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Changeset 6275 for branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters – NEMO

Ignore:
Timestamp:
2016-02-01T03:35:04+01:00 (8 years ago)
Author:
gm
Message:

#1629: DOC of v3.6_stable. Upadate, see associated wiki page for description

Location:
branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters
Files:
15 edited

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  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Abstracts_Foreword.tex

    r3294 r6275  
    1313be a flexible tool for studying the ocean and its interactions with the others components of  
    1414the earth climate system over a wide range of space and time scales.  
    15 Prognostic variables are the three-dimensional velocity field, a linear  
    16 or non-linear sea surface height, the temperature and the salinity. In the horizontal direction,  
    17 the model uses a curvilinear orthogonal grid and in the vertical direction, a full or partial step  
    18 $z$-coordinate, or $s$-coordinate, or a mixture of the two. The distribution of variables is a  
    19 three-dimensional Arakawa C-type grid. Various physical choices are available to describe  
    20 ocean physics, including TKE, GLS and KPP vertical physics. Within NEMO, the ocean is  
    21 interfaced with a sea-ice model (LIM v2 and v3), passive tracer and biogeochemical models (TOP)  
    22 and, via the OASIS coupler, with several atmospheric general circulation models. It also  
    23 support two-way grid embedding via the AGRIF software. 
     15Prognostic variables are the three-dimensional velocity field, a non-linear sea surface height,  
     16the \textit{Conservative} Temperature and the \textit{Absolute} Salinity.  
     17In the horizontal direction, the model uses a curvilinear orthogonal grid and in the vertical direction,  
     18a full or partial step $z$-coordinate, or $s$-coordinate, or a mixture of the two.  
     19The distribution of variables is a three-dimensional Arakawa C-type grid.  
     20Various physical choices are available to describe ocean physics, including TKE, and GLS vertical physics.  
     21Within NEMO, the ocean is interfaced with a sea-ice model (LIM or CICE), passive tracer and  
     22biogeochemical models (TOP) and, via the OASIS coupler, with several atmospheric general circulation models.  
     23It also support two-way grid embedding via the AGRIF software. 
    2424 
    2525% ================================================================ 
    … …  
    3131interactions avec les autres composantes du syst\`{e}me climatique terrestre.  
    3232Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer  
    33 lin\'{e}aire ou non, la temperature et la salinit\'{e}.  
     33lin\'{e}aire, la Temp\'{e}rature Conservative et la Salinit\'{e} Absolue.  
    3434La distribution des variables se fait sur une grille C d'Arakawa tridimensionnelle utilisant une  
    3535coordonn\'{e}e verticale $z$ \`{a} niveaux entiers ou partiels, ou une coordonn\'{e}e s, ou encore  
    3636une combinaison des deux. Diff\'{e}rents choix sont propos\'{e}s pour d\'{e}crire la physique  
    37 oc\'{e}anique, incluant notamment des physiques verticales TKE, GLS et KPP. A travers l'infrastructure  
    38 NEMO, l'oc\'{e}an est interfac\'{e} avec des mod\`{e}les de glace de mer, de biog\'{e}ochimie  
    39 et de traceurs passifs, et, via le coupleur OASIS, \`{a} plusieurs mod\`{e}les de circulation  
    40 g\'{e}n\'{e}rale atmosph\'{e}rique. Il supporte \'{e}galement l'embo\^{i}tement interactif de  
    41 maillages via le logiciel AGRIF. 
     37oc\'{e}anique, incluant notamment des physiques verticales TKE et GLS. A travers l'infrastructure  
     38NEMO, l'oc\'{e}an est interfac\'{e} avec des mod\`{e}les de glace de mer (LIM ou CICE),  
     39de biog\'{e}ochimie marine et de traceurs passifs, et, via le coupleur OASIS, \`{a} plusieurs  
     40mod\`{e}les de circulation g\'{e}n\'{e}rale atmosph\'{e}rique.  
     41Il supporte \'{e}galement l'embo\^{i}tement interactif de maillages via le logiciel AGRIF. 
    4242}  
    4343 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Annex_C.tex

    r3294 r6275  
    410410\end{aligned}   } \right. 
    411411\end{equation}  
    412 where the indices $i_p$ and $k_p$ take the following value:  
     412where the indices $i_p$ and $j_p$ take the following value:  
    413413$i_p = -1/2$ or $1/2$ and $j_p = -1/2$ or $1/2$, 
    414414and the vorticity triads, ${^i_j}\mathbb{Q}^{i_p}_{j_p}$, defined at $T$-point, are given by:  
    … …  
    11031103The discrete formulation of the horizontal diffusion of momentum ensures the  
    11041104conservation of potential vorticity and the horizontal divergence, and the  
    1105 dissipation of the square of these quantities (i.e. enstrophy and the  
     1105dissipation of the square of these quantities ($i.e.$ enstrophy and the  
    11061106variance of the horizontal divergence) as well as the dissipation of the  
    11071107horizontal kinetic energy. In particular, when the eddy coefficients are  
    … …  
    11271127&\int \limits_D \frac{1} {e_3 } \textbf{k} \cdot \nabla \times  
    11281128   \Bigl[    \nabla_h  \left( A^{\,lm}\;\chi  \right) 
    1129              - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)    \Bigr]\;dv  = 0 
    1130 \end{flalign*} 
     1129           - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)    \Bigr]\;dv   \\  
     1130%\end{flalign*} 
    11311131%%%%%%%%%%  recheck here....  (gm) 
    1132 \begin{flalign*} 
    1133 = \int \limits_D  -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times  
    1134    \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)  \Bigr]\;dv &&& \\  
    1135 \end{flalign*} 
    1136 \begin{flalign*} 
     1132%\begin{flalign*} 
     1133=& \int \limits_D  -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times  
     1134   \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)  \Bigr]\;dv \\  
     1135%\end{flalign*} 
     1136%\begin{flalign*} 
    11371137\equiv& \sum\limits_{i,j} 
    11381138   \left\{ 
    1139    \delta_{i+1/2}  
    1140    \left[  
    1141    \frac {e_{2v}} {e_{1v}\,e_{3v}}  \delta_i 
    1142       \left[ A_f^{\,lm} e_{3f} \zeta  \right] 
    1143     \right] 
    1144    + \delta_{j+1/2}  
    1145    \left[  
    1146    \frac {e_{1u}} {e_{2u}\,e_{3u}} \delta_j  
    1147       \left[ A_f^{\,lm} e_{3f} \zeta  \right] 
    1148    \right] 
    1149    \right\}  
    1150    && \\  
     1139     \delta_{i+1/2} \left[  \frac {e_{2v}} {e_{1v}\,e_{3v}}  \delta_i \left[ A_f^{\,lm} e_{3f} \zeta  \right]  \right] 
     1140   + \delta_{j+1/2} \left[  \frac {e_{1u}} {e_{2u}\,e_{3u}}  \delta_j \left[ A_f^{\,lm} e_{3f} \zeta  \right]  \right] 
     1141   \right\}     \\  
    11511142% 
    11521143\intertext{Using \eqref{DOM_di_adj}, it follows:} 
    … …  
    11541145\equiv& \sum\limits_{i,j,k}  
    11551146   -\,\left\{ 
    1156       \frac{e_{2v}} {e_{1v}\,e_{3v}}  \delta_i 
    1157       \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_i \left[ 1\right] 
    1158    + \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j  
    1159       \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_j \left[ 1\right] 
     1147      \frac{e_{2v}} {e_{1v}\,e_{3v}}  \delta_i  \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_i \left[ 1\right] 
     1148    + \frac{e_{1u}} {e_{2u}\,e_{3u}}  \delta_j  \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_j \left[ 1\right] 
    11601149   \right\} \quad \equiv 0  
    1161    && \\  
     1150    \\  
    11621151\end{flalign*} 
    11631152 
    … …  
    11671156\subsection{Dissipation of Horizontal Kinetic Energy} 
    11681157\label{Apdx_C.3.2} 
    1169  
    11701158 
    11711159The lateral momentum diffusion term dissipates the horizontal kinetic energy: 
    … …  
    12211209\label{Apdx_C.3.3} 
    12221210 
    1223  
    12241211The lateral momentum diffusion term dissipates the enstrophy when the eddy  
    12251212coefficients are horizontally uniform: 
    … …  
    12281215   \left[   \nabla_h \left( A^{\,lm}\;\chi  \right) 
    12291216          - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)   \right]\;dv &&&\\ 
    1230 &= A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times  
     1217&\quad = A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times  
    12311218   \left[    \nabla_h \times \left( \zeta \; \textbf{k} \right)   \right]\;dv &&&\\ 
    1232 &\equiv A^{\,lm} \sum\limits_{i,j,k}  \zeta \;e_{3f}  
     1219&\quad \equiv A^{\,lm} \sum\limits_{i,j,k}  \zeta \;e_{3f}  
    12331220   \left\{     \delta_{i+1/2} \left[  \frac{e_{2v}} {e_{1v}\,e_{3v}} \delta_i \left[ e_{3f} \zeta  \right]   \right] 
    12341221             + \delta_{j+1/2} \left[  \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j \left[ e_{3f} \zeta  \right]   \right]      \right\}   &&&\\  
    … …  
    12361223\intertext{Using \eqref{DOM_di_adj}, it follows:} 
    12371224% 
    1238 &\equiv  - A^{\,lm} \sum\limits_{i,j,k}  
     1225&\quad \equiv  - A^{\,lm} \sum\limits_{i,j,k}  
    12391226   \left\{    \left(  \frac{1} {e_{1v}\,e_{3v}}  \delta_i \left[ e_{3f} \zeta  \right]  \right)^2   b_v 
    1240             + \left(  \frac{1} {e_{2u}\,e_{3u}}  \delta_j \left[ e_{3f} \zeta  \right] \right)^2   b_u  \right\}      &&&\\ 
    1241 & \leq \;0       &&&\\  
     1227            + \left(  \frac{1} {e_{2u}\,e_{3u}}  \delta_j \left[ e_{3f} \zeta  \right] \right)^2   b_u  \right\}  \quad \leq \;0    &&&\\ 
    12421228\end{flalign*} 
    12431229 
    … …  
    12501236When the horizontal divergence of the horizontal diffusion of momentum  
    12511237(discrete sense) is taken, the term associated with the vertical curl of the  
    1252 vorticity is zero locally, due to (!!! II.1.8  !!!!!). The resulting term conserves the  
    1253 $\chi$ and dissipates $\chi^2$ when the eddy coefficients are  
    1254 horizontally uniform. 
     1238vorticity is zero locally, due to \eqref{Eq_DOM_div_curl}.  
     1239The resulting term conserves the $\chi$ and dissipates $\chi^2$  
     1240when the eddy coefficients are horizontally uniform. 
    12551241\begin{flalign*} 
    12561242& \int\limits_D  \nabla_h \cdot  
    12571243   \Bigl[     \nabla_h \left( A^{\,lm}\;\chi \right) 
    12581244             - \nabla_h \times \left( A^{\,lm}\;\zeta \;\textbf{k} \right)    \Bigr]  dv 
    1259 = \int\limits_D  \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi  \right)   dv   &&&\\ 
     1245= \int\limits_D  \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi  \right)   dv   \\ 
    12601246% 
    12611247&\equiv \sum\limits_{i,j,k}  
    12621248   \left\{   \delta_i \left[ A_u^{\,lm} \frac{e_{2u}\,e_{3u}} {e_{1u}}  \delta_{i+1/2} \left[ \chi \right]  \right] 
    1263            + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}}  \delta_{j+1/2} \left[ \chi \right]  \right]    \right\}    &&&\\  
     1249           + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}}  \delta_{j+1/2} \left[ \chi \right]  \right]    \right\}    \\  
    12641250% 
    12651251\intertext{Using \eqref{DOM_di_adj}, it follows:} 
    … …  
    12671253&\equiv \sum\limits_{i,j,k}  
    12681254   - \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]  
    1269              + \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\}  
    1270    \qquad \equiv 0     &&& \\  
     1255             + \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\}  
     1256   \quad \equiv 0      \\  
    12711257\end{flalign*} 
    12721258 
    … …  
    12811267   \left[    \nabla_h              \left( A^{\,lm}\;\chi                    \right) 
    12821268           - \nabla_h   \times  \left( A^{\,lm}\;\zeta \;\textbf{k} \right)    \right]\;  dv 
    1283  = A^{\,lm}   \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\;  dv    &&&\\  
     1269 = A^{\,lm}   \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\;  dv    \\  
    12841270% 
    12851271&\equiv A^{\,lm}  \sum\limits_{i,j,k}  \frac{1} {e_{1t}\,e_{2t}\,e_{3t}}  \chi  
    … …  
    12871273      \delta_i  \left[   \frac{e_{2u}\,e_{3u}} {e_{1u}}  \delta_{i+1/2} \left[ \chi \right]   \right] 
    12881274   + \delta_j  \left[   \frac{e_{1v}\,e_{3v}} {e_{2v}}   \delta_{j+1/2} \left[ \chi \right]   \right] 
    1289    \right\} \;   e_{1t}\,e_{2t}\,e_{3t}    &&&\\  
     1275   \right\} \;   e_{1t}\,e_{2t}\,e_{3t}    \\  
    12901276% 
    12911277\intertext{Using \eqref{DOM_di_adj}, it turns out to be:} 
    … …  
    12931279&\equiv - A^{\,lm} \sum\limits_{i,j,k} 
    12941280   \left\{    \left(  \frac{1} {e_{1u}}  \delta_{i+1/2}  \left[ \chi \right]  \right)^2  b_u 
    1295                  + \left(  \frac{1} {e_{2v}}  \delta_{j+1/2}  \left[ \chi \right]  \right)^2  b_v    \right\} \;    &&&\\ 
    1296 % 
    1297 &\leq 0              &&&\\ 
     1281            + \left(  \frac{1} {e_{2v}}  \delta_{j+1/2}  \left[ \chi \right]  \right)^2  b_v    \right\}     
     1282\quad \leq 0             \\ 
    12981283\end{flalign*} 
    12991284 
    … …  
    13031288\section{Conservation Properties on Vertical Momentum Physics} 
    13041289\label{Apdx_C_4} 
    1305  
    13061290 
    13071291As for the lateral momentum physics, the continuous form of the vertical diffusion  
    … …  
    13191303   \left(   \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k}   \right)\; dv    \quad &\leq 0     \\ 
    13201304\end{align*} 
     1305 
    13211306The first property is obvious. The second results from: 
    1322  
    13231307\begin{flalign*} 
    13241308\int\limits_D  
    … …  
    13591343   e_{1f}\,e_{2f}\,e_{3f} \; \equiv 0   && \\ 
    13601344\end{flalign*} 
     1345 
    13611346If the vertical diffusion coefficient is uniform over the whole domain, the  
    13621347enstrophy is dissipated, $i.e.$ 
    … …  
    13661351      \left( \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k}   \right)   \right)\; dv = 0   &&&\\ 
    13671352\end{flalign*} 
     1353 
    13681354This property is only satisfied in $z$-coordinates: 
    1369  
    13701355\begin{flalign*} 
    13711356\int\limits_D \zeta \, \textbf{k} \cdot \nabla \times  
    … …  
    14771462 
    14781463The numerical schemes used for tracer subgridscale physics are written such  
    1479 that the heat and salt contents are conserved (equations in flux form, second  
    1480 order centered finite differences). Since a flux form is used to compute the  
    1481 temperature and salinity, the quadratic form of these quantities (i.e. their variance)  
    1482 globally tends to diminish. As for the advection term, there is generally no strict  
    1483 conservation of mass, even if in practice the mass is conserved to a very high  
    1484 accuracy.  
     1464that the heat and salt contents are conserved (equations in flux form).  
     1465Since a flux form is used to compute the temperature and salinity,  
     1466the quadratic form of these quantities ($i.e.$ their variance) globally tends to diminish.  
     1467As for the advection term, there is conservation of mass only if the Equation Of Seawater is linear.  
    14851468 
    14861469% ------------------------------------------------------------------------------------------------------------- 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Annex_D.tex

    r3294 r6275  
    120120\hline 
    121121public  \par or  \par module variable&  
    122 \textbf{m n} \par \textit{but not} \par \textbf{nn\_}&  
     122\textbf{m n} \par \textit{but not} \par \textbf{nn\_ np\_}&  
    123123\textbf{a b e f g h o q r} \par \textbf{t} \textit{to} \textbf{x} \par but not \par \textbf{fs rn\_}&  
    124124\textbf{l} \par \textit{but not} \par \textbf{lp ld} \par \textbf{ ll ln\_}&  
    … …  
    156156\hline 
    157157parameter&  
    158 \textbf{jp}&  
     158\textbf{jp np\_}&  
    159159\textbf{pp}&  
    160160\textbf{lp}&  
    … …  
    190190%-------------------------------------------------------------------------------------------------------------- 
    191191 
     192N.B.   Parameter here, in not only parameter in the \textsc{Fortran} acceptation, it is also used for code variables  
     193that are read in namelist and should never been modified during a simulation.  
     194It is the case, for example, for the size of a domain (jpi,jpj,jpk). 
     195 
    192196\newpage 
    193197% ================================================================ 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_DIA.tex

