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Changeset 6850 – NEMO

Changeset 6850


Ignore:
Timestamp:
2016-08-08T10:33:25+02:00 (8 years ago)
Author:
gm
Message:

#1629: SIMPLIF_1: S-EOS + DOC and phasing with trunk rev6826

Location:
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters
Files:
6 edited

Legend:

Unmodified
Added
Removed

  • branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_DOM.tex

    r6347 r6850  
    495495\ifile{bathy\_meter} file, so that the computation of the number of wet ocean point  
    496496in each water column is by-passed}.  
     497If \np{ln\_isfcav}~=~true, an extra file input file describing the ice shelf draft  
     498(in meters) (\ifile{isf\_draft\_meter}) is needed. 
     499 
    497500After reading the bathymetry, the algorithm for vertical grid definition differs  
    498501between the different options: 
    … …  
    890893In case of ice shelf cavities, modifications of the model bathymetry and ice shelf draft into  
    891894the cavities are performed in the \textit{zgr\_isf} routine. The compatibility between ice shelf draft and bathymetry is checked.  
     895All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked).  
    892896If only one cell on the water column is opened at $t$-, $u$- or $v$-points, the bathymetry or the ice shelf draft is dug to fit this constrain. 
    893897If the incompatibility is too strong (need to dig more than 1 cell), the cell is masked.\\  
    894898 
    895 From the \textit{mbathy} array, the mask fields are defined as follows: 
     899From the \textit{mbathy} and \textit{misfdep} array, the mask fields are defined as follows: 
    896900\begin{align*} 
    897901tmask(i,j,k) &= \begin{cases}   \; 0&   \text{ if $k < misfdep(i,j) $ } \\ 

  • branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_DYN.tex

    r6347 r6850  
    637637($e_{3w}$). 
    638638  
     639$\bullet$ Traditional coding with adaptation for ice shelf cavities (\np{ln\_dynhpg\_isf}=true). 
     640This scheme need the activation of ice shelf cavities (\np{ln\_isfcav}=true). 
     641 
    639642$\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}=true) 
    640643 

  • branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_LDF.tex

    r6391 r6850  
    397397\subsubsection{Space and Time Varying Mixing Coefficients} 
    398398 
    399 There are no default specifications of space and time varying mixing coefficient.  One 
    400 available case is specific to the ORCA2 and ORCA05 global ocean configurations. It 
    401 provides only a tracer mixing coefficient for eddy induced velocity (ORCA2) or both 
    402 iso-neutral and eddy induced velocity (ORCA05) that depends on the local growth rate of 
    403 baroclinic instability. This specification is actually used when an ORCA key 
     399There is no default specification of space and time varying mixing coefficient.  
     400The only case available is specific to the ORCA2 and ORCA05 global ocean configurations.  
     401It provides only a tracer mixing coefficient for eddy induced velocity (ORCA2) or both  
     402iso-neutral and eddy induced velocity (ORCA05) that depends on the local growth rate of  
     403baroclinic instability. This specification is actually used when an ORCA key  
    404404and both \key{traldf\_eiv} and \key{traldf\_c2d} are defined. 
    405405 

  • branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_SBC.tex

    r6347 r6850  
    5151\item the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model) (\np{nn\_ice}~=~0,1, 2 or 3) ;  
    5252\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ;  
    53 \item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false)  
    54 or as fluxes applied at the land-ice ocean interface (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true) ;  
     53\item the addition of isf melting as lateral inflow (parameterisation) or as fluxes applied at the land-ice ocean interface (\np{ln\_isf}) ;  
    5554\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ;  
    5655\item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ;  
    … …  
    558557reanalysis and satellite data. They use an inertial dissipative method to compute  
    559558the turbulent transfer coefficients (momentum, sensible heat and evaporation)  
    560 from the 10 meters wind speed, air temperature and specific humidity. 
     559from the 10 meter wind speed, air temperature and specific humidity. 
    561560This \citet{Large_Yeager_Rep04} dataset is available through the  
    562561\href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.  
    … …  
    943942\begin{description} 
    944943\item[\np{nn\_isf}~=~1] 
    945 The ice shelf cavities are explicitly represented. The fwf and heat flux are computed. Two different bulk formula are available: 
     944The ice shelf cavities are explicitly represented (\np{ln\_isfcav}~=~true needed). The fwf and heat flux are computed.  
     945Two different bulk formula are available: 
    946946   \begin{description} 
    947947   \item[\np{nn\_isfblk}~=~1] 
    … …  
    951951   \item[\np{nn\_isfblk}~=~2]  
    952952   The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}. 
    953         This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation). 
     953        This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget  
     954        and a linearised freezing point temperature equation). 
    954955   \end{description} 
    955956 
    … …  
    987988 
    988989\item[\np{nn\_isf}~=~4] 
    989 The ice shelf cavity is opened. However, the fwf is not computed but specified from file \np{sn\_fwfisf}).  
     990The ice shelf cavity is opened (\np{ln\_isfcav}~=~true needed). However, the fwf is not computed but specified from file \np{sn\_fwfisf}).  
    990991The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\ 
    991992\end{description} 
    … …  
    10001001coarse to have realistic melting or for studies where you need to control your heat and fw input.\\  
    10011002 
    1002 Two namelist parameters control how the heat and fw fluxes are passed to NEMO: \np{rn\_hisf\_tbl} and \np{ln\_divisf} 
    1003 \begin{description} 
    1004 \item[\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}.  
     1003A namelist parameters control over how many meters the heat and fw fluxes are spread.  
     1004\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}.  
    10051005This parameter is only used if \np{nn\_isf}~=~1 or \np{nn\_isf}~=~4 
    1006 It allows you to control over which depth you want to spread the heat and fw fluxes.  
    1007  
    1008 If \np{rn\_hisf\_tbl} = 0.0, the fluxes are put in the top level whatever is its tickness.  
    1009  
    1010 If \np{rn\_hisf\_tbl} $>$ 0.0, the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells). 
    1011  
    1012 \item[\np{ln\_divisf}] is a flag to apply the fw flux as a volume flux or as a salt flux.  
    1013  
    1014 \np{ln\_divisf}~=~true applies the fwf as a volume flux. This volume flux is implemented with in the same way as for the runoff. 
     1006 
     1007If \np{rn\_hisf\_tbl} = 0., the fluxes are put in the top level whatever its tickness is.  
     1008 
     1009If \np{rn\_hisf\_tbl} $>$ 0., the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells).\\ 
     1010 
     1011The ice shelf melt is implemented as a volume flux with in the same way as for the runoff. 
    10151012The fw addition due to the ice shelf melting is, at each relevant depth level, added to the horizontal divergence  
    10161013(\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}.  
    10171014See the runoff section \ref{SBC_rnf} for all the details about the divergence correction.  
    10181015 
    1019 \np{ln\_divisf}~=~false applies the fwf and heat flux directly on the salinity and temperature tendancy. 
    1020  
    1021 \item[\np{ln\_conserve}] is a flag for \np{nn\_isf}~=~1. A conservative boundary layer scheme as described in \citet{Jenkins2001}  
    1022 is used if \np{ln\_conserve}=true. It takes into account the fact that the melt water is at freezing T and needs to be warm up to ocean temperature.  
    1023 It is only relevant for \np{ln\_divisf}~=~false.  
    1024 If \np{ln\_divisf}~=~true, \np{ln\_conserve} has to be set to false to avoid a double counting of the contribution.  
    1025   
     1016 
     1017\section{ Ice sheet coupling} 
     1018\label{SBC_iscpl} 
     1019%------------------------------------------namsbc_iscpl---------------------------------------------------- 
     1020\namdisplay{namsbc_iscpl} 
     1021%-------------------------------------------------------------------------------------------------------- 
     1022Ice sheet/ocean coupling is done through file exchange at the restart step. NEMO, at each restart step,  
     1023read the bathymetry and ice shelf draft variable in a netcdf file.  
     1024If \np{ln\_iscpl = ~true}, the isf draft is assume to be different at each restart step  
     1025with potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics. 
     1026The wetting and drying scheme applied on the restart is very simple and described below for the 6 different cases: 
     1027\begin{description} 
     1028\item[Thin a cell down:] 
     1029   T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant ($bt_b=bt_n$). 
     1030\item[Enlarge  a cell:] 
     1031   See case "Thin a cell down" 
     1032\item[Dry a cell:] 
     1033   mask, T/S, U/V and ssh are set to 0. Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$). 
     1034\item[Wet a cell:]  
     1035   mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0. If no neighbours along i,j and k, T/S/U/V and mask are set to 0. 
     1036\item[Dry a column:] 
     1037   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0. 
     1038\item[Wet a column:] 
     1039   set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0. If no neighbour, T/S/U/V and mask set to 0. 
    10261040\end{description} 
     1041The extrapolation is call \np{nn\_drown} times. It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps, 
     1042 the code will be unable to fill all the new wet cells properly. The default number is set up for the MISOMIP idealised experiments.\\ 
     1043This coupling procedure is able to take into account grounding line and calving front migration. However, it is a non-conservative processe.  
     1044This could lead to a trend in heat/salt content and volume. In order to remove the trend and keep the conservation level as close to 0 as possible, 
     1045 a simple conservation scheme is available with \np{ln\_hsb = ~true}. The heat/salt/vol. gain/loss is diagnose, as well as the location.  
     1046Based on what is done on sbcrnf to prescribed a source of heat/salt/vol., the heat/salt/vol. gain/loss is removed/added, 
     1047 over a period of \np{rn\_fiscpl} time step, into the system.  
     1048So after \np{rn\_fiscpl} time step, all the heat/salt/vol. gain/loss due to extrapolation process is canceled.\\ 
     1049 
     1050As the before and now fields are not compatible (modification of the geometry), the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$. 
    10271051% 
    10281052% ================================================================ 

  • branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_TRA.tex

    r6347 r6850  
    11% ================================================================ 
    2 % Chapter 1 ——— Ocean Tracers (TRA) 
     2% Chapter 1 --- Ocean Tracers (TRA) 
    33% ================================================================ 
    44\chapter{Ocean Tracers (TRA)} 
    … …  
    4848freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}). 
    4949 
    50 The different options available to the user are managed by namelist logicals or CPP keys.  
    51 For each equation term  \textit{TTT}, the namelist logicals are \textit{ln\_traTTT\_xxx},  
    52 where \textit{xxx} is a 3 or 4 letter acronym corresponding to each optional scheme.  
    53 The CPP key (when it exists) is \textbf{key\_traTTT}. The equivalent code can be  
    54 found in the \textit{traTTT} or \textit{traTTT\_xxx} module, in the NEMO/OPA/TRA directory. 
     50The different options available to the user are managed by namelist logicals or  
     51CPP keys. For each equation term \textbf{\textit{ttt}}, the namelist logicals are \textit{ln\_tra\textbf{ttt}\_\textbf{xxx}},  
     52where \textbf{\textit{xxx}} is a 3 or 4 letter acronym corresponding to each optional scheme.  
     53The CPP key (when it exists) is \textbf{key\_tra\textit{ttt}}. The equivalent code can be  
     54found in the \textit{tra\textbf{ttt}} or \textit{tra\textbf{ttt}\_\textbf{xxx}} module, in the NEMO/OPA/TRA directory. 
    5555 
    5656The user has the option of extracting each tendency term on the RHS of the tracer  
    … …  
    169169using a same treatment to assess the robustness of their results. 
    170170 
    171 % ------------------------------------------------------------------------------------------------------------- 
     171%------------------------------------------------------------------------------------ 
    172172%        2nd and 4th order centred schemes 
    173 % ------------------------------------------------------------------------------------------------------------- 
     173%------------------------------------------------------------------------------------ 
    174174\subsection [Centred schemes (CEN) (\np{ln\_traadv\_cen})] 
    175175            {Centred schemes (CEN) (\np{ln\_traadv\_cen}=true)} 
    176176\label{TRA_adv_cen} 
    177  
    178 %        2nd order centred scheme   
    179177 
    180178The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}~=~\textit{true}.  
    … …  
    189187\tau _u^{cen2} =\overline T ^{i+1/2} 
    190188\end{equation} 
     189 
     190%        2nd order centred scheme   
    191191 
    192192CEN2 is non diffusive ($i.e.$ it conserves the tracer variance, $\tau^2)$  
    … …  
    241241for these near boundary grid points. 
    242242 
    243 % ------------------------------------------------------------------------------------------------------------- 
     243%------------------------------------------------------------------------------------ 
    244244%        FCT scheme   
    245 % ------------------------------------------------------------------------------------------------------------- 
     245%------------------------------------------------------------------------------------ 
    246246\subsection   [Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct})] 
    247247         {Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct}=true)} 
    … …  
    288288while a forward scheme is used for the diffusive part.  
    289289 
    290 % ------------------------------------------------------------------------------------------------------------- 
     290%------------------------------------------------------------------------------------- 
    291291%        MUSCL scheme   
    292 % ------------------------------------------------------------------------------------------------------------- 
     292%------------------------------------------------------------------------------------ 
    293293\subsection[MUSCL scheme  (\np{ln\_traadv\_mus})] 
    294294   {Monotone Upstream Scheme for Conservative Laws (MUSCL) (\np{ln\_traadv\_mus}=T)} 
    … …  
    321321computed using upstream fluxes (\np{ln\_mus\_ups}~=~\textit{true}). 
    322322 
    323 % ------------------------------------------------------------------------------------------------------------- 
     323%------------------------------------------------------------------------------------- 
    324324%        UBS scheme   
    325 % ------------------------------------------------------------------------------------------------------------- 
     325%------------------------------------------------------------------------------------ 
    326326\subsection   [Upstream-Biased Scheme (UBS) (\np{ln\_traadv\_ubs})] 
    327327         {Upstream-Biased Scheme (UBS) (\np{ln\_traadv\_ubs}=true)} 
    … …  
    348348 the advection scheme is similar to that reported in \cite{Farrow1995}.  
    349349It is a relatively good compromise between accuracy and smoothness.  
    350 Nevertheless the scheme is not \emph{positive}, meaning that false extrema are permitted,  
     350Nevertheless, the scheme is not \emph{positive}, meaning that false extrema are permitted,  
    351351but the amplitude of such are significantly reduced over the centred second  
    352 or fourth order method. therefore it is not recommended that it should be  
     352or fourth order method. Therefore it is not recommended that it should be  
    353353applied to a passive tracer that requires positivity.  
    354354 
    … …  
    396396the computationally more efficient formulation \eqref{Eq_tra_adv_ubs}. 
    397397 
    398 % ------------------------------------------------------------------------------------------------------------- 
     398%------------------------------------------------------------------------------------- 
    399399%        QCK scheme   
    400 % ------------------------------------------------------------------------------------------------------------- 
     400%------------------------------------------------------------------------------------- 
    401401\subsection   [QUICKEST scheme (QCK) (\np{ln\_traadv\_qck})] 
    402402         {QUICKEST scheme (QCK) (\np{ln\_traadv\_qck}=true)} 
    … …  
    429429      {Tracer Lateral Diffusion (\mdl{traldf})} 
    430430\label{TRA_ldf} 
    431 %-----------------------------------------nam_traldf------------------------------------------------------ 
     431%-----------------------------------------nam_traldf---------------------------------- 
    432432\namdisplay{namtra_ldf} 
    433 %------------------------------------------------------------------------------------------------------------- 
     433%------------------------------------------------------------------------------------- 
