/[MITgcm]/manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex

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-revision 1.16 by jmc,
Tue Jan 15 20:04:06 2008 UTC
+revision 1.25 by mlosch,
Wed Nov 25 10:57:41 2015 UTC
 Line 1
  % $Header$
  % $Name$
- \section[Global Ocean MITgcm Exmaple]{Global Ocean Simulation at $4^\circ$ Resolution}
+ \section[Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution}
- \label{www:tutorials}
+ %\label{www:tutorials}
- \label{sect:eg-global}
+ \label{sec:eg-global}
  \begin{rawhtml}
  <!-- CMIREDIR:eg-global: -->
  \end{rawhtml}
 Line 13
  \bodytext{bgcolor="#FFFFFFFF"}
- %\begin{center}
+ \noindent {\bf WARNING: the description of this experiment is not complete.
+  In particular, many parameters are not yet described.}\\
+ %\begin{center}
  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
  %At Four Degree Resolution with Asynchronous Time Stepping}
  %
-Line 23
+Line 26
  %{\large May 2001}
  %\end{center}
+ This example experiment demonstrates using the MITgcm to simulate the
- This example experiment demonstrates using the MITgcm to simulate
+ planetary ocean circulation. The simulation is configured with
- the planetary ocean circulation. The simulation is configured
+ realistic geography and bathymetry on a $4^{\circ} \times 4^{\circ}$
- with realistic geography and bathymetry on a
+ spherical polar grid. The files for this experiment are in the
- $4^{\circ} \times 4^{\circ}$ spherical polar grid.
+ verification directory under tutorial\_global\_oce\_latlon. Fifteen
- The files for this experiment are in the verification directory
+ levels are used in the vertical, ranging in thickness from $50\,{\rm
- under tutorial\_global\_oce\_latlon.
+   m}$ at the surface to $690\,{\rm m}$ at depth, giving a maximum
- Twenty levels are used in the vertical, ranging in thickness
+ model depth of $5200\,{\rm m}$.
- from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,
+ Different time-steps are used to accelerate the convergence to
- giving a maximum model depth of $6\,{\rm km}$.
+ equilibrium \cite[]{bryan:84} so that, at this resolution,
- At this resolution, the configuration
+ the configuration can be integrated forward for thousands of years
- can be integrated forward for thousands of years on a single
+ on a single processor desktop computer.
- processor desktop computer.
  \\
  \subsection{Overview}
- \label{www:tutorials}
+ %\label{www:tutorials}
- The model is forced with climatological wind stress data and surface
+ The model is forced with climatological wind stress data from
- flux data from DaSilva \cite{DaSilva94}. Climatological data
+ \citet{trenberth90} and NCEP surface flux data from
- from Levitus \cite{Levitus94} is used to initialize the model hydrography.
+ \citet{kalnay96}. Climatological data \citep{Levitus94} is
- Levitus seasonal climatology data is also used throughout the calculation
+ used to initialize the model hydrography. \citeauthor{Levitus94} seasonal
- to provide additional air-sea fluxes.
+ climatology data is also used throughout the calculation to provide
- These fluxes are combined with the DaSilva climatological estimates of
+ additional air-sea fluxes.  These fluxes are combined with the NCEP
- surface heat flux and fresh water, resulting in a mixed boundary
+ climatological estimates of surface heat flux, resulting in a mixed
- condition of the style described in Haney \cite{Haney}.
+ boundary condition of the style described in \citet{Haney}.
- Altogether, this yields the following forcing applied
+ Altogether, this yields the following forcing applied in the model
- in the model surface layer.
+ surface layer.
  \begin{eqnarray}
- \label{EQ:eg-global-global_forcing}
+ \label{eq:eg-global-global_forcing}
- \label{EQ:eg-global-global_forcing_fu}
+ \label{eq:eg-global-global_forcing_fu}
  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
  \\
- \label{EQ:eg-global-global_forcing_fv}
+ \label{eq:eg-global-global_forcing_fv}
  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
  \\
- \label{EQ:eg-global-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:eg-global-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 88 
 experiment are $\tau_{x}$, $\tau_{y}$, $
+Line 90 
 experiment are $\tau_{x}$, $\tau_{y}$, $
  $\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$)
  have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields
  ($\theta^{\ast}$ 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. 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}.
