s_examples/barotropic_gyre/baro.tex

% $Header: /u/gcmpack/manual/part3/case_studies/barotropic_gyre/baro.tex,v 1.11 2004/10/13 05:06:26 cnh Exp $
% $Name:  $

\bodytext{bgcolor="#FFFFFFFF"}

%\begin{center} 
%{\Large \bf Using MITgcm to Simulate a Barotropic Ocean Gyre In Cartesian
%Coordinates}
%
%\vspace*{4mm}
%
%\vspace*{3mm}
%{\large May 2001}
%\end{center}

This is the first in a series of tutorials describing
example MITgcm numerical experiments. The example experiments 
include both straightforward examples of idealized geophysical 
fluid simulations and more involved cases encompassing
large scale modeling and
automatic differentiation. Both hydrostatic and non-hydrostatic 
experiments are presented, as well as experiments employing
Cartesian, spherical-polar and cube-sphere coordinate systems.
These ``case study'' documents include information describing
the experimental configuration and detailed information on how to
configure the MITgcm code and input files for each experiment.

\section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}
\label{sect:eg-baro}
\label{www:tutorials}
\begin{rawhtml}
<!-- CMIREDIR:eg-baro: -->
\end{rawhtml}


This example experiment demonstrates using the MITgcm to simulate
a Barotropic, wind-forced, ocean gyre circulation. The experiment 
is a numerical rendition of the gyre circulation problem similar
to the problems described analytically by Stommel in 1966 
\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.

In this experiment the model 
is configured to represent a rectangular enclosed box of fluid,
$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
in the ``north-south'' direction. Topologically the grid is Cartesian and 
the coriolis parameter $f$ is defined according to a mid-latitude beta-plane 
equation

\begin{equation}
\label{EQ:eg-baro-fcori}
f(y) = f_{0}+\beta y
\end{equation}
 
\noindent where $y$ is the distance along the ``north-south'' axis of the 
simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in 
(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. 
\\
\\
 The sinusoidal wind-stress variations are defined according to 

\begin{equation}
\label{EQ:eg-baro-taux}
\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
\end{equation}
 
\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and 
$\tau_0$ is set to $0.1N m^{-2}$. 
\\
\\
Figure \ref{FIG:eg-baro-simulation_config}
summarizes the configuration simulated.

%% === eh3 ===
\begin{figure}
%% \begin{center}
%%  \resizebox{7.5in}{5.5in}{
%%    \includegraphics*[0.2in,0.7in][10.5in,10.5in]
%%     {part3/case_studies/barotropic_gyre/simulation_config.eps} }
%% \end{center}
\centerline{
  \scalefig{.95}
  \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
}
\caption{Schematic of simulation domain and wind-stress forcing function 
for barotropic gyre numerical experiment. The domain is enclosed bu solid
walls at $x=$~0,1200km and at $y=$~0,1200km.}
\label{FIG:eg-baro-simulation_config}
\end{figure}

\subsection{Equations Solved}
\label{www:tutorials}
The model is configured in hydrostatic form. The implicit free surface form of the
pressure equation described in Marshall et. al \cite{marshall:97a} is
employed.
A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
dissipation. The wind-stress momentum input is added to the momentum equation
for the ``zonal flow'', $u$. Other terms in the model
are explicitly switched off for this experiment configuration (see section
\ref{SEC:code_config} ), yielding an active set of equations solved in this
configuration as follows 

\begin{eqnarray}
\label{EQ:eg-baro-model_equations}
\frac{Du}{Dt} - fv +
              g\frac{\partial \eta}{\partial x} -
              A_{h}\nabla_{h}^2u
& = &
\frac{\tau_{x}}{\rho_{0}\Delta z}
\\
\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
              A_{h}\nabla_{h}^2v
& = &
0
\\
\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
&=&
0
\end{eqnarray}

\noindent where $u$ and $v$ and the $x$ and $y$ components of the
flow vector $\vec{u}$.
\\


\subsection{Discrete Numerical Configuration}
\label{www:tutorials}

 The domain is discretised with 
a uniform grid spacing in the horizontal set to
 $\Delta x=\Delta y=20$~km, so 
that there are sixty grid cells in the $x$ and $y$ directions. Vertically the 
model is configured with a single layer with depth, $\Delta z$, of $5000$~m. 

