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revision 1.3 by cnh, Thu Oct 25 18:36:55 2001 UTC revision 1.21 by jmc, Thu Apr 21 21:27:16 2011 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}  \section[Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution}
5    %\label{www:tutorials}
6  \label{sec:eg-global}  \label{sec:eg-global}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-global: -->
9    \end{rawhtml}
10    \begin{center}
11    (in directory: {\it verification/tutorial\_global\_oce\_latlon/})
12    \end{center}
13    
14  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
15    
16    \noindent {\bf WARNING: the description of this experiment is not up-to-date.
17     In particular, most of the parameters description corresponds to an older
18     version of {\it verification/exp2} instead of the current tutorial}\\
19    
20  %\begin{center}  %\begin{center}
21  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
22  %At Four Degree Resolution with Asynchronous Time Stepping}  %At Four Degree Resolution with Asynchronous Time Stepping}
# Line 16  Line 27 
27  %{\large May 2001}  %{\large May 2001}
28  %\end{center}  %\end{center}
29    
 \subsection{Introduction}  
   
 This document describes the third example MITgcm experiment. The first  
 two examples illustrated how to configure the code for hydrostatic idealized  
 geophysical fluids simulations. This example illustrates the use of  
 the MITgcm for large scale ocean circulation simulation.  
   
