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revision 1.18 by jmc, Fri Aug 27 13:25:32 2010 UTC revision 1.19 by jmc, Mon Aug 30 23:09:20 2010 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section[Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution}  \section[Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution}
5  \label{www:tutorials}  %\label{www:tutorials}
6  \label{sect:eg-global}  \label{sec:eg-global}
7  \begin{rawhtml}  \begin{rawhtml}
8  <!-- CMIREDIR:eg-global: -->  <!-- CMIREDIR:eg-global: -->
9  \end{rawhtml}  \end{rawhtml}
# Line 38  can be integrated forward for thousands Line 38  can be integrated forward for thousands
38  processor desktop computer.  processor desktop computer.
39  \\  \\
40  \subsection{Overview}  \subsection{Overview}
41  \label{www:tutorials}  %\label{www:tutorials}
42    
43  The model is forced with climatological wind stress data and surface  The model is forced with climatological wind stress data and surface
44  flux data from DaSilva \cite{DaSilva94}. Climatological data  flux data from DaSilva \cite{DaSilva94}. Climatological data
# Line 52  Altogether, this yields the following fo Line 52  Altogether, this yields the following fo
52  in the model surface layer.  in the model surface layer.
53    
54  \begin{eqnarray}  \begin{eqnarray}
55  \label{EQ:eg-global-global_forcing}  \label{eq:eg-global-global_forcing}
56  \label{EQ:eg-global-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:eg-global-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:eg-global-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:eg-global-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 92  respectively. The salinity forcing field Line 92  respectively. The salinity forcing field
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. The source files and procedures for ingesting this data into the  respectively. The source files and procedures for ingesting this data into the
94  simulation are described in the experiment configuration discussion in section  simulation are described in the experiment configuration discussion in section
95  \ref{SEC:eg-global-clim_ocn_examp_exp_config}.  \ref{sec:eg-global-clim_ocn_examp_exp_config}.
96    
97    
98  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
99  \label{www:tutorials}  %\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 147  The implicit free surface form of the pr Line 147  The implicit free surface form of the pr
147  \cite{marshall:97a} 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 in (\ref{EQ:eg-global-model_equations})  Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations})
151  for both 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
152  (\ref{EQ:eg-global-global_forcing_fu}) and (\ref{EQ:eg-global-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  Thermodynamic forcing inputs are added to the equations
154  in (\ref{EQ:eg-global-model_equations}) for  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:eg-global-global_forcing_ft}) and (\ref{EQ:eg-global-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:eg-global-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 214  elevation $\eta$ and the hydrostatic pre Line 214  elevation $\eta$ and the hydrostatic pre
214  \\  \\
215    
216  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
217  \label{www:tutorials}  %\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:95},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
221  \begin{eqnarray}  \begin{eqnarray}
222  \label{EQ:eg-global-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    
# Line 233  time step $\delta t_{\theta}=30~{\rm hou Line 233  time step $\delta t_{\theta}=30~{\rm hou
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:95}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
235  \begin{eqnarray}  \begin{eqnarray}
236  \label{EQ:eg-global-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    
# Line 245  $\phi=80^{\circ}$ 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:eg-global-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    
# Line 260  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:eg-global-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 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
267  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
268  \begin{eqnarray}  \begin{eqnarray}
269  \label{EQ:eg-global-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 277  of $S_{l} \approx 0.5$. Line 277  of $S_{l} \approx 0.5$.
277  \cite{adcroft:95}  \cite{adcroft:95}
278    
279  \begin{eqnarray}  \begin{eqnarray}
280  \label{EQ:eg-global-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 290  horizontal flow Line 290  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:eg-global-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 303  with a maximum speed of $c_{g}=10~{\rm m Line 303  with a maximum speed of $c_{g}=10~{\rm m
303  \cite{adcroft:95}  \cite{adcroft:95}
304    
305  \begin{eqnarray}  \begin{eqnarray}
306  \label{EQ:eg-global-gfl_stability}  \label{eq:eg-global-gfl_stability}
307  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
308  \end{eqnarray}  \end{eqnarray}
309    
# Line 311  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 311  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
311  stability limit of 0.5.  stability limit of 0.5.
312        
313  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
314  \label{www:tutorials}  %\label{www:tutorials}
315  \label{SEC:eg-global-clim_ocn_examp_exp_config}  \label{sec:eg-global-clim_ocn_examp_exp_config}
316    
317  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
318  directory {\it tutorial\_examples/global\_ocean\_circulation/}.    directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
# Line 338  experiments. Below we describe the custo Line 338  experiments. Below we describe the custo
338  to these files associated with this experiment.  to these files associated with this experiment.
339    
340  \subsubsection{Driving Datasets}  \subsubsection{Driving Datasets}
341  \label{www:tutorials}  %\label{www:tutorials}
342    
343  Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the  Figures ({\it --- missing figures ---})
344  relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,  %(\ref{fig:sim_config_tclim}-\ref{fig:sim_config_empmr})
345  the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)  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  and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used  and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
348  in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures  in equations
349  also indicate the lateral extent and coastline used in the experiment.  (\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}).
