Changeset 10442 for NEMO/trunk


Ignore:
Timestamp:
2018-12-21T15:18:38+01:00 (2 years ago)
Author:
nicolasmartin
Message:

Front page edition, cleaning in custom LaTeX commands and add index for single subfile compilation

  • Use \thanks storing cmd to refer to the ST members list for 2018 in an footnote on the cover page
  • NEMO and Fortran in small capitals
  • Removing of unused or underused custom cmds, move local cmds to their respective .tex file
  • Addition of new ones (\zstar, \ztilde, \sstar, \stilde, \ie, \eg, \fortran, \fninety)
  • Fonts for indexed items: italic font for files (modules and .nc files), preformat for code (CPP keys, routines names and namelists content)
Location:
NEMO/trunk/doc/latex/NEMO
Files:
1 deleted
28 edited

Legend:

Unmodified
Added
Removed
  • NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.sty

    r10146 r10442  
    11%% ============================================================================== 
    2 %% NEMO_manual.sty: all customizations (packages, ) 
     2%% NEMO_manual.sty: all customizations (packages, styles, cmds) 
    33%% ============================================================================== 
    44 
     
    1010\usepackage{caption}          %% caption 
    1111\usepackage{xcolor}           %% color 
    12 \usepackage{silence}          %% compilation 
    1312\usepackage{times}            %% font 
    1413\usepackage{hyperref}         %% hyper 
     
    2423%% Extensions in bundle package 
    2524 
    26 \usepackage{amssymb, graphicx, makeidx, tabularx, xspace} 
     25\usepackage{amssymb, graphicx, makeidx, tabularx} 
    2726 
    2827 
     
    3231\graphicspath{{../../../figures/}} 
    3332\hypersetup{ 
    34    pdftitle={NEMO ocean engine}, pdfauthor={Gurvan Madec, and the NEMO team}, 
     33   pdftitle={NEMO ocean engine}, pdfauthor={Gurvan Madec, and NEMO System Team}, 
    3534   colorlinks 
    3635} 
     
    4544\pagestyle{fancy} 
    4645\bibliographystyle{../main/ametsoc} 
    47  
    4846 
    4947%% Additionnal fonts 
     
    103101 
    104102 
    105 %% Macros (to check) 
     103%% Global custom commands: \newcommand{<name>}[<args>][<first argument value>]{<code>} 
     104%% ============================================================================== 
    106105 
    107 \def\deg{$^{\circ}$} 
    108 \def\degC{$^{\circ}C$} 
    109 \def\degK{$^{\circ}K$} 
    110 \def\degN{$^{\circ}N$} 
    111 \def\degS{$^{\circ}S$} 
     106%% NEMO and Fortran in small capitals 
     107\newcommand{\NEMO}{\textsc{nemo}} 
     108\newcommand{\fortran}{\textsc{Fortran}} 
     109\newcommand{\fninety}{\textsc{Fortran 90}} 
    112110 
    113 \def\half{\textstyle\frac{1}{2}} 
    114 \def\hhalf{\scriptstyle\frac{1}{2}} 
     111%% Common aliases 
     112\renewcommand{\deg}[1][]{\ensuremath{^{\circ}#1}} 
     113\newcommand{\zstar }{\ensuremath{z^\star}} 
     114\newcommand{\sstar }{\ensuremath{s^\star}} 
     115\newcommand{\ztilde}{\ensuremath{\tilde z}} 
     116\newcommand{\stilde}{\ensuremath{\tilde s}} 
     117\newcommand{\ie}{\ensuremath{i.e.}} 
     118\newcommand{\eg}{\ensuremath{e.g.}} 
    115119 
    116 \def\quarter{\textstyle\frac{1}{4}} 
    117 \def\qquarter{\scriptstyle\frac{1}{4}} 
    118 \def\squarter{\sfrac{1}{4}} 
    119 \def\stwelfth{\sfrac{1}{12}} 
    120 \def\sthirtysixth{\sfrac{1}{36}} 
     120%% Inline maths 
     121\newcommand{\fractext}[2]{\textstyle \frac{#1}{#2}} 
     122\newcommand{\rdt}{\Delta t} 
    121123 
    122 \def\bgamma\boldsymbol{\gamma} 
    123 \def\rdt{\Delta t} 
     124%% Text env. for Gurvan 
     125\newcommand{\gmcomment}[1]{} 
     126 
     127%% Index (italic font for files, preformat for code) 
     128\newcommand{\ifile}[1]{\textit{#1.nc}          \index{Input NetCDF files!#1.nc}} 
     129\newcommand{\mdl}[1]{\textit{#1.F90}           \index{Modules!#1}} 
     130\newcommand{\jp}[1]{\texttt{#1}                \index{Model parameters!#1}} 
     131\newcommand{\key}[1]{\texttt{\textbf{key\_#1}} \index{CPP keys!key\_#1}} 
     132\newcommand{\ngn}[1]{\texttt{#1}               \index{Namelist Group Name!#1}} 
     133\newcommand{\np}[1]{\texttt{#1}                \index{Namelist variables!#1}} 
     134\newcommand{\rou}[1]{\texttt{#1}               \index{Routines!#1}} 
     135 
     136%% Maths 
     137\newcommand{\vect}[1]{\ensuremath{\mathbf{#1}}} 
     138\newcommand{\pd}[2][]{\ensuremath{\frac{\partial #1}{\partial #2}}} 
     139 
     140%% Shortened DOI in bibliography 
     141\newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{doi:#1}} 
     142 
     143%% Namelists inclusion 
     144\newcommand{\nlst}[1]{\forfile{../../../namelists/#1}} 
    124145 
    125146 
    126 %% New commands 
     147%% Minted package: syntax highlighting configuration 
     148%% ============================================================================== 
    127149 
    128 \newcommand{\gmcomment}[1]{} 
    129 \newcommand{\sfcomment}[1]{} 
    130 \newcommand{\sgacomment}[1]{} 
     150%% Global highlighting style 
     151\setminted{style=emacs, fontsize=\scriptsize, breaklines, frame=leftline} 
     152\setminted[xml]{style=borland} %% Specific per language 
    131153 
    132 \newcommand{\nl}[1]{\texttt{\small{\textcolor{blue}{#1}}}} 
    133 \newcommand{\NEMO}{\textit{NEMO}\xspace} 
     154%% Oneliner 
     155\newmint[forline]{fortran}{}   % \forline|...| 
     156\newmint[xmlline]{xml}{}       % \xmlline|...| 
     157\newmint[cmd]{console}{}       % \cmd|...| 
    134158 
    135 \newcommand{\hf}[1]{\textit{#1.h90}\index{h90 file!#1}} 
    136 \newcommand{\ifile}[1]{\textit{#1.nc}\index{Input NetCDF files!#1.nc}} 
    137 \newcommand{\jp}[1]{\textit{#1}\index{Model parameters!#1}} 
    138 \newcommand{\key}[1]{\textbf{key\_#1}\index{CPP keys!key\_#1}} 
    139 \newcommand{\mdl}[1]{\textit{#1.F90}\index{Modules!#1}} 
    140 \newcommand{\ngn}[1]{\textit{#1}\index{Namelist Group Name!#1}} 
    141 \newcommand{\np}[1]{\textit{#1}\index{Namelist variables!#1}} 
    142 \newcommand{\rou}[1]{\textit{#1}\index{Routines!#1}} 
     159%% Multi-lines 
     160\newminted[forlines]{fortran}{}   % \begin{forlines} 
     161\newminted[xmllines]{xml}{}       % \begin{xmllines} 
     162\newminted[cmds]{console}{}       % \begin{cmds} 
     163\newminted[clines]{c}{}           % \begin{clines} 
    143164 
    144 \newcommand{\grad}{\nabla} 
    145 \newcommand{\gradh}{\nabla_h} 
     165%% File 
     166\newmintedfile[forfile]{fortran}{}   % \forfile{../namelists/nam...} 
    146167 
    147 \newcommand{\ew}[3]{{e_{3#1}}_{\,#2}^{\,#3} } 
    148 \newcommand{\vect}[1]{\ensuremath{\mathbf{#1}}} 
    149 \newcommand{\Div}{\grad\cdot} 
    150 \newcommand{\curl}{\nabla \times} 
    151 \newcommand{\pd}[2][]{\frac{\partial #1}{\partial #2}} 
    152 \newcommand{\alpbet} {\left(\alpha / \beta \right)} 
    153  
    154 \newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}} 
    155 \newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}} 
    156 \newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}} 
    157 \newcommand{\rtriad}[2][]{\ensuremath{\triad[#1]{i}{k}{#2}{i_p}{k_p}}} 
    158 \newcommand{\rtriadt}[1]{\ensuremath{\triadt{i}{k}{#1}{i_p}{k_p}}} 
    159  
    160 \newcommand{\Alts}{{A}} 
    161 \newcommand{\Alt}{{A^{lT}}} 
    162  
    163 \newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}} 
    164 \newcommand{\rML}[1][i]{r_{\mathrm{ML}\,#1}} 
    165  
    166 \newcommand{\mygstrut}[2]{\rule[#1 em]{0pt}{#2 em}} 
    167 \newcommand{\mystrut}{\rule[-.9 em]{0pt}{1.79 em}} 
    168  
    169 \newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{full-text}} 
    170  
    171 \newcommand{\nlst}[1]{\forfile{../../../namelists/#1}} 
     168%% Inline 
     169\newmintinline[forcode]{fortran}{fontsize=auto, frame=lines}   % \forcode{...} 
     170\newmintinline[xmlcode]{xml}{    fontsize=auto, frame=lines}   % \xmlcode{...} 
     171\newmintinline[snippet]{console}{fontsize=auto, frame=lines}   % \snippet{...} 
  • NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.tex

    r10414 r10442  
    1717%% Custom style 
    1818\usepackage{../main/NEMO_manual} 
    19 \usepackage{../main/NEMO_minted} 
    2019 
    2120\makeindex 
     
    2524%% ============================================================================== 
    2625 
    27 %% Trick to include biblio in subfile compilation 
    28 \newcommand{\biblio}{ 
    29   \bibliographystyle{../main/ametsoc} 
    30   \bibliography{../main/NEMO_manual} 
    31 } 
     26%% Include references and index for single subfile compilation 
     27\newcommand{\biblio}{\bibliography{../main/NEMO_manual}} 
     28\newcommand{\pindex}{\printindex} 
    3229 
    3330\begin{document} 
    3431 
    35 %% Trick to include biblio in subfile compilation 
    36 \def\biblio{} 
     32%% Override custom cmds for full manual compilation 
     33\renewcommand{\biblio}{} 
     34\renewcommand{\pindex}{} 
    3735 
    3836 
     
    5149 
    5250\author{ 
    53 \Large Gurvan Madec, and the NEMO team                                                          \\ 
    54 \texttt{\small\href{mailto:gurvan.madec@locean-ipsl.umpc.fr}{gurvan.madec@locean-ipsl.umpc.fr}} \\ 
     51  \Large Gurvan Madec and NEMO System Team 
     52  \thanks{ 
     53    Yevgeny Aksenov, Mireck Andrejczuk, Mike Bell, Romain Bourdalle-Badie, Cl\'{e}ment Bricaud, 
     54    J\'{e}r\^{o}me Chanut, Stefania Ciliberti, Emanuela Clementi, Andrew Coward, Damiano Delrosso, 
     55    Massimiliano Drudi, Christian Eth\'{e}, Simona Flavoni, Doroteaciro Iovino, Claire L\'{e}vy, Tomas Lovato, 
     56    Nicolas Martin, S\'{e}bastien Masson, Pierre Mathiot, Gelsomina Mattia, Francesca Mele, Silvia Mocavero, 
     57    George Nurser, Enda O'Dea, Julien Paul, Cl\'{e}ment Rousset, Dave Storkey, Martin Vancoppenolle 
     58  }                                                        \\ 
     59                                                           \\ 
     60  \textit{Issue 27, Notes du P\^{o}le de mod\'{e}lisation} \\ 
     61  \textit{Institut Pierre-Simon Laplace (IPSL)}            \\ 
     62  \textit{ISSN 1288-1619} 
    5563} 
    5664 
    57 \date{ 
    58 Decembre 2017                                                                                \\ 
    59 {\small  -- version 4.0 alpha --}                                                            \\ 
    60 ~                                                                                            \\ 
    61 \textit{\small Note du P\^ole de mod\'{e}lisation de l'Institut Pierre-Simon Laplace No 27 } \\ 
    62 \vspace{0.45cm}{ ISSN No 1288-1619.} 
    63 } 
     65\date{Version 4.0 -- January 2019} 
    6466%\date{\today} 
    6567 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_A.tex

    r10414 r10442  
    2020 
    2121In order to establish the set of Primitive Equation in curvilinear $s$-coordinates 
    22 ($i.e.$ an orthogonal curvilinear coordinate in the horizontal and 
     22(\ie an orthogonal curvilinear coordinate in the horizontal and 
    2323an Arbitrary Lagrangian Eulerian (ALE) coordinate in the vertical), 
    2424we start from the set of equations established in \autoref{subsec:PE_zco_Eq} for 
     
    273273\] 
    274274leads to the $s-$coordinate formulation of the total $z-$coordinate time derivative, 
    275 $i.e.$ the total $s-$coordinate time derivative : 
     275\ie the total $s-$coordinate time derivative : 
    276276\begin{align} 
    277277  \label{apdx:A_sco_Dt_vect} 
     
    312312% 
    313313Introducing the vertical scale factor inside the horizontal derivative of the first two terms  
    314 ($i.e.$ the horizontal divergence), it becomes : 
     314(\ie the horizontal divergence), it becomes : 
    315315\begin{align*} 
    316316  { 
     
    355355\end{align*} 
    356356which leads to the $s-$coordinate flux formulation of the total $s-$coordinate time derivative,  
    357 $i.e.$ the total $s-$coordinate time derivative in flux form: 
     357\ie the total $s-$coordinate time derivative in flux form: 
    358358\begin{flalign} 
    359359  \label{apdx:A_sco_Dt_flux} 
     
    513513in particular the pressure gradient. 
    514514By contrast, $\omega$ is not $w$, the third component of the velocity, but the dia-surface velocity component, 
    515 $i.e.$ the volume flux across the moving $s$-surfaces per unit horizontal area.  
     515\ie the volume flux across the moving $s$-surfaces per unit horizontal area.  
    516516 
    517517 
     
    540540\biblio 
    541541 
     542\pindex 
     543 
    542544\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_B.tex

    r10414 r10442  
    402402\biblio 
    403403 
     404\pindex 
     405 
    404406\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_C.tex

    r10414 r10442  
    1010\minitoc 
    1111 
    12 %%%  Appendix put in gmcomment as it has not been updated for z* and s coordinate 
     12%%%  Appendix put in gmcomment as it has not been updated for \zstar and s coordinate 
    1313%I'm writting this appendix. It will be available in a forthcoming release of the documentation 
    1414 
     
    3939$dv=e_1\,e_2\,e_3 \,di\,dj\,dk$  is the volume element, with only $e_3$ that depends on time. 
    4040$D$ and $S$ are the ocean domain volume and surface, respectively. 
    41 No wetting/drying is allow ($i.e.$ $\frac{\partial S}{\partial t} = 0$). 
     41No wetting/drying is allow (\ie $\frac{\partial S}{\partial t} = 0$). 
    4242Let $k_s$ and $k_b$ be the ocean surface and bottom, resp. 
    43 ($i.e.$ $s(k_s) = \eta$ and $s(k_b)=-H$, where $H$ is the bottom depth). 
     43(\ie $s(k_s) = \eta$ and $s(k_b)=-H$, where $H$ is the bottom depth). 
    4444\begin{flalign*} 
    4545  z(k) = \eta - \int\limits_{\tilde{k}=k}^{\tilde{k}=k_s}  e_3(\tilde{k}) \;d\tilde{k} 
     
    9999\label{sec:C.1} 
    100100 
    101 The discretization of pimitive equation in $s$-coordinate ($i.e.$ time and space varying vertical coordinate) 
     101The discretization of pimitive equation in $s$-coordinate (\ie time and space varying vertical coordinate) 
    102102must be chosen so that the discrete equation of the model satisfy integral constrains on energy and enstrophy.  
    103103 
    104104Let us first establish those constraint in the continuous world. 
    105 The total energy ($i.e.$ kinetic plus potential energies) is conserved: 
     105The total energy (\ie kinetic plus potential energies) is conserved: 
    106106\begin{flalign} 
    107107  \label{eq:Tot_Energy} 
     
    487487  +   \frac{1}{2} \int_D {  \frac{{\textbf{U}_h}^2}{e_3} \partial_t ( e_3) \;dv } 
    488488\] 
    489 Indeed, using successively \autoref{eq:DOM_di_adj} ($i.e.$ the skew symmetry property of the $\delta$ operator) 
     489Indeed, using successively \autoref{eq:DOM_di_adj} (\ie the skew symmetry property of the $\delta$ operator) 
    490490and the continuity equation, then \autoref{eq:DOM_di_adj} again, 
    491491then the commutativity of operators $\overline {\,\cdot \,}$ and $\delta$, and finally \autoref{eq:DOM_mi_adj} 
    492 ($i.e.$ the symmetry property of the $\overline {\,\cdot \,}$ operator) 
     492(\ie the symmetry property of the $\overline {\,\cdot \,}$ operator) 
    493493applied in the horizontal and vertical directions, it becomes: 
    494494\begin{flalign*} 
     
    599599 
    600600When the equation of state is linear 
    601 ($i.e.$ when an advection-diffusion equation for density can be derived from those of temperature and salinity) 
     601(\ie when an advection-diffusion equation for density can be derived from those of temperature and salinity) 
    602602the change of KE due to the work of pressure forces is balanced by 
    603603the change of potential energy due to buoyancy forces:  
     
    621621  % 
    622622  \allowdisplaybreaks 
    623   \intertext{Using successively \autoref{eq:DOM_di_adj}, $i.e.$ the skew symmetry property of 
     623  \intertext{Using successively \autoref{eq:DOM_di_adj}, \ie the skew symmetry property of 
    624624    the $\delta$ operator, \autoref{eq:wzv}, the continuity equation, \autoref{eq:dynhpg_sco}, 
    625625    the hydrostatic equation in the $s$-coordinate, and $\delta_{k+1/2} \left[ z_t \right] \equiv e_{3w} $, 
     
    811811 
    812812Let us first consider the first term of the scalar product 
    813 ($i.e.$ just the the terms associated with the i-component of the advection): 
     813(\ie just the the terms associated with the i-component of the advection): 
    814814\begin{flalign*} 
    815815  &  - \int_D u \cdot \nabla \cdot \left(   \textbf{U}\,u   \right) \; dv   \\ 
     
    867867When the UBS scheme is used to evaluate the flux form momentum advection, 
    868868the discrete operator does not contribute to the global budget of linear momentum (flux form). 
    869 The horizontal kinetic energy is not conserved, but forced to decay ($i.e.$ the scheme is diffusive).  
     869The horizontal kinetic energy is not conserved, but forced to decay (\ie the scheme is diffusive).  
    870870 
    871871% ================================================================ 
     
    893893 
    894894The scheme does not allow but the conservation of the total kinetic energy but the conservation of $q^2$, 
    895 the potential enstrophy for a horizontally non-divergent flow ($i.e.$ when $\chi$=$0$). 
     895the potential enstrophy for a horizontally non-divergent flow (\ie when $\chi$=$0$). 
    896896Indeed, using the symmetry or skew symmetry properties of the operators 
    897897( \autoref{eq:DOM_mi_adj} and \autoref{eq:DOM_di_adj}), 
     
    942942  } 
    943943\end{flalign*} 
    944 The later equality is obtain only when the flow is horizontally non-divergent, $i.e.$ $\chi$=$0$.  
     944The later equality is obtain only when the flow is horizontally non-divergent, \ie $\chi$=$0$.  
    945945 
    946946% ------------------------------------------------------------------------------------------------------------- 
     
    971971\end{equation} 
    972972 
    973 This formulation does conserve the potential enstrophy for a horizontally non-divergent flow ($i.e.$ $\chi=0$).  
     973This formulation does conserve the potential enstrophy for a horizontally non-divergent flow (\ie $\chi=0$).  
    974974 
    975975Let consider one of the vorticity triad, for example ${^{i}_j}\mathbb{Q}^{+1/2}_{+1/2} $, 
     
    10261026the internal dynamics and physics (equations in flux form). 
    10271027For advection, 
    1028 only the CEN2 scheme ($i.e.$ $2^{nd}$ order finite different scheme) conserves the global variance of tracer. 
     1028only the CEN2 scheme (\ie $2^{nd}$ order finite different scheme) conserves the global variance of tracer. 
    10291029Nevertheless the other schemes ensure that the global variance decreases 
    1030 ($i.e.$ they are at least slightly diffusive). 
     1030(\ie they are at least slightly diffusive). 
    10311031For diffusion, all the schemes ensure the decrease of the total tracer variance, except the iso-neutral operator. 
    10321032There is generally no strict conservation of mass, 
     
    10721072 
    10731073The conservation of the variance of tracer due to the advection tendency can be achieved only with the CEN2 scheme, 
    1074 $i.e.$ when $\tau_u= \overline T^{\,i+1/2}$, $\tau_v= \overline T^{\,j+1/2}$, and $\tau_w= \overline T^{\,k+1/2}$.  
     1074\ie when $\tau_u= \overline T^{\,i+1/2}$, $\tau_v= \overline T^{\,j+1/2}$, and $\tau_w= \overline T^{\,k+1/2}$.  
    10751075It can be demonstarted as follows: 
    10761076\begin{flalign*} 
     
    11081108the conservation of potential vorticity and the horizontal divergence, 
    11091109and the dissipation of the square of these quantities 
    1110 ($i.e.$ enstrophy and the variance of the horizontal divergence) as well as 
     1110(\ie enstrophy and the variance of the horizontal divergence) as well as 
    11111111the dissipation of the horizontal kinetic energy. 
    11121112In particular, when the eddy coefficients are horizontally uniform, 
     
    13461346\end{flalign*} 
    13471347 
    1348 If the vertical diffusion coefficient is uniform over the whole domain, the enstrophy is dissipated, $i.e.$ 
     1348If the vertical diffusion coefficient is uniform over the whole domain, the enstrophy is dissipated, \ie 
    13491349\begin{flalign*} 
    13501350  \int\limits_D \zeta \, \textbf{k} \cdot \nabla \times 
     
    13961396    \left( \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k} \right) \right)\; dv = 0    &&& 
    13971397\end{flalign*} 
    1398 and the square of the horizontal divergence decreases ($i.e.$ the horizontal divergence is dissipated) if 
     1398and the square of the horizontal divergence decreases (\ie the horizontal divergence is dissipated) if 
    13991399the vertical diffusion coefficient is uniform over the whole domain: 
    14001400 
     
    14631463the heat and salt contents are conserved (equations in flux form). 
    14641464Since a flux form is used to compute the temperature and salinity, 
    1465 the quadratic form of these quantities ($i.e.$ their variance) globally tends to diminish. 
     1465the quadratic form of these quantities (\ie their variance) globally tends to diminish. 
    14661466As for the advection term, there is conservation of mass only if the Equation Of Seawater is linear.  
    14671467 
     
    15301530\biblio 
    15311531 
     1532\pindex 
     1533 
    15321534\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_D.tex

    r10414 r10442  
    7777\label{sec:D_coding} 
    7878 
    79 - Use of the universal language \textsc{Fortran} 90, and try to avoid obsolescent features like statement functions, 
     79- Use of the universal language \fninety, and try to avoid obsolescent features like statement functions, 
    8080do not use GO TO and EQUIVALENCE statements. 
    8181 
     
    188188%-------------------------------------------------------------------------------------------------------------- 
    189189 
    190 N.B. Parameter here, in not only parameter in the \textsc{Fortran} acceptation, 
     190N.B. Parameter here, in not only parameter in the \fortran acceptation, 
    191191it is also used for code variables that are read in namelist and should never been modified during a simulation.  
    192192It is the case, for example, for the size of a domain (jpi,jpj,jpk). 
     
