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02/08/12 17:17:04 (13 years ago)
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cholod
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Load NEMO_TMP into vendor/nemo/current.

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  • vendor/nemo/current/DOC/TexFiles/Chapters/Annex_ISO.tex

    r1 r4  
    22% Iso-neutral diffusion : 
    33% ================================================================ 
    4 \chapter{Griffies's iso-neutral diffusion} 
     4\chapter[Iso-neutral diffusion and eddy advection using 
     5triads]{Iso-neutral diffusion and eddy advection using triads} 
    56\label{sec:triad} 
    67\minitoc 
    7  
    8 \section{Griffies's formulation of iso-neutral diffusion} 
     8\pagebreak 
     9\section{Choice of namelist parameters} 
     10%-----------------------------------------nam_traldf------------------------------------------------------ 
     11\namdisplay{namtra_ldf} 
     12%--------------------------------------------------------------------------------------------------------- 
     13If the namelist variable \np{ln\_traldf\_grif} is set true (and 
     14\key{ldfslp} is set), \NEMO updates both active and passive tracers 
     15using the Griffies triad representation of iso-neutral diffusion and 
     16the eddy-induced advective skew (GM) fluxes. Otherwise (by default) the 
     17filtered version of Cox's original scheme is employed 
     18(\S\ref{LDF_slp}). In the present implementation of the Griffies 
     19scheme, the advective skew fluxes are implemented even if 
     20\key{traldf\_eiv} is not set. 
     21 
     22Values of iso-neutral diffusivity and GM coefficient are set as 
     23described in \S\ref{LDF_coef}. If none of the keys \key{traldf\_cNd}, 
     24N=1,2,3 is set (the default), spatially constant iso-neutral $A_l$ and 
     25GM diffusivity $A_e$ are directly set by \np{rn\_aeih\_0} and 
     26\np{rn\_aeiv\_0}. If 2D-varying coefficients are set with 
     27\key{traldf\_c2d} then $A_l$ is reduced in proportion with horizontal 
     28scale factor according to \eqref{Eq_title} \footnote{Except in global 
     29  $0.5^{\circ}$ runs (\key{orca\_r05}) with \key{traldf\_eiv}, where 
     30  $A_l$ is set like $A_e$ but with a minimum vale of 
     31  $100\;\mathrm{m}^2\;\mathrm{s}^{-1}$}. In idealised setups with 
     32\key{traldf\_c2d}, $A_e$ is reduced similarly, but if \key{traldf\_eiv} 
     33is set in the global configurations \key{orca\_r2}, \key{orca\_r1} or 
     34\key{orca\_r05} with \key{traldf\_c2d}, a horizontally varying $A_e$ is 
     35instead set from the Held-Larichev parameterisation\footnote{In this 
     36  case, $A_e$ at low latitudes $|\theta|<20^{\circ}$ is further 
     37  reduced by a factor $|f/f_{20}|$, where $f_{20}$ is the value of $f$ 
     38  at $20^{\circ}$~N} (\mdl{ldfeiv}) and \np{rn\_aeiv\_0} is ignored 
     39unless it is zero. 
     40 
     41The options specific to the Griffies scheme include: 
     42\begin{description}[font=\normalfont] 
     43\item[\np{ln\_traldf\_gdia}] Default value is false. See \S\ref{sec:triad:sfdiag}. If this is set true, time-mean 
     44  eddy-advective (GM) velocities are output for diagnostic purposes, even 
     45  though the eddy advection is accomplished by means of the skew 
     46  fluxes. 
     47\item[\np{ln\_traldf\_iso}] See \S\ref{sec:triad:taper}. If this is set false (the default), then 
     48  `iso-neutral' mixing is accomplished within the surface mixed-layer 
     49  along slopes linearly decreasing with depth from the value immediately below 
     50  the mixed-layer to zero (flat) at the surface (\S\ref{sec:triad:lintaper}). This is the same 
     51  treatment as used in the default implementation 
     52  \S\ref{LDF_slp_iso}; Fig.~\ref{Fig_eiv_slp}.  Where 
     53  \np{ln\_traldf\_iso} is set true, the vertical skew flux is further 
     54  reduced to ensure no vertical buoyancy flux, giving an almost pure 
     55  horizontal diffusive tracer flux within the mixed layer. This is similar to 
     56  the tapering suggested by \citet{Gerdes1991}. See \S\ref{sec:triad:Gerdes-taper} 
     57\item[\np{ln\_traldf\_botmix}] See \S\ref{sec:triad:iso_bdry}. If this 
     58  is set false (the default) then the lateral diffusive fluxes 
     59  associated with triads partly masked by topography are neglected. If 
     60  it is set true, however, then these lateral diffusive fluxes are 
     61  applied, giving smoother bottom tracer fields at the cost of 
     62  introducing diapycnal mixing. 
     63\end{description} 
     64\section{Triad formulation of iso-neutral diffusion} 
    965\label{sec:triad:iso} 
    10  
    11 We define a scheme inspired by \citet{Griffies_al_JPO98}, but formulated within the \NEMO 
     66We have implemented into \NEMO a scheme inspired by \citet{Griffies_al_JPO98}, but formulated within the \NEMO 
    1267framework, using scale factors rather than grid-sizes. 
    1368 
    … …  
    147202% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    148203\begin{figure}[h] \begin{center} 
    149     \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_triad_fluxes} 
     204    \includegraphics[width=1.05\textwidth]{./TexFiles/Figures/Fig_GRIFF_triad_fluxes} 
    150205    \caption{ \label{fig:triad:ISO_triad} 
    151206      (a) Arrangement of triads $S_i$ and tracer gradients to 
    … …  
    215270% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    216271\begin{figure}[h] \begin{center} 
    217     \includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_qcells} 
     272    \includegraphics[width=0.80\textwidth]{./TexFiles/Figures/Fig_GRIFF_qcells} 
    218273    \caption{   \label{fig:triad:qcells} 
    219     Triad notation for quarter cells.$T$-cells are inside 
     274    Triad notation for quarter cells. $T$-cells are inside 
    220275      boxes, while the  $i+\half,k$ $u$-cell is shaded in green and the 
    221276      $i,k+\half$ $w$-cell is shaded in pink.} 
    … …  
    613668or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$ $u$-point is 
    614669masked. The associated lateral fluxes (grey-black dashed line) are 
    615 masked if \nlv{ln\_botmix\_grif=.false.}, but left unmasked, 
    616 giving bottom mixing, if \nlv{ln\_botmix\_grif=.true.}. 
    617  
    618 The default option \nlv{ln\_botmix\_grif=.false.} is suitable when the 
    619 bbl mixing option is enabled (\key{trabbl}, with \nlv{nn\_bbl\_ldf=1}), 
     670masked if \np{ln\_botmix\_grif}=false, but left unmasked, 
     671giving bottom mixing, if \np{ln\_botmix\_grif}=true. 
     672 
     673The default option \np{ln\_botmix\_grif}=false is suitable when the 
     674bbl mixing option is enabled (\key{trabbl}, with \np{nn\_bbl\_ldf}=1), 
    620675or  for simple idealized  problems. For setups with topography without 
    621 bbl mixing, \nlv{ln\_botmix\_grif=.true.} may be necessary. 
     676bbl mixing, \np{ln\_botmix\_grif}=true may be necessary. 
    622677% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    623678\begin{figure}[h] \begin{center} 
    624     \includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_bdry_triads} 
     679    \includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_GRIFF_bdry_triads} 
    625680    \caption{  \label{fig:triad:bdry_triads} 
    626681      (a) Uppermost model layer $k=1$ with $i,1$ and $i+1,1$ tracer 
    … …  
    636691      or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$ $u$-point 
    637692      is masked. The associated lateral fluxes (grey-black dashed 
    638       line) are masked if \smnlv{ln\_botmix\_grif=.false.}, but left 
    639       unmasked, giving bottom mixing, if \smnlv{ln\_botmix\_grif=.true.}} 
     693      line) are masked if \np{botmix\_grif}=.false., but left 
     694      unmasked, giving bottom mixing, if \np{botmix\_grif}=.true.} 
    640695 \end{center} \end{figure} 
    641696% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    … …  
    665720iso-neutral density flux that drives dianeutral mixing.  In particular this iso-neutral density flux 
    666721is always downwards, and so acts to reduce gravitational potential energy. 
    667 \subsection{Tapering within the surface mixed layer} 
     722\subsection{Tapering within the surface mixed layer}\label{sec:triad:taper} 
     723 
    668724Additional tapering of the iso-neutral fluxes is necessary within the 
    669725surface mixed layer. When the Griffies triads are used, we offer two 
    … …  
    671727\subsubsection{Linear slope tapering within the surface mixed layer}\label{sec:triad:lintaper} 
    672728This is the option activated by the default choice 
