| 77 |
\begin{itemize} |
\begin{itemize} |
| 78 |
\item it can be used to study both atmospheric and oceanic phenomena; one |
\item it can be used to study both atmospheric and oceanic phenomena; one |
| 79 |
hydrodynamical kernel is used to drive forward both atmospheric and oceanic |
hydrodynamical kernel is used to drive forward both atmospheric and oceanic |
| 80 |
models - see fig.1% |
models - see fig% |
| 81 |
\marginpar{ |
\marginpar{ |
| 82 |
Fig.1 One model}\ref{fig:onemodel} |
Fig.1 One model}\ref{fig:onemodel} |
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| 84 |
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%% CNHbegin |
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\input{part1/one_model_figure} |
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%% CNHend |
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\item it has a non-hydrostatic capability and so can be used to study both |
\item it has a non-hydrostatic capability and so can be used to study both |
| 89 |
small-scale and large scale processes - see fig.2% |
small-scale and large scale processes - see fig % |
| 90 |
\marginpar{ |
\marginpar{ |
| 91 |
Fig.2 All scales}\ref{fig:all-scales} |
Fig.2 All scales}\ref{fig:all-scales} |
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| 93 |
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%% CNHbegin |
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\input{part1/all_scales_figure} |
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%% CNHend |
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\item finite volume techniques are employed yielding an intuitive |
\item finite volume techniques are employed yielding an intuitive |
| 98 |
discretization and support for the treatment of irregular geometries using |
discretization and support for the treatment of irregular geometries using |
| 99 |
orthogonal curvilinear grids and shaved cells - see fig.3% |
orthogonal curvilinear grids and shaved cells - see fig % |
| 100 |
\marginpar{ |
\marginpar{ |
| 101 |
Fig.3 Finite volumes}\ref{fig:Finite volumes} |
Fig.3 Finite volumes}\ref{fig:finite-volumes} |
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%% CNHbegin |
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\input{part1/fvol_figure} |
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%% CNHend |
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\item tangent linear and adjoint counterparts are automatically maintained |
\item tangent linear and adjoint counterparts are automatically maintained |
| 108 |
along with the forward model, permitting sensitivity and optimization |
along with the forward model, permitting sensitivity and optimization |
| 140 |
A novel feature of MITgcm is its ability to simulate both atmospheric and |
A novel feature of MITgcm is its ability to simulate both atmospheric and |
| 141 |
oceanographic flows at both small and large scales. |
oceanographic flows at both small and large scales. |
| 142 |
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|
| 143 |
Fig.E1a.\ref{fig:Held-Suarez} shows an instantaneous plot of the 500$mb$ |
Fig.E1a.\ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$ |
| 144 |
temperature field obtained using the atmospheric isomorph of MITgcm run at |
temperature field obtained using the atmospheric isomorph of MITgcm run at |
| 145 |
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 |
| 146 |
(blue) and warm air along an equatorial band (red). Fully developed |
(blue) and warm air along an equatorial band (red). Fully developed |
| 151 |
in Held and Suarez; 1994 designed to test atmospheric hydrodynamical cores - |
in Held and Suarez; 1994 designed to test atmospheric hydrodynamical cores - |
| 152 |
there are no mountains or land-sea contrast. |
there are no mountains or land-sea contrast. |
| 153 |
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| 154 |
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%% CNHbegin |
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\input{part1/cubic_eddies_figure} |
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As described in Adcroft (2001), a `cubed sphere' is used to discretize the |
As described in Adcroft (2001), a `cubed sphere' is used to discretize the |
| 159 |
globe permitting a uniform gridding and obviated the need to fourier filter. |
globe permitting a uniform gridding and obviated the need to fourier filter. |
| 160 |
The `vector-invariant' form of MITgcm supports any orthogonal curvilinear |
The `vector-invariant' form of MITgcm supports any orthogonal curvilinear |
| 167 |
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| 168 |
A regular spherical lat-lon grid can also be used. |
A regular spherical lat-lon grid can also be used. |
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%% CNHbegin |
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\input{part1/hs_zave_u_figure} |
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| 174 |
\subsection{Ocean gyres} |
\subsection{Ocean gyres} |
| 175 |
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| 176 |
Baroclinic instability is a ubiquitous process in the ocean, as well as the |
Baroclinic instability is a ubiquitous process in the ocean, as well as the |
