Changeset 9393 for branches/2017/dev_merge_2017/DOC/tex_sub/chap_DOM.tex
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branches/2017/dev_merge_2017/DOC/tex_sub/chap_DOM.tex
r9392 r9393 4 4 % Chapter 2 ——— Space and Time Domain (DOM) 5 5 % ================================================================ 6 \chapter{Space Domain (DOM) 6 \chapter{Space Domain (DOM)} 7 7 \label{DOM} 8 8 \minitoc … … 31 31 % Fundamentals of the Discretisation 32 32 % ================================================================ 33 \section{Fundamentals of the Discretisation}33 \section{Fundamentals of the discretisation} 34 34 \label{DOM_basics} 35 35 … … 37 37 % Arrangement of Variables 38 38 % ------------------------------------------------------------------------------------------------------------- 39 \subsection{Arrangement of Variables}39 \subsection{Arrangement of variables} 40 40 \label{DOM_cell} 41 41 … … 107 107 % Vector Invariant Formulation 108 108 % ------------------------------------------------------------------------------------------------------------- 109 \subsection{Discrete Operators}109 \subsection{Discrete operators} 110 110 \label{DOM_operators} 111 111 … … 198 198 % Numerical Indexing 199 199 % ------------------------------------------------------------------------------------------------------------- 200 \subsection{Numerical Indexing}200 \subsection{Numerical indexing} 201 201 \label{DOM_Num_Index} 202 202 … … 221 221 % Horizontal Indexing 222 222 % ----------------------------------- 223 \subsubsection{Horizontal Indexing}223 \subsubsection{Horizontal indexing} 224 224 \label{DOM_Num_Index_hor} 225 225 … … 232 232 % Vertical indexing 233 233 % ----------------------------------- 234 \subsubsection{Vertical Indexing}234 \subsubsection{Vertical indexing} 235 235 \label{DOM_Num_Index_vertical} 236 236 … … 264 264 % Domain Size 265 265 % ----------------------------------- 266 \subsubsection{Domain Size}266 \subsubsection{Domain size} 267 267 \label{DOM_size} 268 268 … … 281 281 % Domain: List of fields needed 282 282 % ================================================================ 283 \section [Domain: Needed fields] 284 {Domain: Needed fields} 283 \section{Needed fields} 285 284 \label{DOM_fields} 286 285 The ocean mesh ($i.e.$ the position of all the scalar and vector points) is defined … … 309 308 ie1e2u\_v is a flag to flag set u and v surfaces are neither read nor computed.\\ 310 309 311 These fields can be read in an domain input file which name is setted in \np{cn _domcfg} parameter specified in \ngn{namcfg}.310 These fields can be read in an domain input file which name is setted in \np{cn\_domcfg} parameter specified in \ngn{namcfg}. 312 311 \forfile{../namelists/namcfg} 313 312 or they can be defined in an analytical way in MY\_SRC directory of the configuration. … … 323 322 % Domain: Horizontal Grid (mesh) 324 323 % ================================================================ 325 \section [Domain: Horizontal Grid (mesh) (\textit{domhgr})] 326 {Domain: Horizontal Grid (mesh) \small{(\protect\mdl{domhgr} module)} } 324 \section{Horizontal grid mesh (\protect\mdl{domhgr})} 327 325 \label{DOM_hgr} 328 326 … … 409 407 % Grid files 410 408 % ------------------------------------------------------------------------------------------------------------- 411 \subsection{Output Grid files}409 \subsection{Output grid files} 412 410 \label{DOM_hgr_files} 413 411 414 412 All the arrays relating to a particular ocean model configuration (grid-point 415 position, scale factors, masks) can be saved in files if $nn\_msh\not= 0$413 position, scale factors, masks) can be saved in files if \np{nn\_msh} $\not= 0$ 416 414 (namelist variable in \ngn{namdom}). This can be particularly useful