Changeset 11315


Ignore:
Timestamp:
2019-07-19T19:12:23+02:00 (13 months ago)
Author:
djlea
Message:

#2297 Merge in the latest trunk

Location:
NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex
Files:
4 deleted
8 edited
2 copied

Legend:

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  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/NEMO/main/appendices.tex

    r11187 r11315  
    44\subfile{../subfiles/annex_C}             %% Discrete invariants of the eqs. 
    55\subfile{../subfiles/annex_iso}            %% Isoneutral diffusion using triads 
    6 \subfile{../subfiles/annex_D}             %% Coding rules 
    76 
    87%% Not included 
  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/NEMO/main/bibliography.bib

    r11213 r11315  
    23062306} 
    23072307 
     2308@article{         qiao.yuan.ea_OD10, 
     2309  title         = "A three-dimensional surface wave–ocean circulation coupled  
     2310                  model and its initial testing", 
     2311  pages         = "1339--1335", 
     2312  journal       = "Ocean Dynamics", 
     2313  volume        = "60", 
     2314  number        = "5", 
     2315  author        = "F. Qiao and Y. Yuan and T. Ezer and C. Xia and  
     2316                   Y. Yang and X. Lu and Z. Song ", 
     2317  year          = "2010", 
     2318  month         = "oct", 
     2319  publisher     = "Springer-Verlag", 
     2320  issn          = "1616-7341", 
     2321  doi           = "10.1007/s10236-010-0326-y" 
     2322} 
     2323 
    23082324@article{         redi_JPO82, 
    23092325  title         = "Oceanic isopycnal mixing by coordinate rotation", 
  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/NEMO/subfiles/chap_DIA.tex

    r11218 r11315  
    1515%       Old Model Output  
    1616% ================================================================ 
    17 \section{Old model output (default)} 
     17\section{Model output} 
    1818\label{sec:DIA_io_old} 
    1919 
     
    14941494\textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested. 
    14951495In particular, options associated with \np{ln\_dyn\_mxl}, \np{ln\_vor\_trd}, and \np{ln\_tra\_mxl} are not working, 
    1496 and none of the options have been tested with variable volume (\ie \key{vvl} defined). 
     1496and none of the options have been tested with variable volume (\ie \np{ln\_linssh}\forcode{ = .true.}). 
    14971497 
    14981498% ------------------------------------------------------------------------------------------------------------- 
     
    19301930   
    19311931Third, the discretisation of \autoref{eq:steric_Bq} depends on the type of free surface which is considered. 
    1932 In the non linear free surface case, \ie \key{vvl} defined, it is given by 
     1932In the non linear free surface case, \ie \np{ln\_linssh}\forcode{ = .true.}, it is given by 
    19331933 
    19341934\[ 
     
    19691969where $S_o$ and $p_o$ are the initial salinity and pressure, respectively. 
    19701970 
    1971 Both steric and thermosteric sea level are computed in \mdl{diaar5} which needs the \key{diaar5} defined to 
    1972 be called. 
     1971Both steric and thermosteric sea level are computed in \mdl{diaar5}. 
    19731972 
    19741973% ------------------------------------------------------------------------------------------------------------- 
    19751974%       Other Diagnostics 
    19761975% ------------------------------------------------------------------------------------------------------------- 
    1977 \section[Other diagnostics (\texttt{\textbf{key\_diahth}}, \texttt{\textbf{key\_diaar5}})] 
    1978 {Other diagnostics (\protect\key{diahth}, \protect\key{diaar5})} 
     1976\section[Other diagnostics] 
     1977{Other diagnostics} 
    19791978\label{sec:DIA_diag_others} 
    19801979 
     
    19951994- the depth of the thermocline (maximum of the vertical temperature gradient) (\mdl{diahth}) 
    19961995 
    1997 % ----------------------------------------------------------- 
    1998 %     Poleward heat and salt transports 
    1999 % ----------------------------------------------------------- 
    2000  
    2001 \subsection[Poleward heat and salt transports (\textit{diaptr.F90})] 
    2002 {Poleward heat and salt transports (\protect\mdl{diaptr})} 
    2003  
    2004 %------------------------------------------namptr----------------------------------------- 
    2005  
    2006 \nlst{namptr}  
    2007 %----------------------------------------------------------------------------------------- 
    2008  
    2009 The poleward heat and salt transports, their advective and diffusive component, 
    2010 and the meriodional stream function can be computed on-line in \mdl{diaptr} \np{ln\_diaptr} to true 
    2011 (see the \textit{\ngn{namptr} } namelist below). 
    2012 When \np{ln\_subbas}\forcode{ = .true.}, transports and stream function are computed for the Atlantic, Indian, 
    2013 Pacific and Indo-Pacific Oceans (defined north of 30\deg{S}) as well as for the World Ocean. 
    2014 The sub-basin decomposition requires an input file (\ifile{subbasins}) which contains three 2D mask arrays, 
    2015 the Indo-Pacific mask been deduced from the sum of the Indian and Pacific mask (\autoref{fig:mask_subasins}). 
    20161996 
    20171997%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    20342014%       CMIP specific diagnostics  
    20352015% ----------------------------------------------------------- 
    2036 \subsection[CMIP specific diagnostics (\textit{diaar5.F90})] 
     2016\subsection[CMIP specific diagnostics (\textit{diaar5.F90}, \textit{diaptr.F90})] 
    20372017{CMIP specific diagnostics (\protect\mdl{diaar5})} 
    20382018 
    2039 A series of diagnostics has been added in the \mdl{diaar5}. 
    2040 They corresponds to outputs that are required for AR5 simulations (CMIP5) 
     2019A series of diagnostics has been added in the \mdl{diaar5} and \mdl{diaptr}. 
     2020In \mdl{diaar5} they correspond to outputs that are required for AR5 simulations (CMIP5) 
    20412021(see also \autoref{sec:DIA_steric} for one of them). 
    2042 Activating those outputs requires to define the \key{diaar5} CPP key. 
     2022The module \mdl{diaar5} is active when one of the following outputs is required : global total volume (voltot), global mean ssh (sshtot), global total mass (masstot), global mean temperature (temptot), global mean ssh steric (sshsteric), global mean ssh thermosteric (sshthster), global mean salinity (saltot), sea water pressure at sea floor (botpres), dynamic sea surface height (sshdyn). 
     2023 
     2024In \mdl{diaptr} when \np{ln\_diaptr}\forcode{ = .true.}  
     2025(see the \textit{\ngn{namptr} } namelist below) can be computed on-line the poleward heat and salt transports, their advective and diffusive component, and the meriodional stream function . 
     2026When \np{ln\_subbas}\forcode{ = .true.}, transports and stream function are computed for the Atlantic, Indian, 
     2027Pacific and Indo-Pacific Oceans (defined north of 30\deg{S}) as well as for the World Ocean. 
     2028The sub-basin decomposition requires an input file (\ifile{subbasins}) which contains three 2D mask arrays, 
     2029the Indo-Pacific mask been deduced from the sum of the Indian and Pacific mask (\autoref{fig:mask_subasins}). 
     2030 
     2031%------------------------------------------namptr----------------------------------------- 
     2032 
     2033\nlst{namptr}  
     2034%----------------------------------------------------------------------------------------- 
    20432035 
    20442036% ----------------------------------------------------------- 
  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/NEMO/subfiles/chap_DOM.tex

    r11179 r11315  
    1818%     - domclo:  closed sea and lakes.... management of closea sea area : specific to global configuration, both forced and coupled 
    1919 
     20\vfill 
     21\begin{figure}[b] 
     22\subsubsection*{Changes record} 
     23\begin{tabular}{m{0.08\linewidth}||m{0.32\linewidth}|m{0.6\linewidth}} 
     24    Release   & Author(s)     & Modifications \\ 
     25\hline 
     26    {\em 4.0} & {\em Simon M{\"u}ller \& Andrew Coward} & {\em Compatibility changes for v4.0. Major simplication has moved many of the options to external domain configuration tools. For now this information has been retained in an appendix }  \\ 
     27    {\em 3.x} & {\em Sebastien Masson, Gurvan Madec \& Rashid Benshila } & {\em }  \\ 
     28\end{tabular} 
     29\end{figure} 
     30 
    2031\newpage 
    2132 
    2233Having defined the continuous equations in \autoref{chap:PE} and chosen a time discretization \autoref{chap:STP}, 
    23 we need to choose a discretization on a grid, and numerical algorithms. 
     34we need to choose a grid for spatial discretization and related numerical algorithms. 
    2435In the present chapter, we provide a general description of the staggered grid used in \NEMO, 
    25 and other information relevant to the main directory routines as well as the DOM (DOMain) directory. 
     36and other relevant information about the DOM (DOMain) source-code modules . 
    2637 
    2738% ================================================================ 
     
    5566The numerical techniques used to solve the Primitive Equations in this model are based on the traditional, 
    5667centred second-order finite difference approximation. 
    57 Special attention has been given to the homogeneity of the solution in the three space directions. 
     68Special attention has been given to the homogeneity of the solution in the three spatial directions. 
    5869The arrangement of variables is the same in all directions. 
    5970It consists of cells centred on scalar points ($t$, $S$, $p$, $\rho$) with vector points $(u, v, w)$ defined in 
     
    7182Each scale factor is defined as the local analytical value provided by \autoref{eq:scale_factors}. 
    7283As a result, the mesh on which partial derivatives $\pd[]{\lambda}$, $\pd[]{\varphi}$ and 
    73 $\pd[]{z}$ are evaluated in a uniform mesh with a grid size of unity. 
     84$\pd[]{z}$ are evaluated is a uniform mesh with a grid size of unity. 
    7485Discrete partial derivatives are formulated by the traditional, centred second order finite difference approximation 
    7586while the scale factors are chosen equal to their local analytical value. 
     
