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- 2016-08-08T10:33:25+02:00 (8 years ago)
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- branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters
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branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_DOM.tex
r6347 r6850 495 495 \ifile{bathy\_meter} file, so that the computation of the number of wet ocean point 496 496 in each water column is by-passed}. 497 If \np{ln\_isfcav}~=~true, an extra file input file describing the ice shelf draft 498 (in meters) (\ifile{isf\_draft\_meter}) is needed. 499 497 500 After reading the bathymetry, the algorithm for vertical grid definition differs 498 501 between the different options: … … 890 893 In case of ice shelf cavities, modifications of the model bathymetry and ice shelf draft into 891 894 the cavities are performed in the \textit{zgr\_isf} routine. The compatibility between ice shelf draft and bathymetry is checked. 895 All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked). 892 896 If 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. 893 897 If the incompatibility is too strong (need to dig more than 1 cell), the cell is masked.\\ 894 898 895 From the \textit{mbathy} a rray, the mask fields are defined as follows:899 From the \textit{mbathy} and \textit{misfdep} array, the mask fields are defined as follows: 896 900 \begin{align*} 897 901 tmask(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 637 637 ($e_{3w}$). 638 638 639 $\bullet$ Traditional coding with adaptation for ice shelf cavities (\np{ln\_dynhpg\_isf}=true). 640 This scheme need the activation of ice shelf cavities (\np{ln\_isfcav}=true). 641 639 642 $\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}=true) 640 643 -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_LDF.tex
r6391 r6850 397 397 \subsubsection{Space and Time Varying Mixing Coefficients} 398 398 399 There are no default specifications of space and time varying mixing coefficient. One400 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 399 There is no default specification of space and time varying mixing coefficient. 400 The only case available is specific to the ORCA2 and ORCA05 global ocean configurations. 401 It 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 404 404 and both \key{traldf\_eiv} and \key{traldf\_c2d} are defined. 405 405 -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_SBC.tex
r6347 r6850 51 51 \item the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model) (\np{nn\_ice}~=~0,1, 2 or 3) ; 52 52 \item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ; 53 \item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false) 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}) ; 55 54 \item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ; 56 55 \item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ; … … 558 557 reanalysis and satellite data. They use an inertial dissipative method to compute 559 558 the turbulent transfer coefficients (momentum, sensible heat and evaporation) 560 from the 10 meter swind speed, air temperature and specific humidity.559 from the 10 meter wind speed, air temperature and specific humidity. 561 560 This \citet{Large_Yeager_Rep04} dataset is available through the 562 561 \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. … … 943 942 \begin{description} 944 943 \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: 944 The ice shelf cavities are explicitly represented (\np{ln\_isfcav}~=~true needed). The fwf and heat flux are computed. 945 Two different bulk formula are available: 946 946 \begin{description} 947 947 \item[\np{nn\_isfblk}~=~1] … … 951 951 \item[\np{nn\_isfblk}~=~2] 952 952 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). 954 955 \end{description} 955 956 … … 987 988 988 989 \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}).990 The ice shelf cavity is opened (\np{ln\_isfcav}~=~true needed). However, the fwf is not computed but specified from file \np{sn\_fwfisf}). 990 991 The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\ 991 992 \end{description} … … 1000 1001 coarse to have realistic melting or for studies where you need to control your heat and fw input.\\ 1001 1002 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}. 1003 A 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}. 1005 1005 This 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 1007 If \np{rn\_hisf\_tbl} = 0., the fluxes are put in the top level whatever its tickness is. 1008 1009 If \np{rn\_hisf\_tbl} $>$ 0., the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells).\\ 1010 1011 The ice shelf melt is implemented as a volume flux with in the same way as for the runoff. 1015 1012 The fw addition due to the ice shelf melting is, at each relevant depth level, added to the horizontal divergence 1016 1013 (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}. 