/[MITgcm]/manual/s_phys_pkgs/text/gmredi.tex

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-revision 1.4 by adcroft,
Tue Nov 13 14:54:50 2001 UTC
+revision 1.15 by jmc,
Mon Aug 30 23:09:21 2010 UTC
 Line 1
- \section{Gent/McWiliams/Redi SGS Eddy parameterization}
+ \subsection{GMREDI: Gent/McWiliams/Redi SGS Eddy Parameterization}
+ \label{sec:pkg:gmredi}
+ \begin{rawhtml}
+ <!-- CMIREDIR:gmredi: -->
+ \end{rawhtml}
  There are two parts to the Redi/GM parameterization of geostrophic
  eddies. The first aims to mix tracer properties along isentropes
-Line 31 
 and Redi scheme, substantial cancellatio
+Line 35 
 and Redi scheme, substantial cancellatio
  that the horizontal fluxes are unmodified from the lateral diffusion
  parameterization.
- \subsection{Redi scheme: Isopycnal diffusion}
+ \subsubsection{Redi scheme: Isopycnal diffusion}
  The Redi scheme diffuses tracers along isopycnals and introduces a
  term in the tendency (rhs) of such a tracer (here $\tau$) of the form:
-Line 71 
 S_x & S_y & |S|^2 \\
+Line 75 
 S_x & S_y & |S|^2 \\
  \end{equation}
- \subsection{GM parameterization}
+ \subsubsection{GM parameterization}
  The GM parameterization aims to parameterise the ``advective'' or
  ``transport'' effect of geostrophic eddies by means of a ``bolus''
-Line 100 
 F_y & = & \kappa_{GM} S_y
+Line 104 
 F_y & = & \kappa_{GM} S_y
  This is the form of the GM parameterization as applied by Donabasaglu,
 , in MOM versions 1 and 2.
- \subsection{Griffies Skew Flux}
+ \subsubsection{Griffies Skew Flux}
  Griffies notes that the discretisation of bolus velocities involves
  multiple layers of differencing and interpolation that potentially
-Line 187 
 $S_y$: {\bf SlopeY} (argument on exit)
+Line 191 
 $S_y$: {\bf SlopeY} (argument on exit)
- \subsection{Variable $\kappa_{GM}$}
+ \subsubsection{Variable $\kappa_{GM}$}
  Visbeck et al., 1996, suggest making the eddy coefficient,
  $\kappa_{GM}$, a function of the Eady growth rate,
-Line 213 
 Substituting into the formula for $\kapp
+Line 217 
 Substituting into the formula for $\kapp
  \end{displaymath}
- \subsection{Tapering and stability}
+ \subsubsection{Tapering and stability}
  Experience with the GFDL model showed that the GM scheme has to be
  matched to the convective parameterization. This was originally
-Line 238 
 $z_\sigma^{*}$: {\bf dRdSigmaLtd} (argum
+Line 242 
 $z_\sigma^{*}$: {\bf dRdSigmaLtd} (argum
  \begin{figure}
  \begin{center}
- \resizebox{5.0in}{3.0in}{\includegraphics{part6/tapers.eps}}
+ \resizebox{5.0in}{3.0in}{\includegraphics{s_phys_pkgs/figs/tapers.eps}}
  \end{center}
- \caption{Taper functions used in GKW91 and DM95.}
+ \caption{Taper functions used in GKW99 and DM95.}
  \label{fig:tapers}
  \end{figure}
  \begin{figure}
  \begin{center}
- \resizebox{5.0in}{3.0in}{\includegraphics{part6/effective_slopes.eps}}
+ \resizebox{5.0in}{3.0in}{\includegraphics{s_phys_pkgs/figs/effective_slopes.eps}}
  \end{center}
  \caption{Effective slope as a function of ``true'' slope using Cox
  slope clipping, GKW91 limiting and DM95 limiting.}
-Line 254 
 slope clipping, GKW91 limiting and DM95
+Line 258 
 slope clipping, GKW91 limiting and DM95
  \end{figure}
- \subsubsection{Slope clipping}
+ Slope clipping:
  Deep convection sites and the mixed layer are indicated by
  homogenized, unstable or nearly unstable stratification. The slopes in
-Line 301 
 parameterization. Limiting the slopes al
+Line 305 
 parameterization. Limiting the slopes al
  of the GM/Redi parameterization, re-introducing diabatic fluxes in
  regions where the limiting is in effect.