    7990the continuous properties (see \autoref{apdx:C}). 
    8091A similar, related remark can be made about the domain size: 
    81 when needed, an area, volume, or the total ocean depth must be evaluated as the sum of the relevant scale factors 
     92when needed, an area, volume, or the total ocean depth must be evaluated as the product or sum of the relevant scale factors 
    8293(see \autoref{eq:DOM_bar} in the next section). 
    8394 
     
    8798    \begin{tabular}{|p{46pt}|p{56pt}|p{56pt}|p{56pt}|} 
    8899      \hline 
    89       T  & $i      $ & $j      $ & $k      $ \\ 
     100      t  & $i      $ & $j      $ & $k      $ \\ 
    90101      \hline 
    91102      u  & $i + 1/2$ & $j      $ & $k      $ \\ 
     
    107118      \protect\label{tab:cell} 
    108119      Location of grid-points as a function of integer or integer and a half value of the column, line or level. 
    109       This indexing is only used for the writing of the semi -discrete equation. 
    110       In the code, the indexing uses integer values only and has a reverse direction in the vertical 
     120      This indexing is only used for the writing of the semi -discrete equations. 
     121      In the code, the indexing uses integer values only and is positive downwards in the vertical with $k=1$ at the surface. 
    111122      (see \autoref{subsec:DOM_Num_Index}) 
    112123    } 
    113124  \end{center} 
    114125\end{table} 
     126%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     127 
     128Note that the definition of the scale factors 
     129(\ie as the analytical first derivative of the transformation that 
     130results in $(\lambda,\varphi,z)$ as a function of $(i,j,k)$) 
     131is specific to the \NEMO model \citep{marti.madec.ea_JGR92}. 
     132As an example, a scale factor in the $i$ direction is defined locally at a $t$-point, 
     133whereas many other models on a C grid choose to define such a scale factor as 
     134the distance between the $u$-points on each side of the $t$-point. 
     135Relying on an analytical transformation has two advantages: 
     136firstly, there is no ambiguity in the scale factors appearing in the discrete equations, 
     137since they are first introduced in the continuous equations; 
     138secondly, analytical transformations encourage good practice by the definition of smoothly varying grids 
     139(rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{treguier.dukowicz.ea_JGR96}. 
     140An example of the effect of such a choice is shown in \autoref{fig:zgr_e3}. 
     141%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     142\begin{figure}[!t] 
     143  \begin{center} 
     144    \includegraphics[width=\textwidth]{Fig_zgr_e3} 
     145    \caption{ 
     146      \protect\label{fig:zgr_e3} 
     147      Comparison of (a) traditional definitions of grid-point position and grid-size in the vertical, 
     148      and (b) analytically derived grid-point position and scale factors. 
     149      For both grids here, the same $w$-point depth has been chosen but 
     150      in (a) the $t$-points are set half way between $w$-points while 
     151      in (b) they are defined from an analytical function: 
     152      $z(k) = 5 \, (k - 1/2)^3 - 45 \, (k - 1/2)^2 + 140 \, (k - 1/2) - 150$. 
     153      Note the resulting difference between the value of the grid-size $\Delta_k$ and 
     154      those of the scale factor $e_k$. 
     155    } 
     156  \end{center} 
     157\end{figure} 
    115158%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    116159 
     
    132175Following \autoref{eq:PE_grad} and \autoref{eq:PE_lap}, the gradient of a variable $q$ defined at 
    133176a $t$-point has its three components defined at $u$-, $v$- and $w$-points while 
    134 its Laplacian is defined at $t$-point. 
     177its Laplacian is defined at the $t$-point. 
    135178These operators have the following discrete forms in the curvilinear $s$-coordinates system: 
    136179\[ 
     
    171214\end{equation} 
    172215 
    173 The vertical average over the whole water column denoted by an overbar becomes for a quantity $q$ which 
    174 is a masked field (i.e. equal to zero inside solid area): 
     216The vertical average over the whole water column is denoted by an overbar and is for 
     217a masked field $q$ (\ie a quantity that is equal to zero inside solid areas): 
    175218\begin{equation} 
    176219  \label{eq:DOM_bar} 
     
    178221\end{equation} 
    179222where $H_q$  is the ocean depth, which is the masked sum of the vertical scale factors at $q$ points, 
    180 $k^b$ and $k^o$ are the bottom and surface $k$-indices, and the symbol $k^o$ refers to a summation over 
     223$k^b$ and $k^o$ are the bottom and surface $k$-indices, and the symbol $\sum \limits_k$ refers to a summation over 
    181224all grid points of the same type in the direction indicated by the subscript (here $k$). 
    182225 
     
    193236vector points $(u,v,w)$. 
    194237 
    195 Let $a$ and $b$ be two fields defined on the mesh, with value zero inside continental area. 
    196 Using integration by parts it can be shown that the differencing operators ($\delta_i$, $\delta_j$ and $\delta_k$) 
     238Let $a$ and $b$ be two fields defined on the mesh, with a value of zero inside continental areas. 
     239It can be shown that the differencing operators ($\delta_i$, $\delta_j$ and $\delta_k$) 
    197240are skew-symmetric linear operators, and further that the averaging operators $\overline{\cdots}^{\, i}$, 
    198241$\overline{\cdots}^{\, j}$ and $\overline{\cdots}^{\, k}$) are symmetric linear operators, \ie 
     
    228271%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    229272 
    230 The array representation used in the \fortran code requires an integer indexing while 
    231 the analytical definition of the mesh (see \autoref{subsec:DOM_cell}) is associated with the use of 
    232 integer values for $t$-points and both integer and integer and a half values for all the other points. 
    233 Therefore a specific integer indexing must be defined for points other than $t$-points 
     273The array representation used in the \fortran code requires an integer indexing. 
     274However, the analytical definition of the mesh (see \autoref{subsec:DOM_cell}) is associated with the use of 
     275integer values for $t$-points only while all the other points involve integer and a half values. 
     276Therefore, a specific integer indexing has been defined for points other than $t$-points 
    234277(\ie velocity and vorticity grid-points). 
    235 Furthermore, the direction of the vertical indexing has been changed so that the surface level is at $k = 1$. 
     278Furthermore, the direction of the vertical indexing has been reversed and the surface level set at $k = 1$. 
    236279 
    237280% ----------------------------------- 
     
    253296\label{subsec:DOM_Num_Index_vertical} 
    254297 
    255 In the vertical, the chosen indexing requires special attention since the $k$-axis is re-orientated downward in 
    256 the \fortran code compared to the indexing used in the semi -discrete equations and 
     298In the vertical, the chosen indexing requires special attention since the direction of the $k$-axis in 
     299the \fortran code is the reverse of that used in the semi -discrete equations and 
    257300given in \autoref{subsec:DOM_cell}. 
    258 The sea surface corresponds to the $w$-level $k = 1$ which is the same index as $t$-level just below 
     301The sea surface corresponds to the $w$-level $k = 1$, which is the same index as the $t$-level just below 
    259302(\autoref{fig:index_vert}). 
    260 The last $w$-level ($k = jpk$) either corresponds to the ocean floor or is inside the bathymetry while 
    261 the last $t$-level is always inside the bathymetry (\autoref{fig:index_vert}). 
    262 Note that for an increasing $k$ index, a $w$-point and the $t$-point just below have the same $k$ index, 
    263 in opposition to what is done in the horizontal plane where 
    264 it is the $t$-point and the nearest velocity points in the direction of the horizontal axis that 
    265 have the same $i$ or $j$ index 
     303The last $w$-level ($k = jpk$) either corresponds to or is below the ocean floor while 
     304the last $t$-level is always outside the ocean domain (\autoref{fig:index_vert}). 
     305Note that a $w$-point and the directly underlaying $t$-point have a common $k$ index (\ie $t$-points and their 
     306nearest $w$-point neighbour in negative index direction), in contrast to the indexing on the horizontal plane where 
     307the $t$-point has the same index as the nearest velocity points in the positive direction of the respective horizontal axis index 
    266308(compare the dashed area in \autoref{fig:index_hor} and \autoref{fig:index_vert}). 
    267309Since the scale factors are chosen to be strictly positive, 
    268 a \textit{minus sign} appears in the \fortran code \textit{before all the vertical derivatives} of 
    269 the discrete equations given in this documentation. 
     310a \textit{minus sign} is included in the \fortran implementations of \textit{all the vertical derivatives} of 
     311the discrete equations given in this manual in order to accommodate the opposing vertical index directions in implementation and documentation. 
    270312 
    271313%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    276318      \protect\label{fig:index_vert} 
    277319      Vertical integer indexing used in the \fortran code. 
    278       Note that the $k$-axis is orientated downward. 
    279       The dashed area indicates the cell in which variables contained in arrays have the same $k$-index. 
     320      Note that the $k$-axis is oriented downward. 
     321      The dashed area indicates the cell in which variables contained in arrays have a common $k$-index. 
    280322    } 
    281323  \end{center} 
     
