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revision 1.9 by adcroft, Tue Nov 13 20:13:07 2001 UTC revision 1.15 by cnh, Wed Nov 21 16:33:17 2001 UTC
# Line 83  studies. Line 83  studies.
83  computational platforms.  computational platforms.
84  \end{itemize}  \end{itemize}
85    
86  Key publications reporting on and charting the development of the model are  Key publications reporting on and charting the development of the model are:
87  listed in an Appendix.  
88    \begin{verbatim}
89    
90    Hill, C. and J. Marshall, (1995)
91    Application of a Parallel Navier-Stokes Model to Ocean Circulation in
92    Parallel Computational Fluid Dynamics
93    In Proceedings of Parallel Computational Fluid Dynamics: Implementations
94    and Results Using Parallel Computers, 545-552.
95    Elsevier Science B.V.: New York
96    
97    Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997)
98    Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling,
99    J. Geophysical Res., 102(C3), 5733-5752.
100    
101    Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, (1997)
102    A finite-volume, incompressible Navier Stokes model for studies of the ocean
103    on parallel computers,
104    J. Geophysical Res., 102(C3), 5753-5766.
105    
106    Adcroft, A.J., Hill, C.N. and J. Marshall, (1997)
107    Representation of topography by shaved cells in a height coordinate ocean
108    model
109    Mon Wea Rev, vol 125, 2293-2315
110    
111    Marshall, J., Jones, H. and C. Hill, (1998)
112    Efficient ocean modeling using non-hydrostatic algorithms
113    Journal of Marine Systems, 18, 115-134
114    
115    Adcroft, A., Hill C. and J. Marshall: (1999)
116    A new treatment of the Coriolis terms in C-grid models at both high and low
117    resolutions,
118    Mon. Wea. Rev. Vol 127, pages 1928-1936
119    
120    Hill, C, Adcroft,A., Jamous,D., and J. Marshall, (1999)
121    A Strategy for Terascale Climate Modeling.
122    In Proceedings of the Eighth ECMWF Workshop on the Use of Parallel Processors
123    in Meteorology, pages 406-425
124    World Scientific Publishing Co: UK
125    
126    Marotzke, J, Giering,R., Zhang, K.Q., Stammer,D., Hill,C., and T.Lee, (1999)
127    Construction of the adjoint MIT ocean general circulation model and
128    application to Atlantic heat transport variability
129    J. Geophysical Res., 104(C12), 29,529-29,547.
130    
131    
132    \end{verbatim}
133    
134  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
135  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.
# Line 102  of them here. A more detailed descriptio Line 147  of them here. A more detailed descriptio
147  numerical algorithm and implementation that lie behind these calculations is  numerical algorithm and implementation that lie behind these calculations is
148  given later. Indeed many of the illustrative examples shown below can be  given later. Indeed many of the illustrative examples shown below can be
149  easily reproduced: simply download the model (the minimum you need is a PC  easily reproduced: simply download the model (the minimum you need is a PC
150  running linux, together with a FORTRAN\ 77 compiler) and follow the examples  running Linux, together with a FORTRAN\ 77 compiler) and follow the examples
151  described in detail in the documentation.  described in detail in the documentation.
152    
153  \subsection{Global atmosphere: `Held-Suarez' benchmark}  \subsection{Global atmosphere: `Held-Suarez' benchmark}
# Line 126  there are no mountains or land-sea contr Line 171  there are no mountains or land-sea contr
171  %% CNHend  %% CNHend
172    
173  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
174  globe permitting a uniform gridding and obviated the need to Fourier filter.  globe permitting a uniform griding and obviated the need to Fourier filter.
175  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear
176  grid, of which the cubed sphere is just one of many choices.  grid, of which the cubed sphere is just one of many choices.
177    
# Line 163  warm water northward by the mean flow of Line 208  warm water northward by the mean flow of
208  visible.  visible.
