--- manual/s_phys_pkgs/text/gmredi.tex	2001/09/28 14:09:56	1.2
+++ manual/s_phys_pkgs/text/gmredi.tex	2010/08/27 13:15:37	1.14
@@ -1,4 +1,8 @@
-\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
@@ -31,7 +35,7 @@
 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:
@@ -71,7 +75,7 @@
 \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''
@@ -100,7 +104,7 @@
 This is the form of the GM parameterization as applied by Donabasaglu,
 1997, 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
@@ -167,7 +171,7 @@
 \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}
@@ -187,7 +191,7 @@
 
 
 
-\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,
@@ -213,12 +217,12 @@
 \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.
 
@@ -238,15 +242,15 @@
 
 \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.}
@@ -254,14 +258,14 @@
 \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:
@@ -296,14 +300,14 @@
 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
@@ -325,10 +329,10 @@
 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)
@@ -342,9 +346,9 @@
 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:
@@ -362,13 +366,50 @@
 
 
 \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{sect: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
 
 
 
