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% Section: Overview |
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This document provides the reader with the information necessary to |
This document provides the reader with the information necessary to |
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carry out numerical experiments using MITgcm. It gives a comprehensive |
carry out numerical experiments using MITgcm. It gives a comprehensive |
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description of the continuous equations on which the model is based, the |
description of the continuous equations on which the model is based, the |
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We begin by briefly showing some of the results of the model in action to |
We begin by briefly showing some of the results of the model in action to |
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give a feel for the wide range of problems that can be addressed using it. |
give a feel for the wide range of problems that can be addressed using it. |
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\section{Illustrations of the model in action} |
\section{Illustrations of the model in action} |
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MITgcm has been designed and used to model a wide range of phenomena, |
MITgcm has been designed and used to model a wide range of phenomena, |
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\input{s_overview/text/lab_figure} |
\input{s_overview/text/lab_figure} |
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%%CNHend |
%%CNHend |
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\section{Continuous equations in `r' coordinates} |
\section{Continuous equations in `r' coordinates} |
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\begin{rawhtml} |
\begin{rawhtml} |
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<!-- CMIREDIR:z-p_isomorphism: --> |
<!-- CMIREDIR:z-p_isomorphism: --> |
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Tangent linear and adjoint counterparts of the forward model are described |
Tangent linear and adjoint counterparts of the forward model are described |
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in Chapter 5. |
in Chapter 5. |
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\section{Appendix ATMOSPHERE} |
\section{Appendix ATMOSPHERE} |
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1125 |
\subsection{Hydrostatic Primitive Equations for the Atmosphere in pressure |
\subsection{Hydrostatic Primitive Equations for the Atmosphere in pressure |
1139 |
c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q} \label{eq:atmos-heat} |
c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q} \label{eq:atmos-heat} |
1140 |
\end{eqnarray} |
\end{eqnarray} |
1141 |
where $\vec{\mathbf{v}}_{h}=(u,v,0)$ is the `horizontal' (on pressure |
where $\vec{\mathbf{v}}_{h}=(u,v,0)$ is the `horizontal' (on pressure |
1142 |
surfaces) component of velocity,$\frac{D}{Dt}=\vec{\mathbf{v}}_{h}\cdot |
surfaces) component of velocity, $\frac{D}{Dt}=\frac{\partial}{\partial t} |
1143 |
\mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$ is the total |
+\vec{\mathbf{v}}_{h}\cdot \mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$ |
1144 |
derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter, $\phi =gz$ is |
is the total derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter, |
1145 |
the geopotential, $\alpha =1/\rho $ is the specific volume, $\omega =\frac{Dp |
$\phi =gz$ is the geopotential, $\alpha =1/\rho $ is the specific volume, |
1146 |
}{Dt}$ is the vertical velocity in the $p-$coordinate. Equation(\ref |
$\omega =\frac{Dp }{Dt}$ is the vertical velocity in the $p-$coordinate. |
1147 |
{eq:atmos-heat}) is the first law of thermodynamics where internal energy $ |
Equation(\ref {eq:atmos-heat}) is the first law of thermodynamics where internal |
1148 |
e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass and $ |
energy $e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass |
1149 |
p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing. |
and $p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing. |
1150 |
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1151 |
It is convenient to cast the heat equation in terms of potential temperature |
It is convenient to cast the heat equation in terms of potential temperature |
1152 |
$\theta $ so that it looks more like a generic conservation law. |
$\theta $ so that it looks more like a generic conservation law. |
1246 |
\frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } |
\frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } |
1247 |
\end{eqnarray} |
\end{eqnarray} |
1248 |
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1249 |
\section{Appendix OCEAN} |
\section{Appendix OCEAN} |
1250 |
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1251 |
\subsection{Equations of motion for the ocean} |
\subsection{Equations of motion for the ocean} |
1460 |
_{nh}=0$ form of these equations that are used throughout the ocean modeling |
_{nh}=0$ form of these equations that are used throughout the ocean modeling |
1461 |
community and referred to as the primitive equations (HPE). |
community and referred to as the primitive equations (HPE). |
1462 |
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1463 |
\section{Appendix:OPERATORS} |
\section{Appendix:OPERATORS} |
1464 |
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1465 |
\subsection{Coordinate systems} |
\subsection{Coordinate systems} |