# Changeset 11123

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Timestamp:
2019-06-17T14:22:27+02:00 (17 months ago)
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Modification of LaTeX subfiles accordingly to new citations keys

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

• ## NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.tex

 r11043 %% Chapters \subfile{../subfiles/chap_model_basics} \subfile{../subfiles/chap_time_domain}   % Time discretisation (time stepping strategy) \subfile{../subfiles/chap_DOM}           % Space discretisation \subfile{../subfiles/chap_TRA}           % Tracer advection/diffusion equation \subfile{../subfiles/chap_DYN}           % Dynamics : momentum equation \subfile{../subfiles/chap_SBC}           % Surface Boundary Conditions \subfile{../subfiles/chap_LBC}           % Lateral Boundary Conditions \subfile{../subfiles/chap_LDF}           % Lateral diffusion \subfile{../subfiles/chap_ZDF}           % Vertical diffusion \subfile{../subfiles/chap_DIA}           % Outputs and Diagnostics \subfile{../subfiles/chap_OBS}           % Observation operator \subfile{../subfiles/chap_ASM}           % Assimilation increments \subfile{../subfiles/chap_STO}           % Stochastic param. \subfile{../subfiles/chap_misc}          % Miscellaneous topics \subfile{../subfiles/chap_CONFIG}        % Predefined configurations \subfile{../subfiles/chap_time_domain}    % Time discretisation (time stepping strategy) \subfile{../subfiles/chap_DOM}            % Space discretisation \subfile{../subfiles/chap_TRA}            % Tracer advection/diffusion equation \subfile{../subfiles/chap_DYN}            % Dynamics : momentum equation \subfile{../subfiles/chap_SBC}            % Surface Boundary Conditions \subfile{../subfiles/chap_LBC}            % Lateral Boundary Conditions \subfile{../subfiles/chap_LDF}            % Lateral diffusion \subfile{../subfiles/chap_ZDF}            % Vertical diffusion \subfile{../subfiles/chap_DIA}            % Outputs and Diagnostics \subfile{../subfiles/chap_OBS}            % Observation operator \subfile{../subfiles/chap_ASM}            % Assimilation increments \subfile{../subfiles/chap_STO}            % Stochastic param. \subfile{../subfiles/chap_misc}           % Miscellaneous topics \subfile{../subfiles/chap_CONFIG}         % Predefined configurations %% Appendix \appendix \subfile{../subfiles/annex_A}             % Generalised vertical coordinate \subfile{../subfiles/annex_B}             % Diffusive operator \subfile{../subfiles/annex_C}             % Discrete invariants of the eqs. \subfile{../subfiles/annex_iso}           % Isoneutral diffusion using triads \subfile{../subfiles/annex_D}             % Coding rules \subfile{../subfiles/annex_A}             % Generalised vertical coordinate \subfile{../subfiles/annex_B}             % Diffusive operator \subfile{../subfiles/annex_C}             % Discrete invariants of the eqs. \subfile{../subfiles/annex_iso}            % Isoneutral diffusion using triads \subfile{../subfiles/annex_D}             % Coding rules %% Not included %\subfile{../subfiles/chap_conservation}  % %\subfile{../subfiles/chap_model_basics_zstar} %\subfile{../subfiles/chap_DIU} %\subfile{../subfiles/chap_conservation} %\subfile{../subfiles/annex_E}            % Notes on some on going staff %% Backmatter
• ## NEMO/trunk/doc/latex/NEMO/subfiles

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

 r10442 As in $z$-coordinate, the horizontal pressure gradient can be split in two parts following \citet{Marsaleix_al_OM08}. the horizontal pressure gradient can be split in two parts following \citet{marsaleix.auclair.ea_OM08}. Let defined a density anomaly, $d$, by $d=(\rho - \rho_o)/ \rho_o$, and 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 the ($i$,$j$,$k$) curvilinear coordinate system in which the equations of the ocean circulation model are formulated, takes the following form \citep{Redi_JPO82}: takes the following form \citep{redi_JPO82}: In practice, isopycnal slopes are generally less than $10^{-2}$ in the ocean, so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{Cox1987}: so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{cox_OM87}: \begin{subequations} \label{apdx:B4}
• ## NEMO/trunk/doc/latex/NEMO/subfiles/annex_D.tex

 r10442 To satisfy part of these aims, \NEMO is written with a coding standard which is close to the ECMWF rules, named DOCTOR \citep{Gibson_TR86}. named DOCTOR \citep{gibson_rpt86}. These rules present some advantages like:
• ## NEMO/trunk/doc/latex/NEMO/subfiles/annex_E.tex