    203203\biblio 
    204204 
     205\pindex 
     206 
    205207\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_E.tex

    r10414 r10442  
    4848$\tau "_i =\frac{e_{1T}}{e_{2T}\,e_{3T}}\delta_i \left[ \frac{e_{2u} e_{3u} }{e_{1u} }\delta_{i+1/2}[\tau] \right]$. 
    4949 
    50 This results in a dissipatively dominant (i.e. hyper-diffusive) truncation error 
     50This results in a dissipatively dominant (\ie hyper-diffusive) truncation error 
    5151\citep{Shchepetkin_McWilliams_OM05}. 
    5252The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}. 
     
    135135\end{equation} 
    136136with ${A_u^{lT}}^2 = \frac{1}{12} {e_{1u}}^3\ |u|$,  
    137 $i.e.$ $A_u^{lT} = \frac{1}{\sqrt{12}} \,e_{1u}\ \sqrt{ e_{1u}\,|u|\,}$ 
     137\ie $A_u^{lT} = \frac{1}{\sqrt{12}} \,e_{1u}\ \sqrt{ e_{1u}\,|u|\,}$ 
    138138it comes: 
    139139\begin{equation} 
     
    147147  \end{split} 
    148148\end{equation} 
    149 if the velocity is uniform ($i.e.$ $|u|=cst$) then the diffusive flux is 
     149if the velocity is uniform (\ie $|u|=cst$) then the diffusive flux is 
    150150\begin{equation} 
    151151  \label{eq:tra_ldf_lap} 
     
    166166  \end{split} 
    167167\end{equation} 
    168 if the velocity is uniform ($i.e.$ $|u|=cst$) and 
     168if the velocity is uniform (\ie $|u|=cst$) and 
    169169choosing $\tau "_i =\frac{e_{1T}}{e_{2T}\,e_{3T}}\delta_i \left[ \frac{e_{2u} e_{3u} }{e_{1u} } \delta_{i+1/2}[\tau] \right]$ 
    170170 
     
    218218not $2\rdt$ as it can be found sometimes in literature. 
    219219The leap-Frog time stepping is a second order centered scheme. 
    220 As such it respects the quadratic invariant in integral forms, $i.e.$ the following continuous property, 
     220As such it respects the quadratic invariant in integral forms, \ie the following continuous property, 
    221221\[ 
    222222  % \label{eq:Energy} 
     
    257257Let try to define a scheme that get its inspiration from the \citet{Griffies_al_JPO98} scheme, 
    258258but is formulated within the \NEMO framework 
    259 ($i.e.$ using scale factors rather than grid-size and having a position of $T$-points that 
     259(\ie using scale factors rather than grid-size and having a position of $T$-points that 
    260260is not necessary in the middle of vertical velocity points, see \autoref{fig:zgr_e3}). 
    261261 
     
    271271(see \autoref{chap:LDF}). 
    272272Nevertheless, this technique works fine for $T$ and $S$ as they are active tracers 
    273 ($i.e.$ they enter the computation of density), but it does not work for a passive tracer. 
     273(\ie they enter the computation of density), but it does not work for a passive tracer. 
    274274\citep{Griffies_al_JPO98} introduce a different way to discretise the off-diagonal terms that 
    275275nicely solve the problem. 
     
    386386\item[$\bullet$ implicit treatment in the vertical] 
    387387  In the diagonal term associated with the vertical divergence of the iso-neutral fluxes 
    388   (i.e. the term associated with a second order vertical derivative) 
     388  \ie the term associated with a second order vertical derivative) 
    389389  appears only tracer values associated with a single water column. 
    390390  This is of paramount importance since it means that 
     
    399399 
    400400\item[$\bullet$ pure iso-neutral operator] 
    401   The iso-neutral flux of locally referenced potential density is zero, $i.e.$ 
     401  The iso-neutral flux of locally referenced potential density is zero, \ie 
    402402  \begin{align*} 
    403403    % \label{eq:Gf_property2} 
     
    415415 
    416416\item[$\bullet$ conservation of tracer] 
    417   The iso-neutral diffusion term conserve the total tracer content, $i.e.$ 
     417  The iso-neutral diffusion term conserve the total tracer content, \ie 
    418418  \[ 
    419419    % \label{eq:Gf_property1} 
     
    423423 
    424424\item[$\bullet$ decrease of tracer variance] 
    425   The iso-neutral diffusion term does not increase the total tracer variance, $i.e.$ 
     425  The iso-neutral diffusion term does not increase the total tracer variance, \ie 
    426426  \[ 
    427427    % \label{eq:Gf_property1} 
     
    431431It is a key property for a diffusion term. 
    432432It means that the operator is also a dissipation term, 
    433 $i.e.$ it is a sink term for the square of the quantity on which it is applied. 
     433\ie it is a sink term for the square of the quantity on which it is applied. 
    434434It therfore ensures that, when the diffusivity coefficient is large enough, 
    435435the field on which it is applied become free of grid-point noise. 
    436436 
    437437\item[$\bullet$ self-adjoint operator] 
    438   The iso-neutral diffusion operator is self-adjoint, $i.e.$ 
     438  The iso-neutral diffusion operator is self-adjoint, \ie 
    439439  \[ 
    440440    % \label{eq:Gf_property1} 
     
    457457the formulation of which depends on the slopes of iso-neutral surfaces. 
    458458Contrary to the case of iso-neutral mixing, the slopes used here are referenced to the geopotential surfaces, 
    459 $i.e.$ \autoref{eq:ldfslp_geo} is used in $z$-coordinate, 
     459\ie \autoref{eq:ldfslp_geo} is used in $z$-coordinate, 
    460460and the sum \autoref{eq:ldfslp_geo} + \autoref{eq:ldfslp_iso} in $z^*$ or $s$-coordinates.  
    461461 
     
    578578Nevertheless this property can be used to choose a discret form of \autoref{eq:eiv_skew_continuous} which 
    579579is consistent with the iso-neutral operator \autoref{eq:Gf_operator}. 
    580 Using the slopes \autoref{eq:Gf_slopes} and defining $A_e$ at $T$-point($i.e.$ as $A$, 
     580Using the slopes \autoref{eq:Gf_slopes} and defining $A_e$ at $T$-point(\ie as $A$, 
    581581the eddy diffusivity coefficient), the resulting discret form is given by: 
    582582\begin{equation} 
     
    600600it uses the same definition for the slopes. 
    601601It also ensures the conservation of the tracer variance (see Appendix \autoref{apdx:eiv_skew}), 
    602 $i.e.$ it does not include a diffusive component but is a "pure" advection term. 
     602\ie it does not include a diffusive component but is a "pure" advection term. 
    603603 
    604604$\ $\newpage      %force an empty line 
     
    840840Exactly the same thing occurs for the triad ${_i^k \mathbb{R}_{-1/2}^{+1/2}}$ in the $i$ direction. 
    841841Therefore the sum over the domain is zero, 
    842 $i.e.$ the variance of the tracer is preserved by the discretisation of the skew fluxes. 
     842\ie the variance of the tracer is preserved by the discretisation of the skew fluxes. 
    843843 
    844844\biblio 
    845845 
     846\pindex 
     847 
    846848\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_iso.tex

    r10414 r10442  
    11\documentclass[../main/NEMO_manual]{subfiles} 
     2 
     3%% Local cmds 
     4\newcommand{\rML}[1][i]{\ensuremath{_{\mathrm{ML}\,#1}}} 
     5\newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}} 
     6\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}} 
     7\newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}} 
     8\newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}} 
     9\newcommand{\rtriad}[2][]{\ensuremath{\triad[#1]{i}{k}{#2}{i_p}{k_p}}} 
     10\newcommand{\rtriadt}[1]{\ensuremath{\triadt{i}{k}{#1}{i_p}{k_p}}} 
    211 
    312\begin{document} 
     
    514% Iso-neutral diffusion : 
    615% ================================================================ 
    7 \chapter[Iso-Neutral Diffusion and Eddy Advection using Triads] 
    8          {\texorpdfstring{Iso-Neutral Diffusion and\\ Eddy Advection using Triads}{Iso-Neutral Diffusion and Eddy Advection using Triads}} 
     16\chapter{Iso-Neutral Diffusion and Eddy Advection using Triads} 
    917\label{apdx:triad} 
    1018 
     
    3240even though the eddy advection is accomplished by means of the skew fluxes. 
    3341 
    34  
    3542The options specific to the Griffies scheme include: 
    36 \begin{description}[font=\normalfont] 
     43\begin{description} 
    3744\item[\np{ln\_triad\_iso}] 
    3845  See \autoref{sec:taper}. 
     
    5663\end{description} 
    5764The options shared with the Standard scheme include: 
    58 \begin{description}[font=\normalfont] 
     65\begin{description} 
    5966\item[\np{ln\_traldf\_msc}]   blah blah to be added 
    6067\item[\np{rn\_slpmax}]  blah blah to be added 
     
    7481  \label{eq:iso_tensor_1} 
    7582  \begin{equation} 
    76     D^{lT}=-\Div\vect{f}^{lT}\equiv 
     83    D^{lT}=-\nabla \cdot\vect{f}^{lT}\equiv 
    7784    -\frac{1}{e_1e_2e_3}\left[\pd{i}\left (f_1^{lT}e_2e_3\right) + 
    7885      \pd{j}\left (f_2^{lT}e_2e_3\right) + \pd{k}\left (f_3^{lT}e_1e_2\right)\right], 
     
    8087  where the diffusive flux per unit area of physical space 
    8188  \begin{equation} 
    82     \vect{f}^{lT}=-\Alt\Re\cdot\grad T, 
     89    \vect{f}^{lT}=-{A^{lT}}\Re\cdot\nabla T, 
    8390  \end{equation} 
    8491  \begin{equation} 
     
    8693    \mbox{with}\quad \;\;\Re = 
    8794    \begin{pmatrix} 
    88       1   &  0   & -r_1           \mystrut \\ 
    89       0   &  1   & -r_2           \mystrut \\ 
    90       -r_1 & -r_2 &  r_1 ^2+r_2 ^2 \mystrut 
     95      1   &  0   & -r_1           \rule[-.9 em]{0pt}{1.79 em} \\ 
     96      0   &  1   & -r_2           \rule[-.9 em]{0pt}{1.79 em} \\ 
     97      -r_1 & -r_2 &  r_1 ^2+r_2 ^2 \rule[-.9 em]{0pt}{1.79 em} 
    9198    \end{pmatrix} 
    92     \quad \text{and} \quad\grad T= 
     99    \quad \text{and} \quad\nabla T= 
    93100    \begin{pmatrix} 
    94       \frac{1}{e_1} \pd[T]{i} \mystrut \\ 
    95       \frac{1}{e_2} \pd[T]{j} \mystrut \\ 
    96       \frac{1}{e_3} \pd[T]{k} \mystrut 
     101      \frac{1}{e_1} \pd[T]{i} \rule[-.9 em]{0pt}{1.79 em} \\ 
     102      \frac{1}{e_2} \pd[T]{j} \rule[-.9 em]{0pt}{1.79 em} \\ 
     103      \frac{1}{e_3} \pd[T]{k} \rule[-.9 em]{0pt}{1.79 em} 
    97104    \end{pmatrix} 
    98105    . 
     
    131138\begin{align} 
    132139  \label{eq:i13c} 
    133   f_{13}=&+\Alt r_1\frac{1}{e_3}\frac{\partial T}{\partial k},\qquad f_{23}=+\Alt r_2\frac{1}{e_3}\frac{\partial T}{\partial k}\\ 
     140  f_{13}=&+{A^{lT}} r_1\frac{1}{e_3}\frac{\partial T}{\partial k},\qquad f_{23}=+{A^{lT}} r_2\frac{1}{e_3}\frac{\partial T}{\partial k}\\ 
    134141  \intertext{and in the k-direction resulting from the lateral tracer gradients} 
    135142  \label{eq:i31c} 
    136   f_{31}+f_{32}=& \Alt r_1\frac{1}{e_1}\frac{\partial T}{\partial i}+\Alt r_2\frac{1}{e_1}\frac{\partial T}{\partial i} 
     143  f_{31}+f_{32}=& {A^{lT}} r_1\frac{1}{e_1}\frac{\partial T}{\partial i}+{A^{lT}} r_2\frac{1}{e_1}\frac{\partial T}{\partial i} 
    137144\end{align} 
    138145 
     
    140147\begin{equation} 
    141148  \label{eq:i33c} 
    142   f_{33}=-\Alt(r_1^2 +r_2^2) \frac{1}{e_3}\frac{\partial T}{\partial k}. 
     149  f_{33}=-{A^{lT}}(r_1^2 +r_2^2) \frac{1}{e_3}\frac{\partial T}{\partial k}. 
    143150\end{equation} 
    144151 
     
    165172the $1/{e_{3}}_{i+1/2}^k$ associated with the vertical tracer gradient, is then \autoref{eq:tra_ldf_iso} 
    166173\[ 
    167   \left(F_u^{13} \right)_{i+\hhalf}^k = \Alts_{i+\hhalf}^k 
     174  \left(F_u^{13} \right)_{i+\frac{1}{2}}^k = {A}_{i+\frac{1}{2}}^k 
    168175  {e_{2}}_{i+1/2}^k \overline{\overline 
    169176    r_1} ^{\,i,k}\,\overline{\overline{\delta_k T}}^{\,i,k}, 
     
    175182  \frac{\delta_{i+1/2} [\rho]}{\overline{\overline{\delta_k \rho}}^{\,i,k}}, 
    176183\] 
    177 and here and in the following we drop the $^{lT}$ superscript from $\Alt$ for simplicity. 
     184and here and in the following we drop the $^{lT}$ superscript from ${A^{lT}}$ for simplicity. 
    178185Unfortunately the resulting combination $\overline{\overline{\delta_k\bullet}}^{\,i,k}$ of a $k$ average and 
    179186a $k$ difference of the tracer reduces to $\bullet_{k+1}-\bullet_{k-1}$, 
     
    183190To correct this, we introduced a smoothing of the slopes of the iso-neutral surfaces (see \autoref{chap:LDF}). 
    184191This technique works for $T$ and $S$ in so far as they are active tracers 
    185 ($i.e.$ they enter the computation of density), but it does not work for a passive tracer. 
     192(\ie they enter the computation of density), but it does not work for a passive tracer. 
    186193 
    187194\subsection{Expression of the skew-flux in terms of triad slopes} 
     
    213220\begin{multline} 
    214221  \label{eq:i13} 
    215   \left( F_u^{13}  \right)_{i+\frac{1}{2}}^k = \Alts_{i+1}^k a_1 s_1 
     222  \left( F_u^{13}  \right)_{i+\frac{1}{2}}^k = {A}_{i+1}^k a_1 s_1 
    216223  \delta_{k+\frac{1}{2}} \left[ T^{i+1} 
    217   \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  + \Alts _i^k a_2 s_2 \delta 
     224  \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  + {A} _i^k a_2 s_2 \delta 
    218225  _{k+\frac{1}{2}} \left[ T^i 
    219226  \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}} \\ 
    220   +\Alts _{i+1}^k a_3 s_3 \delta_{k-\frac{1}{2}} \left[ T^{i+1} 
    221   \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  +\Alts _i^k a_4 s_4 \delta 
     227  +{A} _{i+1}^k a_3 s_3 \delta_{k-\frac{1}{2}} \left[ T^{i+1} 
     228  \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}  +{A} _i^k a_4 s_4 \delta 
    222229  _{k-\frac{1}{2}} \left[ T^i \right]/e_{{3w}_{i+1}}^{k+\frac{1}{2}}, 
    223230\end{multline} 
    224231where the contributions of the triad fluxes are weighted by areas $a_1, \dotsc a_4$, 
    225 and $\Alts$ is now defined at the tracer points rather than the $u$-points. 
     232and ${A}$ is now defined at the tracer points rather than the $u$-points. 
    226233This discretization gives a much closer stencil, and disallows the two-point computational modes. 
    227234 
    228235The vertical skew flux \autoref{eq:i31c} from tracer cell $i,k$ to $i,k+1$ at 
    229 the $w$-point $i,k+\hhalf$ is constructed similarly (\autoref{fig:ISO_triad}b) by 
     236the $w$-point $i,k+\frac{1}{2}$ is constructed similarly (\autoref{fig:ISO_triad}b) by 
    230237multiplying lateral tracer gradients from each of the four surrounding $u$-points by the appropriate triad slope: 
    231238\begin{multline} 
    232239  \label{eq:i31} 
    233   \left( F_w^{31} \right) _i ^{k+\frac{1}{2}} =  \Alts_i^{k+1} a_{1}' 
     240  \left( F_w^{31} \right) _i ^{k+\frac{1}{2}} =  {A}_i^{k+1} a_{1}' 
    234241  s_{1}' \delta_{i-\frac{1}{2}} \left[ T^{k+1} \right]/{e_{3u}}_{i-\frac{1}{2}}^{k+1} 
    235   +\Alts_i^{k+1} a_{2}' s_{2}' \delta_{i+\frac{1}{2}} \left[ T^{k+1} \right]/{e_{3u}}_{i+\frac{1}{2}}^{k+1} \\ 
    236   + \Alts_i^k a_{3}' s_{3}' \delta_{i-\frac{1}{2}} \left[ T^k\right]/{e_{3u}}_{i-\frac{1}{2}}^k 
    237   +\Alts_i^k a_{4}' s_{4}' \delta_{i+\frac{1}{2}} \left[ T^k \right]/{e_{3u}}_{i+\frac{1}{2}}^k. 
     242  +{A}_i^{k+1} a_{2}' s_{2}' \delta_{i+\frac{1}{2}} \left[ T^{k+1} \right]/{e_{3u}}_{i+\frac{1}{2}}^{k+1} \\ 
     243  + {A}_i^k a_{3}' s_{3}' \delta_{i-\frac{1}{2}} \left[ T^k\right]/{e_{3u}}_{i-\frac{1}{2}}^k 
     244  +{A}_i^k a_{4}' s_{4}' \delta_{i+\frac{1}{2}} \left[ T^k \right]/{e_{3u}}_{i+\frac{1}{2}}^k. 
    238245\end{multline} 
    239246 
     
    262269      \protect\label{fig:qcells} 
    263270      Triad notation for quarter cells. $T$-cells are inside boxes, 
    264       while the  $i+\half,k$ $u$-cell is shaded in green and 
    265       the $i,k+\half$ $w$-cell is shaded in pink. 
     271      while the  $i+\fractext{1}{2},k$ $u$-cell is shaded in green and 
     272      the $i,k+\fractext{1}{2}$ $w$-cell is shaded in pink. 
    266273    } 
    267274  \end{center} 
     
    272279the intersection of the $i,k$ $T$-cell, the $i+i_p,k$ $u$-cell and the $i,k+k_p$ $w$-cell. 
    273280Expressing the slopes $s_i$ and $s'_i$ in \autoref{eq:i13} and \autoref{eq:i31} in this notation, 
    274 we have $e.g.$ \ $s_1=s'_1={\:}_i^k \mathbb{R}_{1/2}^{1/2}$. 
     281we have \eg \ $s_1=s'_1={\:}_i^k \mathbb{R}_{1/2}^{1/2}$. 
    275282Each triad slope $_i^k\mathbb{R}_{i_p}^{k_p}$ is used once (as an $s$) to 
    276283calculate the lateral flux along its $u$-arm, at $(i+i_p,k)$, 
     
    280287and we notate these areas, similarly to the triad slopes, 
    281288as $_i^k{\mathbb{A}_u}_{i_p}^{k_p}$, $_i^k{\mathbb{A}_w}_{i_p}^{k_p}$, 
    282 where $e.g.$ in \autoref{eq:i13} $a_{1}={\:}_i^k{\mathbb{A}_u}_{1/2}^{1/2}$, 
     289where \eg in \autoref{eq:i13} $a_{1}={\:}_i^k{\mathbb{A}_u}_{1/2}^{1/2}$, 
    283290and in \autoref{eq:i31} $a'_{1}={\:}_i^k{\mathbb{A}_w}_{1/2}^{1/2}$. 
    284291 
     
    292299  \label{eq:i11} 
    293300  \left( F_u^{11} \right) _{i+\frac{1}{2}} ^{k} = 
    294   - \left( \Alts_i^{k+1} a_{1} + \Alts_i^{k+1} a_{2} + \Alts_i^k 
    295     a_{3} + \Alts_i^k a_{4} \right) 
     301  - \left( {A}_i^{k+1} a_{1} + {A}_i^{k+1} a_{2} + {A}_i^k 
     302    a_{3} + {A}_i^k a_{4} \right) 
    296303  \frac{\delta_{i+1/2} \left[ T^k\right]}{{e_{1u}}_{\,i+1/2}^{\,k}}, 
    297304\end{equation} 
     
    301308\begin{equation} 
    302309  \label{eq:latflux-triad} 
    303   _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) = - \Alts_i^k{ \:}_i^k{\mathbb{A}_u}_{i_p}^{k_p} 
     310  _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) = - {A}_i^k{ \:}_i^k{\mathbb{A}_u}_{i_p}^{k_p} 
    304311  \left( 
    305312    \frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} } 
     
    325332  \label{eq:i33} 
    326333  \left( F_w^{33} \right) _i^{k+\frac{1}{2}} = 
    327   - \left( \Alts_i^{k+1} a_{1}' s_{1}'^2 
    328     + \Alts_i^{k+1} a_{2}' s_{2}'^2 
    329     + \Alts_i^k a_{3}' s_{3}'^2 
    330     + \Alts_i^k a_{4}' s_{4}'^2 \right)\delta_{k+\frac{1}{2}} \left[ T^{i+1} \right], 
     334  - \left( {A}_i^{k+1} a_{1}' s_{1}'^2 
     335    + {A}_i^{k+1} a_{2}' s_{2}'^2 
     336    + {A}_i^k a_{3}' s_{3}'^2 
     337    + {A}_i^k a_{4}' s_{4}'^2 \right)\delta_{k+\frac{1}{2}} \left[ T^{i+1} \right], 
    331338\end{equation} 
    332339where the areas $a'$ and slopes $s'$ are the same as in \autoref{eq:i31}. 
     
