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revision 1.8 by cnh, Thu Oct 25 15:24:01 2001 UTC revision 1.17 by edhill, Thu Aug 7 18:27:51 2003 UTC
# Line 37  Line 37 
37  % $Header$  % $Header$
38  % $Name$  % $Name$
39    
40  \section{Introduction}  This document provides the reader with the information necessary to
   
 This documentation provides the reader with the information necessary to  
41  carry out numerical experiments using MITgcm. It gives a comprehensive  carry out numerical experiments using MITgcm. It gives a comprehensive
42  description of the continuous equations on which the model is based, the  description of the continuous equations on which the model is based, the
43  numerical algorithms the model employs and a description of the associated  numerical algorithms the model employs and a description of the associated
# Line 49  are available. A number of examples illu Line 47  are available. A number of examples illu
47  both process and general circulation studies of the atmosphere and ocean are  both process and general circulation studies of the atmosphere and ocean are
48  also presented.  also presented.
49    
50    \section{Introduction}
51    
52  MITgcm has a number of novel aspects:  MITgcm has a number of novel aspects:
53    
54  \begin{itemize}  \begin{itemize}
# Line 84  computational platforms. Line 84  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.  \cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99}:
88    
89    \begin{verbatim}
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    \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 the large scale planetary
298  surface elevation of the ocean obtained by bringing the model in to  circulation and a Hopf-Muller plot of Equatorial sea-surface height.
299    Both are obtained from assimilation bringing the model in to
300  consistency with altimetric and in-situ observations over the period  consistency with altimetric and in-situ observations over the period
301  1992-1997. {\bf CHANGE THIS TEXT - FIG FROM PATRICK/CARL/DETLEF}  1992-1997.
302    
303  %% CNHbegin  %% CNHbegin
304  \input{part1/globes_figure}  \input{part1/assim_figure}
305  %% CNHend  %% CNHend
306    
307  \subsection{Ocean biogeochemical cycles}  \subsection{Ocean biogeochemical cycles}
# Line 277  telescoping to $\frac{1}{3}^{\circ}\time Line 322  telescoping to $\frac{1}{3}^{\circ}\time
322  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
323    
324  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a
325  laboratory experiment enquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An  laboratory experiment inquiring into the dynamics of the Antarctic Circumpolar Current (ACC). An
326  initially homogeneous tank of water ($1m$ in diameter) is driven from its  initially homogeneous tank of water ($1m$ in diameter) is driven from its
327  free surface by a rotating heated disk. The combined action of mechanical  free surface by a rotating heated disk. The combined action of mechanical
328  and thermal forcing creates a lens of fluid which becomes baroclinically  and thermal forcing creates a lens of fluid which becomes baroclinically
# Line 301  One system of hydrodynamical equations i Line 346  One system of hydrodynamical equations i
346  and encoded. The model variables have different interpretations depending on  and encoded. The model variables have different interpretations depending on
347  whether the atmosphere or ocean is being studied. Thus, for example, the  whether the atmosphere or ocean is being studied. Thus, for example, the
348  vertical coordinate `$r$' is interpreted as pressure, $p$, if we are  vertical coordinate `$r$' is interpreted as pressure, $p$, if we are
349  modeling the atmosphere (left hand side of figure \ref{fig:isomorphic-equations})  modeling the atmosphere (right hand side of figure \ref{fig:isomorphic-equations})
350  and height, $z$, if we are modeling the ocean (right hand side of figure  and height, $z$, if we are modeling the ocean (left hand side of figure
351  \ref{fig:isomorphic-equations}).  \ref{fig:isomorphic-equations}).
352    
353  %%CNHbegin  %%CNHbegin
# Line 351  b=b(\theta ,S,r)\text{ equation of state Line 396  b=b(\theta ,S,r)\text{ equation of state
396    
397  \begin{equation}  \begin{equation}
398  \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity}  \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity}
399  \label{eq:humidtity_salt}  \label{eq:humidity_salt}
400  \end{equation}  \end{equation}
401    
402  Here:  Here:
# Line 426  in later chapters. Line 471  in later chapters.
471  at fixed and moving $r$ surfaces we set (see figure \ref{fig:zandp-vert-coord}):  at fixed and moving $r$ surfaces we set (see figure \ref{fig:zandp-vert-coord}):
472    
473  \begin{equation}  \begin{equation}
474  \dot{r}=0atr=R_{fixed}(x,y)\text{ (ocean bottom, top of the atmosphere)}  \dot{r}=0 \text{\ at\ } r=R_{fixed}(x,y)\text{ (ocean bottom, top of the atmosphere)}
475  \label{eq:fixedbc}  \label{eq:fixedbc}
476  \end{equation}  \end{equation}
477    
478  \begin{equation}  \begin{equation}
479  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \  \dot{r}=\frac{Dr}{Dt} \text{\ at\ } r=R_{moving}\text{ \
480  (oceansurface,bottomoftheatmosphere)}  \label{eq:movingbc}  (ocean surface,bottom of the atmosphere)}  \label{eq:movingbc}
481  \end{equation}  \end{equation}
482    
483  Here  Here
# Line 525  The boundary conditions at top and botto Line 570  The boundary conditions at top and botto
570  atmosphere)}  \label{eq:moving-bc-atmos}  atmosphere)}  \label{eq:moving-bc-atmos}
571  \end{eqnarray}  \end{eqnarray}
572    
573  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})
574  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 $p$
575  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).
576    
# Line 562  w &=&\frac{D\eta }{Dt}\text{ at }r=R_{mo Line 607  w &=&\frac{D\eta }{Dt}\text{ at }r=R_{mo
607  \end{eqnarray}  \end{eqnarray}
608  where $\eta $ is the elevation of the free surface.  where $\eta $ is the elevation of the free surface.
609    
610  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
611  of oceanic equations  of oceanic equations
612  which, for convenience, are written out in $z$ coordinates in Appendix Ocean  which, for convenience, are written out in $z$ coordinates in Appendix Ocean
613  - 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 1223  _{h}+\frac{\partial w}{\partial z} &=&0
1223  \label{eq:non-boussinesq}  \label{eq:non-boussinesq}
1224  \end{eqnarray}  \end{eqnarray}
1225  These equations permit acoustics modes, inertia-gravity waves,  These equations permit acoustics modes, inertia-gravity waves,
1226  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermo-haline  non-hydrostatic motions, a geostrophic (Rossby) mode and a thermohaline
1227  mode. As written, they cannot be integrated forward consistently - if we  mode. As written, they cannot be integrated forward consistently - if we
1228  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
1229  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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