    673 \nlv{ln\_triad\_iso=.false.}. Slopes $\tilde{r}_i$ relative to 
     729\np{ln\_triad\_iso}=false. Slopes $\tilde{r}_i$ relative to 
    674730geopotentials are tapered linearly from their value immediately below the mixed layer to zero at the 
    675731surface, as described in option (c) of Fig.~\ref{Fig_eiv_slp}, to values 
    … …  
    794850    different $i_p,k_p$, denoted by different colours, (e.g. the green 
    795851    triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.}} 
    796   {\includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_triad_MLB}} 
     852  {\includegraphics[width=0.60\textwidth]{./TexFiles/Figures/Fig_GRIFF_MLB_triads}} 
    797853\end{figure} 
    798854% >>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    799855 
    800 \subsubsection{Additional truncation of skew iso-neutral flux components} 
    801 The alternative option is activated by setting \nlv{ln\_triad\_iso = 
    802   .true.}. This retains the same tapered slope $\rML$  described above for the 
     856\subsubsection{Additional truncation of skew iso-neutral flux 
     857  components} 
     858\label{sec:triad:Gerdes-taper} 
     859The alternative option is activated by setting \np{ln\_triad\_iso} = 
     860  true. This retains the same tapered slope $\rML$  described above for the 
    803861calculation of the $_{33}$ term of the iso-neutral diffusion tensor (the 
    804862vertical tracer flux driven by vertical tracer gradients), but 
    … …  
    839897% Skew flux formulation for Eddy Induced Velocity : 
    840898% ================================================================ 
    841 \section{Eddy induced advection and its formulation as a skew flux} 
     899\section{Eddy induced advection formulated as a skew flux}\label{sec:triad:skew-flux} 
    842900 
    843901\subsection{The continuous skew flux formulation}\label{sec:triad:continuous-skew-flux} 
    844902 
    845  When Gent and McWilliams's [1990] diffusion is used (\key{traldf\_eiv} defined), 
     903 When Gent and McWilliams's [1990] diffusion is used, 
    846904an additional advection term is added. The associated velocity is the so called 
    847905eddy induced velocity, the formulation of which depends on the slopes of iso- 
    … …  
    852910 
    853911The eddy induced velocity is given by: 
    854 \begin{equation} \label{eq:triad:eiv_v} 
     912\begin{subequations} \label{eq:triad:eiv} 
     913\begin{equation}\label{eq:triad:eiv_v} 
    855914\begin{split} 
    856  u^* & = - \frac{1}{e_{3}}\;          \partial_k \left( A_{e} \; \tilde{r}_1 \right)   \\ 
    857  v^* & = - \frac{1}{e_{3}}\;          \partial_k \left( A_{e} \; \tilde{r}_2 \right)   \\ 
    858 w^* & =    \frac{1}{e_{1}e_{2}}\; \left\{ \partial_i  \left( e_{2} \, A_{e} \; \tilde{r}_1 \right) 
    859                                                             + \partial_j  \left( e_{1} \, A_{e} \;\tilde{r}_2 \right) \right\} 
     915 u^* & = - \frac{1}{e_{3}}\;          \partial_i\psi_1,  \\ 
     916 v^* & = - \frac{1}{e_{3}}\;          \partial_j\psi_2,    \\ 
     917w^* & =    \frac{1}{e_{1}e_{2}}\; \left\{ \partial_i  \left( e_{2} \, \psi_1\right) 
     918                                                            + \partial_j  \left( e_{1} \, \psi_2\right) \right\}, 
    860919\end{split} 
    861920\end{equation} 
    862 where $A_{e}$ is the eddy induced velocity coefficient, and $\tilde{r}_1$ and $\tilde{r}_2$ the slopes between the iso-neutral and the geopotential surfaces. 
    863  
    864 The traditional way to implement this additional advection is to add it to the Eulerian 
    865 velocity prior to computing the tracer advection. This allows us to take advantage of 
    866 all the advection schemes offered for the tracers (see \S\ref{TRA_adv}) and not just 
    867 a $2^{nd}$ order advection scheme. This is particularly useful for passive tracers 
    868 where \emph{positivity} of the advection scheme is of paramount importance. 
    869  
    870 \citet{Griffies_JPO98} introduces another way to implement the eddy induced advection, 
    871 the so-called skew form. It is based on a transformation of the advective fluxes 
     921where the streamfunctions $\psi_i$ are given by 
     922\begin{equation} \label{eq:triad:eiv_psi} 
     923\begin{split} 
     924\psi_1 & = A_{e} \; \tilde{r}_1,   \\ 
     925\psi_2 & = A_{e} \; \tilde{r}_2, 
     926\end{split} 
     927\end{equation} 
     928\end{subequations} 
     929with $A_{e}$ the eddy induced velocity coefficient, and $\tilde{r}_1$ and $\tilde{r}_2$ the slopes between the iso-neutral and the geopotential surfaces. 
     930 
     931The traditional way to implement this additional advection is to add 
     932it to the Eulerian velocity prior to computing the tracer 
     933advection. This is implemented if \key{traldf\_eiv} is set in the 
     934default implementation, where \np{ln\_traldf\_grif} is set 
     935false. This allows us to take advantage of all the advection schemes 
     936offered for the tracers (see \S\ref{TRA_adv}) and not just a $2^{nd}$ 
     937order advection scheme. This is particularly useful for passive 
     938tracers where \emph{positivity} of the advection scheme is of 
     939paramount importance. 
     940 
     941However, when \np{ln\_traldf\_grif} is set true, \NEMO instead 
     942implements eddy induced advection according to the so-called skew form 
     943\citep{Griffies_JPO98}. It is based on a transformation of the advective fluxes 
    872944using the non-divergent nature of the eddy induced velocity. 
    873945For example in the (\textbf{i},\textbf{k}) plane, the tracer advective 
    … …  
    883955&= 
    884956\begin{pmatrix} 
    885                 { - \partial_k \left( e_{2} \, A_{e} \; \tilde{r}_1 \right) \; T \;}            \\ 
    886                 {+ \partial_i  \left( e_{2} \, A_{e} \; \tilde{r}_1 \right) \; T \;}     \\ 
     957                { - \partial_k \left( e_{2} \,\psi_1 \right) \; T \;}           \\ 
     958                {+ \partial_i  \left( e_{2} \, \psi_1 \right) \; T \;}   \\ 
    887959\end{pmatrix}                   \\ 
    888960&= 
    889961\begin{pmatrix} 
    890                 { - \partial_k \left( e_{2} \, A_{e} \; \tilde{r}_1  \; T \right) \;}  \\ 
    891                 {+ \partial_i  \left( e_{2} \, A_{e} \; \tilde{r}_1 \; T \right) \;}    \\ 
     962                { - \partial_k \left( e_{2} \, \psi_1  \; T \right) \;}  \\ 
     963                {+ \partial_i  \left( e_{2} \,\psi_1 \; T \right) \;}    \\ 
    892964\end{pmatrix} 
    893965 + 
    894966\begin{pmatrix} 
    895                 {+ e_{2} \, A_{e} \; \tilde{r}_1  \; \partial_k T}  \\ 
    896                 { - e_{2} \, A_{e} \; \tilde{r}_1  \; \partial_i  T}     \\ 
     967                {+ e_{2} \, \psi_1  \; \partial_k T}  \\ 
     968                { - e_{2} \, \psi_1  \; \partial_i  T}   \\ 
    897969\end{pmatrix} 
    898970\end{split} 
    … …  
    902974\begin{equation} \label{eq:triad:eiv_skew_ijk} 
    903975\textbf{F}_\mathrm{eiv}^T = \begin{pmatrix} 
    904                 {+ e_{2} \, A_{e} \; \tilde{r}_1  \; \partial_k T}   \\ 
    905                 { - e_{2} \, A_{e} \; \tilde{r}_1  \; \partial_i  T}     \\ 
     976                {+ e_{2} \, \psi_1  \; \partial_k T}   \\ 
     977                { - e_{2} \, \psi_1  \; \partial_i  T}   \\ 
    906978                                 \end{pmatrix} 
    907979\end{equation} 
    … …  
    909981\begin{equation}\label{eq:triad:eiv_skew_physical} 
    910982\begin{split} 
    911  f^*_1 & = \frac{1}{e_{3}}\; A_{e} \; \tilde{r}_1 \partial_k T   \\ 
    912  f^*_2 & = \frac{1}{e_{3}}\; A_{e} \; \tilde{r}_2 \partial_k T   \\ 
    913  f^*_3 & =  -\frac{1}{e_{1}e_{2}}\; A_{e} \left\{ e_{2} \tilde{r}_1 \partial_i T 
    914    + e_{1} \tilde{r}_2 \partial_j T \right\}. \\ 
     983 f^*_1 & = \frac{1}{e_{3}}\; \psi_1 \partial_k T   \\ 
     984 f^*_2 & = \frac{1}{e_{3}}\; \psi_2 \partial_k T   \\ 
     985 f^*_3 & =  -\frac{1}{e_{1}e_{2}}\; \left\{ e_{2} \psi_1 \partial_i T 
     986   + e_{1} \psi_2 \partial_j T \right\}. \\ 
    915987\end{split} 
    916988\end{equation} 
    917989Note that Eq.~ \eqref{eq:triad:eiv_skew_physical} takes the same form whatever the 
    918990vertical coordinate, though of course the slopes 
    919 $\tilde{r}_i$ are relative to geopotentials. 
     991$\tilde{r}_i$ which define the $\psi_i$ in \eqref{eq:triad:eiv_psi} are relative to geopotentials. 
    920992The tendency associated with eddy induced velocity is then simply the convergence 
    921993of the fluxes (\ref{eq:triad:eiv_skew_ijk}, \ref{eq:triad:eiv_skew_physical}), so 
    922994\begin{equation} \label{eq:triad:skew_eiv_conv} 