    434434  
    435435Options are defined through the \ngn{namtra\_ldf} namelist variables. 
    … …  
    450450the pure vertical component is split into an explicit and an implicit part \citep{Lemarie_OM2012}. 
    451451 
    452 % ------------------------------------------------------------------------------------------------------------- 
     452%------------------------------------------------------------------------------------ 
    453453%        Type of operator 
    454 % ------------------------------------------------------------------------------------------------------------- 
     454%------------------------------------------------------------------------------------ 
    455455\subsection   [Type of operator (\np{ln\_traldf\_NONE}, \np{ln\_traldf\_lap}, \np{ln\_traldf\_blp})] 
    456456              {Type of operator (\np{ln\_traldf\_NONE}, \np{ln\_traldf\_lap}, or \np{ln\_traldf\_blp} = true) }  
    … …  
    510510 
    511511 
    512 % ------------------------------------------------------------------------------------------------------------- 
     512%------------------------------------------------------------------------------------ 
    513513%       iso-level operator 
    514 % ------------------------------------------------------------------------------------------------------------- 
     514%------------------------------------------------------------------------------------ 
    515515\subsection   [Iso-level (bi-)laplacian operator ( \np{ln\_traldf\_iso})] 
    516516         {Iso-level (bi-)laplacian operator ( \np{ln\_traldf\_iso}) } 
    … …  
    544544 
    545545 
    546 % ------------------------------------------------------------------------------------------------------------- 
     546%------------------------------------------------------------------------------------ 
    547547%         Rotated laplacian operator 
    548 % ------------------------------------------------------------------------------------------------------------- 
     548%------------------------------------------------------------------------------------ 
    549549\subsection   [Standard and triad rotated (bi-)laplacian operator (\mdl{traldf\_iso}, \mdl{traldf\_triad})] 
    550550               {Standard and triad (bi-)laplacian operator (\mdl{traldf\_iso}, \mdl{traldf\_triad}))} 
    … …  
    649649      {Tracer Vertical Diffusion (\mdl{trazdf})} 
    650650\label{TRA_zdf} 
    651 %--------------------------------------------namzdf--------------------------------------------------------- 
     651%--------------------------------------------namzdf----------------------------------- 
    652652\namdisplay{namzdf} 
    653 %-------------------------------------------------------------------------------------------------------------- 
     653%------------------------------------------------------------------------------------- 
    654654 
    655655Options are defined through the \ngn{namzdf} namelist variables. 
    … …  
    697697\label{TRA_sbc_qsr_bbc} 
    698698 
    699 % ------------------------------------------------------------------------------------------------------------- 
     699%------------------------------------------------------------------------------------- 
    700700%        surface boundary condition 
    701 % ------------------------------------------------------------------------------------------------------------- 
     701%------------------------------------------------------------------------------------- 
    702702\subsection   [Surface boundary condition (\textit{trasbc})] 
    703703         {Surface boundary condition (\mdl{trasbc})} 
    … …  
    768768This is the reason why the modified filter is not applied in the linear free surface case (see \S\ref{STP}). 
    769769 
    770 % ------------------------------------------------------------------------------------------------------------- 
     770%------------------------------------------------------------------------------------- 
    771771%        Solar Radiation Penetration  
    772 % ------------------------------------------------------------------------------------------------------------- 
     772%------------------------------------------------------------------------------------- 
    773773\subsection   [Solar Radiation Penetration (\textit{traqsr})] 
    774774         {Solar Radiation Penetration (\mdl{traqsr})} 
    775775\label{TRA_qsr} 
    776 %--------------------------------------------namqsr-------------------------------------------------------- 
     776%--------------------------------------------namqsr----------------------------------- 
    777777\namdisplay{namtra_qsr} 
    778 %-------------------------------------------------------------------------------------------------------------- 
     778%------------------------------------------------------------------------------------- 
    779779 
    780780Options are defined through the  \ngn{namtra\_qsr} namelist variables. 
    … …  
    879879%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    880880 
    881 % ------------------------------------------------------------------------------------------------------------- 
     881%------------------------------------------------------------------------------------- 
    882882%        Bottom Boundary Condition 
    883 % ------------------------------------------------------------------------------------------------------------- 
     883%------------------------------------------------------------------------------------- 
    884884\subsection   [Bottom Boundary Condition (\textit{trabbc})] 
    885885         {Bottom Boundary Condition (\mdl{trabbc})} 
    886886\label{TRA_bbc} 
    887 %--------------------------------------------nambbc-------------------------------------------------------- 
     887%--------------------------------------------nambbc----------------------------------- 
    888888\namdisplay{nambbc} 
    889 %-------------------------------------------------------------------------------------------------------------- 
     889%------------------------------------------------------------------------------------- 
    890890%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    891891\begin{figure}[!t]     \begin{center} 
    … …  
    924924      {Bottom Boundary Layer (\mdl{trabbl} - \key{trabbl})} 
    925925\label{TRA_bbl} 
    926 %--------------------------------------------nambbl--------------------------------------------------------- 
     926%--------------------------------------------nambbl----------------------------------- 
    927927\namdisplay{nambbl} 
    928 %-------------------------------------------------------------------------------------------------------------- 
     928%------------------------------------------------------------------------------------- 