 \subsection{Overview}  
30    
31  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
32  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
33  with realistic geography and bathymetry on a  with realistic geography and bathymetry on a
34  $4^{\circ} \times 4^{\circ}$ spherical polar grid.  $4^{\circ} \times 4^{\circ}$ spherical polar grid.
35    The files for this experiment are in the verification directory
36    under tutorial\_global\_oce\_latlon.
37  Twenty levels are used in the vertical, ranging in thickness  Twenty levels are used in the vertical, ranging in thickness
38  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,
39  giving a maximum model depth of $6\,{\rm km}$.  giving a maximum model depth of $6\,{\rm km}$.
# Line 36  At this resolution, the configuration Line 41  At this resolution, the configuration
41  can be integrated forward for thousands of years on a single  can be integrated forward for thousands of years on a single
42  processor desktop computer.  processor desktop computer.
43  \\  \\
44    \subsection{Overview}
45    %\label{www:tutorials}
46    
47  The model is forced with climatological wind stress data and surface  The model is forced with climatological wind stress data and surface
48  flux data from DaSilva \cite{DaSilva94}. Climatological data  flux data from DaSilva \cite{DaSilva94}. Climatological data
# Line 49  Altogether, this yields the following fo Line 56  Altogether, this yields the following fo
56  in the model surface layer.  in the model surface layer.
57    
58  \begin{eqnarray}  \begin{eqnarray}
59  \label{EQ:global_forcing}  \label{eq:eg-global-global_forcing}
60  \label{EQ:global_forcing_fu}  \label{eq:eg-global-global_forcing_fu}
61  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
62  \\  \\
63  \label{EQ:global_forcing_fv}  \label{eq:eg-global-global_forcing_fv}
64  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
65  \\  \\
66  \label{EQ:global_forcing_ft}  \label{eq:eg-global-global_forcing_ft}
67  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
68   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
69  \\  \\
70  \label{EQ:global_forcing_fs}  \label{eq:eg-global-global_forcing_fs}
71  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
72   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
73  \end{eqnarray}  \end{eqnarray}
# Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 94  have units of ${\rm N}~{\rm m}^{-2}$. Th
94  ($\theta^{\ast}$ 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 ${\rm W}~{\rm m}^{-2}$
95  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
96  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
97  respectively.  respectively. The source files and procedures for ingesting this data into the
98  \\  simulation are described in the experiment configuration discussion in section
99    \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.  
100    
101    
102  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
103    %\label{www:tutorials}
104    
105    
106   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 112  meridional direction. The internal model Line 111  meridional direction. The internal model
111  $x$ and $y$ are initialized according to  $x$ and $y$ are initialized according to
112  \begin{eqnarray}  \begin{eqnarray}
113  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
114  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
115  \end{eqnarray}  \end{eqnarray}
116    
117  Arctic polar regions are not  Arctic polar regions are not
# Line 146  $ Line 145  $
145   \Delta z_{18}=725\,{\rm m},\,   \Delta z_{18}=725\,{\rm m},\,
146   \Delta z_{19}=775\,{\rm m},\,   \Delta z_{19}=775\,{\rm m},\,
147   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
148  $ (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
149    give a total depth, $H$, of $-5450{\rm m}$.
150  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
151  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
152  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
153    
154  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})
155  the zonal flow, $u$ and the meridional flow $v$, according to equations  for both the zonal flow, $u$ and the meridional flow $v$, according to equations
156  (\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}).
157  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations
158    in (\ref{eq:eg-global-model_equations}) for
159  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
160  (\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}).
161  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
162    
163  \begin{eqnarray}  \begin{eqnarray}
164  \label{EQ:model_equations}  \label{eq:eg-global-model_equations}
165  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
166    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
167    \nabla_{h}\cdot A_{h}\nabla_{h}u -    \nabla_{h}\cdot A_{h}\nabla_{h}u -
# Line 210  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d Line 211  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
211  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
212  are the zonal and meridional components of the  are the zonal and meridional components of the
213  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
214  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
215  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
216  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
217  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
218  \\  \\
219    
220  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
221    %\label{www:tutorials}
222    
223  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 $5 \times 10^5 m s^{-1}$.
224  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},
225  \begin{eqnarray}  \begin{eqnarray}
226  \label{EQ:munk_layer}  \label{eq:eg-global-munk_layer}
227  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
228  \end{eqnarray}  \end{eqnarray}
229    
230  \noindent  of $\approx 600$km. This is greater than the model  \noindent  of $\approx 600$km. This is greater than the model
# Line 233  boundary layer is adequately resolved. Line 235  boundary layer is adequately resolved.
235  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
236  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
237  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
238  parameter to the horizontal Laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
239  \begin{eqnarray}  \begin{eqnarray}
240  \label{EQ:laplacian_stability}  \label{eq:eg-global-laplacian_stability}
241  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
242  \end{eqnarray}  \end{eqnarray}
243    
244  \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 247  $\phi=80^{\circ}$ where $\Delta x=r\cos( Line 249  $\phi=80^{\circ}$ where $\Delta x=r\cos(
249  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
250  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
251  \begin{eqnarray}  \begin{eqnarray}
252  \label{EQ:laplacian_stability_z}  \label{eq:eg-global-laplacian_stability_z}
253  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
254  \end{eqnarray}  \end{eqnarray}
255    
# Line 262  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s} Line 264  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
264  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 $\Delta x \approx 77 {\rm km}$.
265  Here the stability parameter  Here the stability parameter
266  \begin{eqnarray}  \begin{eqnarray}
267  \label{EQ:laplacian_stability_xtheta}  \label{eq:eg-global-laplacian_stability_xtheta}
268  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
269  \end{eqnarray}  \end{eqnarray}
270  evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The  evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
271  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
272  \begin{eqnarray}  \begin{eqnarray}
273  \label{EQ:laplacian_stability_ztheta}  \label{eq:eg-global-laplacian_stability_ztheta}
274  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
275  \end{eqnarray}  \end{eqnarray}
276  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 276  of $S_{l} \approx 0.5$. Line 278  of $S_{l} \approx 0.5$.
278  \\  \\
279    
280  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
281  \cite{Adcroft_thesis}  \cite{adcroft:95}
282    
283  \begin{eqnarray}  \begin{eqnarray}
284  \label{EQ:inertial_stability}  \label{eq:eg-global-inertial_stability}
285  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
286  \end{eqnarray}  \end{eqnarray}
287    
# Line 287  S_{i} = f^{2} {\delta t_v}^2 Line 289  S_{i} = f^{2} {\delta t_v}^2
289  the $S_{i} < 1$ upper limit for stability.  the $S_{i} < 1$ upper limit for stability.
290  \\  \\
291    
292  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
293  horizontal flow  horizontal flow
294  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
295    
296  \begin{eqnarray}  \begin{eqnarray}
297  \label{EQ:cfl_stability}  \label{eq:eg-global-cfl_stability}
298  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
299  \end{eqnarray}  \end{eqnarray}
300    
# Line 302  limit of 0.5. Line 304  limit of 0.5.
304    
305  \noindent The stability parameter for internal gravity waves propagating  \noindent The stability parameter for internal gravity waves propagating
306  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
307  \cite{Adcroft_thesis}  \cite{adcroft:95}
308    
309  \begin{eqnarray}  \begin{eqnarray}
310  \label{EQ:cfl_stability}  \label{eq:eg-global-gfl_stability}
311  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
312  \end{eqnarray}  \end{eqnarray}
313    
# Line 313  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 315  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
315  stability limit of 0.5.  stability limit of 0.5.
316        
317  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
318  \label{SEC:clim_ocn_examp_exp_config}  %\label{www:tutorials}
319    \label{sec:eg-global-clim_ocn_examp_exp_config}
320    
321  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
322  directory {\it verification/exp2/}.  The experiment files  directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
323    The experiment files
324    
325  \begin{itemize}  \begin{itemize}
326  \item {\it input/data}  \item {\it input/data}
327  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 336  contain the code customizations and para Line 341  contain the code customizations and para
341  experiments. Below we describe the customizations  experiments. Below we describe the customizations
342  to these files associated with this experiment.  to these files associated with this experiment.
343    
344  \subsubsection{File {\it input/data}}  \subsubsection{Driving Datasets}
345    %\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 Lines 7-10 and 11-14  
 \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  
 $\cdots$ \\  
 set reference values for potential  
 temperature and salinity at each model level in units of $^{\circ}$C and  
 ${\rm ppt}$. The entries are ordered from surface to depth.  
 Density is calculated from anomalies at each level evaluated  
 with respect to the reference values set here.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R INI\_THETA}({\it ini\_theta.F})  
 \end{minipage}  
 }  
   