1017 1014 See the runoff section \ref{SBC_rnf} for all the details about the divergence correction. 1018 1015 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 %-------------------------------------------------------------------------------------------------------- 1022 Ice sheet/ocean coupling is done through file exchange at the restart step. NEMO, at each restart step, 1023 read the bathymetry and ice shelf draft variable in a netcdf file. 1024 If \np{ln\_iscpl = ~true}, the isf draft is assume to be different at each restart step 1025 with potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics. 1026 The 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. 1026 1040 \end{description} 1041 The 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.\\ 1043 This coupling procedure is able to take into account grounding line and calving front migration. However, it is a non-conservative processe. 1044 This 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. 1046 Based 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. 1048 So after \np{rn\_fiscpl} time step, all the heat/salt/vol. gain/loss due to extrapolation process is canceled.\\ 1049 1050 As 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 $fields_b = fields_n$. 1027 1051 % 1028 1052 % ================================================================ -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_TRA.tex
r6347 r6850 1 1 % ================================================================ 2 % Chapter 1 ———Ocean Tracers (TRA)2 % Chapter 1 --- Ocean Tracers (TRA) 3 3 % ================================================================ 4 4 \chapter{Ocean Tracers (TRA)} … … 48 48 freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}). 49 49 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 \text it{xxx} is a 3 or 4 letter acronym corresponding to each optional scheme.53 The CPP key (when it exists) is \textbf{key\_tra TTT}. The equivalent code can be54 found in the \textit{tra TTT} or \textit{traTTT\_xxx} module, in the NEMO/OPA/TRA directory.50 The different options available to the user are managed by namelist logicals or 51 CPP keys. For each equation term \textbf{\textit{ttt}}, the namelist logicals are \textit{ln\_tra\textbf{ttt}\_\textbf{xxx}}, 52 where \textbf{\textit{xxx}} is a 3 or 4 letter acronym corresponding to each optional scheme. 53 The CPP key (when it exists) is \textbf{key\_tra\textit{ttt}}. The equivalent code can be 54 found in the \textit{tra\textbf{ttt}} or \textit{tra\textbf{ttt}\_\textbf{xxx}} module, in the NEMO/OPA/TRA directory. 55 55 56 56 The user has the option of extracting each tendency term on the RHS of the tracer … … 169 169 using a same treatment to assess the robustness of their results. 170 170 171 % -------------------------------------------------------------------------------------------------------------171 %------------------------------------------------------------------------------------ 172 172 % 2nd and 4th order centred schemes 173 % -------------------------------------------------------------------------------------------------------------173 %------------------------------------------------------------------------------------ 174 174 \subsection [Centred schemes (CEN) (\np{ln\_traadv\_cen})] 175 175 {Centred schemes (CEN) (\np{ln\_traadv\_cen}=true)} 176 176 \label{TRA_adv_cen} 177 178 % 2nd order centred scheme179 177 180 178 The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}~=~\textit{true}. … … 189 187 \tau _u^{cen2} =\overline T ^{i+1/2} 190 188 \end{equation} 189 190 % 2nd order centred scheme 191 191 192 192 CEN2 is non diffusive ($i.e.$ it conserves the tracer variance, $\tau^2)$ … … 241 241 for these near boundary grid points. 242 242 243 % -------------------------------------------------------------------------------------------------------------243 %------------------------------------------------------------------------------------ 244 244 % FCT scheme 245 % -------------------------------------------------------------------------------------------------------------245 %------------------------------------------------------------------------------------ 246 246 \subsection [Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct})] 247 247 {Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct}=true)} … … 288 288 while a forward scheme is used for the diffusive part. 289 289 290 % -------------------------------------------------------------------------------------------------------------290 %------------------------------------------------------------------------------------- 291 291 % MUSCL scheme 292 % -------------------------------------------------------------------------------------------------------------292 %------------------------------------------------------------------------------------ 293 293 \subsection[MUSCL scheme (\np{ln\_traadv\_mus})] 294 294 {Monotone Upstream Scheme for Conservative Laws (MUSCL) (\np{ln\_traadv\_mus}=T)} … … 321 321 computed using upstream fluxes (\np{ln\_mus\_ups}~=~\textit{true}). 