Changeset 11123


Ignore:
Timestamp:
2019-06-17T14:22:27+02:00 (17 months ago)
Author:
nicolasmartin
Message:

Modification of LaTeX subfiles accordingly to new citations keys

Location:
NEMO/trunk/doc/latex/NEMO
Files:
27 edited

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  • NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.sty

    r11043 r11123  
    66%% LaTeX packages 
    77%% ============================================================================== 
    8 \usepackage{natbib}           %% bib 
    9 \usepackage{caption}          %% caption 
    10 \usepackage{xcolor}           %% color 
    11 \usepackage{times}            %% font 
    12 \usepackage{hyperref}         %% hyper 
    13 \usepackage{idxlayout}        %% index 
    14 \usepackage{enumitem}         %% list 
    15 \usepackage{minted}           %% listing 
    16 \usepackage{amsmath}          %% maths 
    17 \usepackage{fancyhdr}         %% page 
    18 \usepackage{minitoc}          %% toc 
    19 \usepackage{subfiles}         %% subdocs 
    20 \usepackage[utf8]{inputenc}   %% input encoding 
    21 \usepackage{draftwatermark}   %% watermark 
    22 \usepackage{textcomp}         %% Companion fonts 
     8\usepackage{natbib}                      %% bib 
     9\usepackage{caption}                     %% caption 
     10\usepackage{xcolor}                      %% color 
     11\usepackage{times}                       %% font 
     12\usepackage{hyperref}                    %% hyper 
     13\usepackage{idxlayout}                   %% index 
     14\usepackage{enumitem}                    %% list 
     15\usepackage[outputdir=../build]{minted}   %% listing 
     16\usepackage{amsmath}                     %% maths 
     17\usepackage{fancyhdr}                    %% page 
     18\usepackage{minitoc}                     %% toc 
     19\usepackage{subfiles}                    %% subdocs 
     20\usepackage[utf8]{inputenc}              %% input encoding 
     21\usepackage{draftwatermark}              %% watermark 
     22\usepackage{textcomp}                    %% Companion fonts 
    2323 
    2424%% Extensions in bundle package 
     
    130130\newcommand{\pd}[2][]{\ensuremath{\frac{\partial #1}{\partial #2}}} 
    131131 
    132 %% Shortened DOI in bibliography 
    133 \newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{doi:#1}} 
    134  
    135132%% Namelists inclusion 
    136133\newcommand{\nlst}[1]{\forfile{../../../namelists/#1}} 
  • NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.tex

    r11043 r11123  
    8080%% Chapters 
    8181\subfile{../subfiles/chap_model_basics} 
    82 \subfile{../subfiles/chap_time_domain}   % Time discretisation (time stepping strategy) 
    83 \subfile{../subfiles/chap_DOM}           % Space discretisation 
    84 \subfile{../subfiles/chap_TRA}           % Tracer advection/diffusion equation 
    85 \subfile{../subfiles/chap_DYN}           % Dynamics : momentum equation 
    86 \subfile{../subfiles/chap_SBC}           % Surface Boundary Conditions 
    87 \subfile{../subfiles/chap_LBC}           % Lateral Boundary Conditions 
    88 \subfile{../subfiles/chap_LDF}           % Lateral diffusion 
    89 \subfile{../subfiles/chap_ZDF}           % Vertical diffusion 
    90 \subfile{../subfiles/chap_DIA}           % Outputs and Diagnostics 
    91 \subfile{../subfiles/chap_OBS}           % Observation operator 
    92 \subfile{../subfiles/chap_ASM}           % Assimilation increments 
    93 \subfile{../subfiles/chap_STO}           % Stochastic param. 
    94 \subfile{../subfiles/chap_misc}          % Miscellaneous topics 
    95 \subfile{../subfiles/chap_CONFIG}        % Predefined configurations 
     82\subfile{../subfiles/chap_time_domain}    % Time discretisation (time stepping strategy) 
     83\subfile{../subfiles/chap_DOM}            % Space discretisation 
     84\subfile{../subfiles/chap_TRA}            % Tracer advection/diffusion equation 
     85\subfile{../subfiles/chap_DYN}            % Dynamics : momentum equation 
     86\subfile{../subfiles/chap_SBC}            % Surface Boundary Conditions 
     87\subfile{../subfiles/chap_LBC}            % Lateral Boundary Conditions 
     88\subfile{../subfiles/chap_LDF}            % Lateral diffusion 
     89\subfile{../subfiles/chap_ZDF}            % Vertical diffusion 
     90\subfile{../subfiles/chap_DIA}            % Outputs and Diagnostics 
     91\subfile{../subfiles/chap_OBS}            % Observation operator 
     92\subfile{../subfiles/chap_ASM}            % Assimilation increments 
     93\subfile{../subfiles/chap_STO}            % Stochastic param. 
     94\subfile{../subfiles/chap_misc}           % Miscellaneous topics 
     95\subfile{../subfiles/chap_CONFIG}         % Predefined configurations 
    9696 
    9797%% Appendix 
    9898\appendix 
    99 \subfile{../subfiles/annex_A}             % Generalised vertical coordinate 
    100 \subfile{../subfiles/annex_B}             % Diffusive operator 
    101 \subfile{../subfiles/annex_C}             % Discrete invariants of the eqs. 
    102 \subfile{../subfiles/annex_iso}           % Isoneutral diffusion using triads 
    103 \subfile{../subfiles/annex_D}             % Coding rules 
     99\subfile{../subfiles/annex_A}             % Generalised vertical coordinate 
     100\subfile{../subfiles/annex_B}             % Diffusive operator 
     101\subfile{../subfiles/annex_C}             % Discrete invariants of the eqs. 
     102\subfile{../subfiles/annex_iso}            % Isoneutral diffusion using triads 
     103\subfile{../subfiles/annex_D}             % Coding rules 
    104104 
    105105%% Not included 
    106 %\subfile{../subfiles/chap_conservation}  % 
     106%\subfile{../subfiles/chap_model_basics_zstar} 
     107%\subfile{../subfiles/chap_DIU} 
     108%\subfile{../subfiles/chap_conservation} 
    107109%\subfile{../subfiles/annex_E}            % Notes on some on going staff 
    108  
    109110 
    110111%% Backmatter 
  • NEMO/trunk/doc/latex/NEMO/subfiles

    • Property svn:ignore deleted
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_A.tex

    r10442 r11123  
    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 $p_h'= g \; \int_z^\eta d \; e_3 \; dk$. 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_B.tex

    r10442 r11123  
    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} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/annex_D.tex

    r10442 r11123  
    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/trunk/doc/latex/NEMO/subfiles/annex_E.tex

    r10442 r11123  
    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 
     
    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/trunk/doc/latex/NEMO/subfiles/annex_iso.tex

    r10442 r11123  
    5252  the vertical skew flux is further reduced to ensure no vertical buoyancy flux, 
    5353  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} 
     54  This is similar to the tapering suggested by \citet{gerdes.koberle.ea_CD91}. See \autoref{subsec:Gerdes-taper} 
    5555\item[\np{ln\_botmix\_triad}] 
    5656  See \autoref{sec:iso_bdry}.  
     
    7171\label{sec:iso} 
    7272 
    73 We have implemented into \NEMO a scheme inspired by \citet{Griffies_al_JPO98}, 
     73We have implemented into \NEMO a scheme inspired by \citet{griffies.gnanadesikan.ea_JPO98}, 
    7474but formulated within the \NEMO framework, using scale factors rather than grid-sizes. 
    7575 
     
    194194\subsection{Expression of the skew-flux in terms of triad slopes} 
    195195 
    196 \citep{Griffies_al_JPO98} introduce a different discretization of the off-diagonal terms that 
     196\citep{griffies.gnanadesikan.ea_JPO98} introduce a different discretization of the off-diagonal terms that 
    197197nicely solves the problem. 
    198198% Instead of multiplying the mean slope calculated at the $u$-point by 
     
    473473 
    474474To 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, 
     475\citet{griffies.gnanadesikan.ea_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells, 
    476476defined in terms of the distances between $T$, $u$,$f$ and $w$-points. 
    477477This is the natural discretization of \autoref{eq:cts-var}. 
     
    685685As discussed in \autoref{subsec:LDF_slp_iso}, 
    686686iso-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}. 
     687both for consistency with the small-slope approximation and for numerical stability \citep{cox_OM87, griffies_bk04}. 
    688688The bound chosen in \NEMO is applied to each component of the slope separately and 
    689689has a value of $1/100$ in the ocean interior. 
     
    859859\footnote{ 
    860860  To ensure good behaviour where horizontal density gradients are weak, 
    861   we in fact follow \citet{Gerdes1991} and 
     861  we in fact follow \citet{gerdes.koberle.ea_CD91} and 
    862862  set $\rML^*=\mathrm{sgn}(\tilde{r}_i)\min(|\rMLt^2/\tilde{r}_i|,|\tilde{r}_i|)-\sigma_i$. 
    863863} 
     
    865865This approach is similar to multiplying the iso-neutral diffusion coefficient by 
    866866$\tilde{r}_{\mathrm{max}}^{-2}\tilde{r}_i^{-2}$ for steep slopes, 
    867 as suggested by \citet{Gerdes1991} (see also \citet{Griffies_Bk04}). 
     867as suggested by \citet{gerdes.koberle.ea_CD91} (see also \citet{griffies_bk04}). 
    868868Again it is applied separately to each triad $_i^k\mathbb{R}_{i_p}^{k_p}$ 
    869869 
     
    925925 
    926926However, 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}. 
     927\NEMO instead implements eddy induced advection according to the so-called skew form \citep{griffies_JPO98}. 
    928928It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. 
    929929For example in the (\textbf{i},\textbf{k}) plane, 
     
    11391139it is equivalent to a horizontal eiv (eddy-induced velocity) that is uniform within the mixed layer 
    11401140\autoref{eq:eiv_v}. 
    1141 This ensures that the eiv velocities do not restratify the mixed layer \citep{Treguier1997,Danabasoglu_al_2008}. 
     1141This ensures that the eiv velocities do not restratify the mixed layer \citep{treguier.held.ea_JPO97,danabasoglu.ferrari.ea_JC08}. 
    11421142Equivantly, in terms of the skew-flux formulation we use here, 
    11431143the linear slope tapering within the mixed-layer gives a linearly varying vertical flux, 
     
    11531153$uw$ (integer +1/2 $i$, integer $j$, integer +1/2 $k$) and $vw$ (integer $i$, integer +1/2 $j$, integer +1/2 $k$) 
    11541154points (see Table \autoref{tab:cell}) respectively. 
    1155 We follow \citep{Griffies_Bk04} and calculate the streamfunction at a given $uw$-point from 
     1155We follow \citep{griffies_bk04} and calculate the streamfunction at a given $uw$-point from 
    11561156the surrounding four triads according to: 
    11571157\[ 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex

    r10442 r11123  
    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. 
     
    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/trunk/doc/latex/NEMO/subfiles/chap_CONFIG.tex

    r11112 r11123  
    9696      The two "north pole" are the foci of a series of embedded ellipses (blue curves) which 
    9797      are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes). 
    98       Then, following \citet{Madec_Imbard_CD96}, the normal to the series of ellipses (red curves) is computed which 
     98      Then, following \citet{madec.imbard_CD96}, the normal to the series of ellipses (red curves) is computed which 
    9999      provides the j-lines of the mesh (pseudo longitudes). 
    100100    } 
     
    109109\label{subsec:CFG_orca_grid} 
    110110 
    111 The ORCA grid is a tripolar grid based on the semi-analytical method of \citet{Madec_Imbard_CD96}. 
     111The ORCA grid is a tripolar grid based on the semi-analytical method of \citet{madec.imbard_CD96}. 
    112112It allows to construct a global orthogonal curvilinear ocean mesh which has no singularity point inside 
    113113the computational domain since two north mesh poles are introduced and placed on lands. 
     
    207207%climate change (Marti et al., 2009). 
    208208%It is also the basis for the \NEMO contribution to the Coordinate Ocean-ice Reference Experiments (COREs) 
    209 %documented in \citet{Griffies_al_OM09}.  
     209%documented in \citet{griffies.biastoch.ea_OM09}.  
    210210 
    211211This version of ORCA\_R2 has 31 levels in the vertical, with the highest resolution (10m) in the upper 150m 
    212212(see \autoref{tab:orca_zgr} and \autoref{fig:zgr}).  
    213213The bottom topography and the coastlines are derived from the global atlas of Smith and Sandwell (1997).  
    214 The default forcing uses the boundary forcing from \citet{Large_Yeager_Rep04} (see \autoref{subsec:SBC_blk_core}),  
     214The default forcing uses the boundary forcing from \citet{large.yeager_rpt04} (see \autoref{subsec:SBC_blk_core}),  
    215215which was developed for the purpose of running global coupled ocean-ice simulations without 
    216216an interactive atmosphere. 
    217 This \citet{Large_Yeager_Rep04} dataset is available through 
     217This \citet{large.yeager_rpt04} dataset is available through 
    218218the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. 
    219219The "normal year" of \citet{Large_Yeager_Rep04} has been chosen of the NEMO distribution since release v3.3.  
     
