s_examples/barotropic_gyre/baro.tex

% $Header: /u/gcmpack/mitgcmdoc/part3/case_studies/barotropic_gyre/baro.tex,v 1.8 2002/02/28 19:32:19 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 Ocean Gyre In Cartesian Coordinates}
\label{sect:eg-baro}
\label{www:tutorials}


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.

\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}
\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	adcroft	1.9	% $Header: /u/gcmpack/mitgcmdoc/part3/case_studies/barotropic_gyre/baro.tex,v 1.8 2002/02/28 19:32:19 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	1.8	\section{Barotropic Ocean Gyre In Cartesian Coordinates}
29			\label{sect:eg-baro}
30	adcroft	1.9	\label{www:tutorials}
31	cnh	1.8
32	adcroft	1.1
33			This example experiment demonstrates using the MITgcm to simulate
34	cnh	1.4	a Barotropic, wind-forced, ocean gyre circulation. The experiment
35			is a numerical rendition of the gyre circulation problem similar
36	adcroft	1.1	to the problems described analytically by Stommel in 1966
37			\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
38
39			In this experiment the model
40			is configured to represent a rectangular enclosed box of fluid,
41			$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
42			by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
43	cnh	1.4	in the ``north-south'' direction. Topologically the grid is Cartesian and
44	adcroft	1.1	the coriolis parameter $f$ is defined according to a mid-latitude beta-plane
45			equation
46
47			\begin{equation}
48	cnh	1.8	\label{EQ:eg-baro-fcori}
49	adcroft	1.1	f(y) = f_{0}+\beta y
50			\end{equation}
51
52			\noindent where $y$ is the distance along the ``north-south'' axis of the
53			simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in
54	cnh	1.8	(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
55	adcroft	1.1	\\
56			\\
57			The sinusoidal wind-stress variations are defined according to
58
59			\begin{equation}
60	cnh	1.8	\label{EQ:eg-baro-taux}
61	adcroft	1.1	\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
62			\end{equation}
63
64			\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and
65			$\tau_0$ is set to $0.1N m^{-2}$.
66			\\
67			\\
68	cnh	1.8	Figure \ref{FIG:eg-baro-simulation_config}
69	cnh	1.4	summarizes the configuration simulated.
70	adcroft	1.1
71			\begin{figure}
72	cnh	1.2	\begin{center}
73	adcroft	1.1	\resizebox{7.5in}{5.5in}{
74			\includegraphics*[0.2in,0.7in][10.5in,10.5in]
75			{part3/case_studies/barotropic_gyre/simulation_config.eps} }
76	cnh	1.2	\end{center}
77	adcroft	1.1	\caption{Schematic of simulation domain and wind-stress forcing function
78			for barotropic gyre numerical experiment. The domain is enclosed bu solid
79			walls at $x=$~0,1200km and at $y=$~0,1200km.}
80	cnh	1.8	\label{FIG:eg-baro-simulation_config}
81	adcroft	1.1	\end{figure}
82
83	cnh	1.3	\subsection{Equations Solved}
84	adcroft	1.9	\label{www:tutorials}
85	cnh	1.3	The model is configured in hydrostatic form. The implicit free surface form of the
86	adcroft	1.6	pressure equation described in Marshall et. al \cite{marshall:97a} is
87	cnh	1.3	employed.
88	cnh	1.4	A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
89	adcroft	1.1	dissipation. The wind-stress momentum input is added to the momentum equation
90			for the ``zonal flow'', $u$. Other terms in the model
91	cnh	1.4	are explicitly switched off for this experiment configuration (see section
92	cnh	1.3	\ref{SEC:code_config} ), yielding an active set of equations solved in this
93			configuration as follows
94	adcroft	1.1
95			\begin{eqnarray}
96	cnh	1.8	\label{EQ:eg-baro-model_equations}
97	cnh	1.3	\frac{Du}{Dt} - fv +
98			g\frac{\partial \eta}{\partial x} -
99			A_{h}\nabla_{h}^2u
100	adcroft	1.1	& = &
101			\frac{\tau_{x}}{\rho_{0}\Delta z}
102			\\
103			\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
104	cnh	1.3	A_{h}\nabla_{h}^2v
105	adcroft	1.1	& = &
106			0
107			\\
108			\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
109			&=&
110			0
111			\end{eqnarray}
112
113			\noindent where $u$ and $v$ and the $x$ and $y$ components of the
114	cnh	1.3	flow vector $\vec{u}$.
