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revision 1.3 by cnh, Thu Oct 25 18:36:55 2001 UTC revision 1.13 by edhill, Sat Apr 8 01:50:50 2006 UTC
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1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}  \section[Global Ocean MITgcm Exmaple]{Global Ocean Simulation at $4^\circ$ Resolution}
5  \label{sec:eg-global}  \label{www:tutorials}
6    \label{sect:eg-global}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-global: -->
9    \end{rawhtml}
10    
11  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
12    
# Line 16  Line 20 
20  %{\large May 2001}  %{\large May 2001}
21  %\end{center}  %\end{center}
22    
 \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}  
23    
24  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
25  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
# Line 36  At this resolution, the configuration Line 32  At this resolution, the configuration
32  can be integrated forward for thousands of years on a single  can be integrated forward for thousands of years on a single
33  processor desktop computer.  processor desktop computer.
34  \\  \\
35    \subsection{Overview}
36    \label{www:tutorials}
37    
38  The model is forced with climatological wind stress data and surface  The model is forced with climatological wind stress data and surface
39  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 47  Altogether, this yields the following fo
47  in the model surface layer.  in the model surface layer.
48    
49  \begin{eqnarray}  \begin{eqnarray}
50  \label{EQ:global_forcing}  \label{EQ:eg-global-global_forcing}
51  \label{EQ:global_forcing_fu}  \label{EQ:eg-global-global_forcing_fu}
52  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
53  \\  \\
54  \label{EQ:global_forcing_fv}  \label{EQ:eg-global-global_forcing_fv}
55  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
56  \\  \\
57  \label{EQ:global_forcing_ft}  \label{EQ:eg-global-global_forcing_ft}
58  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
59   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
60  \\  \\
61  \label{EQ:global_forcing_fs}  \label{EQ:eg-global-global_forcing_fs}
62  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
63   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
64  \end{eqnarray}  \end{eqnarray}
# Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 85  have units of ${\rm N}~{\rm m}^{-2}$. Th
85  ($\theta^{\ast}$ 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 ${\rm W}~{\rm m}^{-2}$
86  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
87  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
88  respectively.  respectively. The source files and procedures for ingesting this data into the
89  \\  simulation are described in the experiment configuration discussion in section
90    \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.  
91    
92    
93  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
94    \label{www:tutorials}
95    
96    
97   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 102  meridional direction. The internal model
102  $x$ and $y$ are initialized according to  $x$ and $y$ are initialized according to
103  \begin{eqnarray}  \begin{eqnarray}
104  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
105  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
106  \end{eqnarray}  \end{eqnarray}
107    
108  Arctic polar regions are not  Arctic polar regions are not
# Line 146  $ Line 136  $
136   \Delta z_{18}=725\,{\rm m},\,   \Delta z_{18}=725\,{\rm m},\,
137   \Delta z_{19}=775\,{\rm m},\,   \Delta z_{19}=775\,{\rm m},\,
138   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
139  $ (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
140    give a total depth, $H$, of $-5450{\rm m}$.
141  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
142  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
143  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
144    
145  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})
146  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
147  (\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}).
148  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations
149    in (\ref{EQ:eg-global-model_equations}) for
150  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
151  (\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}).
152  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
153    
154  \begin{eqnarray}  \begin{eqnarray}
155  \label{EQ:model_equations}  \label{EQ:eg-global-model_equations}
156  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
157    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
158    \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 202  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
202  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
203  are the zonal and meridional components of the  are the zonal and meridional components of the
204  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
205  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
206  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
207  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
208  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
209  \\  \\
210    
211  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
212    \label{www:tutorials}
213    
214  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 $5 \times 10^5 m s^{-1}$.
215  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},
216  \begin{eqnarray}  \begin{eqnarray}
217  \label{EQ:munk_layer}  \label{EQ:eg-global-munk_layer}
218  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
219  \end{eqnarray}  \end{eqnarray}
220    
221  \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 226  boundary layer is adequately resolved.
226  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
227  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
228  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
229  parameter to the horizontal Laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
230  \begin{eqnarray}  \begin{eqnarray}
231  \label{EQ:laplacian_stability}  \label{EQ:eg-global-laplacian_stability}
232  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
233  \end{eqnarray}  \end{eqnarray}
234    
235  \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 240  $\phi=80^{\circ}$ where $\Delta x=r\cos(
240  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
241  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
242  \begin{eqnarray}  \begin{eqnarray}
243  \label{EQ:laplacian_stability_z}  \label{EQ:eg-global-laplacian_stability_z}
244  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
245  \end{eqnarray}  \end{eqnarray}
246    
# Line 262  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s} Line 255  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
255  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 $\Delta x \approx 77 {\rm km}$.
