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revision 1.3 by cnh, Thu Oct 25 18:36:55 2001 UTC revision 1.10 by adcroft, Wed Nov 20 14:09:32 2002 UTC
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1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}  \section{Global Ocean Simulation at 4$^\circ$ Resolution}
5  \label{sec:eg-global}  \label{www:tutorials}
6    \label{sect:eg-global}
7    
8  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
9    
# Line 16  Line 17 
17  %{\large May 2001}  %{\large May 2001}
18  %\end{center}  %\end{center}
19    
 \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}  
20    
21  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
22  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
# Line 36  At this resolution, the configuration Line 29  At this resolution, the configuration
29  can be integrated forward for thousands of years on a single  can be integrated forward for thousands of years on a single
30  processor desktop computer.  processor desktop computer.
31  \\  \\
32    \subsection{Overview}
33    \label{www:tutorials}
34    
35  The model is forced with climatological wind stress data and surface  The model is forced with climatological wind stress data and surface
36  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 44  Altogether, this yields the following fo
44  in the model surface layer.  in the model surface layer.
45    
46  \begin{eqnarray}  \begin{eqnarray}
47  \label{EQ:global_forcing}  \label{EQ:eg-global-global_forcing}
48  \label{EQ:global_forcing_fu}  \label{EQ:eg-global-global_forcing_fu}
49  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
50  \\  \\
51  \label{EQ:global_forcing_fv}  \label{EQ:eg-global-global_forcing_fv}
52  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
53  \\  \\
54  \label{EQ:global_forcing_ft}  \label{EQ:eg-global-global_forcing_ft}
55  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
56   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
57  \\  \\
58  \label{EQ:global_forcing_fs}  \label{EQ:eg-global-global_forcing_fs}
59  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
60   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
61  \end{eqnarray}  \end{eqnarray}
# Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 82  have units of ${\rm N}~{\rm m}^{-2}$. Th
82  ($\theta^{\ast}$ 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 ${\rm W}~{\rm m}^{-2}$
83  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
84  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
85  respectively.  respectively. The source files and procedures for ingesting this data into the
86  \\  simulation are described in the experiment configuration discussion in section
87    \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.  
88    
89    
90  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
91    \label{www:tutorials}
92    
93    
94   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 99  meridional direction. The internal model
99  $x$ and $y$ are initialized according to  $x$ and $y$ are initialized according to
100  \begin{eqnarray}  \begin{eqnarray}
101  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
102  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
103  \end{eqnarray}  \end{eqnarray}
104    
105  Arctic polar regions are not  Arctic polar regions are not
# Line 146  $ Line 133  $
133   \Delta z_{18}=725\,{\rm m},\,   \Delta z_{18}=725\,{\rm m},\,
134   \Delta z_{19}=775\,{\rm m},\,   \Delta z_{19}=775\,{\rm m},\,
135   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
136  $ (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
137    give a total depth, $H$, of $-5450{\rm m}$.
138  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
139  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
140  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
141    
142  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})
143  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
144  (\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}).
145  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations
146    in (\ref{EQ:eg-global-model_equations}) for
147  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
148  (\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}).
149  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
150    
151  \begin{eqnarray}  \begin{eqnarray}
152  \label{EQ:model_equations}  \label{EQ:eg-global-model_equations}
153  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
154    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
155    \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 199  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
199  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
200  are the zonal and meridional components of the  are the zonal and meridional components of the
201  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
202  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
203  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
204  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
205  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
206  \\  \\
207    
208  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
209    \label{www:tutorials}
210    
211  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 $5 \times 10^5 m s^{-1}$.
212  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},
213  \begin{eqnarray}  \begin{eqnarray}
214  \label{EQ:munk_layer}  \label{EQ:eg-global-munk_layer}
215  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
216  \end{eqnarray}  \end{eqnarray}
217    
218  \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 223  boundary layer is adequately resolved.
223  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
224  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
225  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
226  parameter to the horizontal Laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
227  \begin{eqnarray}  \begin{eqnarray}
228  \label{EQ:laplacian_stability}  \label{EQ:eg-global-laplacian_stability}
229  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
230  \end{eqnarray}  \end{eqnarray}
231    
232  \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 237  $\phi=80^{\circ}$ where $\Delta x=r\cos(
237  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
238  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
239  \begin{eqnarray}  \begin{eqnarray}
240  \label{EQ:laplacian_stability_z}  \label{EQ:eg-global-laplacian_stability_z}
241  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
242  \end{eqnarray}  \end{eqnarray}
243    
# Line 262  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s} Line 252  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
252  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 $\Delta x \approx 77 {\rm km}$.