115	adcroft	1.1	\\
116	cnh	1.3
117
118			\subsection{Discrete Numerical Configuration}
119	adcroft	1.9	\label{www:tutorials}
120	cnh	1.3
121			The domain is discretised with
122			a uniform grid spacing in the horizontal set to
123			$\Delta x=\Delta y=20$~km, so
124			that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
125			model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
126	adcroft	1.1
127			\subsubsection{Numerical Stability Criteria}
128	adcroft	1.9	\label{www:tutorials}
129	adcroft	1.1
130	cnh	1.4	The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
131	adcroft	1.5	This value is chosen to yield a Munk layer width \cite{adcroft:95},
132	adcroft	1.1
133			\begin{eqnarray}
134	cnh	1.8	\label{EQ:eg-baro-munk_layer}
135	adcroft	1.1	M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
136			\end{eqnarray}
137
138			\noindent of $\approx 100$km. This is greater than the model
139			resolution $\Delta x$, ensuring that the frictional boundary
140			layer is well resolved.
141			\\
142
143			\noindent The model is stepped forward with a
144			time step $\delta t=1200$secs. With this time step the stability
145	adcroft	1.5	parameter to the horizontal Laplacian friction \cite{adcroft:95}
146	adcroft	1.1
147
148
149			\begin{eqnarray}
150	cnh	1.8	\label{EQ:eg-baro-laplacian_stability}
151	adcroft	1.1	S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
152			\end{eqnarray}
153
154			\noindent evaluates to 0.012, which is well below the 0.3 upper limit
155			for stability.
156			\\
157
158			\noindent The numerical stability for inertial oscillations
159	adcroft	1.5	\cite{adcroft:95}
160	adcroft	1.1
161			\begin{eqnarray}
162	cnh	1.8	\label{EQ:eg-baro-inertial_stability}
163	adcroft	1.1	S_{i} = f^{2} {\delta t}^2
164			\end{eqnarray}
165
166			\noindent evaluates to $0.0144$, which is well below the $0.5$ upper
167			limit for stability.
168			\\
169
170	adcroft	1.5	\noindent The advective CFL \cite{adcroft:95} for an extreme maximum
171	adcroft	1.1	horizontal flow speed of $ \| \vec{u} \| = 2 ms^{-1}$
172
173			\begin{eqnarray}
174	cnh	1.8	\label{EQ:eg-baro-cfl_stability}
175	adcroft	1.1	S_{a} = \frac{\| \vec{u} \| \delta t}{ \Delta x}
176			\end{eqnarray}
177
178			\noindent evaluates to 0.12. This is approaching the stability limit
179			of 0.5 and limits $\delta t$ to $1200s$.
180
181			\subsection{Code Configuration}
182	adcroft	1.9	\label{www:tutorials}
183	cnh	1.8	\label{SEC:eg-baro-code_config}
184	adcroft	1.1
185			The model configuration for this experiment resides under the
186			directory {\it verification/exp0/}. The experiment files
187			\begin{itemize}
188			\item {\it input/data}
189			\item {\it input/data.pkg}
190			\item {\it input/eedata},
191			\item {\it input/windx.sin\_y},
192			\item {\it input/topog.box},
193			\item {\it code/CPP\_EEOPTIONS.h}
194			\item {\it code/CPP\_OPTIONS.h},
195			\item {\it code/SIZE.h}.
196			\end{itemize}
197	cnh	1.4	contain the code customizations and parameter settings for this
198			experiments. Below we describe the customizations
199	adcroft	1.1	to these files associated with this experiment.
200
201			\subsubsection{File {\it input/data}}
202	adcroft	1.9	\label{www:tutorials}
203	adcroft	1.1
204			This file, reproduced completely below, specifies the main parameters
205			for the experiment. The parameters that are significant for this configuration
206			are
207
208			\begin{itemize}
209
210			\item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets
211	cnh	1.4	the Laplacian friction coefficient to $400 m^2s^{-1}$
212	adcroft	1.1	\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
213			$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
214
215			\item Lines 15 and 16
216			\begin{verbatim}
217			rigidLid=.FALSE.,
218			implicitFreeSurface=.TRUE.,
219			\end{verbatim}
220			these lines suppress the rigid lid formulation of the surface
221			pressure inverter and activate the implicit free surface form
222			of the pressure inverter.
223
224			\item Line 27,
225			\begin{verbatim}
226			startTime=0,
227			\end{verbatim}
228			this line indicates that the experiment should start from $t=0$
229	cnh	1.4	and implicitly suppresses searching for checkpoint files associated
230	adcroft	1.1	with restarting an numerical integration from a previously saved state.
231
232			\item Line 29,
233			\begin{verbatim}
234			endTime=12000,
235			\end{verbatim}
236			this line indicates that the experiment should start finish at $t=12000s$.
237			A restart file will be written at this time that will enable the
238			simulation to be continued from this point.
239
240			\item Line 30,
241			\begin{verbatim}
242			deltaTmom=1200,
243			\end{verbatim}
244			This line sets the momentum equation timestep to $1200s$.
245
246			\item Line 39,
247			\begin{verbatim}
248			usingCartesianGrid=.TRUE.,
249			\end{verbatim}
250			This line requests that the simulation be performed in a
251	cnh	1.4	Cartesian coordinate system.