 r10442 This results in a dissipatively dominant (\ie hyper-diffusive) truncation error \citep{Shchepetkin_McWilliams_OM05}. The overall performance of the advection scheme is similar to that reported in \cite{Farrow1995}. \citep{shchepetkin.mcwilliams_OM05}. The overall performance of the advection scheme is similar to that reported in \cite{farrow.stevens_JPO95}. It is a relatively good compromise between accuracy and smoothness. It is not a \emph{positive} scheme meaning false extrema are permitted but the second term which is the diffusive part of the scheme, is evaluated using the \textit{before} velocity (forward in time). This is discussed by \citet{Webb_al_JAOT98} in the context of the Quick advection scheme. This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme. UBS and QUICK schemes only differ by one coefficient. Substituting 1/6 with 1/8 in (\autoref{eq:tra_adv_ubs}) leads to the QUICK advection scheme \citep{Webb_al_JAOT98}. Substituting 1/6 with 1/8 in (\autoref{eq:tra_adv_ubs}) leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. This option is not available through a namelist parameter, since the 1/6 coefficient is hard coded. Nevertheless it is quite easy to make the substitution in \mdl{traadv\_ubs} module and obtain a QUICK scheme. $\tau_w^{ubs}$ will be evaluated using either \textit{(a)} a centered $2^{nd}$ order scheme, or \textit{(b)} a TVD scheme, or \textit{(c)} an interpolation based on conservative parabolic splines following \citet{Shchepetkin_McWilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS. \citet{shchepetkin.mcwilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS. The $3^{rd}$ case has dispersion properties similar to an eight-order accurate conventional scheme. \subsection{Griffies iso-neutral diffusion operator} Let try to define a scheme that get its inspiration from the \citet{Griffies_al_JPO98} scheme, Let try to define a scheme that get its inspiration from the \citet{griffies.gnanadesikan.ea_JPO98} scheme, but is formulated within the \NEMO framework (\ie using scale factors rather than grid-size and having a position of $T$-points that Nevertheless, this technique works fine for $T$ and $S$ as they are active tracers (\ie they enter the computation of density), but it does not work for a passive tracer. \citep{Griffies_al_JPO98} introduce a different way to discretise the off-diagonal terms that \citep{griffies.gnanadesikan.ea_JPO98} introduce a different way to discretise the off-diagonal terms that nicely solve the problem. The idea is to get rid of combinations of an averaged in one direction combined with \] \citep{Griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form. \citep{griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form. It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. For example in the (\textbf{i},\textbf{k}) plane, the tracer advective fluxes can be transformed as follows: The horizontal component reduces to the one use for an horizontal laplacian operator and the vertical one keeps the same complexity, but not more. This property has been used to reduce the computational time \citep{Griffies_JPO98}, This property has been used to reduce the computational time \citep{griffies_JPO98}, but it is not of practical use as usually $A \neq A_e$. Nevertheless this property can be used to choose a discret form of \autoref{eq:eiv_skew_continuous} which