322 322 323 % -------------------------------------------------------------------------------------------------------------323 %------------------------------------------------------------------------------------- 324 324 % UBS scheme 325 % -------------------------------------------------------------------------------------------------------------325 %------------------------------------------------------------------------------------ 326 326 \subsection [Upstream-Biased Scheme (UBS) (\np{ln\_traadv\_ubs})] 327 327 {Upstream-Biased Scheme (UBS) (\np{ln\_traadv\_ubs}=true)} … … 348 348 the advection scheme is similar to that reported in \cite{Farrow1995}. 349 349 It is a relatively good compromise between accuracy and smoothness. 350 Nevertheless the scheme is not \emph{positive}, meaning that false extrema are permitted,350 Nevertheless, the scheme is not \emph{positive}, meaning that false extrema are permitted, 351 351 but the amplitude of such are significantly reduced over the centred second 352 or fourth order method. therefore it is not recommended that it should be352 or fourth order method. Therefore it is not recommended that it should be 353 353 applied to a passive tracer that requires positivity. 354 354 … … 396 396 the computationally more efficient formulation \eqref{Eq_tra_adv_ubs}. 397 397 398 % -------------------------------------------------------------------------------------------------------------398 %------------------------------------------------------------------------------------- 399 399 % QCK scheme 400 % -------------------------------------------------------------------------------------------------------------400 %------------------------------------------------------------------------------------- 401 401 \subsection [QUICKEST scheme (QCK) (\np{ln\_traadv\_qck})] 402 402 {QUICKEST scheme (QCK) (\np{ln\_traadv\_qck}=true)} … … 429 429 {Tracer Lateral Diffusion (\mdl{traldf})} 430 430 \label{TRA_ldf} 431 %-----------------------------------------nam_traldf---------------------------------- --------------------431 %-----------------------------------------nam_traldf---------------------------------- 432 432 \namdisplay{namtra_ldf} 433 %------------------------------------------------------------------------------------- ------------------------433 %------------------------------------------------------------------------------------- 434 434 435 435 Options are defined through the \ngn{namtra\_ldf} namelist variables. … … 450 450 the pure vertical component is split into an explicit and an implicit part \citep{Lemarie_OM2012}. 451 451 452 % -------------------------------------------------------------------------------------------------------------452 %------------------------------------------------------------------------------------ 453 453 % Type of operator 454 % -------------------------------------------------------------------------------------------------------------454 %------------------------------------------------------------------------------------ 455 455 \subsection [Type of operator (\np{ln\_traldf\_NONE}, \np{ln\_traldf\_lap}, \np{ln\_traldf\_blp})] 456 456 {Type of operator (\np{ln\_traldf\_NONE}, \np{ln\_traldf\_lap}, or \np{ln\_traldf\_blp} = true) } … … 510 510 511 511 512 % -------------------------------------------------------------------------------------------------------------512 %------------------------------------------------------------------------------------ 513 513 % iso-level operator 514 % -------------------------------------------------------------------------------------------------------------514 %------------------------------------------------------------------------------------ 515 515 \subsection [Iso-level (bi-)laplacian operator ( \np{ln\_traldf\_iso})] 516 516 {Iso-level (bi-)laplacian operator ( \np{ln\_traldf\_iso}) } … … 544 544 545 545 546 % -------------------------------------------------------------------------------------------------------------546 %------------------------------------------------------------------------------------ 547 547 % Rotated laplacian operator 548 % -------------------------------------------------------------------------------------------------------------548 %------------------------------------------------------------------------------------ 549 549 \subsection [Standard and triad rotated (bi-)laplacian operator (\mdl{traldf\_iso}, \mdl{traldf\_triad})] 550 550 {Standard and triad (bi-)laplacian operator (\mdl{traldf\_iso}, \mdl{traldf\_triad}))} … … 649 649 {Tracer Vertical Diffusion (\mdl{trazdf})} 650 650 \label{TRA_zdf} 651 %--------------------------------------------namzdf----------------------------------- ----------------------651 %--------------------------------------------namzdf----------------------------------- 