350  Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model  The figures also indicate the lateral extent and coastline used in the
351  domain.  experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})
352    shows the depth contours of the model domain.
353    
354  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
355  \label{www:tutorials}  %\label{www:tutorials}
356    
357  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
358  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 523  cg2dTargetResidual=1.E-13, Line 524  cg2dTargetResidual=1.E-13,
524  \end{verbatim}  \end{verbatim}
525  Sets the tolerance which the two-dimensional, conjugate  Sets the tolerance which the two-dimensional, conjugate
526  gradient solver will use to test for convergence in equation  gradient solver will use to test for convergence in equation
527  \ref{EQ:congrad_2d_resid} to $1 \times 10^{-13}$.  %- note: Description of Conjugate gradient method (& related params) is missing
528  Solver will iterate until  %  in the mean time, substitute this eq ref:
529  tolerance falls below this value or until the maximum number of  \ref{eq:elliptic-backward-free-surface} %\ref{eq:congrad_2d_resid}
530  solver iterations is reached.\\  to $1 \times 10^{-13}$.
531    Solver will iterate until tolerance falls below this value or until the
532    maximum number of solver iterations is reached.\\
533  \fbox{  \fbox{
534  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
535  {\it S/R CG2D}~({\it cg2d.F})  {\it S/R CG2D}~({\it cg2d.F})
# Line 565  deltaTmom=2400.0, Line 568  deltaTmom=2400.0,
568  \end{verbatim}  \end{verbatim}
569  Sets the timestep $\delta t_{v}$ used in the momentum equations to  Sets the timestep $\delta t_{v}$ used in the momentum equations to
570  $20~{\rm mins}$.  $20~{\rm mins}$.
571  See section \ref{SEC:mom_time_stepping}.  %- note: Distord Physics (using different time-steps) is not described
572    %  in the mean time, put this section ref:
573    See section \ref{sec:time_stepping}. %\ref{sec:mom_time_stepping}.
574    
575  \fbox{  \fbox{
576  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 577  See section \ref{SEC:mom_time_stepping}. Line 582  See section \ref{SEC:mom_time_stepping}.
582  \begin{verbatim}  \begin{verbatim}
583  tauCD=321428.,  tauCD=321428.,
584  \end{verbatim}  \end{verbatim}
585  Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.  Sets the D-grid to C-grid coupling time scale $\tau_{CD}$
586  See section \ref{SEC:cd_scheme}.  used in the momentum equations.
587    %- note: description of CD-scheme pkg (and related params) is missing;
588    %  in the mean time, comment out this ref.
589    %See section \ref{sec:cd_scheme}.
590    
591  \fbox{  \fbox{
592  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 593  deltaTtracer=108000., Line 601  deltaTtracer=108000.,
601  \end{verbatim}  \end{verbatim}
602  Sets the default timestep, $\delta t_{\theta}$, for tracer equations to  Sets the default timestep, $\delta t_{\theta}$, for tracer equations to
603  $30~{\rm hours}$.  $30~{\rm hours}$.
604  See section \ref{SEC:tracer_time_stepping}.  %- note: Distord Physics (using different time-steps) is not described
605    %  in the mean time, put this section ref:
606    See section \ref{sec:time_stepping}. %\ref{sec:tracer_time_stepping}.
607    
608  \fbox{  \fbox{
609  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 641  notes. Line 651  notes.
651  \end{small}  \end{small}
652    
653  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
654  \label{www:tutorials}  %\label{www:tutorials}
655    
656  This file uses standard default values and does not contain  This file uses standard default values and does not contain
657  customisations for this experiment.  customisations for this experiment.
658    
659  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
660  \label{www:tutorials}  %\label{www:tutorials}
661    
662  This file uses standard default values and does not contain  This file uses standard default values and does not contain
663  customisations for this experiment.  customisations for this experiment.
664    
665  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
666  \label{www:tutorials}  %\label{www:tutorials}
667    
668  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
669  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 664  in MITgcm. The included matlab program { Line 674  in MITgcm. The included matlab program {
674  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
675    
676  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
677  \label{www:tutorials}  %\label{www:tutorials}
678    
679    
680  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 676  The included matlab program {\it input/g Line 686  The included matlab program {\it input/g
686  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
687    
688  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
689  \label{www:tutorials}  %\label{www:tutorials}
690    
691  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
692    
# Line 703  the vertical domain extent in grid point Line 713  the vertical domain extent in grid point
713  \end{small}  \end{small}
714    
715  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
716  \label{www:tutorials}  %\label{www:tutorials}
717    
718  This file uses standard default values and does not contain  This file uses standard default values and does not contain
719  customisations for this experiment.  customisations for this experiment.
720    
721    
722  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
723  \label{www:tutorials}  %\label{www:tutorials}
724    
725  This file uses standard default values and does not contain  This file uses standard default values and does not contain
726  customisations for this experiment.  customisations for this experiment.
727    
728  \subsubsection{Other Files }  \subsubsection{Other Files }
729  \label{www:tutorials}  %\label{www:tutorials}
730    
731  Other files relevant to this experiment are  Other files relevant to this experiment are
732  \begin{itemize}  \begin{itemize}
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