:
+\citet{blanke.delecluse_JPO93} notice that this simplification has two major drawbacks:
 it makes no sense for locally unstable stratification and the computation no longer uses all
 the information contained in the vertical density profile.
 To overcome these drawbacks, \citet{Madec1998} introduces the \np{nn\_mxl}\forcode{ = 2..3} cases,
+To overcome these drawbacks, \citet{madec.delecluse.ea_NPM98} introduces the \np{nn\_mxl}\forcode{ = 2, 3} cases,
 which add an extra assumption concerning the vertical gradient of the computed length scale.
 So, the length scales are first evaluated as in \autoref{eq:tke_mxl0_1} and then bounded such that:
 …
 \autoref{eq:tke_mxl_constraint} means that the vertical variations of the length scale cannot be larger than
 the variations of depth.
 It provides a better approximation of the \citet{Gaspar1990} formulation while being much less
+It provides a better approximation of the \citet{gaspar.gregoris.ea_JGR90} formulation while being much less
 time consuming.
 In particular, it allows the length scale to be limited not only by the distance to the surface or
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=1.00\textwidth]{Fig_mixing_length}
+    \includegraphics[width=\textwidth]{Fig_mixing_length}
     \caption{
       \protect\label{fig:mixing_length}
 …
 In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same value:
 $ l_k=  l_\epsilon = \min \left(\ l_{up} \;,\;  l_{dwn}\ \right)$, while in the \np{nn\_mxl}\forcode{ = 3} case,
 the dissipation and mixing turbulent length scales are give as in \citet{Gaspar1990}:
+the dissipation and mixing turbulent length scales are give as in \citet{gaspar.gregoris.ea_JGR90}:
 \[
   % \label{eq:tke_mxl_gaspar}
 …
 Usually the surface scale is given by $l_o = \kappa \,z_o$ where $\kappa = 0.4$ is von Karman's constant and
 $z_o$ the roughness parameter of the surface.
 Assuming $z_o=0.1$~m \citep{Craig_Banner_JPO94} leads to a 0.04~m, the default value of \np{rn\_mxl0}.
+Assuming $z_o=0.1$~m \citep{craig.banner_JPO94} leads to a 0.04~m, the default value of \np{rn\_mxl0}.
 In the ocean interior a minimum length scale is set to recover the molecular viscosity when
 $\bar{e}$ reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ).
 …
 %-----------------------------------------------------------------------%
 Following \citet{Mellor_Blumberg_JPO04}, the TKE turbulence closure model has been modified to
+Following \citet{mellor.blumberg_JPO04}, the TKE turbulence closure model has been modified to
 include the effect of surface wave breaking energetics.
 This results in a reduction of summertime surface temperature when the mixed layer is relatively shallow.
 The \citet{Mellor_Blumberg_JPO04} modifications acts on surface length scale and TKE values and
+The \citet{mellor.blumberg_JPO04} modifications acts on surface length scale and TKE values and
 air-sea drag coefficient.
 The latter concerns the bulk formulea and is not discussed here.
 Following \citet{Craig_Banner_JPO94}, the boundary condition on surface TKE value is :
+The latter concerns the bulk formulae and is not discussed here.
+Following \citet{craig.banner_JPO94}, the boundary condition on surface TKE value is :
 \begin{equation}
   \label{eq:ZDF_Esbc}
   \bar{e}_o = \frac{1}{2}\,\left(  15.8\,\alpha_{CB} \right)^{2/3} \,\frac{|\tau|}{\rho_o}
 \end{equation}
 where $\alpha_{CB}$ is the \citet{Craig_Banner_JPO94} constant of proportionality which depends on the ''wave age'',
 ranging from 57 for mature waves to 146 for younger waves \citep{Mellor_Blumberg_JPO04}.
+where $\alpha_{CB}$ is the \citet{craig.banner_JPO94} constant of proportionality which depends on the ''wave age'',
+ranging from 57 for mature waves to 146 for younger waves \citep{mellor.blumberg_JPO04}.
 The boundary condition on the turbulent length scale follows the Charnock's relation:
 \begin{equation}
 …
 \end{equation}
 where $\kappa=0.40$ is the von Karman constant, and $\beta$ is the Charnock's constant.
 \citet{Mellor_Blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by
 \citet{Stacey_JPO99} citing observation evidence, and
+\citet{mellor.blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by
+\citet{stacey_JPO99} citing observation evidence, and
 $\alpha_{CB} = 100$ the Craig and Banner's value.
 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$,
 with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}\forcode{ = 67.83} corresponds
 to $\alpha_{CB} = 100$.
 Further setting  \np{ln\_mxl0} to true applies \autoref{eq:ZDF_Lsbc} as surface boundary condition on length scale,
+Further setting  \np{ln\_mxl0=.true.},  applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale,
 with $\beta$ hard coded to the Stacey's value.
 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on
+Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on the
 surface $\bar{e}$ value.
 …
 Although LC have nothing to do with convection, the circulation pattern is rather similar to
 so-called convective rolls in the atmospheric boundary layer.
 The detailed physics behind LC is described in, for example, \citet{Craik_Leibovich_JFM76}.
+The detailed physics behind LC is described in, for example, \citet{craik.leibovich_JFM76}.
 The prevailing explanation is that LC arise from a nonlinear interaction between the Stokes drift and
 wind drift currents.
 Here we introduced in the TKE turbulent closure the simple parameterization of Langmuir circulations proposed by
 \citep{Axell_JGR02} for a $k-\epsilon$ turbulent closure.
+\citep{axell_JGR02} for a $k-\epsilon$ turbulent closure.
 The parameterization, tuned against large-eddy simulation, includes the whole effect of LC in
 an extra source terms of TKE, $P_{LC}$.
+an extra source term of TKE, $P_{LC}$.
 The presence of $P_{LC}$ in \autoref{eq:zdftke_e}, the TKE equation, is controlled by setting \np{ln\_lc} to
 \forcode{.true.} in the namtke namelist.
+\forcode{.true.} in the \ngn{namzdf\_tke} namelist.
 By making an analogy with the characteristic convective velocity scale (\eg, \citet{D'Alessio_al_JPO98}),
+By making an analogy with the characteristic convective velocity scale (\eg, \citet{dalessio.abdella.ea_JPO98}),
 $P_{LC}$ is assumed to be :
 \[
 …
 With no information about the wave field, $w_{LC}$ is assumed to be proportional to
 the Stokes drift $u_s = 0.377\,\,|\tau|^{1/2}$, where $|\tau|$ is the surface wind stress module
 \footnote{Following \citet{Li_Garrett_JMR93}, the surface Stoke drift velocity may be expressed as
+\footnote{Following \citet{li.garrett_JMR93}, the surface Stoke drift velocity may be expressed as
   $u_s =  0.016 \,|U_{10m}|$.
   Assuming an air density of $\rho_a=1.22 \,Kg/m^3$ and a drag coefficient of
 …
   \end{cases}
 \]
 where $c_{LC} = 0.15$ has been chosen by \citep{Axell_JGR02} as a good compromise to fit LES data.
+where $c_{LC} = 0.15$ has been chosen by \citep{axell_JGR02} as a good compromise to fit LES data.
 The chosen value yields maximum vertical velocities $w_{LC}$ of the order of a few centimeters per second.
 The value of $c_{LC}$ is set through the \np{rn\_lc} namelist parameter,
 having in mind that it should stay between 0.15 and 0.54 \citep{Axell_JGR02}.
+having in mind that it should stay between 0.15 and 0.54 \citep{axell_JGR02}.
 The $H_{LC}$ is estimated in a similar way as the turbulent length scale of TKE equations:
 $H_{LC}$ is depth to which a water parcel with kinetic energy due to Stoke drift can reach on its own by
+$H_{LC}$ is the depth to which a water parcel with kinetic energy due to Stoke drift can reach on its own by
 converting its kinetic energy to potential energy, according to
 \[
 …
 produce mixed-layer depths that are too shallow during summer months and windy conditions.
 This bias is particularly acute over the Southern Ocean.
 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}.
+To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{rodgers.aumont.ea_B14}.
 The parameterization is an empirical one, \ie not derived from theoretical considerations,
 but rather is meant to account for observed processes that affect the density structure of
 …
 \end{equation}
 where $z$ is the depth, $e_s$ is TKE surface boundary condition, $f_r$ is the fraction of the surface TKE that
 penetrate in the ocean, $h_\tau$ is a vertical mixing length scale that controls exponential shape of
+penetrates in the ocean, $h_\tau$ is a vertical mixing length scale that controls exponential shape of
 the penetration, and $f_i$ is the ice concentration
 (no penetration if $f_i=1$, that is if the ocean is entirely covered by sea-ice).
+(no penetration if $f_i=1$, \ie if the ocean is entirely covered by sea-ice).
 The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter.
 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}\forcode{ = 0}) or
 …
 (\np{nn\_etau}\forcode{ = 1}).
 Note that two other option existe, \np{nn\_etau}\forcode{ = 2..3}.
+Note that two other option exist, \np{nn\_etau}\forcode{ = 2, 3}.
 They correspond to applying \autoref{eq:ZDF_Ehtau} only at the base of the mixed layer,
 or to using the high frequency part of the stress to evaluate the fraction of TKE that penetrate the ocean.
+or to using the high frequency part of the stress to evaluate the fraction of TKE that penetrates the ocean.
 Those two options are obsolescent features introduced for test purposes.
 They will be removed in the next release.
+% This should be explain better below what this rn_eice parameter is meant for:
+In presence of Sea Ice, the value of this mixing can be modulated by the \np{rn\_eice} namelist parameter.
+This parameter varies from \forcode{0} for no effect to \forcode{4} to suppress the TKE input into the ocean when Sea Ice concentration
+is greater than 25\%.
 % from Burchard et al OM 2008 :
 …
 % -------------------------------------------------------------------------------------------------------------
+%        TKE discretization considerations
+% -------------------------------------------------------------------------------------------------------------
+\subsection{TKE discretization considerations (\protect\key{zdftke})}
+%        GLS Generic Length Scale Scheme
+% -------------------------------------------------------------------------------------------------------------
+\subsection[GLS: Generic Length Scale (\forcode{ln_zdfgls = .true.})]
+{GLS: Generic Length Scale (\protect\np{ln\_zdfgls}\forcode{ = .true.})}
+\label{subsec:ZDF_gls}
+%--------------------------------------------namzdf_gls---------------------------------------------------------
+\nlst{namzdf_gls}
+%--------------------------------------------------------------------------------------------------------------
+The Generic Length Scale (GLS) scheme is a turbulent closure scheme based on two prognostic equations:
+one for the turbulent kinetic energy $\bar {e}$, and another for the generic length scale,
+$\psi$ \citep{umlauf.burchard_JMR03, umlauf.burchard_CSR05}.
+This later variable is defined as: $\psi = {C_{0\mu}}^{p} \ {\bar{e}}^{m} \ l^{n}$,
+where the triplet $(p, m, n)$ value given in Tab.\autoref{tab:GLS} allows to recover a number of
+well-known turbulent closures ($k$-$kl$ \citep{mellor.yamada_RG82}, $k$-$\epsilon$ \citep{rodi_JGR87},
+$k$-$\omega$ \citep{wilcox_AJ88} among others \citep{umlauf.burchard_JMR03,kantha.carniel_JMR03}).
+The GLS scheme is given by the following set of equations:
+\begin{equation}
+  \label{eq:zdfgls_e}
+  \frac{\partial \bar{e}}{\partial t} =
+  \frac{K_m}{\sigma_e e_3 }\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2
+      +\left( \frac{\partial v}{\partial k} \right)^2} \right]
+  -K_\rho \,N^2
+  +\frac{1}{e_3}\,\frac{\partial}{\partial k} \left[ \frac{K_m}{e_3}\,\frac{\partial \bar{e}}{\partial k} \right]
+  - \epsilon
+\end{equation}
+\[
+  % \label{eq:zdfgls_psi}
+  \begin{split}
+    \frac{\partial \psi}{\partial t} =& \frac{\psi}{\bar{e}} \left\{
+      \frac{C_1\,K_m}{\sigma_{\psi} {e_3}}\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2
+          +\left( \frac{\partial v}{\partial k} \right)^2} \right]
+      - C_3 \,K_\rho\,N^2   - C_2 \,\epsilon \,Fw   \right\}             \\
+    &+\frac{1}{e_3}  \;\frac{\partial }{\partial k}\left[ {\frac{K_m}{e_3 }
+        \;\frac{\partial \psi}{\partial k}} \right]\;
+  \end{split}
+\]
+\[
+  % \label{eq:zdfgls_kz}
+  \begin{split}
+    K_m    &= C_{\mu} \ \sqrt {\bar{e}} \ l         \\
+    K_\rho &= C_{\mu'}\ \sqrt {\bar{e}} \ l
+  \end{split}
+\]
+\[
+  % \label{eq:zdfgls_eps}
+  {\epsilon} = C_{0\mu} \,\frac{\bar {e}^{3/2}}{l} \;
+\]
+where $N$ is the local Brunt-Vais\"{a}l\"{a} frequency (see \autoref{subsec:TRA_bn2}) and
+$\epsilon$ the dissipation rate.
+The constants $C_1$, $C_2$, $C_3$, ${\sigma_e}$, ${\sigma_{\psi}}$ and the wall function ($Fw$) depends of
+the choice of the turbulence model.
+Four different turbulent models are pre-defined (\autoref{tab:GLS}).
+They are made available through the \np{nn\_clo} namelist parameter.
+%--------------------------------------------------TABLE--------------------------------------------------
+\begin{table}[htbp]
+  \begin{center}
+    % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}c}
+    \begin{tabular}{ccccc}
+      &   $k-kl$   & $k-\epsilon$ & $k-\omega$ &   generic   \\
+      % & \citep{mellor.yamada_RG82} &  \citep{rodi_JGR87}       & \citep{wilcox_AJ88} &                 \\
+      \hline
+      \hline
+      \np{nn\_clo}     & \textbf{0} &   \textbf{1}  &   \textbf{2}   &    \textbf{3}   \\
+      \hline
+      $( p , n , m )$          &   ( 0 , 1 , 1 )   & ( 3 , 1.5 , -1 )   & ( -1 , 0.5 , -1 )    &  ( 2 , 1 , -0.67 )  \\
+      $\sigma_k$      &    2.44         &     1.              &      2.                &      0.8          \\
+      $\sigma_\psi$  &    2.44         &     1.3            &      2.                 &       1.07       \\
+      $C_1$              &      0.9         &     1.44          &      0.555          &       1.           \\
+      $C_2$              &      0.5         &     1.92          &      0.833          &       1.22       \\
+      $C_3$              &      1.           &     1.              &      1.                &       1.           \\
+      $F_{wall}$        &      Yes        &       --             &     --                  &      --          \\
+      \hline
+      \hline
+    \end{tabular}
+    \caption{
+      \protect\label{tab:GLS}
+      Set of predefined GLS parameters, or equivalently predefined turbulence models available with
+      \protect\np{ln\_zdfgls}\forcode{ = .true.} and controlled by the \protect\np{nn\_clos} namelist variable in \protect\ngn{namzdf\_gls}.