256  Here the stability parameter  Here the stability parameter
257  \begin{eqnarray}  \begin{eqnarray}
258  \label{EQ:laplacian_stability_xtheta}  \label{EQ:eg-global-laplacian_stability_xtheta}
259  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
260  \end{eqnarray}  \end{eqnarray}
261  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
262  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
263  \begin{eqnarray}  \begin{eqnarray}
264  \label{EQ:laplacian_stability_ztheta}  \label{EQ:eg-global-laplacian_stability_ztheta}
265  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
266  \end{eqnarray}  \end{eqnarray}
267  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 269  of $S_{l} \approx 0.5$.
269  \\  \\
270    
271  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
272  \cite{Adcroft_thesis}  \cite{adcroft:95}
273    
274  \begin{eqnarray}  \begin{eqnarray}
275  \label{EQ:inertial_stability}  \label{EQ:eg-global-inertial_stability}
276  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
277  \end{eqnarray}  \end{eqnarray}
278    
# Line 287  S_{i} = f^{2} {\delta t_v}^2 Line 280  S_{i} = f^{2} {\delta t_v}^2
280  the $S_{i} < 1$ upper limit for stability.  the $S_{i} < 1$ upper limit for stability.
281  \\  \\
282    
283  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
284  horizontal flow  horizontal flow
285  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
286    
287  \begin{eqnarray}  \begin{eqnarray}
288  \label{EQ:cfl_stability}  \label{EQ:eg-global-cfl_stability}
289  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
290  \end{eqnarray}  \end{eqnarray}
291    
# Line 302  limit of 0.5. Line 295  limit of 0.5.
295    
296  \noindent The stability parameter for internal gravity waves propagating  \noindent The stability parameter for internal gravity waves propagating
297  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
298  \cite{Adcroft_thesis}  \cite{adcroft:95}
299    
300  \begin{eqnarray}  \begin{eqnarray}
301  \label{EQ:cfl_stability}  \label{EQ:eg-global-gfl_stability}
302  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
303  \end{eqnarray}  \end{eqnarray}
304    
# Line 313  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 306  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
306  stability limit of 0.5.  stability limit of 0.5.
307        
308  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
309  \label{SEC:clim_ocn_examp_exp_config}  \label{www:tutorials}
310    \label{SEC:eg-global-clim_ocn_examp_exp_config}
311    
312  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
313  directory {\it verification/exp2/}.  The experiment files  directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
314    The experiment files
315    
316  \begin{itemize}  \begin{itemize}
317  \item {\it input/data}  \item {\it input/data}
318  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 336  contain the code customizations and para Line 332  contain the code customizations and para
332  experiments. Below we describe the customizations  experiments. Below we describe the customizations
333  to these files associated with this experiment.  to these files associated with this experiment.
334    
335    \subsubsection{Driving Datasets}
336    \label{www:tutorials}
337    
338    Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
339    relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
340    the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
341    and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
342    in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures
343    also indicate the lateral extent and coastline used in the experiment.
344    Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
345    domain.
346    
347    
348  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
349    \label{www:tutorials}
350    
351  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
352  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 348  are Line 358  are
358  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}
359  $\cdots$ \\  $\cdots$ \\
360  set reference values for potential  set reference values for potential
361  temperature and salinity at each model level in units of $^{\circ}$C and  temperature and salinity at each model level in units of $^{\circ}\mathrm{C}$ and
362  ${\rm ppt}$. The entries are ordered from surface to depth.  ${\rm ppt}$. The entries are ordered from surface to depth.
363  Density is calculated from anomalies at each level evaluated  Density is calculated from anomalies at each level evaluated
364  with respect to the reference values set here.\\  with respect to the reference values set here.\\
# Line 626  notes. Line 636  notes.
636  \end{small}  \end{small}
637    
638  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
639    \label{www:tutorials}
640    
641  This file uses standard default values and does not contain  This file uses standard default values and does not contain
642  customisations for this experiment.  customisations for this experiment.
643    
644  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
645    \label{www:tutorials}
646    
647  This file uses standard default values and does not contain  This file uses standard default values and does not contain
648  customisations for this experiment.  customisations for this experiment.
649    
650  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
651    \label{www:tutorials}
652    
653  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
654  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 659  in MITgcm. The included matlab program {
659  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
660    
661  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
662    \label{www:tutorials}
663    
664    
665  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 671  The included matlab program {\it input/g
671  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
672    
673  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
674    \label{www:tutorials}
675    
676  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
677    
# Line 683  the vertical domain extent in grid point Line 698  the vertical domain extent in grid point
698  \end{small}  \end{small}
699    
700  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
701    \label{www:tutorials}
702    
703  This file uses standard default values and does not contain  This file uses standard default values and does not contain
704  customisations for this experiment.  customisations for this experiment.
705    
706    
707  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
708    \label{www:tutorials}
709    
710  This file uses standard default values and does not contain  This file uses standard default values and does not contain
711  customisations for this experiment.  customisations for this experiment.
712    
713  \subsubsection{Other Files }  \subsubsection{Other Files }
714    \label{www:tutorials}
715    
716  Other files relevant to this experiment are  Other files relevant to this experiment are
717  \begin{itemize}  \begin{itemize}
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