s_examples/barotropic_gyre/baro.tex

% $Header: /u/u0/gcmpack/manual/part3/case_studies/barotropic_gyre/baro.tex,v 1.7 2001/11/13 20:13:54 adcroft 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}


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}
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}

 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}

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{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}}

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}}

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

\subsubsection{File {\it input/eedata}}

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

\subsubsection{File {\it input/windx.sin\_y}}

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}}


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}}

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}}

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


\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}

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

1	cnh	1.8	% $Header: /u/u0/gcmpack/manual/part3/case_studies/barotropic_gyre/baro.tex,v 1.7 2001/11/13 20:13:54 adcroft 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
31	adcroft	1.1
32			This example experiment demonstrates using the MITgcm to simulate
33	cnh	1.4	a Barotropic, wind-forced, ocean gyre circulation. The experiment
34			is a numerical rendition of the gyre circulation problem similar
35	adcroft	1.1	to the problems described analytically by Stommel in 1966
36			\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
37
38			In this experiment the model
39			is configured to represent a rectangular enclosed box of fluid,
40			$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
41			by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
42	cnh	1.4	in the ``north-south'' direction. Topologically the grid is Cartesian and
43	adcroft	1.1	the coriolis parameter $f$ is defined according to a mid-latitude beta-plane
44			equation
45
46			\begin{equation}
47	cnh	1.8	\label{EQ:eg-baro-fcori}
48	adcroft	1.1	f(y) = f_{0}+\beta y
49			\end{equation}
50
51			\noindent where $y$ is the distance along the ``north-south'' axis of the
52			simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in
53	cnh	1.8	(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
54	adcroft	1.1	\\
55			\\
56			The sinusoidal wind-stress variations are defined according to
57
58			\begin{equation}
59	cnh	1.8	\label{EQ:eg-baro-taux}
60	adcroft	1.1	\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
61			\end{equation}
62
63			\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and
64			$\tau_0$ is set to $0.1N m^{-2}$.
65			\\
66			\\
67	cnh	1.8	Figure \ref{FIG:eg-baro-simulation_config}
68	cnh	1.4	summarizes the configuration simulated.
69	adcroft	1.1
70			\begin{figure}
71	cnh	1.2	\begin{center}
72	adcroft	1.1	\resizebox{7.5in}{5.5in}{
73			\includegraphics*[0.2in,0.7in][10.5in,10.5in]
74			{part3/case_studies/barotropic_gyre/simulation_config.eps} }
75	cnh	1.2	\end{center}
76	adcroft	1.1	\caption{Schematic of simulation domain and wind-stress forcing function
77			for barotropic gyre numerical experiment. The domain is enclosed bu solid
78			walls at $x=$~0,1200km and at $y=$~0,1200km.}
79	cnh	1.8	\label{FIG:eg-baro-simulation_config}
80	adcroft	1.1	\end{figure}
81
82	cnh	1.3	\subsection{Equations Solved}
83			The model is configured in hydrostatic form. The implicit free surface form of the
84	adcroft	1.6	pressure equation described in Marshall et. al \cite{marshall:97a} is
85	cnh	1.3	employed.
86	cnh	1.4	A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
87	adcroft	1.1	dissipation. The wind-stress momentum input is added to the momentum equation
88			for the ``zonal flow'', $u$. Other terms in the model
89	cnh	1.4	are explicitly switched off for this experiment configuration (see section
90	cnh	1.3	\ref{SEC:code_config} ), yielding an active set of equations solved in this
91			configuration as follows
92	adcroft	1.1
93			\begin{eqnarray}
94	cnh	1.8	\label{EQ:eg-baro-model_equations}
95	cnh	1.3	\frac{Du}{Dt} - fv +
96			g\frac{\partial \eta}{\partial x} -
97			A_{h}\nabla_{h}^2u
98	adcroft	1.1	& = &
99			\frac{\tau_{x}}{\rho_{0}\Delta z}
100			\\
101			\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
102	cnh	1.3	A_{h}\nabla_{h}^2v
103	adcroft	1.1	& = &
104			0
105			\\
106			\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
107			&=&
108			0
109			\end{eqnarray}
110
111			\noindent where $u$ and $v$ and the $x$ and $y$ components of the
112	cnh	1.3	flow vector $\vec{u}$.
113	adcroft	1.1	\\
114	cnh	1.3
115
116			\subsection{Discrete Numerical Configuration}
117
118			The domain is discretised with
