Changeset 11263


Ignore:
Timestamp:
2019-07-12T12:47:53+02:00 (13 months ago)
Author:
smasson
Message:

dev_r10984_HPC-13 : merge with trunk@11242, see #2285

Location:
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization
Files:
7 deleted
58 edited
47 copied

Legend:

Unmodified
Added
Removed
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/cfgs/AGRIF_DEMO/EXPREF/1_namelist_cfg

    r10075 r11263  
    2222   cn_exp      = "Pacific" !  experience name 
    2323   nn_it000    =       1   !  first time step 
    24    nn_itend    =      75   !  last  time step (std 5475) 
     24   nn_itend    =      80   !  last  time step (std 5475) 
    2525   nn_istate   =       0   !  output the initial state (1) or not (0) 
    2626/ 
     
    3030   ln_linssh   = .false.   !  =T  linear free surface  ==>>  model level are fixed in time 
    3131   ! 
    32    rn_rdt      = 5760.     !  time step for the dynamics and tracer 
     32   rn_rdt      = 5400.     !  time step for the dynamics and tracer 
    3333/ 
    3434!----------------------------------------------------------------------- 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/cfgs/AGRIF_DEMO/EXPREF/2_namelist_cfg

    r10072 r11263  
    2222   cn_exp      = "Nordic"  !  experience name  
    2323   nn_it000    =    1      !  first time step 
    24    nn_itend    =  300      !  last  time step 
     24   nn_itend    =  320      !  last  time step 
    2525   nn_istate   =      0    !  output the initial state (1) or not (0) 
    2626   ln_clobber  = .true.    !  clobber (overwrite) an existing file 
     
    3131   ln_linssh   = .false.   !  =T  linear free surface  ==>>  model level are fixed in time 
    3232   ! 
    33    rn_rdt      = 1440.     !  time step for the dynamics (and tracer if nn_acc=0) 
     33   rn_rdt      = 1350.     !  time step for the dynamics (and tracer if nn_acc=0) 
    3434/ 
    3535!----------------------------------------------------------------------- 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/cfgs/AGRIF_DEMO/EXPREF/3_namelist_cfg

    r10072 r11263  
    2222   cn_exp      = "Nordic"  !  experience name  
    2323   nn_it000    =    1      !  first time step 
    24    nn_itend    =  900      !  last  time step 
     24   nn_itend    =  960      !  last  time step 
    2525   nn_istate   =      0    !  output the initial state (1) or not (0) 
    2626   ln_clobber  = .true.    !  clobber (overwrite) an existing file 
     
    3131   ln_linssh   = .false.   !  =T  linear free surface  ==>>  model level are fixed in time 
    3232   ! 
    33    rn_rdt      = 480.     !  time step for the dynamics (and tracer if nn_acc=0) 
     33   rn_rdt      = 450.     !  time step for the dynamics (and tracer if nn_acc=0) 
    3434/ 
    3535!----------------------------------------------------------------------- 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/cfgs/AGRIF_DEMO/EXPREF/namelist_cfg

    r10075 r11263  
    2222   cn_exp      =  "ORCA2"  !  experience name 
    2323   nn_it000    =       1   !  first time step 
    24    nn_itend    =      75   !  last  time step (std 5475) 
     24   nn_itend    =      80   !  last  time step (std 5475) 
    2525   nn_istate   =       0   !  output the initial state (1) or not (0) 
    2626/ 
     
    3030   ln_linssh   = .false.   !  =T  linear free surface  ==>>  model level are fixed in time 
    3131   ! 
    32    rn_rdt      = 5760.     !  time step for the dynamics and tracer 
     32   rn_rdt      = 5400.     !  time step for the dynamics and tracer 
    3333/ 
    3434!----------------------------------------------------------------------- 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/cfgs/ORCA2_ICE_PISCES/EXPREF/namelist_cfg

    r10190 r11263  
    2222   cn_exp      =  "ORCA2"  !  experience name 
    2323   nn_it000    =       1   !  first time step 
    24    nn_itend    =    5475   !  last  time step (std 5475) 
     24   nn_itend    =    5840   !  last  time step (std 5475) 
    2525   nn_istate   =       0   !  output the initial state (1) or not (0) 
    2626/ 
     
    2828&namdom        !   time and space domain 
    2929!----------------------------------------------------------------------- 
    30    rn_rdt      = 5760.     !  time step for the dynamics and tracer 
     30   rn_rdt      = 5400.     !  time step for the dynamics and tracer 
    3131/ 
    3232!----------------------------------------------------------------------- 
     
    7575&namsbc        !   Surface Boundary Condition manager                   (default: NO selection) 
    7676!----------------------------------------------------------------------- 
    77    nn_fsbc     = 3         !  frequency of SBC module call 
     77   nn_fsbc     = 4         !  frequency of SBC module call 
    7878                           !     (also = the frequency of sea-ice & iceberg model call) 
    7979                     ! Type of air-sea fluxes  
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/cfgs/SPITZ12/EXPREF/namelist_ice_cfg

    r10911 r11263  
    102102&namdia         !   Diagnostics 
    103103!------------------------------------------------------------------------------ 
     104   ln_icediachk     = .true.         !  check online the heat, mass & salt budgets (T) or not (F) 
    104105/ 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc

    • Property svn:ignore deleted
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex

    • Property svn:ignore
      •  

        old new  
        1 *.aux 
        2 *.bbl 
        3 *.blg 
        4 *.dvi 
        5 *.fdb* 
        6 *.fls 
        7 *.idx 
        8 *.ilg 
        9 *.ind 
        10 *.log 
        11 *.maf 
        12 *.mtc* 
        13 *.out 
        14 *.pdf 
        15 *.toc 
        16 _minted-* 
         1figures 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/DEPS

    r11042 r11263  
    2323helvetic 
    2424hyperref 
    25 idxlayout 
    2625ifplatform 
     26imakeidx 
     27koma-script 
    2728latex 
     29latexconfig 
    2830latex-bin 
    29 latexconfig 
    3031latex-fonts 
    3132latexmk 
     
    3940oberdiek 
    4041parskip 
     42preview 
    4143psnfss 
    4244subfiles 
     
    4446times 
    4547titlesec 
     48titling 
    4649tools 
    4750upquote 
     
    5053wrapfig 
    5154xcolor 
     55xkeyval 
    5256xstring 
    5357zapfchan 
     58 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/HTML_latex2html.sh

    r10146 r11263  
    11#!/bin/bash 
    22 
    3 ./inc/clean.sh 
    4 ./inc/build.sh 
     3#./inc/clean.sh 
     4#./inc/build.sh 
    55 
    6 cd tex_main 
    7 sed -i -e 's#\\documentclass#%\\documentclass#' -e '/{document}/ s/^/%/' \ 
    8    ../tex_sub/*.tex 
    9 sed -i    's#\\subfile{#\\include{#g' \ 
    10    NEMO_manual.tex 
    11 latex2html -local_icons -no_footnode -split 4 -link 2 -mkdir -dir ../html_LaTeX2HTML   \ 
    12             $*                                                                         \ 
    13    NEMO_manual 
    14 sed -i -e 's#%\\documentclass#\\documentclass#' -e '/{document}/ s/^%//' \ 
    15    ../tex_sub/*.tex 
    16 sed -i    's#\\include{#\\subfile{#g' \ 
    17    NEMO_manual.tex 
     6sed -i -e 's#utf8#latin1#'                                 \ 
     7       -e 's#\[outputdir=../build\]{minted}#\[\]{minted}#' \ 
     8       -e '/graphicspath/ s#{../#{../../#g'                \ 
     9          global/packages.tex 
     10 
     11cd ./NEMO/main 
     12sed -i -e 's#\\documentclass#%\\documentclass#' -e '/{document}/ s#^#%#'   ../subfiles/*.tex 
     13sed -i    's#\\subfile{#\\input{#'                                         chapters.tex appendices.tex 
     14 
     15#latex2html                                   -noimages -local_icons -no_footnode -split 4 -link 2 -dir ../html_LaTeX2HTML $* NEMO_manual 
     16latex2html -debug -noreuse -init_file ../../l2hconf.pm -local_icons                               -dir ../build/html               NEMO_manual 
     17 
     18sed -i -e 's#%\\documentclass#\\documentclass#' -e '/{document}/ s#^%##'   ../subfiles/*.tex 
     19sed -i    's#\\input{#\\subfile{#'                                         chapters.tex appendices.tex 
    1820cd - 
    1921 
     22sed -i -e 's#latin1#utf8#'                                 \ 
     23       -e 's#\[\]{minted}#\[outputdir=../build\]{minted}#' \ 
     24       -e '/graphicspath/ s#{../../#{../#g'                \ 
     25     global/packages.tex 
     26 
    2027exit 0 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO

    • Property svn:ignore deleted
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/main

    • Property svn:ignore
      •  

        old new  
        1 *.aux 
        2 *.bbl 
        3 *.blg 
        4 *.dvi 
        5 *.fdb* 
        6 *.fls 
        7 *.idx 
        81*.ilg 
        92*.ind 
        10 *.log 
        11 *.maf 
        12 *.mtc* 
        13 *.out 
        14 *.pdf 
        15 *.toc 
        16 _minted-* 
    • Property svn:externals set to
      ^/utils/dev/bibtool.rsc bibtool.rsc
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_A.tex

    r10442 r11263  
    7979    { 
    8080    \begin{array}{*{20}l} 
    81       \nabla \cdot {\rm {\bf U}} 
     81      \nabla \cdot {\mathrm {\mathbf U}} 
    8282      &= \frac{1}{e_1 \,e_2 }  \left[ \left. {\frac{\partial (e_2 \,u)}{\partial i}} \right|_z 
    8383        +\left. {\frac{\partial(e_1 \,v)}{\partial j}} \right|_z  \right] 
     
    115115      $, it becomes:} 
    116116    % 
    117       \nabla \cdot {\rm {\bf U}} 
     117      \nabla \cdot {\mathrm {\mathbf U}} 
    118118      & = \frac{1}{e_1 \,e_2 \,e_3 }  \left[ 
    119119        \left.  \frac{\partial (e_2 \,e_3 \,u)}{\partial i} \right|_s 
     
    144144    { 
    145145    \begin{array}{*{20}l} 
    146       \nabla \cdot {\rm {\bf U}} 
     146      \nabla \cdot {\mathrm {\mathbf U}} 
    147147      &= \frac{1}{e_1 \,e_2 \,e_3 }    \left[ 
    148148        \left.  \frac{\partial (e_2 \,e_3 \,u)}{\partial i} \right|_s 
     
    346346  % 
    347347    &= \left. {\frac{\partial u }{\partial t}} \right|_s 
    348     &+ \left.  \nabla \cdot \left(   {{\rm {\bf U}}\,u}   \right)    \right|_s 
     348    &+ \left.  \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,u}   \right)    \right|_s 
    349349      + \,u \frac{1}{e_3 } \frac{\partial e_3}{\partial t} 
    350350      - \frac{v}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i} 
     
    359359  \label{apdx:A_sco_Dt_flux} 
    360360  \left. \frac{D u}{D t} \right|_s   = \frac{1}{e_3}  \left. \frac{\partial ( e_3\,u)}{\partial t} \right|_s 
    361   + \left.  \nabla \cdot \left(   {{\rm {\bf U}}\,u}   \right)    \right|_s 
     361  + \left.  \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,u}   \right)    \right|_s 
    362362  - \frac{v}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i} 
    363363    -u  \;\frac{\partial e_1 }{\partial j}            \right) 
     
    399399 
    400400As in $z$-coordinate, 
    401 the horizontal pressure gradient can be split in two parts following \citet{Marsaleix_al_OM08}. 
     401the horizontal pressure gradient can be split in two parts following \citet{marsaleix.auclair.ea_OM08}. 
    402402Let defined a density anomaly, $d$, by $d=(\rho - \rho_o)/ \rho_o$, 
    403403and a hydrostatic pressure anomaly, $p_h'$, by $p_h'= g \; \int_z^\eta d \; e_3 \; dk$. 
     
    483483    \label{apdx:A_PE_dyn_flux_u} 
    484484    \frac{1}{e_3} \frac{\partial \left(  e_3\,u  \right) }{\partial t} = 
    485     \nabla \cdot \left(   {{\rm {\bf U}}\,u}   \right) 
     485    \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,u}   \right) 
    486486    +   \left\{ {f + \frac{1}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i} 
    487487          -u  \;\frac{\partial e_1 }{\partial j}            \right)} \right\} \,v     \\ 
     
    493493    \label{apdx:A_dyn_flux_v} 
    494494    \frac{1}{e_3}\frac{\partial \left(  e_3\,v  \right) }{\partial t}= 
    495     -  \nabla \cdot \left(   {{\rm {\bf U}}\,v}   \right) 
     495    -  \nabla \cdot \left(   {{\mathrm {\mathbf U}}\,v}   \right) 
    496496    +   \left\{ {f + \frac{1}{e_1 e_2 }\left(    v  \;\frac{\partial e_2 }{\partial i} 
    497497          -u  \;\frac{\partial e_1 }{\partial j}            \right)} \right\} \,u     \\ 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_B.tex

    r10442 r11263  
    162162the ($i$,$j$,$k$) curvilinear coordinate system in which 
    163163the equations of the ocean circulation model are formulated, 
    164 takes the following form \citep{Redi_JPO82}: 
     164takes the following form \citep{redi_JPO82}: 
    165165 
    166166\begin{equation} 
     
    184184 
    185185In practice, isopycnal slopes are generally less than $10^{-2}$ in the ocean, 
    186 so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{Cox1987}: 
     186so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{cox_OM87}: 
    187187\begin{subequations} 
    188188  \label{apdx:B4} 
     
    236236  { 
    237237  \begin{array}{*{20}l} 
    238     \nabla T\;.\left( {{\rm {\bf A}}_{\rm {\bf I}} \nabla T} 
     238    \nabla T\;.\left( {{\mathrm {\mathbf A}}_{\mathrm {\mathbf I}} \nabla T} 
    239239    \right)&=A^{lT}\left[ {\left( {\frac{\partial T}{\partial i}} \right)^2-2a_1 
    240240             \frac{\partial T}{\partial i}\frac{\partial T}{\partial k}+\left( 
     
    379379  - \nabla _h \times \left( {A^{lm}\;\zeta \;{\textbf{k}}} \right) 
    380380  + \frac{1}{e_3 }\frac{\partial }{\partial k}\left( {\frac{A^{vm}\;}{e_3 } 
    381       \frac{\partial {\rm {\bf U}}_h }{\partial k}} \right) \\ 
     381      \frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}} \right) \\ 
    382382\end{equation} 
    383383that is, in expanded form: 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_D.tex

    r10442 r11263  
    3232 
    3333To satisfy part of these aims, \NEMO is written with a coding standard which is close to the ECMWF rules, 
    34 named DOCTOR \citep{Gibson_TR86}.  
     34named DOCTOR \citep{gibson_rpt86}.  
    3535These rules present some advantages like: 
    3636 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_E.tex

    r10442 r11263  
    4949 
    5050This results in a dissipatively dominant (\ie hyper-diffusive) truncation error 
    51 \citep{Shchepetkin_McWilliams_OM05}. 
    52 The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}. 
     51\citep{shchepetkin.mcwilliams_OM05}. 
     52The overall performance of the advection scheme is similar to that reported in \cite{farrow.stevens_JPO95}. 
    5353It is a relatively good compromise between accuracy and smoothness. 
    5454It is not a \emph{positive} scheme meaning false extrema are permitted but 
     
    6565the second term which is the diffusive part of the scheme, is evaluated using the \textit{before} velocity 
    6666(forward in time). 
    67 This is discussed by \citet{Webb_al_JAOT98} in the context of the Quick advection scheme. 
     67This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme. 
    6868UBS and QUICK schemes only differ by one coefficient. 
    69 Substituting 1/6 with 1/8 in (\autoref{eq:tra_adv_ubs}) leads to the QUICK advection scheme \citep{Webb_al_JAOT98}. 
     69Substituting 1/6 with 1/8 in (\autoref{eq:tra_adv_ubs}) leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 
    7070This option is not available through a namelist parameter, since the 1/6 coefficient is hard coded. 
    7171Nevertheless it is quite easy to make the substitution in \mdl{traadv\_ubs} module and obtain a QUICK scheme. 
     
    8080$\tau_w^{ubs}$ will be evaluated using either \textit{(a)} a centered $2^{nd}$ order scheme, 
    8181or \textit{(b)} a TVD scheme, or \textit{(c)} an interpolation based on conservative parabolic splines following 
    82 \citet{Shchepetkin_McWilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS. 
     82\citet{shchepetkin.mcwilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS. 
    8383The $3^{rd}$ case has dispersion properties similar to an eight-order accurate conventional scheme. 
    8484 
     
    255255\subsection{Griffies iso-neutral diffusion operator} 
    256256 
    257 Let try to define a scheme that get its inspiration from the \citet{Griffies_al_JPO98} scheme, 
     257Let try to define a scheme that get its inspiration from the \citet{griffies.gnanadesikan.ea_JPO98} scheme, 
    258258but is formulated within the \NEMO framework 
    259259(\ie using scale factors rather than grid-size and having a position of $T$-points that 
     
    272272Nevertheless, this technique works fine for $T$ and $S$ as they are active tracers 
    273273(\ie they enter the computation of density), but it does not work for a passive tracer. 
    274 \citep{Griffies_al_JPO98} introduce a different way to discretise the off-diagonal terms that 
     274\citep{griffies.gnanadesikan.ea_JPO98} introduce a different way to discretise the off-diagonal terms that 
    275275nicely solve the problem. 
    276276The idea is to get rid of combinations of an averaged in one direction combined with 
     
    308308\begin{figure}[!ht] 
    309309  \begin{center} 
    310     \includegraphics[width=0.70\textwidth]{Fig_ISO_triad} 
     310    \includegraphics[width=\textwidth]{Fig_ISO_triad} 
    311311    \caption{ 
    312312      \protect\label{fig:ISO_triad} 
     
    508508\] 
    509509 
    510 \citep{Griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form. 
     510\citep{griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form. 
    511511It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. 
    512512For example in the (\textbf{i},\textbf{k}) plane, the tracer advective fluxes can be transformed as follows: 
     
    574574The horizontal component reduces to the one use for an horizontal laplacian operator and 
    575575the vertical one keeps the same complexity, but not more. 
    576 This property has been used to reduce the computational time \citep{Griffies_JPO98}, 
     576This property has been used to reduce the computational time \citep{griffies_JPO98}, 
    577577but it is not of practical use as usually $A \neq A_e$. 
    578578Nevertheless this property can be used to choose a discret form of \autoref{eq:eiv_skew_continuous} which 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_iso.tex

    r10442 r11263  
    44\newcommand{\rML}[1][i]{\ensuremath{_{\mathrm{ML}\,#1}}} 
    55\newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}} 
    6 \newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}} 
     6%% Move to ../../global/new_cmds.tex to avoid error with \listoffigures 
     7%\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}} 
    78\newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}} 
    89\newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}} 
     
    5253  the vertical skew flux is further reduced to ensure no vertical buoyancy flux, 
    5354  giving an almost pure horizontal diffusive tracer flux within the mixed layer. 
    54   This is similar to the tapering suggested by \citet{Gerdes1991}. See \autoref{subsec:Gerdes-taper} 
     55  This is similar to the tapering suggested by \citet{gerdes.koberle.ea_CD91}. See \autoref{subsec:Gerdes-taper} 
    5556\item[\np{ln\_botmix\_triad}] 
    5657  See \autoref{sec:iso_bdry}.  
     
    7172\label{sec:iso} 
    7273 
    73 We have implemented into \NEMO a scheme inspired by \citet{Griffies_al_JPO98}, 
     74We have implemented into \NEMO a scheme inspired by \citet{griffies.gnanadesikan.ea_JPO98}, 
    7475but formulated within the \NEMO framework, using scale factors rather than grid-sizes. 
    7576 
     
    194195\subsection{Expression of the skew-flux in terms of triad slopes} 
    195196 
    196 \citep{Griffies_al_JPO98} introduce a different discretization of the off-diagonal terms that 
     197\citep{griffies.gnanadesikan.ea_JPO98} introduce a different discretization of the off-diagonal terms that 
    197198nicely solves the problem. 
    198199% Instead of multiplying the mean slope calculated at the $u$-point by 
     
    201202\begin{figure}[tb] 
    202203  \begin{center} 
    203     \includegraphics[width=1.05\textwidth]{Fig_GRIFF_triad_fluxes} 
     204    \includegraphics[width=\textwidth]{Fig_GRIFF_triad_fluxes} 
    204205    \caption{ 
    205206      \protect\label{fig:ISO_triad} 
     
    265266\begin{figure}[tb] 
    266267  \begin{center} 
    267     \includegraphics[width=0.80\textwidth]{Fig_GRIFF_qcells} 
     268    \includegraphics[width=\textwidth]{Fig_GRIFF_qcells} 
    268269    \caption{ 
    269270      \protect\label{fig:qcells} 
     
    473474 
    474475To complete the discretization we now need only specify the triad volumes $_i^k\mathbb{V}_{i_p}^{k_p}$. 
    475 \citet{Griffies_al_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells, 
     476\citet{griffies.gnanadesikan.ea_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells, 
    476477defined in terms of the distances between $T$, $u$,$f$ and $w$-points. 
    477478This is the natural discretization of \autoref{eq:cts-var}. 
     
    658659\begin{figure}[h] 
    659660  \begin{center} 
    660     \includegraphics[width=0.60\textwidth]{Fig_GRIFF_bdry_triads} 
     661    \includegraphics[width=\textwidth]{Fig_GRIFF_bdry_triads} 
    661662    \caption{ 
    662663      \protect\label{fig:bdry_triads} 
     
    685686As discussed in \autoref{subsec:LDF_slp_iso}, 
    686687iso-neutral slopes relative to geopotentials must be bounded everywhere, 
    687 both for consistency with the small-slope approximation and for numerical stability \citep{Cox1987, Griffies_Bk04}. 
     688both for consistency with the small-slope approximation and for numerical stability \citep{cox_OM87, griffies_bk04}. 
    688689The bound chosen in \NEMO is applied to each component of the slope separately and 
    689690has a value of $1/100$ in the ocean interior. 
     
    732733\[ 
    733734  % \label{eq:iso_tensor_ML} 
    734   D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 
     735  D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 
    735736  \mbox{with}\quad \;\;\Re =\left( {{ 
    736737        \begin{array}{*{20}c} 
     
    829830    (\eg the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.} 
    830831  % } 
    831   \includegraphics[width=0.60\textwidth]{Fig_GRIFF_MLB_triads} 
     832  \includegraphics[width=\textwidth]{Fig_GRIFF_MLB_triads} 
    832833\end{figure} 
    833834% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    847848\[ 
    848849  % \label{eq:iso_tensor_ML2} 
    849   D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 
     850  D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 
    850851  \mbox{with}\quad \;\;\Re =\left( {{ 
    851852        \begin{array}{*{20}c} 
     
    859860\footnote{ 
    860861  To ensure good behaviour where horizontal density gradients are weak, 
    861   we in fact follow \citet{Gerdes1991} and 
     862  we in fact follow \citet{gerdes.koberle.ea_CD91} and 
    862863  set $\rML^*=\mathrm{sgn}(\tilde{r}_i)\min(|\rMLt^2/\tilde{r}_i|,|\tilde{r}_i|)-\sigma_i$. 
    863864} 
     
    865866This approach is similar to multiplying the iso-neutral diffusion coefficient by 
    866867$\tilde{r}_{\mathrm{max}}^{-2}\tilde{r}_i^{-2}$ for steep slopes, 
    867 as suggested by \citet{Gerdes1991} (see also \citet{Griffies_Bk04}). 
     868as suggested by \citet{gerdes.koberle.ea_CD91} (see also \citet{griffies_bk04}). 
    868869Again it is applied separately to each triad $_i^k\mathbb{R}_{i_p}^{k_p}$ 
    869870 
     
    925926 
    926927However, when \np{ln\_traldf\_triad} is set true, 
    927 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{Griffies_JPO98}. 
     928\NEMO instead implements eddy induced advection according to the so-called skew form \citep{griffies_JPO98}. 
    928929It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. 
    929930For example in the (\textbf{i},\textbf{k}) plane, 
     
    11391140it is equivalent to a horizontal eiv (eddy-induced velocity) that is uniform within the mixed layer 
    11401141\autoref{eq:eiv_v}. 
    1141 This ensures that the eiv velocities do not restratify the mixed layer \citep{Treguier1997,Danabasoglu_al_2008}. 
     1142This ensures that the eiv velocities do not restratify the mixed layer \citep{treguier.held.ea_JPO97,danabasoglu.ferrari.ea_JC08}. 
    11421143Equivantly, in terms of the skew-flux formulation we use here, 
    11431144the linear slope tapering within the mixed-layer gives a linearly varying vertical flux, 
     
    11531154$uw$ (integer +1/2 $i$, integer $j$, integer +1/2 $k$) and $vw$ (integer $i$, integer +1/2 $j$, integer +1/2 $k$) 
    11541155points (see Table \autoref{tab:cell}) respectively. 
    1155 We follow \citep{Griffies_Bk04} and calculate the streamfunction at a given $uw$-point from 
     1156We follow \citep{griffies_bk04} and calculate the streamfunction at a given $uw$-point from 
    11561157the surrounding four triads according to: 
    11571158\[ 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_ASM.tex

    r10442 r11263  
    3737it may be preferable to introduce the increment gradually into the ocean model in order to 
    3838minimize spurious adjustment processes. 
    39 This technique is referred to as Incremental Analysis Updates (IAU) \citep{Bloom_al_MWR96}. 
     39This technique is referred to as Incremental Analysis Updates (IAU) \citep{bloom.takacs.ea_MWR96}. 
    4040IAU is a common technique used with 3D assimilation methods such as 3D-Var or OI. 
    4141IAU is used when \np{ln\_asmiau} is set to true. 
    4242 
    43 With IAU, the model state trajectory ${\bf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$) 
     43With IAU, the model state trajectory ${\mathbf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$) 
    4444is corrected by adding the analysis increments for temperature, salinity, horizontal velocity and SSH as 
    4545additional tendency terms to the prognostic equations: 
    4646\begin{align*} 
    4747  % \label{eq:wa_traj_iau} 
    48   {\bf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\bf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\bf x}^{a} 
     48  {\mathbf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\mathbf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\mathbf x}^{a} 
    4949\end{align*} 
    50 where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\bf x}^{a}$ defined such that 
     50where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\mathbf x}^{a}$ defined such that 
    5151$\sum_{i=1}^{N} F_{i}=1$. 
    52 ${\bf x}^b$ denotes the model initial state and ${\bf x}^a$ is the model state after the increments are applied. 
     52${\mathbf x}^b$ denotes the model initial state and ${\mathbf x}^a$ is the model state after the increments are applied. 
    5353To control the adjustment time of the model to the increment, 
    5454the increment can be applied over an arbitrary sub-window, $t_{m} \leq t_{i} \leq t_{n}$, 
     
    6262  =\left\{ 
    6363  \begin{array}{ll} 
    64     0     &    {\rm if} \; \; \; t_{i} < t_{m}                \\ 
    65     1/M &    {\rm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\ 
    66     0     &    {\rm if} \; \; \; t_{i} > t_{n} 
     64    0     &    {\mathrm if} \; \; \; t_{i} < t_{m}                \\ 
     65    1/M &    {\mathrm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\ 
     66    0     &    {\mathrm if} \; \; \; t_{i} > t_{n} 
    6767  \end{array} 
    6868            \right.  
     
    7676  =\left\{ 
    7777  \begin{array}{ll} 
    78     0                           &    {\rm if} \; \; \; t_{i}       <     t_{m}                        \\ 
    79     \alpha \, i               &    {\rm if} \; \; \; t_{m}    \leq t_{i}    \leq   t_{M/2}   \\ 
    80     \alpha \, (M - i +1) &    {\rm if} \; \; \; t_{M/2}  <    t_{i}    \leq   t_{n}       \\ 
    81     0                            &   {\rm if} \; \; \; t_{i}        >    t_{n} 
     78    0                           &    {\mathrm if} \; \; \; t_{i}       <     t_{m}                        \\ 
     79    \alpha \, i               &    {\mathrm if} \; \; \; t_{m}    \leq t_{i}    \leq   t_{M/2}   \\ 
     80    \alpha \, (M - i +1) &    {\mathrm if} \; \; \; t_{M/2}  <    t_{i}    \leq   t_{n}       \\ 
     81    0                            &   {\mathrm if} \; \; \; t_{i}        >    t_{n} 
    8282  \end{array} 
    8383                                   \right. 
     
    118118This type of the initialisation reduces the vertical velocity magnitude and 
    119119alleviates the problem of the excessive unphysical vertical mixing in the first steps of the model integration 
    120 \citep{Talagrand_JAS72, Dobricic_al_OS07}. 
     120\citep{talagrand_JAS72, dobricic.pinardi.ea_OS07}. 
    121121Diffusion coefficients are defined as $A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. 
    122122The divergence damping is activated by assigning to \np{nn\_divdmp} in the \textit{nam\_asminc} namelist 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_CONFIG.tex

    r10442 r11263  
    1818\label{sec:CFG_intro} 
    1919 
    20 The purpose of this part of the manual is to introduce the \NEMO reference configurations. 
     20The purpose of this part of the manual is to introduce the NEMO reference configurations. 
    2121These configurations are offered as means to explore various numerical and physical options, 
    2222thus allowing the user to verify that the code is performing in a manner consistent with that we are running. 
     
