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%{\large May 2001} |
%{\large May 2001} |
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%\end{center} |
%\end{center} |
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This is the first in a series of tutorials describing |
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example MITgcm numerical experiments. The example experiments |
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include both straightforward examples of idealized geophysical |
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fluid simulations and more involved cases encompassing |
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large scale modeling and |
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automatic differentiation. Both hydrostatic and non-hydrostatic |
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experiments are presented, as well as experiments employing |
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Cartesian, spherical-polar and cube-sphere coordinate systems. |
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These ``case study'' documents include information describing |
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the experimental configuration and detailed information on how to |
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configure the MITgcm code and input files for each experiment. |
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\section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates} |
\section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates} |
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\label{sect:eg-baro} |
%\label{www:tutorials} |
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\label{www:tutorials} |
\label{sec:eg-baro} |
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\begin{rawhtml} |
\begin{rawhtml} |
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<!-- CMIREDIR:eg-baro: --> |
<!-- CMIREDIR:eg-baro: --> |
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\end{rawhtml} |
\end{rawhtml} |
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\begin{center} |
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(in directory: {\it verification/tutorial\_barotropic\_gyre/}) |
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\end{center} |
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This example experiment demonstrates using the MITgcm to simulate |
This example experiment demonstrates using the MITgcm to simulate |
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a Barotropic, wind-forced, ocean gyre circulation. The experiment |
a Barotropic, wind-forced, ocean gyre circulation. The files for this |
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is a numerical rendition of the gyre circulation problem similar |
experiment can be found in the verification directory tutorial\_barotropic\_gyre. |
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The experiment is a numerical rendition of the gyre circulation problem similar |
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to the problems described analytically by Stommel in 1966 |
to the problems described analytically by Stommel in 1966 |
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\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}. |
\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}. |
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equation |
equation |
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\begin{equation} |
\begin{equation} |
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\label{EQ:eg-baro-fcori} |
\label{eq:eg-baro-fcori} |
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f(y) = f_{0}+\beta y |
f(y) = f_{0}+\beta y |
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\end{equation} |
\end{equation} |
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\noindent where $y$ is the distance along the ``north-south'' axis of the |
\noindent where $y$ is the distance along the ``north-south'' axis of the |
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simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in |
simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in |
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(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. |
(\ref{eq:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. |
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\\ |
\\ |
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\\ |
\\ |
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The sinusoidal wind-stress variations are defined according to |
The sinusoidal wind-stress variations are defined according to |
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\begin{equation} |
\begin{equation} |
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\label{EQ:eg-baro-taux} |
\label{eq:eg-baro-taux} |
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\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y}) |
\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y}) |
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\end{equation} |
\end{equation} |
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$\tau_0$ is set to $0.1N m^{-2}$. |
$\tau_0$ is set to $0.1N m^{-2}$. |
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\\ |
\\ |
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\\ |
\\ |
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Figure \ref{FIG:eg-baro-simulation_config} |
Figure \ref{fig:eg-baro-simulation_config} |
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summarizes the configuration simulated. |
summarizes the configuration simulated. |
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%% === eh3 === |
%% === eh3 === |
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%% \begin{center} |
%% \begin{center} |
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%% \resizebox{7.5in}{5.5in}{ |
%% \resizebox{7.5in}{5.5in}{ |
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%% \includegraphics*[0.2in,0.7in][10.5in,10.5in] |
%% \includegraphics*[0.2in,0.7in][10.5in,10.5in] |
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%% {part3/case_studies/barotropic_gyre/simulation_config.eps} } |
%% {s_examples/barotropic_gyre/simulation_config.eps} } |
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%% \end{center} |
%% \end{center} |
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\centerline{ |
\centerline{ |
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\scalefig{.95} |
\scalefig{.95} |
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\epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps} |
\epsfbox{s_examples/barotropic_gyre/simulation_config.eps} |
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} |
} |
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\caption{Schematic of simulation domain and wind-stress forcing function |
\caption{Schematic of simulation domain and wind-stress forcing function |
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for barotropic gyre numerical experiment. The domain is enclosed bu solid |
for barotropic gyre numerical experiment. The domain is enclosed bu solid |
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walls at $x=$~0,1200km and at $y=$~0,1200km.} |
walls at $x=$~0,1200km and at $y=$~0,1200km.} |
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\label{FIG:eg-baro-simulation_config} |
\label{fig:eg-baro-simulation_config} |
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\end{figure} |
\end{figure} |
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\subsection{Equations Solved} |
\subsection{Equations Solved} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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The model is configured in hydrostatic form. The implicit free surface form of the |
The model is configured in hydrostatic form. The implicit free surface form of the |
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pressure equation described in Marshall et. al \cite{marshall:97a} is |
pressure equation described in Marshall et. al \cite{marshall:97a} is |
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employed. |
employed. |
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dissipation. The wind-stress momentum input is added to the momentum equation |
dissipation. The wind-stress momentum input is added to the momentum equation |
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for the ``zonal flow'', $u$. Other terms in the model |
for the ``zonal flow'', $u$. Other terms in the model |
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are explicitly switched off for this experiment configuration (see section |
