/[MITgcm]/manual/s_examples/baroclinic_gyre/fourlayer.tex
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revision 1.10 by adcroft, Tue Nov 13 19:01:42 2001 UTC revision 1.14 by edhill, Wed Jul 30 13:42:53 2003 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}  \section{Four Layer Baroclinic Ocean Gyre In Spherical Coordinates}
5  \label{sec:eg-fourlayer}  \label{www:tutorials}
6    \label{sect:eg-fourlayer}
7    
8  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
9    
# Line 19  Line 20 
20  This document describes an example experiment using MITgcm  This document describes an example experiment using MITgcm
21  to simulate a baroclinic ocean gyre in spherical  to simulate a baroclinic ocean gyre in spherical
22  polar coordinates. The barotropic  polar coordinates. The barotropic
23  example experiment in section \ref{sec:eg-baro}  example experiment in section \ref{sect:eg-baro}
24  illustrated how to configure the code for a single layer  illustrated how to configure the code for a single layer
25  simulation in a Cartesian grid. In this example a similar physical problem  simulation in a Cartesian grid. In this example a similar physical problem
26  is simulated, but the code is now configured  is simulated, but the code is now configured
27  for four layers and in a spherical polar coordinate system.  for four layers and in a spherical polar coordinate system.
28    
29  \subsection{Overview}  \subsection{Overview}
30    \label{www:tutorials}
31    
32  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
33  a baroclinic, wind-forced, ocean gyre circulation. The experiment  a baroclinic, wind-forced, ocean gyre circulation. The experiment
# Line 43  domain is a sector on a sphere and the c Line 45  domain is a sector on a sphere and the c
45  according to latitude, $\varphi$  according to latitude, $\varphi$
46    
47  \begin{equation}  \begin{equation}
48  \label{EQ:fcori}  \label{EQ:eg-fourlayer-fcori}
49  f(\varphi) = 2 \Omega \sin( \varphi )  f(\varphi) = 2 \Omega \sin( \varphi )
50  \end{equation}  \end{equation}
51    
# Line 61  f(\varphi) = 2 \Omega \sin( \varphi ) Line 63  f(\varphi) = 2 \Omega \sin( \varphi )
63  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
64  \\  \\
65    
66  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:eg-fourlayer-simulation_config}
67  summarizes the configuration simulated.  summarizes the configuration simulated.
68  In contrast to the example in section \ref{sec:eg-baro}, the  In contrast to the example in section \ref{sect:eg-baro}, the
69  current experiment simulates a spherical polar domain. As indicated  current experiment simulates a spherical polar domain. As indicated
70  by the axes in the lower left of the figure the model code works internally  by the axes in the lower left of the figure the model code works internally
71  in a locally orthogonal coordinate $(x,y,z)$. For this experiment description  in a locally orthogonal coordinate $(x,y,z)$. For this experiment description
# Line 82  $\theta_{1750}=6^{\circ}$~C. The equatio Line 84  $\theta_{1750}=6^{\circ}$~C. The equatio
84  linear  linear
85    
86  \begin{equation}  \begin{equation}
87  \label{EQ:linear1_eos}  \label{EQ:eg-fourlayer-linear1_eos}
88  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
89  \end{equation}  \end{equation}
90    
91  \noindent which is implemented in the model as a density anomaly equation  \noindent which is implemented in the model as a density anomaly equation
92    
93  \begin{equation}  \begin{equation}
94  \label{EQ:linear1_eos_pert}  \label{EQ:eg-fourlayer-linear1_eos_pert}
95  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
96  \end{equation}  \end{equation}
97    
# Line 114  An initial stratification is Line 116  An initial stratification is
116  imposed by setting the potential temperature, $\theta$, in each layer.  imposed by setting the potential temperature, $\theta$, in each layer.
117  The vertical spacing, $\Delta z$, is constant and equal to $500$m.  The vertical spacing, $\Delta z$, is constant and equal to $500$m.