    2424The reference configurations also provide a sense for some of the options available in the code, 
    2525though by no means are all options exercised in the reference configurations. 
     26Configuration is defined manually through the \textit{namcfg} namelist variables. 
    2627 
    2728%------------------------------------------namcfg---------------------------------------------------- 
     
    3334% 1D model configuration 
    3435% ================================================================ 
    35 \section{C1D: 1D Water column model (\protect\key{c1d}) } 
     36\section[C1D: 1D Water column model (\texttt{\textbf{key\_c1d}})] 
     37{C1D: 1D Water column model (\protect\key{c1d})} 
    3638\label{sec:CFG_c1d} 
    3739 
    38 BE careful: to be re-written according to suppression of jpizoom and jpjzoom !!!! 
    39  
    40 The 1D model option simulates a stand alone water column within the 3D \NEMO system. 
     40The 1D model option simulates a stand alone water column within the 3D NEMO system. 
    4141It can be applied to the ocean alone or to the ocean-ice system and can include passive tracers or a biogeochemical model. 
    4242It is set up by defining the position of the 1D water column in the grid 
    43 (see \textit{CONFIG/SHARED/namelist\_ref} ).  
     43(see \textit{cfgs/SHARED/namelist\_ref}).  
    4444The 1D model is a very useful tool 
    4545\textit{(a)} to learn about the physics and numerical treatment of vertical mixing processes; 
     
    5050\textit{(d)} to produce extra diagnostics, without the large memory requirement of the full 3D model. 
    5151 
    52 The methodology is based on the use of the zoom functionality over the smallest possible domain: 
    53 a 3x3 domain centered on the grid point of interest, with some extra routines. 
    54 There is no need to define a new mesh, bathymetry, initial state or forcing, 
    55 since the 1D model will use those of the configuration it is a zoom of. 
    56 The chosen grid point is set in \textit{\ngn{namcfg}} namelist by 
    57 setting the \np{jpizoom} and \np{jpjzoom} parameters to the indices of the location of the chosen grid point. 
     52The methodology is based on the configuration of the smallest possible domain: 
     53a 3x3 domain with 75 vertical levels. 
    5854 
    5955The 1D model has some specifies. First, all the horizontal derivatives are assumed to be zero, 
    6056and second, the two components of the velocity are moved on a $T$-point.  
    61 Therefore, defining \key{c1d} changes five main things in the code behaviour:  
     57Therefore, defining \key{c1d} changes some things in the code behaviour:  
    6258\begin{description} 
    6359\item[(1)] 
    64   the lateral boundary condition routine (\rou{lbc\_lnk}) set the value of the central column of 
    65   the 3x3 domain is imposed over the whole domain; 
    66 \item[(3)] 
    67   a call to \rou{lbc\_lnk} is systematically done when reading input data (\ie in \mdl{iom}); 
    68 \item[(3)] 
    6960  a simplified \rou{stp} routine is used (\rou{stp\_c1d}, see \mdl{step\_c1d} module) in which 
    7061  both lateral tendancy terms and lateral physics are not called; 
    71 \item[(4)] 
     62\item[(2)] 
    7263  the vertical velocity is zero 
    7364  (so far, no attempt at introducing a Ekman pumping velocity has been made); 
    74 \item[(5)] 
     65\item[(3)] 
    7566  a simplified treatment of the Coriolis term is performed as $U$- and $V$-points are the same 
    7667  (see \mdl{dyncor\_c1d}). 
    7768\end{description} 
    78 All the relevant \textit{\_c1d} modules can be found in the NEMOGCM/NEMO/OPA\_SRC/C1D directory of 
    79 the \NEMO distribution. 
     69All the relevant \textit{\_c1d} modules can be found in the src/OCE/C1D directory of 
     70the NEMO distribution. 
    8071 
    8172% to be added:  a test case on the yearlong Ocean Weather Station (OWS) Papa dataset of Martin (1985) 
     
    8879 
    8980The ORCA family is a series of global ocean configurations that are run together with 
    90 the LIM sea-ice model (ORCA-LIM) and possibly with PISCES biogeochemical model (ORCA-LIM-PISCES), 
    91 using various resolutions. 
    92 An appropriate namelist is available in \path{CONFIG/ORCA2_LIM3_PISCES/EXP00/namelist_cfg} for ORCA2. 
     81the SI3 model (ORCA-ICE) and possibly with PISCES biogeochemical model (ORCA-ICE-PISCES). 
     82An appropriate namelist is available in \path{cfgs/ORCA2_ICE_PISCES/EXPREF/namelist_cfg} for ORCA2. 
    9383The domain of ORCA2 configuration is defined in \ifile{ORCA\_R2\_zps\_domcfg} file, 
    94 this file is available in tar file in the wiki of NEMO: \\ 
    95 https://forge.ipsl.jussieu.fr/nemo/wiki/Users/ReferenceConfigurations/ORCA2\_LIM3\_PISCES \\ 
     84this file is available in tar file on the NEMO community zenodo platform: \\ 
     85https://doi.org/10.5281/zenodo.2640723 
     86 
    9687In this namelist\_cfg the name of domain input file is set in \ngn{namcfg} block of namelist.  
    9788 
     
    9990\begin{figure}[!t] 
    10091  \begin{center} 
    101     \includegraphics[width=0.98\textwidth]{Fig_ORCA_NH_mesh} 
     92    \includegraphics[width=\textwidth]{Fig_ORCA_NH_mesh} 
    10293    \caption{ 
    10394      \protect\label{fig:MISC_ORCA_msh} 
     
    10697      The two "north pole" are the foci of a series of embedded ellipses (blue curves) which 
    10798      are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes). 
    108       Then, following \citet{Madec_Imbard_CD96}, the normal to the series of ellipses (red curves) is computed which 
     99      Then, following \citet{madec.imbard_CD96}, the normal to the series of ellipses (red curves) is computed which 
    109100      provides the j-lines of the mesh (pseudo longitudes). 
    110101    } 
     
    119110\label{subsec:CFG_orca_grid} 
    120111 
    121 The ORCA grid is a tripolar is based on the semi-analytical method of \citet{Madec_Imbard_CD96}. 
     112The ORCA grid is a tripolar grid based on the semi-analytical method of \citet{madec.imbard_CD96}. 
    122113It allows to construct a global orthogonal curvilinear ocean mesh which has no singularity point inside 
    123114the computational domain since two north mesh poles are introduced and placed on lands. 
     
    131122\begin{figure}[!tbp] 
    132123  \begin{center} 
    133     \includegraphics[width=1.0\textwidth]{Fig_ORCA_NH_msh05_e1_e2} 
    134     \includegraphics[width=0.80\textwidth]{Fig_ORCA_aniso} 
     124    \includegraphics[width=\textwidth]{Fig_ORCA_NH_msh05_e1_e2} 
     125    \includegraphics[width=\textwidth]{Fig_ORCA_aniso} 
    135126    \caption { 
    136127      \protect\label{fig:MISC_ORCA_e1e2} 
     
    158149 
    159150% ------------------------------------------------------------------------------------------------------------- 
    160 %       ORCA-LIM(-PISCES) configurations 
     151%       ORCA-ICE(-PISCES) configurations 
    161152% ------------------------------------------------------------------------------------------------------------- 
    162153\subsection{ORCA pre-defined resolution} 
     
    199190The ORCA\_R2 configuration has the following specificity: starting from a 2\deg~ORCA mesh, 
    200191local mesh refinements were applied to the Mediterranean, Red, Black and Caspian Seas, 
    201 so that the resolution is 1\deg \time 1\deg there. 
     192so that the resolution is 1\deg~ there. 
    202193A local transformation were also applied with in the Tropics in order to refine the meridional resolution up to 
    203 0.5\deg at the Equator. 
     1940.5\deg~ at the Equator. 
    204195 
    205196The ORCA\_R1 configuration has only a local tropical transformation to refine the meridional resolution up to 
     
    211202For ORCA\_R1 and R025, setting the configuration key to 75 allows to use 75 vertical levels, otherwise 46 are used. 
    212203In 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}). 
    214  
    215 Only the ORCA\_R2 is provided with all its input files in the \NEMO distribution. 
    216 It is very similar to that used as part of the climate model developed at IPSL for the 4th IPCC assessment of 
    217 climate change (Marti et al., 2009). 
    218 It is also the basis for the \NEMO contribution to the Coordinate Ocean-ice Reference Experiments (COREs) 
    219 documented in \citet{Griffies_al_OM09}.  
     204(see \autoref{tab:orca_zgr}). %\sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}). 
     205 
     206Only the ORCA\_R2 is provided with all its input files in the NEMO distribution. 
     207%It is very similar to that used as part of the climate model developed at IPSL for the 4th IPCC assessment of 
     208%climate change (Marti et al., 2009). 
     209%It is also the basis for the \NEMO contribution to the Coordinate Ocean-ice Reference Experiments (COREs) 
     210%documented in \citet{griffies.biastoch.ea_OM09}.  
    220211 
    221212This version of ORCA\_R2 has 31 levels in the vertical, with the highest resolution (10m) in the upper 150m 
    222213(see \autoref{tab:orca_zgr} and \autoref{fig:zgr}).  
    223214The bottom topography and the coastlines are derived from the global atlas of Smith and Sandwell (1997).  
    224 The default forcing uses the boundary forcing from \citet{Large_Yeager_Rep04} (see \autoref{subsec:SBC_blk_core}),  
     215The default forcing uses the boundary forcing from \citet{large.yeager_rpt04} (see \autoref{subsec:SBC_blk_core}),  
    225216which was developed for the purpose of running global coupled ocean-ice simulations without 
    226217an interactive atmosphere. 
    227 This \citet{Large_Yeager_Rep04} dataset is available through 
     218This \citet{large.yeager_rpt04} dataset is available through 
    228219the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. 
    229 The "normal year" of \citet{Large_Yeager_Rep04} has been chosen of the \NEMO distribution since release v3.3.  
    230  
    231 ORCA\_R2 pre-defined configuration can also be run with an AGRIF zoom over the Agulhas current area 
    232 (\key{agrif} defined) and, by setting the appropriate variables, see \path{CONFIG/SHARED/namelist_ref}. 
     220The "normal year" of \citet{large.yeager_rpt04} has been chosen of the NEMO distribution since release v3.3.  
     221 
     222ORCA\_R2 pre-defined configuration can also be run with multiply online nested zooms (\ie with AGRIF, \key{agrif} defined). This is available as the AGRIF\_DEMO configuration that can be found in the \path{cfgs/AGRIF_DEMO/} directory. 
     223 
    233224A regional Arctic or peri-Antarctic configuration is extracted from an ORCA\_R2 or R05 configurations using 
    234225sponge layers at open boundaries.  
     
    237228%       GYRE family: double gyre basin 
    238229% ------------------------------------------------------------------------------------------------------------- 
    239 \section{GYRE family: double gyre basin } 
     230\section{GYRE family: double gyre basin} 
    240231\label{sec:CFG_gyre} 
    241232 
    242 The GYRE configuration \citep{Levy_al_OM10} has been built to 
     233The GYRE configuration \citep{levy.klein.ea_OM10} has been built to 
    243234simulate the seasonal cycle of a double-gyre box model. 
    244 It consists in an idealized domain similar to that used in the studies of \citet{Drijfhout_JPO94} and 
    245 \citet{Hazeleger_Drijfhout_JPO98, Hazeleger_Drijfhout_JPO99, Hazeleger_Drijfhout_JGR00, Hazeleger_Drijfhout_JPO00}, 
     235It consists in an idealized domain similar to that used in the studies of \citet{drijfhout_JPO94} and 
     236\citet{hazeleger.drijfhout_JPO98, hazeleger.drijfhout_JPO99, hazeleger.drijfhout_JGR00, hazeleger.drijfhout_JPO00}, 
    246237over which an analytical seasonal forcing is applied. 
    247238This allows to investigate the spontaneous generation of a large number of interacting, transient mesoscale eddies  
    248239and their contribution to the large scale circulation.  
    249240 
     241The GYRE configuration run together with the PISCES biogeochemical model (GYRE-PISCES). 
    250242The domain geometry is a closed rectangular basin on the $\beta$-plane centred at $\sim$ 30\deg{N} and 
    251243rotated by 45\deg, 3180~km long, 2120~km wide and 4~km deep (\autoref{fig:MISC_strait_hand}). 
     
    253245The configuration is meant to represent an idealized North Atlantic or North Pacific basin. 
    254246The circulation is forced by analytical profiles of wind and buoyancy fluxes. 
    255 The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{Levy_al_OM10}.  
     247The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{levy.klein.ea_OM10}.  
    256248The wind stress is zonal and its curl changes sign at 22\deg{N} and 36\deg{N}. 
    257249It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain and 
     
    266258The GYRE configuration is set like an analytical configuration. 
    267259Through \np{ln\_read\_cfg}\forcode{ = .false.} in \textit{namcfg} namelist defined in 
    268 the reference configuration \path{CONFIG/GYRE/EXP00/namelist_cfg} 
     260the reference configuration \path{cfgs/GYRE_PISCES/EXPREF/namelist_cfg} 
    269261analytical definition of grid in GYRE is done in usrdef\_hrg, usrdef\_zgr routines. 
    270262Its horizontal resolution (and thus the size of the domain) is determined by 
    271263setting \np{nn\_GYRE} in \ngn{namusr\_def}: \\ 
     264 
    272265\np{jpiglo} $= 30 \times$ \np{nn\_GYRE} + 2   \\ 
     266 
    273267\np{jpjglo} $= 20 \times$ \np{nn\_GYRE} + 2   \\ 
     268 
    274269Obviously, the namelist parameters have to be adjusted to the chosen resolution, 
    275 see the Configurations pages on the NEMO web site (Using NEMO\/Configurations). 
     270see the Configurations pages on the NEMO web site (NEMO Configurations). 
    276271In the vertical, GYRE uses the default 30 ocean levels (\jp{jpk}\forcode{ = 31}) (\autoref{fig:zgr}). 
    277272 
     
    281276even though the physical integrity of the solution can be compromised. 
    282277Benchmark is activate via \np{ln\_bench}\forcode{ = .true.} in \ngn{namusr\_def} in 
    283 namelist \path{CONFIG/GYRE/EXP00/namelist_cfg}. 
     278namelist \path{cfgs/GYRE_PISCES/EXPREF/namelist_cfg}. 
    284279 
    285280%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    286281\begin{figure}[!t] 
    287282  \begin{center} 
    288     \includegraphics[width=1.0\textwidth]{Fig_GYRE} 
     283    \includegraphics[width=\textwidth]{Fig_GYRE} 
    289284    \caption{ 
    290285      \protect\label{fig:GYRE} 
    291286      Snapshot of relative vorticity at the surface of the model domain in GYRE R9, R27 and R54. 
    292       From \citet{Levy_al_OM10}. 
     287      From \citet{levy.klein.ea_OM10}. 
    293288    } 
    294289  \end{center} 
     
    304299The AMM, Atlantic Margins Model, is a regional model covering the Northwest European Shelf domain on 
    305300a regular lat-lon grid at approximately 12km horizontal resolution. 
    306 The appropriate \textit{\&namcfg} namelist  is available in \textit{CONFIG/AMM12/EXP00/namelist\_cfg}. 
     301The appropriate \textit{\&namcfg} namelist  is available in \textit{cfgs/AMM12/EXPREF/namelist\_cfg}. 
    307302It is used to build the correct dimensions of the AMM domain. 
    308303 
    309304This configuration tests several features of NEMO functionality specific to the shelf seas. 
    310 In particular, the AMM uses $S$-coordinates in the vertical rather than $z$-coordinates and 
    311 is forced with tidal lateral boundary conditions using a flather boundary condition from the BDY module. 
    312 The AMM configuration uses the GLS (\key{zdfgls}) turbulence scheme, 
    313 the VVL non-linear free surface(\key{vvl}) and time-splitting (\key{dynspg\_ts}). 
     305In particular, the AMM uses $s$-coordinates in the vertical rather than $z$-coordinates and 
     306is forced with tidal lateral boundary conditions using a Flather boundary condition from the BDY module. 
     307Also specific to the AMM configuration is the use of the GLS turbulence scheme (\np{ln\_zdfgls} \forcode{= .true.}). 
    314308 
    315309In addition to the tidal boundary condition the model may also take open boundary conditions from 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DIA.tex

    r10509 r11263  
    2525the same run performed in one step. 
    2626It should be noted that this requires that the restart file contains two consecutive time steps for 
    27 all the prognostic variables, and that it is saved in the same binary format as the one used by the computer that 
    28 is to read it (in particular, 32 bits binary IEEE format must not be used for this file). 
     27all the prognostic variables. 
    2928 
    3029The output listing and file(s) are predefined but should be checked and eventually adapted to the user's needs. 
     
    3837the writing work is distributed over the processors in massively parallel computing. 
    3938A complete description of the use of this I/O server is presented in the next section. 
    40  
    41 By default, \key{iomput} is not defined, 
    42 NEMO produces NetCDF with the old IOIPSL library which has been kept for compatibility and its easy installation. 
    43 However, the IOIPSL library is quite inefficient on parallel machines and, since version 3.2, 
    44 many diagnostic options have been added presuming the use of \key{iomput}. 
    45 The usefulness of the default IOIPSL-based option is expected to reduce with each new release. 
    46 If \key{iomput} is not defined, output files and content are defined in the \mdl{diawri} module and 
    47 contain mean (or instantaneous if \key{diainstant} is defined) values over a regular period of 
    48 nn\_write time-steps (namelist parameter).  
    4939 
    5040%\gmcomment{                    % start of gmcomment 
     
    9181in a very easy way. 
    9282All details of iomput functionalities are listed in the following subsections. 
    93 Examples of the XML files that control the outputs can be found in: \path{NEMOGCM/CONFIG/ORCA2_LIM/EXP00/iodef.xml}, 
    94 \path{NEMOGCM/CONFIG/SHARED/field_def.xml} and \path{NEMOGCM/CONFIG/SHARED/domain_def.xml}. \\ 
     83Examples of the XML files that control the outputs can be found in:  
     84\path{cfgs/ORCA2_ICE_PISCES/EXPREF/iodef.xml}, 
     85\path{cfgs/SHARED/field_def_nemo-oce.xml}, 
     86\path{cfgs/SHARED/field_def_nemo-pisces.xml}, 
     87\path{cfgs/SHARED/field_def_nemo-ice.xml} and \path{cfgs/SHARED/domain_def_nemo.xml}. \\ 
    9588 
    9689The second functionality targets output performance when running in parallel (\key{mpp\_mpi}). 
     
    10194 
    10295In version 3.6, the iom\_put interface depends on 
    103 an external code called \href{https://forge.ipsl.jussieu.fr/ioserver/browser/XIOS/branchs/xios-1.0}{XIOS-1.0}  
     96an external code called \href{https://forge.ipsl.jussieu.fr/ioserver/browser/XIOS/branchs/xios-2.5}{XIOS-2.5}  
    10497(use of revision 618 or higher is required). 
    10598This new IO server can take advantage of the parallel I/O functionality of NetCDF4 to 
     
    168161\xmlline|<variable id="using_server" type="bool"></variable>| 
    169162 
    170 The {\tt using\_server} setting determines whether or not the server will be used in \textit{attached mode} 
    171 (as a library) [{\tt> false <}] or in \textit{detached mode} 
    172 (as an external executable on N additional, dedicated cpus) [{\tt > true <}]. 
     163The {\ttfamily using\_server} setting determines whether or not the server will be used in \textit{attached mode} 
     164(as a library) [{\ttfamily> false <}] or in \textit{detached mode} 
     165(as an external executable on N additional, dedicated cpus) [{\ttfamily > true <}]. 
    173166The \textit{attached mode} is simpler to use but much less efficient for massively parallel applications. 
    174167The type of each file can be either ''multiple\_file'' or ''one\_file''. 
     
    207200\subsubsection{Control of XIOS: the context in iodef.xml} 
    208201 
    209 As well as the {\tt using\_server} flag, other controls on the use of XIOS are set in the XIOS context in iodef.xml. 
     202As well as the {\ttfamily using\_server} flag, other controls on the use of XIOS are set in the XIOS context in iodef.xml. 
    210203See the XML basics section below for more details on XML syntax and rules. 
    211204 
     
    257250See the installation guide on the \href{http://forge.ipsl.jussieu.fr/ioserver/wiki}{XIOS} wiki for help and guidance. 
    258251NEMO will need to link to the compiled XIOS library. 
    259 The \href{https://forge.ipsl.jussieu.fr/nemo/wiki/Users/ModelInterfacing/InputsOutputs#Inputs-OutputsusingXIOS} 
    260 {XIOS with NEMO} guide provides an example illustration of how this can be achieved. 
     252The \href{https://forge.ipsl.jussieu.fr/nemo/chrome/site/doc/NEMO/guide/html/install.html#extract-and-install-xios} 
     253{Extract and install XIOS} guide provides an example illustration of how this can be achieved. 
    261254 
    262255\subsubsection{Add your own outputs} 
     
    269262\begin{enumerate} 
    270263\item[1.] 
    271   in NEMO code, add a \forcode{CALL iom\_put( 'identifier', array )} where you want to output a 2D or 3D array. 
     264  in NEMO code, add a \forcode{CALL iom_put( 'identifier', array )} where you want to output a 2D or 3D array. 
    272265\item[2.] 
    273266  If necessary, add \forcode{USE iom ! I/O manager library} to the list of used modules in 
     
    442435\xmlline|<context src="./nemo_def.xml" />| 
    443436  
    444 \noindent In NEMO, by default, the field and domain definition is done in 2 separate files: 
    445 \path{NEMOGCM/CONFIG/SHARED/field_def.xml} and \path{NEMOGCM/CONFIG/SHARED/domain_def.xml} that 
     437\noindent In NEMO, by default, the field definition is done in 3 separate files ( 
     438\path{cfgs/SHARED/field_def_nemo-oce.xml}, 
     439\path{cfgs/SHARED/field_def_nemo-pisces.xml} and 
     440\path{cfgs/SHARED/field_def_nemo-ice.xml} ) and the  domain definition is done in another file ( \path{cfgs/SHARED/domain_def_nemo.xml} ) 
     441that 
    446442are included in the main iodef.xml file through the following commands: 
    447443\begin{xmllines} 
    448 <field_definition src="./field_def.xml" /> 
    449 <domain_definition src="./domain_def.xml" /> 
     444<context id="nemo" src="./context_nemo.xml"/>  
    450445\end{xmllines} 
    451446 
     
    508503 
    509504Secondly, the group can be used to replace a list of elements. 
    510 Several examples of groups of fields are proposed at the end of the file \path{CONFIG/SHARED/field_def.xml}. 
     505Several examples of groups of fields are proposed at the end of the XML field files ( 
     506\path{cfgs/SHARED/field_def_nemo-oce.xml}, 
     507\path{cfgs/SHARED/field_def_nemo-pisces.xml} and 
     508\path{cfgs/SHARED/field_def_nemo-ice.xml} ) . 
    511509For example, a short list of the usual variables related to the U grid: 
    512510 
     
    514512<field_group id="groupU" > 
    515513   <field field_ref="uoce"  /> 
    516    <field field_ref="suoce" /> 
     514   <field field_ref="ssu" /> 
    517515   <field field_ref="utau"  /> 
    518516</field_group> 
     
    538536the tag family domain. 
    539537It must therefore be done in the domain part of the XML file.  
    540 For example, in \path{CONFIG/SHARED/domain_def.xml}, we provide the following example of a definition of  
     538For example, in \path{cfgs/SHARED/domain_def.xml}, we provide the following example of a definition of  
    541539a 5 by 5 box with the bottom left corner at point (10,10). 
    542540 
    543541\begin{xmllines} 
    544 <domain_group id="grid_T"> 
    545    <domain id="myzoom" zoom_ibegin="10" zoom_jbegin="10" zoom_ni="5" zoom_nj="5" /> 
     542<domain id="myzoomT" domain_ref="grid_T"> 
     543   <zoom_domain ibegin="10" jbegin="10" ni="5" nj="5" /> 
    546544\end{xmllines} 
    547545 
     
    551549\begin{xmllines} 
    552550<file id="myfile_vzoom" output_freq="1d" > 
    553    <field field_ref="toce" domain_ref="myzoom"/> 
     551   <field field_ref="toce" domain_ref="myzoomT"/> 
    554552</file> 
    555553\end{xmllines} 
     
    576574\subsubsection{Define vertical zooms} 
    577575 
    578 Vertical zooms are defined through the attributs zoom\_begin and zoom\_end of the tag family axis. 
     576Vertical zooms are defined through the attributs zoom\_begin and zoom\_n of the tag family axis. 
    579577It must therefore be done in the axis part of the XML file. 
    580 For example, in \path{NEMOGCM/CONFIG/ORCA2_LIM/iodef_demo.xml}, we provide the following example: 
    581  
    582 \begin{xmllines} 
    583 <axis_group id="deptht" long_name="Vertical T levels" unit="m" positive="down" > 
    584    <axis id="deptht" /> 
    585    <axis id="deptht_myzoom" zoom_begin="1" zoom_end="10" /> 
     578For example, in \path{cfgs/ORCA2_ICE_PISCES/EXPREF/iodef_demo.xml}, we provide the following example: 
     579 
     580\begin{xmllines} 
     581<axis_definition> 
     582   <axis id="deptht" long_name="Vertical T levels" unit="m" positive="down" /> 
     583   <axis id="deptht_zoom" azix_ref="deptht" > 
     584      <zoom_axis zoom_begin="1" zoom_n="10" /> 
     585   </axis> 
    586586\end{xmllines} 
    587587 
     
    765765\end{xmllines} 
    766766 
    767 Note that, then the code is crashing, writting real4 variables forces a numerical convection from  
     767Note that, then the code is crashing, writting real4 variables forces a numerical conversion from  
    768768real8 to real4 which will create an internal error in NetCDF and will avoid the creation of the output files. 
    769769Forcing double precision outputs with prec="8" (for example in the field\_definition) will avoid this problem. 
     
    938938    \hline 
    939939  \end{tabularx} 
    940   \caption{Field tags ("\tt{field\_*}")} 
     940  \caption{Field tags ("\ttfamily{field\_*}")} 
    941941\end{table} 
    942942 
     
    974974    \hline 
    975975  \end{tabularx} 
    976   \caption{File tags ("\tt{file\_*}")} 
     976  \caption{File tags ("\ttfamily{file\_*}")} 
    977977\end{table} 
    978978 
     
    10071007    \hline 
    10081008  \end{tabularx} 
    1009   \caption{Axis tags ("\tt{axis\_*}")} 
     1009  \caption{Axis tags ("\ttfamily{axis\_*}")} 
    10101010\end{table} 
    10111011 
     
    10401040    \hline 
    10411041  \end{tabularx} 
    1042   \caption{Domain tags ("\tt{domain\_*)}"} 
     1042  \caption{Domain tags ("\ttfamily{domain\_*)}"} 
    10431043\end{table} 
    10441044 
     
    10731073    \hline 
    10741074  \end{tabularx} 
    1075   \caption{Grid tags ("\tt{grid\_*}")} 
     1075  \caption{Grid tags ("\ttfamily{grid\_*}")} 
    10761076\end{table} 
    10771077 
     
    11141114    \hline 
    11151115  \end{tabularx} 
    1116   \caption{Reference attributes ("\tt{*\_ref}")} 
     1116  \caption{Reference attributes ("\ttfamily{*\_ref}")} 
    11171117\end{table} 
    11181118 
     
    11501150    \hline 
    11511151  \end{tabularx} 
    1152   \caption{Domain attributes ("\tt{zoom\_*}")} 
     1152  \caption{Domain attributes ("\ttfamily{zoom\_*}")} 
    11531153\end{table} 
    11541154 
     
    13181318\subsection{CF metadata standard compliance} 
    13191319 
    1320 Output from the XIOS-1.0 IO server is compliant with  
     1320Output from the XIOS IO server is compliant with  
    13211321\href{http://cfconventions.org/Data/cf-conventions/cf-conventions-1.5/build/cf-conventions.html}{version 1.5} of 
    13221322the CF metadata standard.  
     
    13321332%       NetCDF4 support 
    13331333% ================================================================ 
    1334 \section{NetCDF4 support (\protect\key{netcdf4})} 
     1334\section[NetCDF4 support (\texttt{\textbf{key\_netcdf4}})] 
     1335{NetCDF4 support (\protect\key{netcdf4})} 
    13351336\label{sec:DIA_nc4} 
    13361337 
     
    13401341Chunking and compression can lead to significant reductions in file sizes for a small runtime overhead. 
    13411342For a fuller discussion on chunking and other performance issues the reader is referred to 
    1342 the NetCDF4 documentation found \href{http://www.unidata.ucar.edu/software/netcdf/docs/netcdf.html#Chunking}{here}. 
     1343the NetCDF4 documentation found \href{https://www.unidata.ucar.edu/software/netcdf/docs/netcdf_perf_chunking.html}{here}. 
    13431344 
    13441345The new features are only available when the code has been linked with a NetCDF4 library 
     
    13891390\end{forlines} 
    13901391 
    1391 \noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\tt 46x38x1} respectively in 
    1392 the mono-processor case (\ie global domain of {\small\tt 182x149x31}). 
     1392\noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\ttfamily 46x38x1} respectively in 
     1393the mono-processor case (\ie global domain of {\small\ttfamily 182x149x31}). 
    13931394An illustration of the potential space savings that NetCDF4 chunking and compression provides is given in  
    13941395table \autoref{tab:NC4} which compares the results of two short runs of the ORCA2\_LIM reference configuration with 
     
    14501451%       Tracer/Dynamics Trends 
    14511452% ------------------------------------------------------------------------------------------------------------- 
    1452 \section{Tracer/Dynamics trends  (\protect\ngn{namtrd})} 
     1453\section[Tracer/Dynamics trends (\texttt{namtrd})] 
     1454{Tracer/Dynamics trends (\protect\ngn{namtrd})} 
    14531455\label{sec:DIA_trd} 
    14541456 
     
    14621464(\ie at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). 
    14631465This capability is controlled by options offered in \ngn{namtrd} namelist. 
    1464 Note that the output are done with xIOS, and therefore the \key{IOM} is required. 
     1466Note that the output are done with XIOS, and therefore the \key{iomput} is required. 
    14651467 
    14661468What is done depends on the \ngn{namtrd} logical set to \forcode{.true.}: 
     
    14881490 
    14891491Note that the mixed layer tendency diagnostic can also be used on biogeochemical models via  
    1490 the \key{trdtrc} and \key{trdmld\_trc} CPP keys. 
     1492the \key{trdtrc} and \key{trdmxl\_trc} CPP keys. 
    14911493 
    14921494\textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested. 
     