    283325%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    284326 
     327% ------------------------------------------------------------------------------------------------------------- 
     328%        Domain configuration 
     329% ------------------------------------------------------------------------------------------------------------- 
     330\section{Spatial domain configuration} 
     331\label{subsec:DOM_config} 
     332 
     333\nlst{namcfg} 
     334 
     335Two typical methods are available to specify the spatial domain 
     336configuration; they can be selected using parameter \np{ln\_read\_cfg} 
     337parameter in namelist \ngn{namcfg}.  
     338 
     339If \np{ln\_read\_cfg} is set to \forcode{.true.}, the domain-specific parameters 
     340and fields are read from a netCDF input file, whose name (without its .nc 
     341suffix) can be specified as the value of the \np{cn\_domcfg} parameter in 
     342namelist \ngn{namcfg}. 
     343 
     344If \np{ln\_read\_cfg} is set to \forcode{.false.}, the domain-specific 
     345parameters and fields can be provided (\eg analytically computed) by subroutines 
     346\mdl{usrdef\_hgr} and \mdl{usrdef\_zgr}. These subroutines can be supplied in 
     347the \path{MY_SRC} directory of the configuration, and default versions that 
     348configure the spatial domain for the GYRE reference configuration are present in 
     349the \path{src/OCE/USR} directory. 
     350 
     351In version 4.0 there are no longer any options for reading complex bathmetries and  
     352performing a vertical discretization at run-time. Whilst it is occasionally convenient 
     353to have a common bathymetry file and, for example, to run similar models with and 
     354without partial bottom boxes and/or sigma-coordinates, supporting such choices leads to 
     355overly complex code. Worse still is the difficulty of ensuring the model configurations  
     356intended to be identical are indeed so when the model domain itself can be altered by runtime 
     357selections. The code previously used to perform vertical discretization has be incorporated  
     358into an external tool (\path{tools/DOMAINcfg}) which is briefly described in appendix F. 
     359 
     360The next subsections summarise the parameter and fields related to the 
     361configuration of the whole model domain. These represent the minimum information 
     362that must be provided either via the \np{cn\_domcfg} file or set by code 
     363inserted into user-supplied versions of the \mdl{usrdef\_*} subroutines. The 
     364requirements are presented in three sections: the domain size 
     365(\autoref{subsec:DOM_size}), the horizontal mesh 
     366(\autoref{subsec:DOM_hgr}), and the vertical grid 
     367(\autoref{subsec:DOM_zgr}). 
     368 
    285369% ----------------------------------- 
    286370%        Domain Size 
    287371% ----------------------------------- 
    288 \subsubsection{Domain size} 
     372\subsection{Domain size} 
    289373\label{subsec:DOM_size} 
    290374 
    291 The total size of the computational domain is set by the parameters \np{jpiglo}, 
    292 \np{jpjglo} and \np{jpkglo} in the $i$, $j$ and $k$ directions respectively. 
    293 Parameters $jpi$ and $jpj$ refer to the size of each processor subdomain when 
    294 the code is run in parallel using domain decomposition (\key{mpp\_mpi} defined, 
    295 see \autoref{sec:LBC_mpp}). 
    296  
    297 % ================================================================ 
    298 % Domain: List of fields needed 
    299 % ================================================================ 
    300 \section{Needed fields} 
    301 \label{sec:DOM_fields} 
    302 The ocean mesh (\ie the position of all the scalar and vector points) is defined by the transformation that 
    303 gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$. 
    304 The grid-points are located at integer or integer and a half values of as indicated in \autoref{tab:cell}. 
    305 The associated scale factors are defined using the analytical first derivative of the transformation 
    306 \autoref{eq:scale_factors}. 
    307 Necessary fields for configuration definition are: 
    308  
    309 \begin{itemize} 
    310 \item 
    311   Geographic position: 
    312   longitude with \texttt{glamt}, \texttt{glamu}, \texttt{glamv}, \texttt{glamf} and 
    313   latitude  with \texttt{gphit}, \texttt{gphiu}, \texttt{gphiv}, \texttt{gphif} 
    314   (all respectively at T, U, V and F point) 
    315 \item 
    316   Coriolis parameter (if domain not on the sphere): \texttt{ff\_f} and \texttt{ff\_t} 
    317   (at T and F point) 
    318 \item 
    319   Scale factors: 
    320   \texttt{e1t}, \texttt{e1u}, \texttt{e1v} and \texttt{e1f} (on i direction), 
    321   \texttt{e2t}, \texttt{e2u}, \texttt{e2v} and \texttt{e2f} (on j direction) and 
    322   \texttt{ie1e2u\_v}, \texttt{e1e2u}, \texttt{e1e2v}. \\ 
    323   \texttt{e1e2u}, \texttt{e1e2v} are u and v surfaces (if gridsize reduction in some straits),  
    324   \texttt{ie1e2u\_v} is to flag set u and v surfaces are neither read nor computed. 
    325 \end{itemize} 
    326   
    327 These fields can be read in an domain input file which name is setted in \np{cn\_domcfg} parameter specified in 
    328 \ngn{namcfg}. 
    329  
    330 \nlst{namcfg} 
    331  
    332 Or they can be defined in an analytical way in \path{MY_SRC} directory of the configuration. 
    333 For Reference Configurations of NEMO input domain files are supplied by NEMO System Team. 
    334 For analytical definition of input fields two routines are supplied: \mdl{usrdef\_hgr} and \mdl{usrdef\_zgr}. 
    335 They are an example of GYRE configuration parameters, and they are available in \path{src/OCE/USR} directory, 
    336 they provide the horizontal and vertical mesh. 
    337 % ------------------------------------------------------------------------------------------------------------- 
    338 %        Needed fields  
    339 % ------------------------------------------------------------------------------------------------------------- 
    340 %\subsection{List of needed fields to build DOMAIN} 
    341 %\label{subsec:DOM_fields_list} 
    342  
     375The total size of the computational domain is set by the parameters 
     376\np{jpiglo}, \np{jpjglo} and \np{jpkglo} for the $i$, $j$ and $k$ 
     377directions, respectively. Note, that the variables \forcode{jpi} and \forcode{jpj} 
     378refer to the size of each processor subdomain when the code is run in 
     379parallel using domain decomposition (\key{mpp\_mpi} defined, see 
     380\autoref{sec:LBC_mpp}). 
     381 
     382The name of the configuration is set through parameter \np{cn\_cfg}, 
     383and the nominal resolution through parameter \np{nn\_cfg} (unless in 
     384the input file both of variables \forcode{ORCA} and \forcode{ORCA_index} 
     385are present, in which case \np{cn\_cfg} and \np{nn\_cfg} are set from these 
     386values accordingly). 
     387 
     388The global lateral boundary condition type is selected from 8 options 
     389using parameter \np{jperio}. See \autoref{sec:LBC_jperio} for 
     390details on the available options and the corresponding values for 
     391\np{jperio}. 
    343392 
    344393% ================================================================ 
    345394% Domain: Horizontal Grid (mesh)  
    346395% ================================================================ 
    347 \section[Horizontal grid mesh (\textit{domhgr.F90})] 
    348 {Horizontal grid mesh (\protect\mdl{domhgr})} 
    349 \label{sec:DOM_hgr} 
    350  
    351 % ------------------------------------------------------------------------------------------------------------- 
    352 %        Coordinates and scale factors  
    353 % ------------------------------------------------------------------------------------------------------------- 
    354 \subsection{Coordinates and scale factors} 
    355 \label{subsec:DOM_hgr_coord_e} 
    356  
    357 The ocean mesh (\ie the position of all the scalar and vector points) is defined by 
    358 the transformation that gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$. 
    359 The grid-points are located at integer or integer and a half values of as indicated in \autoref{tab:cell}. 
    360 The associated scale factors are defined using the analytical first derivative of the transformation 
    361 \autoref{eq:scale_factors}. 
    362 These definitions are done in two modules, \mdl{domhgr} and \mdl{domzgr}, 
    363 which provide the horizontal and vertical meshes, respectively. 
    364 This section deals with the horizontal mesh parameters. 
    365  
    366 In a horizontal plane, the location of all the model grid points is defined from 
    367 the analytical expressions of the longitude $\lambda$ and latitude $\varphi$ as a function of $(i,j)$. 
    368 The horizontal scale factors are calculated using \autoref{eq:scale_factors}. 
    369 For example, when the longitude and latitude are function of a single value 
    370 ($i$ and $j$, respectively) (geographical configuration of the mesh), 
    371 the horizontal mesh definition reduces to define the wanted $\lambda(i)$, $\varphi(j)$, 
    372 and their derivatives $\lambda'(i) \ \varphi'(j)$ in the \mdl{domhgr} module. 
    373 The model computes the grid-point positions and scale factors in the horizontal plane as follows: 
    374 \begin{align*} 
    375    \lambda_t &\equiv \text{glamt} =      \lambda (i      ) 
    376   &\varphi_t &\equiv \text{gphit} =      \varphi (j      ) \\ 
    377    \lambda_u &\equiv \text{glamu} =      \lambda (i + 1/2) 
    378   &\varphi_u &\equiv \text{gphiu} =      \varphi (j      ) \\ 
    379    \lambda_v &\equiv \text{glamv} =      \lambda (i      ) 
    380   &\varphi_v &\equiv \text{gphiv} =      \varphi (j + 1/2) \\ 
    381    \lambda_f &\equiv \text{glamf} =      \lambda (i + 1/2) 
    382   &\varphi_f &\equiv \text{gphif} =      \varphi (j + 1/2) \\ 
    383    e_{1t}    &\equiv \text{e1t}   = r_a |\lambda'(i      ) \; \cos\varphi(j      ) | 
    384   &e_{2t}    &\equiv \text{e2t}   = r_a |\varphi'(j      )                         | \\ 
    385    e_{1u}    &\equiv \text{e1t}   = r_a |\lambda'(i + 1/2) \; \cos\varphi(j      ) | 
    386   &e_{2u}    &\equiv \text{e2t}   = r_a |\varphi'(j      )                         | \\ 
    387    e_{1v}    &\equiv \text{e1t}   = r_a |\lambda'(i      ) \; \cos\varphi(j + 1/2) | 
    388   &e_{2v}    &\equiv \text{e2t}   = r_a |\varphi'(j + 1/2)                         | \\ 
    389    e_{1f}    &\equiv \text{e1t}   = r_a |\lambda'(i + 1/2) \; \cos\varphi(j + 1/2) | 
    390   &e_{2f}    &\equiv \text{e2t}   = r_a |\varphi'(j + 1/2)                         | 
    391 \end{align*} 
    392 where the last letter of each computational name indicates the grid point considered and 
    393 $r_a$ is the earth radius (defined in \mdl{phycst} along with all universal constants). 
    394 Note that the horizontal position of and scale factors at $w$-points are exactly equal to those of $t$-points, 
    395 thus no specific arrays are defined at $w$-points. 
    396  
    397 Note that the definition of the scale factors 
    398 (\ie as the analytical first derivative of the transformation that 
    399 gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$) 
    400 is specific to the \NEMO model \citep{marti.madec.ea_JGR92}. 
    401 As an example, $e_{1t}$ is defined locally at a $t$-point, 
    402 whereas many other models on a C grid choose to define such a scale factor as 
    403 the distance between the $U$-points on each side of the $t$-point. 
    404 Relying on an analytical transformation has two advantages: 
    405 firstly, there is no ambiguity in the scale factors appearing in the discrete equations, 
    406 since they are first introduced in the continuous equations; 
    407 secondly, analytical transformations encourage good practice by the definition of smoothly varying grids 
    408 (rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{treguier.dukowicz.ea_JGR96}. 
    409 An example of the effect of such a choice is shown in \autoref{fig:zgr_e3}. 
    410 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    411 \begin{figure}[!t] 
    412   \begin{center} 
    413     \includegraphics[width=\textwidth]{Fig_zgr_e3} 
    414     \caption{ 
    415       \protect\label{fig:zgr_e3} 
    416       Comparison of (a) traditional definitions of grid-point position and grid-size in the vertical, 
    417       and (b) analytically derived grid-point position and scale factors. 
    418       For both grids here, the same $w$-point depth has been chosen but 
    419       in (a) the $t$-points are set half way between $w$-points while 
    420       in (b) they are defined from an analytical function: 
    421       $z(k) = 5 \, (k - 1/2)^3 - 45 \, (k - 1/2)^2 + 140 \, (k - 1/2) - 150$. 
    422       Note the resulting difference between the value of the grid-size $\Delta_k$ and 
    423       those of the scale factor $e_k$. 
    424     } 
    425   \end{center} 
    426 \end{figure} 
    427 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    428  
    429 % ------------------------------------------------------------------------------------------------------------- 
    430 %        Choice of horizontal grid 
    431 % ------------------------------------------------------------------------------------------------------------- 
    432 \subsection{Choice of horizontal grid} 
    433 \label{subsec:DOM_hgr_msh_choice} 
    434  
    435 % ------------------------------------------------------------------------------------------------------------- 
    436 %        Grid files 
    437 % ------------------------------------------------------------------------------------------------------------- 
    438 \subsection{Output grid files} 
    439 \label{subsec:DOM_hgr_files} 
    440  
    441 All the arrays relating to a particular ocean model configuration (grid-point position, scale factors, masks) 
    442 can be saved in files if \np{nn\_msh} $\not = 0$ (namelist variable in \ngn{namdom}). 
    443 This can be particularly useful for plots and off-line diagnostics. 
    444 In some cases, the user may choose to make a local modification of a scale factor in the code. 
    445 This is the case in global configurations when restricting the width of a specific strait 
    446 (usually a one-grid-point strait that happens to be too wide due to insufficient model resolution). 
    447 An example is Gibraltar Strait in the ORCA2 configuration. 
    448 When such modifications are done, 
    449 the output grid written when \np{nn\_msh} $\not = 0$ is no more equal to the input grid. 
     396\subsection{Horizontal grid mesh (\protect\mdl{domhgr})} 
     397\label{subsec:DOM_hgr} 
     398 
     399% ================================================================ 
     400% Domain: List of hgr-related fields needed 
     401% ================================================================ 
     402\subsubsection{Required fields} 
     403\label{sec:DOM_hgr_fields} 
     404The explicit specification of a range of mesh-related fields are required for the definition of a configuration. These include: 
     405 
     406\begin{Verbatim}[fontsize=\tiny] 
     407int    jpiglo, jpjglo, jpkglo            /* global domain sizes                                          */ 
     408int    jperio                            /* lateral global domain b.c.                                   */ 
     409double glamt, glamu, glamv, glamf        /* geographic longitude (t,u,v and f points respectively)       */ 
     410double gphit, gphiu, gphiv, gphif        /* geographic latitude                                          */ 
     411double e1t, e1u, e1v, e1f                /* horizontal scale factors                                     */ 
     412double e2t, e2u, e2v, e2f                /* horizontal scale factors                                     */ 
     413\end{Verbatim} 
     414 
     415The values of the geographic longitude and latitude arrays at indices $i,j$ correspond to the analytical expressions of the longitude $\lambda$ and latitude $\varphi$ as a function of $(i,j)$, evaluated at the values as specified in Table \autoref{tab:cell} for the respective grid-point position. The calculation of the values of the horizontal scale factor arrays in general additionally involves partial derivatives of $\lambda$ and $\varphi$ with respect to $i$ and $j$, evaluated for the same arguments as $\lambda$ and $\varphi$. 
     416 
     417\subsubsection{Optional fields} 
     418\begin{Verbatim}[fontsize=\tiny] 
     419                                         /* Optional:                                                    */ 
     420int    ORCA, ORCA_index                  /* configuration name, configuration resolution                 */ 
     421double e1e2u, e1e2v                      /* U and V surfaces (if grid size reduction in some straits)    */ 
     422double ff_f, ff_t                        /* Coriolis parameter (if not on the sphere)                    */ 
     423\end{Verbatim} 
     424 
     425NEMO can support the local reduction of key strait widths by altering individual values of 
     426e1u or e1v at the appropriate locations. This is particularly useful for locations such as 
     427Gibraltar or Indonesian Throughflow pinch-points (see \autoref{sec:MISC_strait} for 
     428illustrated examples). The key is to reduce the faces of $T$-cell (\ie change the value of 
     429the horizontal scale factors at $u$- or $v$-point) but not the volume of the cells. Doing 
     430otherwise can lead to numerical instability issues.  In normal operation the surface areas 
     431are computed from $\texttt{e1u} * \texttt{e2u}$ and $\texttt{e1v} * \texttt{e2v}$ but in 
     432cases where a gridsize reduction is required, the unaltered surface areas at $u$ and $v$ 
     433grid points (\texttt{e1e2u} and \texttt{e1e2v}, respectively) must be read or pre-computed 
     434in \mdl{usrdef\_hgr}. If these arrays are present in the \np{cn\_domcfg} file they are 
     435read and the internal computation is suppressed. Versions of \mdl{usrdef\_hgr} which set 
     436their own values of \texttt{e1e2u} and \texttt{e1e2v} should set the surface-area 
     437computation flag: \texttt{ie1e2u\_v} to a non-zero value to suppress their re-computation. 
     438 
     439\smallskip 
     440Similar logic applies to the other optional fields: \texttt{ff\_f} and \texttt{ff\_t} 
     441which can be used to provide the Coriolis parameter at F- and T-points respectively if the 
     442mesh is not on a sphere. If present these fields will be read and used and the normal 
     443calculation ($2*\Omega*\sin(\varphi)$) suppressed. Versions of \mdl{usrdef\_hgr} which set 
     444their own values of \texttt{ff\_f} and \texttt{ff\_t} should set the Coriolis computation 
     445flag: \texttt{iff} to a non-zero value to suppress their re-computation. 
     446 
     447Note that longitudes, latitudes, and scale factors at $w$ points are exactly 
     448equal to those of $t$ points, thus no specific arrays are defined at $w$ points. 
     449 
    450450 
    451451% ================================================================ 
    452452% Domain: Vertical Grid (domzgr) 
    453453% ================================================================ 
    454 \section[Vertical grid (\textit{domzgr.F90})] 
     454\subsection[Vertical grid (\textit{domzgr.F90})] 
    455455{Vertical grid (\protect\mdl{domzgr})} 
    456 \label{sec:DOM_zgr} 
    457 %-----------------------------------------nam_zgr & namdom------------------------------------------- 
    458 % 
    459 %\nlst{namzgr}  
    460  
    461 \nlst{namdom}  
     456\label{subsec:DOM_zgr} 
     457%-----------------------------------------namdom------------------------------------------- 
     458\nlst{namdom} 
    462459%------------------------------------------------------------------------------------------------------------- 
    463460 
    464 Variables are defined through the \ngn{namzgr} and \ngn{namdom} namelists. 
    465461In the vertical, the model mesh is determined by four things:  