+ \ref{sec:eg-global-clim_ocn_examp_exp_config}.
  \subsection{Discrete Numerical Configuration}
- \label{www:tutorials}
+ %\label{www:tutorials}
-  The model is configured in hydrostatic form.  The domain is discretised with
+ The model is configured in hydrostatic form.  The domain is
- a uniform grid spacing in latitude and longitude on the sphere
+ discretised with a uniform grid spacing in latitude and longitude on
-  $\Delta \phi=\Delta \lambda=4^{\circ}$, so
+ the sphere $\Delta \phi=\Delta \lambda=4^{\circ}$, so that there are
- that there are ninety grid cells in the zonal and forty in the
+ ninety grid cells in the zonal and forty in the meridional
- meridional direction. The internal model coordinate variables
+ direction. The internal model coordinate variables $x$ and $y$ are
- $x$ and $y$ are initialized according to
+ initialized according to
  \begin{eqnarray}
  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
  y=r\lambda,~\Delta y &= &r\Delta \lambda
  \end{eqnarray}
  Arctic polar regions are not
  included in this experiment. Meridionally the model extends from
  $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
- Vertically the model is configured with twenty layers with the
+ Vertically the model is configured with fifteen layers with the
- following thicknesses
+ following thicknesses:
- $\Delta z_{1} = 50\,{\rm m},\,
+ $\Delta z_{1} = 50\,{\rm m},$\\
-  \Delta z_{2} = 50\,{\rm m},\,
+ $\Delta z_{2} = 70\,{\rm m},\,
-  \Delta z_{3} = 55\,{\rm m},\,
+  \Delta z_{3} = 100\,{\rm m},\,
-  \Delta z_{4} = 60\,{\rm m},\,
+  \Delta z_{4} = 140\,{\rm m},\,
-  \Delta z_{5} = 65\,{\rm m},\,
+  \Delta z_{5} = 190\,{\rm m},\,
- $
+  \Delta z_{6} = 240\,{\rm m},\,
- $
+  \Delta z_{7} = 290\,{\rm m},\,
-  \Delta z_{6}~=~70\,{\rm m},\,
+  \Delta z_{8} = 340\,{\rm m},$\\
-  \Delta z_{7}~=~80\,{\rm m},\,
+ $\Delta z_{9} = 390\,{\rm m},\,
-  \Delta z_{8}~=95\,{\rm m},\,
+  \Delta z_{10}= 440\,{\rm m},\,
-  \Delta z_{9}=120\,{\rm m},\,
+  \Delta z_{11}= 490\,{\rm m},\,
-  \Delta z_{10}=155\,{\rm m},\,
+  \Delta z_{12}= 540\,{\rm m},\,
- $
+  \Delta z_{13}= 590\,{\rm m},\,
- $
+  \Delta z_{14}= 640\,{\rm m},\,
-  \Delta z_{11}=200\,{\rm m},\,
+  \Delta z_{15}= 690\,{\rm m}$\\
-  \Delta z_{12}=260\,{\rm m},\,
+ (here the numeric subscript indicates the model level index number, ${\tt k}$) to
-  \Delta z_{13}=320\,{\rm m},\,
+ give a total depth, $H$, of $-5200{\rm m}$.
-  \Delta z_{14}=400\,{\rm m},\,
+ The implicit free surface form of the pressure equation described in
-  \Delta z_{15}=480\,{\rm m},\,
+ \citet{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
- $
- $
-  \Delta z_{16}=570\,{\rm m},\,
-  \Delta z_{17}=655\,{\rm m},\,
-  \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, ${\tt k}$) 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 in (\ref{EQ:eg-global-model_equations})
+ Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations})
  for both the zonal flow, $u$ and the meridional flow $v$, according to equations
- (\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}).