• ## NEMO/trunk/doc/latex/NEMO/subfiles/chap_conservation.tex

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

 r10601 and their propagation and accumulation cause uncertainty in final simulation reproducibility on different numbers of processors. To avoid so, based on \citet{He_Ding_JSC01} review of different technics, To avoid so, based on \citet{he.ding_JS01} review of different technics, we use a so called self-compensated summation method. The 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 If further, an approximative conservation of heat and salt contents is sufficient for the problem solved, then it is sufficient to solve a linearized version of \autoref{eq:PE_ssh}, which still allows to take into account freshwater fluxes applied at the ocean surface \citep{Roullet_Madec_JGR00}. which still allows to take into account freshwater fluxes applied at the ocean surface \citep{roullet.madec_JGR00}. Nevertheless, with the linearization, an exact conservation of heat and salt contents is lost. The filtering of EGWs in models with a free surface is usually a matter of discretisation of the temporal derivatives, using a split-explicit method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92} or the implicit scheme \citep{Dukowicz1994} or the addition of a filtering force in the momentum equation \citep{Roullet_Madec_JGR00}. using a split-explicit method \citep{killworth.webb.ea_JPO91, zhang.endoh_JGR92} or the implicit scheme \citep{dukowicz.smith_JGR94} or the addition of a filtering force in the momentum equation \citep{roullet.madec_JGR00}. With the present release, \NEMO offers the choice between an explicit free surface (see \autoref{subsec:DYN_spg_exp}) or a split-explicit scheme strongly inspired the one proposed by \citet{Shchepetkin_McWilliams_OM05} a split-explicit scheme strongly inspired the one proposed by \citet{shchepetkin.mcwilliams_OM05} (see \autoref{subsec:DYN_spg_ts}). cannot be easily treated in a global model without filtering. A solution consists of introducing an appropriate coordinate transformation that shifts the singular point onto land \citep{Madec_Imbard_CD96, Murray_JCP96}. shifts the singular point onto land \citep{madec.imbard_CD96, murray_JCP96}. As a consequence, it is important to solve the primitive equations in various curvilinear coordinate systems. An efficient way of introducing an appropriate coordinate transform can be found when using a tensorial formalism. Ocean modellers mainly use three-dimensional orthogonal grids on the sphere (spherical earth approximation), with preservation of the local vertical. Here we give the simplified equations for this particular case. The general case is detailed by \citet{Eiseman1980} in their survey of the conservation laws of fluid dynamics. The general case is detailed by \citet{eiseman.stone_SR80} in their survey of the conservation laws of fluid dynamics. Let $(i,j,k)$ be a set of orthogonal curvilinear coordinates on In order to satisfy two or more constrains one can even be tempted to mixed these coordinate systems, as in HYCOM (mixture of $z$-coordinate at the surface, isopycnic coordinate in the ocean interior and $\sigma$ at the ocean bottom) \citep{Chassignet_al_JPO03} or the ocean bottom) \citep{chassignet.smith.ea_JPO03} or OPA (mixture of $z$-coordinate in vicinity the surface and steep topography areas and $\sigma$-coordinate elsewhere) \citep{Madec_al_JPO96} among others. \citep{madec.delecluse.ea_JPO96} among others. In fact one is totally free to choose any space and time vertical coordinate by the $(i,j,s,t)$ generalised coordinate system with $s$ depending on the other three variables through \autoref{eq:PE_s}. This so-called \textit{generalised vertical coordinate} \citep{Kasahara_MWR74} is in fact This so-called \textit{generalised vertical coordinate} \citep{kasahara_MWR74} is in fact an Arbitrary Lagrangian--Eulerian (ALE) coordinate. Indeed, choosing an expression for $s$ is an arbitrary choice that determines which part of the vertical velocity (defined from a fixed referential) will cross the levels (Eulerian part) and which part will be used to move them (Lagrangian part). The coordinate is also sometime referenced as an adaptive coordinate \citep{Hofmeister_al_OM09}, The coordinate is also sometime referenced as an adaptive coordinate \citep{hofmeister.burchard.ea_OM10}, since the coordinate system is adapted in the course of the simulation. Its most often used implementation is via an ALE algorithm, in which a pure lagrangian step is followed by regridding and remapping steps, the later step implicitly embedding the vertical advection \citep{Hirt_al_JCP74, Chassignet_al_JPO03, White_al_JCP09}. Here we follow the \citep{Kasahara_MWR74} strategy: \citep{hirt.amsden.ea_JCP74, chassignet.smith.ea_JPO03, white.adcroft.ea_JCP09}. Here we follow the \citep{kasahara_MWR74} strategy: a regridding step (an update of the vertical coordinate) followed by an eulerian step with an explicit computation of vertical advection relative to the moving s-surfaces. (b) $z$-coordinate in non-linear free surface case ; (c) re-scaled height coordinate (become popular as the \zstar-coordinate \citep{Adcroft_Campin_OM04}). (become popular as the \zstar-coordinate \citep{adcroft.campin_OM04}). } \end{center} In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account. These coordinates systems is presented in a report \citep{Levier2007} available on the \NEMO web site. These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site. The \zstar coordinate approach is an unapproximated, non-linear free surface implementation which allows one to deal with large amplitude free-surface variations relative to the vertical resolution \citep{Adcroft_Campin_OM04}. deal with large amplitude free-surface variations relative to the vertical resolution \citep{adcroft.campin_OM04}. In the \zstar formulation, the variation of the column thickness due to sea-surface undulations is not concentrated in the surface level, The quasi -horizontal nature of the coordinate surfaces also facilitates the implementation of neutral