    923995\frac{\partial T}{\partial t}= -\frac{1}{e_1 \, e_2 \, e_3 }      \left[ 
    924   \frac{\partial}{\partial i} \left( e_2  A_{e} \; \tilde{r}_1 \partial_k T\right) 
    925   + \frac{\partial}{\partial j} \left( e_1  A_{e} \; 
    926     \tilde{r}_2 \partial_k T\right) 
    927  -  \frac{\partial}{\partial k} A_{e} \left( e_{2} \tilde{r}_1 \partial_i T 
    928    + e_{1} \tilde{r}_2 \partial_j T \right)  \right] 
     996  \frac{\partial}{\partial i} \left( e_2 \psi_1 \partial_k T\right) 
     997  + \frac{\partial}{\partial j} \left( e_1  \; 
     998    \psi_2 \partial_k T\right) 
     999 -  \frac{\partial}{\partial k} \left( e_{2} \psi_1 \partial_i T 
     1000   + e_{1} \psi_2 \partial_j T \right)  \right] 
    9291001\end{equation} 
    9301002 It naturally conserves the tracer content, as it is expressed in flux 
    … …  
    9761048The discretization conserves tracer variance, $i.e.$ it does not 
    9771049include a diffusive component but is a `pure' advection term. This can 
    978 be seen either from Appendix \ref{Apdx_eiv_skew} or by considering the 
     1050be seen 
     1051%either from Appendix \ref{Apdx_eiv_skew} or 
     1052by considering the 
    9791053fluxes associated with a given triad slope 
    9801054$_i^k{\mathbb{R}}_{i_p}^{k_p} (T)$. For, following 
    … …  
    10641138and $\triadt{i+1}{k}{R}{-1/2}{1/2}$ are masked when either of the 
    10651139$i,k+1$ or $i+1,k+1$ tracer points is masked, i.e.\ the $i,k+1$ 
    1066 $u$-point is masked. The namelist parameter \nlv{ln\_botmix\_grif} has 
     1140$u$-point is masked. The namelist parameter \np{ln\_botmix\_grif} has 
    10671141no effect on the eddy-induced skew-fluxes. 
    10681142 
    … …  
    10791153option (c) of Fig.~\ref{Fig_eiv_slp}. This linear tapering for the 
    10801154slopes used to calculate the eddy-induced fluxes is 
    1081 unaffected by the value of \nlv{ln\_triad\_iso}. 
     1155unaffected by the value of \np{ln\_triad\_iso}. 
    10821156 
    10831157The justification for this linear slope tapering is that, for $A_e$ 
    … …  
    10941168 
    10951169\subsection{Streamfunction diagnostics}\label{sec:triad:sfdiag} 
    1096 Where the namelist parameter \nlv{ln\_botmix\_grif=.true.}, diagnosed 
     1170Where the namelist parameter \np{ln\_traldf\_gdia}=true, diagnosed 
    10971171mean eddy-induced velocities are output. Each time step, 
    10981172streamfunctions are calculated in the $i$-$k$ and $j$-$k$ planes at 
    … …  
    11041178\begin{equation} 
    11051179  \label{eq:triad:sfdiagi} 
    1106   {\psi_{[i]}}_{i+1/2}^{k+1/2}={\quarter}\sum_{\substack{i_p,\,k_p}} 
    1107   {A_e}_{i+1/2-i_p}^{k+1/2-k_p}\:\triadd{i+1/2-i_p}{k+1/2-k_p}{R}{i_p}{k_p} 
    1108 \end{equation} 
    1109  
    1110 \newpage      %force an empty line 
    1111 % ================================================================ 
    1112 % Discrete Invariants of the skew flux formulation 
    1113 % ================================================================ 
    1114 \subsection{Discrete Invariants of the skew flux formulation} 
    1115 \label{Apdx_eiv_skew} 
    1116  
    1117  
    1118 Demonstration for the conservation of the tracer variance in the (\textbf{i},\textbf{j}) plane. 
    1119  
    1120 This have to be moved in an Appendix. 
    1121  
    1122 The continuous property to be demonstrated is : 
    1123 \begin{align*} 
    1124 \int_D \nabla \cdot \textbf{F}_\mathrm{eiv}(T) \; T \;dv  \equiv 0 
    1125 \end{align*} 
    1126 The discrete form of its left hand side is obtained using \eqref{eq:triad:allskewflux} 
    1127 \begin{align*} 
    1128  \sum\limits_{i,k} \sum_{\substack{i_p,\,k_p}}  \Biggl\{   \;\; 
    1129  \delta_i  &\left[ 
    1130 {e_{2u}}_{i+i_p+1/2}^{k}                                  \;\ \ {A_{e}}_{i+i_p+1/2}^{k} 
    1131 \ \ \ { _{i+i_p+1/2}^k \mathbb{R}_{-i_p}^{k_p} }   \quad \delta_{k+k_p}[T_{i+i_p+1/2}] 
    1132    \right] \; T_i^k      \\ 
    1133 - \delta_k &\left[ 
    1134 {e_{2u}}_i^{k+k_p+1/2}                                     \ \ {A_{e}}_i^{k+k_p+1/2} 
    1135 \ \ { _i^{k+k_p+1/2} \mathbb{R}_{i_p}^{-k_p} }   \ \ \delta_{i+i_p}[T^{k+k_p+1/2}] 
    1136    \right] \; T_i^k      \         \Biggr\} 
    1137 \end{align*} 
    1138 apply the adjoint of delta operator, it becomes 
    1139 \begin{align*} 
    1140  \sum\limits_{i,k} \sum_{\substack{i_p,\,k_p}}  \Biggl\{   \;\; 
    1141   &\left( 
    1142 {e_{2u}}_{i+i_p+1/2}^{k}                                  \;\ \ {A_{e}}_{i+i_p+1/2}^{k} 
    1143 \ \ \ { _{i+i_p+1/2}^k \mathbb{R}_{-i_p}^{k_p} }   \quad \delta_{k+k_p}[T_{i+i_p+1/2}] 
    1144    \right) \; \delta_{i+1/2}[T^{k}]      \\ 
    1145 - &\left( 
    1146 {e_{2u}}_i^{k+k_p+1/2}                                     \ \ {A_{e}}_i^{k+k_p+1/2} 
    1147 \ \ { _i^{k+k_p+1/2} \mathbb{R}_{i_p}^{-k_p} }   \ \ \delta_{i+i_p}[T^{k+k_p+1/2}] 
    1148      \right) \; \delta_{k+1/2}[T_{i}]       \         \Biggr\} 
    1149 \end{align*} 
    1150 Expending the summation on $i_p$ and $k_p$, it becomes: 
    1151 \begin{align*} 
    1152  \begin{matrix} 
    1153 &\sum\limits_{i,k}   \Bigl\{ 
    1154   &+{e_{2u}}_{i+1}^{k}                             &{A_{e}}_{i+1    }^{k} 
    1155   &\ {_{i+1}^k \mathbb{R}_{- 1/2}^{-1/2}} &\delta_{k-1/2}[T_{i+1}]    &\delta_{i+1/2}[T^{k}]   &\\ 
    1156 &&+{e_{2u}}_i^{k\ \ \ \:}                            &{A_{e}}_{i}^{k\ \ \ \:} 
    1157   &\ {\ \ \;_i^k \mathbb{R}_{+1/2}^{-1/2}}  &\delta_{k-1/2}[T_{i\ \ \ \;}]  &\delta_{i+1/2}[T^{k}] &\\ 
    1158 &&+{e_{2u}}_{i+1}^{k}                             &{A_{e}}_{i+1    }^{k} 
    1159   &\ {_{i+1}^k \mathbb{R}_{- 1/2}^{+1/2}} &\delta_{k+1/2}[T_{i+1}]     &\delta_{i+1/2}[T^{k}] &\\ 
    1160 &&+{e_{2u}}_i^{k\ \ \ \:}                            &{A_{e}}_{i}^{k\ \ \ \:} 
    1161     &\ {\ \ \;_i^k \mathbb{R}_{+1/2}^{+1/2}} &\delta_{k+1/2}[T_{i\ \ \ \;}] &\delta_{i+1/2}[T^{k}] &\\ 
    1162 % 
    1163 &&-{e_{2u}}_i^{k+1}                                &{A_{e}}_i^{k+1} 
    1164   &{_i^{k+1} \mathbb{R}_{-1/2}^{- 1/2}}   &\delta_{i-1/2}[T^{k+1}]      &\delta_{k+1/2}[T_{i}] &\\ 
    1165 &&-{e_{2u}}_i^{k\ \ \ \:}                             &{A_{e}}_i^{k\ \ \ \:} 
    1166   &{\ \ \;_i^k  \mathbb{R}_{-1/2}^{+1/2}}   &\delta_{i-1/2}[T^{k\ \ \ \:}]  &\delta_{k+1/2}[T_{i}] &\\ 
    1167 &&-{e_{2u}}_i^{k+1    }                             &{A_{e}}_i^{k+1} 
    1168   &{_i^{k+1} \mathbb{R}_{+1/2}^{- 1/2}}   &\delta_{i+1/2}[T^{k+1}]      &\delta_{k+1/2}[T_{i}] &\\ 
    1169 &&-{e_{2u}}_i^{k\ \ \ \:}                             &{A_{e}}_i^{k\ \ \ \:} 
    1170   &{\ \ \;_i^k  \mathbb{R}_{+1/2}^{+1/2}}   &\delta_{i+1/2}[T^{k\ \ \ \:}]  &\delta_{k+1/2}[T_{i}] 
    1171 &\Bigr\}  \\ 
    1172 \end{matrix} 
    1173 \end{align*} 
    1174 The two terms associated with the triad ${_i^k \mathbb{R}_{+1/2}^{+1/2}}$ are the 
    1175 same but of opposite signs, they cancel out. 
    1176 Exactly the same thing occurs for the triad ${_i^k \mathbb{R}_{-1/2}^{-1/2}}$. 
    1177 The two terms associated with the triad ${_i^k \mathbb{R}_{+1/2}^{-1/2}}$ are the 
    1178 same but both of opposite signs and shifted by 1 in $k$ direction. When summing over $k$ 
    1179 they cancel out with the neighbouring grid points. 
    1180 Exactly the same thing occurs for the triad ${_i^k \mathbb{R}_{-1/2}^{+1/2}}$ in the 
    1181 $i$ direction. Therefore the sum over the domain is zero, $i.e.$ the variance of the 
    1182 tracer is preserved by the discretisation of the skew fluxes. 
    1183  
    1184 %%% Local Variables: 
    1185 %%% TeX-master: "../../NEMO_book-luatex.tex" 
    1186 %%% End: 
     1180  {\psi_1}_{i+1/2}^{k+1/2}={\quarter}\sum_{\substack{i_p,\,k_p}} 
     1181  {A_e}_{i+1/2-i_p}^{k+1/2-k_p}\:\triadd{i+1/2-i_p}{k+1/2-k_p}{R}{i_p}{k_p}. 
     1182\end{equation} 
     1183The streamfunction $\psi_1$ is calculated similarly at $vw$ points. 
     1184The eddy-induced velocities are then calculated from the 
     1185straightforward discretisation of \eqref{eq:triad:eiv_v}: 
     1186\begin{equation}\label{eq:triad:eiv_v_discrete} 
     1187\begin{split} 
     1188 {u^*}_{i+1/2}^{k} & = - \frac{1}{{e_{3u}}_{i}^{k}}\left({\psi_1}_{i+1/2}^{k+1/2}-{\psi_1}_{i+1/2}^{k+1/2}\right),   \\ 
     1189 {v^*}_{j+1/2}^{k} & = - \frac{1}{{e_{3v}}_{j}^{k}}\left({\psi_2}_{j+1/2}^{k+1/2}-{\psi_2}_{j+1/2}^{k+1/2}\right),   \\ 
     1190 {w^*}_{i,j}^{k+1/2} & =    \frac{1}{e_{1t}e_{2t}}\; \left\{ 
     1191 {e_{2u}}_{i+1/2}^{k+1/2} \,{\psi_1}_{i+1/2}^{k+1/2} - 
     1192 {e_{2u}}_{i-1/2}^{k+1/2} \,{\psi_1}_{i-1/2}^{k+1/2} \right. + \\ 
     1193\phantom{=} & \qquad\qquad\left. {e_{2v}}_{j+1/2}^{k+1/2} \,{\psi_2}_{j+1/2}^{k+1/2} - {e_{2v}}_{j-1/2}^{k+1/2} \,{\psi_2}_{j-1/2}^{k+1/2} \right\}, 
     1194\end{split} 
     1195\end{equation} 