+    }
+  \end{center}
+\end{table}
+%--------------------------------------------------------------------------------------------------------------
+In the Mellor-Yamada model, the negativity of $n$ allows to use a wall function to force the convergence of
+the mixing length towards $\kappa z_b$ ($\kappa$ is the Von Karman constant and $z_b$ the rugosity length scale) value near physical boundaries
+(logarithmic boundary layer law).
+$C_{\mu}$ and $C_{\mu'}$ are calculated from stability function proposed by \citet{galperin.kantha.ea_JAS88},
+or by \citet{kantha.clayson_JGR94} or one of the two functions suggested by \citet{canuto.howard.ea_JPO01}
+(\np{nn\_stab\_func}\forcode{ = 0, 3}, resp.).
+The value of $C_{0\mu}$ depends on the choice of the stability function.
+The surface and bottom boundary condition on both $\bar{e}$ and $\psi$ can be calculated thanks to Dirichlet or
+Neumann condition through \np{nn\_bc\_surf} and \np{nn\_bc\_bot}, resp.
+As for TKE closure, the wave effect on the mixing is considered when
+\np{rn\_crban}\forcode{ > 0.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}.
+The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and
+\np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}.
+The $\psi$ equation is known to fail in stably stratified flows, and for this reason
+almost all authors apply a clipping of the length scale as an \textit{ad hoc} remedy.
+With this clipping, the maximum permissible length scale is determined by $l_{max} = c_{lim} \sqrt{2\bar{e}}/ N$.
+A value of $c_{lim} = 0.53$ is often used \citep{galperin.kantha.ea_JAS88}.
+\cite{umlauf.burchard_CSR05} show that the value of the clipping factor is of crucial importance for
+the entrainment depth predicted in stably stratified situations,
+and that its value has to be chosen in accordance with the algebraic model for the turbulent fluxes.
+The clipping is only activated if \np{ln\_length\_lim}\forcode{ = .true.},
+and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value.
+The time and space discretization of the GLS equations follows the same energetic consideration as for
+the TKE case described in \autoref{subsec:ZDF_tke_ene} \citep{burchard_OM02}.
+Evaluation of the 4 GLS turbulent closure schemes can be found in \citet{warner.sherwood.ea_OM05} in ROMS model and
+ in \citet{reffray.guillaume.ea_GMD15} for the \NEMO model.
+% -------------------------------------------------------------------------------------------------------------
+%        OSM OSMOSIS BL Scheme
+% -------------------------------------------------------------------------------------------------------------
+\subsection[OSM: OSMosis boundary layer scheme (\forcode{ln_zdfosm = .true.})]
+{OSM: OSMosis boundary layer scheme (\protect\np{ln\_zdfosm}\forcode{ = .true.})}
+\label{subsec:ZDF_osm}
+%--------------------------------------------namzdf_osm---------------------------------------------------------
+\nlst{namzdf_osm}
+%--------------------------------------------------------------------------------------------------------------
+The OSMOSIS turbulent closure scheme is based on......   TBC
+% -------------------------------------------------------------------------------------------------------------
+%        TKE and GLS discretization considerations
+% -------------------------------------------------------------------------------------------------------------
+\subsection[ Discrete energy conservation for TKE and GLS schemes]
+{Discrete energy conservation for TKE and GLS schemes}
 \label{subsec:ZDF_tke_ene}
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=1.00\textwidth]{Fig_ZDF_TKE_time_scheme}
+    \includegraphics[width=\textwidth]{Fig_ZDF_TKE_time_scheme}
     \caption{
       \protect\label{fig:TKE_time_scheme}
       Illustration of the TKE time integration and its links to the momentum and tracer time integration.
+      Illustration of the subgrid kinetic energy integration in GLS and TKE schemes and its links to the momentum and tracer time integration.
+    }
   \end{center}
 …
 The production of turbulence by vertical shear (the first term of the right hand side of
 \autoref{eq:zdftke_e}) should balance the loss of kinetic energy associated with the vertical momentum diffusion
+\autoref{eq:zdftke_e}) and  \autoref{eq:zdfgls_e}) should balance the loss of kinetic energy associated with the vertical momentum diffusion
 (first line in \autoref{eq:PE_zdf}).
 To do so a special care have to be taken for both the time and space discretization of
 the TKE equation \citep{Burchard_OM02,Marsaleix_al_OM08}.
+To do so a special care has to be taken for both the time and space discretization of
+the kinetic energy equation \citep{burchard_OM02,marsaleix.auclair.ea_OM08}.
 Let us first address the time stepping issue. \autoref{fig:TKE_time_scheme} shows how
 the two-level Leap-Frog time stepping of the momentum and tracer equations interplays with
 the one-level forward time stepping of TKE equation.
+the one-level forward time stepping of the equation for $\bar{e}$.
 With this framework, the total loss of kinetic energy (in 1D for the demonstration) due to
 the vertical momentum diffusion is obtained by multiplying this quantity by $u^t$ and
 …
 A similar consideration applies on the destruction rate of $\bar{e}$ due to stratification
 (second term of the right hand side of \autoref{eq:zdftke_e}).
+(second term of the right hand side of \autoref{eq:zdftke_e} and \autoref{eq:zdfgls_e}).
 This term must balance the input of potential energy resulting from vertical mixing.
 The rate of change of potential energy (in 1D for the demonstration) due vertical mixing is obtained by
 multiplying vertical density diffusion tendency by $g\,z$ and and summing the result vertically:
+The rate of change of potential energy (in 1D for the demonstration) due to vertical mixing is obtained by
+multiplying the vertical density diffusion tendency by $g\,z$ and and summing the result vertically:
 \begin{equation}
   \label{eq:energ2}
 …
 The second term is minus the destruction rate of  $\bar{e}$ due to stratification.
 Therefore \autoref{eq:energ1} implies that, to be energetically consistent,
 the product ${K_\rho}^{t-\rdt}\,(N^2)^t$ should be used in \autoref{eq:zdftke_e}, the TKE equation.
+the product ${K_\rho}^{t-\rdt}\,(N^2)^t$ should be used in \autoref{eq:zdftke_e} and  \autoref{eq:zdfgls_e}.
 Let us now address the space discretization issue.
 …
 By redoing the \autoref{eq:energ1} in the 3D case, it can be shown that the product of eddy coefficient by
 the shear at $t$ and $t-\rdt$ must be performed prior to the averaging.
 Furthermore, the possible time variation of $e_3$ (\key{vvl} case) have to be taken into account.
+Furthermore, the time variation of $e_3$ has be taken into account.
 The above energetic considerations leads to the following final discrete form for the TKE equation:
 …
 are time stepped using a backward scheme (see\autoref{sec:STP_forward_imp}).
 Note that the Kolmogorov term has been linearized in time in order to render the implicit computation possible.
+The restart of the TKE scheme requires the storage of $\bar {e}$, $K_m$, $K_\rho$ and $l_\epsilon$ as
+they all appear in the right hand side of \autoref{eq:zdftke_ene}.
+For the latter, it is in fact the ratio $\sqrt{\bar{e}}/l_\epsilon$ which is stored.
+% -------------------------------------------------------------------------------------------------------------
+%        GLS Generic Length Scale Scheme
+% -------------------------------------------------------------------------------------------------------------
+\subsection{GLS: Generic Length Scale (\protect\key{zdfgls})}
+\label{subsec:ZDF_gls}
+%--------------------------------------------namzdf_gls---------------------------------------------------------
+\nlst{namzdf_gls}
+%--------------------------------------------------------------------------------------------------------------
+The Generic Length Scale (GLS) scheme is a turbulent closure scheme based on two prognostic equations:
+one for the turbulent kinetic energy $\bar {e}$, and another for the generic length scale,
+$\psi$ \citep{Umlauf_Burchard_JMS03, Umlauf_Burchard_CSR05}.
+This later variable is defined as: $\psi = {C_{0\mu}}^{p} \ {\bar{e}}^{m} \ l^{n}$,
+where the triplet $(p, m, n)$ value given in Tab.\autoref{tab:GLS} allows to recover a number of
+well-known turbulent closures ($k$-$kl$ \citep{Mellor_Yamada_1982}, $k$-$\epsilon$ \citep{Rodi_1987},
+$k$-$\omega$ \citep{Wilcox_1988} among others \citep{Umlauf_Burchard_JMS03,Kantha_Carniel_CSR05}).
+The GLS scheme is given by the following set of equations:
+\begin{equation}
+  \label{eq:zdfgls_e}
+  \frac{\partial \bar{e}}{\partial t} =
+  \frac{K_m}{\sigma_e e_3 }\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2
+      +\left( \frac{\partial v}{\partial k} \right)^2} \right]
+  -K_\rho \,N^2
+  +\frac{1}{e_3}\,\frac{\partial}{\partial k} \left[ \frac{K_m}{e_3}\,\frac{\partial \bar{e}}{\partial k} \right]
+  - \epsilon
+\end{equation}
+\[
+  % \label{eq:zdfgls_psi}
+  \begin{split}
+    \frac{\partial \psi}{\partial t} =& \frac{\psi}{\bar{e}} \left\{
+      \frac{C_1\,K_m}{\sigma_{\psi} {e_3}}\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2
+          +\left( \frac{\partial v}{\partial k} \right)^2} \right]
+      - C_3 \,K_\rho\,N^2   - C_2 \,\epsilon \,Fw   \right\}             \\
+    &+\frac{1}{e_3}  \;\frac{\partial }{\partial k}\left[ {\frac{K_m}{e_3 }
+        \;\frac{\partial \psi}{\partial k}} \right]\;
+  \end{split}
+\]
+\[
+  % \label{eq:zdfgls_kz}
+  \begin{split}
+    K_m    &= C_{\mu} \ \sqrt {\bar{e}} \ l         \\
+    K_\rho &= C_{\mu'}\ \sqrt {\bar{e}} \ l
+  \end{split}
+\]
+\[
+  % \label{eq:zdfgls_eps}
+  {\epsilon} = C_{0\mu} \,\frac{\bar {e}^{3/2}}{l} \;
+\]
+where $N$ is the local Brunt-Vais\"{a}l\"{a} frequency (see \autoref{subsec:TRA_bn2}) and
+$\epsilon$ the dissipation rate.
+The constants $C_1$, $C_2$, $C_3$, ${\sigma_e}$, ${\sigma_{\psi}}$ and the wall function ($Fw$) depends of
+the choice of the turbulence model.
+Four different turbulent models are pre-defined (Tab.\autoref{tab:GLS}).
+They are made available through the \np{nn\_clo} namelist parameter.
+%--------------------------------------------------TABLE--------------------------------------------------
+\begin{table}[htbp]
+  \begin{center}
+    % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}c}
+    \begin{tabular}{ccccc}
+      &   $k-kl$   & $k-\epsilon$ & $k-\omega$ &   generic   \\
+      % & \citep{Mellor_Yamada_1982} &  \citep{Rodi_1987}       & \citep{Wilcox_1988} &                 \\
+      \hline
+      \hline
+      \np{nn\_clo}     & \textbf{0} &   \textbf{1}  &   \textbf{2}   &    \textbf{3}   \\
+      \hline
+      $( p , n , m )$          &   ( 0 , 1 , 1 )   & ( 3 , 1.5 , -1 )   & ( -1 , 0.5 , -1 )    &  ( 2 , 1 , -0.67 )  \\
+      $\sigma_k$      &    2.44         &     1.              &      2.                &      0.8          \\
+      $\sigma_\psi$  &    2.44         &     1.3            &      2.                 &       1.07       \\
+      $C_1$              &      0.9         &     1.44          &      0.555          &       1.           \\
+      $C_2$              &      0.5         &     1.92          &      0.833          &       1.22       \\
+      $C_3$              &      1.           &     1.              &      1.                &       1.           \\
+      $F_{wall}$        &      Yes        &       --             &     --                  &      --          \\
+      \hline
+      \hline
+    \end{tabular}
+    \caption{
+      \protect\label{tab:GLS}
+      Set of predefined GLS parameters, or equivalently predefined turbulence models available with
+      \protect\key{zdfgls} and controlled by the \protect\np{nn\_clos} namelist variable in \protect\ngn{namzdf\_gls}.
+    }
+  \end{center}
+\end{table}
+%--------------------------------------------------------------------------------------------------------------
+In the Mellor-Yamada model, the negativity of $n$ allows to use a wall function to force the convergence of
+the mixing length towards $K z_b$ ($K$: Kappa and $z_b$: rugosity length) value near physical boundaries
+(logarithmic boundary layer law).
+$C_{\mu}$ and $C_{\mu'}$ are calculated from stability function proposed by \citet{Galperin_al_JAS88},
+or by \citet{Kantha_Clayson_1994} or one of the two functions suggested by \citet{Canuto_2001}
+(\np{nn\_stab\_func}\forcode{ = 0..3}, resp.).
+The value of $C_{0\mu}$ depends of the choice of the stability function.
+The surface and bottom boundary condition on both $\bar{e}$ and $\psi$ can be calculated thanks to Dirichlet or
+Neumann condition through \np{nn\_tkebc\_surf} and \np{nn\_tkebc\_bot}, resp.
+As for TKE closure, the wave effect on the mixing is considered when
+\np{ln\_crban}\forcode{ = .true.} \citep{Craig_Banner_JPO94, Mellor_Blumberg_JPO04}.
+The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and
+\np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}.
+The $\psi$ equation is known to fail in stably stratified flows, and for this reason
+almost all authors apply a clipping of the length scale as an \textit{ad hoc} remedy.
+With this clipping, the maximum permissible length scale is determined by $l_{max} = c_{lim} \sqrt{2\bar{e}}/ N$.
+A value of $c_{lim} = 0.53$ is often used \citep{Galperin_al_JAS88}.
+\cite{Umlauf_Burchard_CSR05} show that the value of the clipping factor is of crucial importance for
+the entrainment depth predicted in stably stratified situations,
+and that its value has to be chosen in accordance with the algebraic model for the turbulent fluxes.
+The clipping is only activated if \np{ln\_length\_lim}\forcode{ = .true.},
+and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value.
+The time and space discretization of the GLS equations follows the same energetic consideration as for
+the TKE case described in \autoref{subsec:ZDF_tke_ene} \citep{Burchard_OM02}.
+Examples of performance of the 4 turbulent closure scheme can be found in \citet{Warner_al_OM05}.
+% -------------------------------------------------------------------------------------------------------------
+%        OSM OSMOSIS BL Scheme
+% -------------------------------------------------------------------------------------------------------------
+\subsection{OSM: OSMOSIS boundary layer scheme (\protect\key{zdfosm})}
+\label{subsec:ZDF_osm}
+%--------------------------------------------namzdf_osm---------------------------------------------------------
+\nlst{namzdf_osm}
+%--------------------------------------------------------------------------------------------------------------
+The OSMOSIS turbulent closure scheme is based on......   TBC
+%The restart of the TKE scheme requires the storage of $\bar {e}$, $K_m$, $K_\rho$ and $l_\epsilon$ as
+%they all appear in the right hand side of \autoref{eq:zdftke_ene}.
