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revision 1.1 by adcroft, Wed Aug 8 16:16:05 2001 UTC revision 1.14 by molod, Tue Jun 27 19:08:22 2006 UTC
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1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}  \section[Global Ocean MITgcm Exmaple]{Global Ocean Simulation at $4^\circ$ Resolution}
5    \label{www:tutorials}
6    \label{sect:eg-global}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-global: -->
9    \end{rawhtml}
10    
11  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
12    
13  %\begin{center}  %\begin{center}
14  %{\Large \bf Using MITgcm to Simulate Global Climatalogical Ocean Circulation  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
15  %At Four Degree Resolution with Asynchronous Time Stepping}  %At Four Degree Resolution with Asynchronous Time Stepping}
16  %  %
17  %\vspace*{4mm}  %\vspace*{4mm}
# Line 15  Line 20 
20  %{\large May 2001}  %{\large May 2001}
21  %\end{center}  %\end{center}
22    
 \subsection{Introduction}  
   
 This document describes the third example MITgcm experiment. The first  
 two examples illustrated how to configure the code for hydrostatic idealised  
 geophysical fluids simulations. This example iilustrates the use of  
 the MITgcm for large scale ocean circulation simulation.  
   
 \subsection{Overview}  
23    
24  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
25  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
26  with realistic geography and bathymetry on a  with realistic geography and bathymetry on a
27  $4^{\circ} \times 4^{\circ}$ spherical polar grid.  $4^{\circ} \times 4^{\circ}$ spherical polar grid.
28    The files for this experiment are in the verification directory
29    under tutorial\_global\_oce\_latlon.
30  Twenty levels are used in the vertical, ranging in thickness  Twenty levels are used in the vertical, ranging in thickness
31  from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,  from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,
32  giving a maximum model depth of $6\,{\rm km}$.  giving a maximum model depth of $6\,{\rm km}$.
# Line 35  At this resolution, the configuration Line 34  At this resolution, the configuration
34  can be integrated forward for thousands of years on a single  can be integrated forward for thousands of years on a single
35  processor desktop computer.  processor desktop computer.
36  \\  \\
37    \subsection{Overview}
38    \label{www:tutorials}
39    
40  The model is forced with climatalogical wind stress data and surface  The model is forced with climatological wind stress data and surface
41  flux data from DaSilva \cite{DaSilva94}. Climatalogical data  flux data from DaSilva \cite{DaSilva94}. Climatological data
42  from Levitus \cite{Levitus94} is used to initialise the model hydrography.  from Levitus \cite{Levitus94} is used to initialize the model hydrography.
43  Levitus seasonal clmatology data is also used throughout the calculation  Levitus seasonal climatology data is also used throughout the calculation
44  to provide additional air-sea fluxes.  to provide additional air-sea fluxes.
45  These fluxes are combined with the DaSilva climatalogical estimates of  These fluxes are combined with the DaSilva climatological estimates of
46  surface heat flux and fresh water, resulting in a mixed boundary  surface heat flux and fresh water, resulting in a mixed boundary
47  condition of the style decribed in Haney \cite{Haney}.  condition of the style described in Haney \cite{Haney}.
48  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied
49  in the model surface layer.  in the model surface layer.
50    
51  \begin{eqnarray}  \begin{eqnarray}
52  \label{EQ:global_forcing}  \label{EQ:eg-global-global_forcing}
53  \label{EQ:global_forcing_fu}  \label{EQ:eg-global-global_forcing_fu}
54  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
55  \\  \\
56  \label{EQ:global_forcing_fv}  \label{EQ:eg-global-global_forcing_fv}
57  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
58  \\  \\
59  \label{EQ:global_forcing_ft}  \label{EQ:eg-global-global_forcing_ft}
60  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
61   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
62  \\  \\
63  \label{EQ:global_forcing_fs}  \label{EQ:eg-global-global_forcing_fs}
64  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
65   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
66  \end{eqnarray}  \end{eqnarray}
# Line 86  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th
87  ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$  ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$
88  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
89  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
90  respectively.  respectively. The source files and procedures for ingesting this data into the
91  \\  simulation are described in the experiment configuration discussion in section
92    \ref{SEC:eg-global-clim_ocn_examp_exp_config}.
   
 Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the  
 relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,  
 the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)  
 and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used  
 in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures  
 also indicate the lateral extent and coastline used in the experiment.  
 Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model  
 domain.  
93    
94    
95  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
96    \label{www:tutorials}
97    
98    
99   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 108  a uniform grid spacing in latitude and l Line 101  a uniform grid spacing in latitude and l
101   $\Delta \phi=\Delta \lambda=4^{\circ}$, so   $\Delta \phi=\Delta \lambda=4^{\circ}$, so
102  that there are ninety grid cells in the zonal and forty in the  that there are ninety grid cells in the zonal and forty in the
103  meridional direction. The internal model coordinate variables  meridional direction. The internal model coordinate variables
104  $x$ and $y$ are initialised according to  $x$ and $y$ are initialized according to
105  \begin{eqnarray}  \begin{eqnarray}
106  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
107  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
108  \end{eqnarray}  \end{eqnarray}
109    
110  Arctic polar regions are not  Arctic polar regions are not
# Line 145  $ Line 138  $
138   \Delta z_{18}=725\,{\rm m},\,   \Delta z_{18}=725\,{\rm m},\,
139   \Delta z_{19}=775\,{\rm m},\,   \Delta z_{19}=775\,{\rm m},\,
140   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
141  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$) to
142    give a total depth, $H$, of $-5450{\rm m}$.
143  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
144  \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
145  dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
146    
147  Wind-stress forcing is added to the momentum equations for both  Wind-stress forcing is added to the momentum equations in (\ref{EQ:eg-global-model_equations})
148  the zonal flow, $u$ and the merdional flow $v$, according to equations  for both the zonal flow, $u$ and the meridional flow $v$, according to equations
149  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:eg-global-global_forcing_fu}) and (\ref{EQ:eg-global-global_forcing_fv}).
150  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations
151    in (\ref{EQ:eg-global-model_equations}) for
152  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
153  (\ref{EQ:global_forcing_ft}) and (\ref{EQ:global_forcing_fs}).  (\ref{EQ:eg-global-global_forcing_ft}) and (\ref{EQ:eg-global-global_forcing_fs}).
154  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
155    
156  \begin{eqnarray}  \begin{eqnarray}
157  \label{EQ:model_equations}  \label{EQ:eg-global-model_equations}
158  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
159    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
160    \nabla_{h}\cdot A_{h}\nabla_{h}u -    \nabla_{h}\cdot A_{h}\nabla_{h}u -
# Line 209  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d Line 204  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
204  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
205  are the zonal and meridional components of the  are the zonal and meridional components of the
206  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
207  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
208  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
209  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
210  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
211  \\  \\
212    
213  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
214    \label{www:tutorials}
215    
216  The laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
217  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:95},
218  \begin{eqnarray}  \begin{eqnarray}
219  \label{EQ:munk_layer}  \label{EQ:eg-global-munk_layer}
220  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
221  \end{eqnarray}  \end{eqnarray}
222    
223  \noindent  of $\approx 600$km. This is greater than the model  \noindent  of $\approx 600$km. This is greater than the model
# Line 232  boundary layer is adequately resolved. Line 228  boundary layer is adequately resolved.
228  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
229  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
230  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
231  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
232  \begin{eqnarray}  \begin{eqnarray}
233  \label{EQ:laplacian_stability}  \label{EQ:eg-global-laplacian_stability}
234  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
235  \end{eqnarray}  \end{eqnarray}
236    
237  \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the  \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the
# Line 246  $\phi=80^{\circ}$ where $\Delta x=r\cos( Line 242  $\phi=80^{\circ}$ where $\Delta x=r\cos(
242  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
243  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
244  \begin{eqnarray}  \begin{eqnarray}
245  \label{EQ:laplacian_stability_z}  \label{EQ:eg-global-laplacian_stability_z}
246  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
247  \end{eqnarray}  \end{eqnarray}
248    
249  \noindent evaluates to $0.015$ for the smallest model  \noindent evaluates to $0.015$ for the smallest model
250  level spcing ($\Delta z_{1}=50{\rm m}$) which is again well below  level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
251  the upper stability limit.  the upper stability limit.