    336343  \label{eq:vertflux-triad} 
    337344  _i^k {\mathbb{F}_w}_{i_p}^{k_p} (T) 
    338   &= \Alts_i^k{\: }_i^k{\mathbb{A}_w}_{i_p}^{k_p} 
     345  &= {A}_i^k{\: }_i^k{\mathbb{A}_w}_{i_p}^{k_p} 
    339346    \left( 
    340347    {_i^k\mathbb{R}_{i_p}^{k_p}}\frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} } 
     
    383390the $u$-point $i+i_p,k$ and a vertical flux $_i^k{\mathbb{F}_w}_{i_p}^{k_p} (T)$ across the $w$-point $i,k+k_p$. 
    384391The lateral flux drives a net rate of change of variance, 
    385 summed over the two $T$-points $i+i_p-\half,k$ and $i+i_p+\half,k$, of 
     392summed over the two $T$-points $i+i_p-\fractext{1}{2},k$ and $i+i_p+\fractext{1}{2},k$, of 
    386393\begin{multline} 
    387394  {b_T}_{i+i_p-1/2}^k\left(\frac{\partial T}{\partial t}T\right)_{i+i_p-1/2}^k+ 
     
    395402\end{multline} 
    396403while the vertical flux similarly drives a net rate of change of variance summed over 
    397 the $T$-points $i,k+k_p-\half$ (above) and $i,k+k_p+\half$ (below) of 
     404the $T$-points $i,k+k_p-\fractext{1}{2}$ (above) and $i,k+k_p+\fractext{1}{2}$ (below) of 
    398405\begin{equation} 
    399406  \label{eq:dvar_iso_k} 
     
    404411\autoref{eq:latflux-triad} and \autoref{eq:vertflux-triad}, it is 
    405412\begin{multline*} 
    406   -\Alts_i^k\left \{ 
     413  -{A}_i^k\left \{ 
    407414    { } _i^k{\mathbb{A}_u}_{i_p}^{k_p} 
    408415    \left( 
     
    429436\begin{equation} 
    430437  \label{eq:perfect-square} 
    431   -\Alts_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p} 
     438  -{A}_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p} 
    432439  \left( 
    433440    \frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} } 
     
    445452\begin{equation} 
    446453  \label{eq:cts-var} 
    447   \frac{\partial}{\partial t}\int\!\half T^2\, dV = 
     454  \frac{\partial}{\partial t}\int\!\fractext{1}{2} T^2\, dV = 
    448455  \int\!\mathbf{F}\cdot\nabla T\, dV, 
    449456\end{equation} 
     
    474481\begin{equation} 
    475482  \label{eq:V-NEMO} 
    476   _i^k\mathbb{V}_{i_p}^{k_p}=\quarter {b_u}_{i+i_p}^k, 
     483  _i^k\mathbb{V}_{i_p}^{k_p}=\fractext{1}{4} {b_u}_{i+i_p}^k, 
    477484\end{equation} 
    478485as a quarter of the volume of the $u$-cell inside which the triad quarter-cell lies. 
     
    481488\begin{equation} 
    482489  \label{eq:lat-normal} 
    483   -\overline\Alts_{\,i+1/2}^k\; 
     490  -\overline{A}_{\,i+1/2}^k\; 
    484491  \frac{{b_u}_{i+1/2}^k}{{e_{1u}}_{\,i + i_p}^{\,k}} 
    485492  \;\frac{\delta_{i+ 1/2}[T^k] }{{e_{1u}}_{\,i + i_p}^{\,k}} 
    486   = -\overline\Alts_{\,i+1/2}^k\;\frac{{e_{1w}}_{\,i + 1/2}^{\,k}\:{e_{1v}}_{\,i + 1/2}^{\,k}\;\delta_{i+ 1/2}[T^k]}{{e_{1u}}_{\,i + 1/2}^{\,k}}. 
     493  = -\overline{A}_{\,i+1/2}^k\;\frac{{e_{1w}}_{\,i + 1/2}^{\,k}\:{e_{1v}}_{\,i + 1/2}^{\,k}\;\delta_{i+ 1/2}[T^k]}{{e_{1u}}_{\,i + 1/2}^{\,k}}. 
    487494\end{equation} 
    488495In fact if the diffusive coefficient is defined at $u$-points, 
    489 so that we employ $\Alts_{i+i_p}^k$ instead of  $\Alts_i^k$ in the definitions of the triad fluxes 
     496so that we employ ${A}_{i+i_p}^k$ instead of  ${A}_i^k$ in the definitions of the triad fluxes 
    490497\autoref{eq:latflux-triad} and \autoref{eq:vertflux-triad}, 
    491498we can replace $\overline{A}_{\,i+1/2}^k$ by $A_{i+1/2}^k$ in the above. 
     
    509516  \begin{align} 
    510517    \label{eq:triadfluxu} 
    511     _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) &= - \Alts_i^k{ 
     518    _i^k {\mathbb{F}_u}_{i_p}^{k_p} (T) &= - {A}_i^k{ 
    512519                                          \:}\frac{{{}_i^k\mathbb{V}}_{i_p}^{k_p}}{{e_{1u}}_{\,i + i_p}^{\,k}} 
    513520                                          \left( 
     
    518525    \intertext{and} 
    519526    _i^k {\mathbb{F}_w}_{i_p}^{k_p} (T) 
    520                                         &= \Alts_i^k{\: }\frac{{{}_i^k\mathbb{V}}_{i_p}^{k_p}}{{e_{3w}}_{\,i}^{\,k+k_p}} 
     527                                        &= {A}_i^k{\: }\frac{{{}_i^k\mathbb{V}}_{i_p}^{k_p}}{{e_{3w}}_{\,i}^{\,k+k_p}} 
    521528                                          \left( 
    522529                                          {_i^k\mathbb{R}_{i_p}^{k_p}}\frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} } 
     
    528535  \[ 
    529536    % \label{eq:V-NEMO2} 
    530     _i^k{\mathbb{V}}_{i_p}^{k_p}=\quarter {b_u}_{i+i_p}^k. 
     537    _i^k{\mathbb{V}}_{i_p}^{k_p}=\fractext{1}{4} {b_u}_{i+i_p}^k. 
    531538  \] 
    532539\end{subequations} 
     
    551558    D_l^T = \frac{1}{b_T} \ 
    552559    \delta_{i} \left[ \frac{e_{2u}\,e_{3u}}{e_{1u}} \; 
    553       \overline\Alts^{\,i} \; \delta_{i+1/2}[T] \right] \qquad 
     560      \overline{A}^{\,i} \; \delta_{i+1/2}[T] \right] \qquad 
    554561    \text{when} \quad { _i^k \mathbb{R}_{i_p}^{k_p} }=0 
    555562  \] 
     
    563570  \[ 
    564571    \frac{1}{b_w}\sum_{\substack{i_p, \,k_p}} \left\{ 
    565       {\:}_i^k\mathbb{V}_{i_p}^{k_p} \: \Alts_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2 
     572      {\:}_i^k\mathbb{V}_{i_p}^{k_p} \: {A}_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2 
    566573    \right\}  = 
    567574    \frac{1}{4b_w}\sum_{\substack{i_p, \,k_p}} \left\{ 
    568       {b_u}_{i+i_p}^k\: \Alts_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2 
     575      {b_u}_{i+i_p}^k\: {A}_i^k \: \left(_i^k \mathbb{R}_{i_p}^{k_p}\right)^2 
    569576    \right\}, 
    570577  \] 
     
    576583 
    577584\item[$\bullet$ conservation of tracer] 
    578   The iso-neutral diffusion conserves tracer content, $i.e.$ 
     585  The iso-neutral diffusion conserves tracer content, \ie 
    579586  \[ 
    580587    % \label{eq:iso_property1} 
     
    584591 
    585592\item[$\bullet$ no increase of tracer variance] 
    586   The iso-neutral diffusion does not increase the tracer variance, $i.e.$ 
     593  The iso-neutral diffusion does not increase the tracer variance, \ie 
    587594  \[ 
    588595    % \label{eq:iso_property2} 
     
    592599  It is a key property for a diffusion term. 
    593600  It means that it is also a dissipation term, 
    594   $i.e.$ it dissipates the square of the quantity on which it is applied. 
     601  \ie it dissipates the square of the quantity on which it is applied. 
    595602  It therefore ensures that, when the diffusivity coefficient is large enough, 
    596603  the field on which it is applied becomes free of grid-point noise. 
    597604 
    598605\item[$\bullet$ self-adjoint operator] 
    599   The iso-neutral diffusion operator is self-adjoint, $i.e.$ 
     606  The iso-neutral diffusion operator is self-adjoint, \ie 
    600607  \begin{equation} 
    601608    \label{eq:iso_property3} 
     
    610617  \[ 
    611618    % \label{eq:TScovar} 
    612     - \Alts_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p} 
     619    - {A}_i^k{\:} _i^k\mathbb{V}_{i_p}^{k_p} 
    613620    \left( 
    614621      \frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} } 
     
    633640or down into the ocean floor, must be masked out. 
    634641See \autoref{fig:bdry_triads}. 
    635 Surface layer triads $\triad{i}{1}{R}{1/2}{-1/2}$ (magenta) and $\triad{i+1}{1}{R}{-1/2}{-1/2}$ (blue) that 
     642Surface layer triads \triad{i}{1}{R}{1/2}{-1/2} (magenta) and \triad{i+1}{1}{R}{-1/2}{-1/2} (blue) that 
    636643require density to be specified above the ocean surface are masked (\autoref{fig:bdry_triads}a): 
    637644this ensures that lateral tracer gradients produce no flux through the ocean surface. 
    638645However, to prevent surface noise, it is customary to retain the $_{11}$ contributions towards 
    639 the lateral triad fluxes $\triad[u]{i}{1}{F}{1/2}{-1/2}$ and $\triad[u]{i+1}{1}{F}{-1/2}{-1/2}$; 
     646the lateral triad fluxes \triad[u]{i}{1}{F}{1/2}{-1/2} and \triad[u]{i+1}{1}{F}{-1/2}{-1/2}; 
    640647this drives diapycnal tracer fluxes. 
    641648Similar comments apply to triads that would intersect the ocean floor (\autoref{fig:bdry_triads}b). 
    642 Note that both near bottom triad slopes $\triad{i}{k}{R}{1/2}{1/2}$ and 
    643 $\triad{i+1}{k}{R}{-1/2}{1/2}$ are masked when either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, 
    644 i.e.\ the $i,k+1$ $u$-point is masked. 
     649Note that both near bottom triad slopes \triad{i}{k}{R}{1/2}{1/2} and \triad{i+1}{k}{R}{-1/2}{1/2} are masked when 
     650either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, \ie the $i,k+1$ $u$-point is masked. 
    645651The associated lateral fluxes (grey-black dashed line) are masked if \np{ln\_botmix\_triad}\forcode{ = .false.}, 
    646652but left unmasked, giving bottom mixing, if \np{ln\_botmix\_triad}\forcode{ = .true.}. 
     
    657663      (a) Uppermost model layer $k=1$ with $i,1$ and $i+1,1$ tracer points (black dots), 
    658664      and $i+1/2,1$ $u$-point (blue square). 
    659       Triad slopes $\triad{i}{1}{R}{1/2}{-1/2}$ (magenta) and $\triad{i+1}{1}{R}{-1/2}{-1/2}$ (blue) poking through 
     665      Triad slopes \triad{i}{1}{R}{1/2}{-1/2} (magenta) and \triad{i+1}{1}{R}{-1/2}{-1/2} (blue) poking through 
    660666      the ocean surface are masked (faded in figure). 
    661       However, the lateral $_{11}$ contributions towards $\triad[u]{i}{1}{F}{1/2}{-1/2}$ and 
    662       $\triad[u]{i+1}{1}{F}{-1/2}{-1/2}$ (yellow line) are still applied, 
     667      However, the lateral $_{11}$ contributions towards \triad[u]{i}{1}{F}{1/2}{-1/2} and 
     668      \triad[u]{i+1}{1}{F}{-1/2}{-1/2} (yellow line) are still applied, 
    663669      giving diapycnal diffusive fluxes. 
    664670      \newline 
    665       (b) Both near bottom triad slopes $\triad{i}{k}{R}{1/2}{1/2}$ and 
    666       $\triad{i+1}{k}{R}{-1/2}{1/2}$ are masked when either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, 
    667       i.e.\ the $i,k+1$ $u$-point is masked. 
     671      (b) Both near bottom triad slopes \triad{i}{k}{R}{1/2}{1/2} and 
     672      \triad{i+1}{k}{R}{-1/2}{1/2} are masked when either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, 
     673      \ie the $i,k+1$ $u$-point is masked. 
    668674      The associated lateral fluxes (grey-black dashed line) are masked if 
    669675      \protect\np{botmix\_triad}\forcode{ = .false.}, but left unmasked, 
     
    758764  where $i,k_{10}$ is the tracer gridbox within which the depth reaches 10~m. 
    759765  See the left side of \autoref{fig:MLB_triad}. 
    760   We use the $k_{10}$-gridbox instead of the surface gridbox to avoid problems e.g.\ with thin daytime mixed-layers. 
     766  We use the $k_{10}$-gridbox instead of the surface gridbox to avoid problems \eg with thin daytime mixed-layers. 
    761767  Currently we use the same $\Delta\rho_c=0.01\;\mathrm{kg\:m^{-3}}$ for ML triad tapering as is used to 
    762768  output the diagnosed mixed-layer depth $h_{\mathrm{ML}}=|z_{W}|_{k_{\mathrm{ML}}+1/2}$, 
     
    774780                                                       % \label{eq:Rbase} 
    775781    \\ 
    776     \intertext{with e.g.\ the green triad} 
     782    \intertext{with \eg the green triad} 
    777783    {\:}_i{\mathbb{R}_{\mathrm{base}}}_{1/2}^{-1/2}&= 
    778784                                                     {\:}^{k_{\mathrm{ML}}}_i{\mathbb{R}_{\mathrm{base}}}_{\,1/2}^{-1/2}. 
     
    821827    ${\:}_i{\mathbb{R}_{\mathrm{base}}}_{\,i_p}^{k_p}$. 
    822828    Triads with different $i_p,k_p$, denoted by different colours, 
    823     (e.g. the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.} 
     829    (\eg the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.} 
    824830  % } 
    825831  \includegraphics[width=0.60\textwidth]{Fig_GRIFF_MLB_triads} 
     
    882888the formulation of which depends on the slopes of iso-neutral surfaces. 
    883889Contrary to the case of iso-neutral mixing, the slopes used here are referenced to the geopotential surfaces, 
    884 $i.e.$ \autoref{eq:ldfslp_geo} is used in $z$-coordinate, 
     890\ie \autoref{eq:ldfslp_geo} is used in $z$-coordinate, 
    885891and the sum \autoref{eq:ldfslp_geo} + \autoref{eq:ldfslp_iso} in $z^*$ or $s$-coordinates. 
    886892 
     
    10081014  \begin{align} 
    10091015    \label{eq:skewfluxu} 
    1010     _i^k {\mathbb{S}_u}_{i_p}^{k_p} (T) &= + \quarter {A_e}_i^k{ 
     1016    _i^k {\mathbb{S}_u}_{i_p}^{k_p} (T) &= + \fractext{1}{4} {A_e}_i^k{ 
    10111017                                          \:}\frac{{b_u}_{i+i_p}^k}{{e_{1u}}_{\,i + i_p}^{\,k}} 
    10121018                                          \ {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}} \ 
     
    10171023    } 
    10181024    _i^k {\mathbb{S}_w}_{i_p}^{k_p} (T) 
    1019                                         &= -\quarter {A_e}_i^k{\: }\frac{{b_u}_{i+i_p}^k}{{e_{3w}}_{\,i}^{\,k+k_p}} 
     1025                                        &= -\fractext{1}{4} {A_e}_i^k{\: }\frac{{b_u}_{i+i_p}^k}{{e_{3w}}_{\,i}^{\,k+k_p}} 
    10201026                                          {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}}\frac{ \delta_{i+ i_p}[T^k] }{ {e_{1u}}_{\,i + i_p}^{\,k} }.\label{eq:skewfluxw} 
    10211027  \end{align} 
     
    10271033\subsubsection{No change in tracer variance} 
    10281034 
    1029 The discretization conserves tracer variance, $i.e.$ it does not include a diffusive component but is a `pure' advection term. 
     1035The discretization conserves tracer variance, \ie it does not include a diffusive component but is a `pure' advection term. 
    10301036This can be seen %either from Appendix \autoref{apdx:eiv_skew} or 
    10311037by considering the fluxes associated with a given triad slope $_i^k{\mathbb{R}}_{i_p}^{k_p} (T)$. 
    10321038For, following \autoref{subsec:variance} and \autoref{eq:dvar_iso_i}, 
    10331039the associated horizontal skew-flux $_i^k{\mathbb{S}_u}_{i_p}^{k_p} (T)$ drives a net rate of change of variance, 
    1034 summed over the two $T$-points $i+i_p-\half,k$ and $i+i_p+\half,k$, of 
     1040summed over the two $T$-points $i+i_p-\fractext{1}{2},k$ and $i+i_p+\fractext{1}{2},k$, of 
    10351041\begin{equation} 
    10361042  \label{eq:dvar_eiv_i} 
     
    10381044\end{equation} 
    10391045while the associated vertical skew-flux gives a variance change summed over 
    1040 the $T$-points $i,k+k_p-\half$ (above) and $i,k+k_p+\half$ (below) of 
     1046the $T$-points $i,k+k_p-\fractext{1}{2}$ (above) and $i,k+k_p+\fractext{1}{2}$ (below) of 
    10411047\begin{equation} 
    10421048  \label{eq:dvar_eiv_k} 
     
    10661072  % gives two terms. The 
    10671073  % first $\rtriad{R}$ term (the only term for $z$-coordinates) is: 
    1068   &=-\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}} 
     1074  &=-\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k {_i^k\tilde{\mathbb{R}}_{i_p}^{k_p}} 
    10691075    \frac{ -\alpha _i^k\delta_{i+ i_p}[T^k]+ \beta_i^k\delta_{i+ i_p}[S^k]} { {e_{1u}}_{\,i + i_p}^{\,k} } \notag \\ 
    1070   &=+\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k 
     1076  &=+\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k 
    10711077    \left({_i^k\mathbb{R}_{i_p}^{k_p}}+\frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}}\right) {_i^k\mathbb{R}_{i_p}^{k_p}} 
    10721078    \frac{-\alpha_i^k \delta_{k+ k_p}[T^i]+ \beta_i^k\delta_{k+ k_p}[S^i]} {{e_{3w}}_{\,i}^{\,k+k_p}}, 
     
    10831089    -\alpha _i^k {\:}_i^k {\mathbb{S}_u}_{i_p}^{k_p} (T) + \beta_i^k {\:}_i^k {\mathbb{S}_u}_{i_p}^{k_p} (S) 
    10841090  \right] \\ 
    1085   = +\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k 
     1091  = +\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k 
    10861092  \frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}} 
    10871093  \left({_i^k\mathbb{R}_{i_p}^{k_p}}+\frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}}\right) 
     
    10941100  g{e_{3w}}_{\,i}^{\,k+k_p}{\mathbb{S}_w}_{i_p}^{k_p} (\rho) + 
    10951101  g\delta_{i+i_p}[z_T^k] {\:}_i^k {\mathbb{S}_u}_{i_p}^{k_p} (\rho) \\ 
    1096   = +\quarter g{A_e}_i^k{\: }{b_u}_{i+i_p}^k 
     1102  = +\fractext{1}{4} g{A_e}_i^k{\: }{b_u}_{i+i_p}^k 
    10971103  \left({_i^k\mathbb{R}_{i_p}^{k_p}}+\frac{\delta_{i+i_p}[z_T^k]}{{e_{1u}}_{\,i + i_p}^{\,k}}\right)^2 
    10981104  \frac{-\alpha_i^k \delta_{k+ k_p}[T^i]+ \beta_i^k\delta_{k+ k_p}[S^i]} {{e_{3w}}_{\,i}^{\,k+k_p}}. 
     
