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revision 1.1 by adcroft, Wed Aug 8 16:16:16 2001 UTC revision 1.2 by cnh, Thu Oct 25 18:36:54 2001 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: Centenial Time Scale Sensitivities}  \section{Example: Centennial Time Scale Sensitivities}
5    
6  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
7    
8  %\begin{center}  %\begin{center}
9  %{\Large \bf Using MITgcm to Look at Centenial Time Scale  %{\Large \bf Using MITgcm to Look at Centennial Time Scale
10  %Sensitivities}  %Sensitivities}
11  %  %
12  %\vspace*{4mm}  %\vspace*{4mm}
# Line 18  Line 18 
18  \subsection{Introduction}  \subsection{Introduction}
19    
20  This document describes the fourth example MITgcm experiment.  This document describes the fourth example MITgcm experiment.
21  This example iilustrates the use of  This example illustrates the use of
22  the MITgcm to perform sentivity analysis in a  the MITgcm to perform sensitivity analysis in a
23  large scale ocean circulation simulation.  large scale ocean circulation simulation.
24    
25  \subsection{Overview}  \subsection{Overview}
# Line 36  can be integrated forward for thousands Line 36  can be integrated forward for thousands
36  processor desktop computer.  processor desktop computer.
37  \\  \\
38    
39  The model is forced with climatalogical wind stress data and surface  The model is forced with climatological wind stress data and surface
40  flux data from Da Silva \cite{DaSilva94}. Climatalogical data  flux data from Da Silva \cite{DaSilva94}. Climatological data
41  from Levitus \cite{Levitus94} is used to initialise the model hydrography.  from Levitus \cite{Levitus94} is used to initialize the model hydrography.
42  Levitus data is also used throughout the calculation  Levitus data is also used throughout the calculation
43  to derive air-sea fluxes of heat at the ocean surface.  to derive air-sea fluxes of heat at the ocean surface.
44  These fluxes are combined with climatalogical estimates of  These fluxes are combined with climatological estimates of
45  surface heat flux and fresh water, resulting in a mixed boundary  surface heat flux and fresh water, resulting in a mixed boundary
46  condition of the style decribed in Haney \cite{Haney}.  condition of the style described in Haney \cite{Haney}.
47  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied
48  in the model surface layer.  in the model surface layer.
49    
# Line 118  $ Line 118  $
118   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
119  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
120  The implicit free surface form of the pressure equation described in Marshall et. al  The implicit free surface form of the pressure equation described in Marshall et. al
121  \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
122  dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
123  \\  \\
124    
125  Wind-stress momentum inputs are added to the momentum equations for both  Wind-stress momentum inputs are added to the momentum equations for both
126  the zonal flow, $u$ and the merdional flow $v$, according to equations  the zonal flow, $u$ and the meridional flow $v$, according to equations
127  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).
128  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations for
129  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
# Line 175  elevation $\eta$ and the hydrostatic pre Line 175  elevation $\eta$ and the hydrostatic pre
175    
176  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
177    
178  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
179  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},
180    
181  \begin{eqnarray}  \begin{eqnarray}
# Line 190  boundary layer is well resolved. Line 190  boundary layer is well resolved.
190    
191  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
192  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
193  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{Adcroft_thesis}
194    
195  \begin{eqnarray}  \begin{eqnarray}
196  \label{EQ:laplacian_stability}  \label{EQ:laplacian_stability}
# Line 240  S_{a} = \frac{| \vec{u} | \delta t}{ \De Line 240  S_{a} = \frac{| \vec{u} | \delta t}{ \De
240  limit of 0.5.  limit of 0.5.
241  \\  \\
242    
243  \noindent The stbility parameter for internal gravity waves  \noindent The stability parameter for internal gravity waves
244  \cite{Adcroft_thesis}  \cite{Adcroft_thesis}
245    
246  \begin{eqnarray}  \begin{eqnarray}
# Line 266  directory {\it verification/exp1/}.  The Line 266  directory {\it verification/exp1/}.  The
266  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
267  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
268  \end{itemize}  \end{itemize}
269  contain the code customisations and parameter settings for this  contain the code customizations and parameter settings for this
270  experiements. Below we describe the customisations  experiments. Below we describe the customizations
271  to these files associated with this experiment.  to these files associated with this experiment.
272    
273  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
# Line 284  this line sets Line 284  this line sets
284  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
285  level in units of $^{\circ}$C.  level in units of $^{\circ}$C.
286  The entries are ordered from surface to depth. For each  The entries are ordered from surface to depth. For each
287  depth level the inital and reference profiles will be uniform in  depth level the initial and reference profiles will be uniform in
288  $x$ and $y$.  $x$ and $y$.
