Changeset 11597


Ignore:
Timestamp:
2019-09-25T20:20:19+02:00 (12 months ago)
Author:
nicolasmartin
Message:

Continuation of coding rules application
Recovery of some sections deleted by the previous commit

Location:
NEMO/trunk/doc/latex/NEMO/subfiles
Files:
24 edited

Legend:

Unmodified
Added
Removed
  • NEMO/trunk/doc/latex/NEMO/subfiles/apdx_DOMAINcfg.tex

    r11596 r11597  
    88\vfill 
    99\begin{figure}[b] 
     10%% ================================================================================================= 
    1011\subsubsection*{Changes record} 
    1112\begin{tabular}{m{0.08\linewidth}||m{0.32\linewidth}|m{0.6\linewidth}} 
     
    3031of those described elsewhere in this manual. 
    3132 
     33%% ================================================================================================= 
    3234\section{Choice of horizontal grid} 
    3335\label{sec:DOMCFG_hor} 
    3436 
    35 %--------------------------------------------namdom------------------------------------------------------- 
    3637 
    3738\begin{listing} 
     
    4041  \label{lst:namdom_domcfg} 
    4142\end{listing} 
    42 %-------------------------------------------------------------------------------------------------------------- 
    4343 
    4444The user has three options available in defining a horizontal grid, which involve the 
     
    9494(and the number of grid points). 
    9595 
     96%% ================================================================================================= 
    9697\section{Vertical grid} 
    9798\label{sec:DOMCFG_vert} 
    9899 
     100%% ================================================================================================= 
    99101\subsection{Vertical reference coordinate} 
    100102\label{sec:DOMCFG_zref} 
     
    289291%% %        Meter Bathymetry 
    290292%% % ------------------------------------------------------------------------------------------------------------- 
     293%% ================================================================================================= 
    291294\subsection{Model bathymetry} 
    292295\label{subsec:DOMCFG_bathy} 
     
    317320\end{description} 
    318321 
     322%% ================================================================================================= 
    319323\subsection{Choice of vertical grid} 
    320324\label{sec:DOMCFG_vgrd} 
     
    337341%%% 
    338342 
     343%% ================================================================================================= 
    339344\subsubsection[$Z$-coordinate with uniform thickness levels (\forcode{ln_zco})]{$Z$-coordinate with uniform thickness levels (\protect\np{ln_zco}{ln\_zco})} 
    340345\label{subsec:DOMCFG_zco} 
     
    346351rarely used in modern simulations but it can be useful for testing purposes. 
    347352 
     353%% ================================================================================================= 
    348354\subsubsection[$Z$-coordinate with partial step (\forcode{ln_zps})]{$Z$-coordinate with partial step (\protect\np{ln_zps}{ln\_zps})} 
    349355\label{subsec:DOMCFG_zps} 
     
    373379the default thickness $e_{3t}(jk)$). 
    374380 
     381%% ================================================================================================= 
    375382\subsubsection[$S$-coordinate (\forcode{ln_sco})]{$S$-coordinate (\protect\np{ln_sco}{ln\_sco})} 
    376383\label{sec:DOMCFG_sco} 
    377 %------------------------------------------nam_zgr_sco--------------------------------------------------- 
    378384% 
    379385\begin{listing} 
     
    382388  \label{lst:namzgr_sco_domcfg} 
    383389\end{listing} 
    384 %-------------------------------------------------------------------------------------------------------------- 
    385390Options are defined in \nam{zgr_sco}{zgr\_sco} (\texttt{DOMAINcfg} only). 
    386391In $s$-coordinate (\np[=.true.]{ln_sco}{ln\_sco}), the depth and thickness of the model levels are defined from 
     
    519524and is output as part of the model mesh file at the start of the run. 
    520525 
     526%% ================================================================================================= 
    521527\subsubsection[\zstar- or \sstar-coordinate (\forcode{ln_linssh})]{\zstar- or \sstar-coordinate (\protect\np{ln_linssh}{ln\_linssh})} 
    522528\label{subsec:DOMCFG_zgr_star} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/apdx_algos.tex

    r11596 r11597  
    99This appendix some on going consideration on algorithms used or planned to be used in \NEMO. 
    1010 
     11%% ================================================================================================= 
    1112\section{Upstream Biased Scheme (UBS) (\protect\np[=.true.]{ln_traadv_ubs}{ln\_traadv\_ubs})} 
    1213\label{sec:ALGOS_tra_adv_ubs} 
     
    180181which leads to ${A_u^{lT}} = \frac{1}{12} {e_{1u}}^3\ |u|$ 
    181182 
     183%% ================================================================================================= 
    182184\section{Leapfrog energetic} 
    183185\label{sec:ALGOS_LF} 
     
    233235In time this boundary condition is not physical and \textbf{add something here!!!} 
    234236 
     237%% ================================================================================================= 
    235238\section{Lateral diffusion operator} 
    236239 
     240%% ================================================================================================= 
    237241\subsection{Griffies iso-neutral diffusion operator} 
    238242 
     
    426430\end{description} 
    427431 
     432%% ================================================================================================= 
    428433\subsection{Eddy induced velocity and skew flux formulation} 
    429434 
     
    579584 
    580585$\ $\newpage      %force an empty line 
     586%% ================================================================================================= 
    581587\subsection{Discrete invariants of the iso-neutral diffrusion} 
    582588\label{subsec:ALGOS_Gf_operator} 
     
    741747There is no need to develop a specific to obtain it. 
    742748 
     749%% ================================================================================================= 
    743750\subsection{Discrete invariants of the skew flux formulation} 
    744751\label{subsec:ALGOS_eiv_skew} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/apdx_diff_opers.tex

    r11596 r11597  
    77\chaptertoc 
    88 
     9%% ================================================================================================= 
    910\section{Horizontal/Vertical $2^{nd}$ order tracer diffusive operators} 
    1011\label{sec:DIFFOPERS_1} 
    1112 
     13%% ================================================================================================= 
    1214\subsubsection*{In z-coordinates} 
    1315 
     
    2224\end{align} 
    2325 
     26%% ================================================================================================= 
    2427\subsubsection*{In generalized vertical coordinates} 
    2528 
     
    148151%\addtocounter{equation}{-2} 
    149152 
     153%% ================================================================================================= 
    150154\section{Iso/Diapycnal $2^{nd}$ order tracer diffusive operators} 
    151155\label{sec:DIFFOPERS_2} 
    152156 
     157%% ================================================================================================= 
    153158\subsubsection*{In z-coordinates} 
    154159 
     
    252257the property becomes obvious. 
    253258 
     259%% ================================================================================================= 
    254260\subsubsection*{In generalized vertical coordinates} 
    255261 
     
    309315\autoref{sec:DIFFOPERS_1} onto $s$-coordinates is exact, however steep the $s$-surfaces. 
    310316 
     317%% ================================================================================================= 
    311318\section{Lateral/Vertical momentum diffusive operators} 
    312319\label{sec:DIFFOPERS_3} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/apdx_invariants.tex

    r11596 r11597  
    1212%\gmcomment{ 
    1313 
     14%% ================================================================================================= 
    1415\section{Introduction / Notations} 
    1516\label{sec:INVARIANTS_0} 
     
    8586\end{flalign} 
    8687 
     88%% ================================================================================================= 
    8789\section{Continuous conservation} 
    8890\label{sec:INVARIANTS_1} 
     
    311313% 
    312314 
     315%% ================================================================================================= 
    313316\section{Discrete total energy conservation: vector invariant form} 
    314317\label{sec:INVARIANTS_2} 
    315318 
     319%% ================================================================================================= 
    316320\subsection{Total energy conservation} 
    317321\label{subsec:INVARIANTS_KE+PE_vect} 
     
    337341leads to the discrete equivalent of the four equations \autoref{eq:INVARIANTS_E_tot_flux}. 
    338342 
     343%% ================================================================================================= 
    339344\subsection{Vorticity term (coriolis + vorticity part of the advection)} 
    340345\label{subsec:INVARIANTS_vor} 
     
    343348or the planetary ($q=f/e_{3f}$), or the total potential vorticity ($q=(\zeta +f) /e_{3f}$). 
    344349Two discretisation of the vorticity term (ENE and EEN) allows the conservation of the kinetic energy. 
     350%% ================================================================================================= 
    345351\subsubsection{Vorticity term with ENE scheme (\protect\np[=.true.]{ln_dynvor_ene}{ln\_dynvor\_ene})} 
    346352\label{subsec:INVARIANTS_vorENE} 
     
    380386In other words, the domain averaged kinetic energy does not change due to the vorticity term. 
    381387 
     388%% ================================================================================================= 
    382389\subsubsection{Vorticity term with EEN scheme (\protect\np[=.true.]{ln_dynvor_een}{ln\_dynvor\_een})} 
    383390\label{subsec:INVARIANTS_vorEEN_vect} 
     
    449456\end{flalign*} 
    450457 
     458%% ================================================================================================= 
    451459\subsubsection{Gradient of kinetic energy / Vertical advection} 
    452460\label{subsec:INVARIANTS_zad} 
     
    556564Blah blah required on the the step representation of bottom topography..... 
    557565 
     566%% ================================================================================================= 
    558567\subsection{Pressure gradient term} 
    559568\label{subsec:INVARIANTS_2.6} 
     
    698707Nevertheless, it is almost never satisfied since a linear equation of state is rarely used. 
    699708 
     709%% ================================================================================================= 
    700710\section{Discrete total energy conservation: flux form} 
    701711\label{sec:INVARIANTS_3} 
    702712 
     713%% ================================================================================================= 
    703714\subsection{Total energy conservation} 
    704715\label{subsec:INVARIANTS_KE+PE_flux} 
     
    721732vector invariant or in flux form, leads to the discrete equivalent of the ???? 
    722733 
     734%% ================================================================================================= 
    723735\subsection{Coriolis and advection terms: flux form} 
    724736\label{subsec:INVARIANTS_3.2} 
    725737 
     738%% ================================================================================================= 
    726739\subsubsection{Coriolis plus ``metric'' term} 
    727740\label{subsec:INVARIANTS_3.3} 
     
    742755The derivation is the same as for the vorticity term in the vector invariant form (\autoref{subsec:INVARIANTS_vor}). 
    743756 
     757%% ================================================================================================= 
    744758\subsubsection{Flux form advection} 
    745759\label{subsec:INVARIANTS_3.4} 
     
    820834The horizontal kinetic energy is not conserved, but forced to decay (\ie\ the scheme is diffusive). 
    821835 
     836%% ================================================================================================= 
    822837\section{Discrete enstrophy conservation} 
    823838\label{sec:INVARIANTS_4} 
    824839 
     840%% ================================================================================================= 
    825841\subsubsection{Vorticity term with ENS scheme  (\protect\np[=.true.]{ln_dynvor_ens}{ln\_dynvor\_ens})} 
    826842\label{subsec:INVARIANTS_vorENS} 
     
    889905The later equality is obtain only when the flow is horizontally non-divergent, \ie\ $\chi$=$0$. 
    890906 
     907%% ================================================================================================= 
    891908\subsubsection{Vorticity Term with EEN scheme (\protect\np[=.true.]{ln_dynvor_een}{ln\_dynvor\_een})} 
    892909\label{subsec:INVARIANTS_vorEEN} 
     
    959976\end{flalign*} 
    960977 
     978%% ================================================================================================= 
    961979\section{Conservation properties on tracers} 
    962980\label{sec:INVARIANTS_5} 
     
    972990as the equation of state is non linear with respect to $T$ and $S$. 
    973991In practice, the mass is conserved to a very high accuracy. 
     992%% ================================================================================================= 
    974993\subsection{Advection term} 
    975994\label{subsec:INVARIANTS_5.1} 
     
    10351054which is the discrete form of $ \frac{1}{2} \int_D {  T^2 \frac{1}{e_3} \frac{\partial  e_3 }{\partial t} \;dv }$. 
    10361055 
     1056%% ================================================================================================= 
    10371057\section{Conservation properties on lateral momentum physics} 
    10381058\label{sec:INVARIANTS_dynldf_properties} 
     
    10531073the term associated with the horizontal gradient of the divergence is locally zero. 
    10541074 
     1075%% ================================================================================================= 
    10551076\subsection{Conservation of potential vorticity} 
    10561077\label{subsec:INVARIANTS_6.1} 
     
    10841105\end{flalign*} 
    10851106 
     1107%% ================================================================================================= 
    10861108\subsection{Dissipation of horizontal kinetic energy} 
    10871109\label{subsec:INVARIANTS_6.2} 
     
    11331155\] 
    11341156 
     1157%% ================================================================================================= 
    11351158\subsection{Dissipation of enstrophy} 
    11361159\label{subsec:INVARIANTS_6.3} 
     
    11541177\end{flalign*} 
    11551178 
     1179%% ================================================================================================= 
    11561180\subsection{Conservation of horizontal divergence} 
    11571181\label{subsec:INVARIANTS_6.4} 
     
    11781202\end{flalign*} 
    11791203 
     1204%% ================================================================================================= 
    11801205\subsection{Dissipation of horizontal divergence variance} 
    11811206\label{subsec:INVARIANTS_6.5} 
     
    12011226\end{flalign*} 
    12021227 
     1228%% ================================================================================================= 
    12031229\section{Conservation properties on vertical momentum physics} 
    12041230\label{sec:INVARIANTS_7} 
     
    13691395\end{flalign*} 
    13701396 
     1397%% ================================================================================================= 
    13711398\section{Conservation properties on tracer physics} 
    13721399\label{sec:INVARIANTS_8} 
     
    13781405As for the advection term, there is conservation of mass only if the Equation Of Seawater is linear. 
    13791406 
     1407%% ================================================================================================= 
    13801408\subsection{Conservation of tracers} 
    13811409\label{subsec:INVARIANTS_8.1} 
     
    14081436In fact, this property simply results from the flux form of the operator. 
    14091437 
     1438%% ================================================================================================= 
    14101439\subsection{Dissipation of tracer variance} 
    14111440\label{subsec:INVARIANTS_8.2} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/apdx_s_coord.tex

    r11596 r11597  
    1010\vfill 
    1111\begin{figure}[b] 
     12%% ================================================================================================= 
    1213\subsubsection*{Changes record} 
    1314\begin{tabular}{l||l|m{0.65\linewidth}} 
     
    1819\end{figure} 
    1920 
     21%% ================================================================================================= 
    2022\section{Chain rule for $s-$coordinates} 
    2123\label{sec:SCOORD_chain} 
     
    112114\end{equation} 
    113115 
     116%% ================================================================================================= 
    114117\section{Continuity equation in $s-$coordinates} 
    115118\label{sec:SCOORD_continuity} 
     
    227230the contribution of the time variation of the vertical coordinate to the volume budget. 
    228231 
     232%% ================================================================================================= 
    229233\section{Momentum equation in $s-$coordinate} 
    230234\label{sec:SCOORD_momentum} 
     
    554558\ie\ the volume flux across the moving $s$-surfaces per unit horizontal area. 
    555559 
     560%% ================================================================================================= 
    556561\section{Tracer equation} 
    557562\label{sec:SCOORD_tracer} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/apdx_triads.tex

    r11596 r11597  
    1717\chaptertoc 
    1818 
     19%% ================================================================================================= 
    1920\section[Choice of \forcode{namtra\_ldf} namelist parameters]{Choice of \protect\nam{tra_ldf}{tra\_ldf} namelist parameters} 
    20 %-----------------------------------------nam_traldf------------------------------------------------------ 
    21  
    22 %--------------------------------------------------------------------------------------------------------- 
     21 
    2322 
    2423Two scheme are available to perform the iso-neutral diffusion. 
     
    6362\end{description} 
    6463 
     64%% ================================================================================================= 
    6565\section{Triad formulation of iso-neutral diffusion} 
    6666\label{sec:TRIADS_iso} 
     
    6969but formulated within the \NEMO\ framework, using scale factors rather than grid-sizes. 
    7070 
     71%% ================================================================================================= 
    7172\subsection{Iso-neutral diffusion operator} 
    7273 
     
    156157is evaluated at $w$-points but involves horizontal gradients defined at $u$-points. 
    157158 
     159%% ================================================================================================= 
    158160\subsection{Standard discretization} 
    159161 
     
    187189(\ie\ they enter the computation of density), but it does not work for a passive tracer. 
    188190 
     191%% ================================================================================================= 
    189192\subsection{Expression of the skew-flux in terms of triad slopes} 
    190193 
     
    282285and in \autoref{eq:TRIADS_i31} $a'_{1}={\:}_i^k{\mathbb{A}_w}_{1/2}^{1/2}$. 
    283286 
     287%% ================================================================================================= 
    284288\subsection{Full triad fluxes} 
    285289 
     
    365369\end{flalign} 
    366370 
     371%% ================================================================================================= 
    367372\subsection{Ensuring the scheme does not increase tracer variance} 
    368373\label{subsec:TRIADS_variance} 
     
    462467\] 
    463468 
     469%% ================================================================================================= 
    464470\subsection{Triad volumes in Griffes's scheme and in \NEMO} 
    465471 
     
    490496we can replace $\overline{A}_{\,i+1/2}^k$ by $A_{i+1/2}^k$ in the above. 
    491497 
     498%% ================================================================================================= 
    492499\subsection{Summary of the scheme} 
    493500 
     
    625632\end{description} 
    626633 
     634%% ================================================================================================= 
    627635\subsection{Treatment of the triads at the boundaries} 
    628636\label{sec:TRIADS_iso_bdry} 
     
    673681% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    674682 
     683%% ================================================================================================= 
    675684\subsection{ Limiting of the slopes within the interior} 
    676685\label{sec:TRIADS_limit} 
     
    701710and so acts to reduce gravitational potential energy. 
    702711 
     712%% ================================================================================================= 
    703713\subsection{Tapering within the surface mixed layer} 
    704714\label{sec:TRIADS_taper} 
     
    707717When the Griffies triads are used, we offer two options for this. 
    708718 
     719%% ================================================================================================= 
    709720\subsubsection{Linear slope tapering within the surface mixed layer} 
    710721\label{sec:TRIADS_lintaper} 
     
    822833% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    823834 
     835%% ================================================================================================= 
    824836\subsubsection{Additional truncation of skew iso-neutral flux components} 
    825837\label{subsec:TRIADS_Gerdes-taper} 
     
    864876% This may give strange looking results, 
    865877% particularly where the mixed-layer depth varies strongly laterally. 
     878%% ================================================================================================= 
    866879\section{Eddy induced advection formulated as a skew flux} 
    867880\label{sec:TRIADS_skew-flux} 
    868881 
     882%% ================================================================================================= 
    869883\subsection{Continuous skew flux formulation} 
    870884\label{sec:TRIADS_continuous-skew-flux} 
     
    975989Since it has the same divergence as the advective form it also preserves the tracer variance. 
    976990 
     991%% ================================================================================================= 
    977992\subsection{Discrete skew flux formulation} 
    978993 
     
    10171032It also ensures the following two key properties. 
    10181033 
     1034%% ================================================================================================= 
    10191035\subsubsection{No change in tracer variance} 
    10201036 
     
    10391055Hence the two fluxes associated with each triad make no net contribution to the variance budget. 
    10401056 
     1057%% ================================================================================================= 
    10411058\subsubsection{Reduction in gravitational PE} 
    10421059 
     
    10931110\beta_i^k\delta_{k+ k_p}[S^i]<0$, this PE change is negative. 
    10941111 
     1112%% ================================================================================================= 
    10951113\subsection{Treatment of the triads at the boundaries} 
    10961114\label{sec:TRIADS_skew_bdry} 
     
    11041122The namelist parameter \np{ln_botmix_triad}{ln\_botmix\_triad} has no effect on the eddy-induced skew-fluxes. 
    11051123 
     1124%% ================================================================================================= 
    11061125\subsection{Limiting of the slopes within the interior} 
    11071126\label{sec:TRIADS_limitskew} 
     
    11111130Each individual triad \rtriadt{R} is so limited. 
    11121131 
     1132%% ================================================================================================= 
    11131133\subsection{Tapering within the surface mixed layer} 
    11141134\label{sec:TRIADS_taperskew} 
     
    11311151(the horizontal flux convergence is relatively insignificant within the mixed-layer). 
    11321152 
     1153%% ================================================================================================= 
    11331154\subsection{Streamfunction diagnostics} 
    11341155\label{sec:TRIADS_sfdiag} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex

    r11596 r11597  
    99\vfill 
    1010\begin{figure}[b] 
     11%% ================================================================================================= 
    1112\subsubsection*{Changes record} 
    1213\begin{tabular}{l||l|m{0.65\linewidth}} 
     
    2728%=============================================================== 
    2829 
     30%% ================================================================================================= 
    2931\section{Direct initialization} 
    3032\label{sec:ASM_DI} 
     
    3436DI is used when \np{ln_asmdin}{ln\_asmdin} is set to true. 
    3537 
     38%% ================================================================================================= 
    3639\section{Incremental analysis updates} 
    3740\label{sec:ASM_IAU} 
     
    9295%========================================================================== 
    9396% Divergence damping description %%% 
     97%% ================================================================================================= 
    9498\section{Divergence damping initialisation} 
    9599\label{sec:ASM_div_dmp} 
     
    135139%========================================================================== 
    136140 
     141%% ================================================================================================= 
    137142\section{Implementation details} 
    138143\label{sec:ASM_details} 
     
    141146the ORCA2 grid. 
    142147 
    143 %------------------------------------------nam_asminc----------------------------------------------------- 
    144148% 
    145149\begin{listing} 
     