    11091115Thus surface layer triads $\triadt{i}{1}{R}{1/2}{-1/2}$ and $\triadt{i+1}{1}{R}{-1/2}{-1/2}$ are masked,  
    11101116and both near bottom triad slopes $\triadt{i}{k}{R}{1/2}{1/2}$ and $\triadt{i+1}{k}{R}{-1/2}{1/2}$ are masked when  
    1111 either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$ $u$-point is masked.  
     1117either of the $i,k+1$ or $i+1,k+1$ tracer points is masked, \ie the $i,k+1$ $u$-point is masked.  
    11121118The namelist parameter \np{ln\_botmix\_triad} has no effect on the eddy-induced skew-fluxes. 
    11131119 
     
    11511157\[ 
    11521158  % \label{eq:sfdiagi} 
    1153   {\psi_1}_{i+1/2}^{k+1/2}={\quarter}\sum_{\substack{i_p,\,k_p}} 
     1159  {\psi_1}_{i+1/2}^{k+1/2}={\fractext{1}{4}}\sum_{\substack{i_p,\,k_p}} 
    11541160  {A_e}_{i+1/2-i_p}^{k+1/2-k_p}\:\triadd{i+1/2-i_p}{k+1/2-k_p}{R}{i_p}{k_p}. 
    11551161\] 
     
    11701176\biblio 
    11711177 
     1178\pindex 
     1179 
    11721180\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex

    r10414 r10442  
    179179\biblio 
    180180 
     181\pindex 
     182 
    181183\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_CONFIG.tex

    r10414 r10442  
    6565  the 3x3 domain is imposed over the whole domain; 
    6666\item[(3)] 
    67   a call to \rou{lbc\_lnk} is systematically done when reading input data ($i.e.$ in \mdl{iom}); 
     67  a call to \rou{lbc\_lnk} is systematically done when reading input data (\ie in \mdl{iom}); 
    6868\item[(3)] 
    6969  a simplified \rou{stp} routine is used (\rou{stp\_c1d}, see \mdl{step\_c1d} module) in which 
     
    103103      \protect\label{fig:MISC_ORCA_msh} 
    104104      ORCA mesh conception. 
    105       The departure from an isotropic Mercator grid start poleward of 20\degN. 
     105      The departure from an isotropic Mercator grid start poleward of 20\deg{N}. 
    106106      The two "north pole" are the foci of a series of embedded ellipses (blue curves) which 
    107107      are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes). 
     
    138138      \textit{Bottom}: ratio of anisotropy ($e_1 / e_2$) 
    139139      for ORCA 0.5\deg ~mesh. 
    140       South of 20\degN a Mercator grid is used ($e_1 = e_2$) so that the anisotropy ratio is 1. 
    141       Poleward of 20\degN, the two "north pole" introduce a weak anisotropy over the ocean areas ($< 1.2$) except in 
     140      South of 20\deg{N} a Mercator grid is used ($e_1 = e_2$) so that the anisotropy ratio is 1. 
     141      Poleward of 20\deg{N}, the two "north pole" introduce a weak anisotropy over the ocean areas ($< 1.2$) except in 
    142142      vicinity of Victoria Island (Canadian Arctic Archipelago). 
    143143    } 
     
    146146%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    147147 
    148 The method is applied to Mercator grid ($i.e.$ same zonal and meridional grid spacing) poleward of 20\degN, 
     148The method is applied to Mercator grid (\ie same zonal and meridional grid spacing) poleward of 20\deg{N}, 
    149149so that the Equator is a mesh line, which provides a better numerical solution for equatorial dynamics. 
    150150The choice of the series of embedded ellipses (position of the foci and variation of the ellipses) 
     
    211211For ORCA\_R1 and R025, setting the configuration key to 75 allows to use 75 vertical levels, otherwise 46 are used. 
    212212In the other ORCA configurations, 31 levels are used 
    213 (see \autoref{tab:orca_zgr} \sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}). 
     213(see \autoref{tab:orca_zgr} %\sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}). 
    214214 
    215215Only the ORCA\_R2 is provided with all its input files in the \NEMO distribution. 
     
    248248and their contribution to the large scale circulation.  
    249249 
    250 The domain geometry is a closed rectangular basin on the $\beta$-plane centred at $\sim$ 30\degN and 
     250The domain geometry is a closed rectangular basin on the $\beta$-plane centred at $\sim$ 30\deg{N} and 
    251251rotated by 45\deg, 3180~km long, 2120~km wide and 4~km deep (\autoref{fig:MISC_strait_hand}). 
    252252The domain is bounded by vertical walls and by a flat bottom. 
     
    254254The circulation is forced by analytical profiles of wind and buoyancy fluxes. 
    255255The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{Levy_al_OM10}.  
    256 The wind stress is zonal and its curl changes sign at 22\degN and 36\degN. 
     256The wind stress is zonal and its curl changes sign at 22\deg{N} and 36\deg{N}. 
    257257It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain and 
    258258a small recirculation gyre in the southern corner. 
     
    322322\biblio 
    323323 
     324\pindex 
     325 
    324326\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIA.tex

    r10414 r10442  
    8383  The possibility to extract a vertical or an horizontal subdomain. 
    8484\item 
    85   The choice of the temporal operation to perform, $e.g.$: average, accumulate, instantaneous, min, max and once. 
     85  The choice of the temporal operation to perform, \eg: average, accumulate, instantaneous, min, max and once. 
    8686\item 
    8787  Control over metadata via a large XML "database" of possible output fields. 
     
    106106create a single output file and therefore to bypass the rebuilding phase. 
    107107Note that writing in parallel into the same NetCDF files requires that your NetCDF4 library is linked to 
    108 an HDF5 library that has been correctly compiled ($i.e.$ with the configure option $--$enable-parallel). 
     108an HDF5 library that has been correctly compiled (\ie with the configure option $--$enable-parallel). 
    109109Note that the files created by iomput through XIOS are incompatible with NetCDF3. 
    110110All post-processsing and visualization tools must therefore be compatible with NetCDF4 and not only NetCDF3. 
     
    222222 
    223223It is very easy to add your own outputs with iomput. 
    224 Many standard fields and diagnostics are already prepared ($i.e.$, steps 1 to 3 below have been done) and 
     224Many standard fields and diagnostics are already prepared (\ie, steps 1 to 3 below have been done) and 
    225225simply need to be activated by including the required output in a file definition in iodef.xml (step 4). 
    226226To add new output variables, all 4 of the following steps must be taken. 
     
    251251reference grids and axes either defined in the code 
    252252(iom\_set\_domain\_attr and iom\_set\_axis\_attr in \mdl{iom}) or defined in the domain\_def.xml file. 
    253 $e.g.$: 
     253\eg: 
    254254 
    255255\begin{xmllines} 
     
    13491349 
    13501350\noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\tt 46x38x1} respectively in 
    1351 the mono-processor case (i.e. global domain of {\small\tt 182x149x31}). 
     1351the mono-processor case (\ie global domain of {\small\tt 182x149x31}). 
    13521352An illustration of the potential space savings that NetCDF4 chunking and compression provides is given in  
    13531353table \autoref{tab:NC4} which compares the results of two short runs of the ORCA2\_LIM reference configuration with 
     
    14191419Each trend of the dynamics and/or temperature and salinity time evolution equations can be send to 
    14201420\mdl{trddyn} and/or \mdl{trdtra} modules (see TRD directory) just after their computation 
    1421 ($i.e.$ at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). 
     1421(\ie at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). 
    14221422This capability is controlled by options offered in \ngn{namtrd} namelist. 
    14231423Note that the output are done with xIOS, and therefore the \key{IOM} is required. 
     
    14511451\textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested. 
    14521452In particular, options associated with \np{ln\_dyn\_mxl}, \np{ln\_vor\_trd}, and \np{ln\_tra\_mxl} are not working, 
    1453 and none of the options have been tested with variable volume ($i.e.$ \key{vvl} defined). 
     1453and none of the options have been tested with variable volume (\ie \key{vvl} defined). 
    14541454 
    14551455% ------------------------------------------------------------------------------------------------------------- 
     
    16571657 - \texttt{long2 lat2}, coordinates of the second extremity of the section; 
    16581658 
    1659  - \texttt{nclass}    the number of bounds of your classes (e.g. 3 bounds for 2 classes); 
     1659 - \texttt{nclass}    the number of bounds of your classes (\eg bounds for 2 classes); 
    16601660 
    16611661 - \texttt{okstrpond} to compute    heat and       salt transports, \texttt{nostrpond} if no; 
     
    18241824 
    18251825The first term in equation \autoref{eq:ssh_nBq} alters sea level by adding or subtracting mass from the ocean.  
    1826 The second term arises from temporal changes in the global mean density; $i.e.$ from steric effects. 
     1826The second term arises from temporal changes in the global mean density; \ie from steric effects. 
    18271827 
    18281828In a Boussinesq fluid, $\rho$ is replaced by $\rho_o$ in all the equation except when $\rho$ appears multiplied by 
    1829 the gravity ($i.e.$ in the hydrostatic balance of the primitive Equations). 
     1829the gravity (\ie in the hydrostatic balance of the primitive Equations). 
    18301830In particular, the mass conservation equation, \autoref{eq:Co_nBq}, degenerates into the incompressibility equation: 
    18311831 
     
    18741874The above formulation of the steric height of a Boussinesq ocean requires four remarks. 
    18751875First, one can be tempted to define $\rho_o$ as the initial value of $\mathcal{M}/\mathcal{V}$, 
    1876 $i.e.$ set $\mathcal{D}_{t=0}=0$, so that the initial steric height is zero. 
     1876\ie set $\mathcal{D}_{t=0}=0$, so that the initial steric height is zero. 
    18771877We do not recommend that. 
    18781878Indeed, in this case $\rho_o$ depends on the initial state of the ocean. 
     
    18901890   
    18911891Third, the discretisation of \autoref{eq:steric_Bq} depends on the type of free surface which is considered. 
    1892 In the non linear free surface case, $i.e.$ \key{vvl} defined, it is given by 
     1892In the non linear free surface case, \ie \key{vvl} defined, it is given by 
    18931893 
    18941894\[ 
     
    19131913so that there are no associated ocean currents. 
    19141914Hence, the dynamically relevant sea level is the effective sea level, 
    1915 $i.e.$ the sea level as if sea ice (and snow) were converted to liquid seawater \citep{Campin_al_OM08}. 
     1915\ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{Campin_al_OM08}. 
    19161916However, in the current version of \NEMO the sea-ice is levitating above the ocean without mass exchanges between 
    19171917ice and ocean. 
     
    19491949- the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) 
    19501950 
    1951 - the depth of the 20\deg C isotherm (\mdl{diahth}) 
     1951- the depth of the 20\deg{C} isotherm (\mdl{diahth}) 
    19521952 
    19531953- the depth of the thermocline (maximum of the vertical temperature gradient) (\mdl{diahth}) 
     
    19681968(see the \textit{\ngn{namptr} } namelist below). 
    19691969When \np{ln\_subbas}\forcode{ = .true.}, transports and stream function are computed for the Atlantic, Indian, 
    1970 Pacific and Indo-Pacific Oceans (defined north of 30\deg S) as well as for the World Ocean. 
     1970Pacific and Indo-Pacific Oceans (defined north of 30\deg{S}) as well as for the World Ocean. 
    19711971The sub-basin decomposition requires an input file (\ifile{subbasins}) which contains three 2D mask arrays, 
    19721972the Indo-Pacific mask been deduced from the sum of the Indian and Pacific mask (\autoref{fig:mask_subasins}). 
     
    20602060\biblio 
    20612061 
     2062\pindex 
     2063 
    20622064\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIU.tex

    r10414 r10442  
    3131Models are provided for both the warm layer, \mdl{diurnal\_bulk}, and the cool skin, \mdl{cool\_skin}. 
    3232Foundation SST is not considered as it can be obtained either from the main NEMO model 
    33 ($i.e.$ from the temperature of the top few model levels) or from some other source.   
     33(\ie from the temperature of the top few model levels) or from some other source.   
    3434It must be noted that both the cool skin and warm layer models produce estimates of the change in temperature 
    3535($\Delta T_{\rm{cs}}$ and $\Delta T_{\rm{wl}}$) and 
     
    8080and $\rho_a$ is the density of air. 
    8181The symbol $Q$ in equation (\autoref{eq:ecmwf1}) is the instantaneous total thermal energy flux into 
    82 the diurnal layer, $i.e.$ 
     82the diurnal layer, \ie 
    8383\[ 
    8484  Q = Q_{\rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,} 
     
    102102\end{equation} 
    103103where $\zeta=\frac{D_T}{L}$.  It is clear that the first derivative of (\autoref{eq:stab_func_eqn}), 
    104 and thus of (\autoref{eq:ecmwf1}), is discontinuous at $\zeta=0$ ($i.e.$ $Q\rightarrow0$ in 
     104and thus of (\autoref{eq:ecmwf1}), is discontinuous at $\zeta=0$ (\ie $Q\rightarrow0$ in 
    105105equation (\autoref{eq:ecmwf2})). 
    106106 
     
    156156\biblio 
    157157 
     158\pindex 
     159 
    158160\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DOM.tex

    r10414 r10442  
    6464the barotropic stream function $\psi$ is defined at horizontal points overlying the $\zeta$ and $f$-points. 
    6565 
    66 The ocean mesh ($i.e.$ the position of all the scalar and vector points) is defined by 
     66The ocean mesh (\ie the position of all the scalar and vector points) is defined by 
    6767the transformation that gives ($\lambda$ ,$\varphi$ ,$z$) as a function of $(i,j,k)$. 
    6868The grid-points are located at integer or integer and a half value of $(i,j,k)$ as indicated on \autoref{tab:cell}. 
     
    162162 
    163163The vertical average over the whole water column denoted by an overbar becomes for a quantity $q$ which 
    164 is a masked field (i.e. equal to zero inside solid area): 
     164is a masked field (\ie equal to zero inside solid area): 
    165165\begin{equation} 
    166166  \label{eq:DOM_bar} 
     
    191191the differencing operators ($\delta_i$, $\delta_j$ and $\delta_k$) are skew-symmetric linear operators, 
    192192and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$, $\overline{\,\cdot\,}^{\,k}$ and 
    193 $\overline{\,\cdot\,}^{\,k}$) are symmetric linear operators, 
    194 $i.e.$ 
     193$\overline{\,\cdot\,}^{\,k}$) are symmetric linear operators, \ie 
    195194\begin{align} 
    196195  \label{eq:DOM_di_adj} 
     
    219218    \caption{ 
    220219      \protect\label{fig:index_hor} 
    221       Horizontal integer indexing used in the \textsc{Fortran} code. 
     220      Horizontal integer indexing used in the \fortran code. 
    222221      The dashed area indicates the cell in which variables contained in arrays have the same $i$- and $j$-indices 
    223222    } 
     
    226225%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    227226 
    228 The array representation used in the \textsc{Fortran} code requires an integer indexing while 
     227The array representation used in the \fortran code requires an integer indexing while 
    229228the analytical definition of the mesh (see \autoref{subsec:DOM_cell}) is associated with the use of 
    230229integer values for $t$-points and both integer and integer and a half values for all the other points. 
    231230Therefore a specific integer indexing must be defined for points other than $t$-points 
    232 ($i.e.$ velocity and vorticity grid-points). 
     231(\ie velocity and vorticity grid-points). 
    233232Furthermore, the direction of the vertical indexing has been changed so that the surface level is at $k=1$. 
    234233 
     
    252251 
    253252In the vertical, the chosen indexing requires special attention since 
    254 the $k$-axis is re-orientated downward in the \textsc{Fortran} code compared to 
     253the $k$-axis is re-orientated downward in the \fortran code compared to 
    255254the indexing used in the semi-discrete equations and given in \autoref{subsec:DOM_cell}. 
    256255The sea surface corresponds to the $w$-level $k=1$ which is the same index as $t$-level just below 
     
    263262have the same $i$ or $j$ index 
    264263(compare the dashed area in \autoref{fig:index_hor} and \autoref{fig:index_vert}). 
    265 Since the scale factors are chosen to be strictly positive, a \emph{minus sign} appears in the \textsc{Fortran}  
     264Since the scale factors are chosen to be strictly positive, a \emph{minus sign} appears in the \fortran  
    266265code \emph{before all the vertical derivatives} of the discrete equations given in this documentation. 
    267266 
     
    272271    \caption{ 
    273272      \protect\label{fig:index_vert} 
    274       Vertical integer indexing used in the \textsc{Fortran } code. 
     273      Vertical integer indexing used in the \fortran code. 
    275274      Note that the $k$-axis is orientated downward. 
    276275      The dashed area indicates the cell in which variables contained in arrays have the same $k$-index. 
     
    300299\section{Needed fields} 
    301300\label{sec:DOM_fields} 
    302 The ocean mesh ($i.e.$ the position of all the scalar and vector points) is defined by the transformation that gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$. 
     301The ocean mesh (\ie the position of all the scalar and vector points) is defined by the transformation that gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$. 
    303302The grid-points are located at integer or integer and a half values of as indicated in \autoref{tab:cell}. 
    304303The associated scale factors are defined using the analytical first derivative of the transformation 
     
    352351\label{subsec:DOM_hgr_coord_e} 
    353352 
    354 The ocean mesh ($i.e.$ the position of all the scalar and vector points) is defined by 
     353The ocean mesh (\ie the position of all the scalar and vector points) is defined by 
    355354the transformation that gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$. 
    356355The grid-points are located at integer or integer and a half values of as indicated in \autoref{tab:cell}. 
     
    391390 
    392391Note that the definition of the scale factors 
    393 ($i.e.$ as the analytical first derivative of the transformation that 
     392(\ie as the analytical first derivative of the transformation that 
    394393gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$) 
    395394is specific to the \NEMO model \citep{Marti_al_JGR92}. 
     
    461460(2) the number of levels of the model (\jp{jpk});  
    462461(3) the analytical transformation $z(i,j,k)$ and the vertical scale factors (derivatives of the transformation); and 
    463 (4) the masking system, $i.e.$ the number of wet model levels at each  
     462(4) the masking system, \ie the number of wet model levels at each  
    464463$(i,j)$ column of points. 
    465464 
     
    563562  The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) at 
    564563  each grid point of the model grid. 
    565   The bathymetry is usually built by interpolating a standard bathymetry product ($e.g.$ ETOPO2) onto 
     564  The bathymetry is usually built by interpolating a standard bathymetry product (\eg ETOPO2) onto 
    566565  the horizontal ocean mesh. 
    567566  Defining the bathymetry also defines the coastline: where the bathymetry is zero, 
     
    926925 
    927926% ------------------------------------------------------------------------------------------------------------- 
    928 %        z*- or s*-coordinate 
     927%        \zstar- or \sstar-coordinate 
    929928% ------------------------------------------------------------------------------------------------------------- 
    930929\subsection{$Z^*$- or $S^*$-coordinate (\protect\np{ln\_linssh}\forcode{ = .false.}) } 
     
    945944follow the face of the model cells (step like topography) \citep{Madec_al_JPO96}. 
    946945The distribution of the steps in the horizontal is defined in a 2D integer array, mbathy, 
    947 which gives the number of ocean levels ($i.e.$ those that are not masked) at each $t$-point. 
     946which gives the number of ocean levels (\ie those that are not masked) at each $t$-point. 
    948947mbathy is computed from the meter bathymetry using the definiton of gdept as 
    949948the number of $t$-points which gdept $\leq$ bathy. 
     
    961960the cavities are performed in the \textit{zgr\_isf} routine. 
    962961The compatibility between ice shelf draft and bathymetry is checked.  
    963 All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked).  
     962All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded (\ie masked).  
    964963If only one cell on the water column is opened at $t$-, $u$- or $v$-points, 
    965964the bathymetry or the ice shelf draft is dug to fit this constrain. 
     
    10171016\biblio 
    10181017 
     1018\pindex 
     1019 
    10191020\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DYN.tex

    r10414 r10442  
    6868\label{subsec:DYN_divcur} 
    6969 
    70 The vorticity is defined at an $f$-point ($i.e.$ corner point) as follows: 
     70The vorticity is defined at an $f$-point (\ie corner point) as follows: 
    7171\begin{equation} 
    7272  \label{eq:divcur_cur} 
     
    123123the tracer equation \autoref{eq:tra_nxt}: 
    124124a leapfrog scheme in combination with an Asselin time filter, 
    125 $i.e.$ the velocity appearing in \autoref{eq:dynspg_ssh} is centred in time (\textit{now} velocity). 
     125\ie the velocity appearing in \autoref{eq:dynspg_ssh} is centred in time (\textit{now} velocity). 
    126126This is of paramount importance. 
    127127Replacing $T$ by the number $1$ in the tracer equation and summing over the water column must lead to 
     
    149149The upper boundary condition applies at a fixed level $z=0$. 
    150150The top vertical velocity is thus equal to the divergence of the barotropic transport 
    151 ($i.e.$ the first term in the right-hand-side of \autoref{eq:dynspg_ssh}). 
     151(\ie the first term in the right-hand-side of \autoref{eq:dynspg_ssh}). 
    152152 
    153153Note also that whereas the vertical velocity has the same discrete expression in $z$- and $s$-coordinates, 
    154154its physical meaning is not the same: 
    155155in the second case, $w$ is the velocity normal to the $s$-surfaces. 
    156 Note also that the $k$-axis is re-orientated downwards in the \textsc{fortran} code compared to 
     156Note also that the $k$-axis is re-orientated downwards in the \fortran code compared to 
    157157the indexing used in the semi-discrete equations such as \autoref{eq:wzv} 
    158158(see \autoref{subsec:DOM_Num_Index_vertical}).  
     
    174174Options are defined through the \ngn{namdyn\_adv} namelist variables Coriolis and 
    175175momentum advection terms are evaluated using a leapfrog scheme, 
    176 $i.e.$ the velocity appearing in these expressions is centred in time (\textit{now} velocity).  
     176\ie the velocity appearing in these expressions is centred in time (\textit{now} velocity).  
    177177At the lateral boundaries either free slip, no slip or partial slip boundary conditions are applied following 
    178178\autoref{chap:LBC}. 
     
    208208In the enstrophy conserving case (ENS scheme), 
    209209the discrete formulation of the vorticity term provides a global conservation of the enstrophy 
    210 ($ [ (\zeta +f ) / e_{3f} ]^2 $ in $s$-coordinates) for a horizontally non-divergent flow ($i.e.$ $\chi$=$0$), 
     210($ [ (\zeta +f ) / e_{3f} ]^2 $ in $s$-coordinates) for a horizontally non-divergent flow (\ie $\chi$=$0$), 
    211211but does not conserve the total kinetic energy. 
    212212It is given by: 
     
    278278the presence of grid point oscillation structures that will be invisible to the operator. 
    279279These structures are \textit{computational modes} that will be at least partly damped by 
    280 the momentum diffusion operator ($i.e.$ the subgrid-scale advection), but not by the resolved advection term. 
     280the momentum diffusion operator (\ie the subgrid-scale advection), but not by the resolved advection term. 
    281281The ENS and ENE schemes therefore do not contribute to dump any grid point noise in the horizontal velocity field. 
    282282Such noise would result in more noise in the vertical velocity field, an undesirable feature. 
     
