Changeset 7260


Ignore:
Timestamp:
2016-11-18T09:27:42+01:00 (4 years ago)
Author:
cbricaud
Message:

phaze DOC/ directory of the CRS branch with nemo_v3_6_STABLE branch at rev 7213 (09-09-2016) (merge -r 5519:7213 )

Location:
branches/2015/dev_r5003_MERCATOR6_CRS/DOC
Files:
9 deleted
27 edited
9 copied

Legend:

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  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/NEMO_book.tex

    r5602 r7260  
    44% (C) Xavier Perseguers 2002 - xavier.perseguers@epfl.ch 
    55 
    6 \documentclass[a4paper,11pt]{book} 
    7 %\documentclass[a4paper,11pt,makeidx]{book} <== may need this to generate index 
     6% ================================================================ 
     7% PREAMBLE 
     8% ================================================================ 
    89 
    9 %  makeindex NEMO_book     <== to regenerate the index 
    10 %  bibtex         NEMO_book   <== to generate  the bibliography 
     10\include{TexFiles/Preamble} 
    1111 
    1212% ================================================================ 
    13 % HEADERS DEFINITION 
     13% TOP MATTER 
    1414% ================================================================ 
    1515 
    16 \usepackage[french]{babel} 
    17 %\usepackage{color} 
    18 \usepackage{xcolor} 
    19 %\usepackage{graphics}           % allows insertion of pictures 
    20 \usepackage{graphicx}            % allows insertion of pictures 
    21 \usepackage[capbesideposition={top,center}]{floatrow} % allows captions 
    22 \floatsetup[table]{style=plaintop}                                   % beside pictures 
    23 \usepackage[margin=10pt,font={small},labelsep=colon,labelfont={bf}]{caption} % Gives small font for captions 
    24 \usepackage{enumitem}                          % allows non-bold description items 
    25 \usepackage{longtable}                         % allows multipage tables 
    26 %\usepackage{colortbl}                           % gives coloured panels behind table columns 
    27  
    28 %hyperref 
    29 \usepackage[               % 
    30   pdftitle={NEMO ocean engine},  % 
    31   pdfauthor={Gurvan Madec},      % pdfsubject={The preprint document class 
    32                                        % elsart},% pdfkeywords={diapycnal diffusion,numerical mixing,z-level models},% 
    33   pdfstartview=FitH,          % 
    34   bookmarks=true,          % 
    35   bookmarksopen=true,         % 
    36   breaklinks=true,            % 
    37   colorlinks=true,            % 
    38   linkcolor=blue,anchorcolor=blue,  % 
    39   citecolor=blue,filecolor=blue,    % 
    40  menucolor=blue,                    % 
    41   urlcolor=blue]{hyperref} 
    42 %  usage of exteranl hyperlink :  \href{mailto:my_address@wikibooks.org}{my\_address@wikibooks.org} 
    43 %                                                 \url{http://www.wikibooks.org} 
    44 %                                     or         \href{http://www.wikibooks.org}{wikibooks home} 
    45  
    46  
    47  
    48 %%%% page styles etc................ 
    49 \usepackage{fancyhdr} 
    50 \pagestyle{fancy} 
    51 % with this we ensure that the chapter and section 
    52 % headings are in lowercase. 
    53 \renewcommand{\chaptermark}[1]{\markboth{#1}{}} 
    54 \renewcommand{\sectionmark}[1]{\markright{\thesection.\ #1}} 
    55 \fancyhf{}             % delete current setting for header and footer 
    56 \fancyhead[LE,RO]{\bfseries\thepage} 
    57 \fancyhead[LO]{\bfseries\hspace{-0em}\rightmark} 
    58 \fancyhead[RE]{\bfseries\leftmark} 
    59 \renewcommand{\headrulewidth}{0.5pt} 
    60 \renewcommand{\footrulewidth}{0pt} 
    61 \addtolength{\headheight}{2.6pt}   % make space for the rule 
    62 %\addtolength{\headheight}{1.6pt}   % make space for the rule 
    63 \fancypagestyle{plain}{ 
    64   \fancyhead{}         % get rid of headers on plain pages 
    65   \renewcommand{\headrulewidth}{0pt}  % and the line 
    66 } 
    67  
    68  
    69 %%%%  Section number in Margin....... 
    70 % typeset the number of each section in the left margin, with the start of each instance of 
    71 % sectional heading text aligned with the left hand edge of  the body text. 
    72 \makeatletter 
    73 \def\@seccntformat#1{\protect\makebox[0pt][r]{\csname the#1\endcsname\quad}} 
    74 \makeatother 
    75  
    76 % Leave blank pages completely empty, w/o header 
    77 \makeatletter 
    78 \def\cleardoublepage{\clearpage\if@twoside \ifodd\c@page\else 
    79   \hbox{} 
    80   \vspace*{\fill} 
    81   \vspace{\fill} 
    82   \thispagestyle{empty} 
    83   \newpage 
    84   \if@twocolumn\hbox{}\newpage\fi\fi\fi} 
    85 \makeatother 
    86  
    87 %%%% define the chapter  style ................ 
    88 \usepackage{minitoc}          %In French : \usepackage[french]{minitoc} 
    89 %\usepackage{mtcoff}          % invalidate the use of minitocs 
    90 \usepackage{fancybox} 
    91  
    92 \makeatletter 
    93 \def\LigneVerticale{\vrule height 5cm depth 2cm\hspace{0.1cm}\relax} 
    94 \def\LignesVerticales{% 
    95   \let\LV\LigneVerticale\LV\LV\LV\LV\LV\LV\LV\LV\LV\LV} 
    96 \def\GrosCarreAvecUnChiffre#1{% 
    97   \rlap{\vrule height 0.8cm width 1cm depth 0.2cm}% 
    98  \rlap{\hbox to 1cm{\hss\mbox{\color{white} #1}\hss}}% 
    99   \vrule height 0pt width 1cm depth 0pt} 
    100 \def\GrosCarreAvecTroisChiffre#1{% 
    101   \rlap{\vrule height 0.8cm width 1.6cm depth 0.2cm}% 
    102  \rlap{\hbox to 1.5cm{\hss\mbox{\color{white} #1}\hss}}% 
    103   \vrule height 0pt width 1cm depth 0pt} 
    104  
    105 \def\@makechapterhead#1{\hbox{% 
    106    \huge 
    107     \LignesVerticales 
    108     \hspace{-0.5cm}% 
    109     \GrosCarreAvecUnChiffre{\thechapter} 
    110     \hspace{0.2cm}\hbox{#1}% 
    111 %    \GrosCarreAvecTroisChiffre{\thechapter} 
    112 %    \hspace{1cm}\hbox{#1}% 
    113 %}\par\vskip 2cm} 
    114 }\par\vskip 1cm} 
    115 \def\@makeschapterhead#1{\hbox{% 
    116    \huge 
    117     \LignesVerticales 
    118     %\hspace{0.5cm}% 
    119     \hbox{#1}% 
    120 }\par\vskip 2cm} 
    121 \makeatother 
    122  
    123 %\def\thechapter{\Roman{chapter}}      % chapter number to be Roman 
    124  
    125  
    126 %%%%           Mathematics............... 
    127 %\documentclass{amsart} 
    128 \usepackage{xspace}                              % helpd ensure correct spacing after macros 
    129 \usepackage{latexsym} 
    130 \usepackage{amssymb} 
    131 \usepackage{amsmath} 
    132 \allowdisplaybreaks[1]           % allow page breaks in the middle of equations 
    133 \usepackage{./TexFiles/math_abbrev}    % use maths shortcuts 
    134  
    135  
    136 \usepackage{times}                % use times font for text 
    137 %\usepackage{mathtime}                          % font for illustrator to work (belleek fonts ) 
    138 %\usepackage[latin1]{inputenc}                % allows some unicode removed (agn) 
    139  
    140  
    141 %%% essai commande 
    142 \newcommand{\nl} [1] {\texttt{\small {\textcolor{blue}{#1}} } } 
    143 \newcommand{\nlv} [1] {\texttt{\footnotesize#1}\xspace} 
    144 \newcommand{\smnlv} [1] {\texttt{\scriptsize#1}\xspace} 
    145  
    146 %%%% namelist & code display................................ 
    147 \usepackage{alltt}      %%  alltt for namelist 
    148 \usepackage{verbatim}   %%  alltt for namelist 
    149 % namelists 
    150 \newcommand{\namdisplay} [1] { 
    151 \begin{alltt} 
    152 {\tiny \verbatiminput{./TexFiles/Namelist/#1}} 
    153 \end{alltt} 
    154   \vspace{-10pt} 
    155 } 
    156 % code display 
    157 %\newcommand{\codedisplay} [1] { \begin{alltt} {\tiny  {\begin{verbatim} {#1}} \end{verbatim} }  \end{alltt}   } 
    158  
    159  
    160  
    161 %%%% commands for working with text................................ 
    162 % command to "comment out" portions of text ({} argument) or not ({#1} argument) 
    163 \newcommand{\amtcomment}[1]{}    % command to "commented out" portions of text or not (#1 in argument) 
    164 \newcommand{\sgacomment}[1]{}    % command to "commented out" portions of 
    165 \newcommand{\gmcomment}[1]{}     % command to "commented out" portions of 
    166 %                                               % text that span line breaks 
    167 %Red (NR) or Yellow(WARN) 
    168 %\newcommand{\NR} {\colorbox{red}{#1}} 
    169 %\newcommand{\WARN} {{ \colorbox{yellow}{#1}} } 
    170  
    171  
    172  
    173 %%% index commands...................... 
    174 \usepackage{makeidx} 
    175 %\usepackage{showidx}            % show the index entry 
    176  
    177 \newcommand{\mdl} [1] {\textit{#1.F90}\index{Modules!#1}}         %module (mdl) 
    178 \newcommand{\rou} [1] {\textit{#1}\index{Routines!#1}}            %module (routine) 
    179 \newcommand{\hf} [1] {\textit{#1.h90}\index{h90 file!#1}}            %module (h90 files) 
    180 \newcommand{\ngn} [1] {\textit{#1}\index{Namelist Group Name!#1}}    %namelist name (nampar) 
    181 \newcommand{\np} [1] {\textit{#1}\index{Namelist variables!#1}}             %namelist variable 
    182 \newcommand{\jp} [1] {\textit{#1}\index{Model parameters!#1}}        %model parameter (jp) 
    183 \newcommand{\pp} [1] {\textit{#1}\index{Model parameters!#1}}        %namelist parameter (pp) 
    184 \newcommand{\ifile} [1] {\textit{#1.nc}\index{Input NetCDF files!#1.nc}}   %input NetCDF files (.nc) 
    185 \newcommand{\key} [1] {\textbf{key\_#1}\index{CPP keys!key\_#1}}  %key_cpp (key) 
    186 \newcommand{\NEMO} {\textit{NEMO}\xspace}                %NEMO (nemo) 
    187  
    188 %%%%   Bibliography   ............. 
    189 \usepackage[nottoc, notlof, notlot]{tocbibind} 
    190 \usepackage[square, comma]{natbib} 
    191 \bibpunct{[}{]}{,}{a}{}{;}                           %suppress "," after "et al." 
    192 \providecommand{\bibfont}{\small} 
    193  
     16\include{TexFiles/Top_Matter} 
    19417 
    19518% ================================================================ 
    196 % FRONT PAGE 
    197 % ================================================================ 
    198  
    199 %\usepackage{pstricks} 
    200 \title{ 
    201 %\psset{unit=1.1in,linewidth=4pt}   %parameters of the units for pstricks 
    202 % \rput(0,2){ \includegraphics[width=1.1\textwidth]{./TexFiles/Figures/logo_ALL.pdf}             } \\ 
    203 % \vspace{0.1cm} 
    204 \vspace{-6.0cm} 
    205 \includegraphics[width=1.1\textwidth]{./TexFiles/Figures/logo_ALL.pdf}\\ 
    206 \vspace{5.1cm} 
    207 \includegraphics[width=0.9\textwidth]{./TexFiles/Figures/NEMO_logo_Black.pdf} \\ 
    208 \vspace{1.4cm} 
    209 \rule{345pt}{1.5pt} \\ 
    210 \vspace{0.45cm} 
    211 {\Huge NEMO ocean engine} 
    212 \rule{345pt}{1.5pt} \\ 
    213  } 
    214 %{ -- Draft --}   } 
    215 %\date{\today} 
    216 \date{ 
    217 November 2014  \\ 
    218 {\small  -- version 3.6 --} \\ 
    219 ~  \\ 
    220 \textit{\small Note du P\^ole de mod\'{e}lisation de l'Institut Pierre-Simon Laplace No 27 }\\ 
    221 \vspace{0.45cm} 
    222 { ISSN No 1288-1619.} 
    223 } 
    224  
    225  
    226 \author{ 
    227 \Large Gurvan Madec, and the NEMO team  \\ 
    228  \texttt{\small gurvan.madec@locean-ipsl.umpc.fr} \\ 
    229  \texttt{\small nemo\_st@locean-ipsl.umpc.fr} \\ 
    230 %{\small Laboratoire d'Oc\'{e}anographie  et du Climat: Exp\'{e}rimentation et Approches Num\'{e}riques } 
    231 } 
    232  
    233 \dominitoc 
    234 \makeindex        %type this first :     makeindex -s NEMO.ist NEMO_book.idx 
    235  
    236 % ================================================================ 
    237 %      Include ONLY order 
    238 % ================================================================ 
    239  
    240 %\includeonly{./TexFiles/Chapters/Chap_MISC} 
    241 %\includeonly{./TexFiles/Chapters/Chap_ZDF} 
    242 %\includeonly{./TexFiles/Chapters/Chap_STP,./TexFiles/Chapters/Chap_SBC,./TexFiles/Chapters/Chap_TRA} 
    243 %\includeonly{./TexFiles/Chapters/Chap_LBC,./TexFiles/Chapters/Chap_MISC} 
    244 %\includeonly{./TexFiles/Chapters/Chap_Model_Basics} 
    245 %\includeonly{./TexFiles/Chapters/Annex_A,./TexFiles/Chapters/Annex_B,./TexFiles/Chapters/Annex_C,./TexFiles/Chapters/Annex_D} 
    246  
    247 % ================================================================ 
     19% DOCUMENT 
    24820% ================================================================ 
    24921 
     
    26436% ================================================================ 
    26537 
    266 \include{./TexFiles/Chapters/Abstracts_Foreword} 
     38\subfile{TexFiles/Chapters/Abstracts_Foreword} 
    26739 
    26840% ================================================================ 
     
    27042% ================================================================ 
    27143 
    272 \include{./TexFiles/Chapters/Introduction} 
     44\subfile{TexFiles/Chapters/Introduction} 
    27345 
    27446% ================================================================ 
     
    27648% ================================================================ 
    27749 
    278 \include{./TexFiles/Chapters/Chap_Model_Basics} 
     50\subfile{TexFiles/Chapters/Chap_Model_Basics} 
    27951 
    280 \include{./TexFiles/Chapters/Chap_STP}       % Time discretisation (time stepping strategy) 
     52\subfile{TexFiles/Chapters/Chap_STP}         % Time discretisation (time stepping strategy) 
    28153 
    282 \include{./TexFiles/Chapters/Chap_DOM}       % Space discretisation 
     54\subfile{TexFiles/Chapters/Chap_DOM}         % Space discretisation 
    28355 
    284 \include{./TexFiles/Chapters/Chap_TRA}       % Tracer advection/diffusion equation 
     56\subfile{TexFiles/Chapters/Chap_TRA}         % Tracer advection/diffusion equation 
    28557 
    286 \include{./TexFiles/Chapters/Chap_DYN}       % Dynamics : momentum equation 
     58\subfile{TexFiles/Chapters/Chap_DYN}         % Dynamics : momentum equation 
    28759 
    288 \include{./TexFiles/Chapters/Chap_SBC}       % Surface Boundary Conditions 
     60\subfile{TexFiles/Chapters/Chap_SBC}         % Surface Boundary Conditions 
    28961 
    290 \include{./TexFiles/Chapters/Chap_LBC}       % Lateral Boundary Conditions 
     62\subfile{TexFiles/Chapters/Chap_LBC}         % Lateral Boundary Conditions 
    29163 
    292 \include{./TexFiles/Chapters/Chap_LDF}       % Lateral diffusion 
     64\subfile{TexFiles/Chapters/Chap_LDF}         % Lateral diffusion 
    29365 
    294 \include{./TexFiles/Chapters/Chap_ZDF}       % Vertical diffusion 
     66\subfile{TexFiles/Chapters/Chap_ZDF}         % Vertical diffusion 
    29567 
    296 \include{./TexFiles/Chapters/Chap_DIA}       % Outputs and Diagnostics 
     68\subfile{TexFiles/Chapters/Chap_DIA}         % Outputs and Diagnostics 
    29769 
    298 \include{./TexFiles/Chapters/Chap_OBS}          % Observation operator 
     70\subfile{TexFiles/Chapters/Chap_OBS}                    % Observation operator 
    29971 
    300 \include{./TexFiles/Chapters/Chap_ASM}          % Assimilation increments 
     72\subfile{TexFiles/Chapters/Chap_ASM}                    % Assimilation increments 
    30173 
    302 \include{./TexFiles/Chapters/Chap_STO}          % Stochastic param. 
     74\subfile{TexFiles/Chapters/Chap_STO}                    % Stochastic param. 
    30375 
    304 \include{./TexFiles/Chapters/Chap_MISC}         % Miscellaneous topics 
     76\subfile{TexFiles/Chapters/Chap_MISC}        % Miscellaneous topics 
    30577 
    306 \include{./TexFiles/Chapters/Chap_CFG}       % Predefined configurations 
     78\subfile{TexFiles/Chapters/Chap_CFG}         % Predefined configurations 
    30779 
    30880% ================================================================ 
     
    31284\appendix 
    31385 
    314 %\include{./TexFiles/Chapters/Chap_Conservation} 
    315 \include{./TexFiles/Chapters/Annex_A}        % generalised vertical coordinate 
    316 \include{./TexFiles/Chapters/Annex_B}        % diffusive operator 
    317 \include{./TexFiles/Chapters/Annex_C}        % Discrete invariants of the eqs. 
    318 \include{./TexFiles/Chapters/Annex_D}        % Coding rules 
    319 \include{./TexFiles/Chapters/Annex_ISO}                     % Isoneutral diffusion using triads 
    320 %\include{./TexFiles/Chapters/Annex_E}                   % Notes on some on going staff (no included in the DOC) 
    321 %\include{./TexFiles/Chapters/Annex_Fox-Kemper}   % Notes on Fox-Kemper (no included in the DOC) 
    322 %\include{./TexFiles/Chapters/Annex_EVP}           % Notes on EVP (no included in the DOC) 
     86%\subfile{TexFiles/Chapters/Chap_Conservation} 
     87\subfile{TexFiles/Chapters/Annex_A}       % generalised vertical coordinate 
     88\subfile{TexFiles/Chapters/Annex_B}       % diffusive operator 
     89\subfile{TexFiles/Chapters/Annex_C}       % Discrete invariants of the eqs. 
     90\subfile{TexFiles/Chapters/Annex_ISO}                    % Isoneutral diffusion using triads 
     91\subfile{TexFiles/Chapters/Annex_D}       % Coding rules 
     92%\subfile{TexFiles/Chapters/Annex_E}                     % Notes on some on going staff (no included in the DOC) 
     93%\subfile{TexFiles/Chapters/Annex_Fox-Kemper}   % Notes on Fox-Kemper (no included in the DOC) 
     94%\subfile{TexFiles/Chapters/Annex_EVP}          % Notes on EVP (no included in the DOC) 
    32395 
    32496% ================================================================ 
     
    334106 
    335107%%\bibliographystyle{plainat} 
    336 \bibliographystyle{./TexFiles/ametsoc}    % AMS biblio style (JPO) 
    337 \bibliography{./TexFiles/Biblio/Biblio} 
     108\bibliographystyle{TexFiles/Styles/ametsoc}     % AMS biblio style (JPO) 
     109\bibliography{TexFiles/Bibliography/Biblio} 
    338110 
    339111% ================================================================ 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/NEMO_coding.conv.tex

    r2738 r7260  
    77\usepackage{framed}  
    88\usepackage{makeidx}  
    9  
     9\graphicspath{{Figures/}} 
    1010 
    1111%%%%%%% 
     
    3131 
    3232\title{  
    33 \includegraphics[width=0.3\textwidth]{./TexFiles/Figures/NEMO_logo_Black.pdf} \\ 
     33\includegraphics[width=0.3\textwidth]{NEMO_logo_Black} \\ 
    3434\vspace{1.0cm} 
    3535\rule{345pt}{1.5pt} \\ 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Abstracts_Foreword.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13 
    24% ================================================================ 
     
    1315be a flexible tool for studying the ocean and its interactions with the others components of  
    1416the earth climate system over a wide range of space and time scales.  
    15 Prognostic variables are the three-dimensional velocity field, a linear  
    16 or non-linear sea surface height, the temperature and the salinity. In the horizontal direction,  
    17 the model uses a curvilinear orthogonal grid and in the vertical direction, a full or partial step  
    18 $z$-coordinate, or $s$-coordinate, or a mixture of the two. The distribution of variables is a  
    19 three-dimensional Arakawa C-type grid. Various physical choices are available to describe  
    20 ocean physics, including TKE, GLS and KPP vertical physics. Within NEMO, the ocean is  
    21 interfaced with a sea-ice model (LIM v2 and v3), passive tracer and biogeochemical models (TOP)  
    22 and, via the OASIS coupler, with several atmospheric general circulation models. It also  
    23 support two-way grid embedding via the AGRIF software. 
     17Prognostic variables are the three-dimensional velocity field, a non-linear sea surface height,  
     18the \textit{Conservative} Temperature and the \textit{Absolute} Salinity.  
     19In the horizontal direction, the model uses a curvilinear orthogonal grid and in the vertical direction,  
     20a full or partial step $z$-coordinate, or $s$-coordinate, or a mixture of the two.  
     21The distribution of variables is a three-dimensional Arakawa C-type grid.  
     22Various physical choices are available to describe ocean physics, including TKE, and GLS vertical physics.  
     23Within NEMO, the ocean is interfaced with a sea-ice model (LIM or CICE), passive tracer and  
     24biogeochemical models (TOP) and, via the OASIS coupler, with several atmospheric general circulation models.  
     25It also support two-way grid embedding via the AGRIF software. 
    2426 
    2527% ================================================================ 
    26  \vspace{0.5cm} 
     28% \vspace{0.5cm} 
    2729 
    28 Le moteur oc\'{e}anique de NEMO (Nucleus for European Modelling of the Ocean) est un  
    29 mod\`{e}le aux \'{e}quations primitives de la circulation oc\'{e}anique r\'{e}gionale et globale.  
    30 Il se veut un outil flexible pour \'{e}tudier sur un vaste spectre spatiotemporel l'oc\'{e}an et ses  
    31 interactions avec les autres composantes du syst\`{e}me climatique terrestre.  
    32 Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer  
    33 lin\'{e}aire ou non, la temperature et la salinit\'{e}.  
    34 La distribution des variables se fait sur une grille C d'Arakawa tridimensionnelle utilisant une  
    35 coordonn\'{e}e verticale $z$ \`{a} niveaux entiers ou partiels, ou une coordonn\'{e}e s, ou encore  
    36 une combinaison des deux. Diff\'{e}rents choix sont propos\'{e}s pour d\'{e}crire la physique  
    37 oc\'{e}anique, incluant notamment des physiques verticales TKE, GLS et KPP. A travers l'infrastructure  
    38 NEMO, l'oc\'{e}an est interfac\'{e} avec des mod\`{e}les de glace de mer, de biog\'{e}ochimie  
    39 et de traceurs passifs, et, via le coupleur OASIS, \`{a} plusieurs mod\`{e}les de circulation  
    40 g\'{e}n\'{e}rale atmosph\'{e}rique. Il supporte \'{e}galement l'embo\^{i}tement interactif de  
    41 maillages via le logiciel AGRIF. 
     30%Le moteur oc\'{e}anique de NEMO (Nucleus for European Modelling of the Ocean) est un  
     31%mod\`{e}le aux \'{e}quations primitives de la circulation oc\'{e}anique r\'{e}gionale et globale.  
     32%Il se veut un outil flexible pour \'{e}tudier sur un vaste spectre spatiotemporel l'oc\'{e}an et ses  
     33%interactions avec les autres composantes du syst\`{e}me climatique terrestre.  
     34%Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer  
     35%lin\'{e}aire, la Temp\'{e}rature Conservative et la Salinit\'{e} Absolue.  
     36%La distribution des variables se fait sur une grille C d'Arakawa tridimensionnelle utilisant une  
     37%coordonn\'{e}e verticale $z$ \`{a} niveaux entiers ou partiels, ou une coordonn\'{e}e s, ou encore  
     38%une combinaison des deux. Diff\'{e}rents choix sont propos\'{e}s pour d\'{e}crire la physique  
     39%oc\'{e}anique, incluant notamment des physiques verticales TKE et GLS. A travers l'infrastructure  
     40%NEMO, l'oc\'{e}an est interfac\'{e} avec des mod\`{e}les de glace de mer (LIM ou CICE),  
     41%de biog\'{e}ochimie marine et de traceurs passifs, et, via le coupleur OASIS, \`{a} plusieurs  
     42%mod\`{e}les de circulation g\'{e}n\'{e}rale atmosph\'{e}rique.  
     43%Il supporte \'{e}galement l'embo\^{i}tement interactif de maillages via le logiciel AGRIF. 
    4244}  
    4345 
     
    6971 \vspace{0.5cm} 
    7072 
     73\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_A.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13 
    24% ================================================================ 
     
    532534expression of the 3D divergence in the $s-$coordinates established above.  
    533535 
     536\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_B.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter Ñ Appendix B : Diffusive Operators 
     
    364366\eqref{Apdx_B_Lap_U} is used in both $z$- and $s$-coordinate systems, that is 
    365367a Laplacian diffusion is applied on momentum along the coordinate directions. 
     368\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_C.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter Ñ Appendix C : Discrete Invariants of the Equations 
     
    410412\end{aligned}   } \right. 
    411413\end{equation}  
    412 where the indices $i_p$ and $k_p$ take the following value:  
     414where the indices $i_p$ and $j_p$ take the following value:  
    413415$i_p = -1/2$ or $1/2$ and $j_p = -1/2$ or $1/2$, 
    414416and the vorticity triads, ${^i_j}\mathbb{Q}^{i_p}_{j_p}$, defined at $T$-point, are given by:  
     
    11031105The discrete formulation of the horizontal diffusion of momentum ensures the  
    11041106conservation of potential vorticity and the horizontal divergence, and the  
    1105 dissipation of the square of these quantities (i.e. enstrophy and the  
     1107dissipation of the square of these quantities ($i.e.$ enstrophy and the  
    11061108variance of the horizontal divergence) as well as the dissipation of the  
    11071109horizontal kinetic energy. In particular, when the eddy coefficients are  
     
    11271129&\int \limits_D \frac{1} {e_3 } \textbf{k} \cdot \nabla \times  
    11281130   \Bigl[    \nabla_h  \left( A^{\,lm}\;\chi  \right) 
    1129              - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)    \Bigr]\;dv  = 0 
    1130 \end{flalign*} 
     1131           - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)    \Bigr]\;dv   \\  
     1132%\end{flalign*} 
    11311133%%%%%%%%%%  recheck here....  (gm) 
    1132 \begin{flalign*} 
    1133 = \int \limits_D  -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times  
    1134    \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)  \Bigr]\;dv &&& \\  
    1135 \end{flalign*} 
    1136 \begin{flalign*} 
     1134%\begin{flalign*} 
     1135=& \int \limits_D  -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times  
     1136   \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)  \Bigr]\;dv \\  
     1137%\end{flalign*} 
     1138%\begin{flalign*} 
    11371139\equiv& \sum\limits_{i,j} 
    11381140   \left\{ 
    1139    \delta_{i+1/2}  
    1140    \left[  
    1141    \frac {e_{2v}} {e_{1v}\,e_{3v}}  \delta_i 
    1142       \left[ A_f^{\,lm} e_{3f} \zeta  \right] 
    1143     \right] 
    1144    + \delta_{j+1/2}  
    1145    \left[  
    1146    \frac {e_{1u}} {e_{2u}\,e_{3u}} \delta_j  
    1147       \left[ A_f^{\,lm} e_{3f} \zeta  \right] 
    1148    \right] 
    1149    \right\}  
    1150    && \\  
     1141     \delta_{i+1/2} \left[  \frac {e_{2v}} {e_{1v}\,e_{3v}}  \delta_i \left[ A_f^{\,lm} e_{3f} \zeta  \right]  \right] 
     1142   + \delta_{j+1/2} \left[  \frac {e_{1u}} {e_{2u}\,e_{3u}}  \delta_j \left[ A_f^{\,lm} e_{3f} \zeta  \right]  \right] 
     1143   \right\}     \\  
    11511144% 
    11521145\intertext{Using \eqref{DOM_di_adj}, it follows:} 
     
    11541147\equiv& \sum\limits_{i,j,k}  
    11551148   -\,\left\{ 
    1156       \frac{e_{2v}} {e_{1v}\,e_{3v}}  \delta_i 
    1157       \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_i \left[ 1\right] 
    1158    + \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j  
    1159       \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_j \left[ 1\right] 
     1149      \frac{e_{2v}} {e_{1v}\,e_{3v}}  \delta_i  \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_i \left[ 1\right] 
     1150    + \frac{e_{1u}} {e_{2u}\,e_{3u}}  \delta_j  \left[ A_f^{\,lm} e_{3f} \zeta  \right]\;\delta_j \left[ 1\right] 
    11601151   \right\} \quad \equiv 0  
    1161    && \\  
     1152    \\  
    11621153\end{flalign*} 
    11631154 
     
    11671158\subsection{Dissipation of Horizontal Kinetic Energy} 
    11681159\label{Apdx_C.3.2} 
    1169  
    11701160 
    11711161The lateral momentum diffusion term dissipates the horizontal kinetic energy: 
     
    12211211\label{Apdx_C.3.3} 
    12221212 
    1223  
    12241213The lateral momentum diffusion term dissipates the enstrophy when the eddy  
    12251214coefficients are horizontally uniform: 
     
    12281217   \left[   \nabla_h \left( A^{\,lm}\;\chi  \right) 
    12291218          - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right)   \right]\;dv &&&\\ 
    1230 &= A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times  
     1219&\quad = A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times  
    12311220   \left[    \nabla_h \times \left( \zeta \; \textbf{k} \right)   \right]\;dv &&&\\ 
    1232 &\equiv A^{\,lm} \sum\limits_{i,j,k}  \zeta \;e_{3f}  
     1221&\quad \equiv A^{\,lm} \sum\limits_{i,j,k}  \zeta \;e_{3f}  
    12331222   \left\{     \delta_{i+1/2} \left[  \frac{e_{2v}} {e_{1v}\,e_{3v}} \delta_i \left[ e_{3f} \zeta  \right]   \right] 
    12341223             + \delta_{j+1/2} \left[  \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j \left[ e_{3f} \zeta  \right]   \right]      \right\}   &&&\\  
     
    12361225\intertext{Using \eqref{DOM_di_adj}, it follows:} 
    12371226% 
    1238 &\equiv  - A^{\,lm} \sum\limits_{i,j,k}  
     1227&\quad \equiv  - A^{\,lm} \sum\limits_{i,j,k}  
    12391228   \left\{    \left(  \frac{1} {e_{1v}\,e_{3v}}  \delta_i \left[ e_{3f} \zeta  \right]  \right)^2   b_v 
    1240             + \left(  \frac{1} {e_{2u}\,e_{3u}}  \delta_j \left[ e_{3f} \zeta  \right] \right)^2   b_u  \right\}      &&&\\ 
    1241 & \leq \;0       &&&\\  
     1229            + \left(  \frac{1} {e_{2u}\,e_{3u}}  \delta_j \left[ e_{3f} \zeta  \right] \right)^2   b_u  \right\}  \quad \leq \;0    &&&\\ 
    12421230\end{flalign*} 
    12431231 
     