    148152  \label{lst:nam_asminc} 
    149153\end{listing} 
    150 %------------------------------------------------------------------------------------------------------------- 
    151154 
    152155The header of an assimilation increments file produced using the NetCDF tool 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIA.tex

    r11596 r11597  
    99\vfill 
    1010\begin{figure}[b] 
     11%% ================================================================================================= 
    1112\subsubsection*{Changes record} 
    1213\begin{tabular}{l||l|m{0.65\linewidth}} 
     
    2021\end{figure} 
    2122 
     23%% ================================================================================================= 
    2224\section{Model output} 
    2325\label{sec:DIA_io_old} 
     
    4547%\gmcomment{                    % start of gmcomment 
    4648 
     49%% ================================================================================================= 
    4750\section{Standard model output (IOM)} 
    4851\label{sec:DIA_iom} 
     
    103106even without a parallel-enabled NetCDF4 library, simply by employing only one dedicated I/O server. 
    104107 
     108%% ================================================================================================= 
    105109\subsection{XIOS: Reading and writing restart file} 
    106110 
     
    142146An older versions of XIOS do not support reading functionality. It's recommended to use at least XIOS2@1451. 
    143147 
     148%% ================================================================================================= 
    144149\subsection{XIOS: XML Inputs-Outputs Server} 
    145150 
     151%% ================================================================================================= 
    146152\subsubsection{Attached or detached mode?} 
    147153 
     
    178184The following subsection provides a typical example but the syntax will vary in different MPP environments. 
    179185 
     186%% ================================================================================================= 
    180187\subsubsection{Number of cpu used by XIOS in detached mode} 
    181188 
     
    192199\cmd|mpirun -np 62 ./nemo.exe : -np 2 ./xios_server.exe| 
    193200 
     201%% ================================================================================================= 
    194202\subsubsection{Control of XIOS: the context in iodef.xml} 
    195203 
     
    237245\end{table} 
    238246 
     247%% ================================================================================================= 
    239248\subsection{Practical issues} 
    240249 
     250%% ================================================================================================= 
    241251\subsubsection{Installation} 
    242252 
     
    247257{Extract and install XIOS} guide provides an example illustration of how this can be achieved. 
    248258 
     259%% ================================================================================================= 
    249260\subsubsection{Add your own outputs} 
    250261 
     
    303314\end{enumerate} 
    304315 
     316%% ================================================================================================= 
    305317\subsection{XML fundamentals} 
    306318 
     319%% ================================================================================================= 
    307320\subsubsection{ XML basic rules} 
    308321 
     
    314327See \href{http://www.xmlnews.org/docs/xml-basics.html}{here} for more details. 
    315328 
     329%% ================================================================================================= 
    316330\subsubsection{Structure of the XML file used in \NEMO} 
    317331 
     
    419433\end{table} 
    420434 
     435%% ================================================================================================= 
    421436\subsubsection{Nesting XML files} 
    422437 
     
    435450\end{xmllines} 
    436451 
     452%% ================================================================================================= 
    437453\subsubsection{Use of inheritance} 
    438454 
     
    475491Inherit (and overwrite, if needed) the attributes of a tag you are refering to. 
    476492 
     493%% ================================================================================================= 
    477494\subsubsection{Use of groups} 
    478495 
     
    516533\end{xmllines} 
    517534 
     535%% ================================================================================================= 
    518536\subsection{Detailed functionalities} 
    519537 
     
    521539the new functionalities offered by the XML interface of XIOS. 
    522540 
     541%% ================================================================================================= 
    523542\subsubsection{Define horizontal subdomains} 
    524543 
     
    562581We are therefore advising to use the ''one\_file'' type in this case. 
    563582 
     583%% ================================================================================================= 
    564584\subsubsection{Define vertical zooms} 
    565585 
     
    585605\end{xmllines} 
    586606 
     607%% ================================================================================================= 
    587608\subsubsection{Control of the output file names} 
    588609 
     
    657678\noindent will give the following file name radical: \ifile{myfile\_ORCA2\_19891231\_freq1d} 
    658679 
     680%% ================================================================================================= 
    659681\subsubsection{Other controls of the XML attributes from \NEMO} 
    660682 
     
    710732\end{table} 
    711733 
     734%% ================================================================================================= 
    712735\subsubsection{Advanced use of XIOS functionalities} 
    713736 
     737%% ================================================================================================= 
    714738\subsection{XML reference tables} 
    715739\label{subsec:DIA_IOM_xmlref} 
     
    858882field\_ref="sst" means that attributes not explicitely defined, are inherited from sst field. 
    859883 
     884%% ================================================================================================= 
    860885\subsubsection{Tag list per family} 
    861886 
     
    10511076\end{table} 
    10521077 
     1078%% ================================================================================================= 
    10531079\subsubsection{Attributes list per family} 
    10541080 
     
    12861312\end{table} 
    12871313 
     1314%% ================================================================================================= 
    12881315\subsection{CF metadata standard compliance} 
    12891316 
     
    12981325This must be set to true if these metadata are to be included in the output files. 
    12991326 
     1327%% ================================================================================================= 
    13001328\section[NetCDF4 support (\texttt{\textbf{key\_netcdf4}})]{NetCDF4 support (\protect\key{netcdf4})} 
    13011329\label{sec:DIA_nc4} 
     
    13151343setting the \np{ln_nc4zip}{ln\_nc4zip} logical to false in the \nam{nc4}{nc4} namelist: 
    13161344 
    1317 %------------------------------------------namnc4---------------------------------------------------- 
    13181345 
    13191346\begin{listing} 
     
    13221349  \label{lst:namnc4} 
    13231350\end{listing} 
    1324 %------------------------------------------------------------------------------------------------------------- 
    13251351 
    13261352If \key{netcdf4} has not been defined, these namelist parameters are not read. 
     
    13671393each processing region. 
    13681394 
    1369 %------------------------------------------TABLE---------------------------------------------------- 
    13701395\begin{table} 
    13711396  \centering 
     
    14031428  \label{tab:DIA_NC4} 
    14041429\end{table} 
    1405 %---------------------------------------------------------------------------------------------------- 
    14061430 
    14071431When \key{iomput} is activated with \key{netcdf4} chunking and compression parameters for fields produced via 
     
    14141438the invidual processing regions and different chunking choices may be desired. 
    14151439 
     1440%% ================================================================================================= 
    14161441\section[Tracer/Dynamics trends (\forcode{&namtrd})]{Tracer/Dynamics trends (\protect\nam{trd}{trd})} 
    14171442\label{sec:DIA_trd} 
    14181443 
    1419 %------------------------------------------namtrd---------------------------------------------------- 
    14201444 
    14211445\begin{listing} 
     
    14241448  \label{lst:namtrd} 
    14251449\end{listing} 
    1426 %------------------------------------------------------------------------------------------------------------- 
    14271450 
    14281451Each trend of the dynamics and/or temperature and salinity time evolution equations can be send to 
     
    14621485and none of the options have been tested with variable volume (\ie\ \np[=.true.]{ln_linssh}{ln\_linssh}). 
    14631486 
     1487%% ================================================================================================= 
    14641488\section[FLO: On-Line Floats trajectories (\texttt{\textbf{key\_floats}})]{FLO: On-Line Floats trajectories (\protect\key{floats})} 
    14651489\label{sec:DIA_FLO} 
    1466 %--------------------------------------------namflo------------------------------------------------------- 
    14671490 
    14681491\begin{listing} 
     
    14711494  \label{lst:namflo} 
    14721495\end{listing} 
    1473 %-------------------------------------------------------------------------------------------------------------- 
    14741496 
    14751497The on-line computation of floats advected either by the three dimensional velocity field or constraint to 
     
    14811503are consistent with the numeric of the code, so that the trajectories never intercept the bathymetry. 
    14821504 
     1505%% ================================================================================================= 
    14831506\subsubsection{Input data: initial coordinates} 
    14841507 
     
    15381561\np{jpnflnewflo}{jpnflnewflo} can be added in the initialization file. 
    15391562 
     1563%% ================================================================================================= 
    15401564\subsubsection{Output data} 
    15411565 
     
    15641588\end{xmllines} 
    15651589 
     1590%% ================================================================================================= 
    15661591\section[Harmonic analysis of tidal constituents (\texttt{\textbf{key\_diaharm}})]{Harmonic analysis of tidal constituents (\protect\key{diaharm})} 
    15671592\label{sec:DIA_diag_harm} 
    15681593 
    1569 %------------------------------------------nam_diaharm---------------------------------------------------- 
    15701594% 
    15711595\begin{listing} 
     
    15741598  \label{lst:nam_diaharm} 
    15751599\end{listing} 
    1576 %---------------------------------------------------------------------------------------------------------- 
    15771600 
    15781601A module is available to compute the amplitude and phase of tidal waves. 
     
    16121635We obtain in output $C_{j}$ and $S_{j}$ for each tidal wave. 
    16131636 
     1637%% ================================================================================================= 
    16141638\section[Transports across sections (\texttt{\textbf{key\_diadct}})]{Transports across sections (\protect\key{diadct})} 
    16151639\label{sec:DIA_diag_dct} 
    16161640 
    1617 %------------------------------------------nam_diadct---------------------------------------------------- 
    16181641 
    16191642\begin{listing} 
     
    16221645  \label{lst:nam_diadct} 
    16231646\end{listing} 
    1624 %------------------------------------------------------------------------------------------------------------- 
    16251647 
    16261648A module is available to compute the transport of volume, heat and salt through sections. 
     
    16461668\np{nn_debug}{nn\_debug} : debugging of the section 
    16471669 
     1670%% ================================================================================================= 
    16481671\subsubsection{Creating a binary file containing the pathway of each section} 
    16491672 
     
    17171740 } 
    17181741 
     1742%% ================================================================================================= 
    17191743\subsubsection{To read the output files} 
    17201744 
     
    17551779\end{table} 
    17561780 
     1781%% ================================================================================================= 
    17571782\section{Diagnosing the steric effect in sea surface height} 
    17581783\label{sec:DIA_steric} 
     
    19311956Both steric and thermosteric sea level are computed in \mdl{diaar5}. 
    19321957 
     1958%% ================================================================================================= 
    19331959\section{Other diagnostics} 
    19341960\label{sec:DIA_diag_others} 
     
    19371963The available ready-to-add diagnostics modules can be found in directory DIA. 
    19381964 
     1965%% ================================================================================================= 
    19391966\subsection[Depth of various quantities (\textit{diahth.F90})]{Depth of various quantities (\protect\mdl{diahth})} 
    19401967 
     
    19691996%       CMIP specific diagnostics 
    19701997% ----------------------------------------------------------- 
     1998%% ================================================================================================= 
    19711999\subsection[CMIP specific diagnostics (\textit{diaar5.F90}, \textit{diaptr.F90})]{CMIP specific diagnostics (\protect\mdl{diaar5})} 
    19722000 
     
    19872015the Indo-Pacific mask been deduced from the sum of the Indian and Pacific mask (\autoref{fig:DIA_mask_subasins}). 
    19882016 
    1989 %------------------------------------------namptr----------------------------------------- 
    19902017 
    19912018\begin{listing} 
     
    19942021  \label{lst:namptr} 
    19952022\end{listing} 
    1996 %----------------------------------------------------------------------------------------- 
    19972023 
    19982024% ----------------------------------------------------------- 
    19992025%       25 hour mean and hourly Surface, Mid and Bed 
    20002026% ----------------------------------------------------------- 
     2027%% ================================================================================================= 
    20012028\subsection{25 hour mean output for tidal models} 
    20022029 
    2003 %------------------------------------------nam_dia25h------------------------------------- 
    20042030 
    20052031\begin{listing} 
     
    20082034  \label{lst:nam_dia25h} 
    20092035\end{listing} 
    2010 %----------------------------------------------------------------------------------------- 
    20112036 
    20122037A module is available to compute a crudely detided M2 signal by obtaining a 25 hour mean. 
     
    20182043%     Top Middle and Bed hourly output 
    20192044% ----------------------------------------------------------- 
     2045%% ================================================================================================= 
    20202046\subsection{Top middle and bed hourly output} 
    20212047 
    2022 %------------------------------------------nam_diatmb----------------------------------------------------- 
    20232048 
    20242049\begin{listing} 
     
    20272052  \label{lst:nam_diatmb} 
    20282053\end{listing} 
    2029 %---------------------------------------------------------------------------------------------------------- 
    20302054 
    20312055A module is available to output the surface (top), mid water and bed diagnostics of a set of standard variables. 
     
    20382062%     Courant numbers 
    20392063% ----------------------------------------------------------- 
     2064%% ================================================================================================= 
    20402065\subsection{Courant numbers} 
    20412066 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIU.tex

    r11596 r11597  
    5252 
    5353%=============================================================== 
     54%% ================================================================================================= 
    5455\section{Warm layer model} 
    5556\label{sec:DIU_warm_layer_sec} 
     
    109110%=============================================================== 
    110111 
     112%% ================================================================================================= 
    111113\section{Cool skin model} 
    112114\label{sec:DIU_cool_skin_sec} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DOM.tex

    r11596 r11597  
    3838and other relevant information about the DOM (DOMain) source code modules. 
    3939 
     40%% ================================================================================================= 
    4041\section{Fundamentals of the discretisation} 
    4142\label{sec:DOM_basics} 
    4243 
     44%% ================================================================================================= 
    4345\subsection{Arrangement of variables} 
    4446\label{subsec:DOM_cell} 
     
    145147\end{figure} 
    146148 
     149%% ================================================================================================= 
    147150\subsection{Discrete operators} 
    148151\label{subsec:DOM_operators} 
     
    235238demonstrate integral conservative properties of the discrete formulation chosen. 
    236239 
     240%% ================================================================================================= 
    237241\subsection{Numerical indexing} 
    238242\label{subsec:DOM_Num_Index} 
     
    258262%        Horizontal Indexing 
    259263% ----------------------------------- 
     264%% ================================================================================================= 
    260265\subsubsection{Horizontal indexing} 
    261266\label{subsec:DOM_Num_Index_hor} 
     
    270275%        Vertical indexing 
    271276% ----------------------------------- 
     277%% ================================================================================================= 
    272278\subsubsection{Vertical indexing} 
    273279\label{subsec:DOM_Num_Index_vertical} 
     
    301307\end{figure} 
    302308 
     309%% ================================================================================================= 
    303310\section{Spatial domain configuration} 
    304311\label{subsec:DOM_config} 
     
    338345%        Domain Size 
    339346% ----------------------------------- 
     347%% ================================================================================================= 
    340348\subsection{Domain size} 
    341349\label{subsec:DOM_size} 
     
    355363See \autoref{sec:LBC_jperio} for details on the available options and the corresponding values for \jp{jperio}. 
    356364 
     365%% ================================================================================================= 
    357366\subsection[Horizontal grid mesh (\textit{domhgr.F90}]{Horizontal grid mesh (\protect\mdl{domhgr})} 
    358367\label{subsec:DOM_hgr} 
    359368 
     369%% ================================================================================================= 
    360370\subsubsection{Required fields} 
    361371\label{sec:DOM_hgr_fields} 
     
    380390evaluated for the same arguments as $\lambda$ and $\varphi$. 
    381391 
     392%% ================================================================================================= 
    382393\subsubsection{Optional fields} 
    383394 
     
    417428thus no specific arrays are defined at $w$ points. 
    418429 
     430%% ================================================================================================= 
    419431\subsection[Vertical grid (\textit{domzgr.F90})]{Vertical grid (\protect\mdl{domzgr})} 
    420432\label{subsec:DOM_zgr} 
    421 %-----------------------------------------namdom------------------------------------------- 
    422433\begin{listing} 
    423434  \nlst{namdom} 
     
    425436  \label{lst:namdom} 
    426437\end{listing} 
    427 %------------------------------------------------------------------------------------------------------------- 
    428438 
    429439In the vertical, the model mesh is determined by four things: 
     
    506516their reference counterpart and remain fixed. 
    507517 
     518%% ================================================================================================= 
    508519\subsubsection{Required fields} 
    509520\label{sec:DOM_zgr_fields} 
     
    541552With ice cavities, \jp{top\_level} determines the first wet point below the overlying ice shelf. 
    542553 
     554%% ================================================================================================= 
    543555\subsubsection{Level bathymetry and mask} 
    544556\label{subsec:DOM_msk} 
     
    572584%% (see \autoref{fig:LBC_jperio}). 
    573585 
    574 %------------------------------------------------------------------------------------------------- 
    575586%        Closed seas 
    576 %------------------------------------------------------------------------------------------------- 
     587%% ================================================================================================= 
    577588\subsection{Closed seas} 
    578589\label{subsec:DOM_closea} 
     
    595606\end{clines} 
    596607 
     608%% ================================================================================================= 
    597609\subsection{Output grid files} 
    598610\label{subsec:DOM_meshmask} 
     
    613625This file contains additional fields that can be useful for post-processing applications. 
    614626 
     627%% ================================================================================================= 
    615628\section[Initial state (\textit{istate.F90} and \textit{dtatsd.F90})]{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})} 
    616629\label{sec:DOM_DTA_tsd} 
    617 %-----------------------------------------namtsd------------------------------------------- 
    618630\begin{listing} 
    619631  \nlst{namtsd} 
     
    621633  \label{lst:namtsd} 
    622634\end{listing} 
    623 %------------------------------------------------------------------------------------------ 
    624635 
    625636Basic initial state options are defined in \nam{tsd}{tsd}. 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DYN.tex

    r11596 r11597  
    5353MISC correspond to "extracting tendency terms" or "vorticity balance"?} 
    5454 
     55%% ================================================================================================= 
    5556\section{Sea surface height and diagnostic variables ($\eta$, $\zeta$, $\chi$, $w$)} 
    5657\label{sec:DYN_divcur_wzv} 
    5758 
    58 %-------------------------------------------------------------------------------------------------------------- 
    59 %           Horizontal divergence and relative vorticity 
    60 %-------------------------------------------------------------------------------------------------------------- 
     59%% ================================================================================================= 
    6160\subsection[Horizontal divergence and relative vorticity (\textit{divcur.F90})]{Horizontal divergence and relative vorticity (\protect\mdl{divcur})} 
    6261\label{subsec:DYN_divcur} 
     
    9291the nonlinear advection and of the vertical velocity respectively. 
    9392 
    94 %-------------------------------------------------------------------------------------------------------------- 
    95 %           Sea Surface Height evolution 
    96 %-------------------------------------------------------------------------------------------------------------- 
     93%% ================================================================================================= 
    9794\subsection[Horizontal divergence and relative vorticity (\textit{sshwzv.F90})]{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})} 
    9895\label{subsec:DYN_sshwzv} 
     
    152149(see \autoref{subsec:DOM_Num_Index_vertical}). 
    153150 
     151 
     152%% ================================================================================================= 
    154153\section{Coriolis and advection: vector invariant form} 
    155154\label{sec:DYN_adv_cor_vect} 
    156 %-----------------------------------------nam_dynadv---------------------------------------------------- 
    157155 
    158156\begin{listing} 
     
    161159  \label{lst:namdyn_adv} 
    162160\end{listing} 
    163 %------------------------------------------------------------------------------------------------------------- 
    164161 
    165162The vector invariant form of the momentum equations is the one most often used in 
     
    172169\autoref{chap:LBC}. 
    173170 
     171%% ================================================================================================= 
    174172\subsection[Vorticity term (\textit{dynvor.F90})]{Vorticity term (\protect\mdl{dynvor})} 
    175173\label{subsec:DYN_vor} 
    176 %------------------------------------------nam_dynvor---------------------------------------------------- 
    177174 
    178175\begin{listing} 
     
    181178  \label{lst:namdyn_vor} 
    182179\end{listing} 
    183 %------------------------------------------------------------------------------------------------------------- 
    184180 
    185181Options are defined through the \nam{dyn_vor}{dyn\_vor} namelist variables. 
     
    195191The vorticity terms are all computed in dedicated routines that can be found in the \mdl{dynvor} module. 
    196192 
    197 %------------------------------------------------------------- 
    198193%                 enstrophy conserving scheme 
    199 %------------------------------------------------------------- 
     194%% ================================================================================================= 
    200195\subsubsection[Enstrophy conserving scheme (\forcode{ln_dynvor_ens})]{Enstrophy conserving scheme (\protect\np{ln_dynvor_ens}{ln\_dynvor\_ens})} 
    201196\label{subsec:DYN_vor_ens} 
     
    218213\end{equation} 
    219214 
    220 %------------------------------------------------------------- 
    221215%                 energy conserving scheme 
    222 %------------------------------------------------------------- 
     216%% ================================================================================================= 
    223217\subsubsection[Energy conserving scheme (\forcode{ln_dynvor_ene})]{Energy conserving scheme (\protect\np{ln_dynvor_ene}{ln\_dynvor\_ene})} 
    224218\label{subsec:DYN_vor_ene} 
     
    238232\end{equation} 
    239233 
    240 %------------------------------------------------------------- 
    241234%                 mix energy/enstrophy conserving scheme 
    242 %------------------------------------------------------------- 
     235%% ================================================================================================= 
    243236\subsubsection[Mixed energy/enstrophy conserving scheme (\forcode{ln_dynvor_mix})]{Mixed energy/enstrophy conserving scheme (\protect\np{ln_dynvor_mix}{ln\_dynvor\_mix})} 
    244237\label{subsec:DYN_vor_mix} 
     
    263256\] 
    264257 
    265 %------------------------------------------------------------- 
    266258%                 energy and enstrophy conserving scheme 
    267 %------------------------------------------------------------- 
     259%% ================================================================================================= 
    268260\subsubsection[Energy and enstrophy conserving scheme (\forcode{ln_dynvor_een})]{Energy and enstrophy conserving scheme (\protect\np{ln_dynvor_een}{ln\_dynvor\_een})} 
    269261\label{subsec:DYN_vor_een} 
     
    353345leading to a larger topostrophy of the flow \citep{barnier.madec.ea_OD06, penduff.le-sommer.ea_OS07}. 
    354346 
    355 %-------------------------------------------------------------------------------------------------------------- 
    356 %           Kinetic Energy Gradient term 
    357 %-------------------------------------------------------------------------------------------------------------- 
     347%% ================================================================================================= 
    358348\subsection[Kinetic energy gradient term (\textit{dynkeg.F90})]{Kinetic energy gradient term (\protect\mdl{dynkeg})} 
    359349\label{subsec:DYN_keg} 
     
    373363\] 
    374364 
    375 %-------------------------------------------------------------------------------------------------------------- 
    376 %           Vertical advection term 
    377 %-------------------------------------------------------------------------------------------------------------- 
     365%% ================================================================================================= 
    378366\subsection[Vertical advection term (\textit{dynzad.F90})]{Vertical advection term (\protect\mdl{dynzad})} 
    379367\label{subsec:DYN_zad} 
     
    400388an option which is only available with a TVD scheme (see \np{ln_traadv_tvd_zts}{ln\_traadv\_tvd\_zts} in \autoref{subsec:TRA_adv_tvd}). 
    401389 
     390 
     391%% ================================================================================================= 
    402392\section{Coriolis and advection: flux form} 
    403393\label{sec:DYN_adv_cor_flux} 
    404 %------------------------------------------nam_dynadv---------------------------------------------------- 
    405  
    406 %------------------------------------------------------------------------------------------------------------- 
    407394 
    408395Options are defined through the \nam{dyn_adv}{dyn\_adv} namelist variables. 
     