118  }  }
119  \label{FIG:simulation_config}  \label{FIG:eg-fourlayer-simulation_config}
120  \end{figure}  \end{figure}
121    
122  \subsection{Equations solved}  \subsection{Equations solved}
123    \label{www:tutorials}
124  For this problem  For this problem
125  the implicit free surface, {\bf HPE} (see section \ref{sec:hydrostatic_and_quasi-hydrostatic_forms}) form of the  the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the
126  equations described in Marshall et. al \cite{marshall:97a} are  equations described in Marshall et. al \cite{marshall:97a} are
127  employed. The flow is three-dimensional with just temperature, $\theta$, as  employed. The flow is three-dimensional with just temperature, $\theta$, as
128  an active tracer.  The equation of state is linear.  an active tracer.  The equation of state is linear.
# Line 133  solved in this configuration, written in Line 136  solved in this configuration, written in
136  follows  follows
137    
138  \begin{eqnarray}  \begin{eqnarray}
139  \label{EQ:model_equations}  \label{EQ:eg-fourlayer-model_equations}
140  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
141    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} -    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} -
142    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 202  e.g. $\frac{\partial \theta}{\partial \v Line 205  e.g. $\frac{\partial \theta}{\partial \v
205    
206    
207  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
208    \label{www:tutorials}
209    
210   The domain is discretised with   The domain is discretised with
211  a uniform grid spacing in latitude and longitude  a uniform grid spacing in latitude and longitude
# Line 221  y=r\varphi,~\Delta y &= &r\Delta \varphi Line 225  y=r\varphi,~\Delta y &= &r\Delta \varphi
225    
226  The procedure for generating a set of internal grid variables from a  The procedure for generating a set of internal grid variables from a
227  spherical polar grid specification is discussed in section  spherical polar grid specification is discussed in section
228  \ref{sec:spatial_discrete_horizontal_grid}.  \ref{sect:spatial_discrete_horizontal_grid}.
229    
230  \noindent\fbox{ \begin{minipage}{5.5in}  \noindent\fbox{ \begin{minipage}{5.5in}
231  {\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em  {\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em
# Line 242  $\Delta x_v$, $\Delta y_u$: {\bf DXv}, { Line 246  $\Delta x_v$, $\Delta y_u$: {\bf DXv}, {
246    
247    
248    
249  As described in \ref{sec:tracer_equations}, the time evolution of potential  As described in \ref{sect:tracer_equations}, the time evolution of potential
250  temperature,  temperature,
251  $\theta$, (equation \ref{eq:eg_fourl_theta})  $\theta$, (equation \ref{eq:eg_fourl_theta})
252  is evaluated prognostically. The centered second-order scheme with  is evaluated prognostically. The centered second-order scheme with
253  Adams-Bashforth time stepping described in section  Adams-Bashforth time stepping described in section
254  \ref{sec:tracer_equations_abII} is used to step forward the temperature  \ref{sect:tracer_equations_abII} is used to step forward the temperature
255  equation. Prognostic terms in  equation. Prognostic terms in
256  the momentum equations are solved using flux form as  the momentum equations are solved using flux form as
257  described in section \ref{sec:flux-form_momentum_eqautions}.  described in section \ref{sect:flux-form_momentum_eqautions}.
258  The pressure forces that drive the fluid motions, (  The pressure forces that drive the fluid motions, (
259  $\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface  $\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface
260  elevation $\eta$ and the hydrostatic pressure. The hydrostatic part of the  elevation $\eta$ and the hydrostatic pressure. The hydrostatic part of the
# Line 258  pressure is diagnosed explicitly by inte Line 262  pressure is diagnosed explicitly by inte
262  height, $\eta$, is diagnosed using an implicit scheme. The pressure  height, $\eta$, is diagnosed using an implicit scheme. The pressure
263  field solution method is described in sections  field solution method is described in sections
264  \ref{sect:pressure-method-linear-backward} and  \ref{sect:pressure-method-linear-backward} and
265  \ref{sec:finding_the_pressure_field}.  \ref{sect:finding_the_pressure_field}.
