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2016-02-05T00:47:05+01:00 (8 years ago)

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#1673 DOC of the trunk - Update, see associated wiki page for description

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trunk/DOC/TexFiles/Chapters

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: 17 edited

Abstracts_Foreword.tex (modified) (2 diffs)
Annex_C.tex (modified) (17 diffs)
Annex_D.tex (modified) (3 diffs)
Annex_ISO.tex (modified) (11 diffs)
Chap_DIA.tex (modified) (27 diffs)
Chap_DIU.tex (modified) (5 diffs)
Chap_DOM.tex (modified) (12 diffs)
Chap_DYN.tex (modified) (12 diffs)
Chap_LBC.tex (modified) (11 diffs)
Chap_LDF.tex (modified) (2 diffs)
Chap_MISC.tex (modified) (7 diffs)
Chap_Model_Basics.tex (modified) (8 diffs)
Chap_SBC.tex (modified) (17 diffs)
Chap_STO.tex (modified) (1 diff)
Chap_TRA.tex (modified) (19 diffs)
Chap_ZDF.tex (modified) (7 diffs)
Introduction.tex (modified) (1 diff)

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trunk/DOC/TexFiles/Chapters/Abstracts_Foreword.tex

-                      r6140
+                      r6289
 the earth climate system over a wide range of space and time scales.
 Prognostic variables are the three-dimensional velocity field, a non-linear sea surface height,
 the \textit{Conservative} Temperature and the \textit{Absolut} Salinity.
+the \textit{Conservative} Temperature and the \textit{Absolute} Salinity.
 In the horizontal direction, the model uses a curvilinear orthogonal grid and in the vertical direction,
 a full or partial step $z$-coordinate, or $s$-coordinate, or a mixture of the two.
 …
 interactions avec les autres composantes du syst\`{e}me climatique terrestre.
 Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer
 lin\'{e}aire, la Ttemperature Conservative et la Salinit\'{e} Absolue.
+lin\'{e}aire, la Temp\'{e}erature Conservative et la Salinit\'{e} Absolue.
 La distribution des variables se fait sur une grille C d'Arakawa tridimensionnelle utilisant une
 coordonn\'{e}e verticale $z$ \`{a} niveaux entiers ou partiels, ou une coordonn\'{e}e s, ou encore

trunk/DOC/TexFiles/Chapters/Annex_C.tex

-                      r6140
+                      r6289
 The discrete formulation of the horizontal diffusion of momentum ensures the
 conservation of potential vorticity and the horizontal divergence, and the
 dissipation of the square of these quantities (i.e. enstrophy and the
+dissipation of the square of these quantities ($i.e.$ enstrophy and the
 variance of the horizontal divergence) as well as the dissipation of the
 horizontal kinetic energy. In particular, when the eddy coefficients are
 …
 &\int \limits_D \frac{1} {e_3 } \textbf{k} \cdot \nabla \times
    \Bigl[    \nabla_h  \left( A^{\,lm}\;\chi  \right)
              - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)    \Bigr]\;dv  = 0
 \end{flalign*}
+           - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)    \Bigr]\;dv   \\
+%\end{flalign*}
 %%%%%%%%%%  recheck here....  (gm)
 \begin{flalign*}
 = \int \limits_D  -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times
    \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)  \Bigr]\;dv &&& \\
 \end{flalign*}
 \begin{flalign*}
+%\begin{flalign*}
+=& \int \limits_D  -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times
+   \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)  \Bigr]\;dv  \\
+%\end{flalign*}
+%\begin{flalign*}
 \equiv& \sum\limits_{i,j}
    \left\{
+   \delta_{i+1/2}
+   \left[
+   \frac {e_{2v}} {e_{1v}\,e_{3v}}  \delta_i
+      \left[ A_f^{\,lm} e_{3f} \zeta  \right]
+    \right]
+   + \delta_{j+1/2}
+   \left[
+   \frac {e_{1u}} {e_{2u}\,e_{3u}} \delta_j
+      \left[ A_f^{\,lm} e_{3f} \zeta  \right]
+   \right]
+   \right\}
+   && \\
+     \delta_{i+1/2} \left[  \frac {e_{2v}} {e_{1v}\,e_{3v}}  \delta_i \left[ A_f^{\,lm} e_{3f} \zeta  \right]  \right]
+   + \delta_{j+1/2} \left[  \frac {e_{1u}} {e_{2u}\,e_{3u}}  \delta_j \left[ A_f^{\,lm} e_{3f} \zeta  \right]  \right]
+   \right\}     \\
+%
 \intertext{Using \eqref{DOM_di_adj}, it follows:}
 …
 \equiv& \sum\limits_{i,j,k}
    -\,\left\{
+      \frac{e_{2v}} {e_{1v}\,e_{3v}}  \delta_i
+      \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_i \left[ 1\right]
+   + \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j
+      \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_j \left[ 1\right]
+      \frac{e_{2v}} {e_{1v}\,e_{3v}}  \delta_i  \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_i \left[ 1\right]
+    + \frac{e_{1u}} {e_{2u}\,e_{3u}}  \delta_j  \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_j \left[ 1\right]
    \right\} \quad \equiv 0
    && \\
+    \\
 \end{flalign*}
 …
 \subsection{Dissipation of Horizontal Kinetic Energy}
 \label{Apdx_C.3.2}
 The lateral momentum diffusion term dissipates the horizontal kinetic energy:
 …
 \label{Apdx_C.3.3}
 The lateral momentum diffusion term dissipates the enstrophy when the eddy
 coefficients are horizontally uniform:
 …
    \left[   \nabla_h \left( A^{\,lm}\;\chi  \right)
           - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)   \right]\;dv &&&\\
 &= A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times
+&\quad = A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times
    \left[    \nabla_h \times \left( \zeta \; \textbf{k} \right)   \right]\;dv &&&\\
 &\equiv A^{\,lm} \sum\limits_{i,j,k}  \zeta \;e_{3f}
+&\quad \equiv A^{\,lm} \sum\limits_{i,j,k}  \zeta \;e_{3f}
    \left\{     \delta_{i+1/2} \left[  \frac{e_{2v}} {e_{1v}\,e_{3v}} \delta_i \left[ e_{3f} \zeta  \right]   \right]
              + \delta_{j+1/2} \left[  \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j \left[ e_{3f} \zeta  \right]   \right]      \right\}   &&&\\
 …
 \intertext{Using \eqref{DOM_di_adj}, it follows:}
+%
 &\equiv  - A^{\,lm} \sum\limits_{i,j,k}
+&\quad \equiv  - A^{\,lm} \sum\limits_{i,j,k}
    \left\{    \left(  \frac{1} {e_{1v}\,e_{3v}}  \delta_i \left[ e_{3f} \zeta  \right]  \right)^2   b_v
+            + \left(  \frac{1} {e_{2u}\,e_{3u}}  \delta_j \left[ e_{3f} \zeta  \right] \right)^2   b_u  \right\}      &&&\\
+& \leq \;0       &&&\\
+            + \left(  \frac{1} {e_{2u}\,e_{3u}}  \delta_j \left[ e_{3f} \zeta  \right] \right)^2   b_u  \right\}  \quad \leq \;0    &&&\\
 \end{flalign*}
 …
 When the horizontal divergence of the horizontal diffusion of momentum
 (discrete sense) is taken, the term associated with the vertical curl of the
 vorticity is zero locally, due to (!!! II.1.8  !!!!!). The resulting term conserves the
 $\chi$ and dissipates $\chi^2$ when the eddy coefficients are
 horizontally uniform.
+vorticity is zero locally, due to \eqref{Eq_DOM_div_curl}.
+The resulting term conserves the $\chi$ and dissipates $\chi^2$
+when the eddy coefficients are horizontally uniform.
 \begin{flalign*}
 & \int\limits_D  \nabla_h \cdot
    \Bigl[     \nabla_h \left( A^{\,lm}\;\chi \right)
              - \nabla_h \times \left( A^{\,lm}\;\zeta \;\textbf{k} \right)    \Bigr]  dv
 = \int\limits_D  \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi  \right)   dv   &&&\\
+= \int\limits_D  \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi  \right)   dv   \\
+%
 &\equiv \sum\limits_{i,j,k}
    \left\{   \delta_i \left[ A_u^{\,lm} \frac{e_{2u}\,e_{3u}} {e_{1u}}  \delta_{i+1/2} \left[ \chi \right]  \right]
            + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}}  \delta_{j+1/2} \left[ \chi \right]  \right]    \right\}    &&&\\
+           + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}}  \delta_{j+1/2} \left[ \chi \right]  \right]    \right\}    \\
+%
 \intertext{Using \eqref{DOM_di_adj}, it follows:}
 …
 &\equiv \sum\limits_{i,j,k}
    - \left\{   \frac{e_{2u}\,e_{3u}} {e_{1u}}  A_u^{\,lm} \delta_{i+1/2} \left[ \chi \right] \delta_{i+1/2} \left[ 1 \right]
              + \frac{e_{1v}\,e_{3v}}  {e_{2v}}  A_v^{\,lm} \delta_{j+1/2} \left[ \chi \right] \delta_{j+1/2} \left[ 1 \right]    \right\}
    \qquad \equiv 0     &&& \\
+             + \frac{e_{1v}\,e_{3v}} {e_{2v}}  A_v^{\,lm} \delta_{j+1/2} \left[ \chi \right] \delta_{j+1/2} \left[ 1 \right]    \right\}
+   \quad \equiv 0      \\
 \end{flalign*}
 …
    \left[    \nabla_h              \left( A^{\,lm}\;\chi                    \right)
            - \nabla_h   \times  \left( A^{\,lm}\;\zeta \;\textbf{k} \right)    \right]\;  dv
  = A^{\,lm}   \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\;  dv    &&&\\
+ = A^{\,lm}   \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\;  dv    \\
+%
 &\equiv A^{\,lm}  \sum\limits_{i,j,k}  \frac{1} {e_{1t}\,e_{2t}\,e_{3t}}  \chi
 …
       \delta_i  \left[   \frac{e_{2u}\,e_{3u}} {e_{1u}}  \delta_{i+1/2} \left[ \chi \right]   \right]
    + \delta_j  \left[   \frac{e_{1v}\,e_{3v}} {e_{2v}}   \delta_{j+1/2} \left[ \chi \right]   \right]
    \right\} \;   e_{1t}\,e_{2t}\,e_{3t}    &&&\\
+   \right\} \;   e_{1t}\,e_{2t}\,e_{3t}    \\
+%
 \intertext{Using \eqref{DOM_di_adj}, it turns out to be:}
 …
 &\equiv - A^{\,lm} \sum\limits_{i,j,k}
    \left\{    \left(  \frac{1} {e_{1u}}  \delta_{i+1/2}  \left[ \chi \right]  \right)^2  b_u
+                 + \left(  \frac{1} {e_{2v}}  \delta_{j+1/2}  \left[ \chi \right]  \right)^2  b_v    \right\} \;    &&&\\
+%
+&\leq 0              &&&\\
+            + \left(  \frac{1} {e_{2v}}  \delta_{j+1/2}  \left[ \chi \right]  \right)^2  b_v    \right\}
+\quad \leq 0             \\
 \end{flalign*}
 …
 \section{Conservation Properties on Vertical Momentum Physics}
 \label{Apdx_C_4}
 As for the lateral momentum physics, the continuous form of the vertical diffusion
 …
    \left(   \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k}   \right)\; dv    \quad &\leq 0     \\
 \end{align*}
 The first property is obvious. The second results from:
 \begin{flalign*}
 \int\limits_D
 …
    e_{1f}\,e_{2f}\,e_{3f} \; \equiv 0   && \\
 \end{flalign*}
 If the vertical diffusion coefficient is uniform over the whole domain, the
 enstrophy is dissipated, $i.e.$
 …
       \left( \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k}   \right)   \right)\; dv = 0   &&&\\
 \end{flalign*}
 This property is only satisfied in $z$-coordinates:
 \begin{flalign*}
 \int\limits_D \zeta \, \textbf{k} \cdot \nabla \times
 …
 The numerical schemes used for tracer subgridscale physics are written such
+that the heat and salt contents are conserved (equations in flux form, second
+order centered finite differences). Since a flux form is used to compute the
+temperature and salinity, the quadratic form of these quantities (i.e. their variance)
+globally tends to diminish. As for the advection term, there is generally no strict
+conservation of mass, even if in practice the mass is conserved to a very high
+accuracy.
+that the heat and salt contents are conserved (equations in flux form).
+Since a flux form is used to compute the temperature and salinity,
+the quadratic form of these quantities ($i.e.$ their variance) globally tends to diminish.
+As for the advection term, there is conservation of mass only if the Equation Of Seawater is linear.
 % -------------------------------------------------------------------------------------------------------------

trunk/DOC/TexFiles/Chapters/Annex_D.tex

-                      r3294
+                      r6289
 \hline
 public  \par or  \par module variable&
 \textbf{m n} \par \textit{but not} \par \textbf{nn\_}&
+\textbf{m n} \par \textit{but not} \par \textbf{nn\_ np\_}&
 \textbf{a b e f g h o q r} \par \textbf{t} \textit{to} \textbf{x} \par but not \par \textbf{fs rn\_}&
 \textbf{l} \par \textit{but not} \par \textbf{lp ld} \par \textbf{ ll ln\_}&
 …
 \hline
 parameter&
 \textbf{jp}&
+\textbf{jp np\_}&
 \textbf{pp}&
 \textbf{lp}&
 …
 %--------------------------------------------------------------------------------------------------------------
+N.B.   Parameter here, in not only parameter in the \textsc{Fortran} acceptation, it is also used for code variables
+that are read in namelist and should never been modified during a simulation.
+It is the case, for example, for the size of a domain (jpi,jpj,jpk).
 \newpage
 % ================================================================

trunk/DOC/TexFiles/Chapters/Annex_ISO.tex

-                      r4147
+                      r6289
 \namdisplay{namtra_ldf}
 %---------------------------------------------------------------------------------------------------------
+If the namelist variable \np{ln\_traldf\_grif} is set true (and
+\key{ldfslp} is set), \NEMO updates both active and passive tracers
+using the Griffies triad representation of iso-neutral diffusion and
+the eddy-induced advective skew (GM) fluxes. Otherwise (by default) the
+filtered version of Cox's original scheme is employed
+(\S\ref{LDF_slp}). In the present implementation of the Griffies
+scheme, the advective skew fluxes are implemented even if
+\key{traldf\_eiv} is not set.
+Two scheme are available to perform the iso-neutral diffusion.
+If the namelist logical \np{ln\_traldf\_triad} is set true,
+\NEMO updates both active and passive tracers using the Griffies triad representation
+of iso-neutral diffusion and the eddy-induced advective skew (GM) fluxes.
+If the namelist logical \np{ln\_traldf\_iso} is set true,
+the filtered version of Cox's original scheme (the Standard scheme) is employed (\S\ref{LDF_slp}).
+In the present implementation of the Griffies scheme,
+the advective skew fluxes are implemented even if \np{ln\_traldf\_eiv} is false.
 Values of iso-neutral diffusivity and GM coefficient are set as
+described in \S\ref{LDF_coef}. If none of the keys \key{traldf\_cNd},
+N=1,2,3 is set (the default), spatially constant iso-neutral $A_l$ and
+GM diffusivity $A_e$ are directly set by \np{rn\_aeih\_0} and
+\np{rn\_aeiv\_0}. If 2D-varying coefficients are set with
+\key{traldf\_c2d} then $A_l$ is reduced in proportion with horizontal
+scale factor according to \eqref{Eq_title} \footnote{Except in global ORCA
+  $0.5^{\circ}$ runs with \key{traldf\_eiv}, where
+  $A_l$ is set like $A_e$ but with a minimum vale of
+  $100\;\mathrm{m}^2\;\mathrm{s}^{-1}$}. In idealised setups with
+\key{traldf\_c2d}, $A_e$ is reduced similarly, but if \key{traldf\_eiv}
+is set in the global configurations with \key{traldf\_c2d}, a horizontally varying $A_e$ is
+instead set from the Held-Larichev parameterisation\footnote{In this
+  case, $A_e$ at low latitudes $|\theta|<20^{\circ}$ is further
+  reduced by a factor $|f/f_{20}|$, where $f_{20}$ is the value of $f$
+  at $20^{\circ}$~N} (\mdl{ldfeiv}) and \np{rn\_aeiv\_0} is ignored
+unless it is zero.
+described in \S\ref{LDF_coef}. Note that when GM fluxes are used,
+the eddy-advective (GM) velocities are output for diagnostic purposes using xIOS,
+even though the eddy advection is accomplished by means of the skew fluxes.
 The options specific to the Griffies scheme include:
 \begin{description}[font=\normalfont]
+\item[\np{ln\_traldf\_gdia}] Default value is false. See \S\ref{sec:triad:sfdiag}. If this is set true, time-mean
+  eddy-advective (GM) velocities are output for diagnostic purposes, even
+  though the eddy advection is accomplished by means of the skew
+  fluxes.
+\item[\np{ln\_traldf\_iso}] See \S\ref{sec:triad:taper}. If this is set false (the default), then
+\item[\np{ln\_triad\_iso}] See \S\ref{sec:triad:taper}. If this is set false (the default), then
   `iso-neutral' mixing is accomplished within the surface mixed-layer
   along slopes linearly decreasing with depth from the value immediately below
+  the mixed-layer to zero (flat) at the surface (\S\ref{sec:triad:lintaper}). This is the same
+  treatment as used in the default implementation
+  \S\ref{LDF_slp_iso}; Fig.~\ref{Fig_eiv_slp}.  Where
+  \np{ln\_traldf\_iso} is set true, the vertical skew flux is further
+  reduced to ensure no vertical buoyancy flux, giving an almost pure
+  the mixed-layer to zero (flat) at the surface (\S\ref{sec:triad:lintaper}).
+  This is the same treatment as used in the default implementation \S\ref{LDF_slp_iso}; Fig.~\ref{Fig_eiv_slp}.
+  Where \np{ln\_triad\_iso} is set true, 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 \S\ref{sec:triad:Gerdes-taper}
+\item[\np{ln\_traldf\_botmix}] See \S\ref{sec:triad:iso_bdry}. If this
+  is set false (the default) then the lateral diffusive fluxes
+  associated with triads partly masked by topography are neglected. If
+  it is set true, however, then these lateral diffusive fluxes are
+  applied, giving smoother bottom tracer fields at the cost of
+  introducing diapycnal mixing.
+\item[\np{ln\_botmix\_triad}] See \S\ref{sec:triad:iso_bdry}.
+  If this is set false (the default) then the lateral diffusive fluxes
+  associated with triads partly masked by topography are neglected.
+  If it is set true, however, then these lateral diffusive fluxes are applied,
+  giving smoother bottom tracer fields at the cost of introducing diapycnal mixing.
+\item[\np{rn\_sw\_triad}]  blah blah to be added....
+\end{description}
+The options shared with the Standard scheme include:
+\begin{description}[font=\normalfont]
+\item[\np{ln\_traldf\_msc}]   blah blah to be added
+\item[\np{rn\_slpmax}]  blah blah to be added
 \end{description}
 \section{Triad formulation of iso-neutral diffusion}
 \label{sec:triad:iso}
 We have implemented into \NEMO a scheme inspired by \citet{Griffies_al_JPO98}, but formulated within the \NEMO
 framework, using scale factors rather than grid-sizes.
+We have implemented into \NEMO a scheme inspired by \citet{Griffies_al_JPO98},
+but formulated within the \NEMO framework, using scale factors rather than grid-sizes.
 \subsection{The iso-neutral diffusion operator}
 …
     \mbox{with}\quad \;\;\Re =
     \begin{pmatrix}
 &0&-r_1\mystrut \\
 &1&-r_2\mystrut \\
       -r_1&-r_2&r_1 ^2+r_2 ^2\mystrut
+   &  0   & -r_1           \mystrut \\
+   &  1   & -r_2           \mystrut \\
+      -r_1 & -r_2 &  r_1 ^2+r_2 ^2 \mystrut
     \end{pmatrix}
     \quad \text{and} \quad\grad T=
     \begin{pmatrix}
       \frac{1}{e_1}\pd[T]{i}\mystrut \\
       \frac{1}{e_2}\pd[T]{j}\mystrut \\
       \frac{1}{e_3}\pd[T]{k}\mystrut
+      \frac{1}{e_1} \pd[T]{i} \mystrut \\
+      \frac{1}{e_2} \pd[T]{j} \mystrut \\
+      \frac{1}{e_3} \pd[T]{k} \mystrut
     \end{pmatrix}.
   \end{equation}
 …
 %  {-r_1 } \hfill & {-r_2 } \hfill & {r_1 ^2+r_2 ^2} \hfill \\
 % \end{array} }} \right)
  Here \eqref{Eq_PE_iso_slopes}
+ Here \eqref{Eq_PE_iso_slopes}
 \begin{align*}
   r_1 &=-\frac{e_3 }{e_1 } \left( \frac{\partial \rho }{\partial i}
 …
 % the mean vertical gradient at the $u$-point,
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[h] \begin{center}
+\begin{figure}[tb] \begin{center}
     \includegraphics[width=1.05\textwidth]{./TexFiles/Figures/Fig_GRIFF_triad_fluxes}
     \caption{ \label{fig:triad:ISO_triad}
 …
+  \
   \frac
+  {\left(\alpha / \beta \right)_i^k  \ \delta_{i + i_p}[T^k] - \delta_{i + i_p}[S^k] }
+  {\left(\alpha / \beta \right)_i^k  \ \delta_{k+k_p}[T^i ] - \delta_{k+k_p}[S^i ] }.
+\end{equation}
+In calculating the slopes of the local neutral
+surfaces, the expansion coefficients $\alpha$ and $\beta$ are
+evaluated at the anchor points of the triad \footnote{Note that in \eqref{eq:triad:R} we use the ratio $\alpha / \beta$
+instead of multiplying the temperature derivative by $\alpha$ and the
+salinity derivative by $\beta$. This is more efficient as the ratio
+$\alpha / \beta$ can to be evaluated directly}, while the metrics are
+calculated at the $u$- and $w$-points on the arms.
+  { \alpha_i^k  \ \delta_{i+i_p}[T^k] - \beta_i^k \ \delta_{i+i_p}[S^k] }
+  { \alpha_i^k  \ \delta_{k+k_p}[T^i] - \beta_i^k \ \delta_{k+k_p}[S^i] }.
+\end{equation}
+In calculating the slopes of the local neutral surfaces,
+the expansion coefficients $\alpha$ and $\beta$ are evaluated at the anchor points of the triad,
+while the metrics are calculated at the $u$- and $w$-points on the arms.
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[h] \begin{center}
+\begin{figure}[tb] \begin{center}
     \includegraphics[width=0.80\textwidth]{./TexFiles/Figures/Fig_GRIFF_qcells}
     \caption{   \label{fig:triad:qcells}
 …
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
+Each triad $\{_i^k\:_{i_p}^{k_p}\}$ is associated (Fig.~\ref{fig:triad:qcells}) with the quarter
+cell that is the intersection of the $i,k$ $T$-cell, the $i+i_p,k$
+$u$-cell and the $i,k+k_p$ $w$-cell. Expressing the slopes $s_i$ and
+$s'_i$ in \eqref{eq:triad:i13} and \eqref{eq:triad:i31} in this notation, we have
+e.g.\ $s_1=s'_1={\:}_i^k \mathbb{R}_{1/2}^{1/2}$. Each triad slope $_i^k
+\mathbb{R}_{i_p}^{k_p}$ is used once (as an $s$) to calculate the
+lateral flux along its $u$-arm, at $(i+i_p,k)$, and then again as an
+$s'$ to calculate the vertical flux along its $w$-arm at
+$(i,k+k_p)$. Each vertical area $a_i$ used to calculate the lateral
+flux and horizontal area $a'_i$ used to calculate the vertical flux
+can also be identified as the area across the $u$- and $w$-arms of a
+unique triad, and we notate these areas, similarly to the triad
+slopes, as $_i^k{\mathbb{A}_u}_{i_p}^{k_p}$,
+$_i^k{\mathbb{A}_w}_{i_p}^{k_p}$, where e.g. in \eqref{eq:triad:i13}
+$a_{1}={\:}_i^k{\mathbb{A}_u}_{1/2}^{1/2}$, and in \eqref{eq:triad:i31}
+$a'_{1}={\:}_i^k{\mathbb{A}_w}_{1/2}^{1/2}$.
+Each triad $\{_i^{k}\:_{i_p}^{k_p}\}$ is associated (Fig.~\ref{fig:triad:qcells}) with the quarter
+cell that is the intersection of the $i,k$ $T$-cell, the $i+i_p,k$ $u$-cell and the $i,k+k_p$ $w$-cell.
+Expressing the slopes $s_i$ and $s'_i$ in \eqref{eq:triad:i13} and \eqref{eq:triad:i31} in this notation,
+we have $e.g.$ \ $s_1=s'_1={\:}_i^k \mathbb{R}_{1/2}^{1/2}$.
+Each triad slope $_i^k\mathbb{R}_{i_p}^{k_p}$ is used once (as an $s$)
+to calculate the lateral flux along its $u$-arm, at $(i+i_p,k)$,
+and then again as an $s'$ to calculate the vertical flux along its $w$-arm at $(i,k+k_p)$.
+Each vertical area $a_i$ used to calculate the lateral flux and horizontal area $a'_i$ used
+to calculate the vertical flux can also be identified as the area across the $u$- and $w$-arms
+of a unique triad, and we notate these areas, similarly to the triad slopes,
+as $_i^k{\mathbb{A}_u}_{i_p}^{k_p}$, $_i^k{\mathbb{A}_w}_{i_p}^{k_p}$,
+where $e.g.$ in \eqref{eq:triad:i13} $a_{1}={\:}_i^k{\mathbb{A}_u}_{1/2}^{1/2}$,
+and in \eqref{eq:triad:i31} $a'_{1}={\:}_i^k{\mathbb{A}_w}_{1/2}^{1/2}$.
 \subsection{The full triad fluxes}
 …
 or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$ $u$-point is
 masked. The associated lateral fluxes (grey-black dashed line) are
 masked if \np{ln\_botmix\_grif}=false, but left unmasked,
 giving bottom mixing, if \np{ln\_botmix\_grif}=true.
 The default option \np{ln\_botmix\_grif}=false is suitable when the
+masked if \np{ln\_botmix\_triad}=false, but left unmasked,
+giving bottom mixing, if \np{ln\_botmix\_triad}=true.
+The default option \np{ln\_botmix\_triad}=false is suitable when the
 bbl mixing option is enabled (\key{trabbl}, with \np{nn\_bbl\_ldf}=1),
 or  for simple idealized  problems. For setups with topography without
 bbl mixing, \np{ln\_botmix\_grif}=true may be necessary.
+bbl mixing, \np{ln\_botmix\_triad}=true may be necessary.
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[h] \begin{center}
 …
       or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$ $u$-point
       is masked. The associated lateral fluxes (grey-black dashed
       line) are masked if \np{botmix\_grif}=.false., but left
       unmasked, giving bottom mixing, if \np{botmix\_grif}=.true.}
+      line) are masked if \np{botmix\_triad}=.false., but left
+      unmasked, giving bottom mixing, if \np{botmix\_triad}=.true.}
  \end{center} \end{figure}
 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 it to the Eulerian velocity prior to computing the tracer
 advection. This is implemented if \key{traldf\_eiv} is set in the
 default implementation, where \np{ln\_traldf\_grif} is set
+default implementation, where \np{ln\_traldf\_triad} is set
 false. This allows us to take advantage of all the advection schemes
 offered for the tracers (see \S\ref{TRA_adv}) and not just a $2^{nd}$
 …
 paramount importance.
 However, when \np{ln\_traldf\_grif} is set true, \NEMO instead
+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}. It is based on a transformation of the advective fluxes
 …
 and $\triadt{i+1}{k}{R}{-1/2}{1/2}$ are masked when either of the
 $i,k+1$ or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$
 $u$-point is masked. The namelist parameter \np{ln\_botmix\_grif} has
+$u$-point is masked. The namelist parameter \np{ln\_botmix\_triad} has
 no effect on the eddy-induced skew-fluxes.