  Thermodynamic forcing inputs are added to the equations
- in (\ref{EQ:eg-global-model_equations}) for
+ in (\ref{eq:eg-global-model_equations}) for
  potential temperature, $\theta$, and salinity, $S$, according to equations
- (\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}).
  This produces a set of equations solved in this configuration as follows:
  \begin{eqnarray}
- \label{EQ:eg-global-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 -
    \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}
   & = &
  \begin{cases}
  {\cal F}_u & \text{(surface)} \\
 & \text{(interior)}
  \end{cases}
  \\
  \frac{Dv}{Dt} + fu +
    \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
    \nabla_{h}\cdot A_{h}\nabla_{h}v -
    \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}
  & = &
  \begin{cases}
  {\cal F}_v & \text{(surface)} \\
-Line 184 
 This produces a set of equations solved
+Line 175 
 This produces a set of equations solved
  \\
  \frac{D\theta}{Dt} -
   \nabla_{h}\cdot K_{h}\nabla_{h}\theta
   - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}
  & = &
  \begin{cases}
  {\cal F}_\theta & \text{(surface)} \\
-Line 193 
 This produces a set of equations solved
+Line 184 
 This produces a set of equations solved
  \\
  \frac{D s}{Dt} -
   \nabla_{h}\cdot K_{h}\nabla_{h}s
   - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}
  & = &
  \begin{cases}
  {\cal F}_s & \text{(surface)} \\
-Line 203 
 This produces a set of equations solved
+Line 194 
 This produces a set of equations solved
  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
  \end{eqnarray}
  \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
  are the zonal and meridional components of the
  flow vector, $\vec{u}$, on the sphere. As described in
  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
  evolution of potential temperature, $\theta$, equation is solved prognostically.
  The total pressure, $p$, is diagnosed by summing pressure due to surface
  elevation $\eta$ and the hydrostatic pressure.
  \\
  \subsubsection{Numerical Stability Criteria}
- \label{www:tutorials}
+ %\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},
+ This value is chosen to yield a Munk layer width \citep{adcroft:95},
  \begin{eqnarray}
- \label{EQ:eg-global-munk_layer}
+ \label{eq:eg-global-munk_layer}
  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
  \end{eqnarray}
  \noindent  of $\approx 600$km. This is greater than the model
  resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional
  boundary layer is adequately resolved.
  \\
- \noindent The model is stepped forward with a
+ \noindent The model is stepped forward with a time step $\Delta
- time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
+ t_{\theta}=24~{\rm hours}$ for thermodynamic variables and $\Delta
- $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
+ t_{v}=30~{\rm minutes}$ for momentum terms. With this time step,
- parameter to the horizontal Laplacian friction \cite{adcroft:95}
+ the stability parameter to the horizontal Laplacian friction
+ \citep{adcroft:95}
  \begin{eqnarray}
- \label{EQ:eg-global-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
+ \noindent evaluates to 0.6 at a latitude of $\phi=80^{\circ}$, which
-.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at
+ is above the 0.3 upper limit for stability, but the zonal grid spacing
- $\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.
+ $\Delta x$ is smallest at $\phi=80^{\circ}$ where $\Delta
- \\
+ x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$ and the stability
+ criterion is already met 1 grid cell equatorwards (at $\phi=76^{\circ}$).
  \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:eg-global-laplacian_stability_z}
+ \label{eq:eg-global-laplacian_stability_z}
- S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
+ && S_{l} = 4 \frac{A_{z} \Delta t_{v}}{{\Delta z}^2}
  \end{eqnarray}
- \noindent evaluates to $0.015$ for the smallest model
+ \noindent evaluates to $0.0029$ for the smallest model
- level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
+ level spacing ($\Delta z_{1}=50{\rm m}$) which is well below
  the upper stability limit.
  \\
- The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
+ % The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
- for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
+ % for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
- and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
+ % and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
- 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 $\Delta x \approx 77 {\rm km}$.