652 652 \namdisplay{namzdf} 653 %------------------------------------------------------------------------------------- -------------------------653 %------------------------------------------------------------------------------------- 654 654 655 655 Options are defined through the \ngn{namzdf} namelist variables. … … 697 697 \label{TRA_sbc_qsr_bbc} 698 698 699 % -------------------------------------------------------------------------------------------------------------699 %------------------------------------------------------------------------------------- 700 700 % surface boundary condition 701 % -------------------------------------------------------------------------------------------------------------701 %------------------------------------------------------------------------------------- 702 702 \subsection [Surface boundary condition (\textit{trasbc})] 703 703 {Surface boundary condition (\mdl{trasbc})} … … 768 768 This is the reason why the modified filter is not applied in the linear free surface case (see \S\ref{STP}). 769 769 770 % -------------------------------------------------------------------------------------------------------------770 %------------------------------------------------------------------------------------- 771 771 % Solar Radiation Penetration 772 % -------------------------------------------------------------------------------------------------------------772 %------------------------------------------------------------------------------------- 773 773 \subsection [Solar Radiation Penetration (\textit{traqsr})] 774 774 {Solar Radiation Penetration (\mdl{traqsr})} 775 775 \label{TRA_qsr} 776 %--------------------------------------------namqsr----------------------------------- ---------------------776 %--------------------------------------------namqsr----------------------------------- 777 777 \namdisplay{namtra_qsr} 778 %------------------------------------------------------------------------------------- -------------------------778 %------------------------------------------------------------------------------------- 779 779 780 780 Options are defined through the \ngn{namtra\_qsr} namelist variables. … … 879 879 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 880 880 881 % -------------------------------------------------------------------------------------------------------------881 %------------------------------------------------------------------------------------- 882 882 % Bottom Boundary Condition 883 % -------------------------------------------------------------------------------------------------------------883 %------------------------------------------------------------------------------------- 884 884 \subsection [Bottom Boundary Condition (\textit{trabbc})] 885 885 {Bottom Boundary Condition (\mdl{trabbc})} 886 886 \label{TRA_bbc} 887 %--------------------------------------------nambbc----------------------------------- ---------------------887 %--------------------------------------------nambbc----------------------------------- 888 888 \namdisplay{nambbc} 889 %------------------------------------------------------------------------------------- -------------------------889 %------------------------------------------------------------------------------------- 890 890 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 891 891 \begin{figure}[!t] \begin{center} … … 924 924 {Bottom Boundary Layer (\mdl{trabbl} - \key{trabbl})} 925 925 \label{TRA_bbl} 926 %--------------------------------------------nambbl----------------------------------- ----------------------926 %--------------------------------------------nambbl----------------------------------- 927 927 \namdisplay{nambbl} 928 %------------------------------------------------------------------------------------- -------------------------928 %------------------------------------------------------------------------------------- 929 929 930 930 Options are defined through the \ngn{nambbl} namelist variables. … … 954 954 all the improvements introduced by \citet{Campin_Goosse_Tel99}. 955 955 956 % -------------------------------------------------------------------------------------------------------------956 %------------------------------------------------------------------------------------- 957 957 % Diffusive BBL 958 % -------------------------------------------------------------------------------------------------------------958 %------------------------------------------------------------------------------------- 959 959 \subsection{Diffusive Bottom Boundary layer (\np{nn\_bbl\_ldf}=1)} 960 960 \label{TRA_bbl_diff} … … 989 989 salinity and depth, respectively. 