trunk/DOC/TexFiles/Chapters/Chap_DIA.tex

-                      r6140
+                      r6289
 %       Old Model Output
 % ================================================================
 \section{Old Model Output (default or \key{dimgout})}
+\section{Old Model Output (default)}
 \label{DIA_io_old}
 …
 "\textit{grep -i numout}" in the source code directory.
+By default, diagnostic output files are written in NetCDF format but an IEEE binary output format, called DIMG, can be chosen by defining \key{dimgout}.
+Since version 3.2, when defining \key{iomput}, an I/O server has been added which provides more flexibility in the choice of the fields to be written as well as how the writing work is distributed over the processors in massively parallel computing. The complete description of the use of this I/O server is presented in the next section.
+By default, if neither \key{iomput} nor \key{dimgout} are 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).
+By default, diagnostic output files are written in NetCDF format.
+Since version 3.2, when defining \key{iomput}, an I/O server has been added
+which provides more flexibility in the choice of the fields to be written
+as well as how 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
 …
+Since version 3.2, iomput is the NEMO output interface of choice. It has been designed to be simple to use, flexible and efficient. The two main purposes of iomput are:
+Since version 3.2, iomput is the NEMO output interface of choice.
+It has been designed to be simple to use, flexible and efficient.
+The two main purposes of iomput are:
 \begin{enumerate}
+\item The complete and flexible control of the output files through external XML files adapted by the user from standard templates.
+\item To achieve high performance and scalable output through the optional distribution of all diagnostic output related tasks to dedicated processes.
+\item The complete and flexible control of the output files through external XML files
+adapted by the user from standard templates.
+\item To achieve high performance and scalable output through the optional distribution
+of all diagnostic output related tasks to dedicated processes.
 \end{enumerate}
+The first functionality allows the user to specify, without code changes or recompilation, aspects of the diagnostic output stream, such as:
+The first functionality allows the user to specify, without code changes or recompilation,
+aspects of the diagnostic output stream, such as:
 \begin{itemize}
 \item The choice of output frequencies that can be different for each file (including real months and years).
+\item The choice of file contents; includes complete flexibility over which data are written in which files (the same data can be written in different files).
+\item The choice of file contents; includes complete flexibility over which data are written in which files
+(the same data can be written in different files).
 \item The possibility to split output files at a chosen frequency.
 \item The possibility to extract a vertical or an horizontal subdomain.
 …
 \item Control over metadata via a large XML "database" of possible output fields.
 \end{itemize}
+In addition, iomput allows the user to add the output of any new variable (scalar, 2D or 3D) in the code 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:
+In addition, iomput allows the user to add in the code the output of any new variable (scalar, 2D or 3D)
+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:
 \begin{alltt}
 \begin{verbatim}
 …
 \end{alltt}
+The second functionality targets output performance when running in parallel (\key{mpp\_mpi}). Iomput provides the possibility to specify N dedicated I/O processes (in addition to the NEMO processes) to collect and write the outputs. With an appropriate choice of N by the user, the bottleneck associated with the writing of the output files can be greatly reduced.
+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} (use of revision 618 or higher is required). This new IO server can take advantage of the parallel I/O functionality of NetCDF4 to create a single output file and therefore to bypass the rebuilding phase. Note that writing in parallel into the same NetCDF files requires that your NetCDF4 library is linked to an HDF5 library that has been correctly compiled (i.e. with the configure option $--$enable-parallel). Note that the files created by iomput through XIOS are incompatible with NetCDF3. All post-processsing and visualization tools must therefore be compatible with NetCDF4 and not only NetCDF3.
+Even if not using the parallel I/O functionality of NetCDF4, using N dedicated I/O servers, where N is typically much less than the number of NEMO processors, will reduce the number of output files created. This can greatly reduce the post-processing burden usually associated with using large numbers of NEMO processors. Note that for smaller configurations, the rebuilding phase can be avoided, even without a parallel-enabled NetCDF4 library, simply by employing only one dedicated I/O server.
+The second functionality targets output performance when running in parallel (\key{mpp\_mpi}).
+Iomput provides the possibility to specify N dedicated I/O processes (in addition to the NEMO processes)
+to collect and write the outputs. With an appropriate choice of N by the user,
+the bottleneck associated with the writing of the output files can be greatly reduced.
+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}
+(use of revision 618 or higher is required). This new IO server can take advantage of
+the parallel I/O functionality of NetCDF4 to create a single output file and therefore
+to bypass the rebuilding phase. Note that writing in parallel into the same NetCDF files
+requires that your NetCDF4 library is linked to an HDF5 library that has been correctly compiled
+($i.e.$ with the configure option $--$enable-parallel).
+Note that the files created by iomput through XIOS are incompatible with NetCDF3.
+All post-processsing and visualization tools must therefore be compatible with NetCDF4 and not only NetCDF3.
+Even if not using the parallel I/O functionality of NetCDF4, using N dedicated I/O servers,
+where N is typically much less than the number of NEMO processors, will reduce the number of output files created.
+This can greatly reduce the post-processing burden usually associated with using large numbers of NEMO processors.
+Note that for smaller configurations, the rebuilding phase can be avoided,
+even without a parallel-enabled NetCDF4 library, simply by employing only one dedicated I/O server.
 \subsection{XIOS: the IO\_SERVER}
 …
 \subsubsection{Attached or detached mode?}
+Iomput is based on \href{http://forge.ipsl.jussieu.fr/ioserver/wiki}{XIOS}, the io\_server developed by Yann Meurdesoif from IPSL. The behaviour of the io subsystem is controlled by settings in the external XML files listed above. Key settings in the iodef.xml file are {\tt using\_server} and the {\tt type} tag associated with each defined file. The {\tt using\_server} setting determines whether or not the server will be used in ''attached mode'' (as a library) [{\tt false}] or in ''detached mode'' (as an external executable on N additional, dedicated cpus) [{\tt true}]. The ''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''.
+In attached mode and if the type of file is ''multiple\_file'', then each NEMO process will also act as an IO server and produce its own set of output files. Superficially, this emulates the standard behaviour in previous versions, However, the subdomain written out by each process does not correspond to the {\tt jpi x jpj x jpk} domain actually computed by the process (although it may if {\tt jpni=1}). Instead each process will have collected and written out a number of complete longitudinal strips. If the ''one\_file'' option is chosen then all processes will collect their longitudinal strips and write (in parallel) to a single output file.
+In detached mode and if the type of file is ''multiple\_file'', then each stand-alone XIOS process will collect data for a range of complete longitudinal strips and write to its own set of output files. If the ''one\_file'' option is chosen then all XIOS processes will collect their longitudinal strips and write (in parallel) to a single output file. Note running in detached mode requires launching a Multiple Process Multiple Data (MPMD) parallel job. The following subsection provides a typical example but the syntax will vary in different MPP environments.
+Iomput is based on \href{http://forge.ipsl.jussieu.fr/ioserver/wiki}{XIOS},
+the io\_server developed by Yann Meurdesoif from IPSL.
+The behaviour of the I/O subsystem is controlled by settings in the external XML files listed above.
+Key settings in the iodef.xml file are {\tt using\_server} and the {\tt type} tag associated with each defined file.
+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 \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''.
+In \textit{attached mode} and if the type of file is ''multiple\_file'',
+then each NEMO process will also act as an IO server and produce its own set of output files.
+Superficially, this emulates the standard behaviour in previous versions.
+However, the subdomain written out by each process does not correspond to the {\tt jpi x jpj x jpk}
+domain actually computed by the process (although it may if {\tt jpni=1}).
+Instead each process will have collected and written out a number of complete longitudinal strips.
+If the ''one\_file'' option is chosen then all processes will collect their longitudinal strips
+and write (in parallel) to a single output file.
+In \textit{detached mode} and if the type of file is ''multiple\_file'',
+then each stand-alone XIOS process will collect data for a range of complete longitudinal strips
+and write to its own set of output files. If the ''one\_file'' option is chosen then
+all XIOS processes will collect their longitudinal strips and write (in parallel) to a single output file.
+Note running in detached mode requires launching a Multiple Process Multiple Data (MPMD) parallel job.
+The following subsection provides a typical example but the syntax will vary in different MPP environments.
 \subsubsection{Number of cpu used by XIOS in detached mode}
+The number of cores used by the XIOS is specified when launching the model. The number of cores dedicated to XIOS should be from ~1/10 to ~1/50 of the number or cores dedicated to NEMO. Some manufacturers suggest using O($\sqrt{N}$) dedicated IO processors for N processors but this is a general recommendation and not specific to NEMO. It is difficult to provide precise recommendations because the optimal choice will depend on the particular hardware properties of the target system (parallel filesystem performance, available memory, memory bandwidth etc.) and the volume and frequency of data to be created. Here is an example of 2 cpus for the io\_server and 62 cpu for nemo using mpirun:
+The number of cores used by the XIOS is specified when launching the model.
+The number of cores dedicated to XIOS should be from ~1/10 to ~1/50 of the number or cores dedicated to NEMO.
+Some manufacturers suggest using O($\sqrt{N}$) dedicated IO processors for N processors
+but this is a general recommendation and not specific to NEMO.
+It is difficult to provide precise recommendations because the optimal choice will depend on
+the particular hardware properties of the target system (parallel filesystem performance, available memory,
+memory bandwidth etc.) and the volume and frequency of data to be created.
+Here is an example of 2 cpus for the io\_server and 62 cpu for nemo using mpirun:
 \texttt{ mpirun -np 62 ./nemo.exe : -np 2 ./xios\_server.exe }
 …
 \subsubsection{Control of XIOS: the XIOS 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. See the XML basics section below for more details on XML syntax and rules.
+As well as the {\tt 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.
 \begin{tabular}{|p{4cm}|p{6.0cm}|p{2.0cm}|}
 …
    \hline
    buffer\_size &
+   buffer size used by XIOS to send data from NEMO to XIOS. Larger is more efficient. Note that needed/used buffer sizes are summarized at the end of the job &
+   buffer size used by XIOS to send data from NEMO to XIOS. Larger is more efficient.
+   Note that needed/used buffer sizes are summarized at the end of the job &
    25000000 \\
    \hline
 …
 \subsubsection{Installation}
+As mentioned, XIOS is supported separately and must be downloaded and compiled before it can be used with NEMO. 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{http://www.nemo-ocean.eu/Using-NEMO/User-Guides/Basics/XIOS-IO-server-installation-and-use}{XIOS with NEMO} guide provides an example illustration of how this can be achieved.
+As mentioned, XIOS is supported separately and must be downloaded and compiled before it can be used with NEMO.
+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{http://www.nemo-ocean.eu/Using-NEMO/User-Guides/Basics/XIOS-IO-server-installation-and-use}{XIOS with NEMO}
+guide provides an example illustration of how this can be achieved.
 \subsubsection{Add your own outputs}
+It is very easy to add your own outputs with iomput. Many standard fields and diagnostics are already prepared (i.e., steps 1 to 3 below have been done) and simply need to be activated by including the required output in a file definition in iodef.xml (step 4). To add new output variables, all 4 of the following steps must be taken.
+It is very easy to add your own outputs with iomput.
+Many standard fields and diagnostics are already prepared ($i.e.$, steps 1 to 3 below have been done)
+and simply need to be activated by including the required output in a file definition in iodef.xml (step 4).
+To add new output variables, all 4 of the following steps must be taken.
 \begin{description}
 \item[1.] in NEMO code, add a \\
 …
 to the list of used modules in the upper part of your module.
+\item[3.] in the field\_def.xml file, add the definition of your variable using the same identifier you used in the f90 code (see subsequent sections for a details of the XML syntax and rules). For example:
+\item[3.] in the field\_def.xml file, add the definition of your variable using the same identifier
+you used in the f90 code (see subsequent sections for a details of the XML syntax and rules).
+For example:
 \vspace{-20pt}
 \begin{alltt}  {{\scriptsize
 …
 \end{verbatim}
 }}\end{alltt}
+Note your definition must be added to the field\_group whose reference grid is consistent with the size of the array passed to iomput. The grid\_ref attribute refers to definitions set in iodef.xml which, in turn, reference grids and axes either defined in the code (iom\_set\_domain\_attr and iom\_set\_axis\_attr in iom.F90) or defined in the domain\_def.xml file. E.g.:
+Note your definition must be added to the field\_group whose reference grid is consistent
+with the size of the array passed to iomput.
+The grid\_ref attribute refers to definitions set in iodef.xml which, in turn, reference grids
+and axes either defined in the code (iom\_set\_domain\_attr and iom\_set\_axis\_attr in iom.F90)
+or defined in the domain\_def.xml file. $e.g.$:
 \vspace{-20pt}
 \begin{alltt}  {{\scriptsize
 …
 }}\end{alltt}
 Note, if your array is computed within the surface module each nn\_fsbc time\_step,
+add the field definition within the field\_group defined with the id ''SBC'': $<$field\_group id=''SBC''...$>$ which has been defined with the correct frequency of operations (iom\_set\_field\_attr in iom.F90)
+add the field definition within the field\_group defined with the id ''SBC'': $<$field\_group id=''SBC''...$>$
+which has been defined with the correct frequency of operations (iom\_set\_field\_attr in iom.F90)
 \item[4.] add your field in one of the output files defined in iodef.xml (again see subsequent sections for syntax and rules)   \\
 …
 \subsubsection{Structure of the xml file used in NEMO}
+The XML file used in XIOS is structured by 7 families of tags: context, axis, domain, grid, field, file and variable. Each tag family has hierarchy of three flavors (except for context):
+The XML file used in XIOS is structured by 7 families of tags: context, axis, domain, grid, field, file and variable.
+Each tag family has hierarchy of three flavors (except for context):
 \\
 \begin{tabular}{|p{3.0cm}|p{4.5cm}|p{4.5cm}|}
 …
 \\
+Each element may have several attributes. Some attributes are mandatory, other are optional but have a default value and other are are completely optional. Id is a special attribute used to identify an element or a group of elements. It must be unique for a kind of element. It is optional, but no reference to the corresponding element can be done if it is not defined.
+The XML file is split into context tags that are used to isolate IO definition from different codes or different parts of a code. No interference is possible between 2 different contexts. Each context has its own calendar and an associated timestep. In NEMO, we used the following contexts (that can be defined in any order):\\
+Each element may have several attributes.
+Some attributes are mandatory, other are optional but have a default value and other are are completely optional.
+Id is a special attribute used to identify an element or a group of elements.
+It must be unique for a kind of element.
+It is optional, but no reference to the corresponding element can be done if it is not defined.
+The XML file is split into context tags that are used to isolate IO definition from different codes
+or different parts of a code. No interference is possible between 2 different contexts.
+Each context has its own calendar and an associated timestep.
+In \NEMO, we used the following contexts (that can be defined in any order):\\
 \\
 \begin{tabular}{|p{3.0cm}|p{4.5cm}|p{4.5cm}|}
 …
 \\
+\noindent Each context tag related to NEMO (mother or child grids) is divided into 5 parts (that can be defined in any order):\\
+\noindent Each context tag related to NEMO (mother or child grids) is divided into 5 parts
+(that can be defined in any order):\\
 \\
 \begin{tabular}{|p{3.0cm}|p{4.5cm}|p{4.5cm}|}
 …
 \subsubsection{Nesting XML files}
+The XML file can be split in different parts to improve its readability and facilitate its use. The inclusion of XML files into the main XML file can be done through the attribute src: \\
+The XML file can be split in different parts to improve its readability and facilitate its use.
+The inclusion of XML files into the main XML file can be done through the attribute src: \\
 {\scriptsize \verb? <context src="./nemo_def.xml" /> ?}\\
 …
 \subsubsection{Use of inheritance}
+XML extensively uses the concept of inheritance. XML has a tree based structure with a parent-child oriented relation: all children inherit attributes from parent, but an attribute defined in a child replace the inherited attribute value. Note that the special attribute ''id'' is never inherited.  \\
+XML extensively uses the concept of inheritance.
+XML has a tree based structure with a parent-child oriented relation:
+all children inherit attributes from parent, but an attribute defined in a child replace the inherited attribute value.
+Note that the special attribute ''id'' is never inherited.  \\
 \\
 example 1: Direct inheritance.
 …
 \subsubsection{Use of Groups}
+Groups can be used for 2 purposes. Firstly, the group can be used to define common attributes to be shared by the elements of the group through inheritance. In the following example, we define a group of field that will share a common grid ''grid\_T\_2D''. Note that for the field ''toce'', we overwrite the grid definition inherited from the group by ''grid\_T\_3D''.
+Groups can be used for 2 purposes.
+Firstly, the group can be used to define common attributes to be shared by the elements of the group through inheritance.
+In the following example, we define a group of field that will share a common grid ''grid\_T\_2D''.
+Note that for the field ''toce'', we overwrite the grid definition inherited from the group by ''grid\_T\_3D''.
 \vspace{-20pt}
 \begin{alltt}  {{\scriptsize
 …
 }}\end{alltt}
+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 {\tt CONFIG/SHARED/field\_def.xml}. For example, a short list of the usual variables related to the U grid:
+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 {\tt CONFIG/SHARED/field\_def.xml}.
+For example, a short list of the usual variables related to the U grid:
 \vspace{-20pt}
 \begin{alltt}  {{\scriptsize
 …
 \subsection{Detailed functionalities }
+The file {\tt NEMOGCM/CONFIG/ORCA2\_LIM/iodef\_demo.xml} provides several examples of the use of the new functionalities offered by the XML interface of XIOS.
+The file {\tt NEMOGCM/CONFIG/ORCA2\_LIM/iodef\_demo.xml} provides several examples of the use
+of the new functionalities offered by the XML interface of XIOS.
 \subsubsection{Define horizontal subdomains}
+Horizontal subdomains are defined through the attributs zoom\_ibegin, zoom\_jbegin, zoom\_ni, zoom\_nj of the tag family domain. It must therefore be done in the domain part of the XML file. For example, in {\tt CONFIG/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).
+Horizontal subdomains are defined through the attributs zoom\_ibegin, zoom\_jbegin, zoom\_ni, zoom\_nj of the tag family domain.
+It must therefore be done in the domain part of the XML file.
+For example, in {\tt CONFIG/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).
 \vspace{-20pt}
 \begin{alltt}  {{\scriptsize
 …
 \end{verbatim}
 }}\end{alltt}
+Moorings are seen as an extrem case corresponding to a 1 by 1 subdomain. The Equatorial section, the TAO, RAMA and PIRATA moorings are alredy registered in the code and can therefore be outputted without taking care of their (i,j) position in the grid. These predefined domains can be activated by the use of specific domain\_ref: ''EqT'', ''EqU'' or ''EqW'' for the equatorial sections and the mooring position for TAO, RAMA and PIRATA followed by ''T'' (for example: ''8s137eT'', ''1.5s80.5eT'' ...)
+Moorings are seen as an extrem case corresponding to a 1 by 1 subdomain.
+The Equatorial section, the TAO, RAMA and PIRATA moorings are alredy registered in the code
+and can therefore be outputted without taking care of their (i,j) position in the grid.
+These predefined domains can be activated by the use of specific domain\_ref: ''EqT'', ''EqU'' or ''EqW''
+for the equatorial sections and the mooring position for TAO, RAMA and PIRATA followed
+by ''T'' (for example: ''8s137eT'', ''1.5s80.5eT'' ...)
 \vspace{-20pt}
 \begin{alltt}  {{\scriptsize
 …
 % -------------------------------------------------------------------------------------------------------------
 \section[Tracer/Dynamics Trends (TRD)]
+                  {Tracer/Dynamics Trends  (\key{trdtra}, \key{trddyn},    \\
+                                                             \key{trddvor}, \key{trdmld})}
+                  {Tracer/Dynamics Trends  (\ngn{namtrd})}
 \label{DIA_trd}
 …
 %-------------------------------------------------------------------------------------------------------------
+When \key{trddyn} and/or \key{trddyn} CPP variables are defined, each
+trend of the dynamics and/or temperature and salinity time evolution equations
+is stored in three-dimensional arrays just after their computation ($i.e.$ at the end
+of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). Options are defined by
+\ngn{namtrd} namelist variables. These trends are then
+used in \mdl{trdmod} (see TRD directory) every \textit{nn\_trd } time-steps.
+What is done depends on the CPP keys defined:
+Each trend of the dynamics and/or temperature and salinity time evolution equations
+can be send to \mdl{trddyn} and/or \mdl{trdtra} modules (see TRD directory) just after their computation
+($i.e.$ at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines).
+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.
+What is done depends on the \ngn{namtrd} logical set to \textit{true}:
 \begin{description}
+\item[\key{trddyn}, \key{trdtra}] : a check of the basin averaged properties of the momentum
+and/or tracer equations is performed ;
+\item[\key{trdvor}] : a vertical summation of the moment tendencies is performed,
+then the curl is computed to obtain the barotropic vorticity tendencies which are output ;
+\item[\key{trdmld}] : output of the tracer tendencies averaged vertically
+either over the mixed layer (\np{nn\_ctls}=0),
+or       over a fixed number of model levels (\np{nn\_ctls}$>$1 provides the number of level),
+or       over a spatially varying but temporally fixed number of levels (typically the base
+of the winter mixed layer) read in \ifile{ctlsurf\_idx} (\np{nn\_ctls}=1) ;
+\item[\np{ln\_glo\_trd}] : at each \np{nn\_trd} time-step a check of the basin averaged properties
+of the momentum and tracer equations is performed. This also includes a check of $T^2$, $S^2$,
+$\tfrac{1}{2} (u^2+v2)$, and potential energy time evolution equations properties ;
+\item[\np{ln\_dyn\_trd}] : each 3D trend of the evolution of the two momentum components is output ;
+\item[\np{ln\_dyn\_mxl}] : each 3D trend of the evolution of the two momentum components averaged
+                           over the mixed layer is output  ;
+\item[\np{ln\_vor\_trd}] : a vertical summation of the moment tendencies is performed,
+                           then the curl is computed to obtain the barotropic vorticity tendencies which are output ;
+\item[\np{ln\_KE\_trd}]  : each 3D trend of the Kinetic Energy equation is output ;
+\item[\np{ln\_tra\_trd}] : each 3D trend of the evolution of temperature and salinity is output ;
+\item[\np{ln\_tra\_mxl}] : each 2D trend of the evolution of temperature and salinity averaged
+                           over the mixed layer is output ;
 \end{description}
-The units in the output file can be changed using the \np{nn\_ucf} namelist parameter.
-For example, in case of salinity tendency the units are given by PSU/s/\np{nn\_ucf}.
-Setting \np{nn\_ucf}=86400 ($i.e.$ the number of second in a day) provides the tendencies in PSU/d.
-When \key{trdmld} is defined, two time averaging procedure are proposed.
-Setting \np{ln\_trdmld\_instant} to \textit{true}, a simple time averaging is performed,
-so that the resulting tendency is the contribution to the change of a quantity between
-the two instantaneous values taken at the extremities of the time averaging period.
-Setting \np{ln\_trdmld\_instant} to \textit{false}, a double time averaging is performed,
-so that the resulting tendency is the contribution to the change of a quantity between
-two \textit{time mean} values. The later option requires the use of an extra file, \ifile{restart\_mld}
-(\np{ln\_trdmld\_restart}=true), to restart a run.
 Note that the mixed layer tendency diagnostic can also be used on biogeochemical models
 via the \key{trdtrc} and \key{trdmld\_trc} CPP keys.
+\textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested.
+In particular, options associated with \np{ln\_dyn\_mxl}, \np{ln\_vor\_trd}, and \np{ln\_tra\_mxl}
+are not working, and none of the option have been tested with variable volume ($i.e.$ \key{vvl} defined).
 % -------------------------------------------------------------------------------------------------------------
 …
 \label{DIA_diag_harm}
-A module is available to compute the amplitude and phase for tidal waves.
-This diagnostic is actived with \key{diaharm}.
 %------------------------------------------namdia_harm----------------------------------------------------
 \namdisplay{namdia_harm}
 %----------------------------------------------------------------------------------------------------------
+Concerning the on-line Harmonic analysis, some parameters are available in namelist
+\ngn{namdia\_harm} :
+- \texttt{nit000\_han} is the first time step used for harmonic analysis
+- \texttt{nitend\_han} is the last time step used for harmonic analysis
+- \texttt{nstep\_han} is the time step frequency for harmonic analysis
+- \texttt{nb\_ana} is the number of harmonics to analyse
+- \texttt{tname} is an array with names of tidal constituents to analyse
+\texttt{nit000\_han} and \texttt{nitend\_han} must be between \texttt{nit000} and \texttt{nitend} of the simulation.
+A module is available to compute the amplitude and phase of tidal waves.
+This on-line Harmonic analysis is actived with \key{diaharm}.
+Some parameters are available in namelist \ngn{namdia\_harm} :
+- \np{nit000\_han} is the first time step used for harmonic analysis
+- \np{nitend\_han} is the last time step used for harmonic analysis
+- \np{nstep\_han} is the time step frequency for harmonic analysis
+- \np{nb\_ana} is the number of harmonics to analyse
+- \np{tname} is an array with names of tidal constituents to analyse
+\np{nit000\_han} and \np{nitend\_han} must be between \np{nit000} and \np{nitend} of the simulation.
 The restart capability is not implemented.
 The Harmonic analysis solve this equation:
+The Harmonic analysis solve the following equation:
 \begin{equation}
 h_{i} - A_{0} + \sum^{nb\_ana}_{j=1}[A_{j}cos(\nu_{j}t_{j}-\phi_{j})] = e_{i}
 …
 \label{DIA_diag_dct}
 A module is available to compute the transport of volume, heat and salt through sections. This diagnostic
 is actived with \key{diadct}.
+A module is available to compute the transport of volume, heat and salt through sections.
+This diagnostic is actived with \key{diadct}.
 Each section is defined by the coordinates of its 2 extremities. The pathways between them are contructed
 …
 %-------------------------------------------------------------------------------------------------------------
 \texttt{nn\_dct}: frequency of instantaneous transports computing
 \texttt{nn\_dctwri}: frequency of writing ( mean of instantaneous transports )
 \texttt{nn\_debug}: debugging of the section
+\np{nn\_dct}: frequency of instantaneous transports computing
+\np{nn\_dctwri}: frequency of writing ( mean of instantaneous transports )
+\np{nn\_debug}: debugging of the section
 \subsubsection{ To create a binary file containing the pathway of each section }
 …
 the \key{diahth} CPP key:
 - the mixed layer depth (based on a density criterion, \citet{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth})
+- the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth})
 - the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth})