- Here the stability parameter
+ % Here the stability parameter
- \begin{eqnarray}
+ % \begin{eqnarray}
- \label{EQ:eg-global-laplacian_stability_xtheta}
+ % \label{eq:eg-global-laplacian_stability_xtheta}
- S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
+ % S_{l} = \frac{4 K_{h} \Delta t_{\theta}}{{\Delta x}^2}
- \end{eqnarray}
+ % \end{eqnarray}
- 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
- stability parameter related to $K_{z}$
+ % stability parameter related to $K_{z}$
- \begin{eqnarray}
+ % \begin{eqnarray}
- \label{EQ:eg-global-laplacian_stability_ztheta}
+ % \label{eq:eg-global-laplacian_stability_ztheta}
- S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
+ % S_{l} = \frac{4 K_{z} \Delta t_{\theta}}{{\Delta z}^2}
- \end{eqnarray}
+ % \end{eqnarray}
- 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
- of $S_{l} \approx 0.5$.
+ % of $S_{l} \approx 0.5$.
- \\
+ % \\
  \noindent The numerical stability for inertial oscillations
- \cite{adcroft:95}
+ \citep{adcroft:95}
  \begin{eqnarray}
- \label{EQ:eg-global-inertial_stability}
+ \label{eq:eg-global-inertial_stability}
- S_{i} = f^{2} {\delta t_v}^2
+ && S_{i} = f^{2} {\Delta t_v}^2
  \end{eqnarray}
- \noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to
+ \noindent evaluates to $0.07$ for
- the $S_{i} < 1$ upper limit for stability.
+ $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is
+ below the $S_{i} < 1$ upper limit for stability.
  \\
- \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
+ \noindent The advective CFL \citep{adcroft:95} for a extreme maximum
  horizontal flow
  speed of $ | \vec{u} | = 2 ms^{-1}$
  \begin{eqnarray}
- \label{EQ:eg-global-cfl_stability}
+ \label{eq:eg-global-cfl_stability}
- S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
+ && S_{a} = \frac{| \vec{u} | \Delta t_{v}}{ \Delta x}
  \end{eqnarray}
- \noindent evaluates to $6 \times 10^{-2}$. This is well below the stability
+ \noindent evaluates to $5 \times 10^{-2}$. This is well below the stability
  limit of 0.5.
  \\
  \noindent The stability parameter for internal gravity waves propagating
- with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
+  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
- \cite{adcroft:95}
+ \citep{adcroft:95}
  \begin{eqnarray}
- \label{EQ:eg-global-gfl_stability}
+ \label{eq:eg-global-gfl_stability}
- S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
+ && S_{c} = \frac{c_{g} \Delta t_{v}}{ \Delta x}
  \end{eqnarray}
- \noindent evaluates to $3 \times 10^{-1}$. This is close to the linear
+ \noindent evaluates to $2.3 \times 10^{-1}$. This is close to the linear
  stability limit of 0.5.
  \subsection{Experiment Configuration}
- \label{www:tutorials}
+ %\label{www:tutorials}
- \label{SEC:eg-global-clim_ocn_examp_exp_config}
+ \label{sec:eg-global-clim_ocn_examp_exp_config}
  The model configuration for this experiment resides under the
- directory {\it tutorial\_examples/global\_ocean\_circulation/}.
+ directory {\it tutorial\_global\_oce\_latlon/}. The experiment files
- The experiment files
  \begin{itemize}
  \item {\it input/data}
  \item {\it input/data.pkg}
  \item {\it input/eedata},
- \item {\it input/windx.bin},
+ \item {\it input/trenberth\_taux.bin},
- \item {\it input/windy.bin},
+ \item {\it input/trenberth\_tauy.bin},
- \item {\it input/salt.bin},
+ \item {\it input/lev\_s.bin},
- \item {\it input/theta.bin},
+ \item {\it input/lev\_t.bin},
- \item {\it input/SSS.bin},
+ \item {\it input/lev\_sss.bin},
- \item {\it input/SST.bin},
+ \item {\it input/lev\_sst.bin},
- \item {\it input/topog.bin},
+ \item {\it input/bathymetry.bin},
- \item {\it code/CPP\_EEOPTIONS.h}
+ %\item {\it code/CPP\_EEOPTIONS.h}
- \item {\it code/CPP\_OPTIONS.h},
+ %\item {\it code/CPP\_OPTIONS.h},
  \item {\it code/SIZE.h}.
