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revision 1.2 by cnh, Mon Oct 22 11:55:48 2001 UTC revision 1.20 by jmc, Thu Apr 21 20:05:12 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  %\begin{center}  %\begin{center}
17  %{\Large \bf Using MITgcm to Simulate Global Climatalogical Ocean Circulation  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
18  %At Four Degree Resolution with Asynchronous Time Stepping}  %At Four Degree Resolution with Asynchronous Time Stepping}
19  %  %
20  %\vspace*{4mm}  %\vspace*{4mm}
# Line 16  Line 23 
23  %{\large May 2001}  %{\large May 2001}
24  %\end{center}  %\end{center}
25    
 \subsection{Introduction}  
   
 This document describes the third example MITgcm experiment. The first  
 two examples illustrated how to configure the code for hydrostatic idealised  
 geophysical fluids simulations. This example iilustrates the use of  
 the MITgcm for large scale ocean circulation simulation.  
   
 \subsection{Overview}  
26    
27  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
28  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
29  with realistic geography and bathymetry on a  with realistic geography and bathymetry on a
30  $4^{\circ} \times 4^{\circ}$ spherical polar grid.  $4^{\circ} \times 4^{\circ}$ spherical polar grid.
31    The files for this experiment are in the verification directory
32    under tutorial\_global\_oce\_latlon.
33  Twenty levels are used in the vertical, ranging in thickness  Twenty levels are used in the vertical, ranging in thickness
34  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,
35  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 37  At this resolution, the configuration
37  can be integrated forward for thousands of years on a single  can be integrated forward for thousands of years on a single
38  processor desktop computer.  processor desktop computer.
39  \\  \\
40    \subsection{Overview}
41    %\label{www:tutorials}
42    
43  The model is forced with climatalogical wind stress data and surface  The model is forced with climatological wind stress data and surface
44  flux data from DaSilva \cite{DaSilva94}. Climatalogical data  flux data from DaSilva \cite{DaSilva94}. Climatological data
45  from Levitus \cite{Levitus94} is used to initialise the model hydrography.  from Levitus \cite{Levitus94} is used to initialize the model hydrography.
46  Levitus seasonal clmatology data is also used throughout the calculation  Levitus seasonal climatology data is also used throughout the calculation
47  to provide additional air-sea fluxes.  to provide additional air-sea fluxes.
48  These fluxes are combined with the DaSilva climatalogical estimates of  These fluxes are combined with the DaSilva climatological estimates of
49  surface heat flux and fresh water, resulting in a mixed boundary  surface heat flux and fresh water, resulting in a mixed boundary
50  condition of the style decribed in Haney \cite{Haney}.  condition of the style described in Haney \cite{Haney}.
51  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied
52  in the model surface layer.  in the model surface layer.
53    
54  \begin{eqnarray}  \begin{eqnarray}
55  \label{EQ:global_forcing}  \label{eq:eg-global-global_forcing}
56  \label{EQ:global_forcing_fu}  \label{eq:eg-global-global_forcing_fu}
57  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
58  \\  \\
59  \label{EQ:global_forcing_fv}  \label{eq:eg-global-global_forcing_fv}
60  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
61  \\  \\
62  \label{EQ:global_forcing_ft}  \label{eq:eg-global-global_forcing_ft}
63  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
64   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
65  \\  \\
66  \label{EQ:global_forcing_fs}  \label{eq:eg-global-global_forcing_fs}
67  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
68   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
69  \end{eqnarray}  \end{eqnarray}
# Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 90  have units of ${\rm N}~{\rm m}^{-2}$. Th
90  ($\theta^{\ast}$ 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 ${\rm W}~{\rm m}^{-2}$
91  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
92  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
93  respectively.  respectively. The source files and procedures for ingesting this data into the
94  \\  simulation are described in the experiment configuration discussion in section
95    \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.  
96    
97    
98  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
99    %\label{www:tutorials}
100    
101    
102   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 109  a uniform grid spacing in latitude and l Line 104  a uniform grid spacing in latitude and l
104   $\Delta \phi=\Delta \lambda=4^{\circ}$, so   $\Delta \phi=\Delta \lambda=4^{\circ}$, so
105  that there are ninety grid cells in the zonal and forty in the  that there are ninety grid cells in the zonal and forty in the
106  meridional direction. The internal model coordinate variables  meridional direction. The internal model coordinate variables
107  $x$ and $y$ are initialised according to  $x$ and $y$ are initialized according to
108  \begin{eqnarray}  \begin{eqnarray}
109  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
110  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
111  \end{eqnarray}  \end{eqnarray}
112    
113  Arctic polar regions are not  Arctic polar regions are not
# Line 146  $ Line 141  $
141   \Delta z_{18}=725\,{\rm m},\,   \Delta z_{18}=725\,{\rm m},\,
142   \Delta z_{19}=775\,{\rm m},\,   \Delta z_{19}=775\,{\rm m},\,
143   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
144  $ (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
145    give a total depth, $H$, of $-5450{\rm m}$.
