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revision 1.5 by adcroft, Tue Nov 13 19:01:42 2001 UTC revision 1.10 by molod, Tue Jun 27 19:08:22 2006 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: Centennial Time Scale Sensitivities}  \section{Centennial Time Scale Tracer Injection}
5    \label{www:tutorials}
6    \label{sect:eg-simple-tracer}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-simple-tracer: -->
9    \end{rawhtml}
10    
11  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
12    
# Line 16  Line 21 
21  %\end{center}  %\end{center}
22    
23  \subsection{Introduction}  \subsection{Introduction}
24    \label{www:tutorials}
25    
 This document describes the fourth example MITgcm experiment.  
26  This example illustrates the use of  This example illustrates the use of
27  the MITgcm to perform sensitivity analysis in a  the MITgcm to perform sensitivity analysis in a
28  large scale ocean circulation simulation.  large scale ocean circulation simulation.
29    The files for this experiment can be found in the
30    verification directory under tutorial\_tracer\_adjsens.
31    
32  \subsection{Overview}  \subsection{Overview}
33    \label{www:tutorials}
34    
35  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
36  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
# Line 48  Altogether, this yields the following fo Line 56  Altogether, this yields the following fo
56  in the model surface layer.  in the model surface layer.
57    
58  \begin{eqnarray}  \begin{eqnarray}
59  \label{EQ:global_forcing}  \label{EQ:eg-simple-tracer-global_forcing}
60  \label{EQ:global_forcing_fu}  \label{EQ:eg-simple-tracer-global_forcing_fu}
61  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
62  \\  \\
63  \label{EQ:global_forcing_fv}  \label{EQ:eg-simple-tracer-global_forcing_fv}
64  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
65  \\  \\
66  \label{EQ:global_forcing_ft}  \label{EQ:eg-simple-tracer-global_forcing_ft}
67  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
68   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
69  \\  \\
70  \label{EQ:global_forcing_fs}  \label{EQ:eg-simple-tracer-global_forcing_fs}
71  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
72   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
73  \end{eqnarray}  \end{eqnarray}
# Line 81  The configuration is illustrated in figu Line 89  The configuration is illustrated in figu
89    
90    
91  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
92    \label{www:tutorials}
93    
94    
95   The model is configured in hydrostatic form.  The domain is discretised with   The model is configured in hydrostatic form.  The domain is discretised with
# Line 124  dissipation. Thermal and haline diffusio Line 133  dissipation. Thermal and haline diffusio
133    
134  Wind-stress momentum inputs are added to the momentum equations for both  Wind-stress momentum inputs are added to the momentum equations for both
135  the zonal flow, $u$ and the meridional flow $v$, according to equations  the zonal flow, $u$ and the meridional flow $v$, according to equations
136  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:eg-simple-tracer-global_forcing_fu}) and (\ref{EQ:eg-simple-tracer-global_forcing_fv}).
137  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations for
138  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
139  (\ref{EQ:global_forcing_ft}) and (\ref{EQ:global_forcing_fs}).  (\ref{EQ:eg-simple-tracer-global_forcing_ft}) and (\ref{EQ:eg-simple-tracer-global_forcing_fs}).
140  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
141  % {\fracktur}  % {\fracktur}
142    
143    
144  \begin{eqnarray}  \begin{eqnarray}
145  \label{EQ:model_equations}  \label{EQ:eg-simple-tracer-model_equations}
146  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
147    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
148    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}
# Line 174  elevation $\eta$ and the hydrostatic pre Line 183  elevation $\eta$ and the hydrostatic pre
183  \\  \\
184    
185  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
186    \label{www:tutorials}
187    
188  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
189  This value is chosen to yield a Munk layer width \cite{adcroft:95},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
190    
191  \begin{eqnarray}  \begin{eqnarray}
192  \label{EQ:munk_layer}  \label{EQ:eg-simple-tracer-munk_layer}
193  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
194  \end{eqnarray}  \end{eqnarray}
195    
# Line 193  time step $\delta t=1200$secs. With this Line 203  time step $\delta t=1200$secs. With this
203  parameter to the horizontal Laplacian friction \cite{adcroft:95}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
204    
205  \begin{eqnarray}  \begin{eqnarray}
206  \label{EQ:laplacian_stability}  \label{EQ:eg-simple-tracer-laplacian_stability}