+%For the latter, it is in fact the ratio $\sqrt{\bar{e}}/l_\epsilon$ which is stored.
 % ================================================================
 …
 \section{Convection}
 \label{sec:ZDF_conv}
-%--------------------------------------------namzdf--------------------------------------------------------
-\nlst{namzdf}
-%--------------------------------------------------------------------------------------------------------------
 Static instabilities (\ie light potential densities under heavy ones) may occur at particular ocean grid points.
 …
 %       Non-Penetrative Convective Adjustment
 % -------------------------------------------------------------------------------------------------------------
 \subsection[Non-penetrative convective adjmt (\protect\np{ln\_tranpc}\forcode{ = .true.})]
             {Non-penetrative convective adjustment (\protect\np{ln\_tranpc}\forcode{ = .true.})}
+\subsection[Non-penetrative convective adjustment (\forcode{ln_tranpc = .true.})]
+{Non-penetrative convective adjustment (\protect\np{ln\_tranpc}\forcode{ = .true.})}
 \label{subsec:ZDF_npc}
-%--------------------------------------------namzdf--------------------------------------------------------
-\nlst{namzdf}
-%--------------------------------------------------------------------------------------------------------------
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!htb]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_npc}
+    \includegraphics[width=\textwidth]{Fig_npc}
     \caption{
       \protect\label{fig:npc}
 …
 the water column, but only until the density structure becomes neutrally stable
 (\ie until the mixed portion of the water column has \textit{exactly} the density of the water just below)
 \citep{Madec_al_JPO91}.
+\citep{madec.delecluse.ea_JPO91}.
 The associated algorithm is an iterative process used in the following way (\autoref{fig:npc}):
 starting from the top of the ocean, the first instability is found.
 …
 the algorithm used in \NEMO converges for any profile in a number of iterations which is less than
 the number of vertical levels.
 This property is of paramount importance as pointed out by \citet{Killworth1989}:
+This property is of paramount importance as pointed out by \citet{killworth_iprc89}:
 it avoids the existence of permanent and unrealistic static instabilities at the sea surface.
 This non-penetrative convective algorithm has been proved successful in studies of the deep water formation in
 the north-western Mediterranean Sea \citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}.
+the north-western Mediterranean Sea \citep{madec.delecluse.ea_JPO91, madec.chartier.ea_DAO91, madec.crepon_iprc91}.
 The current implementation has been modified in order to deal with any non linear equation of seawater
 …
 Two main differences have been introduced compared to the original algorithm:
 $(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency
 (not the the difference in potential density);
+(not the difference in potential density);
 $(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients are vertically mixed in
 the same way their temperature and salinity has been mixed.
 …
 %       Enhanced Vertical Diffusion
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Enhanced vertical diffusion (\protect\np{ln\_zdfevd}\forcode{ = .true.})}
+\subsection[Enhanced vertical diffusion (\forcode{ln_zdfevd = .true.})]
+{Enhanced vertical diffusion (\protect\np{ln\_zdfevd}\forcode{ = .true.})}
 \label{subsec:ZDF_evd}
-%--------------------------------------------namzdf--------------------------------------------------------
-\nlst{namzdf}
-%--------------------------------------------------------------------------------------------------------------
 Options are defined through the  \ngn{namzdf} namelist variables.
 The enhanced vertical diffusion parameterisation is used when \np{ln\_zdfevd}\forcode{ = .true.}.
 In this case, the vertical eddy mixing coefficients are assigned very large values
 (a typical value is $10\;m^2s^{-1})$ in regions where the stratification is unstable
 (\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}.
+In this case, the vertical eddy mixing coefficients are assigned very large values
+in regions where the stratification is unstable
+(\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{lazar_phd97, lazar.madec.ea_JPO99}.
 This is done either on tracers only (\np{nn\_evdm}\forcode{ = 0}) or
 on both momentum and tracers (\np{nn\_evdm}\forcode{ = 1}).
 …
 the convective adjustment algorithm presented above when mixing both tracers and
 momentum in the case of static instabilities.
-It requires the use of an implicit time stepping on vertical diffusion terms
-(\ie np{ln\_zdfexp}\forcode{ = .false.}).
 Note that the stability test is performed on both \textit{before} and \textit{now} values of $N^2$.
 This removes a potential source of divergence of odd and even time step in
 a leapfrog environment \citep{Leclair_PhD2010} (see \autoref{sec:STP_mLF}).
+a leapfrog environment \citep{leclair_phd10} (see \autoref{sec:STP_mLF}).
 % -------------------------------------------------------------------------------------------------------------
 %       Turbulent Closure Scheme
 % -------------------------------------------------------------------------------------------------------------
+\subsection[Turbulent closure scheme (\protect\key{zdf}\{tke,gls,osm\})]{Turbulent Closure Scheme (\protect\key{zdftke}, \protect\key{zdfgls} or \protect\key{zdfosm})}
+\subsection[Handling convection with turbulent closure schemes (\forcode{ln_zdf/tke/gls/osm = .true.})]
+{Handling convection with turbulent closure schemes (\protect\np{ln\_zdf/tke/gls/osm}\forcode{ = .true.})}
 \label{subsec:ZDF_tcs}
+The turbulent closure scheme presented in \autoref{subsec:ZDF_tke} and \autoref{subsec:ZDF_gls}
+(\key{zdftke} or \key{zdftke} is defined) in theory solves the problem of statically unstable density profiles.
+The turbulent closure schemes presented in \autoref{subsec:ZDF_tke}, \autoref{subsec:ZDF_gls} and
+\autoref{subsec:ZDF_osm} (\ie \np{ln\_zdftke} or \np{ln\_zdfgls} or \np{ln\_zdfosm} defined) deal, in theory,
+with statically unstable density profiles.
 In such a case, the term corresponding to the destruction of turbulent kinetic energy through stratification in
 \autoref{eq:zdftke_e} or \autoref{eq:zdfgls_e} becomes a source term, since $N^2$ is negative.
 It results in large values of $A_T^{vT}$ and  $A_T^{vT}$, and also the four neighbouring $A_u^{vm} {and}\;A_v^{vm}$
 (up to $1\;m^2s^{-1}$).
+It results in large values of $A_T^{vT}$ and  $A_T^{vT}$, and also of the four neighboring values at
+velocity points $A_u^{vm} {and}\;A_v^{vm}$ (up to $1\;m^2s^{-1}$).
 These large values restore the static stability of the water column in a way similar to that of
 the enhanced vertical diffusion parameterisation (\autoref{subsec:ZDF_evd}).
 …
 It can thus be useful to combine the enhanced vertical diffusion with the turbulent closure scheme,
 \ie setting the \np{ln\_zdfnpc} namelist parameter to true and
 defining the turbulent closure CPP key all together.
 The KPP turbulent closure scheme already includes enhanced vertical diffusion in the case of convection,
 as governed by the variables $bvsqcon$ and $difcon$ found in \mdl{zdfkpp},
 therefore \np{ln\_zdfevd}\forcode{ = .false.} should be used with the KPP scheme.
+defining the turbulent closure (\np{ln\_zdftke} or \np{ln\_zdfgls} = \forcode{.true.}) all together.
+The OSMOSIS turbulent closure scheme already includes enhanced vertical diffusion in the case of convection,
+%as governed by the variables $bvsqcon$ and $difcon$ found in \mdl{zdfkpp},
+therefore \np{ln\_zdfevd}\forcode{ = .false.} should be used with the OSMOSIS scheme.
 % gm%  + one word on non local flux with KPP scheme trakpp.F90 module...
 …
 % Double Diffusion Mixing
 % ================================================================
+\section{Double diffusion mixing (\protect\key{zdfddm})}
+\label{sec:ZDF_ddm}
+\section[Double diffusion mixing (\forcode{ln_zdfddm = .true.})]
+{Double diffusion mixing (\protect\np{ln\_zdfddm}\forcode{ = .true.})}
+\label{subsec:ZDF_ddm}
 %-------------------------------------------namzdf_ddm-------------------------------------------------
 …
 %--------------------------------------------------------------------------------------------------------------
+Options are defined through the  \ngn{namzdf\_ddm} namelist variables.
+This parameterisation has been introduced in \mdl{zdfddm} module and is controlled by the namelist parameter
+\np{ln\_zdfddm} in \ngn{namzdf}.
 Double diffusion occurs when relatively warm, salty water overlies cooler, fresher water, or vice versa.
 The former condition leads to salt fingering and the latter to diffusive convection.
 Double-diffusive phenomena contribute to diapycnal mixing in extensive regions of the ocean.
 \citet{Merryfield1999} include a parameterisation of such phenomena in a global ocean model and show that
+\citet{merryfield.holloway.ea_JPO99} include a parameterisation of such phenomena in a global ocean model and show that
 it leads to relatively minor changes in circulation but exerts significant regional influences on
 temperature and salinity.
+This parameterisation has been introduced in \mdl{zdfddm} module and is controlled by the \key{zdfddm} CPP key.
 Diapycnal mixing of S and T are described by diapycnal diffusion coefficients
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.99\textwidth]{Fig_zdfddm}
+    \includegraphics[width=\textwidth]{Fig_zdfddm}
     \caption{
       \protect\label{fig:zdfddm}
       From \citet{Merryfield1999} :
+      From \citet{merryfield.holloway.ea_JPO99} :
       (a) Diapycnal diffusivities $A_f^{vT}$ and $A_f^{vS}$ for temperature and salt in regions of salt fingering.
       Heavy curves denote $A^{\ast v} = 10^{-3}~m^2.s^{-1}$ and thin curves $A^{\ast v} = 10^{-4}~m^2.s^{-1}$;
 …
 The factor 0.7 in \autoref{eq:zdfddm_f_T} reflects the measured ratio $\alpha F_T /\beta F_S \approx  0.7$ of
 buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{McDougall_Taylor_JMR84}).
 Following  \citet{Merryfield1999}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$.
+buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{mcdougall.taylor_JMR84}).
+Following  \citet{merryfield.holloway.ea_JPO99}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$.
 To represent mixing of S and T by diffusive layering,  the diapycnal diffusivities suggested by
 …
 % Bottom Friction
 % ================================================================
+\section{Bottom and top friction (\protect\mdl{zdfbfr})}
+\label{sec:ZDF_bfr}
+ \section[Bottom and top friction (\textit{zdfdrg.F90})]
+ {Bottom and top friction (\protect\mdl{zdfdrg})}
+ \label{sec:ZDF_drg}
 %--------------------------------------------nambfr--------------------------------------------------------
+%
+%\nlst{nambfr}
+\nlst{namdrg}
+\nlst{namdrg_top}
+\nlst{namdrg_bot}
 %--------------------------------------------------------------------------------------------------------------
 Options to define the top and bottom friction are defined through the \ngn{nambfr} namelist variables.
+Options to define the top and bottom friction are defined through the \ngn{namdrg} namelist variables.
 The bottom friction represents the friction generated by the bathymetry.
 The top friction represents the friction generated by the ice shelf/ocean interface.
 As the friction processes at the top and bottom are treated in similar way,
 only the bottom friction is described in detail below.
+As the friction processes at the top and the bottom are treated in and identical way,
+the description below considers mostly the bottom friction case, if not stated otherwise.
 …
 a condition on the vertical diffusive flux.
 For the bottom boundary layer, one has:
 \[
   % \label{eq:zdfbfr_flux}
   A^{vm} \left( \partial {\textbf U}_h / \partial z \right) = {{\cal F}}_h^{\textbf U}
 \]
+ \[
+   % \label{eq:zdfbfr_flux}
+   A^{vm} \left( \partial {\textbf U}_h / \partial z \right) = {{\cal F}}_h^{\textbf U}
+ \]
 where ${\cal F}_h^{\textbf U}$ is represents the downward flux of horizontal momentum outside
 the logarithmic turbulent boundary layer (thickness of the order of 1~m in the ocean).
 …
 To illustrate this, consider the equation for $u$ at $k$, the last ocean level:
 \begin{equation}
   \label{eq:zdfbfr_flux2}
+  \label{eq:zdfdrg_flux2}
   \frac{\partial u_k}{\partial t} = \frac{1}{e_{3u}} \left[ \frac{A_{uw}^{vm}}{e_{3uw}} \delta_{k+1/2}\;[u] - {\cal F}^u_h \right] \approx - \frac{{\cal F}^u_{h}}{e_{3u}}
 \end{equation}
 …
 In the code, the bottom friction is imposed by adding the trend due to the bottom friction to
 the general momentum trend in \mdl{dynbfr}.
+ the general momentum trend in \mdl{dynzdf}.
 For the time-split surface pressure gradient algorithm, the momentum trend due to
 the barotropic component needs to be handled separately.
 For this purpose it is convenient to compute and store coefficients which can be simply combined with
 bottom velocities and geometric values to provide the momentum trend due to bottom friction.
 These coefficients are computed in \mdl{zdfbfr} and generally take the form $c_b^{\textbf U}$ where:
+ These coefficients are computed in \mdl{zdfdrg} and generally take the form $c_b^{\textbf U}$ where:
 \begin{equation}
   \label{eq:zdfbfr_bdef}
 …
   - \frac{{\cal F}^{\textbf U}_{h}}{e_{3u}} = \frac{c_b^{\textbf U}}{e_{3u}} \;{\textbf U}_h^b
 \end{equation}
+where $\textbf{U}_h^b = (u_b\;,\;v_b)$ is the near-bottom, horizontal, ocean velocity.
+where $\textbf{U}_h^b = (u_b\;,\;v_b)$ is the near-bottom, horizontal, ocean velocity.
+Note than from \NEMO 4.0, drag coefficients are only computed at cell centers (\ie at T-points) and refer to as $c_b^T$ in the following. These are then linearly interpolated in space to get $c_b^\textbf{U}$ at velocity points.
 % -------------------------------------------------------------------------------------------------------------
 %       Linear Bottom Friction
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Linear bottom friction (\protect\np{nn\_botfr}\forcode{ = 0..1})}
+\label{subsec:ZDF_bfr_linear}
+The linear bottom friction parameterisation (including the special case of a free-slip condition) assumes that
+the bottom friction is proportional to the interior velocity (\ie the velocity of the last model level):
+ \subsection[Linear top/bottom friction (\forcode{ln_lin = .true.})]
+ {Linear top/bottom friction (\protect\np{ln\_lin}\forcode{ = .true.)}}
+ \label{subsec:ZDF_drg_linear}
+The linear friction parameterisation (including the special case of a free-slip condition) assumes that
+the friction is proportional to the interior velocity (\ie the velocity of the first/last model level):
 \[
   % \label{eq:zdfbfr_linear}
   {\cal F}_h^\textbf{U} = \frac{A^{vm}}{e_3} \; \frac{\partial \textbf{U}_h}{\partial k} = r \; \textbf{U}_h^b
 \]
 where $r$ is a friction coefficient expressed in ms$^{-1}$.
+where $r$ is a friction coefficient expressed in $m s^{-1}$.
 This coefficient is generally estimated by setting a typical decay time $\tau$ in the deep ocean,
 and setting $r = H / \tau$, where $H$ is the ocean depth.