    466 (1) the bathymetry given in meters;  
    467 (2) the number of levels of the model (\jp{jpk});  
    468 (3) the analytical transformation $z(i,j,k)$ and the vertical scale factors (derivatives of the transformation); and 
    469 (4) the masking system, \ie the number of wet model levels at each  
    470 $(i,j)$ column of points. 
     462\begin{enumerate} 
     463  \item the bathymetry given in meters;  
     464  \item the number of levels of the model (\jp{jpk});  
     465  \item the analytical transformation $z(i,j,k)$ and the vertical scale factors (derivatives of the transformation); and 
     466  \item the masking system, \ie the number of wet model levels at each  
     467$(i,j)$ location of the horizontal grid. 
     468\end{enumerate} 
    471469 
    472470%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    489487%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    490488 
    491 The choice of a vertical coordinate, even if it is made through \ngn{namzgr} namelist parameters,  
    492 must be done once of all at the beginning of an experiment. 
    493 It is not intended as an option which can be enabled or disabled in the middle of an experiment. 
    494 Three main choices are offered (\autoref{fig:z_zps_s_sps}): 
    495 $z$-coordinate with full step bathymetry (\np{ln\_zco}\forcode{ = .true.}), 
    496 $z$-coordinate with partial step bathymetry (\np{ln\_zps}\forcode{ = .true.}), 
    497 or generalized, $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}). 
    498 Hybridation of the three main coordinates are available: 
    499 $s-z$ or $s-zps$ coordinate (\autoref{fig:z_zps_s_sps} and \autoref{fig:z_zps_s_sps}). 
    500 By default a non-linear free surface is used: the coordinate follow the time-variation of the free surface so that 
    501 the transformation is time dependent: $z(i,j,k,t)$ (\autoref{fig:z_zps_s_sps}). 
    502 When a linear free surface is assumed (\np{ln\_linssh}\forcode{ = .true.}), 
    503 the vertical coordinate are fixed in time, but the seawater can move up and down across the $z_0$ surface 
    504 (in other words, the top of the ocean in not a rigid-lid). 
    505 The last choice in terms of vertical coordinate concerns the presence (or not) in 
    506 the model domain of ocean cavities beneath ice shelves. 
    507 Setting \np{ln\_isfcav} to true allows to manage ocean cavities, otherwise they are filled in. 
    508 This option is currently only available in $z$- or $zps$-coordinate, 
    509 and partial step are also applied at the ocean/ice shelf interface. 
    510  
    511 Contrary to the horizontal grid, the vertical grid is computed in the code and no provision is made for 
    512 reading it from a file. 
    513 The only input file is the bathymetry (in meters) (\ifile{bathy\_meter}) 
    514 \footnote{ 
    515   N.B. in full step $z$-coordinate, a \ifile{bathy\_level} file can replace the \ifile{bathy\_meter} file, 
    516   so that the computation of the number of wet ocean point in each water column is by-passed}. 
    517 If \np{ln\_isfcav}\forcode{ = .true.}, an extra file input file (\ifile{isf\_draft\_meter}) describing 
    518 the ice shelf draft (in meters) is needed. 
    519  
    520 After reading the bathymetry, the algorithm for vertical grid definition differs between the different options: 
    521 \begin{description} 
    522 \item[\textit{zco}] 
    523   set a reference coordinate transformation $z_0(k)$, and set $z(i,j,k,t) = z_0(k)$. 
    524 \item[\textit{zps}] 
    525   set a reference coordinate transformation $z_0(k)$, and calculate the thickness of the deepest level at 
    526   each $(i,j)$ point using the bathymetry, to obtain the final three-dimensional depth and scale factor arrays. 
    527 \item[\textit{sco}] 
    528   smooth the bathymetry to fulfill the hydrostatic consistency criteria and 
    529   set the three-dimensional transformation. 
    530 \item[\textit{s-z} and \textit{s-zps}] 
    531   smooth the bathymetry to fulfill the hydrostatic consistency criteria and 
    532   set the three-dimensional transformation $z(i,j,k)$, 
    533   and possibly introduce masking of extra land points to better fit the original bathymetry file. 
    534 \end{description} 
    535 %%% 
    536 \gmcomment{   add the description of the smoothing:  envelop topography...} 
    537 %%% 
    538  
    539 Unless a linear free surface is used (\np{ln\_linssh}\forcode{ = .false.}), 
    540 the arrays describing the grid point depths and vertical scale factors are three set of 
    541 three dimensional arrays $(i,j,k)$ defined at \textit{before}, \textit{now} and \textit{after} time step. 
    542 The time at which they are defined is indicated by a suffix: $\_b$, $\_n$, or $\_a$, respectively. 
    543 They are updated at each model time step using a fixed reference coordinate system which 
    544 computer names have a $\_0$ suffix. 
    545 When the linear free surface option is used (\np{ln\_linssh}\forcode{ = .true.}), \textit{before}, 
    546 \textit{now} and \textit{after} arrays are simply set one for all to their reference counterpart. 
    547  
    548 % ------------------------------------------------------------------------------------------------------------- 
    549 %        Meter Bathymetry 
    550 % ------------------------------------------------------------------------------------------------------------- 
    551 \subsection{Meter bathymetry} 
    552 \label{subsec:DOM_bathy} 
    553  
    554 Three options are possible for defining the bathymetry, according to the namelist variable \np{nn\_bathy} 
    555 (found in \ngn{namdom} namelist):  
    556 \begin{description} 
    557 \item[\np{nn\_bathy}\forcode{ = 0}]: 
    558   a flat-bottom domain is defined. 
    559   The total depth $z_w (jpk)$ is given by the coordinate transformation. 
    560   The domain can either be a closed basin or a periodic channel depending on the parameter \np{jperio}. 
    561 \item[\np{nn\_bathy}\forcode{ = -1}]: 
    562   a domain with a bump of topography one third of the domain width at the central latitude. 
    563   This is meant for the "EEL-R5" configuration, a periodic or open boundary channel with a seamount. 
    564 \item[\np{nn\_bathy}\forcode{ = 1}]: 
    565   read a bathymetry and ice shelf draft (if needed). 
    566   The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) at 
    567   each grid point of the model grid. 
    568   The bathymetry is usually built by interpolating a standard bathymetry product (\eg ETOPO2) onto 
    569   the horizontal ocean mesh. 
    570   Defining the bathymetry also defines the coastline: where the bathymetry is zero, 
    571   no model levels are defined (all levels are masked). 
    572  
    573   The \ifile{isfdraft\_meter} file (Netcdf format) provides the ice shelf draft (positive, in meters) at 
    574   each grid point of the model grid. 
    575   This file is only needed if \np{ln\_isfcav}\forcode{ = .true.}. 
    576   Defining the ice shelf draft will also define the ice shelf edge and the grounding line position. 
    577 \end{description} 
    578  
    579 When a global ocean is coupled to an atmospheric model it is better to represent all large water bodies 
    580 (\eg great lakes, Caspian sea...) even if the model resolution does not allow their communication with 
    581 the rest of the ocean. 
    582 This is unnecessary when the ocean is forced by fixed atmospheric conditions, 
    583 so these seas can be removed from the ocean domain. 
    584 The user has the option to set the bathymetry in closed seas to zero (see \autoref{sec:MISC_closea}), 
    585 but the code has to be adapted to the user's configuration. 
    586  
    587 % ------------------------------------------------------------------------------------------------------------- 
    588 %        z-coordinate  and reference coordinate transformation 
    589 % ------------------------------------------------------------------------------------------------------------- 
    590 \subsection[$Z$-coordinate (\forcode{ln_zco = .true.}) and ref. coordinate] 
    591 {$Z$-coordinate (\protect\np{ln\_zco}\forcode{ = .true.}) and reference coordinate} 
    592 \label{subsec:DOM_zco} 
    593  
    594 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    595 \begin{figure}[!tb] 
    596   \begin{center} 
    597     \includegraphics[width=\textwidth]{Fig_zgr} 
    598     \caption{ 
    599       \protect\label{fig:zgr} 
    600       Default vertical mesh for ORCA2: 30 ocean levels (L30). 
    601       Vertical level functions for (a) T-point depth and (b) the associated scale factor as computed from 
    602       \autoref{eq:DOM_zgr_ana_1} using \autoref{eq:DOM_zgr_coef} in $z$-coordinate. 
    603     } 
    604   \end{center} 
    605 \end{figure} 
    606 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    607  
    608 The reference coordinate transformation $z_0(k)$ defines the arrays $gdept_0$ and $gdepw_0$ for $t$- and $w$-points, 
    609 respectively. 
    610 As indicated on \autoref{fig:index_vert} \jp{jpk} is the number of $w$-levels. 
    611 $gdepw_0(1)$ is the ocean surface. 
    612 There are at most \jp{jpk}-1 $t$-points inside the ocean, 
    613 the additional $t$-point at $jk = jpk$ is below the sea floor and is not used. 
    614 The vertical location of $w$- and $t$-levels is defined from the analytic expression of the depth $z_0(k)$ whose 
    615 analytical derivative with respect to $k$ provides the vertical scale factors. 
    616 The user must provide the analytical expression of both $z_0$ and its first derivative with respect to $k$. 
    617 This is done in routine \mdl{domzgr} through statement functions, 
    618 using parameters provided in the \ngn{namcfg} namelist. 
    619  
    620 It is possible to define a simple regular vertical grid by giving zero stretching (\np{ppacr}\forcode{ = 0}). 
    621 In that case, the parameters \jp{jpk} (number of $w$-levels) and 
    622 \np{pphmax} (total ocean depth in meters) fully define the grid. 
    623  
    624 For climate-related studies it is often desirable to concentrate the vertical resolution near the ocean surface. 
    625 The following function is proposed as a standard for a $z$-coordinate (with either full or partial steps):  
    626 \begin{gather} 
    627   \label{eq:DOM_zgr_ana_1} 
    628     z_0  (k) = h_{sur} - h_0 \; k - \; h_1 \; \log  \big[ \cosh ((k - h_{th}) / h_{cr}) \big] \\ 
    629     e_3^0(k) = \lt|    - h_0      -    h_1 \; \tanh \big[        (k - h_{th}) / h_{cr}  \big] \rt| 
    630 \end{gather} 
    631 where $k = 1$ to \jp{jpk} for $w$-levels and $k = 1$ to $k = 1$ for $T-$levels. 
    632 Such an expression allows us to define a nearly uniform vertical location of levels at the ocean top and bottom with 
    633 a smooth hyperbolic tangent transition in between (\autoref{fig:zgr}). 
    634  
    635 If the ice shelf cavities are opened (\np{ln\_isfcav}\forcode{ = .true.}), the definition of $z_0$ is the same. 
    636 However, definition of $e_3^0$ at $t$- and $w$-points is respectively changed to: 
    637 \begin{equation} 
    638   \label{eq:DOM_zgr_ana_2} 
    639   \begin{split} 
    640     e_3^T(k) &= z_W (k + 1) - z_W (k    ) \\ 
    641     e_3^W(k) &= z_T (k    ) - z_T (k - 1) 
    642   \end{split} 
    643 \end{equation} 
    644 This formulation decrease the self-generated circulation into the ice shelf cavity  
    645 (which can, in extreme case, leads to blow up).\\ 
    646   
    647 The most used vertical grid for ORCA2 has $10~m$ ($500~m$) resolution in the surface (bottom) layers and 
    648 a depth which varies from 0 at the sea surface to a minimum of $-5000~m$. 
    649 This leads to the following conditions: 
    650 \begin{equation} 
    651   \label{eq:DOM_zgr_coef} 
    652   \begin{array}{ll} 
    653     e_3 (1   + 1/2) =  10. & z(1  ) =     0. \\ 
    654     e_3 (jpk - 1/2) = 500. & z(jpk) = -5000. 
    655   \end{array} 
    656 \end{equation} 
    657  
    658 With the choice of the stretching $h_{cr} = 3$ and the number of levels \jp{jpk}~$= 31$, 
    659 the four coefficients $h_{sur}$, $h_0$, $h_1$, and $h_{th}$ in 
    660 \autoref{eq:DOM_zgr_ana_2} have been determined such that 
    661 \autoref{eq:DOM_zgr_coef} is satisfied, through an optimisation procedure using a bisection method. 
    662 For the first standard ORCA2 vertical grid this led to the following values: 
    663 $h_{sur} = 4762.96$, $h_0 = 255.58, h_1 = 245.5813$, and $h_{th} = 21.43336$. 
    664 The resulting depths and scale factors as a function of the model levels are shown in 
    665 \autoref{fig:zgr} and given in \autoref{tab:orca_zgr}. 
    666 Those values correspond to the parameters \np{ppsur}, \np{ppa0}, \np{ppa1}, \np{ppkth} in \ngn{namcfg} namelist. 
    667  
    668 Rather than entering parameters $h_{sur}$, $h_0$, and $h_1$ directly, it is possible to recalculate them. 
    669 In that case the user sets \np{ppsur}~$=$~\np{ppa0}~$=$~\np{ppa1}~$= 999999$., 
    670 in \ngn{namcfg} namelist, and specifies instead the four following parameters: 
     489The choice of a vertical coordinate is made when setting up the configuration; 
     490it is not intended to be an option which can be changed in the middle of an 
     491experiment. The one exception to this statement being the choice of linear or 
     492non-linear free surface. In v4.0 the linear free surface option is implemented 
     493as a special case of the non-linear free surface. This is computationally 
     494wasteful since it uses the structures for time-varying 3D metrics for fields 
     495that (in the linear free surface case) are fixed. However, the linear 
     496free-surface is rarely used and implementing it this way means a single configuration 
     497file can support both options. 
     498 
     499By default a non-linear free surface is used (\np{ln\_linssh} set to \forcode{ = 
     500.false.} in \ngn{namdom}): the coordinate follow the time-variation of the free 
     501surface so that the transformation is time dependent: $z(i,j,k,t)$ 
     502(\eg \autoref{fig:z_zps_s_sps}f).  When a linear free surface is assumed 
     503(\np{ln\_linssh} set to \forcode{ = .true.} in \ngn{namdom}), the vertical 
     504coordinates are fixed in time, but the seawater can move up and down across the 
     505$z_0$ surface (in other words, the top of the ocean in not a rigid lid). 
     506 
     507Note that settings: \np{ln\_zco}, \np{ln\_zps}, \np{ln\_sco} and \np{ln\_isfcav} mentioned 
     508in the following sections appear to be namelist options but they are no longer truly 
     509namelist options for NEMO. Their value is written to and read from the domain configuration file 
     510and they should be treated as fixed parameters for a particular configuration. They are 
     511namelist options for the \forcode{DOMAINcfg} tool that can be used to build the 
     512configuration file and serve both to provide a record of the choices made whilst building the 
     513configuration and to trigger appropriate code blocks within NEMO. 
     514These values should not be altered in the \np{cn\_domcfg} file. 
     515 
     516\medskip 
     517The decision on these choices must be made when the \np{cn\_domcfg} file is constructed. 
     518Three main choices are offered (\autoref{fig:z_zps_s_sps}a-c): 
     519 
    671520\begin{itemize} 
    672 \item 
    673   \np{ppacr}~$= h_{cr}$: stretching factor (nondimensional). 
    674   The larger \np{ppacr}, the smaller the stretching. 
    675   Values from $3$ to $10$ are usual. 
    676 \item 
    677   \np{ppkth}~$= h_{th}$: is approximately the model level at which maximum stretching occurs 
    678   (nondimensional, usually of order 1/2 or 2/3 of \jp{jpk}) 
    679 \item 
    680   \np{ppdzmin}: minimum thickness for the top layer (in meters). 
    681 \item 
    682   \np{pphmax}: total depth of the ocean (meters). 
     521\item $z$-coordinate with full step bathymetry (\np{ln\_zco}\forcode{ = .true.}), 
     522\item $z$-coordinate with partial step ($zps$) bathymetry (\np{ln\_zps}\forcode{ = .true.}), 
     523\item Generalized, $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}). 
    683524\end{itemize} 
    684 As an example, for the $45$ layers used in the DRAKKAR configuration those parameters are: 
    685 \jp{jpk}~$= 46$, \np{ppacr}~$= 9$, \np{ppkth}~$= 23.563$, \np{ppdzmin}~$= 6~m$, \np{pphmax}~$= 5750~m$. 
    686  
    687 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    688 \begin{table} 
    689   \begin{center} 
    690     \begin{tabular}{c||r|r|r|r} 
    691       \hline 
    692       \textbf{LEVEL} & \textbf{gdept\_1d} & \textbf{gdepw\_1d} & \textbf{e3t\_1d } & \textbf{e3w\_1d} \\ 
    693       \hline 
    694       1              & \textbf{     5.00} &               0.00 & \textbf{   10.00} &            10.00 \\ 
    695       \hline 
    696       2              & \textbf{    15.00} &              10.00 & \textbf{   10.00} &            10.00 \\ 
    697       \hline 
    698       3              & \textbf{    25.00} &              20.00 & \textbf{   10.00} &            10.00 \\ 
    699       \hline 
    700       4              & \textbf{    35.01} &              30.00 & \textbf{   10.01} &            10.00 \\ 
    701       \hline 
    702       5              & \textbf{    45.01} &              40.01 & \textbf{   10.01} &            10.01 \\ 
    703       \hline 
    704       6              & \textbf{    55.03} &              50.02 & \textbf{   10.02} &            10.02 \\ 
    705       \hline 
    706       7              & \textbf{    65.06} &              60.04 & \textbf{   10.04} &            10.03 \\ 
    707       \hline 
    708       8              & \textbf{    75.13} &              70.09 & \textbf{   10.09} &            10.06 \\ 
    709       \hline 
    710       9              & \textbf{    85.25} &              80.18 & \textbf{   10.17} &            10.12 \\ 
    711       \hline 
    712       10             & \textbf{    95.49} &              90.35 & \textbf{   10.33} &            10.24 \\ 
    713       \hline 
    714       11             & \textbf{   105.97} &             100.69 & \textbf{   10.65} &            10.47 \\ 
    715       \hline 
    716       12             & \textbf{   116.90} &             111.36 & \textbf{   11.27} &            10.91 \\ 
    717       \hline 
    718       13             & \textbf{   128.70} &             122.65 & \textbf{   12.47} &            11.77 \\ 
    719       \hline 
    720       14             & \textbf{   142.20} &             135.16 & \textbf{   14.78} &            13.43 \\ 
    721       \hline 
    722       15             & \textbf{   158.96} &             150.03 & \textbf{   19.23} &            16.65 \\ 
    723       \hline 
    724       16             & \textbf{   181.96} &             169.42 & \textbf{   27.66} &            22.78 \\ 
    725       \hline 
    726       17             & \textbf{   216.65} &             197.37 & \textbf{   43.26} &            34.30 \\ 
    727       \hline 
    728       18             & \textbf{   272.48} &             241.13 & \textbf{   70.88} &            55.21 \\ 
    729       \hline 
    730       19             & \textbf{   364.30} &             312.74 & \textbf{  116.11} &            90.99 \\ 
    731       \hline 
    732       20             & \textbf{   511.53} &             429.72 & \textbf{  181.55} &           146.43 \\ 
    733       \hline 
    734       21             & \textbf{   732.20} &             611.89 & \textbf{  261.03} &           220.35 \\ 
    735       \hline 
    736       22             & \textbf{  1033.22} &             872.87 & \textbf{  339.39} &           301.42 \\ 
    737       \hline 
    738       23             & \textbf{  1405.70} &            1211.59 & \textbf{  402.26} &           373.31 \\ 
    739       \hline 
    740       24             & \textbf{  1830.89} &            1612.98 & \textbf{  444.87} &           426.00 \\ 
    741       \hline 
    742       25             & \textbf{  2289.77} &            2057.13 & \textbf{  470.55} &           459.47 \\ 
    743       \hline 
    744       26             & \textbf{  2768.24} &            2527.22 & \textbf{  484.95} &           478.83 \\ 
    745       \hline 