   
 \item Line 15,  
 \begin{verbatim} viscAz=1.E-3, \end{verbatim}  
 this line sets the vertical Laplacian dissipation coefficient to  
 $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions  
 for this operator are specified later. This variable is copied into  
 model general vertical coordinate variable {\bf viscAr}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})  
 \end{minipage}  
 }  
   
 \item Line 16,  
 \begin{verbatim}  
 viscAh=5.E5,  
 \end{verbatim}  
 this line sets the horizontal Laplacian frictional dissipation coefficient to  
 $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions  
 for this operator are specified later.  
   
 \item Lines 17,  
 \begin{verbatim}  
 no_slip_sides=.FALSE.  
 \end{verbatim}  
 this line selects a free-slip lateral boundary condition for  
 the horizontal Laplacian friction operator  
 e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and  
 $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  
   
 \item Lines 9,  
 \begin{verbatim}  
 no_slip_bottom=.TRUE.  
 \end{verbatim}  
 this line selects a no-slip boundary condition for bottom  
 boundary condition in the vertical Laplacian friction operator  
 e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.  
   
 \item Line 19,  
 \begin{verbatim}  
 diffKhT=1.E3,  
 \end{verbatim}  
 this line sets the horizontal diffusion coefficient for temperature  
 to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this  
 operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on  
 all boundaries.  
   
 \item Line 20,  
 \begin{verbatim}  
 diffKzT=3.E-5,  
 \end{verbatim}  
 this line sets the vertical diffusion coefficient for temperature  
 to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary  
 condition on this operator is $\frac{\partial}{\partial z}=0$ at both  
 the upper and lower boundaries.  
   
 \item Line 21,  
 \begin{verbatim}  
 diffKhS=1.E3,  
 \end{verbatim}  
 this line sets the horizontal diffusion coefficient for salinity  
 to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this  
 operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on  
 all boundaries.  
   
 \item Line 22,  
 \begin{verbatim}  
 diffKzS=3.E-5,  
 \end{verbatim}  
 this line sets the vertical diffusion coefficient for salinity  
 to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary  
 condition on this operator is $\frac{\partial}{\partial z}=0$ at both  
 the upper and lower boundaries.  
   
 \item Lines 23-26  
 \begin{verbatim}  
 beta=1.E-11,  
 \end{verbatim}  
 \vspace{-5mm}$\cdots$\\  
 These settings do not apply for this experiment.  
   
 \item Line 27,  
 \begin{verbatim}  
 gravity=9.81,  
 \end{verbatim}  
 Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\  
 {\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\  
 {\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\  
 {\it S/R INI\_PARMS}~({\it ini\_parms.F})\\  
 {\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})  
 \end{minipage}  
 }  
   
   
 \item Line 28-29,  
 \begin{verbatim}  
 rigidLid=.FALSE.,  
 implicitFreeSurface=.TRUE.,  
 \end{verbatim}  
 Selects the barotropic pressure equation to be the implicit free surface  
 formulation.  
   
 \item Line 30,  
 \begin{verbatim}  
 eosType='POLY3',  
 \end{verbatim}  
 Selects the third order polynomial form of the equation of state.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R FIND\_RHO}~({\it find\_rho.F})\\  
 {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})  
 \end{minipage}  
 }  
   
 \item Line 31,  
 \begin{verbatim}  
 readBinaryPrec=32,  
 \end{verbatim}  
 Sets format for reading binary input datasets holding model fields to  
 use 32-bit representation for floating-point numbers.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\  
 {\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})  
 \end{minipage}  
 }  
   
 \item Line 36,  
 \begin{verbatim}  
 cg2dMaxIters=1000,  
 \end{verbatim}  
 Sets maximum number of iterations the two-dimensional, conjugate  
 gradient solver will use, {\bf irrespective of convergence  
 criteria being met}.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R CG2D}~({\it cg2d.F})  
 \end{minipage}  
 }  
   
 \item Line 37,  
 \begin{verbatim}  
 cg2dTargetResidual=1.E-13,  
 \end{verbatim}  
 Sets the tolerance which the two-dimensional, conjugate  
 gradient solver will use to test for convergence in equation  
 \ref{EQ:congrad_2d_resid} to $1 \times 10^{-13}$.  
 Solver will iterate until  
 tolerance falls below this value or until the maximum number of  
 solver iterations is reached.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R CG2D}~({\it cg2d.F})  
 \end{minipage}  
 }  
   
 \item Line 42,  
 \begin{verbatim}  
 startTime=0,  
 \end{verbatim}  
 Sets the starting time for the model internal time counter.  
 When set to non-zero this option implicitly requests a  
 checkpoint file be read for initial state.  
 By default the checkpoint file is named according to  
 the integer number of time steps in the {\bf startTime} value.  
 The internal time counter works in seconds.  
   