  • vendor/nemo/current/DOC/TexFiles/Chapters/Chap_CFG.tex

    r1 r4  
    269269 
    270270% ------------------------------------------------------------------------------------------------------------- 
    271 %       POMME configuration 
    272 % ------------------------------------------------------------------------------------------------------------- 
    273 \section{POMME: mid-latitude sub-domain} 
    274 \label{MISC_config_POMME} 
    275  
    276  
    277 \key{pomme\_r025} : to be described.... 
    278  
    279  
    280  
     271%       AMM configuration 
     272% ------------------------------------------------------------------------------------------------------------- 
     273\section{AMM: atlantic margin configuration (\key{amm\_12km})} 
     274\label{MISC_config_AMM} 
     275 
     276The AMM, Atlantic Margins Model, is a regional model covering the 
     277Northwest European Shelf domain on a regular lat-lon grid at 
     278approximately 12km horizontal resolution. The key \key{amm\_12km} 
     279is used to create the correct dimensions of the AMM domain. 
     280 
     281This configuration tests several features of NEMO functionality specific 
     282to the shelf seas. 
     283In particular, the AMM uses $S$-coordinates in the vertical rather than 
     284$z$-coordinates and is forced with tidal lateral boundary conditions 
     285using a flather boundary condition from the BDY module (key\_bdy). 
     286The AMM configuration  uses the GLS (key\_zdfgls) turbulence scheme, the 
     287VVL non-linear free surface(key\_vvl) and time-splitting 
     288(key\_dynspg\_ts). 
     289 
     290In addition to the tidal boundary condition the model may also take 
     291open boundary conditions from a North Atlantic model. Boundaries may be 
     292completely ommited by removing the BDY key (key\_bdy). 
     293Sample surface fluxes, river forcing and a sample initial restart file 
     294are included to test a realistic model run. The Baltic boundary is 
     295included within the river input file and is specified as a river source. 
     296Unlike ordinary river points the Baltic inputs also include salinity and 
     297temperature data. 
     298 

  • vendor/nemo/current/DOC/TexFiles/Chapters/Chap_DIA.tex

    r1 r4  
    943943The output format is : 
    944944  
    945 \small{\texttt{date, time-step number, section number, section name, section slope coefficient, class number,  
     945{\small\texttt{date, time-step number, section number, section name, section slope coefficient, class number,  
    946946class name, class bound 1 , classe bound2, transport\_direction1 ,  transport\_direction2, transport\_total}}\\ 
    947947 

  • vendor/nemo/current/DOC/TexFiles/Chapters/Chap_DOM.tex

    r1 r4  
    123123the following discrete forms in the curvilinear $s$-coordinate system: 
    124124\begin{equation} \label{Eq_DOM_grad} 
    125 \nabla q\equiv  \frac{1}{e_{1u} } \delta _{i+1/2 } [q] \;\,{\rm {\bf i}} 
    126                 +       \frac{1}{e_{2v} } \delta _{j+1/2 } [q] \;\,{\rm {\bf j}} 
    127                 +       \frac{1}{e_{3w}} \delta _{k+1/2} [q] \;\,{\rm {\bf k}} 
     125\nabla q\equiv  \frac{1}{e_{1u} } \delta _{i+1/2 } [q] \;\,\mathbf{i} 
     126                +       \frac{1}{e_{2v} } \delta _{j+1/2 } [q] \;\,\mathbf{j} 
     127                +       \frac{1}{e_{3w}} \delta _{k+1/2} [q] \;\,\mathbf{k} 
    128128\end{equation} 
    129129\begin{multline} \label{Eq_DOM_lap} 
    130 \Delta q\equiv \frac{1}{e_{1t}\,e_{2t}\,e_{3t} }  
     130\Delta q\equiv \frac{1}{e_{1t}\,e_{2t}\,e_{3t} } 
    131131       \;\left(          \delta_i  \left[ \frac{e_{2u}\,e_{3u}} {e_{1u}} \;\delta_{i+1/2} [q] \right] 
    132132+                        \delta_j  \left[ \frac{e_{1v}\,e_{3v}}  {e_{2v}} \;\delta_{j+1/2} [q] \right] \;  \right)              \\ 
    … …  
    139139\begin{eqnarray}  \label{Eq_DOM_curl} 
    140140 \nabla \times {\rm {\bf A}}\equiv & 
    141       \frac{1}{e_{2v}\,e_{3vw} } \ \left( \delta_{j +1/2} \left[e_{3w}\,a_3 \right] -\delta_{k+1/2} \left[e_{2v} \,a_2 \right] \right)  &\ \rm{\bf i} \\  
    142  +& \frac{1}{e_{2u}\,e_{3uw}} \ \left( \delta_{k+1/2} \left[e_{1u}\,a_1  \right] -\delta_{i +1/2} \left[e_{3w}\,a_3 \right] \right)  &\ \rm{\bf j} \\  
    143  +& \frac{1}{e_{1f} \,e_{2f}    } \ \left( \delta_{i +1/2} \left[e_{2v}\,a_2  \right] -\delta_{j +1/2} \left[e_{1u}\,a_1 \right] \right)  &\ \rm{\bf k} 
     141      \frac{1}{e_{2v}\,e_{3vw} } \ \left( \delta_{j +1/2} \left[e_{3w}\,a_3 \right] -\delta_{k+1/2} \left[e_{2v} \,a_2 \right] \right)  &\ \mathbf{i} \\  
     142 +& \frac{1}{e_{2u}\,e_{3uw}} \ \left( \delta_{k+1/2} \left[e_{1u}\,a_1  \right] -\delta_{i +1/2} \left[e_{3w}\,a_3 \right] \right)  &\ \mathbf{j} \\ 
     143 +& \frac{1}{e_{1f} \,e_{2f}    } \ \left( \delta_{i +1/2} \left[e_{2v}\,a_2  \right] -\delta_{j +1/2} \left[e_{1u}\,a_1 \right] \right)  &\ \mathbf{k} 
    144144 \end{eqnarray} 
    145145\begin{equation} \label{Eq_DOM_div} 