990 990 991 % -------------------------------------------------------------------------------------------------------------991 %------------------------------------------------------------------------------------- 992 992 % Advective BBL 993 % -------------------------------------------------------------------------------------------------------------993 %------------------------------------------------------------------------------------- 994 994 \subsection {Advective Bottom Boundary Layer (\np{nn\_bbl\_adv}= 1 or 2)} 995 995 \label{TRA_bbl_adv} … … 1084 1084 {Tracer damping (\mdl{tradmp})} 1085 1085 \label{TRA_dmp} 1086 %--------------------------------------------namtra_dmp------------------------------- ------------------1086 %--------------------------------------------namtra_dmp------------------------------- 1087 1087 \namdisplay{namtra_dmp} 1088 %------------------------------------------------------------------------------------- -------------------------1088 %------------------------------------------------------------------------------------- 1089 1089 1090 1090 In some applications it can be useful to add a Newtonian damping term … … 1137 1137 The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 1138 1138 1139 %--------------------------------------------nam_dmp_create--------------------------- ----------------------1139 %--------------------------------------------nam_dmp_create--------------------------- 1140 1140 \namtools{namelist_dmp} 1141 %------------------------------------------------------------------------------------- ------------------1141 %------------------------------------------------------------------------------------- 1142 1142 1143 1143 \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. … … 1169 1169 {Tracer time evolution (\mdl{tranxt})} 1170 1170 \label{TRA_nxt} 1171 %--------------------------------------------namdom----------------------------------- ------------------1171 %--------------------------------------------namdom----------------------------------- 1172 1172 \namdisplay{namdom} 1173 %------------------------------------------------------------------------------------- -------------------------1173 %------------------------------------------------------------------------------------- 1174 1174 1175 1175 Options are defined through the \ngn{namdom} namelist variables. … … 1208 1208 {Equation of State (\mdl{eosbn2}) } 1209 1209 \label{TRA_eosbn2} 1210 %--------------------------------------------nameos----------------------------------- ------------------1210 %--------------------------------------------nameos----------------------------------- 1211 1211 \namdisplay{nameos} 1212 %------------------------------------------------------------------------------------- -------------------------1213 1214 % -------------------------------------------------------------------------------------------------------------1212 %------------------------------------------------------------------------------------- 1213 1214 %------------------------------------------------------------------------------------- 1215 1215 % 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})} 1218 1218 \label{TRA_eos} 1219 1219 1220 1220 The Equation Of Seawater (EOS) is an empirical nonlinear thermodynamic relationship 1221 linking seawater density, $\rho$, to a number of state variables, 1222 most typicallytemperature, salinity and pressure.1221 linking seawater density, $\rho$, to a number of state variables, most typically 1222 temperature, salinity and pressure. 1223 1223 Because density gradients control the pressure gradient force through the hydrostatic balance, 1224 1224 the equation of state provides a fundamental bridge between the distribution of active tracers 1225 1225 and the fluid dynamics. Nonlinearities of the EOS are of major importance, in particular 1226 1226 influencing the circulation through determination of the static stability below the mixed layer, 1227 thus controlling rates of exchange between the atmosphere 1227 thus controlling rates of exchange between the atmosphere and the ocean interior \citep{Roquet_JPO2015}. 1228 1228 Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{UNESCO1983}) 1229 1229 or TEOS-10 \citep{TEOS10} standards should be used anytime a simulation of the real 1230 1230 ocean circulation is attempted \citep{Roquet_JPO2015}. 1231 The 1980 International Equation of Seawater (EOS-80) has served the community very well for 30 years. 1232 Since the 1$^{st}$ January 2010, TEOS-10 (Thermodynamic Equation Of Seawater - 2010) has been 1233 adopted as the new standard definition of the thermodynamic properties of seawater in oceanography 1234 by the Intergovernmental Oceanographic Commission. Its main novelty is the introduction of concepts of 1235 Conservative Temperature ($\Theta$) and Absolute Salinity ($S_A$), replacing Potential 1236 Temperature ($\theta$) and Practical Salinity ($S_P$), respectively. 1231 1237 The use of TEOS-10 is highly recommended because 1232 1238 \textit{(i)} it is the new official EOS, 1233 1239 \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 1241 conservative thus more suitable for use as model variables \citep{TEOS10, Graham_McDougall_JPO13}. 