for plots and off-line 417 415 diagnostics. In some cases, the user may choose to make a local modification … … 420 418 happens to be too wide due to insufficient model resolution). An example 421 419 is Gibraltar Strait in the ORCA2 configuration. When such modifications are done, 422 the output grid written when $nn\_msh\not= 0$ is no more equal to the input grid.420 the output grid written when \np{nn\_msh} $\not= 0$ is no more equal to the input grid. 423 421 424 422 $\ $\newline % force a new line … … 427 425 % Domain: Vertical Grid (domzgr) 428 426 % ================================================================ 429 \section [Domain: Vertical Grid (\textit{domzgr})] 430 {Domain: Vertical Grid \small{(\protect\mdl{domzgr} module)} } 427 \section{Vertical grid (\protect\mdl{domzgr})} 431 428 \label{DOM_zgr} 432 429 %-----------------------------------------nam_zgr & namdom------------------------------------------- … … 454 451 (d) hybrid $s-z$ coordinate, 455 452 (e) hybrid $s-z$ coordinate with partial step, and 456 (f) same as (e) but in the non-linear free surface (\ protect\forcode{ln_linssh= .false.}).453 (f) same as (e) but in the non-linear free surface (\np{ln\_linssh}\forcode{ = .false.}). 457 454 Note that the non-linear free surface can be used with any of the 458 455 5 coordinates (a) to (e).} … … 464 461 option which can be enabled or disabled in the middle of an experiment. Three main 465 462 choices are offered (Fig.~\ref{Fig_z_zps_s_sps}a to c): $z$-coordinate with full step 466 bathymetry (\np{ln _zco}~=~true), $z$-coordinate with partial step bathymetry467 (\np{ln _zps}~=~true), or generalized, $s$-coordinate (\np{ln_sco}~=~true).463 bathymetry (\np{ln\_zco}\forcode{ = .true.}), $z$-coordinate with partial step bathymetry 464 (\np{ln\_zps}\forcode{ = .true.}), or generalized, $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}). 468 465 Hybridation of the three main coordinates are available: $s-z$ or $s-zps$ coordinate 469 466 (Fig.~\ref{Fig_z_zps_s_sps}d and \ref{Fig_z_zps_s_sps}e). By default a non-linear free surface is used: 470 467 the coordinate follow the time-variation of the free surface so that the transformation is time dependent: 471 $z(i,j,k,t)$ (Fig.~\ref{Fig_z_zps_s_sps}f). When a linear free surface is assumed (\ forcode{ln_linssh= .true.}),468 $z(i,j,k,t)$ (Fig.~\ref{Fig_z_zps_s_sps}f). When a linear free surface is assumed (\np{ln\_linssh}\forcode{ = .true.}), 472 469 the vertical coordinate are fixed in time, but the seawater can move up and down across the z=0 surface 473 470 (in other words, the top of the ocean in not a rigid-lid). 474 471 The last choice in terms of vertical coordinate concerns the presence (or not) in the model domain 475 of ocean cavities beneath ice shelves. Setting \np{ln _isfcav} to true allows to manage ocean cavities,472 of ocean cavities beneath ice shelves. Setting \np{ln\_isfcav} to true allows to manage ocean cavities, 476 473 otherwise they are filled in. This option is currently only available in $z$- or $zps$-coordinate, 477 474 and partial step are also applied at the ocean/ice shelf interface. … … 483 480 \ifile{bathy\_meter} file, so that the computation of the number of wet ocean point 484 481 in each water column is by-passed}. 485 If \np{ln _isfcav}~=~true, an extra file input file describing the ice shelf draft482 If \np{ln\_isfcav}\forcode{ = .true.}, an extra file input file describing the ice shelf draft 486 483 (in meters) (\ifile{isf\_draft\_meter}) is needed. 487 484 … … 503 500 %%% 504 501 505 Unless a linear free surface is used (\ forcode{ln_linssh= .false.}), the arrays describing502 Unless a linear free surface is used (\np{ln\_linssh}\forcode{ = .false.