    r5515 r6275  
    22% Chapter I/O & Diagnostics 
    33% ================================================================ 
    4 \chapter{Ouput and Diagnostics (IOM, DIA, TRD, FLO)} 
     4\chapter{Output and Diagnostics (IOM, DIA, TRD, FLO)} 
    55\label{DIA} 
    66\minitoc 
    77 
    88\newpage 
    9 $\ $\newline    % force a new ligne 
     9$\ $\newline    % force a new line 
    1010 
    1111% ================================================================ 
    … …  
    4848 
    4949 
    50 Since version 3.2, iomput is the NEMO output interface of choice. It has been designed to be simple to use, flexible and efficient. The two main purposes of iomput are:  
     50Since version 3.2, iomput is the NEMO output interface of choice.  
     51It has been designed to be simple to use, flexible and efficient.  
     52The two main purposes of iomput are:  
    5153\begin{enumerate} 
    5254\item The complete and flexible control of the output files through external XML files adapted by the user from standard templates.  
    … …  
    11161118% ------------------------------------------------------------------------------------------------------------- 
    11171119\section[Tracer/Dynamics Trends (TRD)] 
    1118                   {Tracer/Dynamics Trends  (\key{trdtra}, \key{trddyn},    \\  
    1119                                                              \key{trddvor}, \key{trdmld})} 
     1120                  {Tracer/Dynamics Trends  (\ngn{namtrd})} 
    11201121\label{DIA_trd} 
    11211122 
    … …  
    11241125%------------------------------------------------------------------------------------------------------------- 
    11251126 
    1126 When \key{trddyn} and/or \key{trddyn} CPP variables are defined, each  
    1127 trend of the dynamics and/or temperature and salinity time evolution equations  
    1128 is stored in three-dimensional arrays just after their computation ($i.e.$ at the end  
    1129 of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). Options are defined by 
    1130 \ngn{namtrd} namelist variables. These trends are then  
    1131 used in \mdl{trdmod} (see TRD directory) every \textit{nn\_trd } time-steps. 
    1132  
    1133 What is done depends on the CPP keys defined: 
     1127Each trend of the dynamics and/or temperature and salinity time evolution equations  
     1128can be send to \mdl{trddyn} and/or \mdl{trdtra} modules (see TRD directory) just after their computation  
     1129($i.e.$ at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines).  
     1130This capability is controlled by options offered in \ngn{namtrd} namelist.  
     1131Note that the output are done with xIOS, and therefore the \key{IOM} is required. 
     1132 
     1133What is done depends on the \ngn{namtrd} logical set to \textit{true}: 
    11341134\begin{description} 
    1135 \item[\key{trddyn}, \key{trdtra}] : a check of the basin averaged properties of the momentum  
    1136 and/or tracer equations is performed ;  
    1137 \item[\key{trdvor}] : a vertical summation of the moment tendencies is performed,  
    1138 then the curl is computed to obtain the barotropic vorticity tendencies which are output ; 
    1139 \item[\key{trdmld}] : output of the tracer tendencies averaged vertically   
    1140 either over the mixed layer (\np{nn\_ctls}=0),  
    1141 or       over a fixed number of model levels (\np{nn\_ctls}$>$1 provides the number of level),  
    1142 or       over a spatially varying but temporally fixed number of levels (typically the base  
    1143 of the winter mixed layer) read in \ifile{ctlsurf\_idx} (\np{nn\_ctls}=1) ; 
     1135\item[\np{ln\_glo\_trd}] : at each \np{nn\_trd} time-step a check of the basin averaged properties  
     1136of the momentum and tracer equations is performed. This also includes a check of $T^2$, $S^2$,  
     1137$\tfrac{1}{2} (u^2+v2)$, and potential energy time evolution equations properties ;  
     1138\item[\np{ln\_dyn\_trd}] : each 3D trend of the evolution of the two momentum components is output ;  
     1139\item[\np{ln\_dyn\_mxl}] : each 3D trend of the evolution of the two momentum components averaged  
     1140                           over the mixed layer is output  ;  
     1141\item[\np{ln\_vor\_trd}] : a vertical summation of the moment tendencies is performed,  
     1142                           then the curl is computed to obtain the barotropic vorticity tendencies which are output ; 
     1143\item[\np{ln\_KE\_trd}]  : each 3D trend of the Kinetic Energy equation is output ; 
     1144\item[\np{ln\_tra\_trd}] : each 3D trend of the evolution of temperature and salinity is output ; 
     1145\item[\np{ln\_tra\_mxl}] : each 2D trend of the evolution of temperature and salinity averaged  
     1146                           over the mixed layer is output ; 
    11441147\end{description} 
    1145  
    1146 The units in the output file can be changed using the \np{nn\_ucf} namelist parameter.  
    1147 For example, in case of salinity tendency the units are given by PSU/s/\np{nn\_ucf}. 
    1148 Setting \np{nn\_ucf}=86400 ($i.e.$ the number of second in a day) provides the tendencies in PSU/d. 
    1149  
    1150 When \key{trdmld} is defined, two time averaging procedure are proposed. 
    1151 Setting \np{ln\_trdmld\_instant} to \textit{true}, a simple time averaging is performed,  
    1152 so that the resulting tendency is the contribution to the change of a quantity between  
    1153 the two instantaneous values taken at the extremities of the time averaging period. 
    1154 Setting \np{ln\_trdmld\_instant} to \textit{false}, a double time averaging is performed,  
    1155 so that the resulting tendency is the contribution to the change of a quantity between  
    1156 two \textit{time mean} values. The later option requires the use of an extra file, \ifile{restart\_mld}   
    1157 (\np{ln\_trdmld\_restart}=true), to restart a run. 
    1158  
    11591148 
    11601149Note that the mixed layer tendency diagnostic can also be used on biogeochemical models  
    11611150via the \key{trdtrc} and \key{trdmld\_trc} CPP keys. 
     1151 
     1152\textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested.  
     1153In particular, options associated with \np{ln\_dyn\_mxl}, \np{ln\_vor\_trd}, and \np{ln\_tra\_mxl}  
     1154are not working, and none of the option have been tested with variable volume ($i.e.$ \key{vvl} defined). 
     1155 
    11621156 
    11631157% ------------------------------------------------------------------------------------------------------------- 
    … …  
    12801274\label{DIA_diag_harm} 
    12811275 
    1282 A module is available to compute the amplitude and phase for tidal waves.  
    1283 This diagnostic is actived with \key{diaharm}. 
    1284  
    12851276%------------------------------------------namdia_harm---------------------------------------------------- 
    12861277\namdisplay{namdia_harm} 
    12871278%---------------------------------------------------------------------------------------------------------- 
    12881279 
    1289 Concerning the on-line Harmonic analysis, some parameters are available in namelist 
    1290 \ngn{namdia\_harm} : 
    1291  
    1292 - \texttt{nit000\_han} is the first time step used for harmonic analysis 
    1293  
    1294 - \texttt{nitend\_han} is the last time step used for harmonic analysis 
    1295  
    1296 - \texttt{nstep\_han} is the time step frequency for harmonic analysis 
    1297  
    1298 - \texttt{nb\_ana} is the number of harmonics to analyse 
    1299  
    1300 - \texttt{tname} is an array with names of tidal constituents to analyse 
    1301  
    1302 \texttt{nit000\_han} and \texttt{nitend\_han} must be between \texttt{nit000} and \texttt{nitend} of the simulation. 
     1280A module is available to compute the amplitude and phase of tidal waves.  
     1281This on-line Harmonic analysis is actived with \key{diaharm}. 
     1282Some parameters are available in namelist \ngn{namdia\_harm} : 
     1283 
     1284- \np{nit000\_han} is the first time step used for harmonic analysis 
     1285 
     1286- \np{nitend\_han} is the last time step used for harmonic analysis 
     1287 
     1288- \np{nstep\_han} is the time step frequency for harmonic analysis 
     1289 
     1290- \np{nb\_ana} is the number of harmonics to analyse 
     1291 
     1292- \np{tname} is an array with names of tidal constituents to analyse 
     1293 
     1294\np{nit000\_han} and \np{nitend\_han} must be between \np{nit000} and \np{nitend} of the simulation. 
    13031295The restart capability is not implemented. 
    13041296 
    1305 The Harmonic analysis solve this equation: 
     1297The Harmonic analysis solve the following equation: 
    13061298\begin{equation} 
    13071299h_{i} - A_{0} + \sum^{nb\_ana}_{j=1}[A_{j}cos(\nu_{j}t_{j}-\phi_{j})] = e_{i} 
    … …  
    13241316\label{DIA_diag_dct} 
    13251317 
    1326 A module is available to compute the transport of volume, heat and salt through sections. This diagnostic 
    1327 is actived with \key{diadct}. 
     1318A module is available to compute the transport of volume, heat and salt through sections.  
     1319This diagnostic is actived with \key{diadct}. 
    13281320 
    13291321Each section is defined by the coordinates of its 2 extremities. The pathways between them are contructed 
    … …  
    13471339%------------------------------------------------------------------------------------------------------------- 
    13481340 
    1349 \texttt{nn\_dct}: frequency of instantaneous transports computing 
    1350  
    1351 \texttt{nn\_dctwri}: frequency of writing ( mean of instantaneous transports ) 
    1352  
    1353 \texttt{nn\_debug}: debugging of the section 
     1341\np{nn\_dct}: frequency of instantaneous transports computing 
     1342 
     1343\np{nn\_dctwri}: frequency of writing ( mean of instantaneous transports ) 
     1344 
     1345\np{nn\_debug}: debugging of the section 
    13541346 
    13551347\subsubsection{ To create a binary file containing the pathway of each section } 
    … …  
    14821474the \key{diahth} CPP key:  
    14831475 
    1484 - the mixed layer depth (based on a density criterion, \citet{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 
     1476- the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 
    14851477 
    14861478- the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_DOM.tex

    r5120 r6275  
    11% ================================================================ 
    2 % Chapter 2 � Space and Time Domain (DOM) 
     2% Chapter 2 ——— Space and Time Domain (DOM) 
    33% ================================================================ 
    44\chapter{Space Domain (DOM) } 
    … …  
    138138and $f$-points, and its divergence defined at $t$-points: 
    139139\begin{eqnarray}  \label{Eq_DOM_curl} 
    140  \nabla \times {\rm {\bf A}}\equiv & 
     140 \nabla \times {\rm{\bf A}}\equiv & 
    141141      \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} \\  
    142142 +& \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} \\ 
    … …  
    183183Let $a$ and $b$ be two fields defined on the mesh, with value zero inside  
    184184continental area. Using integration by parts it can be shown that the differencing  
    185 operators ($\delta_i$, $\delta_j$ and $\delta_k$) are anti-symmetric linear  
    186 operators, and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$,  
     185operators ($\delta_i$, $\delta_j$ and $\delta_k$) are skew-symmetric linear operators,  
     186and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$,  
    187187$\overline{\,\cdot\,}^{\,k}$ and $\overline{\,\cdot\,}^{\,k}$) are symmetric linear  
    188188operators, $i.e.$ 
    … …  
    364364For both grids here,  the same $w$-point depth has been chosen but in (a) the  
    365365$t$-points are set half way between $w$-points while in (b) they are defined from  
    366 an analytical function: $z(k)=5\,(i-1/2)^3 - 45\,(i-1/2)^2 + 140\,(i-1/2) - 150$.  
     366an analytical function: $z(k)=5\,(k-1/2)^3 - 45\,(k-1/2)^2 + 140\,(k-1/2) - 150$.  
    367367Note the resulting difference between the value of the grid-size $\Delta_k$ and  
    368368those of the scale factor $e_k$. } 
    … …  
    425425 
    426426The choice of the grid must be consistent with the boundary conditions specified  
    427 by the parameter \np{jperio} (see {\S\ref{LBC}). 
     427by \np{jperio}, a parameter found in \ngn{namcfg} namelist (see {\S\ref{LBC}). 
    428428 
    429429% ------------------------------------------------------------------------------------------------------------- 
    … …  
    481481%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    482482 
    483 The choice of a vertical coordinate, even if it is made through a namelist parameter,  
     483The choice of a vertical coordinate, even if it is made through \ngn{namzgr} namelist parameters,  
    484484must be done once of all at the beginning of an experiment. It is not intended as an  
    485485option which can be enabled or disabled in the middle of an experiment. Three main  
    … …  
    498498Contrary to the horizontal grid, the vertical grid is computed in the code and no  
    499499provision is made for reading it from a file. The only input file is the bathymetry  
    500 (in meters) (\ifile{bathy\_meter})  
     500(in meters) (\ifile{bathy\_meter}).  
    501501\footnote{N.B. in full step $z$-coordinate, a \ifile{bathy\_level} file can replace the  
    502502\ifile{bathy\_meter} file, so that the computation of the number of wet ocean point  
    … …  
    540540 
    541541Three options are possible for defining the bathymetry, according to the  
    542 namelist variable \np{nn\_bathy}:  
     542namelist variable \np{nn\_bathy} (found in \ngn{namdom} namelist):  
    543543\begin{description} 
    544544\item[\np{nn\_bathy} = 0] a flat-bottom domain is defined. The total depth $z_w (jpk)$  
    … …  
    721721usually 10\%, of the default thickness $e_{3t}(jk)$). 
    722722 
    723  \colorbox{yellow}{Add a figure here of pstep especially at last ocean level } 
     723\gmcomment{ \colorbox{yellow}{Add a figure here of pstep especially at last ocean level } } 
    724724 
    725725% ------------------------------------------------------------------------------------------------------------- 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_DYN.tex

