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% $Name$ |
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\section{Example: Centennial Time Scale Sensitivities} |
\section{Centennial Time Scale Tracer Injection} |
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\label{www:tutorials} |
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\label{sect:eg-simple-tracer} |
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\begin{rawhtml} |
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<!-- CMIREDIR:eg-simple-tracer: --> |
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\end{rawhtml} |
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\bodytext{bgcolor="#FFFFFFFF"} |
\bodytext{bgcolor="#FFFFFFFF"} |
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%\end{center} |
%\end{center} |
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\subsection{Introduction} |
\subsection{Introduction} |
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\label{www:tutorials} |
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This document describes the fourth example MITgcm experiment. |
This document describes the fourth example MITgcm experiment. |
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This example illustrates the use of |
This example illustrates the use of |
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large scale ocean circulation simulation. |
large scale ocean circulation simulation. |
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\subsection{Overview} |
\subsection{Overview} |
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\label{www:tutorials} |
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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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the planetary ocean circulation. The simulation is configured |
the planetary ocean circulation. The simulation is configured |
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in the model surface layer. |
in the model surface layer. |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:global_forcing} |
\label{EQ:eg-simple-tracer-global_forcing} |
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\label{EQ:global_forcing_fu} |
\label{EQ:eg-simple-tracer-global_forcing_fu} |
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{\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}} |
{\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}} |
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\\ |
\\ |
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\label{EQ:global_forcing_fv} |
\label{EQ:eg-simple-tracer-global_forcing_fv} |
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{\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}} |
{\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}} |
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\\ |
\\ |
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\label{EQ:global_forcing_ft} |
\label{EQ:eg-simple-tracer-global_forcing_ft} |
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{\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} ) |
{\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} ) |
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- \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q} |
- \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q} |
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\\ |
\\ |
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\label{EQ:global_forcing_fs} |
\label{EQ:eg-simple-tracer-global_forcing_fs} |
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{\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} ) |
{\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} ) |
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+ \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R}) |
+ \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R}) |
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\end{eqnarray} |
\end{eqnarray} |
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\subsection{Discrete Numerical Configuration} |
\subsection{Discrete Numerical Configuration} |
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\label{www:tutorials} |
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The model is configured in hydrostatic form. The domain is discretised with |
The model is configured in hydrostatic form. The domain is discretised with |
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\Delta z_{20}=815\,{\rm m} |
\Delta z_{20}=815\,{\rm m} |
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$ (here the numeric subscript indicates the model level index number, ${\tt k}$). |
$ (here the numeric subscript indicates the model level index number, ${\tt k}$). |
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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 |
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\cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous |
\cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous |
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dissipation. Thermal and haline diffusion is also represented by a Laplacian operator. |
dissipation. Thermal and haline diffusion is also represented by a Laplacian operator. |
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\\ |
\\ |
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Wind-stress momentum inputs are added to the momentum equations for both |
Wind-stress momentum inputs are added to the momentum equations for both |
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the zonal flow, $u$ and the meridional flow $v$, according to equations |
the zonal flow, $u$ and the meridional flow $v$, according to equations |
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(\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}). |
(\ref{EQ:eg-simple-tracer-global_forcing_fu}) and (\ref{EQ:eg-simple-tracer-global_forcing_fv}). |
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Thermodynamic forcing inputs are added to the equations for |
Thermodynamic forcing inputs are added to the equations for |
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potential temperature, $\theta$, and salinity, $S$, according to equations |
potential temperature, $\theta$, and salinity, $S$, according to equations |
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(\ref{EQ:global_forcing_ft}) and (\ref{EQ:global_forcing_fs}). |
(\ref{EQ:eg-simple-tracer-global_forcing_ft}) and (\ref{EQ:eg-simple-tracer-global_forcing_fs}). |
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This produces a set of equations solved in this configuration as follows: |
This produces a set of equations solved in this configuration as follows: |
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% {\fracktur} |
% {\fracktur} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:model_equations} |
\label{EQ:eg-simple-tracer-model_equations} |
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\frac{Du}{Dt} - fv + |
\frac{Du}{Dt} - fv + |
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\frac{1}{\rho}\frac{\partial p^{'}}{\partial x} - |
\frac{1}{\rho}\frac{\partial p^{'}}{\partial x} - |
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A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}} |
A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}} |
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\noindent where $u$ and $v$ are the $x$ and $y$ components of the |
\noindent where $u$ and $v$ are the $x$ and $y$ components of the |
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flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and |
flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and |
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interior model levels respectively. As described in |
interior model levels respectively. As described in |
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MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time |
MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time |
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evolution of potential temperature, $\theta$, equation is solved prognostically. |
evolution of potential temperature, $\theta$, equation is solved prognostically. |
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The total pressure, $p$, is diagnosed by summing pressure due to surface |
The total pressure, $p$, is diagnosed by summing pressure due to surface |
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elevation $\eta$ and the hydrostatic pressure. |
elevation $\eta$ and the hydrostatic pressure. |
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\\ |
\\ |
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\subsubsection{Numerical Stability Criteria} |
\subsubsection{Numerical Stability Criteria} |
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\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:munk_layer} |
\label{EQ:eg-simple-tracer-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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parameter to the horizontal Laplacian friction \cite{adcroft:95} |
parameter to the horizontal Laplacian friction \cite{adcroft:95} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:laplacian_stability} |
\label{EQ:eg-simple-tracer-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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$1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit |
$1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:laplacian_stability_z} |
\label{EQ:eg-simple-tracer-laplacian_stability_z} |
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S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2} |
S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^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:inertial_stability} |
\label{EQ:eg-simple-tracer-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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speed of $ | \vec{u} | = 2 ms^{-1}$ |
speed of $ | \vec{u} | = 2 ms^{-1}$ |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:cfl_stability} |
\label{EQ:eg-simple-tracer-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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\cite{adcroft:95} |
\cite{adcroft:95} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:cfl_stability} |
\label{EQ:eg-simple-tracer-igw_stability} |
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S_{c} = \frac{c_{g} \delta t}{ \Delta x} |
S_{c} = \frac{c_{g} \delta t}{ \Delta x} |
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\end{eqnarray} |
\end{eqnarray} |
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stability limit of 0.25. |
stability limit of 0.25. |
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\subsection{Code Configuration} |
\subsection{Code Configuration} |
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\label{www:tutorials} |
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\label{SEC:code_config} |
\label{SEC: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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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} |
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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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\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} |
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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} |
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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} |
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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} |
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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} |
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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{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} |
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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} |
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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{Other Files } |
\subsubsection{Other Files } |
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\label{www:tutorials} |
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Other files relevant to this experiment are |
Other files relevant to this experiment are |
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\begin{itemize} |
\begin{itemize} |
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