252	adcroft	1.1
253			\item Line 41,
254			\begin{verbatim}
255			delX=60*20E3,
256			\end{verbatim}
257			This line sets the horizontal grid spacing between each x-coordinate line
258			in the discrete grid. The syntax indicates that the discrete grid
259			should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$
260			($20$~km).
261
262			\item Line 42,
263			\begin{verbatim}
264			delY=60*20E3,
265			\end{verbatim}
266			This line sets the horizontal grid spacing between each y-coordinate line
267			in the discrete grid to $20 \times 10^{3}m$ ($20$~km).
268
269			\item Line 43,
270			\begin{verbatim}
271			delZ=5000,
272			\end{verbatim}
273			This line sets the vertical grid spacing between each z-coordinate line
274			in the discrete grid to $5000m$ ($5$~km).
275
276			\item Line 46,
277			\begin{verbatim}
278			bathyFile='topog.box'
279			\end{verbatim}
280			This line specifies the name of the file from which the domain
281			bathymetry is read. This file is a two-dimensional ($x,y$) map of
282			depths. This file is assumed to contain 64-bit binary numbers
283			giving the depth of the model at each grid cell, ordered with the x
284			coordinate varying fastest. The points are ordered from low coordinate
285			to high coordinate for both axes. The units and orientation of the
286			depths in this file are the same as used in the MITgcm code. In this
287			experiment, a depth of $0m$ indicates a solid wall and a depth
288			of $-5000m$ indicates open ocean. The matlab program
289			{\it input/gendata.m} shows an example of how to generate a
290			bathymetry file.
291
292
293			\item Line 49,
294			\begin{verbatim}
295			zonalWindFile='windx.sin_y'
296			\end{verbatim}
297			This line specifies the name of the file from which the x-direction
298			surface wind stress is read. This file is also a two-dimensional
299			($x,y$) map and is enumerated and formatted in the same manner as the
300			bathymetry file. The matlab program {\it input/gendata.m} includes example
301			code to generate a valid {\bf zonalWindFile} file.
302
303			\end{itemize}
304
305			\noindent other lines in the file {\it input/data} are standard values
306			that are described in the MITgcm Getting Started and MITgcm Parameters
307			notes.
308
309			\begin{small}
310			\input{part3/case_studies/barotropic_gyre/input/data}
311			\end{small}
312
313			\subsubsection{File {\it input/data.pkg}}
314	adcroft	1.9	\label{www:tutorials}
315	adcroft	1.1
316			This file uses standard default values and does not contain
317	cnh	1.4	customizations for this experiment.
318	adcroft	1.1
319			\subsubsection{File {\it input/eedata}}
320	adcroft	1.9	\label{www:tutorials}
321	adcroft	1.1
322			This file uses standard default values and does not contain
323	cnh	1.4	customizations for this experiment.
324	adcroft	1.1
325			\subsubsection{File {\it input/windx.sin\_y}}
326	adcroft	1.9	\label{www:tutorials}
327	adcroft	1.1
328			The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
329			map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
330			Although $\tau_{x}$ is only a function of $y$n in this experiment
331			this file must still define a complete two-dimensional map in order
332			to be compatible with the standard code for loading forcing fields
333			in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
334			code for creating the {\it input/windx.sin\_y} file.
335
336			\subsubsection{File {\it input/topog.box}}
337	adcroft	1.9	\label{www:tutorials}
338	adcroft	1.1
339
340			The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
341			map of depth values. For this experiment values are either
342			$0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep
343			ocean. The file contains a raw binary stream of data that is enumerated
344			in the same way as standard MITgcm two-dimensional, horizontal arrays.
345			The included matlab program {\it input/gendata.m} gives a complete
346			code for creating the {\it input/topog.box} file.
347
348			\subsubsection{File {\it code/SIZE.h}}
349	adcroft	1.9	\label{www:tutorials}
350	adcroft	1.1
351			Two lines are customized in this file for the current experiment
352
353			\begin{itemize}
354
355			\item Line 39,
356			\begin{verbatim} sNx=60, \end{verbatim} this line sets
357			the lateral domain extent in grid points for the
358			axis aligned with the x-coordinate.
359
360			\item Line 40,
361			\begin{verbatim} sNy=60, \end{verbatim} this line sets
362			the lateral domain extent in grid points for the
363			axis aligned with the y-coordinate.
364
365			\end{itemize}
366
367			\begin{small}
368			\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
369			\end{small}
370
371			\subsubsection{File {\it code/CPP\_OPTIONS.h}}
372	adcroft	1.9	\label{www:tutorials}
373	adcroft	1.1
374			This file uses standard default values and does not contain
375	cnh	1.4	customizations for this experiment.
376	adcroft	1.1
377
378			\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
379	adcroft	1.9	\label{www:tutorials}
380	adcroft	1.1
381			This file uses standard default values and does not contain
382	cnh	1.4	customizations for this experiment.
383	adcroft	1.1