1237 1242 EOS-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 purpose d,1239 a simplified EOS (S-EOS) inspired by \citet{Vallis06} isalso available.1243 For process studies, it is often convenient to use an approximation of the EOS. To that purpose, 1244 the simplified EOS (S-EOS) proposed by \citep{Roquet_JPO2015} and a Linear EOS (L-EOS) are also available. 1240 1245 1241 1246 In the computer code, a density anomaly, $d_a= \rho / \rho_o - 1$, 1242 1247 is 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 $1,026~Kg/m^3$.1248 in the code, $\rho_o$ is set in \mdl{eosbn2} module to a value of $1,026~kg/m^3$. 1244 1249 This 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, 1250 climate 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). 1252 With the exception of only a small percentage of the ocean, 1246 1253 density in the World Ocean varies by no more than 2$\%$ from that value \citep{Gill1982}. 1247 1254 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). 1255 Options are defined through the \ngn{nameos} namelist variables, and in particular by setting to \textit{true} 1256 one of following logicals: \np{ln\_TEOS10}, \np{ln\_EOS80}, \np{ln\_SEOS}, or \np{ln\_LEOS}, 1257 the logicals that control the EOS used. 1258 1250 1259 \begin{description} 1251 1260 1252 \item[\np{ nn\_eos}$=-1$] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used.1253 Th e 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 quantities1256 which make themmore adapted for use in ocean models.1257 Note that a slightly higher precision polynomial form is now used replacement of theTEOS-101258 rational function approximation for hydrographic data analysis \citep{TEOS10}.1259 A key point is that conservativestate variables are used:1261 \item[\np{ln\_TEOS10} = \textit{true}] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used. 1262 This equation of state consists in a 55-term polynomial approximation of the reference TEOS-10 expression, 1263 optimized for a Boussinesq fluid by giving density as a function of Conservative Temperature, Absolute Salinity, 1264 and pressure. The polynomial expression has a simple and computationally efficient expression 1265 for its derived quantities (derivatives and primitives) which makes it more adapted for use in ocean models. 1266 Note that a higher precision approximation (75-term, also polynomial form) is now used as the standard TEOS-10 1267 approximation for hydrographic data analysis \citep{Roquet_OM2015, TEOS10}. 1268 A key point is that \textit{conservative} state variables are used: 1260 1269 Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: $\degres C$, notation: $\Theta$). 1261 1270 The pressure in decibars is approximated by the depth in meters. 1262 With TEOS 10, the specific heat capacity of sea water, $C_p$, is a constant. It is set to1263 $C_p=3991.86795711963~J \,Kg^{-1}\,\degres K^{-1}$, according to \citet{TEOS10}.1271 With 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}. 1264 1273 1265 1274 Choosing 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 1276 have to be given as \textit{Conservative} Temperature and \textit{Absolute} Salinity. 1277 In addition, the Conservative Sea Surface Temperature (SST) is automatically converted to 1278 potential SST prior to either computing the air-sea and ice-sea fluxes (forced mode) 1279 or sending the SST field to the atmosphere (coupled mode). 1280 This conversion is performed in \mdl{sbcssm} and \mdl{sbccpl} modules 1281 using \rou{eos\_pt\_from\_ct} routine. 1282 1283 1284 \item[\np{ln\_EOS80} = \textit{true}] the polyEOS80-bsq equation of seawater is used. 1273 1285 It 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: $\theta$). 1286 to accurately fit EOS-80 (Roquet, personal comm.). In this case, the state variables 1287 used in both the EOS-80 and the ocean model are: 1288 the Practical Salinity (unit: psu, notation: $S_p$) and 1289 the Potential Temperature (unit: $\degres C$, notation: $\theta$). 1277 1290 The pressure in decibars is approximated by the depth in meters. 1278 With th si 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 to1280 have a heat content ($C_p T_p$) which is conserved by the model: $C_p$ is set to a constant1281 value, the TEOS10 value.1291 With this EOS, the specific heat capacity of sea water, $C_p$, should be a function 1292 of temperature, salinity and pressure \citep{UNESCO1983}. Nevertheless, a severe 1293 assumption is made in the model in order to have a heat content ($C_p \theta$) 1294 which is conserved by the model: $C_p$ is set to a constant value, the TEOS-10 value. 1282 1295 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 EOS1287 in theoretical studies \citep{Roquet_JPO2015}. 1288 With such an equation of state there is no longer a distinction between1289 \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 1298 to fit the behavior of TEOS-10, and thus which uses \textit{conservative} state variables ($S_A$ and $\Theta$). 