  • vendor/nemo/current/DOC/TexFiles/Chapters/Chap_LBC.tex

    r1 r4  
    742742 
    743743%-----------------------------------------nambdy-------------------------------------------- 
    744 %-    cn_mask    =  ''                        !  name of mask file (if ln_bdy_mask=.TRUE.) 
    745 %-    cn_dta_frs_T  = 'bdydata_grid_T.nc'     !  name of data file (T-points) 
    746 %-    cn_dta_frs_U  = 'bdydata_grid_U.nc'     !  name of data file (U-points) 
    747 %-    cn_dta_frs_V  = 'bdydata_grid_V.nc'     !  name of data file (V-points) 
    748 %-    cn_dta_fla_T  = 'bdydata_bt_grid_T.nc'  !  name of data file for Flather condition (T-points) 
    749 %-    cn_dta_fla_U  = 'bdydata_bt_grid_U.nc'  !  name of data file for Flather condition (U-points) 
    750 %-    cn_dta_fla_V  = 'bdydata_bt_grid_V.nc'  !  name of data file for Flather condition (V-points) 
    751 %-    ln_clim    = .false.                    !  contain 1 (T) or 12 (F) time dumps and be cyclic 
    752 %-    ln_vol     = .true.                     !  total volume correction (see volbdy parameter) 
    753 %-    ln_mask    = .false.                    !  boundary mask from filbdy_mask (T) or boundaries are on edges of domain (F) 
    754 %-    ln_tides   = .true.                     !  Apply tidal harmonic forcing with Flather condition 
    755 %-    ln_dyn_fla = .true.                     !  Apply Flather condition to velocities 
    756 %-    ln_tra_frs = .false.                    !  Apply FRS condition to temperature and salinity 
    757 %-    ln_dyn_frs = .false.                    !  Apply FRS condition to velocities 
    758 %-    nn_rimwidth    =  9                     !  width of the relaxation zone 
    759 %-    nn_dtactl      =  1                     !  = 0, bdy data are equal to the initial state 
    760 %-                                            !  = 1, bdy data are read in 'bdydata   .nc' files 
    761 %-    nn_volctl      =  0                     !  = 0, the total water flux across open boundaries is zero 
    762 %-                                            !  = 1, the total volume of the system is conserved 
    763744\namdisplay{nambdy}  
     745%----------------------------------------------------------------------------------------------- 
     746%-----------------------------------------nambdy_index-------------------------------------------- 
     747\namdisplay{nambdy_index}  
     748%----------------------------------------------------------------------------------------------- 
     749%-----------------------------------------nambdy_dta-------------------------------------------- 
     750\namdisplay{nambdy_dta}  
     751%----------------------------------------------------------------------------------------------- 
     752%-----------------------------------------nambdy_dta-------------------------------------------- 
     753\namdisplay{nambdy_dta2}  
    764754%----------------------------------------------------------------------------------------------- 
    765755 
    … …  
    774764The BDY module was modelled on the OBC module and shares many features 
    775765and a similar coding structure \citep{Chanut2005}. 
     766 
     767The BDY module is completely rewritten at NEMO 3.4 and there is a new 
     768set of namelists. Boundary data files used with earlier versions of 
     769NEMO may need to be re-ordered to work with this version. See the 
     770section on the Input Boundary Data Files for details. 
     771 
     772%---------------------------------------------- 
     773\subsection{The namelists} 
     774\label{BDY_namelist} 
     775 
     776It is possible to define more than one boundary ``set'' and apply 
     777different boundary conditions to each set. The number of boundary 
     778sets is defined by \np{nb\_bdy}.  Each boundary set may be defined 
     779as a set of straight line segments in a namelist 
     780(\np{ln\_coords\_file}=.false.) or read in from a file 
     781(\np{ln\_coords\_file}=.true.). If the set is defined in a namelist, 
     782then the namelists nambdy\_index must be included separately, one for 
     783each set. If the set is defined by a file, then a 
     784``coordinates.bdy.nc'' file must be provided. The coordinates.bdy file 
     785is analagous to the usual NEMO ``coordinates.nc'' file. In the example 
     786above, there are two boundary sets, the first of which is defined via 
     787a file and the second is defined in a namelist. For more details of 
     788the definition of the boundary geometry see section 
     789\ref{BDY_geometry}. 
     790 
     791For each boundary set a boundary 
     792condition has to be chosen for the barotropic solution (``u2d'': 
     793sea-surface height and barotropic velocities), for the baroclinic 
     794velocities (``u3d''), and for the active tracers\footnote{The BDY 
     795  module does not deal with passive tracers at this version} 
     796(``tra''). For each set of variables there is a choice of algorithm 
     797and a choice for the data, eg. for the active tracers the algorithm is 
     798set by \np{nn\_tra} and the choice of data is set by 
     799\np{nn\_tra\_dta}.  
     800 
     801The choice of algorithm is currently as follows: 
     802 
     803\mbox{} 
     804 
     805\begin{itemize} 
     806\item[0.] No boundary condition applied. So the solution will ``see'' 
     807  the land points around the edge of the edge of the domain. 
     808\item[1.] Flow Relaxation Scheme (FRS) available for all variables.  
     809\item[2.] Flather radiation scheme for the barotropic variables. The 
     810  Flather scheme is not compatible with the filtered free surface 
     811  ({\it dynspg\_ts}).  
     812\end{itemize} 
     813 
     814\mbox{} 
     815 
     816The main choice for the boundary data is 
     817to use initial conditions as boundary data (\np{nn\_tra\_dta}=0) or to 
     818use external data from a file (\np{nn\_tra\_dta}=1). For the 
     819barotropic solution there is also the option to use tidal 
     820harmonic forcing either by itself or in addition to other external 
     821data.  
     822 
     823If external boundary data is required then the nambdy\_dta namelist 
     824must be defined. One nambdy\_dta namelist is required for each boundary 
     825set in the order in which the boundary sets are defined in nambdy. In 
     826the example given, two boundary sets have been defined and so there 
     827are two nambdy\_dta namelists. The boundary data is read in using the 
     828fldread module, so the nambdy\_dta namelist is in the format required 
     829for fldread. For each variable required, the filename, the frequency 
     830of the files and the frequency of the data in the files is given. Also 
     831whether or not time-interpolation is required and whether the data is 
     832climatological (time-cyclic) data. Note that on-the-fly spatial 
     833interpolation of boundary data is not available at this version.  
     834 
     835In the example namelists given, two boundary sets are defined. The 
     836first set is defined via a file and applies FRS conditions to 
     837temperature and salinity and Flather conditions to the barotropic 
     838variables. External data is provided in daily files (from a 
     839large-scale model). Tidal harmonic forcing is also used. The second 
     840set is defined in a namelist. FRS conditions are applied on 
     841temperature and salinity and climatological data is read from external 
     842files.  
    776843 
    777844%---------------------------------------------- 
    … …  
    832899Note that the sea-surface height gradient in \eqref{Eq_bdy_fla1} 
    833900is a spatial gradient across the model boundary, so that $\eta_{e}$ is 
    834 defined on the $T$ points with $nbrdta=1$ and $\eta$ is defined on the 
    835 $T$ points with $nbrdta=2$. $U$ and $U_{e}$ are defined on the $U$ or 
    836 $V$ points with $nbrdta=1$, $i.e.$ between the two $T$ grid points. 
    837  
    838 %---------------------------------------------- 
    839 \subsection{Choice of schemes} 
    840 \label{BDY_choice_of_schemes} 
    841  
    842 The Flow Relaxation Scheme may be applied separately to the 
    843 temperature and salinity (\np{ln\_tra\_frs} = true) and 
    844 the velocity fields (\np{ln\_dyn\_frs} = true). Flather 
    845 radiation conditions may be applied using externally defined 
    846 barotropic velocities and sea-surface height (\np{ln\_dyn\_fla} = true)  
    847 or using tidal harmonics fields (\np{ln\_tides} = true)  
    848 or both. FRS and Flather conditions may be applied simultaneously.  
    849 A typical configuration where all possible conditions might be used is a tidal,  
    850 shelf-seas model, where the barotropic boundary conditions are fixed  
    851 with the Flather scheme using tidal harmonics and possibly output  
    852 from a large-scale model, and FRS conditions are applied to the tracers  
    853 and baroclinic velocity fields, using fields from a large-scale model. 
    854  
    855 Note that FRS conditions will work with the filtered 
    856 (\key{dynspg\_flt}) or time-split (\key{dynspg\_ts}) solutions for the 
    857 surface pressure gradient. The Flather condition will only work for 
    858 the time-split solution (\key{dynspg\_ts}). FRS conditions are applied 
    859 at the end of the main model time step. Flather conditions are applied 
    860 during the barotropic subcycle in the time-split solution.  
     901defined on the $T$ points with $nbr=1$ and $\eta$ is defined on the 