  \end{itemize}
  contain the code customizations and parameter settings for these
  experiments. Below we describe the customizations
  to these files associated with this experiment.
  \subsubsection{Driving Datasets}
- \label{www:tutorials}
+ %\label{www:tutorials}
- Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
+ %% New figures are included before
- relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
+ %% Relaxation temperature
- the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
+ %\begin{figure}
+ %\centering
+ %\includegraphics[]{relax_temperature.eps}
+ %\caption{Relaxation temperature for January}
+ %\label{fig:relax_temperature}
+ %\end{figure}
+ %% Relaxation salinity
+ %\begin{figure}
+ %\centering
+ %\includegraphics[]{relax_salinity.eps}
+ %\caption{Relaxation salinity for January}
+ %\label{fig:relax_salinity}
+ %\end{figure}
+ %% tau_x
+ %\begin{figure}
+ %\centering
+ %\includegraphics[]{tau_x.eps}
+ %\caption{zonal wind stress for January}
+ %\label{fig:tau_x}
+ %\end{figure}
+ %% tau_y
+ %\begin{figure}
+ %\centering
+ %\includegraphics[]{tau_y.eps}
+ %\caption{meridional wind stress for January}
+ %\label{fig:tau_y}
+ %\end{figure}
+ %% Qnet
+ %\begin{figure}
+ %\centering
+ %\includegraphics[]{qnet.eps}
+ %\caption{Heat flux for January}
+ %\label{fig:qnet}
+ %\end{figure}
+ %% EmPmR
+ %\begin{figure}
+ %\centering
+ %\includegraphics[]{empmr.eps}
+ %\caption{Fresh water flux for January}
+ %\label{fig:empmr}
+ %\end{figure}
+ %% Bathymetry
+ %\begin{figure}
+ %\centering
+ %\includegraphics[]{bathymetry.eps}
+ %\caption{Bathymetry}
+ %\label{fig:bathymetry}
+ %\end{figure}
+ Figures (\ref{fig:sim_config_tclim_pcoord}-\ref{fig:sim_config_empmr_pcoord})
+ %(\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
+ in equations
- 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}).
- Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
+ The figures also indicate the lateral extent and coastline used in the
- domain.
+ experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})
+ shows the depth contours of the model domain.
  \subsubsection{File {\it input/data}}
- \label{www:tutorials}
+ %\label{www:tutorials}
- This file, reproduced completely below, specifies the main parameters
- for the experiment. The parameters that are significant for this configuration
- are
- \begin{itemize}
- \item Lines 7-10 and 11-14
- \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 $^{\circ}\mathrm{C}$ 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.\\
- \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 coefficient 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 MOM\_FLUXFORM}({\it mom\_fluxform.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}
- \noindent other lines in the file {\it input/data} are standard values
+ \input{s_examples/global_oce_latlon/inp_data}
- that are described in the MITgcm Getting Started and MITgcm Parameters
- notes.
- \begin{small}
- \input{part3/case_studies/climatalogical_ogcm/input/data}
- \end{small}
  \subsubsection{File {\it input/data.pkg}}
- \label{www:tutorials}
+ %\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}
+ %\label{www:tutorials}
  This file uses standard default values and does not contain
  customisations for this experiment.
- \subsubsection{File {\it input/windx.sin\_y}}
+ \subsubsection{Files{\it input/trenberth\_taux.bin} and {\it
- \label{www:tutorials}
+   input/trenberth\_tauy.bin}}
+ %\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 $Nm^{-2}$.