1299 It provides a simplistic linear representation of both cabbeling and thermobaricity effects 1300 which is enough for a proper treatment of the EOS in theoretical studies. 1301 This simplified EOS has been validated with a forced ORCA2 configuration, 1302 and it has been found that the simulated circulation satisfactorily reproduces the simulated circulation 1303 obtained with TEOS-10, with tracer and velocity fields generally differing by less than 10\%. 1304 S-EOS takes the following form: 1292 1305 \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 \\ 1299 1308 \end{equation} 1300 where the computer name of the coefficients as well as their standard value are given in \ref{Tab_SEOS}. 1309 with $\Delta \Theta = \Theta-\Theta_o$, $\Delta S = S_A-35$ and $\rho_o = 1026~Kg/m^3$. 1310 Equation (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 1314 The computer name of the coefficients as they appear in \ngn{nameos} namelist 1315 as well as their standard value are given in \ref{Tab_SEOS}. 1301 1316 In fact, when choosing S-EOS, various approximation of EOS can be specified simply by changing 1302 1317 the 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 1318 Setting to zero the thermobaric coefficients ($T_h$) removes all thermobaric effects from S-EOS. 1319 Setting to zero the cabbeling coefficients ($C_b$) removes all cabbeling effects from S-EOS. 1320 Setting to zero both cabbeling and thermobaric coefficients ($C_b$ and $T_h$) removes nonlinearities from S-EOS. 1321 Nevertheless, in the setting $C_b$ to zero removes the dependency of $d_a$ with temperature at $z=0$. 1322 A 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 1327 optimized to fit the behavior of TEOS-10 and thus which uses \textit{conservative} state variables ($S_A$ and $\Theta$). 1328 Such a linear equation has neither cabbeling nor thermobaric effects. 1329 L-EOS uses \eqref{Eq_tra_S-EOS} with all the coefficients but $a_0$ and $b_0$ set to zero. 1330 It 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} 1334 with $\Delta \Theta = \Theta-10$, $\Delta S = S_A-35$ and $\rho_o = 1026~Kg/m^3$. 1335 The computer name of the $a_0$ and $b_0$ coefficients as they appear in \ngn{nameos} namelist 1336 as well as their standard value are given in \ref{Tab_SEOS}. 1307 1337 \end{description} 1308 1338 … … 1310 1340 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1311 1341 \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}} 1313 1343 \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 1344 coeff. & 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 1322 1353 \end{tabular} 1323 1354 \caption{ \label{Tab_SEOS} 1324 Standard value of S-EOS coefficients. } 1355 Standard values of S-EOS and L-EOS coefficients \citep{Roquet_JPO2015}. 1356 In S-EOS case, only four parameters are usually needed. 1357 The parameter $a_o$ should be set to zero, unless cabbeling effect are removed ($i.e.$ $C_b=0$). 1358 In L-EOS case, only two parameters are used and $C_b= \Theta=T_h=0$ } 1325 1359 \end{center} 1326 1360 \end{table} 1327 1361 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1328 1329 1330 % ------------------------------------------------------------------------------------------------------------- 1362 \vspace{1.cm} 1363 %$\ $\newline % force a new ligne 1364 1365 1366 In TEOS-10 (as well as in S-EOS and L-EOS), the density of seawater is a 1367 function of the absolute salinity $S_A$, defined as the mass fraction of salt (units: $g/kg$): 1368 \begin{equation} \label{Eq_tra_SA} 1369 S_A= 1.00471 \times S_P + \delta S_A 1370 \end{equation} 1371 where $\delta S_A$ is a correction accounting for ionic composition changes. 1372 On average, $S_A$ and $S_P$ differ numerically by about 0.5\%. 1373 1374 When 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 %------------------------------------------------------------------------------------- 1331 1382 % 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} 1334 1385 \label{TRA_bn2} 1335 1386 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 determinethe ocean stratification and1387 An 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 1338 1389 is used in several ocean parameterisations (namely TKE, GLS, Richardson number dependent 1339 1390 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 pressure1341 (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 $N^2$ 1342 1393 is given by: 1343 1394 \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)1395 N^2 = \frac{g}{e_{3w}} \left( b \;\delta_{k+1/2}[S] - a \;\delta_{k+1/2}[T] \right) 1345 1396 \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. 