    12501238When the horizontal divergence of the horizontal diffusion of momentum  
    12511239(discrete sense) is taken, the term associated with the vertical curl of the  
    1252 vorticity is zero locally, due to (!!! II.1.8  !!!!!). The resulting term conserves the  
    1253 $\chi$ and dissipates $\chi^2$ when the eddy coefficients are  
    1254 horizontally uniform. 
     1240vorticity is zero locally, due to \eqref{Eq_DOM_div_curl}.  
     1241The resulting term conserves the $\chi$ and dissipates $\chi^2$  
     1242when the eddy coefficients are horizontally uniform. 
    12551243\begin{flalign*} 
    12561244& \int\limits_D  \nabla_h \cdot  
    12571245   \Bigl[     \nabla_h \left( A^{\,lm}\;\chi \right) 
    12581246             - \nabla_h \times \left( A^{\,lm}\;\zeta \;\textbf{k} \right)    \Bigr]  dv 
    1259 = \int\limits_D  \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi  \right)   dv   &&&\\ 
     1247= \int\limits_D  \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi  \right)   dv   \\ 
    12601248% 
    12611249&\equiv \sum\limits_{i,j,k}  
    12621250   \left\{   \delta_i \left[ A_u^{\,lm} \frac{e_{2u}\,e_{3u}} {e_{1u}}  \delta_{i+1/2} \left[ \chi \right]  \right] 
    1263            + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}}  \delta_{j+1/2} \left[ \chi \right]  \right]    \right\}    &&&\\  
     1251           + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}}  \delta_{j+1/2} \left[ \chi \right]  \right]    \right\}    \\  
    12641252% 
    12651253\intertext{Using \eqref{DOM_di_adj}, it follows:} 
     
    12671255&\equiv \sum\limits_{i,j,k}  
    12681256   - \left\{   \frac{e_{2u}\,e_{3u}} {e_{1u}}  A_u^{\,lm} \delta_{i+1/2} \left[ \chi \right] \delta_{i+1/2} \left[ 1 \right]  
    1269              + \frac{e_{1v}\,e_{3v}}  {e_{2v}}  A_v^{\,lm} \delta_{j+1/2} \left[ \chi \right] \delta_{j+1/2} \left[ 1 \right]    \right\}  
    1270    \qquad \equiv 0     &&& \\  
     1257             + \frac{e_{1v}\,e_{3v}} {e_{2v}}  A_v^{\,lm} \delta_{j+1/2} \left[ \chi \right] \delta_{j+1/2} \left[ 1 \right]    \right\}  
     1258   \quad \equiv 0      \\  
    12711259\end{flalign*} 
    12721260 
     
    12811269   \left[    \nabla_h              \left( A^{\,lm}\;\chi                    \right) 
    12821270           - \nabla_h   \times  \left( A^{\,lm}\;\zeta \;\textbf{k} \right)    \right]\;  dv 
    1283  = A^{\,lm}   \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\;  dv    &&&\\  
     1271 = A^{\,lm}   \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\;  dv    \\  
    12841272% 
    12851273&\equiv A^{\,lm}  \sum\limits_{i,j,k}  \frac{1} {e_{1t}\,e_{2t}\,e_{3t}}  \chi  
     
    12871275      \delta_i  \left[   \frac{e_{2u}\,e_{3u}} {e_{1u}}  \delta_{i+1/2} \left[ \chi \right]   \right] 
    12881276   + \delta_j  \left[   \frac{e_{1v}\,e_{3v}} {e_{2v}}   \delta_{j+1/2} \left[ \chi \right]   \right] 
    1289    \right\} \;   e_{1t}\,e_{2t}\,e_{3t}    &&&\\  
     1277   \right\} \;   e_{1t}\,e_{2t}\,e_{3t}    \\  
    12901278% 
    12911279\intertext{Using \eqref{DOM_di_adj}, it turns out to be:} 
     
    12931281&\equiv - A^{\,lm} \sum\limits_{i,j,k} 
    12941282   \left\{    \left(  \frac{1} {e_{1u}}  \delta_{i+1/2}  \left[ \chi \right]  \right)^2  b_u 
    1295                  + \left(  \frac{1} {e_{2v}}  \delta_{j+1/2}  \left[ \chi \right]  \right)^2  b_v    \right\} \;    &&&\\ 
    1296 % 
    1297 &\leq 0              &&&\\ 
     1283            + \left(  \frac{1} {e_{2v}}  \delta_{j+1/2}  \left[ \chi \right]  \right)^2  b_v    \right\}     
     1284\quad \leq 0             \\ 
    12981285\end{flalign*} 
    12991286 
     
    13031290\section{Conservation Properties on Vertical Momentum Physics} 
    13041291\label{Apdx_C_4} 
    1305  
    13061292 
    13071293As for the lateral momentum physics, the continuous form of the vertical diffusion  
     
    13191305   \left(   \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k}   \right)\; dv    \quad &\leq 0     \\ 
    13201306\end{align*} 
     1307 
    13211308The first property is obvious. The second results from: 
    1322  
    13231309\begin{flalign*} 
    13241310\int\limits_D  
     
    13591345   e_{1f}\,e_{2f}\,e_{3f} \; \equiv 0   && \\ 
    13601346\end{flalign*} 
     1347 
    13611348If the vertical diffusion coefficient is uniform over the whole domain, the  
    13621349enstrophy is dissipated, $i.e.$ 
     
    13661353      \left( \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k}   \right)   \right)\; dv = 0   &&&\\ 
    13671354\end{flalign*} 
     1355 
    13681356This property is only satisfied in $z$-coordinates: 
    1369  
    13701357\begin{flalign*} 
    13711358\int\limits_D \zeta \, \textbf{k} \cdot \nabla \times  
     
    14771464 
    14781465The numerical schemes used for tracer subgridscale physics are written such  
    1479 that the heat and salt contents are conserved (equations in flux form, second  
    1480 order centered finite differences). Since a flux form is used to compute the  
    1481 temperature and salinity, the quadratic form of these quantities (i.e. their variance)  
    1482 globally tends to diminish. As for the advection term, there is generally no strict  
    1483 conservation of mass, even if in practice the mass is conserved to a very high  
    1484 accuracy.  
     1466that the heat and salt contents are conserved (equations in flux form).  
     1467Since a flux form is used to compute the temperature and salinity,  
     1468the quadratic form of these quantities ($i.e.$ their variance) globally tends to diminish.  
     1469As for the advection term, there is conservation of mass only if the Equation Of Seawater is linear.  
    14851470 
    14861471% ------------------------------------------------------------------------------------------------------------- 
     
    15481533%%%%  end of appendix in gm comment 
    15491534%} 
     1535\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_D.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Appendix D Ñ Coding Rules 
     
    120122\hline 
    121123public  \par or  \par module variable&  
    122 \textbf{m n} \par \textit{but not} \par \textbf{nn\_}&  
     124\textbf{m n} \par \textit{but not} \par \textbf{nn\_ np\_}&  
    123125\textbf{a b e f g h o q r} \par \textbf{t} \textit{to} \textbf{x} \par but not \par \textbf{fs rn\_}&  
    124126\textbf{l} \par \textit{but not} \par \textbf{lp ld} \par \textbf{ ll ln\_}&  
     
    156158\hline 
    157159parameter&  
    158 \textbf{jp}&  
     160\textbf{jp np\_}&  
    159161\textbf{pp}&  
    160162\textbf{lp}&  
     
    190192%-------------------------------------------------------------------------------------------------------------- 
    191193 
     194N.B.   Parameter here, in not only parameter in the \textsc{Fortran} acceptation, it is also used for code variables  
     195that are read in namelist and should never been modified during a simulation.  
     196It is the case, for example, for the size of a domain (jpi,jpj,jpk). 
     197 
    192198\newpage 
    193199% ================================================================ 
     
    198204 
    199205To be done.... 
     206\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_E.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Appendix E : Note on some algorithms 
     
    299301\begin{figure}[!ht] \label{Fig_ISO_triad} 
    300302\begin{center} 
    301 \includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_ISO_triad.pdf} 
     303\includegraphics[width=0.70\textwidth]{Fig_ISO_triad} 
    302304\caption{  \label{Fig_ISO_triad}    
    303305Triads used in the Griffies's like iso-neutral diffision scheme for  
     
    806808tracer is preserved by the discretisation of the skew fluxes. 
    807809 
     810\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_ISO.tex

    r4147 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Iso-neutral diffusion : 
     
    201203% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    202204\begin{figure}[h] \begin{center} 
    203     \includegraphics[width=1.05\textwidth]{./TexFiles/Figures/Fig_GRIFF_triad_fluxes} 
     205    \includegraphics[width=1.05\textwidth]{Fig_GRIFF_triad_fluxes} 
    204206    \caption{ \label{fig:triad:ISO_triad} 
    205207      (a) Arrangement of triads $S_i$ and tracer gradients to 
     
    269271% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    270272\begin{figure}[h] \begin{center} 
    271     \includegraphics[width=0.80\textwidth]{./TexFiles/Figures/Fig_GRIFF_qcells} 
     273    \includegraphics[width=0.80\textwidth]{Fig_GRIFF_qcells} 
    272274    \caption{   \label{fig:triad:qcells} 
    273275    Triad notation for quarter cells. $T$-cells are inside 
     
    676678% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    677679\begin{figure}[h] \begin{center} 
    678     \includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_GRIFF_bdry_triads} 
     680    \includegraphics[width=0.60\textwidth]{Fig_GRIFF_bdry_triads} 
    679681    \caption{  \label{fig:triad:bdry_triads} 
    680682      (a) Uppermost model layer $k=1$ with $i,1$ and $i+1,1$ tracer 
     
    849851    different $i_p,k_p$, denoted by different colours, (e.g. the green 
    850852    triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.}} 
    851   {\includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_GRIFF_MLB_triads}} 
     853  {\includegraphics[width=0.60\textwidth]{Fig_GRIFF_MLB_triads}} 
    852854\end{figure} 
    853855% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    11931195\end{split} 
    11941196\end{equation} 
     1197\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_ASM.tex

    r4147 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter Assimilation increments (ASM) 
     
    172174\end{verbatim} 
    173175\end{alltt} 
     176\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_CFG.tex

    r4147 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter � Configurations 
     
    8890%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    8991\begin{figure}[!t]   \begin{center} 
    90 \includegraphics[width=0.98\textwidth]{./TexFiles/Figures/Fig_ORCA_NH_mesh.pdf} 
     92\includegraphics[width=0.98\textwidth]{Fig_ORCA_NH_mesh} 
    9193\caption{  \label{Fig_MISC_ORCA_msh}      
    92 ORCA mesh conception. The departure from an isotropic Mercator grid start poleward of 20\deg N. 
     94ORCA mesh conception. The departure from an isotropic Mercator grid start poleward of 20\degN. 
    9395The two "north pole" are the foci of a series of embedded ellipses (blue curves)  
    9496which are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes).  
     
    115117%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    116118\begin{figure}[!tbp]  \begin{center} 
    117 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_ORCA_NH_msh05_e1_e2.pdf} 
    118 \includegraphics[width=0.80\textwidth]{./TexFiles/Figures/Fig_ORCA_aniso.pdf} 
     119\includegraphics[width=1.0\textwidth]{Fig_ORCA_NH_msh05_e1_e2} 
     120\includegraphics[width=0.80\textwidth]{Fig_ORCA_aniso} 
    119121\caption {  \label{Fig_MISC_ORCA_e1e2} 
    120122\textit{Top}: Horizontal scale factors ($e_1$, $e_2$) and  
    121123\textit{Bottom}: ratio of anisotropy ($e_1 / e_2$) 
    122 for ORCA 0.5\deg ~mesh. South of 20\deg N a Mercator grid is used ($e_1 = e_2$)  
    123 so that the anisotropy ratio is 1. Poleward of 20\deg N, the two "north pole"  
     124for ORCA 0.5\deg ~mesh. South of 20\degN a Mercator grid is used ($e_1 = e_2$)  
     125so that the anisotropy ratio is 1. Poleward of 20\degN, the two "north pole"  
    124126introduce a weak anisotropy over the ocean areas ($< 1.2$) except in vicinity of Victoria Island  
    125127(Canadian Arctic Archipelago). } 
     
    129131 
    130132The method is applied to Mercator grid ($i.e.$ same zonal and meridional grid spacing) poleward  
    131 of $20\deg$N, so that the Equator is a mesh line, which provides a better numerical solution  
     133of 20\degN, so that the Equator is a mesh line, which provides a better numerical solution  
    132134for equatorial dynamics. The choice of the series of embedded ellipses (position of the foci and  
    133135variation of the ellipses) is a compromise between maintaining  the ratio of mesh anisotropy  
     
    178180The ORCA\_R2 configuration has the following specificity : starting from a 2\deg~ORCA mesh,  
    179181local mesh refinements were applied to the Mediterranean, Red, Black and Caspian Seas,  
    180 so that the resolution is $1\deg \time 1\deg$ there. A local transformation were also applied  
     182so that the resolution is 1\deg \time 1\deg there. A local transformation were also applied  
    181183with in the Tropics in order to refine the meridional resolution up to 0.5\deg at the Equator. 
    182184 
     
    227229 
    228230The domain geometry is a closed rectangular basin on the $\beta$-plane centred  
    229 at $\sim 30\deg$N and rotated by 45\deg, 3180~km long, 2120~km wide  
     231at $\sim$ 30\degN and rotated by 45\deg, 3180~km long, 2120~km wide  
    230232and 4~km deep (Fig.~\ref{Fig_MISC_strait_hand}).  
    231233The domain is bounded by vertical walls and by a flat bottom. The configuration is  
     
    234236The applied forcings vary seasonally in a sinusoidal manner between winter  
    235237and summer extrema \citep{Levy_al_OM10}.  
    236 The wind stress is zonal and its curl changes sign at 22\deg N and 36\deg N.  
     238The wind stress is zonal and its curl changes sign at 22\degN and 36\degN.  
    237239It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain  
    238240and a small recirculation gyre in the southern corner.  
     
    261263%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    262264\begin{figure}[!t]   \begin{center} 
    263 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_GYRE.pdf} 
     265\includegraphics[width=1.0\textwidth]{Fig_GYRE} 
    264266\caption{  \label{Fig_GYRE}    
    265267Snapshot of relative vorticity at the surface of the model domain  
     
    311313temperature data. 
    312314 
     315\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_Conservation.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13 
    24% ================================================================ 
     
    333335not been implemented. 
    334336 
     337\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_DIA.tex

    r5602 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter I/O & Diagnostics 
    35% ================================================================ 
    4 \chapter{Ouput and Diagnostics (IOM, DIA, TRD, FLO)} 
     6\chapter{Output and Diagnostics (IOM, DIA, TRD, FLO)} 
    57\label{DIA} 
    68\minitoc 
    79 
    810\newpage 
    9 $\ $\newline    % force a new ligne 
     11$\ $\newline    % force a new line 
    1012 
    1113% ================================================================ 
     
    4850 
    4951 
    50 Since version 3.2, iomput is the NEMO output interface of choice. It has been designed to be simple to use, flexible and efficient. The two main purposes of iomput are:  
     52Since version 3.2, iomput is the NEMO output interface of choice.  
     53It has been designed to be simple to use, flexible and efficient.  
     54The two main purposes of iomput are:  
    5155\begin{enumerate} 
    5256\item The complete and flexible control of the output files through external XML files adapted by the user from standard templates.  
     
    11161120% ------------------------------------------------------------------------------------------------------------- 
    11171121\section[Tracer/Dynamics Trends (TRD)] 
    1118                   {Tracer/Dynamics Trends  (\key{trdtra}, \key{trddyn},    \\  
    1119                                                              \key{trddvor}, \key{trdmld})} 
     1122                  {Tracer/Dynamics Trends  (\ngn{namtrd})} 
    11201123\label{DIA_trd} 
    11211124 
     
    11241127%------------------------------------------------------------------------------------------------------------- 
    11251128 
    1126 When \key{trddyn} and/or \key{trddyn} CPP variables are defined, each  
    1127 trend of the dynamics and/or temperature and salinity time evolution equations  
    1128 is stored in three-dimensional arrays just after their computation ($i.e.$ at the end  
    1129 of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). Options are defined by 
    1130 \ngn{namtrd} namelist variables. These trends are then  
    1131 used in \mdl{trdmod} (see TRD directory) every \textit{nn\_trd } time-steps. 
    1132  
    1133 What is done depends on the CPP keys defined: 
     1129Each trend of the dynamics and/or temperature and salinity time evolution equations  
     1130can be send to \mdl{trddyn} and/or \mdl{trdtra} modules (see TRD directory) just after their computation  
     1131($i.e.$ at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines).  
     1132This capability is controlled by options offered in \ngn{namtrd} namelist.  
     1133Note that the output are done with xIOS, and therefore the \key{IOM} is required. 
     1134 
     1135What is done depends on the \ngn{namtrd} logical set to \textit{true}: 
    11341136\begin{description} 
    1135 \item[\key{trddyn}, \key{trdtra}] : a check of the basin averaged properties of the momentum  
    1136 and/or tracer equations is performed ;  
    1137 \item[\key{trdvor}] : a vertical summation of the moment tendencies is performed,  
    1138 then the curl is computed to obtain the barotropic vorticity tendencies which are output ; 
    1139 \item[\key{trdmld}] : output of the tracer tendencies averaged vertically   
    1140 either over the mixed layer (\np{nn\_ctls}=0),  
    1141 or       over a fixed number of model levels (\np{nn\_ctls}$>$1 provides the number of level),  
    1142 or       over a spatially varying but temporally fixed number of levels (typically the base  
    1143 of the winter mixed layer) read in \ifile{ctlsurf\_idx} (\np{nn\_ctls}=1) ; 
     1137\item[\np{ln\_glo\_trd}] : at each \np{nn\_trd} time-step a check of the basin averaged properties  
     1138of the momentum and tracer equations is performed. This also includes a check of $T^2$, $S^2$,  
     1139$\tfrac{1}{2} (u^2+v2)$, and potential energy time evolution equations properties ;  
     1140\item[\np{ln\_dyn\_trd}] : each 3D trend of the evolution of the two momentum components is output ;  
     1141\item[\np{ln\_dyn\_mxl}] : each 3D trend of the evolution of the two momentum components averaged  
     1142                           over the mixed layer is output  ;  
     1143\item[\np{ln\_vor\_trd}] : a vertical summation of the moment tendencies is performed,  
     1144                           then the curl is computed to obtain the barotropic vorticity tendencies which are output ; 
     1145\item[\np{ln\_KE\_trd}]  : each 3D trend of the Kinetic Energy equation is output ; 
     1146\item[\np{ln\_tra\_trd}] : each 3D trend of the evolution of temperature and salinity is output ; 
     1147\item[\np{ln\_tra\_mxl}] : each 2D trend of the evolution of temperature and salinity averaged  
     1148                           over the mixed layer is output ; 
    11441149\end{description} 
    1145  
    1146 The units in the output file can be changed using the \np{nn\_ucf} namelist parameter.  
    1147 For example, in case of salinity tendency the units are given by PSU/s/\np{nn\_ucf}. 
    1148 Setting \np{nn\_ucf}=86400 ($i.e.$ the number of second in a day) provides the tendencies in PSU/d. 
    1149  
    1150 When \key{trdmld} is defined, two time averaging procedure are proposed. 
    1151 Setting \np{ln\_trdmld\_instant} to \textit{true}, a simple time averaging is performed,  
    1152 so that the resulting tendency is the contribution to the change of a quantity between  
    1153 the two instantaneous values taken at the extremities of the time averaging period. 
    1154 Setting \np{ln\_trdmld\_instant} to \textit{false}, a double time averaging is performed,  
    1155 so that the resulting tendency is the contribution to the change of a quantity between  
    1156 two \textit{time mean} values. The later option requires the use of an extra file, \ifile{restart\_mld}   
    1157 (\np{ln\_trdmld\_restart}=true), to restart a run. 
    1158  
    11591150 
    11601151Note that the mixed layer tendency diagnostic can also be used on biogeochemical models  
    11611152via the \key{trdtrc} and \key{trdmld\_trc} CPP keys. 
     1153 
     1154\textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested.  
     1155In particular, options associated with \np{ln\_dyn\_mxl}, \np{ln\_vor\_trd}, and \np{ln\_tra\_mxl}  
     1156are not working, and none of the option have been tested with variable volume ($i.e.$ \key{vvl} defined). 
     1157 
    11621158 
    11631159% ------------------------------------------------------------------------------------------------------------- 
     
    12801276\label{DIA_diag_harm} 
    12811277 
    1282 A module is available to compute the amplitude and phase for tidal waves.  
    1283 This diagnostic is actived with \key{diaharm}. 
    1284  
    12851278%------------------------------------------namdia_harm---------------------------------------------------- 
    12861279\namdisplay{namdia_harm} 
    12871280%---------------------------------------------------------------------------------------------------------- 
    12881281 
    1289 Concerning the on-line Harmonic analysis, some parameters are available in namelist 
    1290 \ngn{namdia\_harm} : 
    1291  
    1292 - \texttt{nit000\_han} is the first time step used for harmonic analysis 
    1293  
    1294 - \texttt{nitend\_han} is the last time step used for harmonic analysis 
    1295  
    1296 - \texttt{nstep\_han} is the time step frequency for harmonic analysis 
    1297  
    1298 - \texttt{nb\_ana} is the number of harmonics to analyse 
    1299  
    1300 - \texttt{tname} is an array with names of tidal constituents to analyse 
    1301  
    1302 \texttt{nit000\_han} and \texttt{nitend\_han} must be between \texttt{nit000} and \texttt{nitend} of the simulation. 
     1282A module is available to compute the amplitude and phase of tidal waves.  
     1283This on-line Harmonic analysis is actived with \key{diaharm}. 
     1284Some parameters are available in namelist \ngn{namdia\_harm} : 
     1285 
     1286- \np{nit000\_han} is the first time step used for harmonic analysis 
     1287 
     1288- \np{nitend\_han} is the last time step used for harmonic analysis 
     1289 
     1290- \np{nstep\_han} is the time step frequency for harmonic analysis 
     1291 
     1292- \np{nb\_ana} is the number of harmonics to analyse 
     1293 
     1294- \np{tname} is an array with names of tidal constituents to analyse 
     1295 
     1296\np{nit000\_han} and \np{nitend\_han} must be between \np{nit000} and \np{nitend} of the simulation. 
    13031297The restart capability is not implemented. 
    13041298 
    1305 The Harmonic analysis solve this equation: 
     1299The Harmonic analysis solve the following equation: 
    13061300\begin{equation} 
    13071301h_{i} - A_{0} + \sum^{nb\_ana}_{j=1}[A_{j}cos(\nu_{j}t_{j}-\phi_{j})] = e_{i} 
     
    13241318\label{DIA_diag_dct} 
    13251319 
    1326 A module is available to compute the transport of volume, heat and salt through sections. This diagnostic 
    1327 is actived with \key{diadct}. 
     1320A module is available to compute the transport of volume, heat and salt through sections.  
     1321This diagnostic is actived with \key{diadct}. 
    13281322 
    13291323Each section is defined by the coordinates of its 2 extremities. The pathways between them are contructed 
     
    13471341%------------------------------------------------------------------------------------------------------------- 
    13481342 
    1349 \texttt{nn\_dct}: frequency of instantaneous transports computing 
    1350  
    1351 \texttt{nn\_dctwri}: frequency of writing ( mean of instantaneous transports ) 
    1352  
    1353 \texttt{nn\_debug}: debugging of the section 
     1343\np{nn\_dct}: frequency of instantaneous transports computing 
     1344 
     1345\np{nn\_dctwri}: frequency of writing ( mean of instantaneous transports ) 
     1346 
     1347\np{nn\_debug}: debugging of the section 
    13541348 
    13551349\subsubsection{ To create a binary file containing the pathway of each section } 
     
    14821476the \key{diahth} CPP key:  
    14831477 
    1484 - the mixed layer depth (based on a density criterion, \citet{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 
     1478- the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 
    14851479 
    14861480- the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) 
    14871481 
    1488 - the depth of the 20\deg C isotherm (\mdl{diahth}) 
     1482- the depth of the 20\degC isotherm (\mdl{diahth}) 
    14891483 
    14901484- the depth of the thermocline (maximum of the vertical temperature gradient) (\mdl{diahth}) 
     
    14941488\np{ln\_diaptr} to true (see the \textit{\ngn{namptr} } namelist below).   
    14951489When \np{ln\_subbas}~=~true, transports and stream function are computed  
    1496 for the Atlantic, Indian, Pacific and Indo-Pacific Oceans (defined north of 30\deg S)  
     1490for the Atlantic, Indian, Pacific and Indo-Pacific Oceans (defined north of 30\degS)  
    14971491as well as for the World Ocean. The sub-basin decomposition requires an input file  
    14981492(\ifile{subbasins}) which contains three 2D mask arrays, the Indo-Pacific mask  
     
    15041498%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    15051499\begin{figure}[!t]     \begin{center} 
    1506 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_mask_subasins.pdf} 
     1500\includegraphics[width=1.0\textwidth]{Fig_mask_subasins} 
    15071501\caption{   \label{Fig_mask_subasins} 
    15081502Decomposition of the World Ocean (here ORCA2) into sub-basin used in to compute 
     
    16901684 
    16911685 
     1686\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_DOM.tex

    r5602 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    2 % Chapter 2 Space and Time Domain (DOM) 
     4% Chapter 2 ——— Space and Time Domain (DOM) 
    35% ================================================================ 
    46\chapter{Space Domain (DOM) } 
     
    4042%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    4143\begin{figure}[!tb]    \begin{center} 
    42 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_cell.pdf} 
     44\includegraphics[width=0.90\textwidth]{Fig_cell} 
    4345\caption{ \label{Fig_cell}     
    4446Arrangement of variables. $t$ indicates scalar points where temperature,  
     
    138140and $f$-points, and its divergence defined at $t$-points: 
    139141\begin{eqnarray}  \label{Eq_DOM_curl} 
    140  \nabla \times {\rm {\bf A}}\equiv & 
     142 \nabla \times {\rm{\bf A}}\equiv & 
    141143      \frac{1}{e_{2v}\,e_{3vw} } \ \left( \delta_{j +1/2} \left[e_{3w}\,a_3 \right] -\delta_{k+1/2} \left[e_{2v} \,a_2 \right] \right)  &\ \mathbf{i} \\  
    142144 +& \frac{1}{e_{2u}\,e_{3uw}} \ \left( \delta_{k+1/2} \left[e_{1u}\,a_1  \right] -\delta_{i +1/2} \left[e_{3w}\,a_3 \right] \right)  &\ \mathbf{j} \\ 
     
    183185Let $a$ and $b$ be two fields defined on the mesh, with value zero inside  
    184186continental area. Using integration by parts it can be shown that the differencing  
    185 operators ($\delta_i$, $\delta_j$ and $\delta_k$) are anti-symmetric linear  
    186 operators, and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$,  
     187operators ($\delta_i$, $\delta_j$ and $\delta_k$) are skew-symmetric linear operators,  
     188and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$,  
    187189$\overline{\,\cdot\,}^{\,k}$ and $\overline{\,\cdot\,}^{\,k}$) are symmetric linear  
    188190operators, $i.e.$ 
     
    210212%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    211213\begin{figure}[!tb]  \begin{center} 
    212 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_index_hor.pdf} 
     214\includegraphics[width=0.90\textwidth]{Fig_index_hor} 
    213215\caption{   \label{Fig_index_hor}     
    214216Horizontal integer indexing used in the \textsc{Fortran} code. The dashed area indicates  
     
    260262%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    261263\begin{figure}[!pt]    \begin{center} 
    262 \includegraphics[width=.90\textwidth]{./TexFiles/Figures/Fig_index_vert.pdf} 
     264\includegraphics[width=.90\textwidth]{Fig_index_vert} 
    263265\caption{ \label{Fig_index_vert}      
    264266Vertical integer indexing used in the \textsc{Fortran } code. Note that  
     
    358360%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    359361\begin{figure}[!t]     \begin{center} 
    360 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_zgr_e3.pdf} 
     362\includegraphics[width=0.90\textwidth]{Fig_zgr_e3} 
    361363\caption{ \label{Fig_zgr_e3}     
    362364Comparison of (a) traditional definitions of grid-point position and grid-size in the vertical,  
     
    364366For both grids here,  the same $w$-point depth has been chosen but in (a) the  
    365367$t$-points are set half way between $w$-points while in (b) they are defined from  
    366 an analytical function: $z(k)=5\,(i-1/2)^3 - 45\,(i-1/2)^2 + 140\,(i-1/2) - 150$.  
     368an analytical function: $z(k)=5\,(k-1/2)^3 - 45\,(k-1/2)^2 + 140\,(k-1/2) - 150$.  
    367369Note the resulting difference between the value of the grid-size $\Delta_k$ and  
    368370those of the scale factor $e_k$. } 
     
    425427 
    426428The choice of the grid must be consistent with the boundary conditions specified  
    427 by the parameter \np{jperio} (see {\S\ref{LBC}). 
     429by \np{jperio}, a parameter found in \ngn{namcfg} namelist (see {\S\ref{LBC}). 
    428430 
    429431% ------------------------------------------------------------------------------------------------------------- 
     
    467469%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    468470\begin{figure}[!tb]    \begin{center} 
    469 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_z_zps_s_sps.pdf} 
     471\includegraphics[width=1.0\textwidth]{Fig_z_zps_s_sps} 
    470472\caption{  \label{Fig_z_zps_s_sps}    
    471473The ocean bottom as seen by the model:  
     
    481483%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    482484 
    483 The choice of a vertical coordinate, even if it is made through a namelist parameter,  
     485The choice of a vertical coordinate, even if it is made through \ngn{namzgr} namelist parameters,  
    484486must be done once of all at the beginning of an experiment. It is not intended as an  
    485487option which can be enabled or disabled in the middle of an experiment. Three main  
     
    494496bathymetry or $s$-coordinate (hybrid and partial step coordinates have not  
    495497yet been tested in NEMO v2.3). If using $z$-coordinate with partial step bathymetry 
    496 (\np{ln\_zps}~=~true), ocean cavity beneath ice shelves can be open (\np{ln\_isfcav}~=~true). 
     498(\np{ln\_zps}~=~true), ocean cavity beneath ice shelves can be open (\np{ln\_isfcav}~=~true)  
     499and partial step are also applied at the ocean/ice shelf interface.  
    497500 
    498501Contrary to the horizontal grid, the vertical grid is computed in the code and no  
    499502provision is made for reading it from a file. The only input file is the bathymetry  
    500 (in meters) (\ifile{bathy\_meter})  
     503(in meters) (\ifile{bathy\_meter}).  
    501504\footnote{N.B. in full step $z$-coordinate, a \ifile{bathy\_level} file can replace the  
    502505\ifile{bathy\_meter} file, so that the computation of the number of wet ocean point  
     
    540543 
    541544Three options are possible for defining the bathymetry, according to the  
    542 namelist variable \np{nn\_bathy}:  
     545namelist variable \np{nn\_bathy} (found in \ngn{namdom} namelist):  
    543546\begin{description} 
    544547\item[\np{nn\_bathy} = 0] a flat-bottom domain is defined. The total depth $z_w (jpk)$  
     
    548551domain width at the central latitude. This is meant for the "EEL-R5" configuration,  
    549552a periodic or open boundary channel with a seamount.  
    550 \item[\np{nn\_bathy} = 1] read a bathymetry. The \ifile{bathy\_meter} file (Netcdf format)  
    551 provides the ocean depth (positive, in meters) at each grid point of the model grid.  
    552 The bathymetry is usually built by interpolating a standard bathymetry product  
     553\item[\np{nn\_bathy} = 1] read a bathymetry and ice shelf draft (if needed). 
     554 The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) 
     555 at each grid point of the model grid. The bathymetry is usually built by interpolating a standard bathymetry product  
    553556($e.g.$ ETOPO2) onto the horizontal ocean mesh. Defining the bathymetry also  
    554557defines the coastline: where the bathymetry is zero, no model levels are defined  
    555558(all levels are masked). 
     559 
     560The \ifile{isfdraft\_meter} file (Netcdf format) provides the ice shelf draft (positive, in meters) 
     561 at each grid point of the model grid. This file is only needed if \np{ln\_isfcav}~=~true.  
     562Defining the ice shelf draft will also define the ice shelf edge and the grounding line position. 
    556563\end{description} 
    557564 
     