    230230\label{sec:CFG_gyre} 
    231231 
    232 The GYRE configuration \citep{Levy_al_OM10} has been built to 
     232The GYRE configuration \citep{levy.klein.ea_OM10} has been built to 
    233233simulate the seasonal cycle of a double-gyre box model. 
    234 It consists in an idealized domain similar to that used in the studies of \citet{Drijfhout_JPO94} and 
    235 \citet{Hazeleger_Drijfhout_JPO98, Hazeleger_Drijfhout_JPO99, Hazeleger_Drijfhout_JGR00, Hazeleger_Drijfhout_JPO00}, 
     234It consists in an idealized domain similar to that used in the studies of \citet{drijfhout_JPO94} and 
     235\citet{hazeleger.drijfhout_JPO98, hazeleger.drijfhout_JPO99, hazeleger.drijfhout_JGR00, hazeleger.drijfhout_JPO00}, 
    236236over which an analytical seasonal forcing is applied. 
    237237This allows to investigate the spontaneous generation of a large number of interacting, transient mesoscale eddies  
     
    244244The configuration is meant to represent an idealized North Atlantic or North Pacific basin. 
    245245The circulation is forced by analytical profiles of wind and buoyancy fluxes. 
    246 The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{Levy_al_OM10}.  
     246The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{levy.klein.ea_OM10}.  
    247247The wind stress is zonal and its curl changes sign at 22\deg{N} and 36\deg{N}. 
    248248It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain and 
     
    284284      \protect\label{fig:GYRE} 
    285285      Snapshot of relative vorticity at the surface of the model domain in GYRE R9, R27 and R54. 
    286       From \citet{Levy_al_OM10}. 
     286      From \citet{levy.klein.ea_OM10}. 
    287287    } 
    288288  \end{center} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIA.tex

    r10509 r11123  
    15071507remain at a given depth ($w = 0$ in the computation) have been introduced in the system during the CLIPPER project. 
    15081508Options are defined by \ngn{namflo} namelis variables. 
    1509 The algorithm used is based either on the work of \cite{Blanke_Raynaud_JPO97} (default option), 
     1509The algorithm used is based either on the work of \cite{blanke.raynaud_JPO97} (default option), 
    15101510or 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 
     1511Note that the \cite{blanke.raynaud_JPO97} algorithm have the advantage of providing trajectories which 
    15121512are consistent with the numeric of the code, so that the trajectories never intercept the bathymetry. 
    15131513 
     
    18091809The steric effect is therefore not explicitely represented. 
    18101810This 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, 
     1811\citep{greatbatch_JGR94}, but extra attention is required when investigating sea level, 
    18121812as steric changes are an important contribution to local changes in sea level on seasonal and climatic time scales. 
    18131813This is especially true for investigation into sea level rise due to global warming. 
    18141814 
    18151815Fortunately, 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}. 
     1816can be diagnosed by considering the mass budget of the world ocean \citep{greatbatch_JGR94}. 
    18171817In order to better understand how global mean sea level evolves and thus how the steric sea level can be diagnosed, 
    18181818we compare, in the following, the non-Boussinesq and Boussinesq cases. 
     
    18881888the ocean surface, not by changes in mean mass of the ocean: the steric effect is missing in a Boussinesq fluid. 
    18891889 
    1890 Nevertheless, following \citep{Greatbatch_JGR94}, the steric effect on the volume can be diagnosed by 
     1890Nevertheless, following \citep{greatbatch_JGR94}, the steric effect on the volume can be diagnosed by 
    18911891considering the mass budget of the ocean.  
    18921892The apparent changes in $\mathcal{M}$, mass of the ocean, which are not induced by surface mass flux 
    18931893must be compensated by a spatially uniform change in the mean sea level due to expansion/contraction of the ocean 
    1894 \citep{Greatbatch_JGR94}. 
     1894\citep{greatbatch_JGR94}. 
    18951895In others words, the Boussinesq mass, $\mathcal{M}_o$, can be related to $\mathcal{M}$, 
    18961896the total mass of the ocean seen by the Boussinesq model, via the steric contribution to the sea level, 
     
    19241924This value is a sensible choice for the reference density used in a Boussinesq ocean climate model since, 
    19251925with 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). 
     19262$\%$ from this value (\cite{gill_bk82}, page 47). 
    19271927 
    19281928Second, we have assumed here that the total ocean surface, $\mathcal{A}$, 
     
    19541954so that there are no associated ocean currents. 
    19551955Hence, 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}. 
     1956\ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{campin.marshall.ea_OM08}. 
    19571957However, in the current version of \NEMO the sea-ice is levitating above the ocean without mass exchanges between 
    19581958ice and ocean. 
     
    19861986Among the available diagnostics the following ones are obtained when defining the \key{diahth} CPP key: 
    19871987 
    1988 - the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 
     1988- the mixed layer depth (based on a density criterion \citep{de-boyer-montegut.madec.ea_JGR04}) (\mdl{diahth}) 
    19891989 
    19901990- the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DIU.tex

    r10442 r11123  
    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} 
     
    8787where $Q_{\rm{h}}$ is the sensible and latent heat flux, $Q_{\rm{lw}}$ is the long wave flux, 
    8888and $Q_{\rm{sol}}$ 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. 
     89For $Q_{\rm{sol}}$ 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 $u^*_{w}$. 
     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 $u^*_{w}$. 
    121121As 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 
    122122\[ 
     
    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/trunk/doc/latex/NEMO/subfiles/chap_DOM.tex

    r10502 r11123  
    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. 
     
    397397(\ie as the analytical first derivative of the transformation that 
    398398gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$) 
    399 is specific to the \NEMO model \citep{Marti_al_JGR92}. 
     399is specific to the \NEMO model \citep{marti.madec.ea_JGR92}. 
    400400As an example, $e_{1t}$ is defined locally at a $t$-point, 
    401401whereas many other models on a C grid choose to define such a scale factor as 
     
    405405since they are first introduced in the continuous equations; 
    406406secondly, 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}. 
     407(rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{treguier.dukowicz.ea_JGR96}. 
    408408An example of the effect of such a choice is shown in \autoref{fig:zgr_e3}. 
    409409%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    827827The original default NEMO s-coordinate stretching is available if neither of the other options are specified as true 
    828828(\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}: 
     829This uses a depth independent $\tanh$ function for the stretching \citep{madec.delecluse.ea_JPO96}: 
    830830 
    831831\[ 
     
    846846 
    847847A stretching function, 
    848 modified from the commonly used \citet{Song_Haidvogel_JCP94} stretching (\np{ln\_s\_SH94}~\forcode{= .true.}), 
     848modified from the commonly used \citet{song.haidvogel_JCP94} stretching (\np{ln\_s\_SH94}~\forcode{= .true.}), 
    849849is also available and is more commonly used for shelf seas modelling: 
    850850 
     
    876876 
    877877Another 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}. 
     878an analytical terrain-following stretching \citet{siddorn.furner_OM13}. 
    879879In this case the a stretching function $\gamma$ is defined such that: 
    880880 
     
    913913  \includegraphics[]{Fig_DOM_compare_coordinates_surface} 
    914914  \caption{ 
    915     A comparison of the \citet{Song_Haidvogel_JCP94} $S$-coordinate (solid lines), 
     915    A comparison of the \citet{song.haidvogel_JCP94} $S$-coordinate (solid lines), 
    916916    a 50 level $Z$-coordinate (contoured surfaces) and 
    917     the \citet{Siddorn_Furner_OM12} $S$-coordinate (dashed lines) in the surface $100~m$ for 
     917    the \citet{siddorn.furner_OM13} $S$-coordinate (dashed lines) in the surface $100~m$ for 
    918918    a idealised bathymetry that goes from $50~m$ to $5500~m$ depth. 
    919919    For clarity every third coordinate surface is shown. 
     
    929929creating a non-analytical vertical coordinate that 
    930930therefore may suffer from large gradients in the vertical resolutions. 
    931 This stretching is less straightforward to implement than the \citet{Song_Haidvogel_JCP94} stretching, 
     931This stretching is less straightforward to implement than the \citet{song.haidvogel_JCP94} stretching, 
    932932but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes. 
    933933 
    934 As with the \citet{Song_Haidvogel_JCP94} stretching the stretch is only applied at depths greater than 
     934As with the \citet{song.haidvogel_JCP94} stretching the stretch is only applied at depths greater than 
    935935the critical depth $h_c$. 
    936936In this example two options are available in depths shallower than $h_c$, 
     
    940940Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as 
    941941large slopes lead to hydrostatic consistency. 
    942 A hydrostatic consistency parameter diagnostic following \citet{Haney1991} has been implemented, 
     942A hydrostatic consistency parameter diagnostic following \citet{haney_JPO91} has been implemented, 
    943943and is output as part of the model mesh file at the start of the run. 
    944944 
     
    960960 
    961961Whatever 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}. 
     962steps that follow the face of the model cells (step like topography) \citep{madec.delecluse.ea_JPO96}. 
    963963The distribution of the steps in the horizontal is defined in a 2D integer array, mbathy, which 
    964964gives the number of ocean levels (\ie those that are not masked) at each $t$-point. 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_DYN.tex

    r10499 r11123  
    127127Replacing $T$ by the number $1$ in the tracer equation and summing over the water column must lead to 
    128128the sea surface height equation otherwise tracer content will not be conserved 
    129 \citep{Griffies_al_MWR01, Leclair_Madec_OM09}. 
     129\citep{griffies.pacanowski.ea_MWR01, leclair.madec_OM09}. 
    130130 
    131131The vertical velocity is computed by an upward integration of the horizontal divergence starting at the bottom, 
     
    287287Nevertheless, this technique strongly distort the phase and group velocity of Rossby waves....} 
    288288 
    289 A very nice solution to the problem of double averaging was proposed by \citet{Arakawa_Hsu_MWR90}. 
     289A very nice solution to the problem of double averaging was proposed by \citet{arakawa.hsu_MWR90}. 
    290290The idea is to get rid of the double averaging by considering triad combinations of vorticity. 
    291291It 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.  
     292\citep{griffies.gnanadesikan.ea_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}). 
     293 
     294The \citet{arakawa.hsu_MWR90} vorticity advection scheme for a single layer is modified  
     295for spherical coordinates as described by \citet{arakawa.lamb_MWR81} to obtain the EEN scheme.  
    296296First consider the discrete expression of the potential vorticity, $q$, defined at an $f$-point:  
    297297\[ 
     
    327327(with a systematic reduction of $e_{3f}$ when a model level intercept the bathymetry) 
    328328that tends to reinforce the topostrophy of the flow 
    329 (\ie the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}.  
     329(\ie the tendency of the flow to follow the isobaths) \citep{penduff.le-sommer.ea_OS07}.  
    330330 
    331331Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as 
     
    356356(\ie $\chi$=$0$) (see \autoref{subsec:C_vorEEN}).  
    357357Applied to a realistic ocean configuration, it has been shown that it leads to a significant reduction of 
    358 the noise in the vertical velocity field \citep{Le_Sommer_al_OM09}. 
     358the noise in the vertical velocity field \citep{le-sommer.penduff.ea_OM09}. 
    359359Furthermore, used in combination with a partial steps representation of bottom topography, 
    360360it improves the interaction between current and topography, 
    361 leading to a larger topostrophy of the flow \citep{Barnier_al_OD06, Penduff_al_OS07}.  
     361leading to a larger topostrophy of the flow \citep{barnier.madec.ea_OD06, penduff.le-sommer.ea_OS07}.  
    362362 
    363363%-------------------------------------------------------------------------------------------------------------- 
     
    403403When \np{ln\_dynzad\_zts}\forcode{ = .true.}, 
    404404a 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}.  
     405This option can be useful when the value of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}.  
    406406Note that in this case, 
    407407a similar split-explicit time stepping should be used on vertical advection of tracer to ensure a better stability, 
     
    475475a $2^{nd}$ order centered finite difference scheme, CEN2, 
    476476or a $3^{rd}$ order upstream biased scheme, UBS. 
    477 The latter is described in \citet{Shchepetkin_McWilliams_OM05}. 
     477The latter is described in \citet{shchepetkin.mcwilliams_OM05}. 
    478478The schemes are selected using the namelist logicals \np{ln\_dynadv\_cen2} and \np{ln\_dynadv\_ubs}.  
    479479In flux form, the schemes differ by the choice of a space and time interpolation to define the value of 
     
    523523where $u"_{i+1/2} =\delta_{i+1/2} \left[ {\delta_i \left[ u \right]} \right]$. 
    524524This 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}. 
     525\citep{shchepetkin.mcwilliams_OM05}. 
     526The overall performance of the advection scheme is similar to that reported in \citet{farrow.stevens_JPO95}. 
    527527It is a relatively good compromise between accuracy and smoothness. 
    528528It is not a \emph{positive} scheme, meaning that false extrema are permitted. 
     
    542542while the second term, which is the diffusion part of the scheme, 
    543543is 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. 
     544This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme. 
    545545 
    546546Note that the UBS and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes only differ by 
    547547one coefficient. 
    548 Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{Webb_al_JAOT98}. 
     548Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 
    549549This option is not available through a namelist parameter, since the $1/6$ coefficient is hard coded. 
    550550Nevertheless it is quite easy to make the substitution in the \mdl{dynadv\_ubs} module and obtain a QUICK scheme. 
     
    652652 
    653653Pressure gradient formulations in an $s$-coordinate have been the subject of a vast number of papers 
    654 (\eg, \citet{Song1998, Shchepetkin_McWilliams_OM05}).  
     654(\eg, \citet{song_MWR98, shchepetkin.mcwilliams_OM05}).  
    655655A number of different pressure gradient options are coded but the ROMS-like, 
    656656density Jacobian with cubic polynomial method is currently disabled whilst known bugs are under investigation. 
    657657 
    658 $\bullet$ Traditional coding (see for example \citet{Madec_al_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.}) 
     658$\bullet$ Traditional coding (see for example \citet{madec.delecluse.ea_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.}) 
    659659\begin{equation} 
    660660  \label{eq:dynhpg_sco} 
     
    679679$\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) 
    680680 
    681 $\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{Shchepetkin_McWilliams_OM05}  
     681$\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{shchepetkin.mcwilliams_OM05}  
    682682(\np{ln\_dynhpg\_djc}\forcode{ = .true.}) (currently disabled; under development) 
    683683 
    684684Note that expression \autoref{eq:dynhpg_sco} is commonly used when the variable volume formulation is activated 
    685685(\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}. 
     686the coordinate surfaces are not horizontal but follow the free surface \citep{levier.treguier.ea_rpt07}. 
    687687The pressure jacobian scheme (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) is available as 
    688688an improved option to \np{ln\_dynhpg\_sco}\forcode{ = .true.} when \key{vvl} is active. 
     
    704704corresponds to the water replaced by the ice shelf. 
    705705This top pressure is constant over time. 
    706 A detailed description of this method is described in \citet{Losch2008}.\\ 
     706A detailed description of this method is described in \citet{losch_JGR08}.\\ 
    707707 
    708708The pressure gradient due to ocean load is computed using the expression \autoref{eq:dynhpg_sco} described in 
     
    722722the physical phenomenon that controls the time-step is internal gravity waves (IGWs). 
    723723A semi-implicit scheme for doubling the stability limit associated with IGWs can be used 
    724 \citep{Brown_Campana_MWR78, Maltrud1998}. 
     724\citep{brown.campana_MWR78, maltrud.smith.ea_JGR98}. 
    725725It involves the evaluation of the hydrostatic pressure gradient as 
    726726an average over the three time levels $t-\rdt$, $t$, and $t+\rdt$ 
     
    790790which imposes a very small time step when an explicit time stepping is used. 
    791791Two 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}),  
     792the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt?}),  
    793793and the split-explicit free surface described below. 
    794794The extra term introduced in the filtered method is calculated implicitly,  
     
    845845 
    846846The 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}. 
     847also called the time-splitting formulation, follows the one proposed by \citet{shchepetkin.mcwilliams_OM05}. 
    848848The general idea is to solve the free surface equation and the associated barotropic velocity equations with 
    849849a smaller time step than $\rdt$, the time step used for the three dimensional prognostic variables 
     
    876876(see section \autoref{sec:ZDF_bfr}), explicitly accounted for at each barotropic iteration. 
    877877Temporal discretization of the system above follows a three-time step Generalized Forward Backward algorithm 
    878 detailed in \citet{Shchepetkin_McWilliams_OM05}. 
     878detailed in \citet{shchepetkin.mcwilliams_OM05}. 
    879879AB3-AM4 coefficients used in \NEMO follow the second-order accurate, 
    880 "multi-purpose" stability compromise as defined in \citet{Shchepetkin_McWilliams_Bk08} 
     880"multi-purpose" stability compromise as defined in \citet{shchepetkin.mcwilliams_ibk09} 
    881881(see their figure 12, lower left).  
    882882 
     
    936936and time splitting not compatible. 
    937937Advective 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}). 
     938uniquely defined from the filter coefficients used for the time averaging (\citet{shchepetkin.mcwilliams_OM05}). 
    939939Consistency between the time averaged continuity equation and the time stepping of tracers is here the key to 
    940940obtain exact conservation. 
     