     902$T$ points with $nbr=2$. $U$ and $U_{e}$ are defined on the $U$ or 
     903$V$ points with $nbr=1$, $i.e.$ between the two $T$ grid points. 
    861904 
    862905%---------------------------------------------- 
    … …  
    864907\label{BDY_geometry} 
    865908 
    866 The definition of the open boundary is completely flexible. An example 
    867 is shown in Fig.~\ref{Fig_LBC_bdy_geom}. The boundary zone is 
    868 defined by a series of index arrays read in from the input boundary 
    869 data files: $nbidta$, $nbjdta$, and $nbrdta$. The first two of these 
    870 define the global $(i,j)$ indices of each point in the boundary zone 
    871 and the $nbrdta$ array defines the discrete distance from the boundary 
    872 with $nbrdta=1$ meaning that the point is next to the edge of the 
    873 model domain and $nbrdta>1$ showing that the point is increasingly 
    874 further away from the edge of the model domain. These arrays are 
    875 defined separately for each of the $T$, $U$ and $V$ grids, but the 
    876 relationship between the points is assumed to be as in Fig. 
    877 \ref{Fig_LBC_bdy_geom} with the $T$ points forming the outermost row 
    878 of the boundary and the first row of velocities normal to the boundary 
    879 being inside the first row of $T$ points. The order in which the 
    880 points are defined is unimportant.  
     909Each open boundary set is defined as a list of points. The information 
     910is stored in the arrays $nbi$, $nbj$, and $nbr$ in the $idx\_bdy$ 
     911structure.  The $nbi$ and $nbj$ arrays 
     912define the local $(i,j)$ indices of each point in the boundary zone 
     913and the $nbr$ array defines the discrete distance from the boundary 
     914with $nbr=1$ meaning that the point is next to the edge of the 
     915model domain and $nbr>1$ showing that the point is increasingly 
     916further away from the edge of the model domain. A set of $nbi$, $nbj$, 
     917and $nbr$ arrays is defined for each of the $T$, $U$ and $V$ 
     918grids. Figure \ref{Fig_LBC_bdy_geom} shows an example of an irregular 
     919boundary.  
     920 
     921The boundary geometry for each set may be defined in a namelist 
     922nambdy\_index or by reading in a ``coordinates.bdy.nc'' file. The 
     923nambdy\_index namelist defines a series of straight-line segments for 
     924north, east, south and west boundaries. For the northern boundary, 
     925\np{nbdysegn} gives the number of segments, \np{jpjnob} gives the $j$ 
     926index for each segment and \np{jpindt} and \np{jpinft} give the start 
     927and end $i$ indices for each segment with similar for the other 
     928boundaries. These segments define a list of $T$ grid points along the 
     929outermost row of the boundary ($nbr\,=\, 1$). The code deduces the $U$ and 
     930$V$ points and also the points for $nbr\,>\, 1$ if 
     931$nn\_rimwidth\,>\,1$. 
     932 
     933The boundary geometry may also be defined from a 
     934``coordinates.bdy.nc'' file. Figure \ref{Fig_LBC_nc_header} 
     935gives an example of the header information from such a file. The file 
     936should contain the index arrays for each of the $T$, $U$ and $V$ 
     937grids. The arrays must be in order of increasing $nbr$. Note that the 
     938$nbi$, $nbj$ values in the file are global values and are converted to 
     939local values in the code. Typically this file will be used to generate 
     940external boundary data via interpolation and so will also contain the 
     941latitudes and longitudes of each point as shown. However, this is not 
     942necessary to run the model.  
     943 
     944For some choices of irregular boundary the model domain may contain 
     945areas of ocean which are not part of the computational domain. For 
     946example if an open boundary is defined along an isobath, say at the 
     947shelf break, then the areas of ocean outside of this boundary will 
     948need to be masked out. This can be done by reading a mask file defined 
     949as \np{cn\_mask\_file} in the nam\_bdy namelist. Only one mask file is 
     950used even if multiple boundary sets are defined. 
    881951 
    882952%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    … …  
    892962\label{BDY_data} 
    893963 
    894 The input data files for the FRS conditions are defined in the 
    895 namelist as \np{cn\_dta\_frs\_T}, \np{cn\_dta\_frs\_U},  
    896 \np{cn\_dta\_frs\_V}. The input data files for the Flather conditions 
    897 are defined in the namelist as \np{cn\_dta\_fla\_T},  
    898 \np{cn\_dta\_fla\_U}, \np{cn\_dta\_fla\_V}.  
    899  
    900 The netcdf header of a typical input data file is shown in Fig.~\ref{Fig_LBC_nc_header}.  
    901 The file contains the index arrays which define the boundary geometry  
    902 as noted above and the data arrays for each field.   
    903 The data arrays are dimensioned on: a time dimension; $xb$  
    904 which is the index of the boundary data point in the horizontal;  
    905 and $yb$ which is a degenerate dimension of 1 to enable 
    906 the file to be read by the standard NEMO I/O routines. The 3D fields 
    907 also have a depth dimension. 
    908  
    909 If \np{ln\_clim} is set to \textit{false}, the model expects the 
    910 units of the time axis to have the form shown in 
    911 Fig.~\ref{Fig_LBC_nc_header}, $i.e.$ {\it ``seconds since yyyy-mm-dd 
    912 hh:mm:ss''} The fields are then linearly interpolated to the model 
    913 time at each timestep. Note that for this option, the time axis of the 
    914 input files must completely span the time period of the model 
    915 integration. If \np{ln\_clim} is set to \textit{true} (climatological 
    916 boundary forcing), the model will expect either a single set of annual 
    917 mean fields (constant boundary forcing) or 12 sets of monthly mean 
    918 fields in the input files. 
    919  
    920 As in the OBC module there is an option to use initial conditions as 
    921 boundary conditions. This is chosen by setting 
    922 \np{nn\_dtactl}~=~0. However, since the model defines the boundary 
    923 geometry by reading the boundary index arrays from the input files, 
    924 it is still necessary to provide a set of input files in this 
    925 case. They need only contain the boundary index arrays, $nbidta$, 
    926 \textit{nbjdta}, \textit{nbrdta}. 
     964The data files contain the data arrays 
     965in the order in which the points are defined in the $nbi$ and $nbj$ 
     966arrays. The data arrays are dimensioned on: a time dimension; 
     967$xb$ which is the index of the boundary data point in the horizontal; 
     968and $yb$ which is a degenerate dimension of 1 to enable the file to be 
     969read by the standard NEMO I/O routines. The 3D fields also have a 
     970depth dimension.  
     971 
     972At Version 3.4 there are new restrictions on the order in which the 
     973boundary points are defined (and therefore restrictions on the order 
     974of the data in the file). In particular: 
     975 
     976\mbox{} 
     977 
     978\begin{enumerate} 
     979\item The data points must be in order of increasing $nbr$, ie. all 
     980  the $nbr=1$ points, then all the $nbr=2$ points etc. 
     981\item All the data for a particular boundary set must be in the same 
     982  order. (Prior to 3.4 it was possible to define barotropic data in a 
     983  different order to the data for tracers and baroclinic velocities).  
     984\end{enumerate} 
     985 
     986\mbox{} 
     987 
     988These restrictions mean that data files used with previous versions of 
     989the model may not work with version 3.4. A fortran utility 
     990{\it bdy\_reorder} exists in the TOOLS directory which will re-order the 
     991data in old BDY data files.  
    927992 
    928993%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    … …  
    930995\includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_LBC_nc_header.pdf} 
    931996\caption {     \label{Fig_LBC_nc_header}  
    932 Example of header of netcdf input data file for BDY} 
     997Example of the header for a coordinates.bdy.nc file} 
    933998\end{center}   \end{figure} 
    934999%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    … …  
    9401005There is an option to force the total volume in the regional model to be constant,  
    9411006similar to the option in the OBC module. This is controlled  by the \np{nn\_volctl}  
    942 parameter in the namelist. A value of\np{nn\_volctl}~=~0 indicates that this option is not used.  
     1007parameter in the namelist. A value of \np{nn\_volctl}~=~0 indicates that this option is not used.  
    9431008If  \np{nn\_volctl}~=~1 then a correction is applied to the normal velocities  
    9441009around the boundary at each timestep to ensure that the integrated volume flow  
    … …  
    9471012flux across the surface and the correction velocity corrects for this as well. 
    9481013 
    949  
     1014If more than one boundary set is used then volume correction is 
     1015applied to all boundaries at once. 
     1016 
     1017\newpage 
    9501018%---------------------------------------------- 
    9511019\subsection{Tidal harmonic forcing} 
    9521020\label{BDY_tides} 
    9531021 
     1022%-----------------------------------------nambdy_tide-------------------------------------------- 
     1023\namdisplay{nambdy_tide}  
     1024%----------------------------------------------------------------------------------------------- 
     1025 
    9541026To be written.... 
    9551027 