    573580%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    574581\begin{figure}[!tb]    \begin{center} 
    575 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_zgr.pdf} 
     582\includegraphics[width=0.90\textwidth]{Fig_zgr} 
    576583\caption{ \label{Fig_zgr}     
    577584Default vertical mesh for ORCA2: 30 ocean levels (L30). Vertical level functions for  
     
    610617(Fig.~\ref{Fig_zgr}). 
    611618 
     619If the ice shelf cavities are opened (\np{ln\_isfcav}=~true~}), the definition of $z_0$ is the same.  
     620However, definition of $e_3^0$ at $t$- and $w$-points is respectively changed to: 
     621\begin{equation} \label{DOM_zgr_ana} 
     622\begin{split} 
     623 e_3^T(k) &= z_W (k+1) - z_W (k)   \\ 
     624 e_3^W(k) &= z_T (k)   - z_T (k-1) \\ 
     625\end{split} 
     626\end{equation} 
     627This formulation decrease the self-generated circulation into the ice shelf cavity  
     628(which can, in extreme case, leads to blow up).\\ 
     629 
     630  
    612631The most used vertical grid for ORCA2 has $10~m$ ($500~m)$ resolution in the  
    613632surface (bottom) layers and a depth which varies from 0 at the sea surface to a  
     
    721740usually 10\%, of the default thickness $e_{3t}(jk)$). 
    722741 
    723  \colorbox{yellow}{Add a figure here of pstep especially at last ocean level } 
     742\gmcomment{ \colorbox{yellow}{Add a figure here of pstep especially at last ocean level } } 
    724743 
    725744% ------------------------------------------------------------------------------------------------------------- 
     
    785804%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    786805\begin{figure}[!ht]    \begin{center} 
    787 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_sco_function.pdf} 
     806\includegraphics[width=1.0\textwidth]{Fig_sco_function} 
    788807\caption{  \label{Fig_sco_function}    
    789808Examples of the stretching function applied to a seamount; from left to right:  
     
    825844%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    826845\begin{figure}[!ht] 
    827    \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/FIG_DOM_compare_coordinates_surface.pdf} 
     846   \includegraphics[width=1.0\textwidth]{FIG_DOM_compare_coordinates_surface} 
    828847        \caption{A comparison of the \citet{Song_Haidvogel_JCP94} $S$-coordinate (solid lines), a 50 level $Z$-coordinate (contoured surfaces) and the \citet{Siddorn_Furner_OM12} $S$-coordinate (dashed lines) in the surface 100m for a idealised bathymetry that goes from 50m to 5500m depth. For clarity every third coordinate surface is shown.} 
    829848    \label{fig_compare_coordinates_surface} 
     
    860879gives the number of ocean levels ($i.e.$ those that are not masked) at each  
    861880$t$-point. mbathy is computed from the meter bathymetry using the definiton of  
    862 gdept as the number of $t$-points which gdept $\leq$ bathy.  
     881gdept as the number of $t$-points which gdept $\leq$ bathy. 
    863882 
    864883Modifications of the model bathymetry are performed in the \textit{bat\_ctl}  
    865884routine (see \mdl{domzgr} module) after mbathy is computed. Isolated grid points  
    866 that do not communicate with another ocean point at the same level are eliminated. 
     885that do not communicate with another ocean point at the same level are eliminated.\\ 
     886 
     887As for the representation of bathymetry, a 2D integer array, misfdep, is created.  
     888misfdep defines the level of the first wet $t$-point. All the cells between $k=1$ and $misfdep(i,j)-1$ are masked.  
     889By default, misfdep(:,:)=1 and no cells are masked. 
     890 
     891In case of ice shelf cavities (\np{ln\_isfcav}~=~true), modifications of the model bathymetry and ice shelf draft in  
     892the cavities are performed through the \textit{zgr\_isf} routine. The compatibility between ice shelf draft and bathymetry is checked:  
     893if 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 have a 2-level water column  
     894(i.e. two unmasked levels). If the incompatibility is too strong (i.e. need to dig more than one cell), the entire water column is masked.\\  
    867895 
    868896From the \textit{mbathy} array, the mask fields are defined as follows: 
    869897\begin{align*} 
    870 tmask(i,j,k) &= \begin{cases}   \; 1&   \text{ if $k\leq mbathy(i,j)$  }    \\ 
    871                                                 \; 0&   \text{ if $k\leq mbathy(i,j)$  }    \end{cases}     \\ 
     898tmask(i,j,k) &= \begin{cases}   \; 0&   \text{ if $k < misfdep(i,j) $ } \\ 
     899                                \; 1&   \text{ if $misfdep(i,j) \leq k\leq mbathy(i,j)$  }    \\ 
     900                                \; 0&   \text{ if $k > mbathy(i,j)$  }    \end{cases}     \\ 
    872901umask(i,j,k) &=         \; tmask(i,j,k) \ * \ tmask(i+1,j,k)   \\ 
    873902vmask(i,j,k) &=         \; tmask(i,j,k) \ * \ tmask(i,j+1,k)   \\ 
    874903fmask(i,j,k) &=         \; tmask(i,j,k) \ * \ tmask(i+1,j,k)   \\ 
    875                    & \ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) 
     904                   & \ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 
     905wmask(i,j,k) &=         \; tmask(i,j,k) \ * \ tmask(i,j,k-1) \text{ with } wmask(i,j,1) = tmask(i,j,1)  
    876906\end{align*} 
    877907 
    878 Note that \textit{wmask} is not defined as it is exactly equal to \textit{tmask} with  
    879 the numerical indexing used (\S~\ref{DOM_Num_Index}). Moreover, the  
    880 specification of closed lateral boundaries requires that at least the first and last  
     908Note, wmask is now defined. It allows, in case of ice shelves,  
     909to deal with the top boundary (ice shelf/ocean interface) exactly in the same way as for the bottom boundary.  
     910 
     911The specification of closed lateral boundaries requires that at least the first and last  
    881912rows and columns of the \textit{mbathy} array are set to zero. In the particular  
    882913case of an east-west cyclical boundary condition, \textit{mbathy} has its last  
     
    910941(typical of the tropical ocean), see \rou{istate\_t\_s} subroutine called from \mdl{istate} module. 
    911942\end{description} 
     943\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_DYN.tex

    r5602 r7260  
    1 % ================================================================ 
    2 % Chapter � Ocean Dynamics (DYN) 
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
     3% ================================================================ 
     4% Chapter ——— Ocean Dynamics (DYN) 
    35% ================================================================ 
    46\chapter{Ocean Dynamics (DYN)} 
    57\label{DYN} 
    68\minitoc 
    7  
    8 % add a figure for  dynvor ens, ene latices 
    99 
    1010%\vspace{2.cm} 
     
    165165%------------------------------------------------------------------------------------------------------------- 
    166166 
    167 The vector invariant form of the momentum equations is the one most  
    168 often used in applications of the \NEMO ocean model. The flux form option  
    169 (see next section) has been present since version $2$. Options are defined 
    170 through the \ngn{namdyn\_adv} namelist variables 
    171 Coriolis and momentum advection terms are evaluated using a leapfrog  
    172 scheme, $i.e.$ the velocity appearing in these expressions is centred in  
    173 time (\textit{now} velocity).  
     167The vector invariant form of the momentum equations (\np{ln\_dynhpg\_vec}~=~true) is the one most  
     168often used in applications of the \NEMO ocean model. The flux form option (\np{ln\_dynhpg\_vec}~=false) 
     169(see next section) has been present since version $2$.  
     170Options are defined through the \ngn{namdyn\_adv} namelist variables. 
     171Coriolis and momentum advection terms are evaluated using a leapfrog scheme,  
     172$i.e.$ the velocity appearing in these expressions is centred in time (\textit{now} velocity).  
    174173At the lateral boundaries either free slip, no slip or partial slip boundary  
    175174conditions are applied following Chap.\ref{LBC}. 
     
    296295%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    297296\begin{figure}[!ht]    \begin{center} 
    298 \includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_DYN_een_triad.pdf} 
     297\includegraphics[width=0.70\textwidth]{Fig_DYN_een_triad} 
    299298\caption{ \label{Fig_DYN_een_triad}   
    300299Triads used in the energy and enstrophy conserving scheme (een) for  
     
    303302%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    304303 
    305 Note that a key point in \eqref{Eq_een_e3f} is that the averaging in the \textbf{i}- and  
    306 \textbf{j}- directions uses the masked vertical scale factor but is always divided by  
    307 $4$, not by the sum of the masks at the four $T$-points. This preserves the continuity of  
    308 $e_{3f}$ when one or more of the neighbouring $e_{3t}$ tends to zero and  
    309 extends by continuity the value of $e_{3f}$ into the land areas. This feature is essential for  
    310 the $z$-coordinate with partial steps. 
     304A key point in \eqref{Eq_een_e3f} is how the averaging in the \textbf{i}- and \textbf{j}- directions is made.  
     305It uses the sum of masked t-point vertical scale factor divided either  
     306by the sum of the four t-point masks (\np{ln\_dynvor\_een\_old}~=~false),  
     307or  just by $4$ (\np{ln\_dynvor\_een\_old}~=~true). 
     308The latter case preserves the continuity of $e_{3f}$ when one or more of the neighbouring $e_{3t}$  
     309tends to zero and extends by continuity the value of $e_{3f}$ into the land areas.  
     310This case introduces a sub-grid-scale topography at f-points (with a systematic reduction of $e_{3f}$  
     311when a model level intercept the bathymetry) that tends to reinforce the topostrophy of the flow  
     312($i.e.$ the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.  
    311313 
    312314Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as  
     
    374376\end{aligned}         \right. 
    375377\end{equation}  
     378When \np{ln\_dynzad\_zts}~=~\textit{true}, a split-explicit time stepping with 5 sub-timesteps is used  
     379on the vertical advection term. 
     380This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}.  
     381Note that in this case, a similar split-explicit time stepping should be used on  
     382vertical advection of tracer to ensure a better stability,  
     383an option which is only available with a TVD scheme (see \np{ln\_traadv\_tvd\_zts} in \S\ref{TRA_adv_tvd}). 
     384 
    376385 
    377386% ================================================================ 
     
    491500those in the centred second order method. As the scheme already includes  
    492501a diffusion component, it can be used without explicit  lateral diffusion on momentum  
    493 ($i.e.$ \np{ln\_dynldf\_lap}=\np{ln\_dynldf\_bilap}=false), and it is recommended to do so. 
     502($i.e.$ setting both \np{ln\_dynldf\_lap} and \np{ln\_dynldf\_bilap} to \textit{false}),  
     503and it is recommended to do so. 
    494504 
    495505The UBS scheme is not used in all directions. In the vertical, the centred $2^{nd}$  
     
    629639($e_{3w}$). 
    630640  
    631 $\bullet$ Traditional coding with adaptation for ice shelf cavities (\np{ln\_dynhpg\_isf}=true). 
    632 This scheme need the activation of ice shelf cavities (\np{ln\_isfcav}=true). 
    633  
    634641$\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}=true) 
    635642 
     
    646653pressure Jacobian method is used to solve the horizontal pressure gradient. This method can provide 
    647654a more accurate calculation of the horizontal pressure gradient than the standard scheme. 
     655 
     656\subsection{Ice shelf cavity} 
     657\label{DYN_hpg_isf} 
     658Beneath an ice shelf, the total pressure gradient is the sum of the pressure gradient due to the ice shelf load and 
     659 the pressure gradient due to the ocean load. If cavities are present (\np{ln\_isfcav}~=~true) these two terms can be 
     660 calculated by setting \np{ln\_dynhpg\_isf}~=~true. No other scheme is working with ice shelves.\\ 
     661 
     662$\bullet$ The main hypothesis to compute the ice shelf load is that the ice shelf is in isostatic equilibrium. 
     663 The top pressure is computed integrating a reference density profile (prescribed as density of a water at 34.4  
     664PSU and -1.9$^{\circ}C$) from the sea surface to the ice shelf base, which corresponds to the load of the water 
     665column in which the ice shelf is floatting. This top pressure is constant over time. A detailed description of  
     666this method is described in \citet{Losch2008}.\\ 
     667 
     668$\bullet$ The ocean load is computed using the expression \eqref{Eq_dynhpg_sco} described in \ref{DYN_hpg_sco}.  
     669A treatment of the top and bottom partial cells similar to the one described in \ref{DYN_hpg_zps} is done  
     670to reduce the residual circulation generated by the top partial cell.  
    648671 
    649672%-------------------------------------------------------------------------------------------------------------- 
     
    718741$\ $\newline      %force an empty line 
    719742 
    720 %%% 
    721743Options are defined through the \ngn{namdyn\_spg} namelist variables. 
    722 The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}). The main distinction is between the fixed volume case (linear free surface) and the variable volume case (nonlinear free surface, \key{vvl} is defined). In the linear free surface case (\S\ref{PE_free_surface}) the vertical scale factors $e_{3}$ are fixed in time, while they are time-dependent in the nonlinear case (\S\ref{PE_free_surface}). With both linear and nonlinear free surface, external gravity waves are allowed in the equations, which imposes a very small time step when an explicit time stepping is used. Two methods are proposed to allow a longer time step for the three-dimensional equations: the filtered free surface, which is a modification of the continuous equations (see \eqref{Eq_PE_flt}), and the split-explicit free surface described below. The extra term introduced in the filtered method is calculated implicitly, so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 
    723  
    724 %%% 
     744The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}).  
     745The main distinction is between the fixed volume case (linear free surface) and the variable volume case  
     746(nonlinear free surface, \key{vvl} is defined). In the linear free surface case (\S\ref{PE_free_surface})  
     747the vertical scale factors $e_{3}$ are fixed in time, while they are time-dependent in the nonlinear case  
     748(\S\ref{PE_free_surface}).  
     749With both linear and nonlinear free surface, external gravity waves are allowed in the equations,  
     750which imposes a very small time step when an explicit time stepping is used.  
     751Two methods are proposed to allow a longer time step for the three-dimensional equations:  
     752the filtered free surface, which is a modification of the continuous equations (see \eqref{Eq_PE_flt}),  
     753and the split-explicit free surface described below.  
     754The extra term introduced in the filtered method is calculated implicitly,  
     755so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 
    725756 
    726757 
     
    736767implicitly, so that a solver is used to compute it. As a consequence the update of the $next$  
    737768velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 
    738  
    739769 
    740770 
     
    779809$\rdt_e = \rdt / nn\_baro$. This parameter can be optionally defined automatically (\np{ln\_bt\_nn\_auto}=true)  
    780810considering that the stability of the barotropic system is essentially controled by external waves propagation.  
    781 Maximum allowed Courant number is in that case time independent, and easily computed online from the input bathymetry. 
     811Maximum Courant number is in that case time independent, and easily computed online from the input bathymetry. 
     812Therefore, $\rdt_e$ is adjusted so that the Maximum allowed Courant number is smaller than \np{rn\_bt\_cmax}. 
    782813 
    783814%%% 
     
    798829%>   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   > 
    799830\begin{figure}[!t]    \begin{center} 
    800 \includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_DYN_dynspg_ts.pdf} 
     831\includegraphics[width=0.7\textwidth]{Fig_DYN_dynspg_ts} 
    801832\caption{  \label{Fig_DYN_dynspg_ts} 
    802833Schematic of the split-explicit time stepping scheme for the external  
    803834and internal modes. Time increases to the right. In this particular exemple,  
    804 a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_filt=1$) and $nn\_baro=5$. 
     835a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_flt=1$) and $nn\_baro=5$. 
    805836Internal mode time steps (which are also the model time steps) are denoted  
    806837by $t-\rdt$, $t$ and $t+\rdt$. Variables with $k$ superscript refer to instantaneous barotropic variables,  
     
    808839The former are used to obtain time filtered quantities at $t+\rdt$ while the latter are used to obtain time averaged  
    809840transports to advect tracers. 
    810 a) Forward time integration: \np{ln\_bt\_fw}=true, \np{ln\_bt\_ave}=true.  
    811 b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_ave}=true.  
    812 c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_ave}=false. } 
     841a) Forward time integration: \np{ln\_bt\_fw}=true, \np{ln\_bt\_av}=true.  
     842b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_av}=true.  
     843c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_av}=false. } 
    813844\end{center}    \end{figure} 
    814845%>   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   > 
     
    816847In the default case (\np{ln\_bt\_fw}=true), the external mode is integrated  
    817848between \textit{now} and  \textit{after} baroclinic time-steps (Fig.~\ref{Fig_DYN_dynspg_ts}a). To avoid aliasing of fast barotropic motions into three dimensional equations, time filtering is eventually applied on barotropic  
    818 quantities (\np{ln\_bt\_ave}=true). In that case, the integration is extended slightly beyond  \textit{after} time step to provide time filtered quantities.  
     849quantities (\np{ln\_bt\_av}=true). In that case, the integration is extended slightly beyond  \textit{after} time step to provide time filtered quantities.  
    819850These are used for the subsequent initialization of the barotropic mode in the following baroclinic step.  
    820851Since external mode equations written at baroclinic time steps finally follow a forward time stepping scheme,  
     
    837868%%% 
    838869 
    839 One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_ave}=false).  
     870One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_av}=false).  
    840871In that case, external mode equations are continuous in time, ie they are not re-initialized when starting a new  
    841872sub-stepping sequence. This is the method used so far in the POM model, the stability being maintained by refreshing at (almost)  
     
    11581189 
    11591190Besides the surface and bottom stresses (see the above section) which are  
    1160 introduced as boundary conditions on the vertical mixing, two other forcings  
    1161 enter the dynamical equations.  
    1162  
    1163 One is the effect of atmospheric pressure on the ocean dynamics. 
    1164 Another forcing term is the tidal potential. 
    1165 Both of which will be introduced into the reference version soon.  
    1166  
    1167 \gmcomment{atmospheric pressure is there!!!!    include its description } 
     1191introduced as boundary conditions on the vertical mixing, three other forcings  
     1192may enter the dynamical equations by affecting the surface pressure gradient.  
     1193 
     1194(1) When \np{ln\_apr\_dyn}~=~true (see \S\ref{SBC_apr}), the atmospheric pressure is taken  
     1195into account when computing the surface pressure gradient. 
     1196 
     1197(2) When \np{ln\_tide\_pot}~=~true and \key{tide} is defined (see \S\ref{SBC_tide}),  
     1198the tidal potential is taken into account when computing the surface pressure gradient. 
     1199 
     1200(3) When \np{nn\_ice\_embd}~=~2 and LIM or CICE is used ($i.e.$ when the sea-ice is embedded in the ocean),  
     1201the snow-ice mass is taken into account when computing the surface pressure gradient. 
     1202 
     1203 
     1204\gmcomment{ missing : the lateral boundary condition !!!   another external forcing 
     1205 } 
    11681206 
    11691207% ================================================================ 
     
    12961334 
    12971335% ================================================================ 
     1336\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_LBC.tex

    r4147 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    2 % Chapter Lateral Boundary Condition (LBC)  
     4% Chapter Lateral Boundary Condition (LBC)  
    35% ================================================================ 
    46\chapter{Lateral Boundary Condition (LBC) } 
     
    5355%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    5456\begin{figure}[!t]     \begin{center} 
    55 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_LBC_uv.pdf} 
     57\includegraphics[width=0.90\textwidth]{Fig_LBC_uv} 
    5658\caption{  \label{Fig_LBC_uv} 
    5759Lateral boundary (thick line) at T-level. The velocity normal to the boundary is set to zero.} 
     
    7678%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    7779\begin{figure}[!p] \begin{center} 
    78 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_LBC_shlat.pdf} 
     80\includegraphics[width=0.90\textwidth]{Fig_LBC_shlat} 
    7981\caption{     \label{Fig_LBC_shlat}  
    8082lateral boundary condition (a) free-slip ($rn\_shlat=0$) ; (b) no-slip ($rn\_shlat=2$)  
     
    195197%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    196198\begin{figure}[!t]     \begin{center} 
    197 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_LBC_jperio.pdf} 
     199\includegraphics[width=1.0\textwidth]{Fig_LBC_jperio} 
    198200\caption{    \label{Fig_LBC_jperio} 
    199201setting of (a) east-west cyclic  (b) symmetric across the equator boundary conditions.} 
     
    204206%        North fold (\textit{jperio = 3 }to $6)$  
    205207% ------------------------------------------------------------------------------------------------------------- 
    206 \subsection{North-fold (\textit{jperio = 3 }to $6)$ } 
     208\subsection{North-fold (\textit{jperio = 3 }to $6$) } 
    207209\label{LBC_north_fold} 
    208210 
    209211The north fold boundary condition has been introduced in order to handle the north  
    210 boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere.  
    211 \colorbox{yellow}{to be completed...} 
     212boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere  
     213(Fig.\ref{Fig_MISC_ORCA_msh}, and thus requires a specific treatment illustrated in Fig.\ref{Fig_North_Fold_T}.  
     214Further information can be found in \mdl{lbcnfd} module which applies the north fold boundary condition. 
    212215 
    213216%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    214217\begin{figure}[!t]    \begin{center} 
    215 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_North_Fold_T.pdf} 
     218\includegraphics[width=0.90\textwidth]{Fig_North_Fold_T} 
    216219\caption{    \label{Fig_North_Fold_T}  
    217220North fold boundary with a $T$-point pivot and cyclic east-west boundary condition  
     
    250253ocean model. Second order finite difference schemes lead to local discrete  
    251254operators that depend at the very most on one neighbouring point. The only  
    252 non-local computations concern the vertical physics (implicit diffusion, 1.5  
     255non-local computations concern the vertical physics (implicit diffusion,  
    253256turbulent closure scheme, ...) (delocalization over the whole water column),  
    254257and the solving of the elliptic equation associated with the surface pressure  
    255258gradient computation (delocalization over the whole horizontal domain).  
    256259Therefore, a pencil strategy is used for the data sub-structuration  
    257 \gmcomment{no idea what this means!} 
    258260: the 3D initial domain is laid out on local processor  
    259261memories following a 2D horizontal topological splitting. Each sub-domain  
     
    264266phase starts: each processor sends to its neighbouring processors the update  
    265267values of the points corresponding to the interior overlapping area to its  
    266 neighbouring sub-domain (i.e. the innermost of the two overlapping rows).  
    267 The communication is done through message passing. Usually the parallel virtual  
    268 language, PVM, is used as it is a standard language available on  nearly  all  
    269 MPP computers. More specific languages (i.e. computer dependant languages)  
    270 can be easily used to speed up the communication, such as SHEM on a T3E  
    271 computer. The data exchanges between processors are required at the very  
     268neighbouring sub-domain ($i.e.$ the innermost of the two overlapping rows).  
     269The communication is done through the Message Passing Interface (MPI).  
     270The data exchanges between processors are required at the very  
    272271place where lateral domain boundary conditions are set in the mono-domain  
    273 computation (\S III.10-c): the lbc\_lnk routine which manages such conditions  
    274 is substituted by mpplnk.F or mpplnk2.F routine when running on an MPP  
    275 computer (\key{mpp\_mpi} defined). It has to be pointed out that when using  
    276 the MPP version of the model, the east-west cyclic boundary condition is done  
    277 implicitly, whilst the south-symmetric boundary condition option is not available. 
     272computation : the \rou{lbc\_lnk} routine (found in \mdl{lbclnk} module)  
     273which manages such conditions is interfaced with routines found in \mdl{lib\_mpp} module  
     274when running on an MPP computer ($i.e.$ when \key{mpp\_mpi} defined).  
     275It has to be pointed out that when using the MPP version of the model,  
     276the east-west cyclic boundary condition is done implicitly,  
     277whilst the south-symmetric boundary condition option is not available. 
    278278 
    279279%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    280280\begin{figure}[!t]    \begin{center} 
    281 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_mpp.pdf} 
     281\includegraphics[width=0.90\textwidth]{Fig_mpp} 
    282282\caption{   \label{Fig_mpp}  
    283283Positioning of a sub-domain when massively parallel processing is used. } 
     
    285285%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    286286 
    287 In the standard version of the OPA model, the splitting is regular and arithmetic. 
    288  the i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors  
    289  \jp{jpnij} most often equal to $jpni \times jpnj$ (model parameters set in  
    290  \mdl{par\_oce}). Each processor is independent and without message passing  
    291  or synchronous process  
    292  \gmcomment{how does a synchronous process relate to this?},  
    293  programs run alone and access just its own local memory. For this reason, the  
    294  main model dimensions are now the local dimensions of the subdomain (pencil)  
     287In the standard version of \NEMO, the splitting is regular and arithmetic. 
     288The i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors  
     289\jp{jpnij} most often equal to $jpni \times jpnj$ (parameters set in  
     290 \ngn{nammpp} namelist). Each processor is independent and without message passing  
     291 or synchronous process, programs run alone and access just its own local memory.  
     292 For this reason, the main model dimensions are now the local dimensions of the subdomain (pencil)  
    295293 that are named \jp{jpi}, \jp{jpj}, \jp{jpk}. These dimensions include the internal  
    296294 domain and the overlapping rows. The number of rows to exchange (known as  
     
    304302where \jp{jpni}, \jp{jpnj} are the number of processors following the i- and j-axis. 
    305303 
    306 \colorbox{yellow}{Figure IV.3: example of a domain splitting with 9 processors and  
    307 no east-west cyclic boundary conditions.} 
    308  
    309 One also defines variables nldi and nlei which correspond to the internal  
    310 domain bounds, and the variables nimpp and njmpp which are the position  
    311 of the (1,1) grid-point in the global domain. An element of $T_{l}$, a local array  
    312 (subdomain) corresponds to an element of $T_{g}$, a global array  
    313 (whole domain) by the relationship:  
     304One also defines variables nldi and nlei which correspond to the internal domain bounds,  
     305and the variables nimpp and njmpp which are the position of the (1,1) grid-point in the global domain.  
     306An element of $T_{l}$, a local array (subdomain) corresponds to an element of $T_{g}$,  
     307a global array (whole domain) by the relationship:  
    314308\begin{equation} \label{Eq_lbc_nimpp} 
    315309T_{g} (i+nimpp-1,j+njmpp-1,k) = T_{l} (i,j,k), 
     
    320314nproc. In the standard version, a processor has no more than four neighbouring  
    321315processors named nono (for north), noea (east), noso (south) and nowe (west)  
    322 and two variables, nbondi and nbondj, indicate the relative position of the processor  
    323 \colorbox{yellow}{(see Fig.IV.3)}: 
     316and two variables, nbondi and nbondj, indicate the relative position of the processor : 
    324317\begin{itemize} 
    325318\item       nbondi = -1    an east neighbour, no west processor, 
     
    332325processor on its overlapping row, and sends the data issued from internal  
    333326domain corresponding to the overlapping row of the other processor. 
    334         
    335 \colorbox{yellow}{Figure IV.4: pencil splitting with the additional outer halos } 
    336327 
    337328 
     
    343334global ocean where more than 50 \% of points are land points. For this reason, a  
    344335pre-processing tool can be used to choose the mpp domain decomposition with a  
    345 maximum number of only land points processors, which can then be eliminated.  
    346 (For example, the mpp\_optimiz tools, available from the DRAKKAR web site.)  
     336maximum number of only land points processors, which can then be eliminated (Fig. \ref{Fig_mppini2}) 
     337(For example, the mpp\_optimiz tools, available from the DRAKKAR web site).  
    347338This optimisation is dependent on the specific bathymetry employed. The user  
    348339then chooses optimal parameters \jp{jpni}, \jp{jpnj} and \jp{jpnij} with  
    349340$jpnij < jpni \times jpnj$, leading to the elimination of $jpni \times jpnj - jpnij$  
    350 land processors. When those parameters are specified in module \mdl{par\_oce},  
     341land processors. When those parameters are specified in \ngn{nammpp} namelist,  
    351342the algorithm in the \rou{inimpp2} routine sets each processor's parameters (nbound,  
    352343nono, noea,...) so that the land-only processors are not taken into account.  
    353344 
    354 \colorbox{yellow}{Note that the inimpp2 routine is general so that the original inimpp  
     345\gmcomment{Note that the inimpp2 routine is general so that the original inimpp  
    355346routine should be suppressed from the code.} 
    356347 
    357348When land processors are eliminated, the value corresponding to these locations in  
    358 the model output files is zero. Note that this is a problem for a mesh output file written  
    359 by such a model configuration, because model users often divide by the scale factors  
    360 ($e1t$, $e2t$, etc) and do not expect the grid size to be zero, even on land. It may be  
    361 best not to eliminate land processors when running the model especially to write the  
    362 mesh files as outputs (when \np{nn\_msh} namelist parameter differs from 0). 
    363 %% 
    364 \gmcomment{Steven : dont understand this, no land processor means no output file  
    365 covering this part of globe; its only when files are stitched together into one that you  
    366 can leave a hole} 
    367 %% 
     349the model output files is undefined. Note that this is a problem for the meshmask file  
     350which requires to be defined over the whole domain. Therefore, user should not eliminate  
     351land processors when creating a meshmask file ($i.e.$ when setting a non-zero value to \np{nn\_msh}). 
    368352 
    369353%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    370354\begin{figure}[!ht]     \begin{center} 
    371 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_mppini2.pdf} 
     355\includegraphics[width=0.90\textwidth]{Fig_mppini2} 
    372356\caption {    \label{Fig_mppini2} 
    373357Example of Atlantic domain defined for the CLIPPER projet. Initial grid is  
     