    746       27             & \textbf{  3257.48} &            3011.90 & \textbf{  492.70} &           489.44 \\ 
    747       \hline 
    748       28             & \textbf{  3752.44} &            3504.46 & \textbf{  496.78} &           495.07 \\ 
    749       \hline 
    750       29             & \textbf{  4250.40} &            4001.16 & \textbf{  498.90} &           498.02 \\ 
    751       \hline 
    752       30             & \textbf{  4749.91} &            4500.02 & \textbf{  500.00} &           499.54 \\ 
    753       \hline 
    754       31             & \textbf{  5250.23} &            5000.00 & \textbf{  500.56} &           500.33 \\ 
    755       \hline 
    756     \end{tabular} 
    757   \end{center} 
    758   \caption{ 
    759     \protect\label{tab:orca_zgr} 
    760     Default vertical mesh in $z$-coordinate for 30 layers ORCA2 configuration as computed from 
    761     \autoref{eq:DOM_zgr_ana_2} using the coefficients given in \autoref{eq:DOM_zgr_coef} 
    762   } 
    763 \end{table} 
    764 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    765  
    766 % ------------------------------------------------------------------------------------------------------------- 
    767 %        z-coordinate with partial step 
    768 % ------------------------------------------------------------------------------------------------------------- 
    769 \subsection[$Z$-coordinate with partial step (\forcode{ln_zps = .true.})] 
    770 {$Z$-coordinate with partial step (\protect\np{ln\_zps}\forcode{ = .true.})} 
    771 \label{subsec:DOM_zps} 
    772 %--------------------------------------------namdom------------------------------------------------------- 
    773  
    774 \nlst{namdom}  
    775 %-------------------------------------------------------------------------------------------------------------- 
    776  
    777 In $z$-coordinate partial step, 
    778 the depths of the model levels are defined by the reference analytical function $z_0(k)$ as described in 
    779 the previous section, \textit{except} in the bottom layer. 
    780 The thickness of the bottom layer is allowed to vary as a function of geographical location $(\lambda,\varphi)$ to 
    781 allow a better representation of the bathymetry, especially in the case of small slopes 
    782 (where the bathymetry varies by less than one level thickness from one grid point to the next). 
    783 The reference layer thicknesses $e_{3t}^0$ have been defined in the absence of bathymetry. 
    784 With partial steps, layers from 1 to \jp{jpk}-2 can have a thickness smaller than $e_{3t}(jk)$. 
    785 The model deepest layer (\jp{jpk}-1) is allowed to have either a smaller or larger thickness than $e_{3t}(jpk)$: 
    786 the maximum thickness allowed is $2*e_{3t}(jpk - 1)$. 
    787 This has to be kept in mind when specifying values in \ngn{namdom} namelist, 
    788 as the maximum depth \np{pphmax} in partial steps: 
    789 for example, with \np{pphmax}~$= 5750~m$ for the DRAKKAR 45 layer grid, 
    790 the maximum ocean depth allowed is actually $6000~m$ (the default thickness $e_{3t}(jpk - 1)$ being $250~m$). 
    791 Two variables in the namdom namelist are used to define the partial step vertical grid. 
    792 The mimimum water thickness (in meters) allowed for a cell partially filled with bathymetry at level jk is 
    793 the minimum of \np{rn\_e3zps\_min} (thickness in meters, usually $20~m$) or $e_{3t}(jk)*$\np{rn\_e3zps\_rat} 
    794 (a fraction, usually 10\%, of the default thickness $e_{3t}(jk)$). 
    795  
    796 \gmcomment{ \colorbox{yellow}{Add a figure here of pstep especially at last ocean level }  } 
    797  
    798 % ------------------------------------------------------------------------------------------------------------- 
    799 %        s-coordinate 
    800 % ------------------------------------------------------------------------------------------------------------- 
    801 \subsection[$S$-coordinate (\forcode{ln_sco = .true.})] 
    802 {$S$-coordinate (\protect\np{ln\_sco}\forcode{ = .true.})} 
    803 \label{subsec:DOM_sco} 
    804 %------------------------------------------nam_zgr_sco--------------------------------------------------- 
    805 % 
    806 %\nlst{namzgr_sco}  
    807 %-------------------------------------------------------------------------------------------------------------- 
    808 Options are defined in \ngn{namzgr\_sco}. 
    809 In $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}), the depth and thickness of the model levels are defined from 
    810 the product of a depth field and either a stretching function or its derivative, respectively: 
    811  
    812 \begin{align*} 
    813   % \label{eq:DOM_sco_ana} 
    814   z(k)   &= h(i,j) \; z_0 (k) \\ 
    815   e_3(k) &= h(i,j) \; z_0'(k) 
    816 \end{align*} 
    817  
    818 where $h$ is the depth of the last $w$-level ($z_0(k)$) defined at the $t$-point location in the horizontal and 
    819 $z_0(k)$ is a function which varies from $0$ at the sea surface to $1$ at the ocean bottom. 
    820 The depth field $h$ is not necessary the ocean depth, 
    821 since a mixed step-like and bottom-following representation of the topography can be used 
    822 (\autoref{fig:z_zps_s_sps}) or an envelop bathymetry can be defined (\autoref{fig:z_zps_s_sps}). 
    823 The namelist parameter \np{rn\_rmax} determines the slope at which 
    824 the terrain-following coordinate intersects the sea bed and becomes a pseudo z-coordinate. 
    825 The coordinate can also be hybridised by specifying \np{rn\_sbot\_min} and \np{rn\_sbot\_max} as 
    826 the minimum and maximum depths at which the terrain-following vertical coordinate is calculated. 
    827  
    828 Options for stretching the coordinate are provided as examples, 
    829 but care must be taken to ensure that the vertical stretch used is appropriate for the application. 
    830  
    831 The original default NEMO s-coordinate stretching is available if neither of the other options are specified as true 
    832 (\np{ln\_s\_SH94}\forcode{ = .false.} and \np{ln\_s\_SF12}\forcode{ = .false.}). 
    833 This uses a depth independent $\tanh$ function for the stretching \citep{madec.delecluse.ea_JPO96}: 
    834  
    835 \[ 
    836   z = s_{min} + C (s) (H - s_{min}) 
    837   % \label{eq:SH94_1} 
    838 \] 
    839  
    840 where $s_{min}$ is the depth at which the $s$-coordinate stretching starts and 
    841 allows a $z$-coordinate to placed on top of the stretched coordinate, 
    842 and $z$ is the depth (negative down from the asea surface). 
    843 \begin{gather*} 
    844   s = - \frac{k}{n - 1} \quad \text{and} \quad 0 \leq k \leq n - 1 
    845   % \label{eq:DOM_s} 
    846  \\ 
    847   % \label{eq:DOM_sco_function} 
    848   C(s) = \frac{[\tanh(\theta \, (s + b)) - \tanh(\theta \, b)]}{2 \; \sinh(\theta)} 
    849 \end{gather*} 
    850  
    851 A stretching function, 
    852 modified from the commonly used \citet{song.haidvogel_JCP94} stretching (\np{ln\_s\_SH94}\forcode{ = .true.}), 
    853 is also available and is more commonly used for shelf seas modelling: 
    854  
    855 \[ 
    856   C(s) =   (1 - b) \frac{\sinh(\theta s)}{\sinh(\theta)} 
    857          + b       \frac{\tanh \lt[ \theta \lt(s + \frac{1}{2} \rt) \rt] -   \tanh \lt( \frac{\theta}{2} \rt)} 
    858                         {                                                  2 \tanh \lt( \frac{\theta}{2} \rt)} 
    859   % \label{eq:SH94_2} 
    860 \] 
    861  
    862 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    863 \begin{figure}[!ht] 
    864   \begin{center} 
    865     \includegraphics[width=\textwidth]{Fig_sco_function} 
    866     \caption{ 
    867       \protect\label{fig:sco_function} 
    868       Examples of the stretching function applied to a seamount; 
    869       from left to right: surface, surface and bottom, and bottom intensified resolutions 
    870     } 
    871   \end{center} 
    872 \end{figure} 
    873 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    874  
    875 where $H_c$ is the critical depth (\np{rn\_hc}) at which the coordinate transitions from pure $\sigma$ to 
    876 the stretched coordinate, and $\theta$ (\np{rn\_theta}) and $b$ (\np{rn\_bb}) are the surface and 
    877 bottom control parameters such that $0 \leqslant \theta \leqslant 20$, and $0 \leqslant b \leqslant 1$. 
    878 $b$ has been designed to allow surface and/or bottom increase of the vertical resolution 
    879 (\autoref{fig:sco_function}). 
    880  
    881 Another example has been provided at version 3.5 (\np{ln\_s\_SF12}) that allows a fixed surface resolution in 
    882 an analytical terrain-following stretching \citet{siddorn.furner_OM13}. 
    883 In this case the a stretching function $\gamma$ is defined such that: 
    884  
    885 \begin{equation} 
    886   z = - \gamma h \quad \text{with} \quad 0 \leq \gamma \leq 1 
    887   % \label{eq:z} 
    888 \end{equation} 
    889  
    890 The function is defined with respect to $\sigma$, the unstretched terrain-following coordinate: 
    891  
    892 \begin{gather*} 
    893   % \label{eq:DOM_gamma_deriv} 
    894   \gamma =   A \lt( \sigma   - \frac{1}{2} (\sigma^2     + f (\sigma)) \rt) 
    895            + B \lt( \sigma^3 - f           (\sigma) \rt) + f (\sigma)       \\ 
    896   \intertext{Where:} 
    897   % \label{eq:DOM_gamma} 
    898   f(\sigma) = (\alpha + 2) \sigma^{\alpha + 1} - (\alpha + 1) \sigma^{\alpha + 2} 
    899   \quad \text{and} \quad \sigma = \frac{k}{n - 1} 
    900 \end{gather*} 
    901  
    902 This gives an analytical stretching of $\sigma$ that is solvable in $A$ and $B$ as a function of 
    903 the user prescribed stretching parameter $\alpha$ (\np{rn\_alpha}) that stretches towards 
    904 the surface ($\alpha > 1.0$) or the bottom ($\alpha < 1.0$) and 
    905 user prescribed surface (\np{rn\_zs}) and bottom depths. 
    906 The bottom cell depth in this example is given as a function of water depth: 
    907  
    908 \[ 
    909   % \label{eq:DOM_zb} 
    910   Z_b = h a + b 
    911 \] 
    912  
    913 where the namelist parameters \np{rn\_zb\_a} and \np{rn\_zb\_b} are $a$ and $b$ respectively. 
    914  
    915 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    916 \begin{figure}[!ht] 
    917   \includegraphics[width=\textwidth]{Fig_DOM_compare_coordinates_surface} 
    918   \caption{ 
    919     A comparison of the \citet{song.haidvogel_JCP94} $S$-coordinate (solid lines), 
    920     a 50 level $Z$-coordinate (contoured surfaces) and 
    921     the \citet{siddorn.furner_OM13} $S$-coordinate (dashed lines) in the surface $100~m$ for 
    922     a idealised bathymetry that goes from $50~m$ to $5500~m$ depth. 
    923     For clarity every third coordinate surface is shown. 
    924   } 
    925   \label{fig:fig_compare_coordinates_surface} 
    926 \end{figure} 
    927  % >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    928  
    929 This gives a smooth analytical stretching in computational space that is constrained to 
    930 given specified surface and bottom grid cell thicknesses in real space. 
    931 This is not to be confused with the hybrid schemes that 
    932 superimpose geopotential coordinates on terrain following coordinates thus 
    933 creating a non-analytical vertical coordinate that 
    934 therefore may suffer from large gradients in the vertical resolutions. 
    935 This stretching is less straightforward to implement than the \citet{song.haidvogel_JCP94} stretching, 
    936 but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes. 
    937  
    938 As with the \citet{song.haidvogel_JCP94} stretching the stretch is only applied at depths greater than 
    939 the critical depth $h_c$. 
    940 In this example two options are available in depths shallower than $h_c$, 
    941 with pure sigma being applied if the \np{ln\_sigcrit} is true and pure z-coordinates if it is false 
    942 (the z-coordinate being equal to the depths of the stretched coordinate at $h_c$). 
    943  
    944 Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as 
    945 large slopes lead to hydrostatic consistency. 
    946 A hydrostatic consistency parameter diagnostic following \citet{haney_JPO91} has been implemented, 
    947 and is output as part of the model mesh file at the start of the run. 
    948  
    949 % ------------------------------------------------------------------------------------------------------------- 
    950 %        z*- or s*-coordinate 
    951 % ------------------------------------------------------------------------------------------------------------- 
    952 \subsection[\zstar- or \sstar-coordinate (\forcode{ln_linssh = .false.})] 
    953 {\zstar- or \sstar-coordinate (\protect\np{ln\_linssh}\forcode{ = .false.})} 
    954 \label{subsec:DOM_zgr_star} 
    955  
    956 This option is described in the Report by Levier \textit{et al.} (2007), available on the \NEMO web site. 
    957  
    958 %gm% key advantage: minimise the diffusion/dispertion associated with advection in response to high frequency surface disturbances 
     525 
     526Additionally, hybrid combinations of the three main coordinates are available: 
     527$s-z$ or $s-zps$ coordinate (\autoref{fig:z_zps_s_sps}d and \autoref{fig:z_zps_s_sps}e). 
     528 
     529A further choice related to vertical coordinate concerns the presence (or not) of ocean 
     530cavities beneath ice shelves within the model domain.  A setting of \np{ln\_isfcav} as 
     531\forcode{.true.} indicates that the domain contains  ocean cavities, otherwise the top, 
     532wet layer of the ocean will always be at the ocean surface.  This option is currently only 
     533available for $z$- or $zps$-coordinates. In the latter case, partial steps are also applied 
     534at the ocean/ice shelf interface. 
     535 
     536Within the model, the arrays describing the grid point depths and vertical scale factors 
     537are three set of three dimensional arrays $(i,j,k)$ defined at \textit{before}, 
     538\textit{now} and \textit{after} time step.  The time at which they are defined is 
     539indicated by a suffix: $\_b$, $\_n$, or $\_a$, respectively.  They are updated at each 
     540model time step. The initial fixed reference coordinate system is held in variable names 
     541with a $\_0$ suffix.  When the linear free surface option is used 
     542(\np{ln\_linssh}\forcode{ = .true.}), \textit{before}, \textit{now} and \textit{after} 
     543arrays are initially set to their reference counterpart and remain fixed. 
     544 
     545\subsubsection{Required fields} 
     546\label{sec:DOM_zgr_fields} 
     547The explicit specification of a range of fields related to the vertical grid are required for the definition of a configuration. These include: 
     548 
     549\begin{Verbatim}[fontsize=\tiny] 
     550int    ln_zco, ln_zps, ln_sco            /* flags for z-coord, z-coord with partial steps and s-coord    */ 
     551int    ln_isfcav                         /* flag  for ice shelf cavities                                 */ 
     552double e3t_1d, e3w_1d                    /* reference vertical scale factors at T and W points           */ 
     553double e3t_0, e3u_0, e3v_0, e3f_0, e3w_0 /* vertical scale factors 3D coordinate at T,U,V,F and W points */ 
     554double e3uw_0, e3vw_0                    /* vertical scale factors 3D coordinate at UW and VW points     */ 
     555int    bottom_level, top_level           /* last wet T-points, 1st wet T-points (for ice shelf cavities) */ 
     556                                         /* For reference:                                               */ 
     557float  bathy_metry                       /* bathymetry used in setting top and bottom levels             */ 
     558\end{Verbatim} 
     559 
     560This set of vertical metrics is sufficient to describe the initial depth and thickness of 
     561every gridcell in the model regardless of the choice of vertical coordinate. With constant 
     562z-levels, e3 metrics will be uniform across each horizontal level. In the partial step 
     563case each e3 at the \np{bottom\_level} (and, possibly, \np{top\_level} if ice cavities are 
     564present) may vary from its horizontal neighbours. And, in s-coordinates, variations can 
     565occur throughout the water column. With the non-linear free-surface, all the coordinates 
     566behave more like the s-coordinate in that variations occurr throughout the water column 
     567with displacements related to the sea surface height. These variations are typically much 
     568smaller than those arising from bottom fitted coordinates. The values for vertical metrics 
     569supplied in the domain configuration file can be considered as those arising from a flat 
     570sea surface with zero elevation. 
     571 
     572The \np{bottom\_level} and \np{top\_level} 2D arrays define the \np{bottom\_level} and top 
     573wet levels in each grid column. Without ice cavities, \np{top\_level} is essentially a land 
     574mask (0 on land; 1 everywhere else). With ice cavities, \np{top\_level} determines the 
     575first wet point below the overlying ice shelf. 
     576 
     577 
    959578 
    960579% ------------------------------------------------------------------------------------------------------------- 
    961580%        level bathymetry and mask  
    962581% ------------------------------------------------------------------------------------------------------------- 
    963 \subsection{Level bathymetry and mask} 
     582\subsubsection{Level bathymetry and mask} 
    964583\label{subsec:DOM_msk} 
    965584 
    966 Whatever the vertical coordinate used, the model offers the possibility of representing the bottom topography with 
    967 steps that follow the face of the model cells (step like topography) \citep{madec.delecluse.ea_JPO96}. 
    968 The distribution of the steps in the horizontal is defined in a 2D integer array, mbathy, which 
    969 gives the number of ocean levels (\ie those that are not masked) at each $t$-point. 
    970 mbathy is computed from the meter bathymetry using the definiton of gdept as the number of $t$-points which 
    971 gdept $\leq$ bathy. 
    972  
    973 Modifications of the model bathymetry are performed in the \textit{bat\_ctl} routine (see \mdl{domzgr} module) after 
    974 mbathy is computed. 
    975 Isolated grid points that do not communicate with another ocean point at the same level are eliminated. 
    976  
    977 As for the representation of bathymetry, a 2D integer array, misfdep, is created. 
    978 misfdep defines the level of the first wet $t$-point. 
    979 All the cells between $k = 1$ and $misfdep(i,j) - 1$ are masked. 
    980 By default, $misfdep(:,:) = 1$ and no cells are masked. 
    981  
    982 In case of ice shelf cavities, modifications of the model bathymetry and ice shelf draft into  
    983 the cavities are performed in the \textit{zgr\_isf} routine. 
    984 The compatibility between ice shelf draft and bathymetry is checked. 
    985 All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded (\ie masked). 
    986 If only one cell on the water column is opened at $t$-, $u$- or $v$-points, 
    987 the bathymetry or the ice shelf draft is dug to fit this constrain. 
    988 If the incompatibility is too strong (need to dig more than 1 cell), the cell is masked. 
    989  
    990 From the \textit{mbathy} and \textit{misfdep} array, the mask fields are defined as follows: 
     585 
     586From \np{top\_level} and \np{bottom\_level} fields, the mask fields are defined as follows: 
    991587\begin{alignat*}{2} 
    992588  tmask(i,j,k) &= &  & 
    993589    \begin{cases} 
    994                   0 &\text{if $                  k  <    misfdep(i,j)$} \\ 
    995                   1 &\text{if $misfdep(i,j) \leq k \leq   mbathy(i,j)$} \\ 
    996                   0 &\text{if $                  k  >     mbathy(i,j)$} 
     590                  0 &\text{if $                  k  <    top\_level(i,j)$} \\ 
     591                  1 &\text{if $bottom\_level(i,j) \leq k \leq   top\_level(i,j)$} \\ 
     592                  0 &\text{if $                  k  >     bottom\_level(i,j)$} 
    997593    \end{cases} 
    998594  \\ 
     