+ The {\it input/trenberth\_taux.bin} and {\it
- Although $\tau_{x}$ is only a function of $y$n in this experiment
+   input/trenberth\_tauy.bin} files specify a three-dimensional
- this file must still define a complete two-dimensional map in order
+ ($x,y,time$) map of wind stress, $(\tau_{x},\tau_{y})$, values
- to be compatible with the standard code for loading forcing fields
+ \citep{trenberth90}. The units used are $Nm^{-2}$.
- in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
- code for creating the {\it input/windx.sin\_y} file.
+ \subsubsection{File {\it input/bathymetry.bin}}
+ %\label{www:tutorials}
- \subsubsection{File {\it input/topog.box}}
- \label{www:tutorials}
+ The {\it input/bathymetry.bin} file specifies a two-dimensional
+ ($x,y$) map of depth values. For this experiment values range
+ between~$0$ and $-5200\,{\rm m}$, and have been derived from
- The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
+ ETOPO5. The file contains a raw binary stream of data that is
- map of depth values. For this experiment values are either
+ enumerated in the same way as standard MITgcm two-dimensional,
- $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep
+ horizontal arrays.
- ocean. The file contains a raw binary stream of data that is enumerated
- in the same way as standard MITgcm two-dimensional, horizontal arrays.
- The included matlab program {\it input/gendata.m} gives a complete
- code for creating the {\it input/topog.box} file.
  \subsubsection{File {\it code/SIZE.h}}
- \label{www:tutorials}
+ %\label{www:tutorials}
- Two lines are customized in this file for the current experiment
- \begin{itemize}
- \item Line 39,
- \begin{verbatim} sNx=60, \end{verbatim} this line sets
- the lateral domain extent in grid points for the
- axis aligned with the x-coordinate.
- \item Line 40,
- \begin{verbatim} sNy=60, \end{verbatim} this line sets
- the lateral domain extent in grid points for the
- axis aligned with the y-coordinate.
- \item Line 49,
- \begin{verbatim} Nr=4,   \end{verbatim} this line sets
- the vertical domain extent in grid points.
- \end{itemize}
- \begin{small}
+ \input{s_examples/global_oce_latlon/cod_SIZE.h}
- \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}
- \end{small}
- \subsubsection{File {\it code/CPP\_OPTIONS.h}}
+ %\subsubsection{File {\it code/CPP\_OPTIONS.h}}
- \label{www:tutorials}
+ %\label{www:tutorials}
- This file uses standard default values and does not contain
+ %This file uses standard default values and does not contain
- customisations for this experiment.
+ %customisations for this experiment.
- \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
+ %\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
- \label{www:tutorials}
+ %\label{www:tutorials}
- This file uses standard default values and does not contain
+ %This file uses standard default values and does not contain
- customisations for this experiment.
+ %customisations for this experiment.
  \subsubsection{Other Files }
- \label{www:tutorials}
+ %\label{www:tutorials}
- Other files relevant to this experiment are
+ % Other files relevant to this experiment are
- \begin{itemize}
+ % \begin{itemize}
- \item {\it model/src/ini\_cori.F}. This file initializes the model
+ % \item {\it model/src/ini\_cori.F}. This file initializes the model
- coriolis variables {\bf fCorU}.
+ % coriolis variables {\bf fCorU}.
- \item {\it model/src/ini\_spherical\_polar\_grid.F}
+ % \item {\it model/src/ini\_spherical\_polar\_grid.F}
- \item {\it model/src/ini\_parms.F},
+ % \item {\it model/src/ini\_parms.F},
- \item {\it input/windx.sin\_y},
+ % \item {\it input/windx.sin\_y},
- \end{itemize}
+ % \end{itemize}
- contain the code customisations and parameter settings for this
+ % contain the code customisations and parameter settings for this
- experiments. Below we describe the customisations
+ % experiments. Below we describe the customisations
- to these files associated with this experiment.
+ % to these files associated with this experiment.

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