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revision 1.9 by heimbach, Thu Jul 14 21:04:52 2005 UTC revision 1.11 by molod, Wed Apr 5 03:35:15 2006 UTC
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1  \section{GMREDI: Gent/McWiliams/Redi SGS Eddy Parameterization}  \subsection{GMREDI: Gent/McWiliams/Redi SGS Eddy Parameterization}
2  \label{sec:pkg:gmredi}  \label{sec:pkg:gmredi}
3  \begin{rawhtml}  \begin{rawhtml}
4  <!-- CMIREDIR:gmredi: -->  <!-- CMIREDIR:gmredi: -->
# Line 35  and Redi scheme, substantial cancellatio Line 35  and Redi scheme, substantial cancellatio
35  that the horizontal fluxes are unmodified from the lateral diffusion  that the horizontal fluxes are unmodified from the lateral diffusion
36  parameterization.  parameterization.
37    
38  \subsection{Redi scheme: Isopycnal diffusion}  \subsubsection{Redi scheme: Isopycnal diffusion}
39    
40  The Redi scheme diffuses tracers along isopycnals and introduces a  The Redi scheme diffuses tracers along isopycnals and introduces a
41  term in the tendency (rhs) of such a tracer (here $\tau$) of the form:  term in the tendency (rhs) of such a tracer (here $\tau$) of the form:
# Line 75  S_x & S_y & |S|^2 \\ Line 75  S_x & S_y & |S|^2 \\
75  \end{equation}  \end{equation}
76    
77    
78  \subsection{GM parameterization}  \subsubsection{GM parameterization}
79    
80  The GM parameterization aims to parameterise the ``advective'' or  The GM parameterization aims to parameterise the ``advective'' or
81  ``transport'' effect of geostrophic eddies by means of a ``bolus''  ``transport'' effect of geostrophic eddies by means of a ``bolus''
# Line 104  F_y & = & \kappa_{GM} S_y Line 104  F_y & = & \kappa_{GM} S_y
104  This is the form of the GM parameterization as applied by Donabasaglu,  This is the form of the GM parameterization as applied by Donabasaglu,
105  1997, in MOM versions 1 and 2.  1997, in MOM versions 1 and 2.
106    
107  \subsection{Griffies Skew Flux}  \subsubsection{Griffies Skew Flux}
108    
109  Griffies notes that the discretisation of bolus velocities involves  Griffies notes that the discretisation of bolus velocities involves
110  multiple layers of differencing and interpolation that potentially  multiple layers of differencing and interpolation that potentially
# Line 191  $S_y$: {\bf SlopeY} (argument on exit) Line 191  $S_y$: {\bf SlopeY} (argument on exit)
191    
192    
193    
194  \subsection{Variable $\kappa_{GM}$}  \subsubsection{Variable $\kappa_{GM}$}
195    
196  Visbeck et al., 1996, suggest making the eddy coefficient,  Visbeck et al., 1996, suggest making the eddy coefficient,
197  $\kappa_{GM}$, a function of the Eady growth rate,  $\kappa_{GM}$, a function of the Eady growth rate,
# Line 217  Substituting into the formula for $\kapp Line 217  Substituting into the formula for $\kapp
217  \end{displaymath}  \end{displaymath}
218    
219    
220  \subsection{Tapering and stability}  \subsubsection{Tapering and stability}
221    
222  Experience with the GFDL model showed that the GM scheme has to be  Experience with the GFDL model showed that the GM scheme has to be
223  matched to the convective parameterization. This was originally  matched to the convective parameterization. This was originally
# Line 258  slope clipping, GKW91 limiting and DM95 Line 258  slope clipping, GKW91 limiting and DM95
258  \end{figure}  \end{figure}
259    
260    
261  \subsubsection{Slope clipping}  Slope clipping:
262    
263  Deep convection sites and the mixed layer are indicated by  Deep convection sites and the mixed layer are indicated by
264  homogenized, unstable or nearly unstable stratification. The slopes in  homogenized, unstable or nearly unstable stratification. The slopes in
# Line 305  parameterization. Limiting the slopes al Line 305  parameterization. Limiting the slopes al
305  of the GM/Redi parameterization, re-introducing diabatic fluxes in  of the GM/Redi parameterization, re-introducing diabatic fluxes in
306  regions where the limiting is in effect.  regions where the limiting is in effect.