    r5120 r6275  
    11% ================================================================ 
    2 % Chapter � Ocean Dynamics (DYN) 
     2% Chapter ——— Ocean Dynamics (DYN) 
    33% ================================================================ 
    44\chapter{Ocean Dynamics (DYN)} 
    55\label{DYN} 
    66\minitoc 
    7  
    8 % add a figure for  dynvor ens, ene latices 
    97 
    108%\vspace{2.cm} 
    … …  
    165163%------------------------------------------------------------------------------------------------------------- 
    166164 
    167 The vector invariant form of the momentum equations is the one most  
    168 often used in applications of the \NEMO ocean model. The flux form option  
    169 (see next section) has been present since version $2$. Options are defined 
    170 through the \ngn{namdyn\_adv} namelist variables 
    171 Coriolis and momentum advection terms are evaluated using a leapfrog  
    172 scheme, $i.e.$ the velocity appearing in these expressions is centred in  
    173 time (\textit{now} velocity).  
     165The vector invariant form of the momentum equations (\np{ln\_dynhpg\_vec}~=~true) is the one most  
     166often used in applications of the \NEMO ocean model. The flux form option (\np{ln\_dynhpg\_vec}~=false) 
     167(see next section) has been present since version $2$.  
     168Options are defined through the \ngn{namdyn\_adv} namelist variables. 
     169Coriolis and momentum advection terms are evaluated using a leapfrog scheme,  
     170$i.e.$ the velocity appearing in these expressions is centred in time (\textit{now} velocity).  
    174171At the lateral boundaries either free slip, no slip or partial slip boundary  
    175172conditions are applied following Chap.\ref{LBC}. 
    … …  
    303300%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    304301 
    305 Note that a key point in \eqref{Eq_een_e3f} is that the averaging in the \textbf{i}- and  
    306 \textbf{j}- directions uses the masked vertical scale factor but is always divided by  
    307 $4$, not by the sum of the masks at the four $T$-points. This preserves the continuity of  
    308 $e_{3f}$ when one or more of the neighbouring $e_{3t}$ tends to zero and  
    309 extends by continuity the value of $e_{3f}$ into the land areas. This feature is essential for  
    310 the $z$-coordinate with partial steps. 
     302A key point in \eqref{Eq_een_e3f} is how the averaging in the \textbf{i}- and \textbf{j}- directions is made.  
     303It uses the sum of masked t-point vertical scale factor divided either  
     304by the sum of the four t-point masks (\np{ln\_dynvor\_een\_old}~=~false),  
     305or  just by $4$ (\np{ln\_dynvor\_een\_old}~=~true). 
     306The latter case preserves the continuity of $e_{3f}$ when one or more of the neighbouring $e_{3t}$  
     307tends to zero and extends by continuity the value of $e_{3f}$ into the land areas.  
     308This case introduces a sub-grid-scale topography at f-points (with a systematic reduction of $e_{3f}$  
     309when a model level intercept the bathymetry) that tends to reinforce the topostrophy of the flow  
     310($i.e.$ the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.  
    311311 
    312312Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as  
    … …  
    374374\end{aligned}         \right. 
    375375\end{equation}  
     376When \np{ln\_dynzad\_zts}~=~\textit{true}, a split-explicit time stepping with 5 sub-timesteps is used  
     377on the vertical advection term. 
     378This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}.  
     379Note that in this case, a similar split-explicit time stepping should be used on  
     380vertical advection of tracer to ensure a better stability,  
     381an option which is only available with a TVD scheme (see \np{ln\_traadv\_tvd\_zts} in \S\ref{TRA_adv_tvd}). 
     382 
    376383 
    377384% ================================================================ 
    … …  
    491498those in the centred second order method. As the scheme already includes  
    492499a diffusion component, it can be used without explicit  lateral diffusion on momentum  
    493 ($i.e.$ \np{ln\_dynldf\_lap}=\np{ln\_dynldf\_bilap}=false), and it is recommended to do so. 
     500($i.e.$ setting both \np{ln\_dynldf\_lap} and \np{ln\_dynldf\_bilap} to \textit{false}),  
     501and it is recommended to do so. 
    494502 
    495503The UBS scheme is not used in all directions. In the vertical, the centred $2^{nd}$  
    … …  
    629637($e_{3w}$). 
    630638  
    631 $\bullet$ Traditional coding with adaptation for ice shelf cavities (\np{ln\_dynhpg\_isf}=true). 
     639$\bullet$ Traditional coding with adaptation for ice shelf cavities (\np{ln\_hpg\_isf}=true). 
    632640This scheme need the activation of ice shelf cavities (\np{ln\_isfcav}=true). 
    633641 
    … …  
    718726$\ $\newline      %force an empty line 
    719727 
    720 %%% 
    721728Options are defined through the \ngn{namdyn\_spg} namelist variables. 
    722 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}. 
    723  
    724 %%% 
     729The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}).  
     730The main distinction is between the fixed volume case (linear free surface) and the variable volume case  
     731(nonlinear free surface, \key{vvl} is defined). In the linear free surface case (\S\ref{PE_free_surface})  
     732the vertical scale factors $e_{3}$ are fixed in time, while they are time-dependent in the nonlinear case  
     733(\S\ref{PE_free_surface}).  
     734With both linear and nonlinear free surface, external gravity waves are allowed in the equations,  
     735which imposes a very small time step when an explicit time stepping is used.  
     736Two methods are proposed to allow a longer time step for the three-dimensional equations:  
     737the filtered free surface, which is a modification of the continuous equations (see \eqref{Eq_PE_flt}),  
     738and the split-explicit free surface described below.  
     739The extra term introduced in the filtered method is calculated implicitly,  
     740so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 
    725741 
    726742 
    … …  
    736752implicitly, so that a solver is used to compute it. As a consequence the update of the $next$  
    737753velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 
    738  
    739754 
    740755 
    … …  
    779794$\rdt_e = \rdt / nn\_baro$. This parameter can be optionally defined automatically (\np{ln\_bt\_nn\_auto}=true)  
    780795considering that the stability of the barotropic system is essentially controled by external waves propagation.  
    781 Maximum allowed Courant number is in that case time independent, and easily computed online from the input bathymetry. 
     796Maximum Courant number is in that case time independent, and easily computed online from the input bathymetry. 
     797Therefore, $\rdt_e$ is adjusted so that the Maximum allowed Courant number is smaller than \np{rn\_bt\_cmax}. 
    782798 
    783799%%% 
    … …  
    802818Schematic of the split-explicit time stepping scheme for the external  
    803819and internal modes. Time increases to the right. In this particular exemple,  
    804 a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_filt=1$) and $nn\_baro=5$. 
     820a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_flt=1$) and $nn\_baro=5$. 
    805821Internal mode time steps (which are also the model time steps) are denoted  
    806822by $t-\rdt$, $t$ and $t+\rdt$. Variables with $k$ superscript refer to instantaneous barotropic variables,  
    … …  
    808824The former are used to obtain time filtered quantities at $t+\rdt$ while the latter are used to obtain time averaged  
    809825transports to advect tracers. 
    810 a) Forward time integration: \np{ln\_bt\_fw}=true, \np{ln\_bt\_ave}=true.  
    811 b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_ave}=true.  
    812 c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_ave}=false. } 
     826a) Forward time integration: \np{ln\_bt\_fw}=true, \np{ln\_bt\_av}=true.  
     827b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_av}=true.  
     828c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_av}=false. } 
    813829\end{center}    \end{figure} 
    814830%>   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   > 
    … …  
    816832In the default case (\np{ln\_bt\_fw}=true), the external mode is integrated  
    817833between \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  
    818 quantities (\np{ln\_bt\_ave}=true). In that case, the integration is extended slightly beyond  \textit{after} time step to provide time filtered quantities.  
     834quantities (\np{ln\_bt\_av}=true). In that case, the integration is extended slightly beyond  \textit{after} time step to provide time filtered quantities.  
    819835These are used for the subsequent initialization of the barotropic mode in the following baroclinic step.  
    820836Since external mode equations written at baroclinic time steps finally follow a forward time stepping scheme,  
    … …  
    837853%%% 
    838854 
    839 One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_ave}=false).  
     855One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_av}=false).  
    840856In that case, external mode equations are continuous in time, ie they are not re-initialized when starting a new  
    841857sub-stepping sequence. This is the method used so far in the POM model, the stability being maintained by refreshing at (almost)  
    … …  
    11581174 
    11591175Besides the surface and bottom stresses (see the above section) which are  
    1160 introduced as boundary conditions on the vertical mixing, two other forcings  
    1161 enter the dynamical equations.  
    1162  
    1163 One is the effect of atmospheric pressure on the ocean dynamics. 
    1164 Another forcing term is the tidal potential. 
    1165 Both of which will be introduced into the reference version soon.  
    1166  
    1167 \gmcomment{atmospheric pressure is there!!!!    include its description } 
     1176introduced as boundary conditions on the vertical mixing, three other forcings  
     1177may enter the dynamical equations by affecting the surface pressure gradient.  
     1178 
     1179(1) When \np{ln\_apr\_dyn}~=~true (see \S\ref{SBC_apr}), the atmospheric pressure is taken  
     1180into account when computing the surface pressure gradient. 
     1181 
     1182(2) When \np{ln\_tide\_pot}~=~true and \key{tide} is defined (see \S\ref{SBC_tide}),  
     1183the tidal potential is taken into account when computing the surface pressure gradient. 
     1184 
     1185(3) When \np{nn\_ice\_embd}~=~2 and LIM or CICE is used ($i.e.$ when the sea-ice is embedded in the ocean),  
     1186the snow-ice mass is taken into account when computing the surface pressure gradient. 
     1187 
     1188 
     1189\gmcomment{ missing : the lateral boundary condition !!!   another external forcing 
     1190 } 
    11681191 
    11691192% ================================================================ 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_LBC.tex