    14971499%       On-line Floats trajectories 
    14981500% ------------------------------------------------------------------------------------------------------------- 
    1499 \section{FLO: On-Line Floats trajectories (\protect\key{floats})} 
     1501\section[FLO: On-Line Floats trajectories (\texttt{\textbf{key\_floats}})] 
     1502{FLO: On-Line Floats trajectories (\protect\key{floats})} 
    15001503\label{sec:FLO} 
    15011504%--------------------------------------------namflo------------------------------------------------------- 
     
    15061509The on-line computation of floats advected either by the three dimensional velocity field or constraint to 
    15071510remain at a given depth ($w = 0$ in the computation) have been introduced in the system during the CLIPPER project. 
    1508 Options are defined by \ngn{namflo} namelis variables. 
    1509 The algorithm used is based either on the work of \cite{Blanke_Raynaud_JPO97} (default option), 
     1511Options are defined by \ngn{namflo} namelist variables. 
     1512The algorithm used is based either on the work of \cite{blanke.raynaud_JPO97} (default option), 
    15101513or on a $4^th$ Runge-Hutta algorithm (\np{ln\_flork4}\forcode{ = .true.}). 
    1511 Note that the \cite{Blanke_Raynaud_JPO97} algorithm have the advantage of providing trajectories which 
     1514Note that the \cite{blanke.raynaud_JPO97} algorithm have the advantage of providing trajectories which 
    15121515are consistent with the numeric of the code, so that the trajectories never intercept the bathymetry. 
    15131516 
     
    15191522In case of Ariane convention, input filename is \np{init\_float\_ariane}. 
    15201523Its format is: \\ 
    1521 {\scriptsize \texttt{I J K nisobfl itrash itrash}} 
     1524{\scriptsize \texttt{I J K nisobfl itrash}} 
    15221525 
    15231526\noindent with: 
     
    15771580In that case, output filename is trajec\_float. 
    15781581 
    1579 Another possiblity of writing format is Netcdf (\np{ln\_flo\_ascii}\forcode{ = .false.}). 
    1580 There are 2 possibilities: 
    1581  
    1582 - if (\key{iomput}) is used, outputs are selected in  iodef.xml. 
     1582Another possiblity of writing format is Netcdf (\np{ln\_flo\_ascii}\forcode{ = .false.}) with 
     1583\key{iomput} and outputs selected in iodef.xml. 
    15831584Here it is an example of specification to put in files description section: 
    15841585 
     
    15971598\end{xmllines} 
    15981599 
    1599  -  if (\key{iomput}) is not used, a file called \ifile{trajec\_float} will be created by IOIPSL library. 
    1600  
    1601  See also \href{http://stockage.univ-brest.fr/~grima/Ariane/}{here} the web site describing the off-line use of 
    1602  this marvellous diagnostic tool. 
    16031600 
    16041601% ------------------------------------------------------------------------------------------------------------- 
    16051602%       Harmonic analysis of tidal constituents 
    16061603% ------------------------------------------------------------------------------------------------------------- 
    1607 \section{Harmonic analysis of tidal constituents (\protect\key{diaharm}) } 
     1604\section[Harmonic analysis of tidal constituents (\texttt{\textbf{key\_diaharm}})] 
     1605{Harmonic analysis of tidal constituents (\protect\key{diaharm})} 
    16081606\label{sec:DIA_diag_harm} 
    16091607 
    1610 %------------------------------------------namdia_harm---------------------------------------------------- 
     1608%------------------------------------------nam_diaharm---------------------------------------------------- 
    16111609% 
    16121610\nlst{nam_diaharm} 
     
    16161614This on-line Harmonic analysis is actived with \key{diaharm}. 
    16171615 
    1618 Some parameters are available in namelist \ngn{namdia\_harm}: 
     1616Some parameters are available in namelist \ngn{nam\_diaharm}: 
    16191617 
    16201618 - \np{nit000\_han} is the first time step used for harmonic analysis 
     
    16521650%       Sections transports 
    16531651% ------------------------------------------------------------------------------------------------------------- 
    1654 \section{Transports across sections (\protect\key{diadct}) } 
     1652\section[Transports across sections (\texttt{\textbf{key\_diadct}})] 
     1653{Transports across sections (\protect\key{diadct})} 
    16551654\label{sec:DIA_diag_dct} 
    16561655 
     
    16641663 
    16651664Each section is defined by the coordinates of its 2 extremities. 
    1666 The pathways between them are contructed using tools which can be found in \texttt{NEMOGCM/TOOLS/SECTIONS\_DIADCT} 
    1667 and are written in a binary file \texttt{section\_ijglobal.diadct\_ORCA2\_LIM} which is later read in by 
     1665The pathways between them are contructed using tools which can be found in \texttt{tools/SECTIONS\_DIADCT} 
     1666and are written in a binary file \texttt{section\_ijglobal.diadct} which is later read in by 
    16681667NEMO to compute on-line transports. 
    16691668 
     
    16841683\subsubsection{Creating a binary file containing the pathway of each section} 
    16851684 
    1686 In \texttt{NEMOGCM/TOOLS/SECTIONS\_DIADCT/run}, 
     1685In \texttt{tools/SECTIONS\_DIADCT/run}, 
    16871686the file \textit{ {list\_sections.ascii\_global}} contains a list of all the sections that are to be computed 
    16881687(this list of sections is based on MERSEA project metrics). 
     
    17331732   
    17341733 The script \texttt{job.ksh} computes the pathway for each section and creates a binary file 
    1735  \texttt{section\_ijglobal.diadct\_ORCA2\_LIM} which is read by NEMO. \\ 
     1734 \texttt{section\_ijglobal.diadct} which is read by NEMO. \\ 
    17361735 
    17371736 It is possible to use this tools for new configuations: \texttt{job.ksh} has to be updated with 
     
    18091808The steric effect is therefore not explicitely represented. 
    18101809This approximation does not represent a serious error with respect to the flow field calculated by the model 
    1811 \citep{Greatbatch_JGR94}, but extra attention is required when investigating sea level, 
     1810\citep{greatbatch_JGR94}, but extra attention is required when investigating sea level, 
    18121811as steric changes are an important contribution to local changes in sea level on seasonal and climatic time scales. 
    18131812This is especially true for investigation into sea level rise due to global warming. 
    18141813 
    18151814Fortunately, the steric contribution to the sea level consists of a spatially uniform component that 
    1816 can be diagnosed by considering the mass budget of the world ocean \citep{Greatbatch_JGR94}. 
     1815can be diagnosed by considering the mass budget of the world ocean \citep{greatbatch_JGR94}. 
    18171816In order to better understand how global mean sea level evolves and thus how the steric sea level can be diagnosed, 
    18181817we compare, in the following, the non-Boussinesq and Boussinesq cases. 
     
    18881887the ocean surface, not by changes in mean mass of the ocean: the steric effect is missing in a Boussinesq fluid. 
    18891888 
    1890 Nevertheless, following \citep{Greatbatch_JGR94}, the steric effect on the volume can be diagnosed by 
     1889Nevertheless, following \citep{greatbatch_JGR94}, the steric effect on the volume can be diagnosed by 
    18911890considering the mass budget of the ocean.  
    18921891The apparent changes in $\mathcal{M}$, mass of the ocean, which are not induced by surface mass flux 
    18931892must be compensated by a spatially uniform change in the mean sea level due to expansion/contraction of the ocean 
    1894 \citep{Greatbatch_JGR94}. 
     1893\citep{greatbatch_JGR94}. 
    18951894In others words, the Boussinesq mass, $\mathcal{M}_o$, can be related to $\mathcal{M}$, 
    18961895the total mass of the ocean seen by the Boussinesq model, via the steric contribution to the sea level, 
     
    19241923This value is a sensible choice for the reference density used in a Boussinesq ocean climate model since, 
    19251924with the exception of only a small percentage of the ocean, density in the World Ocean varies by no more than 
    1926 2$\%$ from this value (\cite{Gill1982}, page 47). 
     19252$\%$ from this value (\cite{gill_bk82}, page 47). 
    19271926 
    19281927Second, we have assumed here that the total ocean surface, $\mathcal{A}$, 
     
    19541953so that there are no associated ocean currents. 
    19551954Hence, the dynamically relevant sea level is the effective sea level, 
    1956 \ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{Campin_al_OM08}. 
     1955\ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{campin.marshall.ea_OM08}. 
    19571956However, in the current version of \NEMO the sea-ice is levitating above the ocean without mass exchanges between 
    19581957ice and ocean. 
     
    19761975%       Other Diagnostics 
    19771976% ------------------------------------------------------------------------------------------------------------- 
    1978 \section{Other diagnostics (\protect\key{diahth}, \protect\key{diaar5})} 
     1977\section[Other diagnostics (\texttt{\textbf{key\_diahth}}, \texttt{\textbf{key\_diaar5}})] 
     1978{Other diagnostics (\protect\key{diahth}, \protect\key{diaar5})} 
    19791979\label{sec:DIA_diag_others} 
    19801980 
     
    19821982The available ready-to-add diagnostics modules can be found in directory DIA. 
    19831983 
    1984 \subsection{Depth of various quantities (\protect\mdl{diahth})} 
     1984\subsection[Depth of various quantities (\textit{diahth.F90})] 
     1985{Depth of various quantities (\protect\mdl{diahth})} 
    19851986 
    19861987Among the available diagnostics the following ones are obtained when defining the \key{diahth} CPP key: 
    19871988 
    1988 - the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 
     1989- the mixed layer depth (based on a density criterion \citep{de-boyer-montegut.madec.ea_JGR04}) (\mdl{diahth}) 
    19891990 
    19901991- the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) 
     
    19981999% ----------------------------------------------------------- 
    19992000 
    2000 \subsection{Poleward heat and salt transports (\protect\mdl{diaptr})} 
     2001\subsection[Poleward heat and salt transports (\textit{diaptr.F90})] 
     2002{Poleward heat and salt transports (\protect\mdl{diaptr})} 
    20012003 
    20022004%------------------------------------------namptr----------------------------------------- 
     
    20162018\begin{figure}[!t] 
    20172019  \begin{center} 
    2018     \includegraphics[width=1.0\textwidth]{Fig_mask_subasins} 
     2020    \includegraphics[width=\textwidth]{Fig_mask_subasins} 
    20192021    \caption{ 
    20202022      \protect\label{fig:mask_subasins} 
     
    20322034%       CMIP specific diagnostics  
    20332035% ----------------------------------------------------------- 
    2034 \subsection{CMIP specific diagnostics (\protect\mdl{diaar5})} 
     2036\subsection[CMIP specific diagnostics (\textit{diaar5.F90})] 
     2037{CMIP specific diagnostics (\protect\mdl{diaar5})} 
    20352038 
    20362039A series of diagnostics has been added in the \mdl{diaar5}. 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DIU.tex

    r10442 r11263  
    3333(\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 
    35 ($\Delta T_{\rm{cs}}$ and $\Delta T_{\rm{wl}}$) and 
     35($\Delta T_{\mathrm{cs}}$ and $\Delta T_{\mathrm{wl}}$) and 
    3636both must be added to a foundation SST to obtain the true skin temperature. 
    3737 
     
    6060%=============================================================== 
    6161 
    62 The warm layer is calculated using the model of \citet{Takaya_al_JGR10} (TAKAYA10 model hereafter). 
     62The warm layer is calculated using the model of \citet{takaya.bidlot.ea_JGR10} (TAKAYA10 model hereafter). 
    6363This is a simple flux based model that is defined by the equations 
    6464\begin{align} 
    65 \frac{\partial{\Delta T_{\rm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p 
     65\frac{\partial{\Delta T_{\mathrm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p 
    6666\nu}-\frac{(\nu+1)ku^*_{w}f(L_a)\Delta T}{D_T\Phi\!\left(\frac{D_T}{L}\right)} \mbox{,} 
    6767\label{eq:ecmwf1} \\ 
    6868L&=&\frac{\rho_w c_p u^{*^3}_{w}}{\kappa g \alpha_w Q }\mbox{,}\label{eq:ecmwf2} 
    6969\end{align} 
    70 where $\Delta T_{\rm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal. 
     70where $\Delta T_{\mathrm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal. 
    7171In equation (\autoref{eq:ecmwf1}) $\alpha_w=2\times10^{-4}$ is the thermal expansion coefficient of water, 
    7272$\kappa=0.4$ is von K\'{a}rm\'{a}n's constant, $c_p$ is the heat capacity at constant pressure of sea water, 
    7373$\rho_w$ is the water density, and $L$ is the Monin-Obukhov length. 
    7474The tunable variable $\nu$ is a shape parameter that defines the expected subskin temperature profile via 
    75 $T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\rm{wl}}$, 
     75$T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\mathrm{wl}}$, 
    7676where $T$ is the absolute temperature and $z\le D_T$ is the depth below the top of the warm layer. 
    7777The influence of wind on TAKAYA10 comes through the magnitude of the friction velocity of the water $u^*_{w}$, 
     
    8282the diurnal layer, \ie 
    8383\[ 
    84   Q = Q_{\rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,} 
     84  Q = Q_{\mathrm{sol}} + Q_{\mathrm{lw}} + Q_{\mathrm{h}}\mbox{,} 
    8585  % \label{eq:e_flux_eqn} 
    8686\] 
    87 where $Q_{\rm{h}}$ is the sensible and latent heat flux, $Q_{\rm{lw}}$ is the long wave flux, 
    88 and $Q_{\rm{sol}}$ is the solar flux absorbed within the diurnal warm layer. 
    89 For $Q_{\rm{sol}}$ the 9 term representation of \citet{Gentemann_al_JGR09} is used. 
     87where $Q_{\mathrm{h}}$ is the sensible and latent heat flux, $Q_{\mathrm{lw}}$ is the long wave flux, 
     88and $Q_{\mathrm{sol}}$ is the solar flux absorbed within the diurnal warm layer. 
     89For $Q_{\mathrm{sol}}$ the 9 term representation of \citet{gentemann.minnett.ea_JGR09} is used. 
    9090In equation \autoref{eq:ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$, 
    9191where $L_a=0.3$\footnote{ 
     
    118118%=============================================================== 
    119119 
    120 The cool skin is modelled using the framework of \citet{Saunders_JAS82} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$. 
    121 As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\rm{cs}}$ becomes 
     120The cool skin is modelled using the framework of \citet{saunders_JAS67} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$. 
     121As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\mathrm{cs}}$ becomes 
    122122\[ 
    123123  % \label{eq:sunders_eqn} 
    124   \Delta T_{\rm{cs}}=\frac{Q_{\rm{ns}}\delta}{k_t} \mbox{,} 
     124  \Delta T_{\mathrm{cs}}=\frac{Q_{\mathrm{ns}}\delta}{k_t} \mbox{,} 
    125125\] 
    126 where $Q_{\rm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and 
     126where $Q_{\mathrm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and 
    127127$k_t$ is the thermal conductivity of sea water. 
    128128$\delta$ is the thickness of the skin layer and is given by 
     
    132132\end{equation} 
    133133where $\mu$ is the kinematic viscosity of sea water and $\lambda$ is a constant of proportionality which 
    134 \citet{Saunders_JAS82} suggested varied between 5 and 10. 
     134\citet{saunders_JAS67} suggested varied between 5 and 10. 
    135135 
    136 The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{Artale_al_JGR02}, 
    137 which is shown in \citet{Tu_Tsuang_GRL05} to outperform a number of other parametrisations at 
     136The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{artale.iudicone.ea_JGR02}, 
     137which is shown in \citet{tu.tsuang_GRL05} to outperform a number of other parametrisations at 
    138138both low and high wind speeds. 
    139139Specifically, 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DOM.tex

    r10502 r11263  
    4040\begin{figure}[!tb] 
    4141  \begin{center} 
    42     \includegraphics[]{Fig_cell} 
     42    \includegraphics[width=\textwidth]{Fig_cell} 
    4343    \caption{ 
    4444      \protect\label{fig:cell} 
     
    6060the centre of each face of the cells (\autoref{fig:cell}). 
    6161This is the generalisation to three dimensions of the well-known ``C'' grid in Arakawa's classification 
    62 \citep{Mesinger_Arakawa_Bk76}. 
     62\citep{mesinger.arakawa_bk76}. 
    6363The relative and planetary vorticity, $\zeta$ and $f$, are defined in the centre of each vertical edge and 
    6464the barotropic stream function $\psi$ is defined at horizontal points overlying the $\zeta$ and $f$-points. 
     
    218218\begin{figure}[!tb] 
    219219  \begin{center} 
    220     \includegraphics[]{Fig_index_hor} 
     220    \includegraphics[width=\textwidth]{Fig_index_hor} 
    221221    \caption{ 
    222222      \protect\label{fig:index_hor} 
     
    272272\begin{figure}[!pt] 
    273273  \begin{center} 
    274     \includegraphics[]{Fig_index_vert} 
     274    \includegraphics[width=\textwidth]{Fig_index_vert} 
    275275    \caption{ 
    276276      \protect\label{fig:index_vert} 
     
    345345% Domain: Horizontal Grid (mesh)  
    346346% ================================================================ 
    347 \section{Horizontal grid mesh (\protect\mdl{domhgr})} 
     347\section[Horizontal grid mesh (\textit{domhgr.F90})] 
     348{Horizontal grid mesh (\protect\mdl{domhgr})} 
    348349\label{sec:DOM_hgr} 
    349350 
     
    397398(\ie as the analytical first derivative of the transformation that 
    398399gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$) 
    399 is specific to the \NEMO model \citep{Marti_al_JGR92}. 
     400is specific to the \NEMO model \citep{marti.madec.ea_JGR92}. 
    400401As an example, $e_{1t}$ is defined locally at a $t$-point, 
    401402whereas many other models on a C grid choose to define such a scale factor as 
     
    405406since they are first introduced in the continuous equations; 
    406407secondly, analytical transformations encourage good practice by the definition of smoothly varying grids 
    407 (rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{Treguier1996}. 
     408(rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{treguier.dukowicz.ea_JGR96}. 
    408409An example of the effect of such a choice is shown in \autoref{fig:zgr_e3}. 
    409410%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    410411\begin{figure}[!t] 
    411412  \begin{center} 
    412     \includegraphics[]{Fig_zgr_e3} 
     413    \includegraphics[width=\textwidth]{Fig_zgr_e3} 
    413414    \caption{ 
    414415      \protect\label{fig:zgr_e3} 
     
    451452% Domain: Vertical Grid (domzgr) 
    452453% ================================================================ 
    453 \section{Vertical grid (\protect\mdl{domzgr})} 
     454\section[Vertical grid (\textit{domzgr.F90})] 
     455{Vertical grid (\protect\mdl{domzgr})} 
    454456\label{sec:DOM_zgr} 
    455457%-----------------------------------------nam_zgr & namdom------------------------------------------- 
     
    471473\begin{figure}[!tb] 
    472474  \begin{center} 
    473     \includegraphics[]{Fig_z_zps_s_sps} 
     475    \includegraphics[width=\textwidth]{Fig_z_zps_s_sps} 
    474476    \caption{ 
    475477      \protect\label{fig:z_zps_s_sps} 
     
    480482      (d) hybrid $s-z$ coordinate, 
    481483      (e) hybrid $s-z$ coordinate with partial step, and 
    482       (f) same as (e) but in the non-linear free surface (\protect\np{ln\_linssh}~\forcode{= .false.}). 
     484      (f) same as (e) but in the non-linear free surface (\protect\np{ln\_linssh}\forcode{ = .false.}). 
    483485      Note that the non-linear free surface can be used with any of the 5 coordinates (a) to (e). 
    484486    } 
     
    491493It is not intended as an option which can be enabled or disabled in the middle of an experiment. 
    492494Three main choices are offered (\autoref{fig:z_zps_s_sps}): 
    493 $z$-coordinate with full step bathymetry (\np{ln\_zco}~\forcode{= .true.}), 
    494 $z$-coordinate with partial step bathymetry (\np{ln\_zps}~\forcode{= .true.}), 
    495 or generalized, $s$-coordinate (\np{ln\_sco}~\forcode{= .true.}). 
     495$z$-coordinate with full step bathymetry (\np{ln\_zco}\forcode{ = .true.}), 
     496$z$-coordinate with partial step bathymetry (\np{ln\_zps}\forcode{ = .true.}), 
     497or generalized, $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}). 
    496498Hybridation of the three main coordinates are available: 
    497499$s-z$ or $s-zps$ coordinate (\autoref{fig:z_zps_s_sps} and \autoref{fig:z_zps_s_sps}). 
    498500By default a non-linear free surface is used: the coordinate follow the time-variation of the free surface so that 
    499501the transformation is time dependent: $z(i,j,k,t)$ (\autoref{fig:z_zps_s_sps}). 
    500 When a linear free surface is assumed (\np{ln\_linssh}~\forcode{= .true.}), 
     502When a linear free surface is assumed (\np{ln\_linssh}\forcode{ = .true.}), 
    501503the vertical coordinate are fixed in time, but the seawater can move up and down across the $z_0$ surface 
    502504(in other words, the top of the ocean in not a rigid-lid). 
     
    513515  N.B. in full step $z$-coordinate, a \ifile{bathy\_level} file can replace the \ifile{bathy\_meter} file, 
    514516  so that the computation of the number of wet ocean point in each water column is by-passed}. 
    515 If \np{ln\_isfcav}~\forcode{= .true.}, an extra file input file (\ifile{isf\_draft\_meter}) describing 
     517If \np{ln\_isfcav}\forcode{ = .true.}, an extra file input file (\ifile{isf\_draft\_meter}) describing 
    516518the ice shelf draft (in meters) is needed. 
    517519 
     
    535537%%% 
    536538 
    537 Unless a linear free surface is used (\np{ln\_linssh}~\forcode{= .false.}), 
     539Unless a linear free surface is used (\np{ln\_linssh}\forcode{ = .false.}), 
    538540the arrays describing the grid point depths and vertical scale factors are three set of 
    539541three dimensional arrays $(i,j,k)$ defined at \textit{before}, \textit{now} and \textit{after} time step. 
     
    541543They are updated at each model time step using a fixed reference coordinate system which 
    542544computer names have a $\_0$ suffix. 
    543 When the linear free surface option is used (\np{ln\_linssh}~\forcode{= .true.}), \textit{before}, 
     545When the linear free surface option is used (\np{ln\_linssh}\forcode{ = .true.}), \textit{before}, 
    544546\textit{now} and \textit{after} arrays are simply set one for all to their reference counterpart. 
    545547 
     
    553555(found in \ngn{namdom} namelist):  
    554556\begin{description} 
    555 \item[\np{nn\_bathy}~\forcode{= 0}]: 
     557\item[\np{nn\_bathy}\forcode{ = 0}]: 
    556558  a flat-bottom domain is defined. 
    557559  The total depth $z_w (jpk)$ is given by the coordinate transformation. 
    558560  The domain can either be a closed basin or a periodic channel depending on the parameter \np{jperio}. 
    559 \item[\np{nn\_bathy}~\forcode{= -1}]: 
     561\item[\np{nn\_bathy}\forcode{ = -1}]: 
    560562  a domain with a bump of topography one third of the domain width at the central latitude. 
    561563  This is meant for the "EEL-R5" configuration, a periodic or open boundary channel with a seamount. 
    562 \item[\np{nn\_bathy}~\forcode{= 1}]: 
     564\item[\np{nn\_bathy}\forcode{ = 1}]: 
    563565  read a bathymetry and ice shelf draft (if needed). 
    564566  The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) at 
     
    571573  The \ifile{isfdraft\_meter} file (Netcdf format) provides the ice shelf draft (positive, in meters) at 
    572574  each grid point of the model grid. 
    573   This file is only needed if \np{ln\_isfcav}~\forcode{= .true.}. 
     575  This file is only needed if \np{ln\_isfcav}\forcode{ = .true.}. 
    574576  Defining the ice shelf draft will also define the ice shelf edge and the grounding line position. 
    575577\end{description} 
     
    586588%        z-coordinate  and reference coordinate transformation 
    587589% ------------------------------------------------------------------------------------------------------------- 
    588 \subsection[$Z$-coordinate (\protect\np{ln\_zco}~\forcode{= .true.}) and ref. coordinate] 
    589             {$Z$-coordinate (\protect\np{ln\_zco}~\forcode{= .true.}) and reference coordinate} 
     590\subsection[$Z$-coordinate (\forcode{ln_zco = .true.}) and ref. coordinate] 
     591{$Z$-coordinate (\protect\np{ln\_zco}\forcode{ = .true.}) and reference coordinate} 
    590592\label{subsec:DOM_zco} 
    591593 
     
    593595\begin{figure}[!tb] 
    594596  \begin{center} 
    595     \includegraphics[]{Fig_zgr} 
     597    \includegraphics[width=\textwidth]{Fig_zgr} 
    596598    \caption{ 
    597599      \protect\label{fig:zgr} 
     
    616618using parameters provided in the \ngn{namcfg} namelist. 
    617619 
    618 It is possible to define a simple regular vertical grid by giving zero stretching (\np{ppacr}~\forcode{= 0}). 
     620It is possible to define a simple regular vertical grid by giving zero stretching (\np{ppacr}\forcode{ = 0}). 
    619621In that case, the parameters \jp{jpk} (number of $w$-levels) and 
    620622\np{pphmax} (total ocean depth in meters) fully define the grid. 
     
    631633a smooth hyperbolic tangent transition in between (\autoref{fig:zgr}). 
    632634 
    633 If the ice shelf cavities are opened (\np{ln\_isfcav}~\forcode{= .true.}), the definition of $z_0$ is the same. 
     635If the ice shelf cavities are opened (\np{ln\_isfcav}\forcode{ = .true.}), the definition of $z_0$ is the same. 
    634636However, definition of $e_3^0$ at $t$- and $w$-points is respectively changed to: 
    635637\begin{equation} 
     
    765767%        z-coordinate with partial step 
    766768% ------------------------------------------------------------------------------------------------------------- 
    767 \subsection{$Z$-coordinate with partial step (\protect\np{ln\_zps}~\forcode{= .true.})} 
     769\subsection[$Z$-coordinate with partial step (\forcode{ln_zps = .true.})] 
     770{$Z$-coordinate with partial step (\protect\np{ln\_zps}\forcode{ = .true.})} 
    768771\label{subsec:DOM_zps} 
    769772%--------------------------------------------namdom------------------------------------------------------- 
     
    796799%        s-coordinate 
    797800% ------------------------------------------------------------------------------------------------------------- 
    798 \subsection{$S$-coordinate (\protect\np{ln\_sco}~\forcode{= .true.})} 
     801\subsection[$S$-coordinate (\forcode{ln_sco = .true.})] 
     802{$S$-coordinate (\protect\np{ln\_sco}\forcode{ = .true.})} 
    799803\label{subsec:DOM_sco} 
    800804%------------------------------------------nam_zgr_sco--------------------------------------------------- 
     
    803807%-------------------------------------------------------------------------------------------------------------- 
    804808Options are defined in \ngn{namzgr\_sco}. 
    805 In $s$-coordinate (\np{ln\_sco}~\forcode{= .true.}), the depth and thickness of the model levels are defined from 
     809In $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}), the depth and thickness of the model levels are defined from 
    806810the product of a depth field and either a stretching function or its derivative, respectively: 
    807811 
     
    826830 
    827831The original default NEMO s-coordinate stretching is available if neither of the other options are specified as true 
    828 (\np{ln\_s\_SH94}~\forcode{= .false.} and \np{ln\_s\_SF12}~\forcode{= .false.}). 
    829 This uses a depth independent $\tanh$ function for the stretching \citep{Madec_al_JPO96}: 
     832(\np{ln\_s\_SH94}\forcode{ = .false.} and \np{ln\_s\_SF12}\forcode{ = .false.}). 
     833This uses a depth independent $\tanh$ function for the stretching \citep{madec.delecluse.ea_JPO96}: 
    830834 
    831835\[ 
     
    846850 
    847851A stretching function, 
    848 modified from the commonly used \citet{Song_Haidvogel_JCP94} stretching (\np{ln\_s\_SH94}~\forcode{= .true.}), 
     852modified from the commonly used \citet{song.haidvogel_JCP94} stretching (\np{ln\_s\_SH94}\forcode{ = .true.}), 
    849853is also available and is more commonly used for shelf seas modelling: 
    850854 
     
    859863\begin{figure}[!ht] 
    860864  \begin{center} 
    861     \includegraphics[]{Fig_sco_function} 
     865    \includegraphics[width=\textwidth]{Fig_sco_function} 
    862866    \caption{ 
    863867      \protect\label{fig:sco_function} 
     
    876880 
    877881Another example has been provided at version 3.5 (\np{ln\_s\_SF12}) that allows a fixed surface resolution in 
    878 an analytical terrain-following stretching \citet{Siddorn_Furner_OM12}. 
     882an analytical terrain-following stretching \citet{siddorn.furner_OM13}. 
    879883In this case the a stretching function $\gamma$ is defined such that: 
    880884 
     
    911915%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    912916\begin{figure}[!ht] 
    913   \includegraphics[]{Fig_DOM_compare_coordinates_surface} 
     917  \includegraphics[width=\textwidth]{Fig_DOM_compare_coordinates_surface} 
    914918  \caption{ 
    915     A comparison of the \citet{Song_Haidvogel_JCP94} $S$-coordinate (solid lines), 
     919    A comparison of the \citet{song.haidvogel_JCP94} $S$-coordinate (solid lines), 
    916920    a 50 level $Z$-coordinate (contoured surfaces) and 
    917     the \citet{Siddorn_Furner_OM12} $S$-coordinate (dashed lines) in the surface $100~m$ for 
     921    the \citet{siddorn.furner_OM13} $S$-coordinate (dashed lines) in the surface $100~m$ for 
    918922    a idealised bathymetry that goes from $50~m$ to $5500~m$ depth. 
    919923    For clarity every third coordinate surface is shown. 
     