physics parameterizations in \zstar models using the same techniques as in $z$-models (see Chapters 13-16 of \cite{Griffies_Bk04}) for a discussion of neutral physics in $z$-models, (see Chapters 13-16 of \cite{griffies_bk04}) for a discussion of neutral physics in $z$-models, as well as \autoref{sec:LDF_slp} in this document for treatment in \NEMO). The response to such a velocity field often leads to numerical dispersion effects. One solution to strongly reduce this error is to use a partial step representation of bottom topography instead of a full step one \cite{Pacanowski_Gnanadesikan_MWR98}. a full step one \cite{pacanowski.gnanadesikan_MWR98}. Another solution is to introduce a terrain-following coordinate system (hereafter $s$-coordinate). introduces a truncation error that is not present in a $z$-model. In the special case of a $\sigma$-coordinate (i.e. a depth-normalised coordinate system $\sigma = z/H$), \citet{Haney1991} and \citet{Beckmann1993} have given estimates of the magnitude of this truncation error. \citet{haney_JPO91} and \citet{beckmann.haidvogel_JPO93} have given estimates of the magnitude of this truncation error. It depends on topographic slope, stratification, horizontal and vertical resolution, the equation of state, and the finite difference scheme. The large-scale slopes require high horizontal resolution, and the computational cost becomes prohibitive. This problem can be at least partially overcome by mixing $s$-coordinate and step-like representation of bottom topography \citep{Gerdes1993a,Gerdes1993b,Madec_al_JPO96}. step-like representation of bottom topography \citep{gerdes_JGR93*a,gerdes_JGR93*b,madec.delecluse.ea_JPO96}. However, the definition of the model domain vertical coordinate becomes then a non-trivial thing for a realistic bottom topography: In contrast, the ocean will stay at rest in a $z$-model. As for the truncation error, the problem can be reduced by introducing the terrain-following coordinate below the strongly stratified portion of the water column (\ie the main thermocline) \citep{Madec_al_JPO96}. the strongly stratified portion of the water column (\ie the main thermocline) \citep{madec.delecluse.ea_JPO96}. An alternate solution consists of rotating the lateral diffusive tensor to geopotential or to isoneutral surfaces (see \autoref{subsec:PE_ldf}). strongly exceeding the stability limit of such a operator when it is discretized (see \autoref{chap:LDF}). The $s$-coordinates introduced here \citep{Lott_al_OM90,Madec_al_JPO96} differ mainly in two aspects from The $s$-coordinates introduced here \citep{lott.madec.ea_OM90,madec.delecluse.ea_JPO96} differ mainly in two aspects from similar models: it allows a representation of bottom topography with mixed full or partial step-like/terrain following topography; \label{subsec:PE_zco_tilde} The \ztilde -coordinate has been developed by \citet{Leclair_Madec_OM11}. The \ztilde -coordinate has been developed by \citet{leclair.madec_OM11}. It is available in \NEMO since the version 3.4. Nevertheless, it is currently not robust enough to be used in all possible configurations. The resulting lateral diffusive and dissipative operators are of second order. Observations show that lateral mixing induced by mesoscale turbulence tends to be along isopycnal surfaces (or more precisely neutral surfaces \cite{McDougall1987}) rather than across them. (or more precisely neutral surfaces \cite{mcdougall_JPO87}) rather than across them. As the slope of neutral surfaces is small in the ocean, a common approximation is to assume that the `lateral' direction is the horizontal, \ie the lateral mixing is performed along geopotential surfaces. both horizontal and isoneutral operators have no effect on mean (\ie large scale) potential energy whereas potential energy is a main source of turbulence (through baroclinic instabilities). \citet{Gent1990} have proposed a parameterisation of mesoscale eddy-induced turbulence which \citet{gent.mcwilliams_JPO90} have proposed a parameterisation of mesoscale eddy-induced turbulence which associates an eddy-induced velocity to the isoneutral diffusion. Its mean effect is to reduce the mean potential energy of the ocean. There are not all available in \NEMO. For active tracers (temperature and salinity) the main ones are: Laplacian and bilaplacian operators acting along geopotential or iso-neutral surfaces, \citet{Gent1990} parameterisation, and various slightly diffusive advection schemes. \citet{gent.mcwilliams_JPO90} parameterisation, and various slightly diffusive advection schemes. For momentum, the main ones are: Laplacian and bilaplacian operators acting along geopotential surfaces, and UBS advection schemes when flux form is chosen for the momentum advection. the rotation between geopotential and $s$-surfaces, while it is only an approximation for the rotation between isoneutral and $z$- or $s$-surfaces. Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{Cox1987}. Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{cox_OM87}. First, the horizontal contribution of the dianeutral mixing is neglected since the ratio between iso and dia-neutral diffusive coefficients is known to be several orders of magnitude smaller than unity. \subsubsection{Eddy induced velocity} When the \textit{eddy induced velocity} parametrisation (eiv) \citep{Gent1990} is used, When the \textit{eddy induced velocity} parametrisation (eiv) \citep{gent.mcwilliams_JPO90} is used, an additional tracer advection is introduced in combination with the isoneutral diffusion of tracers: \[ \ie on a $f$- or $\beta$-plane, not on the sphere. It is also a very good approximation in vicinity of the Equator in a geographical coordinate system \citep{Lengaigne_al_JGR03}. a geographical coordinate system \citep{lengaigne.madec.ea_JGR03}. \subsubsection{lateral bilaplacian momentum diffusive operator}
• ## NEMO/trunk/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex

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

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

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