    929929 
    930930Options are defined through the  \ngn{nambbl} namelist variables. 
    … …  
    954954all the improvements introduced by \citet{Campin_Goosse_Tel99}. 
    955955 
    956 % ------------------------------------------------------------------------------------------------------------- 
     956%------------------------------------------------------------------------------------- 
    957957%        Diffusive BBL 
    958 % ------------------------------------------------------------------------------------------------------------- 
     958%------------------------------------------------------------------------------------- 
    959959\subsection{Diffusive Bottom Boundary layer (\np{nn\_bbl\_ldf}=1)} 
    960960\label{TRA_bbl_diff} 
    … …  
    989989salinity and depth, respectively. 
    990990 
    991 % ------------------------------------------------------------------------------------------------------------- 
     991%------------------------------------------------------------------------------------- 
    992992%        Advective BBL 
    993 % ------------------------------------------------------------------------------------------------------------- 
     993%------------------------------------------------------------------------------------- 
    994994\subsection   {Advective Bottom Boundary Layer  (\np{nn\_bbl\_adv}= 1 or 2)} 
    995995\label{TRA_bbl_adv} 
    … …  
    10841084      {Tracer damping (\mdl{tradmp})} 
    10851085\label{TRA_dmp} 
    1086 %--------------------------------------------namtra_dmp------------------------------------------------- 
     1086%--------------------------------------------namtra_dmp------------------------------- 
    10871087\namdisplay{namtra_dmp} 
    1088 %-------------------------------------------------------------------------------------------------------------- 
     1088%------------------------------------------------------------------------------------- 
    10891089 
    10901090In some applications it can be useful to add a Newtonian damping term  
    … …  
    11371137The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 
    11381138 
    1139 %--------------------------------------------nam_dmp_create------------------------------------------------- 
     1139%--------------------------------------------nam_dmp_create--------------------------- 
    11401140\namtools{namelist_dmp} 
    1141 %------------------------------------------------------------------------------------------------------- 
     1141%------------------------------------------------------------------------------------- 
    11421142 
    11431143\np{cp\_cfg}, \np{cp\_cpz}, \np{jp\_cfg} and \np{jperio} specify the model configuration being used and should be the same as specified in \nl{namcfg}. The variable \nl{lzoom} is used to specify that the damping is being used as in case \textit{a} above to provide boundary conditions to a zoom configuration. In the case of the arctic or antarctic zoom configurations this includes some specific treatment. Otherwise damping is applied to the 6 grid points along the ocean boundaries. The open boundaries are specified by the variables \np{lzoom\_n}, \np{lzoom\_e}, \np{lzoom\_s}, \np{lzoom\_w} in the \nl{nam\_zoom\_dmp} name list. 
    … …  
    11691169      {Tracer time evolution (\mdl{tranxt})} 
    11701170\label{TRA_nxt} 
    1171 %--------------------------------------------namdom----------------------------------------------------- 
     1171%--------------------------------------------namdom----------------------------------- 
    11721172\namdisplay{namdom} 
    1173 %-------------------------------------------------------------------------------------------------------------- 
     1173%------------------------------------------------------------------------------------- 
    11741174 
    11751175Options are defined through the  \ngn{namdom} namelist variables. 
    … …  
    12081208      {Equation of State (\mdl{eosbn2}) } 
    12091209\label{TRA_eosbn2} 
    1210 %--------------------------------------------nameos----------------------------------------------------- 
     1210%--------------------------------------------nameos----------------------------------- 
    12111211\namdisplay{nameos} 
    1212 %-------------------------------------------------------------------------------------------------------------- 
    1213  
    1214 % ------------------------------------------------------------------------------------------------------------- 
     1212%------------------------------------------------------------------------------------- 
     1213 
     1214%------------------------------------------------------------------------------------- 
    12151215%        Equation of State 
    1216 % ------------------------------------------------------------------------------------------------------------- 
    1217 \subsection{Equation Of Seawater (\np{nn\_eos} = -1, 0, or 1)} 
     1216%------------------------------------------------------------------------------------- 
     1217\subsection{Equation Of Seawater (\np{ln\_TEOS10}, \np{ln\_EOS80}, \np{ln\_SEOS}, or \np{ln\_LEOS})} 
    12181218\label{TRA_eos} 
    12191219 
    12201220The Equation Of Seawater (EOS) is an empirical nonlinear thermodynamic relationship  
    1221 linking seawater density, $\rho$, to a number of state variables,  
    1222 most typically temperature, salinity and pressure.  
     1221linking seawater density, $\rho$, to a number of state variables, most typically  
     1222temperature, salinity and pressure.  
    12231223Because density gradients control the pressure gradient force through the hydrostatic balance,  
    12241224the equation of state provides a fundamental bridge between the distribution of active tracers  
    12251225and the fluid dynamics. Nonlinearities of the EOS are of major importance, in particular  
    12261226influencing the circulation through determination of the static stability below the mixed layer,  
    1227 thus controlling rates of exchange between the atmosphere  and the ocean interior \citep{Roquet_JPO2015}.  
     1227thus controlling rates of exchange between the atmosphere and the ocean interior \citep{Roquet_JPO2015}.  
    12281228Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{UNESCO1983})  
    12291229or TEOS-10 \citep{TEOS10} standards should be used anytime a simulation of the real  
    12301230ocean circulation is attempted \citep{Roquet_JPO2015}.  
     1231The 1980 International Equation of Seawater (EOS-80) has served the community very well for 30 years. 
     1232Since the 1$^{st}$ January 2010, TEOS-10 (Thermodynamic Equation Of Seawater - 2010) has been  
     1233adopted as the new standard definition of the thermodynamic properties of seawater in oceanography  