    380364%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    381365 
    382  
    383 % ================================================================ 
    384 % Open Boundary Conditions  
    385 % ================================================================ 
    386 \section{Open Boundary Conditions (\key{obc}) (OBC)} 
    387 \label{LBC_obc} 
    388 %-----------------------------------------nam_obc  ------------------------------------------- 
    389 %-    nobc_dta    =    0     !  = 0 the obc data are equal to the initial state 
    390 %-                           !  = 1 the obc data are read in 'obc   .dta' files 
    391 %-    rn_dpein      =    1.    !  ??? 
    392 %-    rn_dpwin      =    1.    !  ??? 
    393 %-    rn_dpnin      =   30.    !  ??? 
    394 %-    rn_dpsin      =    1.    !  ??? 
    395 %-    rn_dpeob      = 1500.    !  time relaxation (days) for the east  open boundary 
    396 %-    rn_dpwob      =   15.    !    "        "           for the west  open boundary 
    397 %-    rn_dpnob      =  150.    !    "        "           for the north open boundary 
    398 %-    rn_dpsob      =   15.    !    "        "           for the south open boundary 
    399 %-    ln_obc_clim = .true.   !  climatological obc data files (default T) 
    400 %-    ln_vol_cst  = .true.   !  total volume conserved 
    401 \namdisplay{namobc}  
    402  
    403 It is often necessary to implement a model configuration limited to an oceanic  
    404 region or a basin, which communicates with the rest of the global ocean through  
    405 ''open boundaries''. As stated by \citet{Roed1986}, an open boundary is a  
    406 computational border where the aim of the calculations is to allow the perturbations  
    407 generated inside the computational domain to leave it without deterioration of the  
    408 inner model solution. However, an open boundary also has to let information from  
    409 the outer ocean enter the model and should support inflow and outflow conditions.  
    410  
    411 The open boundary package OBC is the first open boundary option developed in  
    412 NEMO (originally in OPA8.2). It allows the user to  
    413 \begin{itemize} 
    414 \item tell the model that a boundary is ''open'' and not closed by a wall, for example  
    415 by modifying the calculation of the divergence of velocity there; 
    416 \item impose values of tracers and velocities at that boundary (values which may  
    417 be taken from a climatology): this is the``fixed OBC'' option.  
    418 \item calculate boundary values by a sophisticated algorithm combining radiation  
    419 and relaxation (``radiative OBC'' option) 
    420 \end{itemize} 
    421  
    422 Options are defined through the \ngn{namobc} namelist variables. 
    423 The package resides in the OBC directory. It is described here in four parts: the  
    424 boundary geometry (parameters to be set in \mdl{obc\_par}), the forcing data at  
    425 the boundaries (module \mdl{obcdta}),  the radiation algorithm involving the  
    426 namelist and module \mdl{obcrad}, and a brief presentation of boundary update  
    427 and restart files. 
    428  
    429 %---------------------------------------------- 
    430 \subsection{Boundary geometry} 
    431 \label{OBC_geom} 
    432 % 
    433 First one has to realize that open boundaries may not necessarily be located  
    434 at the extremities of the computational domain. They may exist in the middle  
    435 of the domain, for example at Gibraltar Straits if one wants to avoid including  
    436 the Mediterranean in an Atlantic domain. This flexibility has been found necessary  
    437 for the CLIPPER project \citep{Treguier_al_JGR01}. Because of the complexity of the  
    438 geometry of ocean basins, it may even be necessary to have more than one  
    439 ''west'' open boundary, more than one ''north'', etc. This is not possible with  
    440 the OBC option: only one open boundary of each kind, west, east, south and  
    441 north is allowed; these names refer to the grid geometry (not to the direction  
    442 of the geographical ''west'', ''east'', etc). 
    443  
    444 The open boundary geometry is set by a series of parameters in the module  
    445 \mdl{obc\_par}. For an eastern open boundary, parameters are \jp{lp\_obc\_east}  
    446 (true if an east open boundary exists), \jp{jpieob} the $i$-index along which  
    447 the eastern open boundary (eob) is located, \jp{jpjed} the $j$-index at which  
    448 it starts, and \jp{jpjef} the $j$-index where it ends (note $d$ is for ''d\'{e}but''  
    449 and $f$ for ''fin'' in French). Similar parameters exist for the west, south and  
    450 north cases (Table~\ref{Tab_obc_param}). 
    451  
    452  
    453 %--------------------------------------------------TABLE-------------------------------------------------- 
    454 \begin{table}[htbp]     \begin{center}    \begin{tabular}{|l|c|c|c|} 
    455 \hline 
    456 Boundary and  & Constant index  & Starting index (d\'{e}but) & Ending index (fin) \\ 
    457 Logical flag  &                 &                            &                     \\ 
    458 \hline 
    459 West          & \jp{jpiwob} $>= 2$         &  \jp{jpjwd}$>= 2$          &  \jp{jpjwf}<= \np{jpjglo}-1 \\ 
    460 lp\_obc\_west & $i$-index of a $u$ point   & $j$ of a $T$ point   &$j$ of a $T$ point \\ 
    461 \hline 
    462 East            & \jp{jpieob}$<=$\np{jpiglo}-2&\jp{jpjed} $>= 2$         & \jp{jpjef}$<=$ \np{jpjglo}-1 \\ 
    463  lp\_obc\_east  & $i$-index of a $u$ point    & $j$ of a $T$ point & $j$ of a $T$ point \\ 
    464 \hline 
    465 South           & \jp{jpjsob} $>= 2$         & \jp{jpisd} $>= 2$          & \jp{jpisf}$<=$\np{jpiglo}-1 \\ 
    466 lp\_obc\_south  & $j$-index of a $v$ point   & $i$ of a $T$ point   & $i$ of a $T$ point \\ 
    467 \hline 
    468 North           & \jp{jpjnob} $<=$ \np{jpjglo}-2& \jp{jpind} $>= 2$        & \jp{jpinf}$<=$\np{jpiglo}-1 \\ 
    469 lp\_obc\_north  & $j$-index of a $v$ point      & $i$  of a $T$ point & $i$ of a $T$ point \\ 
    470 \hline 
    471 \end{tabular}    \end{center} 
    472 \caption{     \label{Tab_obc_param} 
    473 Names of different indices relating to the open boundaries. In the case  
    474 of a completely open ocean domain with four ocean boundaries, the parameters  
    475 take exactly the values indicated.} 
    476 \end{table} 
    477 %------------------------------------------------------------------------------------------------------------ 
    478  
    479 The open boundaries must be along coordinate lines. On the C-grid, the boundary  
    480 itself is along a line of normal velocity points: $v$ points for a zonal open boundary  
    481 (the south or north one), and $u$ points for a meridional open boundary (the west  
    482 or east one). Another constraint is that there still must be a row of masked points  
    483 all around the domain, as if the domain were a closed basin (unless periodic conditions  
    484 are used together with open boundary conditions). Therefore, an open boundary  
    485 cannot be located at the first/last index, namely, 1, \jp{jpiglo} or \jp{jpjglo}. Also,  
    486 the open boundary algorithm involves calculating the normal velocity points situated  
    487 just on the boundary, as well as the tangential velocity and temperature and salinity  
    488 just outside the boundary. This means that for a west/south boundary, normal  
    489 velocities and temperature are calculated at the same index \jp{jpiwob} and  
    490 \jp{jpjsob}, respectively. For an east/north boundary, the normal velocity is  
    491 calculated at index \jp{jpieob} and \jp{jpjnob}, but the ``outside'' temperature is  
    492 at index \jp{jpieob}+1 and \jp{jpjnob}+1. This means that \jp{jpieob}, \jp{jpjnob}  
    493 cannot be bigger than \jp{jpiglo}-2, \jp{jpjglo}-2.  
    494  
    495  
    496 The starting and ending indices are to be thought of as $T$ point indices: in many  
    497 cases they indicate the first land $T$-point, at the extremity of an open boundary  
    498 (the coast line follows the $f$ grid points, see Fig.~\ref{Fig_obc_north} for an example  
    499 of a northern open boundary). All indices are relative to the global domain. In the  
    500 free surface case it is possible to have ``ocean corners'', that is, an open boundary  
    501 starting and ending in the ocean. 
    502  
    503 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    504 \begin{figure}[!t]     \begin{center} 
    505 \includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_obc_north.pdf} 
    506 \caption{    \label{Fig_obc_north} 
    507 Localization of the North open boundary points.} 
    508 \end{center}     \end{figure} 
    509 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    510  
    511 Although not compulsory, it is highly recommended that the bathymetry in the  
    512 vicinity of an open boundary follows the following rule: in the direction perpendicular  
    513 to the open line, the water depth should be constant for 4 grid points. This is in  
    514 order to ensure that the radiation condition, which involves model variables next  
    515 to the boundary, is calculated in a consistent way. On Fig.\ref{Fig_obc_north} we  
    516 indicate by an $=$ symbol, the points which should have the same depth. It means  
    517 that at the 4 points near the boundary, the bathymetry is cylindrical \gmcomment{not sure  
    518 why cylindrical}. The line behind the open $T$-line must be 0 in the bathymetry file  
    519 (as shown on Fig.\ref{Fig_obc_north} for example). 
    520  
    521 %---------------------------------------------- 
    522 \subsection{Boundary data} 
    523 \label{OBC_data} 
    524  
    525 It is necessary to provide information at the boundaries. The simplest case is  
    526 when this information does not change in time and is equal to the initial conditions  
    527 (namelist variable \np{nn\_obcdta}=0). This is the case for the standard configuration  
    528 EEL5 with open boundaries. When (\np{nn\_obcdta}=1), open boundary information  
    529 is read from netcdf files. For convenience the input files are supposed to be similar  
    530 to the ''history'' NEMO output files, for dimension names and variable names.  
    531 Open boundary arrays must be dimensioned according to the parameters of table~ 
    532 \ref{Tab_obc_param}: for example, at the western boundary, arrays have a  
    533 dimension of \jp{jpwf}-\jp{jpwd}+1 in the horizontal and \jp{jpk} in the vertical.  
    534  
    535 When ocean observations are used to generate the boundary data (a hydrographic  
    536 section for example, as in \citet{Treguier_al_JGR01}) it happens often that only the velocity  
    537 normal to the boundary is known, which is the reason why the initial OBC code  
    538 assumes that only $T$, $S$, and the normal velocity ($u$ or $v$) needs to be  
    539 specified. As more and more global model solutions and ocean analysis products  
    540 become available, it will be possible to provide information about all the variables  
    541 (including the tangential velocity) so that the specification of four variables at each  
    542 boundaries will become standard. For the sea surface height, one must distinguish  
    543 between the filtered free surface case and the time-splitting or explicit treatment of  
    544 the free surface. 
    545  In the first case, it is assumed that the user does not wish to represent high  
    546  frequency motions such as tides. The boundary condition is thus one of zero  
    547  normal gradient of sea surface height at the open boundaries, following \citet{Marchesiello2001}.  
    548 No information other than the total velocity needs to be provided at the open  
    549 boundaries in that case. In the other two cases (time splitting or explicit free surface),  
    550 the user must provide barotropic information (sea surface height and barotropic  
    551 velocities) and the use of the Flather algorithm for barotropic variables is  
    552 recommanded. However, this algorithm has not yet been fully tested and bugs  
    553 remain in NEMO v2.3. Users should read the code carefully before using it. Finally,  
    554 in the case of the rigid lid approximation the barotropic streamfunction must be  
    555 provided, as documented in \citet{Treguier_al_JGR01}). This option is no longer  
    556 recommended but remains in NEMO V2.3. 
    557  
    558 One frequently encountered case is when an open boundary domain is constructed  
    559 from a global or larger scale NEMO configuration. Assuming the domain corresponds  
    560 to indices $ib:ie$, $jb:je$ of the global domain, the bathymetry and forcing of the  
    561 small domain can be created by using the following netcdf utility on the global files:  
    562 ncks -F $-d\;x,ib,ie$ $-d\;y,jb,je$ (part of the nco series of utilities,  
    563 see their \href{http://nco.sourceforge.net}{website}).  
    564 The open boundary files can be constructed using ncks  
    565 commands, following table~\ref{Tab_obc_ind}.  
    566  
    567 %--------------------------------------------------TABLE-------------------------------------------------- 
    568 \begin{table}[htbp]     \begin{center}      \begin{tabular}{|l|c|c|c|c|c|} 
    569 \hline 
    570 OBC  & Variable   & file name      & Index  & Start  & end  \\ 
    571 West &  T,S       &   obcwest\_TS.nc &  $ib$+1     &   $jb$+1 &  $je-1$  \\ 
    572      &    U       &   obcwest\_U.nc  &  $ib$+1     &   $jb$+1 &  $je-1$  \\  
    573      &    V       &   obcwest\_V.nc  &  $ib$+1     &   $jb$+1 &  $je-1$  \\        
    574 \hline 
    575 East &  T,S       &   obceast\_TS.nc &  $ie$-1     &   $jb$+1 &  $je-1$  \\ 
    576      &    U       &   obceast\_U.nc  &  $ie$-2     &   $jb$+1 &  $je-1$  \\  
    577      &    V       &   obceast\_V.nc  &  $ie$-1     &   $jb$+1 &  $je-1$  \\        
    578 \hline          
    579 South &  T,S      &   obcsouth\_TS.nc &  $jb$+1     &  $ib$+1 &  $ie-1$  \\ 
    580       &    U      &   obcsouth\_U.nc  &  $jb$+1     &  $ib$+1 &  $ie-1$  \\  
    581       &    V      &   obcsouth\_V.nc  &  $jb$+1     &  $ib$+1 &  $ie-1$  \\     
    582 \hline 
    583 North &  T,S      &   obcnorth\_TS.nc &  $je$-1     &  $ib$+1 &  $ie-1$  \\ 
    584       &    U      &   obcnorth\_U.nc  &  $je$-1     &  $ib$+1 &  $ie-1$  \\  
    585       &    V      &   obcnorth\_V.nc  &  $je$-2     &  $ib$+1 &  $ie-1$  \\   
    586 \hline 
    587 \end{tabular}     \end{center} 
    588 \caption{    \label{Tab_obc_ind} 
    589 Requirements for creating open boundary files from a global configuration,  
    590 appropriate for the subdomain of indices $ib:ie$, $jb:je$. ``Index'' designates the  
    591 $i$ or $j$ index along which the $u$ of $v$ boundary point is situated in the global  
    592 configuration, starting and ending with the $j$ or $i$ indices indicated.  
    593 For example, to generate file obcnorth\_V.nc, use the command ncks  
    594 $-F$ $-d\;y,je-2$  $-d\;x,ib+1,ie-1$ }  
    595 \end{table} 
    596 %----------------------------------------------------------------------------------------------------------- 
    597  
    598 It is assumed that the open boundary files contain the variables for the period of  
    599 the model integration. If the boundary files contain one time frame, the boundary  
    600 data is held fixed in time. If the files contain 12 values, it is assumed that the input  
    601 is a climatology for a repeated annual cycle (corresponding to the case \np{ln\_obc\_clim}  
    602 =true). The case of an arbitrary number of time frames is not yet implemented  
    603 correctly; the user is required to write his own code in the module \mdl{obc\_dta}  
    604 to deal with this situation.  
    605  
    606 \subsection{Radiation algorithm} 
    607 \label{OBC_rad} 
    608  
    609 The art of open boundary management consists in applying a constraint strong  
    610 enough that the inner domain "feels" the rest of the ocean, but weak enough 
    611 that perturbations are allowed to leave the domain with minimum false reflections  
    612 of energy. The constraints are specified separately at each boundary as time  
    613 scales for ''inflow'' and ''outflow'' as defined below. The time scales are set (in days)  
    614 by namelist parameters such as \np{rn\_dpein}, \np{rn\_dpeob} for the eastern open  
    615 boundary for example. When both time scales are zero for a given boundary  
    616 ($e.g.$ for the western boundary, \jp{lp\_obc\_west}=true, \np{rn\_dpwob}=0 and  
    617 \np{rn\_dpwin}=0) this means that the boundary in question is a ''fixed '' boundary  
    618 where the solution is set exactly by the boundary data. This is not recommended,  
    619 except in combination with increased viscosity in a ''sponge'' layer next to the  
    620 boundary in order to avoid spurious reflections.   
    621  
    622  
    623 The radiation\/relaxation \gmcomment{the / doesnt seem to appear in the output}  
    624 algorithm is applied when either relaxation time (for ''inflow'' or ''outflow'') is  
    625 non-zero. It has been developed and tested in the SPEM model and its  
    626 successor ROMS \citep{Barnier1996, Marchesiello2001}, which is an  
    627 $s$-coordinate model on an Arakawa C-grid. Although the algorithm has  
    628 been numerically successful in the CLIPPER Atlantic models, the physics  
    629 do not work as expected \citep{Treguier_al_JGR01}. Users are invited to consider  
    630 open boundary conditions (OBC hereafter) with some scepticism  
    631 \citep{Durran2001, Blayo2005}. 
    632  
    633 The first part of the algorithm calculates a phase velocity to determine  
    634 whether perturbations tend to propagate toward, or away from, the  
    635 boundary. Let us consider a model variable $\phi$.  
    636 The phase velocities ($C_{\phi x}$,$C_{\phi y}$) for the variable $\phi$,  
    637 in the directions normal and tangential to the boundary are 
    638 \begin{equation} \label{Eq_obc_cphi} 
    639 C_{\phi x} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{x}  
    640 \;\;\;\;\; \;\;\;  
    641 C_{\phi y} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{y}.  
    642 \end{equation} 
    643 Following \citet{Treguier_al_JGR01} and \citet{Marchesiello2001} we retain only  
    644 the normal component of the velocity, $C_{\phi x}$, setting $C_{\phi y} =0$  
    645 (but unlike the original Orlanski radiation algorithm we retain $\phi_{y}$ in  
    646 the expression for $C_{\phi x}$).   
    647  
    648 The discrete form of (\ref{Eq_obc_cphi}), described by \citet{Barnier1998}, 
    649 takes into account the two rows of grid points situated inside the domain  
    650 next to the boundary, and the three previous time steps ($n$, $n-1$, 
    651 and $n-2$). The same equation can then be discretized at the boundary at 
    652 time steps $n-1$, $n$ and $n+1$ \gmcomment{since the original was three time-level}  
    653 in order to extrapolate for the new boundary value $\phi^{n+1}$.  
    654  
    655 In the open boundary algorithm as implemented in NEMO v2.3, the new boundary  
    656 values are updated differently depending on the sign of $C_{\phi x}$. Let us take  
    657 an eastern boundary as an example. The solution for variable $\phi$ at the  
    658 boundary is given by a generalized wave equation with phase velocity $C_{\phi}$,  
    659 with the addition of a relaxation term, as: 
    660 \begin{eqnarray} 
    661 \phi_{t} &  =  & -C_{\phi x} \phi_{x} + \frac{1}{\tau_{o}} (\phi_{c}-\phi)  
    662                         \;\;\; \;\;\; \;\;\; (C_{\phi x} > 0), \label{Eq_obc_rado} \\ 
    663 \phi_{t} &  =  & \frac{1}{\tau_{i}} (\phi_{c}-\phi)  
    664 \;\;\; \;\;\; \;\;\;\;\;\; (C_{\phi x} < 0), \label{Eq_obc_radi} 
    665 \end{eqnarray} 
    666 where $\phi_{c}$ is the estimate of $\phi$ at the boundary, provided as boundary  
    667 data. Note that in (\ref{Eq_obc_rado}), $C_{\phi x}$ is bounded by the ratio  
    668 $\delta x/\delta t$ for stability reasons. When $C_{\phi x}$ is eastward (outward  
    669 propagation), the radiation condition (\ref{Eq_obc_rado}) is used.  
    670 When  $C_{\phi x}$ is westward (inward propagation), (\ref{Eq_obc_radi}) is  
    671 used with a strong relaxation to climatology (usually $\tau_{i}=\np{rn\_dpein}=$1~day). 
    672 Equation (\ref{Eq_obc_radi}) is solved with a Euler time-stepping scheme. As a  
    673 consequence, setting $\tau_{i}$ smaller than, or equal to the time step is equivalent  
    674 to a fixed boundary condition. A time scale of one day is usually a good compromise  
    675 which guarantees that the inflow conditions remain close to climatology while ensuring  
    676 numerical stability.  
    677  
    678 In  the case of a western boundary located in the Eastern Atlantic, \citet{Penduff_al_JGR00}  
    679 have been able to implement the radiation algorithm without any boundary data,  
    680 using persistence from the previous time step instead. This solution has not worked  
    681 in other cases \citep{Treguier_al_JGR01}, so that the use of boundary data is recommended.  
    682 Even in the outflow condition (\ref{Eq_obc_rado}), we have found it desirable to  
    683 maintain a weak relaxation to climatology. The time step is usually chosen so as to  
    684 be larger than typical turbulent scales (of order 1000~days \gmcomment{or maybe seconds?}). 
    685  
    686 The radiation condition is applied to the model variables: temperature, salinity,  
    687 tangential and normal velocities. For normal and tangential velocities, $u$ and $v$,  
    688 radiation is applied with phase velocities calculated from $u$ and $v$ respectively.   
    689 For the radiation of tracers, we use the phase velocity calculated from the tangential  
    690 velocity in order to avoid calculating too many independent radiation velocities and  
    691 because tangential velocities and tracers have the same position along the boundary  
    692 on a C-grid.   
    693  
    694 \subsection{Domain decomposition (\key{mpp\_mpi})} 
    695 \label{OBC_mpp} 
    696 When \key{mpp\_mpi} is active in the code, the computational domain is divided  
    697 into rectangles that are attributed each to a different processor. The open boundary  
    698 code is ``mpp-compatible'' up to a certain point. The radiation algorithm will not  
    699 work if there is an mpp subdomain boundary parallel to the open boundary at the  
    700 index of the boundary, or the grid point after (outside), or three grid points before  
    701 (inside). On the other hand, there is no problem if an mpp subdomain boundary  
    702 cuts the open boundary perpendicularly. These geometrical limitations must be  
    703 checked for by the user (there is no safeguard in the code).   
    704 The general principle for the open boundary mpp code is that loops over the open  
    705 boundaries {not sure what this means} are performed on local indices (nie0,  
    706 nie1, nje0, nje1 for an eastern boundary for instance) that are initialized in module  
    707 \mdl{obc\_ini}. Those indices have relevant values on the processors that contain  
    708 a segment of an open boundary. For processors that do not include an open  
    709 boundary segment, the indices are such that the calculations within the loops are  
    710 not performed. 
    711 \gmcomment{I dont understand most of the last few sentences} 
    712   
    713 Arrays of climatological data that are read from files are seen by all processors  
    714 and have the same dimensions for all (for instance, for the eastern boundary,  
    715 uedta(jpjglo,jpk,2)). On the other hand, the arrays for the calculation of radiation  
    716 are local to each processor (uebnd(jpj,jpk,3,3) for instance).  This allowed the  
    717 CLIPPER model for example, to save on memory where the eastern boundary  
    718 crossed 8 processors so that \jp{jpj} was much smaller than (\jp{jpjef}-\jp{jpjed}+1).  
    719  
    720 \subsection{Volume conservation} 
    721 \label{OBC_vol} 
    722  
    723 It is necessary to control the volume inside a domain when using open boundaries.  
    724 With fixed boundaries, it is enough to ensure that the total inflow/outflow has  
    725 reasonable values (either zero or a value compatible with an observed volume  
    726 balance). When using radiative boundary conditions it is necessary to have a  
    727 volume constraint because each open boundary works independently from the  
    728 others. The methodology used to control this volume is identical to the one  
    729 coded in the ROMS model \citep{Marchesiello2001}. 
    730  
    731  
    732 %---------------------------------------- EXTRAS 
    733 \colorbox{yellow}{Explain obc\_vol{\ldots}} 
    734  
    735 \colorbox{yellow}{OBC algorithm for update, OBC restart, list of routines where obc key appears{\ldots}} 
    736  
    737 \colorbox{yellow}{OBC rigid lid? {\ldots}} 
    738366 
    739367% ==================================================================== 
     
    956584%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    957585\begin{figure}[!t]      \begin{center} 
    958 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_LBC_bdy_geom.pdf} 
     586\includegraphics[width=1.0\textwidth]{Fig_LBC_bdy_geom} 
    959587\caption {      \label{Fig_LBC_bdy_geom} 
    960588Example of geometry of unstructured open boundary} 
     
    997625%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    998626\begin{figure}[!t]     \begin{center} 
    999 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_LBC_nc_header.pdf} 
     627\includegraphics[width=1.0\textwidth]{Fig_LBC_nc_header} 
    1000628\caption {     \label{Fig_LBC_nc_header}  
    1001629Example of the header for a coordinates.bdy.nc file} 
     
    1034662 
    1035663 
     664\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_LDF.tex

    r4147 r7260  
    1  
    2 % ================================================================ 
    3 % Chapter � Lateral Ocean Physics (LDF) 
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
     3 
     4% ================================================================ 
     5% Chapter ———  Lateral Ocean Physics (LDF) 
    46% ================================================================ 
    57\chapter{Lateral Ocean Physics (LDF)} 
     
    6870When none of the \textbf{key\_dynldf\_...} and \textbf{key\_traldf\_...} keys are  
    6971defined, a constant value is used over the whole ocean for momentum and  
    70 tracers, which is specified through the \np{rn\_ahm0} and \np{rn\_aht0} namelist  
     72tracers, which is specified through the \np{rn\_ahm\_0\_lap} and \np{rn\_aht\_0} namelist  
    7173parameters. 
    7274 
     
    7779mixing coefficients will require 3D arrays. In the 1D option, a hyperbolic variation  
    7880of the lateral mixing coefficient is introduced in which the surface value is  
    79 \np{rn\_aht0} (\np{rn\_ahm0}), the bottom value is 1/4 of the surface value,  
     81\np{rn\_aht\_0} (\np{rn\_ahm\_0\_lap}), the bottom value is 1/4 of the surface value,  
    8082and the transition takes place around z=300~m with a width of 300~m  
    8183($i.e.$ both the depth and the width of the inflection point are set to 300~m).  
     
    9395\end{equation} 
    9496where $e_{max}$ is the maximum of $e_1$ and $e_2$ taken over the whole masked  
    95 ocean domain, and $A_o^l$ is the \np{rn\_ahm0} (momentum) or \np{rn\_aht0} (tracer)  
     97ocean domain, and $A_o^l$ is the \np{rn\_ahm\_0\_lap} (momentum) or \np{rn\_aht\_0} (tracer)  
    9698namelist parameter. This variation is intended to reflect the lesser need for subgrid  
    9799scale eddy mixing where the grid size is smaller in the domain. It was introduced in  
     
    105107Other formulations can be introduced by the user for a given configuration.  
    106108For example, in the ORCA2 global ocean model (see Configurations), the laplacian  
    107 viscosity operator uses \np{rn\_ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$  
    108 north and south and decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s  
     109viscosity operator uses \np{rn\_ahm\_0\_lap}~= 4.10$^4$ m$^2$/s poleward of 20\deg  
     110north and south and decreases linearly to \np{rn\_aht\_0}~= 2.10$^3$ m$^2$/s  
    109111at the equator \citep{Madec_al_JPO96, Delecluse_Madec_Bk00}. This modification  
    110112can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}.  
     
    120122\subsubsection{Space and Time Varying Mixing Coefficients} 
    121123 
    122 There is no default specification of space and time varying mixing coefficient.  
    123 The only case available is specific to the ORCA2 and ORCA05 global ocean  
    124 configurations. It provides only a tracer  
    125 mixing coefficient for eddy induced velocity (ORCA2) or both iso-neutral and  
    126 eddy induced velocity (ORCA05) that depends on the local growth rate of  
    127 baroclinic instability. This specification is actually used when an ORCA key  
     124There are no default specifications of space and time varying mixing coefficient.  One 
     125available case is specific to the ORCA2 and ORCA05 global ocean configurations. It 
     126provides only a tracer mixing coefficient for eddy induced velocity (ORCA2) or both 
     127iso-neutral and eddy induced velocity (ORCA05) that depends on the local growth rate of 
     128baroclinic instability. This specification is actually used when an ORCA key 
    128129and both \key{traldf\_eiv} and \key{traldf\_c2d} are defined. 
     130 
     131\subsubsection{Smagorinsky viscosity (\key{dynldf\_c3d} and \key{dynldf\_smag})} 
     132 
     133The \key{dynldf\_smag} key activates a 3D, time-varying viscosity that depends on the 
     134resolved motions. Following \citep{Smagorinsky_93} the viscosity coefficient is set 
     135proportional to a local deformation rate based on the horizontal shear and tension, 
     136namely: 
     137 
     138\begin{equation} 
     139A_{m_{Smag}} = \left(\frac{{\sf CM_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert 
     140\end{equation} 
     141 
     142\noindent where the deformation rate $\vert{D}\vert$ is given by  
     143 
     144\begin{equation} 
     145\vert{D}\vert=\sqrt{\left({\frac{\partial{u}} {\partial{x}}} 
     146                         -{\frac{\partial{v}} {\partial{y}}}\right)^2 
     147                 +  \left({\frac{\partial{u}} {\partial{y}}} 
     148                         +{\frac{\partial{v}} {\partial{x}}}\right)^2}  
     149\end{equation} 
     150 
     151\noindent and $L$ is the local gridscale given by: 
     152 
     153\begin{equation} 
     154L^2 = \frac{2{e_1}^2 {e_2}^2}{\left ( {e_1}^2 + {e_2}^2 \right )} 
     155\end{equation} 
     156 
     157\citep{Griffies_Hallberg_MWR00} suggest values in the range 2.2 to 4.0 of the coefficient 
     158$\sf CM_{Smag}$ for oceanic flows. This value is set via the \np{rn\_cmsmag\_1} namelist 
     159parameter. An additional parameter: \np{rn\_cmsh} is included in NEMO for experimenting 
     160with the contribution of the shear term. A value of 1.0 (the default) calculates the 
     161deformation rate as above; a value of 0.0 will discard the shear term entirely. 
     162 
     163For numerical stability, the calculated viscosity is bounded according to the following: 
     164 
     165\begin{equation} 
     166{\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_ahm\_m\_lap\right ) \geq A_{m_{Smag}}  
     167                                                                  \geq rn\_ahm\_0\_lap 
     168\end{equation} 
     169 
     170\noindent with both parameters for the upper and lower bounds being provided via the 
     171indicated namelist parameters. 
     172 
     173\bigskip When $ln\_dynldf\_bilap = .true.$, a biharmonic version of the Smagorinsky 
     174viscosity is also available which sets a coefficient for the biharmonic viscosity as: 
     175 
     176\begin{equation} 
     177B_{m_{Smag}} = - \left(\frac{{\sf CM_{bSmag}}}{\pi}\right)^2 {L^4\over 8}\vert{D}\vert 
     178\end{equation} 
     179 
     180\noindent which is bounded according to: 
     181 
     182\begin{equation} 
     183{\rm MAX}\left (-{ L^4\over {64\Delta{t}}}, rn\_ahm\_m\_blp\right ) \leq B_{m_{Smag}}  
     184                                                                    \leq rn\_ahm\_0\_blp 
     185\end{equation} 
     186 
     187\noindent Note the reversal of the inequalities here because NEMO requires the biharmonic 
     188coefficients as negative numbers. $\sf CM_{bSmag}$ is set via the \np{rn\_cmsmag\_2} 
     189namelist parameter and the bounding values have corresponding entries in the namelist too. 
     190 
     191\bigskip The current implementation in NEMO also allows for 3D, time-varying diffusivities 
     192to be set using the Smagorinsky approach. Users should note that this option is not 
     193recommended for many applications since diffusivities will tend to be largest near 
     194boundaries (where shears are greatest) leading to spurious upwellings 
     195(\citep{Griffies_Bk04}, chapter 18.3.4). Nevertheless the option is there for those 
     196wishing to experiment. This choice requires both \key{traldf\_c3d} and \key{traldf\_smag} 
     197and uses the \np{rn\_chsmag} (${\sf CH_{Smag}}$), \np{rn\_smsh} and \np{rn\_aht\_m} 
     198namelist parameters in an analogous way to \np{rn\_cmsmag\_1}, \np{rn\_cmsh} and 
     199\np{rn\_ahm\_m\_lap} (see above) to set the diffusion coefficient: 
     200 
     201\begin{equation} 
     202A_{h_{Smag}} = \left(\frac{{\sf CH_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert 
     203\end{equation} 
     204 
     205  
     206For numerical stability, the calculated diffusivity is bounded according to the following: 
     207 
     208\begin{equation} 
     209{\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_aht\_m\right ) \geq A_{h_{Smag}}  
     210                                                             \geq rn\_aht\_0 
     211\end{equation} 
     212 
     213 
    129214 
    130215$\ $\newline    % force a new ligne 
     
    144229(3) for isopycnal diffusion on momentum or tracers, an additional purely  
    145230horizontal background diffusion with uniform coefficient can be added by  
    146 setting a non zero value of \np{rn\_ahmb0} or \np{rn\_ahtb0}, a background horizontal  
     231setting a non zero value of \np{rn\_ahmb\_0} or \np{rn\_ahtb\_0}, a background horizontal  
    147232eddy viscosity or diffusivity coefficient (namelist parameters whose default  
    148233values are $0$). However, the technique used to compute the isopycnal  
    149234slopes is intended to get rid of such a background diffusion, since it introduces  
    150 spurious diapycnal diffusion (see {\S\ref{LDF_slp}). 
     235spurious diapycnal diffusion (see \S\ref{LDF_slp}). 
    151236 
    152237(4) when an eddy induced advection term is used (\key{traldf\_eiv}), $A^{eiv}$,  
     
    361446%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    362447\begin{figure}[!ht]      \begin{center} 
    363 \includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_LDF_ZDF1.pdf} 
     448\includegraphics[width=0.70\textwidth]{Fig_LDF_ZDF1} 
    364449\caption {    \label{Fig_LDF_ZDF1} 
    365450averaging procedure for isopycnal slope computation.} 
     
    389474%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    390475\begin{figure}[!ht]     \begin{center} 
    391 \includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_eiv_slp.pdf} 
     476\includegraphics[width=0.70\textwidth]{Fig_eiv_slp} 
    392477\caption {     \label{Fig_eiv_slp} 
    393478Vertical profile of the slope used for lateral mixing in the mixed layer :  
     
    431516diffusion along model level surfaces, i.e. using the shear computed along  
    432517the model levels and with no additional friction at the ocean bottom (see  
    433 {\S\ref{LBC_coast}). 
     518\S\ref{LBC_coast}). 
    434519 
    435520 
     
    472557 
    473558 
     559\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_MISC.tex

    r5602 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter � Miscellaneous Topics 
     
    3436has been made to set them in a generic way. However, examples of how  
    3537they can be set up is given in the ORCA 2\deg and 0.5\deg configurations. For example,  
    36 for details of implementation in ORCA2, search: 
    37 \vspace{-10pt}   
    38 \begin{alltt}   
    39 \tiny     
    40 \begin{verbatim} 
    41 IF( cp_cfg == "orca" .AND. jp_cfg == 2 ) 
    42 \end{verbatim}   
    43 \end{alltt} 
     38for details of implementation in ORCA2, search:  
     39\texttt{ IF( cp\_cfg == "orca" .AND. jp\_cfg == 2 ) } 
    4440 
    4541% ------------------------------------------------------------------------------------------------------------- 
     
    6662%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    6763\begin{figure}[!tbp]     \begin{center} 
    68 \includegraphics[width=0.80\textwidth]{./TexFiles/Figures/Fig_Gibraltar.pdf} 
    69 \includegraphics[width=0.80\textwidth]{./TexFiles/Figures/Fig_Gibraltar2.pdf} 
     64\includegraphics[width=0.80\textwidth]{Fig_Gibraltar} 
     65\includegraphics[width=0.80\textwidth]{Fig_Gibraltar2} 
    7066\caption{   \label{Fig_MISC_strait_hand}  
    71 Example of the Gibraltar strait defined in a $1\deg \times 1\deg$ mesh.  
     67Example of the Gibraltar strait defined in a $1^{\circ} \times 1^{\circ}$ mesh.  
    7268\textit{Top}: using partially open cells. The meridional scale factor at $v$-point  
    7369is reduced on both sides of the strait to account for the real width of the strait  
     
    8985%-------------------------------------------------------------------------------------------------------------- 
    9086 
    91 \colorbox{yellow}{Add a short description of CLA staff here or in lateral boundary condition chapter?} 
    9287Options are defined through the  \ngn{namcla} namelist variables. 
     88This option is an obsolescent feature that will be removed in version 3.7 and followings.  
    9389 
    9490%The problem is resolved here by allowing the mixing of tracers and mass/volume between non-adjacent water columns at nominated regions within the model. Momentum is not mixed. The scheme conserves total tracer content, and total volume (the latter in $z*$- or $s*$-coordinate), and maintains compatibility between the tracer and mass/volume budgets.   
     
