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revision 1.5 by adcroft, Tue Nov 13 19:01:42 2001 UTC revision 1.9 by edhill, Sat Apr 8 01:50:49 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    
26  This document describes the fourth example MITgcm experiment.  This document describes the fourth example MITgcm experiment.
27  This example illustrates the use of  This example illustrates the use of
# Line 23  the MITgcm to perform sensitivity analys Line 29  the MITgcm to perform sensitivity analys
29  large scale ocean circulation simulation.  large scale ocean circulation simulation.
30    
31  \subsection{Overview}  \subsection{Overview}
32    \label{www:tutorials}
33    
34  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
35  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 55  Altogether, this yields the following fo
55  in the model surface layer.  in the model surface layer.
56    
57  \begin{eqnarray}  \begin{eqnarray}
58  \label{EQ:global_forcing}  \label{EQ:eg-simple-tracer-global_forcing}
59  \label{EQ:global_forcing_fu}  \label{EQ:eg-simple-tracer-global_forcing_fu}
60  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
61  \\  \\
62  \label{EQ:global_forcing_fv}  \label{EQ:eg-simple-tracer-global_forcing_fv}
63  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
64  \\  \\
65  \label{EQ:global_forcing_ft}  \label{EQ:eg-simple-tracer-global_forcing_ft}
66  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
67   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
68  \\  \\
69  \label{EQ:global_forcing_fs}  \label{EQ:eg-simple-tracer-global_forcing_fs}
70  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
71   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
72  \end{eqnarray}  \end{eqnarray}
# Line 81  The configuration is illustrated in figu Line 88  The configuration is illustrated in figu
88    
89    
90  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
91    \label{www:tutorials}
92    
93    
94   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 132  dissipation. Thermal and haline diffusio
132    
133  Wind-stress momentum inputs are added to the momentum equations for both  Wind-stress momentum inputs are added to the momentum equations for both
134  the zonal flow, $u$ and the meridional flow $v$, according to equations  the zonal flow, $u$ and the meridional flow $v$, according to equations
135  (\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}).
136  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations for
137  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
138  (\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}).
139  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
140  % {\fracktur}  % {\fracktur}
141    
142    
143  \begin{eqnarray}  \begin{eqnarray}
144  \label{EQ:model_equations}  \label{EQ:eg-simple-tracer-model_equations}
145  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
146    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
147    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 182  elevation $\eta$ and the hydrostatic pre
182  \\  \\
183    
184  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
185    \label{www:tutorials}
186    
187  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
188  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},
189    
190  \begin{eqnarray}  \begin{eqnarray}
191  \label{EQ:munk_layer}  \label{EQ:eg-simple-tracer-munk_layer}
192  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
193  \end{eqnarray}  \end{eqnarray}
194    
# Line 193  time step $\delta t=1200$secs. With this Line 202  time step $\delta t=1200$secs. With this
202  parameter to the horizontal Laplacian friction \cite{adcroft:95}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
203    
204  \begin{eqnarray}  \begin{eqnarray}
205  \label{EQ:laplacian_stability}  \label{EQ:eg-simple-tracer-laplacian_stability}
206  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
207  \end{eqnarray}  \end{eqnarray}
208    
# Line 205  for stability. Line 214  for stability.
214  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
215    
216  \begin{eqnarray}  \begin{eqnarray}
217  \label{EQ:laplacian_stability_z}  \label{EQ:eg-simple-tracer-laplacian_stability_z}
218  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
219  \end{eqnarray}  \end{eqnarray}
220    
# Line 219  and vertical ($K_{z}$) diffusion coeffic Line 228  and vertical ($K_{z}$) diffusion coeffic
228  \cite{adcroft:95}  \cite{adcroft:95}
229    
230  \begin{eqnarray}  \begin{eqnarray}
231  \label{EQ:inertial_stability}  \label{EQ:eg-simple-tracer-inertial_stability}
232  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
233  \end{eqnarray}  \end{eqnarray}
234    
# Line 232  horizontal flow Line 241  horizontal flow
241  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
242    
243  \begin{eqnarray}  \begin{eqnarray}
244  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-cfl_stability}
245  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
246  \end{eqnarray}  \end{eqnarray}
247    
# Line 244  limit of 0.5. Line 253  limit of 0.5.
253  \cite{adcroft:95}  \cite{adcroft:95}
254    
255  \begin{eqnarray}  \begin{eqnarray}
256  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-igw_stability}
257  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
258  \end{eqnarray}  \end{eqnarray}
259    
# Line 252  S_{c} = \frac{c_{g} \delta t}{ \Delta x} Line 261  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
261  stability limit of 0.25.  stability limit of 0.25.
262        
263  \subsection{Code Configuration}  \subsection{Code Configuration}
264    \label{www:tutorials}
265  \label{SEC:code_config}  \label{SEC:code_config}
266    
267  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 281  experiments. Below we describe the custo
281  to these files associated with this experiment.  to these files associated with this experiment.
282    
283  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
284    \label{www:tutorials}
285    
286  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
287  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 293  are
293  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}
294  this line sets  this line sets
295  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
296  level in units of $^{\circ}$C.  level in units of $^{\circ}\mathrm{C}$.
297  The entries are ordered from surface to depth. For each  The entries are ordered from surface to depth. For each
298  depth level the initial and reference profiles will be uniform in  depth level the initial and reference profiles will be uniform in
299  $x$ and $y$.  $x$ and $y$.
# Line 473  notes. Line 484  notes.
484  \end{small}  \end{small}
485    
486  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
487    \label{www:tutorials}
488    
489  This file uses standard default values and does not contain  This file uses standard default values and does not contain
490  customizations for this experiment.  customizations for this experiment.
491    
492  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
493    \label{www:tutorials}
494    
495  This file uses standard default values and does not contain  This file uses standard default values and does not contain
496  customizations for this experiment.  customizations for this experiment.
497    
498  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
499    \label{www:tutorials}
500    
501  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
502  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 507  in MITgcm. The included matlab program {
507  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
508    
509  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
510    \label{www:tutorials}
511    
512    
513  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 519  The included matlab program {\it input/g
519  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
520    
521  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
522    \label{www:tutorials}
523    
524  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
525    
# Line 530  the vertical domain extent in grid point Line 546  the vertical domain extent in grid point
546  \end{small}  \end{small}
547    
548  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
549    \label{www:tutorials}
550    
551  This file uses standard default values and does not contain  This file uses standard default values and does not contain
552  customizations for this experiment.  customizations for this experiment.
553    
554    
555  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
556    \label{www:tutorials}
557    
558  This file uses standard default values and does not contain  This file uses standard default values and does not contain
559  customizations for this experiment.  customizations for this experiment.
560    
561  \subsubsection{Other Files }  \subsubsection{Other Files }
562    \label{www:tutorials}
563    
564  Other files relevant to this experiment are  Other files relevant to this experiment are
565  \begin{itemize}  \begin{itemize}
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