}), the arrays describing 506 503 the grid point depths and vertical scale factors are three set of three dimensional arrays $(i,j,k)$ 507 504 defined at \textit{before}, \textit{now} and \textit{after} time step. The time at which they are 508 505 defined is indicated by a suffix:$\_b$, $\_n$, or $\_a$, respectively. They are updated at each model time step 509 506 using a fixed reference coordinate system which computer names have a $\_0$ suffix. 510 When the linear free surface option is used (\ forcode{ln_linssh= .true.}), \textit{before}, \textit{now}507 When the linear free surface option is used (\np{ln\_linssh}\forcode{ = .true.}), \textit{before}, \textit{now} 511 508 and \textit{after} arrays are simply set one for all to their reference counterpart. 512 509 … … 515 512 % Meter Bathymetry 516 513 % ------------------------------------------------------------------------------------------------------------- 517 \subsection{Meter Bathymetry}514 \subsection{Meter bathymetry} 518 515 \label{DOM_bathy} 519 516 520 517 Three options are possible for defining the bathymetry, according to the 521 namelist variable \np{nn _bathy} (found in \ngn{namdom} namelist):518 namelist variable \np{nn\_bathy} (found in \ngn{namdom} namelist): 522 519 \begin{description} 523 \item[\np{nn _bathy} = 0]a flat-bottom domain is defined. The total depth $z_w (jpk)$520 \item[\np{nn\_bathy}\forcode{ = 0}]: a flat-bottom domain is defined. The total depth $z_w (jpk)$ 524 521 is given by the coordinate transformation. The domain can either be a closed 525 522 basin or a periodic channel depending on the parameter \np{jperio}. 526 \item[\np{nn _bathy} = -1]a domain with a bump of topography one third of the523 \item[\np{nn\_bathy}\forcode{ = -1}]: a domain with a bump of topography one third of the 527 524 domain width at the central latitude. This is meant for the "EEL-R5" configuration, 528 525 a periodic or open boundary channel with a seamount. 529 \item[\np{nn _bathy} = 1]read a bathymetry and ice shelf draft (if needed).526 \item[\np{nn\_bathy}\forcode{ = 1}]: read a bathymetry and ice shelf draft (if needed). 530 527 The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) 531 528 at each grid point of the model grid. The bathymetry is usually built by interpolating a standard bathymetry product … … 535 532 536 533 The \ifile{isfdraft\_meter} file (Netcdf format) provides the ice shelf draft (positive, in meters) 537 at each grid point of the model grid. This file is only needed if \np{ln _isfcav}~=~true.534 at each grid point of the model grid. This file is only needed if \np{ln\_isfcav}\forcode{ = .true.}. 538 535 Defining the ice shelf draft will also define the ice shelf edge and the grounding line position. 539 536 \end{description} … … 550 547 % z-coordinate and reference coordinate transformation 551 548 % ------------------------------------------------------------------------------------------------------------- 552 \subsection[$ z$-coordinate (\protect\np{ln_zco}]553 {$z$-coordinate (\protect\forcode{ln_zco= .true.}) and reference coordinate}549 \subsection[$Z$-coordinate (\protect\np{ln\_zco}\forcode{ = .true.}) and ref. coordinate] 550 {$Z$-coordinate (\protect\np{ln\_zco}\forcode{ = .true.}) and reference coordinate} 554 551 \label{DOM_zco} 555 552 … … 593 590 (Fig.~\ref{Fig_zgr}). 594 591 595 If the ice shelf cavities are opened (\np{ln _isfcav}=~true~), the definition of $z_0$ is the same.592 If the ice shelf cavities are opened (\np{ln\_isfcav}\forcode{ = .true.