    r4147 r6275  
    11% ================================================================ 
    2 % Chapter � Lateral Boundary Condition (LBC)  
     2% Chapter — Lateral Boundary Condition (LBC)  
    33% ================================================================ 
    44\chapter{Lateral Boundary Condition (LBC) } 
    … …  
    204204%        North fold (\textit{jperio = 3 }to $6)$  
    205205% ------------------------------------------------------------------------------------------------------------- 
    206 \subsection{North-fold (\textit{jperio = 3 }to $6)$ } 
     206\subsection{North-fold (\textit{jperio = 3 }to $6$) } 
    207207\label{LBC_north_fold} 
    208208 
    209209The north fold boundary condition has been introduced in order to handle the north  
    210 boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere.  
    211 \colorbox{yellow}{to be completed...} 
     210boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere  
     211(Fig.\ref{Fig_MISC_ORCA_msh}, and thus requires a specific treatment illustrated in Fig.\ref{Fig_North_Fold_T}.  
     212Further information can be found in \mdl{lbcnfd} module which applies the north fold boundary condition. 
    212213 
    213214%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    … …  
    250251ocean model. Second order finite difference schemes lead to local discrete  
    251252operators that depend at the very most on one neighbouring point. The only  
    252 non-local computations concern the vertical physics (implicit diffusion, 1.5  
     253non-local computations concern the vertical physics (implicit diffusion,  
    253254turbulent closure scheme, ...) (delocalization over the whole water column),  
    254255and the solving of the elliptic equation associated with the surface pressure  
    255256gradient computation (delocalization over the whole horizontal domain).  
    256257Therefore, a pencil strategy is used for the data sub-structuration  
    257 \gmcomment{no idea what this means!} 
    258258: the 3D initial domain is laid out on local processor  
    259259memories following a 2D horizontal topological splitting. Each sub-domain  
    … …  
    264264phase starts: each processor sends to its neighbouring processors the update  
    265265values of the points corresponding to the interior overlapping area to its  
    266 neighbouring sub-domain (i.e. the innermost of the two overlapping rows).  
    267 The communication is done through message passing. Usually the parallel virtual  
    268 language, PVM, is used as it is a standard language available on  nearly  all  
    269 MPP computers. More specific languages (i.e. computer dependant languages)  
    270 can be easily used to speed up the communication, such as SHEM on a T3E  
    271 computer. The data exchanges between processors are required at the very  
     266neighbouring sub-domain ($i.e.$ the innermost of the two overlapping rows).  
     267The communication is done through the Message Passing Interface (MPI).  
     268The data exchanges between processors are required at the very  
    272269place where lateral domain boundary conditions are set in the mono-domain  
    273 computation (\S III.10-c): the lbc\_lnk routine which manages such conditions  
    274 is substituted by mpplnk.F or mpplnk2.F routine when running on an MPP  
    275 computer (\key{mpp\_mpi} defined). It has to be pointed out that when using  
    276 the MPP version of the model, the east-west cyclic boundary condition is done  
    277 implicitly, whilst the south-symmetric boundary condition option is not available. 
     270computation : the \rou{lbc\_lnk} routine (found in \mdl{lbclnk} module)  
     271which manages such conditions is interfaced with routines found in \mdl{lib\_mpp} module  
     272when running on an MPP computer ($i.e.$ when \key{mpp\_mpi} defined).  
     273It has to be pointed out that when using the MPP version of the model,  
     274the east-west cyclic boundary condition is done implicitly,  
     275whilst the south-symmetric boundary condition option is not available. 
    278276 
    279277%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    … …  
    285283%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    286284 
    287 In the standard version of the OPA model, the splitting is regular and arithmetic. 
    288  the i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors  
    289  \jp{jpnij} most often equal to $jpni \times jpnj$ (model parameters set in  
    290  \mdl{par\_oce}). Each processor is independent and without message passing  
    291  or synchronous process  
    292  \gmcomment{how does a synchronous process relate to this?},  
    293  programs run alone and access just its own local memory. For this reason, the  
    294  main model dimensions are now the local dimensions of the subdomain (pencil)  
     285In the standard version of \NEMO, the splitting is regular and arithmetic. 
     286The i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors  
     287\jp{jpnij} most often equal to $jpni \times jpnj$ (parameters set in  
     288 \ngn{nammpp} namelist). Each processor is independent and without message passing  
     289 or synchronous process, programs run alone and access just its own local memory.  
     290 For this reason, the main model dimensions are now the local dimensions of the subdomain (pencil)  
    295291 that are named \jp{jpi}, \jp{jpj}, \jp{jpk}. These dimensions include the internal  
    296292 domain and the overlapping rows. The number of rows to exchange (known as  
    … …  
    304300where \jp{jpni}, \jp{jpnj} are the number of processors following the i- and j-axis. 
    305301 
    306 \colorbox{yellow}{Figure IV.3: example of a domain splitting with 9 processors and  
    307 no east-west cyclic boundary conditions.} 
    308  
    309 One also defines variables nldi and nlei which correspond to the internal  
    310 domain bounds, and the variables nimpp and njmpp which are the position  
    311 of the (1,1) grid-point in the global domain. An element of $T_{l}$, a local array  
    312 (subdomain) corresponds to an element of $T_{g}$, a global array  
    313 (whole domain) by the relationship:  
     302One also defines variables nldi and nlei which correspond to the internal domain bounds,  
     303and the variables nimpp and njmpp which are the position of the (1,1) grid-point in the global domain.  
     304An element of $T_{l}$, a local array (subdomain) corresponds to an element of $T_{g}$,  
     305a global array (whole domain) by the relationship:  
    314306\begin{equation} \label{Eq_lbc_nimpp} 
    315307T_{g} (i+nimpp-1,j+njmpp-1,k) = T_{l} (i,j,k), 
    … …  
    320312nproc. In the standard version, a processor has no more than four neighbouring  
    321313processors named nono (for north), noea (east), noso (south) and nowe (west)  
    322 and two variables, nbondi and nbondj, indicate the relative position of the processor  
    323 \colorbox{yellow}{(see Fig.IV.3)}: 
     314and two variables, nbondi and nbondj, indicate the relative position of the processor : 
    324315\begin{itemize} 
    325316\item       nbondi = -1    an east neighbour, no west processor, 
    … …  
    332323processor on its overlapping row, and sends the data issued from internal  
    333324domain corresponding to the overlapping row of the other processor. 
    334         
    335 \colorbox{yellow}{Figure IV.4: pencil splitting with the additional outer halos } 
    336325 
    337326 
    … …  
    343332global ocean where more than 50 \% of points are land points. For this reason, a  
    344333pre-processing tool can be used to choose the mpp domain decomposition with a  
    345 maximum number of only land points processors, which can then be eliminated.  
    346 (For example, the mpp\_optimiz tools, available from the DRAKKAR web site.)  
     334maximum number of only land points processors, which can then be eliminated (Fig. \ref{Fig_mppini2}) 
     335(For example, the mpp\_optimiz tools, available from the DRAKKAR web site).  
    347336This optimisation is dependent on the specific bathymetry employed. The user  
    348337then chooses optimal parameters \jp{jpni}, \jp{jpnj} and \jp{jpnij} with  
    349338$jpnij < jpni \times jpnj$, leading to the elimination of $jpni \times jpnj - jpnij$  
    350 land processors. When those parameters are specified in module \mdl{par\_oce},  
     339land processors. When those parameters are specified in \ngn{nammpp} namelist,  
    351340the algorithm in the \rou{inimpp2} routine sets each processor's parameters (nbound,  
    352341nono, noea,...) so that the land-only processors are not taken into account.  
    353342 
    354 \colorbox{yellow}{Note that the inimpp2 routine is general so that the original inimpp  
     343\gmcomment{Note that the inimpp2 routine is general so that the original inimpp  
    355344routine should be suppressed from the code.} 
    356345 
    357346When land processors are eliminated, the value corresponding to these locations in  
    358 the model output files is zero. Note that this is a problem for a mesh output file written  
    359 by such a model configuration, because model users often divide by the scale factors  
    360 ($e1t$, $e2t$, etc) and do not expect the grid size to be zero, even on land. It may be  
    361 best not to eliminate land processors when running the model especially to write the  
    362 mesh files as outputs (when \np{nn\_msh} namelist parameter differs from 0). 
    363 %% 
    364 \gmcomment{Steven : dont understand this, no land processor means no output file  
    365 covering this part of globe; its only when files are stitched together into one that you  
    366 can leave a hole} 
    367 %% 
     347the model output files is undefined. Note that this is a problem for the meshmask file  
     348which requires to be defined over the whole domain. Therefore, user should not eliminate  
     349land processors when creating a meshmask file ($i.e.$ when setting a non-zero value to \np{nn\_msh}). 
    368350 
    369351%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    … …  
    380362%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    381363 
    382  
    383 % ================================================================ 
    384 % Open Boundary Conditions  
    385 % ================================================================ 
    386 \section{Open Boundary Conditions (\key{obc}) (OBC)} 
    387 \label{LBC_obc} 
    388 %-----------------------------------------nam_obc  ------------------------------------------- 
    389 %-    nobc_dta    =    0     !  = 0 the obc data are equal to the initial state 
    390 %-                           !  = 1 the obc data are read in 'obc   .dta' files 
    391 %-    rn_dpein      =    1.    !  ??? 
    392 %-    rn_dpwin      =    1.    !  ??? 
    393 %-    rn_dpnin      =   30.    !  ??? 
    394 %-    rn_dpsin      =    1.    !  ??? 
    395 %-    rn_dpeob      = 1500.    !  time relaxation (days) for the east  open boundary 
    396 %-    rn_dpwob      =   15.    !    "        "           for the west  open boundary 
    397 %-    rn_dpnob      =  150.    !    "        "           for the north open boundary 
    398 %-    rn_dpsob      =   15.    !    "        "           for the south open boundary 
    399 %-    ln_obc_clim = .true.   !  climatological obc data files (default T) 
    400 %-    ln_vol_cst  = .true.   !  total volume conserved 
    401 \namdisplay{namobc}  
    402  
    403 It is often necessary to implement a model configuration limited to an oceanic  
    404 region or a basin, which communicates with the rest of the global ocean through  
    405 ''open boundaries''. As stated by \citet{Roed1986}, an open boundary is a  
    406 computational border where the aim of the calculations is to allow the perturbations  
    407 generated inside the computational domain to leave it without deterioration of the  
    408 inner model solution. However, an open boundary also has to let information from  
    409 the outer ocean enter the model and should support inflow and outflow conditions.  
    410  
    411 The open boundary package OBC is the first open boundary option developed in  
    412 NEMO (originally in OPA8.2). It allows the user to  
    413 \begin{itemize} 
    414 \item tell the model that a boundary is ''open'' and not closed by a wall, for example  
    415 by modifying the calculation of the divergence of velocity there; 
    416 \item impose values of tracers and velocities at that boundary (values which may  
    417 be taken from a climatology): this is the``fixed OBC'' option.  
    418 \item calculate boundary values by a sophisticated algorithm combining radiation  
    419 and relaxation (``radiative OBC'' option) 
    420 \end{itemize} 
    421  
    422 Options are defined through the \ngn{namobc} namelist variables. 
    423 The package resides in the OBC directory. It is described here in four parts: the  
    424 boundary geometry (parameters to be set in \mdl{obc\_par}), the forcing data at  
    425 the boundaries (module \mdl{obcdta}),  the radiation algorithm involving the  
    426 namelist and module \mdl{obcrad}, and a brief presentation of boundary update  
    427 and restart files. 
    428  
    429 %---------------------------------------------- 
    430 \subsection{Boundary geometry} 
    431 \label{OBC_geom} 
    432 % 
    433 First one has to realize that open boundaries may not necessarily be located  
    434 at the extremities of the computational domain. They may exist in the middle  
    435 of the domain, for example at Gibraltar Straits if one wants to avoid including  
    436 the Mediterranean in an Atlantic domain. This flexibility has been found necessary  
    437 for the CLIPPER project \citep{Treguier_al_JGR01}. Because of the complexity of the  
    438 geometry of ocean basins, it may even be necessary to have more than one  
    439 ''west'' open boundary, more than one ''north'', etc. This is not possible with  
    440 the OBC option: only one open boundary of each kind, west, east, south and  
    441 north is allowed; these names refer to the grid geometry (not to the direction  
    442 of the geographical ''west'', ''east'', etc). 
    443  
    444 The open boundary geometry is set by a series of parameters in the module  
    445 \mdl{obc\_par}. For an eastern open boundary, parameters are \jp{lp\_obc\_east}  
    446 (true if an east open boundary exists), \jp{jpieob} the $i$-index along which  
    447 the eastern open boundary (eob) is located, \jp{jpjed} the $j$-index at which  
    448 it starts, and \jp{jpjef} the $j$-index where it ends (note $d$ is for ''d\'{e}but''  
    449 and $f$ for ''fin'' in French). Similar parameters exist for the west, south and  
    450 north cases (Table~\ref{Tab_obc_param}). 
    451  
    452  
    453 %--------------------------------------------------TABLE-------------------------------------------------- 
    454 \begin{table}[htbp]     \begin{center}    \begin{tabular}{|l|c|c|c|} 
    455 \hline 
    456 Boundary and  & Constant index  & Starting index (d\'{e}but) & Ending index (fin) \\ 
    457 Logical flag  &                 &                            &                     \\ 
    458 \hline 
    459 West          & \jp{jpiwob} $>= 2$         &  \jp{jpjwd}$>= 2$          &  \jp{jpjwf}<= \np{jpjglo}-1 \\ 
    460 lp\_obc\_west & $i$-index of a $u$ point   & $j$ of a $T$ point   &$j$ of a $T$ point \\ 
    461 \hline 
    462 East            & \jp{jpieob}$<=$\np{jpiglo}-2&\jp{jpjed} $>= 2$         & \jp{jpjef}$<=$ \np{jpjglo}-1 \\ 
    463  lp\_obc\_east  & $i$-index of a $u$ point    & $j$ of a $T$ point & $j$ of a $T$ point \\ 
    464 \hline 
    465 South           & \jp{jpjsob} $>= 2$         & \jp{jpisd} $>= 2$          & \jp{jpisf}$<=$\np{jpiglo}-1 \\ 
    466 lp\_obc\_south  & $j$-index of a $v$ point   & $i$ of a $T$ point   & $i$ of a $T$ point \\ 
    467 \hline 
    468 North           & \jp{jpjnob} $<=$ \np{jpjglo}-2& \jp{jpind} $>= 2$        & \jp{jpinf}$<=$\np{jpiglo}-1 \\ 
    469 lp\_obc\_north  & $j$-index of a $v$ point      & $i$  of a $T$ point & $i$ of a $T$ point \\ 
    470 \hline 
    471 \end{tabular}    \end{center} 
    472 \caption{     \label{Tab_obc_param} 
    473 Names of different indices relating to the open boundaries. In the case  
    474 of a completely open ocean domain with four ocean boundaries, the parameters  
    475 take exactly the values indicated.} 
    476 \end{table} 
    477 %------------------------------------------------------------------------------------------------------------ 
    478  
    479 The open boundaries must be along coordinate lines. On the C-grid, the boundary  
    480 itself is along a line of normal velocity points: $v$ points for a zonal open boundary  
    481 (the south or north one), and $u$ points for a meridional open boundary (the west  
    482 or east one). Another constraint is that there still must be a row of masked points  
    483 all around the domain, as if the domain were a closed basin (unless periodic conditions  
    484 are used together with open boundary conditions). Therefore, an open boundary  
    485 cannot be located at the first/last index, namely, 1, \jp{jpiglo} or \jp{jpjglo}. Also,  
    486 the open boundary algorithm involves calculating the normal velocity points situated  
    487 just on the boundary, as well as the tangential velocity and temperature and salinity  
    488 just outside the boundary. This means that for a west/south boundary, normal  
    489 velocities and temperature are calculated at the same index \jp{jpiwob} and  
    490 \jp{jpjsob}, respectively. For an east/north boundary, the normal velocity is  
    491 calculated at index \jp{jpieob} and \jp{jpjnob}, but the ``outside'' temperature is  
    492 at index \jp{jpieob}+1 and \jp{jpjnob}+1. This means that \jp{jpieob}, \jp{jpjnob}  
    493 cannot be bigger than \jp{jpiglo}-2, \jp{jpjglo}-2.  
    494  
    495  
    496 The starting and ending indices are to be thought of as $T$ point indices: in many  
    497 cases they indicate the first land $T$-point, at the extremity of an open boundary  
    498 (the coast line follows the $f$ grid points, see Fig.~\ref{Fig_obc_north} for an example  
    499 of a northern open boundary). All indices are relative to the global domain. In the  
    500 free surface case it is possible to have ``ocean corners'', that is, an open boundary  
    501 starting and ending in the ocean. 
    502  
    503 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    504 \begin{figure}[!t]     \begin{center} 
    505 \includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_obc_north.pdf} 
    506 \caption{    \label{Fig_obc_north} 
    507 Localization of the North open boundary points.} 
    508 \end{center}     \end{figure} 
    509 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    510  
    511 Although not compulsory, it is highly recommended that the bathymetry in the  
    512 vicinity of an open boundary follows the following rule: in the direction perpendicular  
    513 to the open line, the water depth should be constant for 4 grid points. This is in  
    514 order to ensure that the radiation condition, which involves model variables next  
    515 to the boundary, is calculated in a consistent way. On Fig.\ref{Fig_obc_north} we  
    516 indicate by an $=$ symbol, the points which should have the same depth. It means  
    517 that at the 4 points near the boundary, the bathymetry is cylindrical \gmcomment{not sure  
    518 why cylindrical}. The line behind the open $T$-line must be 0 in the bathymetry file  
    519 (as shown on Fig.\ref{Fig_obc_north} for example). 
    520  
    521 %---------------------------------------------- 
    522 \subsection{Boundary data} 
    523 \label{OBC_data} 
    524  
    525 It is necessary to provide information at the boundaries. The simplest case is  
    526 when this information does not change in time and is equal to the initial conditions  
    527 (namelist variable \np{nn\_obcdta}=0). This is the case for the standard configuration  
    528 EEL5 with open boundaries. When (\np{nn\_obcdta}=1), open boundary information  
    529 is read from netcdf files. For convenience the input files are supposed to be similar  
    530 to the ''history'' NEMO output files, for dimension names and variable names.  
    531 Open boundary arrays must be dimensioned according to the parameters of table~ 
    532 \ref{Tab_obc_param}: for example, at the western boundary, arrays have a  
    533 dimension of \jp{jpwf}-\jp{jpwd}+1 in the horizontal and \jp{jpk} in the vertical.  
    534  
    535 When ocean observations are used to generate the boundary data (a hydrographic  
    536 section for example, as in \citet{Treguier_al_JGR01}) it happens often that only the velocity  
    537 normal to the boundary is known, which is the reason why the initial OBC code  
    538 assumes that only $T$, $S$, and the normal velocity ($u$ or $v$) needs to be  
    539 specified. As more and more global model solutions and ocean analysis products  
    540 become available, it will be possible to provide information about all the variables  
    541 (including the tangential velocity) so that the specification of four variables at each  
    542 boundaries will become standard. For the sea surface height, one must distinguish  
    543 between the filtered free surface case and the time-splitting or explicit treatment of  
    544 the free surface. 
    545  In the first case, it is assumed that the user does not wish to represent high  
    546  frequency motions such as tides. The boundary condition is thus one of zero  
    547  normal gradient of sea surface height at the open boundaries, following \citet{Marchesiello2001}.  
    548 No information other than the total velocity needs to be provided at the open  
    549 boundaries in that case. In the other two cases (time splitting or explicit free surface),  
    550 the user must provide barotropic information (sea surface height and barotropic  
    551 velocities) and the use of the Flather algorithm for barotropic variables is  
    552 recommanded. However, this algorithm has not yet been fully tested and bugs  
    553 remain in NEMO v2.3. Users should read the code carefully before using it. Finally,  
    554 in the case of the rigid lid approximation the barotropic streamfunction must be  
    555 provided, as documented in \citet{Treguier_al_JGR01}). This option is no longer  
    556 recommended but remains in NEMO V2.3. 
    557  
    558 One frequently encountered case is when an open boundary domain is constructed  
    559 from a global or larger scale NEMO configuration. Assuming the domain corresponds  
    560 to indices $ib:ie$, $jb:je$ of the global domain, the bathymetry and forcing of the  
    561 small domain can be created by using the following netcdf utility on the global files:  
    562 ncks -F $-d\;x,ib,ie$ $-d\;y,jb,je$ (part of the nco series of utilities,  
    563 see their \href{http://nco.sourceforge.net}{website}).  
    564 The open boundary files can be constructed using ncks  
    565 commands, following table~\ref{Tab_obc_ind}.  
    566  
    567 %--------------------------------------------------TABLE-------------------------------------------------- 
    568 \begin{table}[htbp]     \begin{center}      \begin{tabular}{|l|c|c|c|c|c|} 
    569 \hline 
    570 OBC  & Variable   & file name      & Index  & Start  & end  \\ 
    571 West &  T,S       &   obcwest\_TS.nc &  $ib$+1     &   $jb$+1 &  $je-1$  \\ 
    572      &    U       &   obcwest\_U.nc  &  $ib$+1     &   $jb$+1 &  $je-1$  \\  
    573      &    V       &   obcwest\_V.nc  &  $ib$+1     &   $jb$+1 &  $je-1$  \\        
    574 \hline 
    575 East &  T,S       &   obceast\_TS.nc &  $ie$-1     &   $jb$+1 &  $je-1$  \\ 
    576      &    U       &   obceast\_U.nc  &  $ie$-2     &   $jb$+1 &  $je-1$  \\  
    577      &    V       &   obceast\_V.nc  &  $ie$-1     &   $jb$+1 &  $je-1$  \\        
    578 \hline          
    579 South &  T,S      &   obcsouth\_TS.nc &  $jb$+1     &  $ib$+1 &  $ie-1$  \\ 
    580       &    U      &   obcsouth\_U.nc  &  $jb$+1     &  $ib$+1 &  $ie-1$  \\  
    581       &    V      &   obcsouth\_V.nc  &  $jb$+1     &  $ib$+1 &  $ie-1$  \\     
    582 \hline 
    583 North &  T,S      &   obcnorth\_TS.nc &  $je$-1     &  $ib$+1 &  $ie-1$  \\ 
    584       &    U      &   obcnorth\_U.nc  &  $je$-1     &  $ib$+1 &  $ie-1$  \\  
    585       &    V      &   obcnorth\_V.nc  &  $je$-2     &  $ib$+1 &  $ie-1$  \\   
    586 \hline 
    587 \end{tabular}     \end{center} 
    588 \caption{    \label{Tab_obc_ind} 
    589 Requirements for creating open boundary files from a global configuration,  
    590 appropriate for the subdomain of indices $ib:ie$, $jb:je$. ``Index'' designates the  
    591 $i$ or $j$ index along which the $u$ of $v$ boundary point is situated in the global  
    592 configuration, starting and ending with the $j$ or $i$ indices indicated.  
    593 For example, to generate file obcnorth\_V.nc, use the command ncks  
    594 $-F$ $-d\;y,je-2$  $-d\;x,ib+1,ie-1$ }  
    595 \end{table} 
    596 %----------------------------------------------------------------------------------------------------------- 
    597  
    598 It is assumed that the open boundary files contain the variables for the period of  
    599 the model integration. If the boundary files contain one time frame, the boundary  
    600 data is held fixed in time. If the files contain 12 values, it is assumed that the input  
    601 is a climatology for a repeated annual cycle (corresponding to the case \np{ln\_obc\_clim}  
    602 =true). The case of an arbitrary number of time frames is not yet implemented  
    603 correctly; the user is required to write his own code in the module \mdl{obc\_dta}  
    604 to deal with this situation.  
    605  
    606 \subsection{Radiation algorithm} 
    607 \label{OBC_rad} 
    608  
    609 The art of open boundary management consists in applying a constraint strong  
    610 enough that the inner domain "feels" the rest of the ocean, but weak enough 
    611 that perturbations are allowed to leave the domain with minimum false reflections  
    612 of energy. The constraints are specified separately at each boundary as time  
    613 scales for ''inflow'' and ''outflow'' as defined below. The time scales are set (in days)  
    614 by namelist parameters such as \np{rn\_dpein}, \np{rn\_dpeob} for the eastern open  
    615 boundary for example. When both time scales are zero for a given boundary  
    616 ($e.g.$ for the western boundary, \jp{lp\_obc\_west}=true, \np{rn\_dpwob}=0 and  
    617 \np{rn\_dpwin}=0) this means that the boundary in question is a ''fixed '' boundary  
    618 where the solution is set exactly by the boundary data. This is not recommended,  
    619 except in combination with increased viscosity in a ''sponge'' layer next to the  
    620 boundary in order to avoid spurious reflections.   
    621  
    622  
    623 The radiation\/relaxation \gmcomment{the / doesnt seem to appear in the output}  
    624 algorithm is applied when either relaxation time (for ''inflow'' or ''outflow'') is  
    625 non-zero. It has been developed and tested in the SPEM model and its  
    626 successor ROMS \citep{Barnier1996, Marchesiello2001}, which is an  
    627 $s$-coordinate model on an Arakawa C-grid. Although the algorithm has  
    628 been numerically successful in the CLIPPER Atlantic models, the physics  
    629 do not work as expected \citep{Treguier_al_JGR01}. Users are invited to consider  
    630 open boundary conditions (OBC hereafter) with some scepticism  
    631 \citep{Durran2001, Blayo2005}. 
    632  
    633 The first part of the algorithm calculates a phase velocity to determine  
    634 whether perturbations tend to propagate toward, or away from, the  
    635 boundary. Let us consider a model variable $\phi$.  
    636 The phase velocities ($C_{\phi x}$,$C_{\phi y}$) for the variable $\phi$,  
    637 in the directions normal and tangential to the boundary are 
    638 \begin{equation} \label{Eq_obc_cphi} 
    639 C_{\phi x} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{x}  
    640 \;\;\;\;\; \;\;\;  
    641 C_{\phi y} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{y}.  
    642 \end{equation} 
    643 Following \citet{Treguier_al_JGR01} and \citet{Marchesiello2001} we retain only  
    644 the normal component of the velocity, $C_{\phi x}$, setting $C_{\phi y} =0$  
    645 (but unlike the original Orlanski radiation algorithm we retain $\phi_{y}$ in  
    646 the expression for $C_{\phi x}$).   
    647  
    648 The discrete form of (\ref{Eq_obc_cphi}), described by \citet{Barnier1998}, 
    649 takes into account the two rows of grid points situated inside the domain  
    650 next to the boundary, and the three previous time steps ($n$, $n-1$, 
    651 and $n-2$). The same equation can then be discretized at the boundary at 
    652 time steps $n-1$, $n$ and $n+1$ \gmcomment{since the original was three time-level}  
    653 in order to extrapolate for the new boundary value $\phi^{n+1}$.  
    654  
    655 In the open boundary algorithm as implemented in NEMO v2.3, the new boundary  
    656 values are updated differently depending on the sign of $C_{\phi x}$. Let us take  
    657 an eastern boundary as an example. The solution for variable $\phi$ at the  
    658 boundary is given by a generalized wave equation with phase velocity $C_{\phi}$,  
    659 with the addition of a relaxation term, as: 
    660 \begin{eqnarray} 
    661 \phi_{t} &  =  & -C_{\phi x} \phi_{x} + \frac{1}{\tau_{o}} (\phi_{c}-\phi)  
    662                         \;\;\; \;\;\; \;\;\; (C_{\phi x} > 0), \label{Eq_obc_rado} \\ 
    663 \phi_{t} &  =  & \frac{1}{\tau_{i}} (\phi_{c}-\phi)  
    664 \;\;\; \;\;\; \;\;\;\;\;\; (C_{\phi x} < 0), \label{Eq_obc_radi} 
    665 \end{eqnarray} 
    666 where $\phi_{c}$ is the estimate of $\phi$ at the boundary, provided as boundary  
    667 data. Note that in (\ref{Eq_obc_rado}), $C_{\phi x}$ is bounded by the ratio  
    668 $\delta x/\delta t$ for stability reasons. When $C_{\phi x}$ is eastward (outward  
    669 propagation), the radiation condition (\ref{Eq_obc_rado}) is used.  
    670 When  $C_{\phi x}$ is westward (inward propagation), (\ref{Eq_obc_radi}) is  
    671 used with a strong relaxation to climatology (usually $\tau_{i}=\np{rn\_dpein}=$1~day). 
    672 Equation (\ref{Eq_obc_radi}) is solved with a Euler time-stepping scheme. As a  
    673 consequence, setting $\tau_{i}$ smaller than, or equal to the time step is equivalent  
    674 to a fixed boundary condition. A time scale of one day is usually a good compromise  
    675 which guarantees that the inflow conditions remain close to climatology while ensuring  
    676 numerical stability.  
    677  
    678 In  the case of a western boundary located in the Eastern Atlantic, \citet{Penduff_al_JGR00}  
    679 have been able to implement the radiation algorithm without any boundary data,  
    680 using persistence from the previous time step instead. This solution has not worked  
    681 in other cases \citep{Treguier_al_JGR01}, so that the use of boundary data is recommended.  
    682 Even in the outflow condition (\ref{Eq_obc_rado}), we have found it desirable to  
    683 maintain a weak relaxation to climatology. The time step is usually chosen so as to  
    684 be larger than typical turbulent scales (of order 1000~days \gmcomment{or maybe seconds?}). 
    685  
    686 The radiation condition is applied to the model variables: temperature, salinity,  
    687 tangential and normal velocities. For normal and tangential velocities, $u$ and $v$,  
    688 radiation is applied with phase velocities calculated from $u$ and $v$ respectively.   
    689 For the radiation of tracers, we use the phase velocity calculated from the tangential  
    690 velocity in order to avoid calculating too many independent radiation velocities and  
    691 because tangential velocities and tracers have the same position along the boundary  
    692 on a C-grid.   
    693  
    694 \subsection{Domain decomposition (\key{mpp\_mpi})} 
    695 \label{OBC_mpp} 
    696 When \key{mpp\_mpi} is active in the code, the computational domain is divided  
    697 into rectangles that are attributed each to a different processor. The open boundary  
    698 code is ``mpp-compatible'' up to a certain point. The radiation algorithm will not  
    699 work if there is an mpp subdomain boundary parallel to the open boundary at the  
    700 index of the boundary, or the grid point after (outside), or three grid points before  
    701 (inside). On the other hand, there is no problem if an mpp subdomain boundary  
    702 cuts the open boundary perpendicularly. These geometrical limitations must be  
    703 checked for by the user (there is no safeguard in the code).   
    704 The general principle for the open boundary mpp code is that loops over the open  
    705 boundaries {not sure what this means} are performed on local indices (nie0,  
    706 nie1, nje0, nje1 for an eastern boundary for instance) that are initialized in module  
    707 \mdl{obc\_ini}. Those indices have relevant values on the processors that contain  
    708 a segment of an open boundary. For processors that do not include an open  
    709 boundary segment, the indices are such that the calculations within the loops are  
    710 not performed. 
    711 \gmcomment{I dont understand most of the last few sentences} 
    712   
    713 Arrays of climatological data that are read from files are seen by all processors  
    714 and have the same dimensions for all (for instance, for the eastern boundary,  
    715 uedta(jpjglo,jpk,2)). On the other hand, the arrays for the calculation of radiation  
    716 are local to each processor (uebnd(jpj,jpk,3,3) for instance).  This allowed the  
    717 CLIPPER model for example, to save on memory where the eastern boundary  
    718 crossed 8 processors so that \jp{jpj} was much smaller than (\jp{jpjef}-\jp{jpjed}+1).  
    719  
    720 \subsection{Volume conservation} 
    721 \label{OBC_vol} 
    722  
    723 It is necessary to control the volume inside a domain when using open boundaries.  
    724 With fixed boundaries, it is enough to ensure that the total inflow/outflow has  
    725 reasonable values (either zero or a value compatible with an observed volume  
    726 balance). When using radiative boundary conditions it is necessary to have a  
    727 volume constraint because each open boundary works independently from the  
    728 others. The methodology used to control this volume is identical to the one  
    729 coded in the ROMS model \citep{Marchesiello2001}. 
    730  
    731  
    732 %---------------------------------------- EXTRAS 
    733 \colorbox{yellow}{Explain obc\_vol{\ldots}} 
    734  
    735 \colorbox{yellow}{OBC algorithm for update, OBC restart, list of routines where obc key appears{\ldots}} 
    736  
    737 \colorbox{yellow}{OBC rigid lid? {\ldots}} 
    738364 
    739365% ==================================================================== 