    929933creating a non-analytical vertical coordinate that 
    930934therefore may suffer from large gradients in the vertical resolutions. 
    931 This stretching is less straightforward to implement than the \citet{Song_Haidvogel_JCP94} stretching, 
     935This stretching is less straightforward to implement than the \citet{song.haidvogel_JCP94} stretching, 
    932936but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes. 
    933937 
    934 As with the \citet{Song_Haidvogel_JCP94} stretching the stretch is only applied at depths greater than 
     938As with the \citet{song.haidvogel_JCP94} stretching the stretch is only applied at depths greater than 
    935939the critical depth $h_c$. 
    936940In this example two options are available in depths shallower than $h_c$, 
     
    940944Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as 
    941945large slopes lead to hydrostatic consistency. 
    942 A hydrostatic consistency parameter diagnostic following \citet{Haney1991} has been implemented, 
     946A hydrostatic consistency parameter diagnostic following \citet{haney_JPO91} has been implemented, 
    943947and is output as part of the model mesh file at the start of the run. 
    944948 
     
    946950%        z*- or s*-coordinate 
    947951% ------------------------------------------------------------------------------------------------------------- 
    948 \subsection{\zstar- or \sstar-coordinate (\protect\np{ln\_linssh}~\forcode{= .false.})} 
     952\subsection[\zstar- or \sstar-coordinate (\forcode{ln_linssh = .false.})] 
     953{\zstar- or \sstar-coordinate (\protect\np{ln\_linssh}\forcode{ = .false.})} 
    949954\label{subsec:DOM_zgr_star} 
    950955 
     
    960965 
    961966Whatever the vertical coordinate used, the model offers the possibility of representing the bottom topography with 
    962 steps that follow the face of the model cells (step like topography) \citep{Madec_al_JPO96}. 
     967steps that follow the face of the model cells (step like topography) \citep{madec.delecluse.ea_JPO96}. 
    963968The distribution of the steps in the horizontal is defined in a 2D integer array, mbathy, which 
    964969gives the number of ocean levels (\ie those that are not masked) at each $t$-point. 
     
    10141019% Domain: Initial State (dtatsd & istate) 
    10151020% ================================================================ 
    1016 \section{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})} 
     1021\section[Initial state (\textit{istate.F90} and \textit{dtatsd.F90})] 
     1022{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})} 
    10171023\label{sec:DTA_tsd} 
    10181024%-----------------------------------------namtsd------------------------------------------- 
     
    10251031salinity fields is controlled through the \np{ln\_tsd\_ini} namelist parameter. 
    10261032\begin{description} 
    1027 \item[\np{ln\_tsd\_init}~\forcode{= .true.}] 
     1033\item[\np{ln\_tsd\_init}\forcode{ = .true.}] 
    10281034  use a T and S input files that can be given on the model grid itself or on their native input data grid. 
    10291035  In the latter case, 
     
    10321038  The information relative to the input files are given in the \np{sn\_tem} and \np{sn\_sal} structures. 
    10331039  The computation is done in the \mdl{dtatsd} module. 
    1034 \item[\np{ln\_tsd\_init}~\forcode{= .false.}] 
     1040\item[\np{ln\_tsd\_init}\forcode{ = .false.}] 
    10351041  use constant salinity value of $35.5~psu$ and an analytical profile of temperature 
    10361042  (typical of the tropical ocean), see \rou{istate\_t\_s} subroutine called from \mdl{istate} module. 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DYN.tex

    r10499 r11263  
    6565%           Horizontal divergence and relative vorticity 
    6666%-------------------------------------------------------------------------------------------------------------- 
    67 \subsection{Horizontal divergence and relative vorticity (\protect\mdl{divcur})} 
     67\subsection[Horizontal divergence and relative vorticity (\textit{divcur.F90})] 
     68{Horizontal divergence and relative vorticity (\protect\mdl{divcur})} 
    6869\label{subsec:DYN_divcur} 
    6970 
     
    101102%           Sea Surface Height evolution 
    102103%-------------------------------------------------------------------------------------------------------------- 
    103 \subsection{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})} 
     104\subsection[Horizontal divergence and relative vorticity (\textit{sshwzv.F90})] 
     105{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})} 
    104106\label{subsec:DYN_sshwzv} 
    105107 
     
    127129Replacing $T$ by the number $1$ in the tracer equation and summing over the water column must lead to 
    128130the sea surface height equation otherwise tracer content will not be conserved 
    129 \citep{Griffies_al_MWR01, Leclair_Madec_OM09}. 
     131\citep{griffies.pacanowski.ea_MWR01, leclair.madec_OM09}. 
    130132 
    131133The vertical velocity is computed by an upward integration of the horizontal divergence starting at the bottom, 
     
    181183%        Vorticity term  
    182184% ------------------------------------------------------------------------------------------------------------- 
    183 \subsection{Vorticity term (\protect\mdl{dynvor})} 
     185\subsection[Vorticity term (\textit{dynvor.F90})] 
     186{Vorticity term (\protect\mdl{dynvor})} 
    184187\label{subsec:DYN_vor} 
    185188%------------------------------------------nam_dynvor---------------------------------------------------- 
     
    203206%                 enstrophy conserving scheme 
    204207%------------------------------------------------------------- 
    205 \subsubsection{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})} 
     208\subsubsection[Enstrophy conserving scheme (\forcode{ln_dynvor_ens = .true.})] 
     209{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})} 
    206210\label{subsec:DYN_vor_ens} 
    207211 
     
    226230%                 energy conserving scheme 
    227231%------------------------------------------------------------- 
    228 \subsubsection{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})} 
     232\subsubsection[Energy conserving scheme (\forcode{ln_dynvor_ene = .true.})] 
     233{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})} 
    229234\label{subsec:DYN_vor_ene} 
    230235 
     
    246251%                 mix energy/enstrophy conserving scheme 
    247252%------------------------------------------------------------- 
    248 \subsubsection{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.}) } 
     253\subsubsection[Mixed energy/enstrophy conserving scheme (\forcode{ln_dynvor_mix = .true.})] 
     254{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.})} 
    249255\label{subsec:DYN_vor_mix} 
    250256 
     
    271277%                 energy and enstrophy conserving scheme 
    272278%------------------------------------------------------------- 
    273 \subsubsection{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.}) } 
     279\subsubsection[Energy and enstrophy conserving scheme (\forcode{ln_dynvor_een = .true.})] 
     280{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.})} 
    274281\label{subsec:DYN_vor_een} 
    275282 
     
    287294Nevertheless, this technique strongly distort the phase and group velocity of Rossby waves....} 
    288295 
    289 A very nice solution to the problem of double averaging was proposed by \citet{Arakawa_Hsu_MWR90}. 
     296A very nice solution to the problem of double averaging was proposed by \citet{arakawa.hsu_MWR90}. 
    290297The idea is to get rid of the double averaging by considering triad combinations of vorticity. 
    291298It is noteworthy that this solution is conceptually quite similar to the one proposed by 
    292 \citep{Griffies_al_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}). 
    293  
    294 The \citet{Arakawa_Hsu_MWR90} vorticity advection scheme for a single layer is modified  
    295 for spherical coordinates as described by \citet{Arakawa_Lamb_MWR81} to obtain the EEN scheme.  
     299\citep{griffies.gnanadesikan.ea_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}). 
     300 
     301The \citet{arakawa.hsu_MWR90} vorticity advection scheme for a single layer is modified  
     302for spherical coordinates as described by \citet{arakawa.lamb_MWR81} to obtain the EEN scheme.  
    296303First consider the discrete expression of the potential vorticity, $q$, defined at an $f$-point:  
    297304\[ 
     
    309316\begin{figure}[!ht] 
    310317  \begin{center} 
    311     \includegraphics[width=0.70\textwidth]{Fig_DYN_een_triad} 
     318    \includegraphics[width=\textwidth]{Fig_DYN_een_triad} 
    312319    \caption{ 
    313320      \protect\label{fig:DYN_een_triad} 
     
    327334(with a systematic reduction of $e_{3f}$ when a model level intercept the bathymetry) 
    328335that tends to reinforce the topostrophy of the flow 
    329 (\ie the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.  
     336(\ie the tendency of the flow to follow the isobaths) \citep{penduff.le-sommer.ea_OS07}.  
    330337 
    331338Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as 
     
    356363(\ie $\chi$=$0$) (see \autoref{subsec:C_vorEEN}).  
    357364Applied to a realistic ocean configuration, it has been shown that it leads to a significant reduction of 
    358 the noise in the vertical velocity field \citep{Le_Sommer_al_OM09}. 
     365the noise in the vertical velocity field \citep{le-sommer.penduff.ea_OM09}. 
    359366Furthermore, used in combination with a partial steps representation of bottom topography, 
    360367it improves the interaction between current and topography, 
    361 leading to a larger topostrophy of the flow \citep{Barnier_al_OD06, Penduff_al_OS07}.  
     368leading to a larger topostrophy of the flow \citep{barnier.madec.ea_OD06, penduff.le-sommer.ea_OS07}.  
    362369 
    363370%-------------------------------------------------------------------------------------------------------------- 
    364371%           Kinetic Energy Gradient term 
    365372%-------------------------------------------------------------------------------------------------------------- 
    366 \subsection{Kinetic energy gradient term (\protect\mdl{dynkeg})} 
     373\subsection[Kinetic energy gradient term (\textit{dynkeg.F90})] 
     374{Kinetic energy gradient term (\protect\mdl{dynkeg})} 
    367375\label{subsec:DYN_keg} 
    368376 
     
    384392%           Vertical advection term 
    385393%-------------------------------------------------------------------------------------------------------------- 
    386 \subsection{Vertical advection term (\protect\mdl{dynzad}) } 
     394\subsection[Vertical advection term (\textit{dynzad.F90})] 
     395{Vertical advection term (\protect\mdl{dynzad})} 
    387396\label{subsec:DYN_zad} 
    388397 
     
    403412When \np{ln\_dynzad\_zts}\forcode{ = .true.}, 
    404413a split-explicit time stepping with 5 sub-timesteps is used on the vertical advection term. 
    405 This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}.  
     414This option can be useful when the value of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}.  
    406415Note that in this case, 
    407416a similar split-explicit time stepping should be used on vertical advection of tracer to ensure a better stability, 
     
    430439%           Coriolis plus curvature metric terms 
    431440%-------------------------------------------------------------------------------------------------------------- 
    432 \subsection{Coriolis plus curvature metric terms (\protect\mdl{dynvor}) } 
     441\subsection[Coriolis plus curvature metric terms (\textit{dynvor.F90})] 
     442{Coriolis plus curvature metric terms (\protect\mdl{dynvor})} 
    433443\label{subsec:DYN_cor_flux} 
    434444 
     
    451461%           Flux form Advection term 
    452462%-------------------------------------------------------------------------------------------------------------- 
    453 \subsection{Flux form advection term (\protect\mdl{dynadv}) } 
     463\subsection[Flux form advection term (\textit{dynadv.F90})] 
     464{Flux form advection term (\protect\mdl{dynadv})} 
    454465\label{subsec:DYN_adv_flux} 
    455466 
     
    475486a $2^{nd}$ order centered finite difference scheme, CEN2, 
    476487or a $3^{rd}$ order upstream biased scheme, UBS. 
    477 The latter is described in \citet{Shchepetkin_McWilliams_OM05}. 
     488The latter is described in \citet{shchepetkin.mcwilliams_OM05}. 
    478489The schemes are selected using the namelist logicals \np{ln\_dynadv\_cen2} and \np{ln\_dynadv\_ubs}.  
    479490In flux form, the schemes differ by the choice of a space and time interpolation to define the value of 
     
    484495%                 2nd order centred scheme 
    485496%------------------------------------------------------------- 
    486 \subsubsection{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})} 
     497\subsubsection[CEN2: $2^{nd}$ order centred scheme (\forcode{ln_dynadv_cen2 = .true.})] 
     498{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})} 
    487499\label{subsec:DYN_adv_cen2} 
    488500 
     
    507519%                 UBS scheme 
    508520%------------------------------------------------------------- 
    509 \subsubsection{UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})} 
     521\subsubsection[UBS: Upstream Biased Scheme (\forcode{ln_dynadv_ubs = .true.})] 
     522{UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})} 
    510523\label{subsec:DYN_adv_ubs} 
    511524 
     
    523536where $u"_{i+1/2} =\delta_{i+1/2} \left[ {\delta_i \left[ u \right]} \right]$. 
    524537This results in a dissipatively dominant (\ie hyper-diffusive) truncation error 
    525 \citep{Shchepetkin_McWilliams_OM05}. 
    526 The overall performance of the advection scheme is similar to that reported in \citet{Farrow1995}. 
     538\citep{shchepetkin.mcwilliams_OM05}. 
     539The overall performance of the advection scheme is similar to that reported in \citet{farrow.stevens_JPO95}. 
    527540It is a relatively good compromise between accuracy and smoothness. 
    528541It is not a \emph{positive} scheme, meaning that false extrema are permitted. 
     
    542555while the second term, which is the diffusion part of the scheme, 
    543556is evaluated using the \textit{before} velocity (forward in time). 
    544 This is discussed by \citet{Webb_al_JAOT98} in the context of the Quick advection scheme. 
     557This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme. 
    545558 
    546559Note that the UBS and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes only differ by 
    547560one coefficient. 
    548 Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{Webb_al_JAOT98}. 
     561Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 
    549562This option is not available through a namelist parameter, since the $1/6$ coefficient is hard coded. 
    550563Nevertheless it is quite easy to make the substitution in the \mdl{dynadv\_ubs} module and obtain a QUICK scheme. 
     
    560573%           Hydrostatic pressure gradient term 
    561574% ================================================================ 
    562 \section{Hydrostatic pressure gradient (\protect\mdl{dynhpg})} 
     575\section[Hydrostatic pressure gradient (\textit{dynhpg.F90})] 
     576{Hydrostatic pressure gradient (\protect\mdl{dynhpg})} 
    563577\label{sec:DYN_hpg} 
    564578%------------------------------------------nam_dynhpg--------------------------------------------------- 
     
    582596%           z-coordinate with full step 
    583597%-------------------------------------------------------------------------------------------------------------- 
    584 \subsection{Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})} 
     598\subsection[Full step $Z$-coordinate (\forcode{ln_dynhpg_zco = .true.})] 
     599{Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})} 
    585600\label{subsec:DYN_hpg_zco} 
    586601 
     
    627642%           z-coordinate with partial step 
    628643%-------------------------------------------------------------------------------------------------------------- 
    629 \subsection{Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})} 
     644\subsection[Partial step $Z$-coordinate (\forcode{ln_dynhpg_zps = .true.})] 
     645{Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})} 
    630646\label{subsec:DYN_hpg_zps} 
    631647 
     
    652668 
    653669Pressure gradient formulations in an $s$-coordinate have been the subject of a vast number of papers 
    654 (\eg, \citet{Song1998, Shchepetkin_McWilliams_OM05}).  
     670(\eg, \citet{song_MWR98, shchepetkin.mcwilliams_OM05}).  
    655671A number of different pressure gradient options are coded but the ROMS-like, 
    656672density Jacobian with cubic polynomial method is currently disabled whilst known bugs are under investigation. 
    657673 
    658 $\bullet$ Traditional coding (see for example \citet{Madec_al_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.}) 
     674$\bullet$ Traditional coding (see for example \citet{madec.delecluse.ea_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.}) 
    659675\begin{equation} 
    660676  \label{eq:dynhpg_sco} 
     
    679695$\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) 
    680696 
    681 $\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{Shchepetkin_McWilliams_OM05}  
     697$\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{shchepetkin.mcwilliams_OM05}  
    682698(\np{ln\_dynhpg\_djc}\forcode{ = .true.}) (currently disabled; under development) 
    683699 
    684700Note that expression \autoref{eq:dynhpg_sco} is commonly used when the variable volume formulation is activated 
    685701(\key{vvl}) because in that case, even with a flat bottom, 
    686 the coordinate surfaces are not horizontal but follow the free surface \citep{Levier2007}. 
     702the coordinate surfaces are not horizontal but follow the free surface \citep{levier.treguier.ea_rpt07}. 
    687703The pressure jacobian scheme (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) is available as 
    688704an improved option to \np{ln\_dynhpg\_sco}\forcode{ = .true.} when \key{vvl} is active. 
     
    704720corresponds to the water replaced by the ice shelf. 
    705721This top pressure is constant over time. 
    706 A detailed description of this method is described in \citet{Losch2008}.\\ 
     722A detailed description of this method is described in \citet{losch_JGR08}.\\ 
    707723 
    708724The pressure gradient due to ocean load is computed using the expression \autoref{eq:dynhpg_sco} described in 
     
    712728%           Time-scheme 
    713729%-------------------------------------------------------------------------------------------------------------- 
    714 \subsection{Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .true./.false.})} 
     730\subsection[Time-scheme (\forcode{ln_dynhpg_imp = .{true,false}.})] 
     731{Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .\{true,false\}}.)} 
    715732\label{subsec:DYN_hpg_imp} 
    716733 
     
    722739the physical phenomenon that controls the time-step is internal gravity waves (IGWs). 
    723740A semi-implicit scheme for doubling the stability limit associated with IGWs can be used 
    724 \citep{Brown_Campana_MWR78, Maltrud1998}. 
     741\citep{brown.campana_MWR78, maltrud.smith.ea_JGR98}. 
    725742It involves the evaluation of the hydrostatic pressure gradient as 
    726743an average over the three time levels $t-\rdt$, $t$, and $t+\rdt$ 
     
    773790% Surface Pressure Gradient 
    774791% ================================================================ 
    775 \section{Surface pressure gradient (\protect\mdl{dynspg})} 
     792\section[Surface pressure gradient (\textit{dynspg.F90})] 
     793{Surface pressure gradient (\protect\mdl{dynspg})} 
    776794\label{sec:DYN_spg} 
    777795%-----------------------------------------nam_dynspg---------------------------------------------------- 
     
    790808which imposes a very small time step when an explicit time stepping is used. 
    791809Two methods are proposed to allow a longer time step for the three-dimensional equations:  
    792 the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt}),  
     810the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt?}),  
    793811and the split-explicit free surface described below. 
    794812The extra term introduced in the filtered method is calculated implicitly,  
     
    811829% Explicit free surface formulation 
    812830%-------------------------------------------------------------------------------------------------------------- 
    813 \subsection{Explicit free surface (\protect\key{dynspg\_exp})} 
     831\subsection[Explicit free surface (\texttt{\textbf{key\_dynspg\_exp}})] 
     832{Explicit free surface (\protect\key{dynspg\_exp})} 
    814833\label{subsec:DYN_spg_exp} 
    815834 
     
    837856% Split-explict free surface formulation 
    838857%-------------------------------------------------------------------------------------------------------------- 
    839 \subsection{Split-explicit free surface (\protect\key{dynspg\_ts})} 
     858\subsection[Split-explicit free surface (\texttt{\textbf{key\_dynspg\_ts}})] 
     859{Split-explicit free surface (\protect\key{dynspg\_ts})} 
    840860\label{subsec:DYN_spg_ts} 
    841861%------------------------------------------namsplit----------------------------------------------------------- 
     
    845865 
    846866The split-explicit free surface formulation used in \NEMO (\key{dynspg\_ts} defined), 
    847 also called the time-splitting formulation, follows the one proposed by \citet{Shchepetkin_McWilliams_OM05}. 
     867also called the time-splitting formulation, follows the one proposed by \citet{shchepetkin.mcwilliams_OM05}. 
    848868The general idea is to solve the free surface equation and the associated barotropic velocity equations with 
    849869a smaller time step than $\rdt$, the time step used for the three dimensional prognostic variables 
     
    862882\begin{equation} 
    863883  \label{eq:BT_dyn} 
    864   \frac{\partial {\rm \overline{{\bf U}}_h} }{\partial t}= 
    865   -f\;{\rm {\bf k}}\times {\rm \overline{{\bf U}}_h} 
    866   -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \rm {\overline{{\bf U}}_h} + \rm {\overline{\bf G}} 
     884  \frac{\partial {\mathrm \overline{{\mathbf U}}_h} }{\partial t}= 
     885  -f\;{\mathrm {\mathbf k}}\times {\mathrm \overline{{\mathbf U}}_h} 
     886  -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \mathrm {\overline{{\mathbf U}}_h} + \mathrm {\overline{\mathbf G}} 
    867887\end{equation} 
    868888\[ 
    869889  % \label{eq:BT_ssh} 
    870   \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\rm{\bf \overline{U}}}_h \,} \right]+P-E 
     890  \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\mathrm{\mathbf \overline{U}}}_h \,} \right]+P-E 
    871891\] 
    872892% \end{subequations} 
    873 where $\rm {\overline{\bf G}}$ is a forcing term held constant, containing coupling term between modes, 
     893where $\mathrm {\overline{\mathbf G}}$ is a forcing term held constant, containing coupling term between modes, 
    874894surface atmospheric forcing as well as slowly varying barotropic terms not explicitly computed to gain efficiency. 
    875895The third term on the right hand side of \autoref{eq:BT_dyn} represents the bottom stress 
    876896(see section \autoref{sec:ZDF_bfr}), explicitly accounted for at each barotropic iteration. 
    877897Temporal discretization of the system above follows a three-time step Generalized Forward Backward algorithm 
    878 detailed in \citet{Shchepetkin_McWilliams_OM05}. 
     898detailed in \citet{shchepetkin.mcwilliams_OM05}. 
    879899AB3-AM4 coefficients used in \NEMO follow the second-order accurate, 
    880 "multi-purpose" stability compromise as defined in \citet{Shchepetkin_McWilliams_Bk08} 
     900"multi-purpose" stability compromise as defined in \citet{shchepetkin.mcwilliams_ibk09} 
    881901(see their figure 12, lower left).  
    882902 
     
    884904\begin{figure}[!t] 
    885905  \begin{center} 
    886     \includegraphics[width=0.7\textwidth]{Fig_DYN_dynspg_ts} 
     906    \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts} 
    887907    \caption{ 
    888908      \protect\label{fig:DYN_dynspg_ts} 
     
    936956and time splitting not compatible. 
    937957Advective barotropic velocities are obtained by using a secondary set of filtering weights, 
    938 uniquely defined from the filter coefficients used for the time averaging (\citet{Shchepetkin_McWilliams_OM05}). 
     958uniquely defined from the filter coefficients used for the time averaging (\citet{shchepetkin.mcwilliams_OM05}). 
    939959Consistency between the time averaged continuity equation and the time stepping of tracers is here the key to 
    940960obtain exact conservation. 
     
    953973external gravity waves in idealized or weakly non-linear cases. 
    954974Although the damping is lower than for the filtered free surface, 
    955 it is still significant as shown by \citet{Levier2007} in the case of an analytical barotropic Kelvin wave. 
     975it is still significant as shown by \citet{levier.treguier.ea_rpt07} in the case of an analytical barotropic Kelvin wave. 
    956976 
    957977%>>>>>=============== 
     
    10511071the leap-frog splitting mode in equation \autoref{eq:DYN_spg_ts_ssh}. 
    10521072We have tried various forms of such filtering, 
    1053 with the following method discussed in \cite{Griffies_al_MWR01} chosen due to 
     1073with the following method discussed in \cite{griffies.pacanowski.ea_MWR01} chosen due to 
    10541074its stability and reasonably good maintenance of tracer conservation properties (see ??). 
    10551075 
     
    10811101% Filtered free surface formulation 
    10821102%-------------------------------------------------------------------------------------------------------------- 
    1083 \subsection{Filtered free surface (\protect\key{dynspg\_flt})} 
     1103\subsection[Filtered free surface (\texttt{\textbf{key\_dynspg\_flt}})] 
     1104{Filtered free surface (\protect\key{dynspg\_flt})} 
    10841105\label{subsec:DYN_spg_fltp} 
    10851106 
    1086 The filtered formulation follows the \citet{Roullet_Madec_JGR00} implementation.  
     1107The filtered formulation follows the \citet{roullet.madec_JGR00} implementation.  
    10871108The extra term introduced in the equations (see \autoref{subsec:PE_free_surface}) is solved implicitly.  
    10881109The elliptic solvers available in the code are documented in \autoref{chap:MISC}. 
     
    10921113  \[ 
    10931114    % \label{eq:spg_flt} 
    1094     \frac{\partial {\rm {\bf U}}_h }{\partial t}= {\rm {\bf M}} 
     1115    \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= {\mathrm {\mathbf M}} 
    10951116    - g \nabla \left( \tilde{\rho} \ \eta \right) 
    10961117    - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right) 
     
    10981119  where $T_c$, is a parameter with dimensions of time which characterizes the force, 
    10991120  $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density, 
    1100   and $\rm {\bf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient, 
     1121  and $\mathrm {\mathbf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient, 
    11011122  non-linear and viscous terms in \autoref{eq:PE_dyn}. 
    11021123}   %end gmcomment 
     
    11091130% Lateral diffusion term 
    11101131% ================================================================ 
    1111 \section{Lateral diffusion term and operators (\protect\mdl{dynldf})} 
     1132\section[Lateral diffusion term and operators (\textit{dynldf.F90})] 
     1133{Lateral diffusion term and operators (\protect\mdl{dynldf})} 
    11121134\label{sec:DYN_ldf} 
    11131135%------------------------------------------nam_dynldf---------------------------------------------------- 
     
    11431165 
    11441166% ================================================================ 
    1145 \subsection[Iso-level laplacian (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})] 
    1146             {Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})} 
     1167\subsection[Iso-level laplacian (\forcode{ln_dynldf_lap = .true.})] 
     1168{Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})} 
    11471169\label{subsec:DYN_ldf_lap} 
    11481170 
     
    11521174  \left\{ 
    11531175    \begin{aligned} 
    1154       D_u^{l{\rm {\bf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm} 
     1176      D_u^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm} 
    11551177          \;\chi } \right]-\frac{1}{e_{2u} {\kern 1pt}e_{3u} }\delta_j \left[  
    11561178        {A_f^{lm} \;e_{3f} \zeta } \right] \\ \\ 
    1157       D_v^{l{\rm {\bf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm} 
     1179      D_v^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm} 
    11581180          \;\chi } \right]+\frac{1}{e_{1v} {\kern 1pt}e_{3v} }\delta_i \left[  
    11591181        {A_f^{lm} \;e_{3f} \zeta } \right] 
     
    11691191%           Rotated laplacian operator 
    11701192%-------------------------------------------------------------------------------------------------------------- 
    1171 \subsection[Rotated laplacian (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})] 
    1172             {Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})} 
     1193\subsection[Rotated laplacian (\forcode{ln_dynldf_iso = .true.})] 
     1194{Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})} 
    11731195\label{subsec:DYN_ldf_iso} 
    11741196 
     
    12281250%           Iso-level bilaplacian operator 
    12291251%-------------------------------------------------------------------------------------------------------------- 
    1230 \subsection[Iso-level bilaplacian (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})] 
    1231             {Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})} 
     1252\subsection[Iso-level bilaplacian (\forcode{ln_dynldf_bilap = .true.})] 
     1253{Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})} 
    12321254\label{subsec:DYN_ldf_bilap} 
    12331255 
     
    12431265%           Vertical diffusion term 
    12441266% ================================================================ 
    1245 \section{Vertical diffusion term (\protect\mdl{dynzdf})} 
     1267\section[Vertical diffusion term (\textit{dynzdf.F90})] 
     1268{Vertical diffusion term (\protect\mdl{dynzdf})} 
    12461269\label{sec:DYN_zdf} 
    12471270%----------------------------------------------namzdf------------------------------------------------------ 
     
    13261349There are two main options for wetting and drying code (wd): 
    13271350(a) an iterative limiter (il) and (b) a directional limiter (dl). 
    1328 The directional limiter is based on the scheme developed by \cite{WarnerEtal13} for RO 
     1351The directional limiter is based on the scheme developed by \cite{warner.defne.ea_CG13} for RO 
    13291352MS 
    1330 which was in turn based on ideas developed for POM by \cite{Oey06}. The iterative 
     1353which was in turn based on ideas developed for POM by \cite{oey_OM06}. The iterative 
    13311354limiter is a new scheme.  The iterative limiter is activated by setting $\mathrm{ln\_wd\_il} = \mathrm{.true.}$ 
    13321355and $\mathrm{ln\_wd\_dl} = \mathrm{.false.}$. The directional limiter is activated 
     
    13721395%   Iterative limiters 
    13731396%----------------------------------------------------------------------------------------- 
    1374 \subsection   [Directional limiter (\textit{wet\_dry})] 
    1375          {Directional limiter (\mdl{wet\_dry})} 
     1397\subsection[Directional limiter (\textit{wet\_dry.F90})] 
     1398{Directional limiter (\mdl{wet\_dry})} 
    13761399\label{subsec:DYN_wd_directional_limiter} 
    13771400The principal idea of the directional limiter is that 
     
    14001423 
    14011424 
    1402 \cite{WarnerEtal13} state that in their scheme the velocity masks at the cell faces for the baroclinic 
     1425\cite{warner.defne.ea_CG13} state that in their scheme the velocity masks at the cell faces for the baroclinic 
    14031426timesteps are set to 0 or 1 depending on whether the average of the masks over the barotropic sub-steps is respectively less than 
    14041427or greater than 0.5. That scheme does not conserve tracers in integrations started from constant tracer 
     
    14121435%----------------------------------------------------------------------------------------- 
    14131436 
    1414 \subsection   [Iterative limiter (\textit{wet\_dry})] 
    1415          {Iterative limiter (\mdl{wet\_dry})} 
     1437\subsection[Iterative limiter (\textit{wet\_dry.F90})] 
     1438{Iterative limiter (\mdl{wet\_dry})} 
    14161439\label{subsec:DYN_wd_iterative_limiter} 
    14171440 
    1418 \subsubsection [Iterative flux limiter (\textit{wet\_dry})] 
    1419          {Iterative flux limiter (\mdl{wet\_dry})} 
     1441\subsubsection[Iterative flux limiter (\textit{wet\_dry.F90})] 
     1442{Iterative flux limiter (\mdl{wet\_dry})} 
    14201443\label{subsubsec:DYN_wd_il_spg_limiter} 
    14211444 
     
