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-revision 1.7 by adcroft,
Tue Nov 13 20:13:54 2001 UTC
+revision 1.15 by jmc,
Wed Jun 28 18:57:15 2006 UTC
 Line 1
  % $Header$
  % $Name$
- \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}
+ \section[Global Ocean MITgcm Exmaple]{Global Ocean Simulation at $4^\circ$ Resolution}
+ \label{www:tutorials}
  \label{sect:eg-global}
+ \begin{rawhtml}
+ <!-- CMIREDIR:eg-global: -->
+ \end{rawhtml}
  \bodytext{bgcolor="#FFFFFFFF"}
-Line 16
+Line 20
  %{\large May 2001}
  %\end{center}
- \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}
  This example experiment demonstrates using the MITgcm to simulate
  the planetary ocean circulation. The simulation is configured
  with realistic geography and bathymetry on a
  $4^{\circ} \times 4^{\circ}$ spherical polar grid.
+ The files for this experiment are in the verification directory
+ under tutorial\_global\_oce\_latlon.
  Twenty levels are used in the vertical, ranging in thickness
  from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,
  giving a maximum model depth of $6\,{\rm km}$.
-Line 36 
 At this resolution, the configuration
+Line 34 
 At this resolution, the configuration
  can be integrated forward for thousands of years on a single
  processor desktop computer.
  \\
+ \subsection{Overview}
+ \label{www:tutorials}
  The model is forced with climatological wind stress data and surface
  flux data from DaSilva \cite{DaSilva94}. Climatological data
 Line 49 
 Altogether, this yields the following fo
  in the model surface layer.
  \begin{eqnarray}
- \label{EQ:global_forcing}
+ \label{EQ:eg-global-global_forcing}
- \label{EQ:global_forcing_fu}
+ \label{EQ:eg-global-global_forcing_fu}
  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
  \\
- \label{EQ:global_forcing_fv}
+ \label{EQ:eg-global-global_forcing_fv}
  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
  \\
- \label{EQ:global_forcing_ft}
+ \label{EQ:eg-global-global_forcing_ft}
  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
  \\
- \label{EQ:global_forcing_fs}
+ \label{EQ:eg-global-global_forcing_fs}
  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
  \end{eqnarray}
 Line 87 
 have units of ${\rm N}~{\rm m}^{-2}$. Th
  ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$
  respectively. The salinity forcing fields ($S^{\ast}$ and
  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
- respectively.
+ respectively. The source files and procedures for ingesting this data into the
- \\
+ simulation are described in the experiment configuration discussion in section
+ \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.
  \subsection{Discrete Numerical Configuration}
+ \label{www:tutorials}
   The model is configured in hydrostatic form.  The domain is discretised with
-Line 112 
 meridional direction. The internal model
+Line 104 
 meridional direction. The internal model
  $x$ and $y$ are initialized according to
  \begin{eqnarray}
  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
- y=r\lambda,~\Delta x &= &r\Delta \lambda
+ y=r\lambda,~\Delta y &= &r\Delta \lambda
  \end{eqnarray}
  Arctic polar regions are not
-Line 146 
 $
+Line 138 
 $
   \Delta z_{18}=725\,{\rm m},\,
   \Delta z_{19}=775\,{\rm m},\,
   \Delta z_{20}=815\,{\rm m}
- $ (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
+ give a total depth, $H$, of $-5450{\rm m}$.
  The implicit free surface form of the pressure equation described in Marshall et. al
  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
- 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})
- 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
- (\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}).
- Thermodynamic forcing inputs are added to the equations for
+ Thermodynamic forcing inputs are added to the equations
+ in (\ref{EQ:eg-global-model_equations}) for
  potential temperature, $\theta$, and salinity, $S$, according to equations
- (\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}).