    413400no slip or partial slip boundary conditions are applied following \autoref{chap:LBC}. 
    414401 
    415 %-------------------------------------------------------------------------------------------------------------- 
    416 %           Coriolis plus curvature metric terms 
    417 %-------------------------------------------------------------------------------------------------------------- 
     402%% ================================================================================================= 
    418403\subsection[Coriolis plus curvature metric terms (\textit{dynvor.F90})]{Coriolis plus curvature metric terms (\protect\mdl{dynvor})} 
    419404\label{subsec:DYN_cor_flux} 
     
    434419This term is evaluated using a leapfrog scheme, \ie\ the velocity is centred in time (\textit{now} velocity). 
    435420 
    436 %-------------------------------------------------------------------------------------------------------------- 
    437 %           Flux form Advection term 
    438 %-------------------------------------------------------------------------------------------------------------- 
     421%% ================================================================================================= 
    439422\subsection[Flux form advection term (\textit{dynadv.F90})]{Flux form advection term (\protect\mdl{dynadv})} 
    440423\label{subsec:DYN_adv_flux} 
     
    467450and $uw$-points for $u$ and at the $f$-, $T$- and $vw$-points for $v$. 
    468451 
    469 %------------------------------------------------------------- 
    470452%                 2nd order centred scheme 
    471 %------------------------------------------------------------- 
     453%% ================================================================================================= 
    472454\subsubsection[CEN2: $2^{nd}$ order centred scheme (\forcode{ln_dynadv_cen2})]{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln_dynadv_cen2}{ln\_dynadv\_cen2})} 
    473455\label{subsec:DYN_adv_cen2} 
     
    490472so $u$ and $v$ are the \emph{now} velocities. 
    491473 
    492 %------------------------------------------------------------- 
    493474%                 UBS scheme 
    494 %------------------------------------------------------------- 
     475%% ================================================================================================= 
    495476\subsubsection[UBS: Upstream Biased Scheme (\forcode{ln_dynadv_ubs})]{UBS: Upstream Biased Scheme (\protect\np{ln_dynadv_ubs}{ln\_dynadv\_ubs})} 
    496477\label{subsec:DYN_adv_ubs} 
     
    543524%%% 
    544525 
     526%% ================================================================================================= 
    545527\section[Hydrostatic pressure gradient (\textit{dynhpg.F90})]{Hydrostatic pressure gradient (\protect\mdl{dynhpg})} 
    546528\label{sec:DYN_hpg} 
    547 %------------------------------------------nam_dynhpg--------------------------------------------------- 
    548529 
    549530\begin{listing} 
     
    552533  \label{lst:namdyn_hpg} 
    553534\end{listing} 
    554 %------------------------------------------------------------------------------------------------------------- 
    555535 
    556536Options are defined through the \nam{dyn_hpg}{dyn\_hpg} namelist variables. 
     
    566546At the lateral boundaries either free slip, no slip or partial slip boundary conditions are applied. 
    567547 
    568 %-------------------------------------------------------------------------------------------------------------- 
    569 %           z-coordinate with full step 
    570 %-------------------------------------------------------------------------------------------------------------- 
     548%% ================================================================================================= 
    571549\subsection[Full step $Z$-coordinate (\forcode{ln_dynhpg_zco})]{Full step $Z$-coordinate (\protect\np{ln_dynhpg_zco}{ln\_dynhpg\_zco})} 
    572550\label{subsec:DYN_hpg_zco} 
     
    611589\autoref{eq:DYN_hpg_zco} through the space and time variations of the vertical scale factor $e_{3w}$. 
    612590 
    613 %-------------------------------------------------------------------------------------------------------------- 
    614 %           z-coordinate with partial step 
    615 %-------------------------------------------------------------------------------------------------------------- 
     591%% ================================================================================================= 
    616592\subsection[Partial step $Z$-coordinate (\forcode{ln_dynhpg_zps})]{Partial step $Z$-coordinate (\protect\np{ln_dynhpg_zps}{ln\_dynhpg\_zps})} 
    617593\label{subsec:DYN_hpg_zps} 
     
    632608module \mdl{zpsdhe} located in the TRA directory and described in \autoref{sec:TRA_zpshde}. 
    633609 
    634 %-------------------------------------------------------------------------------------------------------------- 
    635 %           s- and s-z-coordinates 
    636 %-------------------------------------------------------------------------------------------------------------- 
     610%% ================================================================================================= 
    637611\subsection{$S$- and $Z$-$S$-coordinates} 
    638612\label{subsec:DYN_hpg_sco} 
     
    681655This method can provide a more accurate calculation of the horizontal pressure gradient than the standard scheme. 
    682656 
     657%% ================================================================================================= 
    683658\subsection{Ice shelf cavity} 
    684659\label{subsec:DYN_hpg_isf} 
     
    697672\autoref{subsec:DYN_hpg_sco}. 
    698673 
    699 %-------------------------------------------------------------------------------------------------------------- 
    700 %           Time-scheme 
    701 %-------------------------------------------------------------------------------------------------------------- 
     674%% ================================================================================================= 
    702675\subsection[Time-scheme (\forcode{ln_dynhpg_imp})]{Time-scheme (\protect\np{ln_dynhpg_imp}{ln\_dynhpg\_imp})} 
    703676\label{subsec:DYN_hpg_imp} 
     
    758731This option is controlled by  \np{nn_dynhpg_rst}{nn\_dynhpg\_rst}, a namelist parameter. 
    759732 
     733%% ================================================================================================= 
    760734\section[Surface pressure gradient (\textit{dynspg.F90})]{Surface pressure gradient (\protect\mdl{dynspg})} 
    761735\label{sec:DYN_spg} 
    762 %-----------------------------------------nam_dynspg---------------------------------------------------- 
    763736 
    764737\begin{listing} 
     
    767740  \label{lst:namdyn_spg} 
    768741\end{listing} 
    769 %------------------------------------------------------------------------------------------------------------ 
    770742 
    771743Options are defined through the \nam{dyn_spg}{dyn\_spg} namelist variables. 
     
    795767As a consequence the update of the $next$ velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 
    796768 
    797 %-------------------------------------------------------------------------------------------------------------- 
    798 % Explicit free surface formulation 
    799 %-------------------------------------------------------------------------------------------------------------- 
     769%% ================================================================================================= 
    800770\subsection[Explicit free surface (\forcode{ln_dynspg_exp})]{Explicit free surface (\protect\np{ln_dynspg_exp}{ln\_dynspg\_exp})} 
    801771\label{subsec:DYN_spg_exp} 
     
    821791Thus, nothing is done in the \mdl{dynspg\_exp} module. 
    822792 
    823 %-------------------------------------------------------------------------------------------------------------- 
    824 % Split-explict free surface formulation 
    825 %-------------------------------------------------------------------------------------------------------------- 
     793%% ================================================================================================= 
    826794\subsection[Split-explicit free surface (\forcode{ln_dynspg_ts})]{Split-explicit free surface (\protect\np{ln_dynspg_ts}{ln\_dynspg\_ts})} 
    827795\label{subsec:DYN_spg_ts} 
    828 %------------------------------------------namsplit----------------------------------------------------------- 
    829796% 
    830797%\nlst{namsplit} 
    831 %------------------------------------------------------------------------------------------------------------- 
    832798 
    833799The split-explicit free surface formulation used in \NEMO\ (\np{ln_dynspg_ts}{ln\_dynspg\_ts} set to true), 
     
    10651031%>>>>>=============== 
    10661032 
    1067 %-------------------------------------------------------------------------------------------------------------- 
    1068 % Filtered free surface formulation 
    1069 %-------------------------------------------------------------------------------------------------------------- 
     1033%% ================================================================================================= 
    10701034\subsection{Filtered free surface (\forcode{dynspg_flt?})} 
    10711035\label{subsec:DYN_spg_fltp} 
     
    10931057It is computed once and for all and applies to all ocean time steps. 
    10941058 
     1059%% ================================================================================================= 
    10951060\section[Lateral diffusion term and operators (\textit{dynldf.F90})]{Lateral diffusion term and operators (\protect\mdl{dynldf})} 
    10961061\label{sec:DYN_ldf} 
    1097 %------------------------------------------nam_dynldf---------------------------------------------------- 
    10981062 
    10991063\begin{listing} 
     
    11021066  \label{lst:namdyn_ldf} 
    11031067\end{listing} 
    1104 %------------------------------------------------------------------------------------------------------------- 
    11051068 
    11061069Options are defined through the \nam{dyn_ldf}{dyn\_ldf} namelist variables. 
     