\subsubsection{Numerical Stability Criteria}
\label{www:tutorials}

The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
This value is chosen to yield a Munk layer width \cite{adcroft:95},

\begin{eqnarray}
\label{EQ:eg-baro-munk_layer}
M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
\end{eqnarray}

\noindent  of $\approx 100$km. This is greater than the model
resolution $\Delta x$, ensuring that the frictional boundary
layer is well resolved.
\\

\noindent The model is stepped forward with a 
time step $\delta t=1200$secs. With this time step the stability 
parameter to the horizontal Laplacian friction \cite{adcroft:95}


\begin{eqnarray}
\label{EQ:eg-baro-laplacian_stability}
S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
\end{eqnarray}

\noindent evaluates to 0.012, which is well below the 0.3 upper limit
for stability. 
\\

\noindent The numerical stability for inertial oscillations  
\cite{adcroft:95} 

\begin{eqnarray}
\label{EQ:eg-baro-inertial_stability}
S_{i} = f^{2} {\delta t}^2
\end{eqnarray}

\noindent evaluates to $0.0144$, which is well below the $0.5$ upper 
limit for stability.
\\

\noindent The advective CFL \cite{adcroft:95} for an extreme maximum 
horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$

\begin{eqnarray}
\label{EQ:eg-baro-cfl_stability}
S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
\end{eqnarray}

\noindent evaluates to 0.12. This is approaching the stability limit
of 0.5 and limits $\delta t$ to $1200s$.

\subsection{Code Configuration}
\label{www:tutorials}
\label{SEC:eg-baro-code_config}

The model configuration for this experiment resides under the 
directory {\it verification/exp0/}.  The experiment files 
\begin{itemize}
\item {\it input/data}
\item {\it input/data.pkg}
\item {\it input/eedata},
\item {\it input/windx.sin\_y},
\item {\it input/topog.box},
\item {\it code/CPP\_EEOPTIONS.h}
\item {\it code/CPP\_OPTIONS.h},
\item {\it code/SIZE.h}. 
\end{itemize}
contain the code customizations and parameter settings for this 
experiments. Below we describe the customizations
to these files associated with this experiment.

\subsubsection{File {\it input/data}}
\label{www:tutorials}

This file, reproduced completely below, specifies the main parameters 
for the experiment. The parameters that are significant for this configuration
are

\begin{itemize}

\item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets
the Laplacian friction coefficient to $400 m^2s^{-1}$
\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$

\item Lines 15 and 16
\begin{verbatim}
rigidLid=.FALSE.,
implicitFreeSurface=.TRUE.,
\end{verbatim}
these lines suppress the rigid lid formulation of the surface
pressure inverter and activate the implicit free surface form
of the pressure inverter.

\item Line 27,
\begin{verbatim}
startTime=0,
\end{verbatim}
this line indicates that the experiment should start from $t=0$
and implicitly suppresses searching for checkpoint files associated
with restarting an numerical integration from a previously saved state.

\item Line 29,
\begin{verbatim}
endTime=12000,
\end{verbatim}
this line indicates that the experiment should start finish at $t=12000s$.
A restart file will be written at this time that will enable the
simulation to be continued from this point.

\item Line 30,
\begin{verbatim}
deltaTmom=1200,
\end{verbatim}
This line sets the momentum equation timestep to $1200s$.

\item Line 39,
\begin{verbatim}
usingCartesianGrid=.TRUE.,
\end{verbatim}
This line requests that the simulation be performed in a 
Cartesian coordinate system.

\item Line 41,
\begin{verbatim}
delX=60*20E3,
\end{verbatim}
This line sets the horizontal grid spacing between each x-coordinate line
in the discrete grid. The syntax indicates that the discrete grid
should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$
($20$~km).

\item Line 42,
\begin{verbatim}
delY=60*20E3,
\end{verbatim}
This line sets the horizontal grid spacing between each y-coordinate line
in the discrete grid to $20 \times 10^{3}m$ ($20$~km).

\item Line 43,
\begin{verbatim}
delZ=5000,
\end{verbatim}
This line sets the vertical grid spacing between each z-coordinate line
in the discrete grid to $5000m$ ($5$~km).

\item Line 46,
\begin{verbatim}
bathyFile='topog.box'
\end{verbatim}
This line specifies the name of the file from which the domain
bathymetry is read. This file is a two-dimensional ($x,y$) map of
depths. This file is assumed to contain 64-bit binary numbers 
giving the depth of the model at each grid cell, ordered with the x 
coordinate varying fastest. The points are ordered from low coordinate
to high coordinate for both axes. The units and orientation of the
depths in this file are the same as used in the MITgcm code. In this
experiment, a depth of $0m$ indicates a solid wall and a depth
of $-5000m$ indicates open ocean. The matlab program
{\it input/gendata.m} shows an example of how to generate a
bathymetry file.