    327327(with a systematic reduction of $e_{3f}$ when a model level intercept the bathymetry) 
    328328that tends to reinforce the topostrophy of the flow 
    329 ($i.e.$ the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.  
     329(\ie the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.  
    330330 
    331331Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as 
     
    354354This EEN scheme in fact combines the conservation properties of the ENS and ENE schemes. 
    355355It conserves both total energy and potential enstrophy in the limit of horizontally nondivergent flow 
    356 ($i.e.$ $\chi$=$0$) (see \autoref{subsec:C_vorEEN}).  
     356(\ie $\chi$=$0$) (see \autoref{subsec:C_vorEEN}).  
    357357Applied to a realistic ocean configuration, it has been shown that it leads to a significant reduction of 
    358358the noise in the vertical velocity field \citep{Le_Sommer_al_OM09}. 
     
    422422In the flux form (as in the vector invariant form), 
    423423the Coriolis and momentum advection terms are evaluated using a leapfrog scheme, 
    424 $i.e.$ the velocity appearing in their expressions is centred in time (\textit{now} velocity). 
     424\ie the velocity appearing in their expressions is centred in time (\textit{now} velocity). 
    425425At the lateral boundaries either free slip, 
    426426no slip or partial slip boundary conditions are applied following \autoref{chap:LBC}. 
     
    446446compute the product of the Coriolis parameter and the vorticity. 
    447447However, the energy-conserving scheme (\autoref{eq:dynvor_een}) has exclusively been used to date. 
    448 This term is evaluated using a leapfrog scheme, $i.e.$ the velocity is centred in time (\textit{now} velocity). 
     448This term is evaluated using a leapfrog scheme, \ie the velocity is centred in time (\textit{now} velocity). 
    449449 
    450450%-------------------------------------------------------------------------------------------------------------- 
     
    478478The schemes are selected using the namelist logicals \np{ln\_dynadv\_cen2} and \np{ln\_dynadv\_ubs}.  
    479479In flux form, the schemes differ by the choice of a space and time interpolation to define the value of 
    480 $u$ and $v$ at the centre of each face of $u$- and $v$-cells, $i.e.$ at the $T$-, $f$-, 
     480$u$ and $v$ at the centre of each face of $u$- and $v$-cells, \ie at the $T$-, $f$-, 
    481481and $uw$-points for $u$ and at the $f$-, $T$- and $vw$-points for $v$.  
    482482 
     
    498498\end{equation}  
    499499 
    500 The scheme is non diffusive (i.e. conserves the kinetic energy) but dispersive ($i.e.$ it may create false extrema). 
     500The scheme is non diffusive (\ie conserves the kinetic energy) but dispersive (\ie it may create false extrema). 
    501501It is therefore notoriously noisy and must be used in conjunction with an explicit diffusion operator to 
    502502produce a sensible solution. 
     
    522522\end{equation} 
    523523where $u"_{i+1/2} =\delta_{i+1/2} \left[ {\delta_i \left[ u \right]} \right]$. 
    524 This results in a dissipatively dominant ($i.e.$ hyper-diffusive) truncation error 
     524This results in a dissipatively dominant (\ie hyper-diffusive) truncation error 
    525525\citep{Shchepetkin_McWilliams_OM05}. 
    526526The overall performance of the advection scheme is similar to that reported in \citet{Farrow1995}. 
     
    529529But the amplitudes of the false extrema are significantly reduced over those in the centred second order method. 
    530530As the scheme already includes a diffusion component, it can be used without explicit lateral diffusion on momentum  
    531 ($i.e.$ \np{ln\_dynldf\_lap}\forcode{ = }\np{ln\_dynldf\_bilap}\forcode{ = .false.}), 
     531(\ie \np{ln\_dynldf\_lap}\forcode{ = }\np{ln\_dynldf\_bilap}\forcode{ = .false.}), 
    532532and it is recommended to do so. 
    533533 
    534534The UBS scheme is not used in all directions. 
    535 In the vertical, the centred $2^{nd}$ order evaluation of the advection is preferred, $i.e.$ $u_{uw}^{ubs}$ and 
     535In the vertical, the centred $2^{nd}$ order evaluation of the advection is preferred, \ie $u_{uw}^{ubs}$ and 
    536536$u_{vw}^{ubs}$ in \autoref{eq:dynadv_cen2} are used. 
    537537UBS is diffusive and is associated with vertical mixing of momentum. \gmcomment{ gm  pursue the  
     
    570570The key distinction between the different algorithms used for 
    571571the hydrostatic pressure gradient is the vertical coordinate used, 
    572 since HPG is a \emph{horizontal} pressure gradient, $i.e.$ computed along geopotential surfaces. 
     572since HPG is a \emph{horizontal} pressure gradient, \ie computed along geopotential surfaces. 
    573573As a result, any tilt of the surface of the computational levels will require a specific treatment to 
    574574compute the hydrostatic pressure gradient. 
    575575 
    576576The hydrostatic pressure gradient term is evaluated either using a leapfrog scheme, 
    577 $i.e.$ the density appearing in its expression is centred in time (\emph{now} $\rho$), 
     577\ie the density appearing in its expression is centred in time (\emph{now} $\rho$), 
    578578or a semi-implcit scheme. 
    579579At the lateral boundaries either free slip, no slip or partial slip boundary conditions are applied. 
     
    652652 
    653653Pressure gradient formulations in an $s$-coordinate have been the subject of a vast number of papers 
    654 ($e.g.$, \citet{Song1998, Shchepetkin_McWilliams_OM05}).  
     654(\eg, \citet{Song1998, Shchepetkin_McWilliams_OM05}).  
    655655A number of different pressure gradient options are coded but the ROMS-like, 
    656656density Jacobian with cubic polynomial method is currently disabled whilst known bugs are under investigation. 
     
    704704$\bullet$ The main hypothesis to compute the ice shelf load is that the ice shelf is in an isostatic equilibrium. 
    705705The top pressure is computed integrating from surface to the base of the ice shelf a reference density profile 
    706 (prescribed as density of a water at 34.4 PSU and -1.9\degC) and 
     706(prescribed as density of a water at 34.4 PSU and -1.9\deg{C}) and 
    707707corresponds to the water replaced by the ice shelf. 
    708708This top pressure is constant over time. 
     
    728728It involves the evaluation of the hydrostatic pressure gradient as 
    729729an average over the three time levels $t-\rdt$, $t$, and $t+\rdt$ 
    730 ($i.e.$  \textit{before}, \textit{now} and  \textit{after} time-steps), 
     730(\ie \textit{before}, \textit{now} and  \textit{after} time-steps), 
    731731rather than at the central time level $t$ only, as in the standard leapfrog scheme.  
    732732 
     
    820820the model time step is chosen to be small enough to resolve the external gravity waves 
    821821(typically a few tens of seconds). 
    822 The surface pressure gradient, evaluated using a leap-frog scheme ($i.e.$ centered in time), 
     822The surface pressure gradient, evaluated using a leap-frog scheme (\ie centered in time), 
    823823is thus simply given by : 
    824824\begin{equation} 
     
    832832\end{equation}  
    833833 
    834 Note that in the non-linear free surface case ($i.e.$ \key{vvl} defined), 
     834Note that in the non-linear free surface case (\ie \key{vvl} defined), 
    835835the surface pressure gradient is already included in the momentum tendency through 
    836836the level thickness variation allowed in the computation of the hydrostatic pressure gradient. 
     
    948948(\np{ln\_bt\_av}\forcode{ = .false.}).  
    949949In that case, external mode equations are continuous in time, 
    950 $i.e.$ they are not re-initialized when starting a new sub-stepping sequence. 
     950\ie they are not re-initialized when starting a new sub-stepping sequence. 
    951951This is the method used so far in the POM model, the stability being maintained by 
    952952refreshing at (almost) each barotropic time step advection and horizontal diffusion terms. 
     
    11241124the description of the coefficients is found in the chapter on lateral physics (\autoref{chap:LDF}). 
    11251125The lateral diffusion of momentum is evaluated using a forward scheme, 
    1126 $i.e.$ the velocity appearing in its expression is the \textit{before} velocity in time, 
     1126\ie the velocity appearing in its expression is the \textit{before} velocity in time, 
    11271127except for the pure vertical component that appears when a tensor of rotation is used. 
    11281128This latter term is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}). 
     
    11401140  In finite difference methods, 
    11411141  the biharmonic operator is frequently the method of choice to achieve this scale selective dissipation since 
    1142   its damping time ($i.e.$ its spin down time) scale like $\lambda^{-4}$ for disturbances of wavelength $\lambda$ 
     1142  its damping time (\ie its spin down time) scale like $\lambda^{-4}$ for disturbances of wavelength $\lambda$ 
    11431143  (so that short waves damped more rapidelly than long ones), 
    11441144  whereas the Laplace operator damping time scales only like $\lambda^{-2}$. 
     
    13151315 
    13161316(3) When \np{nn\_ice\_embd}\forcode{ = 2} and LIM or CICE is used 
    1317 ($i.e.$ when the sea-ice is embedded in the ocean), 
     1317(\ie when the sea-ice is embedded in the ocean), 
    13181318the snow-ice mass is taken into account when computing the surface pressure gradient. 
    13191319 
     
    13351335Options are defined through the \ngn{namdom} namelist variables. 
    13361336The general framework for dynamics time stepping is a leap-frog scheme, 
    1337 $i.e.$ a three level centred time scheme associated with an Asselin time filter (cf. \autoref{chap:STP}). 
     1337\ie a three level centred time scheme associated with an Asselin time filter (cf. \autoref{chap:STP}). 
    13381338The scheme is applied to the velocity, except when 
    13391339using the flux form of momentum advection (cf. \autoref{sec:DYN_adv_cor_flux}) 
     
    13791379\biblio 
    13801380 
     1381\pindex 
     1382 
    13811383\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_LBC.tex

    r10414 r10442  
    2626%The lateral ocean boundary conditions contiguous to coastlines are Neumann conditions for heat and salt (no flux across boundaries) and Dirichlet conditions for momentum (ranging from free-slip to "strong" no-slip). They are handled automatically by the mask system (see \autoref{subsec:DOM_msk}).  
    2727 
    28 %OPA allows land and topography grid points in the computational domain due to the presence of continents or islands, and includes the use of a full or partial step representation of bottom topography. The computation is performed over the whole domain, i.e. we do not try to restrict the computation to ocean-only points. This choice has two motivations. Firstly, working on ocean only grid points overloads the code and harms the code readability. Secondly, and more importantly, it drastically reduces the vector portion of the computation, leading to a dramatic increase of CPU time requirement on vector computers.  The current section describes how the masking affects the computation of the various terms of the equations with respect to the boundary condition at solid walls. The process of defining which areas are to be masked is described in \autoref{subsec:DOM_msk}. 
     28%OPA allows land and topography grid points in the computational domain due to the presence of continents or islands, and includes the use of a full or partial step representation of bottom topography. The computation is performed over the whole domain, \ie we do not try to restrict the computation to ocean-only points. This choice has two motivations. Firstly, working on ocean only grid points overloads the code and harms the code readability. Secondly, and more importantly, it drastically reduces the vector portion of the computation, leading to a dramatic increase of CPU time requirement on vector computers.  The current section describes how the masking affects the computation of the various terms of the equations with respect to the boundary condition at solid walls. The process of defining which areas are to be masked is described in \autoref{subsec:DOM_msk}. 
    2929 
    3030Options are defined through the \ngn{namlbc} namelist variables. 
     
    4040Since most of the boundary conditions consist of a zero flux across the solid boundaries, 
    4141they can be simply applied by multiplying variables by the correct mask arrays, 
    42 $i.e.$ the mask array of the grid point where the flux is evaluated. 
     42\ie the mask array of the grid point where the flux is evaluated. 
    4343For example, the heat flux in the \textbf{i}-direction is evaluated at $u$-points. 
    4444Evaluating this quantity as, 
     
    103103\item[free-slip boundary condition (\np{rn\_shlat}\forcode{ = 0}):] the tangential velocity at 
    104104  the coastline is equal to the offshore velocity, 
    105   $i.e.$ the normal derivative of the tangential velocity is zero at the coast, 
     105  \ie the normal derivative of the tangential velocity is zero at the coast, 
    106106  so the vorticity: mask$_{f}$ array is set to zero inside the land and just at the coast 
    107107  (\autoref{fig:LBC_shlat}-a). 
     
    129129 
    130130\item["partial" free-slip boundary condition (0$<$\np{rn\_shlat}$<$2):] the tangential velocity at 
    131   the coastline is smaller than the offshore velocity, $i.e.$ there is a lateral friction but 
     131  the coastline is smaller than the offshore velocity, \ie there is a lateral friction but 
    132132  not strong enough to make the tangential velocity at the coast vanish (\autoref{fig:LBC_shlat}-c). 
    133133  This can be selected by providing a value of mask$_{f}$ strictly inbetween $0$ and $2$. 
     
    165165Each time such a boundary condition is needed, it is set by a call to routine \mdl{lbclnk}. 
    166166The computation of momentum and tracer trends proceeds from $i=2$ to $i=jpi-1$ and from $j=2$ to $j=jpj-1$, 
    167 $i.e.$ in the model interior. 
     167\ie in the model interior. 
    168168To choose a lateral model boundary condition is to specify the first and last rows and columns of 
    169169the model variables.  
     
    242242are organized by explicit statements (message passing method). 
    243243 
    244 A big advantage is that the method does not need many modifications of the initial FORTRAN code. 
     244A big advantage is that the method does not need many modifications of the initial \fortran code. 
    245245From the modeller's point of view, each sub domain running on a processor is identical to the "mono-domain" code. 
    246246In addition, the programmer manages the communications between subdomains, 
     
    267267After a computation, a communication phase starts: 
    268268each processor sends to its neighbouring processors the update values of the points corresponding to 
    269 the interior overlapping area to its neighbouring sub-domain ($i.e.$ the innermost of the two overlapping rows). 
     269the interior overlapping area to its neighbouring sub-domain (\ie the innermost of the two overlapping rows). 
    270270The communication is done through the Message Passing Interface (MPI). 
    271271The data exchanges between processors are required at the very place where 
    272272lateral domain boundary conditions are set in the mono-domain computation: 
    273273the \rou{lbc\_lnk} routine (found in \mdl{lbclnk} module) which manages such conditions is interfaced with 
    274 routines found in \mdl{lib\_mpp} module when running on an MPP computer ($i.e.$ when \key{mpp\_mpi} defined). 
     274routines found in \mdl{lib\_mpp} module when running on an MPP computer (\ie when \key{mpp\_mpi} defined). 
    275275It has to be pointed out that when using the MPP version of the model, 
    276276the east-west cyclic boundary condition is done implicitly, 
     
    355355Note that this is a problem for the meshmask file which requires to be defined over the whole domain. 
    356356Therefore, user should not eliminate land processors when creating a meshmask file 
    357 ($i.e.$ when setting a non-zero value to \np{nn\_msh}). 
     357(\ie when setting a non-zero value to \np{nn\_msh}). 
    358358 
    359359%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    518518Note that the sea-surface height gradient in \autoref{eq:bdy_fla1} is a spatial gradient across the model boundary, 
    519519so that $\eta_{e}$ is defined on the $T$ points with $nbr=1$ and $\eta$ is defined on the $T$ points with $nbr=2$. 
    520 $U$ and $U_{e}$ are defined on the $U$ or $V$ points with $nbr=1$, $i.e.$ between the two $T$ grid points. 
     520$U$ and $U_{e}$ are defined on the $U$ or $V$ points with $nbr=1$, \ie between the two $T$ grid points. 
    521521 
    522522%---------------------------------------------- 
     
    594594 
    595595These restrictions mean that data files used with previous versions of the model may not work with version 3.4. 
    596 A fortran utility {\it bdy\_reorder} exists in the TOOLS directory which 
     596A\fortran utility {\it bdy\_reorder} exists in the TOOLS directory which 
    597597will re-order the data in old BDY data files.  
    598598 
     
    641641\biblio 
    642642 
     643\pindex 
     644 
    643645\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_LDF.tex

    r10414 r10442  
    2222(3) the space and time variations of the eddy coefficients. 
    2323These three aspects of the lateral diffusion are set through namelist parameters 
    24 (see the \textit{\ngn{nam\_traldf}} and \textit{\ngn{nam\_dynldf}} below). 
     24(see the \ngn{nam\_traldf} and \ngn{nam\_dynldf} below). 
    2525Note that this chapter describes the standard implementation of iso-neutral tracer mixing, 
    2626and Griffies's implementation, which is used if \np{traldf\_grif}\forcode{ = .true.}, 
     
    6262\subsection{Slopes for tracer geopotential mixing in the $s$-coordinate} 
    6363 
    64 In $s$-coordinates, geopotential mixing ($i.e.$ horizontal mixing) $r_1$ and $r_2$ are the slopes between 
     64In $s$-coordinates, geopotential mixing (\ie horizontal mixing) $r_1$ and $r_2$ are the slopes between 
    6565the geopotential and computational surfaces. 
    6666Their discrete formulation is found by locally solving \autoref{eq:tra_ldf_iso} when 
    6767the diffusive fluxes in the three directions are set to zero and $T$ is assumed to be horizontally uniform, 
    68 $i.e.$ a linear function of $z_T$, the depth of a $T$-point.  
     68\ie a linear function of $z_T$, the depth of a $T$-point.  
    6969%gm { Steven : My version is obviously wrong since I'm left with an arbitrary constant which is the local vertical temperature gradient} 
    7070 
     
    9696Their formulation does not depend on the vertical coordinate used. 
    9797Their discrete formulation is found using the fact that the diffusive fluxes of 
    98 locally referenced potential density ($i.e.$ $in situ$ density) vanish. 
     98locally referenced potential density (\ie $in situ$ density) vanish. 
    9999So, substituting $T$ by $\rho$ in \autoref{eq:tra_ldf_iso} and setting the diffusive fluxes in 
    100100the three directions to zero leads to the following definition for the neutral slopes: 
     
    255255      \textit{(a)} in the real ocean the slope is the iso-neutral slope in the ocean interior, 
    256256      which has to be adjusted at the surface boundary 
    257       (i.e. it must tend to zero at the surface since there is no mixing across the air-sea interface: 
     257      \ie it must tend to zero at the surface since there is no mixing across the air-sea interface: 
    258258      wall boundary condition). 
    259259      Nevertheless, the profile between the surface zero value and the interior iso-neutral one is unknown, 
     
    280280\textit{vw}- points for the $v$-component. 
    281281They are computed from the slopes used for tracer diffusion, 
    282 $i.e.$ \autoref{eq:ldfslp_geo} and \autoref{eq:ldfslp_iso} : 
     282\ie \autoref{eq:ldfslp_geo} and \autoref{eq:ldfslp_iso}: 
    283283 
    284284\[ 
     
    294294The major issue remaining is in the specification of the boundary conditions. 
    295295The same boundary conditions are chosen as those used for lateral diffusion along model level surfaces, 
    296 $i.e.$ using the shear computed along the model levels and with no additional friction at the ocean bottom 
     296\ie using the shear computed along the model levels and with no additional friction at the ocean bottom 
    297297(see \autoref{sec:LBC_coast}). 
    298298 
     
    327327Changes in the computer code when switching from one option to another have been minimized by 
    328328introducing the eddy coefficients as statement functions 
    329 (include file \hf{ldftra\_substitute} and \hf{ldfdyn\_substitute}). 
     329(include file \textit{ldftra\_substitute.h90} and \textit{ldfdyn\_substitute.h90}). 
    330330The functions are replaced by their actual meaning during the preprocessing step (CPP). 
    331331The specification of the space variation of the coefficient is made in \mdl{ldftra} and \mdl{ldfdyn}, 
    332 or more precisely in include files \hf{traldf\_cNd} and \hf{dynldf\_cNd}, with N=1, 2 or 3. 
     332or more precisely in include files \textit{traldf\_cNd.h90} and \textit{dynldf\_cNd.h90}, with N=1, 2 or 3. 
    333333The user can modify these include files as he/she wishes. 
    334334The way the mixing coefficient are set in the reference version can be briefly described as follows: 
     
    347347the surface value is \np{rn\_aht0} (\np{rn\_ahm0}), the bottom value is 1/4 of the surface value, 
    348348and the transition takes place around z=300~m with a width of 300~m 
    349 ($i.e.$ both the depth and the width of the inflection point are set to 300~m). 
    350 This profile is hard coded in file \hf{traldf\_c1d}, but can be easily modified by users. 
     349(\ie both the depth and the width of the inflection point are set to 300~m). 
     350This profile is hard coded in file \textit{traldf\_c1d.h90}, but can be easily modified by users. 
    351351 
    352352\subsubsection{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 
     
    384384 
    385385The 3D space variation of the mixing coefficient is simply the combination of the 1D and 2D cases, 
    386 $i.e.$ a hyperbolic tangent variation with depth associated with a grid size dependence of 
     386\ie a hyperbolic tangent variation with depth associated with a grid size dependence of 
    387387the magnitude of the coefficient.  
    388388 
     
    416416$A^{eiv}$, the eddy induced coefficient has to be defined. 
    417417Its space variations are controlled by the same CPP variable as for the eddy diffusivity coefficient 
    418 ($i.e.$ \key{traldf\_cNd}).  
     418(\ie \key{traldf\_cNd}).  
    419419 
    420420(5) the eddy coefficient associated with a biharmonic operator must be set to a \emph{negative} value. 
     
    457457the formulation of which depends on the slopes of iso-neutral surfaces. 
    458458Contrary to the case of iso-neutral mixing, the slopes used here are referenced to the geopotential surfaces, 
    459 $i.e.$ \autoref{eq:ldfslp_geo} is used in $z$-coordinates, 
     459\ie \autoref{eq:ldfslp_geo} is used in $z$-coordinates, 
    460460and the sum \autoref{eq:ldfslp_geo} + \autoref{eq:ldfslp_iso} in $s$-coordinates. 
    461461The eddy induced velocity is given by:  
     
    484484\biblio 
    485485 
     486\pindex 
     487 
    486488\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_OBS.tex

    r10414 r10442  
    3030This now works in a generalised vertical coordinate system.  
    3131 
    32 Some profile observation types (e.g. tropical moored buoys) are made available as daily averaged quantities. 
     32Some profile observation types (\eg tropical moored buoys) are made available as daily averaged quantities. 
    3333The observation operator code can be set-up to calculate the equivalent daily average model temperature fields using 
    3434the \np{nn\_profdavtypes} namelist array. 
     