trunk/DOC/TexFiles/Chapters/Chap_DIU.tex

-                      r6140
+                      r6289
 Code to produce an estimate of the diurnal warming and cooling of the sea surface skin
 temperature (skin SST) is found in the DIU directory.  The skin
 temperature can be split into three parts:
+temperature (skin SST) is found in the DIU directory.
+The skin temperature can be split into three parts:
 \begin{itemize}
 \item A foundation SST which is free from diurnal warming.
 …
 Models are provided for both the warm layer, diurnal\_bulk.F90, and the cool skin,
 cool\_skin.F90.  Foundation SST is not considered as it can be obtained
+either from the main NEMO model (i.e. from the temperature of the top few model levels)
+or from
+some other source.  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 both must
+be added to a foundation SST to obtain the true skin temperature.
+either from the main NEMO model ($i.e.$ 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 both must be added to a foundation SST to obtain the true skin temperature.
 Both the cool skin and warm layer models are controlled through the namelist `namdiu':
+Both the cool skin and warm layer models are controlled through the namelist \ngn{namdiu}:
 \namdisplay{namdiu}
 This namelist contains only two variables:
 \begin{description}
 \item[ln\_diurnal] A logical switch for turning on/off both the cool skin and warm layer.
 \item[ln\_diurnal\_only] A logical switch which if .TRUE. will run the diurnal model
 without the other dynamical parts of NEMO.  ln\_diurnal\_only must be
 .FALSE. if ln\_diurnal is .FALSE.
+\item[\np{ln\_diurnal}] A logical switch for turning on/off both the cool skin and warm layer.
+\item[\np{ln\_diurnal\_only}] A logical switch which if .TRUE. will run the diurnal model
+without the other dynamical parts of NEMO.
+\np{ln\_diurnal\_only} must be .FALSE. if \np{ln\_diurnal} is .FALSE.
 \end{description}
 …
 output if they are specified in the iodef.xml file.
+Initialisation is through the restart file.  Specifically the code will expect the presence of the 2-D variable ``Dsst'' to initialise the warm layer.  The cool skin model, which is determined purely by the instantaneous fluxes, has no initialisation variable.
+Initialisation is through the restart file.  Specifically the code will expect
+the presence of the 2-D variable ``Dsst'' to initialise the warm layer.
+The cool skin model, which is determined purely by the instantaneous fluxes,
+has no initialisation variable.
 %===============================================================
 \section{Warm Layer model}
 \label{warm_layer_sec}
 %===============================================================
 …
 (\ref{ecmwf1}) is the instantaneous total thermal energy
 flux into
 the diurnal layer, i.e.
+the diurnal layer, $i.e.$
 \begin{equation}
 Q = Q_{\rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,} \label{e_flux_eqn}
 …
 where $\zeta=\frac{D_T}{L}$.  It is clear that the first derivative of
 (\ref{stab_func_eqn}), and thus of (\ref{ecmwf1}),
 is discontinuous at $\zeta=0$ (i.e. $Q\rightarrow0$ in equation (\ref{ecmwf2})).
+is discontinuous at $\zeta=0$ ($i.e.$ $Q\rightarrow0$ in equation (\ref{ecmwf2})).
 The two terms on the right hand side of (\ref{ecmwf1}) represent different processes.

trunk/DOC/TexFiles/Chapters/Chap_DOM.tex

-                      r6140
+                      r6289
 and $f$-points, and its divergence defined at $t$-points:
 \begin{eqnarray}  \label{Eq_DOM_curl}
  \nabla \times {\rm {\bf A}}\equiv &
+ \nabla \times {\rm{\bf A}}\equiv &
       \frac{1}{e_{2v}\,e_{3vw} } \ \left( \delta_{j +1/2} \left[e_{3w}\,a_3 \right] -\delta_{k+1/2} \left[e_{2v} \,a_2 \right] \right)  &\ \mathbf{i} \\
  +& \frac{1}{e_{2u}\,e_{3uw}} \ \left( \delta_{k+1/2} \left[e_{1u}\,a_1  \right] -\delta_{i +1/2} \left[e_{3w}\,a_3 \right] \right)  &\ \mathbf{j} \\
  +& \frac{1}{e_{1f} \,e_{2f}    } \ \left( \delta_{i +1/2} \left[e_{2v}\,a_2  \right] -\delta_{j +1/2} \left[e_{1u}\,a_1 \right] \right)  &\ \mathbf{k}
  \end{eqnarray}
+\begin{equation} \label{Eq_DOM_div}
+\nabla \cdot \rm{\bf A}=\frac{1}{e_{1t}\,e_{2t}\,e_{3t}}\left( \delta_i \left[e_{2u}\,e_{3u}\,a_1 \right]
+                                                                                         +\delta_j \left[e_{1v}\,e_{3v}\,a_2 \right] \right)+\frac{1}{e_{3t} }\delta_k \left[a_3 \right]
+\end{equation}
+In the special case of a pure $z$-coordinate system, \eqref{Eq_DOM_lap} and
+\eqref{Eq_DOM_div} can be simplified. In this case, the vertical scale factor
+becomes a function of the single variable $k$ and thus does not depend on the
+horizontal location of a grid point. For example \eqref{Eq_DOM_div} reduces to:
+\begin{equation*}
+\nabla \cdot \rm{\bf A}=\frac{1}{e_{1t}\,e_{2t}} \left( \delta_i \left[e_{2u}\,a_1 \right]
+                                                                              +\delta_j \left[e_{1v}\, a_2 \right]  \right)
+                                                     +\frac{1}{e_{3t}} \delta_k \left[             a_3 \right]
+\end{equation*}
+\begin{eqnarray} \label{Eq_DOM_div}
+\nabla \cdot \rm{\bf A} \equiv
+    \frac{1}{e_{1t}\,e_{2t}\,e_{3t}} \left( \delta_i \left[e_{2u}\,e_{3u}\,a_1 \right]
+                                           +\delta_j \left[e_{1v}\,e_{3v}\,a_2 \right] \right)+\frac{1}{e_{3t} }\delta_k \left[a_3 \right]
+\end{eqnarray}
 The vertical average over the whole water column denoted by an overbar becomes
 …
 Let $a$ and $b$ be two fields defined on the mesh, with value zero inside
 continental area. Using integration by parts it can be shown that the differencing
 operators ($\delta_i$, $\delta_j$ and $\delta_k$) are anti-symmetric linear
 operators, and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$,
+operators ($\delta_i$, $\delta_j$ and $\delta_k$) are skew-symmetric linear operators,
+and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$,
 $\overline{\,\cdot\,}^{\,k}$ and $\overline{\,\cdot\,}^{\,k}$) are symmetric linear
 operators, $i.e.$
 …
 The choice of the grid must be consistent with the boundary conditions specified
 by the parameter \np{jperio} (see {\S\ref{LBC}).
+by \np{jperio}, a parameter found in \ngn{namcfg} namelist (see {\S\ref{LBC}).
 % -------------------------------------------------------------------------------------------------------------
 …
 If \np{ln\_isfcav}~=~true, an extra file input file describing the ice shelf draft
 (in meters) (\ifile{isf\_draft\_meter}) is needed and all the location where the isf cavity thinnest
  than \np{rn\_isfhmin} meters are grounded (ie masked).
+ than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked).
 After reading the bathymetry, the algorithm for vertical grid definition differs
 …
 Three options are possible for defining the bathymetry, according to the
 namelist variable \np{nn\_bathy}:
+namelist variable \np{nn\_bathy} (found in \ngn{namdom} namelist):
 \begin{description}
 \item[\np{nn\_bathy} = 0] a flat-bottom domain is defined. The total depth $z_w (jpk)$
 …
 usually 10\%, of the default thickness $e_{3t}(jk)$).
  \colorbox{yellow}{Add a figure here of pstep especially at last ocean level }
+\gmcomment{ \colorbox{yellow}{Add a figure here of pstep especially at last ocean level }  }
 % -------------------------------------------------------------------------------------------------------------
 …
 depth, since a mixed step-like and bottom-following representation of the
 topography can be used (Fig.~\ref{Fig_z_zps_s_sps}d-e) or an envelop bathymetry can be defined (Fig.~\ref{Fig_z_zps_s_sps}f).
+The namelist parameter \np{rn\_rmax} determines the slope at which the terrain-following coordinate intersects the sea bed and becomes a pseudo z-coordinate. The coordinate can also be hybridised by specifying \np{rn\_sbot\_min} and \np{rn\_sbot\_max} as the minimum and maximum depths at which the terrain-following vertical coordinate is calculated.
+Options for stretching the coordinate are provided as examples, but care must be taken to ensure that the vertical stretch used is appropriate for the application.
+The original default NEMO s-coordinate stretching is available if neither of the other options are specified as true (\np{ln\_sco\_SH94}~=~false and \np{ln\_sco\_SF12}~=~false.) This uses a depth independent $\tanh$ function for the stretching \citep{Madec_al_JPO96}:
+The namelist parameter \np{rn\_rmax} determines the slope at which the terrain-following coordinate intersects
+the sea bed and becomes a pseudo z-coordinate.
+The coordinate can also be hybridised by specifying \np{rn\_sbot\_min} and \np{rn\_sbot\_max}
+as the minimum and maximum depths at which the terrain-following vertical coordinate is calculated.
+Options for stretching the coordinate are provided as examples, but care must be taken to ensure
+that the vertical stretch used is appropriate for the application.
+The original default NEMO s-coordinate stretching is available if neither of the other options
+are specified as true (\np{ln\_s\_SH94}~=~false and \np{ln\_s\_SF12}~=~false).
+This uses a depth independent $\tanh$ function for the stretching \citep{Madec_al_JPO96}:
 \begin{equation}
 …
 \end{equation}
+where $s_{min}$ is the depth at which the s-coordinate stretching starts and allows a z-coordinate to placed on top of the stretched coordinate, and z is the depth (negative down from the asea surface).
+where $s_{min}$ is the depth at which the s-coordinate stretching starts and
+allows a z-coordinate to placed on top of the stretched coordinate,
+and z is the depth (negative down from the asea surface).
 \begin{equation}
 …
 \end{equation}
+A stretching function, modified from the commonly used \citet{Song_Haidvogel_JCP94} stretching (\np{ln\_sco\_SH94}~=~true), is also available and is more commonly used for shelf seas modelling:
+A stretching function, modified from the commonly used \citet{Song_Haidvogel_JCP94}
+stretching (\np{ln\_s\_SH94}~=~true), is also available and is more commonly used for shelf seas modelling:
 \begin{equation}
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
+where $H_c$ is the critical depth (\np{rn\_hc}) at which the coordinate transitions from pure $\sigma$ to the stretched coordinate,  and $\theta$ (\np{rn\_theta}) and $b$ (\np{rn\_bb}) are the surface and
+bottom control parameters such that $0\leqslant \theta \leqslant 20$, and
+where $H_c$ is the critical depth (\np{rn\_hc}) at which the coordinate transitions from
+pure $\sigma$ to the stretched coordinate,  and $\theta$ (\np{rn\_theta}) and $b$ (\np{rn\_bb})
+are the surface and bottom control parameters such that $0\leqslant \theta \leqslant 20$, and
 $0\leqslant b\leqslant 1$. $b$ has been designed to allow surface and/or bottom
 increase of the vertical resolution (Fig.~\ref{Fig_sco_function}).
+Another example has been provided at version 3.5 (\np{ln\_sco\_SF12}) that allows a fixed surface resolution in an analytical terrain-following stretching \citet{Siddorn_Furner_OM12}. In this case the a stretching function $\gamma$ is defined such that:
+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}.
+In this case the a stretching function $\gamma$ is defined such that:
 \begin{equation}
 …
 \end{equation}
+This gives an analytical stretching of $\sigma$ that is solvable in $A$ and $B$ as a function of the user prescribed stretching parameter $\alpha$ (\np{rn\_alpha}) that stretches towards the surface ($\alpha > 1.0$) or the bottom ($\alpha < 1.0$) and user prescribed surface (\np{rn\_zs}) and bottom depths. The bottom cell depth in this example is given as a function of water depth:
+This gives an analytical stretching of $\sigma$ that is solvable in $A$ and $B$ as a function of
+the user prescribed stretching parameter $\alpha$ (\np{rn\_alpha}) that stretches towards
+the surface ($\alpha > 1.0$) or the bottom ($\alpha < 1.0$) and user prescribed surface (\np{rn\_zs})
+and bottom depths. The bottom cell depth in this example is given as a function of water depth:
 \begin{equation} \label{DOM_zb}
 …
 \label{DOM_zgr_star}
+This option is described in the Report by Levier \textit{et al.} (2007), available on
+the \NEMO web site.
+This option is described in the Report by Levier \textit{et al.} (2007), available on the \NEMO web site.
 %gm% key advantage: minimise the diffusion/dispertion associated with advection in response to high frequency surface disturbances