253  Here the stability parameter  Here the stability parameter
254  \begin{eqnarray}  \begin{eqnarray}
255  \label{EQ:laplacian_stability_xtheta}  \label{EQ:eg-global-laplacian_stability_xtheta}
256  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
257  \end{eqnarray}  \end{eqnarray}
258  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
259  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
260  \begin{eqnarray}  \begin{eqnarray}
261  \label{EQ:laplacian_stability_ztheta}  \label{EQ:eg-global-laplacian_stability_ztheta}
262  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
263  \end{eqnarray}  \end{eqnarray}
264  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 266  of $S_{l} \approx 0.5$.
266  \\  \\
267    
268  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
269  \cite{Adcroft_thesis}  \cite{adcroft:95}
270    
271  \begin{eqnarray}  \begin{eqnarray}
272  \label{EQ:inertial_stability}  \label{EQ:eg-global-inertial_stability}
273  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
274  \end{eqnarray}  \end{eqnarray}
275    
# Line 287  S_{i} = f^{2} {\delta t_v}^2 Line 277  S_{i} = f^{2} {\delta t_v}^2
277  the $S_{i} < 1$ upper limit for stability.  the $S_{i} < 1$ upper limit for stability.
278  \\  \\
279    
280  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
281  horizontal flow  horizontal flow
282  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
283    
284  \begin{eqnarray}  \begin{eqnarray}
285  \label{EQ:cfl_stability}  \label{EQ:eg-global-cfl_stability}
286  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
287  \end{eqnarray}  \end{eqnarray}
288    
# Line 302  limit of 0.5. Line 292  limit of 0.5.
292    
293  \noindent The stability parameter for internal gravity waves propagating  \noindent The stability parameter for internal gravity waves propagating
294  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
295  \cite{Adcroft_thesis}  \cite{adcroft:95}
296    
297  \begin{eqnarray}  \begin{eqnarray}
298  \label{EQ:cfl_stability}  \label{EQ:eg-global-gfl_stability}
299  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
300  \end{eqnarray}  \end{eqnarray}
301    
# Line 313  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 303  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
303  stability limit of 0.5.  stability limit of 0.5.
304        
305  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
306  \label{SEC:clim_ocn_examp_exp_config}  \label{www:tutorials}
307    \label{SEC:eg-global-clim_ocn_examp_exp_config}
308    
309  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
310  directory {\it verification/exp2/}.  The experiment files  directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
311    The experiment files
312    
313  \begin{itemize}  \begin{itemize}
314  \item {\it input/data}  \item {\it input/data}
315  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 336  contain the code customizations and para Line 329  contain the code customizations and para
329  experiments. Below we describe the customizations  experiments. Below we describe the customizations
330  to these files associated with this experiment.  to these files associated with this experiment.
331    
332    \subsubsection{Driving Datasets}
333    \label{www:tutorials}
334    
335    Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
336    relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
337    the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
338    and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
339    in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures
340    also indicate the lateral extent and coastline used in the experiment.
341    Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
342    domain.
343    
344    
345  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
346    \label{www:tutorials}
347    
348  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
349  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 626  notes. Line 633  notes.
633  \end{small}  \end{small}
634    
635  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
636    \label{www:tutorials}
637    
638  This file uses standard default values and does not contain  This file uses standard default values and does not contain
639  customisations for this experiment.  customisations for this experiment.
640    
641  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
642    \label{www:tutorials}
643    
644  This file uses standard default values and does not contain  This file uses standard default values and does not contain
645  customisations for this experiment.  customisations for this experiment.
646    
647  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
648    \label{www:tutorials}
649    
650  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
651  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 656  in MITgcm. The included matlab program {
656  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
657    
658  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
659    \label{www:tutorials}
660    
661    
662  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 668  The included matlab program {\it input/g
668  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
669    
670  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
671    \label{www:tutorials}
672    
673  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
674    
# Line 683  the vertical domain extent in grid point Line 695  the vertical domain extent in grid point
695  \end{small}  \end{small}
696    
697  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
698    \label{www:tutorials}
699    
700  This file uses standard default values and does not contain  This file uses standard default values and does not contain
701  customisations for this experiment.  customisations for this experiment.
702    
703    
704  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
705    \label{www:tutorials}
706    
707  This file uses standard default values and does not contain  This file uses standard default values and does not contain
708  customisations for this experiment.  customisations for this experiment.
709    
710  \subsubsection{Other Files }  \subsubsection{Other Files }
711    \label{www:tutorials}
712    
713  Other files relevant to this experiment are  Other files relevant to this experiment are
714  \begin{itemize}  \begin{itemize}
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