| 191 |
warm water northward by the mean flow of the Gulf Stream is also clearly |
warm water northward by the mean flow of the Gulf Stream is also clearly |
| 192 |
visible. |
visible. |
| 193 |
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| 194 |
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%% CNHbegin |
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\input{part1/ocean_gyres_figure} |
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| 199 |
\subsection{Global ocean circulation} |
\subsection{Global ocean circulation} |
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| 201 |
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$^{\circ }$ |
| 209 |
Fig.E2b shows the meridional overturning circulation of the global ocean in |
Fig.E2b shows the meridional overturning circulation of the global ocean in |
| 210 |
Sverdrups. |
Sverdrups. |
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%%CNHbegin |
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\input{part1/global_circ_figure} |
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%%CNHend |
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| 216 |
\subsection{Convection and mixing over topography} |
\subsection{Convection and mixing over topography} |
| 217 |
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| 218 |
Dense plumes generated by localized cooling on the continental shelf of the |
Dense plumes generated by localized cooling on the continental shelf of the |
| 227 |
strong, and replaced by lateral entrainment due to the baroclinic |
strong, and replaced by lateral entrainment due to the baroclinic |
| 228 |
instability of the along-slope current. |
instability of the along-slope current. |
| 229 |
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%%CNHbegin |
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\input{part1/convect_and_topo} |
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%%CNHend |
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| 234 |
\subsection{Boundary forced internal waves} |
\subsection{Boundary forced internal waves} |
| 235 |
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| 236 |
The unique ability of MITgcm to treat non-hydrostatic dynamics in the |
The unique ability of MITgcm to treat non-hydrostatic dynamics in the |
| 245 |
using MITgcm's finite volume spatial discretization) where they break under |
using MITgcm's finite volume spatial discretization) where they break under |
| 246 |
nonhydrostatic dynamics. |
nonhydrostatic dynamics. |
| 247 |
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| 248 |
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%%CNHbegin |
| 249 |
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\input{part1/boundary_forced_waves} |
| 250 |
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%%CNHend |
| 251 |
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| 252 |
\subsection{Parameter sensitivity using the adjoint of MITgcm} |
\subsection{Parameter sensitivity using the adjoint of MITgcm} |
| 253 |
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| 254 |
Forward and tangent linear counterparts of MITgcm are supported using an |
Forward and tangent linear counterparts of MITgcm are supported using an |
| 263 |
of deep water for the thermohaline circulations. This calculation also |
of deep water for the thermohaline circulations. This calculation also |
| 264 |
yields sensitivities to all other model parameters. |
yields sensitivities to all other model parameters. |
| 265 |
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| 266 |
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%%CNHbegin |
| 267 |
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\input{part1/adj_hf_ocean_figure} |
| 268 |
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%%CNHend |
| 269 |
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| 270 |
\subsection{Global state estimation of the ocean} |
\subsection{Global state estimation of the ocean} |
| 271 |
|
|
| 272 |
An important application of MITgcm is in state estimation of the global |
An important application of MITgcm is in state estimation of the global |
| 278 |
ocean obtained by bringing the model in to consistency with altimetric and |
ocean obtained by bringing the model in to consistency with altimetric and |
| 279 |
in-situ observations over the period 1992-1997. |
in-situ observations over the period 1992-1997. |
| 280 |
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| 281 |
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%% CNHbegin |
| 282 |
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\input{part1/globes_figure} |
| 283 |
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%% CNHend |
| 284 |
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| 285 |
\subsection{Ocean biogeochemical cycles} |
\subsection{Ocean biogeochemical cycles} |
| 286 |
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|
| 287 |
MITgcm is being used to study global biogeochemical cycles in the ocean. For |
MITgcm is being used to study global biogeochemical cycles in the ocean. For |
| 291 |
flux of oxygen and its relation to density outcrops in the southern oceans |