     1234by the Intergovernmental Oceanographic Commission. Its main novelty is the introduction of concepts of  
     1235Conservative Temperature ($\Theta$) and Absolute Salinity ($S_A$), replacing Potential  
     1236Temperature ($\theta$) and Practical Salinity ($S_P$), respectively.  
    12311237The use of TEOS-10 is highly recommended because  
    12321238\textit{(i)} it is the new official EOS,  
    12331239\textit{(ii)} it is more accurate, being based on an updated database of laboratory measurements, and  
    1234 \textit{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature  
    1235 and practical salinity for EOS-980, both variables being more suitable for use as model variables  
    1236 \citep{TEOS10, Graham_McDougall_JPO13}.  
     1240\textit{(iii)} it uses $\Theta$ and $S_A$ (instead of $\theta$ and $S_P$ for EOS-80), both variables being more  
     1241conservative thus more suitable for use as model variables \citep{TEOS10, Graham_McDougall_JPO13}.  
    12371242EOS-80 is an obsolescent feature of the NEMO system, kept only for backward compatibility. 
    1238 For process studies, it is often convenient to use an approximation of the EOS. To that purposed,  
    1239 a simplified EOS (S-EOS) inspired by \citet{Vallis06} is also available. 
     1243For process studies, it is often convenient to use an approximation of the EOS. To that purpose,  
     1244the simplified EOS (S-EOS) proposed by \citep{Roquet_JPO2015} and a Linear EOS (L-EOS) are also available. 
    12401245 
    12411246In the computer code, a density anomaly, $d_a= \rho / \rho_o - 1$,  
    12421247is computed, with $\rho_o$ a reference density. Called \textit{rau0}  
    1243 in the code, $\rho_o$ is set in \mdl{phycst} to a value of $1,026~Kg/m^3$.  
     1248in the code, $\rho_o$ is set in \mdl{eosbn2} module to a value of $1,026~kg/m^3$.  
    12441249This is a sensible choice for the reference density used in a Boussinesq ocean  
    1245 climate model, as, with the exception of only a small percentage of the ocean,  
     1250climate model, as it is a typical value of surface densities where the freshwater flux is applied  
     1251(see \citep{Roquet_OM2015} for a more complete discussion of this value).  
     1252With the exception of only a small percentage of the ocean,  
    12461253density in the World Ocean varies by no more than 2$\%$ from that value \citep{Gill1982}. 
    12471254 
    1248 Options are defined through the  \ngn{nameos} namelist variables, and in particular \np{nn\_eos}  
    1249 which controls the EOS used (=-1 for TEOS10 ; =0 for EOS-80 ; =1 for S-EOS). 
     1255Options are defined through the  \ngn{nameos} namelist variables, and in particular by setting to \textit{true}  
     1256one of following logicals: \np{ln\_TEOS10}, \np{ln\_EOS80}, \np{ln\_SEOS}, or \np{ln\_LEOS},  
     1257the logicals that control the EOS used. 
     1258 
    12501259\begin{description} 
    12511260 
    1252 \item[\np{nn\_eos}$=-1$] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used.   
    1253 The accuracy of this approximation is comparable to the TEOS-10 rational function approximation,  
    1254 but it is optimized for a boussinesq fluid and the polynomial expressions have simpler  
    1255 and more computationally efficient expressions for their derived quantities  
    1256 which make them more adapted for use in ocean models.  
    1257 Note that a slightly higher precision polynomial form is now used replacement of the TEOS-10  
    1258 rational function approximation for hydrographic data analysis  \citep{TEOS10}.  
    1259 A key point is that conservative state variables are used:  
     1261\item[\np{ln\_TEOS10} = \textit{true}] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used.   
     1262This equation of state consists in a 55-term polynomial approximation of the reference TEOS-10 expression,  
     1263optimized for a Boussinesq fluid by giving density as a function of Conservative Temperature, Absolute Salinity, 
     1264and pressure. The polynomial expression has a simple and computationally efficient expression  
     1265for its derived quantities (derivatives and primitives) which makes it more adapted for use in ocean models.  
     1266Note that a higher precision approximation (75-term, also polynomial form) is now used as the standard TEOS-10  
     1267approximation for hydrographic data analysis \citep{Roquet_OM2015, TEOS10}.  
     1268A key point is that \textit{conservative} state variables are used:  
    12601269Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: $\degres C$, notation: $\Theta$). 
    12611270The pressure in decibars is approximated by the depth in meters.  
    1262 With TEOS10, the specific heat capacity of sea water, $C_p$, is a constant. It is set to  
    1263 $C_p=3991.86795711963~J\,Kg^{-1}\,\degres K^{-1}$, according to \citet{TEOS10}. 
     1271With TEOS-10, the specific heat capacity of sea water, $C_p$, is a constant. It is set to  
     1272$C_p=3991.86795711963~J/kg/\degres K$, according to \citet{TEOS10}. 
    12641273 
    12651274Choosing polyTEOS10-bsq implies that the state variables used by the model are  
    1266 $\Theta$ and $S_A$. In particular, the initial state deined by the user have to be given as  
    1267 \textit{Conservative} Temperature and \textit{Absolute} Salinity.  
    1268 In addition, setting \np{ln\_useCT} to \textit{true} convert the Conservative SST to potential SST  
    1269 prior to either computing the air-sea and ice-sea fluxes (forced mode)  
    1270 or sending the SST field to the atmosphere (coupled mode). 
    1271  
    1272 \item[\np{nn\_eos}$=0$] the polyEOS80-bsq equation of seawater is used. 
     1275$\Theta$ and $S_A$. In particular, the initial and restoring state defined by the user  
     1276have to be given as \textit{Conservative} Temperature and \textit{Absolute} Salinity.  
     1277In addition, the Conservative Sea Surface Temperature (SST) is automatically converted to  
     1278potential SST prior to either computing the air-sea and ice-sea fluxes (forced mode)  
     1279or sending the SST field to the atmosphere (coupled mode).  
     1280This conversion is performed in \mdl{sbcssm} and \mdl{sbccpl} modules  
     1281using \rou{eos\_pt\_from\_ct} routine. 
     1282 
     1283 
     1284\item[\np{ln\_EOS80} = \textit{true}] the polyEOS80-bsq equation of seawater is used. 
    12731285It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized  
    1274 to accurately fit EOS80 (Roquet, personal comm.). The state variables used in both the EOS80  
    1275 and the ocean model are:  
    1276 the Practical Salinity ((unit: psu, notation: $S_p$)) and Potential Temperature (unit: $\degres C$, notation: $\theta$). 
     1286to accurately fit EOS-80 (Roquet, personal comm.). In this case, the state variables  