trunk/DOC/TexFiles/Chapters/Chap_DYN.tex

-                      r6140
+                      r6289
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
+Note that a key point in \eqref{Eq_een_e3f} is that the averaging in the \textbf{i}- and
+\textbf{j}- directions uses the masked vertical scale factor but is always divided by
+$4$, not by the sum of the masks at the four $T$-points. This preserves the continuity of
+$e_{3f}$ when one or more of the neighbouring $e_{3t}$ tends to zero and
+extends by continuity the value of $e_{3f}$ into the land areas. This feature is essential for
+the $z$-coordinate with partial steps.
+A key point in \eqref{Eq_een_e3f} is how the averaging in the \textbf{i}- and \textbf{j}- directions is made.
+It uses the sum of masked t-point vertical scale factor divided either
+by the sum of the four t-point masks (\np{nn\_een\_e3f}~=~1),
+or  just by $4$ (\np{nn\_een\_e3f}~=~true).
+The latter case preserves the continuity of $e_{3f}$ when one or more of the neighbouring $e_{3t}$
+tends to zero and extends by continuity the value of $e_{3f}$ into the land areas.
+This case introduces a sub-grid-scale topography at f-points (with a systematic reduction of $e_{3f}$
+when a model level intercept the bathymetry) that tends to reinforce the topostrophy of the flow
+($i.e.$ the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.
 Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as
 …
 \end{aligned}         \right.
 \end{equation}
+When \np{ln\_dynzad\_zts}~=~\textit{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}.
+Note that in this case, a similar split-explicit time stepping should be used on
+vertical advection of tracer to ensure a better stability,
+an option which is only available with a TVD scheme (see \np{ln\_traadv\_tvd\_zts} in \S\ref{TRA_adv_tvd}).
 % ================================================================
 …
 $\ $\newline      %force an empty line
-%%%
 Options are defined through the \ngn{namdyn\_spg} namelist variables.
+The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}). The main distinction is between the fixed volume case (linear free surface) and the variable volume case (nonlinear free surface, \key{vvl} is defined). In the linear free surface case (\S\ref{PE_free_surface}) the vertical scale factors $e_{3}$ are fixed in time, while they are time-dependent in the nonlinear case (\S\ref{PE_free_surface}). With both linear and nonlinear free surface, external gravity waves are allowed in the equations, 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 \eqref{Eq_PE_flt}), and the split-explicit free surface described below. The extra term introduced in the filtered method is calculated implicitly, so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}.
+%%%
+The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}).
+The main distinction is between the fixed volume case (linear free surface) and the variable volume case
+(nonlinear free surface, \key{vvl} is defined). In the linear free surface case (\S\ref{PE_free_surface})
+the vertical scale factors $e_{3}$ are fixed in time, while they are time-dependent in the nonlinear case
+(\S\ref{PE_free_surface}).
+With both linear and nonlinear free surface, external gravity waves are allowed in the equations,
+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 \eqref{Eq_PE_flt}),
+and the split-explicit free surface described below.
+The extra term introduced in the filtered method is calculated implicitly,
+so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}.
 …
 implicitly, so that a solver is used to compute it. As a consequence the update of the $next$
 velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}.
 …
 $\rdt_e = \rdt / nn\_baro$. This parameter can be optionally defined automatically (\np{ln\_bt\_nn\_auto}=true)
 considering that the stability of the barotropic system is essentially controled by external waves propagation.
+Maximum allowed Courant number is in that case time independent, and easily computed online from the input bathymetry.
+Maximum Courant number is in that case time independent, and easily computed online from the input bathymetry.
+Therefore, $\rdt_e$ is adjusted so that the Maximum allowed Courant number is smaller than \np{rn\_bt\_cmax}.
 %%%
 …
 Schematic of the split-explicit time stepping scheme for the external
 and internal modes. Time increases to the right. In this particular exemple,
 a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_filt=1$) and $nn\_baro=5$.
+a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_flt=1$) and $nn\_baro=5$.
 Internal mode time steps (which are also the model time steps) are denoted
 by $t-\rdt$, $t$ and $t+\rdt$. Variables with $k$ superscript refer to instantaneous barotropic variables,
 …
 The former are used to obtain time filtered quantities at $t+\rdt$ while the latter are used to obtain time averaged
 transports to advect tracers.
 a) Forward time integration: \np{ln\_bt\_fw}=true, \np{ln\_bt\_ave}=true.
 b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_ave}=true.
 c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_ave}=false. }
+a) Forward time integration: \np{ln\_bt\_fw}=true,  \np{ln\_bt\_av}=true.
+b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_av}=true.
+c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_av}=false. }
 \end{center}    \end{figure}
 %>   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >
 …
 In the default case (\np{ln\_bt\_fw}=true), the external mode is integrated
 between \textit{now} and  \textit{after} baroclinic time-steps (Fig.~\ref{Fig_DYN_dynspg_ts}a). To avoid aliasing of fast barotropic motions into three dimensional equations, time filtering is eventually applied on barotropic
 quantities (\np{ln\_bt\_ave}=true). In that case, the integration is extended slightly beyond  \textit{after} time step to provide time filtered quantities.
+quantities (\np{ln\_bt\_av}=true). In that case, the integration is extended slightly beyond  \textit{after} time step to provide time filtered quantities.
 These are used for the subsequent initialization of the barotropic mode in the following baroclinic step.
 Since external mode equations written at baroclinic time steps finally follow a forward time stepping scheme,
 …
 %%%
 One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_ave}=false).
+One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_av}=false).
 In that case, external mode equations are continuous in time, ie they are not re-initialized when starting a new
 sub-stepping sequence. This is the method used so far in the POM model, the stability being maintained by refreshing at (almost)
 …
 At the lateral boundaries either free slip, no slip or partial slip boundary
 conditions are applied according to the user's choice (see Chap.\ref{LBC}).
+\gmcomment{
+Hyperviscous operators are frequently used in the simulation of turbulent flows to control
+the dissipation of unresolved small scale features.
+Their primary role is to provide strong dissipation at the smallest scale supported by the grid
+while minimizing the impact on the larger scale features.
+Hyperviscous operators are thus designed to be more scale selective than the traditional,
+physically motivated Laplace operator.
+In finite difference methods, the biharmonic operator is frequently the method of choice to achieve
+this scale selective dissipation since its damping time ($i.e.$ its spin down time)
+scale like $\lambda^{-4}$ for disturbances of wavelength $\lambda$
+(so that short waves damped more rapidelly than long ones),
+whereas the Laplace operator damping time scales only like $\lambda^{-2}$.
+}
 % ================================================================
 …
 Besides the surface and bottom stresses (see the above section) which are
+introduced as boundary conditions on the vertical mixing, two other forcings
+enter the dynamical equations.
+One is the effect of atmospheric pressure on the ocean dynamics.
+Another forcing term is the tidal potential.
+Both of which will be introduced into the reference version soon.
+\gmcomment{atmospheric pressure is there!!!!    include its description }
+introduced as boundary conditions on the vertical mixing, three other forcings
+may enter the dynamical equations by affecting the surface pressure gradient.
+(1) When \np{ln\_apr\_dyn}~=~true (see \S\ref{SBC_apr}), the atmospheric pressure is taken
+into account when computing the surface pressure gradient.
+(2) When \np{ln\_tide\_pot}~=~true and \key{tide} is defined (see \S\ref{SBC_tide}),
+the tidal potential is taken into account when computing the surface pressure gradient.
+(3) When \np{nn\_ice\_embd}~=~2 and LIM or CICE is used ($i.e.$ when the sea-ice is embedded in the ocean),
+the snow-ice mass is taken into account when computing the surface pressure gradient.
+\gmcomment{ missing : the lateral boundary condition !!!   another external forcing
+ }
 % ================================================================
 …
 % ================================================================
-% Neptune effect
-% ================================================================
-\section  [Neptune effect (\textit{dynnept})]
-                {Neptune effect (\mdl{dynnept})}
-\label{DYN_nept}
-The "Neptune effect" (thus named in \citep{HollowayOM86}) is a
-parameterisation of the potentially large effect of topographic form stress
-(caused by eddies) in driving the ocean circulation. Originally developed for
-low-resolution models, in which it was applied via a Laplacian (second-order)
-diffusion-like term in the momentum equation, it can also be applied in eddy
-permitting or resolving models, in which a more scale-selective bilaplacian
-(fourth-order) implementation is preferred. This mechanism has a
-significant effect on boundary currents (including undercurrents), and the
-upwelling of deep water near continental shelves.
-The theoretical basis for the method can be found in
-\citep{HollowayJPO92}, including the explanation of why form stress is not
-necessarily a drag force, but may actually drive the flow.
-\citep{HollowayJPO94} demonstrate the effects of the parameterisation in
-the GFDL-MOM model, at a horizontal resolution of about 1.8 degrees.
-\citep{HollowayOM08} demonstrate the biharmonic version of the
-parameterisation in a global run of the POP model, with an average horizontal
-grid spacing of about 32km.
-The NEMO implementation is a simplified form of that supplied by
-Greg Holloway, the testing of which was described in \citep{HollowayJGR09}.
-The major simplification is that a time invariant Neptune velocity
-field is assumed.  This is computed only once, during start-up, and
-made available to the rest of the code via a module.  Vertical
-diffusive terms are also ignored, and the model topography itself
-is used, rather than a separate topographic dataset as in
-\citep{HollowayOM08}.  This implementation is only in the iso-level
-formulation, as is the case anyway for the bilaplacian operator.
-The velocity field is derived from a transport stream function given by:
-\begin{equation} \label{Eq_dynnept_sf}
-\psi = -fL^2H
-\end{equation}
-where $L$ is a latitude-dependant length scale given by:
-\begin{equation} \label{Eq_dynnept_ls}
-L = l_1 + (l_2 -l_1)\left ( {1 + \cos 2\phi \over 2 } \right )
-\end{equation}
-where $\phi$ is latitude and $l_1$ and $l_2$ are polar and equatorial length scales respectively.
-Neptune velocity components, $u^*$, $v^*$ are derived from the stremfunction as:
-\begin{equation} \label{Eq_dynnept_vel}
-u^* = -{1\over H} {\partial \psi \over \partial y}\ \ \  ,\ \ \ v^* = {1\over H} {\partial \psi \over \partial x}
-\end{equation}
-\smallskip
-%----------------------------------------------namdom----------------------------------------------------
-\namdisplay{namdyn_nept}
-%--------------------------------------------------------------------------------------------------------
-\smallskip
-The Neptune effect is enabled when \np{ln\_neptsimp}=true (default=false).
-\np{ln\_smooth\_neptvel} controls whether a scale-selective smoothing is applied
-to the Neptune effect flow field (default=false) (this smoothing method is as
-used by Holloway).  \np{rn\_tslse} and \np{rn\_tslsp} are the equatorial and
-polar values respectively of the length-scale parameter $L$ used in determining
-the Neptune stream function \eqref{Eq_dynnept_sf} and \eqref{Eq_dynnept_ls}.
-Values at intermediate latitudes are given by a cosine fit, mimicking the
-variation of the deformation radius with latitude.  The default values of 12km
-and 3km are those given in \citep{HollowayJPO94}, appropriate for a coarse
-resolution model. The finer resolution study of \citep{HollowayOM08} increased
-the values of L by a factor of $\sqrt 2$ to 17km and 4.2km, thus doubling the
-stream function for a given topography.
-The simple formulation for ($u^*$, $v^*$) can give unacceptably large velocities
-in shallow water, and \citep{HollowayOM08} add an offset to the depth in the
-denominator to control this problem. In this implementation we offer instead (at
-the suggestion of G. Madec) the option of ramping down the Neptune flow field to
-zero over a finite depth range. The switch \np{ln\_neptramp} activates this
-option (default=false), in which case velocities at depths greater than
-\np{rn\_htrmax} are unaltered, but ramp down linearly with depth to zero at a
-depth of \np{rn\_htrmin} (and shallower).
-% ================================================================

trunk/DOC/TexFiles/Chapters/Chap_LBC.tex

-                      r4147
+                      r6289
 % ================================================================
 % Chapter � Lateral Boundary Condition (LBC)
+% Chapter — Lateral Boundary Condition (LBC)
 % ================================================================
 \chapter{Lateral Boundary Condition (LBC) }
 …
 can be quite shallow.
-The alternative numerical implementation of the no-slip boundary conditions for an
-arbitrary coast line of \citet{Shchepetkin1996} is also available through the
-\key{noslip\_accurate} CPP key. It is based on a fourth order evaluation of the shear at the
-coast which, in turn, allows a true second order scheme in the interior of the domain
-($i.e.$ the numerical boundary scheme simulates the truncation error of the numerical
-scheme used in the interior of the domain). \citet{Shchepetkin1996} found that such a
-technique considerably improves the quality of the numerical solution. In \NEMO, such
-spectacular improvements have not been found in the half-degree global ocean
-(ORCA05), but significant reductions of numerically induced coastal upwellings were
-found in an eddy resolving simulation of the Alboran Sea \citep{Olivier_PhD01}.
-Nevertheless, since a no-slip boundary condition is not recommended in an eddy
-permitting or resolving simulation \citep{Penduff_al_OS07}, the use of this option is also
-not recommended.
-In practice, the no-slip accurate option changes the way the curl is evaluated at the
-coast (see \mdl{divcur} module), and requires the nature of each coastline grid point
-(convex or concave corners, straight north-south or east-west coast) to be specified.
-This is performed in routine \rou{dom\_msk\_nsa} in the \mdl{domask} module.
 % ================================================================
 …
 %        North fold (\textit{jperio = 3 }to $6)$
 % -------------------------------------------------------------------------------------------------------------
 \subsection{North-fold (\textit{jperio = 3 }to $6)$ }
+\subsection{North-fold (\textit{jperio = 3 }to $6$) }
 \label{LBC_north_fold}
 The north fold boundary condition has been introduced in order to handle the north
+boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere.
+\colorbox{yellow}{to be completed...}
+boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere
+(Fig.\ref{Fig_MISC_ORCA_msh}, and thus requires a specific treatment illustrated in Fig.\ref{Fig_North_Fold_T}.
+Further information can be found in \mdl{lbcnfd} module which applies the north fold boundary condition.
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 ocean model. Second order finite difference schemes lead to local discrete
 operators that depend at the very most on one neighbouring point. The only
 non-local computations concern the vertical physics (implicit diffusion, 1.5
+non-local computations concern the vertical physics (implicit diffusion,
 turbulent closure scheme, ...) (delocalization over the whole water column),
 and the solving of the elliptic equation associated with the surface pressure
 gradient computation (delocalization over the whole horizontal domain).
 Therefore, a pencil strategy is used for the data sub-structuration
-\gmcomment{no idea what this means!}
 : the 3D initial domain is laid out on local processor
 memories following a 2D horizontal topological splitting. Each sub-domain
 …
 phase starts: each processor sends to its neighbouring processors the update
 values of the points corresponding to the interior overlapping area to its
+neighbouring sub-domain (i.e. the innermost of the two overlapping rows).
+The communication is done through message passing. Usually the parallel virtual
+language, PVM, is used as it is a standard language available on  nearly  all
+MPP computers. More specific languages (i.e. computer dependant languages)
+can be easily used to speed up the communication, such as SHEM on a T3E
+computer. The data exchanges between processors are required at the very
+neighbouring sub-domain ($i.e.$ the innermost of the two overlapping rows).
+The communication is done through the Message Passing Interface (MPI).
+The data exchanges between processors are required at the very
 place where lateral domain boundary conditions are set in the mono-domain
+computation (\S III.10-c): the lbc\_lnk routine which manages such conditions
+is substituted by mpplnk.F or mpplnk2.F routine when running on an MPP
+computer (\key{mpp\_mpi} defined). It has to be pointed out that when using
+the MPP version of the model, the east-west cyclic boundary condition is done
+implicitly, whilst the south-symmetric boundary condition option is not available.
+computation : the \rou{lbc\_lnk} routine (found in \mdl{lbclnk} module)
+which manages such conditions is interfaced with routines found in \mdl{lib\_mpp} module
+when running on an MPP computer ($i.e.$ when \key{mpp\_mpi} defined).
+It has to be pointed out that when using the MPP version of the model,
+the east-west cyclic boundary condition is done implicitly,
+whilst the south-symmetric boundary condition option is not available.
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
+In the standard version of the OPA model, the splitting is regular and arithmetic.
+ the i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors
+ \jp{jpnij} most often equal to $jpni \times jpnj$ (model parameters set in
+ \mdl{par\_oce}). Each processor is independent and without message passing
+ or synchronous process
+ \gmcomment{how does a synchronous process relate to this?},
+ programs run alone and access just its own local memory. For this reason, the
+ main model dimensions are now the local dimensions of the subdomain (pencil)
+In the standard version of \NEMO, the splitting is regular and arithmetic.
+The i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors
+\jp{jpnij} most often equal to $jpni \times jpnj$ (parameters set in
+ \ngn{nammpp} namelist). Each processor is independent and without message passing
+ or synchronous process, programs run alone and access just its own local memory.
+ For this reason, the main model dimensions are now the local dimensions of the subdomain (pencil)
  that are named \jp{jpi}, \jp{jpj}, \jp{jpk}. These dimensions include the internal
  domain and the overlapping rows. The number of rows to exchange (known as
 …
 where \jp{jpni}, \jp{jpnj} are the number of processors following the i- and j-axis.
+\colorbox{yellow}{Figure IV.3: example of a domain splitting with 9 processors and
+no east-west cyclic boundary conditions.}
+One also defines variables nldi and nlei which correspond to the internal
+domain bounds, and the variables nimpp and njmpp which are the position
+of the (1,1) grid-point in the global domain. An element of $T_{l}$, a local array
+(subdomain) corresponds to an element of $T_{g}$, a global array
+(whole domain) by the relationship:
+One also defines variables nldi and nlei which correspond to the internal domain bounds,
+and the variables nimpp and njmpp which are the position of the (1,1) grid-point in the global domain.
+An element of $T_{l}$, a local array (subdomain) corresponds to an element of $T_{g}$,
+a global array (whole domain) by the relationship:
 \begin{equation} \label{Eq_lbc_nimpp}
 T_{g} (i+nimpp-1,j+njmpp-1,k) = T_{l} (i,j,k),
 …
 nproc. In the standard version, a processor has no more than four neighbouring
 processors named nono (for north), noea (east), noso (south) and nowe (west)
+and two variables, nbondi and nbondj, indicate the relative position of the processor
+\colorbox{yellow}{(see Fig.IV.3)}:
+and two variables, nbondi and nbondj, indicate the relative position of the processor :
 \begin{itemize}
 \item       nbondi = -1    an east neighbour, no west processor,
 …
 processor on its overlapping row, and sends the data issued from internal
 domain corresponding to the overlapping row of the other processor.
-\colorbox{yellow}{Figure IV.4: pencil splitting with the additional outer halos }
 …
 global ocean where more than 50 \% of points are land points. For this reason, a
 pre-processing tool can be used to choose the mpp domain decomposition with a
 maximum number of only land points processors, which can then be eliminated.
 (For example, the mpp\_optimiz tools, available from the DRAKKAR web site.)
+maximum number of only land points processors, which can then be eliminated (Fig. \ref{Fig_mppini2})
+(For example, the mpp\_optimiz tools, available from the DRAKKAR web site).
 This optimisation is dependent on the specific bathymetry employed. The user
 then chooses optimal parameters \jp{jpni}, \jp{jpnj} and \jp{jpnij} with
 $jpnij < jpni \times jpnj$, leading to the elimination of $jpni \times jpnj - jpnij$
 land processors. When those parameters are specified in module \mdl{par\_oce},
+land processors. When those parameters are specified in \ngn{nammpp} namelist,
 the algorithm in the \rou{inimpp2} routine sets each processor's parameters (nbound,
 nono, noea,...) so that the land-only processors are not taken into account.
 \colorbox{yellow}{Note that the inimpp2 routine is general so that the original inimpp
+\gmcomment{Note that the inimpp2 routine is general so that the original inimpp
 routine should be suppressed from the code.}
 When land processors are eliminated, the value corresponding to these locations in
+the model output files is zero. Note that this is a problem for a mesh output file written
+by such a model configuration, because model users often divide by the scale factors
+($e1t$, $e2t$, etc) and do not expect the grid size to be zero, even on land. It may be
+best not to eliminate land processors when running the model especially to write the
+mesh files as outputs (when \np{nn\_msh} namelist parameter differs from 0).
+%%
+\gmcomment{Steven : dont understand this, no land processor means no output file
+covering this part of globe; its only when files are stitched together into one that you
+can leave a hole}
+%%
+the model output files is undefined. Note that this is a problem for the meshmask file
+which requires to be defined over the whole domain. Therefore, user should not eliminate
+land processors when creating a meshmask file ($i.e.$ when setting a non-zero value to \np{nn\_msh}).
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-% ================================================================
-% Open Boundary Conditions
-% ================================================================
-\section{Open Boundary Conditions (\key{obc}) (OBC)}
-\label{LBC_obc}
-%-----------------------------------------nam_obc  -------------------------------------------
-%-    nobc_dta    =    0     !  = 0 the obc data are equal to the initial state
-%-                           !  = 1 the obc data are read in 'obc   .dta' files
-%-    rn_dpein      =    1.    !  ???
-%-    rn_dpwin      =    1.    !  ???
-%-    rn_dpnin      =   30.    !  ???
-%-    rn_dpsin      =    1.    !  ???
-%-    rn_dpeob      = 1500.    !  time relaxation (days) for the east  open boundary
-%-    rn_dpwob      =   15.    !    "        "           for the west  open boundary
-%-    rn_dpnob      =  150.    !    "        "           for the north open boundary
-%-    rn_dpsob      =   15.    !    "        "           for the south open boundary
-%-    ln_obc_clim = .true.   !  climatological obc data files (default T)
-%-    ln_vol_cst  = .true.   !  total volume conserved
-\namdisplay{namobc}
-It is often necessary to implement a model configuration limited to an oceanic
-region or a basin, which communicates with the rest of the global ocean through
-''open boundaries''. As stated by \citet{Roed1986}, an open boundary is a
-computational border where the aim of the calculations is to allow the perturbations
-generated inside the computational domain to leave it without deterioration of the
-inner model solution. However, an open boundary also has to let information from
-the outer ocean enter the model and should support inflow and outflow conditions.
-The open boundary package OBC is the first open boundary option developed in
-NEMO (originally in OPA8.2). It allows the user to
-\begin{itemize}
-\item tell the model that a boundary is ''open'' and not closed by a wall, for example
-by modifying the calculation of the divergence of velocity there;
-\item impose values of tracers and velocities at that boundary (values which may
-be taken from a climatology): this is the``fixed OBC'' option.
-\item calculate boundary values by a sophisticated algorithm combining radiation
-and relaxation (``radiative OBC'' option)
-\end{itemize}
-Options are defined through the \ngn{namobc} namelist variables.
-The package resides in the OBC directory. It is described here in four parts: the
-boundary geometry (parameters to be set in \mdl{obc\_par}), the forcing data at
-the boundaries (module \mdl{obcdta}),  the radiation algorithm involving the
-namelist and module \mdl{obcrad}, and a brief presentation of boundary update
-and restart files.
-%----------------------------------------------
-\subsection{Boundary geometry}
-\label{OBC_geom}
+%
-First one has to realize that open boundaries may not necessarily be located
-at the extremities of the computational domain. They may exist in the middle
-of the domain, for example at Gibraltar Straits if one wants to avoid including
-the Mediterranean in an Atlantic domain. This flexibility has been found necessary
-for the CLIPPER project \citep{Treguier_al_JGR01}. Because of the complexity of the
-geometry of ocean basins, it may even be necessary to have more than one
-''west'' open boundary, more than one ''north'', etc. This is not possible with
-the OBC option: only one open boundary of each kind, west, east, south and
-north is allowed; these names refer to the grid geometry (not to the direction
-of the geographical ''west'', ''east'', etc).
-The open boundary geometry is set by a series of parameters in the module
-\mdl{obc\_par}. For an eastern open boundary, parameters are \jp{lp\_obc\_east}
-(true if an east open boundary exists), \jp{jpieob} the $i$-index along which
-the eastern open boundary (eob) is located, \jp{jpjed} the $j$-index at which
-it starts, and \jp{jpjef} the $j$-index where it ends (note $d$ is for ''d\'{e}but''
-and $f$ for ''fin'' in French). Similar parameters exist for the west, south and
-north cases (Table~\ref{Tab_obc_param}).
-%--------------------------------------------------TABLE--------------------------------------------------
-\begin{table}[htbp]     \begin{center}    \begin{tabular}{|l|c|c|c|}
-\hline
-Boundary and  & Constant index  & Starting index (d\'{e}but) & Ending index (fin) \\
-Logical flag  &                 &                            &                     \\
-\hline
-West          & \jp{jpiwob} $>= 2$         &  \jp{jpjwd}$>= 2$          &  \jp{jpjwf}<= \np{jpjglo}-1 \\
-lp\_obc\_west & $i$-index of a $u$ point   & $j$ of a $T$ point   &$j$ of a $T$ point \\
-\hline
-East            & \jp{jpieob}$<=$\np{jpiglo}-2&\jp{jpjed} $>= 2$         & \jp{jpjef}$<=$ \np{jpjglo}-1 \\
- lp\_obc\_east  & $i$-index of a $u$ point    & $j$ of a $T$ point & $j$ of a $T$ point \\
-\hline
-South           & \jp{jpjsob} $>= 2$         & \jp{jpisd} $>= 2$          & \jp{jpisf}$<=$\np{jpiglo}-1 \\
-lp\_obc\_south  & $j$-index of a $v$ point   & $i$ of a $T$ point   & $i$ of a $T$ point \\
-\hline
-North           & \jp{jpjnob} $<=$ \np{jpjglo}-2& \jp{jpind} $>= 2$        & \jp{jpinf}$<=$\np{jpiglo}-1 \\
-lp\_obc\_north  & $j$-index of a $v$ point      & $i$  of a $T$ point & $i$ of a $T$ point \\
-\hline
-\end{tabular}    \end{center}
-\caption{     \label{Tab_obc_param}
-Names of different indices relating to the open boundaries. In the case
-of a completely open ocean domain with four ocean boundaries, the parameters
-take exactly the values indicated.}
-\end{table}
-%------------------------------------------------------------------------------------------------------------
-The open boundaries must be along coordinate lines. On the C-grid, the boundary
-itself is along a line of normal velocity points: $v$ points for a zonal open boundary
-(the south or north one), and $u$ points for a meridional open boundary (the west
-or east one). Another constraint is that there still must be a row of masked points
-all around the domain, as if the domain were a closed basin (unless periodic conditions
-are used together with open boundary conditions). Therefore, an open boundary
-cannot be located at the first/last index, namely, 1, \jp{jpiglo} or \jp{jpjglo}. Also,
-the open boundary algorithm involves calculating the normal velocity points situated
-just on the boundary, as well as the tangential velocity and temperature and salinity
-just outside the boundary. This means that for a west/south boundary, normal
-velocities and temperature are calculated at the same index \jp{jpiwob} and
-\jp{jpjsob}, respectively. For an east/north boundary, the normal velocity is
-calculated at index \jp{jpieob} and \jp{jpjnob}, but the ``outside'' temperature is
-at index \jp{jpieob}+1 and \jp{jpjnob}+1. This means that \jp{jpieob}, \jp{jpjnob}
-cannot be bigger than \jp{jpiglo}-2, \jp{jpjglo}-2.
-The starting and ending indices are to be thought of as $T$ point indices: in many
-cases they indicate the first land $T$-point, at the extremity of an open boundary
-(the coast line follows the $f$ grid points, see Fig.~\ref{Fig_obc_north} for an example
-of a northern open boundary). All indices are relative to the global domain. In the
-free surface case it is possible to have ``ocean corners'', that is, an open boundary
-starting and ending in the ocean.
-%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}[!t]     \begin{center}
-\includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_obc_north.pdf}
-\caption{    \label{Fig_obc_north}
-Localization of the North open boundary points.}
-\end{center}     \end{figure}
-%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-Although not compulsory, it is highly recommended that the bathymetry in the
-vicinity of an open boundary follows the following rule: in the direction perpendicular
-to the open line, the water depth should be constant for 4 grid points. This is in
-order to ensure that the radiation condition, which involves model variables next
-to the boundary, is calculated in a consistent way. On Fig.\ref{Fig_obc_north} we
-indicate by an $=$ symbol, the points which should have the same depth. It means
-that at the 4 points near the boundary, the bathymetry is cylindrical \gmcomment{not sure
-why cylindrical}. The line behind the open $T$-line must be 0 in the bathymetry file
-(as shown on Fig.\ref{Fig_obc_north} for example).
-%----------------------------------------------
-\subsection{Boundary data}
-\label{OBC_data}
-It is necessary to provide information at the boundaries. The simplest case is
-when this information does not change in time and is equal to the initial conditions
-(namelist variable \np{nn\_obcdta}=0). This is the case for the standard configuration
-EEL5 with open boundaries. When (\np{nn\_obcdta}=1), open boundary information
-is read from netcdf files. For convenience the input files are supposed to be similar
-to the ''history'' NEMO output files, for dimension names and variable names.
-Open boundary arrays must be dimensioned according to the parameters of table~
-\ref{Tab_obc_param}: for example, at the western boundary, arrays have a
-dimension of \jp{jpwf}-\jp{jpwd}+1 in the horizontal and \jp{jpk} in the vertical.
-When ocean observations are used to generate the boundary data (a hydrographic
-section for example, as in \citet{Treguier_al_JGR01}) it happens often that only the velocity
-normal to the boundary is known, which is the reason why the initial OBC code
-assumes that only $T$, $S$, and the normal velocity ($u$ or $v$) needs to be
-specified. As more and more global model solutions and ocean analysis products
-become available, it will be possible to provide information about all the variables
-(including the tangential velocity) so that the specification of four variables at each
-boundaries will become standard. For the sea surface height, one must distinguish
-between the filtered free surface case and the time-splitting or explicit treatment of
-the free surface.
- In the first case, it is assumed that the user does not wish to represent high
- frequency motions such as tides. The boundary condition is thus one of zero
- normal gradient of sea surface height at the open boundaries, following \citet{Marchesiello2001}.
-No information other than the total velocity needs to be provided at the open
-boundaries in that case. In the other two cases (time splitting or explicit free surface),
-the user must provide barotropic information (sea surface height and barotropic
-velocities) and the use of the Flather algorithm for barotropic variables is
-recommanded. However, this algorithm has not yet been fully tested and bugs
-remain in NEMO v2.3. Users should read the code carefully before using it. Finally,
-in the case of the rigid lid approximation the barotropic streamfunction must be
-provided, as documented in \citet{Treguier_al_JGR01}). This option is no longer
-recommended but remains in NEMO V2.3.
-One frequently encountered case is when an open boundary domain is constructed
-from a global or larger scale NEMO configuration. Assuming the domain corresponds
-to indices $ib:ie$, $jb:je$ of the global domain, the bathymetry and forcing of the
-small domain can be created by using the following netcdf utility on the global files:
-ncks -F $-d\;x,ib,ie$ $-d\;y,jb,je$ (part of the nco series of utilities,
-see their \href{http://nco.sourceforge.net}{website}).
-The open boundary files can be constructed using ncks
-commands, following table~\ref{Tab_obc_ind}.
-%--------------------------------------------------TABLE--------------------------------------------------
-\begin{table}[htbp]     \begin{center}      \begin{tabular}{|l|c|c|c|c|c|}
-\hline
-OBC  & Variable   & file name      & Index  & Start  & end  \\
-West &  T,S       &   obcwest\_TS.nc &  $ib$+1     &   $jb$+1 &  $je-1$  \\
-     &    U       &   obcwest\_U.nc  &  $ib$+1     &   $jb$+1 &  $je-1$  \\
-     &    V       &   obcwest\_V.nc  &  $ib$+1     &   $jb$+1 &  $je-1$  \\
-\hline
-East &  T,S       &   obceast\_TS.nc &  $ie$-1     &   $jb$+1 &  $je-1$  \\
-     &    U       &   obceast\_U.nc  &  $ie$-2     &   $jb$+1 &  $je-1$  \\
-     &    V       &   obceast\_V.nc  &  $ie$-1     &   $jb$+1 &  $je-1$  \\
-\hline
-South &  T,S      &   obcsouth\_TS.nc &  $jb$+1     &  $ib$+1 &  $ie-1$  \\
-      &    U      &   obcsouth\_U.nc  &  $jb$+1     &  $ib$+1 &  $ie-1$  \\
-      &    V      &   obcsouth\_V.nc  &  $jb$+1     &  $ib$+1 &  $ie-1$  \\
-\hline
-North &  T,S      &   obcnorth\_TS.nc &  $je$-1     &  $ib$+1 &  $ie-1$  \\
-      &    U      &   obcnorth\_U.nc  &  $je$-1     &  $ib$+1 &  $ie-1$  \\
-      &    V      &   obcnorth\_V.nc  &  $je$-2     &  $ib$+1 &  $ie-1$  \\
-\hline
-\end{tabular}     \end{center}
-\caption{    \label{Tab_obc_ind}
-Requirements for creating open boundary files from a global configuration,
-appropriate for the subdomain of indices $ib:ie$, $jb:je$. ``Index'' designates the
-$i$ or $j$ index along which the $u$ of $v$ boundary point is situated in the global
-configuration, starting and ending with the $j$ or $i$ indices indicated.
-For example, to generate file obcnorth\_V.nc, use the command ncks
-$-F$ $-d\;y,je-2$  $-d\;x,ib+1,ie-1$ }
-\end{table}
-%-----------------------------------------------------------------------------------------------------------
-It is assumed that the open boundary files contain the variables for the period of
-the model integration. If the boundary files contain one time frame, the boundary
-data is held fixed in time. If the files contain 12 values, it is assumed that the input
-is a climatology for a repeated annual cycle (corresponding to the case \np{ln\_obc\_clim}
-=true). The case of an arbitrary number of time frames is not yet implemented
-correctly; the user is required to write his own code in the module \mdl{obc\_dta}
-to deal with this situation.
-\subsection{Radiation algorithm}
-\label{OBC_rad}
-The art of open boundary management consists in applying a constraint strong
-enough that the inner domain "feels" the rest of the ocean, but weak enough
-that perturbations are allowed to leave the domain with minimum false reflections
-of energy. The constraints are specified separately at each boundary as time
-scales for ''inflow'' and ''outflow'' as defined below. The time scales are set (in days)
-by namelist parameters such as \np{rn\_dpein}, \np{rn\_dpeob} for the eastern open
-boundary for example. When both time scales are zero for a given boundary
-($e.g.$ for the western boundary, \jp{lp\_obc\_west}=true, \np{rn\_dpwob}=0 and
-\np{rn\_dpwin}=0) this means that the boundary in question is a ''fixed '' boundary
-where the solution is set exactly by the boundary data. This is not recommended,
-except in combination with increased viscosity in a ''sponge'' layer next to the
-boundary in order to avoid spurious reflections.
-The radiation\/relaxation \gmcomment{the / doesnt seem to appear in the output}
-algorithm is applied when either relaxation time (for ''inflow'' or ''outflow'') is
-non-zero. It has been developed and tested in the SPEM model and its
-successor ROMS \citep{Barnier1996, Marchesiello2001}, which is an
-$s$-coordinate model on an Arakawa C-grid. Although the algorithm has
-been numerically successful in the CLIPPER Atlantic models, the physics
-do not work as expected \citep{Treguier_al_JGR01}. Users are invited to consider
-open boundary conditions (OBC hereafter) with some scepticism
-\citep{Durran2001, Blayo2005}.
-The first part of the algorithm calculates a phase velocity to determine
-whether perturbations tend to propagate toward, or away from, the
-boundary. Let us consider a model variable $\phi$.
-The phase velocities ($C_{\phi x}$,$C_{\phi y}$) for the variable $\phi$,
-in the directions normal and tangential to the boundary are
-\begin{equation} \label{Eq_obc_cphi}
-C_{\phi x} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{x}
-\;\;\;\;\; \;\;\;
-C_{\phi y} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{y}.
-\end{equation}
-Following \citet{Treguier_al_JGR01} and \citet{Marchesiello2001} we retain only
-the normal component of the velocity, $C_{\phi x}$, setting $C_{\phi y} =0$
-(but unlike the original Orlanski radiation algorithm we retain $\phi_{y}$ in
-the expression for $C_{\phi x}$).
-The discrete form of (\ref{Eq_obc_cphi}), described by \citet{Barnier1998},
-takes into account the two rows of grid points situated inside the domain
-next to the boundary, and the three previous time steps ($n$, $n-1$,
-and $n-2$). The same equation can then be discretized at the boundary at
-time steps $n-1$, $n$ and $n+1$ \gmcomment{since the original was three time-level}
-in order to extrapolate for the new boundary value $\phi^{n+1}$.
-In the open boundary algorithm as implemented in NEMO v2.3, the new boundary
-values are updated differently depending on the sign of $C_{\phi x}$. Let us take
-an eastern boundary as an example. The solution for variable $\phi$ at the
-boundary is given by a generalized wave equation with phase velocity $C_{\phi}$,
-with the addition of a relaxation term, as:
-\begin{eqnarray}
-\phi_{t} &  =  & -C_{\phi x} \phi_{x} + \frac{1}{\tau_{o}} (\phi_{c}-\phi)
-                        \;\;\; \;\;\; \;\;\; (C_{\phi x} > 0), \label{Eq_obc_rado} \\
-\phi_{t} &  =  & \frac{1}{\tau_{i}} (\phi_{c}-\phi)
-\;\;\; \;\;\; \;\;\;\;\;\; (C_{\phi x} < 0), \label{Eq_obc_radi}
-\end{eqnarray}
-where $\phi_{c}$ is the estimate of $\phi$ at the boundary, provided as boundary
-data. Note that in (\ref{Eq_obc_rado}), $C_{\phi x}$ is bounded by the ratio
-$\delta x/\delta t$ for stability reasons. When $C_{\phi x}$ is eastward (outward
-propagation), the radiation condition (\ref{Eq_obc_rado}) is used.
-When  $C_{\phi x}$ is westward (inward propagation), (\ref{Eq_obc_radi}) is
-used with a strong relaxation to climatology (usually $\tau_{i}=\np{rn\_dpein}=$1~day).
-Equation (\ref{Eq_obc_radi}) is solved with a Euler time-stepping scheme. As a
-consequence, setting $\tau_{i}$ smaller than, or equal to the time step is equivalent
-to a fixed boundary condition. A time scale of one day is usually a good compromise
-which guarantees that the inflow conditions remain close to climatology while ensuring
-numerical stability.
-In  the case of a western boundary located in the Eastern Atlantic, \citet{Penduff_al_JGR00}
-have been able to implement the radiation algorithm without any boundary data,
-using persistence from the previous time step instead. This solution has not worked
-in other cases \citep{Treguier_al_JGR01}, so that the use of boundary data is recommended.
-Even in the outflow condition (\ref{Eq_obc_rado}), we have found it desirable to
-maintain a weak relaxation to climatology. The time step is usually chosen so as to
-be larger than typical turbulent scales (of order 1000~days \gmcomment{or maybe seconds?}).
-The radiation condition is applied to the model variables: temperature, salinity,
-tangential and normal velocities. For normal and tangential velocities, $u$ and $v$,
-radiation is applied with phase velocities calculated from $u$ and $v$ respectively.
-For the radiation of tracers, we use the phase velocity calculated from the tangential
-velocity in order to avoid calculating too many independent radiation velocities and
-because tangential velocities and tracers have the same position along the boundary
-on a C-grid.
-\subsection{Domain decomposition (\key{mpp\_mpi})}
-\label{OBC_mpp}
-When \key{mpp\_mpi} is active in the code, the computational domain is divided
-into rectangles that are attributed each to a different processor. The open boundary
-code is ``mpp-compatible'' up to a certain point. The radiation algorithm will not
-work if there is an mpp subdomain boundary parallel to the open boundary at the
-index of the boundary, or the grid point after (outside), or three grid points before
-(inside). On the other hand, there is no problem if an mpp subdomain boundary
-cuts the open boundary perpendicularly. These geometrical limitations must be
-checked for by the user (there is no safeguard in the code).
-The general principle for the open boundary mpp code is that loops over the open
-boundaries {not sure what this means} are performed on local indices (nie0,
-nie1, nje0, nje1 for an eastern boundary for instance) that are initialized in module
-\mdl{obc\_ini}. Those indices have relevant values on the processors that contain
-a segment of an open boundary. For processors that do not include an open
-boundary segment, the indices are such that the calculations within the loops are
-not performed.
-\gmcomment{I dont understand most of the last few sentences}
-Arrays of climatological data that are read from files are seen by all processors
-and have the same dimensions for all (for instance, for the eastern boundary,
-uedta(jpjglo,jpk,2)). On the other hand, the arrays for the calculation of radiation
-are local to each processor (uebnd(jpj,jpk,3,3) for instance).  This allowed the
-CLIPPER model for example, to save on memory where the eastern boundary
-crossed 8 processors so that \jp{jpj} was much smaller than (\jp{jpjef}-\jp{jpjed}+1).
-\subsection{Volume conservation}
-\label{OBC_vol}
-It is necessary to control the volume inside a domain when using open boundaries.
-With fixed boundaries, it is enough to ensure that the total inflow/outflow has
-reasonable values (either zero or a value compatible with an observed volume
-balance). When using radiative boundary conditions it is necessary to have a
-volume constraint because each open boundary works independently from the
-others. The methodology used to control this volume is identical to the one
-coded in the ROMS model \citep{Marchesiello2001}.
-%---------------------------------------- EXTRAS
-\colorbox{yellow}{Explain obc\_vol{\ldots}}
-\colorbox{yellow}{OBC algorithm for update, OBC restart, list of routines where obc key appears{\ldots}}
-\colorbox{yellow}{OBC rigid lid? {\ldots}}
 % ====================================================================

