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

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-revision 1.2 by adcroft,
Fri Sep 28 14:09:56 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 167 
 In the instance that $\kappa_{GM} = \kap
+Line 171 
 In the instance that $\kappa_{GM} = \kap
  \end{array}
  \right)
  \end{equation}
- which differs from the variable laplacian diffusion tensor by only
+ which differs from the variable Laplacian diffusion tensor by only
  two non-zero elements in the $z$-row.
  \fbox{ \begin{minipage}{4.75in}
-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
  expressed in connection with the introduction of the KPP boundary
- layer scheme (Large et al., 97) but infact, as subsequent experience
+ layer scheme (Large et al., 97) but in fact, as subsequent experience
  with the MIT model has found, is necessary for any convective
  parameterization.
-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
  such regions can be either infinite, very large with a sign reversal
  or simply very large. From a numerical point of view, large slopes
  lead to large variations in the tensor elements (implying large bolus
- flow) and can be numerically unstable. This was first reognized by
+ flow) and can be numerically unstable. This was first recognized by
  Cox, 1987, who implemented ``slope clipping'' in the isopycnal mixing
  tensor. Here, the slope magnitude is simply restricted by an upper
  limit:
-Line 296 
 a) using the GM scheme with clipping and
+Line 300 
 a) using the GM scheme with clipping and
  diffusion). The classic result of dramatically reduced mixed layers is
  evident. Indeed, the deep convection sites to just one or two points
  each and are much shallower than we might prefer. This, it turns out,
- is due to the over zealous restratification due to the bolus transport
+ is due to the over zealous re-stratification due to the bolus transport
  parameterization. Limiting the slopes also breaks the adiabatic nature
  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 362 
 GM\_tap\-er\_scheme = 'ldd97'} in {\em d
+Line 366 
 GM\_tap\-er\_scheme = 'ldd97'} in {\em d
  \begin{figure}
+ \begin{center}
  %\includegraphics{mixedlayer-cox.eps}
  %\includegraphics{mixedlayer-diff.eps}
+ Figure missing.
+ \end{center}
  \caption{Mixed layer depth using GM parameterization with a) Cox slope
  clipping and for comparison b) using horizontal constant diffusion.}
- \ref{fig-mixedlayer}
+ \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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