119			a uniform grid spacing in the horizontal set to
120			$\Delta x=\Delta y=20$~km, so
121			that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
122			model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
123	adcroft	1.1
124			\subsubsection{Numerical Stability Criteria}
125
126	cnh	1.4	The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
127	adcroft	1.5	This value is chosen to yield a Munk layer width \cite{adcroft:95},
128	adcroft	1.1
129			\begin{eqnarray}
130	cnh	1.8	\label{EQ:eg-baro-munk_layer}
131	adcroft	1.1	M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
132			\end{eqnarray}
133
134			\noindent of $\approx 100$km. This is greater than the model
135			resolution $\Delta x$, ensuring that the frictional boundary
136			layer is well resolved.
137			\\
138
139			\noindent The model is stepped forward with a
140			time step $\delta t=1200$secs. With this time step the stability
141	adcroft	1.5	parameter to the horizontal Laplacian friction \cite{adcroft:95}
142	adcroft	1.1
143
144
145			\begin{eqnarray}
146	cnh	1.8	\label{EQ:eg-baro-laplacian_stability}
147	adcroft	1.1	S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
148			\end{eqnarray}
149
150			\noindent evaluates to 0.012, which is well below the 0.3 upper limit
151			for stability.
152			\\
153
154			\noindent The numerical stability for inertial oscillations
155	adcroft	1.5	\cite{adcroft:95}
156	adcroft	1.1
157			\begin{eqnarray}
158	cnh	1.8	\label{EQ:eg-baro-inertial_stability}
159	adcroft	1.1	S_{i} = f^{2} {\delta t}^2
160			\end{eqnarray}
161
162			\noindent evaluates to $0.0144$, which is well below the $0.5$ upper
163			limit for stability.
164			\\
165
166	adcroft	1.5	\noindent The advective CFL \cite{adcroft:95} for an extreme maximum
167	adcroft	1.1	horizontal flow speed of $ \| \vec{u} \| = 2 ms^{-1}$
168
169			\begin{eqnarray}
170	cnh	1.8	\label{EQ:eg-baro-cfl_stability}
171	adcroft	1.1	S_{a} = \frac{\| \vec{u} \| \delta t}{ \Delta x}
172			\end{eqnarray}
173
174			\noindent evaluates to 0.12. This is approaching the stability limit
175			of 0.5 and limits $\delta t$ to $1200s$.
176
177			\subsection{Code Configuration}
178	cnh	1.8	\label{SEC:eg-baro-code_config}
179	adcroft	1.1
180			The model configuration for this experiment resides under the
181			directory {\it verification/exp0/}. The experiment files
182			\begin{itemize}
183			\item {\it input/data}
184			\item {\it input/data.pkg}
185			\item {\it input/eedata},
186			\item {\it input/windx.sin\_y},
187			\item {\it input/topog.box},
188			\item {\it code/CPP\_EEOPTIONS.h}
189			\item {\it code/CPP\_OPTIONS.h},
190			\item {\it code/SIZE.h}.
191			\end{itemize}
192	cnh	1.4	contain the code customizations and parameter settings for this
193			experiments. Below we describe the customizations
194	adcroft	1.1	to these files associated with this experiment.
195
196			\subsubsection{File {\it input/data}}
197
198			This file, reproduced completely below, specifies the main parameters
199			for the experiment. The parameters that are significant for this configuration
200			are
201
202			\begin{itemize}
203
204			\item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets
205	cnh	1.4	the Laplacian friction coefficient to $400 m^2s^{-1}$
206	adcroft	1.1	\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
207			$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
208
209			\item Lines 15 and 16
210			\begin{verbatim}
211			rigidLid=.FALSE.,
212			implicitFreeSurface=.TRUE.,
213			\end{verbatim}
214			these lines suppress the rigid lid formulation of the surface
215			pressure inverter and activate the implicit free surface form
216			of the pressure inverter.
217
218			\item Line 27,
219			\begin{verbatim}
220			startTime=0,
221			\end{verbatim}
222			this line indicates that the experiment should start from $t=0$
223	cnh	1.4	and implicitly suppresses searching for checkpoint files associated
224	adcroft	1.1	with restarting an numerical integration from a previously saved state.
225
226			\item Line 29,
227			\begin{verbatim}
228			endTime=12000,
229			\end{verbatim}
230			this line indicates that the experiment should start finish at $t=12000s$.
231			A restart file will be written at this time that will enable the
232			simulation to be continued from this point.
233
234			\item Line 30,
235			\begin{verbatim}
236			deltaTmom=1200,
237			\end{verbatim}
238			This line sets the momentum equation timestep to $1200s$.
239
240			\item Line 39,
241			\begin{verbatim}
242			usingCartesianGrid=.TRUE.,
243			\end{verbatim}
244			This line requests that the simulation be performed in a
245	cnh	1.4	Cartesian coordinate system.
246	adcroft	1.1
247			\item Line 41,
248			\begin{verbatim}
249			delX=60*20E3,