    14941517\end{equation} 
    14951518 
    1496 Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\it [Q: Why is 
     1519Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\itshape [Q: Why is 
    14971520this necessary/desirable?]}. Substituting from (\ref{dyn_wd_continuity_coef}) gives an 
    14981521expression for the coefficient needed to multiply the outward flux at this cell in order 
     
    15221545%      Surface pressure gradients 
    15231546%---------------------------------------------------------------------------------------- 
    1524 \subsubsection   [Modification of surface pressure gradients (\textit{dynhpg})] 
    1525          {Modification of surface pressure gradients (\mdl{dynhpg})} 
     1547\subsubsection[Modification of surface pressure gradients (\textit{dynhpg.F90})] 
     1548{Modification of surface pressure gradients (\mdl{dynhpg})} 
    15261549\label{subsubsec:DYN_wd_il_spg} 
    15271550 
     
    15411564%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    15421565\begin{figure}[!ht] \begin{center} 
    1543 \includegraphics[width=0.8\textwidth]{Fig_WAD_dynhpg} 
     1566\includegraphics[width=\textwidth]{Fig_WAD_dynhpg} 
    15441567\caption{ \label{Fig_WAD_dynhpg} 
    15451568Illustrations of the three possible combinations of the logical variables controlling the 
     
    15881611conditions. 
    15891612 
    1590 \subsubsection   [Additional considerations (\textit{usrdef\_zgr})] 
    1591          {Additional considerations (\mdl{usrdef\_zgr})} 
     1613\subsubsection[Additional considerations (\textit{usrdef\_zgr.F90})] 
     1614{Additional considerations (\mdl{usrdef\_zgr})} 
    15921615\label{subsubsec:WAD_additional} 
    15931616 
     
    16031626%      The WAD test cases 
    16041627%---------------------------------------------------------------------------------------- 
    1605 \subsection   [The WAD test cases (\textit{usrdef\_zgr})] 
    1606          {The WAD test cases (\mdl{usrdef\_zgr})} 
     1628\subsection[The WAD test cases (\textit{usrdef\_zgr.F90})] 
     1629{The WAD test cases (\mdl{usrdef\_zgr})} 
    16071630\label{WAD_test_cases} 
    16081631 
     
    16141637% Time evolution term  
    16151638% ================================================================ 
    1616 \section{Time evolution term (\protect\mdl{dynnxt})} 
     1639\section[Time evolution term (\textit{dynnxt.F90})] 
     1640{Time evolution term (\protect\mdl{dynnxt})} 
    16171641\label{sec:DYN_nxt} 
    16181642 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_LBC.tex

    r10614 r11263  
    1717% Boundary Condition at the Coast 
    1818% ================================================================ 
    19 \section{Boundary condition at the coast (\protect\np{rn\_shlat})} 
     19\section[Boundary condition at the coast (\texttt{rn\_shlat})] 
     20{Boundary condition at the coast (\protect\np{rn\_shlat})} 
    2021\label{sec:LBC_coast} 
    2122%--------------------------------------------nam_lbc------------------------------------------------------- 
     
    5657\begin{figure}[!t] 
    5758  \begin{center} 
    58     \includegraphics[width=0.90\textwidth]{Fig_LBC_uv} 
     59    \includegraphics[width=\textwidth]{Fig_LBC_uv} 
    5960    \caption{ 
    6061      \protect\label{fig:LBC_uv} 
     
    8586\begin{figure}[!p] 
    8687  \begin{center} 
    87     \includegraphics[width=0.90\textwidth]{Fig_LBC_shlat} 
     88    \includegraphics[width=\textwidth]{Fig_LBC_shlat} 
    8889    \caption{ 
    8990      \protect\label{fig:LBC_shlat} 
     
    147148% Boundary Condition around the Model Domain 
    148149% ================================================================ 
    149 \section{Model domain boundary condition (\protect\np{jperio})} 
     150\section[Model domain boundary condition (\texttt{jperio})] 
     151{Model domain boundary condition (\protect\np{jperio})} 
    150152\label{sec:LBC_jperio} 
    151153 
     
    158160%        Closed, cyclic (\np{jperio}\forcode{ = 0..2})  
    159161% ------------------------------------------------------------------------------------------------------------- 
    160 \subsection{Closed, cyclic (\protect\np{jperio}\forcode{= [0127]})} 
     162\subsection[Closed, cyclic (\forcode{jperio = [0127]})] 
     163{Closed, cyclic (\protect\np{jperio}\forcode{ = [0127]})} 
    161164\label{subsec:LBC_jperio012} 
    162165 
     
    194197\begin{figure}[!t] 
    195198  \begin{center} 
    196     \includegraphics[width=1.0\textwidth]{Fig_LBC_jperio} 
     199    \includegraphics[width=\textwidth]{Fig_LBC_jperio} 
    197200    \caption{ 
    198201      \protect\label{fig:LBC_jperio} 
     
    206209%        North fold (\textit{jperio = 3 }to $6)$  
    207210% ------------------------------------------------------------------------------------------------------------- 
    208 \subsection{North-fold (\protect\np{jperio}\forcode{ = 3..6})} 
     211\subsection[North-fold (\forcode{jperio = [3-6]})] 
     212{North-fold (\protect\np{jperio}\forcode{ = [3-6]})} 
    209213\label{subsec:LBC_north_fold} 
    210214 
     
    218222\begin{figure}[!t] 
    219223  \begin{center} 
    220     \includegraphics[width=0.90\textwidth]{Fig_North_Fold_T} 
     224    \includegraphics[width=\textwidth]{Fig_North_Fold_T} 
    221225    \caption{ 
    222226      \protect\label{fig:North_Fold_T} 
     
    232236% Exchange with neighbouring processors  
    233237% ==================================================================== 
    234 \section{Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})} 
     238\section[Exchange with neighbouring processors (\textit{lbclnk.F90}, \textit{lib\_mpp.F90})] 
     239{Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})} 
    235240\label{sec:LBC_mpp} 
    236241 
     
    280285\begin{figure}[!t] 
    281286  \begin{center} 
    282     \includegraphics[width=0.90\textwidth]{Fig_mpp} 
     287    \includegraphics[width=\textwidth]{Fig_mpp} 
    283288    \caption{ 
    284289      \protect\label{fig:mpp} 
     
    360365\begin{figure}[!ht] 
    361366  \begin{center} 
    362     \includegraphics[width=0.90\textwidth]{Fig_mppini2} 
     367    \includegraphics[width=\textwidth]{Fig_mppini2} 
    363368    \caption { 
    364369      \protect\label{fig:mppini2} 
     
    395400 
    396401The BDY module was modelled on the OBC module (see NEMO 3.4) and shares many features and 
    397 a similar coding structure \citep{Chanut2005}. 
     402a similar coding structure \citep{chanut_rpt05}. 
    398403The specification of the location of the open boundary is completely flexible and 
    399404allows for example the open boundary to follow an isobath or other irregular contour.  
     
    475480\label{subsec:BDY_FRS_scheme} 
    476481 
    477 The Flow Relaxation Scheme (FRS) \citep{Davies_QJRMS76,Engerdahl_Tel95}, 
     482The Flow Relaxation Scheme (FRS) \citep{davies_QJRMS76,engedahl_T95}, 
    478483applies a simple relaxation of the model fields to externally-specified values over 
    479484a zone next to the edge of the model domain. 
     
    514519\label{subsec:BDY_flather_scheme} 
    515520 
    516 The \citet{Flather_JPO94} scheme is a radiation condition on the normal, 
     521The \citet{flather_JPO94} scheme is a radiation condition on the normal, 
    517522depth-mean transport across the open boundary. 
    518523It takes the form 
     
    535540\label{subsec:BDY_orlanski_scheme} 
    536541 
    537 The Orlanski scheme is based on the algorithm described by \citep{Marchesiello2001}, hereafter MMS. 
     542The Orlanski scheme is based on the algorithm described by \citep{marchesiello.mcwilliams.ea_OM01}, hereafter MMS. 
    538543 
    539544The adaptive Orlanski condition solves a wave plus relaxation equation at the boundary: 
     
    636641\begin{figure}[!t] 
    637642  \begin{center} 
    638     \includegraphics[width=1.0\textwidth]{Fig_LBC_bdy_geom} 
     643    \includegraphics[width=\textwidth]{Fig_LBC_bdy_geom} 
    639644    \caption { 
    640645      \protect\label{fig:LBC_bdy_geom} 
     
    670675These restrictions mean that data files used with versions of the 
    671676model prior to Version 3.4 may not work with Version 3.4 onwards. 
    672 A \fortran utility {\it bdy\_reorder} exists in the TOOLS directory which 
     677A \fortran utility {\itshape bdy\_reorder} exists in the TOOLS directory which 
    673678will re-order the data in old BDY data files. 
    674679 
     
    676681\begin{figure}[!t] 
    677682  \begin{center} 
    678     \includegraphics[width=1.0\textwidth]{Fig_LBC_nc_header} 
     683    \includegraphics[width=\textwidth]{Fig_LBC_nc_header} 
    679684    \caption { 
    680685      \protect\label{fig:LBC_nc_header} 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_LDF.tex

    r10442 r11263  
    3838% Direction of lateral Mixing 
    3939% ================================================================ 
    40 \section{Direction of lateral mixing (\protect\mdl{ldfslp})} 
     40\section[Direction of lateral mixing (\textit{ldfslp.F90})] 
     41{Direction of lateral mixing (\protect\mdl{ldfslp})} 
    4142\label{sec:LDF_slp} 
    4243 
     
    4445\gmcomment{ 
    4546  we should emphasize here that the implementation is a rather old one. 
    46   Better work can be achieved by using \citet{Griffies_al_JPO98, Griffies_Bk04} iso-neutral scheme. 
     47  Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} iso-neutral scheme. 
    4748} 
    4849 
     
    119120%In practice, \autoref{eq:ldfslp_iso} is of little help in evaluating the neutral surface slopes. Indeed, for an unsimplified equation of state, the density has a strong dependancy on pressure (here approximated as the depth), therefore applying \autoref{eq:ldfslp_iso} using the $in situ$ density, $\rho$, computed at T-points leads to a flattening of slopes as the depth increases. This is due to the strong increase of the $in situ$ density with depth.  
    120121 
    121 %By definition, neutral surfaces are tangent to the local $in situ$ density \citep{McDougall1987}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters). 
     122%By definition, neutral surfaces are tangent to the local $in situ$ density \citep{mcdougall_JPO87}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters). 
    122123 
    123124%In the $z$-coordinate, the derivative of the  \autoref{eq:ldfslp_iso} numerator is evaluated at the same depth \nocite{as what?} ($T$-level, which is the same as the $u$- and $v$-levels), so  the $in situ$ density can be used for its evaluation.  
     
    135136  thus the $in situ$ density can be used. 
    136137  This is not the case for the vertical derivatives: $\delta_{k+1/2}[\rho]$ is replaced by $-\rho N^2/g$, 
    137   where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{McDougall1987} 
     138  where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{mcdougall_JPO87} 
    138139  (see \autoref{subsec:TRA_bn2}).  
    139140 
     
    154155  Note: The solution for $s$-coordinate passes trough the use of different (and better) expression for 
    155156  the constraint on iso-neutral fluxes. 
    156   Following \citet{Griffies_Bk04}, instead of specifying directly that there is a zero neutral diffusive flux of 
     157  Following \citet{griffies_bk04}, instead of specifying directly that there is a zero neutral diffusive flux of 
    157158  locally referenced potential density, we stay in the $T$-$S$ plane and consider the balance between 
    158159  the neutral direction diffusive fluxes of potential temperature and salinity: 
     
    201202a minimum background horizontal diffusion for numerical stability reasons. 
    202203To overcome this problem, several techniques have been proposed in which the numerical schemes of 
    203 the ocean model are modified \citep{Weaver_Eby_JPO97, Griffies_al_JPO98}. 
     204the ocean model are modified \citep{weaver.eby_JPO97, griffies.gnanadesikan.ea_JPO98}. 
    204205Griffies's scheme is now available in \NEMO if \np{traldf\_grif\_iso} is set true; see Appdx \autoref{apdx:triad}. 
    205 Here, another strategy is presented \citep{Lazar_PhD97}: 
     206Here, another strategy is presented \citep{lazar_phd97}: 
    206207a local filtering of the iso-neutral slopes (made on 9 grid-points) prevents the development of 
    207208grid point noise generated by the iso-neutral diffusion operator (\autoref{fig:LDF_ZDF1}). 
     
    212213 
    213214Nevertheless, this iso-neutral operator does not ensure that variance cannot increase, 
    214 contrary to the \citet{Griffies_al_JPO98} operator which has that property.  
     215contrary to the \citet{griffies.gnanadesikan.ea_JPO98} operator which has that property.  
    215216 
    216217%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    217218\begin{figure}[!ht] 
    218219  \begin{center} 
    219     \includegraphics[width=0.70\textwidth]{Fig_LDF_ZDF1} 
     220    \includegraphics[width=\textwidth]{Fig_LDF_ZDF1} 
    220221    \caption { 
    221222      \protect\label{fig:LDF_ZDF1} 
     
    235236 
    236237 
    237 % In addition and also for numerical stability reasons \citep{Cox1987, Griffies_Bk04},  
     238% In addition and also for numerical stability reasons \citep{cox_OM87, griffies_bk04},  
    238239% the slopes are bounded by $1/100$ everywhere. This limit is decreasing linearly  
    239240% to zero fom $70$ meters depth and the surface (the fact that the eddies "feel" the  
    240241% surface motivates this flattening of isopycnals near the surface). 
    241242 
    242 For numerical stability reasons \citep{Cox1987, Griffies_Bk04}, the slopes must also be bounded by 
     243For numerical stability reasons \citep{cox_OM87, griffies_bk04}, the slopes must also be bounded by 
    243244$1/100$ everywhere. 
    244245This constraint is applied in a piecewise linear fashion, increasing from zero at the surface to 
     
    249250\begin{figure}[!ht] 
    250251  \begin{center} 
    251     \includegraphics[width=0.70\textwidth]{Fig_eiv_slp} 
     252    \includegraphics[width=\textwidth]{Fig_eiv_slp} 
    252253    \caption{ 
    253254      \protect\label{fig:eiv_slp} 
     
    301302% Lateral Mixing Operator 
    302303% ================================================================ 
    303 \section{Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf}) } 
     304\section[Lateral mixing operators (\textit{traldf.F90})] 
     305{Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf})} 
    304306\label{sec:LDF_op} 
    305307 
     
    309311% Lateral Mixing Coefficients 
    310312% ================================================================ 
    311 \section{Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn}) } 
     313\section[Lateral mixing coefficient (\textit{ldftra.F90}, \textit{ldfdyn.F90})] 
     314{Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn})} 
    312315\label{sec:LDF_coef} 
    313316 
     
    339342which is specified through the \np{rn\_ahm0} and \np{rn\_aht0} namelist parameters. 
    340343 
    341 \subsubsection{Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})}  
     344\subsubsection[Vertically varying mixing coefficients (\texttt{\textbf{key\_traldf\_c1d}} and \texttt{\textbf{key\_dynldf\_c1d}})] 
     345{Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})} 
    342346The 1D option is only available when using the $z$-coordinate with full step. 
    343347Indeed in all the other types of vertical coordinate, 
     
    350354This profile is hard coded in file \textit{traldf\_c1d.h90}, but can be easily modified by users. 
    351355 
    352 \subsubsection{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 
     356\subsubsection[Horizontally varying mixing coefficients (\texttt{\textbf{key\_traldf\_c2d}} and \texttt{\textbf{key\_dynldf\_c2d}})] 
     357{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 
    353358By default the horizontal variation of the eddy coefficient depends on the local mesh size and 
    354359the type of operator used: 
     
    366371This variation is intended to reflect the lesser need for subgrid scale eddy mixing where 
    367372the grid size is smaller in the domain. 
    368 It was introduced in the context of the DYNAMO modelling project \citep{Willebrand_al_PO01}. 
     373It was introduced in the context of the DYNAMO modelling project \citep{willebrand.barnier.ea_PO01}. 
    369374Note that such a grid scale dependance of mixing coefficients significantly increase the range of stability of 
    370375model configurations presenting large changes in grid pacing such as global ocean models. 
     
    376381For example, in the ORCA2 global ocean model (see Configurations), 
    377382the laplacian viscosity operator uses \np{rn\_ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$ north and south and 
    378 decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{Madec_al_JPO96, Delecluse_Madec_Bk00}. 
     383decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{madec.delecluse.ea_JPO96, delecluse.madec_icol99}. 
    379384This modification can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}. 
    380385Similar modified horizontal variations can be found with the Antarctic or Arctic sub-domain options of 
    381386ORCA2 and ORCA05 (see \&namcfg namelist). 
    382387 
    383 \subsubsection{Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})} 
     388\subsubsection[Space varying mixing coefficients (\texttt{\textbf{key\_traldf\_c3d}} and \texttt{\textbf{key\_dynldf\_c3d}})] 
     389{Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})} 
    384390 
    385391The 3D space variation of the mixing coefficient is simply the combination of the 1D and 2D cases, 
     
    430436% Eddy Induced Mixing 
    431437% ================================================================ 
    432 \section{Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 
     438\section[Eddy induced velocity (\textit{traadv\_eiv.F90}, \textit{ldfeiv.F90})] 
     439{Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 
    433440\label{sec:LDF_eiv} 
    434441 
     
    475482since it allows us to take advantage of all the advection schemes offered for the tracers 
    476483(see \autoref{sec:TRA_adv}) and not just the $2^{nd}$ order advection scheme as in 
    477 previous releases of OPA \citep{Madec1998}. 
     484previous releases of OPA \citep{madec.delecluse.ea_NPM98}. 
    478485This is particularly useful for passive tracers where \emph{positivity} of the advection scheme is of 
    479486paramount importance.  
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_OBS.tex

    r10442 r11263  
    573573\subsubsection{Horizontal interpolation} 
    574574 
    575 Consider an observation point ${\rm P}$ with with longitude and latitude $({\lambda_{}}_{\rm P}, \phi_{\rm P})$ and 
    576 the four nearest neighbouring model grid points ${\rm A}$, ${\rm B}$, ${\rm C}$ and ${\rm D}$ with 
    577 longitude and latitude ($\lambda_{\rm A}$, $\phi_{\rm A}$),($\lambda_{\rm B}$, $\phi_{\rm B}$) etc. 
     575Consider an observation point ${\mathrm P}$ with with longitude and latitude $({\lambda_{}}_{\mathrm P}, \phi_{\mathrm P})$ and 
     576the four nearest neighbouring model grid points ${\mathrm A}$, ${\mathrm B}$, ${\mathrm C}$ and ${\mathrm D}$ with 
     577longitude and latitude ($\lambda_{\mathrm A}$, $\phi_{\mathrm A}$),($\lambda_{\mathrm B}$, $\phi_{\mathrm B}$) etc. 
    578578All horizontal interpolation methods implemented in NEMO estimate the value of a model variable $x$ at point $P$ as 
    579 a weighted linear combination of the values of the model variables at the grid points ${\rm A}$, ${\rm B}$ etc.: 
     579a weighted linear combination of the values of the model variables at the grid points ${\mathrm A}$, ${\mathrm B}$ etc.: 
    580580\begin{align*} 
    581   {x_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & 
    582                                                    \frac{1}{w} \left( {w_{}}_{\rm A} {x_{}}_{\rm A} + 
    583                                                    {w_{}}_{\rm B} {x_{}}_{\rm B} + 
    584                                                    {w_{}}_{\rm C} {x_{}}_{\rm C} + 
    585                                                    {w_{}}_{\rm D} {x_{}}_{\rm D} \right) 
     581  {x_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & 
     582                                                   \frac{1}{w} \left( {w_{}}_{\mathrm A} {x_{}}_{\mathrm A} + 
     583                                                   {w_{}}_{\mathrm B} {x_{}}_{\mathrm B} + 
     584                                                   {w_{}}_{\mathrm C} {x_{}}_{\mathrm C} + 
     585                                                   {w_{}}_{\mathrm D} {x_{}}_{\mathrm D} \right) 
    586586\end{align*} 
    587 where ${w_{}}_{\rm A}$, ${w_{}}_{\rm B}$ etc. are the respective weights for the model field at 
    588 points ${\rm A}$, ${\rm B}$ etc., and $w = {w_{}}_{\rm A} + {w_{}}_{\rm B} + {w_{}}_{\rm C} + {w_{}}_{\rm D}$. 
     587where ${w_{}}_{\mathrm A}$, ${w_{}}_{\mathrm B}$ etc. are the respective weights for the model field at 
     588points ${\mathrm A}$, ${\mathrm B}$ etc., and $w = {w_{}}_{\mathrm A} + {w_{}}_{\mathrm B} + {w_{}}_{\mathrm C} + {w_{}}_{\mathrm D}$. 
    589589 
    590590Four different possibilities are available for computing the weights. 
     
    592592\begin{enumerate} 
    593593 
    594 \item[1.] {\bf Great-Circle distance-weighted interpolation.} 
     594\item[1.] {\bfseries Great-Circle distance-weighted interpolation.} 
    595595  The weights are computed as a function of the great-circle distance $s(P, \cdot)$ between $P$ and 
    596596  the model grid points $A$, $B$ etc. 
    597   For example, the weight given to the field ${x_{}}_{\rm A}$ is specified as the product of the distances 
    598   from ${\rm P}$ to the other points: 
     597  For example, the weight given to the field ${x_{}}_{\mathrm A}$ is specified as the product of the distances 
     598  from ${\mathrm P}$ to the other points: 
    599599  \begin{align*} 
    600     {w_{}}_{\rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D}) 
     600    {w_{}}_{\mathrm A} = s({\mathrm P}, {\mathrm B}) \, s({\mathrm P}, {\mathrm C}) \, s({\mathrm P}, {\mathrm D}) 
    601601  \end{align*} 
    602602  where  
    603603  \begin{align*} 
    604     s\left ({\rm P}, {\rm M} \right )  
     604    s\left ({\mathrm P}, {\mathrm M} \right )  
    605605     & \hspace{-2mm} = \hspace{-2mm} &  
    606606      \cos^{-1} \! \left\{  
    607                \sin {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm M} 
    608              + \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm M}  
    609                \cos ({\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P})  
     607               \sin {\phi_{}}_{\mathrm P} \sin {\phi_{}}_{\mathrm M} 
     608             + \cos {\phi_{}}_{\mathrm P} \cos {\phi_{}}_{\mathrm M}  
     609               \cos ({\lambda_{}}_{\mathrm M} - {\lambda_{}}_{\mathrm P})  
    610610                   \right\} 
    611611   \end{align*} 
    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 (\eg 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*} 
    616      s\left( {\rm P}, {\rm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\} 
     616     s\left( {\mathrm P}, {\mathrm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\} 
    617617   \end{align*} 
    618618   where 
    619619   \begin{align*} 
    620620     x & \hspace{-2mm} = \hspace{-2mm} & 
    621                                          {a_{}}_{\rm M} {a_{}}_{\rm P} + {b_{}}_{\rm M} {b_{}}_{\rm P} + {c_{}}_{\rm M} {c_{}}_{\rm P} 
     621                                         {a_{}}_{\mathrm M} {a_{}}_{\mathrm P} + {b_{}}_{\mathrm M} {b_{}}_{\mathrm P} + {c_{}}_{\mathrm M} {c_{}}_{\mathrm P} 
    622622   \end{align*} 
    623623   and  
    624624   \begin{align*} 
    625       {a_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, \\ 
    626       {a_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm P}, \\ 
    627       {b_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \cos {\phi_{}}_{\rm M}, \\ 
    628       {b_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm P}, \\ 
    629       {c_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \sin {\phi_{}}_{\rm M}, \\ 
    630       {c_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm P}. 
     625      {a_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\mathrm M}, \\ 
     626      {a_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\mathrm P}, \\ 
     627      {b_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm M} \cos {\phi_{}}_{\mathrm M}, \\ 
     628      {b_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm P} \cos {\phi_{}}_{\mathrm P}, \\ 
     629      {c_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm M} \sin {\phi_{}}_{\mathrm M}, \\ 
     630      {c_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm P} \sin {\phi_{}}_{\mathrm P}. 
    631631  \end{align*} 
    632632 
    633 \item[2.] {\bf Great-Circle distance-weighted interpolation with small angle approximation.} 
     633\item[2.] {\bfseries Great-Circle distance-weighted interpolation with small angle approximation.} 
    634634  Similar to the previous interpolation but with the distance $s$ computed as 
    635635  \begin{align*} 
    636     s\left( {\rm P}, {\rm M} \right) 
     636    s\left( {\mathrm P}, {\mathrm M} \right) 
    637637    & \hspace{-2mm} = \hspace{-2mm} & 
    638                                       \sqrt{ \left( {\phi_{}}_{\rm M} - {\phi_{}}_{\rm P} \right)^{2} 
    639                                       + \left( {\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P} \right)^{2} 
    640                                       \cos^{2} {\phi_{}}_{\rm M} } 
     638                                      \sqrt{ \left( {\phi_{}}_{\mathrm M} - {\phi_{}}_{\mathrm P} \right)^{2} 
     639                                      + \left( {\lambda_{}}_{\mathrm M} - {\lambda_{}}_{\mathrm P} \right)^{2} 
     640                                      \cos^{2} {\phi_{}}_{\mathrm M} } 
    641641  \end{align*} 
    642642  where $M$ corresponds to $A$, $B$, $C$ or $D$. 
    643643 
    644 \item[3.] {\bf Bilinear interpolation for a regular spaced grid.} 
     644\item[3.] {\bfseries Bilinear interpolation for a regular spaced grid.} 
    645645  The interpolation is split into two 1D interpolations in the longitude and latitude directions, respectively. 
    646646 
    647 \item[4.] {\bf Bilinear remapping interpolation for a general grid.} 
     647\item[4.] {\bfseries Bilinear remapping interpolation for a general grid.} 
    648648  An iterative scheme that involves first mapping a quadrilateral cell into 
    649649  a cell with coordinates (0,0), (1,0), (0,1) and (1,1). 
    650   This method is based on the SCRIP interpolation package \citep{Jones_1998}. 
     650  This method is based on the \href{https://github.com/SCRIP-Project/SCRIP}{SCRIP interpolation package}. 
    651651   
    652652\end{enumerate} 
     
    678678\begin{figure} 
    679679  \begin{center} 
    680     \includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rec} 
     680    \includegraphics[width=\textwidth]{Fig_OBS_avg_rec} 
    681681    \caption{ 
    682682      \protect\label{fig:obsavgrec} 
     
    691691\begin{figure} 
    692692  \begin{center} 
    693     \includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rad} 
     693    \includegraphics[width=\textwidth]{Fig_OBS_avg_rad} 
    694694    \caption{ 
    695695      \protect\label{fig:obsavgrad} 
     
    710710This is the most difficult and time consuming part of the 2D interpolation procedure.  
    711711A robust test for determining if an observation falls within a given quadrilateral cell is as follows. 
    712 Let ${\rm P}({\lambda_{}}_{\rm P} ,{\phi_{}}_{\rm P} )$ denote the observation point, 
    713 and let ${\rm A}({\lambda_{}}_{\rm A} ,{\phi_{}}_{\rm A} )$, ${\rm B}({\lambda_{}}_{\rm B} ,{\phi_{}}_{\rm B} )$, 
    714 ${\rm C}({\lambda_{}}_{\rm C} ,{\phi_{}}_{\rm C} )$ and ${\rm D}({\lambda_{}}_{\rm D} ,{\phi_{}}_{\rm D} )$ 
     712Let ${\mathrm P}({\lambda_{}}_{\mathrm P} ,{\phi_{}}_{\mathrm P} )$ denote the observation point, 
     713and let ${\mathrm A}({\lambda_{}}_{\mathrm A} ,{\phi_{}}_{\mathrm A} )$, ${\mathrm B}({\lambda_{}}_{\mathrm B} ,{\phi_{}}_{\mathrm B} )$, 
     714${\mathrm C}({\lambda_{}}_{\mathrm C} ,{\phi_{}}_{\mathrm C} )$ and ${\mathrm D}({\lambda_{}}_{\mathrm D} ,{\phi_{}}_{\mathrm D} )$ 
    715715denote the bottom left, bottom right, top left and top right corner points of the cell, respectively.  
    716716To determine if P is inside the cell, we verify that the cross-products  
    717717\begin{align*} 
    718718  \begin{array}{lllll} 
    719     {{\bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC} 
    720     & = & [({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} ) 
    721           ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} ) 
    722           - ({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} ) 
    723           ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ 
    724     {{\bf r}_{}}_{\rm PB} \times {{\bf r}_{}}_{\rm PA} 
    725     & = & [({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} ) 
    726           ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} ) 
    727           - ({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} ) 
    728           ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ 
    729     {{\bf r}_{}}_{\rm PC} \times {{\bf r}_{}}_{\rm PD} 
    730     & = & [({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} ) 
    731           ({\phi_{}}_{\rm D}   \; -\; {\phi_{}}_{\rm P} ) 
    732           - ({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} ) 
    733           ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ 
    734     {{\bf r}_{}}_{\rm PD} \times {{\bf r}_{}}_{\rm PB} 
    735     & = & [({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} ) 
    736           ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} ) 
    737           - ({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} ) 
    738           ({\phi_{}}_{\rm D}  \;  - \; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\ 
     719    {{\mathbf r}_{}}_{\mathrm PA} \times {{\mathbf r}_{}}_{\mathrm PC} 
     720    & = & [({\lambda_{}}_{\mathrm A}\; -\; {\lambda_{}}_{\mathrm P} ) 
     721          ({\phi_{}}_{\mathrm C}   \; -\; {\phi_{}}_{\mathrm P} ) 
     722          - ({\lambda_{}}_{\mathrm C}\; -\; {\lambda_{}}_{\mathrm P} ) 
     723          ({\phi_{}}_{\mathrm A}   \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 
     724    {{\mathbf r}_{}}_{\mathrm PB} \times {{\mathbf r}_{}}_{\mathrm PA} 
     725    & = & [({\lambda_{}}_{\mathrm B}\; -\; {\lambda_{}}_{\mathrm P} ) 
     726          ({\phi_{}}_{\mathrm A}   \; -\; {\phi_{}}_{\mathrm P} ) 
     727          - ({\lambda_{}}_{\mathrm A}\; -\; {\lambda_{}}_{\mathrm P} ) 
     728          ({\phi_{}}_{\mathrm B}   \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 
     729    {{\mathbf r}_{}}_{\mathrm PC} \times {{\mathbf r}_{}}_{\mathrm PD} 
     730    & = & [({\lambda_{}}_{\mathrm C}\; -\; {\lambda_{}}_{\mathrm P} ) 
     731          ({\phi_{}}_{\mathrm D}   \; -\; {\phi_{}}_{\mathrm P} ) 
     732          - ({\lambda_{}}_{\mathrm D}\; -\; {\lambda_{}}_{\mathrm P} ) 
     733          ({\phi_{}}_{\mathrm C}   \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 
     734    {{\mathbf r}_{}}_{\mathrm PD} \times {{\mathbf r}_{}}_{\mathrm PB} 
     735    & = & [({\lambda_{}}_{\mathrm D}\; -\; {\lambda_{}}_{\mathrm P} ) 
     736          ({\phi_{}}_{\mathrm B}   \; -\; {\phi_{}}_{\mathrm P} ) 
     737          - ({\lambda_{}}_{\mathrm B}\; -\; {\lambda_{}}_{\mathrm P} ) 
     738          ({\phi_{}}_{\mathrm D}  \;  - \; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 
    739739  \end{array} 
    740740  % \label{eq:cross} 
    741741\end{align*} 
    742 point in the opposite direction to the unit normal $\widehat{\bf k}$ 
    743 (\ie that the coefficients of $\widehat{\bf k}$ are negative), 
    744 where ${{\bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, etc. correspond to 
     742point in the opposite direction to the unit normal $\widehat{\mathbf k}$ 
     743(\ie that the coefficients of $\widehat{\mathbf k}$ are negative), 
     744where ${{\mathbf r}_{}}_{\mathrm PA}$, ${{\mathbf r}_{}}_{\mathrm PB}$, etc. correspond to 
    745745the vectors between points P and A, P and B, etc.. 
    746 The method used is similar to the method used in the SCRIP interpolation package \citep{Jones_1998}. 
     746The method used is similar to the method used in the \href{https://github.com/SCRIP-Project/SCRIP}{SCRIP interpolation package}. 
    747747 
    748748In order to speed up the grid search, there is the possibility to construct a lookup table for a user specified resolution. 
     