    953953external gravity waves in idealized or weakly non-linear cases. 
    954954Although 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. 
     955it is still significant as shown by \citet{levier.treguier.ea_rpt07} in the case of an analytical barotropic Kelvin wave. 
    956956 
    957957%>>>>>=============== 
     
    10511051the leap-frog splitting mode in equation \autoref{eq:DYN_spg_ts_ssh}. 
    10521052We have tried various forms of such filtering, 
    1053 with the following method discussed in \cite{Griffies_al_MWR01} chosen due to 
     1053with the following method discussed in \cite{griffies.pacanowski.ea_MWR01} chosen due to 
    10541054its stability and reasonably good maintenance of tracer conservation properties (see ??). 
    10551055 
     
    10841084\label{subsec:DYN_spg_fltp} 
    10851085 
    1086 The filtered formulation follows the \citet{Roullet_Madec_JGR00} implementation.  
     1086The filtered formulation follows the \citet{roullet.madec_JGR00} implementation.  
    10871087The extra term introduced in the equations (see \autoref{subsec:PE_free_surface}) is solved implicitly.  
    10881088The elliptic solvers available in the code are documented in \autoref{chap:MISC}. 
     
    13261326There are two main options for wetting and drying code (wd): 
    13271327(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 
     1328The directional limiter is based on the scheme developed by \cite{warner.defne.ea_CG13} for RO 
    13291329MS 
    1330 which was in turn based on ideas developed for POM by \cite{Oey06}. The iterative 
     1330which was in turn based on ideas developed for POM by \cite{oey_OM06}. The iterative 
    13311331limiter is a new scheme.  The iterative limiter is activated by setting $\mathrm{ln\_wd\_il} = \mathrm{.true.}$ 
    13321332and $\mathrm{ln\_wd\_dl} = \mathrm{.false.}$. The directional limiter is activated 
     
    14001400 
    14011401 
    1402 \cite{WarnerEtal13} state that in their scheme the velocity masks at the cell faces for the baroclinic 
     1402\cite{warner.defne.ea_CG13} state that in their scheme the velocity masks at the cell faces for the baroclinic 
    14031403timesteps are set to 0 or 1 depending on whether the average of the masks over the barotropic sub-steps is respectively less than 
    14041404or greater than 0.5. That scheme does not conserve tracers in integrations started from constant tracer 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_LBC.tex

    r10614 r11123  
    395395 
    396396The BDY module was modelled on the OBC module (see NEMO 3.4) and shares many features and 
    397 a similar coding structure \citep{Chanut2005}. 
     397a similar coding structure \citep{chanut_rpt05}. 
    398398The specification of the location of the open boundary is completely flexible and 
    399399allows for example the open boundary to follow an isobath or other irregular contour.  
     
    475475\label{subsec:BDY_FRS_scheme} 
    476476 
    477 The Flow Relaxation Scheme (FRS) \citep{Davies_QJRMS76,Engerdahl_Tel95}, 
     477The Flow Relaxation Scheme (FRS) \citep{davies_QJRMS76,engedahl_T95}, 
    478478applies a simple relaxation of the model fields to externally-specified values over 
    479479a zone next to the edge of the model domain. 
     
    514514\label{subsec:BDY_flather_scheme} 
    515515 
    516 The \citet{Flather_JPO94} scheme is a radiation condition on the normal, 
     516The \citet{flather_JPO94} scheme is a radiation condition on the normal, 
    517517depth-mean transport across the open boundary. 
    518518It takes the form 
     
    535535\label{subsec:BDY_orlanski_scheme} 
    536536 
    537 The Orlanski scheme is based on the algorithm described by \citep{Marchesiello2001}, hereafter MMS. 
     537The Orlanski scheme is based on the algorithm described by \citep{marchesiello.mcwilliams.ea_OM01}, hereafter MMS. 
    538538 
    539539The adaptive Orlanski condition solves a wave plus relaxation equation at the boundary: 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_LDF.tex

    r10442 r11123  
    4444\gmcomment{ 
    4545  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. 
     46  Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} iso-neutral scheme. 
    4747} 
    4848 
     
    119119%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.  
    120120 
    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). 
     121%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). 
    122122 
    123123%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.  
     
    135135  thus the $in situ$ density can be used. 
    136136  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} 
     137  where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{mcdougall_JPO87} 
    138138  (see \autoref{subsec:TRA_bn2}).  
    139139 
     
    154154  Note: The solution for $s$-coordinate passes trough the use of different (and better) expression for 
    155155  the constraint on iso-neutral fluxes. 
    156   Following \citet{Griffies_Bk04}, instead of specifying directly that there is a zero neutral diffusive flux of 
     156  Following \citet{griffies_bk04}, instead of specifying directly that there is a zero neutral diffusive flux of 
    157157  locally referenced potential density, we stay in the $T$-$S$ plane and consider the balance between 
    158158  the neutral direction diffusive fluxes of potential temperature and salinity: 
     
    201201a minimum background horizontal diffusion for numerical stability reasons. 
    202202To 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}. 
     203the ocean model are modified \citep{weaver.eby_JPO97, griffies.gnanadesikan.ea_JPO98}. 
    204204Griffies'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}: 
     205Here, another strategy is presented \citep{lazar_phd97}: 
    206206a local filtering of the iso-neutral slopes (made on 9 grid-points) prevents the development of 
    207207grid point noise generated by the iso-neutral diffusion operator (\autoref{fig:LDF_ZDF1}). 
     
    212212 
    213213Nevertheless, this iso-neutral operator does not ensure that variance cannot increase, 
    214 contrary to the \citet{Griffies_al_JPO98} operator which has that property.  
     214contrary to the \citet{griffies.gnanadesikan.ea_JPO98} operator which has that property.  
    215215 
    216216%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    235235 
    236236 
    237 % In addition and also for numerical stability reasons \citep{Cox1987, Griffies_Bk04},  
     237% In addition and also for numerical stability reasons \citep{cox_OM87, griffies_bk04},  
    238238% the slopes are bounded by $1/100$ everywhere. This limit is decreasing linearly  
    239239% to zero fom $70$ meters depth and the surface (the fact that the eddies "feel" the  
    240240% surface motivates this flattening of isopycnals near the surface). 
    241241 
    242 For numerical stability reasons \citep{Cox1987, Griffies_Bk04}, the slopes must also be bounded by 
     242For numerical stability reasons \citep{cox_OM87, griffies_bk04}, the slopes must also be bounded by 
    243243$1/100$ everywhere. 
    244244This constraint is applied in a piecewise linear fashion, increasing from zero at the surface to 
     
    366366This variation is intended to reflect the lesser need for subgrid scale eddy mixing where 
    367367the grid size is smaller in the domain. 
    368 It was introduced in the context of the DYNAMO modelling project \citep{Willebrand_al_PO01}. 
     368It was introduced in the context of the DYNAMO modelling project \citep{willebrand.barnier.ea_PO01}. 
    369369Note that such a grid scale dependance of mixing coefficients significantly increase the range of stability of 
    370370model configurations presenting large changes in grid pacing such as global ocean models. 
     
    376376For example, in the ORCA2 global ocean model (see Configurations), 
    377377the 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}. 
     378decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{madec.delecluse.ea_JPO96, delecluse.madec_icol99}. 
    379379This modification can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}. 
    380380Similar modified horizontal variations can be found with the Antarctic or Arctic sub-domain options of 
     
    475475since it allows us to take advantage of all the advection schemes offered for the tracers 
    476476(see \autoref{sec:TRA_adv}) and not just the $2^{nd}$ order advection scheme as in 
    477 previous releases of OPA \citep{Madec1998}. 
     477previous releases of OPA \citep{madec.delecluse.ea_NPM98}. 
    478478This is particularly useful for passive tracers where \emph{positivity} of the advection scheme is of 
    479479paramount importance.  
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_OBS.tex

    r10442 r11123  
    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*} 
    616616     s\left( {\rm P}, {\rm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\} 
     
    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} 
     
    744744where ${{\bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, 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. 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex

    r10614 r11123  
    313313The only tricky point is therefore to specify the date at which we need to do the interpolation and 
    314314the 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. 
     315Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step. 
    316316For example, for an experiment starting at 0h00'00" with a one hour time-step, 
    317317a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc. 
     
    632632%------------------------------------------------------------------------------------------------------------- 
    633633 
    634 The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}. 
     634The CORE bulk formulae have been developed by \citet{large.yeager_rpt04}. 
    635635They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data. 
    636636They use an inertial dissipative method to compute the turbulent transfer coefficients 
    637637(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 
     638This \citet{large.yeager_rpt04} dataset is available through 
    639639the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. 
    640640 
    641641Note 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}. 
     642This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 
    643643 
    644644Options are defined through the  \ngn{namsbc\_core} namelist variables. 
     
    696696 
    697697The CLIO bulk formulae were developed several years ago for the Louvain-la-neuve coupled ice-ocean model 
    698 (CLIO, \cite{Goosse_al_JGR99}).  
     698(CLIO, \cite{goosse.deleersnijder.ea_JGR99}).  
    699699They are simpler bulk formulae. 
    700700They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover.  
     
    839839 
    840840The SAL term should in principle be computed online as it depends on 
    841 the model tidal prediction itself (see \citet{Arbic2004} for a 
     841the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a 
    842842discussion about the practical implementation of this term). 
    843843Nevertheless, the complex calculations involved would make this 
     
    871871%coastal modelling and becomes more and more often open ocean and climate modelling  
    872872%\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}.}. 
     873%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}. 
    874874 
    875875 
     
    892892\footnote{ 
    893893  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}. 
     894  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. 
    895895  see also \autoref{fig:SBC_dcy}.}. 
    896896 
     
    989989%-------------------------------------------------------------------------------------------------------- 
    990990The 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}.  
     991Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.  
    992992The different options are illustrated in \autoref{fig:SBC_isf}. 
    993993 
     
    10011001   \item[\np{nn\_isfblk}\forcode{ = 1}]: 
    10021002     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}. 
     1003     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}. 
    10041004   \item[\np{nn\_isfblk}\forcode{ = 2}]: 
    10051005     The melt rate and the heat flux are based on a 3 equations formulation 
    10061006     (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}. 
     1007     A complete description is available in \citet{jenkins_JGR91}. 
    10081008   \end{description} 
    10091009 
    1010      Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{Losch2008}.  
     1010     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.  
    10111011     Its thickness is defined by \np{rn\_hisf\_tbl}. 
    10121012     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m. 
     
    10381038\] 
    10391039     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. 
     1040     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application. 
    10411041   \item[\np{nn\_gammablk}\forcode{ = 2}]: 
    10421042     The salt and heat exchange coefficients are velocity and stability dependent and defined as: 
     
    10471047     $\Gamma_{Turb}$ the contribution of the ocean stability and 
    10481048     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 
    1049      See \citet{Holland1999} for all the details on this formulation.  
     1049     See \citet{holland.jenkins_JPO99} for all the details on this formulation.  
    10501050     This formulation has not been extensively tested in NEMO (not recommended). 
    10511051   \end{description} 
    10521052 \item[\np{nn\_isf}\forcode{ = 2}]: 
    10531053   The ice shelf cavity is not represented. 
    1054    The fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting. 
     1054   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting. 
    10551055   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL) 
    10561056   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front 
     
    11661166%------------------------------------------------------------------------------------------------------------- 
    11671167 
    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} ). 
     1168Icebergs are modelled as lagrangian particles in NEMO \citep{marsh.ivchenko.ea_GMD15}. 
     1169Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ). 
    11701170(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 
    11711171Icebergs are initially spawned into one of ten classes which have specific mass and thickness as 
     
    12651265Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,  
    12661266the drag coefficient is computed according to the stable/unstable conditions of the  
    1267 air-sea interface following \citet{Large_Yeager_Rep04}.  
     1267air-sea interface following \citet{large.yeager_rpt04}.  
    12681268 
    12691269 
     
    12741274\label{subsec:SBC_wave_sdw} 
    12751275 
    1276 The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}.  
     1276The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.  
    12771277It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)  
    12781278and the current measured at a fixed point (Eulerian velocity).  
     
    13071307\begin{description} 
    13081308\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by  
    1309 \citet{Breivik_al_JPO2014}: 
     1309\citet{breivik.janssen.ea_JPO14}: 
    13101310 
    13111311\[ 
     
    13271327\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a  
    13281328reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface 
    1329 \citep{Breivik_al_OM2016}: 
     1329\citep{breivik.bidlot.ea_OM16}: 
    13301330 
    13311331\[ 
     
    13851385 
    13861386The 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  
     1387into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not  
    13881388available for forcing the mean circulation, while in the opposite case of a decaying sea  
    13891389state more momentum is available for forcing the ocean.  
     
    14451445      the mean value of the analytical cycle (blue line) over a time step, 
    14461446      not as the mid time step value of the analytically cycle (red square). 
    1447       From \citet{Bernie_al_CD07}. 
     1447      From \citet{bernie.guilyardi.ea_CD07}. 
    14481448    } 
    14491449  \end{center} 
     
    14511451%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    14521452 
    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. 
     1453\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. 
    14541454Unfortunately high frequency forcing fields are rare, not to say inexistent. 
    14551455Nevertheless, 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}. 
     1456high frequency \citep{bernie.guilyardi.ea_CD07}. 
    14571457Furthermore, only the knowledge of daily mean value of SWF is needed, 
    14581458as higher frequency variations can be reconstructed from them, 
    14591459assuming 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 
     1460The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO by 
    14611461setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when 
    14621462using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or 
    14631463the flux formulation (\np{ln\_flx}\forcode{ = .true.}). 
    14641464The 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}. 
     1465The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}. 
    14661466The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at 
    14671467a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}). 
     