    542542the model equivalent of the observation is calculated by interpolating from 
    543543the four surrounding grid points to the observation location. 
    544 Some satellite observations (e.g. microwave satellite SST data, or satellite SSS data) have a footprint which 
     544Some satellite observations (\eg microwave satellite SST data, or satellite SSS data) have a footprint which 
    545545is similar in size or larger than the model grid size (particularly when the grid size is small). 
    546546In those cases the model counterpart should be calculated by averaging the model grid points over 
     
    612612   and $M$ corresponds to $B$, $C$ or $D$. 
    613613   A more stable form of the great-circle distance formula for small distances ($x$ near 1) 
    614    involves the arcsine function ($e.g.$ see p.~101 of \citet{Daley_Barker_Bk01}: 
     614   involves the arcsine function (\eg see p.~101 of \citet{Daley_Barker_Bk01}: 
    615615   \begin{align*} 
    616616     s\left( {\rm P}, {\rm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\} 
     
    682682      \protect\label{fig:obsavgrec} 
    683683      Weights associated with each model grid box (blue lines and numbers) 
    684       for an observation at -170.5E, 56.0N with a rectangular footprint of 1\deg x 1\deg. 
     684      for an observation at -170.5\deg{E}, 56.0\deg{N} with a rectangular footprint of 1\deg x 1\deg. 
    685685    } 
    686686  \end{center} 
     
    695695      \protect\label{fig:obsavgrad} 
    696696      Weights associated with each model grid box (blue lines and numbers) 
    697       for an observation at -170.5E, 56.0N with a radial footprint with diameter 1\deg. 
     697      for an observation at -170.5\deg{E}, 56.0\deg{N} with a radial footprint with diameter 1\deg. 
    698698    }  
    699699  \end{center} 
     
    741741\end{align*} 
    742742point in the opposite direction to the unit normal $\widehat{\bf k}$ 
    743 (i.e., that the coefficients of $\widehat{\bf k}$ are negative), 
     743(\ie that the coefficients of $\widehat{\bf k}$ are negative), 
    744744where ${{\bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, etc. correspond to 
    745745the vectors between points P and A, P and B, etc.. 
     
    790790any MPP communication. 
    791791Of course, this is under the assumption that we are only using a $2 \times 2$ grid-point stencil for 
    792 the interpolation (e.g., bilinear interpolation). 
     792the interpolation (\eg bilinear interpolation). 
    793793For higher order interpolation schemes this is no longer valid. 
    794794A disadvantage with the above scheme is that the number of observations on each processor can be very different. 
     
    995995\begin{description} 
    996996\item[cl4\_prefix] 
    997   Prefix for class 4 files e.g. class4 
     997  Prefix for class 4 files \eg class4 
    998998\item[cl4\_date] 
    999999  YYYYMMDD validity date 
    10001000\item[cl4\_sys] 
    1001   The name of the class 4 model system e.g. FOAM 
     1001  The name of the class 4 model system \eg FOAM 
    10021002\item[cl4\_cfg] 
    1003   The name of the class 4 model configuration e.g. orca025 
     1003  The name of the class 4 model configuration \eg orca025 
    10041004\item[cl4\_vn] 
    1005   The name of the class 4 model version e.g. 12.0 
     1005  The name of the class 4 model version \eg 12.0 
    10061006\end{description} 
    10071007 
     
    10211021  The name of the producers institution. 
    10221022\item[cl4\_cfg] 
    1023   The name of the class 4 model configuration e.g. orca025 
     1023  The name of the class 4 model configuration \eg orca025 
    10241024\item[cl4\_vn] 
    1025   The name of the class 4 model version e.g. 12.0 
     1025  The name of the class 4 model version \eg 12.0 
    10261026\end{description} 
    10271027 
     
    11641164Some tools for viewing and processing of observation and feedback files are provided in 
    11651165the NEMO repository for convenience. 
    1166 These include OBSTOOLS which are a collection of Fortran programs which are helpful to deal with feedback files. 
     1166These include OBSTOOLS which are a collection of \fortran programs which are helpful to deal with feedback files. 
    11671167They do such tasks as observation file conversion, printing of file contents, 
    11681168some basic statistical analysis of feedback files. 
     
    11731173\subsection{Obstools} 
    11741174 
    1175 A series of Fortran utilities is provided with NEMO called OBSTOOLS. 
     1175A series of \fortran utilities is provided with NEMO called OBSTOOLS. 
    11761176This are helpful in handling observation files and the feedback file output from the NEMO observation operator. 
    11771177The utilities are as follows 
     
    13981398\biblio 
    13991399 
     1400\pindex 
     1401 
    14001402\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex

    r10414 r10442  
    4040a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler) 
    4141(\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}).  
    42 When used ($i.e.$ \np{ln\_apr\_dyn}\forcode{ = .true.}), 
     42When used (\ie \np{ln\_apr\_dyn}\forcode{ = .true.}), 
    4343the atmospheric pressure forces both ocean and ice dynamics. 
    4444 
     
    105105the momentum vertical mixing trend (see \autoref{eq:dynzdf_sbc} in \autoref{sec:DYN_zdf}). 
    106106As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh, 
    107 $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points. 
     107\ie resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points. 
    108108 
    109109The surface heat flux is decomposed into two parts, a non solar and a solar heat flux, 
    110110$Q_{ns}$ and $Q_{sr}$, respectively. 
    111111The former is the non penetrative part of the heat flux 
    112 ($i.e.$ the sum of sensible, latent and long wave heat fluxes plus 
     112(\ie the sum of sensible, latent and long wave heat fluxes plus 
    113113the heat content of the mass exchange with the atmosphere and sea-ice). 
    114114It is applied in \mdl{trasbc} module as a surface boundary condition trend of 
     
    137137% 
    138138%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu  
    139 %ssv) i.e. information required by flux computation or sea-ice 
     139%ssv) \ie information required by flux computation or sea-ice 
    140140% 
    141141%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add  
     
    175175      Ocean variables provided by the ocean to the surface module (SBC). 
    176176      The variable are averaged over nn{\_}fsbc time step, 
    177       $i.e.$ the frequency of computation of surface fluxes. 
     177      \ie the frequency of computation of surface fluxes. 
    178178    } 
    179179  \end{center} 
     
    258258      The stem name is assumed to be 'fn'. 
    259259      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week 
    260       ($i.e.$ 'sun','sat','fri','thu','wed','tue','mon'). 
     260      (\ie 'sun','sat','fri','thu','wed','tue','mon'). 
    261261      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits. 
    262262      Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc', 
     
    518518  This has been cut down and now only calculates surface forcing and the ice model required. 
    519519  New surface modules that can function when only the surface level of the ocean state is defined can also be added 
    520   (e.g. icebergs). 
     520  (\eg icebergs). 
    521521\item 
    522522  \mdl{daymod}: 
     
    790790A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. 
    791791In this case $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain, 
    792 $i.e.$ the mean value of $\eta_{ib}$ is kept to zero at all time step. 
     792\ie the mean value of $\eta_{ib}$ is kept to zero at all time step. 
    793793 
    794794The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean). 
     
    918918The variable \textit{h\_dep} is then calculated to be the depth (in metres) of 
    919919the bottom of the lowest box the river water is being added to 
    920 (i.e. the total depth that river water is being added to in the model). 
     920(\ie the total depth that river water is being added to in the model). 
    921921 
    922922The mass/volume addition due to the river runoff is, at each relevant depth level, added to 
     
    955955 
    956956It is also possible for runnoff to be specified as a negative value for modelling flow through straits, 
    957 i.e. modelling the Baltic flow in and out of the North Sea. 
     957\ie modelling the Baltic flow in and out of the North Sea. 
    958958When the flow is out of the domain there is no change in temperature and salinity, 
    959959regardless of the namelist options used, 
     
    11521152  At each time step, a test is performed to see if there is enough ice mass to 
    11531153  calve an iceberg of each class in order (1 to 10). 
    1154   Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling). 
     1154  Note that this is the initial mass multiplied by the number each particle represents (\ie the scaling). 
    11551155  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly. 
    11561156\end{description} 
     
    12191219\label{subsec:SBC_wave_cdgw} 
    12201220 
    1221 The neutral surface drag coefficient provided from an external data source ($i.e.$ a wave model),  
     1221The neutral surface drag coefficient provided from an external data source (\ie a wave model),  
    12221222can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist.  
    12231223Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,  
     
    14251425a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}). 
    14261426The use of diurnal cycle reconstruction requires the input SWF to be daily 
    1427 ($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter). 
     1427(\ie a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter). 
    14281428Furthermore, it is recommended to have a least 8 surface module time step per day, 
    14291429that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$. 
     
    15461546  Note that the activation of a sea-ice model is is done by defining a CPP key (\key{lim3} or \key{cice}). 
    15471547  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value 
    1548   ($i.e.$ $2$ for LIM-3 or $3$ for CICE). 
     1548  (\ie $2$ for LIM-3 or $3$ for CICE). 
    15491549\end{description} 
    15501550 
     
    16301630\biblio 
    16311631 
     1632\pindex 
     1633 
    16321634\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_STO.tex

    r10414 r10442  
    169169The simulation will continue exactly as if it was not interrupted only 
    170170when \np{ln\_rstseed} is set to \forcode{.true.}, 
    171 $i.e.$ when the state of the random number generator is read in the restart file. 
     171\ie when the state of the random number generator is read in the restart file. 
    172172 
    173173\biblio 
    174174 
     175\pindex 
     176 
    175177\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_TRA.tex

    r10414 r10442  
    3939The terms QSR, BBC, BBL and DMP are optional. 
    4040The external forcings and parameterisations require complex inputs and complex calculations 
    41 ($e.g.$ bulk formulae, estimation of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and  
     41(\eg bulk formulae, estimation of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and  
    4242described in \autoref{chap:SBC}, \autoref{chap:LDF} and \autoref{chap:ZDF}, respectively. 
    4343Note that \mdl{tranpc}, the non-penetrative convection module, although located in the NEMO/OPA/TRA directory as 
     
    6969%------------------------------------------------------------------------------------------------------------- 
    7070 
    71 When considered ($i.e.$ when \np{ln\_traadv\_NONE} is not set to \forcode{.true.}), 
     71When considered (\ie when \np{ln\_traadv\_NONE} is not set to \forcode{.true.}), 
    7272the advection tendency of a tracer is expressed in flux form, 
    73 $i.e.$ as the divergence of the advective fluxes. 
     73\ie as the divergence of the advective fluxes. 
    7474Its discrete expression is given by : 
    7575\begin{equation} 
     
    8585$\nabla \cdot \left( \vect{U}\,T \right)=\vect{U} \cdot \nabla T$ which 
    8686results from the use of the continuity equation,  $\partial _t e_3 + e_3\;\nabla \cdot \vect{U}=0$ 
    87 (which reduces to $\nabla \cdot \vect{U}=0$ in linear free surface, $i.e.$ \np{ln\_linssh}\forcode{ = .true.}). 
     87(which reduces to $\nabla \cdot \vect{U}=0$ in linear free surface, \ie \np{ln\_linssh}\forcode{ = .true.}). 
    8888Therefore it is of paramount importance to design the discrete analogue of the advection tendency so that 
    8989it is consistent with the continuity equation in order to enforce the conservation properties of 
     
    127127  There is a non-zero advective flux which is set for all advection schemes as 
    128128  $\left. {\tau_w } \right|_{k=1/2} =T_{k=1} $, 
    129   $i.e.$ the product of surface velocity (at $z=0$) by the first level tracer value. 
     129  \ie the product of surface velocity (at $z=0$) by the first level tracer value. 
    130130\item[non-linear free surface:] 
    131131  (\np{ln\_linssh}\forcode{ = .false.}) 
     
    141141The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco}) 
    142142is the centred (\textit{now}) \textit{effective} ocean velocity, 
    143 $i.e.$ the \textit{eulerian} velocity (see \autoref{chap:DYN}) plus 
     143\ie the \textit{eulerian} velocity (see \autoref{chap:DYN}) plus 
    144144the eddy induced velocity (\textit{eiv}) and/or 
    145145the mixed layer eddy induced velocity (\textit{eiv}) when 
     
    156156The corresponding code can be found in the \mdl{traadv\_xxx} module, 
    157157where \textit{xxx} is a 3 or 4 letter acronym corresponding to each scheme. 
    158 By default ($i.e.$ in the reference namelist, \ngn{namelist\_ref}), all the logicals are set to \forcode{.false.}. 
     158By default (\ie in the reference namelist, \ngn{namelist\_ref}), all the logicals are set to \forcode{.false.}. 
    159159If the user does not select an advection scheme in the configuration namelist (\ngn{namelist\_cfg}), 
    160160the tracers will \textit{not} be advected! 
     
    199199\end{equation} 
    200200 
    201 CEN2 is non diffusive ($i.e.$ it conserves the tracer variance, $\tau^2)$ but dispersive 
    202 ($i.e.$ it may create false extrema). 
     201CEN2 is non diffusive (\ie it conserves the tracer variance, $\tau^2)$ but dispersive 
     202(\ie it may create false extrema). 
    203203It is therefore notoriously noisy and must be used in conjunction with an explicit diffusion operator to 
    204204produce a sensible solution. 
     
    234234 
    235235A direct consequence of the pseudo-fourth order nature of the scheme is that it is not non-diffusive, 
    236 $i.e.$ the global variance of a tracer is not preserved using CEN4. 
     236\ie the global variance of a tracer is not preserved using CEN4. 
    237237Furthermore, it must be used in conjunction with an explicit diffusion operator to produce a sensible solution. 
    238238As in CEN2 case, the time-stepping is performed using a leapfrog scheme in conjunction with an Asselin time-filter, 
     
    274274where $c_u$ is a flux limiter function taking values between 0 and 1. 
    275275The FCT order is the one of the centred scheme used 
    276 ($i.e.$ it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}). 
     276(\ie it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}). 
    277277There exist many ways to define $c_u$, each corresponding to a different FCT scheme. 
    278278The one chosen in \NEMO is described in \citet{Zalesak_JCP79}. 
     
    356356where $\tau "_i =\delta_i \left[ {\delta_{i+1/2} \left[ \tau \right]} \right]$. 
    357357 
    358 This results in a dissipatively dominant (i.e. hyper-diffusive) truncation error 
     358This results in a dissipatively dominant (\ie hyper-diffusive) truncation error 
    359359\citep{Shchepetkin_McWilliams_OM05}. 
    360360The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}. 
     
    447447$(i)$   the type of operator used (none, laplacian, bilaplacian), 
    448448$(ii)$  the direction along which the operator acts (iso-level, horizontal, iso-neutral), 
    449 $(iii)$ some specific options related to the rotated operators ($i.e.$ non-iso-level operator), and 
     449$(iii)$ some specific options related to the rotated operators (\ie non-iso-level operator), and 
    450450$(iv)$  the specification of eddy diffusivity coefficient (either constant or variable in space and time). 
    451451Item $(iv)$ will be described in \autoref{chap:LDF}. 
     
    455455 
    456456The lateral diffusion of tracers is evaluated using a forward scheme, 
    457 $i.e.$ the tracers appearing in its expression are the \textit{before} tracers in time, 
     457\ie the tracers appearing in its expression are the \textit{before} tracers in time, 
    458458except for the pure vertical component that appears when a rotation tensor is used. 
    459459This latter component is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}). 
     
    491491minimizing the impact on the larger scale features. 
    492492The main difference between the two operators is the scale selectiveness. 
    493 The bilaplacian damping time ($i.e.$ its spin down time) scales like $\lambda^{-4}$ for 
     493The bilaplacian damping time (\ie its spin down time) scales like $\lambda^{-4}$ for 
    494494disturbances of wavelength $\lambda$ (so that short waves damped more rapidelly than long ones), 
    495495whereas the laplacian damping time scales only like $\lambda^{-2}$. 
     
    506506The operator is a simple (re-entrant) laplacian acting in the (\textbf{i},\textbf{j}) plane when 
    507507iso-level option is used (\np{ln\_traldf\_lev}\forcode{ = .true.}) or 
    508 when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{z}-coordinate 
     508when a horizontal (\ie geopotential) operator is demanded in \zstar-coordinate 
    509509(\np{ln\_traldf\_hor} and \np{ln\_zco} equal \forcode{.true.}). 
    510510The associated code can be found in the \mdl{traldf\_lap\_blp} module. 
     
    514514(\np{ln\_traldf\_iso} or \np{ln\_traldf\_triad} equals \forcode{.true.}, 
    515515see \mdl{traldf\_iso} or \mdl{traldf\_triad} module, resp.), or 
    516 when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{s}-coordinate 
     516when a horizontal (\ie geopotential) operator is demanded in \textit{s}-coordinate 
    517517(\np{ln\_traldf\_hor} and \np{ln\_sco} equal \forcode{.true.}) 
    518518\footnote{In this case, the standard iso-neutral operator will be automatically selected}. 
     
    544544compute the iso-level bilaplacian operator.  
    545545 
    546 It is a \emph{horizontal} operator ($i.e.$ acting along geopotential surfaces) in 
     546It is a \emph{horizontal} operator (\ie acting along geopotential surfaces) in 
    547547the $z$-coordinate with or without partial steps, but is simply an iso-level operator in the $s$-coordinate. 
    548548It is thus used when, in addition to \np{ln\_traldf\_lap} or \np{ln\_traldf\_blp}\forcode{ = .true.}, 
     
    593593where $b_t$=$e_{1t}\,e_{2t}\,e_{3t}$  is the volume of $T$-cells, 
    594594$r_1$ and $r_2$ are the slopes between the surface of computation ($z$- or $s$-surfaces) and 
    595 the surface along which the diffusion operator acts ($i.e.$ horizontal or iso-neutral surfaces). 
     595the surface along which the diffusion operator acts (\ie horizontal or iso-neutral surfaces). 
    596596It is thus used when, in addition to \np{ln\_traldf\_lap}\forcode{ = .true.}, 
    597597we have \np{ln\_traldf\_iso}\forcode{ = .true.}, 
     
    676676where $A_w^{vT}$ and $A_w^{vS}$ are the vertical eddy diffusivity coefficients on temperature and salinity, 
    677677respectively. 
    678 Generally, $A_w^{vT}=A_w^{vS}$ except when double diffusive mixing is parameterised ($i.e.$ \key{zdfddm} is defined). 
     678Generally, $A_w^{vT}=A_w^{vS}$ except when double diffusive mixing is parameterised (\ie \key{zdfddm} is defined). 
    679679The way these coefficients are evaluated is given in \autoref{chap:ZDF} (ZDF). 
    680680Furthermore, when iso-neutral mixing is used, both mixing coefficients are increased by 
     
    715715 
    716716Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components 
    717 ($i.e.$ atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer of the ocean is due 
     717(\ie atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer of the ocean is due 
    718718both to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$) and 
    719719to the heat and salt content of the mass exchange. 
     
    725725 
    726726$\bullet$ $Q_{ns}$, the non-solar part of the net surface heat flux that crosses the sea surface 
    727 (i.e. the difference between the total surface heat flux and the fraction of the short wave flux that  
     727(\ie the difference between the total surface heat flux and the fraction of the short wave flux that  
    728728penetrates into the water column, see \autoref{subsec:TRA_qsr}) 
    729729plus the heat content associated with of the mass exchange with the atmosphere and lands. 
     
    796796  \end{split} 
    797797\end{equation} 
    798 where $Q_{sr}$ is the penetrative part of the surface heat flux ($i.e.$ the shortwave radiation) and 
     798where $Q_{sr}$ is the penetrative part of the surface heat flux (\ie the shortwave radiation) and 
    799799$I$ is the downward irradiance ($\left. I \right|_{z=\eta}=Q_{sr}$). 
    800800The additional term in \autoref{eq:PE_qsr} is discretized as follows: 
     
    843843 
    844844The RGB formulation is used when \np{ln\_qsr\_rgb}\forcode{ = .true.}. 
    845 The RGB attenuation coefficients ($i.e.$ the inverses of the extinction length scales) are tabulated over 
     845The RGB attenuation coefficients (\ie the inverses of the extinction length scales) are tabulated over 
    84684661 nonuniform chlorophyll classes ranging from 0.01 to 10 g.Chl/L 
    847847(see the routine \rou{trc\_oce\_rgb} in \mdl{trc\_oce} module). 
     
    867867the depth of $w-$levels does not significantly vary with location. 
    868868The level at which the light has been totally absorbed 
    869 ($i.e.$ it is less than the computer precision) is computed once, 
     869(\ie it is less than the computer precision) is computed once, 
    870870and the trend associated with the penetration of the solar radiation is only added down to that level. 
    871871Finally, note that when the ocean is shallow ($<$ 200~m), part of the solar radiation can reach the ocean floor. 
    872872In this case, we have chosen that all remaining radiation is absorbed in the last ocean level 
    873 ($i.e.$ $I$ is masked).  
     873(\ie $I$ is masked).  
    874874 
    875875%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    914914 
    915915Usually it is assumed that there is no exchange of heat or salt through the ocean bottom, 
    916 $i.e.$ a no flux boundary condition is applied on active tracers at the bottom. 
     916\ie a no flux boundary condition is applied on active tracers at the bottom. 
    917917This is the default option in \NEMO, and it is implemented using the masking technique. 
    918918However, there is a non-zero heat flux across the seafloor that is associated with solid earth cooling. 
     
    920920but it warms systematically the ocean and acts on the densest water masses. 
    921921Taking this flux into account in a global ocean model increases the deepest overturning cell 
    922 ($i.e.$ the one associated with the Antarctic Bottom Water) by a few Sverdrups  \citep{Emile-Geay_Madec_OS09}.  
     922(\ie the one associated with the Antarctic Bottom Water) by a few Sverdrups  \citep{Emile-Geay_Madec_OS09}.  
    923923 
    924924Options are defined through the  \ngn{namtra\_bbc} namelist variables. 
     