266    
267  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
268    \label{www:tutorials}
269    
270  The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
271  This value is chosen to yield a Munk layer width,  This value is chosen to yield a Munk layer width,
272    
273  \begin{eqnarray}  \begin{eqnarray}
274  \label{EQ:munk_layer}  \label{EQ:eg-fourlayer-munk_layer}
275  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
276  \end{eqnarray}  \end{eqnarray}
277    
# Line 282  time step $\delta t=1200$secs. With this Line 287  time step $\delta t=1200$secs. With this
287  parameter to the horizontal Laplacian friction  parameter to the horizontal Laplacian friction
288    
289  \begin{eqnarray}  \begin{eqnarray}
290  \label{EQ:laplacian_stability}  \label{EQ:eg-fourlayer-laplacian_stability}
291  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
292  \end{eqnarray}  \end{eqnarray}
293    
# Line 294  for stability for this term under ABII t Line 299  for stability for this term under ABII t
299  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
300    
301  \begin{eqnarray}  \begin{eqnarray}
302  \label{EQ:laplacian_stability_z}  \label{EQ:eg-fourlayer-laplacian_stability_z}
303  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
304  \end{eqnarray}  \end{eqnarray}
305    
# Line 307  and vertical ($K_{z}$) diffusion coeffic Line 312  and vertical ($K_{z}$) diffusion coeffic
312  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
313    
314  \begin{eqnarray}  \begin{eqnarray}
315  \label{EQ:inertial_stability}  \label{EQ:eg-fourlayer-inertial_stability}
316  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
317  \end{eqnarray}  \end{eqnarray}
318    
# Line 320  horizontal flow Line 325  horizontal flow
325  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
326    
327  \begin{eqnarray}  \begin{eqnarray}
328  \label{EQ:cfl_stability}  \label{EQ:eg-fourlayer-cfl_stability}
329  C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
330  \end{eqnarray}  \end{eqnarray}
331    
# Line 332  limit of 0.5. Line 337  limit of 0.5.
337  propagating at $2~{\rm m}~{\rm s}^{-1}$  propagating at $2~{\rm m}~{\rm s}^{-1}$
338    
339  \begin{eqnarray}  \begin{eqnarray}
340  \label{EQ:igw_stability}  \label{EQ:eg-fourlayer-igw_stability}
341  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
342  \end{eqnarray}  \end{eqnarray}
343    
# Line 340  S_{c} = \frac{c_{g} \delta t}{ \Delta x} Line 345  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
345  stability limit of 0.25.  stability limit of 0.25.
346        
347  \subsection{Code Configuration}  \subsection{Code Configuration}
348    \label{www:tutorials}
349  \label{SEC:eg_fourl_code_config}  \label{SEC:eg_fourl_code_config}
350    
351  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
# Line 359  experiments. Below we describe the custo Line 365  experiments. Below we describe the custo
365  to these files associated with this experiment.  to these files associated with this experiment.
366    
367  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
368    \label{www:tutorials}
369    
370  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
371  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 376  depth level the initial and reference pr Line 383  depth level the initial and reference pr
383  $x$ and $y$. The values specified here are read into the  $x$ and $y$. The values specified here are read into the
384  variable  variable
385  {\bf  {\bf
386  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
387  tRef  tRef
388  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
389  }  }
390  in the model code, by procedure  in the model code, by procedure
391  {\it  {\it
392  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
393  INI\_PARMS  INI\_PARMS
394  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
395  }.  }.
# Line 395  INI\_PARMS Line 402  INI\_PARMS
402  %% \file{ini_parms}  %% \file{ini_parms}
403  \newcommand{\VARtref}{  \newcommand{\VARtref}{
404  {\bf  {\bf
405  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
406  tRef  tRef
407  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
408  }  }
# Line 410  tRef Line 417  tRef
417  \end{minipage}  \end{minipage}
418  }  }
419  {\bf  {\bf
420  \begin{rawhtml} <A href=../../../code_reference/vdb/code/98.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/98.htm> \end{rawhtml}
421  goto code  goto code
422  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
423  }  }
# Line 423  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Bo Line 430  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Bo
430  for this operator are specified later.  for this operator are specified later.