\item Line 49,
\begin{verbatim}
zonalWindFile='windx.sin_y'
\end{verbatim}
This line specifies the name of the file from which the x-direction
surface wind stress is read. This file is also a two-dimensional
($x,y$) map and is enumerated and formatted in the same manner as the 
bathymetry file. The matlab program {\it input/gendata.m} includes example 
code to generate a valid {\bf zonalWindFile} file.  

\end{itemize}

\noindent other lines in the file {\it input/data} are standard values
that are described in the MITgcm Getting Started and MITgcm Parameters
notes.

\begin{small}
\input{part3/case_studies/barotropic_gyre/input/data}
\end{small}

\subsubsection{File {\it input/data.pkg}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.

\subsubsection{File {\it input/eedata}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.

\subsubsection{File {\it input/windx.sin\_y}}
\label{www:tutorials}

The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) 
map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
Although $\tau_{x}$ is only a function of $y$n in this experiment
this file must still define a complete two-dimensional map in order
to be compatible with the standard code for loading forcing fields 
in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
code for creating the {\it input/windx.sin\_y} file.

\subsubsection{File {\it input/topog.box}}
\label{www:tutorials}


The {\it input/topog.box} file specifies a two-dimensional ($x,y$) 
map of depth values. For this experiment values are either
$0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep
ocean. The file contains a raw binary stream of data that is enumerated
in the same way as standard MITgcm two-dimensional, horizontal arrays.
The included matlab program {\it input/gendata.m} gives a complete
code for creating the {\it input/topog.box} file.

\subsubsection{File {\it code/SIZE.h}}
\label{www:tutorials}

Two lines are customized in this file for the current experiment

\begin{itemize}

\item Line 39, 
\begin{verbatim} sNx=60, \end{verbatim} this line sets
the lateral domain extent in grid points for the
axis aligned with the x-coordinate.

\item Line 40, 
\begin{verbatim} sNy=60, \end{verbatim} this line sets
the lateral domain extent in grid points for the
axis aligned with the y-coordinate.

\end{itemize}

\begin{small}
\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
\end{small}

\subsubsection{File {\it code/CPP\_OPTIONS.h}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.


\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.