 Commonly accepted values of $\tau$ are of the order of 100 to 200 days \citep{Weatherly_JMR84}.
+Commonly accepted values of $\tau$ are of the order of 100 to 200 days \citep{weatherly_JMR84}.
 A value $\tau^{-1} = 10^{-7}$~s$^{-1}$ equivalent to 115 days, is usually used in quasi-geostrophic models.
 One may consider the linear friction as an approximation of quadratic friction, $r \approx 2\;C_D\;U_{av}$
 (\citet{Gill1982}, Eq. 9.6.6).
+(\citet{gill_bk82}, Eq. 9.6.6).
 For example, with a drag coefficient $C_D = 0.002$, a typical speed of tidal currents of $U_{av} =0.1$~m\;s$^{-1}$,
 and assuming an ocean depth $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$.
 This is the default value used in \NEMO. It corresponds to a decay time scale of 115~days.
 It can be changed by specifying \np{rn\_bfri1} (namelist parameter).
 For the linear friction case the coefficients defined in the general expression \autoref{eq:zdfbfr_bdef} are:
+It can be changed by specifying \np{rn\_Uc0} (namelist parameter).
+ For the linear friction case the drag coefficient used in the general expression \autoref{eq:zdfbfr_bdef} is:
 \[
   % \label{eq:zdfbfr_linbfr_b}
+  \begin{split}
+    c_b^u &= - r\\
+    c_b^v &= - r\\
+  \end{split}
+\]
+When \np{nn\_botfr}\forcode{ = 1}, the value of $r$ used is \np{rn\_bfri1}.
+Setting \np{nn\_botfr}\forcode{ = 0} is equivalent to setting $r=0$ and
+leads to a free-slip bottom boundary condition.
+These values are assigned in \mdl{zdfbfr}.
+From v3.2 onwards there is support for local enhancement of these values via an externally defined 2D mask array
+(\np{ln\_bfr2d}\forcode{ = .true.}) given in the \ifile{bfr\_coef} input NetCDF file.
+    c_b^T = - r
+\]
+When \np{ln\_lin} \forcode{= .true.}, the value of $r$ used is \np{rn\_Uc0}*\np{rn\_Cd0}.
+Setting \np{ln\_OFF} \forcode{= .true.} (and \forcode{ln_lin = .true.}) is equivalent to setting $r=0$ and leads to a free-slip boundary condition.
+These values are assigned in \mdl{zdfdrg}.
+Note that there is support for local enhancement of these values via an externally defined 2D mask array
+(\np{ln\_boost}\forcode{ = .true.}) given in the \ifile{bfr\_coef} input NetCDF file.
 The mask values should vary from 0 to 1.
 Locations with a non-zero mask value will have the friction coefficient increased by
 $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri1}.
+$mask\_value$ * \np{rn\_boost} * \np{rn\_Cd0}.
 % -------------------------------------------------------------------------------------------------------------
 %       Non-Linear Bottom Friction
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Non-linear bottom friction (\protect\np{nn\_botfr}\forcode{ = 2})}
+\label{subsec:ZDF_bfr_nonlinear}
+The non-linear bottom friction parameterisation assumes that the bottom friction is quadratic:
+\[
+  % \label{eq:zdfbfr_nonlinear}
+ \subsection[Non-linear top/bottom friction (\forcode{ln_no_lin = .true.})]
+ {Non-linear top/bottom friction (\protect\np{ln\_no\_lin}\forcode{ = .true.})}
+ \label{subsec:ZDF_drg_nonlinear}
+The non-linear bottom friction parameterisation assumes that the top/bottom friction is quadratic:
+\[
+  % \label{eq:zdfdrg_nonlinear}
   {\cal F}_h^\textbf{U} = \frac{A^{vm}}{e_3 }\frac{\partial \textbf {U}_h
   }{\partial k}=C_D \;\sqrt {u_b ^2+v_b ^2+e_b } \;\; \textbf {U}_h^b
 \]
 where $C_D$ is a drag coefficient, and $e_b $ a bottom turbulent kinetic energy due to tides,
+where $C_D$ is a drag coefficient, and $e_b $ a top/bottom turbulent kinetic energy due to tides,
 internal waves breaking and other short time scale currents.
 A typical value of the drag coefficient is $C_D = 10^{-3} $.
 As an example, the CME experiment \citep{Treguier_JGR92} uses $C_D = 10^{-3}$ and
 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992} uses $C_D = 1.4\;10^{-3}$ and
+As an example, the CME experiment \citep{treguier_JGR92} uses $C_D = 10^{-3}$ and
+$e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{killworth_JPO92} uses $C_D = 1.4\;10^{-3}$ and
 $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$.
+The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} namelist parameters).
+As for the linear case, the bottom friction is imposed in the code by adding the trend due to
+the bottom friction to the general momentum trend in \mdl{dynbfr}.
+For the non-linear friction case the terms computed in \mdl{zdfbfr} are:
+\[
+  % \label{eq:zdfbfr_nonlinbfr}
+  \begin{split}
+    c_b^u &= - \; C_D\;\left[ u^2 + \left(\bar{\bar{v}}^{i+1,j}\right)^2 + e_b \right]^{1/2}\\
+    c_b^v &= - \; C_D\;\left[  \left(\bar{\bar{u}}^{i,j+1}\right)^2 + v^2 + e_b \right]^{1/2}\\
+  \end{split}
+\]
+The coefficients that control the strength of the non-linear bottom friction are initialised as namelist parameters:
+$C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}.
+Note for applications which treat tides explicitly a low or even zero value of \np{rn\_bfeb2} is recommended.
+From v3.2 onwards a local enhancement of $C_D$ is possible via an externally defined 2D mask array
+(\np{ln\_bfr2d}\forcode{ = .true.}).
+This works in the same way as for the linear bottom friction case with non-zero masked locations increased by
+$mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}.
+The CME choices have been set as default values (\np{rn\_Cd0} and \np{rn\_ke0} namelist parameters).
+As for the linear case, the friction is imposed in the code by adding the trend due to
+the friction to the general momentum trend in \mdl{dynzdf}.
+For the non-linear friction case the term computed in \mdl{zdfdrg} is:
+\[
+  % \label{eq:zdfdrg_nonlinbfr}
+    c_b^T = - \; C_D\;\left[ \left(\bar{u_b}^{i}\right)^2 + \left(\bar{v_b}^{j}\right)^2 + e_b \right]^{1/2}
+\]
+The coefficients that control the strength of the non-linear friction are initialised as namelist parameters:
+$C_D$= \np{rn\_Cd0}, and $e_b$ =\np{rn\_bfeb2}.
+Note that for applications which consider tides explicitly, a low or even zero value of \np{rn\_bfeb2} is recommended. A local enhancement of $C_D$ is again possible via an externally defined 2D mask array
+(\np{ln\_boost}\forcode{ = .true.}).
+This works in the same way as for the linear friction case with non-zero masked locations increased by
+$mask\_value$ * \np{rn\_boost} * \np{rn\_Cd0}.
 % -------------------------------------------------------------------------------------------------------------
 %       Bottom Friction Log-layer
 % -------------------------------------------------------------------------------------------------------------
+\subsection[Log-layer btm frict enhncmnt (\protect\np{nn\_botfr}\forcode{ = 2}, \protect\np{ln\_loglayer}\forcode{ = .true.})]
+            {Log-layer bottom friction enhancement (\protect\np{nn\_botfr}\forcode{ = 2}, \protect\np{ln\_loglayer}\forcode{ = .true.})}
+\label{subsec:ZDF_bfr_loglayer}
+In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally enhanced using
+a "law of the wall" scaling.
+If  \np{ln\_loglayer} = .true., $C_D$ is no longer constant but is related to the thickness of
+the last wet layer in each column by:
+\[
+  C_D = \left ( {\kappa \over {\rm log}\left ( 0.5e_{3t}/rn\_bfrz0 \right ) } \right )^2
+\]
+\noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness length provided via
+the namelist.
+For stability, the drag coefficient is bounded such that it is kept greater or equal to
+the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional namelist parameter:
+\np{rn\_bfri2\_max}, \ie
+\[
+  rn\_bfri2 \leq C_D \leq rn\_bfri2\_max
+\]
+\noindent Note also that a log-layer enhancement can also be applied to the top boundary friction if
+under ice-shelf cavities are in use (\np{ln\_isfcav}\forcode{ = .true.}).
+In this case, the relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} and \np{rn\_tfri2\_max}.
+% -------------------------------------------------------------------------------------------------------------
+%       Bottom Friction stability
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Bottom friction stability considerations}
+\label{subsec:ZDF_bfr_stability}
+Some care needs to exercised over the choice of parameters to ensure that the implementation of
+bottom friction does not induce numerical instability.
+For the purposes of stability analysis, an approximation to \autoref{eq:zdfbfr_flux2} is:
+ \subsection[Log-layer top/bottom friction (\forcode{ln_loglayer = .true.})]
+ {Log-layer top/bottom friction (\protect\np{ln\_loglayer}\forcode{ = .true.})}
+ \label{subsec:ZDF_drg_loglayer}
+In the non-linear friction case, the drag coefficient, $C_D$, can be optionally enhanced using
+a "law of the wall" scaling. This assumes that the model vertical resolution can capture the logarithmic layer which typically occur for layers thinner than 1 m or so.
+If  \np{ln\_loglayer} \forcode{= .true.}, $C_D$ is no longer constant but is related to the distance to the wall (or equivalently to the half of the top/bottom layer thickness):
+\[
+  C_D = \left ( {\kappa \over {\mathrm log}\left ( 0.5 \; e_{3b} / rn\_{z0} \right ) } \right )^2
+\]
+\noindent where $\kappa$ is the von-Karman constant and \np{rn\_z0} is a roughness length provided via the namelist.
+The drag coefficient is bounded such that it is kept greater or equal to
+the base \np{rn\_Cd0} value which occurs where layer thicknesses become large and presumably logarithmic layers are not resolved at all. For stability reason, it is also not allowed to exceed the value of an additional namelist parameter:
+\np{rn\_Cdmax}, \ie
+\[
+  rn\_Cd0 \leq C_D \leq rn\_Cdmax
+\]
+\noindent The log-layer enhancement can also be applied to the top boundary friction if
+under ice-shelf cavities are activated (\np{ln\_isfcav}\forcode{ = .true.}).
+%In this case, the relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} and \np{rn\_tfri2\_max}.
+% -------------------------------------------------------------------------------------------------------------
+%       Explicit bottom Friction
+% -------------------------------------------------------------------------------------------------------------
+ \subsection{Explicit top/bottom friction (\forcode{ln_drgimp = .false.})}
+ \label{subsec:ZDF_drg_stability}
+Setting \np{ln\_drgimp} \forcode{= .false.} means that bottom friction is treated explicitly in time, which has the advantage of simplifying the interaction with the split-explicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic sub-iteration, which becomes less straightforward in the implicit case. In the explicit case, top/bottom stresses can be computed using \textit{before} velocities and inserted in the overall momentum tendency budget. This reads:
+At the top (below an ice shelf cavity):
+\[
+  \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{t}
+  = c_{t}^{\textbf{U}}\textbf{u}^{n-1}_{t}
+\]
+At the bottom (above the sea floor):
+\[
+  \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{b}
+  = c_{b}^{\textbf{U}}\textbf{u}^{n-1}_{b}
+\]
+Since this is conditionally stable, some care needs to exercised over the choice of parameters to ensure that the implementation of explicit top/bottom friction does not induce numerical instability.
+For the purposes of stability analysis, an approximation to \autoref{eq:zdfdrg_flux2} is:
 \begin{equation}
   \label{eq:Eqn_bfrstab}
+  \label{eq:Eqn_drgstab}
   \begin{split}
     \Delta u &= -\frac{{{\cal F}_h}^u}{e_{3u}}\;2 \rdt    \\
 …
   \end{split}
 \end{equation}
 \noindent where linear bottom friction and a leapfrog timestep have been assumed.
 To ensure that the bottom friction cannot reverse the direction of flow it is necessary to have:
+\noindent where linear friction and a leapfrog timestep have been assumed.
+To ensure that the friction cannot reverse the direction of flow it is necessary to have:
 \[
   |\Delta u| < \;|u|
 \]
 \noindent which, using \autoref{eq:Eqn_bfrstab}, gives:
+\noindent which, using \autoref{eq:Eqn_drgstab}, gives:
 \[
   r\frac{2\rdt}{e_{3u}} < 1 \qquad  \Rightarrow \qquad r < \frac{e_{3u}}{2\rdt}\\
 …
 For most applications, with physically sensible parameters these restrictions should not be of concern.
 But caution may be necessary if attempts are made to locally enhance the bottom friction parameters.
 To ensure stability limits are imposed on the bottom friction coefficients both
+To ensure stability limits are imposed on the top/bottom friction coefficients both
 during initialisation and at each time step.
 Checks at initialisation are made in \mdl{zdfbfr} (assuming a 1 m.s$^{-1}$ velocity in the non-linear case).
+Checks at initialisation are made in \mdl{zdfdrg} (assuming a 1 m.s$^{-1}$ velocity in the non-linear case).
 The number of breaches of the stability criterion are reported as well as
 the minimum and maximum values that have been set.
 The criterion is also checked at each time step, using the actual velocity, in \mdl{dynbfr}.
 Values of the bottom friction coefficient are reduced as necessary to ensure stability;
+The criterion is also checked at each time step, using the actual velocity, in \mdl{dynzdf}.
+Values of the friction coefficient are reduced as necessary to ensure stability;
 these changes are not reported.
 Limits on the bottom friction coefficient are not imposed if the user has elected to
 handle the bottom friction implicitly (see \autoref{subsec:ZDF_bfr_imp}).
+Limits on the top/bottom friction coefficient are not imposed if the user has elected to
+handle the friction implicitly (see \autoref{subsec:ZDF_drg_imp}).
 The number of potential breaches of the explicit stability criterion are still reported for information purposes.
 …
 %       Implicit Bottom Friction
 % -------------------------------------------------------------------------------------------------------------
+\subsection{Implicit bottom friction (\protect\np{ln\_bfrimp}\forcode{ = .true.})}
+\label{subsec:ZDF_bfr_imp}
+ \subsection[Implicit top/bottom friction (\forcode{ln_drgimp = .true.})]
+ {Implicit top/bottom friction (\protect\np{ln\_drgimp}\forcode{ = .true.})}
+ \label{subsec:ZDF_drg_imp}
 An optional implicit form of bottom friction has been implemented to improve model stability.
+We recommend this option for shelf sea and coastal ocean applications, especially for split-explicit time splitting.
+This option can be invoked by setting \np{ln\_bfrimp} to \forcode{.true.} in the \textit{nambfr} namelist.
+This option requires \np{ln\_zdfexp} to be \forcode{.false.} in the \textit{namzdf} namelist.
+This implementation is realised in \mdl{dynzdf\_imp} and \mdl{dynspg\_ts}. In \mdl{dynzdf\_imp},
+the bottom boundary condition is implemented implicitly.
