| 87 |
computational platforms. |
computational platforms. |
| 88 |
\end{itemize} |
\end{itemize} |
| 89 |
|
|
| 90 |
|
|
| 91 |
Key publications reporting on and charting the development of the model are |
Key publications reporting on and charting the development of the model are |
| 92 |
\cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99,adcroft:04a,adcroft:04b,marshall:04}: |
\cite{hill:95,marshall:97a,marshall:97b,adcroft:97,mars-eta:98,adcroft:99,hill:99,maro-eta:99,adcroft:04a,adcroft:04b,marshall:04} |
| 93 |
|
(an overview on the model formulation can also be found in \cite{adcroft:04c}): |
| 94 |
|
|
| 95 |
\begin{verbatim} |
\begin{verbatim} |
| 96 |
Hill, C. and J. Marshall, (1995) |
Hill, C. and J. Marshall, (1995) |
| 167 |
|
|
| 168 |
Figure \ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$ |
Figure \ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$ |
| 169 |
temperature field obtained using the atmospheric isomorph of MITgcm run at |
temperature field obtained using the atmospheric isomorph of MITgcm run at |
| 170 |
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 |
| 171 |
(blue) and warm air along an equatorial band (red). Fully developed |
(blue) and warm air along an equatorial band (red). Fully developed |
| 172 |
baroclinic eddies spawned in the northern hemisphere storm track are |
baroclinic eddies spawned in the northern hemisphere storm track are |
| 173 |
evident. There are no mountains or land-sea contrast in this calculation, |
evident. There are no mountains or land-sea contrast in this calculation, |
| 212 |
increased until the baroclinic instability process is resolved, numerical |
increased until the baroclinic instability process is resolved, numerical |
| 213 |
solutions of a different and much more realistic kind, can be obtained. |
solutions of a different and much more realistic kind, can be obtained. |
| 214 |
|
|
| 215 |
Figure \ref{fig:ocean-gyres} shows the surface temperature and velocity |
Figure \ref{fig:ocean-gyres} shows the surface temperature and |
| 216 |
field obtained from MITgcm run at $\frac{1}{6}^{\circ }$ horizontal |
velocity field obtained from MITgcm run at $\frac{1}{6}^{\circ }$ |
| 217 |
resolution on a $lat-lon$ |
horizontal resolution on a \textit{lat-lon} grid in which the pole has |
| 218 |
grid in which the pole has been rotated by 90$^{\circ }$ on to the equator |
been rotated by $90^{\circ }$ on to the equator (to avoid the |
| 219 |
(to avoid the converging of meridian in northern latitudes). 21 vertical |
converging of meridian in northern latitudes). 21 vertical levels are |
| 220 |
levels are used in the vertical with a `lopped cell' representation of |
used in the vertical with a `lopped cell' representation of |
| 221 |
topography. The development and propagation of anomalously warm and cold |
topography. The development and propagation of anomalously warm and |
| 222 |
eddies can be clearly seen in the Gulf Stream region. The transport of |
cold eddies can be clearly seen in the Gulf Stream region. The |
| 223 |
warm water northward by the mean flow of the Gulf Stream is also clearly |
transport of warm water northward by the mean flow of the Gulf Stream |
| 224 |
visible. |
is also clearly visible. |
| 225 |
|
|
| 226 |
%% CNHbegin |
%% CNHbegin |
| 227 |
\input{part1/atl6_figure} |
\input{part1/atl6_figure} |
| 233 |
<!-- CMIREDIR:global_ocean_circulation: --> |
<!-- CMIREDIR:global_ocean_circulation: --> |
| 234 |
\end{rawhtml} |
\end{rawhtml} |
| 235 |
|
|
| 236 |
Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean currents at |
Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean |
| 237 |
the surface of a 4$^{\circ }$ |
currents at the surface of a $4^{\circ }$ global ocean model run with |
| 238 |
global ocean model run with 15 vertical levels. Lopped cells are used to |
15 vertical levels. Lopped cells are used to represent topography on a |
| 239 |
represent topography on a regular $lat-lon$ grid extending from 70$^{\circ |
regular \textit{lat-lon} grid extending from $70^{\circ }N$ to |
| 240 |
}N $ to 70$^{\circ }S$. The model is driven using monthly-mean winds with |
$70^{\circ }S$. The model is driven using monthly-mean winds with |
| 241 |
mixed boundary conditions on temperature and salinity at the surface. The |
mixed boundary conditions on temperature and salinity at the surface. |
| 242 |
transfer properties of ocean eddies, convection and mixing is parameterized |
The transfer properties of ocean eddies, convection and mixing is |
| 243 |
in this model. |
parameterized in this model. |
| 244 |
|
|
| 245 |
Figure \ref{fig:large-scale-circ} (bottom) shows the meridional overturning |
Figure \ref{fig:large-scale-circ} (bottom) shows the meridional overturning |
| 246 |
circulation of the global ocean in Sverdrups. |
circulation of the global ocean in Sverdrups. |
| 303 |
`automatic adjoint compiler'. These can be used in parameter sensitivity and |
`automatic adjoint compiler'. These can be used in parameter sensitivity and |
| 304 |
data assimilation studies. |
data assimilation studies. |
| 305 |
|
|
| 306 |