1	edhill	1.12	% $Header: /u/gcmpack/manual/part3/case_studies/barotropic_gyre/baro.tex,v 1.11 2004/10/13 05:06:26 cnh Exp $
2	cnh	1.2	% $Name: $
3	adcroft	1.1
4			\bodytext{bgcolor="#FFFFFFFF"}
5
6			%\begin{center}
7			%{\Large \bf Using MITgcm to Simulate a Barotropic Ocean Gyre In Cartesian
8			%Coordinates}
9			%
10			%\vspace*{4mm}
11			%
12			%\vspace*{3mm}
13			%{\large May 2001}
14			%\end{center}
15
16	cnh	1.8	This is the first in a series of tutorials describing
17	adcroft	1.1	example MITgcm numerical experiments. The example experiments
18	cnh	1.4	include both straightforward examples of idealized geophysical
19	adcroft	1.1	fluid simulations and more involved cases encompassing
20			large scale modeling and
21			automatic differentiation. Both hydrostatic and non-hydrostatic
22	cnh	1.3	experiments are presented, as well as experiments employing
23	cnh	1.4	Cartesian, spherical-polar and cube-sphere coordinate systems.
24	adcroft	1.1	These ``case study'' documents include information describing
25			the experimental configuration and detailed information on how to
26			configure the MITgcm code and input files for each experiment.
27
28	cnh	1.11	\section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}
29	cnh	1.8	\label{sect:eg-baro}
30	adcroft	1.9	\label{www:tutorials}
31	edhill	1.12	\begin{rawhtml}
32			<!-- CMIREDIR:eg-baro: -->
33			\end{rawhtml}
34	cnh	1.8
35	adcroft	1.1
36			This example experiment demonstrates using the MITgcm to simulate
37	cnh	1.4	a Barotropic, wind-forced, ocean gyre circulation. The experiment
38			is a numerical rendition of the gyre circulation problem similar
39	adcroft	1.1	to the problems described analytically by Stommel in 1966
40			\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
41
42			In this experiment the model
43			is configured to represent a rectangular enclosed box of fluid,
44			$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
45			by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
46	cnh	1.4	in the ``north-south'' direction. Topologically the grid is Cartesian and
47	adcroft	1.1	the coriolis parameter $f$ is defined according to a mid-latitude beta-plane
48			equation
49
50			\begin{equation}
51	cnh	1.8	\label{EQ:eg-baro-fcori}
52	adcroft	1.1	f(y) = f_{0}+\beta y
53			\end{equation}
54
55			\noindent where $y$ is the distance along the ``north-south'' axis of the
56			simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in
57	cnh	1.8	(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
58	adcroft	1.1	\\
59			\\
60			The sinusoidal wind-stress variations are defined according to
61
62			\begin{equation}
63	cnh	1.8	\label{EQ:eg-baro-taux}
64	adcroft	1.1	\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
65			\end{equation}
66
67			\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and
68			$\tau_0$ is set to $0.1N m^{-2}$.
69			\\
70			\\
71	cnh	1.8	Figure \ref{FIG:eg-baro-simulation_config}
72	cnh	1.4	summarizes the configuration simulated.
73	adcroft	1.1
74	edhill	1.10	%% === eh3 ===
75	adcroft	1.1	\begin{figure}
76	edhill	1.10	%% \begin{center}
77			%% \resizebox{7.5in}{5.5in}{
78			%% \includegraphics*[0.2in,0.7in][10.5in,10.5in]
79			%% {part3/case_studies/barotropic_gyre/simulation_config.eps} }
80			%% \end{center}
81			\centerline{
82			\scalefig{.95}
83			\epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
84			}
85	adcroft	1.1	\caption{Schematic of simulation domain and wind-stress forcing function
86			for barotropic gyre numerical experiment. The domain is enclosed bu solid
87			walls at $x=$~0,1200km and at $y=$~0,1200km.}
88	cnh	1.8	\label{FIG:eg-baro-simulation_config}
89	adcroft	1.1	\end{figure}
90
91	cnh	1.3	\subsection{Equations Solved}
92	adcroft	1.9	\label{www:tutorials}
93	cnh	1.3	The model is configured in hydrostatic form. The implicit free surface form of the
94	adcroft	1.6	pressure equation described in Marshall et. al \cite{marshall:97a} is
95	cnh	1.3	employed.
96	cnh	1.4	A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
97	adcroft	1.1	dissipation. The wind-stress momentum input is added to the momentum equation
98			for the ``zonal flow'', $u$. Other terms in the model
99	cnh	1.4	are explicitly switched off for this experiment configuration (see section
100	cnh	1.3	\ref{SEC:code_config} ), yielding an active set of equations solved in this
101			configuration as follows
102	adcroft	1.1
103			\begin{eqnarray}
104	cnh	1.8	\label{EQ:eg-baro-model_equations}
105	cnh	1.3	\frac{Du}{Dt} - fv +
106			g\frac{\partial \eta}{\partial x} -
107			A_{h}\nabla_{h}^2u
108	adcroft	1.1	& = &
109			\frac{\tau_{x}}{\rho_{0}\Delta z}
110			\\
111			\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
112	cnh	1.3	A_{h}\nabla_{h}^2v
113	adcroft	1.1	& = &
114			0
115			\\
116			\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
117			&=&
118			0
119			\end{eqnarray}
120
121			\noindent where $u$ and $v$ and the $x$ and $y$ components of the
122	cnh	1.3	flow vector $\vec{u}$.
123	adcroft	1.1	\\
124	cnh	1.3
125
126			\subsection{Discrete Numerical Configuration}