146  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
147  \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
148  dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
149    
150  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})
151  the zonal flow, $u$ and the merdional flow $v$, according to equations  for both the zonal flow, $u$ and the meridional flow $v$, according to equations
152  (\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}).
153  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations
154    in (\ref{eq:eg-global-model_equations}) for
155  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
156  (\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}).
157  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
158    
159  \begin{eqnarray}  \begin{eqnarray}
160  \label{EQ:model_equations}  \label{eq:eg-global-model_equations}
161  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
162    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
163    \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 207  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
207  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
208  are the zonal and meridional components of the  are the zonal and meridional components of the
209  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
210  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
211  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
212  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
213  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
214  \\  \\
215    
216  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
217    %\label{www:tutorials}
218    
219  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 $5 \times 10^5 m s^{-1}$.
220  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},
221  \begin{eqnarray}  \begin{eqnarray}
222  \label{EQ:munk_layer}  \label{eq:eg-global-munk_layer}
223  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
224  \end{eqnarray}  \end{eqnarray}
225    
226  \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 231  boundary layer is adequately resolved.
231  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
232  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
233  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
234  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
235  \begin{eqnarray}  \begin{eqnarray}
236  \label{EQ:laplacian_stability}  \label{eq:eg-global-laplacian_stability}
237  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
238  \end{eqnarray}  \end{eqnarray}
239    
240  \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 245  $\phi=80^{\circ}$ where $\Delta x=r\cos(
245  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
246  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
247  \begin{eqnarray}  \begin{eqnarray}
248  \label{EQ:laplacian_stability_z}  \label{eq:eg-global-laplacian_stability_z}
249  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
250  \end{eqnarray}  \end{eqnarray}
251    
252  \noindent evaluates to $0.015$ for the smallest model  \noindent evaluates to $0.015$ for the smallest model
253  level spcing ($\Delta z_{1}=50{\rm m}$) which is again well below  level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
254  the upper stability limit.  the upper stability limit.
255  \\  \\
256    
# Line 262  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s} Line 260  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
260  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 $\Delta x \approx 77 {\rm km}$.
261  Here the stability parameter  Here the stability parameter
262  \begin{eqnarray}  \begin{eqnarray}
263  \label{EQ:laplacian_stability_xtheta}  \label{eq:eg-global-laplacian_stability_xtheta}
264  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
265  \end{eqnarray}  \end{eqnarray}
266  evaluates to $0.07$, well below the stabilit limit of $S_{l} \approx 0.5$. The  evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
267  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
268  \begin{eqnarray}  \begin{eqnarray}
269  \label{EQ:laplacian_stability_ztheta}  \label{eq:eg-global-laplacian_stability_ztheta}
270  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
271  \end{eqnarray}  \end{eqnarray}
272  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 274  of $S_{l} \approx 0.5$.
274  \\  \\
275    
276  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
277  \cite{Adcroft_thesis}  \cite{adcroft:95}
278    
279  \begin{eqnarray}  \begin{eqnarray}
280  \label{EQ:inertial_stability}  \label{eq:eg-global-inertial_stability}
281  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
282  \end{eqnarray}  \end{eqnarray}
283    
# Line 287  S_{i} = f^{2} {\delta t_v}^2 Line 285  S_{i} = f^{2} {\delta t_v}^2
285  the $S_{i} < 1$ upper limit for stability.  the $S_{i} < 1$ upper limit for stability.
286  \\  \\
287    
288  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
289  horizontal flow  horizontal flow
290  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
291    
292  \begin{eqnarray}  \begin{eqnarray}
293  \label{EQ:cfl_stability}  \label{eq:eg-global-cfl_stability}
294  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
295  \end{eqnarray}  \end{eqnarray}
296    
# Line 300  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ Line 298  S_{a} = \frac{| \vec{u} | \delta t_{v}}{
298  limit of 0.5.  limit of 0.5.
