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\section{Example: Centenial Time Scale Sensitivities} |
\section{Example: Centennial Time Scale Sensitivities} |
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\bodytext{bgcolor="#FFFFFFFF"} |
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%\begin{center} |
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%{\Large \bf Using MITgcm to Look at Centenial Time Scale |
%{\Large \bf Using MITgcm to Look at Centennial Time Scale |
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%Sensitivities} |
%Sensitivities} |
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%\vspace*{4mm} |
%\vspace*{4mm} |
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\subsection{Introduction} |
\subsection{Introduction} |
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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 iilustrates the use of |
This example illustrates the use of |
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the MITgcm to perform sentivity analysis in a |
the MITgcm to perform sensitivity analysis in a |
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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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processor desktop computer. |
processor desktop computer. |
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The model is forced with climatalogical wind stress data and surface |
The model is forced with climatological wind stress data and surface |
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flux data from Da Silva \cite{DaSilva94}. Climatalogical data |
flux data from Da Silva \cite{DaSilva94}. Climatological data |
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from Levitus \cite{Levitus94} is used to initialise the model hydrography. |
from Levitus \cite{Levitus94} is used to initialize the model hydrography. |
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Levitus data is also used throughout the calculation |
Levitus data is also used throughout the calculation |
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to derive air-sea fluxes of heat at the ocean surface. |
to derive air-sea fluxes of heat at the ocean surface. |
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These fluxes are combined with climatalogical estimates of |
These fluxes are combined with climatological estimates of |
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surface heat flux and fresh water, resulting in a mixed boundary |
surface heat flux and fresh water, resulting in a mixed boundary |
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condition of the style decribed in Haney \cite{Haney}. |
condition of the style described in Haney \cite{Haney}. |
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Altogether, this yields the following forcing applied |
Altogether, this yields the following forcing applied |
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in the model surface layer. |
in the model surface layer. |
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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{Marshall97a} 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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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 merdional 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:global_forcing_fu}) and (\ref{EQ: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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\subsubsection{Numerical Stability Criteria} |
\subsubsection{Numerical Stability Criteria} |
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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_thesis}, |
This value is chosen to yield a Munk layer width \cite{Adcroft_thesis}, |
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\begin{eqnarray} |
\begin{eqnarray} |
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\noindent The model is stepped forward with a |
\noindent The model is stepped forward with a |
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time step $\delta t=1200$secs. With this time step the stability |
time step $\delta t=1200$secs. With this time step the stability |
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parameter to the horizontal laplacian friction \cite{Adcroft_thesis} |
parameter to the horizontal Laplacian friction \cite{Adcroft_thesis} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:laplacian_stability} |
\label{EQ:laplacian_stability} |
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limit of 0.5. |
limit of 0.5. |
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\noindent The stbility parameter for internal gravity waves |
\noindent The stability parameter for internal gravity waves |
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\cite{Adcroft_thesis} |
\cite{Adcroft_thesis} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\item {\it code/CPP\_OPTIONS.h}, |
\item {\it code/CPP\_OPTIONS.h}, |
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\item {\it code/SIZE.h}. |
\item {\it code/SIZE.h}. |
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\end{itemize} |
\end{itemize} |
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contain the code customisations and parameter settings for this |
contain the code customizations and parameter settings for this |
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experiements. Below we describe the customisations |
experiments. Below we describe the customizations |
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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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the initial and reference values of potential temperature at each model |
the initial and reference values of potential temperature at each model |
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level in units of $^{\circ}$C. |
level in units of $^{\circ}$C. |
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The entries are ordered from surface to depth. For each |
The entries are ordered from surface to depth. For each |
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depth level the inital and reference profiles will be uniform in |
depth level the initial and reference profiles will be uniform in |
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$x$ and $y$. |
$x$ and $y$. |
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\fbox{ |
\fbox{ |
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\item Line 6, |
\item Line 6, |
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\begin{verbatim} viscAz=1.E-2, \end{verbatim} |
\begin{verbatim} viscAz=1.E-2, \end{verbatim} |
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this line sets the vertical laplacian dissipation coefficient to |
this line sets the vertical Laplacian dissipation coefficient to |
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$1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions |
$1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions |