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    r4147 r6275  
    11 
    22% ================================================================ 
    3 % Chapter � Lateral Ocean Physics (LDF) 
     3% Chapter ——— Lateral Ocean Physics (LDF) 
    44% ================================================================ 
    55\chapter{Lateral Ocean Physics (LDF)} 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_MISC.tex

    r5118 r6275  
    3434has been made to set them in a generic way. However, examples of how  
    3535they can be set up is given in the ORCA 2\deg and 0.5\deg configurations. For example,  
    36 for details of implementation in ORCA2, search: 
    37 \vspace{-10pt}   
    38 \begin{alltt}   
    39 \tiny     
    40 \begin{verbatim} 
    41 IF( cp_cfg == "orca" .AND. jp_cfg == 2 ) 
    42 \end{verbatim}   
    43 \end{alltt} 
     36for details of implementation in ORCA2, search:  
     37\texttt{ IF( cp\_cfg == "orca" .AND. jp\_cfg == 2 ) } 
    4438 
    4539% ------------------------------------------------------------------------------------------------------------- 
    … …  
    8983%-------------------------------------------------------------------------------------------------------------- 
    9084 
    91 \colorbox{yellow}{Add a short description of CLA staff here or in lateral boundary condition chapter?} 
    9285Options are defined through the  \ngn{namcla} namelist variables. 
     86This option is an obsolescent feature that will be removed in version 3.7 and followings.  
    9387 
    9488%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.   

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_Model_Basics.tex

    r3294 r6275  
    247247sufficient to solve a linearized version of (\ref{Eq_PE_ssh}), which still allows  
    248248to take into account freshwater fluxes applied at the ocean surface \citep{Roullet_Madec_JGR00}. 
     249Nevertheless, with the linearization, an exact conservation of heat and salt contents is lost. 
    249250 
    250251The filtering of EGWs in models with a free surface is usually a matter of discretisation  
    251 of the temporal derivatives, using the time splitting method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92}  
    252 or the implicit scheme \citep{Dukowicz1994}. In \NEMO, we use a slightly different approach  
    253 developed by \citet{Roullet_Madec_JGR00}: the damping of EGWs is ensured by introducing an  
    254 additional force in the momentum equation. \eqref{Eq_PE_dyn} becomes:  
    255 \begin{equation} \label{Eq_PE_flt} 
    256 \frac{\partial {\rm {\bf U}}_h }{\partial t}= {\rm {\bf M}} 
    257 - g \nabla \left( \tilde{\rho} \ \eta \right)  
    258 - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right)  
    259 \end{equation} 
    260 where $T_c$, is a parameter with dimensions of time which characterizes the force,  
    261 $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density, and $\rm {\bf M}$  
    262 represents the collected contributions of the Coriolis, hydrostatic pressure gradient,  
    263 non-linear and viscous terms in \eqref{Eq_PE_dyn}. 
    264  
    265 The new force can be interpreted as a diffusion of vertically integrated volume flux divergence.  
    266 The time evolution of $D$ is thus governed by a balance of two terms, $-g$ \textbf{A} $\eta$  
    267 and $g \, T_c \,$ \textbf{A} $D$, associated with a propagative regime and a diffusive regime  
    268 in the temporal spectrum, respectively. In the diffusive regime, the EGWs no longer propagate,  
    269 $i.e.$ they are stationary and damped. The diffusion regime applies to the modes shorter than  
    270 $T_c$. For longer ones, the diffusion term vanishes. Hence, the temporally unresolved EGWs  
    271 can be damped by choosing $T_c > \rdt$. \citet{Roullet_Madec_JGR00} demonstrate that  
    272 (\ref{Eq_PE_flt}) can be integrated with a leap frog scheme except the additional term which  
    273 has to be computed implicitly. This is not surprising since the use of a large time step has a  
    274 necessarily numerical cost. Two gains arise in comparison with the previous formulations.  
    275 Firstly, the damping of EGWs can be quantified through the magnitude of the additional term.  
    276 Secondly, the numerical scheme does not need any tuning. Numerical stability is ensured as  
    277 soon as $T_c > \rdt$. 
    278  
    279 When the variations of free surface elevation are small compared to the thickness of the first  
    280 model layer, the free surface equation (\ref{Eq_PE_ssh}) can be linearized. As emphasized  
    281 by \citet{Roullet_Madec_JGR00} the linearization of (\ref{Eq_PE_ssh}) has consequences on the  
    282 conservation of salt in the model. With the nonlinear free surface equation, the time evolution  
    283 of the total salt content is  
    284 \begin{equation} \label{Eq_PE_salt_content} 
    285     \frac{\partial }{\partial t}\int\limits_{D\eta } {S\;dv}  
    286                         =\int\limits_S {S\;(-\frac{\partial \eta }{\partial t}-D+P-E)\;ds} 
    287 \end{equation} 
    288 where $S$ is the salinity, and the total salt is integrated over the whole ocean volume  
    289 $D_\eta$ bounded by the time-dependent free surface. The right hand side (which is an  
    290 integral over the free surface) vanishes when the nonlinear equation (\ref{Eq_PE_ssh})  
    291 is satisfied, so that the salt is perfectly conserved. When the free surface equation is  
    292 linearized, \citet{Roullet_Madec_JGR00} show that the total salt content integrated in the fixed  
    293 volume $D$ (bounded by the surface $z=0$) is no longer conserved: 
    294 \begin{equation} \label{Eq_PE_salt_content_linear} 
    295          \frac{\partial }{\partial t}\int\limits_D {S\;dv}  
    296                = - \int\limits_S {S\;\frac{\partial \eta }{\partial t}ds}  
    297 \end{equation} 
    298  
    299 The right hand side of (\ref{Eq_PE_salt_content_linear}) is small in equilibrium solutions  
    300 \citep{Roullet_Madec_JGR00}. It can be significant when the freshwater forcing is not balanced and  
    301 the globally averaged free surface is drifting. An increase in sea surface height \textit{$\eta $}  
    302 results in a decrease of the salinity in the fixed volume $D$. Even in that case though,  
    303 the total salt integrated in the variable volume $D_{\eta}$ varies much less, since  
    304 (\ref{Eq_PE_salt_content_linear}) can be rewritten as  
    305 \begin{equation} \label{Eq_PE_salt_content_corrected} 
    306 \frac{\partial }{\partial t}\int\limits_{D\eta } {S\;dv}  
    307 =\frac{\partial}{\partial t} \left[ \;{\int\limits_D {S\;dv} +\int\limits_S {S\eta \;ds} } \right] 
    308 =\int\limits_S {\eta \;\frac{\partial S}{\partial t}ds} 
    309 \end{equation} 
    310  
    311 Although the total salt content is not exactly conserved with the linearized free surface,  
    312 its variations are driven by correlations of the time variation of surface salinity with the  
    313 sea surface height, which is a negligible term. This situation contrasts with the case of  
    314 the rigid lid approximation in which case freshwater forcing is represented by a virtual  
    315 salt flux, leading to a spurious source of salt at the ocean surface  
    316 \citep{Huang_JPO93, Roullet_Madec_JGR00}. 
    317  
    318 \newpage 
    319 $\ $\newline    % force a new ligne 
     252of the temporal derivatives, using a split-explicit method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92}  
     253or the implicit scheme \citep{Dukowicz1994} or the addition of a filtering force in the momentum equation  
     254\citep{Roullet_Madec_JGR00}. With the present release, \NEMO offers the choice between  
     255an explicit free surface (see \S\ref{DYN_spg_exp}) or a split-explicit scheme strongly  
     256inspired the one proposed by \citet{Shchepetkin_McWilliams_OM05} (see \S\ref{DYN_spg_ts}). 
     257 
     258%\newpage 
     259%$\ $\newline    % force a new line 
    320260 
    321261% ================================================================ 
    … …  
    773713\end{equation} 
    774714 
    775 The equations solved by the ocean model \eqref{Eq_PE} in $s-$coordinate can be written as follows: 
     715The equations solved by the ocean model \eqref{Eq_PE} in $s-$coordinate can be written as follows (see Appendix~\ref{Apdx_A_momentum}): 
    776716 
    777717 \vspace{0.5cm} 
    778 * momentum equation: 
     718$\bullet$ Vector invariant form of the momentum equation : 
    779719\begin{multline} \label{Eq_PE_sco_u} 
    780 \frac{1}{e_3} \frac{\partial \left(  e_3\,u  \right) }{\partial t}= 
     720\frac{\partial  u  }{\partial t}= 
    781721   +   \left( {\zeta +f} \right)\,v                                     
    782722   -   \frac{1}{2\,e_1} \frac{\partial}{\partial i} \left(  u^2+v^2   \right)  
    … …  
    787727\end{multline} 
    788728\begin{multline} \label{Eq_PE_sco_v} 
    789 \frac{1}{e_3} \frac{\partial \left(  e_3\,v  \right) }{\partial t}= 
     729\frac{\partial v }{\partial t}= 
    790730   -   \left( {\zeta +f} \right)\,u    
    791731   -   \frac{1}{2\,e_2 }\frac{\partial }{\partial j}\left(  u^2+v^2  \right)         
    … …  
    795735   +  D_v^{\vect{U}}  +   F_v^{\vect{U}} \quad 
    796736\end{multline} 
     737 
     738 \vspace{0.5cm} 
     739$\bullet$ Vector invariant form of the momentum equation : 
     740\begin{multline} \label{Eq_PE_sco_u} 
     741\frac{1}{e_3} \frac{\partial \left(  e_3\,u  \right) }{\partial t}= 
     742   +   \left( { f + \frac{1}{e_1 \; e_2 } 
     743               \left(    v \frac{\partial e_2}{\partial i} 
     744                  -u \frac{\partial e_1}{\partial j}  \right)}    \right) \, v    \\ 
     745   - \frac{1}{e_1 \; e_2 \; e_3 }   \left(  
     746               \frac{\partial \left( {e_2 \, e_3 \, u\,u} \right)}{\partial i} 
     747      +        \frac{\partial \left( {e_1 \, e_3 \, v\,u} \right)}{\partial j}   \right) 
     748   - \frac{1}{e_3 }\frac{\partial \left( { \omega\,u} \right)}{\partial k}    \\ 
     749   - \frac{1}{e_1} \frac{\partial}{\partial i} \left( \frac{p_s + p_h}{\rho _o}    \right)     
     750   +  g\frac{\rho }{\rho _o}\sigma _1  
     751   +   D_u^{\vect{U}}  +   F_u^{\vect{U}} \quad 
     752\end{multline} 
     753\begin{multline} \label{Eq_PE_sco_v} 
     754\frac{1}{e_3} \frac{\partial \left(  e_3\,v  \right) }{\partial t}= 
     755   -   \left( { f + \frac{1}{e_1 \; e_2} 
     756               \left(    v \frac{\partial e_2}{\partial i} 
     757                  -u \frac{\partial e_1}{\partial j}  \right)}    \right) \, u   \\ 
     758   - \frac{1}{e_1 \; e_2 \; e_3 }   \left(  
     759               \frac{\partial \left( {e_2 \; e_3  \,u\,v} \right)}{\partial i} 
     760      +        \frac{\partial \left( {e_1 \; e_3  \,v\,v} \right)}{\partial j}   \right) 
     761                 - \frac{1}{e_3 } \frac{\partial \left( { \omega\,v} \right)}{\partial k}    \\ 
     762   -   \frac{1}{e_2 }\frac{\partial }{\partial j}\left( \frac{p_s+p_h }{\rho _o}  \right)  
     763    +  g\frac{\rho }{\rho _o }\sigma _2    
     764   +  D_v^{\vect{U}}  +   F_v^{\vect{U}} \quad 
     765\end{multline} 
     766 
    797767where the relative vorticity, \textit{$\zeta $}, the surface pressure gradient, and the hydrostatic  
    798768pressure have the same expressions as in $z$-coordinates although they do not represent  
    799769exactly the same quantities. $\omega$ is provided by the continuity equation  
    800770(see Appendix~\ref{Apdx_A}): 
    801  
    802771\begin{equation} \label{Eq_PE_sco_continuity} 
    803772\frac{\partial e_3}{\partial t} + e_3 \; \chi + \frac{\partial \omega }{\partial s} = 0    
    … …  
    809778 
    810779 \vspace{0.5cm} 
    811 * tracer equations: 
     780$\bullet$ tracer equations: 
    812781\begin{multline} \label{Eq_PE_sco_t} 
    813782\frac{1}{e_3} \frac{\partial \left(  e_3\,T  \right) }{\partial t}= 
    … …  
    1024993 
    1025994The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM10s}. 
    1026 It is not available in the current version of \NEMO. 
     995It is available in \NEMO since the version 3.4. Nevertheless, it is currently not robust enough  
     996to be used in all possible configurations. Its use is therefore not recommended. 
     997 
    1027998 
    1028999\newpage  
    … …  
    11571128operator acting along $s-$surfaces (see \S\ref{LDF}). 
    11581129 
    1159 \subsubsection{Lateral second order tracer diffusive operator} 
    1160  
    1161 The lateral second order tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}): 
     1130\subsubsection{Lateral Laplacian tracer diffusive operator} 
     1131 
     1132The lateral Laplacian tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}): 
    11621133\begin{equation} \label{Eq_PE_iso_tensor} 
    11631134D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad  
    … …  
    11801151ocean (see Appendix~\ref{Apdx_B}). 
    11811152 
     1153For \textit{iso-level} diffusion, $r_1$ and $r_2 $ are zero. $\Re $ reduces to the identity  
     1154in the horizontal direction, no rotation is applied.  
     1155 
    11821156For \textit{geopotential} diffusion, $r_1$ and $r_2 $ are the slopes between the  
    1183 geopotential and computational surfaces: in $z$-coordinates they are zero  
    1184 ($r_1 = r_2 = 0$) while in $s$-coordinate (including $\textit{z*}$ case) they are  
    1185 equal to $\sigma _1$ and $\sigma _2$, respectively (see \eqref{Eq_PE_sco_slope} ). 
     1157geopotential and computational surfaces: they are equal to $\sigma _1$ and $\sigma _2$,  
     1158respectively (see \eqref{Eq_PE_sco_slope} ). 
    11861159 
    11871160For \textit{isoneutral} diffusion $r_1$ and $r_2$ are the slopes between the isoneutral  
    … …  
    12311204to zero in the vicinity of the boundaries. The latter strategy is used in \NEMO (cf. Chap.~\ref{LDF}). 
    12321205 
    1233 \subsubsection{Lateral fourth order tracer diffusive operator} 
    1234  
    1235 The lateral fourth order tracer diffusive operator is defined by: 
     1206\subsubsection{Lateral bilaplacian tracer diffusive operator} 
     1207 
     1208The lateral bilaplacian tracer diffusive operator is defined by: 
    12361209\begin{equation} \label{Eq_PE_bilapT} 
    12371210D^{lT}=\Delta \left( {A^{lT}\;\Delta T} \right)  
    12381211\qquad \text{where} \  D^{lT}=\Delta \left( {A^{lT}\;\Delta T} \right) 
    12391212 \end{equation} 
    1240  
    12411213It is the second order operator given by \eqref{Eq_PE_iso_tensor} applied twice with  
    12421214the eddy diffusion coefficient correctly placed.  
    12431215 
    1244  
    1245 \subsubsection{Lateral second order momentum diffusive operator} 
    1246  
    1247 The second order momentum diffusive operator along $z$- or $s$-surfaces is found by  
     1216\subsubsection{Lateral Laplacian momentum diffusive operator} 
     1217 
     1218The Laplacian momentum diffusive operator along $z$- or $s$-surfaces is found by  
    12481219applying \eqref{Eq_PE_lap_vector} to the horizontal velocity vector (see Appendix~\ref{Apdx_B}): 
    12491220\begin{equation} \label{Eq_PE_lapU} 
    … …  
    12791250of the Equator in a geographical coordinate system \citep{Lengaigne_al_JGR03}. 
    12801251 
    1281 \subsubsection{lateral fourth order momentum diffusive operator} 
     1252\subsubsection{lateral bilaplacian momentum diffusive operator} 
    12821253 
    12831254As for tracers, the fourth order momentum diffusive operator along $z$ or $s$-surfaces  