    772772\begin{figure} 
    773773  \begin{center} 
    774     \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_local} 
     774    \includegraphics[width=\textwidth]{Fig_ASM_obsdist_local} 
    775775    \caption{ 
    776776      \protect\label{fig:obslocal} 
     
    801801\begin{figure} 
    802802  \begin{center} 
    803     \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_global} 
     803    \includegraphics[width=\textwidth]{Fig_ASM_obsdist_global} 
    804804    \caption{ 
    805805      \protect\label{fig:obsglobal} 
     
    13701370\begin{figure} 
    13711371  \begin{center} 
    1372     % \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_main} 
    1373     \includegraphics[width=9cm,angle=-90.]{Fig_OBS_dataplot_main} 
     1372    % \includegraphics[width=\textwidth]{Fig_OBS_dataplot_main} 
     1373    \includegraphics[width=\textwidth]{Fig_OBS_dataplot_main} 
    13741374    \caption{ 
    13751375      \protect\label{fig:obsdataplotmain} 
     
    13861386\begin{figure} 
    13871387  \begin{center} 
    1388     % \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_prof} 
    1389     \includegraphics[width=7cm,angle=-90.]{Fig_OBS_dataplot_prof} 
     1388    % \includegraphics[width=\textwidth]{Fig_OBS_dataplot_prof} 
     1389    \includegraphics[width=\textwidth]{Fig_OBS_dataplot_prof} 
    13901390    \caption{ 
    13911391      \protect\label{fig:obsdataplotprofile} 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_SBC.tex

    r10614 r11263  
    55% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)  
    66% ================================================================ 
    7 \chapter{Surface Boundary Condition (SBC, ISF, ICB) } 
     7\chapter{Surface Boundary Condition (SBC, ISF, ICB)} 
    88\label{chap:SBC} 
    99\minitoc 
     
    226226% Input Data specification (\mdl{fldread}) 
    227227% ------------------------------------------------------------------------------------------------------------- 
    228 \subsection{Input data specification (\protect\mdl{fldread})} 
     228\subsection[Input data specification (\textit{fldread.F90})] 
     229{Input data specification (\protect\mdl{fldread})} 
    229230\label{subsec:SBC_fldread} 
    230231 
     
    313314The only tricky point is therefore to specify the date at which we need to do the interpolation and 
    314315the date of the records read in the input files. 
    315 Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the time step. 
     316Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step. 
    316317For example, for an experiment starting at 0h00'00" with a one hour time-step, 
    317318a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc. 
     
    559560% Analytical formulation (sbcana module)  
    560561% ================================================================ 
    561 \section{Analytical formulation (\protect\mdl{sbcana})} 
     562\section[Analytical formulation (\textit{sbcana.F90})] 
     563{Analytical formulation (\protect\mdl{sbcana})} 
    562564\label{sec:SBC_ana} 
    563565 
     
    584586% Flux formulation  
    585587% ================================================================ 
    586 \section{Flux formulation (\protect\mdl{sbcflx})} 
     588\section[Flux formulation (\textit{sbcflx.F90})] 
     589{Flux formulation (\protect\mdl{sbcflx})} 
    587590\label{sec:SBC_flx} 
    588591%------------------------------------------namsbc_flx---------------------------------------------------- 
     
    606609% ================================================================ 
    607610\section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}] 
    608                         {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}} 
     611{Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}} 
    609612\label{sec:SBC_blk} 
    610613 
     
    625628%        CORE Bulk formulea 
    626629% ------------------------------------------------------------------------------------------------------------- 
    627 \subsection{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})} 
     630\subsection[CORE formulea (\textit{sbcblk\_core.F90}, \forcode{ln_core = .true.})] 
     631{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})} 
    628632\label{subsec:SBC_blk_core} 
    629633%------------------------------------------namsbc_core---------------------------------------------------- 
     
    632636%------------------------------------------------------------------------------------------------------------- 
    633637 
    634 The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}. 
     638The CORE bulk formulae have been developed by \citet{large.yeager_rpt04}. 
    635639They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data. 
    636640They use an inertial dissipative method to compute the turbulent transfer coefficients 
    637641(momentum, sensible heat and evaporation) from the 10 metre wind speed, air temperature and specific humidity. 
    638 This \citet{Large_Yeager_Rep04} dataset is available through 
     642This \citet{large.yeager_rpt04} dataset is available through 
    639643the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. 
    640644 
    641645Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 
    642 This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}. 
     646This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 
    643647 
    644648Options are defined through the  \ngn{namsbc\_core} namelist variables. 
     
    688692%        CLIO Bulk formulea 
    689693% ------------------------------------------------------------------------------------------------------------- 
    690 \subsection{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})} 
     694\subsection[CLIO formulea (\textit{sbcblk\_clio.F90}, \forcode{ln_clio = .true.})] 
     695{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})} 
    691696\label{subsec:SBC_blk_clio} 
    692697%------------------------------------------namsbc_clio---------------------------------------------------- 
     
    696701 
    697702The CLIO bulk formulae were developed several years ago for the Louvain-la-neuve coupled ice-ocean model 
    698 (CLIO, \cite{Goosse_al_JGR99}).  
     703(CLIO, \cite{goosse.deleersnijder.ea_JGR99}).  
    699704They are simpler bulk formulae. 
    700705They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover.  
     
    729734% Coupled formulation 
    730735% ================================================================ 
    731 \section{Coupled formulation (\protect\mdl{sbccpl})} 
     736\section[Coupled formulation (\textit{sbccpl.F90})] 
     737{Coupled formulation (\protect\mdl{sbccpl})} 
    732738\label{sec:SBC_cpl} 
    733739%------------------------------------------namsbc_cpl---------------------------------------------------- 
     
    770776%        Atmospheric pressure 
    771777% ================================================================ 
    772 \section{Atmospheric pressure (\protect\mdl{sbcapr})} 
     778\section[Atmospheric pressure (\textit{sbcapr.F90})] 
     779{Atmospheric pressure (\protect\mdl{sbcapr})} 
    773780\label{sec:SBC_apr} 
    774781%------------------------------------------namsbc_apr---------------------------------------------------- 
     
    806813%        Surface Tides Forcing 
    807814% ================================================================ 
    808 \section{Surface tides (\protect\mdl{sbctide})} 
     815\section[Surface tides (\textit{sbctide.F90})] 
     816{Surface tides (\protect\mdl{sbctide})} 
    809817\label{sec:SBC_tide} 
    810818 
     
    819827\[ 
    820828  % \label{eq:PE_dyn_tides} 
    821   \frac{\partial {\rm {\bf U}}_h }{\partial t}= ... 
     829  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ... 
    822830  +g\nabla (\Pi_{eq} + \Pi_{sal}) 
    823831\] 
     
    839847 
    840848The SAL term should in principle be computed online as it depends on 
    841 the model tidal prediction itself (see \citet{Arbic2004} for a 
     849the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a 
    842850discussion about the practical implementation of this term). 
    843851Nevertheless, the complex calculations involved would make this 
     
    857865%        River runoffs 
    858866% ================================================================ 
    859 \section{River runoffs (\protect\mdl{sbcrnf})} 
     867\section[River runoffs (\textit{sbcrnf.F90})] 
     868{River runoffs (\protect\mdl{sbcrnf})} 
    860869\label{sec:SBC_rnf} 
    861870%------------------------------------------namsbc_rnf---------------------------------------------------- 
     
    871880%coastal modelling and becomes more and more often open ocean and climate modelling  
    872881%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are 
    873 %required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}. 
     882%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}. 
    874883 
    875884 
     
    892901\footnote{ 
    893902  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to 
    894   properly represent the diurnal cycle \citep{Bernie_al_JC05}. 
     903  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. 
    895904  see also \autoref{fig:SBC_dcy}.}. 
    896905 
     
    982991%        Ice shelf melting 
    983992% ================================================================ 
    984 \section{Ice shelf melting (\protect\mdl{sbcisf})} 
     993\section[Ice shelf melting (\textit{sbcisf.F90})] 
     994{Ice shelf melting (\protect\mdl{sbcisf})} 
    985995\label{sec:SBC_isf} 
    986996%------------------------------------------namsbc_isf---------------------------------------------------- 
     
    989999%-------------------------------------------------------------------------------------------------------- 
    9901000The namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation. 
    991 Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{Mathiot2017}.  
     1001Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.  
    9921002The different options are illustrated in \autoref{fig:SBC_isf}. 
    9931003 
     
    10011011   \item[\np{nn\_isfblk}\forcode{ = 1}]: 
    10021012     The melt rate is based on a balance between the upward ocean heat flux and 
    1003      the latent heat flux at the ice shelf base. A complete description is available in \citet{Hunter2006}. 
     1013     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}. 
    10041014   \item[\np{nn\_isfblk}\forcode{ = 2}]: 
    10051015     The melt rate and the heat flux are based on a 3 equations formulation 
    10061016     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).  
    1007      A complete description is available in \citet{Jenkins1991}. 
     1017     A complete description is available in \citet{jenkins_JGR91}. 
    10081018   \end{description} 
    10091019 
    1010      Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{Losch2008}.  
     1020     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.  
    10111021     Its thickness is defined by \np{rn\_hisf\_tbl}. 
    10121022     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m. 
     
    10381048\] 
    10391049     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters). 
    1040      See \citet{Jenkins2010} for all the details on this formulation. It is the recommended formulation for realistic application. 
     1050     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application. 
    10411051   \item[\np{nn\_gammablk}\forcode{ = 2}]: 
    10421052     The salt and heat exchange coefficients are velocity and stability dependent and defined as: 
     
    10471057     $\Gamma_{Turb}$ the contribution of the ocean stability and 
    10481058     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 
    1049      See \citet{Holland1999} for all the details on this formulation.  
     1059     See \citet{holland.jenkins_JPO99} for all the details on this formulation.  
    10501060     This formulation has not been extensively tested in NEMO (not recommended). 
    10511061   \end{description} 
    10521062 \item[\np{nn\_isf}\forcode{ = 2}]: 
    10531063   The ice shelf cavity is not represented. 
    1054    The fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting. 
     1064   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting. 
    10551065   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL) 
    10561066   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front 
     
    10891099\begin{figure}[!t] 
    10901100  \begin{center} 
    1091     \includegraphics[width=0.8\textwidth]{Fig_SBC_isf} 
     1101    \includegraphics[width=\textwidth]{Fig_SBC_isf} 
    10921102    \caption{ 
    10931103      \protect\label{fig:SBC_isf} 
     
    11661176%------------------------------------------------------------------------------------------------------------- 
    11671177 
    1168 Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}. 
    1169 Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ). 
     1178Icebergs are modelled as lagrangian particles in NEMO \citep{marsh.ivchenko.ea_GMD15}. 
     1179Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ). 
    11701180(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 
    11711181Icebergs are initially spawned into one of ten classes which have specific mass and thickness as 
     
    12271237%        Interactions with waves (sbcwave.F90, ln_wave) 
    12281238% ------------------------------------------------------------------------------------------------------------- 
    1229 \section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 
     1239\section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})] 
     1240{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 
    12301241\label{sec:SBC_wave} 
    12311242%------------------------------------------namsbc_wave-------------------------------------------------------- 
     
    12581269 
    12591270% ================================================================ 
    1260 \subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 
     1271\subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})] 
     1272{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 
    12611273\label{subsec:SBC_wave_cdgw} 
    12621274 
     
    12651277Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,  
    12661278the drag coefficient is computed according to the stable/unstable conditions of the  
    1267 air-sea interface following \citet{Large_Yeager_Rep04}.  
     1279air-sea interface following \citet{large.yeager_rpt04}.  
    12681280 
    12691281 
     
    12711283% 3D Stokes Drift (ln_sdw, nn_sdrift) 
    12721284% ================================================================ 
    1273 \subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 
     1285\subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})] 
     1286{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 
    12741287\label{subsec:SBC_wave_sdw} 
    12751288 
    1276 The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}.  
     1289The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.  
    12771290It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)  
    12781291and the current measured at a fixed point (Eulerian velocity).  
     
    13071320\begin{description} 
    13081321\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by  
    1309 \citet{Breivik_al_JPO2014}: 
     1322\citet{breivik.janssen.ea_JPO14}: 
    13101323 
    13111324\[ 
     
    13271340\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a  
    13281341reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface 
    1329 \citep{Breivik_al_OM2016}: 
     1342\citep{breivik.bidlot.ea_OM16}: 
    13301343 
    13311344\[ 
     
    13671380% Stokes-Coriolis term (ln_stcor) 
    13681381% ================================================================ 
    1369 \subsection{Stokes-Coriolis term (\protect\np{ln\_stcor})} 
     1382\subsection[Stokes-Coriolis term (\texttt{ln\_stcor})] 
     1383{Stokes-Coriolis term (\protect\np{ln\_stcor})} 
    13701384\label{subsec:SBC_wave_stcor} 
    13711385 
     
    13811395% Waves modified stress (ln_tauwoc, ln_tauw) 
    13821396% ================================================================ 
    1383 \subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}  
     1397\subsection[Wave modified sress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})] 
     1398{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 
    13841399\label{subsec:SBC_wave_tauw} 
    13851400 
    13861401The surface stress felt by the ocean is the atmospheric stress minus the net stress going  
    1387 into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not  
     1402into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not  
    13881403available for forcing the mean circulation, while in the opposite case of a decaying sea  
    13891404state more momentum is available for forcing the ocean.  
     
    14281443%        Diurnal cycle 
    14291444% ------------------------------------------------------------------------------------------------------------- 
    1430 \subsection{Diurnal cycle (\protect\mdl{sbcdcy})} 
     1445\subsection[Diurnal cycle (\textit{sbcdcy.F90})] 
     1446{Diurnal cycle (\protect\mdl{sbcdcy})} 
    14311447\label{subsec:SBC_dcy} 
    14321448%------------------------------------------namsbc_rnf---------------------------------------------------- 
     
    14381454\begin{figure}[!t] 
    14391455  \begin{center} 
    1440     \includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal} 
     1456    \includegraphics[width=\textwidth]{Fig_SBC_diurnal} 
    14411457    \caption{ 
    14421458      \protect\label{fig:SBC_diurnal} 
     
    14451461      the mean value of the analytical cycle (blue line) over a time step, 
    14461462      not as the mid time step value of the analytically cycle (red square). 
    1447       From \citet{Bernie_al_CD07}. 
     1463      From \citet{bernie.guilyardi.ea_CD07}. 
    14481464    } 
    14491465  \end{center} 
     
    14511467%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    14521468 
    1453 \cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less. 
     1469\cite{bernie.woolnough.ea_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less. 
    14541470Unfortunately high frequency forcing fields are rare, not to say inexistent. 
    14551471Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at 
    1456 high frequency \citep{Bernie_al_CD07}. 
     1472high frequency \citep{bernie.guilyardi.ea_CD07}. 
    14571473Furthermore, only the knowledge of daily mean value of SWF is needed, 
    14581474as higher frequency variations can be reconstructed from them, 
    14591475assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF. 
    1460 The \cite{Bernie_al_CD07} reconstruction algorithm is available in \NEMO by 
     1476The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO by 
    14611477setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when 
    14621478using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or 
    14631479the flux formulation (\np{ln\_flx}\forcode{ = .true.}). 
    14641480The reconstruction is performed in the \mdl{sbcdcy} module. 
    1465 The detail of the algoritm used can be found in the appendix~A of \cite{Bernie_al_CD07}. 
     1481The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}. 
    14661482The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at 
    14671483a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}). 
     
    14761492\begin{figure}[!t] 
    14771493  \begin{center} 
    1478     \includegraphics[width=0.7\textwidth]{Fig_SBC_dcy} 
     1494    \includegraphics[width=\textwidth]{Fig_SBC_dcy} 
    14791495    \caption{ 
    14801496      \protect\label{fig:SBC_dcy} 
     
    15141530%        Surface restoring to observed SST and/or SSS 
    15151531% ------------------------------------------------------------------------------------------------------------- 
    1516 \subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 
     1532\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})] 
     1533{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 
    15171534\label{subsec:SBC_ssr} 
    15181535%------------------------------------------namsbc_ssr---------------------------------------------------- 
     
    15461563(observed, climatological or an atmospheric model product), 
    15471564\textit{SSS}$_{Obs}$ is a sea surface salinity 
    1548 (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}), 
     1565(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}), 
    15491566$\left.S\right|_{k=1}$ is the model surface layer salinity and 
    15501567$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter. 
    15511568Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as 
    1552 the atmosphere does not care about ocean surface salinity \citep{Madec1997}. 
     1569the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}. 
    15531570The SSS restoring term should be viewed as a flux correction on freshwater fluxes to 
    15541571reduce the uncertainties we have on the observed freshwater budget. 
     
    15931610% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?} 
    15941611 
    1595 \subsection{Interface to CICE (\protect\mdl{sbcice\_cice})} 
     1612\subsection[Interface to CICE (\textit{sbcice\_cice.F90})] 
     1613{Interface to CICE (\protect\mdl{sbcice\_cice})} 
    15961614\label{subsec:SBC_cice} 
    15971615 
     
    16261644%        Freshwater budget control  
    16271645% ------------------------------------------------------------------------------------------------------------- 
    1628 \subsection{Freshwater budget control (\protect\mdl{sbcfwb})} 
     1646\subsection[Freshwater budget control (\textit{sbcfwb.F90})] 
     1647{Freshwater budget control (\protect\mdl{sbcfwb})} 
    16291648\label{subsec:SBC_fwb} 
    16301649 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_STO.tex

    r10442 r11263  
    1515 
    1616The stochastic parametrization module aims to explicitly simulate uncertainties in the model. 
    17 More particularly, \cite{Brankart_OM2013} has shown that, 
     17More particularly, \cite{brankart_OM13} has shown that, 
    1818because of the nonlinearity of the seawater equation of state, unresolved scales represent a major source of 
    1919uncertainties in the computation of the large scale horizontal density gradient (from T/S large scale fields), 
     
    4646A generic approach is thus to add one single new module in NEMO, 
    4747generating processes with appropriate statistics to simulate each kind of uncertainty in the model 
    48 (see \cite{Brankart_al_GMD2015} for more details). 
     48(see \cite{brankart.candille.ea_GMD15} for more details). 
    4949 
    5050In practice, at every model grid point, 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_TRA.tex

    r10544 r11263  
    5555 
    5656The user has the option of extracting each tendency term on the RHS of the tracer equation for output 
    57 (\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}~\forcode{= .true.}), as described in \autoref{chap:DIA}. 
     57(\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}\forcode{ = .true.}), as described in \autoref{chap:DIA}. 
    5858 
    5959% ================================================================ 
    6060% Tracer Advection 
    6161% ================================================================ 
    62 \section{Tracer advection (\protect\mdl{traadv})} 
     62\section[Tracer advection (\textit{traadv.F90})] 
     63{Tracer advection (\protect\mdl{traadv})} 
    6364\label{sec:TRA_adv} 
    6465%------------------------------------------namtra_adv----------------------------------------------------- 
     
    8182Indeed, it is obtained by using the following equality: $\nabla \cdot (\vect U \, T) = \vect U \cdot \nabla T$ which 
    8283results from the use of the continuity equation, $\partial_t e_3 + e_3 \; \nabla \cdot \vect U = 0$ 
    83 (which reduces to $\nabla \cdot \vect U = 0$ in linear free surface, \ie \np{ln\_linssh}~\forcode{= .true.}). 
     84(which reduces to $\nabla \cdot \vect U = 0$ in linear free surface, \ie \np{ln\_linssh}\forcode{ = .true.}). 
    8485Therefore it is of paramount importance to design the discrete analogue of the advection tendency so that 
    8586it is consistent with the continuity equation in order to enforce the conservation properties of 
     
    9091\begin{figure}[!t] 
    9192  \begin{center} 
    92     \includegraphics[]{Fig_adv_scheme} 
     93    \includegraphics[width=\textwidth]{Fig_adv_scheme} 
    9394    \caption{ 
    9495      \protect\label{fig:adv_scheme} 
     
    119120\begin{description} 
    120121\item[linear free surface:] 
    121   (\np{ln\_linssh}~\forcode{= .true.}) 
     122  (\np{ln\_linssh}\forcode{ = .true.}) 
    122123  the first level thickness is constant in time: 
    123124  the vertical boundary condition is applied at the fixed surface $z = 0$ rather than on 
     
    127128  the first level tracer value. 
    128129\item[non-linear free surface:] 
    129   (\np{ln\_linssh}~\forcode{= .false.}) 
     130  (\np{ln\_linssh}\forcode{ = .false.}) 
    130131  convergence/divergence in the first ocean level moves the free surface up/down. 
    131132  There is no tracer advection through it so that the advective fluxes through the surface are also zero. 
     
    136137Nevertheless, in the latter case, it is achieved to a good approximation since 
    137138the non-conservative term is the product of the time derivative of the tracer and the free surface height, 
    138 two quantities that are not correlated \citep{Roullet_Madec_JGR00, Griffies_al_MWR01, Campin2004}. 
    139  
    140 The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco}) is 
     139two quantities that are not correlated \citep{roullet.madec_JGR00, griffies.pacanowski.ea_MWR01, campin.adcroft.ea_OM04}. 
     140 
     141The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco?}) is 
    141142the centred (\textit{now}) \textit{effective} ocean velocity, \ie the \textit{eulerian} velocity 
    142143(see \autoref{chap:DYN}) plus the eddy induced velocity (\textit{eiv}) and/or 
     
    183184%        2nd and 4th order centred schemes 
    184185% ------------------------------------------------------------------------------------------------------------- 
    185 \subsection{CEN: Centred scheme (\protect\np{ln\_traadv\_cen}~\forcode{= .true.})} 
     186\subsection[CEN: Centred scheme (\forcode{ln_traadv_cen = .true.})] 
     187{CEN: Centred scheme (\protect\np{ln\_traadv\_cen}\forcode{ = .true.})} 
    186188\label{subsec:TRA_adv_cen} 
    187189 
    188190%        2nd order centred scheme   
    189191 
    190 The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}~\forcode{= .true.}. 
     192The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}\forcode{ = .true.}. 
    191193Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by 
    192194setting \np{nn\_cen\_h} and \np{nn\_cen\_v} to $2$ or $4$. 
     
    220222  \tau_u^{cen4} = \overline{T - \frac{1}{6} \, \delta_i \Big[ \delta_{i + 1/2}[T] \, \Big]}^{\,i + 1/2} 
    221223\end{equation} 
    222 In the vertical direction (\np{nn\_cen\_v}~\forcode{= 4}), 
    223 a $4^{th}$ COMPACT interpolation has been prefered \citep{Demange_PhD2014}. 
     224In the vertical direction (\np{nn\_cen\_v}\forcode{ = 4}), 
     225a $4^{th}$ COMPACT interpolation has been prefered \citep{demange_phd14}. 
    224226In the COMPACT scheme, both the field and its derivative are interpolated, which leads, after a matrix inversion, 
    225 spectral characteristics similar to schemes of higher order \citep{Lele_JCP1992}.  
     227spectral characteristics similar to schemes of higher order \citep{lele_JCP92}.  
    226228 
    227229Strictly speaking, the CEN4 scheme is not a $4^{th}$ order advection scheme but 
     
    250252%        FCT scheme   
    251253% ------------------------------------------------------------------------------------------------------------- 
    252 \subsection{FCT: Flux Corrected Transport scheme (\protect\np{ln\_traadv\_fct}~\forcode{= .true.})} 
     254\subsection[FCT: Flux Corrected Transport scheme (\forcode{ln_traadv_fct = .true.})] 
     255{FCT: Flux Corrected Transport scheme (\protect\np{ln\_traadv\_fct}\forcode{ = .true.})} 
    253256\label{subsec:TRA_adv_tvd} 
    254257 
    255 The Flux Corrected Transport schemes (FCT) is used when \np{ln\_traadv\_fct}~\forcode{= .true.}. 
     258The Flux Corrected Transport schemes (FCT) is used when \np{ln\_traadv\_fct}\forcode{ = .true.}. 
    256259Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by 
    257260setting \np{nn\_fct\_h} and \np{nn\_fct\_v} to $2$ or $4$. 
     
    277280(\ie it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}). 
    278281There exist many ways to define $c_u$, each corresponding to a different FCT scheme. 
    279 The one chosen in \NEMO is described in \citet{Zalesak_JCP79}. 
     282The one chosen in \NEMO is described in \citet{zalesak_JCP79}. 
    280283$c_u$ only departs from $1$ when the advective term produces a local extremum in the tracer field. 
    281284The resulting scheme is quite expensive but \textit{positive}. 
    282285It can be used on both active and passive tracers. 
    283 A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{Levy_al_GRL01}. 
     286A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{levy.estublier.ea_GRL01}. 
    284287 
    285288An additional option has been added controlled by \np{nn\_fct\_zts}. 
     
    287290a $2^{nd}$ order FCT scheme is used on both horizontal and vertical direction, but on the latter, 
    288291a split-explicit time stepping is used, with a number of sub-timestep equals to \np{nn\_fct\_zts}. 
    289 This option can be useful when the size of the timestep is limited by vertical advection \citep{Lemarie_OM2015}. 
     292This option can be useful when the size of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}. 
    290293Note that in this case, a similar split-explicit time stepping should be used on vertical advection of momentum to 
    291294insure a better stability (see \autoref{subsec:DYN_zad}). 
     
    300303%        MUSCL scheme   
    301304% ------------------------------------------------------------------------------------------------------------- 
    302 \subsection{MUSCL: Monotone Upstream Scheme for Conservative Laws (\protect\np{ln\_traadv\_mus}~\forcode{= .true.})} 
     305\subsection[MUSCL: Monotone Upstream Scheme for Conservative Laws (\forcode{ln_traadv_mus = .true.})] 
     306{MUSCL: Monotone Upstream Scheme for Conservative Laws (\protect\np{ln\_traadv\_mus}\forcode{ = .true.})} 
    303307\label{subsec:TRA_adv_mus} 
    304308 
    305 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln\_traadv\_mus}~\forcode{= .true.}. 
     309The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln\_traadv\_mus}\forcode{ = .true.}. 
    306310MUSCL implementation can be found in the \mdl{traadv\_mus} module. 
    307311 
    308 MUSCL has been first implemented in \NEMO by \citet{Levy_al_GRL01}. 
     312MUSCL has been first implemented in \NEMO by \citet{levy.estublier.ea_GRL01}. 
    309313In its formulation, the tracer at velocity points is evaluated assuming a linear tracer variation between 
    310314two $T$-points (\autoref{fig:adv_scheme}). 
     