431  The variable  The variable
432  {\bf  {\bf
433  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZQ.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZQ.htm> \end{rawhtml}
434  viscAz  viscAz
435  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
436  }  }
437  is read in the routine  is read in the routine
438  {\it  {\it
439  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
440  INI\_PARMS  INI\_PARMS
441  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
442  }  }
443  and is copied into model general vertical coordinate variable  and is copied into model general vertical coordinate variable
444  {\bf  {\bf
445  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PF.htm> \end{rawhtml}
446  viscAr  viscAr
447  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
448  }. At each time step, the viscous term contribution to the momentum equations  }. At each time step, the viscous term contribution to the momentum equations
# Line 448  is calculated in routine Line 455  is calculated in routine
455  \end{minipage}  \end{minipage}
456  }  }
457  {\bf  {\bf
458  \begin{rawhtml} <A href=../../../code_reference/vdb/code/53.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/53.htm> \end{rawhtml}
459  goto code  goto code
460  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
461  }  }
# Line 462  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Bo Line 469  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Bo
469  for this operator are specified later.  for this operator are specified later.
470  The variable  The variable
471  {\bf  {\bf
472  \begin{rawhtml} <A href=../../../code_reference/vdb/names/SI.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/SI.htm> \end{rawhtml}
473  viscAh  viscAh
474  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
475  }  }
476  is read in the routine  is read in the routine
477  {\it  {\it
478  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
479  INI\_PARMS  INI\_PARMS
480  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
481  } and applied in routines {\it CALC\_MOM\_RHS} and {\it CALC\_GW}.  } and applied in routines {\it CALC\_MOM\_RHS} and {\it CALC\_GW}.
# Line 479  INI\_PARMS Line 486  INI\_PARMS
486  \end{minipage}  \end{minipage}
487  }  }
488  {\bf  {\bf
489  \begin{rawhtml} <A href=../../../code_reference/vdb/code/60.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/60.htm> \end{rawhtml}
490  goto code  goto code
491  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
492  }  }
# Line 490  goto code Line 497  goto code
497  \end{minipage}  \end{minipage}
498  }  }
499  {\bf  {\bf
500  \begin{rawhtml} <A href=../../../code_reference/vdb/code/58.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/58.htm> \end{rawhtml}
501  goto code  goto code
502  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
503  }  }
# Line 505  e.g. $\frac{\partial u}{\partial y}$=0 a Line 512  e.g. $\frac{\partial u}{\partial y}$=0 a
512  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
513  The variable  The variable
514  {\bf  {\bf
515  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UT.htm> \end{rawhtml}
516  no\_slip\_sides  no\_slip\_sides
517  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
518  }  }
519  is read in the routine  is read in the routine
520  {\it  {\it
521  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
522  INI\_PARMS  INI\_PARMS
523  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
524  } and the boundary condition is evaluated in routine  } and the boundary condition is evaluated in routine
# Line 524  INI\_PARMS Line 531  INI\_PARMS
531  \end{minipage}  \end{minipage}
532  }  }
533  {\bf  {\bf
534  \begin{rawhtml} <A href=../../../code_reference/vdb/code/60.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/60.htm> \end{rawhtml}
535  goto code  goto code
536  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
537  }  }
# Line 538  boundary condition in the vertical lapla Line 545  boundary condition in the vertical lapla
545  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.
546  The variable  The variable
547  {\bf  {\bf
548  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UK.htm> \end{rawhtml}
549  no\_slip\_bottom  no\_slip\_bottom
550  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
551  }  }
552  is read in the routine  is read in the routine
553  {\it  {\it
554  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
555  INI\_PARMS  INI\_PARMS
556  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
557  } and is applied in the routine {\it S/R CALC\_MOM\_RHS}.  } and is applied in the routine {\it S/R CALC\_MOM\_RHS}.
# Line 555  INI\_PARMS Line 562  INI\_PARMS
562  \end{minipage}  \end{minipage}
563  }  }
564  {\bf  {\bf
565  \begin{rawhtml} <A href=../../../code_reference/vdb/code/60.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/60.htm> \end{rawhtml}
566  goto code  goto code
567  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
568  }  }
# Line 570  operator is $\frac{\partial}{\partial x} Line 577  operator is $\frac{\partial}{\partial x}
577  all boundaries.  all boundaries.
578  The variable  The variable
579  {\bf  {\bf
580  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
581  diffKhT  diffKhT
582  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
583  }  }
584  is read in the routine  is read in the routine
585  {\it  {\it
586  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
587  INI\_PARMS  INI\_PARMS
588  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
589  } and used in routine {\it S/R CALC\_GT}.  } and used in routine {\it S/R CALC\_GT}.