trunk/DOC/TexFiles/Chapters/Chap_LDF.tex

-                      r6140
+                      r6289
  r_{1u} &= \frac{e_{3u}}{ \left( e_{1u}\;\overline{\overline{e_{3w}}}^{\,i+1/2,\,k} \right)}
            \;\delta_{i+1/2}[z_t]
       &\approx \frac{1}{e_{1u}}\; \delta_{i+1/2}[z_t]
+      &\approx \frac{1}{e_{1u}}\; \delta_{i+1/2}[z_t] \ \ \
 \\
  r_{2v} &= \frac{e_{3v}}{\left( e_{2v}\;\overline{\overline{e_{3w}}}^{\,j+1/2,\,k} \right)}
            \;\delta_{j+1/2} [z_t]
       &\approx \frac{1}{e_{2v}}\; \delta_{j+1/2}[z_t]
+      &\approx \frac{1}{e_{2v}}\; \delta_{j+1/2}[z_t] \ \ \
 \\
  r_{1w} &= \frac{1}{e_{1w}}\;\overline{\overline{\delta_{i+1/2}[z_t]}}^{\,i,\,k+1/2}
 …
 \label{LDF_eiv}
+%%gm  from Triad appendix  : to be incorporated....
+\gmcomment{
+Values of iso-neutral diffusivity and GM coefficient are set as
+described in \S\ref{LDF_coef}. If none of the keys \key{traldf\_cNd},
+N=1,2,3 is set (the default), spatially constant iso-neutral $A_l$ and
+GM diffusivity $A_e$ are directly set by \np{rn\_aeih\_0} and
+\np{rn\_aeiv\_0}. If 2D-varying coefficients are set with
+\key{traldf\_c2d} then $A_l$ is reduced in proportion with horizontal
+scale factor according to \eqref{Eq_title} \footnote{Except in global ORCA
+  $0.5^{\circ}$ runs with \key{traldf\_eiv}, where
+  $A_l$ is set like $A_e$ but with a minimum vale of
+  $100\;\mathrm{m}^2\;\mathrm{s}^{-1}$}. In idealised setups with
+\key{traldf\_c2d}, $A_e$ is reduced similarly, but if \key{traldf\_eiv}
+is set in the global configurations with \key{traldf\_c2d}, a horizontally varying $A_e$ is
+instead set from the Held-Larichev parameterisation\footnote{In this
+  case, $A_e$ at low latitudes $|\theta|<20^{\circ}$ is further
+  reduced by a factor $|f/f_{20}|$, where $f_{20}$ is the value of $f$
+  at $20^{\circ}$~N} (\mdl{ldfeiv}) and \np{rn\_aeiv\_0} is ignored
+unless it is zero.
+}
 When Gent and McWilliams [1990] diffusion is used (\key{traldf\_eiv} defined),
 an eddy induced tracer advection term is added, the formulation of which