     1287used in both the EOS-80 and the ocean model are:  
     1288the Practical Salinity (unit: psu, notation: $S_p$) and  
     1289the Potential Temperature (unit: $\degres C$, notation: $\theta$). 
    12771290The pressure in decibars is approximated by the depth in meters.   
    1278 With thsi EOS, the specific heat capacity of sea water, $C_p$, is a function of temperature,  
    1279 salinity and pressure \citep{UNESCO1983}. Nevertheless, a severe assumption is made in order to  
    1280 have a heat content ($C_p T_p$) which is conserved by the model: $C_p$ is set to a constant  
    1281 value, the TEOS10 value.  
     1291With this EOS, the specific heat capacity of sea water, $C_p$, should be a function  
     1292of temperature, salinity and pressure \citep{UNESCO1983}. Nevertheless, a severe  
     1293assumption is made in the model in order to have a heat content ($C_p \theta$)  
     1294which is conserved by the model: $C_p$ is set to a constant value, the TEOS-10 value.  
    12821295  
    1283 \item[\np{nn\_eos}$=1$] a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen,  
    1284 the coefficients of which has been optimized to fit the behavior of TEOS10 (Roquet, personal comm.)  
    1285 (see also \citet{Roquet_JPO2015}). It provides a simplistic linear representation of both  
    1286 cabbeling and thermobaricity effects which is enough for a proper treatment of the EOS  
    1287 in theoretical studies \citep{Roquet_JPO2015}. 
    1288 With such an equation of state there is no longer a distinction between  
    1289 \textit{conservative} and \textit{potential} temperature, as well as between \textit{absolute}  
    1290 and \textit{practical} salinity. 
    1291 S-EOS takes the following expression: 
     1296\item[\np{ln\_SEOS} = \textit{true}] the Simplified EOS (S-EOS) proposed by  
     1297\citep{Roquet_JPO2015} is chosen (see their Eq. 17), the coefficients of which have been optimized  
     1298to fit the behavior of TEOS-10, and thus which uses \textit{conservative} state variables ($S_A$ and $\Theta$). 
     1299It provides a simplistic linear representation of both cabbeling and thermobaricity effects  
     1300which is enough for a proper treatment of the EOS in theoretical studies.  
     1301This simplified EOS has been validated with a forced ORCA2 configuration,  
     1302and it has been found that the simulated circulation satisfactorily reproduces the simulated circulation  
     1303obtained with TEOS-10, with tracer and velocity fields generally differing by less than 10\%. 
     1304S-EOS takes the following form: 
    12921305\begin{equation} \label{Eq_tra_S-EOS} 
    1293 \begin{split} 
    1294   d_a(T,S,z)  =  ( & - a_0 \; ( 1 + 0.5 \; \lambda_1 \; T_a + \mu_1 \; z ) * T_a  \\ 
    1295                                 & + b_0 \; ( 1 - 0.5 \; \lambda_2 \; S_a - \mu_2 \; z ) * S_a  \\ 
    1296                                 & - \nu \; T_a \; S_a \;  ) \; / \; \rho_o                     \\ 
    1297   with \ \  T_a = T-10  \; ;  & \;  S_a = S-35  \; ;\;  \rho_o = 1026~Kg/m^3 
    1298 \end{split} 
     1306  d_a(\Theta,S_A,z)  =  ( - a_0 \; \Delta \Theta - 0.5\;C_b\; \Delta \Theta^2   \\ 
     1307                              -\;T_h\; \Theta\;z \;+\; b_0 \; \Delta S \; ) \, / \, \rho_o   \\ 
    12991308\end{equation}  
    1300 where the computer name of the coefficients as well as their standard value are given in \ref{Tab_SEOS}. 
     1309with $\Delta \Theta = \Theta-\Theta_o$, $\Delta S = S_A-35$ and  $\rho_o = 1026~Kg/m^3$. 
     1310Equation (17) of \citep{Roquet_JPO2015} is obtained by setting in \eqref{Eq_tra_S-EOS} $a_0$ to zero,  
     1311$i.e.$ by removing the linear temperature dependent term which has been introduced to allow 
     1312\eqref{Eq_tra_S-EOS} to account for both Simplified and Linear EOS (see \np{ln\_LEOS} = \textit{true} case). 
     1313 
     1314The computer name of the coefficients as they appear in  \ngn{nameos} namelist  
     1315as well as their standard value are given in \ref{Tab_SEOS}. 
    13011316In fact, when choosing S-EOS, various approximation of EOS can be specified simply by changing  
    13021317the associated coefficients.  
    1303 Setting to zero the two thermobaric coefficients ($\mu_1$, $\mu_2$) remove thermobaric effect from S-EOS. 
    1304 setting to zero the three cabbeling coefficients ($\lambda_1$, $\lambda_2$, $\nu$) remove cabbeling effect from S-EOS. 
    1305 Keeping non-zero value to $a_0$ and $b_0$ provide a linear EOS function of T and S. 
    1306  
     1318Setting to zero the thermobaric coefficients ($T_h$) removes all thermobaric effects from S-EOS. 
     1319Setting to zero the cabbeling coefficients ($C_b$) removes all cabbeling effects from S-EOS. 
     1320Setting to zero both cabbeling and thermobaric coefficients ($C_b$ and $T_h$) removes nonlinearities from S-EOS.  
     1321Nevertheless, in the setting $C_b$ to zero removes the dependency of $d_a$ with temperature at $z=0$.  
     1322A non-zero value of $a_o$ must be provided to obtain a linear variation of density with temperature, 
     1323 otherwise the model will crash. A typical choice would be the same as in the linear EOS case:  
     1324 $a_o=0.16\,kg/m^{3}/K$ (see table \ref{Tab_SEOS}). 
     1325 
     1326\item[\np{ln\_LEOS} = \textit{true}] a Linear EOS (L-EOS) is chosen, the coefficients of which have been  
     1327optimized to fit the behavior of TEOS-10 and thus which uses \textit{conservative} state variables ($S_A$ and $\Theta$).  
     1328Such a linear equation has neither cabbeling nor thermobaric effects. 
     1329L-EOS uses \eqref{Eq_tra_S-EOS} with all the coefficients but $a_0$ and $b_0$ set to zero.  
     1330It thereore takes the following form: 
     1331\begin{equation} \label{Eq_tra_L-EOS} 
     1332  d_a(\Theta,S_A,z)  =  ( - a_0 \; \Delta \Theta +  b_0 \; \Delta S) \; / \; \rho_o   \\ 
     1333\end{equation}  
     1334with $\Delta \Theta = \Theta-10$, $\Delta S = S_A-35$ and  $\rho_o = 1026~Kg/m^3$. 
     1335The computer name of the $a_0$ and $b_0$ coefficients as they appear in  \ngn{nameos} namelist  
     1336as well as their standard value are given in \ref{Tab_SEOS}. 
    13071337\end{description} 
    13081338 
    … …  
    13101340%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    13111341\begin{table}[!tb] 
    1312 \begin{center} \begin{tabular}{|p{26pt}|p{72pt}|p{56pt}|p{136pt}|} 
     1342\begin{center} \begin{tabular}{p{20pt}|p{24pt}|p{64pt}|p{39pt}|p{32pt}|p{162pt}} 
    13131343\hline 
    1314 coeff.   & computer name   & S-EOS     &  description                      \\ \hline 
    1315 $a_0$       & \np{rn\_a0}     & 1.6550 $10^{-1}$ &  linear thermal expansion coeff.    \\ \hline 
    1316 $b_0$       & \np{rn\_b0}     & 7.6554 $10^{-1}$ &  linear haline  expansion coeff.    \\ \hline 