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    11% ================================================================ 
    2 % Chapter 1 � Model Basics 
     2% Chapter 1 ——— Model Basics 
    33% ================================================================ 
    44% ================================================================ 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_SBC.tex

    r5120 r6275  
    11% ================================================================ 
    2 % Chapter � Surface Boundary Condition (SBC, ISF, ICB)  
     2% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)  
    33% ================================================================ 
    44\chapter{Surface Boundary Condition (SBC, ISF, ICB) } 
    … …  
    1717   \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 
    1818   \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 
    19    \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 
     19   \item the surface freshwater budget $\left( {\textit{emp}} \right)$ 
     20   \item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$ 
    2021\end{itemize} 
    2122plus an optional field: 
    … …  
    2728are controlled by namelist \ngn{namsbc} variables: an analytical formulation (\np{ln\_ana}~=~true),  
    2829a flux formulation (\np{ln\_flx}~=~true), a bulk formulae formulation (CORE  
    29 (\np{ln\_core}~=~true), CLIO (\np{ln\_clio}~=~true) or MFS 
     30(\np{ln\_blk\_core}~=~true), CLIO (\np{ln\_blk\_clio}~=~true) or MFS 
    3031\footnote { Note that MFS bulk formulae compute fluxes only for the ocean component} 
    31 (\np{ln\_mfs}~=~true) bulk formulae) and a coupled  
    32 formulation (exchanges with a atmospheric model via the OASIS coupler)  
    33 (\np{ln\_cpl}~=~true). When used, the atmospheric pressure forces both  
    34 ocean and ice dynamics (\np{ln\_apr\_dyn}~=~true). 
    35 The frequency at which the six or seven fields have to be updated is the \np{nn\_fsbc}  
    36 namelist parameter.  
     32(\np{ln\_blk\_mfs}~=~true) bulk formulae) and a coupled or mixed forced/coupled formulation  
     33(exchanges with a atmospheric model via the OASIS coupler) (\np{ln\_cpl} or \np{ln\_mixcpl}~=~true).  
     34When used ($i.e.$ \np{ln\_apr\_dyn}~=~true), the atmospheric pressure forces both ocean and ice dynamics. 
     35 
     36The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.  
    3737When the fields are supplied from data files (flux and bulk formulations), the input fields  
    38 need not be supplied on the model grid.  Instead a file of coordinates and weights can  
     38need not be supplied on the model grid. Instead a file of coordinates and weights can  
    3939be supplied which maps the data from the supplied grid to the model points  
    4040(so called "Interpolation on the Fly", see \S\ref{SBC_iof}). 
    … …  
    4242can be masked to avoid spurious results in proximity of the coasts  as large sea-land gradients characterize 
    4343most of the atmospheric variables. 
     44 
    4445In addition, the resulting fields can be further modified using several namelist options.  
    45 These options control  the rotation of vector components supplied relative to an east-north  
    46 coordinate system onto the local grid directions in the model; the addition of a surface  
    47 restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes  
    48 below ice-covered areas (using observed ice-cover or a sea-ice model)  
    49 (\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater  
    50 fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of isf melting as lateral inflow (parameterisation)  
    51 (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false) or as surface flux at the land-ice ocean interface 
    52 (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true);  
    53 the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the  
    54 transformation of the solar radiation (if provided as daily mean) into a diurnal  
    55 cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave  
    56 model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or mfs bulk formulas are selected. 
     46These options control  
     47\begin{itemize} 
     48\item the rotation of vector components supplied relative to an east-north  
     49coordinate system onto the local grid directions in the model ;  
     50\item the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true) ;  
     51\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) ;  
     52\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ;  
     53\item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false)  
     54or as fluxes applied at the land-ice ocean interface (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true) ;  
     55\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ;  
     56\item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ;  
     57and a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}~=~true).  
     58\end{itemize} 
     59The latter option is possible only in case core or mfs bulk formulas are selected. 
    5760 
    5861In this chapter, we first discuss where the surface boundary condition appears in the 
    … …  
    7376 
    7477The surface ocean stress is the stress exerted by the wind and the sea-ice  
    75 on the ocean. The two components of stress are assumed to be interpolated  
    76 onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction  
    77 at $u$- and $v$-points They are applied as a surface boundary condition of the  
    78 computation of the momentum vertical mixing trend (\mdl{dynzdf} module) : 
    79 \begin{equation} \label{Eq_sbc_dynzdf} 
    80 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1} 
    81     = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v } 
    82 \end{equation} 
    83 where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind  
    84 stress vector in the $(\textbf{i},\textbf{j})$ coordinate system. 
     78on the ocean. It is applied in \mdl{dynzdf} module as a surface boundary condition of the  
     79computation of the momentum vertical mixing trend (see \eqref{Eq_dynzdf_sbc} in \S\ref{DYN_zdf}). 
     80As such, it has to be provided as a 2D vector interpolated  
     81onto the horizontal velocity ocean mesh, $i.e.$ resolved onto the model  
     82(\textbf{i},\textbf{j}) direction at $u$- and $v$-points. 
    8583 
    8684The surface heat flux is decomposed into two parts, a non solar and a solar heat  
    8785flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part  
    88 of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).  
    89 It is applied as a surface boundary condition trend of the first level temperature  
    90 time evolution equation (\mdl{trasbc} module).  
    91 \begin{equation} \label{Eq_sbc_trasbc_q} 
    92 \frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho  
    93 _o \;C_p \;e_{3t} }} \right|_{k=1} \quad 
    94 \end{equation} 
    95 $Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D  
    96 trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True. 
    97  
    98 \begin{equation} \label{Eq_sbc_traqsr} 
    99 \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right] 
    100 \end{equation} 
    101 where $I_w$ is a non-dimensional function that describes the way the light  
    102 penetrates inside the water column. It is generally a sum of decreasing  
    103 exponentials (see \S\ref{TRA_qsr}). 
    104  
    105 The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which  
    106 may or may not be identical. Indeed, a surface freshwater flux has two effects:  
    107 it changes the volume of the ocean and it changes the surface concentration of  
    108 salt (and other tracers). Therefore it appears in the sea surface height as a volume  
    109 flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations  
    110 as a concentration/dilution effect,  
    111 $\textit{emp}_{S}$ (\mdl{trasbc} module).  
    112 \begin{equation} \label{Eq_trasbc_emp} 
    113 \begin{aligned} 
    114 &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\  
    115 \\ 
    116  &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\  
    117  \end{aligned} 
    118 \end{equation}  
    119  
    120 In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,  
    121 but it exist several numerical reasons why this equality should be broken.  
    122 For example, when the ocean is coupled to a sea-ice model, the water exchanged between  
    123 ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,  
    124 $\textit{emp}_{S}$ take into account both concentration/dilution effect associated with  
    125 freezing/melting and the salt flux between ice and ocean, while \textit{emp} is  
    126 only the volume flux. In addition, in the current version of \NEMO, the sea-ice is  
    127 assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does  
    128 not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS. 
    129 %gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}. 
    130  
    131 Note that SST can also be modified by a freshwater flux. Precipitation (in  
    132 particular solid precipitation) may have a temperature significantly different from  
    133 the SST. Due to the lack of information about the temperature of  
    134 precipitation, we assume it is equal to the SST. Therefore, no  
    135 concentration/dilution term appears in the temperature equation. It has to  
    136 be emphasised that this absence does not mean that there is no heat flux  
    137 associated with precipitation! Precipitation can change the ocean volume and thus the 
    138 ocean heat content. It is therefore associated with a heat flux (not yet   
    139 diagnosed in the model) \citep{Roullet_Madec_JGR00}). 
     86of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes  
     87plus the heat content of the mass exchange with the atmosphere and sea-ice).  
     88It is applied in \mdl{trasbc} module as a surface boundary condition trend of  
     89the first level temperature time evolution equation (see \eqref{Eq_tra_sbc}  
     90and \eqref{Eq_tra_sbc_lin} in \S\ref{TRA_sbc}).  
     91The latter is the penetrative part of the heat flux. It is applied as a 3D  
     92trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=\textit{true}. 
     93The way the light penetrates inside the water column is generally a sum of decreasing  
     94exponentials (see \S\ref{TRA_qsr}).  
     95 
     96The surface freshwater budget is provided by the \textit{emp} field. 
     97It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation)  
     98and possibly with the sea-ice and ice shelves (freezing minus melting of ice).  
     99It affects both the ocean in two different ways:  
     100$(i)$   it changes the volume of the ocean and therefore appears in the sea surface height  
     101equation as a volume flux, and  
     102$(ii)$  it changes the surface temperature and salinity through the heat and salt contents  
     103of the mass exchanged with the atmosphere, the sea-ice and the ice shelves.  
     104 
    140105 
    141106%\colorbox{yellow}{Miss: } 
    … …  
    157122% 
    158123%Explain here all the namlist namsbc variable{\ldots}. 
     124%  
     125% explain : use or not of surface currents 
    159126% 
    160127%\colorbox{yellow}{End Miss } 
    161128 
    162 The ocean model provides the surface currents, temperature and salinity  
    163 averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the  
    164 mean is done in \mdl{sbcmod} module. 
     129The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})  
     130the surface currents, temperature and salinity.   
     131These variables are averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}),  
     132and it is these averaged fields which are used to computes the surface fluxes  
     133at a frequency of \np{nf\_sbc} time-step. 
     134 
    165135 
    166136%-------------------------------------------------TABLE--------------------------------------------------- 
    … …  
    459429%-------------------------------------------------------------------------------------------------------------- 
    460430 
    461 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.   
    462 Options are defined through the  \ngn{namsbc\_sas} namelist variables. 
     431In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields  
     432and simply read them in from a previous run or receive them from OASIS.   
    463433For example: 
    464434 
    465 \begin{enumerate} 
    466 \item  Multiple runs of the model are required in code development to see the affect of different algorithms in 
     435\begin{itemize} 
     436\item  Multiple runs of the model are required in code development to see the effect of different algorithms in 
    467437       the bulk formulae. 
    468438\item  The effect of different parameter sets in the ice model is to be examined. 
    469 \end{enumerate} 
     439\item  Development of sea-ice algorithms or parameterizations. 
     440\item  spinup of the iceberg floats 
     441\item  ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}~=~\textit{true}) 
     442\end{itemize} 
    470443 
    471444The StandAlone Surface scheme provides this utility. 
     445Its options are defined through the \ngn{namsbc\_sas} namelist variables. 
    472446A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM. 
    473447However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0) 
    … …  
    475449Routines replaced are: 
    476450 
    477 \begin{enumerate} 
    478 \item  \mdl{nemogcm} 
    479  
    480        This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90) 
     451\begin{itemize} 
     452\item \mdl{nemogcm} : This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90) 
    481453       Since the ocean state is not calculated all associated initialisations have been removed. 
    482 \item  \mdl{step} 
    483  
    484        The main time stepping routine now only needs to call the sbc routine (and a few utility functions). 
    485 \item  \mdl{sbcmod} 
    486  
    487        This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules 
     454\item  \mdl{step} : The main time stepping routine now only needs to call the sbc routine (and a few utility functions). 
     455\item  \mdl{sbcmod} : This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules 
    488456       that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs). 
    489 \item  \mdl{daymod} 
    490  
    491        No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions 
     457\item  \mdl{daymod} : No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions 
    492458       have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user 
    493459       must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes. 
    494 \item  \mdl{stpctl} 
    495  
    496        Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module. 
    497 \item  \mdl{diawri} 
    498  
    499        All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which 
     460\item  \mdl{stpctl} : Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module. 
     461\item  \mdl{diawri} : All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which 
    500462       have been read in) are written along with relevant forcing and ice data. 
    501 \end{enumerate} 
     463\end{itemize} 
    502464 
    503465One new routine has been added: 
    504466 
    505 \begin{enumerate} 
    506 \item  \mdl{sbcsas} 
    507        This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface. 
     467\begin{itemize} 
     468\item  \mdl{sbcsas} : This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface. 
    508469       These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module, 
    509470       the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level. 
    510471       Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution. 
    511 \end{enumerate} 
     472\end{itemize} 
     473 
     474 
     475% Missing the description of the 2 following variables: 
     476%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field 
     477%   ln_read_frq = .false.    !  specify whether we must read frq or not 
     478 
     479 
    512480 
    513481% ================================================================ 
    … …  
    720688are sent to the atmospheric component. 
    721689 
    722 A generalised coupled interface has been developed. It is currently interfaced with OASIS 3 
    723 (\key{oasis3}) and does not support OASIS 4 
    724 \footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}.  
     690A generalised coupled interface has been developed.  
     691It is currently interfaced with OASIS-3-MCT (\key{oasis3}).  
    725692It has been successfully used to interface \NEMO to most of the European atmospheric  
    726693GCM (ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz),  
    … …  
    787754\label{SBC_tide} 
    788755 
    789 A module is available to use the tidal potential forcing and is activated with with \key{tide}. 
    790  
    791  
    792 %------------------------------------------nam_tide---------------------------------------------------- 
     756%------------------------------------------nam_tide--------------------------------------- 
    793757\namdisplay{nam_tide} 
    794 %------------------------------------------------------------------------------------------------------------- 
    795  
    796 Concerning the tidal potential, some parameters are available in namelist \ngn{nam\_tide}: 
     758%----------------------------------------------------------------------------------------- 
     759 
     760A module is available to compute the tidal potential and use it in the momentum equation. 
     761This option is activated when \key{tide} is defined. 
     762 
     763Some parameters are available in namelist \ngn{nam\_tide}: 
    797764 
    798765- \np{ln\_tide\_pot} activate the tidal potential forcing 
    … …  
    801768 
    802769- \np{clname} is the name of constituent 
    803  
    804770 
    805771The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem; 
    … …  
    958924\namdisplay{namsbc_isf} 
    959925%-------------------------------------------------------------------------------------------------------- 
    960 Namelist variable in \ngn{namsbc}, \np{nn\_isf},  control the kind of ice shelf representation used.  
     926Namelist variable in \ngn{namsbc}, \np{nn\_isf}, control the kind of ice shelf representation used.  
    961927\begin{description} 
    962928\item[\np{nn\_isf}~=~1] 
    … …  
    987953\np{nn\_isf}~=~3 and \np{nn\_isf}~=~4 read the melt rate and heat flux from a file. You have total control of the fwf scenario. 
    988954 
    989  This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too  
     955This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too  
    990956coarse to have realistic melting or for sensitivity studies where you want to control your input.  
    991957Full description, sensitivity and validation in preparation.  
    … …  
    1000966%        Handling of icebergs 
    1001967% ================================================================ 
    1002 \section{ Handling of icebergs (ICB) } 
     968\section{Handling of icebergs (ICB)} 
    1003969\label{ICB_icebergs} 
    1004970%------------------------------------------namberg---------------------------------------------------- 
    … …  
    1006972%------------------------------------------------------------------------------------------------------------- 
    1007973 
    1008 Icebergs are modelled as lagrangian particles in NEMO. 
    1009 Their physical behaviour is controlled by equations as described in  \citet{Martin_Adcroft_OM10} ). 
    1010 (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO.) 
    1011 Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described in the \ngn{namberg} namelist:  
     974Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}. 
     975Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ). 
     976(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 
     977Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described  
     978in the \ngn{namberg} namelist:  
    1012979\np{rn\_initial\_mass} and \np{rn\_initial\_thickness}. 
    1013980Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs  
    … …  
    11931160The presence at the sea surface of an ice covered area modifies all the fluxes  
    11941161transmitted to the ocean. There are several way to handle sea-ice in the system  
    1195 depending on the value of the \np{nn{\_}ice} namelist parameter.   
     1162depending on the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist.   
    11961163\begin{description} 
    11971164\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.  
    … …  
    12681235% ------------------------------------------------------------------------------------------------------------- 
    12691236\subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})] 
    1270                         {Neutral drag coefficient from external wave model (\mdl{sbcwave})} 
     1237              {Neutral drag coefficient from external wave model (\mdl{sbcwave})} 
    12711238\label{SBC_wave} 
    12721239%------------------------------------------namwave---------------------------------------------------- 
    12731240\namdisplay{namsbc_wave} 
    12741241%------------------------------------------------------------------------------------------------------------- 
    1275 \begin{description} 
    1276  
    1277 \item [??] In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the  
    1278 logical variable \np{ln\_cdgw} 
    1279  in $namsbc$ namelist must be defined ${.true.}$.  
     1242 
     1243In order to read a neutral drag coeff, from an external data source ($i.e.$ a wave model), the  
     1244logical variable \np{ln\_cdgw} in \ngn{namsbc} namelist must be set to \textit{true}.  
    12801245The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the 
    12811246namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all  
    12821247the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input})  
    1283 and a 2D field of neutral drag coefficient. Then using the routine  
    1284 TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according  
    1285 to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}. 
    1286  
    1287 \end{description} 
     1248and a 2D field of neutral drag coefficient.  
     1249Then using the routine TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided,  
     1250the drag coefficient is computed according to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}. 
     1251 
    12881252 
    12891253% Griffies doc: 
    1290 % 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.  
    1291 %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.  
    1292 %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.  
    1293  
    1294  
     1254% When running ocean-ice simulations, we are not explicitly representing land processes,  
     1255% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,  
     1256% it is important to balance the hydrological cycle in ocean-ice models.  
     1257% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.  
     1258% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over  
     1259% a chosen time scale.  
     1260%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,  
     1261% so that there is always a zero net input of water to the ocean-ice system.  
     1262% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used  
     1263% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.  
     1264% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.  
     1265% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean  
     1266% and ice models when aiming to balance the hydrological cycle.  
     1267% 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,  
     1268% not the water in any one sub-component. As an extreme example to illustrate the issue,  
     1269% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,  
     1270% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.  
     1271% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between  
     1272% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle  
     1273% in ocean-ice models.  
     1274 
     1275 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_TRA.tex