trunk/DOC/TexFiles/Chapters/Chap_MISC.tex

-                      r5118
+                      r6289
 % ================================================================
 % Chapter � Miscellaneous Topics
+% Chapter ——— Miscellaneous Topics
 % ================================================================
 \chapter{Miscellaneous Topics}
 …
 has been made to set them in a generic way. However, examples of how
 they can be set up is given in the ORCA 2\deg and 0.5\deg configurations. For example,
+for details of implementation in ORCA2, search:
+\vspace{-10pt}
+\begin{alltt}
+\tiny
+\begin{verbatim}
+IF( cp_cfg == "orca" .AND. jp_cfg == 2 )
+\end{verbatim}
+\end{alltt}
+for details of implementation in ORCA2, search:
+\texttt{ IF( cp\_cfg == "orca" .AND. jp\_cfg == 2 ) }
 % -------------------------------------------------------------------------------------------------------------
 …
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-% -------------------------------------------------------------------------------------------------------------
-% Cross Land Advection
-% -------------------------------------------------------------------------------------------------------------
-\subsection{Cross Land Advection (\mdl{tracla})}
-\label{MISC_strait_cla}
-%--------------------------------------------namcla--------------------------------------------------------
-\namdisplay{namcla}
-%--------------------------------------------------------------------------------------------------------------
-\colorbox{yellow}{Add a short description of CLA staff here or in lateral boundary condition chapter?}
-Options are defined through the  \ngn{namcla} namelist variables.
-%The problem is resolved here by allowing the mixing of tracers and mass/volume between non-adjacent water columns at nominated regions within the model. Momentum is not mixed. The scheme conserves total tracer content, and total volume (the latter in $z*$- or $s*$-coordinate), and maintains compatibility between the tracer and mass/volume budgets.
 % ================================================================
 …
 % ================================================================
-% Accelerating the Convergence
-% ================================================================
-\section{Accelerating the Convergence (\np{nn\_acc} = 1)}
-\label{MISC_acc}
-%--------------------------------------------namdom-------------------------------------------------------
-\namdisplay{namdom}
-%--------------------------------------------------------------------------------------------------------------
-Searching an equilibrium state with an global ocean model requires a very long time
-integration period (a few thousand years for a global model). Due to the size of
-the time step required for numerical stability (less than a few hours),
-this usually requires a large elapsed time. In order to overcome this problem,
-\citet{Bryan1984} introduces a technique that is intended to accelerate
-the spin up to equilibrium. It uses a larger time step in
-the tracer evolution equations than in the momentum evolution
-equations. It does not affect the equilibrium solution but modifies the
-trajectory to reach it.
-Options are defined through the  \ngn{namdom} namelist variables.
-The acceleration of convergence option is used when \np{nn\_acc}=1. In that case,
-$\rdt=rn\_rdt$ is the time step of dynamics while $\widetilde{\rdt}=rdttra$ is the
-tracer time-step. the former is set from the \np{rn\_rdt} namelist parameter while the latter
-is computed using a hyperbolic tangent profile and the following namelist parameters :
-\np{rn\_rdtmin}, \np{rn\_rdtmax} and \np{rn\_rdth}. Those three parameters correspond
-to the surface value the deep ocean value and the depth at which the transition occurs, respectively.
-The set of prognostic equations to solve becomes:
-\begin{equation} \label{Eq_acc}
-\begin{split}
-\frac{\partial \textbf{U}_h }{\partial t}
-   &\equiv \frac{\textbf{U}_h ^{t+1}-\textbf{U}_h^{t-1} }{2\rdt} = \ldots \\
-\frac{\partial T}{\partial t} &\equiv \frac{T^{t+1}-T^{t-1}}{2 \widetilde{\rdt}} = \ldots \\
-\frac{\partial S}{\partial t} &\equiv \frac{S^{t+1} -S^{t-1}}{2 \widetilde{\rdt}} = \ldots \\
-\end{split}
-\end{equation}
-\citet{Bryan1984} has examined the consequences of this distorted physics.
-Free waves have a slower phase speed, their meridional structure is slightly
-modified, and the growth rate of baroclinically unstable waves is reduced
-but with a wider range of instability. This technique is efficient for
-searching for an equilibrium state in coarse resolution models. However its
-application is not suitable for many oceanic problems: it cannot be used for
-transient or time evolving problems (in particular, it is very questionable
-to use this technique when there is a seasonal cycle in the forcing fields),
-and it cannot be used in high-resolution models where baroclinically
-unstable processes are important. Moreover, the vertical variation of
-$\widetilde{ \rdt}$ implies that the heat and salt contents are no longer
-conserved due to the vertical coupling of the ocean level through both
-advection and diffusion. Therefore \np{rn\_rdtmin} = \np{rn\_rdtmax} should be
-a more clever choice.
-% ================================================================
 % Accuracy and Reproducibility
 % ================================================================
 …
 the source of differences between mono and multi processor runs.
+- \key{esopa} (to be rename key\_nemo) : which is another option for model
+management. When defined, this key forces the activation of all options and
+CPP keys. For example, all tracer and momentum advection schemes are called!
+Therefore the model results have no physical meaning.
+However, this option forces both the compiler and the model to run through
+all the \textsc{Fortran} lines of the model. This allows the user to check for obvious
+compilation or execution errors with all CPP options, and errors in namelist options.
+- last digit comparison (\np{nn\_bit\_cmp}). In an MPP simulation, the computation of
+%%gm   to be removed both here and in the code
+- last digit comparison (\np{nn\_bit\_cmp}). In an MPP simulation, the computation of
 a sum over the whole domain is performed as the summation over all processors of
 each of their sums over their interior domains. This double sum never gives exactly
 …
 %THIS is to be updated with the mpp_sum_glo  introduced in v3.3
 % nn_bit_cmp  today only check that the nn_cla = 0 (no cross land advection)
+%%gm end
 $\bullet$  Benchmark (\np{nn\_bench}). This option defines a benchmark run based on
 …
 or the physical parameterisations.
+% ================================================================
+% Elliptic solvers (SOL)
+% ================================================================
+\section{Elliptic solvers (SOL)}
+\label{MISC_sol}
+%--------------------------------------------namdom-------------------------------------------------------
+\namdisplay{namsol}
+%--------------------------------------------------------------------------------------------------------------
+When the filtered sea surface height option is used, the surface pressure gradient is
+computed in \mdl{dynspg\_flt}. The force added in the momentum equation is solved implicitely.
+It is thus solution of an elliptic equation \eqref{Eq_PE_flt} for which two solvers are available:
+a Successive-Over-Relaxation scheme (SOR) and a preconditioned conjugate gradient
+scheme(PCG) \citep{Madec_al_OM88, Madec_PhD90}. The solver is selected trough the
+the value of \np{nn\_solv}   \ngn{namsol} namelist variable.
+The PCG is a very efficient method for solving elliptic equations on vector computers.
+It is a fast and rather easy method to use; which are attractive features for a large
+number of ocean situations (variable bottom topography, complex coastal geometry,
+variable grid spacing, open or cyclic boundaries, etc ...). It does not require
+a search for an optimal parameter as in the SOR method. However, the SOR has
+been retained because it is a linear solver, which is a very useful property when
+using the adjoint model of \NEMO.
+At each time step, the time derivative of the sea surface height at time step $t+1$
+(or equivalently the divergence of the \textit{after} barotropic transport) that appears
+in the filtering forced is the solution of the elliptic equation obtained from the horizontal
+divergence of the vertical summation of \eqref{Eq_PE_flt}.
+Introducing the following coefficients:
+\begin{equation}  \label{Eq_sol_matrix}
+\begin{aligned}
+&c_{i,j}^{NS}  &&= {2 \rdt }^2 \; \frac{H_v (i,j) \; e_{1v} (i,j)}{e_{2v}(i,j)}              \\
+&c_{i,j}^{EW} &&= {2 \rdt }^2 \; \frac{H_u (i,j) \; e_{2u} (i,j)}{e_{1u}(i,j)}            \\
+&b_{i,j} &&= \delta_i \left[ e_{2u}M_u \right] - \delta_j \left[ e_{1v}M_v \right]\ ,   \\
+\end{aligned}
+\end{equation}
+the resulting five-point finite difference equation is given by:
+\begin{equation}  \label{Eq_solmat}
+\begin{split}
+       c_{i+1,j}^{NS} D_{i+1,j}  + \;  c_{i,j+1}^{EW} D_{i,j+1}
+  +   c_{i,j}    ^{NS} D_{i-1,j}   + \;  c_{i,j}    ^{EW} D_{i,j-1}                                          &    \\
+  -    \left(c_{i+1,j}^{NS} + c_{i,j+1}^{EW} + c_{i,j}^{NS} + c_{i,j}^{EW} \right)   D_{i,j}  &=  b_{i,j}
+\end{split}
+\end{equation}
+\eqref{Eq_solmat} is a linear symmetric system of equations. All the elements of
+the corresponding matrix \textbf{A} vanish except those of five diagonals. With
+the natural ordering of the grid points (i.e. from west to east and from
+south to north), the structure of \textbf{A} is block-tridiagonal with
+tridiagonal or diagonal blocks. \textbf{A} is a positive-definite symmetric
+matrix of size $(jpi \cdot jpj)^2$, and \textbf{B}, the right hand side of
+\eqref{Eq_solmat}, is a vector.
+Note that in the linear free surface case, the depth that appears in \eqref{Eq_sol_matrix}
+does not vary with time, and thus the matrix can be computed once for all. In non-linear free surface
+(\key{vvl} defined) the matrix have to be updated at each time step.
+% -------------------------------------------------------------------------------------------------------------
+%       Successive Over Relaxation
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Successive Over Relaxation (\np{nn\_solv}=2, \mdl{solsor})}
+\label{MISC_solsor}
+Let us introduce the four cardinal coefficients:
+\begin{align*}
+a_{i,j}^S &= c_{i,j    }^{NS}/d_{i,j}     &\qquad  a_{i,j}^W &= c_{i,j}^{EW}/d_{i,j}       \\
+a_{i,j}^E &= c_{i,j+1}^{EW}/d_{i,j}    &\qquad   a_{i,j}^N &= c_{i+1,j}^{NS}/d_{i,j}
+\end{align*}
+where $d_{i,j} = c_{i,j}^{NS}+ c_{i+1,j}^{NS} + c_{i,j}^{EW} + c_{i,j+1}^{EW}$
+(i.e. the diagonal of the matrix). \eqref{Eq_solmat} can be rewritten as:
+\begin{equation}  \label{Eq_solmat_p}
+\begin{split}
+a_{i,j}^{N}  D_{i+1,j} +\,a_{i,j}^{E}  D_{i,j+1} +\, a_{i,j}^{S}  D_{i-1,j} +\,a_{i,j}^{W} D_{i,j-1}  -  D_{i,j} = \tilde{b}_{i,j}
+\end{split}
+\end{equation}
+with $\tilde b_{i,j} = b_{i,j}/d_{i,j}$. \eqref{Eq_solmat_p} is the equation actually solved
+with the SOR method. This method used is an iterative one. Its algorithm can be
+summarised as follows (see \citet{Haltiner1980} for a further discussion):
+initialisation (evaluate a first guess from previous time step computations)
+\begin{equation}
+D_{i,j}^0 = 2 \, D_{i,j}^t - D_{i,j}^{t-1}
+\end{equation}
+iteration $n$, from $n=0$ until convergence, do :
+\begin{equation} \label{Eq_sor_algo}
+\begin{split}
+R_{i,j}^n  = &a_{i,j}^{N} D_{i+1,j}^n       +\,a_{i,j}^{E}  D_{i,j+1} ^n
+         +\, a_{i,j}^{S}  D_{i-1,j} ^{n+1}+\,a_{i,j}^{W} D_{i,j-1} ^{n+1}
+                 -  D_{i,j}^n - \tilde{b}_{i,j}                                           \\
+D_{i,j} ^{n+1}  = &D_{i,j} ^{n}   + \omega \;R_{i,j}^n
+\end{split}
+\end{equation}
+where \textit{$\omega $ }satisfies $1\leq \omega \leq 2$. An optimal value exists for
+\textit{$\omega$} which significantly accelerates the convergence, but it has to be
+adjusted empirically for each model domain (except for a uniform grid where an
+analytical expression for \textit{$\omega$} can be found \citep{Richtmyer1967}).
+The value of $\omega$ is set using \np{rn\_sor}, a \textbf{namelist} parameter.
+The convergence test is of the form:
+\begin{equation}
+\delta = \frac{\sum\limits_{i,j}{R_{i,j}^n}{R_{i,j}^n}}
+                    {\sum\limits_{i,j}{ \tilde{b}_{i,j}^n}{\tilde{b}_{i,j}^n}} \leq \epsilon
+\end{equation}
+where $\epsilon$ is the absolute precision that is required. It is recommended
+that a value smaller or equal to $10^{-6}$ is used for $\epsilon$ since larger
+values may lead to numerically induced basin scale barotropic oscillations.
+The precision is specified by setting \np{rn\_eps} (\textbf{namelist} parameter).
+In addition, two other tests are used to halt the iterative algorithm. They involve
+the number of iterations and the modulus of the right hand side. If the former
+exceeds a specified value, \np{nn\_max} (\textbf{namelist} parameter),
+or the latter is greater than $10^{15}$, the whole model computation is stopped
+and the last computed time step fields are saved in a abort.nc NetCDF file.
+In both cases, this usually indicates that there is something wrong in the model
+configuration (an error in the mesh, the initial state, the input forcing,
+or the magnitude of the time step or of the mixing coefficients). A typical value of
+$nn\_max$ is a few hundred when $\epsilon = 10^{-6}$, increasing to a few
+thousand when $\epsilon = 10^{-12}$.
+The vectorization of the SOR algorithm is not straightforward. The scheme
+contains two linear recurrences on $i$ and $j$. This inhibits the vectorisation.
+\eqref{Eq_sor_algo} can be been rewritten as:
+\begin{equation}
+\begin{split}
+R_{i,j}^n
+= &a_{i,j}^{N}  D_{i+1,j}^n +\,a_{i,j}^{E}  D_{i,j+1} ^n
+ +\,a_{i,j}^{S}  D_{i-1,j} ^{n}+\,_{i,j}^{W} D_{i,j-1} ^{n} -  D_{i,j}^n - \tilde{b}_{i,j}      \\
+R_{i,j}^n = &R_{i,j}^n - \omega \;a_{i,j}^{S}\; R_{i,j-1}^n                                             \\
+R_{i,j}^n = &R_{i,j}^n - \omega \;a_{i,j}^{W}\; R_{i-1,j}^n
+\end{split}
+\end{equation}
+This technique slightly increases the number of iteration required to reach the convergence,
+but this is largely compensated by the gain obtained by the suppression of the recurrences.
+Another technique have been chosen, the so-called red-black SOR. It consist in solving successively
+\eqref{Eq_sor_algo} for odd and even grid points. It also slightly reduced the convergence rate
+but allows the vectorisation. In addition, and this is the reason why it has been chosen, it is able to handle the north fold boundary condition used in ORCA configuration ($i.e.$ tri-polar global ocean mesh).
+The SOR method is very flexible and can be used under a wide range of conditions,
+including irregular boundaries, interior boundary points, etc. Proofs of convergence, etc.
+may be found in the standard numerical methods texts for partial differential equations.
+% -------------------------------------------------------------------------------------------------------------
+%       Preconditioned Conjugate Gradient
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Preconditioned Conjugate Gradient  (\np{nn\_solv}=1, \mdl{solpcg}) }
+\label{MISC_solpcg}
+\textbf{A} is a definite positive symmetric matrix, thus solving the linear
+system \eqref{Eq_solmat} is equivalent to the minimisation of a quadratic
+functional:
+\begin{equation*}
+\textbf{Ax} = \textbf{b} \leftrightarrow \textbf{x} =\text{inf}_{y} \,\phi (\textbf{y})
+\quad , \qquad
+\phi (\textbf{y}) = 1/2 \langle \textbf{Ay},\textbf{y}\rangle - \langle \textbf{b},\textbf{y} \rangle
+\end{equation*}
+where $\langle , \rangle$ is the canonical dot product. The idea of the
+conjugate gradient method is to search for the solution in the following
+iterative way: assuming that $\textbf{x}^n$ has been obtained, $\textbf{x}^{n+1}$
+is found from $\textbf {x}^{n+1}={\textbf {x}}^n+\alpha^n{\textbf {d}}^n$ which satisfies:
+\begin{equation*}
+{\textbf{ x}}^{n+1}=\text{inf} _{{\textbf{ y}}={\textbf{ x}}^n+\alpha^n \,{\textbf{ d}}^n} \,\phi ({\textbf{ y}})\;\;\Leftrightarrow \;\;\frac{d\phi }{d\alpha}=0
+\end{equation*}
+and expressing $\phi (\textbf{y})$ as a function of \textit{$\alpha $}, we obtain the
+value that minimises the functional:
+\begin{equation*}
+\alpha ^n = \langle{ \textbf{r}^n , \textbf{r}^n} \rangle  / \langle {\textbf{ A d}^n, \textbf{d}^n} \rangle
+\end{equation*}
+where $\textbf{r}^n = \textbf{b}-\textbf{A x}^n = \textbf{A} (\textbf{x}-\textbf{x}^n)$
+is the error at rank $n$. The descent vector $\textbf{d}^n$ s chosen to be dependent
+on the error: $\textbf{d}^n = \textbf{r}^n + \beta^n \,\textbf{d}^{n-1}$. $\beta ^n$
+is searched such that the descent vectors form an orthogonal basis for the dot
+product linked to \textbf{A}. Expressing the condition
+$\langle \textbf{A d}^n, \textbf{d}^{n-1} \rangle = 0$ the value of $\beta ^n$ is found:
+ $\beta ^n = \langle{ \textbf{r}^n , \textbf{r}^n} \rangle  / \langle {\textbf{r}^{n-1}, \textbf{r}^{n-1}} \rangle$.
+ As a result, the errors $ \textbf{r}^n$ form an orthogonal
+base for the canonic dot product while the descent vectors $\textbf{d}^n$ form
+an orthogonal base for the dot product linked to \textbf{A}. The resulting
+algorithm is thus the following one:
+initialisation :
+\begin{equation*}
+\begin{split}
+\textbf{x}^0 &= D_{i,j}^0   = 2 D_{i,j}^t - D_{i,j}^{t-1}       \quad, \text{the initial guess }     \\
+\textbf{r}^0 &= \textbf{d}^0 = \textbf{b} - \textbf{A x}^0       \\
+\gamma_0 &= \langle{ \textbf{r}^0 , \textbf{r}^0} \rangle
+\end{split}
+\end{equation*}
+iteration $n,$ from $n=0$ until convergence, do :
+\begin{equation}
+\begin{split}
+\text{z}^n& = \textbf{A d}^n \\
+\alpha_n &= \gamma_n /  \langle{ \textbf{z}^n , \textbf{d}^n} \rangle \\
+\textbf{x}^{n+1} &= \textbf{x}^n + \alpha_n \,\textbf{d}^n \\
+\textbf{r}^{n+1} &= \textbf{r}^n - \alpha_n \,\textbf{z}^n \\
+\gamma_{n+1} &= \langle{ \textbf{r}^{n+1} , \textbf{r}^{n+1}} \rangle \\
+\beta_{n+1} &= \gamma_{n+1}/\gamma_{n}  \\
+\textbf{d}^{n+1} &= \textbf{r}^{n+1} + \beta_{n+1}\; \textbf{d}^{n}\\
+\end{split}
+\end{equation}
+The convergence test is:
+\begin{equation}
+\delta = \gamma_{n}\; / \langle{ \textbf{b} , \textbf{b}} \rangle \leq \epsilon
+\end{equation}
+where $\epsilon $ is the absolute precision that is required. As for the SOR algorithm,
+the whole model computation is stopped when the number of iterations, \np{nn\_max}, or
+the modulus of the right hand side of the convergence equation exceeds a
+specified value (see \S\ref{MISC_solsor} for a further discussion). The required
+precision and the maximum number of iterations allowed are specified by setting
+\np{rn\_eps} and \np{nn\_max} (\textbf{namelist} parameters).
+It can be demonstrated that the above algorithm is optimal, provides the exact
+solution in a number of iterations equal to the size of the matrix, and that
+the convergence rate is faster as the matrix is closer to the identity matrix,
+$i.e.$ its eigenvalues are closer to 1. Therefore, it is more efficient to solve
+a better conditioned system which has the same solution. For that purpose,
+we introduce a preconditioning matrix \textbf{Q} which is an approximation
+of \textbf{A} but much easier to invert than \textbf{A}, and solve the system:
+\begin{equation} \label{Eq_pmat}
+\textbf{Q}^{-1} \textbf{A x} = \textbf{Q}^{-1} \textbf{b}
+\end{equation}
+The same algorithm can be used to solve \eqref{Eq_pmat} if instead of the
+canonical dot product the following one is used:
+${\langle{ \textbf{a} , \textbf{b}} \rangle}_Q = \langle{ \textbf{a} , \textbf{Q b}} \rangle$, and
+if $\textbf{\~{b}} = \textbf{Q}^{-1}\;\textbf{b}$ and $\textbf{\~{A}} = \textbf{Q}^{-1}\;\textbf{A}$
+are substituted to \textbf{b} and \textbf{A} \citep{Madec_al_OM88}.
+In \NEMO, \textbf{Q} is chosen as the diagonal of \textbf{ A}, i.e. the simplest form for
+\textbf{Q} so that it can be easily inverted. In this case, the discrete formulation of
+\eqref{Eq_pmat} is in fact given by \eqref{Eq_solmat_p} and thus the matrix and
+right hand side are computed independently from the solver used.
+% ================================================================
+% ================================================================

trunk/DOC/TexFiles/Chapters/Chap_Model_Basics.tex

-                      r6140
+                      r6289
 %\newpage
 %$\ $\newline    % force a new ligne
+%$\ $\newline    % force a new line
 % ================================================================
 …
 \label{PE_zco_tilde}
 The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM10s}.
+The $\tilde{z}$-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. Its use is therefore not recommended.
+We
 \newpage
 …
 All these parameterisations of subgrid scale physics have advantages and
+drawbacks. There are not all available in \NEMO. In the $z$-coordinate
+formulation, five options are offered for active tracers (temperature and
+salinity): second order geopotential operator, second order isoneutral
+operator, \citet{Gent1990} parameterisation, fourth order
+geopotential operator, and various slightly diffusive advection schemes.
+The same options are available for momentum, except
+\citet{Gent1990} parameterisation which only involves tracers. In the
+$s$-coordinate formulation, additional options are offered for tracers: second
+order operator acting along $s-$surfaces, and for momentum: fourth order
+operator acting along $s-$surfaces (see \S\ref{LDF}).
+\subsubsection{Lateral second order tracer diffusive operator}
+The lateral second order tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}):
+drawbacks. 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.
+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.
+\subsubsection{Lateral Laplacian tracer diffusive operator}
+The lateral Laplacian tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}):
 \begin{equation} \label{Eq_PE_iso_tensor}
 D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad
 …
 but have similar expressions in $z$- and $s$-coordinates. In $z$-coordinates:
 \begin{equation} \label{Eq_PE_iso_slopes}
+r_1 =\frac{e_3 }{e_1 }  \left( {\frac{\partial \rho }{\partial i}} \right)
+                  \left( {\frac{\partial \rho }{\partial k}} \right)^{-1} \ , \quad
+r_1 =\frac{e_3 }{e_1 }  \left( {\frac{\partial \rho }{\partial i}} \right)
+                  \left( {\frac{\partial \rho }{\partial k}} \right)^{-1},
+\end{equation}
+while in $s$-coordinates $\partial/\partial k$ is replaced by
+$\partial/\partial s$.
+r_1 =\frac{e_3 }{e_1 }  \left( \pd[\rho]{i} \right) \left( \pd[\rho]{k} \right)^{-1} \, \quad
+r_2 =\frac{e_3 }{e_2 }  \left( \pd[\rho]{j} \right) \left( \pd[\rho]{k} \right)^{-1} \,
+\end{equation}
+while in $s$-coordinates $\pd[]{k}$ is replaced by $\pd[]{s}$.
 \subsubsection{Eddy induced velocity}
 …
  w^\ast &=  -\frac{1}{e_1 e_2 }\left[
                       \frac{\partial }{\partial i}\left( {A^{eiv}\;e_2\,\tilde{r}_1 } \right)
                     +\frac{\partial }{\partial j}\left( {A^{eiv}\;e_1\,\tilde{r}_2 } \right)      \right]
+                     +\frac{\partial }{\partial j}\left( {A^{eiv}\;e_1\,\tilde{r}_2 } \right)      \right]
    \end{split}
 \end{equation}
 …
 \begin{align} \label{Eq_PE_slopes_eiv}
 \tilde{r}_n = \begin{cases}
    r_n                  &      \text{in $z$-coordinate}    \\
+   r_n            &      \text{in $z$-coordinate}    \\
    r_n + \sigma_n &      \text{in \textit{z*} and $s$-coordinates}
                    \end{cases}
+              \end{cases}
 \quad \text{where } n=1,2
 \end{align}
 …
 to zero in the vicinity of the boundaries. The latter strategy is used in \NEMO (cf. Chap.~\ref{LDF}).
 \subsubsection{Lateral fourth order tracer diffusive operator}
 The lateral fourth order tracer diffusive operator is defined by:
+\subsubsection{Lateral bilaplacian tracer diffusive operator}
+The lateral bilaplacian tracer diffusive operator is defined by:
 \begin{equation} \label{Eq_PE_bilapT}
 D^{lT}=\Delta \left( \;\Delta T \right)
+D^{lT}= - \Delta \left( \;\Delta T \right)
 \qquad \text{where} \;\; \Delta \bullet = \nabla \left( {\sqrt{B^{lT}\,}\;\Re \;\nabla \bullet} \right)
  \end{equation}
 It is the second order operator given by \eqref{Eq_PE_iso_tensor} applied twice with
+It is the Laplacian operator given by \eqref{Eq_PE_iso_tensor} applied twice with
 the harmonic eddy diffusion coefficient set to the square root of the biharmonic one.
 \subsubsection{Lateral second order momentum diffusive operator}
 The second order momentum diffusive operator along $z$- or $s$-surfaces is found by
+\subsubsection{Lateral Laplacian momentum diffusive operator}
+The Laplacian momentum diffusive operator along $z$- or $s$-surfaces is found by
 applying \eqref{Eq_PE_lap_vector} to the horizontal velocity vector (see Appendix~\ref{Apdx_B}):
 \begin{equation} \label{Eq_PE_lapU}
 …
 of the Equator in a geographical coordinate system \citep{Lengaigne_al_JGR03}.
+\subsubsection{lateral fourth order momentum diffusive operator}
+As for tracers, the fourth order momentum diffusive operator along $z$ or $s$-surfaces
+is a re-entering second order operator \eqref{Eq_PE_lapU} or \eqref{Eq_PE_lapU_iso}
+with the harmonic eddy diffusion coefficient set to the square root of the biharmonic one.
+\subsubsection{lateral bilaplacian momentum diffusive operator}
+As for tracers, the bilaplacian order momentum diffusive operator is a
+re-entering Laplacian operator with the harmonic eddy diffusion coefficient
+set to the square root of the biharmonic one. Nevertheless it is currently
+not available in the iso-neutral case.