    1010606exactly in the same way as for the bottom boundary. 
    1011607 
    1012 The specification of closed lateral boundaries requires that at least 
    1013 the first and last rows and columns of the \textit{mbathy} array are set to zero. 
    1014 In the particular case of an east-west cyclical boundary condition, \textit{mbathy} has its last column equal to 
    1015 the second one and its first column equal to the last but one (and so too the mask arrays) 
    1016 (see \autoref{fig:LBC_jperio}). 
     608%% The specification of closed lateral boundaries requires that at least 
     609%% the first and last rows and columns of the \textit{mbathy} array are set to zero. 
     610%% In the particular case of an east-west cyclical boundary condition, \textit{mbathy} has its last column equal to 
     611%% the second one and its first column equal to the last but one (and so too the mask arrays) 
     612%% (see \autoref{fig:LBC_jperio}). 
     613 
     614 
     615%------------------------------------------------------------------------------------------------- 
     616%        Closed seas  
     617%------------------------------------------------------------------------------------------------- 
     618\subsection{Closed seas} \label{subsec:DOM_closea}  
     619 
     620When a global ocean is coupled to an atmospheric model it is better to represent all large 
     621water bodies (\eg great lakes, Caspian sea...) even if the model resolution does not allow 
     622their communication with the rest of the ocean.  This is unnecessary when the ocean is 
     623forced by fixed atmospheric conditions, so these seas can be removed from the ocean 
     624domain.  The user has the option to set the bathymetry in closed seas to zero (see 
     625\autoref{sec:MISC_closea}) and to optionally decide on the fate of any freshwater 
     626imbalance over the area. The options are explained in \autoref{sec:MISC_closea} but it 
     627should be noted here that a successful use of these options requires appropriate mask 
     628fields to be present in the domain configuration file. Among the possibilities are: 
     629 
     630\begin{Verbatim}[fontsize=\tiny] 
     631int    closea_mask          /* non-zero values in closed sea areas for optional masking                  */ 
     632int    closea_mask_rnf      /* non-zero values in closed sea areas with runoff locations (precip only)   */ 
     633int    closea_mask_emp      /* non-zero values in closed sea areas with runoff locations (total emp)     */ 
     634\end{Verbatim} 
     635 
     636% ------------------------------------------------------------------------------------------------------------- 
     637%        Grid files 
     638% ------------------------------------------------------------------------------------------------------------- 
     639\subsection{Output grid files} 
     640\label{subsec:DOM_meshmask} 
     641 
     642\nlst{namcfg} 
     643 
     644Most of the arrays relating to a particular ocean model configuration dicussed in this 
     645chapter (grid-point position, scale factors) can be saved in a file if namelist parameter 
     646\np{ln\_write\_cfg} (namelist \ngn{namcfg}) is set to \forcode{.true.}; the output 
     647filename is set thorugh parameter \np{cn\_domcfg\_out}. This is only really useful 
     648if the fields are computed in subroutines \mdl{usrdef\_hgr} or \mdl{usrdef\_zgr} and 
     649checking or confirmation is required. 
     650 
     651\nlst{namdom} 
     652 
     653Alternatively, all the arrays relating to a particular ocean model configuration 
     654(grid-point position, scale factors, depths and masks) can be saved in a file called 
     655\texttt{mesh\_mask} if namelist parameter \np{ln\_meshmask} (namelist \ngn{namdom}) is set 
     656to \forcode{.true.}. This file contains additional fields that can be useful for 
     657post-processing applications 
    1017658 
    1018659% ================================================================ 
     