+\[
+  % \label{eq:dynzdf_bfr}
+  \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{mbk}
+  = \binom{c_{b}^{u}u^{n+1}_{mbk}}{c_{b}^{v}v^{n+1}_{mbk}}
+\]
+where $mbk$ is the layer number of the bottom wet layer.
+Superscript $n+1$ means the velocity used in the friction formula is to be calculated, so, it is implicit.
+If split-explicit time splitting is used, care must be taken to avoid the double counting of the bottom friction in
+the 2-D barotropic momentum equations.
+As NEMO only updates the barotropic pressure gradient and Coriolis' forcing terms in the 2-D barotropic calculation,
+we need to remove the bottom friction induced by these two terms which has been included in the 3-D momentum trend
+and update it with the latest value.
+On the other hand, the bottom friction contributed by the other terms
+(\eg the advection term, viscosity term) has been included in the 3-D momentum equations and
+should not be added in the 2-D barotropic mode.
+The implementation of the implicit bottom friction in \mdl{dynspg\_ts} is done in two steps as the following:
+\[
+  % \label{eq:dynspg_ts_bfr1}
+  \frac{\textbf{U}_{med}-\textbf{U}^{m-1}}{2\Delta t}=-g\nabla\eta-f\textbf{k}\times\textbf{U}^{m}+c_{b}
+  \left(\textbf{U}_{med}-\textbf{U}^{m-1}\right)
+\]
+\[
+  \frac{\textbf{U}^{m+1}-\textbf{U}_{med}}{2\Delta t}=\textbf{T}+
+  \left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{U}^{'}\right)-
+\Delta t_{bc}c_{b}\left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{u}_{b}\right)
+\]
+where $\textbf{T}$ is the vertical integrated 3-D momentum trend.
+We assume the leap-frog time-stepping is used here.
+$\Delta t$ is the barotropic mode time step and $\Delta t_{bc}$ is the baroclinic mode time step.
+$c_{b}$ is the friction coefficient.
+$\eta$ is the sea surface level calculated in the barotropic loops while $\eta^{'}$ is the sea surface level used in
+the 3-D baroclinic mode.
+$\textbf{u}_{b}$ is the bottom layer horizontal velocity.
+% -------------------------------------------------------------------------------------------------------------
+%       Bottom Friction with split-explicit time splitting
+% -------------------------------------------------------------------------------------------------------------
+\subsection[Bottom friction w/ split-explicit time splitting (\protect\np{ln\_bfrimp})]
+            {Bottom friction with split-explicit time splitting (\protect\np{ln\_bfrimp})}
+\label{subsec:ZDF_bfr_ts}
+When calculating the momentum trend due to bottom friction in \mdl{dynbfr},
+the bottom velocity at the before time step is used.
+This velocity includes both the baroclinic and barotropic components which is appropriate when
+using either the explicit or filtered surface pressure gradient algorithms
+(\key{dynspg\_exp} or \key{dynspg\_flt}).
+Extra attention is required, however, when using split-explicit time stepping (\key{dynspg\_ts}).
+In this case the free surface equation is solved with a small time step \np{rn\_rdt}/\np{nn\_baro},
+while the three dimensional prognostic variables are solved with the longer time step of \np{rn\_rdt} seconds.
+The trend in the barotropic momentum due to bottom friction appropriate to this method is that given by
+the selected parameterisation (\ie linear or non-linear bottom friction) computed with
+the evolving velocities at each barotropic timestep.
+In the case of non-linear bottom friction, we have elected to partially linearise the problem by
+keeping the coefficients fixed throughout the barotropic time-stepping to those computed in
+\mdl{zdfbfr} using the now timestep.
+This decision allows an efficient use of the $c_b^{\vect{U}}$ coefficients to:
+We recommend this option for shelf sea and coastal ocean applications. %, especially for split-explicit time splitting.
+This option can be invoked by setting \np{ln\_drgimp} to \forcode{.true.} in the \textit{namdrg} namelist.
+%This option requires \np{ln\_zdfexp} to be \forcode{.false.} in the \textit{namzdf} namelist.
+This implementation is performed in \mdl{dynzdf} where the following boundary conditions are set while solving the fully implicit diffusion step:
+At the top (below an ice shelf cavity):
+\[
+  % \label{eq:dynzdf_drg_top}
+  \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{t}
+  = c_{t}^{\textbf{U}}\textbf{u}^{n+1}_{t}
+\]
+At the bottom (above the sea floor):
+\[
+  % \label{eq:dynzdf_drg_bot}
+  \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{b}
+  = c_{b}^{\textbf{U}}\textbf{u}^{n+1}_{b}
+\]
+where $t$ and $b$ refers to top and bottom layers respectively.
+Superscript $n+1$ means the velocity used in the friction formula is to be calculated, so it is implicit.
+% -------------------------------------------------------------------------------------------------------------
+%       Bottom Friction with split-explicit free surface
+% -------------------------------------------------------------------------------------------------------------
+ \subsection[Bottom friction with split-explicit free surface]
+ {Bottom friction with split-explicit free surface}
+ \label{subsec:ZDF_drg_ts}
+With split-explicit free surface, the sub-stepping of barotropic equations needs the knowledge of top/bottom stresses. An obvious way to satisfy this is to take them as constant over the course of the barotropic integration and equal to the value used to update the baroclinic momentum trend. Provided \np{ln\_drgimp}\forcode{= .false.} and a centred or \textit{leap-frog} like integration of barotropic equations is used (\ie \forcode{ln_bt_fw = .false.}, cf \autoref{subsec:DYN_spg_ts}), this does ensure that barotropic and baroclinic dynamics feel the same stresses during one leapfrog time step. However, if \np{ln\_drgimp}\forcode{= .true.},  stresses depend on the \textit{after} value of the velocities which themselves depend on the barotropic iteration result. This cyclic dependency makes difficult obtaining consistent stresses in 2d and 3d dynamics. Part of this mismatch is then removed when setting the final barotropic component of 3d velocities to the time splitting estimate. This last step can be seen as a necessary evil but should be minimized since it interferes with the adjustment to the boundary conditions.
+The strategy to handle top/bottom stresses with split-explicit free surface in \NEMO is as follows:
 \begin{enumerate}
+\item On entry to \rou{dyn\_spg\_ts}, remove the contribution of the before barotropic velocity to
+  the bottom friction component of the vertically integrated momentum trend.
+  Note the same stability check that is carried out on the bottom friction coefficient in \mdl{dynbfr} has to
+  be applied here to ensure that the trend removed matches that which was added in \mdl{dynbfr}.
+\item At each barotropic step, compute the contribution of the current barotropic velocity to
+  the trend due to bottom friction.
+  Add this contribution to the vertically integrated momentum trend.
+  This contribution is handled implicitly which eliminates the need to impose a stability criteria on
+  the values of the bottom friction coefficient within the barotropic loop.
+\end{enumerate}
+Note that the use of an implicit formulation within the barotropic loop for the bottom friction trend means that
+any limiting of the bottom friction coefficient in \mdl{dynbfr} does not adversely affect the solution when
+using split-explicit time splitting.
+This is because the major contribution to bottom friction is likely to come from the barotropic component which
+uses the unrestricted value of the coefficient.
+However, if the limiting is thought to be having a major effect
+(a more likely prospect in coastal and shelf seas applications) then
+the fully implicit form of the bottom friction should be used (see \autoref{subsec:ZDF_bfr_imp})
+which can be selected by setting \np{ln\_bfrimp} $=$ \forcode{.true.}.
+Otherwise, the implicit formulation takes the form:
+\[
+  % \label{eq:zdfbfr_implicitts}
+  \bar{U}^{t+ \rdt} = \; \left [ \bar{U}^{t-\rdt}\; + 2 \rdt\;RHS \right ] / \left [ 1 - 2 \rdt \;c_b^{u} / H_e \right ]
+\]
+where $\bar U$ is the barotropic velocity, $H_e$ is the full depth (including sea surface height),
+$c_b^u$ is the bottom friction coefficient as calculated in \rou{zdf\_bfr} and
+$RHS$ represents all the components to the vertically integrated momentum trend except for
+that due to bottom friction.
+% ================================================================
+% Tidal Mixing
+% ================================================================
+\section{Tidal mixing (\protect\key{zdftmx})}
+\label{sec:ZDF_tmx}
+%--------------------------------------------namzdf_tmx--------------------------------------------------
+\item To extend the stability of the barotropic sub-stepping, bottom stresses are refreshed at each sub-iteration. The baroclinic part of the flow entering the stresses is frozen at the initial time of the barotropic iteration. In case of non-linear friction, the drag coefficient is also constant.
+\item In case of an implicit drag, specific computations are performed in \mdl{dynzdf} which renders the overall scheme mixed explicit/implicit: the barotropic components of 3d velocities are removed before seeking for the implicit vertical diffusion result. Top/bottom stresses due to the barotropic components are explicitly accounted for thanks to the updated values of barotropic velocities. Then the implicit solution of 3d velocities is obtained. Lastly, the residual barotropic component is replaced by the time split estimate.
+\end{enumerate}
+Note that other strategies are possible, like considering vertical diffusion step in advance, \ie prior barotropic integration.
+% ================================================================
+% Internal wave-driven mixing
+% ================================================================
+\section[Internal wave-driven mixing (\forcode{ln_zdfiwm = .true.})]
+{Internal wave-driven mixing (\protect\np{ln\_zdfiwm}\forcode{ = .true.})}
+\label{subsec:ZDF_tmx_new}
+%--------------------------------------------namzdf_iwm------------------------------------------
+%
 %\nlst{namzdf_tmx}
+\nlst{namzdf_iwm}
 %--------------------------------------------------------------------------------------------------------------
-% -------------------------------------------------------------------------------------------------------------
-%        Bottom intensified tidal mixing
-% -------------------------------------------------------------------------------------------------------------
-\subsection{Bottom intensified tidal mixing}
-\label{subsec:ZDF_tmx_bottom}
-Options are defined through the  \ngn{namzdf\_tmx} namelist variables.
-The parameterization of tidal mixing follows the general formulation for the vertical eddy diffusivity proposed by
-\citet{St_Laurent_al_GRL02} and first introduced in an OGCM by \citep{Simmons_al_OM04}.
-In this formulation an additional vertical diffusivity resulting from internal tide breaking,
-$A^{vT}_{tides}$ is expressed as a function of $E(x,y)$,
-the energy transfer from barotropic tides to baroclinic tides:
-\begin{equation}
-  \label{eq:Ktides}
-  A^{vT}_{tides} =  q \,\Gamma \,\frac{ E(x,y) \, F(z) }{ \rho \, N^2 }
-\end{equation}
-where $\Gamma$ is the mixing efficiency, $N$ the Brunt-Vais\"{a}l\"{a} frequency (see \autoref{subsec:TRA_bn2}),
-$\rho$ the density, $q$ the tidal dissipation efficiency, and $F(z)$ the vertical structure function.
-The mixing efficiency of turbulence is set by $\Gamma$ (\np{rn\_me} namelist parameter) and
-is usually taken to be the canonical value of $\Gamma = 0.2$ (Osborn 1980).
-The tidal dissipation efficiency is given by the parameter $q$ (\np{rn\_tfe} namelist parameter)
-represents the part of the internal wave energy flux $E(x, y)$ that is dissipated locally,
-with the remaining $1-q$ radiating away as low mode internal waves and
-contributing to the background internal wave field.
-A value of $q=1/3$ is typically used \citet{St_Laurent_al_GRL02}.
-The vertical structure function $F(z)$ models the distribution of the turbulent mixing in the vertical.
-It is implemented as a simple exponential decaying upward away from the bottom,
-with a vertical scale of $h_o$ (\np{rn\_htmx} namelist parameter,
-with a typical value of $500\,m$) \citep{St_Laurent_Nash_DSR04},
-\[
-  % \label{eq:Fz}
-  F(i,j,k) = \frac{ e^{ -\frac{H+z}{h_o} } }{ h_o \left( 1- e^{ -\frac{H}{h_o} } \right) }
-\]
-and is normalized so that vertical integral over the water column is unity.
-The associated vertical viscosity is calculated from the vertical diffusivity assuming a Prandtl number of 1,
-\ie $A^{vm}_{tides}=A^{vT}_{tides}$.
-In the limit of $N \rightarrow 0$ (or becoming negative), the vertical diffusivity is capped at $300\,cm^2/s$ and
-impose a lower limit on $N^2$ of \np{rn\_n2min} usually set to $10^{-8} s^{-2}$.
-These bounds are usually rarely encountered.
-The internal wave energy map, $E(x, y)$ in \autoref{eq:Ktides}, is derived from a barotropic model of
-the tides utilizing a parameterization of the conversion of barotropic tidal energy into internal waves.
-The essential goal of the parameterization is to represent the momentum exchange between the barotropic tides and
-the unrepresented internal waves induced by the tidal flow over rough topography in a stratified ocean.
-In the current version of \NEMO, the map is built from the output of
-the barotropic global ocean tide model MOG2D-G \citep{Carrere_Lyard_GRL03}.
-This model provides the dissipation associated with internal wave energy for the M2 and K1 tides component
-(\autoref{fig:ZDF_M2_K1_tmx}).
-The S2 dissipation is simply approximated as being $1/4$ of the M2 one.
-The internal wave energy is thus : $E(x, y) = 1.25 E_{M2} + E_{K1}$.
-Its global mean value is $1.1$ TW,
-in agreement with independent estimates \citep{Egbert_Ray_Nat00, Egbert_Ray_JGR01}.
-%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}[!t]
-  \begin{center}
-    \includegraphics[width=0.90\textwidth]{Fig_ZDF_M2_K1_tmx}
-    \caption{
-      \protect\label{fig:ZDF_M2_K1_tmx}
-      (a) M2 and (b) K1 internal wave drag energy from \citet{Carrere_Lyard_GRL03} ($W/m^2$).
+    }
-  \end{center}
-\end{figure}
-%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-% -------------------------------------------------------------------------------------------------------------
-%        Indonesian area specific treatment
-% -------------------------------------------------------------------------------------------------------------
-\subsection{Indonesian area specific treatment (\protect\np{ln\_zdftmx\_itf})}
-\label{subsec:ZDF_tmx_itf}
-When the Indonesian Through Flow (ITF) area is included in the model domain,
-a specific treatment of tidal induced mixing in this area can be used.
-It is activated through the namelist logical \np{ln\_tmx\_itf}, and the user must provide an input NetCDF file,
-\ifile{mask\_itf}, which contains a mask array defining the ITF area where the specific treatment is applied.
-When \np{ln\_tmx\_itf}\forcode{ = .true.}, the two key parameters $q$ and $F(z)$ are adjusted following
-the parameterisation developed by \citet{Koch-Larrouy_al_GRL07}:
-First, the Indonesian archipelago is a complex geographic region with a series of
-large, deep, semi-enclosed basins connected via numerous narrow straits.
-Once generated, internal tides remain confined within this semi-enclosed area and hardly radiate away.
-Therefore all the internal tides energy is consumed within this area.
-So it is assumed that $q = 1$, \ie all the energy generated is available for mixing.