trunk/DOC/TexFiles/Chapters/Chap_SBC.tex

-                      r6140
+                      r6289
 % ================================================================
 % Chapter � Surface Boundary Condition (SBC, ISF, ICB)
+% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)
 % ================================================================
 \chapter{Surface Boundary Condition (SBC, ISF, ICB) }
 …
    \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$
    \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
+   \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$
+   \item the surface freshwater budget $\left( {\textit{emp}} \right)$
+   \item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
 \end{itemize}
 plus an optional field:
 …
 are controlled by namelist \ngn{namsbc} variables: an analytical formulation (\np{ln\_ana}~=~true),
 a flux formulation (\np{ln\_flx}~=~true), a bulk formulae formulation (CORE
 (\np{ln\_core}~=~true), CLIO (\np{ln\_clio}~=~true) or MFS
+(\np{ln\_blk\_core}~=~true), CLIO (\np{ln\_blk\_clio}~=~true) or MFS
 \footnote { Note that MFS bulk formulae compute fluxes only for the ocean component}
+(\np{ln\_mfs}~=~true) bulk formulae) and a coupled
+formulation (exchanges with a atmospheric model via the OASIS coupler)
+(\np{ln\_cpl}~=~true). When used, the atmospheric pressure forces both
+ocean and ice dynamics (\np{ln\_apr\_dyn}~=~true).
+The frequency at which the six or seven fields have to be updated is the \np{nn\_fsbc}
+namelist parameter.
+(\np{ln\_blk\_mfs}~=~true) bulk formulae) and a coupled or mixed forced/coupled formulation
+(exchanges with a atmospheric model via the OASIS coupler) (\np{ln\_cpl} or \np{ln\_mixcpl}~=~true).
+When used ($i.e.$ \np{ln\_apr\_dyn}~=~true), the atmospheric pressure forces both ocean and ice dynamics.
+The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.
 When the fields are supplied from data files (flux and bulk formulations), the input fields
 need not be supplied on the model grid.  Instead a file of coordinates and weights can
+need not be supplied on the model grid. Instead a file of coordinates and weights can
 be supplied which maps the data from the supplied grid to the model points
 (so called "Interpolation on the Fly", see \S\ref{SBC_iof}).
 …
 can be masked to avoid spurious results in proximity of the coasts  as large sea-land gradients characterize
 most of the atmospheric variables.
 In addition, the resulting fields can be further modified using several namelist options.
+These options control  the rotation of vector components supplied relative to an east-north
+coordinate system onto the local grid directions in the model; the addition of a surface
+restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes
+below ice-covered areas (using observed ice-cover or a sea-ice model)
+(\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater
+fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of isf melting as lateral inflow (parameterisation)
+ or as surface flux at the land-ice ocean interface (\np{ln\_isf}=~true);
+the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the
+transformation of the solar radiation (if provided as daily mean) into a diurnal
+cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave
+model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or mfs bulk formulas are selected.
+These options control
+\begin{itemize}
+\item the rotation of vector components supplied relative to an east-north
+coordinate system onto the local grid directions in the model ;
+\item the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true) ;
+\item the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model) (\np{nn\_ice}~=~0,1, 2 or 3) ;
+\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ;
+\item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false)
+or as fluxes applied at the land-ice ocean interface (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true) ;
+\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ;
+\item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ;
+and a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}~=~true).
+\end{itemize}
+The latter option is possible only in case core or mfs bulk formulas are selected.
 In this chapter, we first discuss where the surface boundary condition appears in the
 …
 The surface ocean stress is the stress exerted by the wind and the sea-ice
+on the ocean. The two components of stress are assumed to be interpolated
+onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
+at $u$- and $v$-points They are applied as a surface boundary condition of the
+computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
+\begin{equation} \label{Eq_sbc_dynzdf}
+\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
+    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
+\end{equation}
+where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
+stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
+on the ocean. It is applied in \mdl{dynzdf} module as a surface boundary condition of the
+computation of the momentum vertical mixing trend (see \eqref{Eq_dynzdf_sbc} in \S\ref{DYN_zdf}).
+As such, it has to be provided as a 2D vector interpolated
+onto the horizontal velocity ocean mesh, $i.e.$ resolved onto the model
+(\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
 The surface heat flux is decomposed into two parts, a non solar and a solar heat
 flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
+of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
+It is applied as a surface boundary condition trend of the first level temperature
+time evolution equation (\mdl{trasbc} module).
+\begin{equation} \label{Eq_sbc_trasbc_q}
+\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho
+_o \;C_p \;e_{3t} }} \right|_{k=1} \quad
+\end{equation}
+$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
+trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
+\begin{equation} \label{Eq_sbc_traqsr}
+\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right]
+\end{equation}
+where $I_w$ is a non-dimensional function that describes the way the light
+penetrates inside the water column. It is generally a sum of decreasing
+exponentials (see \S\ref{TRA_qsr}).
+The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which
+may or may not be identical. Indeed, a surface freshwater flux has two effects:
+it changes the volume of the ocean and it changes the surface concentration of
+salt (and other tracers). Therefore it appears in the sea surface height as a volume
+flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
+as a concentration/dilution effect,
+$\textit{emp}_{S}$ (\mdl{trasbc} module).
+\begin{equation} \label{Eq_trasbc_emp}
+\begin{aligned}
+&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\
+\\
+ &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\
+ \end{aligned}
+\end{equation}
+In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,
+but it exist several numerical reasons why this equality should be broken.
+For example, when the ocean is coupled to a sea-ice model, the water exchanged between
+ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,
+$\textit{emp}_{S}$ take into account both concentration/dilution effect associated with
+freezing/melting and the salt flux between ice and ocean, while \textit{emp} is
+only the volume flux. In addition, in the current version of \NEMO, the sea-ice is
+assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does
+not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS.
+%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
+Note that SST can also be modified by a freshwater flux. Precipitation (in
+particular solid precipitation) may have a temperature significantly different from
+the SST. Due to the lack of information about the temperature of
+precipitation, we assume it is equal to the SST. Therefore, no
+concentration/dilution term appears in the temperature equation. It has to
+be emphasised that this absence does not mean that there is no heat flux
+associated with precipitation! Precipitation can change the ocean volume and thus the
+ocean heat content. It is therefore associated with a heat flux (not yet
+diagnosed in the model) \citep{Roullet_Madec_JGR00}).
+of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes
+plus the heat content of the mass exchange with the atmosphere and sea-ice).
+It is applied in \mdl{trasbc} module as a surface boundary condition trend of
+the first level temperature time evolution equation (see \eqref{Eq_tra_sbc}
+and \eqref{Eq_tra_sbc_lin} in \S\ref{TRA_sbc}).
+The latter is the penetrative part of the heat flux. It is applied as a 3D
+trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=\textit{true}.
+The way the light penetrates inside the water column is generally a sum of decreasing
+exponentials (see \S\ref{TRA_qsr}).
+The surface freshwater budget is provided by the \textit{emp} field.
+It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation)
+and possibly with the sea-ice and ice shelves (freezing minus melting of ice).
+It affects both the ocean in two different ways:
+$(i)$   it changes the volume of the ocean and therefore appears in the sea surface height
+equation as a volume flux, and
+$(ii)$  it changes the surface temperature and salinity through the heat and salt contents
+of the mass exchanged with the atmosphere, the sea-ice and the ice shelves.
 %\colorbox{yellow}{Miss: }
 …
+%
 %Explain here all the namlist namsbc variable{\ldots}.
+%
+% explain : use or not of surface currents
+%
 %\colorbox{yellow}{End Miss }
+The ocean model provides the surface currents, temperature and salinity
+averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
+mean is done in \mdl{sbcmod} module.
+The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
+the surface currents, temperature and salinity.
+These variables are averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}),
+and it is these averaged fields which are used to computes the surface fluxes
+at a frequency of \np{nf\_sbc} time-step.
 %-------------------------------------------------TABLE---------------------------------------------------
 …
 %--------------------------------------------------------------------------------------------------------------
 In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields and simply read them in from  a previous run.
+Options are defined through the  \ngn{namsbc\_sas} namelist variables.
+In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields
+and simply read them in from a previous run or receive them from OASIS.
 For example:
 \begin{enumerate}
 \item  Multiple runs of the model are required in code development to see the affect of different algorithms in
+\begin{itemize}
+\item  Multiple runs of the model are required in code development to see the effect of different algorithms in
        the bulk formulae.
 \item  The effect of different parameter sets in the ice model is to be examined.
+\end{enumerate}
+\item  Development of sea-ice algorithms or parameterizations.
+\item  spinup of the iceberg floats
+\item  ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}~=~\textit{true})
+\end{itemize}
 The StandAlone Surface scheme provides this utility.
+Its options are defined through the \ngn{namsbc\_sas} namelist variables.
 A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
 However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0)
 …
 Routines replaced are:
+\begin{enumerate}
+\item  \mdl{nemogcm}
+       This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90)
+\begin{itemize}
+\item \mdl{nemogcm} : This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90)
        Since the ocean state is not calculated all associated initialisations have been removed.
+\item  \mdl{step}
+       The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
+\item  \mdl{sbcmod}
+       This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules
+\item  \mdl{step} : The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
+\item  \mdl{sbcmod} : This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules
        that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs).
+\item  \mdl{daymod}
+       No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions
+\item  \mdl{daymod} : No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions
        have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user
        must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
+\item  \mdl{stpctl}
+       Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
+\item  \mdl{diawri}
+       All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which
+\item  \mdl{stpctl} : Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
+\item  \mdl{diawri} : All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which
        have been read in) are written along with relevant forcing and ice data.
 \end{enumerate}
+\end{itemize}
 One new routine has been added:
+\begin{enumerate}
+\item  \mdl{sbcsas}
+       This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface.
+\begin{itemize}
+\item  \mdl{sbcsas} : This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface.
        These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module,
        the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level.
        Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
+\end{enumerate}
+\end{itemize}
+% Missing the description of the 2 following variables:
+%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field
+%   ln_read_frq = .false.    !  specify whether we must read frq or not
 % ================================================================
 …
 are sent to the atmospheric component.
+A generalised coupled interface has been developed. It is currently interfaced with OASIS 3
+(\key{oasis3}) and does not support OASIS 4
+\footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}.
+A generalised coupled interface has been developed.
+It is currently interfaced with OASIS-3-MCT (\key{oasis3}).
 It has been successfully used to interface \NEMO to most of the European atmospheric
 GCM (ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz),
 …
 \label{SBC_tide}
+A module is available to use the tidal potential forcing and is activated with with \key{tide}.
+%------------------------------------------nam_tide----------------------------------------------------
+%------------------------------------------nam_tide---------------------------------------
 \namdisplay{nam_tide}
+%-------------------------------------------------------------------------------------------------------------
+Concerning the tidal potential, some parameters are available in namelist \ngn{nam\_tide}:
+%-----------------------------------------------------------------------------------------
+A module is available to compute the tidal potential and use it in the momentum equation.
+This option is activated when \key{tide} is defined.
+Some parameters are available in namelist \ngn{nam\_tide}:
 - \np{ln\_tide\_pot} activate the tidal potential forcing
 …
 - \np{clname} is the name of constituent
 The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem;
 …
 \begin{description}
 \item[\np{nn\_isf}~=~1]
+The ice shelf cavity is represented. The fwf and heat flux are computed. 2 bulk formulations are available: the ISOMIP one (\np{nn\_isfblk = 1}) described in (\np{nn\_isfblk = 2}), the 3 equation formulation described in \citet{Jenkins1991}. In addition to this,
+different way to compute the exchange coefficient are available. $\gamma\_{T/S}$ is constant (\np{nn\_gammablk = 0}), $\gamma\_{T/S}$ is velocity dependant \citep{Jenkins2010} (\np{nn\_gammablk = 1}) and $\gamma\_{T/S}$ is velocity dependant and stratification dependent \citep{Holland1999} (\np{nn\_gammablk = 2}). For each of them, the thermal/salt exchange coefficient (\np{rn\_gammat0} and \np{rn\_gammas0}) have to be specified (the default values are for the ISOMIP case).
+The ice shelf cavity is represented. The fwf and heat flux are computed. 2 bulk formulations are available:
+the ISOMIP one (\np{nn\_isfblk = 1}) described in (\np{nn\_isfblk = 2}),
+the 3 equation formulation described in \citet{Jenkins1991}.
+In addition to this, 3 different ways to compute the exchange coefficient are available.
+$\gamma\_{T/S}$ is constant (\np{nn\_gammablk = 0}), $\gamma\_{T/S}$ is velocity dependant
+\citep{Jenkins2010} (\np{nn\_gammablk = 1}) and $\gamma\_{T/S}$ is velocity dependant
+and stratification dependent \citep{Holland1999} (\np{nn\_gammablk = 2}).
+For each of them, the thermal/salt exchange coefficient (\np{rn\_gammat0} and \np{rn\_gammas0})
+have to be specified (the default values are for the ISOMIP case).
 Full description, sensitivity and validation in preparation.
 …
 (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}~=~3).
 Furthermore the fwf is computed using the \citet{Beckmann2003} parameterisation of isf melting.
+The effective melting length (\np{sn\_Leff\_isf}) is read from a file and the exchange coefficients are set as (\np{rn\_gammat0}) and (\np{rn\_gammas0}).
+The effective melting length (\np{sn\_Leff\_isf}) is read from a file and the exchange coefficients
+are set as (\np{rn\_gammat0}) and (\np{rn\_gammas0}).
 \item[\np{nn\_isf}~=~3]
 …
 %        Handling of icebergs
 % ================================================================
 \section{ Handling of icebergs (ICB) }
+\section{Handling of icebergs (ICB)}
 \label{ICB_icebergs}
 %------------------------------------------namberg----------------------------------------------------
 …
 %-------------------------------------------------------------------------------------------------------------
+Icebergs are modelled as lagrangian particles in NEMO.
+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 described in the \ngn{namberg} namelist:
+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} ).
+(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 described
+in the \ngn{namberg} namelist:
 \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
 Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs
 …
 The presence at the sea surface of an ice covered area modifies all the fluxes
 transmitted to the ocean. There are several way to handle sea-ice in the system
 depending on the value of the \np{nn{\_}ice} namelist parameter.
+depending on the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist.
 \begin{description}
 \item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
 …
 % -------------------------------------------------------------------------------------------------------------
 \subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})]
                         {Neutral drag coefficient from external wave model (\mdl{sbcwave})}
+              {Neutral drag coefficient from external wave model (\mdl{sbcwave})}
 \label{SBC_wave}
 %------------------------------------------namwave----------------------------------------------------
 \namdisplay{namsbc_wave}
 %-------------------------------------------------------------------------------------------------------------
+\begin{description}
+\item [??] In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the
+logical variable \np{ln\_cdgw}
+ in $namsbc$ namelist must be defined ${.true.}$.
+In order to read a neutral drag coeff, from an external data source ($i.e.$ a wave model), the
+logical variable \np{ln\_cdgw} in \ngn{namsbc} namelist must be set to \textit{true}.
 The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the
 namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all
 the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input})
+and a 2D field of neutral drag coefficient. Then using the routine
+TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according
+to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
+\end{description}
+and a 2D field of neutral drag coefficient.
+Then using the routine TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided,
+the drag coefficient is computed according to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
 % Griffies doc:
+% When running ocean-ice simulations, we are not explicitly representing land processes, such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, it is important to balance the hydrological cycle in ocean-ice models. We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. The result of the normalization should be a global integrated zero net water input to the ocean-ice system over a chosen time scale.
+%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, so that there is always a zero net input of water to the ocean-ice system. Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
+%When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean and ice models when aiming to balance the hydrological cycle. The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running ocean-ice models, not the water in any one sub-component. As an extreme example to illustrate the issue, consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up, there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. The total water contained in the ocean plus ice system is constant, but there is an exchange of water between the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle in ocean-ice models.
+% When running ocean-ice simulations, we are not explicitly representing land processes,
+% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
+% it is important to balance the hydrological cycle in ocean-ice models.
+% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
+% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
+% a chosen time scale.
+%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
+% so that there is always a zero net input of water to the ocean-ice system.
+% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
+% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
+% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
+% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
+% and ice models when aiming to balance the hydrological cycle.
+% The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running ocean-ice models,
+% not the water in any one sub-component. As an extreme example to illustrate the issue,
+% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
+% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
+% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
+% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
+% in ocean-ice models.

trunk/DOC/TexFiles/Chapters/Chap_STO.tex

-                      r5404
+                      r6289
 \newpage
 $\ $\newline    % force a new line
+%---------------------------------------namsbc--------------------------------------------------
+\namdisplay{namsto}
+%--------------------------------------------------------------------------------------------------------------
+$\ $\newline    % force a new ligne
+See \cite{Brankart_OM2013} and \cite{Brankart_al_GMD2015} papers for a description of the parameterization.