}), the definition of $z_0$ is the same. 596 593 However, definition of $e_3^0$ at $t$- and $w$-points is respectively changed to: 597 594 \begin{equation} \label{DOM_zgr_ana} … … 629 626 Rather than entering parameters $h_{sur}$, $h_{0}$, and $h_{1}$ directly, it is 630 627 possible to recalculate them. In that case the user sets 631 \np{ppsur} =\np{ppa0}=\forcode{ppa1= 999999}., in \ngn{namcfg} namelist,628 \np{ppsur}\forcode{ = }\np{ppa0}\forcode{ = }\np{ppa1}\forcode{ = 999999}., in \ngn{namcfg} namelist, 632 629 and specifies instead the four following parameters: 633 630 \begin{itemize} … … 640 637 \end{itemize} 641 638 As an example, for the $45$ layers used in the DRAKKAR configuration those 642 parameters are: \jp{jpk}=46, \forcode{ppacr = 9}, \forcode{ppkth = 23}.563, \forcode{ppdzmin = 6}m, 643 \forcode{pphmax = 5750}m. 639 parameters are: \jp{jpk}\forcode{ = 46}, \np{ppacr}\forcode{ = 9}, \np{ppkth}\forcode{ = 23.563}, \np{ppdzmin}\forcode{ = 6}m, \np{pphmax}\forcode{ = 5750}m. 644 640 645 641 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 688 684 % z-coordinate with partial step 689 685 % ------------------------------------------------------------------------------------------------------------- 690 \subsection [$z$-coordinate with partial step (\protect\np{ln_zps})] 691 {$z$-coordinate with partial step (\protect\np{ln_zps}=.true.)} 686 \subsection{$Z$-coordinate with partial step (\protect\np{ln\_zps}\forcode{ = .true.})} 692 687 \label{DOM_zps} 693 688 %--------------------------------------------namdom------------------------------------------------------- … … 712 707 Two variables in the namdom namelist are used to define the partial step 713 708 vertical grid. The mimimum water thickness (in meters) allowed for a cell 714 partially filled with bathymetry at level jk is the minimum of \np{rn _e3zps_min}715 (thickness in meters, usually $20~m$) or $e_{3t}(jk)* rn\_e3zps\_rat$(a fraction,709 partially filled with bathymetry at level jk is the minimum of \np{rn\_e3zps\_min} 710 (thickness in meters, usually $20~m$) or $e_{3t}(jk)*$\np{rn\_e3zps\_rat} (a fraction, 716 711 usually 10\%, of the default thickness $e_{3t}(jk)$). 717 712 … … 721 716 % s-coordinate 722 717 % ------------------------------------------------------------------------------------------------------------- 723 \subsection [$s$-coordinate (\protect\np{ln_sco})] 724 {$s$-coordinate (\protect\forcode{ln_sco = .true.})} 718 \subsection{$S$-coordinate (\protect\np{ln\_sco}\forcode{ = .true.})} 725 719 \label{DOM_sco} 726 720 %------------------------------------------nam_zgr_sco--------------------------------------------------- … … 728 722 %-------------------------------------------------------------------------------------------------------------- 729 723 Options are defined in \ngn{namzgr\_sco}. 730 In $s$-coordinate (\np{ln _sco}~=~true), the depth and thickness of the model724 In $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}), the depth and thickness of the model 731 725 levels are defined from the product of a depth field and either a stretching 732 726 function or its derivative, respectively: … … 744 738 depth, since a mixed step-like and bottom-following representation of the 745 739 topography can be used (Fig.~\ref{Fig_z_zps_s_sps}d-e) or an envelop bathymetry can be defined (Fig.~\ref{Fig_z_zps_s_sps}f). 746 The namelist parameter \np{rn _rmax} determines the slope at which the terrain-following coordinate intersects740 The namelist parameter \np{rn\_rmax} determines the slope at which the terrain-following coordinate intersects 747 741 the sea bed and becomes a pseudo z-coordinate. 748 The coordinate can also be hybridised by specifying \np{rn _sbot_min} and \np{rn_sbot_max}742 The coordinate can also be hybridised by specifying \np{rn\_sbot\_min} and \np{rn\_sbot\_max} 749 743 as the minimum and maximum depths at which the terrain-following vertical coordinate is calculated. 