# Line 586  INI\_PARMS Line 593  INI\_PARMS
593  \end{minipage}  \end{minipage}
594  }  }
595  {\bf  {\bf
596  \begin{rawhtml} <A href=../../../code_reference/vdb/code/57.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/57.htm> \end{rawhtml}
597  goto code  goto code
598  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
599  }  }
# Line 600  to $10^{-2}\,{\rm m^{2}s^{-1}}$. The bou Line 607  to $10^{-2}\,{\rm m^{2}s^{-1}}$. The bou
607  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
608  The variable  The variable
609  {\bf  {\bf
610  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
611  diffKzT  diffKzT
612  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
613  }  }
614  is read in the routine  is read in the routine
615  {\it  {\it
616  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
617  INI\_PARMS  INI\_PARMS
618  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
619  }.  }.
620  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
621  {\bf  {\bf
622  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
623  diffKrT  diffKrT
624  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
625  } which is used in routine {\it S/R CALC\_DIFFUSIVITY}.  } which is used in routine {\it S/R CALC\_DIFFUSIVITY}.
# Line 622  diffKrT Line 629  diffKrT
629  \end{minipage}  \end{minipage}
630  }  }
631  {\bf  {\bf
632  \begin{rawhtml} <A href=../../../code_reference/vdb/code/53.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/53.htm> \end{rawhtml}
633  goto code  goto code
634  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
635  }  }
# Line 637  This line sets the thermal expansion coe Line 644  This line sets the thermal expansion coe
644  to $2 \times 10^{-4}\,{\rm degrees}^{-1}$  to $2 \times 10^{-4}\,{\rm degrees}^{-1}$
645  The variable  The variable
646  {\bf  {\bf
647  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZV.htm> \end{rawhtml}
648  tAlpha  tAlpha
649  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
650  }  }
651  is read in the routine  is read in the routine
652  {\it  {\it
653  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
654  INI\_PARMS  INI\_PARMS
655  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
656  }. The routine {\it S/R FIND\_RHO} makes use of {\bf tAlpha}.  }. The routine {\it S/R FIND\_RHO} makes use of {\bf tAlpha}.
# Line 654  INI\_PARMS Line 661  INI\_PARMS
661  \end{minipage}  \end{minipage}
662  }  }
663  {\bf  {\bf
664  \begin{rawhtml} <A href=../../../code_reference/vdb/code/79.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/79.htm> \end{rawhtml}
665  goto code  goto code
666  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
667  }  }
# Line 666  eosType='LINEAR' Line 673  eosType='LINEAR'
673  This line selects the linear form of the equation of state.  This line selects the linear form of the equation of state.
674  The variable  The variable
675  {\bf  {\bf
676  \begin{rawhtml} <A href=../../../code_reference/vdb/names/WV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/WV.htm> \end{rawhtml}
677  eosType  eosType
678  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
679  }  }
680  is read in the routine  is read in the routine
681  {\it  {\it
682  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
683  INI\_PARMS  INI\_PARMS
684  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
685  }. The values of {\bf eosType} sets which formula in routine  }. The values of {\bf eosType} sets which formula in routine
# Line 684  INI\_PARMS Line 691  INI\_PARMS
691  \end{minipage}  \end{minipage}
692  }  }
693  {\bf  {\bf
694  \begin{rawhtml} <A href=../../../code_reference/vdb/code/79.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/79.htm> \end{rawhtml}
695  goto code  goto code
696  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
697  }  }
# Line 702  causes the grid generation routines to i Line 709  causes the grid generation routines to i
709  on spherical polar geometry.  on spherical polar geometry.
710  The variable  The variable
711  {\bf  {\bf
712  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10T.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10T.htm> \end{rawhtml}
713  usingSphericalPolarGrid  usingSphericalPolarGrid
714  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
715  }  }
716  is read in the routine  is read in the routine
717  {\it  {\it
718  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
719  INI\_PARMS  INI\_PARMS
720  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
721  }. When set to {\bf .TRUE.} the settings of {\bf delX} and {\bf delY} are  }. When set to {\bf .TRUE.} the settings of {\bf delX} and {\bf delY} are
# Line 721  routine {\it INI\_SPEHRICAL\_POLAR\_GRID Line 728  routine {\it INI\_SPEHRICAL\_POLAR\_GRID
728  \end{minipage}  \end{minipage}
729  }  }
730  {\bf  {\bf
731  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
732  goto code  goto code
733  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
734  }  }
# Line 739  a longitude boundary, since the absolute Line 746  a longitude boundary, since the absolute
746  not alter the kernel equation discretisation.  not alter the kernel equation discretisation.