    15461546(observed, climatological or an atmospheric model product), 
    15471547\textit{SSS}$_{Obs}$ is a sea surface salinity 
    1548 (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}), 
     1548(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}), 
    15491549$\left.S\right|_{k=1}$ is the model surface layer salinity and 
    15501550$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter. 
    15511551Unlike 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}. 
     1552the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}. 
    15531553The SSS restoring term should be viewed as a flux correction on freshwater fluxes to 
    15541554reduce the uncertainties we have on the observed freshwater budget. 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_STO.tex

    r10442 r11123  
    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/trunk/doc/latex/NEMO/subfiles/chap_TRA.tex

    r10544 r11123  
    136136Nevertheless, in the latter case, it is achieved to a good approximation since 
    137137the 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 
     138two quantities that are not correlated \citep{roullet.madec_JGR00, griffies.pacanowski.ea_MWR01, campin.adcroft.ea_OM04}. 
     139 
     140The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco?}) is 
    141141the centred (\textit{now}) \textit{effective} ocean velocity, \ie the \textit{eulerian} velocity 
    142142(see \autoref{chap:DYN}) plus the eddy induced velocity (\textit{eiv}) and/or 
     
    221221\end{equation} 
    222222In the vertical direction (\np{nn\_cen\_v}~\forcode{= 4}), 
    223 a $4^{th}$ COMPACT interpolation has been prefered \citep{Demange_PhD2014}. 
     223a $4^{th}$ COMPACT interpolation has been prefered \citep{demange_phd14}. 
    224224In 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}.  
     225spectral characteristics similar to schemes of higher order \citep{lele_JCP92}.  
    226226 
    227227Strictly speaking, the CEN4 scheme is not a $4^{th}$ order advection scheme but 
     
    277277(\ie it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}). 
    278278There 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}. 
     279The one chosen in \NEMO is described in \citet{zalesak_JCP79}. 
    280280$c_u$ only departs from $1$ when the advective term produces a local extremum in the tracer field. 
    281281The resulting scheme is quite expensive but \textit{positive}. 
    282282It 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}. 
     283A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{levy.estublier.ea_GRL01}. 
    284284 
    285285An additional option has been added controlled by \np{nn\_fct\_zts}. 
     
    287287a $2^{nd}$ order FCT scheme is used on both horizontal and vertical direction, but on the latter, 
    288288a 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}. 
     289This option can be useful when the size of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}. 
    290290Note that in this case, a similar split-explicit time stepping should be used on vertical advection of momentum to 
    291291insure a better stability (see \autoref{subsec:DYN_zad}). 
     
    306306MUSCL implementation can be found in the \mdl{traadv\_mus} module. 
    307307 
    308 MUSCL has been first implemented in \NEMO by \citet{Levy_al_GRL01}. 
     308MUSCL has been first implemented in \NEMO by \citet{levy.estublier.ea_GRL01}. 
    309309In its formulation, the tracer at velocity points is evaluated assuming a linear tracer variation between 
    310310two $T$-points (\autoref{fig:adv_scheme}). 
     
    358358 
    359359This 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}. 
     360\citep{shchepetkin.mcwilliams_OM05}. 
     361The overall performance of the advection scheme is similar to that reported in \cite{farrow.stevens_JPO95}. 
    362362It is a relatively good compromise between accuracy and smoothness. 
    363363Nevertheless the scheme is not \textit{positive}, meaning that false extrema are permitted, 
     
    367367The intrinsic diffusion of UBS makes its use risky in the vertical direction where 
    368368the control of artificial diapycnal fluxes is of paramount importance 
    369 \citep{Shchepetkin_McWilliams_OM05, Demange_PhD2014}. 
     369\citep{shchepetkin.mcwilliams_OM05, demange_phd14}. 
    370370Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme or a $4^th$ order COMPACT scheme 
    371371(\np{nn\_cen\_v}~\forcode{= 2 or 4}). 
     
    376376(which is the diffusive part of the scheme), 
    377377is 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. 
     378This choice is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the QUICK advection scheme. 
    379379UBS 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}. 
     380Replacing 1/6 with 1/8 in \autoref{eq:tra_adv_ubs} leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 
    381381This option is not available through a namelist parameter, since the 1/6 coefficient is hard coded. 
    382382Nevertheless it is quite easy to make the substitution in the \mdl{traadv\_ubs} module and obtain a QUICK scheme. 
     
    412412 
    413413The 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.}. 
     414proposed by \citet{leonard_CMAME79} is used when \np{ln\_traadv\_qck}~\forcode{= .true.}. 
    415415QUICKEST implementation can be found in the \mdl{traadv\_qck} module. 
    416416 
    417417QUICKEST is the third order Godunov scheme which is associated with the ULTIMATE QUICKEST limiter 
    418 \citep{Leonard1991}. 
     418\citep{leonard_CMAME91}. 
    419419It has been implemented in NEMO by G. Reffray (MERCATOR-ocean) and can be found in the \mdl{traadv\_qck} module. 
    420420The resulting scheme is quite expensive but \textit{positive}. 
     
    454454This latter component is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}). 
    455455When \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}. 
     456the pure vertical component is split into an explicit and an implicit part \citep{lemarie.debreu.ea_OM12}. 
    457457 
    458458% ------------------------------------------------------------------------------------------------------------- 
     
    590590This formulation conserves the tracer but does not ensure the decrease of the tracer variance. 
    591591Nevertheless 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}. 
     592any additional background horizontal diffusion \citep{guilyardi.madec.ea_CD01}. 
    593593 
    594594Note that in the partial step $z$-coordinate (\np{ln\_zps}~\forcode{= .true.}), 
     
    603603If the Griffies triad scheme is employed (\np{ln\_traldf\_triad}~\forcode{= .true.}; see \autoref{apdx:triad}) 
    604604 
    605 An alternative scheme developed by \cite{Griffies_al_JPO98} which ensures tracer variance decreases 
     605An alternative scheme developed by \cite{griffies.gnanadesikan.ea_JPO98} which ensures tracer variance decreases 
    606606is also available in \NEMO (\np{ln\_traldf\_grif}~\forcode{= .true.}). 
    607607A complete description of the algorithm is given in \autoref{apdx:triad}. 
     
    747747Note that an exact conservation of heat and salt content is only achieved with non-linear free surface. 
    748748In 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}. 
     749The imbalance is larger than the imbalance associated with the Asselin time filter \citep{leclair.madec_OM09}. 
    750750This is the reason why the modified filter is not applied in the linear free surface case (see \autoref{chap:STP}). 
    751751 
     
    794794In the simple 2-waveband light penetration scheme (\np{ln\_qsr\_2bd}~\forcode{= .true.}) 
    795795a chlorophyll-independent monochromatic formulation is chosen for the shorter wavelengths, 
    796 leading to the following expression \citep{Paulson1977}: 
     796leading to the following expression \citep{paulson.simpson_JPO77}: 
    797797\[ 
    798798  % \label{eq:traqsr_iradiance} 
     
    805805 
    806806Such 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}). 
     807observed light penetration profiles (\cite{morel_JGR88}, see also \autoref{fig:traqsr_irradiance}). 
    808808Light 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 
     809\cite{morel_JGR88} has shown that an accurate representation of light penetration can be provided by 
    810810a 61 waveband formulation. 
    811811Unfortunately, such a model is very computationally expensive. 
    812 Thus, \cite{Lengaigne_al_CD07} have constructed a simplified version of this formulation in which 
     812Thus, \cite{lengaigne.menkes.ea_CD07} have constructed a simplified version of this formulation in which 
    813813visible light is split into three wavebands: blue (400-500 nm), green (500-600 nm) and red (600-700nm). 
    814814For 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}), 
     815the full spectral model of \cite{morel_JGR88} (as modified by \cite{morel.maritorena_JGR01}), 
    816816assuming the same power-law relationship. 
    817817As shown in \autoref{fig:traqsr_irradiance}, this formulation, called RGB (Red-Green-Blue), 
     
    834834\item[\np{nn\_chdta}~\forcode{= 2}] 
    835835  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; 
     836  Following \cite{morel.berthon_LO89}, the profile is computed from the local surface chlorophyll value; 
    837837\item[\np{ln\_qsr\_bio}~\forcode{= .true.}] 
    838838  simulated time varying chlorophyll by TOP biogeochemical model. 
     
    865865      61 waveband Morel (1988) formulation (black) for a chlorophyll concentration of 
    866866      (a) Chl=0.05 mg/m$^3$ and (b) Chl=0.5 mg/m$^3$. 
    867       From \citet{Lengaigne_al_CD07}. 
     867      From \citet{lengaigne.menkes.ea_CD07}. 
    868868    } 
    869869  \end{center} 
     
    886886    \caption{ 
    887887      \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}. 
     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_N92}. 
    890890    } 
    891891  \end{center} 
     
    897897This is the default option in \NEMO, and it is implemented using the masking technique. 
    898898However, 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}), 
     899This flux is weak compared to surface fluxes (a mean global value of $\sim 0.1 \, W/m^2$ \citep{stein.stein_N92}), 
    900900but it warms systematically the ocean and acts on the densest water masses. 
    901901Taking 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}. 
     902(\ie the one associated with the Antarctic Bottom Water) by a few Sverdrups \citep{emile-geay.madec_OS09}. 
    903903 
    904904Options are defined through the  \ngn{namtra\_bbc} namelist variables. 
     
    907907the \np{nn\_geoflx\_cst}, which is also a namelist parameter. 
    908908When \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}. 
     909the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:geothermal}) \citep{emile-geay.madec_OS09}. 
    910910 
    911911% ================================================================ 
     
    931931sometimes over a thickness much larger than the thickness of the observed gravity plume. 
    932932A 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}, 
     933a sill \citep{willebrand.barnier.ea_PO01}, and the thickness of the plume is not resolved. 
     934 
     935The idea of the bottom boundary layer (BBL) parameterisation, first introduced by \citet{beckmann.doscher_JPO97}, 
    936936is to allow a direct communication between two adjacent bottom cells at different levels, 
    937937whenever the densest water is located above the less dense water. 
     
    939939In the current implementation of the BBL, only the tracers are modified, not the velocities. 
    940940Furthermore, it only connects ocean bottom cells, and therefore does not include all the improvements introduced by 
    941 \citet{Campin_Goosse_Tel99}. 
     941\citet{campin.goosse_T99}. 
    942942 
    943943% ------------------------------------------------------------------------------------------------------------- 
     
    955955with $\nabla_\sigma$ the lateral gradient operator taken between bottom cells, and 
    956956$A_l^\sigma$ the lateral diffusivity in the BBL. 
    957 Following \citet{Beckmann_Doscher1997}, the latter is prescribed with a spatial dependence, 
     957Following \citet{beckmann.doscher_JPO97}, the latter is prescribed with a spatial dependence, 
    958958\ie in the conditional form 
    959959\begin{equation} 
     
    10201020\np{nn\_bbl\_adv}~\forcode{= 1}: 
    10211021the 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}. 
     1022(see black arrow in \autoref{fig:bbl}) \citep{beckmann.doscher_JPO97}. 
    10231023It is a \textit{conditional advection}, that is, advection is allowed only 
    10241024if dense water overlies less dense water on the slope (\ie $\nabla_\sigma \rho \cdot \nabla H < 0$) and 
     
    10271027\np{nn\_bbl\_adv}~\forcode{= 2}: 
    10281028the 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}. 
     1029the density difference between the higher cell and lower cell densities \citep{campin.goosse_T99}. 
    10301030The advection is allowed only  if dense water overlies less dense water on the slope 
    10311031(\ie $\nabla_\sigma \rho \cdot \nabla H < 0$). 
     
    10411041The parameter $\gamma$ should take a different value for each bathymetric step, but for simplicity, 
    10421042and 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}. 
     1043The possible values for $\gamma$ range between 1 and $10~s$ \citep{campin.goosse_T99}. 
    10441044 
    10451045Scalar properties are advected by this additional transport $(u^{tr}_{bbl},v^{tr}_{bbl})$ using the upwind scheme. 
     
    11091109In the vicinity of these walls, $\gamma$ takes large values (equivalent to a time scale of a few days) whereas 
    11101110it is zero in the interior of the model domain. 
    1111 The second case corresponds to the use of the robust diagnostic method \citep{Sarmiento1982}. 
     1111The second case corresponds to the use of the robust diagnostic method \citep{sarmiento.bryan_JGR82}. 
    11121112It allows us to find the velocity field consistent with the model dynamics whilst 
    11131113having a $T$, $S$ field close to a given climatological field ($T_o$, $S_o$). 
     
    11211121only below the mixed layer (defined either on a density or $S_o$ criterion). 
    11221122It 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}. 
     1123\citep{madec.delecluse.ea_JPO96}. 
    11241124 
    11251125For generating \ifile{resto}, see the documentation for the DMP tool provided with the source code under 
     
    11371137 
    11381138Options 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}, 
     1139The general framework for tracer time stepping is a modified leap-frog scheme \citep{leclair.madec_OM09}, 
    11401140\ie a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:STP_mLF}): 
    11411141\begin{equation} 
     
    11861186Nonlinearities of the EOS are of major importance, in particular influencing the circulation through 
    11871187determination 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}. 
     1188thus controlling rates of exchange between the atmosphere and the ocean interior \citep{roquet.madec.ea_JPO15}. 
     1189Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{fofonoff.millard_bk83}) or 
     1190TEOS-10 \citep{ioc.iapso_bk10} standards should be used anytime a simulation of the real ocean circulation is attempted 
     1191\citep{roquet.madec.ea_JPO15}. 
    11921192The use of TEOS-10 is highly recommended because 
    11931193\textit{(i)}   it is the new official EOS, 
     
    11951195\textit{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature and 
    11961196practical salinity for EOS-980, both variables being more suitable for use as model variables 
    1197 \citep{TEOS10, Graham_McDougall_JPO13}. 
     1197\citep{ioc.iapso_bk10, graham.mcdougall_JPO13}. 
    11981198EOS-80 is an obsolescent feature of the NEMO system, kept only for backward compatibility. 
    11991199For 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. 
     1200To that purposed, a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is also available. 
    12011201 
    12021202In the computer code, a density anomaly, $d_a = \rho / \rho_o - 1$, is computed, with $\rho_o$ a reference density. 
     