750 744 … … 753 747 754 748 The original default NEMO s-coordinate stretching is available if neither of the other options 755 are specified as true (\np{ln _s_SH94}~=~false and \np{ln_s_SF12}~=~false).749 are specified as true (\np{ln\_s\_SH94}\forcode{ = .false.} and \np{ln\_s\_SF12}\forcode{ = .false.}). 756 750 This uses a depth independent $\tanh$ function for the stretching \citep{Madec_al_JPO96}: 757 751 … … 779 773 780 774 A stretching function, modified from the commonly used \citet{Song_Haidvogel_JCP94} 781 stretching (\np{ln _s_SH94}~=~true), is also available and is more commonly used for shelf seas modelling:775 stretching (\np{ln\_s\_SH94}\forcode{ = .true.}), is also available and is more commonly used for shelf seas modelling: 782 776 783 777 \begin{equation} … … 796 790 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 797 791 798 where $H_c$ is the critical depth (\np{rn _hc}) at which the coordinate transitions from799 pure $\sigma$ to the stretched coordinate, and $\theta$ (\np{rn _theta}) and $b$ (\np{rn_bb})792 where $H_c$ is the critical depth (\np{rn\_hc}) at which the coordinate transitions from 793 pure $\sigma$ to the stretched coordinate, and $\theta$ (\np{rn\_theta}) and $b$ (\np{rn\_bb}) 800 794 are the surface and bottom control parameters such that $0\leqslant \theta \leqslant 20$, and 801 795 $0\leqslant b\leqslant 1$. $b$ has been designed to allow surface and/or bottom 802 796 increase of the vertical resolution (Fig.~\ref{Fig_sco_function}). 803 797 804 Another example has been provided at version 3.5 (\np{ln _s_SF12}) that allows798 Another example has been provided at version 3.5 (\np{ln\_s\_SF12}) that allows 805 799 a fixed surface resolution in an analytical terrain-following stretching \citet{Siddorn_Furner_OM12}. 806 800 In this case the a stretching function $\gamma$ is defined such that: … … 823 817 824 818 This gives an analytical stretching of $\sigma$ that is solvable in $A$ and $B$ as a function of 825 the user prescribed stretching parameter $\alpha$ (\np{rn _alpha}) that stretches towards826 the surface ($\alpha > 1.0$) or the bottom ($\alpha < 1.0$) and user prescribed surface (\np{rn _zs})819 the user prescribed stretching parameter $\alpha$ (\np{rn\_alpha}) that stretches towards 820 the surface ($\alpha > 1.0$) or the bottom ($\alpha < 1.0$) and user prescribed surface (\np{rn\_zs}) 827 821 and bottom depths. The bottom cell depth in this example is given as a function of water depth: 828 822 … … 831 825 \end{equation} 832 826 833 where the namelist parameters \np{rn _zb_a} and \np{rn_zb_b} are $a$ and $b$ respectively.827 where the namelist parameters \np{rn\_zb\_a} and \np{rn\_zb\_b} are $a$ and $b$ respectively. 834 828 835 829 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 843 837 This gives a smooth analytical stretching in computational space that is constrained to given specified surface and bottom grid cell thicknesses in real space. This is not to be confused with the hybrid schemes that superimpose geopotential coordinates on terrain following coordinates thus creating a non-analytical vertical coordinate that therefore may suffer from large gradients in the vertical resolutions. This stretching is less straightforward to implement than the \citet{Song_Haidvogel_JCP94} stretching, but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes. 844 838 845 As with the \citet{Song_Haidvogel_JCP94} stretching the stretch is only applied at depths greater than the critical depth $h_c$. In this example two options are available in depths shallower than $h_c$, with pure sigma being applied if the \np{ln _sigcrit} is true and pure z-coordinates if it is false (the z-coordinate being equal to the depths of the stretched coordinate at $h_c$.839 As with the \citet{Song_Haidvogel_JCP94} stretching the stretch is only applied at depths greater than the critical depth $h_c$. In this example two options are available in depths shallower than $h_c$, with pure sigma being applied if the \np{ln\_sigcrit} is true and pure z-coordinates if it is false (the z-coordinate being equal to the depths of the stretched coordinate at $h_c$. 