    11301093} 
    11311094 
    1132 %           Vertical diffusion term 
    1133 % External Forcing 
    1134 % Wetting and drying 
    1135 % Time evolution term 
     1095%% ================================================================================================= 
     1096\subsection[Iso-level laplacian (\forcode{ln_dynldf_lap})]{Iso-level laplacian operator (\protect\np{ln_dynldf_lap}{ln\_dynldf\_lap})} 
     1097\label{subsec:DYN_ldf_lap} 
     1098 
     1099For lateral iso-level diffusion, the discrete operator is: 
     1100\begin{equation} 
     1101  \label{eq:DYN_ldf_lap} 
     1102  \left\{ 
     1103    \begin{aligned} 
     1104      D_u^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm} 
     1105          \;\chi } \right]-\frac{1}{e_{2u} {\kern 1pt}e_{3u} }\delta_j \left[ 
     1106        {A_f^{lm} \;e_{3f} \zeta } \right] \\ \\ 
     1107      D_v^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm} 
     1108          \;\chi } \right]+\frac{1}{e_{1v} {\kern 1pt}e_{3v} }\delta_i \left[ 
     1109        {A_f^{lm} \;e_{3f} \zeta } \right] 
     1110    \end{aligned} 
     1111  \right. 
     1112\end{equation} 
     1113 
     1114As explained in \autoref{subsec:MB_ldf}, 
     1115this formulation (as the gradient of a divergence and curl of the vorticity) preserves symmetry and 
     1116ensures a complete separation between the vorticity and divergence parts of the momentum diffusion. 
     1117 
     1118%% ================================================================================================= 
     1119\subsection[Rotated laplacian (\forcode{ln_dynldf_iso})]{Rotated laplacian operator (\protect\np{ln_dynldf_iso}{ln\_dynldf\_iso})} 
     1120\label{subsec:DYN_ldf_iso} 
     1121 
     1122A rotation of the lateral momentum diffusion operator is needed in several cases: 
     1123for iso-neutral diffusion in the $z$-coordinate (\np[=.true.]{ln_dynldf_iso}{ln\_dynldf\_iso}) and 
     1124for either iso-neutral (\np[=.true.]{ln_dynldf_iso}{ln\_dynldf\_iso}) or 
     1125geopotential (\np[=.true.]{ln_dynldf_hor}{ln\_dynldf\_hor}) diffusion in the $s$-coordinate. 
     1126In the partial step case, coordinates are horizontal except at the deepest level and 
     1127no rotation is performed when \np[=.true.]{ln_dynldf_hor}{ln\_dynldf\_hor}. 
     1128The diffusion operator is defined simply as the divergence of down gradient momentum fluxes on 
     1129each momentum component. 
     1130It must be emphasized that this formulation ignores constraints on the stress tensor such as symmetry. 
     1131The resulting discrete representation is: 
     1132\begin{equation} 
     1133  \label{eq:DYN_ldf_iso} 
     1134  \begin{split} 
     1135    D_u^{l\textbf{U}} &= \frac{1}{e_{1u} \, e_{2u} \, e_{3u} } \\ 
     1136    &  \left\{\quad  {\delta_{i+1/2} \left[ {A_T^{lm}  \left( 
     1137              {\frac{e_{2t} \; e_{3t} }{e_{1t} } \,\delta_{i}[u] 
     1138                -e_{2t} \; r_{1t} \,\overline{\overline {\delta_{k+1/2}[u]}}^{\,i,\,k}} 
     1139            \right)} \right]}    \right. \\ 
     1140    & \qquad +\ \delta_j \left[ {A_f^{lm} \left( {\frac{e_{1f}\,e_{3f} }{e_{2f} 
     1141            }\,\delta_{j+1/2} [u] - e_{1f}\, r_{2f} 
     1142            \,\overline{\overline {\delta_{k+1/2} [u]}} ^{\,j+1/2,\,k}} 
     1143        \right)} \right] \\ 
     1144    &\qquad +\ \delta_k \left[ {A_{uw}^{lm} \left( {-e_{2u} \, r_{1uw} \,\overline{\overline 
     1145              {\delta_{i+1/2} [u]}}^{\,i+1/2,\,k+1/2} } 
     1146        \right.} \right. \\ 
     1147    &  \ \qquad \qquad \qquad \quad\ 
     1148    - e_{1u} \, r_{2uw} \,\overline{\overline {\delta_{j+1/2} [u]}} ^{\,j,\,k+1/2} \\ 
     1149    & \left. {\left. { \ \qquad \qquad \qquad \ \ \ \left. {\ 
     1150                +\frac{e_{1u}\, e_{2u} }{e_{3uw} }\,\left( {r_{1uw}^2+r_{2uw}^2} 
     1151                \right)\,\delta_{k+1/2} [u]} \right)} \right]\;\;\;} \right\} \\ \\ 
     1152    D_v^{l\textbf{V}} &= \frac{1}{e_{1v} \, e_{2v} \, e_{3v} } \\ 
     1153    &  \left\{\quad  {\delta_{i+1/2} \left[ {A_f^{lm}  \left( 
     1154              {\frac{e_{2f} \; e_{3f} }{e_{1f} } \,\delta_{i+1/2}[v] 
     1155                -e_{2f} \; r_{1f} \,\overline{\overline {\delta_{k+1/2}[v]}}^{\,i+1/2,\,k}} 
     1156            \right)} \right]}    \right. \\ 
     1157    & \qquad +\ \delta_j \left[ {A_T^{lm} \left( {\frac{e_{1t}\,e_{3t} }{e_{2t} 
     1158            }\,\delta_{j} [v] - e_{1t}\, r_{2t} 
     1159            \,\overline{\overline {\delta_{k+1/2} [v]}} ^{\,j,\,k}} 
     1160        \right)} \right] \\ 
     1161    & \qquad +\ \delta_k \left[ {A_{vw}^{lm} \left( {-e_{2v} \, r_{1vw} \,\overline{\overline 
     1162              {\delta_{i+1/2} [v]}}^{\,i+1/2,\,k+1/2} }\right.} \right. \\ 
     1163    &  \ \qquad \qquad \qquad \quad\ 
     1164    - e_{1v} \, r_{2vw} \,\overline{\overline {\delta_{j+1/2} [v]}} ^{\,j+1/2,\,k+1/2} \\ 
     1165    & \left. {\left. { \ \qquad \qquad \qquad \ \ \ \left. {\ 
     1166                +\frac{e_{1v}\, e_{2v} }{e_{3vw} }\,\left( {r_{1vw}^2+r_{2vw}^2} 
     1167                \right)\,\delta_{k+1/2} [v]} \right)} \right]\;\;\;} \right\} 
     1168  \end{split} 
     1169\end{equation} 
     1170where $r_1$ and $r_2$ are the slopes between the surface along which the diffusion operator acts and 
     1171the surface of computation ($z$- or $s$-surfaces). 
     1172The way these slopes are evaluated is given in the lateral physics chapter (\autoref{chap:LDF}). 
     1173 
     1174%% ================================================================================================= 
     1175\subsection[Iso-level bilaplacian (\forcode{ln_dynldf_bilap})]{Iso-level bilaplacian operator (\protect\np{ln_dynldf_bilap}{ln\_dynldf\_bilap})} 
     1176\label{subsec:DYN_ldf_bilap} 
     1177 
     1178The lateral fourth order operator formulation on momentum is obtained by applying \autoref{eq:DYN_ldf_lap} twice. 
     1179It requires an additional assumption on boundary conditions: 
     1180the first derivative term normal to the coast depends on the free or no-slip lateral boundary conditions chosen, 
     1181while the third derivative terms normal to the coast are set to zero (see \autoref{chap:LBC}). 
     1182%%% 
     1183\gmcomment{add a remark on the the change in the position of the coefficient} 
     1184%%% 
     1185 
     1186%% ================================================================================================= 
     1187\section[Vertical diffusion term (\textit{dynzdf.F90})]{Vertical diffusion term (\protect\mdl{dynzdf})} 
     1188\label{sec:DYN_zdf} 
     1189 
     1190Options are defined through the \nam{zdf}{zdf} namelist variables. 
     1191The large vertical diffusion coefficient found in the surface mixed layer together with high vertical resolution implies that in the case of explicit time stepping there would be too restrictive a constraint on the time step. 
     1192Two time stepping schemes can be used for the vertical diffusion term: 
     1193$(a)$ a forward time differencing scheme 
     1194(\np[=.true.]{ln_zdfexp}{ln\_zdfexp}) using a time splitting technique (\np{nn_zdfexp}{nn\_zdfexp} $>$ 1) or 
     1195$(b)$ a backward (or implicit) time differencing scheme (\np[=.false.]{ln_zdfexp}{ln\_zdfexp}) 
     1196(see \autoref{chap:TD}). 
     1197Note that namelist variables \np{ln_zdfexp}{ln\_zdfexp} and \np{nn_zdfexp}{nn\_zdfexp} apply to both tracers and dynamics. 
     1198 
     1199The formulation of the vertical subgrid scale physics is the same whatever the vertical coordinate is. 
     1200The vertical diffusion operators given by \autoref{eq:MB_zdf} take the following semi-discrete space form: 
     1201\[ 
     1202  % \label{eq:DYN_zdf} 
     1203  \left\{ 
     1204    \begin{aligned} 
     1205      D_u^{vm} &\equiv \frac{1}{e_{3u}} \ \delta_k \left[ \frac{A_{uw}^{vm} }{e_{3uw} } 
     1206        \ \delta_{k+1/2} [\,u\,]         \right]     \\ 
     1207      \\ 
     1208      D_v^{vm} &\equiv \frac{1}{e_{3v}} \ \delta_k \left[ \frac{A_{vw}^{vm} }{e_{3vw} } 
     1209        \ \delta_{k+1/2} [\,v\,]         \right] 
     1210    \end{aligned} 
     1211  \right. 
     1212\] 
     1213where $A_{uw}^{vm} $ and $A_{vw}^{vm} $ are the vertical eddy viscosity and diffusivity coefficients. 
     1214The way these coefficients are evaluated depends on the vertical physics used (see \autoref{chap:ZDF}). 
     1215 
     1216The surface boundary condition on momentum is the stress exerted by the wind. 
     1217At the surface, the momentum fluxes are prescribed as the boundary condition on 
     1218the vertical turbulent momentum fluxes, 
     1219\begin{equation} 
     1220  \label{eq:DYN_zdf_sbc} 
     1221  \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1} 
     1222  = \frac{1}{\rho_o} \binom{\tau_u}{\tau_v } 
     1223\end{equation} 
     1224where $\left( \tau_u ,\tau_v \right)$ are the two components of the wind stress vector in 
     1225the (\textbf{i},\textbf{j}) coordinate system. 
     1226The high mixing coefficients in the surface mixed layer ensure that the surface wind stress is distributed in 
     1227the vertical over the mixed layer depth. 
     1228If the vertical mixing coefficient is small (when no mixed layer scheme is used) 
     1229the surface stress enters only the top model level, as a body force. 
     1230The surface wind stress is calculated in the surface module routines (SBC, see \autoref{chap:SBC}). 
     1231 
     1232The turbulent flux of momentum at the bottom of the ocean is specified through a bottom friction parameterisation 
     1233(see \autoref{sec:ZDF_drg}) 
     1234 
     1235%% ================================================================================================= 
     1236\section{External forcings} 
     1237\label{sec:DYN_forcing} 
     1238 
     1239Besides the surface and bottom stresses (see the above section) 
     1240which are introduced as boundary conditions on the vertical mixing, 
     1241three other forcings may enter the dynamical equations by affecting the surface pressure gradient. 
     1242 
     1243(1) When \np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn} (see \autoref{sec:SBC_apr}), 
     1244the atmospheric pressure is taken into account when computing the surface pressure gradient. 
     1245 
     1246(2) When \np[=.true.]{ln_tide_pot}{ln\_tide\_pot} and \np[=.true.]{ln_tide}{ln\_tide} (see \autoref{sec:SBC_tide}), 
     1247the tidal potential is taken into account when computing the surface pressure gradient. 
     1248 
     1249(3) When \np[=2]{nn_ice_embd}{nn\_ice\_embd} and LIM or CICE is used 
     1250(\ie\ when the sea-ice is embedded in the ocean), 
     1251the snow-ice mass is taken into account when computing the surface pressure gradient. 
     1252 
     1253 
     1254\gmcomment{ missing : the lateral boundary condition !!!   another external forcing 
     1255 } 
     1256 
     1257%% ================================================================================================= 
     1258\section{Wetting and drying } 
     1259\label{sec:DYN_wetdry} 
     1260 
     1261There are two main options for wetting and drying code (wd): 
     1262(a) an iterative limiter (il) and (b) a directional limiter (dl). 
     1263The directional limiter is based on the scheme developed by \cite{warner.defne.ea_CG13} for RO 
     1264MS 
     1265which was in turn based on ideas developed for POM by \cite{oey_OM06}. The iterative 
     1266limiter is a new scheme.  The iterative limiter is activated by setting $\mathrm{ln\_wd\_il} = \mathrm{.true.}$ 
     1267and $\mathrm{ln\_wd\_dl} = \mathrm{.false.}$. The directional limiter is activated 
     1268by setting $\mathrm{ln\_wd\_dl} = \mathrm{.true.}$ and $\mathrm{ln\_wd\_il} = \mathrm{.false.}$. 
     1269 
     1270\begin{listing} 
     1271  \nlst{namwad} 
     1272  \caption{\forcode{&namwad}} 
     1273  \label{lst:namwad} 
     1274\end{listing} 
     1275 
     1276The following terminology is used. The depth of the topography (positive downwards) 
     1277at each $(i,j)$ point is the quantity stored in array $\mathrm{ht\_wd}$ in the \NEMO\ code. 
     1278The height of the free surface (positive upwards) is denoted by $ \mathrm{ssh}$. Given the sign 
     1279conventions used, the water depth, $h$, is the height of the free surface plus the depth of the 
     1280topography (i.e. $\mathrm{ssh} + \mathrm{ht\_wd}$). 
     1281 
     1282Both wd schemes take all points in the domain below a land elevation of $\mathrm{rn\_wdld}$ to be 
     1283covered by water. They require the topography specified with a model 
     1284configuration to have negative depths at points where the land is higher than the 
     1285topography's reference sea-level. The vertical grid in \NEMO\ is normally computed relative to an 
     1286initial state with zero sea surface height elevation. 
     1287The user can choose to compute the vertical grid and heights in the model relative to 
     1288a non-zero reference height for the free surface. This choice affects the calculation of the metrics and depths 
     1289(i.e. the $\mathrm{e3t\_0, ht\_0}$ etc. arrays). 
     1290 
     1291Points where the water depth is less than $\mathrm{rn\_wdmin1}$ are interpreted as ``dry''. 
     1292$\mathrm{rn\_wdmin1}$ is usually chosen to be of order $0.05$m but extreme topographies 
     1293with very steep slopes require larger values for normal choices of time-step. Surface fluxes 
     1294are also switched off for dry cells to prevent freezing, boiling etc. of very thin water layers. 
     1295The fluxes are tappered down using a $\mathrm{tanh}$ weighting function 
     1296to no flux as the dry limit $\mathrm{rn\_wdmin1}$ is approached. Even wet cells can be very shallow. 
     1297The depth at which to start tapering is controlled by the user by setting $\mathrm{rn\_wd\_sbcdep}$. 
     1298The fraction $(<1)$ of sufrace fluxes to use at this depth is set by $\mathrm{rn\_wd\_sbcfra}$. 
     1299 
     1300Both versions of the code have been tested in six test cases provided in the WAD\_TEST\_CASES configuration 
     1301and in ``realistic'' configurations covering parts of the north-west European shelf. 
     1302All these configurations have used pure sigma coordinates. It is expected that 
     1303the wetting and drying code will work in domains with more general s-coordinates provided 
     1304the coordinates are pure sigma in the region where wetting and drying actually occurs. 
     1305 
     1306The next sub-section descrbies the directional limiter and the following sub-section the iterative limiter. 
     1307The final sub-section covers some additional considerations that are relevant to both schemes. 
     1308 
     1309 
     1310%   Iterative limiters 
     1311%% ================================================================================================= 
     1312\subsection[Directional limiter (\textit{wet\_dry.F90})]{Directional limiter (\mdl{wet\_dry})} 
     1313\label{subsec:DYN_wd_directional_limiter} 
     1314 
     1315The principal idea of the directional limiter is that 
     1316water should not be allowed to flow out of a dry tracer cell (i.e. one whose water depth is less than \np{rn_wdmin1}{rn\_wdmin1}). 
     1317 
     1318All the changes associated with this option are made to the barotropic solver for the non-linear 
     1319free surface code within dynspg\_ts. 
     1320On each barotropic sub-step the scheme determines the direction of the flow across each face of all the tracer cells 
     1321and sets the flux across the face to zero when the flux is from a dry tracer cell. This prevents cells 
     1322whose depth is rn\_wdmin1 or less from drying out further. The scheme does not force $h$ (the water depth) at tracer cells 
     1323to be at least the minimum depth and hence is able to conserve mass / volume. 
     1324 
     1325The flux across each $u$-face of a tracer cell is multiplied by a factor zuwdmask (an array which depends on ji and jj). 
     1326If the user sets \np[=.false.]{ln_wd_dl_ramp}{ln\_wd\_dl\_ramp} then zuwdmask is 1 when the 
     1327flux is from a cell with water depth greater than \np{rn_wdmin1}{rn\_wdmin1} and 0 otherwise. If the user sets 
     1328\np[=.true.]{ln_wd_dl_ramp}{ln\_wd\_dl\_ramp} the flux across the face is ramped down as the water depth decreases 
     1329from 2 * \np{rn_wdmin1}{rn\_wdmin1} to \np{rn_wdmin1}{rn\_wdmin1}. The use of this ramp reduced grid-scale noise in idealised test cases. 
     1330 
     1331At the point where the flux across a $u$-face is multiplied by zuwdmask , we have chosen 
     1332also to multiply the corresponding velocity on the ``now'' step at that face by zuwdmask. We could have 
     1333chosen not to do that and to allow fairly large velocities to occur in these ``dry'' cells. 
     1334The rationale for setting the velocity to zero is that it is the momentum equations that are being solved 
     1335and the total momentum of the upstream cell (treating it as a finite volume) should be considered 
     1336to be its depth times its velocity. This depth is considered to be zero at ``dry'' $u$-points consistent with its 
     1337treatment in the calculation of the flux of mass across the cell face. 
     1338 
     1339 
     1340\cite{warner.defne.ea_CG13} state that in their scheme the velocity masks at the cell faces for the baroclinic 
     1341timesteps are set to 0 or 1 depending on whether the average of the masks over the barotropic sub-steps is respectively less than 
     1342or greater than 0.5. That scheme does not conserve tracers in integrations started from constant tracer 
     1343fields (tracers independent of $x$, $y$ and $z$). Our scheme conserves constant tracers because 
     1344the velocities used at the tracer cell faces on the baroclinic timesteps are carefully calculated by dynspg\_ts 
     1345to equal their mean value during the barotropic steps. If the user sets \np[=.true.]{ln_wd_dl_bc}{ln\_wd\_dl\_bc}, the 
     1346baroclinic velocities are also multiplied by a suitably weighted average of zuwdmask. 
     1347 
     1348%   Iterative limiters 
     1349 
     1350%% ================================================================================================= 
     1351\subsection[Iterative limiter (\textit{wet\_dry.F90})]{Iterative limiter (\mdl{wet\_dry})} 
     1352\label{subsec:DYN_wd_iterative_limiter} 
     1353 
     1354%% ================================================================================================= 
     1355\subsubsection[Iterative flux limiter (\textit{wet\_dry.F90})]{Iterative flux limiter (\mdl{wet\_dry})} 
     1356\label{subsec:DYN_wd_il_spg_limiter} 
     1357 
     1358The iterative limiter modifies the fluxes across the faces of cells that are either already ``dry'' 
     1359or may become dry within the next time-step using an iterative method. 
     1360 
     1361The flux limiter for the barotropic flow (devised by Hedong Liu) can be understood as follows: 
     1362 
     1363The continuity equation for the total water depth in a column 
     1364\begin{equation} 
     1365  \label{eq:DYN_wd_continuity} 
     1366  \frac{\partial h}{\partial t} + \mathbf{\nabla.}(h\mathbf{u}) = 0 . 
     1367\end{equation} 
     1368can be written in discrete form  as 
     1369 
     1370\begin{align} 
     1371  \label{eq:DYN_wd_continuity_2} 
     1372  \frac{e_1 e_2}{\Delta t} ( h_{i,j}(t_{n+1}) - h_{i,j}(t_e) ) 
     1373  &= - ( \mathrm{flxu}_{i+1,j} - \mathrm{flxu}_{i,j}  + \mathrm{flxv}_{i,j+1} - \mathrm{flxv}_{i,j} ) \\ 
     1374  &= \mathrm{zzflx}_{i,j} . 
     1375\end{align} 
     1376 
     1377In the above $h$ is the depth of the water in the column at point $(i,j)$, 
     1378$\mathrm{flxu}_{i+1,j}$ is the flux out of the ``eastern'' face of the cell and 
     1379$\mathrm{flxv}_{i,j+1}$ the flux out of the ``northern'' face of the cell; $t_{n+1}$ is 
     1380the new timestep, $t_e$ is the old timestep (either $t_b$ or $t_n$) and $ \Delta t = 
     1381t_{n+1} - t_e$; $e_1 e_2$ is the area of the tracer cells centred at $(i,j)$ and 
     1382$\mathrm{zzflx}$ is the sum of the fluxes through all the faces. 
     1383 
     1384The flux limiter splits the flux $\mathrm{zzflx}$ into fluxes that are out of the cell 
     1385(zzflxp) and fluxes that are into the cell (zzflxn).  Clearly 
     1386 
     1387\begin{equation} 
     1388  \label{eq:DYN_wd_zzflx_p_n_1} 
     1389  \mathrm{zzflx}_{i,j} = \mathrm{zzflxp}_{i,j} + \mathrm{zzflxn}_{i,j} . 
     1390\end{equation} 
     1391 
     1392The flux limiter iteratively adjusts the fluxes $\mathrm{flxu}$ and $\mathrm{flxv}$ until 
     1393none of the cells will ``dry out''. To be precise the fluxes are limited until none of the 
     1394cells has water depth less than $\mathrm{rn\_wdmin1}$ on step $n+1$. 
     1395 
     1396Let the fluxes on the $m$th iteration step be denoted by $\mathrm{flxu}^{(m)}$ and 
     1397$\mathrm{flxv}^{(m)}$.  Then the adjustment is achieved by seeking a set of coefficients, 
     1398$\mathrm{zcoef}_{i,j}^{(m)}$ such that: 
     1399 
     1400\begin{equation} 
     1401  \label{eq:DYN_wd_continuity_coef} 
     1402  \begin{split} 
     1403    \mathrm{zzflxp}^{(m)}_{i,j} =& \mathrm{zcoef}_{i,j}^{(m)} \mathrm{zzflxp}^{(0)}_{i,j} \\ 
     1404    \mathrm{zzflxn}^{(m)}_{i,j} =& \mathrm{zcoef}_{i,j}^{(m)} \mathrm{zzflxn}^{(0)}_{i,j} 
     1405  \end{split} 
     1406\end{equation} 
     1407 
     1408where the coefficients are $1.0$ generally but can vary between $0.0$ and $1.0$ around 
     1409cells that would otherwise dry. 
     1410 
     1411The iteration is initialised by setting 
     1412 
     1413\begin{equation} 
     1414  \label{eq:DYN_wd_zzflx_initial} 
     1415  \mathrm{zzflxp^{(0)}}_{i,j} = \mathrm{zzflxp}_{i,j} , \quad  \mathrm{zzflxn^{(0)}}_{i,j} = \mathrm{zzflxn}_{i,j} . 
     1416\end{equation} 
     1417 
     1418The fluxes out of cell $(i,j)$ are updated at the $m+1$th iteration if the depth of the 
     1419cell on timestep $t_e$, namely $h_{i,j}(t_e)$, is less than the total flux out of the cell 
     1420times the timestep divided by the cell area. Using (\autoref{eq:DYN_wd_continuity_2}) this 
     1421condition is 
     1422 
     1423\begin{equation} 
     1424  \label{eq:DYN_wd_continuity_if} 
     1425  h_{i,j}(t_e)  - \mathrm{rn\_wdmin1} <  \frac{\Delta t}{e_1 e_2} ( \mathrm{zzflxp}^{(m)}_{i,j} + \mathrm{zzflxn}^{(m)}_{i,j} ) . 
     1426\end{equation} 
     1427 
     1428Rearranging (\autoref{eq:DYN_wd_continuity_if}) we can obtain an expression for the maximum 
     1429outward flux that can be allowed and still maintain the minimum wet depth: 
     1430 
     1431\begin{equation} 
     1432  \label{eq:DYN_wd_max_flux} 
     1433  \begin{split} 
     1434    \mathrm{zzflxp}^{(m+1)}_{i,j} = \Big[ (h_{i,j}(t_e) & - \mathrm{rn\_wdmin1} - \mathrm{rn\_wdmin2})  \frac{e_1 e_2}{\Delta t} \phantom{]} \\ 
     1435    \phantom{[} & -  \mathrm{zzflxn}^{(m)}_{i,j} \Big] 
     1436  \end{split} 
     1437\end{equation} 
     1438 
     1439Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\itshape [Q: Why is 
     1440this necessary/desirable?]}. Substituting from (\autoref{eq:DYN_wd_continuity_coef}) gives an 
     1441expression for the coefficient needed to multiply the outward flux at this cell in order 
     1442to avoid drying. 
     1443 
     1444\begin{equation} 
     1445  \label{eq:DYN_wd_continuity_nxtcoef} 
     1446  \begin{split} 
     1447    \mathrm{zcoef}^{(m+1)}_{i,j} = \Big[ (h_{i,j}(t_e) & - \mathrm{rn\_wdmin1} - \mathrm{rn\_wdmin2})  \frac{e_1 e_2}{\Delta t} \phantom{]} \\ 
     1448    \phantom{[} & -  \mathrm{zzflxn}^{(m)}_{i,j} \Big] \frac{1}{ \mathrm{zzflxp}^{(0)}_{i,j} } 
     1449  \end{split} 
     1450\end{equation} 
     1451 
     1452Only the outward flux components are altered but, of course, outward fluxes from one cell 
     1453are inward fluxes to adjacent cells and the balance in these cells may need subsequent 
     1454adjustment; hence the iterative nature of this scheme.  Note, for example, that the flux 
     1455across the ``eastern'' face of the $(i,j)$th cell is only updated at the $m+1$th iteration 
     1456if that flux at the $m$th iteration is out of the $(i,j)$th cell. If that is the case then 
     1457the flux across that face is into the $(i+1,j)$ cell and that flux will not be updated by 
     1458the calculation for the $(i+1,j)$th cell. In this sense the updates to the fluxes across 
     1459the faces of the cells do not ``compete'' (they do not over-write each other) and one 
     1460would expect the scheme to converge relatively quickly. The scheme is flux based so 
     1461conserves mass. It also conserves constant tracers for the same reason that the 
     1462directional limiter does. 
     1463 
     1464 
     1465%      Surface pressure gradients 
     1466%% ================================================================================================= 
     1467\subsubsection[Modification of surface pressure gradients (\textit{dynhpg.F90})]{Modification of surface pressure gradients (\mdl{dynhpg})} 
     1468\label{subsec:DYN_wd_il_spg} 
     1469 
     1470At ``dry'' points the water depth is usually close to $\mathrm{rn\_wdmin1}$. If the 
     1471topography is sloping at these points the sea-surface will have a similar slope and there 
     1472will hence be very large horizontal pressure gradients at these points. The WAD modifies 
     1473the magnitude but not the sign of the surface pressure gradients (zhpi and zhpj) at such 
     1474points by mulitplying them by positive factors (zcpx and zcpy respectively) that lie 
     1475between $0$ and $1$. 
     1476 
     1477We describe how the scheme works for the ``eastward'' pressure gradient, zhpi, calculated 
     1478at the $(i,j)$th $u$-point. The scheme uses the ht\_wd depths and surface heights at the 
     1479neighbouring $(i+1,j)$ and $(i,j)$ tracer points.  zcpx is calculated using two logicals 
     1480variables, $\mathrm{ll\_tmp1}$ and $\mathrm{ll\_tmp2}$ which are evaluated for each grid 
     1481column.  The three possible combinations are illustrated in \autoref{fig:DYN_WAD_dynhpg}. 
     1482 
     1483%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     1484\begin{figure}[!ht] 
     1485  \centering 
     1486  \includegraphics[width=0.66\textwidth]{Fig_WAD_dynhpg} 
     1487  \caption[Combinations controlling the limiting of the horizontal pressure gradient in 
     1488  wetting and drying regimes]{ 
     1489    Three possible combinations of the logical variables controlling the 
     1490    limiting of the horizontal pressure gradient in wetting and drying regimes} 
     1491  \label{fig:DYN_WAD_dynhpg} 
     1492\end{figure} 
     1493%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     1494 
     1495The first logical, $\mathrm{ll\_tmp1}$, is set to true if and only if the water depth at 
     1496both neighbouring points is greater than $\mathrm{rn\_wdmin1} + \mathrm{rn\_wdmin2}$ and 
     1497the minimum height of the sea surface at the two points is greater than the maximum height 
     1498of the topography at the two points: 
     1499 
     1500\begin{equation} 
     1501  \label{eq:DYN_ll_tmp1} 
     1502  \begin{split} 
     1503    \mathrm{ll\_tmp1}  = & \mathrm{MIN(sshn(ji,jj), sshn(ji+1,jj))} > \\ 
     1504                     & \quad \mathrm{MAX(-ht\_wd(ji,jj), -ht\_wd(ji+1,jj))\  .and.} \\ 
     1505                     & \mathrm{MAX(sshn(ji,jj) + ht\_wd(ji,jj),} \\ 
     1506                     & \mathrm{\phantom{MAX(}sshn(ji+1,jj) + ht\_wd(ji+1,jj))} >\\ 
     1507                     & \quad\quad\mathrm{rn\_wdmin1 + rn\_wdmin2 } 
     1508  \end{split} 
     1509\end{equation} 
     1510 
     1511The second logical, $\mathrm{ll\_tmp2}$, is set to true if and only if the maximum height 
     1512of the sea surface at the two points is greater than the maximum height of the topography 
     1513at the two points plus $\mathrm{rn\_wdmin1} + \mathrm{rn\_wdmin2}$ 
     1514 
     1515\begin{equation} 
     1516  \label{eq:DYN_ll_tmp2} 
     1517  \begin{split} 
     1518    \mathrm{ ll\_tmp2 } = & \mathrm{( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 )\ .AND.}\\ 
     1519    & \mathrm{( MAX(sshn(ji,jj), sshn(ji+1,jj)) > } \\ 
     1520    & \mathrm{\phantom{(} MAX(-ht\_wd(ji,jj), -ht\_wd(ji+1,jj)) + rn\_wdmin1 + rn\_wdmin2}) . 
     1521  \end{split} 
     1522\end{equation} 
     1523 
     1524If $\mathrm{ll\_tmp1}$ is true then the surface pressure gradient, zhpi at the $(i,j)$ 
     1525point is unmodified. If both logicals are false zhpi is set to zero. 
     1526 
     1527If $\mathrm{ll\_tmp1}$ is true and $\mathrm{ll\_tmp2}$ is false then the surface pressure 
     1528gradient is multiplied through by zcpx which is the absolute value of the difference in 
     1529the water depths at the two points divided by the difference in the surface heights at the 
     1530two points. Thus the sign of the sea surface height gradient is retained but the magnitude 
     1531of the pressure force is determined by the difference in water depths rather than the 
     1532difference in surface height between the two points. Note that dividing by the difference 
     1533between the sea surface heights can be problematic if the heights approach parity. An 
     1534additional condition is applied to $\mathrm{ ll\_tmp2 }$ to ensure it is .false. in such 
     1535conditions. 
     1536 
     1537%% ================================================================================================= 
     1538\subsubsection[Additional considerations (\textit{usrdef\_zgr.F90})]{Additional considerations (\mdl{usrdef\_zgr})} 
     1539\label{subsec:DYN_WAD_additional} 
     1540 
     1541In the very shallow water where wetting and drying occurs the parametrisation of 
     1542bottom drag is clearly very important. In order to promote stability 
     1543it is sometimes useful to calculate the bottom drag using an implicit time-stepping approach. 
     1544 
     1545Suitable specifcation of the surface heat flux in wetting and drying domains in forced and 
     1546coupled simulations needs further consideration. In order to prevent freezing or boiling 
     1547in uncoupled integrations the net surface heat fluxes need to be appropriately limited. 
     1548 
     1549%      The WAD test cases 
     1550%% ================================================================================================= 
     1551\subsection[The WAD test cases (\textit{usrdef\_zgr.F90})]{The WAD test cases (\mdl{usrdef\_zgr})} 
     1552\label{subsec:DYN_WAD_test_cases} 
     1553 
     1554See the WAD tests MY\_DOC documention for details of the WAD test cases. 
     1555 
     1556 
     1557 
     1558%% ================================================================================================= 
     1559\section[Time evolution term (\textit{dynnxt.F90})]{Time evolution term (\protect\mdl{dynnxt})} 
     1560\label{sec:DYN_nxt} 
     1561 
     1562 
     1563Options are defined through the \nam{dom}{dom} namelist variables. 
     1564The general framework for dynamics time stepping is a leap-frog scheme, 
     1565\ie\ a three level centred time scheme associated with an Asselin time filter (cf. \autoref{chap:TD}). 
     1566The scheme is applied to the velocity, except when 
     1567using the flux form of momentum advection (cf. \autoref{sec:DYN_adv_cor_flux}) 
     1568in the variable volume case (\texttt{vvl?} defined), 
     1569where it has to be applied to the thickness weighted velocity (see \autoref{sec:SCOORD_momentum}) 
     1570 
     1571$\bullet$ vector invariant form or linear free surface 
     1572(\np[=.true.]{ln_dynhpg_vec}{ln\_dynhpg\_vec} ; \texttt{vvl?} not defined): 
     1573\[ 
     1574  % \label{eq:DYN_nxt_vec} 
     1575  \left\{ 
     1576    \begin{aligned} 
     1577      &u^{t+\rdt} = u_f^{t-\rdt} + 2\rdt  \ \text{RHS}_u^t     \\ 
     1578      &u_f^t \;\quad = u^t+\gamma \,\left[ {u_f^{t-\rdt} -2u^t+u^{t+\rdt}} \right] 
     1579    \end{aligned} 
     1580  \right. 
     1581\] 
     1582 
     1583$\bullet$ flux form and nonlinear free surface 
     1584(\np[=.false.]{ln_dynhpg_vec}{ln\_dynhpg\_vec} ; \texttt{vvl?} defined): 
     1585\[ 
     1586  % \label{eq:DYN_nxt_flux} 
     1587  \left\{ 
     1588    \begin{aligned} 
     1589      &\left(e_{3u}\,u\right)^{t+\rdt} = \left(e_{3u}\,u\right)_f^{t-\rdt} + 2\rdt \; e_{3u} \;\text{RHS}_u^t     \\ 
     1590      &\left(e_{3u}\,u\right)_f^t \;\quad = \left(e_{3u}\,u\right)^t 
     1591      +\gamma \,\left[ {\left(e_{3u}\,u\right)_f^{t-\rdt} -2\left(e_{3u}\,u\right)^t+\left(e_{3u}\,u\right)^{t+\rdt}} \right] 
     1592    \end{aligned} 
     1593  \right. 
     1594\] 
     1595where RHS is the right hand side of the momentum equation, 
     1596the subscript $f$ denotes filtered values and $\gamma$ is the Asselin coefficient. 
     1597$\gamma$ is initialized as \np{nn_atfp}{nn\_atfp} (namelist parameter). 
     1598Its default value is \np[=10.e-3]{nn_atfp}{nn\_atfp}. 
     1599In both cases, the modified Asselin filter is not applied since perfect conservation is not an issue for 
     1600the momentum equations. 
     1601 
     1602Note that with the filtered free surface, 
     1603the update of the \textit{after} velocities is done in the \mdl{dynsp\_flt} module, 
     1604and only array swapping and Asselin filtering is done in \mdl{dynnxt}. 
     1605 
     1606\onlyinsubfile{\input{../../global/epilogue}} 
     1607 
     1608\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_LBC.tex