are explicitly switched off for this experiment configuration (see section |
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\ref{SEC:code_config} ), yielding an active set of equations solved in this |
\ref{sec:eg-baro-code_config} ), yielding an active set of equations solved |
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configuration as follows |
in this configuration as follows |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-baro-model_equations} |
\label{eq:eg-baro-model_equations} |
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\frac{Du}{Dt} - fv + |
\frac{Du}{Dt} - fv + |
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g\frac{\partial \eta}{\partial x} - |
g\frac{\partial \eta}{\partial x} - |
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A_{h}\nabla_{h}^2u |
A_{h}\nabla_{h}^2u |
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\subsection{Discrete Numerical Configuration} |
\subsection{Discrete Numerical Configuration} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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The domain is discretised with |
The domain is discretised with |
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a uniform grid spacing in the horizontal set to |
a uniform grid spacing in the horizontal set to |
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model is configured with a single layer with depth, $\Delta z$, of $5000$~m. |
model is configured with a single layer with depth, $\Delta z$, of $5000$~m. |
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\subsubsection{Numerical Stability Criteria} |
\subsubsection{Numerical Stability Criteria} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$. |
The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$. |
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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}, |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-baro-munk_layer} |
\label{eq:eg-baro-munk_layer} |
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M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} |
M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} |
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\end{eqnarray} |
\end{eqnarray} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-baro-laplacian_stability} |
\label{eq:eg-baro-laplacian_stability} |
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S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} |
S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} |
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\end{eqnarray} |
\end{eqnarray} |
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\cite{adcroft:95} |
\cite{adcroft:95} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-baro-inertial_stability} |
\label{eq:eg-baro-inertial_stability} |
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S_{i} = f^{2} {\delta t}^2 |
S_{i} = f^{2} {\delta t}^2 |
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\end{eqnarray} |
\end{eqnarray} |
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horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ |
horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-baro-cfl_stability} |
\label{eq:eg-baro-cfl_stability} |
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S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} |
S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} |
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\end{eqnarray} |
\end{eqnarray} |
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of 0.5 and limits $\delta t$ to $1200s$. |
of 0.5 and limits $\delta t$ to $1200s$. |
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\subsection{Code Configuration} |
\subsection{Code Configuration} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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\label{SEC:eg-baro-code_config} |
\label{sec:eg-baro-code_config} |
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The model configuration for this experiment resides under the |
The model configuration for this experiment resides under the |
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directory {\it verification/exp0/}. The experiment files |
directory {\it verification/tutorial\_barotropic\_gyre/}. |
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The experiment files |
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\begin{itemize} |
\begin{itemize} |
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\item {\it input/data} |
\item {\it input/data} |
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\item {\it input/data.pkg} |
\item {\it input/data.pkg} |
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to these files associated with this experiment. |
to these files associated with this experiment. |
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\subsubsection{File {\it input/data}} |
\subsubsection{File {\it input/data}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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This file, reproduced completely below, specifies the main parameters |
This file, reproduced completely below, specifies the main parameters |
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for the experiment. The parameters that are significant for this configuration |
for the experiment. The parameters that are significant for this configuration |
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notes. |
notes. |
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\begin{small} |
\begin{small} |
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\input{part3/case_studies/barotropic_gyre/input/data} |
\input{s_examples/barotropic_gyre/input/data} |
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\end{small} |
\end{small} |
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\subsubsection{File {\it input/data.pkg}} |
\subsubsection{File {\it input/data.pkg}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
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customizations for this experiment. |
customizations for this experiment. |
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\subsubsection{File {\it input/eedata}} |
\subsubsection{File {\it input/eedata}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
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customizations for this experiment. |
customizations for this experiment. |
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\subsubsection{File {\it input/windx.sin\_y}} |
\subsubsection{File {\it input/windx.sin\_y}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) |
The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) |
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map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$. |
map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$. |
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code for creating the {\it input/windx.sin\_y} file. |
code for creating the {\it input/windx.sin\_y} file. |
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\subsubsection{File {\it input/topog.box}} |
\subsubsection{File {\it input/topog.box}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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The {\it input/topog.box} file specifies a two-dimensional ($x,y$) |
The {\it input/topog.box} file specifies a two-dimensional ($x,y$) |
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code for creating the {\it input/topog.box} file. |
code for creating the {\it input/topog.box} file. |
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\subsubsection{File {\it code/SIZE.h}} |
\subsubsection{File {\it code/SIZE.h}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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Two lines are customized in this file for the current experiment |
Two lines are customized in this file for the current experiment |
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\end{itemize} |
\end{itemize} |
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\begin{small} |
\begin{small} |
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\input{part3/case_studies/barotropic_gyre/code/SIZE.h} |
\input{s_examples/barotropic_gyre/code/SIZE.h} |
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\end{small} |
\end{small} |
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\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
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customizations for this experiment. |
customizations for this experiment. |
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\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
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customizations for this experiment. |
customizations for this experiment. |