    1317 $\lambda_1$ & \np{rn\_lambda1}& 5.9520 $10^{-2}$ &  cabbeling coeff. in $T^2$          \\ \hline 
    1318 $\lambda_2$ & \np{rn\_lambda2}& 5.4914 $10^{-4}$ &  cabbeling coeff. in $S^2$       \\ \hline 
    1319 $\nu$       & \np{rn\_nu}     & 2.4341 $10^{-3}$ &  cabbeling coeff. in $T \, S$       \\ \hline 
    1320 $\mu_1$     & \np{rn\_mu1}    & 1.4970 $10^{-4}$ &  thermobaric coeff. in T         \\ \hline 
    1321 $\mu_2$     & \np{rn\_mu2}    & 1.1090 $10^{-5}$ &  thermobaric coeff. in S            \\ \hline 
     1344coeff.     &    model     & unit                       & S-EOS          & L-EOS &  description                                   \\  
     1345           &    name      &                            &            &    &                                              \\ \hline 
     1346$C_b$        & \np{rn\_cb} & $kg/m^{3}/K^{2}$ & 0.011             & 0       & cabbeling coefficient                           \\  
     1347$\Theta_o$ & \np{rn\_t0} & $^oC$                  & -4.5                & 0       & zero thermal exp. at  $(\Theta,z)=(\Theta_o,0)$  \\ 
     1348$T_h$         & \np{rn\_th} & $kg/m^{4}/K$       & 2.5 $10^{-5}$ & 0       & thermobaric coeff.                               \\  
     1349$b_0$         & \np{rn\_b0} & $kg/m^{3}/(g/kg)$  & 0.77             & -  & haline contraction coefficient         \\  
     1350$a_0$         & \np{rn\_a0} & $kg/m^{3}/K$       & 0                   & -   & \textit{linear} thermal expansion coefficient  \\ \hline 
     1351$b_0$         & \np{rn\_bl} & $kg/m^{3}/(g/kg)$  & -                  & 0.77  &  \textit{linear} haline contraction coefficient        \\  
     1352$a_0$         & \np{rn\_al} & $kg/m^{3}/K$       & -                   & 0.16   & \textit{linear} thermal expansion coefficient  \\ \hline 
    13221353\end{tabular} 
    13231354\caption{ \label{Tab_SEOS} 
    1324 Standard value of S-EOS coefficients. } 
     1355Standard values of S-EOS and L-EOS coefficients  \citep{Roquet_JPO2015}.  
     1356In S-EOS case, only four parameters are usually needed.  
     1357The parameter $a_o$ should be set to zero, unless cabbeling effect are removed ($i.e.$ $C_b=0$). 
     1358In L-EOS case, only two parameters are used and $C_b= \Theta=T_h=0$  } 
    13251359\end{center} 
    13261360\end{table} 
    13271361%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    1328  
    1329  
    1330 % ------------------------------------------------------------------------------------------------------------- 
     1362\vspace{1.cm} 
     1363%$\ $\newline    % force a new ligne 
     1364 
     1365 
     1366In TEOS-10 (as well as in S-EOS and L-EOS), the density of seawater is a  
     1367function of the absolute salinity $S_A$, defined as the mass fraction of salt (units: $g/kg$): 
     1368\begin{equation} \label{Eq_tra_SA} 
     1369S_A= 1.00471 \times S_P + \delta S_A 
     1370\end{equation}  
     1371where $\delta S_A$ is a correction accounting for ionic composition changes. 
     1372On average, $S_A$ and $S_P$ differ numerically by about 0.5\%. 
     1373 
     1374When needed, converting T/S fields from EOS-80 to TEOS-10 standards is easy: 
     1375\begin{itemize} 
     1376\item[*] $S_A \approx 1.00471 * S_P$  (excellent approximation in practice). 
     1377\item[*] $\Theta=f(\theta,S_A)$ is a simple polynomial expression (very fast conversion) \citep{TEOS10} .  
     1378\end{itemize} 
     1379 
     1380 
     1381%------------------------------------------------------------------------------------- 
    13311382%        Brunt-V\"{a}is\"{a}l\"{a} Frequency 
    1332 % ------------------------------------------------------------------------------------------------------------- 
    1333 \subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)} 
     1383%-------------------------------------------------------------------------------------- 
     1384\subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency} 
    13341385\label{TRA_bn2} 
    13351386 
    1336 An accurate computation of the ocean stability (i.e. of $N$, the brunt-V\"{a}is\"{a}l\"{a} 
    1337  frequency) is of paramount importance as determine the ocean stratification and  
     1387An accurate computation of the ocean stability (i.e. of $N$, the Brunt-V\"{a}is\"{a}l\"{a} 
     1388 frequency) is of paramount importance as $N^2$ determines the ocean stratification and  
    13381389 is used in several ocean parameterisations (namely TKE, GLS, Richardson number dependent  
    13391390 vertical diffusion, enhanced vertical diffusion, non-penetrative convection, tidal mixing  
    1340  parameterisation, iso-neutral diffusion). In particular, $N^2$ has to be computed at the local pressure  
    1341  (pressure in decibar being approximated by the depth in meters). The expression for $N^2$  
     1391 parameterisation, iso-neutral diffusion, ...). In particular, $N^2$ has to be computed at the local pressure  
     1392 (pressure in decibars being approximated by the depth in meters). The expression for $N^2$  
    13421393 is given by:  
    13431394\begin{equation} \label{Eq_tra_bn2} 
    1344 N^2 = \frac{g}{e_{3w}} \left(   \beta \;\delta_{k+1/2}[S] - \alpha \;\delta_{k+1/2}[T]   \right) 
     1395N^2 = \frac{g}{e_{3w}} \left(   b \;\delta_{k+1/2}[S] - a \;\delta_{k+1/2}[T]   \right) 
    13451396\end{equation}  
    1346 where $(T,S) = (\Theta, S_A)$ for TEOS10, $= (\theta, S_p)$ for TEOS-80, or $=(T,S)$ for S-EOS,  
    1347 and, $\alpha$ and $\beta$ are the thermal and haline expansion coefficients.  
     1397where $(T,S) = (\Theta, S_A)$ for TEOS-10, S-EOS, and L-EOS, or $= (\theta, S_p)$ for TEOS-80,  
     1398and, $a$ and $b$ are the "thermal expansion" and "haline contraction"  coefficients, respectively, 
     1399\begin{equation} \label{Eq_tra_rab} 
     1400a(T,S,z) =  - \left( \frac{\partial \rho}{\partial T} \right)_{S,z}  \quad ;  \quad   
     1401b(T,S,z) =   \left( \frac{\partial \rho}{\partial S} \right)_{T,z} 
     1402\end{equation}  
     1403Note that we use here definitions that differ slightly from the usual ones, as they are not divided by density.  
     1404This form is indeed more suitable for a Boussinesq model such as \NEMO.  
     1405As a consequence, $a$ and $b$ have here units of [$kg/m^3 /K$] and [$kg/m^3/(g/kg)$], respectively. 
    13481406The coefficients are a polynomial function of temperature, salinity and depth which expression  
    1349 depends on the chosen EOS. They are computed through \textit{eos\_rab}, a \textsc{Fortran}  
     1407depends on the chosen EOS. They are computed through \rou{eos\_rab}, a \textsc{Fortran}  
    13501408function that can be found in \mdl{eosbn2}. 
    13511409 
    1352 % ------------------------------------------------------------------------------------------------------------- 
