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revision 1.8 by cnh, Thu Oct 25 15:24:01 2001 UTC revision 1.12 by cnh, Mon Nov 19 14:33:44 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 Eight ECMWF Workshop on the Use of Parallel Processors
123    in Meteorology
124    
125    Marotzke, J, Giering,R., Zhang, K.Q., Stammer,D., Hill,C., and T.Lee, (1999)
126    Construction of the adjoint MIT ocean general circulation model and
127    application to Atlantic heat transport variability
128    J. Geophysical Res., 104(C12), 29,529-29,547.
129    
130    
131    \end{verbatim}
132    
133  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
134  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 146  of them here. A more detailed descriptio
146  numerical algorithm and implementation that lie behind these calculations is  numerical algorithm and implementation that lie behind these calculations is
147  given later. Indeed many of the illustrative examples shown below can be  given later. Indeed many of the illustrative examples shown below can be
148  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
149  running linux, together with a FORTRAN\ 77 compiler) and follow the examples  running Linux, together with a FORTRAN\ 77 compiler) and follow the examples
150  described in detail in the documentation.  described in detail in the documentation.
151    
152  \subsection{Global atmosphere: `Held-Suarez' benchmark}  \subsection{Global atmosphere: `Held-Suarez' benchmark}
# Line 126  there are no mountains or land-sea contr Line 170  there are no mountains or land-sea contr
170  %% CNHend  %% CNHend
171    
172  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
173  globe permitting a uniform gridding and obviated the need to Fourier filter.  globe permitting a uniform griding and obviated the need to Fourier filter.
174  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear
175  grid, of which the cubed sphere is just one of many choices.  grid, of which the cubed sphere is just one of many choices.
176    
# Line 163  warm water northward by the mean flow of Line 207  warm water northward by the mean flow of
207  visible.  visible.
208    
209  %% CNHbegin  %% CNHbegin
210  \input{part1/ocean_gyres_figure}  \input{part1/atl6_figure}
211  %% CNHend  %% CNHend
212    
213    
# Line 191  Dense plumes generated by localized cool Line 235  Dense plumes generated by localized cool
235  ocean may be influenced by rotation when the deformation radius is smaller  ocean may be influenced by rotation when the deformation radius is smaller
236  than the width of the cooling region. Rather than gravity plumes, the  than the width of the cooling region. Rather than gravity plumes, the
237  mechanism for moving dense fluid down the shelf is then through geostrophic  mechanism for moving dense fluid down the shelf is then through geostrophic
238  eddies. The simulation shown in the figure \ref{fig::convect-and-topo}  eddies. The simulation shown in the figure \ref{fig:convect-and-topo}
239  (blue is cold dense fluid, red is  (blue is cold dense fluid, red is
240  warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to  warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to
241  trigger convection by surface cooling. The cold, dense water falls down the  trigger convection by surface cooling. The cold, dense water falls down the
# Line 231  data assimilation studies. Line 275  data assimilation studies.
275    
276  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}
277  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
278  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}
279  at 60$^{\circ }$N and $  at 60$^{\circ }$N and $
280  \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
281  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 292  yields sensitivities to all other model
292  An important application of MITgcm is in state estimation of the global  An important application of MITgcm is in state estimation of the global
293  ocean circulation. An appropriately defined `cost function', which measures  ocean circulation. An appropriately defined `cost function', which measures
294  the departure of the model from observations (both remotely sensed and  the departure of the model from observations (both remotely sensed and
295  insitu) over an interval of time, is minimized by adjusting `control  in-situ) over an interval of time, is minimized by adjusting `control
296  parameters' such as air-sea fluxes, the wind field, the initial conditions  parameters' such as air-sea fluxes, the wind field, the initial conditions
297  etc. Figure \ref{fig:assimilated-globes} shows an estimate of the time-mean  etc. Figure \ref{fig:assimilated-globes} shows an estimate of the time-mean
298  surface elevation of the ocean obtained by bringing the model in to  surface elevation of the ocean obtained by bringing the model in to
# Line 277  telescoping to $\frac{1}{3}^{\circ}\time Line 321  telescoping to $\frac{1}{3}^{\circ}\time
321  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
322    
323  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a
324  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
325  initially homogeneous tank of water ($1m$ in diameter) is driven from its  initially homogeneous tank of water ($1m$ in diameter) is driven from its
326  free surface by a rotating heated disk. The combined action of mechanical  free surface by a rotating heated disk. The combined action of mechanical
327  and thermal forcing creates a lens of fluid which becomes baroclinically  and thermal forcing creates a lens of fluid which becomes baroclinically
# Line 351  b=b(\theta ,S,r)\text{ equation of state Line 395  b=b(\theta ,S,r)\text{ equation of state
395    
396  \begin{equation}  \begin{equation}
397  \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity}  \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity}
398  \label{eq:humidtity_salt}  \label{eq:humidity_salt}
399  \end{equation}  \end{equation}
400    
401  Here:  Here:
# Line 432  at fixed and moving $r$ surfaces we set Line 476  at fixed and moving $r$ surfaces we set
476    
477  \begin{equation}  \begin{equation}
478  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \
479  (oceansurface,bottomoftheatmosphere)}  \label{eq:movingbc}  (ocean surface,bottom of the atmosphere)}  \label{eq:movingbc}
480  \end{equation}  \end{equation}
481    
482  Here  Here
# Line 525  The boundary conditions at top and botto Line 569  The boundary conditions at top and botto
569  atmosphere)}  \label{eq:moving-bc-atmos}  atmosphere)}  \label{eq:moving-bc-atmos}
570  \end{eqnarray}  \end{eqnarray}
571    
572  Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_slainty})  Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt})
573  yields a consistent set of atmospheric equations which, for convenience, are written out in $p$  yields a consistent set of atmospheric equations which, for convenience, are written out in $p$
574  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).
575    
# Line 562  w &=&\frac{D\eta }{Dt}\text{ at }r=R_{mo Line 606  w &=&\frac{D\eta }{Dt}\text{ at }r=R_{mo
606  \end{eqnarray}  \end{eqnarray}
607  where $\eta $ is the elevation of the free surface.  where $\eta $ is the elevation of the free surface.
608    
609  Then equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_slainty}) yield a consistent set  Then equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yield a consistent set
610  of oceanic equations  of oceanic equations
611  which, for convenience, are written out in $z$ coordinates in Appendix Ocean  which, for convenience, are written out in $z$ coordinates in Appendix Ocean
612  - see eqs(\ref{eq:ocean-mom}) to (\ref{eq:ocean-salt}).  - see eqs(\ref{eq:ocean-mom}) to (\ref{eq:ocean-salt}).
# Line 1178  _{h}+\frac{\partial w}{\partial z} &=&0 Line 1222  _{h}+\frac{\partial w}{\partial z} &=&0
1222  \label{eq:non-boussinesq}  \label{eq:non-boussinesq}
1223  \end{eqnarray}  \end{eqnarray}
1224  These equations permit acoustics modes, inertia-gravity waves,  These equations permit acoustics modes, inertia-gravity waves,
1225  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermo-haline  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermohaline
1226  mode. As written, they cannot be integrated forward consistently - if we  mode. As written, they cannot be integrated forward consistently - if we
1227  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
1228  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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