--- manual/s_phys_pkgs/text/gmredi.tex 2001/10/25 18:36:56 1.3 +++ manual/s_phys_pkgs/text/gmredi.tex 2010/08/30 23:09:21 1.15 @@ -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} + +\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 @@ -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, @@ -213,7 +217,7 @@ \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 @@ -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.} @@ -254,7 +258,7 @@ \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 @@ -301,9 +305,9 @@ 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{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