    12041204This is a sensible choice for the reference density used in a Boussinesq ocean climate model, as, 
    12051205with 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}. 
     1206density in the World Ocean varies by no more than 2$\%$ from that value \citep{gill_bk82}. 
    12071207 
    12081208Options are defined through the \ngn{nameos} namelist variables, and in particular \np{nn\_eos} which 
     
    12111211\begin{description} 
    12121212\item[\np{nn\_eos}~\forcode{= -1}] 
    1213   the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used. 
     1213  the polyTEOS10-bsq equation of seawater \citep{roquet.madec.ea_OM15} is used. 
    12141214  The accuracy of this approximation is comparable to the TEOS-10 rational function approximation, 
    12151215  but it is optimized for a boussinesq fluid and the polynomial expressions have simpler and 
     
    12171217  use in ocean models. 
    12181218  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}. 
     1219  the TEOS-10 rational function approximation for hydrographic data analysis \citep{ioc.iapso_bk10}. 
    12201220  A key point is that conservative state variables are used: 
    12211221  Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \deg{C}, notation: $\Theta$). 
    12221222  The pressure in decibars is approximated by the depth in meters. 
    12231223  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}. 
     1224  It is set to $C_p = 3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{ioc.iapso_bk10}. 
    12251225  Choosing polyTEOS10-bsq implies that the state variables used by the model are $\Theta$ and $S_A$. 
    12261226  In particular, the initial state deined by the user have to be given as \textit{Conservative} Temperature and 
     
    12381238  The pressure in decibars is approximated by the depth in meters. 
    12391239  With thsi EOS, the specific heat capacity of sea water, $C_p$, is a function of temperature, salinity and 
    1240   pressure \citep{UNESCO1983}. 
     1240  pressure \citep{fofonoff.millard_bk83}. 
    12411241  Nevertheless, a severe assumption is made in order to have a heat content ($C_p T_p$) which 
    12421242  is conserved by the model: $C_p$ is set to a constant value, the TEOS10 value. 
    12431243\item[\np{nn\_eos}~\forcode{= 1}] 
    1244   a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen, 
     1244  a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is chosen, 
    12451245  the coefficients of which has been optimized to fit the behavior of TEOS10 
    1246   (Roquet, personal comm.) (see also \citet{Roquet_JPO2015}). 
     1246  (Roquet, personal comm.) (see also \citet{roquet.madec.ea_JPO15}). 
    12471247  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}. 
     1248  is enough for a proper treatment of the EOS in theoretical studies \citep{roquet.madec.ea_JPO15}. 
    12491249  With such an equation of state there is no longer a distinction between 
    12501250  \textit{conservative} and \textit{potential} temperature, 
     
    13291329\label{subsec:TRA_fzp} 
    13301330 
    1331 The freezing point of seawater is a function of salinity and pressure \citep{UNESCO1983}: 
     1331The freezing point of seawater is a function of salinity and pressure \citep{fofonoff.millard_bk83}: 
    13321332\begin{equation} 
    13331333  \label{eq:tra_eos_fzp} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r10442 r11123  
    8787a dependency between the vertical eddy coefficients and the local Richardson number 
    8888(\ie the ratio of stratification to vertical shear). 
    89 Following \citet{Pacanowski_Philander_JPO81}, the following formulation has been implemented: 
     89Following \citet{pacanowski.philander_JPO81}, the following formulation has been implemented: 
    9090\[ 
    9191  % \label{eq:zdfric} 
     
    124124The final $h_{e}$ is further constrained by the adjustable bounds \np{rn\_mldmin} and \np{rn\_mldmax}. 
    125125Once $h_{e}$ 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}. 
     126the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{lermusiaux_JMS01}. 
    127127 
    128128% ------------------------------------------------------------------------------------------------------------- 
     
    140140a prognostic equation for $\bar{e}$, the turbulent kinetic energy, 
    141141and 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 
     142This turbulent closure model has been developed by \citet{bougeault.lacarrere_MWR89} in the atmospheric case, 
     143adapted by \citet{gaspar.gregoris.ea_JGR90} for the oceanic case, and embedded in OPA, the ancestor of NEMO, 
     144by \citet{blanke.delecluse_JPO93} for equatorial Atlantic simulations. 
     145Since then, significant modifications have been introduced by \citet{madec.delecluse.ea_NPM98} in both the implementation and 
    146146the formulation of the mixing length scale. 
    147147The 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: 
     148its destruction through stratification, its vertical diffusion, and its dissipation of \citet{kolmogorov_IANS42} type: 
    149149\begin{equation} 
    150150  \label{eq:zdftke_e} 
     
    168168$P_{rt}$ is the Prandtl number, $K_m$ and $K_\rho$ are the vertical eddy viscosity and diffusivity coefficients. 
    169169The 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}.  
     170vertical mixing at any depth \citep{gaspar.gregoris.ea_JGR90}.  
    171171They 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, $R_i$: 
     172$P_{rt}$ can be set to unity or, following \citet{blanke.delecluse_JPO93}, be a function of the local Richardson number, $R_i$: 
    173173\begin{align*} 
    174174  % \label{eq:prt} 
     
    185185At the sea surface, the value of $\bar{e}$ is prescribed from the wind stress field as 
    186186$\bar{e}_o = e_{bb} |\tau| / \rho_o$, 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 
     187The default value of $e_{bb}$ is 3.75. \citep{gaspar.gregoris.ea_JGR90}), however a much larger value can be used when 
    188188taking into account the surface wave breaking (see below Eq. \autoref{eq:ZDF_Esbc}). 
    189189The bottom value of TKE is assumed to be equal to the value of the level just above. 
     
    191191the numerical scheme does not ensure its positivity. 
    192192To 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 
     193Following \citet{gaspar.gregoris.ea_JGR90}, the cut-off value is set to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$. 
     194This allows the subsequent formulations to match that of \citet{gargett_JMR84} for the diffusion in 
    195195the thermocline and deep ocean :  $K_\rho = 10^{-3} / N$. 
    196196In addition, a cut-off is applied on $K_m$ and $K_\rho$ to avoid numerical instabilities associated with 
     
    202202 
    203203For computational efficiency, the original formulation of the turbulent length scales proposed by 
    204 \citet{Gaspar1990} has been simplified. 
     204\citet{gaspar.gregoris.ea_JGR90} has been simplified. 
    205205Four 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}: 
     206The first two are based on the following first order approximation \citep{blanke.delecluse_JPO93}: 
    207207\begin{equation} 
    208208  \label{eq:tke_mxl0_1} 
     
    212212The resulting length scale is bounded by the distance to the surface or to the bottom 
    213213(\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: 
     214\citet{blanke.delecluse_JPO93} notice that this simplification has two major drawbacks: 
    215215it makes no sense for locally unstable stratification and the computation no longer uses all 
    216216the information contained in the vertical density profile. 
    217 To overcome these drawbacks, \citet{Madec1998} introduces the \np{nn\_mxl}\forcode{ = 2..3} cases, 
     217To overcome these drawbacks, \citet{madec.delecluse.ea_NPM98} introduces the \np{nn\_mxl}\forcode{ = 2..3} cases, 
    218218which add an extra assumption concerning the vertical gradient of the computed length scale. 
    219219So, the length scales are first evaluated as in \autoref{eq:tke_mxl0_1} and then bounded such that: 
     
    225225\autoref{eq:tke_mxl_constraint} means that the vertical variations of the length scale cannot be larger than 
    226226the variations of depth. 
    227 It provides a better approximation of the \citet{Gaspar1990} formulation while being much less  
     227It provides a better approximation of the \citet{gaspar.gregoris.ea_JGR90} formulation while being much less  
    228228time consuming. 
    229229In particular, it allows the length scale to be limited not only by the distance to the surface or 
     
    258258In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same value: 
    259259$ 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}: 
     260the dissipation and mixing turbulent length scales are give as in \citet{gaspar.gregoris.ea_JGR90}: 
    261261\[ 
    262262  % \label{eq:tke_mxl_gaspar} 
     
    270270Usually the surface scale is given by $l_o = \kappa \,z_o$ where $\kappa = 0.4$ is von Karman's constant and 
    271271$z_o$ 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}. 
     272Assuming $z_o=0.1$~m \citep{craig.banner_JPO94} leads to a 0.04~m, the default value of \np{rn\_mxl0}. 
    273273In the ocean interior a minimum length scale is set to recover the molecular viscosity when 
    274274$\bar{e}$ reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). 
     
    277277%-----------------------------------------------------------------------% 
    278278 
    279 Following \citet{Mellor_Blumberg_JPO04}, the TKE turbulence closure model has been modified to 
     279Following \citet{mellor.blumberg_JPO04}, the TKE turbulence closure model has been modified to 
    280280include the effect of surface wave breaking energetics. 
    281281This 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 
     282The \citet{mellor.blumberg_JPO04} modifications acts on surface length scale and TKE values and 
    283283air-sea drag coefficient.  
    284284The latter concerns the bulk formulea and is not discussed here.  
    285285 
    286 Following \citet{Craig_Banner_JPO94}, the boundary condition on surface TKE value is : 
     286Following \citet{craig.banner_JPO94}, the boundary condition on surface TKE value is : 
    287287\begin{equation} 
    288288  \label{eq:ZDF_Esbc} 
    289289  \bar{e}_o = \frac{1}{2}\,\left(  15.8\,\alpha_{CB} \right)^{2/3} \,\frac{|\tau|}{\rho_o} 
    290290\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}.  
     291where $\alpha_{CB}$ is the \citet{craig.banner_JPO94} constant of proportionality which depends on the ''wave age'', 
     292ranging from 57 for mature waves to 146 for younger waves \citep{mellor.blumberg_JPO04}.  
    293293The boundary condition on the turbulent length scale follows the Charnock's relation: 
    294294\begin{equation} 
     
    297297\end{equation} 
    298298where $\kappa=0.40$ 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 
     299\citet{mellor.blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by 
     300\citet{stacey_JPO99} citing observation evidence, and 
    301301$\alpha_{CB} = 100$ the Craig and Banner's value. 
    302302As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 
     
    315315Although LC have nothing to do with convection, the circulation pattern is rather similar to 
    316316so-called convective rolls in the atmospheric boundary layer. 
    317 The detailed physics behind LC is described in, for example, \citet{Craik_Leibovich_JFM76}. 
     317The detailed physics behind LC is described in, for example, \citet{craik.leibovich_JFM76}. 
    318318The prevailing explanation is that LC arise from a nonlinear interaction between the Stokes drift and 
    319319wind drift currents.  
    320320 
    321321Here we introduced in the TKE turbulent closure the simple parameterization of Langmuir circulations proposed by 
    322 \citep{Axell_JGR02} for a $k-\epsilon$ turbulent closure. 
     322\citep{axell_JGR02} for a $k-\epsilon$ turbulent closure. 
    323323The parameterization, tuned against large-eddy simulation, includes the whole effect of LC in 
    324324an extra source terms of TKE, $P_{LC}$. 
     
    326326\forcode{.true.} in the namtke namelist. 
    327327  
    328 By making an analogy with the characteristic convective velocity scale (\eg, \citet{D'Alessio_al_JPO98}), 
     328By making an analogy with the characteristic convective velocity scale (\eg, \citet{dalessio.abdella.ea_JPO98}), 
    329329$P_{LC}$ is assumed to be :  
    330330\[ 
     
    334334With no information about the wave field, $w_{LC}$ is assumed to be proportional to  
    335335the Stokes drift $u_s = 0.377\,\,|\tau|^{1/2}$, where $|\tau|$ is the surface wind stress module  
    336 \footnote{Following \citet{Li_Garrett_JMR93}, the surface Stoke drift velocity may be expressed as 
     336\footnote{Following \citet{li.garrett_JMR93}, the surface Stoke drift velocity may be expressed as 
    337337  $u_s =  0.016 \,|U_{10m}|$. 
    338338  Assuming an air density of $\rho_a=1.22 \,Kg/m^3$ and a drag coefficient of 
     
    350350  \end{cases} 
    351351\] 
    352 where $c_{LC} = 0.15$ has been chosen by \citep{Axell_JGR02} as a good compromise to fit LES data. 
     352where $c_{LC} = 0.15$ has been chosen by \citep{axell_JGR02} as a good compromise to fit LES data. 
    353353The chosen value yields maximum vertical velocities $w_{LC}$ of the order of a few centimeters per second. 
    354354The value of $c_{LC}$ is set through the \np{rn\_lc} namelist parameter, 
    355 having in mind that it should stay between 0.15 and 0.54 \citep{Axell_JGR02}.  
     355having in mind that it should stay between 0.15 and 0.54 \citep{axell_JGR02}.  
    356356 
    357357The $H_{LC}$ is estimated in a similar way as the turbulent length scale of TKE equations: 
     
    368368produce mixed-layer depths that are too shallow during summer months and windy conditions. 
    369369This bias is particularly acute over the Southern Ocean. 
    370 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}.  
     370To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{rodgers.aumont.ea_B14}.  
    371371The parameterization is an empirical one, \ie not derived from theoretical considerations, 
    372372but rather is meant to account for observed processes that affect the density structure of  
     
    427427(first line in \autoref{eq:PE_zdf}). 
    428428To do so a special care have to be taken for both the time and space discretization of 
    429 the TKE equation \citep{Burchard_OM02,Marsaleix_al_OM08}. 
     429the TKE equation \citep{burchard_OM02,marsaleix.auclair.ea_OM08}. 
    430430 
    431431Let us first address the time stepping issue. \autoref{fig:TKE_time_scheme} shows how 
     
    524524The Generic Length Scale (GLS) scheme is a turbulent closure scheme based on two prognostic equations: 
    525525one for the turbulent kinetic energy $\bar {e}$, and another for the generic length scale, 
    526 $\psi$ \citep{Umlauf_Burchard_JMS03, Umlauf_Burchard_CSR05}. 
     526$\psi$ \citep{umlauf.burchard_JMR03, umlauf.burchard_CSR05}. 
    527527This later variable is defined as: $\psi = {C_{0\mu}}^{p} \ {\bar{e}}^{m} \ l^{n}$,  
    528528where the triplet $(p, m, n)$ value given in Tab.\autoref{tab:GLS} allows to recover a number of 
    529 well-known turbulent closures ($k$-$kl$ \citep{Mellor_Yamada_1982}, $k$-$\epsilon$ \citep{Rodi_1987}, 
    530 $k$-$\omega$ \citep{Wilcox_1988} among others \citep{Umlauf_Burchard_JMS03,Kantha_Carniel_CSR05}).  
     529well-known turbulent closures ($k$-$kl$ \citep{mellor.yamada_RG82}, $k$-$\epsilon$ \citep{rodi_JGR87}, 
     530$k$-$\omega$ \citep{wilcox_AJ88} among others \citep{umlauf.burchard_JMR03,kantha.carniel_JMR03}).  
    531531The GLS scheme is given by the following set of equations: 
    532532\begin{equation} 
     
    577577    \begin{tabular}{ccccc} 
    578578      &   $k-kl$   & $k-\epsilon$ & $k-\omega$ &   generic   \\ 
    579       % & \citep{Mellor_Yamada_1982} &  \citep{Rodi_1987}       & \citep{Wilcox_1988} &                 \\ 
     579      % & \citep{mellor.yamada_RG82} &  \citep{rodi_JGR87}       & \citep{wilcox_AJ88} &                 \\ 
    580580      \hline 
    581581      \hline 
     
    604604the mixing length towards $K z_b$ ($K$: Kappa and $z_b$: rugosity length) value near physical boundaries 
    605605(logarithmic boundary layer law). 
    606 $C_{\mu}$ and $C_{\mu'}$ are calculated from stability function proposed by \citet{Galperin_al_JAS88}, 
    607 or by \citet{Kantha_Clayson_1994} or one of the two functions suggested by \citet{Canuto_2001} 
     606$C_{\mu}$ and $C_{\mu'}$ are calculated from stability function proposed by \citet{galperin.kantha.ea_JAS88}, 
     607or by \citet{kantha.clayson_JGR94} or one of the two functions suggested by \citet{canuto.howard.ea_JPO01} 
    608608(\np{nn\_stab\_func}\forcode{ = 0..3}, resp.).  
    609609The value of $C_{0\mu}$ depends of the choice of the stability function. 
     