  This produces a set of equations solved in this configuration as follows:
  \begin{eqnarray}
- \label{EQ:model_equations}
+ \label{EQ:eg-global-model_equations}
  \frac{Du}{Dt} - fv +
    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
    \nabla_{h}\cdot A_{h}\nabla_{h}u -
-Line 217 
 elevation $\eta$ and the hydrostatic pre
+Line 211 
 elevation $\eta$ and the hydrostatic pre
  \\
  \subsubsection{Numerical Stability Criteria}
+ \label{www:tutorials}
  The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
  This value is chosen to yield a Munk layer width \cite{adcroft:95},
  \begin{eqnarray}
- \label{EQ:munk_layer}
+ \label{EQ:eg-global-munk_layer}
- M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
+ && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
  \end{eqnarray}
  \noindent  of $\approx 600$km. This is greater than the model
-Line 235 
 time step $\delta t_{\theta}=30~{\rm hou
+Line 230 
 time step $\delta t_{\theta}=30~{\rm hou
  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
  parameter to the horizontal Laplacian friction \cite{adcroft:95}
  \begin{eqnarray}
- \label{EQ:laplacian_stability}
+ \label{EQ:eg-global-laplacian_stability}
- S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
+ && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
  \end{eqnarray}
  \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 242 
 $\phi=80^{\circ}$ where $\Delta x=r\cos(
  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
  \begin{eqnarray}
- \label{EQ:laplacian_stability_z}
+ \label{EQ:eg-global-laplacian_stability_z}
  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
  \end{eqnarray}
-Line 262 
 and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
+Line 257 
 and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
  related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
  Here the stability parameter
  \begin{eqnarray}
- \label{EQ:laplacian_stability_xtheta}
+ \label{EQ:eg-global-laplacian_stability_xtheta}
  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
  \end{eqnarray}
  evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
  stability parameter related to $K_{z}$
  \begin{eqnarray}
- \label{EQ:laplacian_stability_ztheta}
+ \label{EQ:eg-global-laplacian_stability_ztheta}
  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
  \end{eqnarray}
  evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
-Line 279 
 of $S_{l} \approx 0.5$.
+Line 274 
 of $S_{l} \approx 0.5$.
  \cite{adcroft:95}
  \begin{eqnarray}
- \label{EQ:inertial_stability}
+ \label{EQ:eg-global-inertial_stability}
  S_{i} = f^{2} {\delta t_v}^2
  \end{eqnarray}
-Line 292 
 horizontal flow
+Line 287 
 horizontal flow
  speed of $ | \vec{u} | = 2 ms^{-1}$
  \begin{eqnarray}
- \label{EQ:cfl_stability}
+ \label{EQ:eg-global-cfl_stability}
  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
  \end{eqnarray}
-Line 305 
 with a maximum speed of $c_{g}=10~{\rm m
+Line 300 
 with a maximum speed of $c_{g}=10~{\rm m
  \cite{adcroft:95}
  \begin{eqnarray}
- \label{EQ:cfl_stability}
+ \label{EQ:eg-global-gfl_stability}
  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
  \end{eqnarray}
-Line 313 
 S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
+Line 308 
 S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
  stability limit of 0.5.
  \subsection{Experiment Configuration}
- \label{SEC:clim_ocn_examp_exp_config}
+ \label{www:tutorials}
+ \label{SEC:eg-global-clim_ocn_examp_exp_config}
  The model configuration for this experiment resides under the
- directory {\it verification/exp2/}.  The experiment files
+ directory {\it tutorial\_examples/global\_ocean\_circulation/}.
+ The experiment files
  \begin{itemize}
  \item {\it input/data}
  \item {\it input/data.pkg}
-Line 336 
 contain the code customizations and para
+Line 334 
 contain the code customizations and para
  experiments. Below we describe the customizations
  to these files associated with this experiment.
+ \subsubsection{Driving Datasets}
+ \label{www:tutorials}
+ Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
+ relaxation temperature ($\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.
  \subsubsection{File {\it input/data}}
+ \label{www:tutorials}
  This file, reproduced completely below, specifies the main parameters
  for the experiment. The parameters that are significant for this configuration
-Line 348 
 are
+Line 360 
 are
  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}
  $\cdots$ \\
  set reference values for potential
- temperature and salinity at each model level in units of $^{\circ}$C and
+ temperature and salinity at each model level in units of $^{\circ}\mathrm{C}$ 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.\\
-Line 568 
 See section \ref{SEC:cd_scheme}.
+Line 580 
 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})
+ {\it S/R MOM\_FLUXFORM}({\it mom\_fluxform.F})
  \end{minipage}
  }
-Line 626 
 notes.
+Line 638 
 notes.
  \end{small}
  \subsubsection{File {\it input/data.pkg}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
  customisations for this experiment.
  \subsubsection{File {\it input/eedata}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
  customisations for this experiment.
  \subsubsection{File {\it input/windx.sin\_y}}
+ \label{www:tutorials}
  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
-Line 646 
 in MITgcm. The included matlab program {
+Line 661 
 in MITgcm. The included matlab program {
  code for creating the {\it input/windx.sin\_y} file.
  \subsubsection{File {\it input/topog.box}}
+ \label{www:tutorials}
  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
-Line 657 
 The included matlab program {\it input/g
+Line 673 
 The included matlab program {\it input/g
  code for creating the {\it input/topog.box} file.
  \subsubsection{File {\it code/SIZE.h}}
+ \label{www:tutorials}
  Two lines are customized in this file for the current experiment
-Line 683 
 the vertical domain extent in grid point
+Line 700 
 the vertical domain extent in grid point
  \end{small}
  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
  customisations for this experiment.
  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
  customisations for this experiment.
  \subsubsection{Other Files }
+ \label{www:tutorials}
  Other files relevant to this experiment are
  \begin{itemize}

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