307    
308  \subsubsection{Tapering: Gerdes, Koberle and Willebrand, Clim. Dyn. 1991}  Tapering: Gerdes, Koberle and Willebrand, Clim. Dyn. 1991:
309    
310  The tapering scheme used in Gerdes et al., 1999, (\cite{gkw:99})  The tapering scheme used in Gerdes et al., 1999, (\cite{gkw:99})
311  addressed two issues with the clipping method: the introduction of  addressed two issues with the clipping method: the introduction of
# Line 329  that the effective vertical diffusivity Line 329  that the effective vertical diffusivity
329  The GKW tapering scheme is activated in the model by setting {\bf  The GKW tapering scheme is activated in the model by setting {\bf
330  GM\_tap\-er\_scheme = 'gkw91'} in {\em data.gmredi}.  GM\_tap\-er\_scheme = 'gkw91'} in {\em data.gmredi}.
331    
332  \subsection{Tapering: Danabasoglu and McWilliams, J. Clim. 1995}  \subsubsection{Tapering: Danabasoglu and McWilliams, J. Clim. 1995}
333    
334  The tapering scheme used by Danabasoglu and McWilliams, 1995,  The tapering scheme used by Danabasoglu and McWilliams, 1995,
335  \cite{dm:95}, followed a similar procedure but used a different  \cite{dm:95}, followed a similar procedure but used a different
# Line 346  slopes. Line 346  slopes.
346  The DM tapering scheme is activated in the model by setting {\bf  The DM tapering scheme is activated in the model by setting {\bf
347  GM\_tap\-er\_scheme = 'dm95'} in {\em data.gmredi}.  GM\_tap\-er\_scheme = 'dm95'} in {\em data.gmredi}.
348    
349  \subsection{Tapering: Large, Danabasoglu and Doney, JPO 1997}  \subsubsection{Tapering: Large, Danabasoglu and Doney, JPO 1997}
350    
351  The tapering used in Large et al., 1997, \cite{ldd:97}, is based on the  The tapering used in Large et al., 1997, \cite{ldd:97}, is based on the
352  DM95 tapering scheme, but also tapers the scheme with an additional  DM95 tapering scheme, but also tapers the scheme with an additional
# Line 376  clipping and for comparison b) using hor Line 376  clipping and for comparison b) using hor
376  \label{fig-mixedlayer}  \label{fig-mixedlayer}
377  \end{figure}  \end{figure}
378    
379  \subsection{Package Reference}  \subsubsection{Package Reference}
380    \label{sec:pkg:gmredi:diagnostics}
381    
382    \begin{verbatim}
383    ------------------------------------------------------------------------
384    <-Name->|Levs|<-parsing code->|<--  Units   -->|<- Tile (max=80c)
385    ------------------------------------------------------------------------
386    GM_VisbK|  1 |SM P    M1      |m^2/s           |Mixing coefficient from Visbeck etal parameterization
387    GM_Kux  | 15 |UU P 177MR      |m^2/s           |K_11 element (U.point, X.dir) of GM-Redi tensor
388    GM_Kvy  | 15 |VV P 176MR      |m^2/s           |K_22 element (V.point, Y.dir) of GM-Redi tensor
389    GM_Kuz  | 15 |UU   179MR      |m^2/s           |K_13 element (U.point, Z.dir) of GM-Redi tensor
390    GM_Kvz  | 15 |VV   178MR      |m^2/s           |K_23 element (V.point, Z.dir) of GM-Redi tensor
391    GM_Kwx  | 15 |UM   181LR      |m^2/s           |K_31 element (W.point, X.dir) of GM-Redi tensor
392    GM_Kwy  | 15 |VM   180LR      |m^2/s           |K_32 element (W.point, Y.dir) of GM-Redi tensor
393    GM_Kwz  | 15 |WM P    LR      |m^2/s           |K_33 element (W.point, Z.dir) of GM-Redi tensor
394    GM_PsiX | 15 |UU   184LR      |m^2/s           |GM Bolus transport stream-function : X component
395    GM_PsiY | 15 |VV   183LR      |m^2/s           |GM Bolus transport stream-function : Y component
396    GM_KuzTz| 15 |UU   186MR      |degC.m^3/s      |Redi Off-diagonal Tempetature flux: X component
397    GM_KvzTz| 15 |VV   185MR      |degC.m^3/s      |Redi Off-diagonal Tempetature flux: Y component
398    \end{verbatim}
399    
400    \subsubsection{Package Reference}
401  % DO NOT EDIT HERE  % DO NOT EDIT HERE
402    
403    
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