299  \\  \\
300    
301  \noindent The stability parameter for internal gravity waves propogating  \noindent The stability parameter for internal gravity waves propagating
302  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
303  \cite{Adcroft_thesis}  \cite{adcroft:95}
304    
305  \begin{eqnarray}  \begin{eqnarray}
306  \label{EQ:cfl_stability}  \label{eq:eg-global-gfl_stability}
307  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
308  \end{eqnarray}  \end{eqnarray}
309    
# Line 313  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 311  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
311  stability limit of 0.5.  stability limit of 0.5.
312        
313  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
314  \label{SEC:clim_ocn_examp_exp_config}  %\label{www:tutorials}
315    \label{sec:eg-global-clim_ocn_examp_exp_config}
316    
317  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
318  directory {\it verification/exp2/}.  The experiment files  directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
319    The experiment files
320    
321  \begin{itemize}  \begin{itemize}
322  \item {\it input/data}  \item {\it input/data}
323  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 332  directory {\it verification/exp2/}.  The Line 333  directory {\it verification/exp2/}.  The
333  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
334  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
335  \end{itemize}  \end{itemize}
336  contain the code customisations and parameter settings for these  contain the code customizations and parameter settings for these
337  experiements. Below we describe the customisations  experiments. Below we describe the customizations
338  to these files associated with this experiment.  to these files associated with this experiment.
339    
340  \subsubsection{File {\it input/data}}  \subsubsection{Driving Datasets}
341    %\label{www:tutorials}
342    
343  This file, reproduced completely below, specifies the main parameters  Figures ({\it --- missing figures ---})
344  for the experiment. The parameters that are significant for this configuration  %(\ref{fig:sim_config_tclim}-\ref{fig:sim_config_empmr})
345  are  show the relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$)
346    fields, the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
347  \begin{itemize}  and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
348    in equations
349  \item Lines 7-10 and 11-14  (\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}).
350  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  The figures also indicate the lateral extent and coastline used in the
351  $\cdots$ \\  experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})
352  set reference values for potential  shows the depth contours of the model domain.
 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 coeeficient 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.    
   
 \end{itemize}  
353    
354  \noindent other lines in the file {\it input/data} are standard values  \subsubsection{File {\it input/data}}
355  that are described in the MITgcm Getting Started and MITgcm Parameters  %\label{www:tutorials}
 notes.  
356    
357  \begin{small}  \input{s_examples/global_oce_latlon/inp_data}
 \input{part3/case_studies/climatalogical_ogcm/input/data}  
 \end{small}  
358    
359  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
360    %\label{www:tutorials}
361    
362  This file uses standard default values and does not contain  This file uses standard default values and does not contain
363  customisations for this experiment.  customisations for this experiment.
364    
365  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
366    %\label{www:tutorials}
367    
368  This file uses standard default values and does not contain  This file uses standard default values and does not contain
369  customisations for this experiment.  customisations for this experiment.
370    
371  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
372    %\label{www:tutorials}
373    
374  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
375  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 380  in MITgcm. The included matlab program {
380  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
381    
382  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
383    %\label{www:tutorials}
384    
385    
386  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 392  The included matlab program {\it input/g
392  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
393    
394  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
395    %\label{www:tutorials}
396    
397  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
398    
# Line 679  the vertical domain extent in grid point Line 415  the vertical domain extent in grid point
415  \end{itemize}  \end{itemize}
416    
417  \begin{small}  \begin{small}
418  \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}  \input{s_examples/global_oce_latlon/code/SIZE.h}
419  \end{small}  \end{small}
420    
421  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
422    %\label{www:tutorials}
423    
424  This file uses standard default values and does not contain  This file uses standard default values and does not contain
425  customisations for this experiment.  customisations for this experiment.
426    
427    
428  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
429    %\label{www:tutorials}
430    
431  This file uses standard default values and does not contain  This file uses standard default values and does not contain
432  customisations for this experiment.  customisations for this experiment.
433    
434  \subsubsection{Other Files }  \subsubsection{Other Files }
435    %\label{www:tutorials}
436    
437  Other files relevant to this experiment are  Other files relevant to this experiment are
438  \begin{itemize}  \begin{itemize}
# Line 704  coriolis variables {\bf fCorU}. Line 443  coriolis variables {\bf fCorU}.
443  \item {\it input/windx.sin\_y},  \item {\it input/windx.sin\_y},
444  \end{itemize}  \end{itemize}
445  contain the code customisations and parameter settings for this  contain the code customisations and parameter settings for this
446  experiements. Below we describe the customisations  experiments. Below we describe the customisations
447  to these files associated with this experiment.  to these files associated with this experiment.
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