flux of oxygen and its relation to density outcrops in the southern oceans |
| 292 |
from a single year of a global, interannually varying simulation. |
from a single year of a global, interannually varying simulation. |
| 293 |
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|
| 294 |
Chris - get figure here: http://puddle.mit.edu/\symbol{126}% |
%%CNHbegin |
| 295 |
mick/biogeochem.html |
\input{part1/biogeo_figure} |
| 296 |
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%%CNHend |
| 297 |
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| 298 |
\subsection{Simulations of laboratory experiments} |
\subsection{Simulations of laboratory experiments} |
| 299 |
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|
| 306 |
arrested by its instability in a process analogous to that whic sets the |
arrested by its instability in a process analogous to that whic sets the |
| 307 |
stratification of the ACC. |
stratification of the ACC. |
| 308 |
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| 309 |
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%%CNHbegin |
| 310 |
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\input{part1/lab_figure} |
| 311 |
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%%CNHend |
| 312 |
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| 313 |
% $Header$ |
% $Header$ |
| 314 |
% $Name$ |
% $Name$ |
| 315 |
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| 325 |
vertical coordinate `$r$' is interpreted as pressure, $p$, if we are |
vertical coordinate `$r$' is interpreted as pressure, $p$, if we are |
| 326 |
modeling the atmosphere and height, $z$, if we are modeling the ocean. |
modeling the atmosphere and height, $z$, if we are modeling the ocean. |
| 327 |
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| 328 |
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%%CNHbegin |
| 329 |
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\input{part1/zandpcoord_figure.tex} |
| 330 |
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%%CNHend |
| 331 |
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|
| 332 |
The state of the fluid at any time is characterized by the distribution of |
The state of the fluid at any time is characterized by the distribution of |
| 333 |
velocity $\vec{\mathbf{v}}$, active tracers $\theta $ and $S$, a |
velocity $\vec{\mathbf{v}}$, active tracers $\theta $ and $S$, a |
| 334 |
`geopotential' $\phi $ and density $\rho =\rho (\theta ,S,p)$ which may |
`geopotential' $\phi $ and density $\rho =\rho (\theta ,S,p)$ which may |
| 339 |
\marginpar{ |
\marginpar{ |
| 340 |
Fig.5 The vertical coordinate of model}: |
Fig.5 The vertical coordinate of model}: |
| 341 |
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| 342 |
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%%CNHbegin |
| 343 |
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\input{part1/vertcoord_figure.tex} |
| 344 |
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%%CNHend |
| 345 |
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| 346 |
\begin{equation*} |
\begin{equation*} |
| 347 |
\frac{D\vec{\mathbf{v}_{h}}}{Dt}+\left( 2\vec{\Omega}\times \vec{\mathbf{v}}% |
\frac{D\vec{\mathbf{v}_{h}}}{Dt}+\left( 2\vec{\Omega}\times \vec{\mathbf{v}}% |
| 348 |
\right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}}% |
\right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}}% |
| 688 |
\marginpar{ |
\marginpar{ |
| 689 |
Fig.6 Spherical polar coordinate system.} |
Fig.6 Spherical polar coordinate system.} |
| 690 |
|
|
| 691 |
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%%CNHbegin |
| 692 |
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\input{part1/sphere_coord_figure.tex} |
| 693 |
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%%CNHend |
| 694 |
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|
| 695 |
\subsubsection{Shallow atmosphere approximation} |
\subsubsection{Shallow atmosphere approximation} |
| 696 |
|
|
| 697 |
Most models are based on the `hydrostatic primitive equations' (HPE's) in |
Most models are based on the `hydrostatic primitive equations' (HPE's) in |
| 808 |
stepping forward the horizontal momentum equations; $\dot{r}$ is found by |
stepping forward the horizontal momentum equations; $\dot{r}$ is found by |
| 809 |
stepping forward the vertical momentum equation. |
stepping forward the vertical momentum equation. |
| 810 |
|
|
| 811 |
|
%%CNHbegin |
| 812 |
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\input{part1/solution_strategy_figure.tex} |
| 813 |
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%%CNHend |
| 814 |
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|
| 815 |
There is no penalty in implementing \textbf{QH} over \textbf{HPE} except, of |
There is no penalty in implementing \textbf{QH} over \textbf{HPE} except, of |
| 816 |
course, some complication that goes with the inclusion of $\cos \phi \ $% |
course, some complication that goes with the inclusion of $\cos \phi \ $% |
| 817 |
Coriolis terms and the relaxation of the shallow atmosphere approximation. |
Coriolis terms and the relaxation of the shallow atmosphere approximation. |
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