-Note that for test purposed, the ITF tidal dissipation efficiency is a namelist parameter (\np{rn\_tfe\_itf}).
-A value of $1$ or close to is this recommended for this parameter.
-Second, the vertical structure function, $F(z)$, is no more associated with a bottom intensification of the mixing,
-but with a maximum of energy available within the thermocline.
-\citet{Koch-Larrouy_al_GRL07} have suggested that the vertical distribution of
-the energy dissipation proportional to $N^2$ below the core of the thermocline and to $N$ above.
-The resulting $F(z)$ is:
-\[
-  % \label{eq:Fz_itf}
-  F(i,j,k) \sim     \left\{
-    \begin{aligned}
-      \frac{q\,\Gamma E(i,j) } {\rho N \, \int N     dz}    \qquad \text{when $\partial_z N < 0$} \\
-      \frac{q\,\Gamma E(i,j) } {\rho     \, \int N^2 dz}    \qquad \text{when $\partial_z N > 0$}
-    \end{aligned}
-  \right.
-\]
-Averaged over the ITF area, the resulting tidal mixing coefficient is $1.5\,cm^2/s$,
-which agrees with the independent estimates inferred from observations.
-Introduced in a regional OGCM, the parameterization improves the water mass characteristics in
-the different Indonesian seas, suggesting that the horizontal and vertical distributions of
-the mixing are adequately prescribed \citep{Koch-Larrouy_al_GRL07, Koch-Larrouy_al_OD08a, Koch-Larrouy_al_OD08b}.
-Note also that such a parameterisation has a significant impact on the behaviour of
-global coupled GCMs \citep{Koch-Larrouy_al_CD10}.
-% ================================================================
-% Internal wave-driven mixing
-% ================================================================
-\section{Internal wave-driven mixing (\protect\key{zdftmx\_new})}
-\label{sec:ZDF_tmx_new}
-%--------------------------------------------namzdf_tmx_new------------------------------------------
+%
-%\nlst{namzdf_tmx_new}
-%--------------------------------------------------------------------------------------------------------------
 The parameterization of mixing induced by breaking internal waves is a generalization of
 the approach originally proposed by \citet{St_Laurent_al_GRL02}.
+the approach originally proposed by \citet{st-laurent.simmons.ea_GRL02}.
 A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed,
 and the resulting diffusivity is obtained as
 …
 where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution of
 the energy available for mixing.
 If the \np{ln\_mevar} namelist parameter is set to false, the mixing efficiency is taken as constant and
 equal to 1/6 \citep{Osborn_JPO80}.
+If the \np{ln\_mevar} namelist parameter is set to \forcode{.false.}, the mixing efficiency is taken as constant and
+equal to 1/6 \citep{osborn_JPO80}.
 In the opposite (recommended) case, $R_f$ is instead a function of
 the turbulence intensity parameter $Re_b = \frac{ \epsilon}{\nu \, N^2}$,
 with $\nu$ the molecular viscosity of seawater, following the model of \cite{Bouffard_Boegman_DAO2013} and
 the implementation of \cite{de_lavergne_JPO2016_efficiency}.
+with $\nu$ the molecular viscosity of seawater, following the model of \cite{bouffard.boegman_DAO13} and
+the implementation of \cite{de-lavergne.madec.ea_JPO16}.
 Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when
 the mixing efficiency is constant.
 In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary
 as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice.
 This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014},
 is implemented as in \cite{de_lavergne_JPO2016_efficiency}.
+as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to \forcode{.true.}, a recommended choice.
+This parameterization of differential mixing, due to \cite{jackson.rehmann_JPO14},
+is implemented as in \cite{de-lavergne.madec.ea_JPO16}.
 The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$,
 is constructed from three static maps of column-integrated internal wave energy dissipation,
 $E_{cri}(i,j)$, $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures
+(de Lavergne et al., in prep):
+$E_{cri}(i,j)$, $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures:
 \begin{align*}
   F_{cri}(i,j,k) &\propto e^{-h_{ab} / h_{cri} }\\
   F_{pyc}(i,j,k) &\propto N^{n\_p}\\
+  F_{pyc}(i,j,k) &\propto N^{n_p}\\
   F_{bot}(i,j,k) &\propto N^2 \, e^{- h_{wkb} / h_{bot} }
 \end{align*}
 …
   h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz'  } \; ,
 \]
 The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_tmx\_new} namelist)
+The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_iwm} namelist)
 controls the stratification-dependence of the pycnocline-intensified dissipation.
 It can take values of 1 (recommended) or 2.
+It can take values of $1$ (recommended) or $2$.
 Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of
 the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps.
 $h_{cri}$ is related to the large-scale topography of the ocean (etopo2) and
 $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of
+the abyssal hill topography \citep{Goff_JGR2010} and the latitude.
+the abyssal hill topography \citep{goff_JGR10} and the latitude.
+%
+% Jc: input files names ?
+% ================================================================
+% surface wave-induced mixing
+% ================================================================
+\section[Surface wave-induced mixing (\forcode{ln_zdfswm = .true.})]
+{Surface wave-induced mixing (\protect\np{ln\_zdfswm}\forcode{ = .true.})}
+\label{subsec:ZDF_swm}
+TBC ...
+% ================================================================
+% Adaptive-implicit vertical advection
+% ================================================================
+\section[Adaptive-implicit vertical advection (\forcode{ln_zad_Aimp = .true.})]
+{Adaptive-implicit vertical advection(\protect\np{ln\_zad\_Aimp}\forcode{ = .true.})}
+\label{subsec:ZDF_aimp}
+This refers to \citep{shchepetkin_OM15}.
+TBC ...
 % ================================================================

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_conservation.tex

-                      r10442
+                      r11263
 horizontal kinetic energy and/or potential enstrophy of horizontally non-divergent flow,
 and variance of temperature and salinity will be conserved in the absence of dissipative effects and forcing.
 \citet{Arakawa1966} has first pointed out the advantage of this approach.
+\citet{arakawa_JCP66} has first pointed out the advantage of this approach.
 He showed that if integral constraints on energy are maintained,
 the computation will be free of the troublesome "non linear" instability originally pointed out by
 \citet{Phillips1959}.
+\citet{phillips_TAMS59}.
 A consistent formulation of the energetic properties is also extremely important in carrying out
 long-term numerical simulations for an oceanographic model.
 Such a formulation avoids systematic errors that accumulate with time \citep{Bryan1997}.
+Such a formulation avoids systematic errors that accumulate with time \citep{bryan_JCP97}.
 The general philosophy of OPA which has led to the discrete formulation presented in {\S}II.2 and II.3 is to
 …
 Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required.
 In that case, and in that case only, the advective scheme used for passive tracer is a flux correction scheme
 \citep{Marti1992, Levy1996, Levy1998}.
+\citep{Marti1992?, Levy1996?, Levy1998?}.
 % -------------------------------------------------------------------------------------------------------------
 …
   % \label{eq:vor_vorticity}
   \int_D {{\textbf {k}}\cdot \frac{1}{e_3 }\nabla \times \left( {\varsigma
         \;{\rm {\bf k}}\times {\textbf {U}}_h } \right)\;dv} =0
+        \;{\mathrm {\mathbf k}}\times {\textbf {U}}_h } \right)\;dv} =0
 \]
 …
 \[
   % \label{eq:dynldf_dyn}
   \int\limits_D {\frac{1}{e_3 }{\rm {\bf k}}\cdot \nabla \times \left[ {\nabla
+  \int\limits_D {\frac{1}{e_3 }{\mathrm {\mathbf k}}\cdot \nabla \times \left[ {\nabla
         _h \left( {A^{lm}\;\chi } \right)-\nabla _h \times \left( {A^{lm}\;\zeta
             \;{\rm {\bf k}}} \right)} \right]\;dv} =0
+            \;{\mathrm {\mathbf k}}} \right)} \right]\;dv} =0
 \]
 …
   % \label{eq:dynldf_div}
   \int\limits_D {\nabla _h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi }
         \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)}
+        \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)}
     \right]\;dv} =0
 \]
 …
 \[
   % \label{eq:dynldf_curl}
   \int_D {{\rm {\bf U}}_h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi }
         \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)}
+  \int_D {{\mathrm {\mathbf U}}_h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi }
+        \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)}
     \right]\;dv} \leqslant 0
 \]
 …
 \[
   % \label{eq:dynldf_curl2}
   \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\zeta \;{\rm {\bf k}}\cdot
+  \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\zeta \;{\mathrm {\mathbf k}}\cdot
     \nabla \times \left[ {\nabla _h \left( {A^{lm}\;\chi } \right)-\nabla _h
         \times \left( {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)} \right]\;dv}
+        \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} \right]\;dv}
   \leqslant 0
 \]
 …
   \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\chi \;\nabla _h \cdot \left[
       {\nabla _h \left( {A^{lm}\;\chi } \right)-\nabla _h \times \left(
           {A^{lm}\;\zeta \;{\rm {\bf k}}} \right)} \right]\;dv} \leqslant 0
+          {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} \right]\;dv} \leqslant 0
 \]
 …
   % \label{eq:dynzdf_vor}
   \begin{aligned}
     & \int_D {\frac{1}{e_3 }{\rm {\bf k}}\cdot \nabla \times \left( {\frac{1}{e_3
           }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm
                   {\bf U}}_h }{\partial k}} \right)} \right)\;dv} =0 \\
     & \int_D {\zeta \,{\rm {\bf k}}\cdot \nabla \times \left( {\frac{1}{e_3
           }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm
                   {\bf U}}_h }{\partial k}} \right)} \right)\;dv} \leq 0 \\
+    & \int_D {\frac{1}{e_3 }{\mathrm {\mathbf k}}\cdot \nabla \times \left( {\frac{1}{e_3
+          }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm
+                  {\mathbf U}}_h }{\partial k}} \right)} \right)\;dv} =0 \\
+    & \int_D {\zeta \,{\mathrm {\mathbf k}}\cdot \nabla \times \left( {\frac{1}{e_3
+          }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm
+                  {\mathbf U}}_h }{\partial k}} \right)} \right)\;dv} \leq 0 \\
   \end{aligned}
 \]
 …
   \begin{aligned}
     &\int_D {\nabla \cdot \left( {\frac{1}{e_3 }\frac{\partial }{\partial
             k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm {\bf U}}_h }{\partial k}}
+            k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}}
           \right)} \right)\;dv} =0 \\
     & \int_D {\chi \;\nabla \cdot \left( {\frac{1}{e_3 }\frac{\partial }{\partial
             k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\rm {\bf U}}_h }{\partial k}}
+            k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}}
           \right)} \right)\;dv} \leq 0 \\
   \end{aligned}

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_misc.tex

-                      r10601
+                      r11263
 \begin{figure}[!tbp]
   \begin{center}
     \includegraphics[width=0.80\textwidth]{Fig_Gibraltar}
     \includegraphics[width=0.80\textwidth]{Fig_Gibraltar2}
+    \includegraphics[width=\textwidth]{Fig_Gibraltar}
+    \includegraphics[width=\textwidth]{Fig_Gibraltar2}
     \caption{
       \protect\label{fig:MISC_strait_hand}
 …
 \begin{figure}[!tbp]
   \begin{center}
     \includegraphics[width=1.0\textwidth]{Fig_closea_mask_example}
+    \includegraphics[width=\textwidth]{Fig_closea_mask_example}
     \caption{
       \protect\label{fig:closea_mask_example}
 …
 % Closed seas
 % ================================================================
+\section{Closed seas (\protect\mdl{closea})}
+\section[Closed seas (\textit{closea.F90})]
+{Closed seas (\protect\mdl{closea})}
 \label{sec:MISC_closea}
 …
 \begin{enumerate}
 \item{{\bf No ``closea\_mask'' field is included in domain configuration
+\item{{\bfseries No ``closea\_mask'' field is included in domain configuration
   file.} In this case the closea module does nothing.}
 \item{{\bf A field called closea\_mask is included in the domain
+\item{{\bfseries A field called closea\_mask is included in the domain
 configuration file and ln\_closea=.false. in namelist namcfg.} In this
 case the inland seas defined by the closea\_mask field are filled in
 …
 closea\_mask that is nonzero is set to be a land point.}
 \item{{\bf A field called closea\_mask is included in the domain
+\item{{\bfseries A field called closea\_mask is included in the domain
 configuration file and ln\_closea=.true. in namelist namcfg.} Each
 inland sea or group of inland seas is set to a positive integer value
 …
 closea\_mask is zero).}
 \item{{\bf Fields called closea\_mask and closea\_mask\_rnf are
+\item{{\bfseries Fields called closea\_mask and closea\_mask\_rnf are
 included in the domain configuration file and ln\_closea=.true. in
 namelist namcfg.} This option works as for option 3, except that if
 …
 ocean.}
 \item{{\bf Fields called closea\_mask and closea\_mask\_emp are
+\item{{\bfseries Fields called closea\_mask and closea\_mask\_emp are
 included in the domain configuration file and ln\_closea=.true. in
 namelist namcfg.} This option works the same as option 4 except that
 …
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_LBC_zoom}
+    \includegraphics[width=\textwidth]{Fig_LBC_zoom}
     \caption{
       \protect\label{fig:LBC_zoom}
 …
 % Accuracy and Reproducibility
 % ================================================================
+\section{Accuracy and reproducibility (\protect\mdl{lib\_fortran})}
+\section[Accuracy and reproducibility (\textit{lib\_fortran.F90})]
+{Accuracy and reproducibility (\protect\mdl{lib\_fortran})}
 \label{sec:MISC_fortran}
+\subsection{Issues with intrinsinc SIGN function (\protect\key{nosignedzero})}
+\subsection[Issues with intrinsinc SIGN function (\texttt{\textbf{key\_nosignedzero}})]
+{Issues with intrinsinc SIGN function (\protect\key{nosignedzero})}
 \label{subsec:MISC_sign}
 …
 and their propagation and accumulation cause uncertainty in final simulation reproducibility on
 different numbers of processors.
 To avoid so, based on \citet{He_Ding_JSC01} review of different technics,
+To avoid so, based on \citet{he.ding_JS01} review of different technics,
 we use a so called self-compensated summation method.
 The idea is to estimate the roundoff error, store it in a buffer, and then add it back in the next addition.
 …
 This alternative method should give identical results to the default \textsc{ALLGATHER} method and
 is recommended for large values of \np{jpni}.
 The new method is activated by setting \np{ln\_nnogather} to be true ({\bf nammpp}).
+The new method is activated by setting \np{ln\_nnogather} to be true (\ngn{nammpp}).
 The reproducibility of results using the two methods should be confirmed for each new,
 non-reference configuration.

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_model_basics.tex

-                      r10544
+                      r11263
 \begin{figure}[!ht]
   \begin{center}
     \includegraphics[]{Fig_I_ocean_bc}
+    \includegraphics[width=\textwidth]{Fig_I_ocean_bc}
     \caption{
       \protect\label{fig:ocean_bc}
 …
 If further, an approximative conservation of heat and salt contents is sufficient for the problem solved,
 then it is sufficient to solve a linearized version of \autoref{eq:PE_ssh},
 which still allows to take into account freshwater fluxes applied at the ocean surface \citep{Roullet_Madec_JGR00}.