127	adcroft	1.9	\label{www:tutorials}
128	cnh	1.3
129			The domain is discretised with
130			a uniform grid spacing in the horizontal set to
131			$\Delta x=\Delta y=20$~km, so
132			that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
133			model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
134	adcroft	1.1
135			\subsubsection{Numerical Stability Criteria}
136	adcroft	1.9	\label{www:tutorials}
137	adcroft	1.1
138	cnh	1.4	The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
139	adcroft	1.5	This value is chosen to yield a Munk layer width \cite{adcroft:95},
140	adcroft	1.1
141			\begin{eqnarray}
142	cnh	1.8	\label{EQ:eg-baro-munk_layer}
143	adcroft	1.1	M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
144			\end{eqnarray}
145
146			\noindent of $\approx 100$km. This is greater than the model
147			resolution $\Delta x$, ensuring that the frictional boundary
148			layer is well resolved.
149			\\
150
151			\noindent The model is stepped forward with a
152			time step $\delta t=1200$secs. With this time step the stability
153	adcroft	1.5	parameter to the horizontal Laplacian friction \cite{adcroft:95}
154	adcroft	1.1
155
156
157			\begin{eqnarray}
158	cnh	1.8	\label{EQ:eg-baro-laplacian_stability}
159	adcroft	1.1	S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
160			\end{eqnarray}
161
162			\noindent evaluates to 0.012, which is well below the 0.3 upper limit
163			for stability.
164			\\
165
166			\noindent The numerical stability for inertial oscillations
167	adcroft	1.5	\cite{adcroft:95}
168	adcroft	1.1
169			\begin{eqnarray}
170	cnh	1.8	\label{EQ:eg-baro-inertial_stability}
171	adcroft	1.1	S_{i} = f^{2} {\delta t}^2
172			\end{eqnarray}
173
174			\noindent evaluates to $0.0144$, which is well below the $0.5$ upper
175			limit for stability.
176			\\
177
178	adcroft	1.5	\noindent The advective CFL \cite{adcroft:95} for an extreme maximum
179	adcroft	1.1	horizontal flow speed of $ \| \vec{u} \| = 2 ms^{-1}$
180
181			\begin{eqnarray}
182	cnh	1.8	\label{EQ:eg-baro-cfl_stability}
183	adcroft	1.1	S_{a} = \frac{\| \vec{u} \| \delta t}{ \Delta x}
184			\end{eqnarray}
185
186			\noindent evaluates to 0.12. This is approaching the stability limit
187			of 0.5 and limits $\delta t$ to $1200s$.
188
189			\subsection{Code Configuration}
190	adcroft	1.9	\label{www:tutorials}
191	cnh	1.8	\label{SEC:eg-baro-code_config}
192	adcroft	1.1
193			The model configuration for this experiment resides under the
194			directory {\it verification/exp0/}. The experiment files
195			\begin{itemize}
196			\item {\it input/data}
197			\item {\it input/data.pkg}
198			\item {\it input/eedata},
199			\item {\it input/windx.sin\_y},
200			\item {\it input/topog.box},
201			\item {\it code/CPP\_EEOPTIONS.h}
202			\item {\it code/CPP\_OPTIONS.h},
203			\item {\it code/SIZE.h}.
204			\end{itemize}
205	cnh	1.4	contain the code customizations and parameter settings for this
206			experiments. Below we describe the customizations
207	adcroft	1.1	to these files associated with this experiment.
208
209			\subsubsection{File {\it input/data}}
210	adcroft	1.9	\label{www:tutorials}
211	adcroft	1.1
212			This file, reproduced completely below, specifies the main parameters
213			for the experiment. The parameters that are significant for this configuration
214			are
215
216			\begin{itemize}
217
218			\item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets
219	cnh	1.4	the Laplacian friction coefficient to $400 m^2s^{-1}$
220	adcroft	1.1	\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
221			$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
222
223			\item Lines 15 and 16
224			\begin{verbatim}
225			rigidLid=.FALSE.,
226			implicitFreeSurface=.TRUE.,
227			\end{verbatim}
228			these lines suppress the rigid lid formulation of the surface
229			pressure inverter and activate the implicit free surface form
230			of the pressure inverter.
231
232			\item Line 27,
233			\begin{verbatim}
234			startTime=0,
235			\end{verbatim}
236			this line indicates that the experiment should start from $t=0$
237	cnh	1.4	and implicitly suppresses searching for checkpoint files associated
238	adcroft	1.1	with restarting an numerical integration from a previously saved state.
239
240			\item Line 29,
241			\begin{verbatim}
242			endTime=12000,
243			\end{verbatim}
244			this line indicates that the experiment should start finish at $t=12000s$.
245			A restart file will be written at this time that will enable the
246			simulation to be continued from this point.
247
248			\item Line 30,
249			\begin{verbatim}
250			deltaTmom=1200,
251			\end{verbatim}
252			This line sets the momentum equation timestep to $1200s$.
253
254			\item Line 39,
255			\begin{verbatim}
256			usingCartesianGrid=.TRUE.,
257			\end{verbatim}
258			This line requests that the simulation be performed in a
259	cnh	1.4	Cartesian coordinate system.
260	adcroft	1.1
261			\item Line 41,
262			\begin{verbatim}
263			delX=60*20E3,
264			\end{verbatim}