  • vendor/nemo/current/DOC/TexFiles/Chapters/Chap_LDF.tex

    r1 r4  
    2121and for tracers only, eddy induced advection on tracers). These three aspects  
    2222of the lateral diffusion are set through namelist parameters and CPP keys  
    23 (see the \textit{nam\_traldf} and \textit{nam\_dynldf} below). 
     23(see the \textit{nam\_traldf} and \textit{nam\_dynldf} below). Note 
     24that this chapter describes the default implementation of iso-neutral 
     25tracer mixing, and Griffies's implementation, which is used if 
     26\np{traldf\_grif}=true, is described in Appdx\ref{sec:triad} 
    2427 
    2528%-----------------------------------nam_traldf - nam_dynldf-------------------------------------------- 
    … …  
    128131$\ $\newline    % force a new ligne 
    129132 
    130 A space variation in the eddy coefficient appeals several remarks: 
     133The following points are relevant when the eddy coefficient varies spatially: 
    131134 
    132135(1) the momentum diffusion operator acting along model level surfaces is  
    133136written in terms of curl and divergent components of the horizontal current  
    134 (see \S\ref{PE_ldf}). Although the eddy coefficient can be set to different values  
    135 in these two terms, this option is not available.  
     137(see \S\ref{PE_ldf}). Although the eddy coefficient could be set to different values  
     138in these two terms, this option is not currently available.  
    136139 
    137140(2) with an horizontally varying viscosity, the quadratic integral constraints  
    … …  
    275278 
    276279\item[$s$- or hybrid $s$-$z$- coordinate : ] in the current release of \NEMO,  
    277 there is no specific treatment for iso-neutral mixing in the $s$-coordinate.  
     280iso-neutral mixing is only employed for $s$-coordinates if the 
     281Griffies scheme is used (\np{traldf\_grif}=true; see Appdx \ref{sec:triad}).  
    278282In other words, iso-neutral mixing will only be accurately represented with a  
    279283linear equation of state (\np{nn\_eos}=1 or 2). In the case of a "true" equation  
    … …  
    332336\end{description} 
    333337 
    334 This implementation is a rather old one. It is similar to the one proposed  
    335 by Cox [1987], except for the background horizontal diffusion. Indeed,  
    336 the Cox implementation of isopycnal diffusion in GFDL-type models requires  
    337 a minimum background horizontal diffusion for numerical stability reasons.  
    338 To overcome this problem, several techniques have been proposed in which  
    339 the numerical schemes of the ocean model are modified \citep{Weaver_Eby_JPO97,  
    340 Griffies_al_JPO98}. Here, another strategy has been chosen \citep{Lazar_PhD97}:  
    341 a local filtering of the iso-neutral slopes (made on 9 grid-points) prevents  
    342 the development of grid point noise generated by the iso-neutral diffusion  
    343 operator (Fig.~\ref{Fig_LDF_ZDF1}). This allows an iso-neutral diffusion scheme  
    344 without additional background horizontal mixing. This technique can be viewed  
    345 as a diffusion operator that acts along large-scale (2~$\Delta$x)  
    346 \gmcomment{2deltax doesnt seem very large scale}  
    347 iso-neutral surfaces. The diapycnal diffusion required for numerical stability is  
    348 thus minimized and its net effect on the flow is quite small when compared to  
    349 the effect of an horizontal background mixing.  
     338This implementation is a rather old one. It is similar to the one 
     339proposed by Cox [1987], except for the background horizontal 
     340diffusion. Indeed, the Cox implementation of isopycnal diffusion in 
     341GFDL-type models requires a minimum background horizontal diffusion 
     342for numerical stability reasons.  To overcome this problem, several 
     343techniques have been proposed in which the numerical schemes of the 
     344ocean model are modified \citep{Weaver_Eby_JPO97, 
     345  Griffies_al_JPO98}. Griffies's scheme is now available in \NEMO if 
     346\np{traldf\_grif\_iso} is set true; see Appdx \ref{sec:triad}. Here, 
     347another strategy is presented \citep{Lazar_PhD97}: a local 
     348filtering of the iso-neutral slopes (made on 9 grid-points) prevents 
     349the development of grid point noise generated by the iso-neutral 
     350diffusion operator (Fig.~\ref{Fig_LDF_ZDF1}). This allows an 
     351iso-neutral diffusion scheme without additional background horizontal 
     352mixing. This technique can be viewed as a diffusion operator that acts 
     353along large-scale (2~$\Delta$x) \gmcomment{2deltax doesnt seem very 
     354  large scale} iso-neutral surfaces. The diapycnal diffusion required 
     355for numerical stability is thus minimized and its net effect on the 
     356flow is quite small when compared to the effect of an horizontal 
     357background mixing. 
    350358 
    351359Nevertheless, this iso-neutral operator does not ensure that variance cannot increase,  

  • vendor/nemo/current/DOC/TexFiles/Chapters/Chap_TRA.tex

    r1 r4  
    491491\label{TRA_ldf_iso} 
    492492 
    493 The general form of the second order lateral tracer subgrid scale physics  
     493If the Griffies trad scheme is not employed 
     494(\np{ln\_traldf\_grif}=true; see App.\ref{sec:triad}) the general form of the second order lateral tracer subgrid scale physics  
    494495(\ref{Eq_PE_zdf}) takes the following semi-discrete space form in $z$- and  
    495496$s$-coordinates: 
    … …  
    536537(see \S\ref{LDF}) allows the model to run safely without any additional  
    537538background horizontal diffusion \citep{Guilyardi_al_CD01}. An alternative scheme  
    538 developed by \cite{Griffies_al_JPO98} which preserves both tracer and its variance  
     539developed by \cite{Griffies_al_JPO98} which ensures tracer variance decreases  
    539540is also available in \NEMO (\np{ln\_traldf\_grif}=true). A complete description of  
    540 the algorithm is given in App.\ref{Apdx_Griffies}. 
     541the algorithm is given in App.\ref{sec:triad}. 
    541542 
    542543Note that in the partial step $z$-coordinate (\np{ln\_zps}=true), the horizontal  

  • vendor/nemo/current/DOC/TexFiles/Chapters/Introduction.tex

    r1 r4  
    202202concern of improving the model performance.  
    203203 
     204 \vspace{1cm} 
     205$\bullet$ The main modifications from NEMO/OPA v3.3 and  v3.4 are :\\ 
     206\begin{enumerate} 
     207\item finalisation of above iso-neutral mixing \citep{Griffies_al_JPO98}";  
     208\item "Neptune effect" parametrisation; 
     209\item horizontal pressure gradient suitable for s-coordinate;  
     210\item semi-implicit bottom friction; 
     211\item finalisation of the merge of passive and active tracers advection-diffusion modules;  
     212\item a new bulk formulae (so-called MFS); 
     213\item use fldread for the off-line tracer component (OFF\_SRC) ;  
     214\item use MPI point to point communications  for north fold; 
     215\item diagnostic of transport ;  
     216\end{enumerate} 
     217 
     218 