trunk/DOC/TexFiles/Chapters/Chap_TRA.tex

-                      r6140
+                      r6289
 (BBL) parametrisation, and an internal damping (DMP) term. The terms QSR,
 BBC, BBL and DMP are optional. The external forcings and parameterisations
 require complex inputs and complex calculations (e.g. bulk formulae, estimation
+require complex inputs and complex calculations ($e.g.$ bulk formulae, estimation
 of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and
 described in chapters \S\ref{SBC}, \S\ref{LDF} and  \S\ref{ZDF}, respectively.
 Note that \mdl{tranpc}, the non-penetrative convection module,  although
+Note that \mdl{tranpc}, the non-penetrative convection module, although
 located in the NEMO/OPA/TRA directory as it directly modifies the tracer fields,
 is described with the model vertical physics (ZDF) together with other available
 …
 In the present chapter we also describe the diagnostic equations used to compute
 the sea-water properties (density, Brunt-Vais\"{a}l\"{a} frequency, specific heat and
+the sea-water properties (density, Brunt-V\"{a}is\"{a}l\"{a} frequency, specific heat and
 freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}).
 …
 found in the \textit{traTTT} or \textit{traTTT\_xxx} module, in the NEMO/OPA/TRA directory.
 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}~=~true), as described in Chap.~\ref{MISC}.
+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}~=~true), as described in Chap.~\ref{DIA}.
 $\ $\newline    % force a new ligne
 …
 %-------------------------------------------------------------------------------------------------------------
+The advection tendency of a tracer in flux form is the divergence of the advective
+fluxes. Its discrete expression is given by :
+When considered ($i.e.$ when \np{ln\_traadv\_NONE} is not set to \textit{true}),
+the advection tendency of a tracer is expressed in flux form,
+$i.e.$ as the divergence of the advective fluxes. Its discrete expression is given by :
 \begin{equation} \label{Eq_tra_adv}
 ADV_\tau =-\frac{1}{b_t} \left(
 …
 %        2nd and 4th order centred schemes
 % -------------------------------------------------------------------------------------------------------------
 \subsection [centred schemes (CEN) (\np{ln\_traadv\_cen})]
             {centred schemes (CEN) (\np{ln\_traadv\_cen}=true)}
+\subsection [Centred schemes (CEN) (\np{ln\_traadv\_cen})]
+            {Centred schemes (CEN) (\np{ln\_traadv\_cen}=true)}
 \label{TRA_adv_cen}
 …
 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)}. Note that in this case, a similar split-explicit
+by vertical advection \citep{Lemarie_OM2015}. 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 \S\ref{DYN_zad}).
 …
 Estimated Streaming Terms (QUICKEST) scheme proposed by \citet{Leonard1979}
 is used when \np{ln\_traadv\_qck}~=~\textit{true}.
 QUICKEST implementation can be found in the \mdl{traadv\_mus} module.
+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
 …
 direction where the control of artificial diapycnal fluxes is of paramount importance.
 Therefore the vertical flux is evaluated using the CEN2 scheme.
+This no longer guarantees the positivity of the scheme. The use of TVD in the vertical
+direction (as for the UBS case) should be implemented to restore this property.
+This no longer guarantees the positivity of the scheme.
+The use of FCT in the vertical direction (as for the UBS case) should be implemented
+to restore this property.
 %%%gmcomment   :  Cross term are missing in the current implementation....
 …
 %-------------------------------------------------------------------------------------------------------------
+Options are defined through the  \ngn{namtra\_ldf} namelist variables.
+The options available for lateral diffusion are a laplacian (rotated or not)
+or a biharmonic operator, the latter being more scale-selective (more
+diffusive at small scales). The specification of eddy diffusivity
+coefficients (either constant or variable in space and time) as well as the
+computation of the slope along which the operators act, are performed in the
+\mdl{ldftra} and \mdl{ldfslp} modules, respectively. This is described in Chap.~\ref{LDF}.
+Options are defined through the \ngn{namtra\_ldf} namelist variables.
+They are regrouped in four items, allowing to specify
+$(i)$   the type of operator used (none, laplacian, bilaplacian),
+$(ii)$  the direction along which the operator acts (iso-level, horizontal, iso-neutral),
+$(iii)$ some specific options related to the rotated operators ($i.e.$ non-iso-level operator), and
+$(iv)$  the specification of eddy diffusivity coefficient (either constant or variable in space and time).
+Item $(iv)$ will be described in Chap.\ref{LDF} .
+The direction along which the operators act is defined through the slope between this direction and the iso-level surfaces.
+The slope is computed in the \mdl{ldfslp} module and will also be described in Chap.~\ref{LDF}.
 The lateral diffusion of tracers is evaluated using a forward scheme,
 $i.e.$ the tracers appearing in its expression are the \textit{before} tracers in time,
+except for the pure vertical component that appears when a rotation tensor
+is used. This latter term is solved implicitly together with the
+vertical diffusion term (see \S\ref{STP}).
+% -------------------------------------------------------------------------------------------------------------
+%        Iso-level laplacian operator
+% -------------------------------------------------------------------------------------------------------------
+\subsection   [Iso-level laplacian operator (lap) (\np{ln\_traldf\_lap})]
+         {Iso-level laplacian operator (lap) (\np{ln\_traldf\_lap}=true) }
+\label{TRA_ldf_lap}
+A laplacian diffusion operator ($i.e.$ a harmonic operator) acting along the model
+surfaces is given by:
+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 \S\ref{STP}).
+When \np{ln\_traldf\_msc}~=~\textit{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}.
+% -------------------------------------------------------------------------------------------------------------
+%        Type of operator
+% -------------------------------------------------------------------------------------------------------------
+\subsection   [Type of operator (\np{ln\_traldf\_NONE}, \np{ln\_traldf\_lap}, \np{ln\_traldf\_blp})]
+              {Type of operator (\np{ln\_traldf\_NONE}, \np{ln\_traldf\_lap}, or \np{ln\_traldf\_blp} = true) }
+\label{TRA_ldf_op}
+Three operator options are proposed and, one and only one of them must be selected:
+\begin{description}
+\item [\np{ln\_traldf\_NONE}] = 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}] = 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 \S\ref{TRA_ldf_dir}),
+and $A_{ht}$ is the eddy diffusivity coefficient expressed in $m^2/s$ (see Chap.~\ref{LDF}).
+\item [\np{ln\_traldf\_blp}] = true : a bilaplacian operator is selected. This biharmonic operator
+takes the following expression:
+$\mathpzc{B}=- \mathpzc{L}\left(\mathpzc{L}(T) \right) = -\nabla \cdot b\nabla \left( {\nabla \cdot b\nabla T} \right)$
+where the gradient operats along the selected direction,
+and $b^2=B_{ht}$ is the eddy diffusivity coefficient expressed in $m^4/s$  (see Chap.~\ref{LDF}).
+In the code, the bilaplacian operator is obtained by calling the laplacian twice.
+\end{description}
+Both laplacian and bilaplacian operators ensure the total tracer variance decrease.
+Their primary role is to provide strong dissipation at the smallest scale supported
+by the grid while minimizing the impact on the larger scale features.
+The main difference between the two operators is the scale selectiveness.
+The bilaplacian damping time ($i.e.$ its spin down time) scales like $\lambda^{-4}$
+for disturbances of wavelength $\lambda$ (so that short waves damped more rapidelly than long ones),
+whereas the laplacian damping time scales only like $\lambda^{-2}$.
+% -------------------------------------------------------------------------------------------------------------
+%        Direction of action
+% -------------------------------------------------------------------------------------------------------------
+\subsection   [Direction of action (\np{ln\_traldf\_lev}, \np{ln\_traldf\_hor}, \np{ln\_traldf\_iso}, \np{ln\_traldf\_triad})]
+              {Direction of action (\np{ln\_traldf\_lev}, \textit{...\_hor}, \textit{...\_iso}, or \textit{...\_triad} = true) }
+\label{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}~=~\textit{true})
+or when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{z}-coordinate
+(\np{ln\_traldf\_hor} and \np{ln\_zco} equal \textit{true}).
+The associated code can be found in the \mdl{traldf\_lap\_blp} module.
+The operator is a rotated (re-entrant) laplacian when the direction along which it acts
+does not coincide with the iso-level surfaces,
+that is when standard or triad iso-neutral option is used (\np{ln\_traldf\_iso} or
+ \np{ln\_traldf\_triad} equals \textit{true}, see \mdl{traldf\_iso} or \mdl{traldf\_triad} module, resp.),
+or when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{s}-coordinate
+(\np{ln\_traldf\_hor} and \np{ln\_sco} equal \textit{true})
+\footnote{In this case, the standard iso-neutral operator will be automatically selected}.
+In that case, a rotation is applied to the gradient(s) that appears in the operator
+so that diffusive fluxes acts on the three spatial direction.
+The resulting discret form of the three operators (one iso-level and two rotated one)
+is given in the next two sub-sections.
+% -------------------------------------------------------------------------------------------------------------
+%       iso-level operator
+% -------------------------------------------------------------------------------------------------------------
+\subsection   [Iso-level (bi-)laplacian operator ( \np{ln\_traldf\_iso})]
+         {Iso-level (bi-)laplacian operator ( \np{ln\_traldf\_iso}) }
+\label{TRA_ldf_lev}
+The laplacian diffusion operator acting along the model (\textit{i,j})-surfaces is given by:
 \begin{equation} \label{Eq_tra_ldf_lap}
 D_T^{lT} =\frac{1}{b_tT} \left( \;
+D_t^{lT} =\frac{1}{b_t} \left( \;
    \delta _{i}\left[ A_u^{lT} \; \frac{e_{2u}\,e_{3u}}{e_{1u}} \;\delta _{i+1/2} [T] \right]
 + \delta _{j}\left[ A_v^{lT} \;  \frac{e_{1v}\,e_{3v}}{e_{2v}} \;\delta _{j+1/2} [T] \right]  \;\right)
 \end{equation}
+where  $b_t$=$e_{1t}\,e_{2t}\,e_{3t}$  is the volume of $T$-cells.
+It is implemented in the \mdl{traadv\_lap} module.
+This lateral operator is computed in \mdl{traldf\_lap}. It is a \emph{horizontal}
+operator ($i.e.$ 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}=true, we have
+\np{ln\_traldf\_level}=true or \np{ln\_traldf\_hor}=\np{ln\_zco}=true.
+where  $b_t$=$e_{1t}\,e_{2t}\,e_{3t}$  is the volume of $T$-cells
+and where zero diffusive fluxes is assumed across solid boundaries,
+first (and third in bilaplacian case) horizontal tracer derivative are masked.
+It is implemented in the \rou{traldf\_lap} subroutine found in the \mdl{traldf\_lap} module.
+The module also contains \rou{traldf\_blp}, the subroutine calling twice \rou{traldf\_lap}
+in order to compute the iso-level bilaplacian operator.
+It is a \emph{horizontal} operator ($i.e.$ 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}~=~\textit{true},
+we have \np{ln\_traldf\_lev}~=~\textit{true} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}~=~\textit{true}.
 In both cases, it significantly contributes to diapycnal mixing.
 It is therefore not recommended.
+It is therefore never recommended, even when using it in the bilaplacian case.
 Note that in the partial step $z$-coordinate (\np{ln\_zps}=true), tracers in horizontally
 …
 described in \S\ref{TRA_zpshde}.
+% -------------------------------------------------------------------------------------------------------------
+%        Rotated laplacian operator
+% -------------------------------------------------------------------------------------------------------------
+\subsection   [Rotated laplacian operator (iso) (\np{ln\_traldf\_lap})]
+         {Rotated laplacian operator (iso) (\np{ln\_traldf\_lap}=true)}
+% -------------------------------------------------------------------------------------------------------------
+%         Rotated laplacian operator
+% -------------------------------------------------------------------------------------------------------------
+\subsection   [Standard and triad rotated (bi-)laplacian operator (\mdl{traldf\_iso}, \mdl{traldf\_triad})]
+               {Standard and triad (bi-)laplacian operator (\mdl{traldf\_iso}, \mdl{traldf\_triad}))}
+\label{TRA_ldf_iso_triad}
+%&&    Standard rotated (bi-)laplacian operator
+%&& ----------------------------------------------
+\subsubsection   [Standard rotated (bi-)laplacian operator (\mdl{traldf\_iso})]
+                 {Standard rotated (bi-)laplacian operator (\mdl{traldf\_iso})}
 \label{TRA_ldf_iso}
+If the Griffies trad scheme is not employed
+(\np{ln\_traldf\_grif}=true; see App.\ref{sec:triad}) the general form of the second order lateral tracer subgrid scale physics
+(\ref{Eq_PE_zdf}) takes the following semi-discrete space form in $z$- and
+$s$-coordinates:
+The general form of the second order lateral tracer subgrid scale physics
+(\ref{Eq_PE_zdf}) takes the following semi-discrete space form in $z$- and $s$-coordinates:
 \begin{equation} \label{Eq_tra_ldf_iso}
 \begin{split}
 …
 of the tracer variance. Nevertheless the treatment performed on the slopes
 (see \S\ref{LDF}) allows the model to run safely without any additional
+background horizontal diffusion \citep{Guilyardi_al_CD01}. An alternative scheme
+developed by \cite{Griffies_al_JPO98} which ensures tracer variance decreases
+background horizontal diffusion \citep{Guilyardi_al_CD01}.
+Note that in the partial step $z$-coordinate (\np{ln\_zps}=true), the horizontal derivatives
+at the bottom level in \eqref{Eq_tra_ldf_iso} require a specific treatment.
+They are calculated in module zpshde, described in \S\ref{TRA_zpshde}.
+%&&     Triad rotated (bi-)laplacian operator
+%&&  -------------------------------------------
+\subsubsection   [Triad rotated (bi-)laplacian operator (\np{ln\_traldf\_triad})]
+                 {Triad rotated (bi-)laplacian operator (\np{ln\_traldf\_triad})}
+\label{TRA_ldf_triad}
+If the Griffies triad scheme is employed (\np{ln\_traldf\_triad}=true ; see App.\ref{sec:triad})
+An alternative scheme developed by \cite{Griffies_al_JPO98} which ensures tracer variance decreases
 is also available in \NEMO (\np{ln\_traldf\_grif}=true). A complete description of
 the algorithm is given in App.\ref{sec:triad}.
-Note that in the partial step $z$-coordinate (\np{ln\_zps}=true), the horizontal
-derivatives at the bottom level in \eqref{Eq_tra_ldf_iso} require a specific
-treatment. They are calculated in module zpshde, described in \S\ref{TRA_zpshde}.
-% -------------------------------------------------------------------------------------------------------------
-%        Iso-level bilaplacian operator
-% -------------------------------------------------------------------------------------------------------------
-\subsection   [Iso-level bilaplacian operator (bilap) (\np{ln\_traldf\_bilap})]
-         {Iso-level bilaplacian operator (bilap) (\np{ln\_traldf\_bilap}=true)}
-\label{TRA_ldf_bilap}
 The lateral fourth order bilaplacian operator on tracers is obtained by
 applying (\ref{Eq_tra_ldf_lap}) twice. The operator requires an additional assumption
 on boundary conditions: both first and third derivative terms normal to the
+coast are set to zero. It is used when, in addition to \np{ln\_traldf\_bilap}=true,
+we have \np{ln\_traldf\_level}=true, or both \np{ln\_traldf\_hor}=true and
+\np{ln\_zco}=false. In both cases, it can contribute diapycnal mixing,
+although less than in the laplacian case. It is therefore not recommended.
+Note that in the code, the bilaplacian routine does not call the laplacian
+routine twice but is rather a separate routine that can be found in the
+\mdl{traldf\_bilap} module. This is due to the fact that we introduce the
+eddy diffusivity coefficient, A, in the operator as:
+$\nabla \cdot \nabla \left( {A\nabla \cdot \nabla T} \right)$,
+instead of
+$-\nabla \cdot a\nabla \left( {\nabla \cdot a\nabla T} \right)$
+where $a=\sqrt{|A|}$ and $A<0$. This was a mistake: both formulations
+ensure the total variance decrease, but the former requires a larger
+number of code-lines.
+% -------------------------------------------------------------------------------------------------------------
+%        Rotated bilaplacian operator
+% -------------------------------------------------------------------------------------------------------------
+\subsection   [Rotated bilaplacian operator (bilapg) (\np{ln\_traldf\_bilap})]
+         {Rotated bilaplacian operator (bilapg) (\np{ln\_traldf\_bilap}=true)}
+\label{TRA_ldf_bilapg}
+coast are set to zero.
 The lateral fourth order operator formulation on tracers is obtained by
 applying (\ref{Eq_tra_ldf_iso}) twice. It requires an additional assumption
 on boundary conditions: first and third derivative terms normal to the
+coast, normal to the bottom and normal to the surface are set to zero. It can be found in the
+\mdl{traldf\_bilapg}.
+It is used when, in addition to \np{ln\_traldf\_bilap}=true, we have
+\np{ln\_traldf\_iso}= .true, or both \np{ln\_traldf\_hor}=true and \np{ln\_zco}=true.
+This rotated bilaplacian operator has never been seriously
+tested. There are no guarantees that it is either free of bugs or correctly formulated.
+Moreover, the stability range of such an operator will be probably quite
+narrow, requiring a significantly smaller time-step than the one used with an
+unrotated operator.
+coast, normal to the bottom and normal to the surface are set to zero.
+%&&    Option for the rotated operators
+%&& ----------------------------------------------
+\subsubsection   [Option for the rotated operators]
+                 {Option for the rotated operators}
+\label{TRA_ldf_options}
+\np{ln\_traldf\_msc} = Method of Stabilizing Correction (both operators)
+\np{rn\_slpmax} = slope limit (both operators)
+\np{ln\_triad\_iso} = pure horizontal mixing in ML (triad only)
+\np{rn\_sw\_triad} =1 switching triad ; =0 all 4 triads used (triad only)
+\np{ln\_botmix\_triad} = lateral mixing on bottom (triad only)
 % ================================================================
 …
 %--------------------------------------------------------------------------------------------------------------
 Options are defined through the  \ngn{namzdf} namelist variables.
+Options are defined through the \ngn{namzdf} namelist variables.
 The formulation of the vertical subgrid scale tracer physics is the same
 for all the vertical coordinates, and is based on a laplacian operator.
 …
 the thickness of the top model layer.
+Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components ($i.e.$ atmosphere, sea-ice, land),
+the change in the heat and salt content of the surface layer of the ocean is due both
+to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$)
+ and to the heat and salt content of the mass exchange.
+\sgacomment{ the following does not apply to the release to which this documentation is
+attached and so should not be included ....
+In a forthcoming release, these two parts, computed in the surface module (SBC), will be included directly
+in $Q_{ns}$, the surface heat flux and $F_{salt}$, the surface salt flux.
+The specification of these fluxes is further detailed in the SBC chapter (see \S\ref{SBC}).
+This change will provide a forcing formulation which is the same for any tracer (including temperature and salinity).
+In the current version, the situation is a little bit more complicated. }
+Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components
+($i.e.$ atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer
+of the ocean is due both to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$)
+and to the heat and salt content of the mass exchange. They are both included directly in $Q_{ns}$,
+the surface heat flux, and $F_{salt}$, the surface salt flux (see \S\ref{SBC} for further details).
+By doing this, the forcing formulation is the same for any tracer (including temperature and salinity).
 The surface module (\mdl{sbcmod}, see \S\ref{SBC}) provides the following
 …
 $\bullet$ $Q_{ns}$, the non-solar part of the net surface heat flux that crosses the sea surface
 (i.e. the difference between the total surface heat flux and the fraction of the short wave flux that
+penetrates into the water column, see \S\ref{TRA_qsr})
+$\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation)
+$\bullet$ $\textit{emp}_S$, an equivalent mass flux taking into account the effect of ice-ocean mass exchange
+$\bullet$ \textit{rnf}, the mass flux associated with runoff (see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies)
+The $\textit{emp}_S$ field is not simply the budget of evaporation-precipitation+freezing-melting because
+the sea-ice is not currently embedded in the ocean but levitates above it. There is no mass
+exchanged between the sea-ice and the ocean. Instead we only take into account the salt
+flux associated with the non-zero salinity of sea-ice, and the concentration/dilution effect
+due to the freezing/melting (F/M) process. These two parts of the forcing are then converted into
+an equivalent mass flux given by $\textit{emp}_S - \textit{emp}$. As a result of this mess,
+the surface boundary condition on temperature and salinity is applied as follows:
+In the nonlinear free surface case (\key{vvl} is defined):
+penetrates into the water column, see \S\ref{TRA_qsr}) plus the heat content associated with
+of the mass exchange with the atmosphere and lands.
+$\bullet$ $\textit{sfx}$, the salt flux resulting from ice-ocean mass exchange (freezing, melting, ridging...)
+$\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation)
+ and possibly with the sea-ice and ice-shelves.
+$\bullet$ \textit{rnf}, the mass flux associated with runoff
+(see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies)
+The surface boundary condition on temperature and salinity is applied as follows:
 \begin{equation} \label{Eq_tra_sbc}
+\begin{aligned}
+ &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }  &\overline{ Q_{ns}       }^t  & \\
+& F^S =\frac{ 1 }{\rho _o  \,      \left. e_{3t} \right|_{k=1} }  &\overline{ \textit{sfx} }^t   & \\
+ \end{aligned}
+\end{equation}
+where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps
+($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the
+divergence of odd and even time step (see \S\ref{STP}).
+In the linear free surface case (\np{ln\_linssh}~=~\textit{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 $Q_{ns}$. On salinity, this term mimics the concentration/dilution effect that
+would have resulted from a change in the volume of the first level.
+The resulting surface boundary condition is applied as follows:
+\begin{equation} \label{Eq_tra_sbc_lin}
 \begin{aligned}
  &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }
 …
+%
 & F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} }
            &\overline{ \left( (\textit{emp}_S - \textit{emp})\;\left. S \right|_{k=1}  \right) }^t   & \\
+           &\overline{ \left( \;\textit{sfx} - \textit{emp} \;\left. S \right|_{k=1}  \right) }^t   & \\
  \end{aligned}
 \end{equation}
+In the linear free surface case (\key{vvl} not defined):
+\begin{equation} \label{Eq_tra_sbc_lin}
+\begin{aligned}
+ &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }  &\overline{ Q_{ns} }^t  & \\
+%
+& F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} }
+           &\overline{ \left( \textit{emp}_S\;\left. S \right|_{k=1}  \right) }^t   & \\
+ \end{aligned}
+\end{equation}
+where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps
+($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the
+divergence of odd and even time step (see \S\ref{STP}).
+The two set of equations, \eqref{Eq_tra_sbc} and \eqref{Eq_tra_sbc_lin}, are obtained
+by assuming that the temperature of precipitation and evaporation are equal to
+the ocean surface temperature and that their salinity is zero. Therefore, the heat content
+of the \textit{emp} budget must be added to the temperature equation in the variable volume case,
+while it does not appear in the constant volume case. Similarly, the \textit{emp} budget affects
+the ocean surface salinity in the constant volume case (through the concentration dilution effect)
+while it does not appears explicitly in the variable volume case since salinity change will be
+induced by volume change. In both constant and variable volume cases, surface salinity
+will change with ice-ocean salt flux and F/M flux (both contained in $\textit{emp}_S - \textit{emp}$) without mass exchanges.
+Note that the concentration/dilution effect due to F/M is computed using
+a constant ice salinity as well as a constant ocean salinity.
+This approximation suppresses the correlation between \textit{SSS}
+and F/M flux, allowing the ice-ocean salt exchanges to be conservative.
+Indeed, if this approximation is not made, even if the F/M budget is zero
+on average over the whole ocean domain and over the seasonal cycle,
+the associated salt flux is not zero, since sea-surface salinity and F/M flux are
+intrinsically correlated (high \textit{SSS} are found where freezing is
+strong whilst low \textit{SSS} is usually associated with high melting areas).
+Even using this approximation, an exact conservation of heat and salt content
+is only achieved in the variable volume case. In the constant volume case,
+there is a small imbalance associated with the product $(\partial_t\eta - \textit{emp}) * \textit{SSS}$.
+Nevertheless, the salt content variation is quite small and will not induce
+a long term drift as there is no physical reason for $(\partial_t\eta - \textit{emp})$
+and \textit{SSS} to be correlated \citep{Roullet_Madec_JGR00}.
+Note that, while quite small, the imbalance in the constant volume case is larger
+Note that an exact conservation of heat and salt content is only achieved with non-linear free surface.
+In the linear free surface case, there is a small imbalance. The imbalance is larger
 than the imbalance associated with the Asselin time filter \citep{Leclair_Madec_OM09}.
 This is the reason why the modified filter is not applied in the constant volume case.
+This is the reason why the modified filter is not applied in the linear free surface case (see \S\ref{STP}).
 % -------------------------------------------------------------------------------------------------------------
 …
 \label{TRA_bbc}
 %--------------------------------------------nambbc--------------------------------------------------------
 \namdisplay{namtra_bbc}
+\namdisplay{nambbc}
 %--------------------------------------------------------------------------------------------------------------
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 …
 \subsection[DMP\_TOOLS]{Generating resto.nc using DMP\_TOOLS}
+DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$. Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled and run on the same machine as the NEMO model. A mesh\_mask.nc file for the model configuration is required as an input. This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1. The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work. The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient.
+DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$.
+Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled
+and run on the same machine as the NEMO model. A mesh\_mask.nc file for the model configuration is required as an input.
+This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1.
+The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work.
+The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient.
 %--------------------------------------------nam_dmp_create-------------------------------------------------
 \namdisplay{nam_dmp_create}
+\namtools{namelist_dmp}
 %-------------------------------------------------------------------------------------------------------
 \np{cp\_cfg}, \np{cp\_cpz}, \np{jp\_cfg} and \np{jperio} specify the model configuration being used and should be the same as specified in \nl{namcfg}. The variable \nl{lzoom} is used to specify that the damping is being used as in case \textit{a} above to provide boundary conditions to a zoom configuration. In the case of the arctic or antarctic zoom configurations this includes some specific treatment. Otherwise damping is applied to the 6 grid points along the ocean boundaries. The open boundaries are specified by the variables \np{lzoom\_n}, \np{lzoom\_e}, \np{lzoom\_s}, \np{lzoom\_w} in the \nl{nam\_zoom\_dmp} name list.
+The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations. \np{ln\_full\_field} specifies that newtonian damping should be applied to the whole model domain. \np{ln\_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea for the ORCA4, ORCA2 and ORCA05 configurations. If \np{ln\_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference configurations with previous model versions. \np{ln\_coast} specifies that the restoration coefficient should be reduced near to coastlines. This option only has an effect if \np{ln\_full\_field} is true. \np{ln\_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer. Finally \np{ln\_custom} specifies that the custom module will be called. This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region.
+The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn\_hdmp}. Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to the full values of a 10$^{\circ}$ latitud band. This is often used because of the short adjustment time scale in the equatorial region \citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a hyperbolic tangent, with \np{rn\_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}.
+The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations.
+\np{ln\_full\_field} specifies that newtonian damping should be applied to the whole model domain.
+\np{ln\_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea
+for the ORCA4, ORCA2 and ORCA05 configurations.
+If \np{ln\_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as
+a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference
+configurations with previous model versions.
+\np{ln\_coast} specifies that the restoration coefficient should be reduced near to coastlines.
+This option only has an effect if \np{ln\_full\_field} is true.
+\np{ln\_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer.
+Finally \np{ln\_custom} specifies that the custom module will be called.
+This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region.
+The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn\_hdmp}.
+Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to
+the full values of a 10$^{\circ}$ latitud band.
+This is often used because of the short adjustment time scale in the equatorial region
+\citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a
+hyperbolic tangent, with \np{rn\_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}.
 % ================================================================
 …
 % -------------------------------------------------------------------------------------------------------------
 %        Brunt-Vais\"{a}l\"{a} Frequency
 % -------------------------------------------------------------------------------------------------------------
 \subsection{Brunt-Vais\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)}
+%        Brunt-V\"{a}is\"{a}l\"{a} Frequency
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)}
 \label{TRA_bn2}
 An accurate computation of the ocean stability (i.e. of $N$, the brunt-Vais\"{a}l\"{a}
+An accurate computation of the ocean stability (i.e. of $N$, the brunt-V\"{a}is\"{a}l\"{a}
  frequency) is of paramount importance as determine the ocean stratification and
  is used in several ocean parameterisations (namely TKE, GLS, Richardson number dependent
 …
 \label{TRA_zpshde}
+\gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators, I've changed "derivative" to "difference" and "mean" to "average"}
+\gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators,
+                   I've changed "derivative" to "difference" and "mean" to "average"}
 With partial bottom cells (\np{ln\_zps}=true), in general, tracers in horizontally

trunk/DOC/TexFiles/Chapters/Chap_ZDF.tex

-                      r5120
+                      r6289
 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 KPP formulation). The computation of these coefficients is initialized
+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{zdfkpp} modules. The trends due to the vertical momentum and tracer
+\mdl{zdfgls} 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.
 …
 %--------------------------------------------------------------%
+To be add here a description of "penetration of TKE" and the associated namelist parameters
+ \np{nn\_etau}, \np{rn\_efr} and \np{nn\_htau}.
+Vertical mixing parameterizations commonly used in ocean general circulation models
+tend 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}.
+The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations,
+but rather is meant to account for observed processes that affect the density structure of
+the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme
+($i.e.$ near-inertial oscillations and ocean swells and waves).
+When using this parameterization ($i.e.$ when \np{nn\_etau}~=~1), the TKE input to the ocean ($S$)
+imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized
+by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by:
+\begin{equation}  \label{ZDF_Ehtau}
+S = (1-f_i) \; f_r \; e_s \; e^{-z / h_\tau}
+\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 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).
+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}~=~0)
+or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m
+at high latitudes (\np{nn\_etau}~=~1).
+Note that two other option existe, \np{nn\_etau}~=~2, or 3. They correspond to applying
+\eqref{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.
+Those two options are obsolescent features introduced for test purposes.
+They will be removed in the next release.
 % from Burchard et al OM 2008 :
+% the most critical process not reproduced by statistical turbulence models is the activity of internal waves and their interaction with turbulence. After the Reynolds decomposition, internal waves are in principle included in the RANS equations, but later partially excluded by the hydrostatic assumption and the model resolution. Thus far, the representation of internal wave mixing in ocean models has been relatively crude (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002).
+% the most critical process not reproduced by statistical turbulence models is the activity of
+% internal waves and their interaction with turbulence. After the Reynolds decomposition,
+% internal waves are in principle included in the RANS equations, but later partially
+% excluded by the hydrostatic assumption and the model resolution.
+% Thus far, the representation of internal wave mixing in ocean models has been relatively crude
+% (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002).
 …
 Examples of performance of the 4 turbulent closure scheme can be found in \citet{Warner_al_OM05}.
-% -------------------------------------------------------------------------------------------------------------
-%        K Profile Parametrisation (KPP)
-% -------------------------------------------------------------------------------------------------------------
-\subsection{K Profile Parametrisation (KPP) (\key{zdfkpp}) }
-\label{ZDF_kpp}
-%--------------------------------------------namkpp--------------------------------------------------------
-\namdisplay{namzdf_kpp}
-%--------------------------------------------------------------------------------------------------------------
-The KKP scheme has been implemented by J. Chanut ...
-Options are defined through the  \ngn{namzdf\_kpp} namelist variables.
-\colorbox{yellow}{Add a description of KPP here.}
 % ================================================================
 …
 Options are defined through the  \ngn{namzdf} namelist variables.
 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}=true.
+The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}~=~\textit{true}.
 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously
 the statically unstable portion of the water column, but only until the density
 …
 (Fig. \ref{Fig_npc}): starting from the top of the ocean, the first instability is
 found. Assume in the following that the instability is located between levels
 $k$ and $k+1$. The potential temperature and salinity in the two levels are
+$k$ and $k+1$. The temperature and salinity in the two levels are
 vertically mixed, conserving the heat and salt contents of the water column.
 The new density is then computed by a linear approximation. If the new
 …
 \citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}.
+Note that in the current implementation of this algorithm presents several
+limitations. First, potential density referenced to the sea surface is used to
+check whether the density profile is stable or not. This is a strong
+simplification which leads to large errors for realistic ocean simulations.
+Indeed, many water masses of the world ocean, especially Antarctic Bottom
+Water, are unstable when represented in surface-referenced potential density.
+The scheme will erroneously mix them up. Second, the mixing of potential
+density is assumed to be linear. This assures the convergence of the algorithm
+even when the equation of state is non-linear. Small static instabilities can thus
+persist due to cabbeling: they will be treated at the next time step.
+Third, temperature and salinity, and thus density, are mixed, but the
+corresponding velocity fields remain unchanged. When using a Richardson
+Number dependent eddy viscosity, the mixing of momentum is done through
+the vertical diffusion: after a static adjustment, the Richardson Number is zero
+and thus the eddy viscosity coefficient is at a maximum. When this convective
+adjustment algorithm is used with constant vertical eddy viscosity, spurious
+solutions can occur since the vertical momentum diffusion remains small even
+after a static adjustment. In that case, we recommend the addition of momentum
+mixing in a manner that mimics the mixing in temperature and salinity
+\citep{Speich_PhD92, Speich_al_JPO96}.
+The current implementation has been modified in order to deal with any non linear
+equation of seawater (L. Brodeau, personnal communication).
+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) ;
+$(ii)$ 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.
+These two modifications allow the algorithm to perform properly and accurately
+with TEOS10 or EOS-80 without having to recompute the expansion coefficients at each
+mixing iteration.
 % -------------------------------------------------------------------------------------------------------------
 …
 % -------------------------------------------------------------------------------------------------------------
 \subsection   [Enhanced Vertical Diffusion (\np{ln\_zdfevd})]
          {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)}
+              {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)}
 \label{ZDF_evd}

trunk/DOC/TexFiles/Chapters/Introduction.tex

r6140	r6289
32	32	The equations are written in a curvilinear coordinate system, with a choice of vertical
33	33	coordinates ($z$, $s$, \textit{z}, \textit{s}, $\tilde{z}$, $\tilde{s}$, and a mixture of them).
34		Momentum equations are formulated in ~~the vector invariant form or in the~~ flux form.
	34	Momentum equations are formulated in vector invariant or flux form.
35	35	Dimensional units in the meter, kilogram, second (MKS) international system
36	36	are used throughout.

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