209    
210  %% CNHbegin  %% CNHbegin
211  \input{part1/ocean_gyres_figure}  \input{part1/atl6_figure}
212  %% CNHend  %% CNHend
213    
214    
# Line 231  data assimilation studies. Line 276  data assimilation studies.
276    
277  As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity}  As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity}
278  maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude  maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude
279  of the overturning streamfunction shown in figure \ref{fig:large-scale-circ}  of the overturning stream-function shown in figure \ref{fig:large-scale-circ}
280  at 60$^{\circ }$N and $  at 60$^{\circ }$N and $
281  \mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over  \mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over
282  a 100 year period. We see that $J$ is  a 100 year period. We see that $J$ is
# Line 248  yields sensitivities to all other model Line 293  yields sensitivities to all other model
293  An important application of MITgcm is in state estimation of the global  An important application of MITgcm is in state estimation of the global
294  ocean circulation. An appropriately defined `cost function', which measures  ocean circulation. An appropriately defined `cost function', which measures
295  the departure of the model from observations (both remotely sensed and  the departure of the model from observations (both remotely sensed and
296  insitu) over an interval of time, is minimized by adjusting `control  in-situ) over an interval of time, is minimized by adjusting `control
297  parameters' such as air-sea fluxes, the wind field, the initial conditions  parameters' such as air-sea fluxes, the wind field, the initial conditions
298  etc. Figure \ref{fig:assimilated-globes} shows an estimate of the time-mean  etc. Figure \ref{fig:assimilated-globes} shows the large scale planetary
299  surface elevation of the ocean obtained by bringing the model in to  circulation and a Hopf-Muller plot of Equatorial sea-surface height.
300    Both are obtained from assimilation bringing the model in to
301  consistency with altimetric and in-situ observations over the period  consistency with altimetric and in-situ observations over the period
302  1992-1997. {\bf CHANGE THIS TEXT - FIG FROM PATRICK/CARL/DETLEF}  1992-1997.
303    
304  %% CNHbegin  %% CNHbegin
305  \input{part1/globes_figure}  \input{part1/assim_figure}
306  %% CNHend  %% CNHend
307    
308  \subsection{Ocean biogeochemical cycles}  \subsection{Ocean biogeochemical cycles}
# Line 277  telescoping to $\frac{1}{3}^{\circ}\time Line 323  telescoping to $\frac{1}{3}^{\circ}\time
323  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
324    
325  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a
326  laboratory experiment enquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An  laboratory experiment inquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An
327  initially homogeneous tank of water ($1m$ in diameter) is driven from its  initially homogeneous tank of water ($1m$ in diameter) is driven from its
328  free surface by a rotating heated disk. The combined action of mechanical  free surface by a rotating heated disk. The combined action of mechanical
329  and thermal forcing creates a lens of fluid which becomes baroclinically  and thermal forcing creates a lens of fluid which becomes baroclinically
# Line 432  at fixed and moving $r$ surfaces we set Line 478  at fixed and moving $r$ surfaces we set
478    
479  \begin{equation}  \begin{equation}
480  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \
481  (oceansurface,bottomoftheatmosphere)}  \label{eq:movingbc}  (ocean surface,bottom of the atmosphere)}  \label{eq:movingbc}
482  \end{equation}  \end{equation}
483    
484  Here  Here
# Line 1178  _{h}+\frac{\partial w}{\partial z} &=&0 Line 1224  _{h}+\frac{\partial w}{\partial z} &=&0
1224  \label{eq:non-boussinesq}  \label{eq:non-boussinesq}
1225  \end{eqnarray}  \end{eqnarray}
1226  These equations permit acoustics modes, inertia-gravity waves,  These equations permit acoustics modes, inertia-gravity waves,
1227  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermo-haline  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermohaline
1228  mode. As written, they cannot be integrated forward consistently - if we  mode. As written, they cannot be integrated forward consistently - if we
1229  step $\rho $ forward in (\ref{eq-zns-cont}), the answer will not be  step $\rho $ forward in (\ref{eq-zns-cont}), the answer will not be
1230  consistent with that obtained by stepping (\ref{eq-zns-heat}) and (\ref  consistent with that obtained by stepping (\ref{eq-zns-heat}) and (\ref
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