    612612Neumann condition through \np{nn\_tkebc\_surf} and \np{nn\_tkebc\_bot}, resp. 
    613613As for TKE closure, the wave effect on the mixing is considered when 
    614 \np{ln\_crban}\forcode{ = .true.} \citep{Craig_Banner_JPO94, Mellor_Blumberg_JPO04}. 
     614\np{ln\_crban}\forcode{ = .true.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}. 
    615615The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and 
    616616\np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}.  
     
    619619almost all authors apply a clipping of the length scale as an \textit{ad hoc} remedy. 
    620620With this clipping, the maximum permissible length scale is determined by $l_{max} = c_{lim} \sqrt{2\bar{e}}/ N$. 
    621 A value of $c_{lim} = 0.53$ is often used \citep{Galperin_al_JAS88}. 
    622 \cite{Umlauf_Burchard_CSR05} show that the value of the clipping factor is of crucial importance for 
     621A value of $c_{lim} = 0.53$ is often used \citep{galperin.kantha.ea_JAS88}. 
     622\cite{umlauf.burchard_CSR05} show that the value of the clipping factor is of crucial importance for 
    623623the entrainment depth predicted in stably stratified situations, 
    624624and that its value has to be chosen in accordance with the algebraic model for the turbulent fluxes. 
     
    627627 
    628628The time and space discretization of the GLS equations follows the same energetic consideration as for 
    629 the TKE case described in \autoref{subsec:ZDF_tke_ene} \citep{Burchard_OM02}. 
    630 Examples of performance of the 4 turbulent closure scheme can be found in \citet{Warner_al_OM05}. 
     629the TKE case described in \autoref{subsec:ZDF_tke_ene} \citep{burchard_OM02}. 
     630Examples of performance of the 4 turbulent closure scheme can be found in \citet{warner.sherwood.ea_OM05}. 
    631631 
    632632% ------------------------------------------------------------------------------------------------------------- 
     
    700700the water column, but only until the density structure becomes neutrally stable 
    701701(\ie until the mixed portion of the water column has \textit{exactly} the density of the water just below) 
    702 \citep{Madec_al_JPO91}. 
     702\citep{madec.delecluse.ea_JPO91}. 
    703703The associated algorithm is an iterative process used in the following way (\autoref{fig:npc}): 
    704704starting from the top of the ocean, the first instability is found. 
     
    718718the algorithm used in \NEMO converges for any profile in a number of iterations which is less than 
    719719the number of vertical levels. 
    720 This property is of paramount importance as pointed out by \citet{Killworth1989}: 
     720This property is of paramount importance as pointed out by \citet{killworth_iprc89}: 
    721721it avoids the existence of permanent and unrealistic static instabilities at the sea surface. 
    722722This non-penetrative convective algorithm has been proved successful in studies of the deep water formation in 
    723 the north-western Mediterranean Sea \citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}. 
     723the north-western Mediterranean Sea \citep{madec.delecluse.ea_JPO91, madec.chartier.ea_DAO91, madec.crepon_iprc91}. 
    724724 
    725725The current implementation has been modified in order to deal with any non linear equation of seawater 
     
    748748In this case, the vertical eddy mixing coefficients are assigned very large values 
    749749(a typical value is $10\;m^2s^{-1})$ in regions where the stratification is unstable 
    750 (\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{Lazar_PhD97, Lazar_al_JPO99}. 
     750(\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{lazar_phd97, lazar.madec.ea_JPO99}. 
    751751This is done either on tracers only (\np{nn\_evdm}\forcode{ = 0}) or 
    752752on both momentum and tracers (\np{nn\_evdm}\forcode{ = 1}). 
     
    764764Note that the stability test is performed on both \textit{before} and \textit{now} values of $N^2$. 
    765765This removes a potential source of divergence of odd and even time step in 
    766 a leapfrog environment \citep{Leclair_PhD2010} (see \autoref{sec:STP_mLF}). 
     766a leapfrog environment \citep{leclair_phd10} (see \autoref{sec:STP_mLF}). 
    767767 
    768768% ------------------------------------------------------------------------------------------------------------- 
     
    807807The former condition leads to salt fingering and the latter to diffusive convection. 
    808808Double-diffusive phenomena contribute to diapycnal mixing in extensive regions of the ocean. 
    809 \citet{Merryfield1999} include a parameterisation of such phenomena in a global ocean model and show that  
     809\citet{merryfield.holloway.ea_JPO99} include a parameterisation of such phenomena in a global ocean model and show that  
    810810it leads to relatively minor changes in circulation but exerts significant regional influences on 
    811811temperature and salinity. 
     
    842842    \caption{ 
    843843      \protect\label{fig:zdfddm} 
    844       From \citet{Merryfield1999} : 
     844      From \citet{merryfield.holloway.ea_JPO99} : 
    845845      (a) Diapycnal diffusivities $A_f^{vT}$ and $A_f^{vS}$ for temperature and salt in regions of salt fingering. 
    846846      Heavy curves denote $A^{\ast v} = 10^{-3}~m^2.s^{-1}$ and thin curves $A^{\ast v} = 10^{-4}~m^2.s^{-1}$; 
     
    855855 
    856856The factor 0.7 in \autoref{eq:zdfddm_f_T} reflects the measured ratio $\alpha F_T /\beta F_S \approx  0.7$ of 
    857 buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{McDougall_Taylor_JMR84}). 
    858 Following  \citet{Merryfield1999}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$. 
     857buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{mcdougall.taylor_JMR84}). 
     858Following  \citet{merryfield.holloway.ea_JPO99}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$. 
    859859 
    860860To represent mixing of S and T by diffusive layering,  the diapycnal diffusivities suggested by 
     
    963963This coefficient is generally estimated by setting a typical decay time $\tau$ in the deep ocean,  
    964964and setting $r = H / \tau$, where $H$ is the ocean depth. 
    965 Commonly accepted values of $\tau$ are of the order of 100 to 200 days \citep{Weatherly_JMR84}. 
     965Commonly accepted values of $\tau$ are of the order of 100 to 200 days \citep{weatherly_JMR84}. 
    966966A value $\tau^{-1} = 10^{-7}$~s$^{-1}$ equivalent to 115 days, is usually used in quasi-geostrophic models. 
    967967One may consider the linear friction as an approximation of quadratic friction, $r \approx 2\;C_D\;U_{av}$ 
    968 (\citet{Gill1982}, Eq. 9.6.6). 
     968(\citet{gill_bk82}, Eq. 9.6.6). 
    969969For example, with a drag coefficient $C_D = 0.002$, a typical speed of tidal currents of $U_{av} =0.1$~m\;s$^{-1}$, 
    970970and assuming an ocean depth $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$. 
     
    10051005internal waves breaking and other short time scale currents. 
    10061006A typical value of the drag coefficient is $C_D = 10^{-3} $. 
    1007 As an example, the CME experiment \citep{Treguier_JGR92} uses $C_D = 10^{-3}$ and 
    1008 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992} uses $C_D = 1.4\;10^{-3}$ and 
     1007As an example, the CME experiment \citep{treguier_JGR92} uses $C_D = 10^{-3}$ and 
     1008$e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{killworth_JPO92} uses $C_D = 1.4\;10^{-3}$ and 
    10091009$e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$. 
    10101010The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} namelist parameters). 
     
    12351235Options are defined through the  \ngn{namzdf\_tmx} namelist variables. 
    12361236The parameterization of tidal mixing follows the general formulation for the vertical eddy diffusivity proposed by 
    1237 \citet{St_Laurent_al_GRL02} and first introduced in an OGCM by \citep{Simmons_al_OM04}.  
     1237\citet{st-laurent.simmons.ea_GRL02} and first introduced in an OGCM by \citep{simmons.jayne.ea_OM04}.  
    12381238In this formulation an additional vertical diffusivity resulting from internal tide breaking, 
    12391239$A^{vT}_{tides}$ is expressed as a function of $E(x,y)$, 
     
    12521252with the remaining $1-q$ radiating away as low mode internal waves and 
    12531253contributing to the background internal wave field. 
    1254 A value of $q=1/3$ is typically used \citet{St_Laurent_al_GRL02}. 
     1254A value of $q=1/3$ is typically used \citet{st-laurent.simmons.ea_GRL02}. 
    12551255The vertical structure function $F(z)$ models the distribution of the turbulent mixing in the vertical. 
    12561256It is implemented as a simple exponential decaying upward away from the bottom, 
    12571257with a vertical scale of $h_o$ (\np{rn\_htmx} namelist parameter, 
    1258 with a typical value of $500\,m$) \citep{St_Laurent_Nash_DSR04},  
     1258with a typical value of $500\,m$) \citep{st-laurent.nash_DSR04},  
    12591259\[ 
    12601260  % \label{eq:Fz} 
     
    12741274the unrepresented internal waves induced by the tidal flow over rough topography in a stratified ocean. 
    12751275In the current version of \NEMO, the map is built from the output of 
    1276 the barotropic global ocean tide model MOG2D-G \citep{Carrere_Lyard_GRL03}. 
     1276the barotropic global ocean tide model MOG2D-G \citep{carrere.lyard_GRL03}. 
    12771277This model provides the dissipation associated with internal wave energy for the M2 and K1 tides component 
    12781278(\autoref{fig:ZDF_M2_K1_tmx}). 
     
    12801280The internal wave energy is thus : $E(x, y) = 1.25 E_{M2} + E_{K1}$. 
    12811281Its global mean value is $1.1$ TW, 
    1282 in agreement with independent estimates \citep{Egbert_Ray_Nat00, Egbert_Ray_JGR01}.  
     1282in agreement with independent estimates \citep{egbert.ray_N00, egbert.ray_JGR01}.  
    12831283 
    12841284%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     
    12881288    \caption{ 
    12891289      \protect\label{fig:ZDF_M2_K1_tmx} 
    1290       (a) M2 and (b) K1 internal wave drag energy from \citet{Carrere_Lyard_GRL03} ($W/m^2$). 
     1290      (a) M2 and (b) K1 internal wave drag energy from \citet{carrere.lyard_GRL03} ($W/m^2$). 
    12911291    } 
    12921292  \end{center} 
     
    13061306 
    13071307When \np{ln\_tmx\_itf}\forcode{ = .true.}, the two key parameters $q$ and $F(z)$ are adjusted following 
    1308 the parameterisation developed by \citet{Koch-Larrouy_al_GRL07}: 
     1308the parameterisation developed by \citet{koch-larrouy.madec.ea_GRL07}: 
    13091309 
    13101310First, the Indonesian archipelago is a complex geographic region with a series of 
     
    13181318Second, the vertical structure function, $F(z)$, is no more associated with a bottom intensification of the mixing, 
    13191319but with a maximum of energy available within the thermocline. 
    1320 \citet{Koch-Larrouy_al_GRL07} have suggested that the vertical distribution of 
     1320\citet{koch-larrouy.madec.ea_GRL07} have suggested that the vertical distribution of 
    13211321the energy dissipation proportional to $N^2$ below the core of the thermocline and to $N$ above.  
    13221322The resulting $F(z)$ is: 
     
    13351335Introduced in a regional OGCM, the parameterization improves the water mass characteristics in 
    13361336the different Indonesian seas, suggesting that the horizontal and vertical distributions of 
    1337 the mixing are adequately prescribed \citep{Koch-Larrouy_al_GRL07, Koch-Larrouy_al_OD08a, Koch-Larrouy_al_OD08b}. 
     1337the mixing are adequately prescribed \citep{koch-larrouy.madec.ea_GRL07, koch-larrouy.madec.ea_OD08*a, koch-larrouy.madec.ea_OD08*b}. 
    13381338Note also that such a parameterisation has a significant impact on the behaviour of 
    1339 global coupled GCMs \citep{Koch-Larrouy_al_CD10}. 
     1339global coupled GCMs \citep{koch-larrouy.lengaigne.ea_CD10}. 
    13401340 
    13411341% ================================================================ 
     
    13511351 
    13521352The parameterization of mixing induced by breaking internal waves is a generalization of 
    1353 the approach originally proposed by \citet{St_Laurent_al_GRL02}. 
     1353the approach originally proposed by \citet{st-laurent.simmons.ea_GRL02}. 
    13541354A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed, 
    13551355and the resulting diffusivity is obtained as  
     
    13611361the energy available for mixing. 
    13621362If the \np{ln\_mevar} namelist parameter is set to false, the mixing efficiency is taken as constant and 
    1363 equal to 1/6 \citep{Osborn_JPO80}. 
     1363equal to 1/6 \citep{osborn_JPO80}. 
    13641364In the opposite (recommended) case, $R_f$ is instead a function of 
    13651365the turbulence intensity parameter $Re_b = \frac{ \epsilon}{\nu \, N^2}$, 
    1366 with $\nu$ the molecular viscosity of seawater, following the model of \cite{Bouffard_Boegman_DAO2013} and 
    1367 the implementation of \cite{de_lavergne_JPO2016_efficiency}. 
     1366with $\nu$ the molecular viscosity of seawater, following the model of \cite{bouffard.boegman_DAO13} and 
     1367the implementation of \cite{de-lavergne.madec.ea_JPO16}. 
    13681368Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when 
    13691369the mixing efficiency is constant. 
     