 \item Line 43,  
 \begin{verbatim}  
 endTime=2808000.,  
 \end{verbatim}  
 Sets the time (in seconds) at which this simulation will terminate.  
 At the end of a simulation a checkpoint file is automatically  
 written so that a numerical experiment can consist of multiple  
 stages.  
   
 \item Line 44,  
 \begin{verbatim}  
 #endTime=62208000000,  
 \end{verbatim}  
 A commented out setting for endTime for a 2000 year simulation.  
   
 \item Line 45,  
 \begin{verbatim}  
 deltaTmom=2400.0,  
 \end{verbatim}  
 Sets the timestep $\delta t_{v}$ used in the momentum equations to  
 $20~{\rm mins}$.  
 See section \ref{SEC:mom_time_stepping}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R TIMESTEP}({\it timestep.F})  
 \end{minipage}  
 }  
   
 \item Line 46,  
 \begin{verbatim}  
 tauCD=321428.,  
 \end{verbatim}  
 Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.  
 See section \ref{SEC:cd_scheme}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R INI\_PARMS}({\it ini\_parms.F})\\  
 {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})  
 \end{minipage}  
 }  
   
 \item Line 47,  
 \begin{verbatim}  
 deltaTtracer=108000.,  
 \end{verbatim}  
 Sets the default timestep, $\delta t_{\theta}$, for tracer equations to  
 $30~{\rm hours}$.  
 See section \ref{SEC:tracer_time_stepping}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})  
 \end{minipage}  
 }  
   
 \item Line 47,  
 \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 $-2000m$ indicates open ocean. The matlab program  
 {\it input/gendata.m} shows an example of how to generate a  
 bathymetry file.  
   
   
 \item Line 50,  
 \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.    
346    
347  \end{itemize}  Figures ({\it --- missing figures ---})
348    %(\ref{fig:sim_config_tclim}-\ref{fig:sim_config_empmr})
349    show the relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$)
350    fields, the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
351    and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
352    in equations
353    (\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}).
354    The figures also indicate the lateral extent and coastline used in the
355    experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})
356    shows the depth contours of the model domain.
357    
358  \noindent other lines in the file {\it input/data} are standard values  \subsubsection{File {\it input/data}}
359  that are described in the MITgcm Getting Started and MITgcm Parameters  %\label{www:tutorials}
 notes.  
360    
361  \begin{small}  \input{s_examples/global_oce_latlon/inp_data}
 \input{part3/case_studies/climatalogical_ogcm/input/data}  
 \end{small}  
362    
363  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
364    %\label{www:tutorials}
365    
366  This file uses standard default values and does not contain  This file uses standard default values and does not contain
367  customisations for this experiment.  customisations for this experiment.
368    
369  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
370    %\label{www:tutorials}
371    
372  This file uses standard default values and does not contain  This file uses standard default values and does not contain
373  customisations for this experiment.  customisations for this experiment.
374    
375  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
376    %\label{www:tutorials}
377    
378  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
379  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 646  in MITgcm. The included matlab program { Line 384  in MITgcm. The included matlab program {
384  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
385    
386  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
387    %\label{www:tutorials}
388    
389    
390  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 657  The included matlab program {\it input/g Line 396  The included matlab program {\it input/g
396  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
397    
398  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
399    %\label{www:tutorials}
400    
401  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
402    
# Line 679  the vertical domain extent in grid point Line 419  the vertical domain extent in grid point
419  \end{itemize}  \end{itemize}
420    
421  \begin{small}  \begin{small}
422  \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}  \input{s_examples/global_oce_latlon/code/SIZE.h}
423  \end{small}  \end{small}
424    
425  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
426    %\label{www:tutorials}
427    
428  This file uses standard default values and does not contain  This file uses standard default values and does not contain
429  customisations for this experiment.  customisations for this experiment.
430    
431    
432  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
433    %\label{www:tutorials}
434    
435  This file uses standard default values and does not contain  This file uses standard default values and does not contain
436  customisations for this experiment.  customisations for this experiment.
437    
438  \subsubsection{Other Files }  \subsubsection{Other Files }
439    %\label{www:tutorials}
440    
441  Other files relevant to this experiment are  Other files relevant to this experiment are
442  \begin{itemize}  \begin{itemize}
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