265			This line sets the horizontal grid spacing between each x-coordinate line
266			in the discrete grid. The syntax indicates that the discrete grid
267			should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$
268			($20$~km).
269
270			\item Line 42,
271			\begin{verbatim}
272			delY=60*20E3,
273			\end{verbatim}
274			This line sets the horizontal grid spacing between each y-coordinate line
275			in the discrete grid to $20 \times 10^{3}m$ ($20$~km).
276
277			\item Line 43,
278			\begin{verbatim}
279			delZ=5000,
280			\end{verbatim}
281			This line sets the vertical grid spacing between each z-coordinate line
282			in the discrete grid to $5000m$ ($5$~km).
283
284			\item Line 46,
285			\begin{verbatim}
286			bathyFile='topog.box'
287			\end{verbatim}
288			This line specifies the name of the file from which the domain
289			bathymetry is read. This file is a two-dimensional ($x,y$) map of
290			depths. This file is assumed to contain 64-bit binary numbers
291			giving the depth of the model at each grid cell, ordered with the x
292			coordinate varying fastest. The points are ordered from low coordinate
293			to high coordinate for both axes. The units and orientation of the
294			depths in this file are the same as used in the MITgcm code. In this
295			experiment, a depth of $0m$ indicates a solid wall and a depth
296			of $-5000m$ indicates open ocean. The matlab program
297			{\it input/gendata.m} shows an example of how to generate a
298			bathymetry file.
299
300
301			\item Line 49,
302			\begin{verbatim}
303			zonalWindFile='windx.sin_y'
304			\end{verbatim}
305			This line specifies the name of the file from which the x-direction
306			surface wind stress is read. This file is also a two-dimensional
307			($x,y$) map and is enumerated and formatted in the same manner as the
308			bathymetry file. The matlab program {\it input/gendata.m} includes example
309			code to generate a valid {\bf zonalWindFile} file.
310
311			\end{itemize}
312
313			\noindent other lines in the file {\it input/data} are standard values
314			that are described in the MITgcm Getting Started and MITgcm Parameters
315			notes.
316
317			\begin{small}
318			\input{part3/case_studies/barotropic_gyre/input/data}
319			\end{small}
320
321			\subsubsection{File {\it input/data.pkg}}
322	adcroft	1.9	\label{www:tutorials}
323	adcroft	1.1
324			This file uses standard default values and does not contain
325	cnh	1.4	customizations for this experiment.
326	adcroft	1.1
327			\subsubsection{File {\it input/eedata}}
328	adcroft	1.9	\label{www:tutorials}
329	adcroft	1.1
330			This file uses standard default values and does not contain
331	cnh	1.4	customizations for this experiment.
332	adcroft	1.1
333			\subsubsection{File {\it input/windx.sin\_y}}
334	adcroft	1.9	\label{www:tutorials}
335	adcroft	1.1
336			The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
337			map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
338			Although $\tau_{x}$ is only a function of $y$n in this experiment
339			this file must still define a complete two-dimensional map in order
340			to be compatible with the standard code for loading forcing fields
341			in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
342			code for creating the {\it input/windx.sin\_y} file.
343
344			\subsubsection{File {\it input/topog.box}}
345	adcroft	1.9	\label{www:tutorials}
346	adcroft	1.1
347
348			The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
349			map of depth values. For this experiment values are either
350			$0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep
351			ocean. The file contains a raw binary stream of data that is enumerated
352			in the same way as standard MITgcm two-dimensional, horizontal arrays.
353			The included matlab program {\it input/gendata.m} gives a complete
354			code for creating the {\it input/topog.box} file.
355
356			\subsubsection{File {\it code/SIZE.h}}
357	adcroft	1.9	\label{www:tutorials}
358	adcroft	1.1
359			Two lines are customized in this file for the current experiment
360
361			\begin{itemize}
362
363			\item Line 39,
364			\begin{verbatim} sNx=60, \end{verbatim} this line sets
365			the lateral domain extent in grid points for the
366			axis aligned with the x-coordinate.
367
368			\item Line 40,
369			\begin{verbatim} sNy=60, \end{verbatim} this line sets
370			the lateral domain extent in grid points for the
371			axis aligned with the y-coordinate.
372
373			\end{itemize}
374
375			\begin{small}
376			\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
377			\end{small}
378
379			\subsubsection{File {\it code/CPP\_OPTIONS.h}}
380	adcroft	1.9	\label{www:tutorials}
381	adcroft	1.1
382			This file uses standard default values and does not contain
383	cnh	1.4	customizations for this experiment.
384	adcroft	1.1
385
386			\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
387	adcroft	1.9	\label{www:tutorials}
388	adcroft	1.1
389			This file uses standard default values and does not contain
390	cnh	1.4	customizations for this experiment.
391	adcroft	1.1