/[MITgcm]/manual/s_overview/text/manual.tex
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revision 1.8 by cnh, Thu Oct 25 15:24:01 2001 UTC revision 1.10 by cnh, Tue Nov 13 20:35:51 2001 UTC
# Line 102  of them here. A more detailed descriptio Line 102  of them here. A more detailed descriptio
102  numerical algorithm and implementation that lie behind these calculations is  numerical algorithm and implementation that lie behind these calculations is
103  given later. Indeed many of the illustrative examples shown below can be  given later. Indeed many of the illustrative examples shown below can be
104  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
105  running linux, together with a FORTRAN\ 77 compiler) and follow the examples  running Linux, together with a FORTRAN\ 77 compiler) and follow the examples
106  described in detail in the documentation.  described in detail in the documentation.
107    
108  \subsection{Global atmosphere: `Held-Suarez' benchmark}  \subsection{Global atmosphere: `Held-Suarez' benchmark}
# Line 126  there are no mountains or land-sea contr Line 126  there are no mountains or land-sea contr
126  %% CNHend  %% CNHend
127    
128  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
129  globe permitting a uniform gridding and obviated the need to Fourier filter.  globe permitting a uniform griding and obviated the need to Fourier filter.
130  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear
131  grid, of which the cubed sphere is just one of many choices.  grid, of which the cubed sphere is just one of many choices.
132    
# Line 191  Dense plumes generated by localized cool Line 191  Dense plumes generated by localized cool
191  ocean may be influenced by rotation when the deformation radius is smaller  ocean may be influenced by rotation when the deformation radius is smaller
192  than the width of the cooling region. Rather than gravity plumes, the  than the width of the cooling region. Rather than gravity plumes, the
193  mechanism for moving dense fluid down the shelf is then through geostrophic  mechanism for moving dense fluid down the shelf is then through geostrophic
194  eddies. The simulation shown in the figure \ref{fig::convect-and-topo}  eddies. The simulation shown in the figure \ref{fig:convect-and-topo}
195  (blue is cold dense fluid, red is  (blue is cold dense fluid, red is
196  warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to  warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to
197  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 231  data assimilation studies.
231    
232  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}
233  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
234  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}
235  at 60$^{\circ }$N and $  at 60$^{\circ }$N and $
236  \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
237  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 248  yields sensitivities to all other model
248  An important application of MITgcm is in state estimation of the global  An important application of MITgcm is in state estimation of the global
249  ocean circulation. An appropriately defined `cost function', which measures  ocean circulation. An appropriately defined `cost function', which measures
250  the departure of the model from observations (both remotely sensed and  the departure of the model from observations (both remotely sensed and
251  insitu) over an interval of time, is minimized by adjusting `control  in-situ) over an interval of time, is minimized by adjusting `control
252  parameters' such as air-sea fluxes, the wind field, the initial conditions  parameters' such as air-sea fluxes, the wind field, the initial conditions
253  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
254  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 277  telescoping to $\frac{1}{3}^{\circ}\time
277  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
278    
279  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a
280  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
281  initially homogeneous tank of water ($1m$ in diameter) is driven from its  initially homogeneous tank of water ($1m$ in diameter) is driven from its
282  free surface by a rotating heated disk. The combined action of mechanical  free surface by a rotating heated disk. The combined action of mechanical
283  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 351  b=b(\theta ,S,r)\text{ equation of state
351    
352  \begin{equation}  \begin{equation}
353  \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity}  \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity}
354  \label{eq:humidtity_salt}  \label{eq:humidity_salt}
355  \end{equation}  \end{equation}
356    
357  Here:  Here:
# Line 432  at fixed and moving $r$ surfaces we set Line 432  at fixed and moving $r$ surfaces we set
432    
433  \begin{equation}  \begin{equation}
434  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \
435  (oceansurface,bottomoftheatmosphere)}  \label{eq:movingbc}  (ocean surface,bottom of the atmosphere)}  \label{eq:movingbc}
436  \end{equation}  \end{equation}
437    
438  Here  Here
# Line 525  The boundary conditions at top and botto Line 525  The boundary conditions at top and botto
525  atmosphere)}  \label{eq:moving-bc-atmos}  atmosphere)}  \label{eq:moving-bc-atmos}
526  \end{eqnarray}  \end{eqnarray}
527    
528  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})
529  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 $p$
530  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).
531    
# Line 562  w &=&\frac{D\eta }{Dt}\text{ at }r=R_{mo Line 562  w &=&\frac{D\eta }{Dt}\text{ at }r=R_{mo
562  \end{eqnarray}  \end{eqnarray}
563  where $\eta $ is the elevation of the free surface.  where $\eta $ is the elevation of the free surface.
564    
565  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
566  of oceanic equations  of oceanic equations
567  which, for convenience, are written out in $z$ coordinates in Appendix Ocean  which, for convenience, are written out in $z$ coordinates in Appendix Ocean
568  - 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 1178  _{h}+\frac{\partial w}{\partial z} &=&0
1178  \label{eq:non-boussinesq}  \label{eq:non-boussinesq}
1179  \end{eqnarray}  \end{eqnarray}
1180  These equations permit acoustics modes, inertia-gravity waves,  These equations permit acoustics modes, inertia-gravity waves,
1181  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermo-haline  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermohaline
1182  mode. As written, they cannot be integrated forward consistently - if we  mode. As written, they cannot be integrated forward consistently - if we
1183  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
1184  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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