    r11596 r11597  
    99%gm% add here introduction to this chapter 
    1010 
     11%% ================================================================================================= 
    1112\section[Boundary condition at the coast (\forcode{rn_shlat})]{Boundary condition at the coast (\protect\np{rn_shlat}{rn\_shlat})} 
    1213\label{sec:LBC_coast} 
    13 %--------------------------------------------namlbc------------------------------------------------------- 
    1414 
    1515\begin{listing} 
     
    1818  \label{lst:namlbc} 
    1919\end{listing} 
    20 %-------------------------------------------------------------------------------------------------------------- 
    2120 
    2221%The lateral ocean boundary conditions contiguous to coastlines are Neumann conditions for heat and salt 
     
    142141it is only applied next to the coast where the minimum water depth can be quite shallow. 
    143142 
     143%% ================================================================================================= 
    144144\section[Model domain boundary condition (\forcode{jperio})]{Model domain boundary condition (\protect\jp{jperio})} 
    145145\label{sec:LBC_jperio} 
     
    150150The north-fold boundary condition is associated with the 3-pole ORCA mesh. 
    151151 
     152%% ================================================================================================= 
    152153\subsection[Closed, cyclic (\forcode{=0,1,2,7})]{Closed, cyclic (\protect\jp{jperio}\forcode{=0,1,2,7})} 
    153154\label{subsec:LBC_jperio012} 
     
    191192\end{figure} 
    192193 
     194%% ================================================================================================= 
    193195\subsection[North-fold (\forcode{=3,6})]{North-fold (\protect\jp{jperio}\forcode{=3,6})} 
    194196\label{subsec:LBC_north_fold} 
     
    210212\end{figure} 
    211213 
     214%% ================================================================================================= 
    212215\section[Exchange with neighbouring processors (\textit{lbclnk.F90}, \textit{lib\_mpp.F90})]{Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})} 
    213216\label{sec:LBC_mpp} 
    214217 
    215 %-----------------------------------------nammpp-------------------------------------------- 
    216218 
    217219\begin{listing} 
     
    220222  \label{lst:nammpp} 
    221223\end{listing} 
    222 %----------------------------------------------------------------------------------------------- 
    223224 
    224225For massively parallel processing (mpp), a domain decomposition method is used. 
     
    321322\end{figure} 
    322323 
     324%% ================================================================================================= 
    323325\section{Unstructured open boundary conditions (BDY)} 
    324326\label{sec:LBC_bdy} 
    325327 
    326 %-----------------------------------------nambdy-------------------------------------------- 
    327328 
    328329\begin{listing} 
     
    331332  \label{lst:nambdy} 
    332333\end{listing} 
    333 %----------------------------------------------------------------------------------------------- 
    334 %-----------------------------------------nambdy_dta-------------------------------------------- 
    335334 
    336335\begin{listing} 
     
    339338  \label{lst:nambdy_dta} 
    340339\end{listing} 
    341 %----------------------------------------------------------------------------------------------- 
    342340 
    343341Options are defined through the \nam{bdy}{bdy} and \nam{bdy_dta}{bdy\_dta} namelist variables. 
     
    352350See the section on the Input Boundary Data Files for details. 
    353351 
    354 %---------------------------------------------- 
     352%% ================================================================================================= 
    355353\subsection{Namelists} 
    356354\label{subsec:LBC_bdy_namelist} 
     
    419417FRS conditions are applied on temperature and salinity and climatological data is read from initial condition files. 
    420418 
    421 %---------------------------------------------- 
     419%% ================================================================================================= 
    422420\subsection{Flow relaxation scheme} 
    423421\label{subsec:LBC_bdy_FRS_scheme} 
     
    458456This is typically set to a value between 8 and 10. 
    459457 
    460 %---------------------------------------------- 
     458%% ================================================================================================= 
    461459\subsection{Flather radiation scheme} 
    462460\label{subsec:LBC_bdy_flather_scheme} 
     
    480478$U$ and $U_{e}$ are defined on the $U$ or $V$ points with $nbr=1$, \ie\ between the two $T$ grid points. 
    481479 
    482 %---------------------------------------------- 
     480%% ================================================================================================= 
    483481\subsection{Orlanski radiation scheme} 
    484482\label{subsec:LBC_bdy_orlanski_scheme} 
     
    528526(\autoref{eq:LBC_wave_continuous}) - (\autoref{eq:LBC_tau_in}) correspond to equations (13) - (15) and (2) - (3) in MMS.\\ 
    529527 
    530 %---------------------------------------------- 
     528%% ================================================================================================= 
    531529\subsection{Relaxation at the boundary} 
    532530\label{subsec:LBC_bdy_relaxation} 
     
    544542The same scaling is applied in the Orlanski damping. 
    545543 
    546 %---------------------------------------------- 
     544%% ================================================================================================= 
    547545\subsection{Boundary geometry} 
    548546\label{subsec:LBC_bdy_geometry} 
     
    590588\end{figure} 
    591589 
    592 %---------------------------------------------- 
     590%% ================================================================================================= 
    593591\subsection{Input boundary data files} 
    594592\label{subsec:LBC_bdy_data} 
     
    626624\end{figure} 
    627625 
    628 %---------------------------------------------- 
     626%% ================================================================================================= 
    629627\subsection{Volume correction} 
    630628\label{subsec:LBC_bdy_vol_corr} 
     
    643641applied to all boundaries at once. 
    644642 
    645 %---------------------------------------------- 
     643%% ================================================================================================= 
    646644\subsection{Tidal harmonic forcing} 
    647645\label{subsec:LBC_bdy_tides} 
    648646 
    649 %-----------------------------------------nambdy_tide-------------------------------------------- 
    650647 
    651648\begin{listing} 
     
    654651  \label{lst:nambdy_tide} 
    655652\end{listing} 
    656 %----------------------------------------------------------------------------------------------- 
    657653 
    658654Tidal forcing at open boundaries requires the activation of surface 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_LDF.tex

    r11596 r11597  
    2222is described in \autoref{apdx:TRIADS} 
    2323 
    24 %-----------------------------------namtra_ldf - namdyn_ldf-------------------------------------------- 
    25  
    26 %-------------------------------------------------------------------------------------------------------------- 
    27  
     24 
     25 
     26%% ================================================================================================= 
    2827\section[Lateral mixing operators]{Lateral mixing operators} 
    2928\label{sec:LDF_op} 
    3029We remind here the different lateral mixing operators that can be used. Further details can be found in \autoref{subsec:TRA_ldf_op} and  \autoref{sec:DYN_ldf}. 
    3130 
     31%% ================================================================================================= 
    3232\subsection[No lateral mixing (\forcode{ln_traldf_OFF} \& \forcode{ln_dynldf_OFF})]{No lateral mixing (\protect\np{ln_traldf_OFF}{ln\_traldf\_OFF} \& \protect\np{ln_dynldf_OFF}{ln\_dynldf\_OFF})} 
    3333 
     
    3737see \autoref{subsec:DYN_adv_ubs}) and can be useful for testing purposes. 
    3838 
     39%% ================================================================================================= 
    3940\subsection[Laplacian mixing (\forcode{ln_traldf_lap} \& \forcode{ln_dynldf_lap})]{Laplacian mixing (\protect\np{ln_traldf_lap}{ln\_traldf\_lap} \& \protect\np{ln_dynldf_lap}{ln\_dynldf\_lap})} 
    4041Setting \protect\np[=.true.]{ln_traldf_lap}{ln\_traldf\_lap} and/or \protect\np[=.true.]{ln_dynldf_lap}{ln\_dynldf\_lap} enables 
     
    4243Laplacian and Bilaplacian operators for the same variable. 
    4344 
     45%% ================================================================================================= 
    4446\subsection[Bilaplacian mixing (\forcode{ln_traldf_blp} \& \forcode{ln_dynldf_blp})]{Bilaplacian mixing (\protect\np{ln_traldf_blp}{ln\_traldf\_blp} \& \protect\np{ln_dynldf_blp}{ln\_dynldf\_blp})} 
    4547Setting \protect\np[=.true.]{ln_traldf_blp}{ln\_traldf\_blp} and/or \protect\np[=.true.]{ln_dynldf_blp}{ln\_dynldf\_blp} enables 
     
    4749We stress again that from \NEMO\ 4, the simultaneous use Laplacian and Bilaplacian operators is not allowed. 
    4850 
     51%% ================================================================================================= 
    4952\section[Direction of lateral mixing (\textit{ldfslp.F90})]{Direction of lateral mixing (\protect\mdl{ldfslp})} 
    5053\label{sec:LDF_slp} 
     
    6972%gm% add here afigure of the slope in i-direction 
    7073 
     74%% ================================================================================================= 
    7175\subsection{Slopes for tracer geopotential mixing in the $s$-coordinate} 
    7276 
     
    99103and either \np[=.true.]{ln_traldf_hor}{ln\_traldf\_hor} or \np[=.true.]{ln_dynldf_hor}{ln\_dynldf\_hor}. 
    100104 
     105%% ================================================================================================= 
    101106\subsection{Slopes for tracer iso-neutral mixing} 
    102107\label{subsec:LDF_slp_iso} 
     
    273278\colorbox{yellow}{add here a discussion about the flattening of the slopes, vs tapering the coefficient.} 
    274279 
     280%% ================================================================================================= 
    275281\subsection{Slopes for momentum iso-neutral mixing} 
    276282 
     
    299305(see \autoref{sec:LBC_coast}). 
    300306 
     307%% ================================================================================================= 
    301308\section[Lateral mixing coefficient (\forcode{nn_aht_ijk_t} \& \forcode{nn_ahm_ijk_t})]{Lateral mixing coefficient (\protect\np{nn_aht_ijk_t}{nn\_aht\_ijk\_t} \& \protect\np{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    302309\label{sec:LDF_coef} 
     
    305312The way the mixing coefficients are set in the reference version can be described as follows: 
    306313 
     314%% ================================================================================================= 
    307315\subsection[Mixing coefficients read from file (\forcode{=-20, -30})]{ Mixing coefficients read from file (\protect\np[=-20, -30]{nn_aht_ijk_t}{nn\_aht\_ijk\_t} \& \protect\np[=-20, -30]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    308316 
     
    313321The provided fields can either be 2d (\np[=-20]{nn_aht_ijk_t}{nn\_aht\_ijk\_t}, \np[=-20]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t}) or 3d (\np[=-30]{nn_aht_ijk_t}{nn\_aht\_ijk\_t},  \np[=-30]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t}). They must be given at U, V points for tracers and T, F points for momentum (see \autoref{tab:LDF_files}). 
    314322 
    315 %-------------------------------------------------TABLE--------------------------------------------------- 
    316323\begin{table}[htb] 
    317324  \centering 
     
    327334  \label{tab:LDF_files} 
    328335\end{table} 
    329 %-------------------------------------------------------------------------------------------------------------- 
    330  
     336 
     337%% ================================================================================================= 
    331338\subsection[Constant mixing coefficients (\forcode{=0})]{ Constant mixing coefficients (\protect\np[=0]{nn_aht_ijk_t}{nn\_aht\_ijk\_t} \& \protect\np[=0]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    332339 
     
    345352 $U_{scl}$ and $L_{scl}$ are given by the namelist parameters \np{rn_Ud}{rn\_Ud}, \np{rn_Uv}{rn\_Uv}, \np{rn_Ld}{rn\_Ld} and \np{rn_Lv}{rn\_Lv}. 
    346353 
     354%% ================================================================================================= 
    347355\subsection[Vertically varying mixing coefficients (\forcode{=10})]{Vertically varying mixing coefficients (\protect\np[=10]{nn_aht_ijk_t}{nn\_aht\_ijk\_t} \& \protect\np[=10]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    348356 
     
    352360This profile is hard coded in module \mdl{ldfc1d\_c2d}, but can be easily modified by users. 
    353361 
     362%% ================================================================================================= 
    354363\subsection[Mesh size dependent mixing coefficients (\forcode{=20})]{Mesh size dependent mixing coefficients (\protect\np[=20]{nn_aht_ijk_t}{nn\_aht\_ijk\_t} \& \protect\np[=20]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    355364 
     
    377386\colorbox{yellow}{CASE \np{nn_aht_ijk_t}{nn\_aht\_ijk\_t} = 21 to be added} 
    378387 
     388%% ================================================================================================= 
    379389\subsection[Mesh size and depth dependent mixing coefficients (\forcode{=30})]{Mesh size and depth dependent mixing coefficients (\protect\np[=30]{nn_aht_ijk_t}{nn\_aht\_ijk\_t} \& \protect\np[=30]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    380390 
     
    383393the magnitude of the coefficient. 
    384394 
     395%% ================================================================================================= 
    385396\subsection[Velocity dependent mixing coefficients (\forcode{=31})]{Flow dependent mixing coefficients (\protect\np[=31]{nn_aht_ijk_t}{nn\_aht\_ijk\_t} \& \protect\np[=31]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    386397In that case, the eddy coefficient is proportional to the local velocity magnitude so that the Reynolds number $Re =  \lvert U \rvert  e / A_l$ is constant (and here hardcoded to $12$): 
     
    397408\end{equation} 
    398409 
     410%% ================================================================================================= 
    399411\subsection[Deformation rate dependent viscosities (\forcode{nn_ahm_ijk_t=32})]{Deformation rate dependent viscosities (\protect\np[=32]{nn_ahm_ijk_t}{nn\_ahm\_ijk\_t})} 
    400412 
     
    433445where $C_{min}$ and $C_{max}$ are adimensional namelist parameters given by \np{rn_minfac}{rn\_minfac} and \np{rn_maxfac}{rn\_maxfac} respectively. 
    434446 
     447%% ================================================================================================= 
    435448\subsection{About space and time varying mixing coefficients} 
    436449 
     
    446459(\autoref{sec:INVARIANTS_dynldf_properties}). 
    447460 
     461%% ================================================================================================= 
    448462\section[Eddy induced velocity (\forcode{ln_ldfeiv})]{Eddy induced velocity (\protect\np{ln_ldfeiv}{ln\_ldfeiv})} 
    449463 
    450464\label{sec:LDF_eiv} 
    451465 
    452 %--------------------------------------------namtra_eiv--------------------------------------------------- 
    453466 
    454467\begin{listing} 
     
    458471\end{listing} 
    459472 
    460 %-------------------------------------------------------------------------------------------------------------- 
    461473 
    462474%%gm  from Triad appendix  : to be incorporated.... 
     
    513525In case of setting \np[=.true.]{ln_traldf_triad}{ln\_traldf\_triad}, a skew form of the eddy induced advective fluxes is used, which is described in \autoref{apdx:TRIADS}. 
    514526 
     527%% ================================================================================================= 
    515528\section[Mixed layer eddies (\forcode{ln_mle})]{Mixed layer eddies (\protect\np{ln_mle}{ln\_mle})} 
    516529\label{sec:LDF_mle} 
    517530 
    518 %--------------------------------------------namtra_eiv--------------------------------------------------- 
    519531 
    520532\begin{listing} 
     
    524536\end{listing} 
    525537 
    526 %-------------------------------------------------------------------------------------------------------------- 
    527538 
    528539If  \np[=.true.]{ln_mle}{ln\_mle} in \nam{tra_mle}{tra\_mle} namelist, a parameterization of the mixing due to unresolved mixed layer instabilities is activated (\citet{foxkemper.ferrari_JPO08}). Additional transport is computed in \rou{ldf\_mle\_trp} and added to the eulerian transport in \rou{tra\_adv} as done for eddy induced advection. 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_OBS.tex

    r11596 r11597  
    99\vfill 
    1010\begin{figure}[b] 
     11%% ================================================================================================= 
    1112\subsubsection*{Changes record} 
    1213\begin{tabular}{l||l|m{0.65\linewidth}} 
     
    5556In \autoref{sec:OBS_obsutils} we describe some utilities to help work with the files produced by the OBS code. 
    5657 
     58%% ================================================================================================= 
    5759\section{Running the observation operator code example} 
    5860\label{sec:OBS_example} 
     
    103105\autoref{sec:OBS_obsutils}. 
    104106 
     107%% ================================================================================================= 
    105108\section{Technical details (feedback type observation file headers)} 
    106109\label{sec:OBS_details} 
     
    109112the observation files that may be used with the observation operator. 
    110113 
    111 %------------------------------------------namobs-------------------------------------------------------- 
    112114 
    113115\begin{listing} 
     
    116118  \label{lst:namobs} 
    117119\end{listing} 
    118 %------------------------------------------------------------------------------------------------------------- 
    119120 
    120121The observation operator code uses the feedback observation file format for all data types. 
     