    200196%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    201197\begin{figure}[!ht]    \begin{center} 
    202 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_LBC_zoom.pdf} 
     198\includegraphics[width=0.90\textwidth]{Fig_LBC_zoom} 
    203199\caption{   \label{Fig_LBC_zoom} 
    204200Position of a model domain compared to the data input domain when the zoom functionality is used.} 
     
    638634 
    639635 
     636\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_Model_Basics.tex

    r3294 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter 1 Ñ Model Basics 
     
    114116%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    115117\begin{figure}[!ht]   \begin{center} 
    116 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_I_ocean_bc.pdf} 
     118\includegraphics[width=0.90\textwidth]{Fig_I_ocean_bc} 
    117119\caption{    \label{Fig_ocean_bc}  
    118120The ocean is bounded by two surfaces, $z=-H(i,j)$ and $z=\eta(i,j,t)$, where $H$  
     
    247249sufficient to solve a linearized version of (\ref{Eq_PE_ssh}), which still allows  
    248250to take into account freshwater fluxes applied at the ocean surface \citep{Roullet_Madec_JGR00}. 
     251Nevertheless, with the linearization, an exact conservation of heat and salt contents is lost. 
    249252 
    250253The filtering of EGWs in models with a free surface is usually a matter of discretisation  
    251 of the temporal derivatives, using the time splitting method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92}  
    252 or the implicit scheme \citep{Dukowicz1994}. In \NEMO, we use a slightly different approach  
    253 developed by \citet{Roullet_Madec_JGR00}: the damping of EGWs is ensured by introducing an  
    254 additional force in the momentum equation. \eqref{Eq_PE_dyn} becomes:  
    255 \begin{equation} \label{Eq_PE_flt} 
    256 \frac{\partial {\rm {\bf U}}_h }{\partial t}= {\rm {\bf M}} 
    257 - g \nabla \left( \tilde{\rho} \ \eta \right)  
    258 - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right)  
    259 \end{equation} 
    260 where $T_c$, is a parameter with dimensions of time which characterizes the force,  
    261 $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density, and $\rm {\bf M}$  
    262 represents the collected contributions of the Coriolis, hydrostatic pressure gradient,  
    263 non-linear and viscous terms in \eqref{Eq_PE_dyn}. 
    264  
    265 The new force can be interpreted as a diffusion of vertically integrated volume flux divergence.  
    266 The time evolution of $D$ is thus governed by a balance of two terms, $-g$ \textbf{A} $\eta$  
    267 and $g \, T_c \,$ \textbf{A} $D$, associated with a propagative regime and a diffusive regime  
    268 in the temporal spectrum, respectively. In the diffusive regime, the EGWs no longer propagate,  
    269 $i.e.$ they are stationary and damped. The diffusion regime applies to the modes shorter than  
    270 $T_c$. For longer ones, the diffusion term vanishes. Hence, the temporally unresolved EGWs  
    271 can be damped by choosing $T_c > \rdt$. \citet{Roullet_Madec_JGR00} demonstrate that  
    272 (\ref{Eq_PE_flt}) can be integrated with a leap frog scheme except the additional term which  
    273 has to be computed implicitly. This is not surprising since the use of a large time step has a  
    274 necessarily numerical cost. Two gains arise in comparison with the previous formulations.  
    275 Firstly, the damping of EGWs can be quantified through the magnitude of the additional term.  
    276 Secondly, the numerical scheme does not need any tuning. Numerical stability is ensured as  
    277 soon as $T_c > \rdt$. 
    278  
    279 When the variations of free surface elevation are small compared to the thickness of the first  
    280 model layer, the free surface equation (\ref{Eq_PE_ssh}) can be linearized. As emphasized  
    281 by \citet{Roullet_Madec_JGR00} the linearization of (\ref{Eq_PE_ssh}) has consequences on the  
    282 conservation of salt in the model. With the nonlinear free surface equation, the time evolution  
    283 of the total salt content is  
    284 \begin{equation} \label{Eq_PE_salt_content} 
    285     \frac{\partial }{\partial t}\int\limits_{D\eta } {S\;dv}  
    286                         =\int\limits_S {S\;(-\frac{\partial \eta }{\partial t}-D+P-E)\;ds} 
    287 \end{equation} 
    288 where $S$ is the salinity, and the total salt is integrated over the whole ocean volume  
    289 $D_\eta$ bounded by the time-dependent free surface. The right hand side (which is an  
    290 integral over the free surface) vanishes when the nonlinear equation (\ref{Eq_PE_ssh})  
    291 is satisfied, so that the salt is perfectly conserved. When the free surface equation is  
    292 linearized, \citet{Roullet_Madec_JGR00} show that the total salt content integrated in the fixed  
    293 volume $D$ (bounded by the surface $z=0$) is no longer conserved: 
    294 \begin{equation} \label{Eq_PE_salt_content_linear} 
    295          \frac{\partial }{\partial t}\int\limits_D {S\;dv}  
    296                = - \int\limits_S {S\;\frac{\partial \eta }{\partial t}ds}  
    297 \end{equation} 
    298  
    299 The right hand side of (\ref{Eq_PE_salt_content_linear}) is small in equilibrium solutions  
    300 \citep{Roullet_Madec_JGR00}. It can be significant when the freshwater forcing is not balanced and  
    301 the globally averaged free surface is drifting. An increase in sea surface height \textit{$\eta $}  
    302 results in a decrease of the salinity in the fixed volume $D$. Even in that case though,  
    303 the total salt integrated in the variable volume $D_{\eta}$ varies much less, since  
    304 (\ref{Eq_PE_salt_content_linear}) can be rewritten as  
    305 \begin{equation} \label{Eq_PE_salt_content_corrected} 
    306 \frac{\partial }{\partial t}\int\limits_{D\eta } {S\;dv}  
    307 =\frac{\partial}{\partial t} \left[ \;{\int\limits_D {S\;dv} +\int\limits_S {S\eta \;ds} } \right] 
    308 =\int\limits_S {\eta \;\frac{\partial S}{\partial t}ds} 
    309 \end{equation} 
    310  
    311 Although the total salt content is not exactly conserved with the linearized free surface,  
    312 its variations are driven by correlations of the time variation of surface salinity with the  
    313 sea surface height, which is a negligible term. This situation contrasts with the case of  
    314 the rigid lid approximation in which case freshwater forcing is represented by a virtual  
    315 salt flux, leading to a spurious source of salt at the ocean surface  
    316 \citep{Huang_JPO93, Roullet_Madec_JGR00}. 
    317  
    318 \newpage 
    319 $\ $\newline    % force a new ligne 
     254of the temporal derivatives, using a split-explicit method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92}  
     255or the implicit scheme \citep{Dukowicz1994} or the addition of a filtering force in the momentum equation  
     256\citep{Roullet_Madec_JGR00}. With the present release, \NEMO offers the choice between  
     257an explicit free surface (see \S\ref{DYN_spg_exp}) or a split-explicit scheme strongly  
     258inspired the one proposed by \citet{Shchepetkin_McWilliams_OM05} (see \S\ref{DYN_spg_ts}). 
     259 
     260%\newpage 
     261%$\ $\newline    % force a new line 
    320262 
    321263% ================================================================ 
     
    372314%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    373315\begin{figure}[!tb]   \begin{center} 
    374 \includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_I_earth_referential.pdf} 
     316\includegraphics[width=0.60\textwidth]{Fig_I_earth_referential} 
    375317\caption{   \label{Fig_referential}  
    376318the geographical coordinate system $(\lambda,\varphi,z)$ and the curvilinear  
     
    773715\end{equation} 
    774716 
    775 The equations solved by the ocean model \eqref{Eq_PE} in $s-$coordinate can be written as follows: 
     717The equations solved by the ocean model \eqref{Eq_PE} in $s-$coordinate can be written as follows (see Appendix~\ref{Apdx_A_momentum}): 
    776718 
    777719 \vspace{0.5cm} 
    778 * momentum equation: 
     720$\bullet$ Vector invariant form of the momentum equation : 
    779721\begin{multline} \label{Eq_PE_sco_u} 
    780 \frac{1}{e_3} \frac{\partial \left(  e_3\,u  \right) }{\partial t}= 
     722\frac{\partial  u  }{\partial t}= 
    781723   +   \left( {\zeta +f} \right)\,v                                     
    782724   -   \frac{1}{2\,e_1} \frac{\partial}{\partial i} \left(  u^2+v^2   \right)  
     
    787729\end{multline} 
    788730\begin{multline} \label{Eq_PE_sco_v} 
    789 \frac{1}{e_3} \frac{\partial \left(  e_3\,v  \right) }{\partial t}= 
     731\frac{\partial v }{\partial t}= 
    790732   -   \left( {\zeta +f} \right)\,u    
    791733   -   \frac{1}{2\,e_2 }\frac{\partial }{\partial j}\left(  u^2+v^2  \right)         
     
    795737   +  D_v^{\vect{U}}  +   F_v^{\vect{U}} \quad 
    796738\end{multline} 
     739 
     740 \vspace{0.5cm} 
     741$\bullet$ Vector invariant form of the momentum equation : 
     742\begin{multline} \label{Eq_PE_sco_u} 
     743\frac{1}{e_3} \frac{\partial \left(  e_3\,u  \right) }{\partial t}= 
     744   +   \left( { f + \frac{1}{e_1 \; e_2 } 
     745               \left(    v \frac{\partial e_2}{\partial i} 
     746                  -u \frac{\partial e_1}{\partial j}  \right)}    \right) \, v    \\ 
     747   - \frac{1}{e_1 \; e_2 \; e_3 }   \left(  
     748               \frac{\partial \left( {e_2 \, e_3 \, u\,u} \right)}{\partial i} 
     749      +        \frac{\partial \left( {e_1 \, e_3 \, v\,u} \right)}{\partial j}   \right) 
     750   - \frac{1}{e_3 }\frac{\partial \left( { \omega\,u} \right)}{\partial k}    \\ 
     751   - \frac{1}{e_1} \frac{\partial}{\partial i} \left( \frac{p_s + p_h}{\rho _o}    \right)     
     752   +  g\frac{\rho }{\rho _o}\sigma _1  
     753   +   D_u^{\vect{U}}  +   F_u^{\vect{U}} \quad 
     754\end{multline} 
     755\begin{multline} \label{Eq_PE_sco_v} 
     756\frac{1}{e_3} \frac{\partial \left(  e_3\,v  \right) }{\partial t}= 
     757   -   \left( { f + \frac{1}{e_1 \; e_2} 
     758               \left(    v \frac{\partial e_2}{\partial i} 
     759                  -u \frac{\partial e_1}{\partial j}  \right)}    \right) \, u   \\ 
     760   - \frac{1}{e_1 \; e_2 \; e_3 }   \left(  
     761               \frac{\partial \left( {e_2 \; e_3  \,u\,v} \right)}{\partial i} 
     762      +        \frac{\partial \left( {e_1 \; e_3  \,v\,v} \right)}{\partial j}   \right) 
     763                 - \frac{1}{e_3 } \frac{\partial \left( { \omega\,v} \right)}{\partial k}    \\ 
     764   -   \frac{1}{e_2 }\frac{\partial }{\partial j}\left( \frac{p_s+p_h }{\rho _o}  \right)  
     765    +  g\frac{\rho }{\rho _o }\sigma _2    
     766   +  D_v^{\vect{U}}  +   F_v^{\vect{U}} \quad 
     767\end{multline} 
     768 
    797769where the relative vorticity, \textit{$\zeta $}, the surface pressure gradient, and the hydrostatic  
    798770pressure have the same expressions as in $z$-coordinates although they do not represent  
    799771exactly the same quantities. $\omega$ is provided by the continuity equation  
    800772(see Appendix~\ref{Apdx_A}): 
    801  
    802773\begin{equation} \label{Eq_PE_sco_continuity} 
    803774\frac{\partial e_3}{\partial t} + e_3 \; \chi + \frac{\partial \omega }{\partial s} = 0    
     
    809780 
    810781 \vspace{0.5cm} 
    811 * tracer equations: 
     782$\bullet$ tracer equations: 
    812783\begin{multline} \label{Eq_PE_sco_t} 
    813784\frac{1}{e_3} \frac{\partial \left(  e_3\,T  \right) }{\partial t}= 
     
    842813%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    843814\begin{figure}[!b]    \begin{center} 
    844 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_z_zstar.pdf} 
     815\includegraphics[width=1.0\textwidth]{Fig_z_zstar} 
    845816\caption{   \label{Fig_z_zstar}  
    846817(a) $z$-coordinate in linear free-surface case ;  
     
    1023994\label{PE_zco_tilde} 
    1024995 
    1025 The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM10s}. 
    1026 It is not available in the current version of \NEMO. 
     996The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM11}. 
     997It is available in \NEMO since the version 3.4. Nevertheless, it is currently not robust enough  
     998to be used in all possible configurations. Its use is therefore not recommended. 
     999 
    10271000 
    10281001\newpage  
     
    11571130operator acting along $s-$surfaces (see \S\ref{LDF}). 
    11581131 
    1159 \subsubsection{Lateral second order tracer diffusive operator} 
    1160  
    1161 The lateral second order tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}): 
     1132\subsubsection{Lateral Laplacian tracer diffusive operator} 
     1133 
     1134The lateral Laplacian tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}): 
    11621135\begin{equation} \label{Eq_PE_iso_tensor} 
    11631136D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad  
     
    11801153ocean (see Appendix~\ref{Apdx_B}). 
    11811154 
     1155For \textit{iso-level} diffusion, $r_1$ and $r_2 $ are zero. $\Re $ reduces to the identity  
     1156in the horizontal direction, no rotation is applied.  
     1157 
    11821158For \textit{geopotential} diffusion, $r_1$ and $r_2 $ are the slopes between the  
    1183 geopotential and computational surfaces: in $z$-coordinates they are zero  
    1184 ($r_1 = r_2 = 0$) while in $s$-coordinate (including $\textit{z*}$ case) they are  
    1185 equal to $\sigma _1$ and $\sigma _2$, respectively (see \eqref{Eq_PE_sco_slope} ). 
     1159geopotential and computational surfaces: they are equal to $\sigma _1$ and $\sigma _2$,  
     1160respectively (see \eqref{Eq_PE_sco_slope} ). 
    11861161 
    11871162For \textit{isoneutral} diffusion $r_1$ and $r_2$ are the slopes between the isoneutral  
     
    12311206to zero in the vicinity of the boundaries. The latter strategy is used in \NEMO (cf. Chap.~\ref{LDF}). 
    12321207 
    1233 \subsubsection{Lateral fourth order tracer diffusive operator} 
    1234  
    1235 The lateral fourth order tracer diffusive operator is defined by: 
     1208\subsubsection{Lateral bilaplacian tracer diffusive operator} 
     1209 
     1210The lateral bilaplacian tracer diffusive operator is defined by: 
    12361211\begin{equation} \label{Eq_PE_bilapT} 
    12371212D^{lT}=\Delta \left( {A^{lT}\;\Delta T} \right)  
    12381213\qquad \text{where} \  D^{lT}=\Delta \left( {A^{lT}\;\Delta T} \right) 
    12391214 \end{equation} 
    1240  
    12411215It is the second order operator given by \eqref{Eq_PE_iso_tensor} applied twice with  
    12421216the eddy diffusion coefficient correctly placed.  
    12431217 
    1244  
    1245 \subsubsection{Lateral second order momentum diffusive operator} 
    1246  
    1247 The second order momentum diffusive operator along $z$- or $s$-surfaces is found by  
     1218\subsubsection{Lateral Laplacian momentum diffusive operator} 
     1219 
     1220The Laplacian momentum diffusive operator along $z$- or $s$-surfaces is found by  
    12481221applying \eqref{Eq_PE_lap_vector} to the horizontal velocity vector (see Appendix~\ref{Apdx_B}): 
    12491222\begin{equation} \label{Eq_PE_lapU} 
     
    12791252of the Equator in a geographical coordinate system \citep{Lengaigne_al_JGR03}. 
    12801253 
    1281 \subsubsection{lateral fourth order momentum diffusive operator} 
     1254\subsubsection{lateral bilaplacian momentum diffusive operator} 
    12821255 
    12831256As for tracers, the fourth order momentum diffusive operator along $z$ or $s$-surfaces  
     
    13091282\end{equation} 
    13101283 
     1284\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_Model_Basics_zstar.tex

    r4147 r7260  
    1 % ================================================================ 
    2 % Chapter 1 � Model Basics 
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
     3% ================================================================ 
     4% Chapter 1 ——— Model Basics 
    35% ================================================================ 
    46% ================================================================ 
     
    121123%>   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   > 
    122124\begin{figure}[!t]   \begin{center} 
    123 \includegraphics[width=0.90\textwidth]{./Figures/Fig_DYN_dynspg_ts.pdf} 
     125\includegraphics[width=0.90\textwidth]{Fig_DYN_dynspg_ts} 
    124126\caption{    \label{Fig_DYN_dynspg_ts} 
    125127Schematic of the split-explicit time stepping scheme for the barotropic and baroclinic modes,  
     
    256258 
    257259 
     260\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_OBS.tex

    r4245 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter observation operator (OBS) 
     
    732734%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    733735\begin{figure}      \begin{center} 
    734 \includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_ASM_obsdist_local} 
     736\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_local} 
    735737\caption{      \label{fig:obslocal} 
    736738Example of the distribution of observations with the geographical distribution of observational data.}  
     
    759761%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    760762\begin{figure}     \begin{center} 
    761 \includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_ASM_obsdist_global} 
     763\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_global} 
    762764\caption{      \label{fig:obsglobal} 
    763765Example of the distribution of observations with the round-robin distribution of observational data.} 
     
    13761378%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    13771379\begin{figure}     \begin{center} 
    1378 %\includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_OBS_dataplot_main} 
    1379 \includegraphics[width=9cm,angle=-90.]{./TexFiles/Figures/Fig_OBS_dataplot_main} 
     1380%\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_main} 
     1381\includegraphics[width=9cm,angle=-90.]{Fig_OBS_dataplot_main} 
    13801382\caption{      \label{fig:obsdataplotmain} 
    13811383Main window of dataplot.} 
     
    13881390%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    13891391\begin{figure}     \begin{center} 
    1390 %\includegraphics[width=10cm,height=12cm,angle=-90.]{./TexFiles/Figures/Fig_OBS_dataplot_prof} 
    1391 \includegraphics[width=7cm,angle=-90.]{./TexFiles/Figures/Fig_OBS_dataplot_prof} 
     1392%\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_prof} 
     1393\includegraphics[width=7cm,angle=-90.]{Fig_OBS_dataplot_prof} 
    13921394\caption{      \label{fig:obsdataplotprofile} 
    13931395Profile plot from dataplot produced by right clicking on a point in the main window.} 
     
    13981400 
    13991401 
     1402\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_SBC.tex

    r5602 r7260  
    1 % ================================================================ 
    2 % Chapter � Surface Boundary Condition (SBC, ISF, ICB)  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
     3% ================================================================ 
     4% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)  
    35% ================================================================ 
    46\chapter{Surface Boundary Condition (SBC, ISF, ICB) } 
     
    1719   \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 
    1820   \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 
    19    \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 
     21   \item the surface freshwater budget $\left( {\textit{emp}} \right)$ 
     22   \item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$ 
    2023\end{itemize} 
    2124plus an optional field: 
     
    2730are controlled by namelist \ngn{namsbc} variables: an analytical formulation (\np{ln\_ana}~=~true),  
    2831a flux formulation (\np{ln\_flx}~=~true), a bulk formulae formulation (CORE  
    29 (\np{ln\_core}~=~true), CLIO (\np{ln\_clio}~=~true) or MFS 
     32(\np{ln\_blk\_core}~=~true), CLIO (\np{ln\_blk\_clio}~=~true) or MFS 
    3033\footnote { Note that MFS bulk formulae compute fluxes only for the ocean component} 
    31 (\np{ln\_mfs}~=~true) bulk formulae) and a coupled  
    32 formulation (exchanges with a atmospheric model via the OASIS coupler)  
    33 (\np{ln\_cpl}~=~true). When used, the atmospheric pressure forces both  
    34 ocean and ice dynamics (\np{ln\_apr\_dyn}~=~true). 
    35 The frequency at which the six or seven fields have to be updated is the \np{nn\_fsbc}  
    36 namelist parameter.  
     34(\np{ln\_blk\_mfs}~=~true) bulk formulae) and a coupled or mixed forced/coupled formulation  
     35(exchanges with a atmospheric model via the OASIS coupler) (\np{ln\_cpl} or \np{ln\_mixcpl}~=~true).  
     36When used ($i.e.$ \np{ln\_apr\_dyn}~=~true), the atmospheric pressure forces both ocean and ice dynamics. 
     37 
     38The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.  
    3739When the fields are supplied from data files (flux and bulk formulations), the input fields  
    38 need not be supplied on the model grid.  Instead a file of coordinates and weights can  
     40need not be supplied on the model grid. Instead a file of coordinates and weights can  
    3941be supplied which maps the data from the supplied grid to the model points  
    4042(so called "Interpolation on the Fly", see \S\ref{SBC_iof}). 
     
    4244can be masked to avoid spurious results in proximity of the coasts  as large sea-land gradients characterize 
    4345most of the atmospheric variables. 
     46 
    4447In addition, the resulting fields can be further modified using several namelist options.  
    45 These options control  the rotation of vector components supplied relative to an east-north  
    46 coordinate system onto the local grid directions in the model; the addition of a surface  
    47 restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes  
    48 below ice-covered areas (using observed ice-cover or a sea-ice model)  
    49 (\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater  
    50 fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of isf melting as lateral inflow (parameterisation)  
    51 (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false) or as surface flux at the land-ice ocean interface 
    52 (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true);  
    53 the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the  
    54 transformation of the solar radiation (if provided as daily mean) into a diurnal  
    55 cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave  
    56 model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or mfs bulk formulas are selected. 
     48These options control  
     49\begin{itemize} 
     50\item the rotation of vector components supplied relative to an east-north  
     51coordinate system onto the local grid directions in the model ;  
     52\item the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true) ;  
     53\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) ;  
     54\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ;  
     55\item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false)  
     56or as fluxes applied at the land-ice ocean interface (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true) ;  
     57\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ;  
     58\item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ;  
     59and a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}~=~true).  
     60\end{itemize} 
     61The latter option is possible only in case core or mfs bulk formulas are selected. 
    5762 
    5863In this chapter, we first discuss where the surface boundary condition appears in the 
     
    7378 
    7479The surface ocean stress is the stress exerted by the wind and the sea-ice  
    75 on the ocean. The two components of stress are assumed to be interpolated  
    76 onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction  
    77 at $u$- and $v$-points They are applied as a surface boundary condition of the  
    78 computation of the momentum vertical mixing trend (\mdl{dynzdf} module) : 
    79 \begin{equation} \label{Eq_sbc_dynzdf} 
    80 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1} 
    81     = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v } 
    82 \end{equation} 
    83 where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind  
    84 stress vector in the $(\textbf{i},\textbf{j})$ coordinate system. 
     80on the ocean. It is applied in \mdl{dynzdf} module as a surface boundary condition of the  
     81computation of the momentum vertical mixing trend (see \eqref{Eq_dynzdf_sbc} in \S\ref{DYN_zdf}). 
     82As such, it has to be provided as a 2D vector interpolated  
     83onto the horizontal velocity ocean mesh, $i.e.$ resolved onto the model  
     84(\textbf{i},\textbf{j}) direction at $u$- and $v$-points. 
    8585 
    8686The surface heat flux is decomposed into two parts, a non solar and a solar heat  
    8787flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part  
    88 of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).  
    89 It is applied as a surface boundary condition trend of the first level temperature  
    90 time evolution equation (\mdl{trasbc} module).  
    91 \begin{equation} \label{Eq_sbc_trasbc_q} 
    92 \frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho  
    93 _o \;C_p \;e_{3t} }} \right|_{k=1} \quad 
    94 \end{equation} 
    95 $Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D  
    96 trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True. 
    97  
    98 \begin{equation} \label{Eq_sbc_traqsr} 
    99 \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right] 
    100 \end{equation} 
    101 where $I_w$ is a non-dimensional function that describes the way the light  
    102 penetrates inside the water column. It is generally a sum of decreasing  
    103 exponentials (see \S\ref{TRA_qsr}). 
    104  
    105 The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which  
    106 may or may not be identical. Indeed, a surface freshwater flux has two effects:  
    107 it changes the volume of the ocean and it changes the surface concentration of  
    108 salt (and other tracers). Therefore it appears in the sea surface height as a volume  
    109 flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations  
    110 as a concentration/dilution effect,  
    111 $\textit{emp}_{S}$ (\mdl{trasbc} module).  
    112 \begin{equation} \label{Eq_trasbc_emp} 
    113 \begin{aligned} 
    114 &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\  
    115 \\ 
    116  &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\  
    117  \end{aligned} 
    118 \end{equation}  
    119  
    120 In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,  
    121 but it exist several numerical reasons why this equality should be broken.  
    122 For example, when the ocean is coupled to a sea-ice model, the water exchanged between  
    123 ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,  
    124 $\textit{emp}_{S}$ take into account both concentration/dilution effect associated with  
    125 freezing/melting and the salt flux between ice and ocean, while \textit{emp} is  
    126 only the volume flux. In addition, in the current version of \NEMO, the sea-ice is  
    127 assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does  
    128 not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS. 
    129 %gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}. 
    130  
    131 Note that SST can also be modified by a freshwater flux. Precipitation (in  
    132 particular solid precipitation) may have a temperature significantly different from  
    133 the SST. Due to the lack of information about the temperature of  
    134 precipitation, we assume it is equal to the SST. Therefore, no  
    135 concentration/dilution term appears in the temperature equation. It has to  
    136 be emphasised that this absence does not mean that there is no heat flux  
    137 associated with precipitation! Precipitation can change the ocean volume and thus the 
    138 ocean heat content. It is therefore associated with a heat flux (not yet   
    139 diagnosed in the model) \citep{Roullet_Madec_JGR00}). 
     88of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes  
     89plus the heat content of the mass exchange with the atmosphere and sea-ice).  
     90It is applied in \mdl{trasbc} module as a surface boundary condition trend of  
     91the first level temperature time evolution equation (see \eqref{Eq_tra_sbc}  
     92and \eqref{Eq_tra_sbc_lin} in \S\ref{TRA_sbc}).  
     93The latter is the penetrative part of the heat flux. It is applied as a 3D  
     94trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=\textit{true}. 
     95The way the light penetrates inside the water column is generally a sum of decreasing  
     96exponentials (see \S\ref{TRA_qsr}).  
     97 
     98The surface freshwater budget is provided by the \textit{emp} field. 
     99It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation)  
     100and possibly with the sea-ice and ice shelves (freezing minus melting of ice).  
     101It affects both the ocean in two different ways:  
     102$(i)$   it changes the volume of the ocean and therefore appears in the sea surface height  
     103equation as a volume flux, and  
     104$(ii)$  it changes the surface temperature and salinity through the heat and salt contents  
     105of the mass exchanged with the atmosphere, the sea-ice and the ice shelves.  
     106 
    140107 
    141108%\colorbox{yellow}{Miss: } 
     
    152119%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields 
    153120% 
    154 %Fluxes update only each nf{\_}sbc time step (namsbc) explain relation  
    155 %between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one  
    156 %nf{\_}sbc 
     121%Fluxes update only each nn{\_}fsbc time step (namsbc) explain relation  
     122%between nn{\_}fsbc and nf{\_}ice, do we define nf{\_}blk??? ? only one  
     123%nn{\_}fsbc 
    157124% 
    158125%Explain here all the namlist namsbc variable{\ldots}. 
     126%  
     127% explain : use or not of surface currents 
    159128% 
    160129%\colorbox{yellow}{End Miss } 
    161130 
    162 The ocean model provides the surface currents, temperature and salinity  
    163 averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the  
    164 mean is done in \mdl{sbcmod} module. 
     131The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})  
     132the surface currents, temperature and salinity.   
     133These variables are averaged over \np{nn\_fsbc} time-step (\ref{Tab_ssm}),  
     134and it is these averaged fields which are used to computes the surface fluxes  
     135at a frequency of \np{nn\_fsbc} time-step. 
     136 
    165137 
    166138%-------------------------------------------------TABLE--------------------------------------------------- 
     
    175147\caption{  \label{Tab_ssm}    
    176148Ocean variables provided by the ocean to the surface module (SBC).  
    177 The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of  
     149The variable are averaged over nn{\_}fsbc time step, $i.e.$ the frequency of  
    178150computation of surface fluxes.} 
    179151\end{center}   \end{table} 
     
    459431%-------------------------------------------------------------------------------------------------------------- 
    460432 
    461 In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields and simply read them in from  a previous run.   
    462 Options are defined through the  \ngn{namsbc\_sas} namelist variables. 
     433In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields  
     434and simply read them in from a previous run or receive them from OASIS.   
    463435For example: 
    464436 
    465 \begin{enumerate} 
    466 \item  Multiple runs of the model are required in code development to see the affect of different algorithms in 
     437\begin{itemize} 
     438\item  Multiple runs of the model are required in code development to see the effect of different algorithms in 
    467439       the bulk formulae. 
    468440\item  The effect of different parameter sets in the ice model is to be examined. 
    469 \end{enumerate} 
     441\item  Development of sea-ice algorithms or parameterizations. 
     442\item  spinup of the iceberg floats 
     443\item  ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}~=~\textit{true}) 
     444\end{itemize} 
    470445 
    471446The StandAlone Surface scheme provides this utility. 
     447Its options are defined through the \ngn{namsbc\_sas} namelist variables. 
    472448A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM. 
    473449However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0) 
     
    475451Routines replaced are: 
    476452 
    477 \begin{enumerate} 
    478 \item  \mdl{nemogcm} 
    479  
    480        This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90) 
     453\begin{itemize} 
     454\item \mdl{nemogcm} : This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90) 
    481455       Since the ocean state is not calculated all associated initialisations have been removed. 
    482 \item  \mdl{step} 
    483  
    484        The main time stepping routine now only needs to call the sbc routine (and a few utility functions). 
    485 \item  \mdl{sbcmod} 
    486  
    487        This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules 
     456\item  \mdl{step} : The main time stepping routine now only needs to call the sbc routine (and a few utility functions). 
     457\item  \mdl{sbcmod} : This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules 
    488458       that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs). 
    489 \item  \mdl{daymod} 
    490  
    491        No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions 
     459\item  \mdl{daymod} : No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions 
    492460       have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user 
    493461       must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes. 
    494 \item  \mdl{stpctl} 
    495  
    496        Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module. 
    497 \item  \mdl{diawri} 
    498  
    499        All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which 
     462\item  \mdl{stpctl} : Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module. 
     463\item  \mdl{diawri} : All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which 
    500464       have been read in) are written along with relevant forcing and ice data. 
    501 \end{enumerate} 
     465\end{itemize} 
    502466 
    503467One new routine has been added: 
    504468 
    505 \begin{enumerate} 
    506 \item  \mdl{sbcsas} 
    507        This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface. 
     469\begin{itemize} 
     470\item  \mdl{sbcsas} : This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface. 
    508471       These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module, 
    509472       the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level. 
    510473       Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution. 
    511 \end{enumerate} 
     474\end{itemize} 
     475 
     476 
     477% Missing the description of the 2 following variables: 
     478%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field 
     479%   ln_read_frq = .false.    !  specify whether we must read frq or not 
     480 
     481 
    512482 
    513483% ================================================================ 
     
    590560reanalysis and satellite data. They use an inertial dissipative method to compute  
    591561the turbulent transfer coefficients (momentum, sensible heat and evaporation)  
    592 from the 10 metre wind speed, air temperature and specific humidity. 
     562from the 10 meters wind speed, air temperature and specific humidity. 
    593563This \citet{Large_Yeager_Rep04} dataset is available through the  
    594564\href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.  
     