    1023664\label{sec:DTA_tsd} 
    1024665%-----------------------------------------namtsd------------------------------------------- 
    1025  
    1026666\nlst{namtsd}  
    1027667%------------------------------------------------------------------------------------------ 
    1028668 
    1029 Options are defined in \ngn{namtsd}. 
    1030 By default, the ocean start from rest (the velocity field is set to zero) and the initialization of temperature and 
    1031 salinity fields is controlled through the \np{ln\_tsd\_ini} namelist parameter. 
     669Basic initial state options are defined in \ngn{namtsd}.  By default, the ocean starts 
     670from rest (the velocity field is set to zero) and the initialization of temperature and 
     671salinity fields is controlled through the \np{ln\_tsd\_init} namelist parameter. 
     672 
    1032673\begin{description} 
    1033 \item[\np{ln\_tsd\_init}\forcode{ = .true.}] 
    1034   use a T and S input files that can be given on the model grid itself or on their native input data grid. 
    1035   In the latter case, 
    1036   the data will be interpolated on-the-fly both in the horizontal and the vertical to the model grid 
    1037   (see \autoref{subsec:SBC_iof}). 
    1038   The information relative to the input files are given in the \np{sn\_tem} and \np{sn\_sal} structures. 
    1039   The computation is done in the \mdl{dtatsd} module. 
    1040 \item[\np{ln\_tsd\_init}\forcode{ = .false.}] 
    1041   use constant salinity value of $35.5~psu$ and an analytical profile of temperature 
    1042   (typical of the tropical ocean), see \rou{istate\_t\_s} subroutine called from \mdl{istate} module. 
     674\item[\np{ln\_tsd\_init}\forcode{= .true.}] 
     675  Use T and S input files that can be given on the model grid itself or on their native 
     676  input data grids.  In the latter case, the data will be interpolated on-the-fly both in 
     677  the horizontal and the vertical to the model grid (see \autoref{subsec:SBC_iof}).  The 
     678  information relating to the input files are specified in the \np{sn\_tem} and 
     679  \np{sn\_sal} structures.  The computation is done in the \mdl{dtatsd} module. 
     680\item[\np{ln\_tsd\_init}\forcode{= .false.}] 
     681  Initial values for T and S are set via a user supplied \rou{usr\_def\_istate} routine 
     682  contained in \mdl{userdef\_istate}. The default version sets horizontally uniform T and 
     683  profiles as used in the  GYRE configuration (see \autoref{sec:CFG_gyre}). 
    1043684\end{description} 
    1044685 
  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r11225 r11315  
    12351235\label{subsec:ZDF_swm} 
    12361236 
    1237 TBC ... 
     1237Surface waves produce an enhanced mixing through wave-turbulence interaction. 
     1238In addition to breaking waves induced turbulence (\autoref{subsec:ZDF_tke}), 
     1239the influence of non-breaking waves can be accounted introducing  
     1240wave-induced viscosity and diffusivity as a function of the wave number spectrum. 
     1241Following \citet{qiao.yuan.ea_OD10}, a formulation of wave-induced mixing coefficient 
     1242is provided  as a function of wave amplitude, Stokes Drift and wave-number: 
     1243 
     1244\begin{equation} 
     1245  \label{eq:Bv} 
     1246  B_{v} = \alpha {A} {U}_{st} {exp(3kz)} 
     1247\end{equation} 
     1248 
     1249Where $B_{v}$ is the wave-induced mixing coefficient, $A$ is the wave amplitude,  
     1250${U}_{st}$ is the Stokes Drift velocity, $k$ is the wave number and $\alpha$  
     1251is a constant which should be determined by observations or  
     1252numerical experiments and is set to be 1. 
     1253 
     1254The coefficient $B_{v}$ is then directly added to the vertical viscosity  
     1255and diffusivity coefficients. 
     1256 
     1257In order to account for this contribution set: \forcode{ln_zdfswm = .true.}, 
     1258then wave interaction has to be activated through \forcode{ln_wave = .true.}, 
     1259the Stokes Drift can be evaluated by setting \forcode{ln_sdw = .true.}  
     1260(see \autoref{subsec:SBC_wave_sdw}) 
     1261and the needed wave fields can be provided either in forcing or coupled mode 
     1262(for more information on wave parameters and settings see \autoref{sec:SBC_wave}) 
    12381263 
    12391264% ================================================================ 
  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/NEMO/subfiles/introduction.tex