    976976and  $A_l^\sigma$ the lateral diffusivity in the BBL. 
    977977Following \citet{Beckmann_Doscher1997}, the latter is prescribed with a spatial dependence, 
    978 $i.e.$ in the conditional form 
     978\ie in the conditional form 
    979979\begin{equation} 
    980980  \label{eq:tra_bbl_coef} 
     
    10061006\label{subsec:TRA_bbl_adv} 
    10071007 
    1008 \sgacomment{"downsloping flow" has been replaced by "downslope flow" in the following 
    1009 if this is not what is meant then "downwards sloping flow" is also a possibility"} 
     1008%\sgacomment{"downsloping flow" has been replaced by "downslope flow" in the following 
     1009%if this is not what is meant then "downwards sloping flow" is also a possibility"} 
    10101010 
    10111011%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    10291029%!!      nn_bbl_adv = 1   use of the ocean velocity as bbl velocity 
    10301030%!!      nn_bbl_adv = 2   follow Campin and Goosse (1999) implentation 
    1031 %!!        i.e. transport proportional to the along-slope density gradient 
     1031%!!        \ie transport proportional to the along-slope density gradient 
    10321032 
    10331033%%%gmcomment   :  this section has to be really written 
     
    10411041(see black arrow in \autoref{fig:bbl}) \citep{Beckmann_Doscher1997}. 
    10421042It is a \textit{conditional advection}, that is, advection is allowed only 
    1043 if dense water overlies less dense water on the slope ($i.e.$ $\nabla_\sigma \rho  \cdot  \nabla H<0$) and 
    1044 if the velocity is directed towards greater depth ($i.e.$ $\vect{U}  \cdot  \nabla H>0$). 
     1043if dense water overlies less dense water on the slope (\ie $\nabla_\sigma \rho  \cdot  \nabla H<0$) and 
     1044if the velocity is directed towards greater depth (\ie $\vect{U}  \cdot  \nabla H>0$). 
    10451045 
    10461046\np{nn\_bbl\_adv}\forcode{ = 2}: 
     
    10481048the density difference between the higher cell and lower cell densities \citep{Campin_Goosse_Tel99}. 
    10491049The advection is allowed only  if dense water overlies less dense water on the slope 
    1050 ($i.e.$ $\nabla_\sigma \rho  \cdot  \nabla H<0$). 
     1050(\ie $\nabla_\sigma \rho  \cdot  \nabla H<0$). 
    10511051For example, the resulting transport of the downslope flow, here in the $i$-direction (\autoref{fig:bbl}), 
    10521052is simply given by the following expression: 
     
    11121112It also requires that both \np{ln\_tsd\_init} and \np{ln\_tsd\_tradmp} are set to true in 
    11131113\textit{namtsd} namelist as well as \np{sn\_tem} and \np{sn\_sal} structures are correctly set 
    1114 ($i.e.$ that $T_o$ and $S_o$ are provided in input files and read using \mdl{fldread}, 
     1114(\ie that $T_o$ and $S_o$ are provided in input files and read using \mdl{fldread}, 
    11151115see \autoref{subsec:SBC_fldread}). 
    11161116The restoring coefficient $\gamma$ is a three-dimensional array read in during the \rou{tra\_dmp\_init} routine. 
     
    11481148This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1. 
    11491149The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work. 
    1150 The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for 
     1150The \ngn{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for 
    11511151the restoration coefficient. 
    11521152 
     
    11561156 
    11571157\np{cp\_cfg}, \np{cp\_cpz}, \np{jp\_cfg} and \np{jperio} specify the model configuration being used and 
    1158 should be the same as specified in \nl{namcfg}. 
    1159 The variable \nl{lzoom} is used to specify that the damping is being used as in case \textit{a} above to 
     1158should be the same as specified in \ngn{namcfg}. 
     1159The variable \np{lzoom} is used to specify that the damping is being used as in case \textit{a} above to 
    11601160provide boundary conditions to a zoom configuration. 
    11611161In the case of the arctic or antarctic zoom configurations this includes some specific treatment. 
    11621162Otherwise damping is applied to the 6 grid points along the ocean boundaries. 
    11631163The open boundaries are specified by the variables \np{lzoom\_n}, \np{lzoom\_e}, \np{lzoom\_s}, \np{lzoom\_w} in 
    1164 the \nl{nam\_zoom\_dmp} name list. 
     1164the \ngn{nam\_zoom\_dmp} name list. 
    11651165 
    11661166The remaining switch namelist variables determine the spatial variation of the restoration coefficient in 
     
    12011201Options are defined through the  \ngn{namdom} namelist variables. 
    12021202The general framework for tracer time stepping is a modified leap-frog scheme \citep{Leclair_Madec_OM09}, 
    1203 $i.e.$ a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:STP_mLF}): 
     1203\ie a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:STP_mLF}): 
    12041204\begin{equation} 
    12051205  \label{eq:tra_nxt} 
     
    12131213where RHS is the right hand side of the temperature equation, the subscript $f$ denotes filtered values, 
    12141214$\gamma$ is the Asselin coefficient, and $S$ is the total forcing applied on $T$ 
    1215 ($i.e.$ fluxes plus content in mass exchanges). 
     1215(\ie fluxes plus content in mass exchanges). 
    12161216$\gamma$ is initialized as \np{rn\_atfp} (\textbf{namelist} parameter). 
    12171217Its default value is \np{rn\_atfp}\forcode{ = 10.e-3}. 
     
    12821282  the TEOS-10 rational function approximation for hydrographic data analysis \citep{TEOS10}. 
    12831283  A key point is that conservative state variables are used: 
    1284   Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \degC, notation: $\Theta$). 
     1284  Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \deg{C}, notation: $\Theta$). 
    12851285  The pressure in decibars is approximated by the depth in meters. 
    12861286  With TEOS10, the specific heat capacity of sea water, $C_p$, is a constant. 
     
    13631363\label{subsec:TRA_bn2} 
    13641364 
    1365 An accurate computation of the ocean stability (i.e. of $N$, the brunt-V\"{a}is\"{a}l\"{a} frequency) is of 
     1365An accurate computation of the ocean stability (\ie of $N$, the brunt-V\"{a}is\"{a}l\"{a} frequency) is of 
    13661366paramount importance as determine the ocean stratification and is used in several ocean parameterisations 
    13671367(namely TKE, GLS, Richardson number dependent vertical diffusion, enhanced vertical diffusion, 
     
    13781378The coefficients are a polynomial function of temperature, salinity and depth which 
    13791379expression depends on the chosen EOS. 
    1380 They are computed through \textit{eos\_rab}, a \textsc{Fortran} function that can be found in \mdl{eosbn2}. 
     1380They are computed through \textit{eos\_rab}, a \fortran function that can be found in \mdl{eosbn2}. 
    13811381 
    13821382% ------------------------------------------------------------------------------------------------------------- 
     
    13961396 
    13971397\autoref{eq:tra_eos_fzp} is only used to compute the potential freezing point of sea water 
    1398 ($i.e.$ referenced to the surface $p=0$), 
     1398(\ie referenced to the surface $p=0$), 
    13991399thus the pressure dependent terms in \autoref{eq:tra_eos_fzp} (last term) have been dropped. 
    14001400The freezing point is computed through \textit{eos\_fzp}, 
    1401 a \textsc{Fortran} function that can be found in \mdl{eosbn2}.   
     1401a \fortran function that can be found in \mdl{eosbn2}.   
    14021402 
    14031403 
     
    15111511\biblio 
    15121512 
     1513\pindex 
     1514 
    15131515\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r10414 r10442  
    2525At the surface they are prescribed from the surface forcing (see \autoref{chap:SBC}), 
    2626while at the bottom they are set to zero for heat and salt, 
    27 unless a geothermal flux forcing is prescribed as a bottom boundary condition ($i.e.$ \key{trabbl} defined, 
     27unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \key{trabbl} defined, 
    2828see \autoref{subsec:TRA_bbc}), and specified through a bottom friction parameterisation for momentum 
    2929(see \autoref{sec:ZDF_bfr}). 
     
    8686The hypothesis of a mixing mainly maintained by the growth of Kelvin-Helmholtz like instabilities leads to 
    8787a dependency between the vertical eddy coefficients and the local Richardson number 
    88 ($i.e.$ the ratio of stratification to vertical shear). 
     88(\ie the ratio of stratification to vertical shear). 
    8989Following \citet{Pacanowski_Philander_JPO81}, the following formulation has been implemented: 
    9090\[ 
     
    254254  \end{aligned} 
    255255\] 
    256 where $l^{(k)}$ is computed using \autoref{eq:tke_mxl0_1}, $i.e.$ $l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$. 
     256where $l^{(k)}$ is computed using \autoref{eq:tke_mxl0_1}, \ie $l^{(k)} = \sqrt {2 {\bar e}^{(k)} / {N^2}^{(k)} }$. 
    257257 
    258258In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same value: 
     
    326326\forcode{.true.} in the namtke namelist. 
    327327  
    328 By making an analogy with the characteristic convective velocity scale ($e.g.$, \citet{D'Alessio_al_JPO98}), 
     328By making an analogy with the characteristic convective velocity scale (\eg, \citet{D'Alessio_al_JPO98}), 
    329329$P_{LC}$ is assumed to be :  
    330330\[ 
     
    369369This bias is particularly acute over the Southern Ocean. 
    370370To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}.  
    371 The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations, 
     371The parameterization is an empirical one, \ie not derived from theoretical considerations, 
    372372but rather is meant to account for observed processes that affect the density structure of  
    373373the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme  
    374 ($i.e.$ near-inertial oscillations and ocean swells and waves). 
    375  
    376 When using this parameterization ($i.e.$ when \np{nn\_etau}\forcode{ = 1}), 
     374(\ie near-inertial oscillations and ocean swells and waves). 
     375 
     376When using this parameterization (\ie when \np{nn\_etau}\forcode{ = 1}), 
    377377the TKE input to the ocean ($S$) imposed by the winds in the form of near-inertial oscillations, 
    378378swell and waves is parameterized by \autoref{eq:ZDF_Esbc} the standard TKE surface boundary condition, 
     
    403403% excluded by the hydrostatic assumption and the model resolution.  
    404404% Thus far, the representation of internal wave mixing in ocean models has been relatively crude  
    405 % (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 
     405% (\eg Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 
    406406 
    407407% ------------------------------------------------------------------------------------------------------------- 
     
    654654%-------------------------------------------------------------------------------------------------------------- 
    655655 
    656 Static instabilities (i.e. light potential densities under heavy ones) may occur at particular ocean grid points. 
     656Static instabilities (\ie light potential densities under heavy ones) may occur at particular ocean grid points. 
    657657In nature, convective processes quickly re-establish the static stability of the water column. 
    658658These processes have been removed from the model via the hydrostatic assumption so they must be parameterized. 
     
    699699It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously the statically unstable portion of 
    700700the water column, but only until the density structure becomes neutrally stable 
    701 ($i.e.$ until the mixed portion of the water column has \textit{exactly} the density of the water just below) 
     701(\ie until the mixed portion of the water column has \textit{exactly} the density of the water just below) 
    702702\citep{Madec_al_JPO91}. 
    703703The associated algorithm is an iterative process used in the following way (\autoref{fig:npc}): 
     
    748748In this case, the vertical eddy mixing coefficients are assigned very large values 
    749749(a typical value is $10\;m^2s^{-1})$ in regions where the stratification is unstable 
    750 ($i.e.$ when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}. 
     750(\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}. 
    751751This is done either on tracers only (\np{nn\_evdm}\forcode{ = 0}) or 
    752752on both momentum and tracers (\np{nn\_evdm}\forcode{ = 1}). 
     
    760760momentum in the case of static instabilities. 
    761761It requires the use of an implicit time stepping on vertical diffusion terms 
    762 (i.e. \np{ln\_zdfexp}\forcode{ = .false.}). 
     762(\ie np{ln\_zdfexp}\forcode{ = .false.}). 
    763763 
    764764Note that the stability test is performed on both \textit{before} and \textit{now} values of $N^2$. 
     
    784784because the mixing length scale is bounded by the distance to the sea surface. 
    785785It can thus be useful to combine the enhanced vertical diffusion with the turbulent closure scheme, 
    786 $i.e.$ setting the \np{ln\_zdfnpc} namelist parameter to true and 
     786\ie setting the \np{ln\_zdfnpc} namelist parameter to true and 
    787787defining the turbulent closure CPP key all together. 
    788788 
     
    855855 
    856856The factor 0.7 in \autoref{eq:zdfddm_f_T} reflects the measured ratio $\alpha F_T /\beta F_S \approx  0.7$ of 
    857 buoyancy flux of heat to buoyancy flux of salt ($e.g.$, \citet{McDougall_Taylor_JMR84}). 
     857buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{McDougall_Taylor_JMR84}). 
    858858Following  \citet{Merryfield1999}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$. 
    859859 
     
    955955 
    956956The linear bottom friction parameterisation (including the special case of a free-slip condition) assumes that 
    957 the bottom friction is proportional to the interior velocity (i.e. the velocity of the last model level): 
     957the bottom friction is proportional to the interior velocity (\ie the velocity of the last model level): 
    958958\[ 
    959959  % \label{eq:zdfbfr_linear} 
     
    10491049For stability, the drag coefficient is bounded such that it is kept greater or equal to 
    10501050the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional namelist parameter: 
    1051 \np{rn\_bfri2\_max}, i.e.: 
     1051\np{rn\_bfri2\_max}, \ie 
    10521052\[ 
    10531053  rn\_bfri2 \leq C_D \leq rn\_bfri2\_max 
     
    11351135and update it with the latest value. 
    11361136On the other hand, the bottom friction contributed by the other terms 
    1137 (e.g. the advection term, viscosity term) has been included in the 3-D momentum equations and 
     1137(\eg the advection term, viscosity term) has been included in the 3-D momentum equations and 
    11381138should not be added in the 2-D barotropic mode. 
    11391139 
     
    11751175while the three dimensional prognostic variables are solved with the longer time step of \np{rn\_rdt} seconds. 
    11761176The trend in the barotropic momentum due to bottom friction appropriate to this method is that given by 
    1177 the selected parameterisation ($i.e.$ linear or non-linear bottom friction) computed with 
     1177the selected parameterisation (\ie linear or non-linear bottom friction) computed with 
    11781178the evolving velocities at each barotropic timestep.  
    11791179 
     
    12641264 
    12651265The associated vertical viscosity is calculated from the vertical diffusivity assuming a Prandtl number of 1, 
    1266 $i.e.$ $A^{vm}_{tides}=A^{vT}_{tides}$. 
     1266\ie $A^{vm}_{tides}=A^{vT}_{tides}$. 
    12671267In the limit of $N \rightarrow 0$ (or becoming negative), the vertical diffusivity is capped at $300\,cm^2/s$ and 
    12681268impose a lower limit on $N^2$ of \np{rn\_n2min} usually set to $10^{-8} s^{-2}$. 
     
    13121312Once generated, internal tides remain confined within this semi-enclosed area and hardly radiate away. 
    13131313Therefore all the internal tides energy is consumed within this area. 
    1314 So it is assumed that $q = 1$, $i.e.$ all the energy generated is available for mixing. 
     1314So it is assumed that $q = 1$, \ie all the energy generated is available for mixing. 
    13151315Note that for test purposed, the ITF tidal dissipation efficiency is a namelist parameter (\np{rn\_tfe\_itf}). 
    13161316A value of $1$ or close to is this recommended for this parameter. 
     
    14011401\biblio 
    14021402 
     1403\pindex 
     1404 
    14031405\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex

    r10414 r10442  
    3535The alternative is to use diffusive schemes such as upstream or flux corrected schemes. 
    3636This last option was rejected because we prefer a complete handling of the model diffusion, 
    37 i.e. of the model physics rather than letting the advective scheme produces its own implicit diffusion without 
     37\ie of the model physics rather than letting the advective scheme produces its own implicit diffusion without 
    3838controlling the space and time structure of this implicit diffusion. 
    3939Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required. 
     
    6060\textbf{* relative, planetary and total vorticity term:} 
    6161 
    62 Let us define as either the relative, planetary and total potential vorticity, i.e. ?, ?, and ?, respectively. 
     62Let us define as either the relative, planetary and total potential vorticity, \ie, ?, and ?, respectively. 
    6363The continuous formulation of the vorticity term satisfies following integral constraints: 
    6464\[ 
     
    122122This properties is satisfied locally with the choice of discretization we have made (property (II.1.9)~). 
    123123In addition, when the equation of state is linear 
    124 (i.e. when an advective-diffusive equation for density can be derived from those of temperature and salinity) 
     124(\ie when an advective-diffusive equation for density can be derived from those of temperature and salinity) 
    125125the change of horizontal kinetic energy due to the work of pressure forces is balanced by the change of 
    126126potential energy due to buoyancy forces: 
     
    164164 
    165165In continuous formulation, the advective terms of the tracer equations conserve the tracer content and 
    166 the quadratic form of the tracer, $i.e.$ 
     166the quadratic form of the tracer, \ie 
    167167\[ 
    168168  % \label{eq:tra_tra2} 
     
    283283In discrete form, all these properties are satisfied in $z$-coordinate (see Appendix C). 
    284284In $s$-coordinates, only first order properties can be demonstrated, 
    285 $i.e.$ the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence. 
     285\ie the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence. 
    286286 
    287287% ------------------------------------------------------------------------------------------------------------- 
     
    294294the heat and salt contents are conserved (equations in flux form, second order centred finite differences). 
    295295As a form flux is used to compute the temperature and salinity, 
    296 the quadratic form of these quantities (i.e. their variance) globally tends to diminish. 
     296the quadratic form of these quantities (\ie their variance) globally tends to diminish. 
    297297As for the advective term, there is generally no strict conservation of mass even if, 
    298298in practice, the mass is conserved with a very good accuracy.  
     
    309309\] 
    310310 
    311 \textbf{* vertical physics: }conservation of tracer, dissipation of tracer variance, $i.e.$ 
     311\textbf{* vertical physics: }conservation of tracer, dissipation of tracer variance, \ie 
    312312 
    313313\[ 
     
    330330\biblio 
    331331 
     332\pindex 
     333 
    332334\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_misc.tex

    r10414 r10442  
    5050This technique is sometime called "partially open face" or "partially closed cells". 
    5151The key issue here is only to reduce the faces of $T$-cell 
    52 ($i.e.$ change the value of the horizontal scale factors at $u$- or $v$-point) but not the volume of the $T$-cell. 
     52(\ie change the value of the horizontal scale factors at $u$- or $v$-point) but not the volume of the $T$-cell. 
    5353Indeed, reducing the volume of strait $T$-cell can easily produce a numerical instability at 
    5454that grid point that would require a reduction of the model time step. 
     
    7474      \textit{Bottom}: using viscous boundary layers. 
    7575      The four fmask parameters along the strait coastlines are set to a value larger than 4, 
    76       $i.e.$ "strong" no-slip case (see \autoref{fig:LBC_shlat}) creating a large viscous boundary layer that 
     76      \ie "strong" no-slip case (see \autoref{fig:LBC_shlat}) creating a large viscous boundary layer that 
    7777      allows a reduced transport through the strait. 
    7878    } 
     
    113113\noindent These files define a horizontal domain of 362x332. 
    114114Assuming the first row with open ocean wet points in the non-isf bathymetry for this set is row 42 
    115 (Fortran indexing) then the formally correct setting for \np{open\_ocean\_jstart} is 41. 
     115(\fortran indexing) then the formally correct setting for \np{open\_ocean\_jstart} is 41. 
    116116Using this value as the first row to be read will result in a 362x292 domain which is the same size as 
    117117the original ORCA1 domain. 
     
    167167\label{subsec:MISC_sign} 
    168168 
    169 The SIGN(A, B) is the \textsc {Fortran} intrinsic function delivers the magnitude of A with the sign of B. 
     169The SIGN(A, B) is the \fortran intrinsic function delivers the magnitude of A with the sign of B. 
    170170For example, SIGN(-3.0,2.0) has the value 3.0. 
    171171The problematic case is when the second argument is zero, because, on platforms that support IEEE arithmetic, 
     
    173173There is a positive zero and a negative zero. 
    174174 
    175 In \textsc{Fortran}~90, the processor was required always to deliver a positive result for SIGN(A, B) if B was zero. 
    176 Nevertheless, in \textsc{Fortran}~95, the processor is allowed to do the correct thing and deliver ABS(A) when 
     175In \fninety, the processor was required always to deliver a positive result for SIGN(A, B) if B was zero. 
     176Nevertheless, in \fninety, the processor is allowed to do the correct thing and deliver ABS(A) when 
    177177B is a positive zero and -ABS(A) when B is a negative zero. 
    178178This change in the specification becomes apparent only when B is of type real, and is zero, 
    179179and the processor is capable of distinguishing between positive and negative zero, 
    180180and B is negative real zero. 
    181 Then SIGN delivers a negative result where, under \textsc{Fortran}~90 rules, it used to return a positive result. 
     181Then SIGN delivers a negative result where, under \fninety rules, it used to return a positive result. 
    182182This change may be especially sensitive for the ice model, 
    183183so we overwrite the intrinsinc function with our own function simply performing :   \\ 
     
    296296\biblio 
    297297 
     298\pindex 
     299 
    298300\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics.tex

    r10414 r10442  
    2828 
    2929The ocean is a fluid that can be described to a good approximation by the primitive equations, 
    30 $i.e.$ the Navier-Stokes equations along with a nonlinear equation of state which 
     30\ie the Navier-Stokes equations along with a nonlinear equation of state which 
    3131couples the two active tracers (temperature and salinity) to the fluid velocity, 
    3232plus the following additional assumptions made from scale considerations: 
     
    5555it is useful to choose an orthogonal set of unit vectors (\textbf{i},\textbf{j},\textbf{k}) linked to 
    5656the earth such that \textbf{k} is the local upward vector and (\textbf{i},\textbf{j}) are two vectors orthogonal to 
    57 \textbf{k}, $i.e.$ tangent to the geopotential surfaces. 
     57\textbf{k}, \ie tangent to the geopotential surfaces. 
    5858Let us define the following variables: \textbf{U} the vector velocity, $\textbf{U}=\textbf{U}_h + w\, \textbf{k}$  
    59 (the subscript $h$ denotes the local horizontal vector, $i.e.$ over the (\textbf{i},\textbf{j}) plane),  
     59(the subscript $h$ denotes the local horizontal vector, \ie over the (\textbf{i},\textbf{j}) plane),  
    6060$T$ the potential temperature, $S$ the salinity, \textit{$\rho $} the \textit{in situ} density. 
    6161The vector invariant form of the primitive equations in the (\textbf{i},\textbf{j},\textbf{k}) vector system 
     
    151151  \footnote{ 
    152152    In fact, it has been shown that the heat flux associated with the solid Earth cooling 
    153     ($i.e.$the geothermal heating) is not negligible for the thermohaline circulation of the world ocean 
     153    (\ie the geothermal heating) is not negligible for the thermohaline circulation of the world ocean 
    154154    (see \autoref{subsec:TRA_bbc}). 
    155155  }. 
    156156  The boundary condition is thus set to no flux of heat and salt across solid boundaries. 
    157157  For momentum, the situation is different. There is no flow across solid boundaries, 
    158   $i.e.$ the velocity normal to the ocean bottom and coastlines is zero (in other words, 
     158  \ie the velocity normal to the ocean bottom and coastlines is zero (in other words, 
    159159  the bottom velocity is parallel to solid boundaries). This kinematic boundary condition 
    160160  can be expressed as: 
     
    225225the time step would have to be very short if they were present in the model. 
    226226The latter strategy filters out these waves since the rigid lid approximation implies $\eta=0$, 
    227 $i.e.$ the sea surface is the surface $z=0$. 
     227\ie the sea surface is the surface $z=0$. 
    228228This well known approximation increases the surface wave speed to infinity and 
    229 modifies certain other longwave dynamics ($e.g.$ barotropic Rossby or planetary waves). 
     229modifies certain other longwave dynamics (\eg barotropic Rossby or planetary waves). 
    230230The rigid-lid hypothesis is an obsolescent feature in modern OGCMs. 
    231231It has been available until the release 3.1 of  \NEMO, and it has been removed in release 3.2 and followings. 
     