252  \\  \\
253    
# Line 261  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s} Line 257  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
257  related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.  related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
258  Here the stability parameter  Here the stability parameter
259  \begin{eqnarray}  \begin{eqnarray}
260  \label{EQ:laplacian_stability_xtheta}  \label{EQ:eg-global-laplacian_stability_xtheta}
261  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
262  \end{eqnarray}  \end{eqnarray}
263  evaluates to $0.07$, well below the stabilit limit of $S_{l} \approx 0.5$. The  evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
264  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
265  \begin{eqnarray}  \begin{eqnarray}
266  \label{EQ:laplacian_stability_ztheta}  \label{EQ:eg-global-laplacian_stability_ztheta}
267  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
268  \end{eqnarray}  \end{eqnarray}
269  evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit  evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
# Line 275  of $S_{l} \approx 0.5$. Line 271  of $S_{l} \approx 0.5$.
271  \\  \\
272    
273  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
274  \cite{Adcroft_thesis}  \cite{adcroft:95}
275    
276  \begin{eqnarray}  \begin{eqnarray}
277  \label{EQ:inertial_stability}  \label{EQ:eg-global-inertial_stability}
278  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
279  \end{eqnarray}  \end{eqnarray}
280    
# Line 286  S_{i} = f^{2} {\delta t_v}^2 Line 282  S_{i} = f^{2} {\delta t_v}^2
282  the $S_{i} < 1$ upper limit for stability.  the $S_{i} < 1$ upper limit for stability.
283  \\  \\
284    
285  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
286  horizontal flow  horizontal flow
287  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
288    
289  \begin{eqnarray}  \begin{eqnarray}
290  \label{EQ:cfl_stability}  \label{EQ:eg-global-cfl_stability}
291  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
292  \end{eqnarray}  \end{eqnarray}
293    
# Line 299  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ Line 295  S_{a} = \frac{| \vec{u} | \delta t_{v}}{
295  limit of 0.5.  limit of 0.5.
296  \\  \\
297    
298  \noindent The stability parameter for internal gravity waves propogating  \noindent The stability parameter for internal gravity waves propagating
299  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
300  \cite{Adcroft_thesis}  \cite{adcroft:95}
301    
302  \begin{eqnarray}  \begin{eqnarray}
303  \label{EQ:cfl_stability}  \label{EQ:eg-global-gfl_stability}
304  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
305  \end{eqnarray}  \end{eqnarray}
306    
# Line 312  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 308  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
308  stability limit of 0.5.  stability limit of 0.5.
309        
310  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
311  \label{SEC:clim_ocn_examp_exp_config}  \label{www:tutorials}
312    \label{SEC:eg-global-clim_ocn_examp_exp_config}
313    
314  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
315  directory {\it verification/exp2/}.  The experiment files  directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
316    The experiment files
317    
318  \begin{itemize}  \begin{itemize}
319  \item {\it input/data}  \item {\it input/data}
320  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 331  directory {\it verification/exp2/}.  The Line 330  directory {\it verification/exp2/}.  The
330  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
331  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
332  \end{itemize}  \end{itemize}
333  contain the code customisations and parameter settings for these  contain the code customizations and parameter settings for these
334  experiements. Below we describe the customisations  experiments. Below we describe the customizations
335  to these files associated with this experiment.  to these files associated with this experiment.
336    
337    \subsubsection{Driving Datasets}
338    \label{www:tutorials}
339    
340    Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
341    relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
342    the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
343    and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
344    in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures
345    also indicate the lateral extent and coastline used in the experiment.
346    Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
347    domain.
348    
349    
350  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
351    \label{www:tutorials}
352    
353  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
354  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 347  are Line 360  are
360  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}
361  $\cdots$ \\  $\cdots$ \\
362  set reference values for potential  set reference values for potential
363  temperature and salinity at each model level in units of $^{\circ}$C and  temperature and salinity at each model level in units of $^{\circ}\mathrm{C}$ and
364  ${\rm ppt}$. The entries are ordered from surface to depth.  ${\rm ppt}$. The entries are ordered from surface to depth.
365  Density is calculated from anomalies at each level evaluated  Density is calculated from anomalies at each level evaluated
366  with respect to the reference values set here.\\  with respect to the reference values set here.\\
# Line 360  with respect to the reference values set Line 373  with respect to the reference values set
373    
374  \item Line 15,  \item Line 15,
375  \begin{verbatim} viscAz=1.E-3, \end{verbatim}  \begin{verbatim} viscAz=1.E-3, \end{verbatim}
376  this line sets the vertical laplacian dissipation coefficient to  this line sets the vertical Laplacian dissipation coefficient to
377  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
378  for this operator are specified later. This variable is copied into  for this operator are specified later. This variable is copied into
379  model general vertical coordinate variable {\bf viscAr}.  model general vertical coordinate variable {\bf viscAr}.