+which still allows to take into account freshwater fluxes applied at the ocean surface \citep{roullet.madec_JGR00}.
 Nevertheless, with the linearization, an exact conservation of heat and salt contents is lost.
 The filtering of EGWs in models with a free surface is usually a matter of discretisation of
 the temporal derivatives,
 using a split-explicit method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92} or
 the implicit scheme \citep{Dukowicz1994} or
 the addition of a filtering force in the momentum equation \citep{Roullet_Madec_JGR00}.
+using a split-explicit method \citep{killworth.webb.ea_JPO91, zhang.endoh_JGR92} or
+the implicit scheme \citep{dukowicz.smith_JGR94} or
+the addition of a filtering force in the momentum equation \citep{roullet.madec_JGR00}.
 With the present release, \NEMO offers the choice between
 an explicit free surface (see \autoref{subsec:DYN_spg_exp}) or
 a split-explicit scheme strongly inspired the one proposed by \citet{Shchepetkin_McWilliams_OM05}
+a split-explicit scheme strongly inspired the one proposed by \citet{shchepetkin.mcwilliams_OM05}
 (see \autoref{subsec:DYN_spg_ts}).
 …
 cannot be easily treated in a global model without filtering.
 A solution consists of introducing an appropriate coordinate transformation that
 shifts the singular point onto land \citep{Madec_Imbard_CD96, Murray_JCP96}.
+shifts the singular point onto land \citep{madec.imbard_CD96, murray_JCP96}.
 As a consequence, it is important to solve the primitive equations in various curvilinear coordinate systems.
 An efficient way of introducing an appropriate coordinate transform can be found when using a tensorial formalism.
 …
 Ocean modellers mainly use three-dimensional orthogonal grids on the sphere (spherical earth approximation),
 with preservation of the local vertical. Here we give the simplified equations for this particular case.
 The general case is detailed by \citet{Eiseman1980} in their survey of the conservation laws of fluid dynamics.
+The general case is detailed by \citet{eiseman.stone_SR80} in their survey of the conservation laws of fluid dynamics.
 Let $(i,j,k)$ be a set of orthogonal curvilinear coordinates on
 …
 \begin{figure}[!tb]
   \begin{center}
     \includegraphics[]{Fig_I_earth_referential}
+    \includegraphics[width=\textwidth]{Fig_I_earth_referential}
     \caption{
       \protect\label{fig:referential}
 …
 In order to satisfy two or more constrains one can even be tempted to mixed these coordinate systems, as in
 HYCOM (mixture of $z$-coordinate at the surface, isopycnic coordinate in the ocean interior and $\sigma$ at
 the ocean bottom) \citep{Chassignet_al_JPO03} or
+the ocean bottom) \citep{chassignet.smith.ea_JPO03} or
 OPA (mixture of $z$-coordinate in vicinity the surface and steep topography areas and $\sigma$-coordinate elsewhere)
 \citep{Madec_al_JPO96} among others.
+\citep{madec.delecluse.ea_JPO96} among others.
 In fact one is totally free to choose any space and time vertical coordinate by
 …
 the $(i,j,s,t)$ generalised coordinate system with $s$ depending on the other three variables through
 \autoref{eq:PE_s}.
 This so-called \textit{generalised vertical coordinate} \citep{Kasahara_MWR74} is in fact
+This so-called \textit{generalised vertical coordinate} \citep{kasahara_MWR74} is in fact
 an Arbitrary Lagrangian--Eulerian (ALE) coordinate.
 Indeed, choosing an expression for $s$ is an arbitrary choice that determines
 which part of the vertical velocity (defined from a fixed referential) will cross the levels (Eulerian part) and
 which part will be used to move them (Lagrangian part).
 The coordinate is also sometime referenced as an adaptive coordinate \citep{Hofmeister_al_OM09},
+The coordinate is also sometime referenced as an adaptive coordinate \citep{hofmeister.burchard.ea_OM10},
 since the coordinate system is adapted in the course of the simulation.
 Its most often used implementation is via an ALE algorithm,
 in which a pure lagrangian step is followed by regridding and remapping steps,
 the later step implicitly embedding the vertical advection
 \citep{Hirt_al_JCP74, Chassignet_al_JPO03, White_al_JCP09}.
 Here we follow the \citep{Kasahara_MWR74} strategy:
+\citep{hirt.amsden.ea_JCP74, chassignet.smith.ea_JPO03, white.adcroft.ea_JCP09}.
+Here we follow the \citep{kasahara_MWR74} strategy:
 a regridding step (an update of the vertical coordinate) followed by an eulerian step with
 an explicit computation of vertical advection relative to the moving s-surfaces.
 …
 \begin{figure}[!b]
   \begin{center}
     \includegraphics[]{Fig_z_zstar}
+    \includegraphics[width=\textwidth]{Fig_z_zstar}
     \caption{
       \protect\label{fig:z_zstar}
 …
       (b) $z$-coordinate in non-linear free surface case ;
       (c) re-scaled height coordinate
       (become popular as the \zstar-coordinate \citep{Adcroft_Campin_OM04}).
+      (become popular as the \zstar-coordinate \citep{adcroft.campin_OM04}).
+    }
   \end{center}
 …
 In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account.
 These coordinates systems is presented in a report \citep{Levier2007} available on the \NEMO web site.
+These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site.
 The \zstar coordinate approach is an unapproximated, non-linear free surface implementation which allows one to
 deal with large amplitude free-surface variations relative to the vertical resolution \citep{Adcroft_Campin_OM04}.
+deal with large amplitude free-surface variations relative to the vertical resolution \citep{adcroft.campin_OM04}.
 In the \zstar formulation,
 the variation of the column thickness due to sea-surface undulations is not concentrated in the surface level,
 …
 The quasi -horizontal nature of the coordinate surfaces also facilitates the implementation of
 neutral physics parameterizations in \zstar models using the same techniques as in $z$-models
 (see Chapters 13-16 of \cite{Griffies_Bk04}) for a discussion of neutral physics in $z$-models,
+(see Chapters 13-16 of \cite{griffies_bk04}) for a discussion of neutral physics in $z$-models,
 as well as \autoref{sec:LDF_slp} in this document for treatment in \NEMO).
 …
 The response to such a velocity field often leads to numerical dispersion effects.
 One solution to strongly reduce this error is to use a partial step representation of bottom topography instead of
 a full step one \cite{Pacanowski_Gnanadesikan_MWR98}.
+a full step one \cite{pacanowski.gnanadesikan_MWR98}.
 Another solution is to introduce a terrain-following coordinate system (hereafter $s$-coordinate).
 …
 introduces a truncation error that is not present in a $z$-model.
 In the special case of a $\sigma$-coordinate (i.e. a depth-normalised coordinate system $\sigma = z/H$),
 \citet{Haney1991} and \citet{Beckmann1993} have given estimates of the magnitude of this truncation error.
+\citet{haney_JPO91} and \citet{beckmann.haidvogel_JPO93} have given estimates of the magnitude of this truncation error.
 It depends on topographic slope, stratification, horizontal and vertical resolution, the equation of state,
 and the finite difference scheme.
 …
 The large-scale slopes require high horizontal resolution, and the computational cost becomes prohibitive.
 This problem can be at least partially overcome by mixing $s$-coordinate and
 step-like representation of bottom topography \citep{Gerdes1993a,Gerdes1993b,Madec_al_JPO96}.
+step-like representation of bottom topography \citep{gerdes_JGR93*a,gerdes_JGR93*b,madec.delecluse.ea_JPO96}.
 However, the definition of the model domain vertical coordinate becomes then a non-trivial thing for
 a realistic bottom topography:
 …
 In contrast, the ocean will stay at rest in a $z$-model.
 As for the truncation error, the problem can be reduced by introducing the terrain-following coordinate below
 the strongly stratified portion of the water column (\ie the main thermocline) \citep{Madec_al_JPO96}.
+the strongly stratified portion of the water column (\ie the main thermocline) \citep{madec.delecluse.ea_JPO96}.
 An alternate solution consists of rotating the lateral diffusive tensor to geopotential or to isoneutral surfaces
 (see \autoref{subsec:PE_ldf}).
 …
 strongly exceeding the stability limit of such a operator when it is discretized (see \autoref{chap:LDF}).
 The $s$-coordinates introduced here \citep{Lott_al_OM90,Madec_al_JPO96} differ mainly in two aspects from
+The $s$-coordinates introduced here \citep{lott.madec.ea_OM90,madec.delecluse.ea_JPO96} differ mainly in two aspects from
 similar models:
 it allows a representation of bottom topography with mixed full or partial step-like/terrain following topography;
 …
 \label{subsec:PE_zco_tilde}
 The \ztilde -coordinate has been developed by \citet{Leclair_Madec_OM11}.
+The \ztilde -coordinate has been developed by \citet{leclair.madec_OM11}.
 It is available in \NEMO since the version 3.4.
 Nevertheless, it is currently not robust enough to be used in all possible configurations.
 …
 The resulting lateral diffusive and dissipative operators are of second order.
 Observations show that lateral mixing induced by mesoscale turbulence tends to be along isopycnal surfaces
 (or more precisely neutral surfaces \cite{McDougall1987}) rather than across them.
+(or more precisely neutral surfaces \cite{mcdougall_JPO87}) rather than across them.
 As the slope of neutral surfaces is small in the ocean, a common approximation is to assume that
 the `lateral' direction is the horizontal, \ie the lateral mixing is performed along geopotential surfaces.
 …
 both horizontal and isoneutral operators have no effect on mean (\ie large scale) potential energy whereas
 potential energy is a main source of turbulence (through baroclinic instabilities).
 \citet{Gent1990} have proposed a parameterisation of mesoscale eddy-induced turbulence which
+\citet{gent.mcwilliams_JPO90} have proposed a parameterisation of mesoscale eddy-induced turbulence which
 associates an eddy-induced velocity to the isoneutral diffusion.
 Its mean effect is to reduce the mean potential energy of the ocean.
 …
 There are not all available in \NEMO. For active tracers (temperature and salinity) the main ones are:
 Laplacian and bilaplacian operators acting along geopotential or iso-neutral surfaces,
 \citet{Gent1990} parameterisation, and various slightly diffusive advection schemes.
+\citet{gent.mcwilliams_JPO90} parameterisation, and various slightly diffusive advection schemes.
 For momentum, the main ones are: Laplacian and bilaplacian operators acting along geopotential surfaces,
 and UBS advection schemes when flux form is chosen for the momentum advection.
 …
 the rotation between geopotential and $s$-surfaces,
 while it is only an approximation for the rotation between isoneutral and $z$- or $s$-surfaces.
 Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{Cox1987}.
+Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{cox_OM87}.
 First, the horizontal contribution of the dianeutral mixing is neglected since the ratio between iso and
 dia-neutral diffusive coefficients is known to be several orders of magnitude smaller than unity.
 …
 \subsubsection{Eddy induced velocity}
 When the \textit{eddy induced velocity} parametrisation (eiv) \citep{Gent1990} is used,
+When the \textit{eddy induced velocity} parametrisation (eiv) \citep{gent.mcwilliams_JPO90} is used,
 an additional tracer advection is introduced in combination with the isoneutral diffusion of tracers:
 \[
 …
 \ie on a $f$- or $\beta$-plane, not on the sphere.
 It is also a very good approximation in vicinity of the Equator in
 a geographical coordinate system \citep{Lengaigne_al_JGR03}.
+a geographical coordinate system \citep{lengaigne.madec.ea_JGR03}.
 \subsubsection{lateral bilaplacian momentum diffusive operator}

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

-                      r10544
+                      r11263
 In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account.
 These coordinates systems is presented in a report \citep{Levier2007} available on the \NEMO web site.
+These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site.
 \colorbox{yellow}{  end of to be updated}
 …
 % Surface Pressure Gradient and Sea Surface Height
 % ================================================================
+\section{Surface pressure gradient and sea surface heigth (\protect\mdl{dynspg})}
+\section[Surface pressure gradient and sea surface heigth (\textit{dynspg.F90})]
+{Surface pressure gradient and sea surface heigth (\protect\mdl{dynspg})}
 \label{sec:DYN_hpg_spg}
 %-----------------------------------------nam_dynspg----------------------------------------------------
 …
 which imposes a very small time step when an explicit time stepping is used.
 Two methods are proposed to allow a longer time step for the three-dimensional equations:
 the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt}),
+the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt?}),
 and the split-explicit free surface described below.
 The extra term introduced in the filtered method is calculated implicitly,
 …
 % Explicit
 %-------------------------------------------------------------
+\subsubsection{Explicit (\protect\key{dynspg\_exp})}
+\subsubsection[Explicit (\texttt{\textbf{key\_dynspg\_exp}})]
+{Explicit (\protect\key{dynspg\_exp})}
 \label{subsec:DYN_spg_exp}
 …
 % Split-explicit time-stepping
 %-------------------------------------------------------------
+\subsubsection{Split-explicit time-stepping (\protect\key{dynspg\_ts})}
+\subsubsection[Split-explicit time-stepping (\texttt{\textbf{key\_dynspg\_ts}})]
+{Split-explicit time-stepping (\protect\key{dynspg\_ts})}
 \label{subsec:DYN_spg_ts}
 %--------------------------------------------namdom----------------------------------------------------
 …
 \nlst{namdom}
 %--------------------------------------------------------------------------------------------------------------
 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004}.
+The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004?}.
 The general idea is to solve the free surface equation with a small time step,
 while the three dimensional prognostic variables are solved with a longer time step that
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[width=0.90\textwidth]{Fig_DYN_dynspg_ts}
+    \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts}
     \caption{
       \protect\label{fig:DYN_dynspg_ts}
       Schematic of the split-explicit time stepping scheme for the barotropic and baroclinic modes,
       after \citet{Griffies2004}.
+      after \citet{Griffies2004?}.
       Time increases to the right.
       Baroclinic time steps are denoted by $t-\Delta t$, $t, t+\Delta t$, and $t+2\Delta t$.
 …
 The split-explicit formulation has a damping effect on external gravity waves,
 which is weaker than the filtered free surface but still significant as shown by \citet{Levier2007} in
+which is weaker than the filtered free surface but still significant as shown by \citet{levier.treguier.ea_rpt07} in
 the case of an analytical barotropic Kelvin wave.
 …
 % Filtered formulation
 %-------------------------------------------------------------
+\subsubsection{Filtered formulation (\protect\key{dynspg\_flt})}
+\subsubsection[Filtered formulation (\texttt{\textbf{key\_dynspg\_flt}})]
+{Filtered formulation (\protect\key{dynspg\_flt})}
 \label{subsec:DYN_spg_flt}
 The filtered formulation follows the \citet{Roullet2000} implementation.
+The filtered formulation follows the \citet{Roullet2000?} implementation.
 The extra term introduced in the equations (see {\S}I.2.2) is solved implicitly.
 The elliptic solvers available in the code are documented in \autoref{chap:MISC}.
 The amplitude of the extra term is given by the namelist variable \np{rnu}.