    13711371In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary  
    13721372as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice.  
    1373 This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014}, 
    1374 is implemented as in \cite{de_lavergne_JPO2016_efficiency}. 
     1373This parameterization of differential mixing, due to \cite{jackson.rehmann_JPO14}, 
     1374is implemented as in \cite{de-lavergne.madec.ea_JPO16}. 
    13751375 
    13761376The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, 
     
    13951395$h_{cri}$ is related to the large-scale topography of the ocean (etopo2) and 
    13961396$h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of 
    1397 the abyssal hill topography \citep{Goff_JGR2010} and the latitude. 
     1397the abyssal hill topography \citep{goff_JGR10} and the latitude. 
    13981398 
    13991399% ================================================================ 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex

    r10442 r11123  
    2121horizontal kinetic energy and/or potential enstrophy of horizontally non-divergent flow, 
    2222and variance of temperature and salinity will be conserved in the absence of dissipative effects and forcing. 
    23 \citet{Arakawa1966} has first pointed out the advantage of this approach. 
     23\citet{arakawa_JCP66} has first pointed out the advantage of this approach. 
    2424He showed that if integral constraints on energy are maintained, 
    2525the computation will be free of the troublesome "non linear" instability originally pointed out by 
    26 \citet{Phillips1959}. 
     26\citet{phillips_TAMS59}. 
    2727A consistent formulation of the energetic properties is also extremely important in carrying out 
    2828long-term numerical simulations for an oceanographic model. 
    29 Such a formulation avoids systematic errors that accumulate with time \citep{Bryan1997}. 
     29Such a formulation avoids systematic errors that accumulate with time \citep{bryan_JCP97}. 
    3030 
    3131The general philosophy of OPA which has led to the discrete formulation presented in {\S}II.2 and II.3 is to 
     
    3939Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required. 
    4040In that case, and in that case only, the advective scheme used for passive tracer is a flux correction scheme 
    41 \citep{Marti1992, Levy1996, Levy1998}. 
     41\citep{Marti1992?, Levy1996?, Levy1998?}. 
    4242 
    4343% ------------------------------------------------------------------------------------------------------------- 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_misc.tex

    r10601 r11123  
    272272and their propagation and accumulation cause uncertainty in final simulation reproducibility on 
    273273different numbers of processors. 
    274 To avoid so, based on \citet{He_Ding_JSC01} review of different technics, 
     274To avoid so, based on \citet{he.ding_JS01} review of different technics, 
    275275we use a so called self-compensated summation method. 
    276276The idea is to estimate the roundoff error, store it in a buffer, and then add it back in the next addition.  
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics.tex

    r10544 r11123  
    258258If further, an approximative conservation of heat and salt contents is sufficient for the problem solved, 
    259259then it is sufficient to solve a linearized version of \autoref{eq:PE_ssh}, 
    260 which still allows to take into account freshwater fluxes applied at the ocean surface \citep{Roullet_Madec_JGR00}. 
     260which still allows to take into account freshwater fluxes applied at the ocean surface \citep{roullet.madec_JGR00}. 
    261261Nevertheless, with the linearization, an exact conservation of heat and salt contents is lost. 
    262262 
    263263The filtering of EGWs in models with a free surface is usually a matter of discretisation of 
    264264the temporal derivatives, 
    265 using a split-explicit method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92} or 
    266 the implicit scheme \citep{Dukowicz1994} or 
    267 the addition of a filtering force in the momentum equation \citep{Roullet_Madec_JGR00}. 
     265using a split-explicit method \citep{killworth.webb.ea_JPO91, zhang.endoh_JGR92} or 
     266the implicit scheme \citep{dukowicz.smith_JGR94} or 
     267the addition of a filtering force in the momentum equation \citep{roullet.madec_JGR00}. 
    268268With the present release, \NEMO offers the choice between 
    269269an explicit free surface (see \autoref{subsec:DYN_spg_exp}) or 
    270 a split-explicit scheme strongly inspired the one proposed by \citet{Shchepetkin_McWilliams_OM05} 
     270a split-explicit scheme strongly inspired the one proposed by \citet{shchepetkin.mcwilliams_OM05} 
    271271(see \autoref{subsec:DYN_spg_ts}). 
    272272 
     
    292292cannot be easily treated in a global model without filtering. 
    293293A solution consists of introducing an appropriate coordinate transformation that 
    294 shifts the singular point onto land \citep{Madec_Imbard_CD96, Murray_JCP96}. 
     294shifts the singular point onto land \citep{madec.imbard_CD96, murray_JCP96}. 
    295295As a consequence, it is important to solve the primitive equations in various curvilinear coordinate systems. 
    296296An efficient way of introducing an appropriate coordinate transform can be found when using a tensorial formalism. 
     
    298298Ocean modellers mainly use three-dimensional orthogonal grids on the sphere (spherical earth approximation), 
    299299with preservation of the local vertical. Here we give the simplified equations for this particular case. 
    300 The general case is detailed by \citet{Eiseman1980} in their survey of the conservation laws of fluid dynamics. 
     300The general case is detailed by \citet{eiseman.stone_SR80} in their survey of the conservation laws of fluid dynamics. 
    301301 
    302302Let $(i,j,k)$ be a set of orthogonal curvilinear coordinates on 
     
    577577In order to satisfy two or more constrains one can even be tempted to mixed these coordinate systems, as in 
    578578HYCOM (mixture of $z$-coordinate at the surface, isopycnic coordinate in the ocean interior and $\sigma$ at 
    579 the ocean bottom) \citep{Chassignet_al_JPO03} or 
     579the ocean bottom) \citep{chassignet.smith.ea_JPO03} or 
    580580OPA (mixture of $z$-coordinate in vicinity the surface and steep topography areas and $\sigma$-coordinate elsewhere) 
    581 \citep{Madec_al_JPO96} among others. 
     581\citep{madec.delecluse.ea_JPO96} among others. 
    582582 
    583583In fact one is totally free to choose any space and time vertical coordinate by 
     
    592592the $(i,j,s,t)$ generalised coordinate system with $s$ depending on the other three variables through 
    593593\autoref{eq:PE_s}. 
    594 This so-called \textit{generalised vertical coordinate} \citep{Kasahara_MWR74} is in fact 
     594This so-called \textit{generalised vertical coordinate} \citep{kasahara_MWR74} is in fact 
    595595an Arbitrary Lagrangian--Eulerian (ALE) coordinate. 
    596596Indeed, choosing an expression for $s$ is an arbitrary choice that determines 
    597597which part of the vertical velocity (defined from a fixed referential) will cross the levels (Eulerian part) and 
    598598which part will be used to move them (Lagrangian part). 
    599 The coordinate is also sometime referenced as an adaptive coordinate \citep{Hofmeister_al_OM09}, 
     599The coordinate is also sometime referenced as an adaptive coordinate \citep{hofmeister.burchard.ea_OM10}, 
    600600since the coordinate system is adapted in the course of the simulation. 
    601601Its most often used implementation is via an ALE algorithm, 
    602602in which a pure lagrangian step is followed by regridding and remapping steps, 
    603603the later step implicitly embedding the vertical advection 
    604 \citep{Hirt_al_JCP74, Chassignet_al_JPO03, White_al_JCP09}. 
    605 Here we follow the \citep{Kasahara_MWR74} strategy: 
     604\citep{hirt.amsden.ea_JCP74, chassignet.smith.ea_JPO03, white.adcroft.ea_JCP09}. 
     605Here we follow the \citep{kasahara_MWR74} strategy: 
    606606a regridding step (an update of the vertical coordinate) followed by an eulerian step with 
    607607an explicit computation of vertical advection relative to the moving s-surfaces. 
     
    744744      (b) $z$-coordinate in non-linear free surface case ; 
    745745      (c) re-scaled height coordinate 
    746       (become popular as the \zstar-coordinate \citep{Adcroft_Campin_OM04}). 
     746      (become popular as the \zstar-coordinate \citep{adcroft.campin_OM04}). 
    747747    } 
    748748  \end{center} 
     
    751751 
    752752In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account. 
    753 These coordinates systems is presented in a report \citep{Levier2007} available on the \NEMO web site. 
     753These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site. 
    754754 
    755755The \zstar coordinate approach is an unapproximated, non-linear free surface implementation which allows one to 
    756 deal with large amplitude free-surface variations relative to the vertical resolution \citep{Adcroft_Campin_OM04}. 
     756deal with large amplitude free-surface variations relative to the vertical resolution \citep{adcroft.campin_OM04}. 
    757757In the \zstar formulation, 
    758758the variation of the column thickness due to sea-surface undulations is not concentrated in the surface level, 
     
    805805The quasi -horizontal nature of the coordinate surfaces also facilitates the implementation of 
    806806neutral physics parameterizations in \zstar models using the same techniques as in $z$-models 
    807 (see Chapters 13-16 of \cite{Griffies_Bk04}) for a discussion of neutral physics in $z$-models, 
     807(see Chapters 13-16 of \cite{griffies_bk04}) for a discussion of neutral physics in $z$-models, 
    808808as well as \autoref{sec:LDF_slp} in this document for treatment in \NEMO). 
    809809 
     
    849849The response to such a velocity field often leads to numerical dispersion effects. 
    850850One solution to strongly reduce this error is to use a partial step representation of bottom topography instead of 
    851 a full step one \cite{Pacanowski_Gnanadesikan_MWR98}. 
     851a full step one \cite{pacanowski.gnanadesikan_MWR98}. 
    852852Another solution is to introduce a terrain-following coordinate system (hereafter $s$-coordinate). 
    853853 
     
    876876introduces a truncation error that is not present in a $z$-model. 
    877877In the special case of a $\sigma$-coordinate (i.e. a depth-normalised coordinate system $\sigma = z/H$), 
    878 \citet{Haney1991} and \citet{Beckmann1993} have given estimates of the magnitude of this truncation error. 
     878\citet{haney_JPO91} and \citet{beckmann.haidvogel_JPO93} have given estimates of the magnitude of this truncation error. 
    879879It depends on topographic slope, stratification, horizontal and vertical resolution, the equation of state, 
    880880and the finite difference scheme. 
     
    884884The large-scale slopes require high horizontal resolution, and the computational cost becomes prohibitive. 
    885885This problem can be at least partially overcome by mixing $s$-coordinate and 
    886 step-like representation of bottom topography \citep{Gerdes1993a,Gerdes1993b,Madec_al_JPO96}. 
     886step-like representation of bottom topography \citep{gerdes_JGR93*a,gerdes_JGR93*b,madec.delecluse.ea_JPO96}. 
    887887However, the definition of the model domain vertical coordinate becomes then a non-trivial thing for 
    888888a realistic bottom topography: 
     
    904904In contrast, the ocean will stay at rest in a $z$-model. 
    905905As for the truncation error, the problem can be reduced by introducing the terrain-following coordinate below 
    906 the strongly stratified portion of the water column (\ie the main thermocline) \citep{Madec_al_JPO96}. 
     906the strongly stratified portion of the water column (\ie the main thermocline) \citep{madec.delecluse.ea_JPO96}. 
    907907An alternate solution consists of rotating the lateral diffusive tensor to geopotential or to isoneutral surfaces 
    908908(see \autoref{subsec:PE_ldf}). 
     
    910910strongly exceeding the stability limit of such a operator when it is discretized (see \autoref{chap:LDF}). 
    911911 
    912 The $s$-coordinates introduced here \citep{Lott_al_OM90,Madec_al_JPO96} differ mainly in two aspects from 
     912The $s$-coordinates introduced here \citep{lott.madec.ea_OM90,madec.delecluse.ea_JPO96} differ mainly in two aspects from 
    913913similar models: 
    914914it allows a representation of bottom topography with mixed full or partial step-like/terrain following topography; 
     
    921921\label{subsec:PE_zco_tilde} 
    922922 
    923 The \ztilde -coordinate has been developed by \citet{Leclair_Madec_OM11}. 
     923The \ztilde -coordinate has been developed by \citet{leclair.madec_OM11}. 
    924924It is available in \NEMO since the version 3.4. 
    925925Nevertheless, it is currently not robust enough to be used in all possible configurations. 
     
    10051005The resulting lateral diffusive and dissipative operators are of second order. 
    10061006Observations show that lateral mixing induced by mesoscale turbulence tends to be along isopycnal surfaces 
    1007 (or more precisely neutral surfaces \cite{McDougall1987}) rather than across them. 
     1007(or more precisely neutral surfaces \cite{mcdougall_JPO87}) rather than across them. 
    10081008As the slope of neutral surfaces is small in the ocean, a common approximation is to assume that 
    10091009the `lateral' direction is the horizontal, \ie the lateral mixing is performed along geopotential surfaces. 
     
    10161016both horizontal and isoneutral operators have no effect on mean (\ie large scale) potential energy whereas 
    10171017potential energy is a main source of turbulence (through baroclinic instabilities). 
    1018 \citet{Gent1990} have proposed a parameterisation of mesoscale eddy-induced turbulence which 
     1018\citet{gent.mcwilliams_JPO90} have proposed a parameterisation of mesoscale eddy-induced turbulence which 
    10191019associates an eddy-induced velocity to the isoneutral diffusion. 
    10201020Its mean effect is to reduce the mean potential energy of the ocean. 
     
    10401040There are not all available in \NEMO. For active tracers (temperature and salinity) the main ones are: 
    10411041Laplacian and bilaplacian operators acting along geopotential or iso-neutral surfaces, 
    1042 \citet{Gent1990} parameterisation, and various slightly diffusive advection schemes. 
     1042\citet{gent.mcwilliams_JPO90} parameterisation, and various slightly diffusive advection schemes. 
    10431043For momentum, the main ones are: Laplacian and bilaplacian operators acting along geopotential surfaces, 
    10441044and UBS advection schemes when flux form is chosen for the momentum advection. 
     
    10621062the rotation between geopotential and $s$-surfaces, 
    10631063while it is only an approximation for the rotation between isoneutral and $z$- or $s$-surfaces. 
    1064 Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{Cox1987}. 
     1064Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{cox_OM87}. 
    10651065First, the horizontal contribution of the dianeutral mixing is neglected since the ratio between iso and 
    10661066dia-neutral diffusive coefficients is known to be several orders of magnitude smaller than unity. 
     