     1410%------------------------------------------------------------------------------------- 
    13531411%        Freezing Point of Seawater 
    1354 % ------------------------------------------------------------------------------------------------------------- 
     1412%------------------------------------------------------------------------------------- 
    13551413\subsection   [Freezing Point of Seawater] 
    13561414         {Freezing Point of Seawater} 
    … …  
    13601418\begin{equation} \label{Eq_tra_eos_fzp} 
    13611419   \begin{split} 
    1362 T_f (S,p) = \left( -0.0575 + 1.710523 \;10^{-3} \, \sqrt{S}  
    1363                        -  2.154996 \;10^{-4} \,S  \right) \ S    \\ 
    1364                - 7.53\,10^{-3} \ \ p  
     1420T_f (S_p,z) = \left( -0.0575 + 1.710523 \;10^{-3} \, \sqrt{S_p}  
     1421                       -  2.154996 \;10^{-4} \,S_p  \right) \ S_p    \\ 
     1422               - 7.53\,10^{-3} \ \ z  
    13651423   \end{split} 
    13661424\end{equation} 
     1425where the depth, $z$, in meters is an approximation of the pressure in decibars, and  
     1426$T_f$ is the \textit{in situ} temperature.  
     1427 
     1428The freezing point is used for both sea-ice/ocean and ice-shelve/ocean interfaces to compute  
     1429the fluxes and determine the sea-ice formation rate. 
     1430In the former case, only the potential freezing point at the surface ($i.e.$ $z=0$) is needed 
     1431which is exactly equals to the $in situ$ freezing point at $z=0$ when using EOS-80 (\np{ln\_eos80} = true). 
     1432With other EOS than EOS-80 ($i.e.$ when \np{ln\_TEOS10}, \np{ln\_SEOS}, or \np{ln\_LEOS} = true),  
     1433the salinity is multiplied by a factor of $35/35.16504$ to convert it from Absolute to Practical.  
     1434This approximation leads to a $~0.003^oC$ rms difference with the exact value of the freezing point.   
     1435In the latter case, potential for EOS-80 or conservative  
     1436  
     1437 
    13671438 
    13681439\eqref{Eq_tra_eos_fzp} is only used to compute the potential freezing point of  
    13691440sea water ($i.e.$ referenced to the surface $p=0$), thus the pressure dependent  
    1370 terms in \eqref{Eq_tra_eos_fzp} (last term) have been dropped. The freezing 
    1371 point is computed through \textit{eos\_fzp}, a \textsc{Fortran} function that can be found  
    1372 in \mdl{eosbn2}.   
    1373  
    1374  
    1375 % ------------------------------------------------------------------------------------------------------------- 
     1441terms in \eqref{Eq_tra_eos_fzp} (last term) have been dropped.  
     1442The freezing point is computed through \rou{eos\_fzp}, a \textsc{Fortran}  
     1443function that can be found in \mdl{eosbn2}.   
     1444 
     1445 
     1446      !! 
     1447      !!       Note1: ptf is the IN SITU freezing temperature. It is equal to the potential 
     1448      !!              one when pdep=0 (or pdep is not present). 
     1449      !!              Potential freezing point is what is needed by sea-ice model 
     1450      !!       Note2: This formulation needs a salinity given in Practical Salinity Units (PSU) 
     1451      !!              With other EOS than EOS-80, the salinity is multiplied by a factor  
     1452      !!              of 35/35.16504 to convert salinity from Absolute to Practical. 
     1453      !!              This approximation leads to a ~0.003.degrees rms difference with the 
     1454      !!              exact value of the freezing point.   
     1455 
     1456 
     1457 
     1458%------------------------------------------------------------------------------------- 
    13761459%        Potential Energy      
    1377 % ------------------------------------------------------------------------------------------------------------- 
     1460%------------------------------------------------------------------------------------- 
    13781461%\subsection{Potential Energy anomalies} 
    13791462%\label{TRA_bn2} 
    … …  
    13931476                   I've changed "derivative" to "difference" and "mean" to "average"} 
    13941477 
    1395 With partial cells (\np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true), in general,  
    1396 tracers in horizontally adjacent cells live at different depths.  
    1397 Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} module)  
    1398 and for the hydrostatic pressure gradient (\mdl{dynhpg} module) to be active.  
    1399 \gmcomment{STEVEN from gm : question: not sure of  what -to be active- means} 
     1478With partial cells (\np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true),  
     1479in general, tracers in horizontally adjacent cells live at different depths.  
     1480Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf}  
     1481module) and the hydrostatic pressure gradient calculations (\mdl{dynhpg} module).  
     1482The partial cell properties at the top (\np{ln\_isfcav}=true) are computed in  
     1483the same way as for the bottom.  
     1484So, only the bottom interpolation is explained below. 
     1485 
    14001486Before taking horizontal gradients between the tracers next to the bottom, a linear  
    14011487interpolation in the vertical is used to approximate the deeper tracer as if it actually  
    … …  
    14731559\gmcomment{gm :   this last remark has to be done} 
    14741560%%% 
    1475  
    1476 If under ice shelf seas opened (\np{ln\_isfcav}=true), the partial cell properties  
    1477 at the top are computed in the same way as for the bottom. Some extra variables are,  
    1478 however, computed to reduce the flow generated at the top and bottom if $z*$ coordinates activated. 
    1479 The extra variables calculated and used by \S\ref{DYN_hpg_isf} are: 
    1480  
    1481 $\bullet$ $\overline{T}_k^{\,i+1/2}$ as described in \eqref{Eq_zps_hde} 
    1482  
    1483 $\bullet$ $\delta _{i+1/2} Z_{T_k} = \widetilde {Z}^{\,i}_{T_k}-Z^{\,i}_{T_k}$ to compute  
    1484 the pressure gradient correction term used by \eqref{Eq_dynhpg_sco} in \S\ref{DYN_hpg_isf}, 
    1485  with $\widetilde {Z}_{T_k}$ the depth of the point $\widetilde {T}_{k}$ in case of $z^*$ coordinates  
    1486 (this term = 0 in z-coordinates) 

  • branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_ZDF.tex

    r6347 r6850  
    852852The bottom friction represents the friction generated by the bathymetry.  
    853853The top friction represents the friction generated by the ice shelf/ocean interface.  
    854 As the friction processes at the top and bottom are represented similarly,  
     854As the friction processes at the top and bottom are treated in similar way,  
    855855only the bottom friction is described in detail below. 
    856856 
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