# Line 375  model general vertical coordinate variab Line 388  model general vertical coordinate variab
388  \begin{verbatim}  \begin{verbatim}
389  viscAh=5.E5,  viscAh=5.E5,
390  \end{verbatim}  \end{verbatim}
391  this line sets the horizontal laplacian frictional dissipation coefficient to  this line sets the horizontal Laplacian frictional dissipation coefficient to
392  $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions  $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
393  for this operator are specified later.  for this operator are specified later.
394    
# Line 384  for this operator are specified later. Line 397  for this operator are specified later.
397  no_slip_sides=.FALSE.  no_slip_sides=.FALSE.
398  \end{verbatim}  \end{verbatim}
399  this line selects a free-slip lateral boundary condition for  this line selects a free-slip lateral boundary condition for
400  the horizontal laplacian friction operator  the horizontal Laplacian friction operator
401  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
402  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
403    
# Line 393  $\frac{\partial v}{\partial x}$=0 along Line 406  $\frac{\partial v}{\partial x}$=0 along
406  no_slip_bottom=.TRUE.  no_slip_bottom=.TRUE.
407  \end{verbatim}  \end{verbatim}
408  this line selects a no-slip boundary condition for bottom  this line selects a no-slip boundary condition for bottom
409  boundary condition in the vertical laplacian friction operator  boundary condition in the vertical Laplacian friction operator
410  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.
411    
412  \item Line 19,  \item Line 19,
# Line 443  These settings do not apply for this exp Line 456  These settings do not apply for this exp
456  \begin{verbatim}  \begin{verbatim}
457  gravity=9.81,  gravity=9.81,
458  \end{verbatim}  \end{verbatim}
459  Sets the gravitational acceleration coeeficient to $9.81{\rm m}{\rm s}^{-1}$.\\  Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
460  \fbox{  \fbox{
461  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
462  {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\  {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
# Line 625  notes. Line 638  notes.
638  \end{small}  \end{small}
639    
640  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
641    \label{www:tutorials}
642    
643  This file uses standard default values and does not contain  This file uses standard default values and does not contain
644  customisations for this experiment.  customisations for this experiment.
645    
646  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
647    \label{www:tutorials}
648    
649  This file uses standard default values and does not contain  This file uses standard default values and does not contain
650  customisations for this experiment.  customisations for this experiment.
651    
652  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
653    \label{www:tutorials}
654    
655  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
656  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 645  in MITgcm. The included matlab program { Line 661  in MITgcm. The included matlab program {
661  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
662    
663  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
664    \label{www:tutorials}
665    
666    
667  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 656  The included matlab program {\it input/g Line 673  The included matlab program {\it input/g
673  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
674    
675  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
676    \label{www:tutorials}
677    
678  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
679    
# Line 682  the vertical domain extent in grid point Line 700  the vertical domain extent in grid point
700  \end{small}  \end{small}
701    
702  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
703    \label{www:tutorials}
704    
705  This file uses standard default values and does not contain  This file uses standard default values and does not contain
706  customisations for this experiment.  customisations for this experiment.
707    
708    
709  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
710    \label{www:tutorials}
711    
712  This file uses standard default values and does not contain  This file uses standard default values and does not contain
713  customisations for this experiment.  customisations for this experiment.
714    
715  \subsubsection{Other Files }  \subsubsection{Other Files }
716    \label{www:tutorials}
717    
718  Other files relevant to this experiment are  Other files relevant to this experiment are
719  \begin{itemize}  \begin{itemize}
# Line 703  coriolis variables {\bf fCorU}. Line 724  coriolis variables {\bf fCorU}.
724  \item {\it input/windx.sin\_y},  \item {\it input/windx.sin\_y},
725  \end{itemize}  \end{itemize}
726  contain the code customisations and parameter settings for this  contain the code customisations and parameter settings for this
727  experiements. Below we describe the customisations  experiments. Below we describe the customisations
728  to these files associated with this experiment.  to these files associated with this experiment.
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