207  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
208  \end{eqnarray}  \end{eqnarray}
209    
# Line 205  for stability. Line 215  for stability.
215  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
216    
217  \begin{eqnarray}  \begin{eqnarray}
218  \label{EQ:laplacian_stability_z}  \label{EQ:eg-simple-tracer-laplacian_stability_z}
219  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
220  \end{eqnarray}  \end{eqnarray}
221    
# Line 219  and vertical ($K_{z}$) diffusion coeffic Line 229  and vertical ($K_{z}$) diffusion coeffic
229  \cite{adcroft:95}  \cite{adcroft:95}
230    
231  \begin{eqnarray}  \begin{eqnarray}
232  \label{EQ:inertial_stability}  \label{EQ:eg-simple-tracer-inertial_stability}
233  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
234  \end{eqnarray}  \end{eqnarray}
235    
# Line 232  horizontal flow Line 242  horizontal flow
242  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
243    
244  \begin{eqnarray}  \begin{eqnarray}
245  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-cfl_stability}
246  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
247  \end{eqnarray}  \end{eqnarray}
248    
# Line 244  limit of 0.5. Line 254  limit of 0.5.
254  \cite{adcroft:95}  \cite{adcroft:95}
255    
256  \begin{eqnarray}  \begin{eqnarray}
257  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-igw_stability}
258  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
259  \end{eqnarray}  \end{eqnarray}
260    
# Line 252  S_{c} = \frac{c_{g} \delta t}{ \Delta x} Line 262  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
262  stability limit of 0.25.  stability limit of 0.25.
263        
264  \subsection{Code Configuration}  \subsection{Code Configuration}
265    \label{www:tutorials}
266  \label{SEC:code_config}  \label{SEC:code_config}
267    
268  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
# Line 271  experiments. Below we describe the custo Line 282  experiments. Below we describe the custo
282  to these files associated with this experiment.  to these files associated with this experiment.
283    
284  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
285    \label{www:tutorials}
286    
287  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
288  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 282  are Line 294  are
294  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}
295  this line sets  this line sets
296  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
297  level in units of $^{\circ}$C.  level in units of $^{\circ}\mathrm{C}$.
298  The entries are ordered from surface to depth. For each  The entries are ordered from surface to depth. For each
299  depth level the initial and reference profiles will be uniform in  depth level the initial and reference profiles will be uniform in
300  $x$ and $y$.  $x$ and $y$.
# Line 473  notes. Line 485  notes.
485  \end{small}  \end{small}
486    
487  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
488    \label{www:tutorials}
489    
490  This file uses standard default values and does not contain  This file uses standard default values and does not contain
491  customizations for this experiment.  customizations for this experiment.
492    
493  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
494    \label{www:tutorials}
495    
496  This file uses standard default values and does not contain  This file uses standard default values and does not contain
497  customizations for this experiment.  customizations for this experiment.
498    
499  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
500    \label{www:tutorials}
501    
502  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
503  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
# Line 493  in MITgcm. The included matlab program { Line 508  in MITgcm. The included matlab program {
508  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
509    
510  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
511    \label{www:tutorials}
512    
513    
514  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
# Line 504  The included matlab program {\it input/g Line 520  The included matlab program {\it input/g
520  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
521    
522  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
523    \label{www:tutorials}
524    
525  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
526    
# Line 530  the vertical domain extent in grid point Line 547  the vertical domain extent in grid point
547  \end{small}  \end{small}
548    
549  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
550    \label{www:tutorials}
551    
552  This file uses standard default values and does not contain  This file uses standard default values and does not contain
553  customizations for this experiment.  customizations for this experiment.
554    
555    
556  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
557    \label{www:tutorials}
558    
559  This file uses standard default values and does not contain  This file uses standard default values and does not contain
560  customizations for this experiment.  customizations for this experiment.
561    
562  \subsubsection{Other Files }  \subsubsection{Other Files }
563    \label{www:tutorials}
564    
565  Other files relevant to this experiment are  Other files relevant to this experiment are
566  \begin{itemize}  \begin{itemize}
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