    123124sea surface temperature are in the following subsections. 
    124125 
     126%% ================================================================================================= 
    125127\subsection{Profile feedback file} 
    126128 
     
    279281\end{clines} 
    280282 
     283%% ================================================================================================= 
    281284\subsection{Sea level anomaly feedback file} 
    282285 
     
    425428\end{clines} 
    426429 
     430%% ================================================================================================= 
    427431\subsection{Sea surface temperature feedback file} 
    428432 
     
    542546\end{clines} 
    543547 
     548%% ================================================================================================= 
    544549\section{Theoretical details} 
    545550\label{sec:OBS_theory} 
    546551 
     552%% ================================================================================================= 
    547553\subsection{Horizontal interpolation and averaging methods} 
    548554 
     
    579585Below is some more detail on the various options for interpolation and averaging available in \NEMO. 
    580586 
     587%% ================================================================================================= 
    581588\subsubsection{Horizontal interpolation} 
    582589 
     
    667674\end{enumerate} 
    668675 
     676%% ================================================================================================= 
    669677\subsubsection{Horizontal averaging} 
    670678 
     
    708716\end{figure} 
    709717 
     718%% ================================================================================================= 
    710719\subsection{Grid search} 
    711720 
     
    758767the $i$ and $j$ ranges of this point searched to determine the precise four points surrounding the observation. 
    759768 
     769%% ================================================================================================= 
    760770\subsection{Parallel aspects of horizontal interpolation} 
    761771\label{subsec:OBS_parallel} 
     
    772782and 2) round-robin. 
    773783 
     784%% ================================================================================================= 
    774785\subsubsection{Geographical distribution of observations among processors} 
    775786 
     
    798809this could lead to load imbalance. 
    799810 
     811%% ================================================================================================= 
    800812\subsubsection{Round-robin distribution of observations among processors} 
    801813 
     
    819831a subroutine has been developed that retrieves any grid points in the global space. 
    820832 
     833%% ================================================================================================= 
    821834\subsection{Vertical interpolation operator} 
    822835 
     
    830843%\usepackage{framed} 
    831844 
     845%% ================================================================================================= 
    832846\section{Standalone observation operator} 
    833847\label{sec:OBS_sao} 
    834848 
     849%% ================================================================================================= 
    835850\subsection{Concept} 
    836851 
     
    849864By forecast, we mean any method which produces an estimate of physical reality which is not an observed value. 
    850865 
    851 %-------------------------------------------------------------------------------------------------------- 
    852866% sao.exe 
    853 %-------------------------------------------------------------------------------------------------------- 
    854  
     867 
     868%% ================================================================================================= 
    855869\subsection{Using the standalone observation operator} 
    856870 
     871%% ================================================================================================= 
    857872\subsubsection{Building} 
    858873 
     
    862877Note this a similar approach to that taken by the standalone surface scheme \emph{SAS\_SRC} and the offline TOP model \emph{OFF\_SRC}. 
    863878 
    864 %-------------------------------------------------------------------------------------------------------- 
    865879% Running 
    866 %-------------------------------------------------------------------------------------------------------- 
     880%% ================================================================================================= 
    867881\subsubsection{Running} 
    868882 
     
    870884a full \NEMO\ namelist and then to run the executable as if it were nemo.exe. 
    871885 
    872 %-------------------------------------------------------------------------------------------------------- 
    873886% Configuration section 
    874 %-------------------------------------------------------------------------------------------------------- 
     887%% ================================================================================================= 
    875888\subsection{Configuring the standalone observation operator} 
    876889The observation files and settings understood by \nam{obs}{obs} have been outlined in the online observation operator section. 
    877890In addition is a further namelist \nam{sao}{sao} which used to set the input model fields for the SAO 
    878891 
     892%% ================================================================================================= 
    879893\subsubsection{Single field} 
    880894 
     
    901915\end{forlines} 
    902916 
     917%% ================================================================================================= 
    903918\subsubsection{Multiple fields per run} 
    904919 
     
    936951This approach is referred to as \emph{Class 4} since it is the fourth metric defined by the GODAE intercomparison project. This requires multiple runs of the SAO and running an additional utility (not currently in the \NEMO\ repository) to combine the feedback files into one class 4 file. 
    937952 
     953%% ================================================================================================= 
    938954\section{Observation utilities} 
    939955\label{sec:OBS_obsutils} 
     
    948964OBSTOOLS and dataplot are described in more detail below. 
    949965 
     966%% ================================================================================================= 
    950967\subsection{Obstools} 
    951968 
     
    953970This are helpful in handling observation files and the feedback file output from the observation operator. A brief description of some of the utilities follows 
    954971 
     972%% ================================================================================================= 
    955973\subsubsection{corio2fb} 
    956974 
     
    962980\end{cmds} 
    963981 
     982%% ================================================================================================= 
    964983\subsubsection{enact2fb} 
    965984 
     
    971990\end{cmds} 
    972991 
     992%% ================================================================================================= 
    973993\subsubsection{fbcomb} 
    974994 
     
    9811001\end{cmds} 
    9821002 
     1003%% ================================================================================================= 
    9831004\subsubsection{fbmatchup} 
    9841005 
     
    9901011\end{cmds} 
    9911012 
     1013%% ================================================================================================= 
    9921014\subsubsection{fbprint} 
    9931015 
     
    10181040\end{cmds} 
    10191041 
     1042%% ================================================================================================= 
    10201043\subsubsection{fbsel} 
    10211044 
     
    10271050\end{cmds} 
    10281051 
     1052%% ================================================================================================= 
    10291053\subsubsection{fbstat} 
    10301054 
     
    10361060\end{cmds} 
    10371061 
     1062%% ================================================================================================= 
    10381063\subsubsection{fbthin} 
    10391064 
     
    10461071\end{cmds} 
    10471072 
     1073%% ================================================================================================= 
    10481074\subsubsection{sla2fb} 
    10491075 
     
    10581084\end{cmds} 
    10591085 
     1086%% ================================================================================================= 
    10601087\subsubsection{vel2fb} 
    10611088 
     
    10671094\end{cmds} 
    10681095 
     1096%% ================================================================================================= 
    10691097\subsection{Building the obstools} 
    10701098 
    10711099To build the obstools use in the tools directory use ./maketools -n OBSTOOLS -m [ARCH]. 
    10721100 
     1101%% ================================================================================================= 
    10731102\subsection{Dataplot} 
    10741103 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex

    r11596 r11597  
    88\chaptertoc 
    99 
    10 %---------------------------------------namsbc-------------------------------------------------- 
    1110 
    1211\begin{listing} 
     
    1514  \label{lst:namsbc} 
    1615\end{listing} 
    17 %-------------------------------------------------------------------------------------------------------------- 
    1816 
    1917The ocean needs seven fields as surface boundary condition: 
     
    8785which provides additional sources of fresh water. 
    8886 
     87%% ================================================================================================= 
    8988\section{Surface boundary condition for the ocean} 
    9089\label{sec:SBC_ocean} 
     
    147146these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps. 
    148147 
    149 %-------------------------------------------------TABLE--------------------------------------------------- 
    150148\begin{table}[tb] 
    151149  \centering 
     
    167165  \label{tab:SBC_ssm} 
    168166\end{table} 
    169 %-------------------------------------------------------------------------------------------------------------- 
    170167 
    171168%\colorbox{yellow}{Penser a} mettre dans le restant l'info nn\_fsbc ET nn\_fsbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt 
    172169 
     170%% ================================================================================================= 
    173171\section{Input data generic interface} 
    174172\label{sec:SBC_input} 
     
    203201By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'. 
    204202 
     203%% ================================================================================================= 
    205204\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})} 
    206205\label{subsec:SBC_fldread} 
     
    220219  whether it is a climatological file or not, and to the open/close frequency (see below for definition). 
    221220 
    222 %--------------------------------------------------TABLE-------------------------------------------------- 
    223221  \begin{table}[htbp] 
    224222    \centering 
     
    247245    \label{tab:SBC_fldread} 
    248246  \end{table} 
    249 %-------------------------------------------------------------------------------------------------------------- 
    250247 
    251248\item [Record frequency]: 
     
    325322a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1. 
    326323 
     324%% ================================================================================================= 
    327325\subsection{Interpolation on-the-fly} 
    328326\label{subsec:SBC_iof} 
     
    347345Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied. 
    348346 
     347%% ================================================================================================= 
    349348\subsubsection{Bilinear interpolation} 
    350349\label{subsec:SBC_iof_bilinear} 
     
    368367and wgt(1) corresponds to variable "wgt01" for example. 
    369368 
     369%% ================================================================================================= 
    370370\subsubsection{Bicubic interpolation} 
    371371\label{subsec:SBC_iof_bicubic} 
     
    386386the spatial dependency has been included into the weights. 
    387387 
     388%% ================================================================================================= 
    388389\subsubsection{Implementation} 
    389390\label{subsec:SBC_iof_imp} 
     
    421422or is a copy of one from the first few columns on the opposite side of the grid (cyclical case). 
    422423 
     424%% ================================================================================================= 
    423425\subsubsection{Limitations} 
    424426\label{subsec:SBC_iof_lim} 
     
    435437\end{enumerate} 
    436438 
     439%% ================================================================================================= 
    437440\subsubsection{Utilities} 
    438441\label{subsec:SBC_iof_util} 
     
    442445(see the directory NEMOGCM/TOOLS/WEIGHTS). 
    443446 
     447%% ================================================================================================= 
    444448\subsection{Standalone surface boundary condition scheme (SAS)} 
    445449\label{subsec:SBC_SAS} 
    446450 
    447 %---------------------------------------namsbc_sas-------------------------------------------------- 
    448451 
    449452\begin{listing} 
     
    452455  \label{lst:namsbc_sas} 
    453456\end{listing} 
    454 %-------------------------------------------------------------------------------------------------------------- 
    455457 
    456458In some circumstances, it may be useful to avoid calculating the 3D temperature, 
     
    513515 (\np[=.true.]{ln_flx}{ln\_flx}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln_flx}{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in. 
    514516 
     517%% ================================================================================================= 
    515518\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})} 
    516519\label{sec:SBC_flx} 
    517 %------------------------------------------namsbc_flx---------------------------------------------------- 
    518520 
    519521\begin{listing} 
     
    522524  \label{lst:namsbc_flx} 
    523525\end{listing} 
    524 %------------------------------------------------------------------------------------------------------------- 
    525526 
    526527In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}), 
     
    534535See \autoref{subsec:SBC_ssr} for its specification. 
    535536 
     537%% ================================================================================================= 
    536538\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})} 
    537539\label{sec:SBC_blk} 
    538 %---------------------------------------namsbc_blk-------------------------------------------------- 
    539540 
    540541\begin{listing} 
     
    543544  \label{lst:namsbc_blk} 
    544545\end{listing} 
    545 %-------------------------------------------------------------------------------------------------------------- 
    546546 
    547547In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields 
     
    562562The required 9 input fields are: 
    563563 
    564 %--------------------------------------------------TABLE-------------------------------------------------- 
    565564\begin{table}[htbp] 
    566565  \centering 
     
    590589  \label{tab:SBC_BULK} 
    591590\end{table} 
    592 %-------------------------------------------------------------------------------------------------------------- 
    593591 
    594592Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points). 
     
    615613the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}). 
    616614 
     615%% ================================================================================================= 
    617616\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.F90, sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})} 
    618617\label{subsec:SBC_blk_ocean} 
     
    640639\end{itemize} 
    641640 
     641%% ================================================================================================= 
    642642\subsection{Ice-Atmosphere Bulk formulae} 
    643643\label{subsec:SBC_blk_ice} 
     
    665665\end{itemize} 
    666666 
     667%% ================================================================================================= 
    667668\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})} 
    668669\label{sec:SBC_cpl} 
    669 %------------------------------------------namsbc_cpl---------------------------------------------------- 
    670670 
    671671\begin{listing} 
     
    674674  \label{lst:namsbc_cpl} 
    675675\end{listing} 
    676 %------------------------------------------------------------------------------------------------------------- 
    677676 
    678677In the coupled formulation of the surface boundary condition, 
     
    702701In cases where this is definitely not possible, the model should abort with an error message. 
    703702 
     703%% ================================================================================================= 
    704704\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})} 
    705705\label{sec:SBC_apr} 
    706 %------------------------------------------namsbc_apr---------------------------------------------------- 
    707706 
    708707\begin{listing} 
     
    711710  \label{lst:namsbc_apr} 
    712711\end{listing} 
    713 %------------------------------------------------------------------------------------------------------------- 
    714712 
    715713The optional atmospheric pressure can be used to force ocean and ice dynamics 
     
    739737\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true. 
    740738 
     739%% ================================================================================================= 
    741740\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})} 
    742741\label{sec:SBC_tide} 
    743742 
    744 %------------------------------------------nam_tide--------------------------------------- 
    745743 
    746744\begin{listing} 
     
    749747  \label{lst:nam_tide} 
    750748\end{listing} 
    751 %----------------------------------------------------------------------------------------- 
    752749 
    753750The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems, 
     
    791788\forcode{.false.} removes the SAL contribution. 
    792789 
     790%% ================================================================================================= 
    793791\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})} 
    794792\label{sec:SBC_rnf} 
    795 %------------------------------------------namsbc_rnf---------------------------------------------------- 
    796793 
    797794\begin{listing} 
     
    800797  \label{lst:namsbc_rnf} 
    801798\end{listing} 
    802 %------------------------------------------------------------------------------------------------------------- 
    803799 
    804800%River runoff generally enters the ocean at a nonzero depth rather than through the surface. 
     
    913909%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the tra_sbc module.  We decided to separate them throughout the code, so that the variable emp represented solely evaporation minus precipitation fluxes, and a new 2d variable rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use emp or emps and the changes made are below: 
    914910 
     911%% ================================================================================================= 
    915912\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})} 
    916913\label{sec:SBC_isf} 
    917 %------------------------------------------namsbc_isf---------------------------------------------------- 
    918914 
    919915\begin{listing} 
     
    922918  \label{lst:namsbc_isf} 
    923919\end{listing} 
    924 %-------------------------------------------------------------------------------------------------------- 
    925920 
    926921The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation. 
     
    10291024\end{figure} 
    10301025 
     1026%% ================================================================================================= 
    10311027\section{Ice sheet coupling} 
    10321028\label{sec:SBC_iscpl} 
    1033 %------------------------------------------namsbc_iscpl---------------------------------------------------- 
    10341029 
    10351030\begin{listing} 
     
    10381033  \label{lst:namsbc_iscpl} 
    10391034\end{listing} 
    1040 %-------------------------------------------------------------------------------------------------------- 
    10411035 
    10421036Ice sheet/ocean coupling is done through file exchange at the restart step. 
     
    10931087The corrective increment is apply into the cell itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry). 
    10941088 
     1089%% ================================================================================================= 
    10951090\section{Handling of icebergs (ICB)} 
    10961091\label{sec:SBC_ICB_icebergs} 
    1097 %------------------------------------------namberg---------------------------------------------------- 
    10981092 
    10991093\begin{listing} 
     
    11021096  \label{lst:namberg} 
    11031097\end{listing} 
    1104 %------------------------------------------------------------------------------------------------------------- 
    11051098 
    11061099Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}. 
     
    11621155since its trajectory data may be spread across multiple files. 
    11631156 
     1157%% ================================================================================================= 
    11641158\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})} 
    11651159\label{sec:SBC_wave} 
    1166 %------------------------------------------namsbc_wave-------------------------------------------------------- 
    11671160 
    11681161\begin{listing} 
     
    11711164  \label{lst:namsbc_wave} 
    11721165\end{listing} 
    1173 %------------------------------------------------------------------------------------------------------------- 
    11741166 
    11751167Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate 
     
    11961188 
    11971189% ---------------------------------------------------------------- 
     1190%% ================================================================================================= 
    11981191\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})} 
    11991192\label{subsec:SBC_wave_cdgw} 
     
    12081201% 3D Stokes Drift (ln_sdw, nn_sdrift) 
    12091202% ---------------------------------------------------------------- 
     1203%% ================================================================================================= 
    12101204\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})} 
    12111205\label{subsec:SBC_wave_sdw} 
     
    13031297% Stokes-Coriolis term (ln_stcor) 
    13041298% ---------------------------------------------------------------- 
     1299%% ================================================================================================= 
    13051300\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})} 
    13061301\label{subsec:SBC_wave_stcor} 
     
    13161311% Waves modified stress (ln_tauwoc, ln_tauw) 
    13171312% ---------------------------------------------------------------- 
     1313%% ================================================================================================= 
    13181314\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})} 
    13191315\label{subsec:SBC_wave_tauw} 
     
    13531349meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}. 
    13541350 
     1351%% ================================================================================================= 
    13551352\section{Miscellaneous options} 
    13561353\label{sec:SBC_misc} 
    13571354 
     1355%% ================================================================================================= 
    13581356\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})} 
    13591357\label{subsec:SBC_dcy} 
    1360 %------------------------------------------namsbc------------------------------------------------------------- 
    13611358% 
    13621359 
    1363 %------------------------------------------------------------------------------------------------------------- 
    13641360 
    13651361\begin{figure}[!t] 
     
    14111407an inconsistency between the scale of the vertical resolution and the forcing acting on that scale. 
    14121408 
     1409%% ================================================================================================= 
    14131410\subsection{Rotation of vector pairs onto the model grid directions} 
    14141411\label{subsec:SBC_rotation} 
     
    14271424The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation. 
    14281425 
     1426%% ================================================================================================= 
    14291427\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 
    14301428\label{subsec:SBC_ssr} 
    1431 %------------------------------------------namsbc_ssr---------------------------------------------------- 
    14321429 
    14331430\begin{listing} 
     
    14361433  \label{lst:namsbc_ssr} 
    14371434\end{listing} 
    1438 %------------------------------------------------------------------------------------------------------------- 
    14391435 
    14401436Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables. 
     
    14711467reduce the uncertainties we have on the observed freshwater budget. 
    14721468 
     1469%% ================================================================================================= 
    14731470\subsection{Handling of ice-covered area  (\textit{sbcice\_...})} 
    14741471\label{subsec:SBC_ice-cover} 
     
    15081505%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc 
    15091506 
     1507%% ================================================================================================= 
    15101508\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})} 
    15111509\label{subsec:SBC_cice} 
     
    15381536there is no sea ice. 
    15391537 
     1538%% ================================================================================================= 
    15401539\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})} 
    15411540\label{subsec:SBC_fwb} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_STO.tex

    r11596 r11597  
    99% \vfill 
    1010% \begin{figure}[b] 
     11%% ================================================================================================= 
    1112% \subsubsection*{Changes record} 
    1213% \begin{tabular}{l||l|m{0.65\linewidth}} 
     
    3940$\mathbf{\xi}$ are uncorrelated over the horizontal and fully correlated along the vertical. 
    4041 
     42%% ================================================================================================= 
    4143\section{Stochastic processes} 
    4244\label{sec:STO_the_details} 
     
    114116for any other configuration or resolution of the model. 
    115117 
     118%% ================================================================================================= 
    116119\section{Implementation details} 
    117120\label{sec:STO_thech_details} 
     
    165168The set of parameters is available in \nam{sto}{sto} namelist 
    166169(only the subset for equation of state stochastic parametrisation is listed below): 
    167 %---------------------------------------namsto-------------------------------------------------- 
    168170 
    169171\begin{listing} 
     
    172174  \label{lst:namsto} 
    173175\end{listing} 
    174 %-------------------------------------------------------------------------------------------------------------- 
    175176 
    176177The variables of stochastic paramtetrisation itself (based on the global 2° experiments as in \cite{brankart_OM13} are: 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_TRA.tex

    r11596 r11597  
    5454(\np{ln_tra_trd}{ln\_tra\_trd} or \np[=.true.]{ln_tra_mxl}{ln\_tra\_mxl}), as described in \autoref{chap:DIA}. 
    5555 
     56%% ================================================================================================= 
    5657\section[Tracer advection (\textit{traadv.F90})]{Tracer advection (\protect\mdl{traadv})} 
    5758\label{sec:TRA_adv} 
    58 %------------------------------------------namtra_adv----------------------------------------------------- 
    5959 
    6060\begin{listing} 
     
    6363  \label{lst:namtra_adv} 
    6464\end{listing} 
    65 %------------------------------------------------------------------------------------------------------------- 
    6665 
    6766When considered (\ie\ when \np{ln_traadv_OFF}{ln\_traadv\_OFF} is not set to \forcode{.true.}), 
     
    171170their results. 
    172171 
     172%% ================================================================================================= 
    173173\subsection[CEN: Centred scheme (\forcode{ln_traadv_cen})]{CEN: Centred scheme (\protect\np{ln_traadv_cen}{ln\_traadv\_cen})} 
    174174\label{subsec:TRA_adv_cen} 
     
    235235these near boundary grid points. 
    236236 
     237%% ================================================================================================= 
    237238\subsection[FCT: Flux Corrected Transport scheme (\forcode{ln_traadv_fct})]{FCT: Flux Corrected Transport scheme (\protect\np{ln_traadv_fct}{ln\_traadv\_fct})} 
    238239\label{subsec:TRA_adv_tvd} 
     
    274275while a forward scheme is used for the diffusive part. 
    275276 
     277%% ================================================================================================= 
    276278\subsection[MUSCL: Monotone Upstream Scheme for Conservative Laws (\forcode{ln_traadv_mus})]{MUSCL: Monotone Upstream Scheme for Conservative Laws (\protect\np{ln_traadv_mus}{ln\_traadv\_mus})} 
    277279\label{subsec:TRA_adv_mus} 
     
    307309(\np[=.true.]{ln_mus_ups}{ln\_mus\_ups}). 
    308310 
     311%% ================================================================================================= 
    309312\subsection[UBS a.k.a. UP3: Upstream-Biased Scheme (\forcode{ln_traadv_ubs})]{UBS a.k.a. UP3: Upstream-Biased Scheme (\protect\np{ln_traadv_ubs}{ln\_traadv\_ubs})} 
    310313\label{subsec:TRA_adv_ubs} 
     
    376379Note the current version of \NEMO\ uses the computationally more efficient formulation \autoref{eq:TRA_adv_ubs}. 
    377380 
     381%% ================================================================================================= 
    378382\subsection[QCK: QuiCKest scheme (\forcode{ln_traadv_qck})]{QCK: QuiCKest scheme (\protect\np{ln_traadv_qck}{ln\_traadv\_qck})} 
    379383\label{subsec:TRA_adv_qck} 
     
    396400%%%gmcomment   :  Cross term are missing in the current implementation.... 
    397401 
     402%% ================================================================================================= 
    398403\section[Tracer lateral diffusion (\textit{traldf.F90})]{Tracer lateral diffusion (\protect\mdl{traldf})} 
    399404\label{sec:TRA_ldf} 
    400 %-----------------------------------------nam_traldf------------------------------------------------------ 
    401405 
    402406\begin{listing} 
     
    405409  \label{lst:namtra_ldf} 
    406410\end{listing} 
    407 %------------------------------------------------------------------------------------------------------------- 
    408411 
    409412Options are defined through the \nam{tra_ldf}{tra\_ldf} namelist variables. 
     