    302302 
    303303In many ocean circulation problems, the flow field has regions of enhanced dynamics 
    304 ($i.e.$ surface layers, western boundary currents, equatorial currents, or ocean fronts). 
     304(\ie surface layers, western boundary currents, equatorial currents, or ocean fronts). 
    305305The representation of such dynamical processes can be improved by 
    306306specifically increasing the model resolution in these regions. 
     
    322322(\textbf{i},\textbf{j},\textbf{k}) linked to the earth such that 
    323323\textbf{k} is the local upward vector and (\textbf{i},\textbf{j}) are two vectors orthogonal to \textbf{k}, 
    324 $i.e.$ along geopotential surfaces (\autoref{fig:referential}). 
     324\ie along geopotential surfaces (\autoref{fig:referential}). 
    325325Let $(\lambda,\varphi,z)$ be the geographical coordinate system in which a position is defined by 
    326326the latitude $\varphi(i,j)$, the longitude $\lambda(i,j)$ and 
     
    487487This is the so-called \textit{vector invariant form} of the momentum advection term. 
    488488For some purposes, it can be advantageous to write this term in the so-called flux form, 
    489 $i.e.$ to write it as the divergence of fluxes. 
     489\ie to write it as the divergence of fluxes. 
    490490For example, the first component of \autoref{eq:PE_vector_form} (the $i$-component) is transformed as follows: 
    491491\begin{flalign*} 
     
    597597 
    598598Note that in the case of geographical coordinate, 
    599 $i.e.$ when $(i,j) \to (\lambda ,\varphi )$ and $(e_1 ,e_2) \to (a \,\cos \varphi ,a)$, 
     599\ie when $(i,j) \to (\lambda ,\varphi )$ and $(e_1 ,e_2) \to (a \,\cos \varphi ,a)$, 
    600600we recover the commonly used modification of the Coriolis parameter $f \to f+(u/a) \tan \varphi$. 
    601601 
     
    720720Therefore, in order to represent the ocean with respect to 
    721721the first point a space and time dependent vertical coordinate that follows the variation of the sea surface height 
    722 $e.g.$ an $z$*-coordinate; 
     722\eg an \zstar-coordinate; 
    723723for the second point, a space variation to fit the change of bottom topography 
    724 $e.g.$ a terrain-following or $\sigma$-coordinate; 
     724\eg a terrain-following or $\sigma$-coordinate; 
    725725and for the third point, one will be tempted to use a space and time dependent coordinate that 
    726 follows the isopycnal surfaces, $e.g.$ an isopycnic coordinate. 
     726follows the isopycnal surfaces, \eg an isopycnic coordinate. 
    727727 
    728728In order to satisfy two or more constrains one can even be tempted to mixed these coordinate systems, as in 
     
    790790 
    791791In this section we first establish the PE in the generalised vertical $s$-coordinate, 
    792 then we discuss the particular cases available in \NEMO, namely $z$, $z$*, $s$, and $\tilde z$ 
     792then we discuss the particular cases available in \NEMO, namely $z$, \zstar, $s$, and \ztilde 
    793793%} 
    794794 
     
    800800Starting from the set of equations established in \autoref{sec:PE_zco} for the special case $k=z$ and thus $e_3=1$, 
    801801we introduce an arbitrary vertical coordinate $s=s(i,j,k,t)$, 
    802 which includes $z$-, \textit{z*}- and $\sigma-$coordinates as special cases 
    803 ($s=z$, $s=\textit{z*}$, and $s=\sigma=z/H$ or $=z/\left(H+\eta \right)$, resp.). 
     802which includes $z$-, \zstar- and $\sigma-$coordinates as special cases 
     803($s=z$, $s=\zstar$, and $s=\sigma=z/H$ or $=z/\left(H+\eta \right)$, resp.). 
    804804A formal derivation of the transformed equations is given in \autoref{apdx:A}. 
    805805Let us define the vertical scale factor by $e_3=\partial_s z$  ($e_3$ is now a function of $(i,j,k,t)$ ), 
     
    917917 
    918918% ------------------------------------------------------------------------------------------------------------- 
    919 % Curvilinear z*-coordinate System 
    920 % ------------------------------------------------------------------------------------------------------------- 
    921 \subsection{Curvilinear \textit{z*}--coordinate system} 
     919% Curvilinear \zstar-coordinate System 
     920% ------------------------------------------------------------------------------------------------------------- 
     921\subsection{Curvilinear \zstar--coordinate system} 
    922922\label{subsec:PE_zco_star} 
    923923 
     
    929929      (a) $z$-coordinate in linear free-surface case ; 
    930930      (b) $z-$coordinate in non-linear free surface case ; 
    931       (c) re-scaled height coordinate (become popular as the \textit{z*-}coordinate 
     931      (c) re-scaled height coordinate (become popular as the \zstar-coordinate 
    932932      \citep{Adcroft_Campin_OM04} ). 
    933933    } 
     
    941941 
    942942%\gmcomment{ 
    943 The \textit{z*} coordinate approach is an unapproximated, non-linear free surface implementation which allows one to 
     943The \zstar coordinate approach is an unapproximated, non-linear free surface implementation which allows one to 
    944944deal with large amplitude free-surface variations relative to the vertical resolution \citep{Adcroft_Campin_OM04}. 
    945 In the \textit{z*} formulation, 
     945In the \zstar formulation, 
    946946the variation of the column thickness due to sea-surface undulations is not concentrated in the surface level, 
    947947as in the $z$-coordinate formulation, but is equally distributed over the full water column. 
    948948Thus vertical levels naturally follow sea-surface variations, with a linear attenuation with depth, 
    949949as illustrated by figure fig.1c. 
    950 Note that with a flat bottom, such as in fig.1c, the bottom-following $z$ coordinate and \textit{z*} are equivalent. 
    951 The definition and modified oceanic equations for the rescaled vertical coordinate  \textit{z*}, 
     950Note that with a flat bottom, such as in fig.1c, the bottom-following $z$ coordinate and \zstar are equivalent. 
     951The definition and modified oceanic equations for the rescaled vertical coordinate  \zstar, 
    952952including the treatment of fresh-water flux at the surface, are detailed in Adcroft and Campin (2004). 
    953953The major points are summarized here. 
    954 The position ( \textit{z*}) and vertical discretization (\textit{z*}) are expressed as: 
     954The position ( \zstar) and vertical discretization (\zstar) are expressed as: 
    955955\[ 
    956956  % \label{eq:z-star} 
    957   H +  \textit{z*} = (H + z) / r \quad \text{and} \ \delta \textit{z*} = \delta z / r \quad \text{with} \ r = \frac{H+\eta} {H} 
     957  H +  \zstar = (H + z) / r \quad \text{and} \ \delta \zstar = \delta z / r \quad \text{with} \ r = \frac{H+\eta} {H} 
    958958\]  
    959 Since the vertical displacement of the free surface is incorporated in the vertical coordinate \textit{z*}, 
    960 the upper and lower boundaries are at fixed  \textit{z*} position, 
    961 $\textit{z*} = 0$ and  $\textit{z*} = -H$ respectively. 
     959Since the vertical displacement of the free surface is incorporated in the vertical coordinate \zstar, 
     960the upper and lower boundaries are at fixed  \zstar position, 
     961$\zstar = 0$ and  $\zstar = -H$ respectively. 
    962962Also the divergence of the flow field is no longer zero as shown by the continuity equation: 
    963963\[  
    964   \frac{\partial r}{\partial t} = \nabla_{\textit{z*}} \cdot \left( r \; \rm{\bf U}_h \right) 
     964  \frac{\partial r}{\partial t} = \nabla_{\zstar} \cdot \left( r \; \rm{\bf U}_h \right) 
    965965  \left( r \; w\textit{*} \right) = 0  
    966966\]  
     
    10691069The second term in \autoref{eq:PE_p_sco} depends on the tilt of the coordinate surface and 
    10701070introduces a truncation error that is not present in a $z$-model. 
    1071 In the special case of a $\sigma-$coordinate (i.e. a depth-normalised coordinate system $\sigma = z/H$), 
     1071In the special case of a $\sigma-$coordinate (\ie depth-normalised coordinate system $\sigma = z/H$), 
    10721072\citet{Haney1991} and \citet{Beckmann1993} have given estimates of the magnitude of this truncation error. 
    10731073It depends on topographic slope, stratification, horizontal and vertical resolution, the equation of state, 
     
    10971097In contrast, the ocean will stay at rest in a $z$-model. 
    10981098As for the truncation error, the problem can be reduced by introducing the terrain-following coordinate below 
    1099 the strongly stratified portion of the water column ($i.e.$ the main thermocline) \citep{Madec_al_JPO96}. 
     1099the strongly stratified portion of the water column (\ie the main thermocline) \citep{Madec_al_JPO96}. 
    11001100An alternate solution consists of rotating the lateral diffusive tensor to geopotential or to isoneutral surfaces 
    11011101(see \autoref{subsec:PE_ldf}). 
     
    11141114% Curvilinear z-tilde coordinate System 
    11151115% ------------------------------------------------------------------------------------------------------------- 
    1116 \subsection{\texorpdfstring{Curvilinear $\tilde{z}$--coordinate}{}} 
     1116\subsection{\texorpdfstring{Curvilinear \ztilde--coordinate}{}} 
    11171117\label{subsec:PE_zco_tilde} 
    11181118 
    1119 The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM11}. 
     1119The \ztilde-coordinate has been developed by \citet{Leclair_Madec_OM11}. 
    11201120It is available in \NEMO since the version 3.4. 
    11211121Nevertheless, it is currently not robust enough to be used in all possible configurations. 
     
    11361136The effects of smaller scale motions (coming from the advective terms in the Navier-Stokes equations) must be represented entirely in terms of large-scale patterns to close the equations. 
    11371137These effects appear in the equations as the divergence of turbulent fluxes 
    1138 ($i.e.$ fluxes associated with the mean correlation of small scale perturbations). 
     1138(\ie fluxes associated with the mean correlation of small scale perturbations). 
    11391139Assuming a turbulent closure hypothesis is equivalent to choose a formulation for these fluxes. 
    11401140It is usually called the subgrid scale physics. 
     
    11811181All the vertical physics is embedded in the specification of the eddy coefficients. 
    11821182They can be assumed to be either constant, or function of the local fluid properties 
    1183 ($e.g.$ Richardson number, Brunt-Vais\"{a}l\"{a} frequency...), 
     1183(\eg Richardson number, Brunt-Vais\"{a}l\"{a} frequency...), 
    11841184or computed from a turbulent closure model. 
    11851185The choices available in \NEMO are discussed in \autoref{chap:ZDF}). 
     
    11961196and a sub mesoscale turbulence which is never explicitly solved even partially, but always parameterized. 
    11971197The formulation of lateral eddy fluxes depends on whether the mesoscale is below or above the grid-spacing 
    1198 ($i.e.$ the model is eddy-resolving or not). 
     1198(\ie the model is eddy-resolving or not). 
    11991199 
    12001200In non-eddy-resolving configurations, the closure is similar to that used for the vertical physics. 
     
    12041204(or more precisely neutral surfaces \cite{McDougall1987}) rather than across them. 
    12051205As the slope of neutral surfaces is small in the ocean, a common approximation is to assume that 
    1206 the `lateral' direction is the horizontal, $i.e.$ the lateral mixing is performed along geopotential surfaces. 
     1206the `lateral' direction is the horizontal, \ie the lateral mixing is performed along geopotential surfaces. 
    12071207This leads to a geopotential second order operator for lateral subgrid scale physics. 
    12081208This assumption can be relaxed: the eddy-induced turbulent fluxes can be better approached by assuming that 
     
    12111211it has components in the three space directions. 
    12121212However, 
    1213 both horizontal and isoneutral operators have no effect on mean ($i.e.$ large scale) potential energy whereas 
     1213both horizontal and isoneutral operators have no effect on mean (\ie large scale) potential energy whereas 
    12141214potential energy is a main source of turbulence (through baroclinic instabilities). 
    12151215\citet{Gent1990} have proposed a parameterisation of mesoscale eddy-induced turbulence which 
     
    13121312  \begin{cases} 
    13131313    r_n            &      \text{in $z$-coordinate}    \\ 
    1314     r_n + \sigma_n &      \text{in \textit{z*} and $s$-coordinates} 
     1314    r_n + \sigma_n &      \text{in \zstar and $s$-coordinates} 
    13151315  \end{cases} 
    13161316                     \quad \text{where } n=1,2 
     
    13591359Unfortunately, it is only available in \textit{iso-level} direction. 
    13601360When a rotation is required 
    1361 ($i.e.$ geopotential diffusion in $s-$coordinates or isoneutral diffusion in both $z$- and $s$-coordinates), 
     1361(\ie geopotential diffusion in $s-$coordinates or isoneutral diffusion in both $z$- and $s$-coordinates), 
    13621362the $u$ and $v-$fields are considered as independent scalar fields, so that the diffusive operator is given by: 
    13631363\[ 
     
    13711371It is the same expression as those used for diffusive operator on tracers. 
    13721372It must be emphasised that such a formulation is only exact in a Cartesian coordinate system, 
    1373 $i.e.$ on a $f-$ or $\beta-$plane, not on the sphere. 
     1373\ie on a $f-$ or $\beta-$plane, not on the sphere. 
    13741374It is also a very good approximation in vicinity of the Equator in 
    13751375a geographical coordinate system \citep{Lengaigne_al_JGR03}. 
     
    13831383\biblio 
    13841384 
     1385\pindex 
     1386 
    13851387\end{document} 
    13861388 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

    r10414 r10442  
    66% ================================================================ 
    77% ================================================================ 
    8 % Curvilinear z*- s*-coordinate System 
    9 % ================================================================ 
    10 \chapter{ essai z* s*} 
    11 \section{Curvilinear \textit{z*}- or \textit{s*} coordinate system} 
     8% Curvilinear \zstar- \sstar-coordinate System 
     9% ================================================================ 
     10\chapter{ essai \zstar \sstar} 
     11\section{Curvilinear \zstar- or \sstar coordinate system} 
    1212 
    1313% ------------------------------------------------------------------------------------------------------------- 
     
    114114and $\rho_w =1,000\,Kg.m^{-3}$ is the volumic mass of pure water. 
    115115The sea-surface height is evaluated using a leapfrog scheme in combination with an Asselin time filter, 
    116 i.e. the velocity appearing in (\autoref{eq:dynspg_ssh}) is centred in time (\textit{now} velocity).  
     116(\ie the velocity appearing in (\autoref{eq:dynspg_ssh}) is centred in time (\textit{now} velocity).  
    117117 
    118118The surface pressure gradient, also evaluated using a leap-frog scheme, is then simply given by: 
     
    316316\biblio 
    317317 
     318\pindex 
     319 
    318320\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_time_domain.tex

    r10414 r10442  
    2222Having defined the continuous equations in \autoref{chap:PE}, we need now to choose a time discretization, 
    2323a key feature of an ocean model as it exerts a strong influence on the structure of the computer code 
    24 ($i.e.$ on its flowchart). 
     24(\ie on its flowchart). 
    2525In the present chapter, we provide a general description of the \NEMO time stepping strategy and 
    2626the consequences for the order in which the equations are solved. 
     
    6767\citep{Mesinger_Arakawa_Bk76}. 
    6868This scheme is widely used for advection processes in low-viscosity fluids. 
    69 It is a time centred scheme, $i.e.$ the RHS in \autoref{eq:STP} is evaluated at time step $t$, the now time step. 
     69It is a time centred scheme, \ie the RHS in \autoref{eq:STP} is evaluated at time step $t$, the now time step. 
    7070It may be used for momentum and tracer advection, pressure gradient, and Coriolis terms, 
    7171but not for diffusion terms. 
     
    229229 
    230230In a classical LF-RA environment, the forcing term is centred in time, 
    231 $i.e.$ it is time-stepped over a $2\rdt$ period: 
     231\ie it is time-stepped over a $2\rdt$ period: 
    232232$x^t  = x^t + 2\rdt Q^t $ where $Q$ is the forcing applied to $x$, 
    233233and the time filter is given by \autoref{eq:STP_asselin} so that $Q$ is redistributed over several time step. 
     
    296296  x^1 = x^0 + \rdt \ \text{RHS}^0 
    297297\] 
    298 This is done simply by keeping the leapfrog environment ($i.e.$ the \autoref{eq:STP} three level time stepping) but 
     298This is done simply by keeping the leapfrog environment (\ie the \autoref{eq:STP} three level time stepping) but 
    299299setting all $x^0$ (\textit{before}) and $x^{1}$ (\textit{now}) fields equal at the first time step and 
    300300using half the value of $\rdt$. 
     
    408408\biblio 
    409409 
     410\pindex 
     411 
    410412\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/foreword.tex

    r10414 r10442  
    5959\biblio 
    6060 
     61\pindex 
     62 
    6163\end{document} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/introduction.tex

    r10414 r10442  
    2828 
    2929This manual is organised in as follows. 
    30 \autoref{chap:PE} presents the model basics, $i.e.$ the equations and their assumptions, 
     30\autoref{chap:PE} presents the model basics, \ie the equations and their assumptions, 
    3131the vertical coordinates used, and the subgrid scale physics. 
    3232This part deals with the continuous equations of the model 
    3333(primitive equations, with temperature, salinity and an equation of seawater). 
    3434The equations are written in a curvilinear coordinate system, with a choice of vertical coordinates 
    35 ($z$, $s$, \textit{z*}, \textit{s*}, $\tilde{z}$, $\tilde{s}$, and a mixture of them). 
     35($z$, $s$, \zstar, \sstar, \ztilde, \stilde, and a mixture of them). 
    3636Momentum equations are formulated in vector invariant or flux form. 
    3737Dimensional units in the meter, kilogram, second (MKS) international system are used throughout. 
     
    4848linear free surface (level position are then fixed in time). 
    4949In non-linear free surface, 
    50 the corresponding rescaled height coordinate formulation (\textit{z*} or \textit{s*}) is used 
     50the corresponding rescaled height coordinate formulation (\zstar or \sstar) is used 
    5151(the level position then vary in time as a function of the sea surface heigh). 
    5252The following two chapters (\autoref{chap:TRA} and \autoref{chap:DYN}) describe the discretisation of 
     
    6464Interactive coupling to Atmospheric models is possible via the OASIS coupler \citep{OASIS2006}. 
    6565Two-way nesting is also available through an interface to the AGRIF package 
    66 (Adaptative Grid Refinement in \textsc{Fortran}) \citep{Debreu_al_CG2008}. 
     66(Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008}. 
    6767The interface code for coupling to an alternative sea ice model (CICE, \citet{Hunke2008}) has now been upgraded so 
    6868that it works for both global and regional domains, although AGRIF is still not available. 
     
    8989 
    9090\noindent \index{CPP keys} CPP keys \newline 
    91 Some CPP keys are implemented in the FORTRAN code to allow code selection at compiling step. 
     91Some CPP keys are implemented in the \fortran code to allow code selection at compiling step. 
    9292This selection of code at compilation time reduces the reliability of the whole platform since 
    9393it changes the code from one set of CPP keys to the other. 
     
    9696\begin{forlines} 
    9797#if defined key_option1 
    98    ! This part of the FORTRAN code will be active 
     98   ! This part of the \fortran code will be active 
    9999   ! only if key_option1 is activated at compiling step 
    100100#endif 
     
    106106There is one namelist file for each component of NEMO (dynamics, sea-ice, biogeochemistry...) 
    107107containing all the FOTRAN namelists needed. 
    108 The implementation in NEMO uses a two step process. For each FORTRAN namelist, two files are read: 
     108The implementation in NEMO uses a two step process. For each \fortran namelist, two files are read: 
    109109\begin{enumerate} 
    110110\item 
     
    135135(water column model, ORCA and GYRE families of configurations). 
    136136 
    137 The model is implemented in \textsc{Fortran 90}, with preprocessing (C-pre-processor). 
     137The model is implemented in \fninety, with preprocessing (C-pre-processor). 
    138138It runs under UNIX. 
    139139It is optimized for vector computers and parallelised by domain decomposition with MPI. 
     
    146146 
    147147The model is organized with a high internal modularity based on physics. 
    148 For example, each trend ($i.e.$, a term in the RHS of the prognostic equation) for momentum and tracers 
     148For example, each trend (\ie, a term in the RHS of the prognostic equation) for momentum and tracers 
    149149is computed in a dedicated module. 
    150150To make it easier for the user to find his way around the code, the module names follow a three-letter rule. 
     
    193193\begin{enumerate} 
    194194\item 
    195   transition to full native \textsc{Fortran} 90, deep code restructuring and drastic reduction of CPP keys;  
     195  transition to full native \fninety, deep code restructuring and drastic reduction of CPP keys;  
    196196\item 
    197197  introduction of partial step representation of bottom topography 
     
    208208  and suppression of the rigid-lid option; 
    209209\item 
    210   non linear free surface associated with the rescaled height coordinate \textit{z*} or \textit{s}; 
     210  non linear free surface associated with the rescaled height coordinate \zstar or \textit{s}; 
    211211\item 
    212212  additional schemes for vector and flux forms of the momentum advection; 
     
    214214  additional advection schemes for tracers; 
    215215\item 
    216   implementation of the AGRIF package (Adaptative Grid Refinement in \textsc{Fortran}) \citep{Debreu_al_CG2008}; 
     216  implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008}; 
    217217\item 
    218218  online diagnostics : tracers trend in the mixed layer and vorticity balance; 
     
    319319\biblio 
    320320 
     321\pindex 
     322 
    321323\end{document} 
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