846 840 847 841 Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as large slopes lead to hydrostatic consistency. A hydrostatic consistency parameter diagnostic following \citet{Haney1991} has been implemented, and is output as part of the model mesh file at the start of the run. … … 850 844 % z*- or s*-coordinate 851 845 % ------------------------------------------------------------------------------------------------------------- 852 \subsection{$ z^*$- or $s^*$-coordinate (\protect\forcode{ln_linssh= .false.}) }846 \subsection{$Z^*$- or $S^*$-coordinate (\protect\np{ln\_linssh}\forcode{ = .false.}) } 853 847 \label{DOM_zgr_star} 854 848 … … 860 854 % level bathymetry and mask 861 855 % ------------------------------------------------------------------------------------------------------------- 862 \subsection{ level bathymetry and mask}856 \subsection{Level bathymetry and mask} 863 857 \label{DOM_msk} 864 858 … … 881 875 In case of ice shelf cavities, modifications of the model bathymetry and ice shelf draft into 882 876 the cavities are performed in the \textit{zgr\_isf} routine. The compatibility between ice shelf draft and bathymetry is checked. 883 All the locations where the isf cavity is thinnest than \np{rn _isfhmin} meters are grounded ($i.e.$ masked).877 All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked). 884 878 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. 885 879 If the incompatibility is too strong (need to dig more than 1 cell), the cell is masked.\\ … … 912 906 % Domain: Initial State (dtatsd & istate) 913 907 % ================================================================ 914 \section [Domain: Initial State (\textit{istate and dtatsd})] 915 {Domain: Initial State \small{(\protect\mdl{istate} and \protect\mdl{dtatsd} modules)} } 908 \section{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})} 916 909 \label{DTA_tsd} 917 910 %-----------------------------------------namtsd------------------------------------------- … … 921 914 Options are defined in \ngn{namtsd}. 922 915 By default, the ocean start from rest (the velocity field is set to zero) and the initialization of 923 temperature and salinity fields is controlled through the \np{ln _tsd_ini} namelist parameter.916 temperature and salinity fields is controlled through the \np{ln\_tsd\_ini} namelist parameter. 924 917 \begin{description} 925 \item[ ln\_tsd\_init = .true.]use a T and S input files that can be given on the model grid itself or918 \item[\np{ln\_tsd\_init}\forcode{ = .true.}] use a T and S input files that can be given on the model grid itself or 926 919 on their native input data grid. In the latter case, the data will be interpolated on-the-fly both in the 927 920 horizontal and the vertical to the model grid (see \S~\ref{SBC_iof}). The information relative to the 928 input files are given in the \np{sn _tem} and \np{sn_sal} structures.921 input files are given in the \np{sn\_tem} and \np{sn\_sal} structures. 929 922 The computation is done in the \mdl{dtatsd} module. 930 \item[ ln\_tsd\_init = .false.] use constant salinity value of 35.5 psu and an analytical profile of temperature923 \item[\np{ln\_tsd\_init}\forcode{ = .false.}] use constant salinity value of 35.5 psu and an analytical profile of temperature 931 924 (typical of the tropical ocean), see \rou{istate\_t\_s} subroutine called from \mdl{istate} module. 932 925 \end{description}
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