747  The variable  The variable
748  {\bf  {\bf
749  \begin{rawhtml} <A href=../../../code_reference/vdb/names/110.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/110.htm> \end{rawhtml}
750  phiMin  phiMin
751  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
752  }  }
753  is read in the routine  is read in the routine
754  {\it  {\it
755  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
756  INI\_PARMS  INI\_PARMS
757  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
758  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
# Line 756  INI\_PARMS Line 763  INI\_PARMS
763  \end{minipage}  \end{minipage}
764  }  }
765  {\bf  {\bf
766  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
767  goto code  goto code
768  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
769  }  }
# Line 769  This line sets the horizontal grid spaci Line 776  This line sets the horizontal grid spaci
776  in the discrete grid to $1^{\circ}$ in longitude.  in the discrete grid to $1^{\circ}$ in longitude.
777  The variable  The variable
778  {\bf  {\bf
779  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10Z.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10Z.htm> \end{rawhtml}
780  delX  delX
781  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
782  }  }
783  is read in the routine  is read in the routine
784  {\it  {\it
785  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
786  INI\_PARMS  INI\_PARMS
787  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
788  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
# Line 786  INI\_PARMS Line 793  INI\_PARMS
793  \end{minipage}  \end{minipage}
794  }  }
795  {\bf  {\bf
796  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
797  goto code  goto code
798  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
799  }  }
# Line 799  This line sets the horizontal grid spaci Line 806  This line sets the horizontal grid spaci
806  in the discrete grid to $1^{\circ}$ in latitude.  in the discrete grid to $1^{\circ}$ in latitude.
807  The variable  The variable
808  {\bf  {\bf
809  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UB.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UB.htm> \end{rawhtml}
810  delY    delY  
811  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
812  }  }
813  is read in the routine  is read in the routine
814  {\it  {\it
815  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
816  INI\_PARMS  INI\_PARMS
817  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
818  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
# Line 816  INI\_PARMS Line 823  INI\_PARMS
823  \end{minipage}  \end{minipage}
824  }  }
825  {\bf  {\bf
826  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
827  goto code  goto code
828  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
829  }  }
# Line 830  in the discrete grid to $500\,{\rm m}$, Line 837  in the discrete grid to $500\,{\rm m}$,
837  is $2\,{\rm km}$.  is $2\,{\rm km}$.
838  The variable  The variable
839  {\bf  {\bf
840  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10W.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10W.htm> \end{rawhtml}
841  delZ  delZ
842  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
843  }  }
844  is read in the routine  is read in the routine
845  {\it  {\it
846  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
847  INI\_PARMS  INI\_PARMS
848  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
849  }.  }.
850  It is copied into the internal  It is copied into the internal
851  model coordinate variable  model coordinate variable
852  {\bf  {\bf
853  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10Y.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10Y.htm> \end{rawhtml}
854  delR  delR
855  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
856  } which is used in routine {\it INI\_VERTICAL\_GRID}.  } which is used in routine {\it INI\_VERTICAL\_GRID}.
# Line 854  delR Line 861  delR
861  \end{minipage}  \end{minipage}
862  }  }
863  {\bf  {\bf
864  \begin{rawhtml} <A href=../../../code_reference/vdb/code/100.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/100.htm> \end{rawhtml}
865  goto code  goto code
866  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
867  }  }
# Line 876  of $-2000m$ indicates open ocean. The ma Line 883  of $-2000m$ indicates open ocean. The ma
883  bathymetry file.  bathymetry file.
884  The variable  The variable
885  {\bf  {\bf
886  \begin{rawhtml} <A href=../../../code_reference/vdb/names/179.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/179.htm> \end{rawhtml}
887  bathyFile  bathyFile
888  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
889  }  }
890  is read in the routine  is read in the routine
891  {\it  {\it
892  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
893  INI\_PARMS  INI\_PARMS
894  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
895  }. The bathymetry file is read in the routine {\it INI\_DEPTHS}.  }. The bathymetry file is read in the routine {\it INI\_DEPTHS}.