1397 where $(T,S) = (\Theta, S_A)$ for TEOS-10, S-EOS, and L-EOS, or $= (\theta, S_p)$ for TEOS-80, 1398 and, $a$ and $b$ are the "thermal expansion" and "haline contraction" coefficients, respectively, 1399 \begin{equation} \label{Eq_tra_rab} 1400 a(T,S,z) = - \left( \frac{\partial \rho}{\partial T} \right)_{S,z} \quad ; \quad 1401 b(T,S,z) = \left( \frac{\partial \rho}{\partial S} \right)_{T,z} 1402 \end{equation} 1403 Note that we use here definitions that differ slightly from the usual ones, as they are not divided by density. 1404 This form is indeed more suitable for a Boussinesq model such as \NEMO. 1405 As a consequence, $a$ and $b$ have here units of [$kg/m^3 /K$] and [$kg/m^3/(g/kg)$], respectively. 1348 1406 The 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}1407 depends on the chosen EOS. They are computed through \rou{eos\_rab}, a \textsc{Fortran} 1350 1408 function that can be found in \mdl{eosbn2}. 1351 1409 1352 % -------------------------------------------------------------------------------------------------------------1410 %------------------------------------------------------------------------------------- 1353 1411 % Freezing Point of Seawater 1354 % -------------------------------------------------------------------------------------------------------------1412 %------------------------------------------------------------------------------------- 1355 1413 \subsection [Freezing Point of Seawater] 1356 1414 {Freezing Point of Seawater} … … 1360 1418 \begin{equation} \label{Eq_tra_eos_fzp} 1361 1419 \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} \ \ p1420 T_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 1365 1423 \end{split} 1366 1424 \end{equation} 1425 where the depth, $z$, in meters is an approximation of the pressure in decibars, and 1426 $T_f$ is the \textit{in situ} temperature. 1427 1428 The freezing point is used for both sea-ice/ocean and ice-shelve/ocean interfaces to compute 1429 the fluxes and determine the sea-ice formation rate. 1430 In the former case, only the potential freezing point at the surface ($i.e.$ $z=0$) is needed 1431 which is exactly equals to the $in situ$ freezing point at $z=0$ when using EOS-80 (\np{ln\_eos80} = true). 1432 With other EOS than EOS-80 ($i.e.$ when \np{ln\_TEOS10}, \np{ln\_SEOS}, or \np{ln\_LEOS} = true), 1433 the salinity is multiplied by a factor of $35/35.16504$ to convert it from Absolute to Practical. 1434 This approximation leads to a $~0.003^oC$ rms difference with the exact value of the freezing point. 1435 In the latter case, potential for EOS-80 or conservative 1436 1437 1367 1438 1368 1439 \eqref{Eq_tra_eos_fzp} is only used to compute the potential freezing point of 1369 1440 sea 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 % ------------------------------------------------------------------------------------------------------------- 1441 terms in \eqref{Eq_tra_eos_fzp} (last term) have been dropped. 1442 The freezing point is computed through \rou{eos\_fzp}, a \textsc{Fortran} 1443 function 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 %------------------------------------------------------------------------------------- 1376 1459 % Potential Energy 1377 % -------------------------------------------------------------------------------------------------------------1460 %------------------------------------------------------------------------------------- 1378 1461 %\subsection{Potential Energy anomalies} 1379 1462 %\label{TRA_bn2} … … 1393 1476 I've changed "derivative" to "difference" and "mean" to "average"} 1394 1477 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} 1478 With partial cells (\np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true), 1479 in general, tracers in horizontally adjacent cells live at different depths. 1480 Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} 1481 module) and the hydrostatic pressure gradient calculations (\mdl{dynhpg} module). 1482 The partial cell properties at the top (\np{ln\_isfcav}=true) are computed in 1483 the same way as for the bottom. 1484 So, only the bottom interpolation is explained below. 1485 1400 1486 Before taking horizontal gradients between the tracers next to the bottom, a linear 1401 1487 interpolation in the vertical is used to approximate the deeper tracer as if it actually … … 1473 1559 \gmcomment{gm : this last remark has to be done} 1474 1560 %%% 1475 1476 If under ice shelf seas opened (\np{ln\_isfcav}=true), the partial cell properties1477 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 compute1484 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 $z^*$ coordinates1486 (this term = 0 in z-coordinates) -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_ZDF.tex
r6347 r6850 852 852 The bottom friction represents the friction generated by the bathymetry. 853 853 The 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,854 As the friction processes at the top and bottom are treated in similar way, 855 855 only the bottom friction is described in detail below. 856 856
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