    425428the pure vertical component is split into an explicit and an implicit part \citep{lemarie.debreu.ea_OM12}. 
    426429 
     430%% ================================================================================================= 
    427431\subsection[Type of operator (\forcode{ln_traldf_}\{\forcode{OFF,lap,blp}\})]{Type of operator (\protect\np{ln_traldf_OFF}{ln\_traldf\_OFF}, \protect\np{ln_traldf_lap}{ln\_traldf\_lap}, or \protect\np{ln_traldf_blp}{ln\_traldf\_blp})} 
    428432\label{subsec:TRA_ldf_op} 
     
    456460whereas the laplacian damping time scales only like $\lambda^{-2}$. 
    457461 
     462%% ================================================================================================= 
    458463\subsection[Action direction (\forcode{ln_traldf_}\{\forcode{lev,hor,iso,triad}\})]{Direction of action (\protect\np{ln_traldf_lev}{ln\_traldf\_lev}, \protect\np{ln_traldf_hor}{ln\_traldf\_hor}, \protect\np{ln_traldf_iso}{ln\_traldf\_iso}, or \protect\np{ln_traldf_triad}{ln\_traldf\_triad})} 
    459464\label{subsec:TRA_ldf_dir} 
     
    479484the next two sub-sections. 
    480485 
     486%% ================================================================================================= 
    481487\subsection[Iso-level (bi-)laplacian operator (\forcode{ln_traldf_iso})]{Iso-level (bi-)laplacian operator ( \protect\np{ln_traldf_iso}{ln\_traldf\_iso})} 
    482488\label{subsec:TRA_ldf_lev} 
     
    507513They are calculated in the \mdl{zpshde} module, described in \autoref{sec:TRA_zpshde}. 
    508514 
     515%% ================================================================================================= 
    509516\subsection{Standard and triad (bi-)laplacian operator} 
    510517\label{subsec:TRA_ldf_iso_triad} 
     
    512519%&&    Standard rotated (bi-)laplacian operator 
    513520%&& ---------------------------------------------- 
     521%% ================================================================================================= 
    514522\subsubsection[Standard rotated (bi-)laplacian operator (\textit{traldf\_iso.F90})]{Standard rotated (bi-)laplacian operator (\protect\mdl{traldf\_iso})} 
    515523\label{subsec:TRA_ldf_iso} 
     
    555563%&&     Triad rotated (bi-)laplacian operator 
    556564%&&  ------------------------------------------- 
     565%% ================================================================================================= 
    557566\subsubsection[Triad rotated (bi-)laplacian operator (\forcode{ln_traldf_triad})]{Triad rotated (bi-)laplacian operator (\protect\np{ln_traldf_triad}{ln\_traldf\_triad})} 
    558567\label{subsec:TRA_ldf_triad} 
     
    573582%&&    Option for the rotated operators 
    574583%&& ---------------------------------------------- 
     584%% ================================================================================================= 
    575585\subsubsection{Option for the rotated operators} 
    576586\label{subsec:TRA_ldf_options} 
     
    584594\end{itemize} 
    585595 
     596%% ================================================================================================= 
    586597\section[Tracer vertical diffusion (\textit{trazdf.F90})]{Tracer vertical diffusion (\protect\mdl{trazdf})} 
    587598\label{sec:TRA_zdf} 
    588 %--------------------------------------------namzdf--------------------------------------------------------- 
    589  
    590 %-------------------------------------------------------------------------------------------------------------- 
     599 
    591600 
    592601Options are defined through the \nam{zdf}{zdf} namelist variables. 
     
    618627it overcomes the stability constraint. 
    619628 
     629%% ================================================================================================= 
    620630\section{External forcing} 
    621631\label{sec:TRA_sbc_qsr_bbc} 
    622632 
     633%% ================================================================================================= 
    623634\subsection[Surface boundary condition (\textit{trasbc.F90})]{Surface boundary condition (\protect\mdl{trasbc})} 
    624635\label{subsec:TRA_sbc} 
     
    686697This is the reason why the modified filter is not applied in the linear free surface case (see \autoref{chap:TD}). 
    687698 
     699%% ================================================================================================= 
    688700\subsection[Solar radiation penetration (\textit{traqsr.F90})]{Solar radiation penetration (\protect\mdl{traqsr})} 
    689701\label{subsec:TRA_qsr} 
    690 %--------------------------------------------namqsr-------------------------------------------------------- 
    691702 
    692703\begin{listing} 
     
    695706  \label{lst:namtra_qsr} 
    696707\end{listing} 
    697 %-------------------------------------------------------------------------------------------------------------- 
    698708 
    699709Options are defined through the \nam{tra_qsr}{tra\_qsr} namelist variables. 
     
    804814\end{figure} 
    805815 
     816%% ================================================================================================= 
    806817\subsection[Bottom boundary condition (\textit{trabbc.F90}) - \forcode{ln_trabbc})]{Bottom boundary condition (\protect\mdl{trabbc} - \protect\np{ln_trabbc}{ln\_trabbc})} 
    807818\label{subsec:TRA_bbc} 
    808 %--------------------------------------------nambbc-------------------------------------------------------- 
    809819 
    810820\begin{listing} 
     
    813823  \label{lst:nambbc} 
    814824\end{listing} 
    815 %-------------------------------------------------------------------------------------------------------------- 
    816825\begin{figure}[!t] 
    817826  \centering 
     
    839848the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:TRA_geothermal}) \citep{emile-geay.madec_OS09}. 
    840849 
     850%% ================================================================================================= 
    841851\section[Bottom boundary layer (\textit{trabbl.F90} - \forcode{ln_trabbl})]{Bottom boundary layer (\protect\mdl{trabbl} - \protect\np{ln_trabbl}{ln\_trabbl})} 
    842852\label{sec:TRA_bbl} 
    843 %--------------------------------------------nambbl--------------------------------------------------------- 
    844853 
    845854\begin{listing} 
     
    848857  \label{lst:nambbl} 
    849858\end{listing} 
    850 %-------------------------------------------------------------------------------------------------------------- 
    851859 
    852860Options are defined through the \nam{bbl}{bbl} namelist variables. 
     
    872880\citet{campin.goosse_T99}. 
    873881 
     882%% ================================================================================================= 
    874883\subsection[Diffusive bottom boundary layer (\forcode{nn_bbl_ldf=1})]{Diffusive bottom boundary layer (\protect\np[=1]{nn_bbl_ldf}{nn\_bbl\_ldf})} 
    875884\label{subsec:TRA_bbl_diff} 
     
    908917$\overline H^\sigma$, the along bottom mean temperature, salinity and depth, respectively. 
    909918 
     919%% ================================================================================================= 
    910920\subsection[Advective bottom boundary layer (\forcode{nn_bbl_adv=1,2})]{Advective bottom boundary layer (\protect\np[=1,2]{nn_bbl_adv}{nn\_bbl\_adv})} 
    911921\label{subsec:TRA_bbl_adv} 
     
    9941004It has to be used to compute the effective velocity as well as the effective overturning circulation. 
    9951005 
     1006%% ================================================================================================= 
    9961007\section[Tracer damping (\textit{tradmp.F90})]{Tracer damping (\protect\mdl{tradmp})} 
    9971008\label{sec:TRA_dmp} 
    998 %--------------------------------------------namtra_dmp------------------------------------------------- 
    9991009 
    10001010\begin{listing} 
     
    10031013  \label{lst:namtra_dmp} 
    10041014\end{listing} 
    1005 %-------------------------------------------------------------------------------------------------------------- 
    10061015 
    10071016In some applications it can be useful to add a Newtonian damping term into the temperature and salinity equations: 
     
    10501059\path{./tools/DMP_TOOLS}. 
    10511060 
     1061%% ================================================================================================= 
    10521062\section[Tracer time evolution (\textit{tranxt.F90})]{Tracer time evolution (\protect\mdl{tranxt})} 
    10531063\label{sec:TRA_nxt} 
    1054 %--------------------------------------------namdom----------------------------------------------------- 
    1055 %-------------------------------------------------------------------------------------------------------------- 
    10561064 
    10571065Options are defined through the \nam{dom}{dom} namelist variables. 
     
    10821090$T^{t - \rdt} = T^t$ and $T^t = T_f$. 
    10831091 
     1092%% ================================================================================================= 
    10841093\section[Equation of state (\textit{eosbn2.F90})]{Equation of state (\protect\mdl{eosbn2})} 
    10851094\label{sec:TRA_eosbn2} 
    1086 %--------------------------------------------nameos----------------------------------------------------- 
    10871095 
    10881096\begin{listing} 
     
    10911099  \label{lst:nameos} 
    10921100\end{listing} 
    1093 %-------------------------------------------------------------------------------------------------------------- 
    1094  
     1101 
     1102%% ================================================================================================= 
    10951103\subsection[Equation of seawater (\forcode{ln_}\{\forcode{teos10,eos80,seos}\})]{Equation of seawater (\protect\np{ln_teos10}{ln\_teos10}, \protect\np{ln_teos80}{ln\_teos80}, or \protect\np{ln_seos}{ln\_seos})} 
    10961104\label{subsec:TRA_eos} 
     
    12121220\end{table} 
    12131221 
     1222%% ================================================================================================= 
    12141223\subsection[Brunt-V\"{a}is\"{a}l\"{a} frequency]{Brunt-V\"{a}is\"{a}l\"{a} frequency} 
    12151224\label{subsec:TRA_bn2} 
     
    12321241They are computed through \textit{eos\_rab}, a \fortran\ function that can be found in \mdl{eosbn2}. 
    12331242 
     1243%% ================================================================================================= 
    12341244\subsection{Freezing point of seawater} 
    12351245\label{subsec:TRA_fzp} 
     
    12511261a \fortran\ function that can be found in \mdl{eosbn2}. 
    12521262 
     1263%% ================================================================================================= 
    12531264%\subsection{Potential Energy anomalies} 
    12541265%\label{subsec:TRA_bn2} 
     
    12571268% 
    12581269 
     1270%% ================================================================================================= 
    12591271\section[Horizontal derivative in \textit{zps}-coordinate (\textit{zpshde.F90})]{Horizontal derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})} 
    12601272\label{sec:TRA_zpshde} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r11596 r11597  
    1212%gm% Add here a small introduction to ZDF and naming of the different physics (similar to what have been written for TRA and DYN. 
    1313 
     14%% ================================================================================================= 
    1415\section{Vertical mixing} 
    1516\label{sec:ZDF} 
     
    3839%and thus of the formulation used (see \autoref{chap:TD}). 
    3940 
    40 %--------------------------------------------namzdf-------------------------------------------------------- 
    4141 
    4242\begin{listing} 
     
    4545  \label{lst:namzdf} 
    4646\end{listing} 
    47 %-------------------------------------------------------------------------------------------------------------- 
    48  
     47 
     48%% ================================================================================================= 
    4949\subsection[Constant (\forcode{ln_zdfcst})]{Constant (\protect\np{ln_zdfcst}{ln\_zdfcst})} 
    5050\label{subsec:ZDF_cst} 
     
    6666$\sim10^{-9}~m^2.s^{-1}$ for salinity. 
    6767 
     68%% ================================================================================================= 
    6869\subsection[Richardson number dependent (\forcode{ln_zdfric})]{Richardson number dependent (\protect\np{ln_zdfric}{ln\_zdfric})} 
    6970\label{subsec:ZDF_ric} 
    7071 
    71 %--------------------------------------------namric--------------------------------------------------------- 
    7272 
    7373\begin{listing} 
     
    7676  \label{lst:namzdf_ric} 
    7777\end{listing} 
    78 %-------------------------------------------------------------------------------------------------------------- 
    7978 
    8079When \np[=.true.]{ln_zdfric}{ln\_zdfric}, a local Richardson number dependent formulation for the vertical momentum and 
     
    124123the empirical values \np{rn_wtmix}{rn\_wtmix} and \np{rn_wvmix}{rn\_wvmix} \citep{lermusiaux_JMS01}. 
    125124 
     125%% ================================================================================================= 
    126126\subsection[TKE turbulent closure scheme (\forcode{ln_zdftke})]{TKE turbulent closure scheme (\protect\np{ln_zdftke}{ln\_zdftke})} 
    127127\label{subsec:ZDF_tke} 
    128 %--------------------------------------------namzdf_tke-------------------------------------------------- 
    129128 
    130129\begin{listing} 
     
    133132  \label{lst:namzdf_tke} 
    134133\end{listing} 
    135 %-------------------------------------------------------------------------------------------------------------- 
    136134 
    137135The vertical eddy viscosity and diffusivity coefficients are computed from a TKE turbulent closure model based on 
     
    196194\np{rn_avt0}{rn\_avt0} (\nam{zdf}{zdf} namelist, see \autoref{subsec:ZDF_cst}). 
    197195 
     196%% ================================================================================================= 
    198197\subsubsection{Turbulent length scale} 
    199198 
     
    266265$\bar{e}$ reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). 
    267266 
     267%% ================================================================================================= 
    268268\subsubsection{Surface wave breaking parameterization} 
    269 %-----------------------------------------------------------------------% 
    270269 
    271270Following \citet{mellor.blumberg_JPO04}, the TKE turbulence closure model has been modified to 
     
    300299surface $\bar{e}$ value. 
    301300 
     301%% ================================================================================================= 
    302302\subsubsection{Langmuir cells} 
    303 %--------------------------------------% 
    304303 
    305304Langmuir circulations (LC) can be described as ordered large-scale vertical motions in 
     
    354353\] 
    355354 
     355%% ================================================================================================= 
    356356\subsubsection{Mixing just below the mixed layer} 
    357 %--------------------------------------------------------------% 
    358357 
    359358Vertical mixing parameterizations commonly used in ocean general circulation models tend to 
     
    402401% (\eg\ Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 
    403402 
     403%% ================================================================================================= 
    404404\subsection[GLS: Generic Length Scale (\forcode{ln_zdfgls})]{GLS: Generic Length Scale (\protect\np{ln_zdfgls}{ln\_zdfgls})} 
    405405\label{subsec:ZDF_gls} 
    406406 
    407 %--------------------------------------------namzdf_gls--------------------------------------------------------- 
    408407 
    409408\begin{listing} 
     
    412411  \label{lst:namzdf_gls} 
    413412\end{listing} 
    414 %-------------------------------------------------------------------------------------------------------------- 
    415413 
    416414The Generic Length Scale (GLS) scheme is a turbulent closure scheme based on two prognostic equations: 
     
    463461They are made available through the \np{nn_clo}{nn\_clo} namelist parameter. 
    464462 
    465 %--------------------------------------------------TABLE-------------------------------------------------- 
    466463\begin{table}[htbp] 
    467464  \centering 
     
    490487  \label{tab:ZDF_GLS} 
    491488\end{table} 
    492 %-------------------------------------------------------------------------------------------------------------- 
    493489 
    494490In the Mellor-Yamada model, the negativity of $n$ allows to use a wall function to force the convergence of 
     
    522518 in \citet{reffray.guillaume.ea_GMD15} for the \NEMO\ model. 
    523519 
     520%% ================================================================================================= 
    524521\subsection[OSM: OSMosis boundary layer scheme (\forcode{ln_zdfosm})]{OSM: OSMosis boundary layer scheme (\protect\np{ln_zdfosm}{ln\_zdfosm})} 
    525522\label{subsec:ZDF_osm} 
    526 %--------------------------------------------namzdf_osm--------------------------------------------------------- 
    527523 
    528524\begin{listing} 
     
    531527  \label{lst:namzdf_osm} 
    532528\end{listing} 
    533 %-------------------------------------------------------------------------------------------------------------- 
    534529 
    535530The OSMOSIS turbulent closure scheme is based on......   TBC 
    536531 
     532%% ================================================================================================= 
    537533\subsection[ Discrete energy conservation for TKE and GLS schemes]{Discrete energy conservation for TKE and GLS schemes} 
    538534\label{subsec:ZDF_tke_ene} 
     
    635631%For the latter, it is in fact the ratio $\sqrt{\bar{e}}/l_\epsilon$ which is stored. 
    636632 
     633%% ================================================================================================= 
    637634\section{Convection} 
    638635\label{sec:ZDF_conv} 
     
    645642or/and the use of a turbulent closure scheme. 
    646643 
     644%% ================================================================================================= 
    647645\subsection[Non-penetrative convective adjustment (\forcode{ln_tranpc})]{Non-penetrative convective adjustment (\protect\np{ln_tranpc}{ln\_tranpc})} 
    648646\label{subsec:ZDF_npc} 
     
    705703having to recompute the expansion coefficients at each mixing iteration. 
    706704 
     705%% ================================================================================================= 
    707706\subsection[Enhanced vertical diffusion (\forcode{ln_zdfevd})]{Enhanced vertical diffusion (\protect\np{ln_zdfevd}{ln\_zdfevd})} 
    708707\label{subsec:ZDF_evd} 
     
    728727a leapfrog environment \citep{leclair_phd10} (see \autoref{sec:TD_mLF}). 
    729728 
     729%% ================================================================================================= 
    730730\subsection[Handling convection with turbulent closure schemes (\forcode{ln_zdf_}\{\forcode{tke,gls,osm}\})]{Handling convection with turbulent closure schemes (\forcode{ln_zdf{tke,gls,osm}})} 
    731731\label{subsec:ZDF_tcs} 
     
    752752% gm%  + one word on non local flux with KPP scheme trakpp.F90 module... 
    753753 
     754%% ================================================================================================= 
    754755\section[Double diffusion mixing (\forcode{ln_zdfddm})]{Double diffusion mixing (\protect\np{ln_zdfddm}{ln\_zdfddm})} 
    755756\label{subsec:ZDF_ddm} 
    756757 
    757 %-------------------------------------------namzdf_ddm------------------------------------------------- 
    758758% 
    759759%\nlst{namzdf_ddm} 
    760 %-------------------------------------------------------------------------------------------------------------- 
    761760 
    762761This parameterisation has been introduced in \mdl{zdfddm} module and is controlled by the namelist parameter 
     
    840839This avoids duplication in the computation of $\alpha$ and $\beta$ (which is usually quite expensive). 
    841840 
     841%% ================================================================================================= 
    842842\section[Bottom and top friction (\textit{zdfdrg.F90})]{Bottom and top friction (\protect\mdl{zdfdrg})} 
    843843\label{sec:ZDF_drg} 
    844844 
    845 %--------------------------------------------namdrg-------------------------------------------------------- 
    846845% 
    847846\begin{listing} 
     
    861860\end{listing} 
    862861 
    863 %-------------------------------------------------------------------------------------------------------------- 
    864862 
    865863Options to define the top and bottom friction are defined through the \nam{drg}{drg} namelist variables. 
     
    916914Note than from \NEMO\ 4.0, drag coefficients are only computed at cell centers (\ie\ at T-points) and refer to as $c_b^T$ in the following. These are then linearly interpolated in space to get $c_b^\textbf{U}$ at velocity points. 
    917915 
     916%% ================================================================================================= 
    918917\subsection[Linear top/bottom friction (\forcode{ln_lin})]{Linear top/bottom friction (\protect\np{ln_lin}{ln\_lin})} 
    919918\label{subsec:ZDF_drg_linear} 
     
    952951$mask\_value$ * \np{rn_boost}{rn\_boost} * \np{rn_Cd0}{rn\_Cd0}. 
    953952 
     953%% ================================================================================================= 
    954954\subsection[Non-linear top/bottom friction (\forcode{ln_non_lin})]{Non-linear top/bottom friction (\protect\np{ln_non_lin}{ln\_non\_lin})} 
    955955\label{subsec:ZDF_drg_nonlinear} 
     
    984984$mask\_value$ * \np{rn_boost}{rn\_boost} * \np{rn_Cd0}{rn\_Cd0}. 
    985985 
     986%% ================================================================================================= 
    986987\subsection[Log-layer top/bottom friction (\forcode{ln_loglayer})]{Log-layer top/bottom friction (\protect\np{ln_loglayer}{ln\_loglayer})} 
    987988\label{subsec:ZDF_drg_loglayer} 
     
    10071008%In this case, the relevant namelist parameters are \np{rn_tfrz0}{rn\_tfrz0}, \np{rn_tfri2}{rn\_tfri2} and \np{rn_tfri2_max}{rn\_tfri2\_max}. 
    10081009 
     1010%% ================================================================================================= 
    10091011\subsection[Explicit top/bottom friction (\forcode{ln_drgimp=.false.})]{Explicit top/bottom friction (\protect\np[=.false.]{ln_drgimp}{ln\_drgimp})} 
    10101012\label{subsec:ZDF_drg_stability} 
     
    10651067The number of potential breaches of the explicit stability criterion are still reported for information purposes. 
    10661068 
     1069%% ================================================================================================= 
    10671070\subsection[Implicit top/bottom friction (\forcode{ln_drgimp=.true.})]{Implicit top/bottom friction (\protect\np[=.true.]{ln_drgimp}{ln\_drgimp})} 
    10681071\label{subsec:ZDF_drg_imp} 
     
    10921095Superscript $n+1$ means the velocity used in the friction formula is to be calculated, so it is implicit. 
    10931096 
     1097%% ================================================================================================= 
    10941098\subsection[Bottom friction with split-explicit free surface]{Bottom friction with split-explicit free surface} 
    10951099\label{subsec:ZDF_drg_ts} 
     
    11051109Note that other strategies are possible, like considering vertical diffusion step in advance, \ie\ prior barotropic integration. 
    11061110 
     1111%% ================================================================================================= 
    11071112\section[Internal wave-driven mixing (\forcode{ln_zdfiwm})]{Internal wave-driven mixing (\protect\np{ln_zdfiwm}{ln\_zdfiwm})} 
    11081113\label{subsec:ZDF_tmx_new} 
    11091114 
    1110 %--------------------------------------------namzdf_iwm------------------------------------------ 
    11111115% 
    11121116\begin{listing} 
     
    11151119  \label{lst:namzdf_iwm} 
    11161120\end{listing} 
    1117 %-------------------------------------------------------------------------------------------------------------- 
    11181121 
    11191122The parameterization of mixing induced by breaking internal waves is a generalization of 
     
    11661169% Jc: input files names ? 
    11671170 
     1171%% ================================================================================================= 
    11681172\section[Surface wave-induced mixing (\forcode{ln_zdfswm})]{Surface wave-induced mixing (\protect\np{ln_zdfswm}{ln\_zdfswm})} 
    11691173\label{subsec:ZDF_swm} 
     