# Line 893  INI\_PARMS Line 900  INI\_PARMS
900  \end{minipage}  \end{minipage}
901  }  }
902  {\bf  {\bf
903  \begin{rawhtml} <A href=../../../code_reference/vdb/code/88.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/88.htm> \end{rawhtml}
904  goto code  goto code
905  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
906  }  }
# Line 912  code to generate a valid Line 919  code to generate a valid
919  file.    file.  
920  The variable  The variable
921  {\bf  {\bf
922  \begin{rawhtml} <A href=../../../code_reference/vdb/names/13W.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/13W.htm> \end{rawhtml}
923  zonalWindFile  zonalWindFile
924  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
925  }  }
926  is read in the routine  is read in the routine
927  {\it  {\it
928  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
929  INI\_PARMS  INI\_PARMS
930  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
931  }.  The wind-stress file is read in the routine  }.  The wind-stress file is read in the routine
# Line 930  INI\_PARMS Line 937  INI\_PARMS
937  \end{minipage}  \end{minipage}
938  }  }
939  {\bf  {\bf
940  \begin{rawhtml} <A href=../../../code_reference/vdb/code/75.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/75.htm> \end{rawhtml}
941  goto code  goto code
942  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
943  }  }
# Line 946  goto code Line 953  goto code
953  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
954    
955  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
956    \label{www:tutorials}
957    
958  This file uses standard default values and does not contain  This file uses standard default values and does not contain
959  customisations for this experiment.  customisations for this experiment.
960    
961  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
962    \label{www:tutorials}
963    
964  This file uses standard default values and does not contain  This file uses standard default values and does not contain
965  customisations for this experiment.  customisations for this experiment.
966    
967  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
968    \label{www:tutorials}
969    
970  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
971  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the
# Line 969  The included matlab program {\it input/g Line 979  The included matlab program {\it input/g
979  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
980    
981  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
982    \label{www:tutorials}
983    
984    
985  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 980  The included matlab program {\it input/g Line 991  The included matlab program {\it input/g
991  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
992    
993  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
994    \label{www:tutorials}
995    
996  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
997    
# Line 1006  the vertical domain extent in grid point Line 1018  the vertical domain extent in grid point
1018  \end{small}  \end{small}
1019    
1020  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
1021    \label{www:tutorials}
1022    
1023  This file uses standard default values and does not contain  This file uses standard default values and does not contain
1024  customisations for this experiment.  customisations for this experiment.
1025    
1026    
1027  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
1028    \label{www:tutorials}
1029    
1030  This file uses standard default values and does not contain  This file uses standard default values and does not contain
1031  customisations for this experiment.  customisations for this experiment.
1032    
1033  \subsubsection{Other Files }  \subsubsection{Other Files }
1034    \label{www:tutorials}
1035    
1036  Other files relevant to this experiment are  Other files relevant to this experiment are
1037  \begin{itemize}  \begin{itemize}
# Line 1029  dxF, dyF, dxG, dyG, dxC, dyC}. Line 1044  dxF, dyF, dxG, dyG, dxC, dyC}.
1044  \end{itemize}  \end{itemize}
1045    
1046  \subsection{Running The Example}  \subsection{Running The Example}
1047    \label{www:tutorials}
1048  \label{SEC:running_the_example}  \label{SEC:running_the_example}
1049    
1050  \subsubsection{Code Download}  \subsubsection{Code Download}
1051    \label{www:tutorials}
1052    
1053   In order to run the examples you must first download the code distribution.   In order to run the examples you must first download the code distribution.
1054  Instructions for downloading the code can be found in section  Instructions for downloading the code can be found in section
1055  \ref{sect:obtainingCode}.  \ref{sect:obtainingCode}.
1056    
1057  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
1058    \label{www:tutorials}
1059    
1060   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
1061    
# Line 1045  Instructions for downloading the code ca Line 1063  Instructions for downloading the code ca
1063  {\it verification/exp2/ }  {\it verification/exp2/ }
1064    
1065  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
1066    \label{www:tutorials}
1067    
1068   To run the experiment   To run the experiment
1069    
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