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\section{Illustrations of the model in action} |
\section{Illustrations of the model in action} |
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The 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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from convection on the scale of meters in the ocean to the global pattern of |
from convection on the scale of meters in the ocean to the global pattern of |
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atmospheric winds - see fig.2\ref{fig:all-scales}. To give a flavor of the |
atmospheric winds - see fig.2\ref{fig:all-scales}. To give a flavor of the |
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kinds of problems the model has been used to study, we briefly describe some |
kinds of problems the model has been used to study, we briefly describe some |
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Fig.E1a.\ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$ |
Fig.E1a.\ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$ |
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temperature field obtained using the atmospheric isomorph of MITgcm run at |
temperature field obtained using the atmospheric isomorph of MITgcm run at |
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2.8$^{\circ }$ resolution on the cubed sphere. We see cold air over the pole |
$2.8^{\circ }$ resolution on the cubed sphere. We see cold air over the pole |
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(blue) and warm air along an equatorial band (red). Fully developed |
(blue) and warm air along an equatorial band (red). Fully developed |
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baroclinic eddies spawned in the northern hemisphere storm track are |
baroclinic eddies spawned in the northern hemisphere storm track are |
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evident. There are no mountains or land-sea contrast in this calculation, |
evident. There are no mountains or land-sea contrast in this calculation, |
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solutions of a different and much more realistic kind, can be obtained. |
solutions of a different and much more realistic kind, can be obtained. |
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Fig. ?.? shows the surface temperature and velocity field obtained from |
Fig. ?.? shows the surface temperature and velocity field obtained from |
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MITgcm run at $\frac{1}{6}^{\circ }$ horizontal resolution on a $lat-lon$ |
MITgcm run at $\frac{1}{6}^{\circ }$ horizontal resolution on a \textit{lat-lon} |
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grid in which the pole has been rotated by 90$^{\circ }$ on to the equator |
grid in which the pole has been rotated by $90^{\circ }$ on to the equator |
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(to avoid the converging of meridian in northern latitudes). 21 vertical |
(to avoid the converging of meridian in northern latitudes). 21 vertical |
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levels are used in the vertical with a `lopped cell' representation of |
levels are used in the vertical with a `lopped cell' representation of |
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topography. The development and propagation of anomalously warm and cold |
topography. The development and propagation of anomalously warm and cold |
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\subsection{Global ocean circulation} |
\subsection{Global ocean circulation} |
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Fig.E2a shows the pattern of ocean currents at the surface of a 4$^{\circ }$ |
Fig.E2a shows the pattern of ocean currents at the surface of a $4^{\circ }$ |
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global ocean model run with 15 vertical levels. Lopped cells are used to |
global ocean model run with 15 vertical levels. Lopped cells are used to |
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represent topography on a regular $lat-lon$ grid extending from 70$^{\circ |
represent topography on a regular \textit{lat-lon} grid extending from $70^{\circ |
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}N $ to 70$^{\circ }S$. The model is driven using monthly-mean winds with |
}N $ to $70^{\circ }S$. The model is driven using monthly-mean winds with |
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mixed boundary conditions on temperature and salinity at the surface. The |
mixed boundary conditions on temperature and salinity at the surface. The |
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transfer properties of ocean eddies, convection and mixing is parameterized |
transfer properties of ocean eddies, convection and mixing is parameterized |
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in this model. |
in this model. |
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As one example of application of the MITgcm adjoint, Fig.E4 maps the |
As one example of application of the MITgcm adjoint, Fig.E4 maps the |
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gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude |
gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude |
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of the overturning streamfunction shown in fig?.? at 40$^{\circ }$N and $ |
of the overturning streamfunction shown in fig?.? at $40^{\circ }N$ and $ |
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\mathcal{H}$ is the air-sea heat flux 100 years before. We see that $J$ is |
\mathcal{H}$ is the air-sea heat flux 100 years before. We see that $J$ is |
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sensitive to heat fluxes over the Labrador Sea, one of the important sources |
sensitive to heat fluxes over the Labrador Sea, one of the important sources |
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of deep water for the thermohaline circulations. This calculation also |
of deep water for the thermohaline circulations. This calculation also |
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\end{equation} |
\end{equation} |
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\qquad \qquad \qquad \qquad \qquad |
\qquad \qquad \qquad \qquad \qquad |
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In the above `${r}$' is the distance from the center of the earth and `$lat$ |
In the above `${r}$' is the distance from the center of the earth and |
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' is latitude. |
`\textit{lat}' is latitude. |
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Grad and div operators in spherical coordinates are defined in appendix |
Grad and div operators in spherical coordinates are defined in appendix |
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OPERATORS. |
OPERATORS. |
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which the vertical momentum equation is reduced to a statement of |
which the vertical momentum equation is reduced to a statement of |
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hydrostatic balance and the `traditional approximation' is made in which the |
hydrostatic balance and the `traditional approximation' is made in which the |
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Coriolis force is treated approximately and the shallow atmosphere |
Coriolis force is treated approximately and the shallow atmosphere |
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approximation is made.\ The MITgcm need not make the `traditional |
approximation is made. MITgcm need not make the `traditional |
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approximation'. To be able to support consistent non-hydrostatic forms the |
approximation'. To be able to support consistent non-hydrostatic forms the |
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shallow atmosphere approximation can be relaxed - when dividing through by $ |
shallow atmosphere approximation can be relaxed - when dividing through by $ |
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r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$, |
r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$, |