    625595or larger than the one of the input atmospheric fields. 
    626596 
     597The  \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair},\np{sn\_humi},\np{sn\_prec}, \np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used (spatial and temporal interpolations).  
     598 
     599\np{cn\_dir} is the directory of location of bulk files 
     600\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.) 
     601\np{rn\_zqt}: is the height of humidity and temperature measurements (m) 
     602\np{rn\_zu}: is the height of wind measurements (m) 
     603The multiplicative factors to activate (value is 1) or deactivate (value is 0) :  
     604\np{rn\_pfac} for precipitations (total and snow) 
     605\np{rn\_efac} for evaporation  
     606\np{rn\_vfac} for for ice/ocean velocities in the calculation of wind stress   
     607 
    627608% ------------------------------------------------------------------------------------------------------------- 
    628609%        CLIO Bulk formulea 
     
    720701are sent to the atmospheric component. 
    721702 
    722 A generalised coupled interface has been developed. It is currently interfaced with OASIS 3 
    723 (\key{oasis3}) and does not support OASIS 4 
    724 \footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}.  
     703A generalised coupled interface has been developed.  
     704It is currently interfaced with OASIS-3-MCT (\key{oasis3}).  
    725705It has been successfully used to interface \NEMO to most of the European atmospheric  
    726706GCM (ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz),  
     
    787767\label{SBC_tide} 
    788768 
    789 A module is available to use the tidal potential forcing and is activated with with \key{tide}. 
    790  
    791  
    792 %------------------------------------------nam_tide---------------------------------------------------- 
     769%------------------------------------------nam_tide--------------------------------------- 
    793770\namdisplay{nam_tide} 
    794 %------------------------------------------------------------------------------------------------------------- 
    795  
    796 Concerning the tidal potential, some parameters are available in namelist \ngn{nam\_tide}: 
     771%----------------------------------------------------------------------------------------- 
     772 
     773A module is available to compute the tidal potential and use it in the momentum equation. 
     774This option is activated when \key{tide} is defined. 
     775 
     776Some parameters are available in namelist \ngn{nam\_tide}: 
    797777 
    798778- \np{ln\_tide\_pot} activate the tidal potential forcing 
     
    801781 
    802782- \np{clname} is the name of constituent 
    803  
    804783 
    805784The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem; 
     
    895874lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model). 
    896875 
     876%Christian: 
     877If the depth information is not provide in the NetCDF file, it can be estimate from the runoff input file at the initial time-step, by setting the namelist parameter \np{ln\_rnf\_depth\_ini} to true. 
     878 
     879This estimation is a simple linear relation between the runoff and a given depth :  
     880\begin{equation}  
     881h\_dep  = \frac{rn\_dep\_max} {rn\_rnf\_max}  rnf 
     882\end{equation} 
     883where  \np{rn\_dep\_max} is the given maximum depth over which the runoffs is spread,  
     884 \np{rn\_rnf\_max} is the maximum value of the runoff climatologie over the global domain 
     885and rnf is the maximum value in time of the runoff climatology at each grid cell (computed online). 
     886 
     887The estimated depth array can be output if needed in a NetCDF file by setting the namelist parameter \np{nn\_rnf\_depth\_file} to 1. 
     888 
    897889The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence  
    898890(\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}). 
     
    958950\namdisplay{namsbc_isf} 
    959951%-------------------------------------------------------------------------------------------------------- 
    960 Namelist variable in \ngn{namsbc}, \np{nn\_isf},  control the kind of ice shelf representation used.  
     952Namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation used (Fig. \ref{Fig_SBC_isf}):  
     953 
     954%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     955\begin{figure}[!h]    \begin{center} 
     956\includegraphics[width=0.8\textwidth]{Fig_SBC_isf} 
     957\caption{ \label{Fig_SBC_isf} 
     958Schematic for all the options available trough \np{nn\_isf}.} 
     959\end{center}   \end{figure} 
     960%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     961 
    961962\begin{description} 
     963\item[\np{nn\_isf}~=~0] 
     964The ice shelf routines are not used. The ice shelf melting is not computed or prescribed, the cavity have to be closed.  
     965If needed, the ice shelf melting should be added to the runoff or the precipitation file. 
     966 
    962967\item[\np{nn\_isf}~=~1] 
    963 The ice shelf cavity is represented. The fwf and heat flux are computed.  
    964 Full description, sensitivity and validation in preparation.  
     968The ice shelf cavity is represented. The fwf and heat flux are computed. Two different bulk formula are available: 
     969   \begin{description} 
     970   \item[\np{nn\_isfblk}~=~1] 
     971   The bulk formula used to compute the melt is based the one described in \citet{Hunter2006}. 
     972        This formulation is based on a balance between the upward ocean heat flux and the latent heat flux at the ice shelf base. 
     973 
     974   \item[\np{nn\_isfblk}~=~2]  
     975   The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}. 
     976        This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation). 
     977   \end{description} 
     978 
     979For this 2 bulk formulations, there are 3 different ways to compute the exchange coeficient: 
     980   \begin{description} 
     981        \item[\np{nn\_gammablk~=~0~}] 
     982   The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0} 
     983 
     984   \item[\np{nn\_gammablk~=~1~}] 
     985   The salt and heat exchange coefficients are velocity dependent and defined as $\np{rn\_gammas0} \times u_{*}$ and $\np{rn\_gammat0} \times u_{*}$ 
     986        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters). 
     987        See \citet{Jenkins2010} for all the details on this formulation. 
     988    
     989   \item[\np{nn\_gammablk~=~2~}] 
     990   The salt and heat exchange coefficients are velocity and stability dependent and defined as  
     991        $\gamma_{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}$ 
     992        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),  
     993        $\Gamma_{Turb}$ the contribution of the ocean stability and  
     994        $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 
     995        See \citet{Holland1999} for all the details on this formulation. 
     996        \end{description} 
    965997 
    966998\item[\np{nn\_isf}~=~2] 
     
    9681000The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL) 
    9691001(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}~=~3).  
    970 Furthermore the fwf is computed using the \citet{Beckmann2003} parameterisation of isf melting.  
     1002Furthermore the fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting.  
    9711003The effective melting length (\np{sn\_Leff\_isf}) is read from a file. 
    9721004 
    9731005\item[\np{nn\_isf}~=~3] 
    9741006A simple parameterisation of isf is used. The ice shelf cavity is not represented.  
    975 The fwf (\np{sn\_rnfisf}) is distributed along the ice shelf edge between the depth of the average grounding line (GL) 
    976 (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}). 
    977 Full description, sensitivity and validation in preparation. 
     1007The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between the depth of the average grounding line (GL) 
     1008(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).  
     1009The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 
    9781010 
    9791011\item[\np{nn\_isf}~=~4] 
    980 The ice shelf cavity is represented. However, the fwf (\np{sn\_fwfisf}) and heat flux (\np{sn\_qisf}) are  
    981 not computed but specified from file.  
     1012The ice shelf cavity is opened. However, the fwf is not computed but specified from file \np{sn\_fwfisf}).  
     1013The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\ 
    9821014\end{description} 
    9831015 
    984 \np{nn\_isf}~=~1 and \np{nn\_isf}~=~2 compute a melt rate based on the water masse properties, ocean velocities and depth. 
    985  This flux is thus highly dependent of the model resolution (horizontal and vertical), realism of the water masse onto the shelf ... 
    986  
    987 \np{nn\_isf}~=~3 and \np{nn\_isf}~=~4 read the melt rate and heat flux from a file. You have total control of the fwf scenario. 
    988  
    989  This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too  
    990 coarse to have realistic melting or for sensitivity studies where you want to control your input.  
    991 Full description, sensitivity and validation in preparation.  
    992  
    993 There is 2 ways to apply the fwf to NEMO. The first possibility (\np{ln\_divisf}~=~false) applied the fwf 
    994  and heat flux directly on the salinity and temperature tendancy. The second possibility (\np{ln\_divisf}~=~true) 
    995  apply the fwf as for the runoff fwf (see \S\ref{SBC_rnf}). The mass/volume addition due to the ice shelf melting is, 
    996  at each relevant depth level, added to the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}  
    997 (called from \mdl{divcur}).  
     1016 
     1017$\bullet$ \np{nn\_isf}~=~1 and \np{nn\_isf}~=~2 compute a melt rate based on the water mass properties, ocean velocities and depth. 
     1018 This flux is thus highly dependent of the model resolution (horizontal and vertical), realism of the water masses onto the shelf ...\\ 
     1019 
     1020$\bullet$ \np{nn\_isf}~=~3 and \np{nn\_isf}~=~4 read the melt rate from a file. You have total control of the fwf forcing. 
     1021This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too  
     1022coarse to have realistic melting or for studies where you need to control your heat and fw input.\\  
     1023 
     1024Two namelist parameters control how the heat and fw fluxes are passed to NEMO: \np{rn\_hisf\_tbl} and \np{ln\_divisf} 
     1025\begin{description} 
     1026\item[\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}.  
     1027This parameter is only used if \np{nn\_isf}~=~1 or \np{nn\_isf}~=~4 
     1028It allows you to control over which depth you want to spread the heat and fw fluxes.  
     1029 
     1030If \np{rn\_hisf\_tbl} = 0.0, the fluxes are put in the top level whatever is its tickness.  
     1031 
     1032If \np{rn\_hisf\_tbl} $>$ 0.0, the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells). 
     1033 
     1034\item[\np{ln\_divisf}] is a flag to apply the fw flux as a volume flux or as a salt flux.  
     1035 
     1036\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. 
     1037The fw addition due to the ice shelf melting is, at each relevant depth level, added to the horizontal divergence  
     1038(\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}.  
     1039See the runoff section \ref{SBC_rnf} for all the details about the divergence correction.  
     1040 
     1041\np{ln\_divisf}~=~false applies the fwf and heat flux directly on the salinity and temperature tendancy. 
     1042 
     1043\item[\np{ln\_conserve}] is a flag for \np{nn\_isf}~=~1. A conservative boundary layer scheme as described in \citet{Jenkins2001}  
     1044is 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.  
     1045It is only relevant for \np{ln\_divisf}~=~false.  
     1046If \np{ln\_divisf}~=~true, \np{ln\_conserve} has to be set to false to avoid a double counting of the contribution.  
     1047  
     1048\end{description} 
    9981049% 
    9991050% ================================================================ 
    10001051%        Handling of icebergs 
    10011052% ================================================================ 
    1002 \section{ Handling of icebergs (ICB) } 
     1053\section{Handling of icebergs (ICB)} 
    10031054\label{ICB_icebergs} 
    10041055%------------------------------------------namberg---------------------------------------------------- 
     
    10061057%------------------------------------------------------------------------------------------------------------- 
    10071058 
    1008 Icebergs are modelled as lagrangian particles in NEMO. 
    1009 Their physical behaviour is controlled by equations as described in  \citet{Martin_Adcroft_OM10} ). 
    1010 (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO.) 
    1011 Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described in the \ngn{namberg} namelist:  
     1059Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}. 
     1060Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ). 
     1061(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 
     1062Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described  
     1063in the \ngn{namberg} namelist:  
    10121064\np{rn\_initial\_mass} and \np{rn\_initial\_thickness}. 
    10131065Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs  
     
    10791131%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    10801132\begin{figure}[!t]    \begin{center} 
    1081 \includegraphics[width=0.8\textwidth]{./TexFiles/Figures/Fig_SBC_diurnal.pdf} 
     1133\includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal} 
    10821134\caption{ \label{Fig_SBC_diurnal}     
    10831135Example of recontruction of the diurnal cycle variation of short wave flux   
     
    11121164%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    11131165\begin{figure}[!t]  \begin{center} 
    1114 \includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_SBC_dcy.pdf} 
     1166\includegraphics[width=0.7\textwidth]{Fig_SBC_dcy} 
    11151167\caption{ \label{Fig_SBC_dcy}    
    11161168Example of recontruction of the diurnal cycle variation of short wave flux   
     
    11931245The presence at the sea surface of an ice covered area modifies all the fluxes  
    11941246transmitted to the ocean. There are several way to handle sea-ice in the system  
    1195 depending on the value of the \np{nn{\_}ice} namelist parameter 
     1247depending on the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist 
    11961248\begin{description} 
    11971249\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.  
     
    12681320% ------------------------------------------------------------------------------------------------------------- 
    12691321\subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})] 
    1270                         {Neutral drag coefficient from external wave model (\mdl{sbcwave})} 
     1322              {Neutral drag coefficient from external wave model (\mdl{sbcwave})} 
    12711323\label{SBC_wave} 
    12721324%------------------------------------------namwave---------------------------------------------------- 
    12731325\namdisplay{namsbc_wave} 
    12741326%------------------------------------------------------------------------------------------------------------- 
    1275 \begin{description} 
    1276  
    1277 \item [??] In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the  
    1278 logical variable \np{ln\_cdgw} 
    1279  in $namsbc$ namelist must be defined ${.true.}$.  
     1327 
     1328In order to read a neutral drag coeff, from an external data source ($i.e.$ a wave model), the  
     1329logical variable \np{ln\_cdgw} in \ngn{namsbc} namelist must be set to \textit{true}.  
    12801330The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the 
    12811331namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all  
    12821332the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input})  
    1283 and a 2D field of neutral drag coefficient. Then using the routine  
    1284 TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according  
    1285 to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}. 
    1286  
    1287 \end{description} 
     1333and a 2D field of neutral drag coefficient.  
     1334Then using the routine TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided,  
     1335the drag coefficient is computed according to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}. 
     1336 
    12881337 
    12891338% Griffies doc: 
    1290 % When running ocean-ice simulations, we are not explicitly representing land processes, such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, it is important to balance the hydrological cycle in ocean-ice models. We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. The result of the normalization should be a global integrated zero net water input to the ocean-ice system over a chosen time scale.  
    1291 %How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, so that there is always a zero net input of water to the ocean-ice system. Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.  
    1292 %When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean and ice models when aiming to balance the hydrological cycle. The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running ocean-ice models, not the water in any one sub-component. As an extreme example to illustrate the issue, consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up, there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. The total water contained in the ocean plus ice system is constant, but there is an exchange of water between the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle in ocean-ice models.  
    1293  
    1294  
     1339% When running ocean-ice simulations, we are not explicitly representing land processes,  
     1340% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,  
     1341% it is important to balance the hydrological cycle in ocean-ice models.  
     1342% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.  
     1343% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over  
     1344% a chosen time scale.  
     1345%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,  
     1346% so that there is always a zero net input of water to the ocean-ice system.  
     1347% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used  
     1348% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.  
     1349% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.  
     1350% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean  
     1351% and ice models when aiming to balance the hydrological cycle.  
     1352% The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running ocean-ice models,  
     1353% not the water in any one sub-component. As an extreme example to illustrate the issue,  
     1354% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,  
     1355% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.  
     1356% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between  
     1357% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle  
     1358% in ocean-ice models.  
     1359 
     1360 
     1361\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_STO.tex

    r5602 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter stochastic parametrization of EOS (STO) 
     
    57\label{STO} 
    68 
     9Authors: P.-A. Bouttier 
     10 
    711\minitoc 
    8  
    912 
    1013\newpage 
    1114$\ $\newline    % force a new line 
     15 
     16The stochastic parametrization module aims to explicitly simulate uncertainties in the model. More particularly, \cite{Brankart_OM2013} has shown that, because of the nonlinearity of the seawater equation of state, unresolved scales represent a major source of uncertainties in the computation of the large scale horizontal density gradient (from T/S large scale fields), and that the impact of these uncertainties can be simulated by random processes representing unresolved T/S fluctuations. 
     17 
     18The stochastic formulation of the equation of state can be written as: 
     19\begin{equation} 
     20 \label{eq:eos_sto} 
     21  \rho = \frac{1}{2} \sum_{i=1}^m\{ \rho[T+\Delta T_i,S+\Delta S_i,p_o(z)] + \rho[T-\Delta T_i,S-\Delta S_i,p_o(z)] \} 
     22\end{equation} 
     23where $p_o(z)$ is the reference pressure depending on the depth and $\Delta T_i$ and $\Delta S_i$ are a set of T/S perturbations defined as the scalar product of the respective local T/S gradients with random walks $\mathbf{\xi}$: 
     24\begin{equation} 
     25 \label{eq:sto_pert} 
     26 \Delta T_i = \mathbf{\xi}_i \cdot \nabla T \qquad \hbox{and} \qquad \Delta S_i = \mathbf{\xi}_i \cdot \nabla S 
     27\end{equation} 
     28$\mathbf{\xi}_i$ are produced by a first-order autoregressive processes (AR-1) with a parametrized decorrelation time scale, and horizontal and vertical standard deviations $\sigma_s$. $\mathbf{\xi}$ are uncorrelated over the horizontal and fully correlated along the vertical. 
     29 
     30 
     31\section{Stochastic processes} 
     32\label{STO_the_details} 
     33 
     34The starting point of our implementation of stochastic parameterizations 
     35in NEMO is to observe that many existing parameterizations are based 
     36on autoregressive processes, which are used as a basic source of randomness 
     37to transform a deterministic model into a probabilistic model. 
     38A generic approach is thus to add one single new module in NEMO, 
     39generating processes with appropriate statistics 
     40to simulate each kind of uncertainty in the model 
     41(see \cite{Brankart_al_GMD2015} for more details). 
     42 
     43In practice, at every model grid point, independent Gaussian autoregressive 
     44processes~$\xi^{(i)},\,i=1,\ldots,m$ are first generated 
     45using the same basic equation: 
     46 
     47\begin{equation} 
     48\label{eq:autoreg} 
     49\xi^{(i)}_{k+1} = a^{(i)} \xi^{(i)}_k + b^{(i)} w^{(i)} + c^{(i)} 
     50\end{equation} 
     51 
     52\noindent 
     53where $k$ is the index of the model timestep; and 
     54$a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are parameters defining 
     55the mean ($\mu^{(i)}$) standard deviation ($\sigma^{(i)}$) 
     56and correlation timescale ($\tau^{(i)}$) of each process: 
     57 
     58\begin{itemize} 
     59\item for order~1 processes, $w^{(i)}$ is a Gaussian white noise, 
     60with zero mean and standard deviation equal to~1, and the parameters 
     61$a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are given by: 
     62 
     63\begin{equation} 
     64\label{eq:ord1} 
     65\left\{ 
     66\begin{array}{l} 
     67a^{(i)} = \varphi \\ 
     68b^{(i)} = \sigma^{(i)} \sqrt{ 1 - \varphi^2 }  
     69 \qquad\qquad\mbox{with}\qquad\qquad 
     70\varphi = \exp \left( - 1 / \tau^{(i)} \right) \\ 
     71c^{(i)} = \mu^{(i)} \left( 1 - \varphi \right) \\ 
     72\end{array} 
     73\right. 
     74\end{equation} 
     75 
     76\item for order~$n>1$ processes, $w^{(i)}$ is an order~$n-1$ autoregressive process, 
     77with zero mean, standard deviation equal to~$\sigma^{(i)}$; correlation timescale 
     78equal to~$\tau^{(i)}$; and the parameters 
     79$a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are given by: 
     80 
     81\begin{equation} 
     82\label{eq:ord2} 
     83\left\{ 
     84\begin{array}{l} 
     85a^{(i)} = \varphi \\ 
     86b^{(i)} = \frac{n-1}{2(4n-3)} \sqrt{ 1 - \varphi^2 }  
     87 \qquad\qquad\mbox{with}\qquad\qquad 
     88\varphi = \exp \left( - 1 / \tau^{(i)} \right) \\ 
     89c^{(i)} = \mu^{(i)} \left( 1 - \varphi \right) \\ 
     90\end{array} 
     91\right. 
     92\end{equation} 
     93 
     94\end{itemize} 
     95 
     96\noindent 
     97In this way, higher order processes can be easily generated recursively using the same piece of code implementing Eq.~(\ref{eq:autoreg}), and using succesively processes from order $0$ to~$n-1$ as~$w^{(i)}$. 
     98The parameters in Eq.~(\ref{eq:ord2}) are computed so that this recursive application 
     99of Eq.~(\ref{eq:autoreg}) leads to processes with the required standard deviation 
     100and correlation timescale, with the additional condition that 
     101the $n-1$ first derivatives of the autocorrelation function 
     102are equal to zero at~$t=0$, so that the resulting processes 
     103become smoother and smoother as $n$ is increased. 
     104 
     105Overall, this method provides quite a simple and generic way of generating a wide class of stochastic processes. However, this also means that new model parameters are needed to specify each of these stochastic processes. As in any parameterization of lacking physics, a very important issues then to tune these new parameters using either first principles, model simulations, or real-world observations. 
     106 
     107\section{Implementation details} 
     108\label{STO_thech_details} 
     109The computer code implementing stochastic parametrisations is made of one single FORTRAN module, 
     110with 3 public routines to be called by the model (in our case, NEMO): 
     111 
     112The first routine ({sto\_par}) is a direct implementation of Eq.~(\ref{eq:autoreg}), 
     113applied at each model grid point (in 2D or 3D), 
     114and called at each model time step ($k$) to update 
     115every autoregressive process ($i=1,\ldots,m$). 
     116This routine also includes a filtering operator, applied to $w^{(i)}$, 
     117to introduce a spatial correlation between the stochastic processes. 
     118 
     119The second routine ({sto\_par\_init}) 
     120is an initialization routine mainly dedicated 
     121to the computation of parameters $a^{(i)}, b^{(i)}, c^{(i)}$ 
     122for each autoregressive process, as a function of the statistical properties 
     123required by the model user (mean, standard deviation, time correlation, 
     124order of the process,\ldots). Parameters for the processes can be specified through the following namelist parameters: 
     125\begin{alltt} 
     126\tiny 
     127\begin{verbatim} 
     128   nn_sto_eos = 1                ! number of independent random walks  
     129   rn_eos_stdxy = 1.4            ! random walk horz. standard deviation (in grid points) 
     130   rn_eos_stdz  = 0.7            ! random walk vert. standard deviation (in grid points) 
     131   rn_eos_tcor  = 1440.0         ! random walk time correlation (in timesteps) 
     132   nn_eos_ord  = 1               ! order of autoregressive processes 
     133   nn_eos_flt  = 0               ! passes of Laplacian filter 
     134   rn_eos_lim  = 2.0             ! limitation factor (default = 3.0) 
     135\end{verbatim} 
     136\end{alltt} 
     137This routine also includes the initialization (seeding) 
     138of the random number generator. 
     139 
     140The third routine ({sto\_rst\_write}) writes a ``restart file'' 
     141with the current value of all autoregressive processes 
     142to allow restarting a simulation from where it has been interrupted. 
     143This file also contains the current state of the random number generator. 
     144In case of a restart, this file is then read by the initialization routine 
     145({sto\_par\_init}), so that the simulation can continue exactly 
     146as if it was not interrupted. 
     147Restart capabilities of the module are driven by the following namelist parameters: 
     148\begin{alltt} 
     149\tiny 
     150\begin{verbatim} 
     151   ln_rststo = .false.           ! start from mean parameter (F) or from restart file (T) 
     152   ln_rstseed = .true.           ! read seed of RNG from restart file 
     153   cn_storst_in  = "restart_sto" !  suffix of stochastic parameter restart file (input) 
     154   cn_storst_out = "restart_sto" !  suffix of stochastic parameter restart file (output) 
     155\end{verbatim} 
     156\end{alltt} 
     157 
     158In the particular case of the stochastic equation of state, there is also an additional module ({sto\_pts}) implementing Eq~\ref{eq:sto_pert} and specific piece of code in the equation of state implementing Eq~\ref{eq:eos_sto}. 
     159 
     160 
     161\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_STP.tex

    r4147 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13 
    24% ================================================================ 
     
    196198%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    197199\begin{figure}[!t]     \begin{center} 
    198 \includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_TimeStepping_flowchart.pdf} 
     200\includegraphics[width=0.7\textwidth]{Fig_TimeStepping_flowchart} 
    199201\caption{   \label{Fig_TimeStep_flowchart} 
    200202Sketch of the leapfrog time stepping sequence in \NEMO from \citet{Leclair_Madec_OM09}.  
     
    288290%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    289291\begin{figure}[!t]     \begin{center} 
    290 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_MLF_forcing.pdf} 
     292\includegraphics[width=0.90\textwidth]{Fig_MLF_forcing} 
    291293\caption{   \label{Fig_MLF_forcing} 
    292294Illustration of forcing integration methods.  
     
    424426} 
    425427%% 
     428\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_TRA.tex

    r5602 r7260  
    1 % ================================================================ 
    2 % Chapter 1 � Ocean Tracers (TRA) 
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
     3% ================================================================ 
     4% Chapter 1 ——— Ocean Tracers (TRA) 
    35% ================================================================ 
    46\chapter{Ocean Tracers (TRA)} 
     
    3638(BBL) parametrisation, and an internal damping (DMP) term. The terms QSR,  
    3739BBC, BBL and DMP are optional. The external forcings and parameterisations  
    38 require complex inputs and complex calculations (e.g. bulk formulae, estimation  
     40require complex inputs and complex calculations ($e.g.$ bulk formulae, estimation  
    3941of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and  
    4042described in chapters \S\ref{SBC}, \S\ref{LDF} and  \S\ref{ZDF}, respectively.  
    41 Note that \mdl{tranpc}, the non-penetrative convection module,  although  
    42 (temporarily) located in the NEMO/OPA/TRA directory, is described with the  
    43 model vertical physics (ZDF). 
    44 %%% 
    45 \gmcomment{change the position of eosbn2 in the reference code} 
    46 %%% 
     43Note that \mdl{tranpc}, the non-penetrative convection module, although  
     44located in the NEMO/OPA/TRA directory as it directly modifies the tracer fields,  
     45is described with the model vertical physics (ZDF) together with other available  
     46parameterization of convection. 
    4747 
    4848In the present chapter we also describe the diagnostic equations used to compute  
    49 the sea-water properties (density, Brunt-Vais\"{a}l\"{a} frequency, specific heat and  
     49the sea-water properties (density, Brunt-V\"{a}is\"{a}l\"{a} frequency, specific heat and  
    5050freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}). 
    5151 
     
    5656found in the \textit{trattt} or \textit{trattt\_xxx} module, in the NEMO/OPA/TRA directory. 
    5757 
    58 The user has the option of extracting each tendency term on the rhs of the tracer  
    59 equation for output (\key{trdtra} is defined), as described in Chap.~\ref{MISC}. 
     58The user has the option of extracting each tendency term on the RHS of the tracer  
     59equation for output (\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}~=~true), as described in Chap.~\ref{DIA}. 
    6060 
    6161$\ $\newline    % force a new ligne 
     
    9191%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    9292\begin{figure}[!t]    \begin{center} 
    93 \includegraphics[width=0.9\textwidth]{./TexFiles/Figures/Fig_adv_scheme.pdf} 
     93\includegraphics[width=0.9\textwidth]{Fig_adv_scheme} 
    9494\caption{   \label{Fig_adv_scheme}  
    9595Schematic representation of some ways used to evaluate the tracer value  
     
    125125\end{description} 
    126126In all cases, this boundary condition retains local conservation of tracer.  
    127 Global conservation is obtained in both rigid-lid and non-linear free surface  
    128 cases, but not in the linear free surface case. Nevertheless, in the latter 
    129 case, it is achieved to a good approximation since the non-conservative  
     127Global conservation is obtained in non-linear free surface case,  
     128but \textit{not} in the linear free surface case. Nevertheless, in the latter case,  
     129it is achieved to a good approximation since the non-conservative  
    130130term is the product of the time derivative of the tracer and the free surface  
    131131height, two quantities that are not correlated (see \S\ref{PE_free_surface},  
     
    133133 
    134134The velocity field that appears in (\ref{Eq_tra_adv}) and (\ref{Eq_tra_adv_zco})  
    135 is the centred (\textit{now}) \textit{eulerian} ocean velocity (see Chap.~\ref{DYN}).  
    136 When eddy induced velocity (\textit{eiv}) parameterisation is used it is the \textit{now}  
    137 \textit{effective} velocity ($i.e.$ the sum of the eulerian and eiv velocities) which is used. 
     135is the centred (\textit{now}) \textit{effective} ocean velocity, $i.e.$ the \textit{eulerian} velocity 
     136(see Chap.~\ref{DYN}) plus the eddy induced velocity (\textit{eiv})  
     137and/or the mixed layer eddy induced velocity (\textit{eiv}) 
     138when those parameterisations are used (see Chap.~\ref{LDF}). 
    138139 
    139140The choice of an advection scheme is made in the \textit{\ngn{nam\_traadv}} namelist, by  
     
    146147 
    147148Note that  
    148 (1) cen2, cen4 and TVD schemes require an explicit diffusion  
     149(1) cen2 and TVD schemes require an explicit diffusion  
    149150operator while the other schemes are diffusive enough so that they do not  
    150151require additional diffusion ;  
    151 (2) cen2, cen4, MUSCL2, and UBS are not \textit{positive} schemes 
     152(2) cen2, MUSCL2, and UBS are not \textit{positive} schemes 
    152153\footnote{negative values can appear in an initially strictly positive tracer field  
    153154which is advected} 
     
    189190temperature is close to the freezing point). 
    190191This combined scheme has been included for specific grid points in the ORCA2  
    191 and ORCA4 configurations only. This is an obsolescent feature as the recommended  
     192configuration only. This is an obsolescent feature as the recommended  
    192193advection scheme for the ORCA configuration is TVD (see  \S\ref{TRA_adv_tvd}). 
    193194 
     