    r11123 r11315  
    151151The coding rules for OPA include conventions for naming variables, 
    152152with different starting letters for different types of variables (real, integer, parameter\ldots). 
    153 Those rules are briefly presented in \autoref{apdx:D} and a more complete document is available . 
     153Those rules are briefly presented in \autoref{apdx:coding} and a more complete document is available . 
    154154 
    155155The model is organized with a high internal modularity based on physics. 
     
    158158To make it easier for the user to find his way around the code, the module names follow a three-letter rule. 
    159159For example, \mdl{traldf} is a module related to the TRAcers equation, computing the Lateral DiFfussion. 
    160 %The complete list of module names is presented in \autoref{apdx:D}.      %====>>>> to be done ! 
     160%The complete list of module names is presented in \autoref{apdx:coding}.      %====>>>> to be done ! 
    161161Furthermore, modules are organized in a few directories that correspond to their category, 
    162162as indicated by the first three letters of their name (\autoref{tab:chapters}). 
  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/global/document.tex

    r11212 r11315  
    8585\include{appendices} 
    8686 
     87%% Append coding rules for every manual 
     88\input{../../global/coding_rules} 
     89 
    8790 
    8891%% Backmatter 
  • NEMO/branches/2019/dev_r11233_obsasm_docfixes/doc/latex/global/highlighting.tex

    r11212 r11315  
    2525 
    2626%% Inline 
    27 \newmintinline[forcode]{fortran}{fontsize=auto, frame=lines}   % \forcode{...} 
    28 \newmintinline[xmlcode]{xml}{    fontsize=auto, frame=lines}   % \xmlcode{...} 
    29 \newmintinline[snippet]{console}{fontsize=auto, frame=lines}   % \snippet{...} 
     27\newmintinline[forcode]{fortran}{bgcolor=, fontsize=auto, frame=lines}   % \forcode{...} 
     28\newmintinline[xmlcode]{xml}{    bgcolor=, fontsize=auto, frame=lines}   % \xmlcode{...} 
     29\newmintinline[snippet]{console}{bgcolor=, fontsize=auto, frame=lines}   % \snippet{...} 
    3030 
    3131%% Namelists inclusion 
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