- \subsubsection{Tapering: Gerdes, Koberle and Willebrand, Clim. Dyn. 1991}
+ Tapering: Gerdes, Koberle and Willebrand, Clim. Dyn. 1991:
- The tapering scheme used in Gerdes et al., 1991, (\cite{gkw91})
+ The tapering scheme used in Gerdes et al., 1999, (\cite{gkw:99})
  addressed two issues with the clipping method: the introduction of
  large vertical fluxes in addition to convective adjustment fluxes is
  avoided by tapering the GM/Redi slopes back to zero in
-Line 325 
 that the effective vertical diffusivity
+Line 329 
 that the effective vertical diffusivity
  The GKW tapering scheme is activated in the model by setting {\bf
  GM\_tap\-er\_scheme = 'gkw91'} in {\em data.gmredi}.
- \subsection{Tapering: Danabasoglu and McWilliams, J. Clim. 1995}
+ \subsubsection{Tapering: Danabasoglu and McWilliams, J. Clim. 1995}
  The tapering scheme used by Danabasoglu and McWilliams, 1995,
- \cite{DM95}, followed a similar procedure but used a different
+ \cite{dm:95}, followed a similar procedure but used a different
  tapering function, $f_1(S)$:
  \begin{equation}
  f_1(S) = \frac{1}{2} \left( 1+\tanh \left[ \frac{S_c - |S|}{S_d} \right] \right)
-Line 342 
 slopes.
+Line 346 
 slopes.
  The DM tapering scheme is activated in the model by setting {\bf
  GM\_tap\-er\_scheme = 'dm95'} in {\em data.gmredi}.
- \subsection{Tapering: Large, Danabasoglu and Doney, JPO 1997}
+ \subsubsection{Tapering: Large, Danabasoglu and Doney, JPO 1997}
- The tapering used in Large et al., 1997, \cite{ldd97}, is based on the
+ The tapering used in Large et al., 1997, \cite{ldd:97}, is based on the
  DM95 tapering scheme, but also tapers the scheme with an additional
  function of height, $f_2(z)$, so that the GM/Redi SGS fluxes are
  reduced near the surface:
-Line 372 
 clipping and for comparison b) using hor
+Line 376 
 clipping and for comparison b) using hor
  \label{fig-mixedlayer}
  \end{figure}
+ \subsubsection{Package Reference}
+ \label{sec:pkg:gmredi:diagnostics}
+ {\footnotesize
+ \begin{verbatim}
+ ------------------------------------------------------------------------
+ <-Name->|Levs|<-parsing code->|<--  Units   -->|<- Tile (max=80c)
+ ------------------------------------------------------------------------
+ GM_VisbK|  1 |SM P    M1      |m^2/s           |Mixing coefficient from Visbeck etal parameterization
+ GM_Kux  | 15 |UU P 177MR      |m^2/s           |K_11 element (U.point, X.dir) of GM-Redi tensor
+ GM_Kvy  | 15 |VV P 176MR      |m^2/s           |K_22 element (V.point, Y.dir) of GM-Redi tensor
+ GM_Kuz  | 15 |UU   179MR      |m^2/s           |K_13 element (U.point, Z.dir) of GM-Redi tensor
+ GM_Kvz  | 15 |VV   178MR      |m^2/s           |K_23 element (V.point, Z.dir) of GM-Redi tensor
+ GM_Kwx  | 15 |UM   181LR      |m^2/s           |K_31 element (W.point, X.dir) of GM-Redi tensor
+ GM_Kwy  | 15 |VM   180LR      |m^2/s           |K_32 element (W.point, Y.dir) of GM-Redi tensor
+ GM_Kwz  | 15 |WM P    LR      |m^2/s           |K_33 element (W.point, Z.dir) of GM-Redi tensor
+ GM_PsiX | 15 |UU   184LR      |m^2/s           |GM Bolus transport stream-function : X component
+ GM_PsiY | 15 |VV   183LR      |m^2/s           |GM Bolus transport stream-function : Y component
+ GM_KuzTz| 15 |UU   186MR      |degC.m^3/s      |Redi Off-diagonal Tempetature flux: X component
+ GM_KvzTz| 15 |VV   185MR      |degC.m^3/s      |Redi Off-diagonal Tempetature flux: Y component
+ \end{verbatim}
+ }
+ \subsubsection{Experiments and tutorials that use gmredi}
+ \label{sec:pkg:gmredi:experiments}
+ \begin{itemize}
+ \item{Global Ocean tutorial, in tutorial\_global\_oce\_latlon verification directory,
+ described in section \ref{sec:eg-global} }
+ \item{ Front Relax experiment, in front\_relax verification directory.}
+ \item{ Ideal 2D Ocean experiment, in ideal\_2D\_oce verification directory.}
+ \end{itemize}
+ % DO NOT EDIT HERE

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