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for this operator are specified later. This variable is copied into |
for this operator are specified later. This variable is copied into |
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model general vertical coordinate variable {\bf viscAr}. |
model general vertical coordinate variable {\bf viscAr}. |
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\begin{verbatim} |
\begin{verbatim} |
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viscAh=4.E2, |
viscAh=4.E2, |
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\end{verbatim} |
\end{verbatim} |
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this line sets the horizontal laplacian frictional dissipation coefficient to |
this line sets the horizontal Laplacian frictional dissipation coefficient to |
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$1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions |
$1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions |
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for this operator are specified later. |
for this operator are specified later. |
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no_slip_sides=.FALSE. |
no_slip_sides=.FALSE. |
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\end{verbatim} |
\end{verbatim} |
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this line selects a free-slip lateral boundary condition for |
this line selects a free-slip lateral boundary condition for |
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the horizontal laplacian friction operator |
the horizontal Laplacian friction operator |
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e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and |
e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and |
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$\frac{\partial v}{\partial x}$=0 along boundaries in $x$. |
$\frac{\partial v}{\partial x}$=0 along boundaries in $x$. |
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no_slip_bottom=.TRUE. |
no_slip_bottom=.TRUE. |
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\end{verbatim} |
\end{verbatim} |
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this line selects a no-slip boundary condition for bottom |
this line selects a no-slip boundary condition for bottom |
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boundary condition in the vertical laplacian friction operator |
boundary condition in the vertical Laplacian friction operator |
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e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain. |
e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain. |
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\item Line 10, |
\item Line 10, |
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\end{verbatim} |
\end{verbatim} |
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This line requests that the simulation be performed in a |
This line requests that the simulation be performed in a |
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spherical polar coordinate system. It affects the interpretation of |
spherical polar coordinate system. It affects the interpretation of |
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grid inoput parameters, for exampl {\bf delX} and {\bf delY} and |
grid input parameters, for example {\bf delX} and {\bf delY} and |
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causes the grid generation routines to initialise an internal grid based |
causes the grid generation routines to initialize an internal grid based |
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on spherical polar geometry. |
on spherical polar geometry. |
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\fbox{ |
\fbox{ |
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This line sets the southern boundary of the modeled |
This line sets the southern boundary of the modeled |
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domain to $0^{\circ}$ latitude. This value affects both the |
domain to $0^{\circ}$ latitude. This value affects both the |
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generation of the locally orthogonal grid that the model |
generation of the locally orthogonal grid that the model |
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uses internally and affects the initialisation of the coriolis force. |
uses internally and affects the initialization of the coriolis force. |
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Note - it is not required to set |
Note - it is not required to set |
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a longitude boundary, since the absolute longitude does |
a longitude boundary, since the absolute longitude does |
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not alter the kernel equation discretisation. |
not alter the kernel equation discretisation. |
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\subsubsection{File {\it input/data.pkg}} |
\subsubsection{File {\it input/data.pkg}} |
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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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customisations 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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This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
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customisations 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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\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
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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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customisations 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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This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
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customisations for this experiment. |
customizations for this experiment. |
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\subsubsection{Other Files } |
\subsubsection{Other Files } |
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\item {\it model/src/ini\_parms.F}, |
\item {\it model/src/ini\_parms.F}, |
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\item {\it input/windx.sin\_y}, |
\item {\it input/windx.sin\_y}, |
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\end{itemize} |
\end{itemize} |
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contain the code customisations and parameter settings for this |
contain the code customizations and parameter settings for this |
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experiements. Below we describe the customisations |
experiments. Below we describe the customizations |
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to these files associated with this experiment. |
to these files associated with this experiment. |