289    
290  \fbox{  \fbox{
# Line 296  $x$ and $y$. Line 296  $x$ and $y$.
296    
297  \item Line 6,  \item Line 6,
298  \begin{verbatim} viscAz=1.E-2, \end{verbatim}  \begin{verbatim} viscAz=1.E-2, \end{verbatim}
299  this line sets the vertical laplacian dissipation coefficient to  this line sets the vertical Laplacian dissipation coefficient to
300  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
301  for this operator are specified later. This variable is copied into  for this operator are specified later. This variable is copied into
302  model general vertical coordinate variable {\bf viscAr}.  model general vertical coordinate variable {\bf viscAr}.
# Line 311  model general vertical coordinate variab Line 311  model general vertical coordinate variab
311  \begin{verbatim}  \begin{verbatim}
312  viscAh=4.E2,  viscAh=4.E2,
313  \end{verbatim}  \end{verbatim}
314  this line sets the horizontal laplacian frictional dissipation coefficient to  this line sets the horizontal Laplacian frictional dissipation coefficient to
315  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
316  for this operator are specified later.  for this operator are specified later.
317    
# Line 320  for this operator are specified later. Line 320  for this operator are specified later.
320  no_slip_sides=.FALSE.  no_slip_sides=.FALSE.
321  \end{verbatim}  \end{verbatim}
322  this line selects a free-slip lateral boundary condition for  this line selects a free-slip lateral boundary condition for
323  the horizontal laplacian friction operator  the horizontal Laplacian friction operator
324  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
325  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
326    
# Line 329  $\frac{\partial v}{\partial x}$=0 along Line 329  $\frac{\partial v}{\partial x}$=0 along
329  no_slip_bottom=.TRUE.  no_slip_bottom=.TRUE.
330  \end{verbatim}  \end{verbatim}
331  this line selects a no-slip boundary condition for bottom  this line selects a no-slip boundary condition for bottom
332  boundary condition in the vertical laplacian friction operator  boundary condition in the vertical Laplacian friction operator
333  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
334    
335  \item Line 10,  \item Line 10,
# Line 382  usingSphericalPolarGrid=.TRUE., Line 382  usingSphericalPolarGrid=.TRUE.,
382  \end{verbatim}  \end{verbatim}
383  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
384  spherical polar coordinate system. It affects the interpretation of  spherical polar coordinate system. It affects the interpretation of
385  grid inoput parameters, for exampl {\bf delX} and {\bf delY} and  grid input parameters, for example {\bf delX} and {\bf delY} and
386  causes the grid generation routines to initialise an internal grid based  causes the grid generation routines to initialize an internal grid based
387  on spherical polar geometry.  on spherical polar geometry.
388    
389  \fbox{  \fbox{
# Line 399  phiMin=0., Line 399  phiMin=0.,
399  This line sets the southern boundary of the modeled  This line sets the southern boundary of the modeled
400  domain to $0^{\circ}$ latitude. This value affects both the  domain to $0^{\circ}$ latitude. This value affects both the
401  generation of the locally orthogonal grid that the model  generation of the locally orthogonal grid that the model
402  uses internally and affects the initialisation of the coriolis force.  uses internally and affects the initialization of the coriolis force.
403  Note - it is not required to set  Note - it is not required to set
404  a longitude boundary, since the absolute longitude does  a longitude boundary, since the absolute longitude does
405  not alter the kernel equation discretisation.  not alter the kernel equation discretisation.
# Line 475  notes. Line 475  notes.
475  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
476    
477  This file uses standard default values and does not contain  This file uses standard default values and does not contain
478  customisations for this experiment.  customizations for this experiment.
479    
480  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
481    
482  This file uses standard default values and does not contain  This file uses standard default values and does not contain
483  customisations for this experiment.  customizations for this experiment.
484    
485  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
486    
# Line 532  the vertical domain extent in grid point Line 532  the vertical domain extent in grid point
532  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
533    
534  This file uses standard default values and does not contain  This file uses standard default values and does not contain
535  customisations for this experiment.  customizations for this experiment.
536    
537    
538  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
539    
540  This file uses standard default values and does not contain  This file uses standard default values and does not contain
541  customisations for this experiment.  customizations for this experiment.
542    
543  \subsubsection{Other Files }  \subsubsection{Other Files }
544    
# Line 550  coriolis variables {\bf fCorU}. Line 550  coriolis variables {\bf fCorU}.
550  \item {\it model/src/ini\_parms.F},  \item {\it model/src/ini\_parms.F},
551  \item {\it input/windx.sin\_y},  \item {\it input/windx.sin\_y},
552  \end{itemize}  \end{itemize}
553  contain the code customisations and parameter settings for this  contain the code customizations and parameter settings for this
554  experiements. Below we describe the customisations  experiments. Below we describe the customizations
555  to these files associated with this experiment.  to these files associated with this experiment.

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