    196197have this order of accuracy. \gmcomment{Note also that ... blah, blah} 
    197198 
    198 % ------------------------------------------------------------------------------------------------------------- 
    199 %        4nd order centred scheme   
    200 % ------------------------------------------------------------------------------------------------------------- 
    201 \subsection   [$4^{nd}$ order centred scheme (cen4) (\np{ln\_traadv\_cen4})] 
    202            {$4^{nd}$ order centred scheme (cen4) (\np{ln\_traadv\_cen4}=true)} 
    203 \label{TRA_adv_cen4} 
    204  
    205 In the $4^{th}$ order formulation (to be implemented), tracer values are  
    206 evaluated at velocity points as a $4^{th}$ order interpolation, and thus depend on  
    207 the four neighbouring $T$-points. For example, in the $i$-direction: 
    208 \begin{equation} \label{Eq_tra_adv_cen4} 
    209 \tau _u^{cen4}  
    210 =\overline{   T - \frac{1}{6}\,\delta _i \left[ \delta_{i+1/2}[T] \,\right]   }^{\,i+1/2} 
    211 \end{equation} 
    212  
    213 Strictly speaking, the cen4 scheme is not a $4^{th}$ order advection scheme  
    214 but a $4^{th}$ order evaluation of advective fluxes, since the divergence of  
    215 advective fluxes \eqref{Eq_tra_adv} is kept at $2^{nd}$ order. The phrase ``$4^{th}$  
    216 order scheme'' used in oceanographic literature is usually associated  
    217 with the scheme presented here. Introducing a \textit{true} $4^{th}$ order advection  
    218 scheme is feasible but, for consistency reasons, it requires changes in the  
    219 discretisation of the tracer advection together with changes in both the  
    220 continuity equation and the momentum advection terms.   
    221  
    222 A direct consequence of the pseudo-fourth order nature of the scheme is that  
    223 it is not non-diffusive, i.e. the global variance of a tracer is not preserved using  
    224 \textit{cen4}. Furthermore, it must be used in conjunction with an explicit  
    225 diffusion operator to produce a sensible solution. The time-stepping is also  
    226 performed using a leapfrog scheme in conjunction with an Asselin time-filter,  
    227 so $T$ in (\ref{Eq_tra_adv_cen4}) is the \textit{now} tracer. 
    228  
    229 At a $T$-grid cell adjacent to a boundary (coastline, bottom and surface), an  
    230 additional hypothesis must be made to evaluate $\tau _u^{cen4}$. This  
    231 hypothesis usually reduces the order of the scheme. Here we choose to set  
    232 the gradient of $T$ across the boundary to zero. Alternative conditions can be  
    233 specified, such as a reduction to a second order scheme for these near boundary  
    234 grid points. 
    235199 
    236200% ------------------------------------------------------------------------------------------------------------- 
     
    270234used for the diffusive part.  
    271235 
     236An additional option has been added controlled by \np{ln\_traadv\_tvd\_zts}.  
     237By setting this logical to true, a TVD scheme is used on both horizontal and vertical direction,  
     238but on the latter, a split-explicit time stepping is used, with 5 sub-timesteps.  
     239This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}.  
     240Note that in this case, a similar split-explicit time stepping should be used on  
     241vertical advection of momentum to ensure a better stability (see \np{ln\_dynzad\_zts} in \S\ref{DYN_zad}). 
     242 
     243 
    272244% ------------------------------------------------------------------------------------------------------------- 
    273245%        MUSCL scheme   
     
    296268 
    297269For an ocean grid point adjacent to land and where the ocean velocity is  
    298 directed toward land, two choices are available: an upstream flux  
    299 (\np{ln\_traadv\_muscl}=true) or a second order flux  
    300 (\np{ln\_traadv\_muscl2}=true). Note that the latter choice does not ensure  
    301 the \textit{positive} character of the scheme. Only the former can be used  
    302 on both active and passive tracers. The two MUSCL schemes are implemented  
    303 in the \mdl{traadv\_tvd} and \mdl{traadv\_tvd2} modules. 
     270directed toward land, two choices are available: an upstream flux (\np{ln\_traadv\_muscl}=true)  
     271or a second order flux (\np{ln\_traadv\_muscl2}=true).  
     272Note that the latter choice does not ensure the \textit{positive} character of the scheme.  
     273Only the former can be used on both active and passive tracers.  
     274The two MUSCL schemes are implemented in the \mdl{traadv\_tvd} and \mdl{traadv\_tvd2} modules. 
     275 
     276Note that when using np{ln\_traadv\_msc\_ups}~=~true in addition to \np{ln\_traadv\_muscl}=true,  
     277the MUSCL fluxes are replaced by upstream fluxes in vicinity of river mouths. 
    304278 
    305279% ------------------------------------------------------------------------------------------------------------- 
     
    416390direction (as for the UBS case) should be implemented to restore this property. 
    417391 
    418  
    419 % ------------------------------------------------------------------------------------------------------------- 
    420 %        PPM scheme   
    421 % ------------------------------------------------------------------------------------------------------------- 
    422 \subsection   [Piecewise Parabolic Method (PPM) (\np{ln\_traadv\_ppm})] 
    423          {Piecewise Parabolic Method (PPM) (\np{ln\_traadv\_ppm}=true)} 
    424 \label{TRA_adv_ppm} 
    425  
    426 The Piecewise Parabolic Method (PPM) proposed by Colella and Woodward (1984)  
    427 \sgacomment{reference?} 
    428 is based on a quadradic piecewise construction. Like the QCK scheme, it is associated  
    429 with the ULTIMATE QUICKEST limiter \citep{Leonard1991}. It has been implemented  
    430 in \NEMO by G. Reffray (MERCATOR-ocean) but is not yet offered in the reference  
    431 version 3.3. 
    432392 
    433393% ================================================================ 
     
    464424surfaces is given by:  
    465425\begin{equation} \label{Eq_tra_ldf_lap} 
    466 D_T^{lT} =\frac{1}{b_tT} \left( \; 
     426D_T^{lT} =\frac{1}{b_t} \left( \; 
    467427   \delta _{i}\left[ A_u^{lT} \; \frac{e_{2u}\,e_{3u}}{e_{1u}} \;\delta _{i+1/2} [T] \right]  
    468428+ \delta _{j}\left[ A_v^{lT} \;  \frac{e_{1v}\,e_{3v}}{e_{2v}} \;\delta _{j+1/2} [T] \right]  \;\right) 
     
    661621the thickness of the top model layer.  
    662622 
    663 Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components ($i.e.$ atmosphere, sea-ice, land), 
    664 the change in the heat and salt content of the surface layer of the ocean is due both  
    665 to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$) 
    666  and to the heat and salt content of the mass exchange. 
    667 \sgacomment{ the following does not apply to the release to which this documentation is  
    668 attached and so should not be included .... 
    669 In a forthcoming release, these two parts, computed in the surface module (SBC), will be included directly 
    670 in $Q_{ns}$, the surface heat flux and $F_{salt}$, the surface salt flux. 
    671 The specification of these fluxes is further detailed in the SBC chapter (see \S\ref{SBC}).  
    672 This change will provide a forcing formulation which is the same for any tracer (including temperature and salinity). 
    673   
    674 In the current version, the situation is a little bit more complicated. } 
     623Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components  
     624($i.e.$ atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer  
     625of the ocean is due both to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$)  
     626and to the heat and salt content of the mass exchange. They are both included directly in $Q_{ns}$,  
     627the surface heat flux, and $F_{salt}$, the surface salt flux (see \S\ref{SBC} for further details). 
     628By doing this, the forcing formulation is the same for any tracer (including temperature and salinity). 
    675629 
    676630The surface module (\mdl{sbcmod}, see \S\ref{SBC}) provides the following  
     
    679633$\bullet$ $Q_{ns}$, the non-solar part of the net surface heat flux that crosses the sea surface  
    680634(i.e. the difference between the total surface heat flux and the fraction of the short wave flux that  
    681 penetrates into the water column, see \S\ref{TRA_qsr}) 
    682  
    683 $\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation) 
    684  
    685 $\bullet$ $\textit{emp}_S$, an equivalent mass flux taking into account the effect of ice-ocean mass exchange 
    686  
    687 $\bullet$ \textit{rnf}, the mass flux associated with runoff (see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies) 
    688  
    689 The $\textit{emp}_S$ field is not simply the budget of evaporation-precipitation+freezing-melting because  
    690 the sea-ice is not currently embedded in the ocean but levitates above it. There is no mass 
    691 exchanged between the sea-ice and the ocean. Instead we only take into account the salt 
    692 flux associated with the non-zero salinity of sea-ice, and the concentration/dilution effect 
    693 due to the freezing/melting (F/M) process. These two parts of the forcing are then converted into  
    694 an equivalent mass flux given by $\textit{emp}_S - \textit{emp}$. As a result of this mess,  
    695 the surface boundary condition on temperature and salinity is applied as follows: 
    696  
    697 In the nonlinear free surface case (\key{vvl} is defined): 
     635penetrates into the water column, see \S\ref{TRA_qsr}) plus the heat content associated with  
     636of the mass exchange with the atmosphere and lands. 
     637 
     638$\bullet$ $\textit{sfx}$, the salt flux resulting from ice-ocean mass exchange (freezing, melting, ridging...) 
     639 
     640$\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation)  
     641 and possibly with the sea-ice and ice-shelves. 
     642 
     643$\bullet$ \textit{rnf}, the mass flux associated with runoff  
     644(see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies) 
     645 
     646$\bullet$ \textit{fwfisf}, the mass flux associated with ice shelf melt, (see \S\ref{SBC_isf} for further details  
     647on how the ice shelf melt is computed and applied).\\ 
     648 
     649In the non-linear free surface case (\key{vvl} is defined), the surface boundary condition  
     650on temperature and salinity is applied as follows: 
    698651\begin{equation} \label{Eq_tra_sbc} 
     652\begin{aligned} 
     653 &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }  &\overline{ Q_{ns}       }^t  & \\  
     654& F^S =\frac{ 1 }{\rho _o  \,      \left. e_{3t} \right|_{k=1} }  &\overline{ \textit{sfx} }^t   & \\    
     655 \end{aligned} 
     656\end{equation}  
     657where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps  
     658($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the  
     659divergence of odd and even time step (see \S\ref{STP}). 
     660 
     661In the linear free surface case (\key{vvl} is \textit{not} defined),  
     662an additional term has to be added on both temperature and salinity.  
     663On temperature, this term remove the heat content associated with mass exchange 
     664that has been added to $Q_{ns}$. On salinity, this term mimics the concentration/dilution effect that 
     665would have resulted from a change in the volume of the first level. 
     666The resulting surface boundary condition is applied as follows: 
     667\begin{equation} \label{Eq_tra_sbc_lin} 
    699668\begin{aligned} 
    700669 &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }    
     
    702671% 
    703672& F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} }  
    704            &\overline{ \left( (\textit{emp}_S - \textit{emp})\;\left. S \right|_{k=1}  \right) }^t   & \\    
     673           &\overline{ \left( \;\textit{sfx} - \textit{emp} \;\left. S \right|_{k=1}  \right) }^t   & \\    
    705674 \end{aligned} 
    706675\end{equation}  
    707  
    708 In the linear free surface case (\key{vvl} not defined): 
    709 \begin{equation} \label{Eq_tra_sbc_lin} 
    710 \begin{aligned} 
    711  &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} }  &\overline{ Q_{ns} }^t  & \\  
    712 % 
    713 & F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} }  
    714            &\overline{ \left( \textit{emp}_S\;\left. S \right|_{k=1}  \right) }^t   & \\    
    715  \end{aligned} 
    716 \end{equation}  
    717 where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps  
    718 ($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the  
    719 divergence of odd and even time step (see \S\ref{STP}). 
    720  
    721 The two set of equations, \eqref{Eq_tra_sbc} and \eqref{Eq_tra_sbc_lin}, are obtained  
    722 by assuming that the temperature of precipitation and evaporation are equal to 
    723 the ocean surface temperature and that their salinity is zero. Therefore, the heat content 
    724 of the \textit{emp} budget must be added to the temperature equation in the variable volume case,  
    725 while it does not appear in the constant volume case. Similarly, the \textit{emp} budget affects  
    726 the ocean surface salinity in the constant volume case (through the concentration dilution effect) 
    727 while it does not appears explicitly in the variable volume case since salinity change will be 
    728 induced by volume change. In both constant and variable volume cases, surface salinity  
    729 will change with ice-ocean salt flux and F/M flux (both contained in $\textit{emp}_S - \textit{emp}$) without mass exchanges. 
    730  
    731 Note that the concentration/dilution effect due to F/M is computed using 
    732 a constant ice salinity as well as a constant ocean salinity.  
    733 This approximation suppresses the correlation between \textit{SSS}  
    734 and F/M flux, allowing the ice-ocean salt exchanges to be conservative. 
    735 Indeed, if this approximation is not made, even if the F/M budget is zero  
    736 on average over the whole ocean domain and over the seasonal cycle,  
    737 the associated salt flux is not zero, since sea-surface salinity and F/M flux are  
    738 intrinsically correlated (high \textit{SSS} are found where freezing is  
    739 strong whilst low \textit{SSS} is usually associated with high melting areas). 
    740  
    741 Even using this approximation, an exact conservation of heat and salt content  
    742 is only achieved in the variable volume case. In the constant volume case,  
    743 there is a small imbalance associated with the product $(\partial_t\eta - \textit{emp}) * \textit{SSS}$. 
    744 Nevertheless, the salt content variation is quite small and will not induce 
    745 a long term drift as there is no physical reason for $(\partial_t\eta - \textit{emp})$  
    746 and \textit{SSS} to be correlated \citep{Roullet_Madec_JGR00}.  
    747 Note that, while quite small, the imbalance in the constant volume case is larger  
     676Note that an exact conservation of heat and salt content is only achieved with non-linear free surface.  
     677In the linear free surface case, there is a small imbalance. The imbalance is larger  
    748678than the imbalance associated with the Asselin time filter \citep{Leclair_Madec_OM09}.  
    749 This is the reason why the modified filter is not applied in the constant volume case. 
     679This is the reason why the modified filter is not applied in the linear free surface case (see \S\ref{STP}). 
    750680 
    751681% ------------------------------------------------------------------------------------------------------------- 
     
    821751($i.e.$ the inverses of the extinction length scales) are tabulated over 61 nonuniform  
    822752chlorophyll classes ranging from 0.01 to 10 g.Chl/L (see the routine \rou{trc\_oce\_rgb}  
    823 in \mdl{trc\_oce} module). Three types of chlorophyll can be chosen in the RGB formulation: 
    824 (1) a constant 0.05 g.Chl/L value everywhere (\np{nn\_chdta}=0) ; (2) an observed  
    825 time varying chlorophyll (\np{nn\_chdta}=1) ; (3) simulated time varying chlorophyll 
    826 by TOP biogeochemical model (\np{ln\_qsr\_bio}=true). In the latter case, the RGB  
    827 formulation is used to calculate both the phytoplankton light limitation in PISCES  
    828 or LOBSTER and the oceanic heating rate.  
    829  
     753in \mdl{trc\_oce} module). Four types of chlorophyll can be chosen in the RGB formulation: 
     754\begin{description}  
     755\item[\np{nn\_chdta}=0]  
     756a constant 0.05 g.Chl/L value everywhere ;  
     757\item[\np{nn\_chdta}=1]   
     758an observed time varying chlorophyll deduced from satellite surface ocean color measurement  
     759spread uniformly in the vertical direction ;  
     760\item[\np{nn\_chdta}=2]   
     761same as previous case except that a vertical profile of chlorophyl is used.  
     762Following \cite{Morel_Berthon_LO89}, the profile is computed from the local surface chlorophyll value ; 
     763\item[\np{ln\_qsr\_bio}=true]   
     764simulated time varying chlorophyll by TOP biogeochemical model.  
     765In this case, the RGB formulation is used to calculate both the phytoplankton  
     766light limitation in PISCES or LOBSTER and the oceanic heating rate.  
     767\end{description}  
    830768The trend in \eqref{Eq_tra_qsr} associated with the penetration of the solar radiation  
    831769is added to the temperature trend, and the surface heat flux is modified in routine \mdl{traqsr}.  
     
    842780%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    843781\begin{figure}[!t]     \begin{center} 
    844 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_TRA_Irradiance.pdf} 
     782\includegraphics[width=1.0\textwidth]{Fig_TRA_Irradiance} 
    845783\caption{    \label{Fig_traqsr_irradiance} 
    846784Penetration profile of the downward solar irradiance calculated by four models.  
     
    859797\label{TRA_bbc} 
    860798%--------------------------------------------nambbc-------------------------------------------------------- 
    861 \namdisplay{namtra_bbc} 
     799\namdisplay{nambbc} 
    862800%-------------------------------------------------------------------------------------------------------------- 
    863801%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    864802\begin{figure}[!t]     \begin{center} 
    865 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_TRA_geoth.pdf} 
     803\includegraphics[width=1.0\textwidth]{Fig_TRA_geoth} 
    866804\caption{   \label{Fig_geothermal} 
    867805Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{Emile-Geay_Madec_OS09}. 
     
    973911%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    974912\begin{figure}[!t]   \begin{center} 
    975 \includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_BBL_adv.pdf} 
     913\includegraphics[width=0.7\textwidth]{Fig_BBL_adv} 
    976914\caption{   \label{Fig_bbl}   
    977915Advective/diffusive Bottom Boundary Layer. The BBL parameterisation is  
     
    11031041\subsection[DMP\_TOOLS]{Generating resto.nc using DMP\_TOOLS} 
    11041042 
    1105 DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$. Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled and run on the same machine as the NEMO model. A mesh\_mask.nc file for the model configuration is required as an input. This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1. The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work. The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 
     1043DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$.  
     1044Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled  
     1045and run on the same machine as the NEMO model. A mesh\_mask.nc file for the model configuration is required as an input.  
     1046This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1.  
     1047The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work.  
     1048The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 
    11061049 
    11071050%--------------------------------------------nam_dmp_create------------------------------------------------- 
     
    11111054\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. 
    11121055 
    1113 The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations. \np{ln\_full\_field} specifies that newtonian damping should be applied to the whole model domain. \np{ln\_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea for the ORCA4, ORCA2 and ORCA05 configurations. If \np{ln\_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference configurations with previous model versions. \np{ln\_coast} specifies that the restoration coefficient should be reduced near to coastlines. This option only has an effect if \np{ln\_full\_field} is true. \np{ln\_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer. Finally \np{ln\_custom} specifies that the custom module will be called. This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region. 
    1114  
    1115 The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn\_hdmp}. Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to the full values of a 10$^{\circ}$ latitud band. This is often used because of the short adjustment time scale in the equatorial region \citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a hyperbolic tangent, with \np{rn\_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}.   
     1056The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations.  
     1057\np{ln\_full\_field} specifies that newtonian damping should be applied to the whole model domain.  
     1058\np{ln\_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea  
     1059for the ORCA4, ORCA2 and ORCA05 configurations.  
     1060If \np{ln\_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as  
     1061a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference  
     1062configurations with previous model versions.  
     1063\np{ln\_coast} specifies that the restoration coefficient should be reduced near to coastlines.  
     1064This option only has an effect if \np{ln\_full\_field} is true.  
     1065\np{ln\_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer.  
     1066Finally \np{ln\_custom} specifies that the custom module will be called.  
     1067This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region. 
     1068 
     1069The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn\_hdmp}.  
     1070Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to  
     1071the full values of a 10\deg latitud band.  
     1072This is often used because of the short adjustment time scale in the equatorial region  
     1073\citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a  
     1074hyperbolic tangent, with \np{rn\_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}.   
    11161075 
    11171076% ================================================================ 
     
    11671126%        Equation of State 
    11681127% ------------------------------------------------------------------------------------------------------------- 
    1169 \subsection{Equation of State (\np{nn\_eos} = 0, 1 or 2)} 
     1128\subsection{Equation Of Seawater (\np{nn\_eos} = -1, 0, or 1)} 
    11701129\label{TRA_eos} 
    11711130 
    1172 It is necessary to know the equation of state for the ocean very accurately  
    1173 to determine stability properties (especially the Brunt-Vais\"{a}l\"{a} frequency),  
    1174 particularly in the deep ocean. The ocean seawater volumic mass, $\rho$,  
    1175 abusively called density, is a non linear empirical function of \textit{in situ}  
    1176 temperature, salinity and pressure. The reference equation of state is that  
    1177 defined by the Joint Panel on Oceanographic Tables and Standards  
    1178 \citep{UNESCO1983}. It was the standard equation of state used in early  
    1179 releases of OPA. However, even though this computation is fully vectorised,  
    1180 it is quite time consuming ($15$ to $20${\%} of the total CPU time) since  
    1181 it requires the prior computation of the \textit{in situ} temperature from the  
    1182 model \textit{potential} temperature using the \citep{Bryden1973} polynomial  
    1183 for adiabatic lapse rate and a $4^th$ order Runge-Kutta integration scheme.  
    1184 Since OPA6, we have used the \citet{JackMcD1995} equation of state for  
    1185 seawater instead. It allows the computation of the \textit{in situ} ocean density  
    1186 directly as a function of \textit{potential} temperature relative to the surface  
    1187 (an \NEMO variable), the practical salinity (another \NEMO variable) and the  
    1188 pressure (assuming no pressure variation along geopotential surfaces, $i.e.$  
    1189 the pressure in decibars is approximated by the depth in meters).  
    1190 Both the \citet{UNESCO1983} and \citet{JackMcD1995} equations of state  
    1191 have exactly the same except that the values of the various coefficients have  
    1192 been adjusted by \citet{JackMcD1995} in order to directly use the \textit{potential}  
    1193 temperature instead of the \textit{in situ} one. This reduces the CPU time of the  
    1194 \textit{in situ} density computation to about $3${\%} of the total CPU time,  
    1195 while maintaining a quite accurate equation of state. 
    1196  
    1197 In the computer code, a \textit{true} density anomaly, $d_a= \rho / \rho_o - 1$,  
    1198 is computed, with $\rho_o$ a reference volumic mass. Called \textit{rau0}  
    1199 in the code, $\rho_o$ is defined in \mdl{phycst}, and a value of $1,035~Kg/m^3$.  
     1131The Equation Of Seawater (EOS) is an empirical nonlinear thermodynamic relationship  
     1132linking seawater density, $\rho$, to a number of state variables,  
     1133most typically temperature, salinity and pressure.  
     1134Because density gradients control the pressure gradient force through the hydrostatic balance,  
     1135the equation of state provides a fundamental bridge between the distribution of active tracers  
     1136and the fluid dynamics. Nonlinearities of the EOS are of major importance, in particular  
     1137influencing the circulation through determination of the static stability below the mixed layer,  
     1138thus controlling rates of exchange between the atmosphere  and the ocean interior \citep{Roquet_JPO2015}.  
     1139Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{UNESCO1983})  
     1140or TEOS-10 \citep{TEOS10} standards should be used anytime a simulation of the real  
     1141ocean circulation is attempted \citep{Roquet_JPO2015}.  
     1142The use of TEOS-10 is highly recommended because  
     1143\textit{(i)} it is the new official EOS,  
     1144\textit{(ii)} it is more accurate, being based on an updated database of laboratory measurements, and  
     1145\textit{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature  
     1146and practical salinity for EOS-980, both variables being more suitable for use as model variables  
     1147\citep{TEOS10, Graham_McDougall_JPO13}.  
     1148EOS-80 is an obsolescent feature of the NEMO system, kept only for backward compatibility. 
     1149For process studies, it is often convenient to use an approximation of the EOS. To that purposed,  
     1150a simplified EOS (S-EOS) inspired by \citet{Vallis06} is also available. 
     1151 
     1152In the computer code, a density anomaly, $d_a= \rho / \rho_o - 1$,  
     1153is computed, with $\rho_o$ a reference density. Called \textit{rau0}  
     1154in the code, $\rho_o$ is set in \mdl{phycst} to a value of $1,026~Kg/m^3$.  
    12001155This is a sensible choice for the reference density used in a Boussinesq ocean  
    12011156climate model, as, with the exception of only a small percentage of the ocean,  
    1202 density in the World Ocean varies by no more than 2$\%$ from $1,035~kg/m^3$  
    1203 \citep{Gill1982}. 
    1204  
    1205 Options are defined through the  \ngn{nameos} namelist variables. 
    1206 The default option (namelist parameter \np{nn\_eos}=0) is the \citet{JackMcD1995}  
    1207 equation of state. Its use is highly recommended. However, for process studies,  
    1208 it is often convenient to use a linear approximation of the density. 
     1157density in the World Ocean varies by no more than 2$\%$ from that value \citep{Gill1982}. 
     1158 
     1159Options are defined through the  \ngn{nameos} namelist variables, and in particular \np{nn\_eos}  
     1160which controls the EOS used (=-1 for TEOS10 ; =0 for EOS-80 ; =1 for S-EOS). 
     1161\begin{description} 
     1162 
     1163\item[\np{nn\_eos}$=-1$] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used.   
     1164The accuracy of this approximation is comparable to the TEOS-10 rational function approximation,  
     1165but it is optimized for a boussinesq fluid and the polynomial expressions have simpler  
     1166and more computationally efficient expressions for their derived quantities  
     1167which make them more adapted for use in ocean models.  
     1168Note that a slightly higher precision polynomial form is now used replacement of the TEOS-10  
     1169rational function approximation for hydrographic data analysis  \citep{TEOS10}.  
     1170A key point is that conservative state variables are used:  
     1171Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \degC, notation: $\Theta$). 
     1172The pressure in decibars is approximated by the depth in meters.  
     1173With TEOS10, the specific heat capacity of sea water, $C_p$, is a constant. It is set to  
     1174$C_p=3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{TEOS10}. 
     1175 
     1176Choosing polyTEOS10-bsq implies that the state variables used by the model are  
     1177$\Theta$ and $S_A$. In particular, the initial state deined by the user have to be given as  
     1178\textit{Conservative} Temperature and \textit{Absolute} Salinity.  
     1179In addition, setting \np{ln\_useCT} to \textit{true} convert the Conservative SST to potential SST  
     1180prior to either computing the air-sea and ice-sea fluxes (forced mode)  
     1181or sending the SST field to the atmosphere (coupled mode). 
     1182 
     1183\item[\np{nn\_eos}$=0$] the polyEOS80-bsq equation of seawater is used. 
     1184It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized  
     1185to accurately fit EOS80 (Roquet, personal comm.). The state variables used in both the EOS80  
     1186and the ocean model are:  
     1187the Practical Salinity ((unit: psu, notation: $S_p$)) and Potential Temperature (unit: $^{\circ}C$, notation: $\theta$). 
     1188The pressure in decibars is approximated by the depth in meters.   
     1189With thsi EOS, the specific heat capacity of sea water, $C_p$, is a function of temperature,  
     1190salinity and pressure \citep{UNESCO1983}. Nevertheless, a severe assumption is made in order to  
     1191have a heat content ($C_p T_p$) which is conserved by the model: $C_p$ is set to a constant  
     1192value, the TEOS10 value.  
     1193  
     1194\item[\np{nn\_eos}$=1$] a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen,  
     1195the coefficients of which has been optimized to fit the behavior of TEOS10 (Roquet, personal comm.)  
     1196(see also \citet{Roquet_JPO2015}). It provides a simplistic linear representation of both  
     1197cabbeling and thermobaricity effects which is enough for a proper treatment of the EOS  
     1198in theoretical studies \citep{Roquet_JPO2015}. 
    12091199With such an equation of state there is no longer a distinction between  
    1210 \textit{in situ} and \textit{potential} density and both cabbeling and thermobaric 
    1211 effects are removed. 
    1212 Two linear formulations are available: a function of $T$ only (\np{nn\_eos}=1)  
    1213 and a function of both $T$ and $S$ (\np{nn\_eos}=2): 
    1214 \begin{equation} \label{Eq_tra_eos_linear} 
     1200\textit{conservative} and \textit{potential} temperature, as well as between \textit{absolute}  
     1201and \textit{practical} salinity. 
     1202S-EOS takes the following expression: 
     1203\begin{equation} \label{Eq_tra_S-EOS} 
    12151204\begin{split} 
    1216   d_a(T)       &=  \rho (T)      /  \rho_o   - 1     =  \  0.0285         -  \alpha   \;T     \\  
    1217   d_a(T,S)    &=  \rho (T,S)   /  \rho_o   - 1     =  \  \beta \; S       -  \alpha   \;T     
     1205  d_a(T,S,z)  =  ( & - a_0 \; ( 1 + 0.5 \; \lambda_1 \; T_a + \mu_1 \; z ) * T_a  \\ 
     1206                                & + b_0 \; ( 1 - 0.5 \; \lambda_2 \; S_a - \mu_2 \; z ) * S_a  \\ 
     1207                                & - \nu \; T_a \; S_a \;  ) \; / \; \rho_o                     \\ 
     1208  with \ \  T_a = T-10  \; ;  & \;  S_a = S-35  \; ;\;  \rho_o = 1026~Kg/m^3 
    12181209\end{split} 
    12191210\end{equation}  
    1220 where $\alpha$ and $\beta$ are the thermal and haline expansion  
    1221 coefficients, and $\rho_o$, the reference volumic mass, $rau0$.  
    1222 ($\alpha$ and $\beta$ can be modified through the \np{rn\_alpha} and  
    1223 \np{rn\_beta} namelist variables). Note that when $d_a$ is a function  
    1224 of $T$ only (\np{nn\_eos}=1), the salinity is a passive tracer and can be  
    1225 used as such. 
    1226  
    1227 % ------------------------------------------------------------------------------------------------------------- 
    1228 %        Brunt-Vais\"{a}l\"{a} Frequency 
    1229 % ------------------------------------------------------------------------------------------------------------- 
    1230 \subsection{Brunt-Vais\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)} 
     1211where the computer name of the coefficients as well as their standard value are given in \ref{Tab_SEOS}. 
     1212In fact, when choosing S-EOS, various approximation of EOS can be specified simply by changing  
     1213the associated coefficients.  
     1214Setting to zero the two thermobaric coefficients ($\mu_1$, $\mu_2$) remove thermobaric effect from S-EOS. 
     1215setting to zero the three cabbeling coefficients ($\lambda_1$, $\lambda_2$, $\nu$) remove cabbeling effect from S-EOS. 
     1216Keeping non-zero value to $a_0$ and $b_0$ provide a linear EOS function of T and S. 
     1217 
     1218\end{description} 
     1219 
     1220 
     1221%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     1222\begin{table}[!tb] 
     1223\begin{center} \begin{tabular}{|p{26pt}|p{72pt}|p{56pt}|p{136pt}|} 
     1224\hline 
     1225coeff.   & computer name   & S-EOS     &  description                      \\ \hline 
     1226$a_0$       & \np{rn\_a0}     & 1.6550 $10^{-1}$ &  linear thermal expansion coeff.    \\ \hline 
     1227$b_0$       & \np{rn\_b0}     & 7.6554 $10^{-1}$ &  linear haline  expansion coeff.    \\ \hline 
     1228$\lambda_1$ & \np{rn\_lambda1}& 5.9520 $10^{-2}$ &  cabbeling coeff. in $T^2$          \\ \hline 
     1229$\lambda_2$ & \np{rn\_lambda2}& 5.4914 $10^{-4}$ &  cabbeling coeff. in $S^2$       \\ \hline 
     1230$\nu$       & \np{rn\_nu}     & 2.4341 $10^{-3}$ &  cabbeling coeff. in $T \, S$       \\ \hline 
     1231$\mu_1$     & \np{rn\_mu1}    & 1.4970 $10^{-4}$ &  thermobaric coeff. in T         \\ \hline 
     1232$\mu_2$     & \np{rn\_mu2}    & 1.1090 $10^{-5}$ &  thermobaric coeff. in S            \\ \hline 
     1233\end{tabular} 
     1234\caption{ \label{Tab_SEOS} 
     1235Standard value of S-EOS coefficients. } 
     1236\end{center} 
     1237\end{table} 
     1238%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     1239 
     1240 
     1241% ------------------------------------------------------------------------------------------------------------- 
     1242%        Brunt-V\"{a}is\"{a}l\"{a} Frequency 
     1243% ------------------------------------------------------------------------------------------------------------- 
     1244\subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)} 
    12311245\label{TRA_bn2} 
    12321246 
    1233 An accurate computation of the ocean stability (i.e. of $N$, the brunt-Vais\"{a}l\"{a} 
    1234  frequency) is of paramount importance as it is used in several ocean  
    1235  parameterisations (namely TKE, KPP, Richardson number dependent  
    1236  vertical diffusion, enhanced vertical diffusion, non-penetrative convection,  
    1237  iso-neutral diffusion). In particular, one must be aware that $N^2$ has to  
    1238  be computed with an \textit{in situ} reference. The expression for $N^2$  
    1239  depends on the type of equation of state used (\np{nn\_eos} namelist parameter). 
    1240  
    1241 For \np{nn\_eos}=0 (\citet{JackMcD1995} equation of state), the \citet{McDougall1987}  
    1242 polynomial expression is used (with the pressure in decibar approximated by  
    1243 the depth in meters):  
     1247An accurate computation of the ocean stability (i.e. of $N$, the brunt-V\"{a}is\"{a}l\"{a} 
     1248 frequency) is of paramount importance as determine the ocean stratification and  
     1249 is used in several ocean parameterisations (namely TKE, GLS, Richardson number dependent  
     1250 vertical diffusion, enhanced vertical diffusion, non-penetrative convection, tidal mixing  
     1251 parameterisation, iso-neutral diffusion). In particular, $N^2$ has to be computed at the local pressure  
     1252 (pressure in decibar being approximated by the depth in meters). The expression for $N^2$  
     1253 is given by:  
    12441254\begin{equation} \label{Eq_tra_bn2} 
    1245 N^2 = \frac{g}{e_{3w}} \; \beta   \  
    1246       \left(  \alpha / \beta \ \delta_{k+1/2}[T]     - \delta_{k+1/2}[S]   \right)  
    1247 \end{equation}  
    1248 where $\alpha$ and $\beta$ are the thermal and haline expansion coefficients.  
    1249 They are a function of  $\overline{T}^{\,k+1/2},\widetilde{S}=\overline{S}^{\,k+1/2} - 35.$,  
    1250 and  $z_w$, with $T$ the \textit{potential} temperature and $\widetilde{S}$ a salinity anomaly.  
    1251 Note that both $\alpha$ and $\beta$ depend on \textit{potential}  
    1252 temperature and salinity which are averaged at $w$-points prior  
    1253 to the computation instead of being computed at $T$-points and  
    1254 then averaged to $w$-points. 
    1255  
    1256 When a linear equation of state is used (\np{nn\_eos}=1 or 2,  
    1257 \eqref{Eq_tra_bn2} reduces to: 
    1258 \begin{equation} \label{Eq_tra_bn2_linear} 
    12591255N^2 = \frac{g}{e_{3w}} \left(   \beta \;\delta_{k+1/2}[S] - \alpha \;\delta_{k+1/2}[T]   \right) 
    12601256\end{equation}  
    1261 where $\alpha$ and $\beta $ are the constant coefficients used to  
    1262 defined the linear equation of state \eqref{Eq_tra_eos_linear}. 
    1263  
    1264 % ------------------------------------------------------------------------------------------------------------- 
    1265 %        Specific Heat 
    1266 % ------------------------------------------------------------------------------------------------------------- 
    1267 \subsection    [Specific Heat (\textit{phycst})] 
    1268          {Specific Heat (\mdl{phycst})} 
    1269 \label{TRA_adv_ldf} 
    1270  
    1271 The specific heat of sea water, $C_p$, is a function of temperature, salinity  
    1272 and pressure \citep{UNESCO1983}. It is only used in the model to convert  
    1273 surface heat fluxes into surface temperature increase and so the pressure  
    1274 dependence is neglected. The dependence on $T$ and $S$ is weak.  
    1275 For example, with $S=35~psu$, $C_p$ increases from $3989$ to $4002$  
    1276 when $T$ varies from -2~\degres C to 31~\degres C. Therefore, $C_p$ has  
    1277 been chosen as a constant: $C_p=4.10^3~J\,Kg^{-1}\,\degres K^{-1}$.  
    1278 Its value is set in \mdl{phycst} module.  
    1279  
     1257where $(T,S) = (\Theta, S_A)$ for TEOS10, $= (\theta, S_p)$ for TEOS-80, or $=(T,S)$ for S-EOS,  
     1258and, $\alpha$ and $\beta$ are the thermal and haline expansion coefficients.  
     1259The coefficients are a polynomial function of temperature, salinity and depth which expression  
     1260depends on the chosen EOS. They are computed through \textit{eos\_rab}, a \textsc{Fortran}  
     1261function that can be found in \mdl{eosbn2}. 
    12801262 
    12811263% ------------------------------------------------------------------------------------------------------------- 
     