250			\end{verbatim}
251			This line sets the horizontal grid spacing between each x-coordinate line
252			in the discrete grid. The syntax indicates that the discrete grid
253			should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$
254			($20$~km).
255
256			\item Line 42,
257			\begin{verbatim}
258			delY=60*20E3,
259			\end{verbatim}
260			This line sets the horizontal grid spacing between each y-coordinate line
261			in the discrete grid to $20 \times 10^{3}m$ ($20$~km).
262
263			\item Line 43,
264			\begin{verbatim}
265			delZ=5000,
266			\end{verbatim}
267			This line sets the vertical grid spacing between each z-coordinate line
268			in the discrete grid to $5000m$ ($5$~km).
269
270			\item Line 46,
271			\begin{verbatim}
272			bathyFile='topog.box'
273			\end{verbatim}
274			This line specifies the name of the file from which the domain
275			bathymetry is read. This file is a two-dimensional ($x,y$) map of
276			depths. This file is assumed to contain 64-bit binary numbers
277			giving the depth of the model at each grid cell, ordered with the x
278			coordinate varying fastest. The points are ordered from low coordinate
279			to high coordinate for both axes. The units and orientation of the
280			depths in this file are the same as used in the MITgcm code. In this
281			experiment, a depth of $0m$ indicates a solid wall and a depth
282			of $-5000m$ indicates open ocean. The matlab program
283			{\it input/gendata.m} shows an example of how to generate a
284			bathymetry file.
285
286
287			\item Line 49,
288			\begin{verbatim}
289			zonalWindFile='windx.sin_y'
290			\end{verbatim}
291			This line specifies the name of the file from which the x-direction
292			surface wind stress is read. This file is also a two-dimensional
293			($x,y$) map and is enumerated and formatted in the same manner as the
294			bathymetry file. The matlab program {\it input/gendata.m} includes example
295			code to generate a valid {\bf zonalWindFile} file.
296
297			\end{itemize}
298
299			\noindent other lines in the file {\it input/data} are standard values
300			that are described in the MITgcm Getting Started and MITgcm Parameters
301			notes.
302
303			\begin{small}
304			\input{part3/case_studies/barotropic_gyre/input/data}
305			\end{small}
306
307			\subsubsection{File {\it input/data.pkg}}
308
309			This file uses standard default values and does not contain
310	cnh	1.4	customizations for this experiment.
311	adcroft	1.1
312			\subsubsection{File {\it input/eedata}}
313
314			This file uses standard default values and does not contain
315	cnh	1.4	customizations for this experiment.
316	adcroft	1.1
317			\subsubsection{File {\it input/windx.sin\_y}}
318
319			The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
320			map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
321			Although $\tau_{x}$ is only a function of $y$n in this experiment
322			this file must still define a complete two-dimensional map in order
323			to be compatible with the standard code for loading forcing fields
324			in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
325			code for creating the {\it input/windx.sin\_y} file.
326
327			\subsubsection{File {\it input/topog.box}}
328
329
330			The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
331			map of depth values. For this experiment values are either
332			$0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep
333			ocean. The file contains a raw binary stream of data that is enumerated
334			in the same way as standard MITgcm two-dimensional, horizontal arrays.
335			The included matlab program {\it input/gendata.m} gives a complete
336			code for creating the {\it input/topog.box} file.
337
338			\subsubsection{File {\it code/SIZE.h}}
339
340			Two lines are customized in this file for the current experiment
341
342			\begin{itemize}
343
344			\item Line 39,
345			\begin{verbatim} sNx=60, \end{verbatim} this line sets
346			the lateral domain extent in grid points for the
347			axis aligned with the x-coordinate.
348
349			\item Line 40,
350			\begin{verbatim} sNy=60, \end{verbatim} this line sets
351			the lateral domain extent in grid points for the
352			axis aligned with the y-coordinate.
353
354			\end{itemize}
355
356			\begin{small}
357			\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
358			\end{small}
359
360			\subsubsection{File {\it code/CPP\_OPTIONS.h}}
361
362			This file uses standard default values and does not contain
363	cnh	1.4	customizations for this experiment.
364	adcroft	1.1
365
366			\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
367
368			This file uses standard default values and does not contain
369	cnh	1.4	customizations for this experiment.
370	adcroft	1.1