    10871087\subsubsection{Eddy induced velocity} 
    10881088 
    1089 When the \textit{eddy induced velocity} parametrisation (eiv) \citep{Gent1990} is used, 
     1089When the \textit{eddy induced velocity} parametrisation (eiv) \citep{gent.mcwilliams_JPO90} is used, 
    10901090an additional tracer advection is introduced in combination with the isoneutral diffusion of tracers: 
    10911091\[ 
     
    11621162\ie on a $f$- or $\beta$-plane, not on the sphere. 
    11631163It is also a very good approximation in vicinity of the Equator in 
    1164 a geographical coordinate system \citep{Lengaigne_al_JGR03}. 
     1164a geographical coordinate system \citep{lengaigne.madec.ea_JGR03}. 
    11651165 
    11661166\subsubsection{lateral bilaplacian momentum diffusive operator} 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

    r10544 r11123  
    1818 
    1919In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account. 
    20 These coordinates systems is presented in a report \citep{Levier2007} available on the \NEMO web site.  
     20These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site.  
    2121 
    2222\colorbox{yellow}{  end of to be updated} 
     
    8989which imposes a very small time step when an explicit time stepping is used. 
    9090Two methods are proposed to allow a longer time step for the three-dimensional equations: 
    91 the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt}), 
     91the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt?}), 
    9292and the split-explicit free surface described below. 
    9393The extra term introduced in the filtered method is calculated implicitly, 
     
    139139\nlst{namdom}  
    140140%-------------------------------------------------------------------------------------------------------------- 
    141 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004}. 
     141The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004?}. 
    142142The general idea is to solve the free surface equation with a small time step, 
    143143while the three dimensional prognostic variables are solved with a longer time step that 
     
    151151      \protect\label{fig:DYN_dynspg_ts} 
    152152      Schematic of the split-explicit time stepping scheme for the barotropic and baroclinic modes, 
    153       after \citet{Griffies2004}. 
     153      after \citet{Griffies2004?}. 
    154154      Time increases to the right. 
    155155      Baroclinic time steps are denoted by $t-\Delta t$, $t, t+\Delta t$, and $t+2\Delta t$. 
     
    171171 
    172172The split-explicit formulation has a damping effect on external gravity waves, 
    173 which is weaker than the filtered free surface but still significant as shown by \citet{Levier2007} in 
     173which is weaker than the filtered free surface but still significant as shown by \citet{levier.treguier.ea_rpt07} in 
    174174the case of an analytical barotropic Kelvin wave.  
    175175 
     
    294294\label{subsec:DYN_spg_flt} 
    295295 
    296 The filtered formulation follows the \citet{Roullet2000} implementation. 
     296The filtered formulation follows the \citet{Roullet2000?} implementation. 
    297297The extra term introduced in the equations (see {\S}I.2.2) is solved implicitly. 
    298298The elliptic solvers available in the code are documented in \autoref{chap:MISC}. 
    299299The amplitude of the extra term is given by the namelist variable \np{rnu}. 
    300 The default value is 1, as recommended by \citet{Roullet2000} 
     300The default value is 1, as recommended by \citet{Roullet2000?} 
    301301 
    302302\colorbox{red}{\np{rnu}\forcode{ = 1} to be suppressed from namelist !} 
     
    309309 
    310310In the non-linear free surface formulation, the variations of volume are fully taken into account. 
    311 This option is presented in a report \citep{Levier2007} available on the NEMO web site. 
     311This option is presented in a report \citep{levier.treguier.ea_rpt07} available on the NEMO web site. 
    312312The three time-stepping methods (explicit, split-explicit and filtered) are the same as in 
    313313\autoref{DYN_spg_linear} except that the ocean depth is now time-dependent. 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_time_domain.tex

    r10501 r11123  
    6464 
    6565The time stepping used for processes other than diffusion is the well-known leapfrog scheme 
    66 \citep{Mesinger_Arakawa_Bk76}. 
     66\citep{mesinger.arakawa_bk76}. 
    6767This scheme is widely used for advection processes in low-viscosity fluids. 
    6868It is a time centred scheme, \ie the RHS in \autoref{eq:STP} is evaluated at time step $t$, the now time step. 
     
    8080To prevent it, the leapfrog scheme is often used in association with a Robert-Asselin time filter 
    8181(hereafter the LF-RA scheme). 
    82 This filter, first designed by \citet{Robert_JMSJ66} and more comprehensively studied by \citet{Asselin_MWR72}, 
     82This filter, first designed by \citet{robert_JMSJ66} and more comprehensively studied by \citet{asselin_MWR72}, 
    8383is a kind of laplacian diffusion in time that mixes odd and even time steps: 
    8484\begin{equation} 
     
    8989$\gamma$ is initialized as \np{rn\_atfp} (namelist parameter). 
    9090Its default value is \np{rn\_atfp}~\forcode{= 10.e-3} (see \autoref{sec:STP_mLF}), 
    91 causing only a weak dissipation of high frequency motions (\citep{Farge1987}). 
     91causing only a weak dissipation of high frequency motions (\citep{farge-coulombier_phd87}). 
    9292The addition of a time filter degrades the accuracy of the calculation from second to first order. 
    9393However, the second order truncation error is proportional to $\gamma$, which is small compared to 1. 
     
    115115 
    116116This is diffusive in time and conditionally stable. 
    117 The conditions for stability of second and fourth order horizontal diffusion schemes are \citep{Griffies_Bk04}: 
     117The conditions for stability of second and fourth order horizontal diffusion schemes are \citep{griffies_bk04}: 
    118118\begin{equation} 
    119119  \label{eq:STP_euler_stability} 
     
    183183$c(k)$ and $d(k)$ are positive and the diagonal term is greater than the sum of the two extra-diagonal terms, 
    184184therefore a special adaptation of the Gauss elimination procedure is used to find the solution 
    185 (see for example \citet{Richtmyer1967}). 
     185(see for example \citet{richtmyer.morton_bk67}). 
    186186 
    187187% ------------------------------------------------------------------------------------------------------------- 
     
    200200    \caption{ 
    201201      \protect\label{fig:TimeStep_flowchart} 
    202       Sketch of the leapfrog time stepping sequence in \NEMO from \citet{Leclair_Madec_OM09}. 
     202      Sketch of the leapfrog time stepping sequence in \NEMO from \citet{leclair.madec_OM09}. 
    203203      The use of a semi -implicit computation of the hydrostatic pressure gradient requires the tracer equation to 
    204204      be stepped forward prior to the momentum equation. 
     
    219219\label{sec:STP_mLF} 
    220220 
    221 Significant changes have been introduced by \cite{Leclair_Madec_OM09} in the LF-RA scheme in order to 
     221Significant changes have been introduced by \cite{leclair.madec_OM09} in the LF-RA scheme in order to 
    222222ensure tracer conservation and to allow the use of a much smaller value of the Asselin filter parameter. 
    223223The modifications affect both the forcing and filtering treatments in the LF-RA scheme. 
     
    237237The change in the forcing formulation given by \autoref{eq:STP_forcing} (see \autoref{fig:MLF_forcing}) 
    238238has a significant effect: 
    239 the forcing term no longer excites the divergence of odd and even time steps \citep{Leclair_Madec_OM09}. 
     239the forcing term no longer excites the divergence of odd and even time steps \citep{leclair.madec_OM09}. 
    240240% forcing seen by the model.... 
    241241This property improves the LF-RA scheme in two respects. 
     
    245245(last term in \autoref{eq:STP_RA} compared to \autoref{eq:STP_asselin}). 
    246246Since the filtering of the forcing was the source of non-conservation in the classical LF-RA scheme, 
    247 the modified formulation becomes conservative \citep{Leclair_Madec_OM09}. 
     247the modified formulation becomes conservative \citep{leclair.madec_OM09}. 
    248248Second, the LF-RA becomes a truly quasi -second order scheme. 
    249249Indeed, \autoref{eq:STP_forcing} used in combination with a careful treatment of static instability 
  • NEMO/trunk/doc/latex/NEMO/subfiles/introduction.tex

    r10544 r11123  
    2727 
    2828The ocean component of \NEMO has been developed from the legacy of the OPA model, release 8.2,  
    29 described in \citet{Madec1998}. 
     29described in \citet{madec.delecluse.ea_NPM98}. 
    3030This model has been used for a wide range of applications, both regional or global, as a forced ocean model and  
    3131as a model coupled with the sea-ice and/or the atmosphere. 
     
    6767Within the \NEMO system the ocean model is interactively coupled with a sea ice model (SI$^3$) and 
    6868a biogeochemistry model (PISCES). 
    69 Interactive coupling to Atmospheric models is possible via the OASIS coupler \citep{OASIS2006}. 
     69Interactive coupling to Atmospheric models is possible via the \href{https://portal.enes.org/oasis}{OASIS coupler}. 
    7070Two-way nesting is also available through an interface to the AGRIF package 
    71 (Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008}. 
     71(Adaptative Grid Refinement in \fortran) \citep{debreu.vouland.ea_CG08}. 
    7272% Needs to be reviewed 
    7373%The interface code for coupling to an alternative sea ice model (CICE, \citet{Hunke2008}) has now been upgraded so 
     
    8383The lateral Laplacian and biharmonic viscosity and diffusion can be rotated following 
    8484a geopotential or neutral direction. 
    85 There is an optional eddy induced velocity \citep{Gent1990} with a space and time variable coefficient 
    86 \citet{Treguier1997}. 
     85There is an optional eddy induced velocity \citep{gent.mcwilliams_JPO90} with a space and time variable coefficient 
     86\citet{treguier.held.ea_JPO97}. 
    8787The model has vertical harmonic viscosity and diffusion with a space and time variable coefficient, 
    88 with options to compute the coefficients with \citet{Blanke1993}, \citet{Pacanowski_Philander_JPO81}, or  
    89 \citet{Umlauf_Burchard_JMS03} mixing schemes. 
     88with options to compute the coefficients with \citet{blanke.delecluse_JPO93}, \citet{pacanowski.philander_JPO81}, or  
     89\citet{umlauf.burchard_JMR03} mixing schemes. 
    9090  
    9191%%gm    To be put somewhere else .... 
     
    213213NEMO/OPA, like all research tools, is in perpetual evolution. 
    214214The present document describes the OPA version include in the release 3.4 of NEMO. 
    215 This release differs significantly from version 8, documented in \citet{Madec1998}. \\ 
     215This release differs significantly from version 8, documented in \citet{madec.delecluse.ea_NPM98}. \\ 
    216216 
    217217The main modifications from OPA v8 and NEMO/OPA v3.2 are : 
     
    222222\item 
    223223  introduction of partial step representation of bottom topography 
    224   \citep{Barnier_al_OD06, Le_Sommer_al_OM09, Penduff_al_OS07}; 
     224  \citep{barnier.madec.ea_OD06, le-sommer.penduff.ea_OM09, penduff.le-sommer.ea_OS07}; 
    225225\item 
    226226  partial reactivation of a terrain-following vertical coordinate ($s$- and hybrid $s$-$z$) with 
     
    242242  additional advection schemes for tracers; 
    243243\item 
    244   implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{Debreu_al_CG2008}; 
     244  implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{debreu.vouland.ea_CG08}; 
    245245\item 
    246246  online diagnostics : tracers trend in the mixed layer and vorticity balance; 
     
    255255  RGB light penetration and optional use of ocean color  
    256256\item 
    257   major changes in the TKE schemes: it now includes a Langmuir cell parameterization \citep{Axell_JGR02}, 
    258   the \citet{Mellor_Blumberg_JPO04} surface wave breaking parameterization, and has a time discretization which 
    259   is energetically consistent with the ocean model equations \citep{Burchard_OM02, Marsaleix_al_OM08}; 
     257  major changes in the TKE schemes: it now includes a Langmuir cell parameterization \citep{axell_JGR02}, 
     258  the \citet{mellor.blumberg_JPO04} surface wave breaking parameterization, and has a time discretization which 
     259  is energetically consistent with the ocean model equations \citep{burchard_OM02, marsaleix.auclair.ea_OM08}; 
    260260\item 
    261261  tidal mixing parametrisation (bottom intensification) + Indonesian specific tidal mixing 
    262   \citep{Koch-Larrouy_al_GRL07}; 
     262  \citep{koch-larrouy.madec.ea_GRL07}; 
    263263\item 
    264264  introduction of LIM-3, the new Louvain-la-Neuve sea-ice model 
    265265  (C-grid rheology and new thermodynamics including bulk ice salinity) 
    266   \citep{Vancoppenolle_al_OM09a, Vancoppenolle_al_OM09b} 
     266  \citep{vancoppenolle.fichefet.ea_OM09*a, vancoppenolle.fichefet.ea_OM09*b} 
    267267\end{itemize} 
    268268 
     
    272272\item 
    273273  introduction of a modified leapfrog-Asselin filter time stepping scheme 
    274   \citep{Leclair_Madec_OM09};  
    275 \item 
    276   additional scheme for iso-neutral mixing \citep{Griffies_al_JPO98}, although it is still a "work in progress"; 
    277 \item 
    278   a rewriting of the bottom boundary layer scheme, following \citet{Campin_Goosse_Tel99}; 
    279 \item 
    280   addition of a Generic Length Scale vertical mixing scheme, following \citet{Umlauf_Burchard_JMS03}; 
     274  \citep{leclair.madec_OM09};  
     275\item 
     276  additional scheme for iso-neutral mixing \citep{griffies.gnanadesikan.ea_JPO98}, although it is still a "work in progress"; 
     277\item 
     278  a rewriting of the bottom boundary layer scheme, following \citet{campin.goosse_T99}; 
     279\item 
     280  addition of a Generic Length Scale vertical mixing scheme, following \citet{umlauf.burchard_JMR03}; 
    281281\item 
    282282  addition of the atmospheric pressure as an external forcing on both ocean and sea-ice dynamics; 
    283283\item 
    284   addition of a diurnal cycle on solar radiation \citep{Bernie_al_CD07}; 
     284  addition of a diurnal cycle on solar radiation \citep{bernie.guilyardi.ea_CD07}; 
    285285\item 
    286286  river runoffs added through a non-zero depth, and having its own temperature and salinity; 
     
    296296  coupling interface adjusted for WRF atmospheric model; 
    297297\item 
    298   C-grid ice rheology now available fro both LIM-2 and LIM-3 \citep{Bouillon_al_OM09}; 
     298  C-grid ice rheology now available fro both LIM-2 and LIM-3 \citep{bouillon.maqueda.ea_OM09}; 
    299299\item 
    300300  LIM-3 ice-ocean momentum coupling applied to LIM-2; 
     
    318318 
    319319\begin{itemize} 
    320 \item finalisation of above iso-neutral mixing \citep{Griffies_al_JPO98}"; 
     320\item finalisation of above iso-neutral mixing \citep{griffies.gnanadesikan.ea_JPO98}"; 
    321321\item "Neptune effect" parametrisation; 
    322322\item horizontal pressure gradient suitable for s-coordinate; 
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