    12981280sea water ($i.e.$ referenced to the surface $p=0$), thus the pressure dependent  
    12991281terms in \eqref{Eq_tra_eos_fzp} (last term) have been dropped. The freezing 
    1300 point is computed through \textit{tfreez}, a \textsc{Fortran} function that can be found  
     1282point is computed through \textit{eos\_fzp}, a \textsc{Fortran} function that can be found  
    13011283in \mdl{eosbn2}.   
    13021284 
     
    13081290\label{TRA_zpshde} 
    13091291 
    1310 \gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators, I've changed "derivative" to "difference" and "mean" to "average"} 
    1311  
    1312 With partial bottom cells (\np{ln\_zps}=true), in general, tracers in horizontally  
     1292\gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators,  
     1293                   I've changed "derivative" to "difference" and "mean" to "average"} 
     1294 
     1295With partial cells (\np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true), in general, tracers in horizontally  
    13131296adjacent cells live at different depths. Horizontal gradients of tracers are needed  
    13141297for horizontal diffusion (\mdl{traldf} module) and for the hydrostatic pressure  
    13151298gradient (\mdl{dynhpg} module) to be active.  
    13161299\gmcomment{STEVEN from gm : question: not sure of  what -to be active- means} 
     1300 
    13171301Before taking horizontal gradients between the tracers next to the bottom, a linear  
    13181302interpolation in the vertical is used to approximate the deeper tracer as if it actually  
     
    13231307%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    13241308\begin{figure}[!p]    \begin{center} 
    1325 \includegraphics[width=0.9\textwidth]{./TexFiles/Figures/Partial_step_scheme.pdf} 
     1309\includegraphics[width=0.9\textwidth]{Partial_step_scheme} 
    13261310\caption{   \label{Fig_Partial_step_scheme}  
    13271311Discretisation of the horizontal difference and average of tracers in the $z$-partial  
     
    13901374\gmcomment{gm :   this last remark has to be done} 
    13911375%%% 
     1376 
     1377If under ice shelf seas opened (\np{ln\_isfcav}=true), the partial cell properties  
     1378at the top are computed in the same way as for the bottom. Some extra variables are,  
     1379however, computed to reduce the flow generated at the top and bottom if $z*$ coordinates activated. 
     1380The extra variables calculated and used by \S\ref{DYN_hpg_isf} are: 
     1381 
     1382$\bullet$ $\overline{T}_k^{\,i+1/2}$ as described in \eqref{Eq_zps_hde} 
     1383 
     1384$\bullet$ $\delta _{i+1/2} Z_{T_k} = \widetilde {Z}^{\,i}_{T_k}-Z^{\,i}_{T_k}$ to compute  
     1385the pressure gradient correction term used by \eqref{Eq_dynhpg_sco} in \S\ref{DYN_hpg_isf}, 
     1386 with $\widetilde {Z}_{T_k}$ the depth of the point $\widetilde {T}_{k}$ in case of $z^*$ coordinates  
     1387(this term = 0 in z-coordinates) 
     1388\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_ZDF.tex

    r5602 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13% ================================================================ 
    24% Chapter  Vertical Ocean Physics (ZDF) 
     
    3335points, respectively (see \S\ref{TRA_zdf} and \S\ref{DYN_zdf}). These  
    3436coefficients can be assumed to be either constant, or a function of the local  
    35 Richardson number, or computed from a turbulent closure model (either  
    36 TKE or KPP formulation). The computation of these coefficients is initialized  
    37 in the \mdl{zdfini} module and performed in the \mdl{zdfric}, \mdl{zdftke} or  
    38 \mdl{zdfkpp} modules. The trends due to the vertical momentum and tracer  
    39 diffusion, including the surface forcing, are computed and added to the  
    40 general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively.  
     37Richardson number, or computed from a turbulent closure model (TKE, GLS or KPP formulation).  
     38The computation of these coefficients is initialized in the \mdl{zdfini} module  
     39and performed in the \mdl{zdfric}, \mdl{zdftke}, \mdl{zdfgls} or \mdl{zdfkpp} modules.  
     40The trends due to the vertical momentum and tracer diffusion, including the surface forcing,  
     41are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively.  
    4142These trends can be computed using either a forward time stepping scheme  
    4243(namelist parameter \np{ln\_zdfexp}=true) or a backward time stepping  
     
    234235%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    235236\begin{figure}[!t] \begin{center} 
    236 \includegraphics[width=1.00\textwidth]{./TexFiles/Figures/Fig_mixing_length.pdf} 
     237\includegraphics[width=1.00\textwidth]{Fig_mixing_length} 
    237238\caption{ \label{Fig_mixing_length}  
    238239Illustration of the mixing length computation. } 
     
    262263\end{equation} 
    263264 
    264 At the ocean surface, a non zero length scale is set through the  \np{rn\_lmin0} namelist  
     265At the ocean surface, a non zero length scale is set through the  \np{rn\_mxl0} namelist  
    265266parameter. Usually the surface scale is given by $l_o = \kappa \,z_o$  
    266267where $\kappa = 0.4$ is von Karman's constant and $z_o$ the roughness  
    267268parameter of the surface. Assuming $z_o=0.1$~m \citep{Craig_Banner_JPO94}  
    268 leads to a 0.04~m, the default value of \np{rn\_lsurf}. In the ocean interior  
     269leads to a 0.04~m, the default value of \np{rn\_mxl0}. In the ocean interior  
    269270a minimum length scale is set to recover the molecular viscosity when $\bar{e}$  
    270271reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). 
     
    295296As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$,  
    296297with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}~=~67.83 corresponds  
    297 to $\alpha_{CB} = 100$. further setting  \np{ln\_lsurf} to true applies \eqref{ZDF_Lsbc}  
    298 as surface boundary condition on length scale, with $\beta$ hard coded to the Stacet's value. 
     298to $\alpha_{CB} = 100$. Further setting  \np{ln\_mxl0} to true applies \eqref{ZDF_Lsbc}  
     299as surface boundary condition on length scale, with $\beta$ hard coded to the Stacey's value. 
    299300Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters)  
    300301is applied on surface $\bar{e}$ value. 
     
    355356%--------------------------------------------------------------% 
    356357 
    357 To be add here a description of "penetration of TKE" and the associated namelist parameters 
    358  \np{nn\_etau}, \np{rn\_efr} and \np{nn\_htau}. 
     358Vertical mixing parameterizations commonly used in ocean general circulation models  
     359tend to produce mixed-layer depths that are too shallow during summer months and windy conditions. 
     360This bias is particularly acute over the Southern Ocean.  
     361To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme  \cite{Rodgers_2014}.  
     362The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations,  
     363but rather is meant to account for observed processes that affect the density structure of  
     364the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme  
     365($i.e.$ near-inertial oscillations and ocean swells and waves). 
     366 
     367When using this parameterization ($i.e.$ when \np{nn\_etau}~=~1), the TKE input to the ocean ($S$)  
     368imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized  
     369by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by: 
     370\begin{equation}  \label{ZDF_Ehtau} 
     371S = (1-f_i) \; f_r \; e_s \; e^{-z / h_\tau}  
     372\end{equation} 
     373where  
     374$z$ is the depth,   
     375$e_s$ is TKE surface boundary condition,  
     376$f_r$ is the fraction of the surface TKE that penetrate in the ocean,  
     377$h_\tau$ is a vertical mixing length scale that controls exponential shape of the penetration,  
     378and $f_i$ is the ice concentration (no penetration if $f_i=1$, that is if the ocean is entirely  
     379covered by sea-ice). 
     380The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter.  
     381The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}~=~0)  
     382or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m  
     383at high latitudes (\np{nn\_etau}~=~1).  
     384 
     385Note that two other option existe, \np{nn\_etau}~=~2, or 3. They correspond to applying  
     386\eqref{ZDF_Ehtau} only at the base of the mixed layer, or to using the high frequency part  
     387of the stress to evaluate the fraction of TKE that penetrate the ocean.  
     388Those two options are obsolescent features introduced for test purposes. 
     389They will be removed in the next release.  
     390 
     391 
    359392 
    360393% from Burchard et al OM 2008 :  
    361 % the most critical process not reproduced by statistical turbulence models is the activity of internal waves and their interaction with turbulence. After the Reynolds decomposition, internal waves are in principle included in the RANS equations, but later partially excluded by the hydrostatic assumption and the model resolution. Thus far, the representation of internal wave mixing in ocean models has been relatively crude (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 
     394% the most critical process not reproduced by statistical turbulence models is the activity of  
     395% internal waves and their interaction with turbulence. After the Reynolds decomposition,  
     396% internal waves are in principle included in the RANS equations, but later partially  
     397% excluded by the hydrostatic assumption and the model resolution.  
     398% Thus far, the representation of internal wave mixing in ocean models has been relatively crude  
     399% (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 
    362400 
    363401 
     
    371409%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    372410\begin{figure}[!t]   \begin{center} 
    373 \includegraphics[width=1.00\textwidth]{./TexFiles/Figures/Fig_ZDF_TKE_time_scheme.pdf} 
     411\includegraphics[width=1.00\textwidth]{Fig_ZDF_TKE_time_scheme} 
    374412\caption{ \label{Fig_TKE_time_scheme}  
    375413Illustration of the TKE time integration and its links to the momentum and tracer time integration. } 
     
    550588value near physical boundaries (logarithmic boundary layer law). $C_{\mu}$ and $C_{\mu'}$  
    551589are calculated from stability function proposed by \citet{Galperin_al_JAS88}, or by \citet{Kantha_Clayson_1994}  
    552 or one of the two functions suggested by \citet{Canuto_2001}  (\np{nn\_stab\_func} = 0, 1, 2 or 3, resp.}).  
     590or one of the two functions suggested by \citet{Canuto_2001}  (\np{nn\_stab\_func} = 0, 1, 2 or 3, resp.).  
    553591The value of $C_{0\mu}$ depends of the choice of the stability function. 
    554592 
     
    586624Options are defined through the  \ngn{namzdf\_kpp} namelist variables. 
    587625 
    588 \colorbox{yellow}{Add a description of KPP here.} 
     626Note that KPP is an obsolescent feature of the \NEMO system.  
     627It will be removed in the next release (v3.7 and followings). 
    589628 
    590629 
     
    621660%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    622661\begin{figure}[!htb]    \begin{center} 
    623 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_npc.pdf} 
     662\includegraphics[width=0.90\textwidth]{Fig_npc} 
    624663\caption{  \label{Fig_npc}  
    625664Example of an unstable density profile treated by the non penetrative  
     
    636675 
    637676Options are defined through the  \ngn{namzdf} namelist variables. 
    638 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}=true.  
     677The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}~=~\textit{true}.  
    639678It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously  
    640679the statically unstable portion of the water column, but only until the density  
     
    644683(Fig. \ref{Fig_npc}): starting from the top of the ocean, the first instability is  
    645684found. Assume in the following that the instability is located between levels  
    646 $k$ and $k+1$. The potential temperature and salinity in the two levels are  
     685$k$ and $k+1$. The temperature and salinity in the two levels are  
    647686vertically mixed, conserving the heat and salt contents of the water column.  
    648687The new density is then computed by a linear approximation. If the new  
     
    664703\citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}. 
    665704 
    666 Note that in the current implementation of this algorithm presents several  
    667 limitations. First, potential density referenced to the sea surface is used to  
    668 check whether the density profile is stable or not. This is a strong  
    669 simplification which leads to large errors for realistic ocean simulations.  
    670 Indeed, many water masses of the world ocean, especially Antarctic Bottom 
    671 Water, are unstable when represented in surface-referenced potential density.  
    672 The scheme will erroneously mix them up. Second, the mixing of potential  
    673 density is assumed to be linear. This assures the convergence of the algorithm  
    674 even when the equation of state is non-linear. Small static instabilities can thus  
    675 persist due to cabbeling: they will be treated at the next time step.  
    676 Third, temperature and salinity, and thus density, are mixed, but the  
    677 corresponding velocity fields remain unchanged. When using a Richardson  
    678 Number dependent eddy viscosity, the mixing of momentum is done through  
    679 the vertical diffusion: after a static adjustment, the Richardson Number is zero  
    680 and thus the eddy viscosity coefficient is at a maximum. When this convective  
    681 adjustment algorithm is used with constant vertical eddy viscosity, spurious  
    682 solutions can occur since the vertical momentum diffusion remains small even  
    683 after a static adjustment. In that case, we recommend the addition of momentum  
    684 mixing in a manner that mimics the mixing in temperature and salinity  
    685 \citep{Speich_PhD92, Speich_al_JPO96}. 
     705The current implementation has been modified in order to deal with any non linear  
     706equation of seawater (L. Brodeau, personnal communication).  
     707Two main differences have been introduced compared to the original algorithm:  
     708$(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency  
     709(not the the difference in potential density) ;  
     710$(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients  
     711are vertically mixed in the same way their temperature and salinity has been mixed. 
     712These two modifications allow the algorithm to perform properly and accurately  
     713with TEOS10 or EOS-80 without having to recompute the expansion coefficients at each  
     714mixing iteration. 
    686715 
    687716% ------------------------------------------------------------------------------------------------------------- 
     
    689718% ------------------------------------------------------------------------------------------------------------- 
    690719\subsection   [Enhanced Vertical Diffusion (\np{ln\_zdfevd})] 
    691          {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 
     720              {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 
    692721\label{ZDF_evd} 
    693722 
     
    787816%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    788817\begin{figure}[!t]   \begin{center} 
    789 \includegraphics[width=0.99\textwidth]{./TexFiles/Figures/Fig_zdfddm.pdf} 
     818\includegraphics[width=0.99\textwidth]{Fig_zdfddm} 
    790819\caption{  \label{Fig_zdfddm} 
    791820From \citet{Merryfield1999} : (a) Diapycnal diffusivities $A_f^{vT}$  
     
    830859% Bottom Friction 
    831860% ================================================================ 
    832 \section  [Bottom and top Friction (\textit{zdfbfr})]   {Bottom Friction (\mdl{zdfbfr} module)} 
     861\section  [Bottom and Top Friction (\textit{zdfbfr})]   {Bottom and Top Friction (\mdl{zdfbfr} module)} 
    833862\label{ZDF_bfr} 
    834863 
     
    838867 
    839868Options to define the top and bottom friction are defined through the  \ngn{nambfr} namelist variables. 
    840 The top friction is activated only if the ice shelf cavities are opened (\np{ln\_isfcav}~=~true). 
    841 As the friction processes at the top and bottom are the represented similarly, only the bottom friction is described in detail. 
     869The bottom friction represents the friction generated by the bathymetry.  
     870The top friction represents the friction generated by the ice shelf/ocean interface.  
     871As the friction processes at the top and bottom are represented similarly, only the bottom friction is described in detail below.\\ 
     872 
    842873 
    843874Both the surface momentum flux (wind stress) and the bottom momentum  
     
    912943$H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$.  
    913944This is the default value used in \NEMO. It corresponds to a decay time scale  
    914 of 115~days. It can be changed by specifying \np{rn\_bfric1} (namelist parameter). 
     945of 115~days. It can be changed by specifying \np{rn\_bfri1} (namelist parameter). 
    915946 
    916947For the linear friction case the coefficients defined in the general  
     
    922953\end{split} 
    923954\end{equation} 
    924 When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfric1}.  
     955When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri1}.  
    925956Setting \np{nn\_botfr}=0 is equivalent to setting $r=0$ and leads to a free-slip  
    926957bottom boundary condition. These values are assigned in \mdl{zdfbfr}.  
     
    929960in the \ifile{bfr\_coef} input NetCDF file. The mask values should vary from 0 to 1.  
    930961Locations with a non-zero mask value will have the friction coefficient increased  
    931 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfric1}. 
     962by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri1}. 
    932963 
    933964% ------------------------------------------------------------------------------------------------------------- 
     
    949980$e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992}  
    950981uses $C_D = 1.4\;10^{-3}$ and $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$.  
    951 The CME choices have been set as default values (\np{rn\_bfric2} and \np{rn\_bfeb2}  
     982The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2}  
    952983namelist parameters). 
    953984 
     
    964995\end{equation} 
    965996 
    966 The coefficients that control the strength of the non-linear bottom friction are  
    967 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}.  
    968 Note for applications which treat tides explicitly a low or even zero value of  
    969 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$  
    970 is possible via an externally defined 2D mask array (\np{ln\_bfr2d}=true).  
    971 See previous section for details. 
     997The coefficients that control the strength of the non-linear bottom friction are 
     998initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 
     999Note for applications which treat tides explicitly a low or even zero value of 
     1000\np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ is possible 
     1001via an externally defined 2D mask array (\np{ln\_bfr2d}=true).  This works in the same way 
     1002as for the linear bottom friction case with non-zero masked locations increased by 
     1003$mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}. 
     1004 
     1005% ------------------------------------------------------------------------------------------------------------- 
     1006%       Bottom Friction Log-layer 
     1007% ------------------------------------------------------------------------------------------------------------- 
     1008\subsection{Log-layer Bottom Friction enhancement (\np{nn\_botfr} = 2, \np{ln\_loglayer} = .true.)} 
     1009\label{ZDF_bfr_loglayer} 
     1010 
     1011In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally 
     1012enhanced using a "law of the wall" scaling. If  \np{ln\_loglayer} = .true., $C_D$ is no 
     1013longer constant but is related to the thickness of the last wet layer in each column by: 
     1014 
     1015\begin{equation} 
     1016C_D = \left ( {\kappa \over {\rm log}\left ( 0.5e_{3t}/rn\_bfrz0 \right ) } \right )^2 
     1017\end{equation} 
     1018 
     1019\noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness 
     1020length provided via the namelist. 
     1021 
     1022For stability, the drag coefficient is bounded such that it is kept greater or equal to 
     1023the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional 
     1024namelist parameter: \np{rn\_bfri2\_max}, i.e.: 
     1025 
     1026\begin{equation} 
     1027rn\_bfri2 \leq C_D \leq rn\_bfri2\_max 
     1028\end{equation} 
     1029 
     1030\noindent Note also that a log-layer enhancement can also be applied to the top boundary 
     1031friction if under ice-shelf cavities are in use (\np{ln\_isfcav}=.true.).  In this case, the 
     1032relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} 
     1033and \np{rn\_tfri2\_max}. 
    9721034 
    9731035% ------------------------------------------------------------------------------------------------------------- 
     
    10831145baroclinic and barotropic components which is appropriate when using either the 
    10841146explicit or filtered surface pressure gradient algorithms (\key{dynspg\_exp} or  
    1085 {\key{dynspg\_flt}). Extra attention is required, however, when using  
     1147\key{dynspg\_flt}). Extra attention is required, however, when using  
    10861148split-explicit time stepping (\key{dynspg\_ts}). In this case the free surface  
    10871149equation is solved with a small time step \np{rn\_rdt}/\np{nn\_baro}, while the three  
     
    11981260%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    11991261\begin{figure}[!t]   \begin{center} 
    1200 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_ZDF_M2_K1_tmx.pdf} 
     1262\includegraphics[width=0.90\textwidth]{Fig_ZDF_M2_K1_tmx} 
    12011263\caption{  \label{Fig_ZDF_M2_K1_tmx}  
    12021264(a) M2 and (b) K1 internal wave drag energy from \citet{Carrere_Lyard_GRL03} ($W/m^2$). } 
     
    12531315 
    12541316% ================================================================ 
     1317% Internal wave-driven mixing 
     1318% ================================================================ 
     1319\section{Internal wave-driven mixing (\key{zdftmx\_new})} 
     1320\label{ZDF_tmx_new} 
     1321 
     1322%--------------------------------------------namzdf_tmx_new------------------------------------------ 
     1323\namdisplay{namzdf_tmx_new} 
     1324%-------------------------------------------------------------------------------------------------------------- 
     1325 
     1326The parameterization of mixing induced by breaking internal waves is a generalization  
     1327of the approach originally proposed by \citet{St_Laurent_al_GRL02}.  
     1328A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed,  
     1329and the resulting diffusivity is obtained as  
     1330\begin{equation} \label{Eq_Kwave} 
     1331A^{vT}_{wave} =  R_f \,\frac{ \epsilon }{ \rho \, N^2 } 
     1332\end{equation} 
     1333where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution  
     1334of the energy available for mixing. If the \np{ln\_mevar} namelist parameter is set to false,  
     1335the mixing efficiency is taken as constant and equal to 1/6 \citep{Osborn_JPO80}.  
     1336In the opposite (recommended) case, $R_f$ is instead a function of the turbulence intensity parameter  
     1337$Re_b = \frac{ \epsilon}{\nu \, N^2}$, with $\nu$ the molecular viscosity of seawater,  
     1338following the model of \cite{Bouffard_Boegman_DAO2013}  
     1339and the implementation of \cite{de_lavergne_JPO2016_efficiency}. 
     1340Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when the mixing efficiency is constant. 
     1341 
     1342In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary  
     1343as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice).  
     1344This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014},  
     1345is implemented as in \cite{de_lavergne_JPO2016_efficiency}. 
     1346 
     1347The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, is constructed  
     1348from three static maps of column-integrated internal wave energy dissipation, $E_{cri}(i,j)$,  
     1349$E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures  
     1350(de Lavergne et al., in prep): 
     1351\begin{align*} 
     1352F_{cri}(i,j,k) &\propto e^{-h_{ab} / h_{cri} }\\ 
     1353F_{pyc}(i,j,k) &\propto N^{n\_p}\\ 
     1354F_{bot}(i,j,k) &\propto N^2 \, e^{- h_{wkb} / h_{bot} } 
     1355\end{align*}  
     1356In the above formula, $h_{ab}$ denotes the height above bottom,  
     1357$h_{wkb}$ denotes the WKB-stretched height above bottom, defined by 
     1358\begin{equation*} 
     1359h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz'  } \; , 
     1360\end{equation*} 
     1361The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_tmx\_new} namelist)  controls the stratification-dependence of the pycnocline-intensified dissipation.  
     1362It can take values of 1 (recommended) or 2. 
     1363Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of  
     1364the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps.  
     1365$h_{cri}$ is related to the large-scale topography of the ocean (etopo2)  
     1366and $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of  
     1367the abyssal hill topography \citep{Goff_JGR2010} and the latitude. 
     1368 
     1369% ================================================================ 
     1370 
     1371 
     1372 
     1373\end{document} 
  • branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Introduction.tex

    r4661 r7260  
     1\documentclass[NEMO_book]{subfiles} 
     2\begin{document} 
    13 
    24% ================================================================ 
     
    2426release 8.2, described in \citet{Madec1998}. This model has been used for a wide  
    2527range of applications, both regional or global, as a forced ocean model and as a  
    26 model coupled with the atmosphere. A complete list of references is found on the  
    27 \NEMO web site.  
     28model coupled with the sea-ice and/or the atmosphere.   
    2829 
    2930This manual is organised in as follows. Chapter~\ref{PE} presents the model basics,  
    3031$i.e.$ the equations and their assumptions, the vertical coordinates used, and the  
    3132subgrid scale physics. This part deals with the continuous equations of the model  
    32 (primitive equations, with potential temperature, salinity and an equation of state).  
     33(primitive equations, with temperature, salinity and an equation of seawater).  
    3334The equations are written in a curvilinear coordinate system, with a choice of vertical  
    3435coordinates ($z$ or $s$, with the rescaled height coordinate formulation \textit{z*}, or   
     
    7980space and time variable coefficient \citet{Treguier1997}. The model has vertical harmonic  
    8081viscosity and diffusion with a space and time variable coefficient, with options to compute  
    81 the coefficients with \citet{Blanke1993}, \citet{Large_al_RG94}, \citet{Pacanowski_Philander_JPO81},  
     82the coefficients with \citet{Blanke1993}, \citet{Pacanowski_Philander_JPO81},  
    8283or \citet{Umlauf_Burchard_JMS03} mixing schemes. 
    8384 \vspace{1cm} 
    8485  
    85   
     86%%gm    To be put somewhere else .... 
     87 
    8688\noindent CPP keys and namelists are used for inputs to the code.  \newline 
    8789 
     
    112114 \vspace{1cm} 
    113115 
     116%%gm  end 
    114117 
    115118Model outputs management and specific online diagnostics are described in chapters~\ref{DIA}. 
     
    227230\item a deep re-writting and simplification of the off-line tracer component (OFF\_SRC) ;  
    228231\item the merge of passive and active advection and diffusion modules ; 
    229 \item  Use of the Flexible Configuration Manager (FCM) to build configurations, generate the Makefile and produce the executable ; 
     232\item Use of the Flexible Configuration Manager (FCM) to build configurations, generate the Makefile and produce the executable ; 
    230233\item Linear-tangent and Adjoint component (TAM) added, phased with v3.0 
    231234\end{enumerate} 
     
    249252 
    250253 
     254 \vspace{1cm} 
     255$\bullet$ The main modifications from NEMO/OPA v3.4 and  v3.6 are :\\ 
     256\begin{enumerate} 
     257\item I/O management: NEMO in now interfaced with XIOS, a Input/Output server having a versatile xml user interface, and  
     258allowing I/O to be performed on dedicated processors thus improving scalability and performance on massively parallel platforms.  
     259\item ICB module \citep{Marsh_GMD2015}: icebergs as lagrangian floats ;  
     260\item SAS: Stand Alone Surface module allowing testing of forcing set with bulk formulae, to run sea-ice models without ocean, to run ICB icebergs module alone, and to test AGRIF with sea-ice 
     261\item ISF : Under ice-selves cavities (parametrisation and/or explicit representation) 
     262\item Coupled interface for next IPCC requirements (multi category sea-ice, calving and iceberg module) 
     263\item Ocean and ice allowed to be explicitly coupled through OASIS, using StandAlone Surface module) 
     264\item On line coarsening of ocean I/O 
     265\item Major evolution of LIM3 sea-ice model \citep{Rousset_GMD2015} 
     266\item Open boundaries: completion of BDY/OBC merge : BDY is now the only Open boundary module available 
     267\item re-visit of the specification of heat/salt(tracers)/mass fluxes ; 
     268\item levitating or fully embedded sea-ice (for LIM and CICE) ; 
     269\item a new parameterization of mixing induced by breaking internal waves (de Lavergne et al. in prep.) 
     270And also: 
     271\item update of AGRIF package and AGRIF compatibility with LIM2 sea-ice model ; 
     272\item A new vertical sigma coordinate stretching function \citep{Siddorn_Furner_OM12} ; 
     273\item Smagorinsky eddy coefficients: the \cite{Griffies_Hallberg_MWR00} Smagorinsky type diffusivity/viscosity for lateral mixing has been introduced ; 
     274\item Standard Fox Kemper parametrisation 
     275\item Analytical tropical cyclones taken in account using track and magnitude observations (Vincent et al. JGR 2012a,b) ; 
     276\item OBS: observation operators improved and now available in Standalone mode ; 
     277\item Log layer option for bottom friction 
     278\item Faster split-explicit time stepping ;  
     279\item Z-tilde ALE coordinates \citep{Leclair_Madec_OM11} ;  
     280\item implicit bottom friction ; 
     281\item Runoff improved and SBC with BGC 
     282\item MPP assessment and optimisation 
     283\item First steps of wave coupling 
     284 
     285Features becoming obsolete: LIM2 (replaced by LIM3 monocategory) ; IOIPSL (replaced by XIOS) ;  
     286 
     287Features that has been removed : LOBSTER (now included in PISCES) ; OBC, replaced by BDY ;    
     288 
     289 
     290 
     291\end{enumerate} 
     292 
     293 
     294\end{document} 
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