    r6039 r6275  
    3636(BBL) parametrisation, and an internal damping (DMP) term. The terms QSR,  
    3737BBC, BBL and DMP are optional. The external forcings and parameterisations  
    38 require complex inputs and complex calculations (e.g. bulk formulae, estimation  
     38require complex inputs and complex calculations ($e.g.$ bulk formulae, estimation  
    3939of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and  
    4040described in chapters \S\ref{SBC}, \S\ref{LDF} and  \S\ref{ZDF}, respectively.  
    41 Note that \mdl{tranpc}, the non-penetrative convection module,  although  
    42 (temporarily) located in the NEMO/OPA/TRA directory, is described with the  
    43 model vertical physics (ZDF). 
    44 %%% 
    45 \gmcomment{change the position of eosbn2 in the reference code} 
    46 %%% 
     41Note that \mdl{tranpc}, the non-penetrative convection module, although  
     42located in the NEMO/OPA/TRA directory as it directly modifies the tracer fields,  
     43is described with the model vertical physics (ZDF) together with other available  
     44parameterization of convection. 
    4745 
    4846In the present chapter we also describe the diagnostic equations used to compute  
    49 the sea-water properties (density, Brunt-Vais\"{a}l\"{a} frequency, specific heat and  
     47the sea-water properties (density, Brunt-V\"{a}is\"{a}l\"{a} frequency, specific heat and  
    5048freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}). 
    5149 
    … …  
    5654found in the \textit{trattt} or \textit{trattt\_xxx} module, in the NEMO/OPA/TRA directory. 
    5755 
    58 The user has the option of extracting each tendency term on the rhs of the tracer  
    59 equation for output (\key{trdtra} is defined), as described in Chap.~\ref{MISC}. 
     56The user has the option of extracting each tendency term on the RHS of the tracer  
     57equation for output (\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}~=~true), as described in Chap.~\ref{DIA}. 
    6058 
    6159$\ $\newline    % force a new ligne 
    … …  
    125123\end{description} 
    126124In all cases, this boundary condition retains local conservation of tracer.  
    127 Global conservation is obtained in both rigid-lid and non-linear free surface  
    128 cases, but not in the linear free surface case. Nevertheless, in the latter 
    129 case, it is achieved to a good approximation since the non-conservative  
     125Global conservation is obtained in non-linear free surface case,  
     126but \textit{not} in the linear free surface case. Nevertheless, in the latter case,  
     127it is achieved to a good approximation since the non-conservative  
    130128term is the product of the time derivative of the tracer and the free surface  
    131129height, two quantities that are not correlated (see \S\ref{PE_free_surface},  
    … …  
    133131 
    134132The velocity field that appears in (\ref{Eq_tra_adv}) and (\ref{Eq_tra_adv_zco})  
    135 is the centred (\textit{now}) \textit{eulerian} ocean velocity (see Chap.~\ref{DYN}).  
    136 When eddy induced velocity (\textit{eiv}) parameterisation is used it is the \textit{now}  
    137 \textit{effective} velocity ($i.e.$ the sum of the eulerian and eiv velocities) which is used. 
     133is the centred (\textit{now}) \textit{effective} ocean velocity, $i.e.$ the \textit{eulerian} velocity 
     134(see Chap.~\ref{DYN}) plus the eddy induced velocity (\textit{eiv})  
     135and/or the mixed layer eddy induced velocity (\textit{eiv}) 
     136when those parameterisations are used (see Chap.~\ref{LDF}). 
    138137 
    139138The choice of an advection scheme is made in the \textit{\ngn{nam\_traadv}} namelist, by  
    … …  
    146145 
    147146Note that  
    148 (1) cen2, cen4 and TVD schemes require an explicit diffusion  
     147(1) cen2 and TVD schemes require an explicit diffusion  
    149148operator while the other schemes are diffusive enough so that they do not  
    150149require additional diffusion ;  
    151 (2) cen2, cen4, MUSCL2, and UBS are not \textit{positive} schemes 
     150(2) cen2, MUSCL2, and UBS are not \textit{positive} schemes 
    152151\footnote{negative values can appear in an initially strictly positive tracer field  
    153152which is advected} 
    … …  
    189188temperature is close to the freezing point). 
    190189This combined scheme has been included for specific grid points in the ORCA2  
    191 and ORCA4 configurations only. This is an obsolescent feature as the recommended  
     190configuration only. This is an obsolescent feature as the recommended  
    192191advection scheme for the ORCA configuration is TVD (see  \S\ref{TRA_adv_tvd}). 
    193192 
    … …  
    196195have this order of accuracy. \gmcomment{Note also that ... blah, blah} 
    197196 
    198 % ------------------------------------------------------------------------------------------------------------- 
    199 %        4nd order centred scheme   
    200 % ------------------------------------------------------------------------------------------------------------- 
    201 \subsection   [$4^{nd}$ order centred scheme (cen4) (\np{ln\_traadv\_cen4})] 
    202            {$4^{nd}$ order centred scheme (cen4) (\np{ln\_traadv\_cen4}=true)} 
    203 \label{TRA_adv_cen4} 
    204  
    205 In the $4^{th}$ order formulation (to be implemented), tracer values are  
    206 evaluated at velocity points as a $4^{th}$ order interpolation, and thus depend on  
    207 the four neighbouring $T$-points. For example, in the $i$-direction: 
    208 \begin{equation} \label{Eq_tra_adv_cen4} 
    209 \tau _u^{cen4}  
    210 =\overline{   T - \frac{1}{6}\,\delta _i \left[ \delta_{i+1/2}[T] \,\right]   }^{\,i+1/2} 
    211 \end{equation} 
    212  
    213 Strictly speaking, the cen4 scheme is not a $4^{th}$ order advection scheme  
    214 but a $4^{th}$ order evaluation of advective fluxes, since the divergence of  
    215 advective fluxes \eqref{Eq_tra_adv} is kept at $2^{nd}$ order. The phrase ``$4^{th}$  
    216 order scheme'' used in oceanographic literature is usually associated  
    217 with the scheme presented here. Introducing a \textit{true} $4^{th}$ order advection  
    218 scheme is feasible but, for consistency reasons, it requires changes in the  
    219 discretisation of the tracer advection together with changes in both the  
    220 continuity equation and the momentum advection terms.   
    221  
    222 A direct consequence of the pseudo-fourth order nature of the scheme is that  
    223 it is not non-diffusive, i.e. the global variance of a tracer is not preserved using  
    224 \textit{cen4}. Furthermore, it must be used in conjunction with an explicit  
    225 diffusion operator to produce a sensible solution. The time-stepping is also  
    226 performed using a leapfrog scheme in conjunction with an Asselin time-filter,  
    227 so $T$ in (\ref{Eq_tra_adv_cen4}) is the \textit{now} tracer. 
    228  
    229 At a $T$-grid cell adjacent to a boundary (coastline, bottom and surface), an  
    230 additional hypothesis must be made to evaluate $\tau _u^{cen4}$. This  
    231 hypothesis usually reduces the order of the scheme. Here we choose to set  
    232 the gradient of $T$ across the boundary to zero. Alternative conditions can be  
    233 specified, such as a reduction to a second order scheme for these near boundary  
    234 grid points. 
    235197 
    236198% ------------------------------------------------------------------------------------------------------------- 
    … …  
    270232used for the diffusive part.  
    271233 
     234An additional option has been added controlled by \np{ln\_traadv\_tvd\_zts}.  
     235By setting this logical to true, a TVD scheme is used on both horizontal and vertical direction,  
     236but on the latter, a split-explicit time stepping is used, with 5 sub-timesteps.  
     237This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}.  
     238Note that in this case, a similar split-explicit time stepping should be used on  
     239vertical advection of momentum to ensure a better stability (see \np{ln\_dynzad\_zts} in \S\ref{DYN_zad}). 
     240 
     241 
    272242% ------------------------------------------------------------------------------------------------------------- 
    273243%        MUSCL scheme   
    … …  
    296266 
    297267For an ocean grid point adjacent to land and where the ocean velocity is  
    298 directed toward land, two choices are available: an upstream flux  
    299 (\np{ln\_traadv\_muscl}=true) or a second order flux  
    300 (\np{ln\_traadv\_muscl2}=true). Note that the latter choice does not ensure  
    301 the \textit{positive} character of the scheme. Only the former can be used  
    302 on both active and passive tracers. The two MUSCL schemes are implemented  
    303 in the \mdl{traadv\_tvd} and \mdl{traadv\_tvd2} modules. 
     268directed toward land, two choices are available: an upstream flux (\np{ln\_traadv\_muscl}=true)  
     269or a second order flux (\np{ln\_traadv\_muscl2}=true).  
     270Note that the latter choice does not ensure the \textit{positive} character of the scheme.  
     271Only the former can be used on both active and passive tracers.  
     272The two MUSCL schemes are implemented in the \mdl{traadv\_tvd} and \mdl{traadv\_tvd2} modules. 
     273 
     274Note that when using np{ln\_traadv\_msc\_ups}~=~true in addition to \np{ln\_traadv\_muscl}=true,  
     275the MUSCL fluxes are replaced by upstream fluxes in vicinity of river mouths. 
    304276 
    305277% ------------------------------------------------------------------------------------------------------------- 
    … …  
    416388direction (as for the UBS case) should be implemented to restore this property. 
    417389 
    418  
    419 % ------------------------------------------------------------------------------------------------------------- 
    420 %        PPM scheme   
    421 % ------------------------------------------------------------------------------------------------------------- 
    422 \subsection   [Piecewise Parabolic Method (PPM) (\np{ln\_traadv\_ppm})] 
    423          {Piecewise Parabolic Method (PPM) (\np{ln\_traadv\_ppm}=true)} 
    424 \label{TRA_adv_ppm} 
    425  
    426 The Piecewise Parabolic Method (PPM) proposed by Colella and Woodward (1984)  
    427 \sgacomment{reference?} 
    428 is based on a quadradic piecewise construction. Like the QCK scheme, it is associated  
    429 with the ULTIMATE QUICKEST limiter \citep{Leonard1991}. It has been implemented  
    430 in \NEMO by G. Reffray (MERCATOR-ocean) but is not yet offered in the reference  
    431 version 3.3. 
    432390 
    433391% ================================================================ 
    … …  
    464422surfaces is given by:  
    465423\begin{equation} \label{Eq_tra_ldf_lap} 
    466 D_T^{lT} =\frac{1}{b_tT} \left( \; 
     424D_T^{lT} =\frac{1}{b_t} \left( \; 
    467425   \delta _{i}\left[ A_u^{lT} \; \frac{e_{2u}\,e_{3u}}{e_{1u}} \;\delta _{i+1/2} [T] \right]  
    468426+ \delta _{j}\left[ A_v^{lT} \;  \frac{e_{1v}\,e_{3v}}{e_{2v}} \;\delta _{j+1/2} [T] \right]  \;\right) 
    … …  
    661619the thickness of the top model layer.  
    662620 
    663 Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components ($i.e.$ atmosphere, sea-ice, land), 
    664 the change in the heat and salt content of the surface layer of the ocean is due both  
    665 to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$) 
    666  and to the heat and salt content of the mass exchange. 
    667 \sgacomment{ the following does not apply to the release to which this documentation is  
    668 attached and so should not be included .... 
    669 In a forthcoming release, these two parts, computed in the surface module (SBC), will be included directly 
    670 in $Q_{ns}$, the surface heat flux and $F_{salt}$, the surface salt flux. 
    671 The specification of these fluxes is further detailed in the SBC chapter (see \S\ref{SBC}).  
    672 This change will provide a forcing formulation which is the same for any tracer (including temperature and salinity). 
    673   
    674 In the current version, the situation is a little bit more complicated. } 
     621Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components  
     622($i.e.$ atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer  
     623of the ocean is due both to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$)  
     624and to the heat and salt content of the mass exchange. They are both included directly in $Q_{ns}$,  
     625the surface heat flux, and $F_{salt}$, the surface salt flux (see \S\ref{SBC} for further details). 
     626By doing this, the forcing formulation is the same for any tracer (including temperature and salinity). 
    675627 
    676628The surface module (\mdl{sbcmod}, see \S\ref{SBC}) provides the following  
    … …  
    679631$\bullet$ $Q_{ns}$, the non-solar part of the net surface heat flux that crosses the sea surface  
    680632(i.e. the difference between the total surface heat flux and the fraction of the short wave flux that  
    681 penetrates into the water column, see \S\ref{TRA_qsr}) 
    682  
    683 $\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation) 
    684  
    685 $\bullet$ $\textit{emp}_S$, an equivalent mass flux taking into account the effect of ice-ocean mass exchange 
    686  
    687 $\bullet$ \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) 
    688  
    689 The $\textit{emp}_S$ field is not simply the budget of evaporation-precipitation+freezing-melting because  
    690 the sea-ice is not currently embedded in the ocean but levitates above it. There is no mass 
    691 exchanged between the sea-ice and the ocean. Instead we only take into account the salt 
    692 flux associated with the non-zero salinity of sea-ice, and the concentration/dilution effect 
    693 due to the freezing/melting (F/M) process. These two parts of the forcing are then converted into  
    694 an equivalent mass flux given by $\textit{emp}_S - \textit{emp}$. As a result of this mess,  
    695 the surface boundary condition on temperature and salinity is applied as follows: 
    696  
    697 In the nonlinear free surface case (\key{vvl} is defined): 
     633penetrates into the water column, see \S\ref{TRA_qsr}) plus the heat content associated with  
     634of the mass exchange with the atmosphere and lands. 
     635 
     636$\bullet$ $\textit{sfx}$, the salt flux resulting from ice-ocean mass exchange (freezing, melting, ridging...) 
     637 
     638$\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation)  
     639 and possibly with the sea-ice and ice-shelves. 
     640 
     641$\bullet$ \textit{rnf}, the mass flux associated with runoff  
     642(see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies) 
     643 
     644In the non-linear free surface case (\key{vvl} is defined), the surface boundary condition  
     645on temperature and salinity is applied as follows: 
    698646\begin{equation} \label{Eq_tra_sbc} 
     647\begin{aligned} 
     648 &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }  &\overline{ Q_{ns}       }^t  & \\  
     649& F^S =\frac{ 1 }{\rho _o  \,      \left. e_{3t} \right|_{k=1} }  &\overline{ \textit{sfx} }^t   & \\    
     650 \end{aligned} 
     651\end{equation}  
     652where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps  
     653($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the  
     654divergence of odd and even time step (see \S\ref{STP}). 
     655 
     656In the linear free surface case (\key{vvl} is \textit{not} defined),  
     657an additional term has to be added on both temperature and salinity.  
     658On temperature, this term remove the heat content associated with mass exchange 
     659that has been added to $Q_{ns}$. On salinity, this term mimics the concentration/dilution effect that 
     660would have resulted from a change in the volume of the first level. 
     661The resulting surface boundary condition is applied as follows: 
     662\begin{equation} \label{Eq_tra_sbc_lin} 
    699663\begin{aligned} 
    700664 &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }    
    … …  
    702666% 
    703667& F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} }  
    704            &\overline{ \left( (\textit{emp}_S - \textit{emp})\;\left. S \right|_{k=1}  \right) }^t   & \\    
     668           &\overline{ \left( \;\textit{sfx} - \textit{emp} \;\left. S \right|_{k=1}  \right) }^t   & \\    
    705669 \end{aligned} 
    706670\end{equation}  
    707  
    708 In the linear free surface case (\key{vvl} not defined): 
    709 \begin{equation} \label{Eq_tra_sbc_lin} 
    710 \begin{aligned} 
    711  &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }  &\overline{ Q_{ns} }^t  & \\  
    712 % 
    713 & F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} }  
    714            &\overline{ \left( \textit{emp}_S\;\left. S \right|_{k=1}  \right) }^t   & \\    
    715  \end{aligned} 
    716 \end{equation}  
    717 where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps  
    718 ($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the  
    719 divergence of odd and even time step (see \S\ref{STP}). 
    720  
    721 The two set of equations, \eqref{Eq_tra_sbc} and \eqref{Eq_tra_sbc_lin}, are obtained  
    722 by assuming that the temperature of precipitation and evaporation are equal to 
    723 the ocean surface temperature and that their salinity is zero. Therefore, the heat content 
    724 of the \textit{emp} budget must be added to the temperature equation in the variable volume case,  
    725 while it does not appear in the constant volume case. Similarly, the \textit{emp} budget affects  
    726 the ocean surface salinity in the constant volume case (through the concentration dilution effect) 
    727 while it does not appears explicitly in the variable volume case since salinity change will be 
    728 induced by volume change. In both constant and variable volume cases, surface salinity  
    729 will change with ice-ocean salt flux and F/M flux (both contained in $\textit{emp}_S - \textit{emp}$) without mass exchanges. 
    730  
    731 Note that the concentration/dilution effect due to F/M is computed using 
    732 a constant ice salinity as well as a constant ocean salinity.  
    733 This approximation suppresses the correlation between \textit{SSS}  
    734 and F/M flux, allowing the ice-ocean salt exchanges to be conservative. 
    735 Indeed, if this approximation is not made, even if the F/M budget is zero  
    736 on average over the whole ocean domain and over the seasonal cycle,  
    737 the associated salt flux is not zero, since sea-surface salinity and F/M flux are  
    738 intrinsically correlated (high \textit{SSS} are found where freezing is  
    739 strong whilst low \textit{SSS} is usually associated with high melting areas). 
    740  
    741 Even using this approximation, an exact conservation of heat and salt content  
    742 is only achieved in the variable volume case. In the constant volume case,  
    743 there is a small imbalance associated with the product $(\partial_t\eta - \textit{emp}) * \textit{SSS}$. 
    744 Nevertheless, the salt content variation is quite small and will not induce 
    745 a long term drift as there is no physical reason for $(\partial_t\eta - \textit{emp})$  
    746 and \textit{SSS} to be correlated \citep{Roullet_Madec_JGR00}.  
    747 Note that, while quite small, the imbalance in the constant volume case is larger  
     671Note that an exact conservation of heat and salt content is only achieved with non-linear free surface.  
     672In the linear free surface case, there is a small imbalance. The imbalance is larger  
    748673than the imbalance associated with the Asselin time filter \citep{Leclair_Madec_OM09}.  
    749 This is the reason why the modified filter is not applied in the constant volume case. 
     674This is the reason why the modified filter is not applied in the linear free surface case (see \S\ref{STP}). 
    750675 
    751676% ------------------------------------------------------------------------------------------------------------- 
    … …  
    11031028\subsection[DMP\_TOOLS]{Generating resto.nc using DMP\_TOOLS} 
    11041029 
    1105 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. 
     1030DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$.  
     1031Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled  
     1032and run on the same machine as the NEMO model. A mesh\_mask.nc file for the model configuration is required as an input.  
     1033This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1.  
     1034The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work.  
     1035The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 
    11061036 
    11071037%--------------------------------------------nam_dmp_create------------------------------------------------- 
    … …  
    11111041\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. 
    11121042 
    1113 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. 
    1114  
    1115 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}.   
     1043The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations.  
     1044\np{ln\_full\_field} specifies that newtonian damping should be applied to the whole model domain.  
     1045\np{ln\_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea  
     1046for the ORCA4, ORCA2 and ORCA05 configurations.  
     1047If \np{ln\_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as  
     1048a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference  
     1049configurations with previous model versions.  
     1050\np{ln\_coast} specifies that the restoration coefficient should be reduced near to coastlines.  
     1051This option only has an effect if \np{ln\_full\_field} is true.  
     1052\np{ln\_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer.  
     1053Finally \np{ln\_custom} specifies that the custom module will be called.  
     1054This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region. 
     1055 
     1056The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn\_hdmp}.  
     1057Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to  
     1058the full values of a 10$^{\circ}$ latitud band.  
     1059This is often used because of the short adjustment time scale in the equatorial region  
     1060\citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a  
     1061hyperbolic tangent, with \np{rn\_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}.   
    11161062 
    11171063% ================================================================ 
    … …  
    12651211\hline 
    12661212coeff.   & computer name   & S-EOS     &  description                      \\ \hline 
    1267 $a_0$       & \np{nn\_a0}     & 1.6550 $10^{-1}$ &  linear thermal expansion coeff.    \\ \hline 
    1268 $b_0$       & \np{nn\_b0}     & 7.6554 $10^{-1}$ &  linear haline  expansion coeff.    \\ \hline 
    1269 $\lambda_1$ & \np{nn\_lambda1}& 5.9520 $10^{-2}$ &  cabbeling coeff. in $T^2$          \\ \hline 
    1270 $\lambda_2$ & \np{nn\_lambda2}& 5.4914 $10^{-4}$ &  cabbeling coeff. in $S^2$       \\ \hline 
    1271 $\nu$       & \np{nn\_nu}     & 2.4341 $10^{-3}$ &  cabbeling coeff. in $T \, S$       \\ \hline 
    1272 $\mu_1$     & \np{nn\_mu1}    & 1.4970 $10^{-4}$ &  thermobaric coeff. in T         \\ \hline 
    1273 $\mu_2$     & \np{nn\_mu2}    & 1.1090 $10^{-5}$ &  thermobaric coeff. in S            \\ \hline 
     1213$a_0$       & \np{rn\_a0}     & 1.6550 $10^{-1}$ &  linear thermal expansion coeff.    \\ \hline 
     1214$b_0$       & \np{rn\_b0}     & 7.6554 $10^{-1}$ &  linear haline  expansion coeff.    \\ \hline 
     1215$\lambda_1$ & \np{rn\_lambda1}& 5.9520 $10^{-2}$ &  cabbeling coeff. in $T^2$          \\ \hline 
     1216$\lambda_2$ & \np{rn\_lambda2}& 5.4914 $10^{-4}$ &  cabbeling coeff. in $S^2$       \\ \hline 
     1217$\nu$       & \np{rn\_nu}     & 2.4341 $10^{-3}$ &  cabbeling coeff. in $T \, S$       \\ \hline 
     1218$\mu_1$     & \np{rn\_mu1}    & 1.4970 $10^{-4}$ &  thermobaric coeff. in T         \\ \hline 
     1219$\mu_2$     & \np{rn\_mu2}    & 1.1090 $10^{-5}$ &  thermobaric coeff. in S            \\ \hline 
    12741220\end{tabular} 
    12751221\caption{ \label{Tab_SEOS} 
    … …  
    12811227 
    12821228% ------------------------------------------------------------------------------------------------------------- 
    1283 %        Brunt-Vais\"{a}l\"{a} Frequency 
    1284 % ------------------------------------------------------------------------------------------------------------- 
    1285 \subsection{Brunt-Vais\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)} 
     1229%        Brunt-V\"{a}is\"{a}l\"{a} Frequency 
     1230% ------------------------------------------------------------------------------------------------------------- 
     1231\subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)} 
    12861232\label{TRA_bn2} 
    12871233 
    1288 An accurate computation of the ocean stability (i.e. of $N$, the brunt-Vais\"{a}l\"{a} 
     1234An accurate computation of the ocean stability (i.e. of $N$, the brunt-V\"{a}is\"{a}l\"{a} 
    12891235 frequency) is of paramount importance as determine the ocean stratification and  
    12901236 is used in several ocean parameterisations (namely TKE, GLS, Richardson number dependent  
    … …  
    13021248function that can be found in \mdl{eosbn2}. 
    13031249 
    1304  
    1305 % ------------------------------------------------------------------------------------------------------------- 
    1306 %        Potential Energy      
    1307 % ------------------------------------------------------------------------------------------------------------- 
    1308 %\subsection{Potential Energy anomalies} 
    1309 %\label{TRA_bn2} 
    1310  
    1311 %    =====>>>>> TO BE written 
    1312 % 
    1313  
    13141250% ------------------------------------------------------------------------------------------------------------- 
    13151251%        Freezing Point of Seawater 
    … …  
    13411277\label{TRA_zpshde} 
    13421278 
    1343 \gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators, I've changed "derivative" to "difference" and "mean" to "average"} 
     1279\gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators,  
     1280                   I've changed "derivative" to "difference" and "mean" to "average"} 
    13441281 
    13451282With partial bottom cells (\np{ln\_zps}=true), in general, tracers in horizontally  