    331335This choice ensure the \textit{positive} character of the scheme. 
    332336In addition, fluxes round a grid-point where a runoff is applied can optionally be computed using upstream fluxes 
    333 (\np{ln\_mus\_ups}~\forcode{= .true.}). 
     337(\np{ln\_mus\_ups}\forcode{ = .true.}). 
    334338 
    335339% ------------------------------------------------------------------------------------------------------------- 
    336340%        UBS scheme   
    337341% ------------------------------------------------------------------------------------------------------------- 
    338 \subsection{UBS a.k.a. UP3: Upstream-Biased Scheme (\protect\np{ln\_traadv\_ubs}~\forcode{= .true.})} 
     342\subsection[UBS a.k.a. UP3: Upstream-Biased Scheme (\forcode{ln_traadv_ubs = .true.})] 
     343{UBS a.k.a. UP3: Upstream-Biased Scheme (\protect\np{ln\_traadv\_ubs}\forcode{ = .true.})} 
    339344\label{subsec:TRA_adv_ubs} 
    340345 
    341 The Upstream-Biased Scheme (UBS) is used when \np{ln\_traadv\_ubs}~\forcode{= .true.}. 
     346The Upstream-Biased Scheme (UBS) is used when \np{ln\_traadv\_ubs}\forcode{ = .true.}. 
    342347UBS implementation can be found in the \mdl{traadv\_mus} module. 
    343348 
     
    358363 
    359364This results in a dissipatively dominant (i.e. hyper-diffusive) truncation error 
    360 \citep{Shchepetkin_McWilliams_OM05}. 
    361 The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}. 
     365\citep{shchepetkin.mcwilliams_OM05}. 
     366The overall performance of the advection scheme is similar to that reported in \cite{farrow.stevens_JPO95}. 
    362367It is a relatively good compromise between accuracy and smoothness. 
    363368Nevertheless the scheme is not \textit{positive}, meaning that false extrema are permitted, 
     
    367372The intrinsic diffusion of UBS makes its use risky in the vertical direction where 
    368373the control of artificial diapycnal fluxes is of paramount importance 
    369 \citep{Shchepetkin_McWilliams_OM05, Demange_PhD2014}. 
     374\citep{shchepetkin.mcwilliams_OM05, demange_phd14}. 
    370375Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme or a $4^th$ order COMPACT scheme 
    371 (\np{nn\_cen\_v}~\forcode{= 2 or 4}). 
     376(\np{nn\_cen\_v}\forcode{ = 2 or 4}). 
    372377 
    373378For stability reasons (see \autoref{chap:STP}), the first term  in \autoref{eq:tra_adv_ubs} 
     
    376381(which is the diffusive part of the scheme), 
    377382is evaluated using the \textit{before} tracer (forward in time). 
    378 This choice is discussed by \citet{Webb_al_JAOT98} in the context of the QUICK advection scheme. 
     383This choice is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the QUICK advection scheme. 
    379384UBS and QUICK schemes only differ by one coefficient. 
    380 Replacing 1/6 with 1/8 in \autoref{eq:tra_adv_ubs} leads to the QUICK advection scheme \citep{Webb_al_JAOT98}. 
     385Replacing 1/6 with 1/8 in \autoref{eq:tra_adv_ubs} leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 
    381386This option is not available through a namelist parameter, since the 1/6 coefficient is hard coded. 
    382387Nevertheless it is quite easy to make the substitution in the \mdl{traadv\_ubs} module and obtain a QUICK scheme. 
     
    408413%        QCK scheme   
    409414% ------------------------------------------------------------------------------------------------------------- 
    410 \subsection{QCK: QuiCKest scheme (\protect\np{ln\_traadv\_qck}~\forcode{= .true.})} 
     415\subsection[QCK: QuiCKest scheme (\forcode{ln_traadv_qck = .true.})] 
     416{QCK: QuiCKest scheme (\protect\np{ln\_traadv\_qck}\forcode{ = .true.})} 
    411417\label{subsec:TRA_adv_qck} 
    412418 
    413419The Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms (QUICKEST) scheme 
    414 proposed by \citet{Leonard1979} is used when \np{ln\_traadv\_qck}~\forcode{= .true.}. 
     420proposed by \citet{leonard_CMAME79} is used when \np{ln\_traadv\_qck}\forcode{ = .true.}. 
    415421QUICKEST implementation can be found in the \mdl{traadv\_qck} module. 
    416422 
    417423QUICKEST is the third order Godunov scheme which is associated with the ULTIMATE QUICKEST limiter 
    418 \citep{Leonard1991}. 
     424\citep{leonard_CMAME91}. 
    419425It has been implemented in NEMO by G. Reffray (MERCATOR-ocean) and can be found in the \mdl{traadv\_qck} module. 
    420426The resulting scheme is quite expensive but \textit{positive}. 
     
    431437% Tracer Lateral Diffusion 
    432438% ================================================================ 
    433 \section{Tracer lateral diffusion (\protect\mdl{traldf})} 
     439\section[Tracer lateral diffusion (\textit{traldf.F90})] 
     440{Tracer lateral diffusion (\protect\mdl{traldf})} 
    434441\label{sec:TRA_ldf} 
    435442%-----------------------------------------nam_traldf------------------------------------------------------ 
     
    453460except for the pure vertical component that appears when a rotation tensor is used. 
    454461This latter component is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}). 
    455 When \np{ln\_traldf\_msc}~\forcode{= .true.}, a Method of Stabilizing Correction is used in which 
    456 the pure vertical component is split into an explicit and an implicit part \citep{Lemarie_OM2012}. 
     462When \np{ln\_traldf\_msc}\forcode{ = .true.}, a Method of Stabilizing Correction is used in which 
     463the pure vertical component is split into an explicit and an implicit part \citep{lemarie.debreu.ea_OM12}. 
    457464 
    458465% ------------------------------------------------------------------------------------------------------------- 
    459466%        Type of operator 
    460467% ------------------------------------------------------------------------------------------------------------- 
    461 \subsection[Type of operator (\protect\np{ln\_traldf}\{\_NONE,\_lap,\_blp\}\})]{Type of operator (\protect\np{ln\_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp}) }  
     468\subsection[Type of operator (\texttt{ln\_traldf}\{\texttt{\_NONE,\_lap,\_blp}\})] 
     469{Type of operator (\protect\np{ln\_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp}) }  
    462470\label{subsec:TRA_ldf_op} 
    463471 
     
    465473 
    466474\begin{description} 
    467 \item[\np{ln\_traldf\_NONE}~\forcode{= .true.}:] 
     475\item[\np{ln\_traldf\_NONE}\forcode{ = .true.}:] 
    468476  no operator selected, the lateral diffusive tendency will not be applied to the tracer equation. 
    469477  This option can be used when the selected advection scheme is diffusive enough (MUSCL scheme for example). 
    470 \item[\np{ln\_traldf\_lap}~\forcode{= .true.}:] 
     478\item[\np{ln\_traldf\_lap}\forcode{ = .true.}:] 
    471479  a laplacian operator is selected. 
    472480  This harmonic operator takes the following expression:  $\mathpzc{L}(T) = \nabla \cdot A_{ht} \; \nabla T $, 
    473481  where the gradient operates along the selected direction (see \autoref{subsec:TRA_ldf_dir}), 
    474482  and $A_{ht}$ is the eddy diffusivity coefficient expressed in $m^2/s$ (see \autoref{chap:LDF}). 
    475 \item[\np{ln\_traldf\_blp}~\forcode{= .true.}]: 
     483\item[\np{ln\_traldf\_blp}\forcode{ = .true.}]: 
    476484  a bilaplacian operator is selected. 
    477485  This biharmonic operator takes the following expression: 
     
    493501%        Direction of action 
    494502% ------------------------------------------------------------------------------------------------------------- 
    495 \subsection[Action direction (\protect\np{ln\_traldf}\{\_lev,\_hor,\_iso,\_triad\})]{Direction of action (\protect\np{ln\_traldf\_lev}, \protect\np{ln\_traldf\_hor}, \protect\np{ln\_traldf\_iso}, or \protect\np{ln\_traldf\_triad}) }  
     503\subsection[Action direction (\texttt{ln\_traldf}\{\texttt{\_lev,\_hor,\_iso,\_triad}\})] 
     504{Direction of action (\protect\np{ln\_traldf\_lev}, \protect\np{ln\_traldf\_hor}, \protect\np{ln\_traldf\_iso}, or \protect\np{ln\_traldf\_triad}) }  
    496505\label{subsec:TRA_ldf_dir} 
    497506 
    498507The choice of a direction of action determines the form of operator used. 
    499508The operator is a simple (re-entrant) laplacian acting in the (\textbf{i},\textbf{j}) plane when 
    500 iso-level option is used (\np{ln\_traldf\_lev}~\forcode{= .true.}) or 
     509iso-level option is used (\np{ln\_traldf\_lev}\forcode{ = .true.}) or 
    501510when a horizontal (\ie geopotential) operator is demanded in \textit{z}-coordinate 
    502511(\np{ln\_traldf\_hor} and \np{ln\_zco} equal \forcode{.true.}). 
     
    519528%       iso-level operator 
    520529% ------------------------------------------------------------------------------------------------------------- 
    521 \subsection{Iso-level (bi -)laplacian operator ( \protect\np{ln\_traldf\_iso}) } 
     530\subsection[Iso-level (bi-)laplacian operator (\texttt{ln\_traldf\_iso})] 
     531{Iso-level (bi-)laplacian operator ( \protect\np{ln\_traldf\_iso})} 
    522532\label{subsec:TRA_ldf_lev} 
    523533 
     
    537547It is a \textit{horizontal} operator (\ie acting along geopotential surfaces) in 
    538548the $z$-coordinate with or without partial steps, but is simply an iso-level operator in the $s$-coordinate. 
    539 It is thus used when, in addition to \np{ln\_traldf\_lap} or \np{ln\_traldf\_blp}~\forcode{= .true.}, 
    540 we have \np{ln\_traldf\_lev}~\forcode{= .true.} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}~\forcode{= .true.}. 
     549It is thus used when, in addition to \np{ln\_traldf\_lap} or \np{ln\_traldf\_blp}\forcode{ = .true.}, 
     550we have \np{ln\_traldf\_lev}\forcode{ = .true.} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}\forcode{ = .true.}. 
    541551In both cases, it significantly contributes to diapycnal mixing. 
    542552It is therefore never recommended, even when using it in the bilaplacian case. 
    543553 
    544 Note that in the partial step $z$-coordinate (\np{ln\_zps}~\forcode{= .true.}), 
     554Note that in the partial step $z$-coordinate (\np{ln\_zps}\forcode{ = .true.}), 
    545555tracers in horizontally adjacent cells are located at different depths in the vicinity of the bottom. 
    546556In this case, horizontal derivatives in (\autoref{eq:tra_ldf_lap}) at the bottom level require a specific treatment. 
     
    550560%         Rotated laplacian operator 
    551561% ------------------------------------------------------------------------------------------------------------- 
    552 \subsection{Standard and triad (bi -)laplacian operator} 
     562\subsection{Standard and triad (bi-)laplacian operator} 
    553563\label{subsec:TRA_ldf_iso_triad} 
    554564 
    555 %&&    Standard rotated (bi -)laplacian operator 
     565%&&    Standard rotated (bi-)laplacian operator 
    556566%&& ---------------------------------------------- 
    557 \subsubsection{Standard rotated (bi -)laplacian operator (\protect\mdl{traldf\_iso})} 
     567\subsubsection[Standard rotated (bi-)laplacian operator (\textit{traldf\_iso.F90})] 
     568{Standard rotated (bi-)laplacian operator (\protect\mdl{traldf\_iso})} 
    558569\label{subsec:TRA_ldf_iso} 
    559570The general form of the second order lateral tracer subgrid scale physics (\autoref{eq:PE_zdf}) 
     
    574585$r_1$ and $r_2$ are the slopes between the surface of computation ($z$- or $s$-surfaces) and 
    575586the surface along which the diffusion operator acts (\ie horizontal or iso-neutral surfaces). 
    576 It is thus used when, in addition to \np{ln\_traldf\_lap}~\forcode{= .true.}, 
    577 we have \np{ln\_traldf\_iso}~\forcode{= .true.}, 
    578 or both \np{ln\_traldf\_hor}~\forcode{= .true.} and \np{ln\_zco}~\forcode{= .true.}. 
     587It is thus used when, in addition to \np{ln\_traldf\_lap}\forcode{ = .true.}, 
     588we have \np{ln\_traldf\_iso}\forcode{ = .true.}, 
     589or both \np{ln\_traldf\_hor}\forcode{ = .true.} and \np{ln\_zco}\forcode{ = .true.}. 
    579590The way these slopes are evaluated is given in \autoref{sec:LDF_slp}. 
    580591At the surface, bottom and lateral boundaries, the turbulent fluxes of heat and salt are set to zero using 
     
    590601This formulation conserves the tracer but does not ensure the decrease of the tracer variance. 
    591602Nevertheless the treatment performed on the slopes (see \autoref{chap:LDF}) allows the model to run safely without 
    592 any additional background horizontal diffusion \citep{Guilyardi_al_CD01}. 
    593  
    594 Note that in the partial step $z$-coordinate (\np{ln\_zps}~\forcode{= .true.}), 
     603any additional background horizontal diffusion \citep{guilyardi.madec.ea_CD01}. 
     604 
     605Note that in the partial step $z$-coordinate (\np{ln\_zps}\forcode{ = .true.}), 
    595606the horizontal derivatives at the bottom level in \autoref{eq:tra_ldf_iso} require a specific treatment. 
    596607They are calculated in module zpshde, described in \autoref{sec:TRA_zpshde}. 
    597608 
    598 %&&     Triad rotated (bi -)laplacian operator 
     609%&&     Triad rotated (bi-)laplacian operator 
    599610%&&  ------------------------------------------- 
    600 \subsubsection{Triad rotated (bi -)laplacian operator (\protect\np{ln\_traldf\_triad})} 
     611\subsubsection[Triad rotated (bi-)laplacian operator (\textit{ln\_traldf\_triad})] 
     612{Triad rotated (bi-)laplacian operator (\protect\np{ln\_traldf\_triad})} 
    601613\label{subsec:TRA_ldf_triad} 
    602614 
    603 If the Griffies triad scheme is employed (\np{ln\_traldf\_triad}~\forcode{= .true.}; see \autoref{apdx:triad}) 
    604  
    605 An alternative scheme developed by \cite{Griffies_al_JPO98} which ensures tracer variance decreases 
    606 is also available in \NEMO (\np{ln\_traldf\_grif}~\forcode{= .true.}). 
     615If the Griffies triad scheme is employed (\np{ln\_traldf\_triad}\forcode{ = .true.}; see \autoref{apdx:triad}) 
     616 
     617An alternative scheme developed by \cite{griffies.gnanadesikan.ea_JPO98} which ensures tracer variance decreases 
     618is also available in \NEMO (\np{ln\_traldf\_grif}\forcode{ = .true.}). 
    607619A complete description of the algorithm is given in \autoref{apdx:triad}. 
    608620 
     
    632644% Tracer Vertical Diffusion 
    633645% ================================================================ 
    634 \section{Tracer vertical diffusion (\protect\mdl{trazdf})} 
     646\section[Tracer vertical diffusion (\textit{trazdf.F90})] 
     647{Tracer vertical diffusion (\protect\mdl{trazdf})} 
    635648\label{sec:TRA_zdf} 
    636649%--------------------------------------------namzdf--------------------------------------------------------- 
     
    663676 
    664677The large eddy coefficient found in the mixed layer together with high vertical resolution implies that 
    665 in the case of explicit time stepping (\np{ln\_zdfexp}~\forcode{= .true.}) 
     678in the case of explicit time stepping (\np{ln\_zdfexp}\forcode{ = .true.}) 
    666679there would be too restrictive a constraint on the time step. 
    667680Therefore, the default implicit time stepping is preferred for the vertical diffusion since 
    668681it overcomes the stability constraint. 
    669 A forward time differencing scheme (\np{ln\_zdfexp}~\forcode{= .true.}) using 
     682A forward time differencing scheme (\np{ln\_zdfexp}\forcode{ = .true.}) using 
    670683a time splitting technique (\np{nn\_zdfexp} $> 1$) is provided as an alternative. 
    671684Namelist variables \np{ln\_zdfexp} and \np{nn\_zdfexp} apply to both tracers and dynamics. 
     
    680693%        surface boundary condition 
    681694% ------------------------------------------------------------------------------------------------------------- 
    682 \subsection{Surface boundary condition (\protect\mdl{trasbc})} 
     695\subsection[Surface boundary condition (\textit{trasbc.F90})] 
     696{Surface boundary condition (\protect\mdl{trasbc})} 
    683697\label{subsec:TRA_sbc} 
    684698 
     
    730744Such time averaging prevents the divergence of odd and even time step (see \autoref{chap:STP}). 
    731745 
    732 In the linear free surface case (\np{ln\_linssh}~\forcode{= .true.}), an additional term has to be added on 
     746In the linear free surface case (\np{ln\_linssh}\forcode{ = .true.}), an additional term has to be added on 
    733747both temperature and salinity. 
    734748On temperature, this term remove the heat content associated with mass exchange that has been added to $Q_{ns}$. 
     
    747761Note that an exact conservation of heat and salt content is only achieved with non-linear free surface. 
    748762In the linear free surface case, there is a small imbalance. 
    749 The imbalance is larger than the imbalance associated with the Asselin time filter \citep{Leclair_Madec_OM09}. 
     763The imbalance is larger than the imbalance associated with the Asselin time filter \citep{leclair.madec_OM09}. 
    750764This is the reason why the modified filter is not applied in the linear free surface case (see \autoref{chap:STP}). 
    751765 
     
    753767%        Solar Radiation Penetration  
    754768% ------------------------------------------------------------------------------------------------------------- 
    755 \subsection{Solar radiation penetration (\protect\mdl{traqsr})} 
     769\subsection[Solar radiation penetration (\textit{traqsr.F90})] 
     770{Solar radiation penetration (\protect\mdl{traqsr})} 
    756771\label{subsec:TRA_qsr} 
    757772%--------------------------------------------namqsr-------------------------------------------------------- 
     
    761776 
    762777Options are defined through the \ngn{namtra\_qsr} namelist variables. 
    763 When the penetrative solar radiation option is used (\np{ln\_flxqsr}~\forcode{= .true.}), 
     778When the penetrative solar radiation option is used (\np{ln\_flxqsr}\forcode{ = .true.}), 
    764779the solar radiation penetrates the top few tens of meters of the ocean. 
    765 If it is not used (\np{ln\_flxqsr}~\forcode{= .false.}) all the heat flux is absorbed in the first ocean level. 
     780If it is not used (\np{ln\_flxqsr}\forcode{ = .false.}) all the heat flux is absorbed in the first ocean level. 
    766781Thus, in the former case a term is added to the time evolution equation of temperature \autoref{eq:PE_tra_T} and 
    767782the surface boundary condition is modified to take into account only the non-penetrative part of the surface  
     
    792807larger depths where it contributes to local heating. 
    793808The way this second part of the solar energy penetrates into the ocean depends on which formulation is chosen. 
    794 In the simple 2-waveband light penetration scheme (\np{ln\_qsr\_2bd}~\forcode{= .true.}) 
     809In the simple 2-waveband light penetration scheme (\np{ln\_qsr\_2bd}\forcode{ = .true.}) 
    795810a chlorophyll-independent monochromatic formulation is chosen for the shorter wavelengths, 
    796 leading to the following expression \citep{Paulson1977}: 
     811leading to the following expression \citep{paulson.simpson_JPO77}: 
    797812\[ 
    798813  % \label{eq:traqsr_iradiance} 
     
    805820 
    806821Such assumptions have been shown to provide a very crude and simplistic representation of 
    807 observed light penetration profiles (\cite{Morel_JGR88}, see also \autoref{fig:traqsr_irradiance}). 
     822observed light penetration profiles (\cite{morel_JGR88}, see also \autoref{fig:traqsr_irradiance}). 
    808823Light absorption in the ocean depends on particle concentration and is spectrally selective. 
    809 \cite{Morel_JGR88} has shown that an accurate representation of light penetration can be provided by 
     824\cite{morel_JGR88} has shown that an accurate representation of light penetration can be provided by 
    810825a 61 waveband formulation. 
    811826Unfortunately, such a model is very computationally expensive. 
    812 Thus, \cite{Lengaigne_al_CD07} have constructed a simplified version of this formulation in which 
     827Thus, \cite{lengaigne.menkes.ea_CD07} have constructed a simplified version of this formulation in which 
    813828visible light is split into three wavebands: blue (400-500 nm), green (500-600 nm) and red (600-700nm). 
    814829For each wave-band, the chlorophyll-dependent attenuation coefficient is fitted to the coefficients computed from 
    815 the full spectral model of \cite{Morel_JGR88} (as modified by \cite{Morel_Maritorena_JGR01}), 
     830the full spectral model of \cite{morel_JGR88} (as modified by \cite{morel.maritorena_JGR01}), 
    816831assuming the same power-law relationship. 
    817832As shown in \autoref{fig:traqsr_irradiance}, this formulation, called RGB (Red-Green-Blue), 
     
    820835The 2-bands formulation does not reproduce the full model very well. 
    821836 
    822 The RGB formulation is used when \np{ln\_qsr\_rgb}~\forcode{= .true.}. 
     837The RGB formulation is used when \np{ln\_qsr\_rgb}\forcode{ = .true.}. 
    823838The RGB attenuation coefficients (\ie the inverses of the extinction length scales) are tabulated over 
    82483961 nonuniform chlorophyll classes ranging from 0.01 to 10 g.Chl/L 
     
    827842 
    828843\begin{description} 
    829 \item[\np{nn\_chdta}~\forcode{= 0}] 
     844\item[\np{nn\_chdta}\forcode{ = 0}] 
    830845  a constant 0.05 g.Chl/L value everywhere ;  
    831 \item[\np{nn\_chdta}~\forcode{= 1}] 
     846\item[\np{nn\_chdta}\forcode{ = 1}] 
    832847  an observed time varying chlorophyll deduced from satellite surface ocean color measurement spread uniformly in 
    833848  the vertical direction; 
    834 \item[\np{nn\_chdta}~\forcode{= 2}] 
     849\item[\np{nn\_chdta}\forcode{ = 2}] 
    835850  same as previous case except that a vertical profile of chlorophyl is used. 
    836   Following \cite{Morel_Berthon_LO89}, the profile is computed from the local surface chlorophyll value; 
    837 \item[\np{ln\_qsr\_bio}~\forcode{= .true.}] 
     851  Following \cite{morel.berthon_LO89}, the profile is computed from the local surface chlorophyll value; 
     852\item[\np{ln\_qsr\_bio}\forcode{ = .true.}] 
    838853  simulated time varying chlorophyll by TOP biogeochemical model. 
    839854  In this case, the RGB formulation is used to calculate both the phytoplankton light limitation in 
     
    856871\begin{figure}[!t] 
    857872  \begin{center} 
    858     \includegraphics[]{Fig_TRA_Irradiance} 
     873    \includegraphics[width=\textwidth]{Fig_TRA_Irradiance} 
    859874    \caption{ 
    860875      \protect\label{fig:traqsr_irradiance} 
     
    865880      61 waveband Morel (1988) formulation (black) for a chlorophyll concentration of 
    866881      (a) Chl=0.05 mg/m$^3$ and (b) Chl=0.5 mg/m$^3$. 
    867       From \citet{Lengaigne_al_CD07}. 
     882      From \citet{lengaigne.menkes.ea_CD07}. 
    868883    } 
    869884  \end{center} 
     
    874889%        Bottom Boundary Condition 
    875890% ------------------------------------------------------------------------------------------------------------- 
    876 \subsection{Bottom boundary condition (\protect\mdl{trabbc})} 
     891\subsection[Bottom boundary condition (\textit{trabbc.F90})] 
     892{Bottom boundary condition (\protect\mdl{trabbc})} 
    877893\label{subsec:TRA_bbc} 
    878894%--------------------------------------------nambbc-------------------------------------------------------- 
     
    883899\begin{figure}[!t] 
    884900  \begin{center} 
    885     \includegraphics[]{Fig_TRA_geoth} 
     901    \includegraphics[width=\textwidth]{Fig_TRA_geoth} 
    886902    \caption{ 
    887903      \protect\label{fig:geothermal} 
    888       Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{Emile-Geay_Madec_OS09}. 
    889       It is inferred from the age of the sea floor and the formulae of \citet{Stein_Stein_Nat92}. 
     904      Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{emile-geay.madec_OS09}. 
     905      It is inferred from the age of the sea floor and the formulae of \citet{stein.stein_N92}. 
    890906    } 
    891907  \end{center} 
     
    897913This is the default option in \NEMO, and it is implemented using the masking technique. 
    898914However, there is a non-zero heat flux across the seafloor that is associated with solid earth cooling. 
    899 This flux is weak compared to surface fluxes (a mean global value of $\sim 0.1 \, W/m^2$ \citep{Stein_Stein_Nat92}), 
     915This flux is weak compared to surface fluxes (a mean global value of $\sim 0.1 \, W/m^2$ \citep{stein.stein_N92}), 
    900916but it warms systematically the ocean and acts on the densest water masses. 
    901917Taking this flux into account in a global ocean model increases the deepest overturning cell 
    902 (\ie the one associated with the Antarctic Bottom Water) by a few Sverdrups \citep{Emile-Geay_Madec_OS09}. 
     918(\ie the one associated with the Antarctic Bottom Water) by a few Sverdrups \citep{emile-geay.madec_OS09}. 
    903919 
    904920Options are defined through the  \ngn{namtra\_bbc} namelist variables. 
     
    907923the \np{nn\_geoflx\_cst}, which is also a namelist parameter. 
    908924When \np{nn\_geoflx} is set to 2, a spatially varying geothermal heat flux is introduced which is provided in 
    909 the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:geothermal}) \citep{Emile-Geay_Madec_OS09}. 
     925the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:geothermal}) \citep{emile-geay.madec_OS09}. 
    910926 
    911927% ================================================================ 
    912928% Bottom Boundary Layer 
    913929% ================================================================ 
    914 \section{Bottom boundary layer (\protect\mdl{trabbl} - \protect\key{trabbl})} 
     930\section[Bottom boundary layer (\textit{trabbl.F90} - \texttt{\textbf{key\_trabbl}})] 
     931{Bottom boundary layer (\protect\mdl{trabbl} - \protect\key{trabbl})} 
    915932\label{sec:TRA_bbl} 
    916933%--------------------------------------------nambbl--------------------------------------------------------- 
     
    931948sometimes over a thickness much larger than the thickness of the observed gravity plume. 
    932949A similar problem occurs in the $s$-coordinate when the thickness of the bottom level varies rapidly downstream of 
    933 a sill \citep{Willebrand_al_PO01}, and the thickness of the plume is not resolved. 
    934  
    935 The idea of the bottom boundary layer (BBL) parameterisation, first introduced by \citet{Beckmann_Doscher1997}, 
     950a sill \citep{willebrand.barnier.ea_PO01}, and the thickness of the plume is not resolved. 
     951 
     952The idea of the bottom boundary layer (BBL) parameterisation, first introduced by \citet{beckmann.doscher_JPO97}, 
    936953is to allow a direct communication between two adjacent bottom cells at different levels, 
    937954whenever the densest water is located above the less dense water. 
     
    939956In the current implementation of the BBL, only the tracers are modified, not the velocities. 
    940957Furthermore, it only connects ocean bottom cells, and therefore does not include all the improvements introduced by 
    941 \citet{Campin_Goosse_Tel99}. 
     958\citet{campin.goosse_T99}. 
    942959 
    943960% ------------------------------------------------------------------------------------------------------------- 
    944961%        Diffusive BBL 
    945962% ------------------------------------------------------------------------------------------------------------- 
    946 \subsection{Diffusive bottom boundary layer (\protect\np{nn\_bbl\_ldf}~\forcode{= 1})} 
     963\subsection[Diffusive bottom boundary layer (\forcode{nn_bbl_ldf = 1})] 
     964{Diffusive bottom boundary layer (\protect\np{nn\_bbl\_ldf}\forcode{ = 1})} 
    947965\label{subsec:TRA_bbl_diff} 
    948966 
     
    955973with $\nabla_\sigma$ the lateral gradient operator taken between bottom cells, and 
    956974$A_l^\sigma$ the lateral diffusivity in the BBL. 
    957 Following \citet{Beckmann_Doscher1997}, the latter is prescribed with a spatial dependence, 
     975Following \citet{beckmann.doscher_JPO97}, the latter is prescribed with a spatial dependence, 
    958976\ie in the conditional form 
    959977\begin{equation} 
     
    9831001%        Advective BBL 
    9841002% ------------------------------------------------------------------------------------------------------------- 
    985 \subsection{Advective bottom boundary layer  (\protect\np{nn\_bbl\_adv}~\forcode{= 1..2})} 
     1003\subsection[Advective bottom boundary layer (\forcode{nn_bbl_adv = [12]})] 
     1004{Advective bottom boundary layer (\protect\np{nn\_bbl\_adv}\forcode{ = [12]})} 
    9861005\label{subsec:TRA_bbl_adv} 
    9871006 
     
    9941013\begin{figure}[!t] 
    9951014  \begin{center} 
    996     \includegraphics[]{Fig_BBL_adv} 
     1015    \includegraphics[width=\textwidth]{Fig_BBL_adv} 
    9971016    \caption{ 
    9981017      \protect\label{fig:bbl} 
     
    10141033%%%gmcomment   :  this section has to be really written 
    10151034 
    1016 When applying an advective BBL (\np{nn\_bbl\_adv}~\forcode{= 1..2}), an overturning circulation is added which 
     1035When applying an advective BBL (\np{nn\_bbl\_adv}\forcode{ = 1..2}), an overturning circulation is added which 
    10171036connects two adjacent bottom grid-points only if dense water overlies less dense water on the slope. 
    10181037The density difference causes dense water to move down the slope. 
    10191038 
    1020 \np{nn\_bbl\_adv}~\forcode{= 1}: 
     1039\np{nn\_bbl\_adv}\forcode{ = 1}: 
    10211040the downslope velocity is chosen to be the Eulerian ocean velocity just above the topographic step 
    1022 (see black arrow in \autoref{fig:bbl}) \citep{Beckmann_Doscher1997}. 
     1041(see black arrow in \autoref{fig:bbl}) \citep{beckmann.doscher_JPO97}. 
    10231042It is a \textit{conditional advection}, that is, advection is allowed only 
    10241043if dense water overlies less dense water on the slope (\ie $\nabla_\sigma \rho \cdot \nabla H < 0$) and 
    10251044if the velocity is directed towards greater depth (\ie $\vect U \cdot \nabla H > 0$). 
    10261045 
    1027 \np{nn\_bbl\_adv}~\forcode{= 2}: 
     1046\np{nn\_bbl\_adv}\forcode{ = 2}: 
    10281047the downslope velocity is chosen to be proportional to $\Delta \rho$, 
    1029 the density difference between the higher cell and lower cell densities \citep{Campin_Goosse_Tel99}. 
     1048the density difference between the higher cell and lower cell densities \citep{campin.goosse_T99}. 
    10301049The advection is allowed only  if dense water overlies less dense water on the slope 
    10311050(\ie $\nabla_\sigma \rho \cdot \nabla H < 0$). 
     