  • vendor/nemo/current/DOC/TexFiles/Namelist/nambdy

    r1 r4  
    22&nambdy        !  unstructured open boundaries                          ("key_bdy") 
    33!----------------------------------------------------------------------- 
    4    cn_mask     =  ''                     !  name of mask file (ln_mask=T) 
    5    cn_dta_frs_T= 'bdydata_grid_T.nc'     !  name of data file (T-points) 
    6    cn_dta_frs_U= 'bdydata_grid_U.nc'     !  name of data file (U-points) 
    7    cn_dta_frs_V= 'bdydata_grid_V.nc'     !  name of data file (V-points) 
    8    cn_dta_fla_T= 'bdydata_bt_grid_T.nc'  !  name of data file for Flather condition (T-points) 
    9    cn_dta_fla_U= 'bdydata_bt_grid_U.nc'  !  name of data file for Flather condition (U-points) 
    10    cn_dta_fla_V= 'bdydata_bt_grid_V.nc'  !  name of data file for Flather condition (V-points) 
    11  
    12    ln_clim     = .false.   !  contain 1 (T) or 12 (F) time dumps and be cyclic 
    13    ln_vol      = .false.   !  total volume correction (see volbdy parameter) 
    14    ln_mask     = .false.   !  boundary mask from filbdy_mask (T), boundaries are on edges of domain (F) 
    15    ln_tides    = .false.   !  Apply tidal harmonic forcing with Flather condition 
    16    ln_dyn_fla  = .false.   !  Apply Flather condition to velocities 
    17    ln_tra_frs  = .false.   !  Apply FRS condition to temperature and salinity  
    18    ln_dyn_frs  = .false.   !  Apply FRS condition to velocities 
    19    nn_rimwidth =  9        !  width of the relaxation zone 
    20    nn_dtactl   =  1        !  = 0, bdy data are equal to the initial state 
    21                            !  = 1, bdy data are read in 'bdydata   .nc' files 
    22    nn_volctl   =  0        !  = 0, the total water flux across open boundaries is zero 
    23                            !  = 1, the total volume of the system is conserved 
     4    nb_bdy = 2                               !  number of open boundary sets        
     5    ln_coords_file = .true.,.false.          !  =T : read bdy coordinates from file 
     6    cn_coords_file = 'coordinates.bdy.nc','' !  bdy coordinates files 
     7    ln_mask_file = .false.                   !  =T : read mask from file 
     8    cn_mask_file = ''                        !  name of mask file (if ln_mask_file=.TRUE.) 
     9    nn_dyn2d      =  2, 0                    !  boundary conditions for barotropic fields 
     10    nn_dyn2d_dta  =  3, 0                    !  = 0, bdy data are equal to the initial state 
     11                                             !  = 1, bdy data are read in 'bdydata   .nc' files 
     12                                             !  = 2, use tidal harmonic forcing data from files 
     13                                             !  = 3, use external data AND tidal harmonic forcing 
     14    nn_dyn3d      =  0, 0                    !  boundary conditions for baroclinic velocities 
     15    nn_dyn3d_dta  =  0, 0                    !  = 0, bdy data are equal to the initial state 
     16                                             !  = 1, bdy data are read in 'bdydata   .nc' files 
     17    nn_tra        =  1, 1                    !  boundary conditions for T and S 
     18    nn_tra_dta    =  1, 1                    !  = 0, bdy data are equal to the initial state 
     19                                             !  = 1, bdy data are read in 'bdydata   .nc' files 
     20    nn_rimwidth  = 10, 5                     !  width of the relaxation zone 
     21    ln_vol     = .false.                     !  total volume correction (see nn_volctl parameter) 
     22    nn_volctl  = 1                           !  = 0, the total water flux across open boundaries is zero 
    2423/ 

  • vendor/nemo/current/DOC/TexFiles/Namelist/nambdy_tide

    r1 r4  
    11!----------------------------------------------------------------------- 
    2 &nambdy_tide   !  tidal forcing at unstructured boundaries               
     2&nambdy_tide     ! tidal forcing at open boundaries               
    33!----------------------------------------------------------------------- 
    4    filtide     = 'bdytide_'           !  file name root of tidal forcing files 
    5    tide_cpt    = 'M2','S1'            !  names of tidal components used 
    6    tide_speed  = 28.984106, 15.000001 !  phase speeds of tidal components (deg/hour) 
    7    ln_tide_date= .false.              !  adjust tidal harmonics for start date of run 
     4   filtide      = 'bdydta/amm12_bdytide_'         !  file name root of tidal forcing files 
     5    tide_cpt(1)   ='Q1'  !  names of tidal components used 
     6    tide_cpt(2)   ='O1'  !  names of tidal components used 
     7    tide_cpt(3)   ='P1'  !  names of tidal components used 
     8    tide_cpt(4)   ='S1'  !  names of tidal components used 
     9    tide_cpt(5)   ='K1'  !  names of tidal components used 
     10    tide_cpt(6)   ='2N2' !  names of tidal components used 
     11    tide_cpt(7)   ='MU2' !  names of tidal components used 
     12    tide_cpt(8)   ='N2'  !  names of tidal components used 
     13    tide_cpt(9)   ='NU2' !  names of tidal components used 
     14    tide_cpt(10)   ='M2'  !  names of tidal components used 
     15    tide_cpt(11)   ='L2'  !  names of tidal components used 
     16    tide_cpt(12)   ='T2'  !  names of tidal components used 
     17    tide_cpt(13)   ='S2'  !  names of tidal components used 
     18    tide_cpt(14)   ='K2'  !  names of tidal components used 
     19    tide_cpt(15)   ='M4'  !  names of tidal components used 
     20    tide_speed(1)   = 13.398661 !  phase speeds of tidal components (deg/hour) 
     21    tide_speed(2)   = 13.943036 !  phase speeds of tidal components (deg/hour) 
     22    tide_speed(3)   = 14.958932 !  phase speeds of tidal components (deg/hour) 
     23    tide_speed(4)   = 15.000001 !  phase speeds of tidal components (deg/hour) 
     24    tide_speed(5)   = 15.041069 !  phase speeds of tidal components (deg/hour) 
     25    tide_speed(6)   = 27.895355 !  phase speeds of tidal components (deg/hour) 
     26    tide_speed(7)   = 27.968210 !  phase speeds of tidal components (deg/hour) 
     27    tide_speed(8)   = 28.439730 !  phase speeds of tidal components (deg/hour) 
     28    tide_speed(9)   = 28.512585 !  phase speeds of tidal components (deg/hour) 
     29    tide_speed(10)   = 28.984106 !  phase speeds of tidal components (deg/hour) 
     30    tide_speed(11)   = 29.528479 !  phase speeds of tidal components (deg/hour) 
     31    tide_speed(12)   = 29.958935 !  phase speeds of tidal components (deg/hour) 
     32    tide_speed(13)   = 30.000002 !  phase speeds of tidal components (deg/hour) 
     33    tide_speed(14)   = 30.082138 !  phase speeds of tidal components (deg/hour) 
     34    tide_speed(15)   = 57.968212 !  phase speeds of tidal components (deg/hour) 
     35    ln_tide_date = .true.               !  adjust tidal harmonics for start date of run 
    836/ 

  • vendor/nemo/current/DOC/TexFiles/Namelist/namtra_ldf

    r1 r4  
    1 !----------------------------------------------------------------------- 
    2 &namtra_ldf    !   lateral diffusion scheme for tracer 
    3 !----------------------------------------------------------------------- 
    4    !                       !  Type of the operator : 
     1!---------------------------------------------------------------------------------- 
     2&namtra_ldf    !   lateral diffusion scheme for tracers 
     3!---------------------------------------------------------------------------------- 
     4   !                       !  Operator type: 
    55   ln_traldf_lap    =  .true.   !  laplacian operator 
    66   ln_traldf_bilap  =  .false.  !  bilaplacian operator 
    7    !                       !  Direction of action  : 
     7   !                       !  Direction of action: 
    88   ln_traldf_level  =  .false.  !  iso-level 
    9    ln_traldf_hor    =  .false.  !  horizontal (geopotential)            (requires "key_ldfslp" when ln_sco=T) 
    10    ln_traldf_iso    =  .true.   !  iso-neutral                          (requires "key_ldfslp") 
    11    !                       !  Griffies parameters 
    12    ln_traldf_grif   =  .false.  !  use griffies triad formulation       (requires "key_ldfslp") 
    13    ln_traldf_gdia   =  .false.  !  output griffies strfn diagnostics    (requires "key_ldfslp") 
    14    ln_triad_iso     =  .false.  !  isoneutral diff'n triads => pure lateral mixing in ML (requires "key_ldfslp") 
    15    ln_botmix_grif   =  .false.  !  griffies operator with lateral mixing on bottom (requires "key_ldfslp") 
     9   ln_traldf_hor    =  .false.  !  horizontal (geopotential)   (needs "key_ldfslp" when ln_sco=T) 
     10   ln_traldf_iso    =  .true.   !  iso-neutral                 (needs "key_ldfslp") 
     11   !                       !  Griffies parameters              (all need "key_ldfslp") 
     12   ln_traldf_grif   =  .false.  !  use griffies triads 
     13   ln_traldf_gdia   =  .false.  !  output griffies eddy velocities 
     14   ln_triad_iso     =  .false.  !  pure lateral mixing in ML 
     15   ln_botmix_grif   =  .false.  !  lateral mixing on bottom 
    1616   !                       !  Coefficients 
    17    ! rn_aeiv_0 is ignored with Held-Larichev spatially varying aeiv (key_traldf_c2d & key_orca_r2, _r1 or _r05) 
    18    rn_aeiv_0        =  2000.    !  eddy induced velocity coefficient [m2/s]    (requires "key_traldf_eiv") 
     17   ! Eddy-induced (GM) advection always used with Griffies; otherwise needs "key_traldf_eiv" 
     18   ! Value rn_aeiv_0 is ignored unless = 0 with Held-Larichev spatially varying aeiv 
     19   !                                  (key_traldf_c2d & key_traldf_eiv & key_orca_r2, _r1 or _r05) 
     20   rn_aeiv_0        =  2000.    !  eddy induced velocity coefficient [m2/s] 
    1921   rn_aht_0         =  2000.    !  horizontal eddy diffusivity for tracers [m2/s] 
    20    rn_ahtb_0        =     0.    !  background eddy diffusivity for ldf_iso [m2/s] (normally=0; not used with Griffies) 
     22   rn_ahtb_0        =     0.    !  background eddy diffusivity for ldf_iso [m2/s] 
     23   !                                           (normally=0; not used with Griffies) 
    2124/ 

  • vendor/nemo/current/DOC/TexFiles/clean.sh

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