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Chap_ZDF.tex

    r5120 r6275  
    3333points, respectively (see \S\ref{TRA_zdf} and \S\ref{DYN_zdf}). These  
    3434coefficients can be assumed to be either constant, or a function of the local  
    35 Richardson number, or computed from a turbulent closure model (either  
    36 TKE or KPP formulation). The computation of these coefficients is initialized  
    37 in the \mdl{zdfini} module and performed in the \mdl{zdfric}, \mdl{zdftke} or  
    38 \mdl{zdfkpp} modules. The trends due to the vertical momentum and tracer  
    39 diffusion, including the surface forcing, are computed and added to the  
    40 general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively.  
     35Richardson number, or computed from a turbulent closure model (TKE, GLS or KPP formulation).  
     36The computation of these coefficients is initialized in the \mdl{zdfini} module  
     37and performed in the \mdl{zdfric}, \mdl{zdftke}, \mdl{zdfgls} or \mdl{zdfkpp} modules.  
     38The trends due to the vertical momentum and tracer diffusion, including the surface forcing,  
     39are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively.  
    4140These trends can be computed using either a forward time stepping scheme  
    4241(namelist parameter \np{ln\_zdfexp}=true) or a backward time stepping  
    … …  
    355354%--------------------------------------------------------------% 
    356355 
    357 To be add here a description of "penetration of TKE" and the associated namelist parameters 
    358  \np{nn\_etau}, \np{rn\_efr} and \np{nn\_htau}. 
     356Vertical mixing parameterizations commonly used in ocean general circulation models  
     357tend to produce mixed-layer depths that are too shallow during summer months and windy conditions. 
     358This bias is particularly acute over the Southern Ocean.  
     359To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme  \cite{Rodgers_2014}.  
     360The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations,  
     361but rather is meant to account for observed processes that affect the density structure of  
     362the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme  
     363($i.e.$ near-inertial oscillations and ocean swells and waves). 
     364 
     365When using this parameterization ($i.e.$ when \np{nn\_etau}~=~1), the TKE input to the ocean ($S$)  
     366imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized  
     367by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by: 
     368\begin{equation}  \label{ZDF_Ehtau} 
     369S = (1-f_i) \; f_r \; e_s \; e^{-z / h_\tau}  
     370\end{equation} 
     371where  
     372$z$ is the depth,   
     373$e_s$ is TKE surface boundary condition,  
     374$f_r$ is the fraction of the surface TKE that penetrate in the ocean,  
     375$h_\tau$ is a vertical mixing length scale that controls exponential shape of the penetration,  
     376and $f_i$ is the ice concentration (no penetration if $f_i=1$, that is if the ocean is entirely  
     377covered by sea-ice). 
     378The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter.  
     379The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}~=~0)  
     380or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m  
     381at high latitudes (\np{nn\_etau}~=~1).  
     382 
     383Note that two other option existe, \np{nn\_etau}~=~2, or 3. They correspond to applying  
     384\eqref{ZDF_Ehtau} only at the base of the mixed layer, or to using the high frequency part  
     385of the stress to evaluate the fraction of TKE that penetrate the ocean.  
     386Those two options are obsolescent features introduced for test purposes. 
     387They will be removed in the next release.  
     388 
     389 
    359390 
    360391% from Burchard et al OM 2008 :  
    361 % 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). 
     392% the most critical process not reproduced by statistical turbulence models is the activity of  
     393% internal waves and their interaction with turbulence. After the Reynolds decomposition,  
     394% internal waves are in principle included in the RANS equations, but later partially  
     395% excluded by the hydrostatic assumption and the model resolution.  
     396% Thus far, the representation of internal wave mixing in ocean models has been relatively crude  
     397% (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 
    362398 
    363399 
    … …  
    586622Options are defined through the  \ngn{namzdf\_kpp} namelist variables. 
    587623 
    588 \colorbox{yellow}{Add a description of KPP here.} 
     624Note that KPP is an obsolescent feature of the \NEMO system.  
     625It will be removed in the next release (v3.7 and followings). 
    589626 
    590627 
    … …  
    636673 
    637674Options are defined through the  \ngn{namzdf} namelist variables. 
    638 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}=true.  
     675The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}~=~\textit{true}.  
    639676It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously  
    640677the statically unstable portion of the water column, but only until the density  
    … …  
    644681(Fig. \ref{Fig_npc}): starting from the top of the ocean, the first instability is  
    645682found. Assume in the following that the instability is located between levels  
    646 $k$ and $k+1$. The potential temperature and salinity in the two levels are  
     683$k$ and $k+1$. The temperature and salinity in the two levels are  
    647684vertically mixed, conserving the heat and salt contents of the water column.  
    648685The new density is then computed by a linear approximation. If the new  
    … …  
    664701\citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}. 
    665702 
    666 Note that in the current implementation of this algorithm presents several  
    667 limitations. First, potential density referenced to the sea surface is used to  
    668 check whether the density profile is stable or not. This is a strong  
    669 simplification which leads to large errors for realistic ocean simulations.  
    670 Indeed, many water masses of the world ocean, especially Antarctic Bottom 
    671 Water, are unstable when represented in surface-referenced potential density.  
    672 The scheme will erroneously mix them up. Second, the mixing of potential  
    673 density is assumed to be linear. This assures the convergence of the algorithm  
    674 even when the equation of state is non-linear. Small static instabilities can thus  
    675 persist due to cabbeling: they will be treated at the next time step.  
    676 Third, temperature and salinity, and thus density, are mixed, but the  
    677 corresponding velocity fields remain unchanged. When using a Richardson  
    678 Number dependent eddy viscosity, the mixing of momentum is done through  
    679 the vertical diffusion: after a static adjustment, the Richardson Number is zero  
    680 and thus the eddy viscosity coefficient is at a maximum. When this convective  
    681 adjustment algorithm is used with constant vertical eddy viscosity, spurious  
    682 solutions can occur since the vertical momentum diffusion remains small even  
    683 after a static adjustment. In that case, we recommend the addition of momentum  
    684 mixing in a manner that mimics the mixing in temperature and salinity  
    685 \citep{Speich_PhD92, Speich_al_JPO96}. 
     703The current implementation has been modified in order to deal with any non linear  
     704equation of seawater (L. Brodeau, personnal communication).  
     705Two main differences have been introduced compared to the original algorithm:  
     706$(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency  
     707(not the the difference in potential density) ;  
     708$(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients  
     709are vertically mixed in the same way their temperature and salinity has been mixed. 
     710These two modifications allow the algorithm to perform properly and accurately  
     711with TEOS10 or EOS-80 without having to recompute the expansion coefficients at each  
     712mixing iteration. 
    686713 
    687714% ------------------------------------------------------------------------------------------------------------- 
    … …  
    689716% ------------------------------------------------------------------------------------------------------------- 
    690717\subsection   [Enhanced Vertical Diffusion (\np{ln\_zdfevd})] 
    691          {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 
     718              {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 
    692719\label{ZDF_evd} 
    693720 

  • branches/2015/nemo_v3_6_STABLE/DOC/TexFiles/Chapters/Introduction.tex

    r4661 r6275  
    2424release 8.2, described in \citet{Madec1998}. This model has been used for a wide  
    2525range of applications, both regional or global, as a forced ocean model and as a  
    26 model coupled with the atmosphere. A complete list of references is found on the  
    27 \NEMO web site.  
     26model coupled with the sea-ice and/or the atmosphere.   
    2827 
    2928This manual is organised in as follows. Chapter~\ref{PE} presents the model basics,  
    3029$i.e.$ the equations and their assumptions, the vertical coordinates used, and the  
    3130subgrid scale physics. This part deals with the continuous equations of the model  
    32 (primitive equations, with potential temperature, salinity and an equation of state).  
     31(primitive equations, with temperature, salinity and an equation of seawater).  
    3332The equations are written in a curvilinear coordinate system, with a choice of vertical  
    3433coordinates ($z$ or $s$, with the rescaled height coordinate formulation \textit{z*}, or   
    … …  
    7978space and time variable coefficient \citet{Treguier1997}. The model has vertical harmonic  
    8079viscosity and diffusion with a space and time variable coefficient, with options to compute  
    81 the coefficients with \citet{Blanke1993}, \citet{Large_al_RG94}, \citet{Pacanowski_Philander_JPO81},  
     80the coefficients with \citet{Blanke1993}, \citet{Pacanowski_Philander_JPO81},  
    8281or \citet{Umlauf_Burchard_JMS03} mixing schemes. 
    8382 \vspace{1cm} 
    8483  
    85   
     84%%gm    To be put somewhere else .... 
     85 
    8686\noindent CPP keys and namelists are used for inputs to the code.  \newline 
    8787 
    … …  
    112112 \vspace{1cm} 
    113113 
     114%%gm  end 
    114115 
    115116Model outputs management and specific online diagnostics are described in chapters~\ref{DIA}. 
    … …  
    249250 
    250251 
     252 \vspace{1cm} 
     253$\bullet$ The main modifications from NEMO/OPA v3.4 and  v3.6 are :\\ 
     254\begin{enumerate} 
     255\item ... ;  
     256\end{enumerate} 
     257 
     258 
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