    10411060The parameter $\gamma$ should take a different value for each bathymetric step, but for simplicity, 
    10421061and because no direct estimation of this parameter is available, a uniform value has been assumed. 
    1043 The possible values for $\gamma$ range between 1 and $10~s$ \citep{Campin_Goosse_Tel99}. 
     1062The possible values for $\gamma$ range between 1 and $10~s$ \citep{campin.goosse_T99}. 
    10441063 
    10451064Scalar properties are advected by this additional transport $(u^{tr}_{bbl},v^{tr}_{bbl})$ using the upwind scheme. 
     
    10741093% Tracer damping 
    10751094% ================================================================ 
    1076 \section{Tracer damping (\protect\mdl{tradmp})} 
     1095\section[Tracer damping (\textit{tradmp.F90})] 
     1096{Tracer damping (\protect\mdl{tradmp})} 
    10771097\label{sec:TRA_dmp} 
    10781098%--------------------------------------------namtra_dmp------------------------------------------------- 
     
    11091129In the vicinity of these walls, $\gamma$ takes large values (equivalent to a time scale of a few days) whereas 
    11101130it is zero in the interior of the model domain. 
    1111 The second case corresponds to the use of the robust diagnostic method \citep{Sarmiento1982}. 
     1131The second case corresponds to the use of the robust diagnostic method \citep{sarmiento.bryan_JGR82}. 
    11121132It allows us to find the velocity field consistent with the model dynamics whilst 
    11131133having a $T$, $S$ field close to a given climatological field ($T_o$, $S_o$). 
     
    11211141only below the mixed layer (defined either on a density or $S_o$ criterion). 
    11221142It is common to set the damping to zero in the mixed layer as the adjustment time scale is short here 
    1123 \citep{Madec_al_JPO96}. 
     1143\citep{madec.delecluse.ea_JPO96}. 
    11241144 
    11251145For generating \ifile{resto}, see the documentation for the DMP tool provided with the source code under 
     
    11291149% Tracer time evolution 
    11301150% ================================================================ 
    1131 \section{Tracer time evolution (\protect\mdl{tranxt})} 
     1151\section[Tracer time evolution (\textit{tranxt.F90})] 
     1152{Tracer time evolution (\protect\mdl{tranxt})} 
    11321153\label{sec:TRA_nxt} 
    11331154%--------------------------------------------namdom----------------------------------------------------- 
     
    11371158 
    11381159Options are defined through the \ngn{namdom} namelist variables. 
    1139 The general framework for tracer time stepping is a modified leap-frog scheme \citep{Leclair_Madec_OM09}, 
     1160The general framework for tracer time stepping is a modified leap-frog scheme \citep{leclair.madec_OM09}, 
    11401161\ie a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:STP_mLF}): 
    11411162\begin{equation} 
     
    11511172(\ie fluxes plus content in mass exchanges). 
    11521173$\gamma$ is initialized as \np{rn\_atfp} (\textbf{namelist} parameter). 
    1153 Its default value is \np{rn\_atfp}~\forcode{= 10.e-3}. 
     1174Its default value is \np{rn\_atfp}\forcode{ = 10.e-3}. 
    11541175Note that the forcing correction term in the filter is not applied in linear free surface 
    1155 (\jp{lk\_vvl}~\forcode{= .false.}) (see \autoref{subsec:TRA_sbc}). 
     1176(\jp{lk\_vvl}\forcode{ = .false.}) (see \autoref{subsec:TRA_sbc}). 
    11561177Not also that in constant volume case, the time stepping is performed on $T$, not on its content, $e_{3t}T$. 
    11571178 
     
    11661187% Equation of State (eosbn2)  
    11671188% ================================================================ 
    1168 \section{Equation of state (\protect\mdl{eosbn2}) } 
     1189\section[Equation of state (\textit{eosbn2.F90})] 
     1190{Equation of state (\protect\mdl{eosbn2})} 
    11691191\label{sec:TRA_eosbn2} 
    11701192%--------------------------------------------nameos----------------------------------------------------- 
     
    11761198%        Equation of State 
    11771199% ------------------------------------------------------------------------------------------------------------- 
    1178 \subsection{Equation of seawater (\protect\np{nn\_eos}~\forcode{= -1..1})} 
     1200\subsection[Equation of seawater (\forcode{nn_eos = {-1,1}})] 
     1201{Equation of seawater (\protect\np{nn\_eos}\forcode{ = {-1,1}})} 
    11791202\label{subsec:TRA_eos} 
    11801203 
     
    11861209Nonlinearities of the EOS are of major importance, in particular influencing the circulation through 
    11871210determination of the static stability below the mixed layer, 
    1188 thus controlling rates of exchange between the atmosphere and the ocean interior \citep{Roquet_JPO2015}. 
    1189 Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{UNESCO1983}) or 
    1190 TEOS-10 \citep{TEOS10} standards should be used anytime a simulation of the real ocean circulation is attempted 
    1191 \citep{Roquet_JPO2015}. 
     1211thus controlling rates of exchange between the atmosphere and the ocean interior \citep{roquet.madec.ea_JPO15}. 
     1212Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{fofonoff.millard_bk83}) or 
     1213TEOS-10 \citep{ioc.iapso_bk10} standards should be used anytime a simulation of the real ocean circulation is attempted 
     1214\citep{roquet.madec.ea_JPO15}. 
    11921215The use of TEOS-10 is highly recommended because 
    11931216\textit{(i)}   it is the new official EOS, 
     
    11951218\textit{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature and 
    11961219practical salinity for EOS-980, both variables being more suitable for use as model variables 
    1197 \citep{TEOS10, Graham_McDougall_JPO13}. 
     1220\citep{ioc.iapso_bk10, graham.mcdougall_JPO13}. 
    11981221EOS-80 is an obsolescent feature of the NEMO system, kept only for backward compatibility. 
    11991222For process studies, it is often convenient to use an approximation of the EOS. 
    1200 To that purposed, a simplified EOS (S-EOS) inspired by \citet{Vallis06} is also available. 
     1223To that purposed, a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is also available. 
    12011224 
    12021225In the computer code, a density anomaly, $d_a = \rho / \rho_o - 1$, is computed, with $\rho_o$ a reference density. 
     
    12041227This is a sensible choice for the reference density used in a Boussinesq ocean climate model, as, 
    12051228with the exception of only a small percentage of the ocean, 
    1206 density in the World Ocean varies by no more than 2$\%$ from that value \citep{Gill1982}. 
     1229density in the World Ocean varies by no more than 2$\%$ from that value \citep{gill_bk82}. 
    12071230 
    12081231Options are defined through the \ngn{nameos} namelist variables, and in particular \np{nn\_eos} which 
     
    12101233 
    12111234\begin{description} 
    1212 \item[\np{nn\_eos}~\forcode{= -1}] 
    1213   the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used. 
     1235\item[\np{nn\_eos}\forcode{ = -1}] 
     1236  the polyTEOS10-bsq equation of seawater \citep{roquet.madec.ea_OM15} is used. 
    12141237  The accuracy of this approximation is comparable to the TEOS-10 rational function approximation, 
    12151238  but it is optimized for a boussinesq fluid and the polynomial expressions have simpler and 
     
    12171240  use in ocean models. 
    12181241  Note that a slightly higher precision polynomial form is now used replacement of 
    1219   the TEOS-10 rational function approximation for hydrographic data analysis \citep{TEOS10}. 
     1242  the TEOS-10 rational function approximation for hydrographic data analysis \citep{ioc.iapso_bk10}. 
    12201243  A key point is that conservative state variables are used: 
    12211244  Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \deg{C}, notation: $\Theta$). 
    12221245  The pressure in decibars is approximated by the depth in meters. 
    12231246  With TEOS10, the specific heat capacity of sea water, $C_p$, is a constant. 
    1224   It is set to $C_p = 3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{TEOS10}. 
     1247  It is set to $C_p = 3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{ioc.iapso_bk10}. 
    12251248  Choosing polyTEOS10-bsq implies that the state variables used by the model are $\Theta$ and $S_A$. 
    12261249  In particular, the initial state deined by the user have to be given as \textit{Conservative} Temperature and 
     
    12291252  either computing the air-sea and ice-sea fluxes (forced mode) or 
    12301253  sending the SST field to the atmosphere (coupled mode). 
    1231 \item[\np{nn\_eos}~\forcode{= 0}] 
     1254\item[\np{nn\_eos}\forcode{ = 0}] 
    12321255  the polyEOS80-bsq equation of seawater is used. 
    12331256  It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized to 
     
    12381261  The pressure in decibars is approximated by the depth in meters. 
    12391262  With thsi EOS, the specific heat capacity of sea water, $C_p$, is a function of temperature, salinity and 
    1240   pressure \citep{UNESCO1983}. 
     1263  pressure \citep{fofonoff.millard_bk83}. 
    12411264  Nevertheless, a severe assumption is made in order to have a heat content ($C_p T_p$) which 
    12421265  is conserved by the model: $C_p$ is set to a constant value, the TEOS10 value. 
    1243 \item[\np{nn\_eos}~\forcode{= 1}] 
    1244   a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen, 
     1266\item[\np{nn\_eos}\forcode{ = 1}] 
     1267  a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is chosen, 
    12451268  the coefficients of which has been optimized to fit the behavior of TEOS10 
    1246   (Roquet, personal comm.) (see also \citet{Roquet_JPO2015}). 
     1269  (Roquet, personal comm.) (see also \citet{roquet.madec.ea_JPO15}). 
    12471270  It provides a simplistic linear representation of both cabbeling and thermobaricity effects which 
    1248   is enough for a proper treatment of the EOS in theoretical studies \citep{Roquet_JPO2015}. 
     1271  is enough for a proper treatment of the EOS in theoretical studies \citep{roquet.madec.ea_JPO15}. 
    12491272  With such an equation of state there is no longer a distinction between 
    12501273  \textit{conservative} and \textit{potential} temperature, 
     
    13031326%        Brunt-V\"{a}is\"{a}l\"{a} Frequency 
    13041327% ------------------------------------------------------------------------------------------------------------- 
    1305 \subsection{Brunt-V\"{a}is\"{a}l\"{a} frequency (\protect\np{nn\_eos}~\forcode{= 0..2})} 
     1328\subsection[Brunt-V\"{a}is\"{a}l\"{a} frequency (\forcode{nn_eos = [0-2]})] 
     1329{Brunt-V\"{a}is\"{a}l\"{a} frequency (\protect\np{nn\_eos}\forcode{ = [0-2]})} 
    13061330\label{subsec:TRA_bn2} 
    13071331 
     
    13291353\label{subsec:TRA_fzp} 
    13301354 
    1331 The freezing point of seawater is a function of salinity and pressure \citep{UNESCO1983}: 
     1355The freezing point of seawater is a function of salinity and pressure \citep{fofonoff.millard_bk83}: 
    13321356\begin{equation} 
    13331357  \label{eq:tra_eos_fzp} 
     
    13571381% Horizontal Derivative in zps-coordinate  
    13581382% ================================================================ 
    1359 \section{Horizontal derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})} 
     1383\section[Horizontal derivative in \textit{zps}-coordinate (\textit{zpshde.F90})] 
     1384{Horizontal derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})} 
    13601385\label{sec:TRA_zpshde} 
    13611386 
     
    13631388I've changed "derivative" to "difference" and "mean" to "average"} 
    13641389 
    1365 With partial cells (\np{ln\_zps}~\forcode{= .true.}) at bottom and top (\np{ln\_isfcav}~\forcode{= .true.}), 
     1390With partial cells (\np{ln\_zps}\forcode{ = .true.}) at bottom and top (\np{ln\_isfcav}\forcode{ = .true.}), 
    13661391in general, tracers in horizontally adjacent cells live at different depths. 
    13671392Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} module) and 
    13681393the hydrostatic pressure gradient calculations (\mdl{dynhpg} module). 
    1369 The partial cell properties at the top (\np{ln\_isfcav}~\forcode{= .true.}) are computed in the same way as 
     1394The partial cell properties at the top (\np{ln\_isfcav}\forcode{ = .true.}) are computed in the same way as 
    13701395for the bottom. 
    13711396So, only the bottom interpolation is explained below. 
     
    13791404\begin{figure}[!p] 
    13801405  \begin{center} 
    1381     \includegraphics[]{Fig_partial_step_scheme} 
     1406    \includegraphics[width=\textwidth]{Fig_partial_step_scheme} 
    13821407    \caption{ 
    13831408      \protect\label{fig:Partial_step_scheme} 
    13841409      Discretisation of the horizontal difference and average of tracers in the $z$-partial step coordinate 
    1385       (\protect\np{ln\_zps}~\forcode{= .true.}) in the case $(e3w_k^{i + 1} - e3w_k^i) > 0$. 
     1410      (\protect\np{ln\_zps}\forcode{ = .true.}) in the case $(e3w_k^{i + 1} - e3w_k^i) > 0$. 
    13861411      A linear interpolation is used to estimate $\widetilde T_k^{i + 1}$, 
    13871412      the tracer value at the depth of the shallower tracer point of the two adjacent bottom $T$-points. 
  • NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r10442 r11263  
    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 (\ie \key{trabbl} defined, 
     27unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \np{ln\_trabbc} defined, 
    2828see \autoref{subsec:TRA_bbc}), and specified through a bottom friction parameterisation for momentum 
    29 (see \autoref{sec:ZDF_bfr}). 
     29(see \autoref{sec:ZDF_drg}).  
    3030 
    3131In this section we briefly discuss the various choices offered to compute the vertical eddy viscosity and 
     
    3333respectively (see \autoref{sec:TRA_zdf} and \autoref{sec:DYN_zdf}). 
    3434These coefficients can be assumed to be either constant, or a function of the local Richardson number, 
    35 or computed from a turbulent closure model (either TKE or GLS formulation). 
    36 The computation of these coefficients is initialized in the \mdl{zdfini} module and performed in 
    37 the \mdl{zdfric}, \mdl{zdftke} or \mdl{zdfgls} modules. 
     35or computed from a turbulent closure model (either TKE or GLS or OSMOSIS formulation). 
     36The computation of these coefficients is initialized in the \mdl{zdfphy} module and performed in 
     37the \mdl{zdfric}, \mdl{zdftke} or \mdl{zdfgls} or \mdl{zdfosm} modules. 
    3838The trends due to the vertical momentum and tracer diffusion, including the surface forcing, 
    3939are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively.  
    40 These trends can be computed using either a forward time stepping scheme 
    41 (namelist parameter \np{ln\_zdfexp}\forcode{ = .true.}) or a backward time stepping scheme 
    42 (\np{ln\_zdfexp}\forcode{ = .false.}) depending on the magnitude of the mixing coefficients, 
    43 and thus of the formulation used (see \autoref{chap:STP}). 
    44  
    45 % ------------------------------------------------------------------------------------------------------------- 
    46 %        Constant  
    47 % ------------------------------------------------------------------------------------------------------------- 
    48 \subsection{Constant (\protect\key{zdfcst})} 
    49 \label{subsec:ZDF_cst} 
    50 %--------------------------------------------namzdf--------------------------------------------------------- 
     40%These trends can be computed using either a forward time stepping scheme 
     41%(namelist parameter \np{ln\_zdfexp}\forcode{ = .true.}) or a backward time stepping scheme 
     42%(\np{ln\_zdfexp}\forcode{ = .false.}) depending on the magnitude of the mixing coefficients, 
     43%and thus of the formulation used (see \autoref{chap:STP}). 
     44 
     45%--------------------------------------------namzdf-------------------------------------------------------- 
    5146 
    5247\nlst{namzdf} 
    5348%-------------------------------------------------------------------------------------------------------------- 
    5449 
     50% ------------------------------------------------------------------------------------------------------------- 
     51%        Constant  
     52% ------------------------------------------------------------------------------------------------------------- 
     53\subsection[Constant (\forcode{ln_zdfcst = .true.})] 
     54{Constant (\protect\np{ln\_zdfcst}\forcode{ = .true.})} 
     55\label{subsec:ZDF_cst} 
     56 
    5557Options are defined through the \ngn{namzdf} namelist variables. 
    56 When \key{zdfcst} is defined, the momentum and tracer vertical eddy coefficients are set to 
     58When \np{ln\_zdfcst} is defined, the momentum and tracer vertical eddy coefficients are set to 
    5759constant values over the whole ocean. 
    5860This is the crudest way to define the vertical ocean physics. 
    59 It is recommended that this option is only used in process studies, not in basin scale simulations. 
     61It is recommended to use this option only in process studies, not in basin scale simulations. 
    6062Typical values used in this case are: 
    6163\begin{align*} 
     
    7274%        Richardson Number Dependent 
    7375% ------------------------------------------------------------------------------------------------------------- 
    74 \subsection{Richardson number dependent (\protect\key{zdfric})} 
     76\subsection[Richardson number dependent (\forcode{ln_zdfric = .true.})] 
     77{Richardson number dependent (\protect\np{ln\_zdfric}\forcode{ = .true.})} 
    7578\label{subsec:ZDF_ric} 
    7679 
     
    8083%-------------------------------------------------------------------------------------------------------------- 
    8184 
    82 When \key{zdfric} is defined, a local Richardson number dependent formulation for the vertical momentum and 
     85When \np{ln\_zdfric}\forcode{ = .true.}, a local Richardson number dependent formulation for the vertical momentum and 
    8386tracer eddy coefficients is set through the \ngn{namzdf\_ric} namelist variables. 
    8487The vertical mixing coefficients are diagnosed from the large scale variables computed by the model.  
     
    8790a dependency between the vertical eddy coefficients and the local Richardson number 
    8891(\ie the ratio of stratification to vertical shear). 
    89 Following \citet{Pacanowski_Philander_JPO81}, the following formulation has been implemented: 
     92Following \citet{pacanowski.philander_JPO81}, the following formulation has been implemented: 
    9093\[ 
    9194  % \label{eq:zdfric} 
     
    124127The final $h_{e}$ is further constrained by the adjustable bounds \np{rn\_mldmin} and \np{rn\_mldmax}. 
    125128Once $h_{e}$ is computed, the vertical eddy coefficients within $h_{e}$ are set to 
    126 the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{Lermusiaux2001}. 
     129the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{lermusiaux_JMS01}. 
    127130 
    128131% ------------------------------------------------------------------------------------------------------------- 
    129132%        TKE Turbulent Closure Scheme  
    130133% ------------------------------------------------------------------------------------------------------------- 
    131 \subsection{TKE turbulent closure scheme (\protect\key{zdftke})} 
     134\subsection[TKE turbulent closure scheme (\forcode{ln_zdftke = .true.})] 
     135{TKE turbulent closure scheme (\protect\np{ln\_zdftke}\forcode{ = .true.})} 
    132136\label{subsec:ZDF_tke} 
    133  
    134137%--------------------------------------------namzdf_tke-------------------------------------------------- 
    135138 
     
    140143a prognostic equation for $\bar{e}$, the turbulent kinetic energy, 
    141144and a closure assumption for the turbulent length scales. 
    142 This turbulent closure model has been developed by \citet{Bougeault1989} in the atmospheric case, 
    143 adapted by \citet{Gaspar1990} for the oceanic case, and embedded in OPA, the ancestor of NEMO, 
    144 by \citet{Blanke1993} for equatorial Atlantic simulations. 
    145 Since then, significant modifications have been introduced by \citet{Madec1998} in both the implementation and 
     145This turbulent closure model has been developed by \citet{bougeault.lacarrere_MWR89} in the atmospheric case, 
     146adapted by \citet{gaspar.gregoris.ea_JGR90} for the oceanic case, and embedded in OPA, the ancestor of NEMO, 
     147by \citet{blanke.delecluse_JPO93} for equatorial Atlantic simulations. 
     148Since then, significant modifications have been introduced by \citet{madec.delecluse.ea_NPM98} in both the implementation and 
    146149the formulation of the mixing length scale. 
    147150The time evolution of $\bar{e}$ is the result of the production of $\bar{e}$ through vertical shear, 
    148 its destruction through stratification, its vertical diffusion, and its dissipation of \citet{Kolmogorov1942} type: 
     151its destruction through stratification, its vertical diffusion, and its dissipation of \citet{kolmogorov_IANS42} type: 
    149152\begin{equation} 
    150153  \label{eq:zdftke_e} 
     
    168171$P_{rt}$ is the Prandtl number, $K_m$ and $K_\rho$ are the vertical eddy viscosity and diffusivity coefficients. 
    169172The constants $C_k =  0.1$ and $C_\epsilon = \sqrt {2} /2$ $\approx 0.7$ are designed to deal with 
    170 vertical mixing at any depth \citep{Gaspar1990}.  
     173vertical mixing at any depth \citep{gaspar.gregoris.ea_JGR90}.  
    171174They are set through namelist parameters \np{nn\_ediff} and \np{nn\_ediss}. 
    172 $P_{rt}$ can be set to unity or, following \citet{Blanke1993}, be a function of the local Richardson number, $R_i$: 
     175$P_{rt}$ can be set to unity or, following \citet{blanke.delecluse_JPO93}, be a function of the local Richardson number, $R_i$: 
    173176\begin{align*} 
    174177  % \label{eq:prt} 
     
    180183  \end{cases} 
    181184\end{align*} 
    182 Options are defined through the  \ngn{namzdfy\_tke} namelist variables. 
    183185The choice of $P_{rt}$ is controlled by the \np{nn\_pdl} namelist variable. 
    184186 
    185187At the sea surface, the value of $\bar{e}$ is prescribed from the wind stress field as 
    186188$\bar{e}_o = e_{bb} |\tau| / \rho_o$, with $e_{bb}$ the \np{rn\_ebb} namelist parameter. 
    187 The default value of $e_{bb}$ is 3.75. \citep{Gaspar1990}), however a much larger value can be used when 
     189The default value of $e_{bb}$ is 3.75. \citep{gaspar.gregoris.ea_JGR90}), however a much larger value can be used when 
    188190taking into account the surface wave breaking (see below Eq. \autoref{eq:ZDF_Esbc}). 
    189191The bottom value of TKE is assumed to be equal to the value of the level just above. 
     
    191193the numerical scheme does not ensure its positivity. 
    192194To overcome this problem, a cut-off in the minimum value of $\bar{e}$ is used (\np{rn\_emin} namelist parameter). 
    193 Following \citet{Gaspar1990}, the cut-off value is set to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$. 
    194 This allows the subsequent formulations to match that of \citet{Gargett1984} for the diffusion in 
     195Following \citet{gaspar.gregoris.ea_JGR90}, the cut-off value is set to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$. 
     196This allows the subsequent formulations to match that of \citet{gargett_JMR84} for the diffusion in 
    195197the thermocline and deep ocean :  $K_\rho = 10^{-3} / N$. 
    196198In addition, a cut-off is applied on $K_m$ and $K_\rho$ to avoid numerical instabilities associated with 
    197199too weak vertical diffusion. 
    198200They must be specified at least larger than the molecular values, and are set through \np{rn\_avm0} and 
    199 \np{rn\_avt0} (namzdf namelist, see \autoref{subsec:ZDF_cst}). 
     201\np{rn\_avt0} (\ngn{namzdf} namelist, see \autoref{subsec:ZDF_cst}). 
    200202 
    201203\subsubsection{Turbulent length scale} 
    202204 
    203205For computational efficiency, the original formulation of the turbulent length scales proposed by 
    204 \citet{Gaspar1990} has been simplified. 
     206\citet{gaspar.gregoris.ea_JGR90} has been simplified. 
    205207Four formulations are proposed, the choice of which is controlled by the \np{nn\_mxl} namelist parameter. 
    206 The first two are based on the following first order approximation \citep{Blanke1993}: 
     208The first two are based on the following first order approximation \citep{blanke.delecluse_JPO93}: 
    207209\begin{equation} 
    208210  \label{eq:tke_mxl0_1} 
     
    212214The resulting length scale is bounded by the distance to the surface or to the bottom 
    213215(\np{nn\_mxl}\forcode{ = 0}) or by the local vertical scale factor (\np{nn\_mxl}\forcode{ = 1}). 
    214 \citet{Blanke1993} notice that this simplification has two major drawbacks: 
     216\citet{blanke.delecluse_JPO93} notice that this simplification has two major drawbacks: 
    215217it makes no sense for locally unstable stratification and the computation no longer uses all 
    216218the information contained in the vertical density profile. 
    217 To overcome these drawbacks, \citet{Madec1998} introduces the \np{nn\_mxl}\forcode{ = 2..3} cases, 
     219To overcome these drawbacks, \citet{madec.delecluse.ea_NPM98} introduces the \np{nn\_mxl}\forcode{ = 2, 3} cases, 
    218220which add an extra assumption concerning the vertical gradient of the computed length scale. 
    219221So, the length scales are first evaluated as in \autoref{eq:tke_mxl0_1} and then bounded such that: 
     
    225227\autoref{eq:tke_mxl_constraint} means that the vertical variations of the length scale cannot be larger than 
    226228the variations of depth. 
    227 It provides a better approximation of the \citet{Gaspar1990} formulation while being much less  
     229It provides a better approximation of the \citet{gaspar.gregoris.ea_JGR90} formulation while being much less  
    228230time consuming. 
    229231In particular, it allows the length scale to be limited not only by the distance to the surface or 
     
    237239\begin{figure}[!t] 
    238240  \begin{center} 
    239     \includegraphics[width=1.00\textwidth]{Fig_mixing_length} 
     241    \includegraphics[width=\textwidth]{Fig_mixing_length} 
    240242    \caption{ 
    241243      \protect\label{fig:mixing_length} 
     
    258260In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same value: 
    259261$ l_k=  l_\epsilon = \min \left(\ l_{up} \;,\;  l_{dwn}\ \right)$, while in the \np{nn\_mxl}\forcode{ = 3} case, 
    260 the dissipation and mixing turbulent length scales are give as in \citet{Gaspar1990}: 
     262the dissipation and mixing turbulent length scales are give as in \citet{gaspar.gregoris.ea_JGR90}: 
    261263\[ 
    262264  % \label{eq:tke_mxl_gaspar} 
     
    270272Usually the surface scale is given by $l_o = \kappa \,z_o$ where $\kappa = 0.4$ is von Karman's constant and 
    271273$z_o$ the roughness parameter of the surface. 
    272 Assuming $z_o=0.1$~m \citep{Craig_Banner_JPO94} leads to a 0.04~m, the default value of \np{rn\_mxl0}. 
     274Assuming $z_o=0.1$~m \citep{craig.banner_JPO94} leads to a 0.04~m, the default value of \np{rn\_mxl0}. 
    273275In the ocean interior a minimum length scale is set to recover the molecular viscosity when 
    274276$\bar{e}$ reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). 
     
    277279%-----------------------------------------------------------------------% 
    278280 
    279 Following \citet{Mellor_Blumberg_JPO04}, the TKE turbulence closure model has been modified to 
     281Following \citet{mellor.blumberg_JPO04}, the TKE turbulence closure model has been modified to 
    280282include the effect of surface wave breaking energetics. 
    281283This results in a reduction of summertime surface temperature when the mixed layer is relatively shallow. 
    282 The \citet{Mellor_Blumberg_JPO04} modifications acts on surface length scale and TKE values and 
     284The \citet{mellor.blumberg_JPO04} modifications acts on surface length scale and TKE values and 
    283285air-sea drag coefficient.  
    284 The latter concerns the bulk formulea and is not discussed here.  
    285  
    286 Following \citet{Craig_Banner_JPO94}, the boundary condition on surface TKE value is : 
     286The latter concerns the bulk formulae and is not discussed here.  
     287 
     288Following \citet{craig.banner_JPO94}, the boundary condition on surface TKE value is : 
    287289\begin{equation} 
    288290  \label{eq:ZDF_Esbc} 
    289291  \bar{e}_o = \frac{1}{2}\,\left(  15.8\,\alpha_{CB} \right)^{2/3} \,\frac{|\tau|}{\rho_o} 
    290292\end{equation} 
    291 where $\alpha_{CB}$ is the \citet{Craig_Banner_JPO94} constant of proportionality which depends on the ''wave age'', 
    292 ranging from 57 for mature waves to 146 for younger waves \citep{Mellor_Blumberg_JPO04}.  
     293where $\alpha_{CB}$ is the \citet{craig.banner_JPO94} constant of proportionality which depends on the ''wave age'', 
     294ranging from 57 for mature waves to 146 for younger waves \citep{mellor.blumberg_JPO04}.  
    293295The boundary condition on the turbulent length scale follows the Charnock's relation: 
    294296\begin{equation} 
     
    297299\end{equation} 
    298300where $\kappa=0.40$ is the von Karman constant, and $\beta$ is the Charnock's constant. 
    299 \citet{Mellor_Blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by 
    300 \citet{Stacey_JPO99} citing observation evidence, and 
     301\citet{mellor.blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by 
     302\citet{stacey_JPO99} citing observation evidence, and 
    301303$\alpha_{CB} = 100$ the Craig and Banner's value. 
    302304As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 
    303305with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}\forcode{ = 67.83} corresponds  
    304306to $\alpha_{CB} = 100$. 
    305 Further setting  \np{ln\_mxl0} to true applies \autoref{eq:ZDF_Lsbc} as surface boundary condition on length scale, 
     307Further setting  \np{ln\_mxl0=.true.},  applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale, 
    306308with $\beta$ hard coded to the Stacey's value. 
    307 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on 
     309Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on the  
    308310surface $\bar{e}$ value. 
    309311 
     
    315317Although LC have nothing to do with convection, the circulation pattern is rather similar to 
    316318so-called convective rolls in the atmospheric boundary layer. 
    317 The detailed physics behind LC is described in, for ex