As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity} |
As one example of application of the MITgcm adjoint, Figure |
| 307 |
maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude |
\ref{fig:hf-sensitivity} maps the gradient $\frac{\partial J}{\partial |
| 308 |
of the overturning stream-function shown in figure \ref{fig:large-scale-circ} |
\mathcal{H}}$where $J$ is the magnitude of the overturning |
| 309 |
at 60$^{\circ }$N and $ |
stream-function shown in figure \ref{fig:large-scale-circ} at |
| 310 |
\mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over |
$60^{\circ }N$ and $ \mathcal{H}(\lambda,\varphi)$ is the mean, local |
| 311 |
a 100 year period. We see that $J$ is |
air-sea heat flux over a 100 year period. We see that $J$ is sensitive |
| 312 |
sensitive to heat fluxes over the Labrador Sea, one of the important sources |
to heat fluxes over the Labrador Sea, one of the important sources of |
| 313 |
of deep water for the thermohaline circulations. This calculation also |
deep water for the thermohaline circulations. This calculation also |
| 314 |
yields sensitivities to all other model parameters. |
yields sensitivities to all other model parameters. |
| 315 |
|
|
| 316 |
%%CNHbegin |
%%CNHbegin |
| 343 |
<!-- CMIREDIR:ocean_biogeo_cycles: --> |
<!-- CMIREDIR:ocean_biogeo_cycles: --> |
| 344 |
\end{rawhtml} |
\end{rawhtml} |
| 345 |
|
|
| 346 |
MITgcm is being used to study global biogeochemical cycles in the ocean. For |
MITgcm is being used to study global biogeochemical cycles in the |
| 347 |
example one can study the effects of interannual changes in meteorological |
ocean. For example one can study the effects of interannual changes in |
| 348 |
forcing and upper ocean circulation on the fluxes of carbon dioxide and |
meteorological forcing and upper ocean circulation on the fluxes of |
| 349 |
oxygen between the ocean and atmosphere. Figure \ref{fig:biogeo} shows |
carbon dioxide and oxygen between the ocean and atmosphere. Figure |
| 350 |
the annual air-sea flux of oxygen and its relation to density outcrops in |
\ref{fig:biogeo} shows the annual air-sea flux of oxygen and its |
| 351 |
the southern oceans from a single year of a global, interannually varying |
relation to density outcrops in the southern oceans from a single year |
| 352 |
simulation. The simulation is run at $1^{\circ}\times1^{\circ}$ resolution |
of a global, interannually varying simulation. The simulation is run |
| 353 |
telescoping to $\frac{1}{3}^{\circ}\times\frac{1}{3}^{\circ}$ in the tropics (not shown). |
at $1^{\circ}\times1^{\circ}$ resolution telescoping to |
| 354 |
|
$\frac{1}{3}^{\circ}\times\frac{1}{3}^{\circ}$ in the tropics (not |
| 355 |
|
shown). |
| 356 |
|
|
| 357 |
%%CNHbegin |
%%CNHbegin |
| 358 |
\input{part1/biogeo_figure} |
\input{part1/biogeo_figure} |
| 1079 |
|
|
| 1080 |
The mixing terms for the temperature and salinity equations have a similar |
The mixing terms for the temperature and salinity equations have a similar |
| 1081 |
form to that of momentum except that the diffusion tensor can be |
form to that of momentum except that the diffusion tensor can be |
| 1082 |
non-diagonal and have varying coefficients. $\qquad $ |
non-diagonal and have varying coefficients. |
| 1083 |
\begin{equation} |
\begin{equation} |
| 1084 |
D_{T,S}=\nabla .[\underline{\underline{K}}\nabla (T,S)]+K_{4}\nabla |
D_{T,S}=\nabla .[\underline{\underline{K}}\nabla (T,S)]+K_{4}\nabla |
| 1085 |
_{h}^{4}(T,S) \label{eq:diffusion} |
_{h}^{4}(T,S) \label{eq:diffusion} |
| 1491 |
\end{equation*} |
\end{equation*} |
| 1492 |
|
|
| 1493 |
\begin{equation*} |
\begin{equation*} |
| 1494 |
v=r\frac{D\varphi }{Dt}\qquad |
v=r\frac{D\varphi }{Dt} |
| 1495 |
\end{equation*} |
\end{equation*} |
|
$\qquad \qquad \qquad \qquad $ |
|
| 1496 |
|
|
| 1497 |
\begin{equation*} |
\begin{equation*} |
| 1498 |
\dot{r}=\frac{Dr}{Dt} |
\dot{r}=\frac{Dr}{Dt} |
| 1502 |
distance of the particle from the center of the earth, $\Omega $ is the |
distance of the particle from the center of the earth, $\Omega $ is the |
| 1503 |
angular speed of rotation of the Earth and $D/Dt$ is the total derivative. |
angular speed of rotation of the Earth and $D/Dt$ is the total derivative. |
| 1504 |
|
|
| 1505 |
The `grad' ($\nabla $) and `div' ($\nabla $.) operators are defined by, in |
The `grad' ($\nabla $) and `div' ($\nabla\cdot$) operators are defined by, in |
| 1506 |
spherical coordinates: |
spherical coordinates: |
| 1507 |
|
|
| 1508 |
\begin{equation*} |
\begin{equation*} |
| 1512 |
\end{equation*} |
\end{equation*} |
| 1513 |
|
|
| 1514 |
\begin{equation*} |
\begin{equation*} |
| 1515 |
\nabla .v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial |
\nabla\cdot v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial |
| 1516 |
\lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\} |
\lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\} |
| 1517 |
+\frac{1}{r^{2}}\frac{\partial \left( r^{2}\dot{r}\right) }{\partial r} |
+\frac{1}{r^{2}}\frac{\partial \left( r^{2}\dot{r}\right) }{\partial r} |
| 1518 |
\end{equation*} |
\end{equation*} |
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