 The default value is 1, as recommended by \citet{Roullet2000}
+The default value is 1, as recommended by \citet{Roullet2000?}
 \colorbox{red}{\np{rnu}\forcode{ = 1} to be suppressed from namelist !}
 …
 % Non-linear free surface formulation
 %-------------------------------------------------------------
+\subsection{Non-linear free surface formulation (\protect\key{vvl})}
+\subsection[Non-linear free surface formulation (\texttt{\textbf{key\_vvl}})]
+{Non-linear free surface formulation (\protect\key{vvl})}
 \label{subsec:DYN_spg_vvl}
 In the non-linear free surface formulation, the variations of volume are fully taken into account.
 This option is presented in a report \citep{Levier2007} available on the NEMO web site.
+This option is presented in a report \citep{levier.treguier.ea_rpt07} available on the NEMO web site.
 The three time-stepping methods (explicit, split-explicit and filtered) are the same as in
 \autoref{DYN_spg_linear} except that the ocean depth is now time-dependent.

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_time_domain.tex

-                      r10501
+                      r11263
 % Missing things:
 %  - daymod: definition of the time domain (nit000, nitend andd the calendar)
+%  - 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,
 …
 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.
 …
 $\rdt$ 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 step depending on the physics with which it is associated.
 The choice of the time step used for this evaluation is discussed below as well as
+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.
 …
 is usually not the variable at the after time step;
 but rather it is used to store the time derivative (RHS in \autoref{eq:STP}) prior to time-stepping the equation.
+Generally, the time stepping is performed once at each time step in the \mdl{tranxt} and \mdl{dynnxt} modules,
+except when using implicit vertical diffusion or calculating sea surface height in which
+case time-splitting options are used.
+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.
 % -------------------------------------------------------------------------------------------------------------
 …
 The time stepping used for processes other than diffusion is the well-known leapfrog scheme
 \citep{Mesinger_Arakawa_Bk76}.
+\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:STP} is evaluated at time step $t$, the now time step.
 …
 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},
+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}
 …
 where the subscript $F$ denotes filtered values and $\gamma$ is the Asselin coefficient.
 $\gamma$ is initialized as \np{rn\_atfp} (namelist parameter).
 Its default value is \np{rn\_atfp}~\forcode{= 10.e-3} (see \autoref{sec:STP_mLF}),
 causing only a weak dissipation of high frequency motions (\citep{Farge1987}).
+Its default value is \np{rn\_atfp}\forcode{ = 10.e-3} (see \autoref{sec:STP_mLF}),
+causing only a weak dissipation of high frequency motions (\citep{farge-coulombier_phd87}).
 The addition of a time filter degrades the accuracy of the calculation from second to first order.
 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.
+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 momentum and tracer equations, LF-RA avoids implicit numerical diffusion:
 …
 The leapfrog differencing scheme is unsuitable for the representation of diffusion and damping processes.
 For a tendancy $D_x$, representing a diffusion term or a restoring term to a tracer climatology
+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:STP_euler_stability}
 …
 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.
+Two solutions are available in \NEMO to overcome the stability constraint:
+$(a)$ a forward time differencing scheme using a time splitting technique (\np{ln\_zdfexp}~\forcode{= .true.}) or
+$(b)$ a backward (or implicit) time differencing scheme                   (\np{ln\_zdfexp}~\forcode{= .false.}).
+In $(a)$, the master time step $\Delta$t is cut into $N$ fractional time steps so that
+the stability criterion is reduced by a factor of $N$.
+The computation is performed as follows:
+\begin{alignat*}{2}
+  % \label{eq:STP_ts}
+  &x_\ast^{t - \rdt}                      &= &x^{t - \rdt} \\
+  &x_\ast^{t - \rdt + L \frac{2 \rdt}{N}} &=   &x_\ast ^{t - \rdt + (L - 1) \frac{2 \rdt}{N}}
+                                             + \frac{2 \rdt}{N} \; DF^{t - \rdt + (L - 1) \frac{2 \rdt}{N}}
+  \quad \text{for $L = 1$ to $N$} \\
+  &x^{t + \rdt}                           &= &x_\ast^{t + \rdt}
+\end{alignat*}
+with DF a vertical diffusion term.
+The number of fractional time steps, $N$, is given by setting \np{nn\_zdfexp}, (namelist parameter).
+The scheme $(b)$ is unconditionally stable but diffusive. It 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:STP_imp}
 …
 %%gm
+This scheme is rather time consuming since it requires a matrix inversion,
+but it becomes attractive since a value of 3 or more is needed for N in the forward time differencing scheme.
+For example, the finite difference approximation of the temperature equation is:
+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:STP_imp_zdf}
 …
 $c(k)$ 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{Richtmyer1967}).
+(see for example \citet{richtmyer.morton_bk67}).
 % -------------------------------------------------------------------------------------------------------------
 …
 \label{sec:STP_spg_ts}
+===>>>>  TO BE written....  :-)
+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{ln\_dynspg\_exp}\forcode{ = .true.}).
+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{ln\_dynspg\_ts}\forcode{ = .true.}) 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: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]
   \begin{center}
     \includegraphics[]{Fig_TimeStepping_flowchart}
+    \includegraphics[width=\textwidth]{Fig_TimeStepping_flowchart_v4}
     \caption{
       \protect\label{fig:TimeStep_flowchart}
+      Sketch of the leapfrog time stepping sequence in \NEMO from \citet{Leclair_Madec_OM09}.
+      The use of a semi -implicit computation of the hydrostatic pressure gradient requires the tracer equation to
+      be stepped forward prior to the momentum equation.
+      The need for knowledge of the vertical scale factor (here denoted as $h$) requires the sea surface height and
+      the continuity equation to be stepped forward prior to the computation of the tracer equation.
+      Note that the method for the evaluation of the surface pressure gradient $\nabla p_s$ is not presented here
+      (see \autoref{sec:DYN_spg}).
+      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. Note the use of time integrated fluxes issued from the barotropic loop  in subsequent calculations
+       of tracer advection and in the continuity equation. Details about the time-splitting scheme can be found
+       in \autoref{subsec:DYN_spg_ts}.
+    }
   \end{center}
 …
 \label{sec:STP_mLF}
 Significant changes have been introduced by \cite{Leclair_Madec_OM09} in the LF-RA scheme in order to
+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.
 …
 The change in the forcing formulation given by \autoref{eq:STP_forcing} (see \autoref{fig: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 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 respects.
+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 be removed by adding a new term in the filter
+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:STP_RA} compared to \autoref{eq:STP_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}.
+the modified formulation becomes conservative \citep{leclair.madec_OM09}.
 Second, the LF-RA becomes a truly quasi -second order scheme.
 Indeed, \autoref{eq:STP_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}),
 the two other main sources of time step divergence,
+(\autoref{subsec:ZDF_evd}) and of the TKE physics (\autoref{subsec:ZDF_tke_ene})
+(the two other main sources of time step divergence),
 allows a reduction by two orders of magnitude of the Asselin filter parameter.
 …
 $Q^{t + \rdt / 2}$ is the forcing applied over the $[t,t + \rdt]$ time interval.
 This and the change in the time filter, \autoref{eq:STP_RA},
 allows an exact evaluation of the contribution due to the forcing term between any two time steps,
+allows for an exact evaluation of the contribution due to the forcing term between any two time steps,
 even if separated by only $\rdt$ since the time filter is no longer applied to the forcing term.
 …
 \begin{figure}[!t]
   \begin{center}
     \includegraphics[]{Fig_MLF_forcing}
+    \includegraphics[width=\textwidth]{Fig_MLF_forcing}
     \caption{
       \protect\label{fig:MLF_forcing}
 …
 This is done simply by keeping the leapfrog environment (\ie the \autoref{eq:STP} three level time stepping) but
 setting all $x^0$ (\textit{before}) and $x^1$ (\textit{now}) fields equal at the first time step and
 using half the value of $\rdt$.
+using half the value of a leapfrog time step ($2 \rdt$).
 It is also possible to restart from a previous computation, by using a restart file.
 …
 This requires saving two time levels and many auxiliary data in the restart files in machine precision.
+Note that when a semi -implicit scheme is used to evaluate the hydrostatic pressure gradient
+(see \autoref{subsec:DYN_hpg_imp}), an extra three-dimensional field has to
+be added to the restart file to ensure an exact restartability.
+This is done optionally via the  \np{nn\_dynhpg\_rst} namelist parameter,
+so that the size of the restart file can be reduced when restartability is not a key issue
+(operational oceanography or in ensemble simulations for seasonal forecasting).
+Note the size of the time step used, $\rdt$, is also saved in the restart file.
+When restarting, if the the time step has been changed, a restart using an Euler time stepping scheme is imposed.
+Options are defined through the  \ngn{namrun} namelist variables.
+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{nn\_euler}\forcode{=0}. Other options to control the time integration of the model
+are defined through the  \ngn{namrun} namelist variables.
 %%%
 \gmcomment{

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/introduction.tex

-                      r10544
+                      r11263
 The ocean component of \NEMO has been developed from the legacy of the OPA model, release 8.2,
 described in \citet{Madec1998}.
+described in \citet{madec.delecluse.ea_NPM98}.
 This model has been used for a wide range of applications, both regional or global, as a forced ocean model and
 as a model coupled with the sea-ice and/or the atmosphere.
 …
 Within the \NEMO system the ocean model is interactively coupled with a sea ice model (SI$^3$) and
 a biogeochemistry model (PISCES).
 Interactive coupling to Atmospheric models is possible via the OASIS coupler \citep{OASIS2006}.
+Interactive coupling to Atmospheric models is possible via the \href{https://portal.enes.org/oasis}{OASIS coupler}.
 Two-way nesting is also available through an interface to the AGRIF package
 (Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008}.
+(Adaptative Grid Refinement in \fortran) \citep{debreu.vouland.ea_CG08}.
 % Needs to be reviewed
 %The interface code for coupling to an alternative sea ice model (CICE, \citet{Hunke2008}) has now been upgraded so
 …
 The lateral Laplacian and biharmonic viscosity and diffusion can be rotated following
 a geopotential or neutral direction.
 There is an optional eddy induced velocity \citep{Gent1990} with a space and time variable coefficient
 \citet{Treguier1997}.
+There is an optional eddy induced velocity \citep{gent.mcwilliams_JPO90} with a space and time variable coefficient
+\citet{treguier.held.ea_JPO97}.
 The model has vertical harmonic viscosity and diffusion with a space and time variable coefficient,
 with options to compute the coefficients with \citet{Blanke1993}, \citet{Pacanowski_Philander_JPO81}, or
 \citet{Umlauf_Burchard_JMS03} mixing schemes.
+with options to compute the coefficients with \citet{blanke.delecluse_JPO93}, \citet{pacanowski.philander_JPO81}, or
+\citet{umlauf.burchard_JMR03} mixing schemes.
 %%gm    To be put somewhere else ....
 …
 NEMO/OPA, like all research tools, is in perpetual evolution.
 The present document describes the OPA version include in the release 3.4 of NEMO.
 This release differs significantly from version 8, documented in \citet{Madec1998}. \\
+This release differs significantly from version 8, documented in \citet{madec.delecluse.ea_NPM98}. \\
 The main modifications from OPA v8 and NEMO/OPA v3.2 are :
 …
 \item
   introduction of partial step representation of bottom topography
   \citep{Barnier_al_OD06, Le_Sommer_al_OM09, Penduff_al_OS07};
+  \citep{barnier.madec.ea_OD06, le-sommer.penduff.ea_OM09, penduff.le-sommer.ea_OS07};
 \item
   partial reactivation of a terrain-following vertical coordinate ($s$- and hybrid $s$-$z$) with
 …
   additional advection schemes for tracers;
 \item
   implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008};
+  implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{debreu.vouland.ea_CG08};
 \item
   online diagnostics : tracers trend in the mixed layer and vorticity balance;
 …
   RGB light penetration and optional use of ocean color
 \item
   major changes in the TKE schemes: it now includes a Langmuir cell parameterization \citep{Axell_JGR02},
   the \citet{Mellor_Blumberg_JPO04} surface wave breaking parameterization, and has a time discretization which
   is energetically consistent with the ocean model equations \citep{Burchard_OM02, Marsaleix_al_OM08};
+  major changes in the TKE schemes: it now includes a Langmuir cell parameterization \citep{axell_JGR02},
+  the \citet{mellor.blumberg_JPO04} surface wave breaking parameterization, and has a time discretization which
+  is energetically consistent with the ocean model equations \citep{burchard_OM02, marsaleix.auclair.ea_OM08};
 \item
   tidal mixing parametrisation (bottom intensification) + Indonesian specific tidal mixing
   \citep{Koch-Larrouy_al_GRL07};
+  \citep{koch-larrouy.madec.ea_GRL07};
 \item
   introduction of LIM-3, the new Louvain-la-Neuve sea-ice model
   (C-grid rheology and new thermodynamics including bulk ice salinity)
   \citep{Vancoppenolle_al_OM09a, Vancoppenolle_al_OM09b}
+  \citep{vancoppenolle.fichefet.ea_OM09*a, vancoppenolle.fichefet.ea_OM09*b}
 \end{itemize}
 …
 \item
   introduction of a modified leapfrog-Asselin filter time stepping scheme
   \citep{Leclair_Madec_OM09};
 \item
   additional scheme for iso-neutral mixing \citep{Griffies_al_JPO98}, although it is still a "work in progress";
 \item
   a rewriting of the bottom boundary layer scheme, following \citet{Campin_Goosse_Tel99};
 \item
   addition of a Generic Length Scale vertical mixing scheme, following \citet{Umlauf_Burchard_JMS03};
+  \citep{leclair.madec_OM09};
+\item
+  additional scheme for iso-neutral mixing \citep{griffies.gnanadesikan.ea_JPO98}, although it is still a "work in progress";
+\item
+  a rewriting of the bottom boundary layer scheme, following \citet{campin.goosse_T99};
+\item
+  addition of a Generic Length Scale vertical mixing scheme, following \citet{umlauf.burchard_JMR03};
 \item
   addition of the atmospheric pressure as an external forcing on both ocean and sea-ice dynamics;
 \item
   addition of a diurnal cycle on solar radiation \citep{Bernie_al_CD07};
+  addition of a diurnal cycle on solar radiation \citep{bernie.guilyardi.ea_CD07};
 \item
   river runoffs added through a non-zero depth, and having its own temperature and salinity;
 …
   coupling interface adjusted for WRF atmospheric model;
 \item
   C-grid ice rheology now available fro both LIM-2 and LIM-3 \citep{Bouillon_al_OM09};
+  C-grid ice rheology now available fro both LIM-2 and LIM-3 \citep{bouillon.maqueda.ea_OM09};
 \item
   LIM-3 ice-ocean momentum coupling applied to LIM-2;
 …
 \begin{itemize}
 \item finalisation of above iso-neutral mixing \citep{Griffies_al_JPO98}";
+\item finalisation of above iso-neutral mixing \citep{griffies.gnanadesikan.ea_JPO98}";
 \item "Neptune effect" parametrisation;
 \item horizontal pressure gradient suitable for s-coordinate;

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