/[MITgcm]/manual/s_examples/tracer_adjsens/co2sens.tex
ViewVC logotype

Diff of /manual/s_examples/tracer_adjsens/co2sens.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.4 by adcroft, Tue Nov 13 18:22:24 2001 UTC revision 1.7 by adcroft, Thu May 16 15:54:37 2002 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    
8  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
9    
# Line 16  Line 18 
18  %\end{center}  %\end{center}
19    
20  \subsection{Introduction}  \subsection{Introduction}
21    \label{www:tutorials}
22    
23  This document describes the fourth example MITgcm experiment.  This document describes the fourth example MITgcm experiment.
24  This example illustrates the use of  This example illustrates the use of
# Line 23  the MITgcm to perform sensitivity analys Line 26  the MITgcm to perform sensitivity analys
26  large scale ocean circulation simulation.  large scale ocean circulation simulation.
27    
28  \subsection{Overview}  \subsection{Overview}
29    \label{www:tutorials}
30    
31  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
32  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 52  Altogether, this yields the following fo
52  in the model surface layer.  in the model surface layer.
53    
54  \begin{eqnarray}  \begin{eqnarray}
55  \label{EQ:global_forcing}  \label{EQ:eg-simple-tracer-global_forcing}
56  \label{EQ:global_forcing_fu}  \label{EQ:eg-simple-tracer-global_forcing_fu}
57  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
58  \\  \\
59  \label{EQ:global_forcing_fv}  \label{EQ:eg-simple-tracer-global_forcing_fv}
60  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
61  \\  \\
62  \label{EQ:global_forcing_ft}  \label{EQ:eg-simple-tracer-global_forcing_ft}
63  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
64   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
65  \\  \\
66  \label{EQ:global_forcing_fs}  \label{EQ:eg-simple-tracer-global_forcing_fs}
67  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
68   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
69  \end{eqnarray}  \end{eqnarray}
# Line 81  The configuration is illustrated in figu Line 85  The configuration is illustrated in figu
85    
86    
87  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
88    \label{www:tutorials}
89    
90    
91   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 118  $ Line 123  $
123   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
124  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
125  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
126  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
127  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
128  \\  \\
129    
130  Wind-stress momentum inputs are added to the momentum equations for both  Wind-stress momentum inputs are added to the momentum equations for both
131  the zonal flow, $u$ and the meridional flow $v$, according to equations  the zonal flow, $u$ and the meridional flow $v$, according to equations
132  (\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}).
133  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations for
134  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
135  (\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}).
136  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
137  % {\fracktur}  % {\fracktur}
138    
139    
140  \begin{eqnarray}  \begin{eqnarray}
141  \label{EQ:model_equations}  \label{EQ:eg-simple-tracer-model_equations}
142  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
143    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
144    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 179  elevation $\eta$ and the hydrostatic pre
179  \\  \\
180    
181  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
182    \label{www:tutorials}
183    
184  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
185  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},
186    
187  \begin{eqnarray}  \begin{eqnarray}
188  \label{EQ:munk_layer}  \label{EQ:eg-simple-tracer-munk_layer}
189  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
190  \end{eqnarray}  \end{eqnarray}
191    
# Line 193  time step $\delta t=1200$secs. With this Line 199  time step $\delta t=1200$secs. With this
199  parameter to the horizontal Laplacian friction \cite{adcroft:95}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
200    
201  \begin{eqnarray}  \begin{eqnarray}
202  \label{EQ:laplacian_stability}  \label{EQ:eg-simple-tracer-laplacian_stability}
203  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
204  \end{eqnarray}  \end{eqnarray}
205    
# Line 205  for stability. Line 211  for stability.
211  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
212    
213  \begin{eqnarray}  \begin{eqnarray}
214  \label{EQ:laplacian_stability_z}  \label{EQ:eg-simple-tracer-laplacian_stability_z}
215  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
216  \end{eqnarray}  \end{eqnarray}
217    
# Line 219  and vertical ($K_{z}$) diffusion coeffic Line 225  and vertical ($K_{z}$) diffusion coeffic
225  \cite{adcroft:95}  \cite{adcroft:95}
226    
227  \begin{eqnarray}  \begin{eqnarray}
228  \label{EQ:inertial_stability}  \label{EQ:eg-simple-tracer-inertial_stability}
229  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
230  \end{eqnarray}  \end{eqnarray}
231    
# Line 232  horizontal flow Line 238  horizontal flow
238  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
239    
240  \begin{eqnarray}  \begin{eqnarray}
241  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-cfl_stability}
242  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
243  \end{eqnarray}  \end{eqnarray}
244    
# Line 244  limit of 0.5. Line 250  limit of 0.5.
250  \cite{adcroft:95}  \cite{adcroft:95}
251    
252  \begin{eqnarray}  \begin{eqnarray}
253  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-igw_stability}
254  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
255  \end{eqnarray}  \end{eqnarray}
256    
# Line 252  S_{c} = \frac{c_{g} \delta t}{ \Delta x} Line 258  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
258  stability limit of 0.25.  stability limit of 0.25.
259        
260  \subsection{Code Configuration}  \subsection{Code Configuration}
261    \label{www:tutorials}
262  \label{SEC:code_config}  \label{SEC:code_config}
263    
264  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 278  experiments. Below we describe the custo
278  to these files associated with this experiment.  to these files associated with this experiment.
279    
280  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
281    \label{www:tutorials}
282    
283  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
284  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 473  notes. Line 481  notes.
481  \end{small}  \end{small}
482    
483  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
484    \label{www:tutorials}
485    
486  This file uses standard default values and does not contain  This file uses standard default values and does not contain
487  customizations for this experiment.  customizations for this experiment.
488    
489  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
490    \label{www:tutorials}
491    
492  This file uses standard default values and does not contain  This file uses standard default values and does not contain
493  customizations for this experiment.  customizations for this experiment.
494    
495  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
496    \label{www:tutorials}
497    
498  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
499  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 504  in MITgcm. The included matlab program {
504  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
505    
506  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
507    \label{www:tutorials}
508    
509    
510  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 516  The included matlab program {\it input/g
516  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
517    
518  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
519    \label{www:tutorials}
520    
521  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
522    
# Line 530  the vertical domain extent in grid point Line 543  the vertical domain extent in grid point
543  \end{small}  \end{small}
544    
545  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
546    \label{www:tutorials}
547    
548  This file uses standard default values and does not contain  This file uses standard default values and does not contain
549  customizations for this experiment.  customizations for this experiment.
550    
551    
552  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
553    \label{www:tutorials}
554    
555  This file uses standard default values and does not contain  This file uses standard default values and does not contain
556  customizations for this experiment.  customizations for this experiment.
557    
558  \subsubsection{Other Files }  \subsubsection{Other Files }
559    \label{www:tutorials}
560    
561  Other files relevant to this experiment are  Other files relevant to this experiment are
562  \begin{itemize}  \begin{itemize}
Legend:
Removed from v.1.4  
changed lines
  Added in v.1.7
  ViewVC Help
Powered by ViewVC 1.1.22