    11961200(for more information on wave parameters and settings see \autoref{sec:SBC_wave}) 
    11971201 
     1202%% ================================================================================================= 
    11981203\section[Adaptive-implicit vertical advection (\forcode{ln_zad_Aimp})]{Adaptive-implicit vertical advection(\protect\np{ln_zad_Aimp}{ln\_zad\_Aimp})} 
    11991204\label{subsec:ZDF_aimp} 
     
    13191324\end{figure} 
    13201325 
     1326%% ================================================================================================= 
    13211327\subsection{Adaptive-implicit vertical advection in the OVERFLOW test-case} 
    13221328 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_cfgs.tex

    r11596 r11597  
    77\chaptertoc 
    88 
     9%% ================================================================================================= 
    910\section{Introduction} 
    1011\label{sec:CFGS_intro} 
     
    1819Configuration is defined manually through the \nam{cfg}{cfg} namelist variables. 
    1920 
    20 %------------------------------------------namcfg---------------------------------------------------- 
    2121 
    2222\begin{listing} 
     
    2525  \label{lst:namcfg} 
    2626\end{listing} 
    27 %------------------------------------------------------------------------------------------------------------- 
    28  
     27 
     28%% ================================================================================================= 
    2929\section[C1D: 1D Water column model (\texttt{\textbf{key\_c1d}})]{C1D: 1D Water column model (\protect\key{c1d})} 
    3030\label{sec:CFGS_c1d} 
     
    6464% to be added:  a test case on the yearlong Ocean Weather Station (OWS) Papa dataset of Martin (1985) 
    6565 
     66%% ================================================================================================= 
    6667\section{ORCA family: global ocean with tripolar grid} 
    6768\label{sec:CFGS_orca} 
     
    9091\end{figure} 
    9192 
     93%% ================================================================================================= 
    9294\subsection{ORCA tripolar grid} 
    9395\label{subsec:CFGS_orca_grid} 
     
    128130while the ratio of anisotropy remains close to one except near the Victoria Island in the Canadian Archipelago. 
    129131 
     132%% ================================================================================================= 
    130133\subsection{ORCA pre-defined resolution} 
    131134\label{subsec:CFGS_orca_resolution} 
     
    138141(\autoref{tab:CFGS_ORCA}). 
    139142 
    140 %--------------------------------------------------TABLE-------------------------------------------------- 
    141143\begin{table}[!t] 
    142144  \centering 
     
    156158  \label{tab:CFGS_ORCA} 
    157159\end{table} 
    158 %-------------------------------------------------------------------------------------------------------------- 
    159160 
    160161The ORCA\_R2 configuration has the following specificity: starting from a 2\deg\ ORCA mesh, 
     
    196197sponge layers at open boundaries. 
    197198 
     199%% ================================================================================================= 
    198200\section{GYRE family: double gyre basin} 
    199201\label{sec:CFGS_gyre} 
     
    255257\end{figure} 
    256258 
     259%% ================================================================================================= 
    257260\section{AMM: atlantic margin configuration} 
    258261\label{sec:CFGS_config_AMM} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex

    r11596 r11597  
    3939\citep{Marti1992?, Levy1996?, Levy1998?}. 
    4040 
     41%% ================================================================================================= 
    4142\section{Conservation properties on ocean dynamics} 
    4243\label{sec:CONS_Invariant_dyn} 
     
    152153otherwise there is no guarantee that the surface pressure force work vanishes. 
    153154 
     155%% ================================================================================================= 
    154156\section{Conservation properties on ocean thermodynamics} 
    155157\label{sec:CONS_Invariant_tra} 
     
    170172In practice, the mass is conserved with a very good accuracy. 
    171173 
     174%% ================================================================================================= 
    172175\subsection{Conservation properties on momentum physics} 
    173176\label{subsec:CONS_Invariant_dyn_physics} 
     
    273276\ie\ the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence. 
    274277 
     278%% ================================================================================================= 
    275279\subsection{Conservation properties on tracer physics} 
    276280\label{subsec:CONS_Invariant_tra_physics} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_misc.tex

    r11596 r11597  
    77\chaptertoc 
    88 
     9%% ================================================================================================= 
    910\section{Representation of unresolved straits} 
    1011\label{sec:MISC_strait} 
     
    2829lateral friction. 
    2930 
     31%% ================================================================================================= 
    3032\subsection{Hand made geometry changes} 
    3133\label{subsec:MISC_strait_hand} 
     
    103105\end{figure} 
    104106 
     107%% ================================================================================================= 
    105108\section[Closed seas (\textit{closea.F90})]{Closed seas (\protect\mdl{closea})} 
    106109\label{sec:MISC_closea} 
     
    167170them to the domain configuration file in the utils/tools/DOMAINcfg directory. 
    168171 
     172%% ================================================================================================= 
    169173\section{Sub-domain functionality} 
    170174\label{sec:MISC_zoom} 
    171175 
     176%% ================================================================================================= 
    172177\subsection{Simple subsetting of input files via NetCDF attributes} 
    173178 
     
    230235conditions. Experimenting with this remains an exercise for the user. 
    231236 
     237%% ================================================================================================= 
    232238\section[Accuracy and reproducibility (\textit{lib\_fortran.F90})]{Accuracy and reproducibility (\protect\mdl{lib\_fortran})} 
    233239\label{sec:MISC_fortran} 
    234240 
     241%% ================================================================================================= 
    235242\subsection[Issues with intrinsinc SIGN function (\texttt{\textbf{key\_nosignedzero}})]{Issues with intrinsinc SIGN function (\protect\key{nosignedzero})} 
    236243\label{subsec:MISC_sign} 
     
    258265some computers/compilers. 
    259266 
     267%% ================================================================================================= 
    260268\subsection{MPP reproducibility} 
    261269\label{subsec:MISC_glosum} 
     
    287295Note also that this implementation may be sensitive to the optimization level. 
    288296 
     297%% ================================================================================================= 
    289298\subsection{MPP scalability} 
    290299\label{subsec:MISC_mppsca} 
     
    311320non-reference configuration. 
    312321 
     322%% ================================================================================================= 
    313323\section{Model optimisation, control print and benchmark} 
    314324\label{sec:MISC_opt} 
    315 %--------------------------------------------namctl------------------------------------------------------- 
    316325 
    317326\begin{listing} 
     
    320329  \label{lst:namctl} 
    321330\end{listing} 
    322 %-------------------------------------------------------------------------------------------------------------- 
    323331 
    324332Options are defined through the  \nam{ctl}{ctl} namelist variables. 
    325333 
     334%% ================================================================================================= 
    326335\subsection{Vector optimisation} 
    327336 
     
    334343% Add also one word on NEC specific optimisation (Novercheck option for example) 
    335344 
     345%% ================================================================================================= 
    336346\subsection{Control print} 
    337347 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics.tex

    r11596 r11597  
    1  
    21\documentclass[../main/NEMO_manual]{subfiles} 
    32 
     
    109 
    1110%% ================================================================================================= 
     11%% ================================================================================================= 
    1212\section{Primitive equations} 
    1313\label{sec:MB_PE} 
    1414 
     15%% ================================================================================================= 
    1516%% ================================================================================================= 
    1617\subsection{Vector invariant formulation} 
     
    9192Their nature and formulation are discussed in \autoref{sec:MB_zdf_ldf} and \autoref{subsec:MB_boundary_condition}. 
    9293 
     94%% ================================================================================================= 
    9395%% ================================================================================================= 
    9496\subsection{Boundary conditions} 
     
    164166 
    165167%% ================================================================================================= 
     168%% ================================================================================================= 
    166169\section{Horizontal pressure gradient} 
    167170\label{sec:MB_hor_pg} 
    168171 
     172%% ================================================================================================= 
    169173%% ================================================================================================= 
    170174\subsection{Pressure formulation} 
     
    200204 
    201205%% ================================================================================================= 
     206%% ================================================================================================= 
    202207\subsection{Free surface formulation} 
    203208\label{subsec:MB_free_surface} 
     
    250255 
    251256%% ================================================================================================= 
     257%% ================================================================================================= 
    252258\section{Curvilinear \textit{z-}coordinate system} 
    253259\label{sec:MB_zco} 
    254260 
     261%% ================================================================================================= 
    255262%% ================================================================================================= 
    256263\subsection{Tensorial formalism} 
     
    337344where $q$ is a scalar quantity and $\vect A = (a_1,a_2,a_3)$ a vector in the $(i,j,k)$ coordinates system. 
    338345 
     346%% ================================================================================================= 
    339347%% ================================================================================================= 
    340348\subsection{Continuous model equations} 
     
    522530 
    523531%% ================================================================================================= 
     532%% ================================================================================================= 
    524533\section{Curvilinear generalised vertical coordinate system} 
    525534\label{sec:MB_gco} 
     
    602611%} 
    603612 
     613%% ================================================================================================= 
    604614%% ================================================================================================= 
    605615\subsection{\textit{S}-coordinate formulation} 
     
    691701 
    692702%% ================================================================================================= 
     703%% ================================================================================================= 
    693704\subsection{Curvilinear \zstar-coordinate system} 
    694705\label{subsec:MB_zco_star} 
     
    777788 
    778789%% ================================================================================================= 
     790%% ================================================================================================= 
    779791\subsection{Curvilinear terrain-following \textit{s}--coordinate} 
    780792\label{subsec:MB_sco} 
    781793 
     794%% ================================================================================================= 
    782795%% ================================================================================================= 
    783796\subsubsection{Introduction} 
     
    862875 
    863876%% ================================================================================================= 
     877%% ================================================================================================= 
    864878\subsection{\texorpdfstring{Curvilinear \ztilde-coordinate}{}} 
    865879\label{subsec:MB_zco_tilde} 
     
    870884Its use is therefore not recommended. 
    871885 
     886%% ================================================================================================= 
    872887%% ================================================================================================= 
    873888\section{Subgrid scale physics} 
     
    894909The formulation of these terms and their underlying physics are briefly discussed in the next two subsections. 
    895910 
     911%% ================================================================================================= 
    896912%% ================================================================================================= 
    897913\subsection{Vertical subgrid scale physics} 
     
    927943 
    928944%% ================================================================================================= 
     945%% ================================================================================================= 
    929946\subsection{Formulation of the lateral diffusive and viscous operators} 
    930947\label{subsec:MB_ldf} 
     
    981998 
    982999%% ================================================================================================= 
     1000%% ================================================================================================= 
    9831001\subsubsection{Lateral laplacian tracer diffusive operator} 
    9841002 
     
    10221040while in $s$-coordinates $\pd[]{k}$ is replaced by $\pd[]{s}$. 
    10231041 
     1042%% ================================================================================================= 
    10241043%% ================================================================================================= 
    10251044\subsubsection{Eddy induced velocity} 
     
    10601079 
    10611080%% ================================================================================================= 
     1081%% ================================================================================================= 
    10621082\subsubsection{Lateral bilaplacian tracer diffusive operator} 
    10631083 
     
    10711091the harmonic eddy diffusion coefficient set to the square root of the biharmonic one. 
    10721092 
     1093%% ================================================================================================= 
    10731094%% ================================================================================================= 
    10741095\subsubsection{Lateral Laplacian momentum diffusive operator} 
     
    11051126 
    11061127%% ================================================================================================= 
     1128%% ================================================================================================= 
    11071129\subsubsection{Lateral bilaplacian momentum diffusive operator} 
    11081130 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

    r11596 r11597  
    33\begin{document} 
    44\chapter{ essai \zstar \sstar} 
     5%% ================================================================================================= 
    56\section{Curvilinear \zstar- or \sstar coordinate system} 
    67 
     
    6061%%% 
    6162 
     63%% ================================================================================================= 
    6264\section[Surface pressure gradient and sea surface heigth (\textit{dynspg.F90})]{Surface pressure gradient and sea surface heigth (\protect\mdl{dynspg})} 
    6365\label{sec:MBZ_dyn_hpg_spg} 
    64 %-----------------------------------------nam_dynspg---------------------------------------------------- 
    6566 
    6667%\nlst{nam_dynspg} 
    67 %------------------------------------------------------------------------------------------------------------ 
    6868Options are defined through the \nam{_dynspg}{\_dynspg} namelist variables. 
    6969The surface pressure gradient term is related to the representation of the free surface (\autoref{sec:MB_hor_pg}). 
     
    8181so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 
    8282 
    83 %------------------------------------------------------------- 
    8483% Explicit 
    85 %------------------------------------------------------------- 
     84%% ================================================================================================= 
    8685\subsubsection[Explicit (\texttt{\textbf{key\_dynspg\_exp}})]{Explicit (\protect\key{dynspg\_exp})} 
    8786\label{subsec:MBZ_dyn_spg_exp} 
     
    117116(\autoref{eq:DYN_spg_exp}). 
    118117 
    119 %------------------------------------------------------------- 
    120118% Split-explicit time-stepping 
    121 %------------------------------------------------------------- 
     119%% ================================================================================================= 
    122120\subsubsection[Split-explicit time-stepping (\texttt{\textbf{key\_dynspg\_ts}})]{Split-explicit time-stepping (\protect\key{dynspg\_ts})} 
    123121\label{subsec:MBZ_dyn_spg_ts} 
    124 %--------------------------------------------namdom---------------------------------------------------- 
    125  
    126 %-------------------------------------------------------------------------------------------------------------- 
     122 
    127123The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004?}. 
    128124The general idea is to solve the free surface equation with a small time step, 
     
    274270be more conservative, and so is recommended. 
    275271 
    276 %------------------------------------------------------------- 
    277272% Filtered formulation 
    278 %------------------------------------------------------------- 
     273%% ================================================================================================= 
    279274\subsubsection[Filtered formulation (\texttt{\textbf{key\_dynspg\_flt}})]{Filtered formulation (\protect\key{dynspg\_flt})} 
    280275\label{subsec:MBZ_dyn_spg_flt} 
     
    288283\colorbox{red}{\np[=1]{rnu}{rnu} to be suppressed from namelist !} 
    289284 
    290 %------------------------------------------------------------- 
    291285% Non-linear free surface formulation 
    292 %------------------------------------------------------------- 
     286%% ================================================================================================= 
    293287\subsection[Non-linear free surface formulation (\texttt{\textbf{key\_vvl}})]{Non-linear free surface formulation (\protect\key{vvl})} 
    294288\label{subsec:MBZ_dyn_spg_vvl} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_time_domain.tex

    r11596 r11597  
    1313  would help  ==> to be added} 
    1414%%%% 
     15 
    1516 
    1617Having defined the continuous equations in \autoref{chap:MB}, we need now to choose a time discretization, 
     
    2021the consequences for the order in which the equations are solved. 
    2122 
     23%% ================================================================================================= 
    2224\section{Time stepping environment} 
    2325\label{sec:TD_environment} 
     
    4749The time stepping itself is performed once at each time step where implicit vertical diffusion is computed, \ie\ in the \mdl{trazdf} and \mdl{dynzdf} modules. 
    4850 
     51%% ================================================================================================= 
    4952\section{Non-diffusive part --- Leapfrog scheme} 
    5053\label{sec:TD_leap_frog} 
     
    8790filter parameter and the viscosity and diffusion coefficients. 
    8891 
     92%% ================================================================================================= 
    8993\section{Diffusive part --- Forward or backward scheme} 
    9094\label{sec:TD_forward_imp} 
     
    151155(see for example \citet{richtmyer.morton_bk67}). 
    152156 
     157%% ================================================================================================= 
    153158\section{Surface pressure gradient} 
    154159\label{sec:TD_spg_ts} 
     
    181186%} 
    182187 
     188%% ================================================================================================= 
    183189\section{Modified Leapfrog -- Asselin filter scheme} 
    184190\label{sec:TD_mLF} 
     
    239245\end{figure} 
    240246 
     247%% ================================================================================================= 
    241248\section{Start/Restart strategy} 
    242249\label{sec:TD_rst} 
    243250 
    244 %--------------------------------------------namrun------------------------------------------- 
    245251\begin{listing} 
    246252  \nlst{namrun} 
     
    248254  \label{lst:namrun} 
    249255\end{listing} 
    250 %-------------------------------------------------------------------------------------------------------------- 
    251256 
    252257The first time step of this three level scheme when starting from initial conditions is a forward step 
     
    286291\gmcomment{       % add a subsection here 
    287292 
    288 %------------------------------------------------------------------------------------------------------------- 
    289293%        Time Domain 
     294% ------------------------------------------------------------------------------------------------------------ 
     295%% ================================================================================================= 
     296\subsection{Time domain} 
     297\label{subsec:TD_time} 
     298 
     299Options are defined through the  \nam{dom}{dom} namelist variables. 
     300 \colorbox{yellow}{add here a few word on nit000 and nitend} 
     301 
     302 \colorbox{yellow}{Write documentation on the calendar and the key variable adatrj} 
     303 
     304add a description of daymod, and the model calandar (leap-year and co) 
     305 
     306}        %% end add 
     307 
     308 
     309 
     310%% 
     311\gmcomment{       % add implicit in vvl case  and Crant-Nicholson scheme 
     312 
     313Implicit time stepping in case of variable volume thickness. 
     314 
     315Tracer case (NB for momentum in vector invariant form take care!) 
     316 
     317\begin{flalign*} 
     318  &\frac{\lt( e_{3t}\,T \rt)_k^{t+1}-\lt( e_{3t}\,T \rt)_k^{t-1}}{2\rdt} 
     319  \equiv \text{RHS}+ \delta_k \lt[ {\frac{A_w^{vt} }{e_{3w}^{t+1} }\delta_{k + 1/2} \lt[ {T^{t+1}} \rt]} 
     320  \rt]      \\ 
     321  &\lt( e_{3t}\,T \rt)_k^{t+1}-\lt( e_{3t}\,T \rt)_k^{t-1} 
     322  \equiv {2\rdt} \ \text{RHS}+ {2\rdt} \ \delta_k \lt[ {\frac{A_w^{vt} }{e_{3w}^{t+1} }\delta_{k + 1/2} \lt[ {T^{t+1}} \rt]} 
     323  \rt]      \\ 
     324  &\lt( e_{3t}\,T \rt)_k^{t+1}-\lt( e_{3t}\,T \rt)_k^{t-1} 
     325  \equiv 2\rdt \ \text{RHS} 
     326  + 2\rdt \ \lt\{ \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k + 1/2} [ T_{k +1}^{t+1} - T_k      ^{t+1} ] 
     327    - \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k - 1/2} [ T_k       ^{t+1} - T_{k -1}^{t+1} ]  \rt\}     \\ 
     328  &\\ 
     329  &\lt( e_{3t}\,T \rt)_k^{t+1} 
     330  -  {2\rdt} \           \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k + 1/2}                  T_{k +1}^{t+1} 
     331  + {2\rdt} \ \lt\{  \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k + 1/2} 
     332    +  \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k - 1/2}     \rt\}   T_{k    }^{t+1} 
     333  -  {2\rdt} \           \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k - 1/2}                  T_{k -1}^{t+1}      \\ 
     334  &\equiv \lt( e_{3t}\,T \rt)_k^{t-1} + {2\rdt} \ \text{RHS}    \\ 
     335  % 
     336\end{flalign*} 
     337\begin{flalign*} 
     338  \allowdisplaybreaks 
     339  \intertext{ Tracer case } 
     340  % 
     341  &  \qquad \qquad  \quad   -  {2\rdt}                  \ \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k + 1/2} 
     342  \qquad \qquad \qquad  \qquad  T_{k +1}^{t+1}   \\ 
     343  &+ {2\rdt} \ \biggl\{  (e_{3t})_{k   }^{t+1}  \bigg. +    \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k + 1/2} 
     344  +   \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k - 1/2} \bigg. \biggr\}  \ \ \ T_{k   }^{t+1}  &&\\ 
     345  & \qquad \qquad  \qquad \qquad \qquad \quad \ \ -  {2\rdt} \                          \lt[ \frac{A_w^{vt}}{e_{3w}^{t+1}} \rt]_{k - 1/2}                          \quad \ \ T_{k -1}^{t+1} 
     346  \ \equiv \ \lt( e_{3t}\,T \rt)_k^{t-1} + {2\rdt} \ \text{RHS}  \\ 
     347  % 
     348\end{flalign*} 
     349\begin{flalign*} 
     350  \allowdisplaybreaks 
     351  \intertext{ Tracer content case } 
     352  % 
     353  & -  {2\rdt} \              & \frac{(A_w^{vt})_{k + 1/2}} {(e_{3w})_{k + 1/2}^{t+1}\;(e_{3t})_{k +1}^{t+1}}  && \  \lt( e_{3t}\,T \rt)_{k +1}^{t+1}   &\\ 
     354  & + {2\rdt} \ \lt[ 1  \rt.+ & \frac{(A_w^{vt})_{k + 1/2}} {(e_{3w})_{k + 1/2}^{t+1}\;(e_{3t})_k^{t+1}} 
     355  + & \frac{(A_w^{vt})_{k - 1/2}} {(e_{3w})_{k - 1/2}^{t+1}\;(e_{3t})_k^{t+1}}  \lt.  \rt]  & \lt( e_{3t}\,T \rt)_{k   }^{t+1}  &\\ 
     356  & -  {2\rdt} \               & \frac{(A_w^{vt})_{k - 1/2}} {(e_{3w})_{k - 1/2}^{t+1}\;(e_{3t})_{k -1}^{t+1}}     &\  \lt( e_{3t}\,T \rt)_{k -1}^{t+1} 
     357  \equiv \lt( e_{3t}\,T \rt)_k^{t-1} + {2\rdt} \ \text{RHS}  & 
     358\end{flalign*} 
     359 
     360%% 
     361} 
     362 
     363\onlyinsubfile{\input{../../global/epilogue}} 
     364 
     365\end{document} 
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