/[MITgcm]/manual/s_overview/text/manual.tex
ViewVC logotype

Diff of /manual/s_overview/text/manual.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.15 by cnh, Wed Nov 21 16:33:17 2001 UTC revision 1.22 by jmc, Sun Oct 17 04:15:13 2004 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    \begin{rawhtml}
52    <!-- CMIREDIR:innovations: -->
53    \end{rawhtml}
54    
55    
56  MITgcm has a number of novel aspects:  MITgcm has a number of novel aspects:
57    
58  \begin{itemize}  \begin{itemize}
# Line 83  studies. Line 87  studies.
87  computational platforms.  computational platforms.
88  \end{itemize}  \end{itemize}
89    
90  Key publications reporting on and charting the development of the model are:  Key publications reporting on and charting the development of the model are
91    \cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99}:
92    
93  \begin{verbatim}  \begin{verbatim}
   
94  Hill, C. and J. Marshall, (1995)  Hill, C. and J. Marshall, (1995)
95  Application of a Parallel Navier-Stokes Model to Ocean Circulation in  Application of a Parallel Navier-Stokes Model to Ocean Circulation in
96  Parallel Computational Fluid Dynamics  Parallel Computational Fluid Dynamics
# Line 95  and Results Using Parallel Computers, 54 Line 99  and Results Using Parallel Computers, 54
99  Elsevier Science B.V.: New York  Elsevier Science B.V.: New York
100    
101  Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997)  Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997)
102  Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling,  Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling
103  J. Geophysical Res., 102(C3), 5733-5752.  J. Geophysical Res., 102(C3), 5733-5752.
104    
105  Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, (1997)  Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, (1997)
# Line 128  Construction of the adjoint MIT ocean ge Line 132  Construction of the adjoint MIT ocean ge
132  application to Atlantic heat transport variability  application to Atlantic heat transport variability
133  J. Geophysical Res., 104(C12), 29,529-29,547.  J. Geophysical Res., 104(C12), 29,529-29,547.
134    
   
135  \end{verbatim}  \end{verbatim}
136    
137  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
# Line 151  running Linux, together with a FORTRAN\ Line 154  running Linux, together with a FORTRAN\
154  described in detail in the documentation.  described in detail in the documentation.
155    
156  \subsection{Global atmosphere: `Held-Suarez' benchmark}  \subsection{Global atmosphere: `Held-Suarez' benchmark}
157    \begin{rawhtml}
158    <!-- CMIREDIR:atmospheric_example: -->
159    \end{rawhtml}
160    
161    
162    
163  A novel feature of MITgcm is its ability to simulate, using one basic algorithm,  A novel feature of MITgcm is its ability to simulate, using one basic algorithm,
164  both atmospheric and oceanographic flows at both small and large scales.  both atmospheric and oceanographic flows at both small and large scales.
# Line 187  latitude-longitude grid. Both grids are Line 195  latitude-longitude grid. Both grids are
195  %% CNHend  %% CNHend
196    
197  \subsection{Ocean gyres}  \subsection{Ocean gyres}
198    \begin{rawhtml}
199    <!-- CMIREDIR:oceanic_example: -->
200    \end{rawhtml}
201    \begin{rawhtml}
202    <!-- CMIREDIR:ocean_gyres: -->
203    \end{rawhtml}
204    
205  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
206  atmosphere. Ocean eddies play an important role in modifying the  atmosphere. Ocean eddies play an important role in modifying the
# Line 213  visible. Line 227  visible.
227    
228    
229  \subsection{Global ocean circulation}  \subsection{Global ocean circulation}
230    \begin{rawhtml}
231    <!-- CMIREDIR:global_ocean_circulation: -->
232    \end{rawhtml}
233    
234  Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean currents at  Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean currents at
235  the surface of a 4$^{\circ }$  the surface of a 4$^{\circ }$
# Line 231  circulation of the global ocean in Sverd Line 248  circulation of the global ocean in Sverd
248  %%CNHend  %%CNHend
249    
250  \subsection{Convection and mixing over topography}  \subsection{Convection and mixing over topography}
251    \begin{rawhtml}
252    <!-- CMIREDIR:mixing_over_topography: -->
253    \end{rawhtml}
254    
255    
256  Dense plumes generated by localized cooling on the continental shelf of the  Dense plumes generated by localized cooling on the continental shelf of the
257  ocean may be influenced by rotation when the deformation radius is smaller  ocean may be influenced by rotation when the deformation radius is smaller
# Line 250  instability of the along-slope current. Line 271  instability of the along-slope current.
271  %%CNHend  %%CNHend
272    
273  \subsection{Boundary forced internal waves}  \subsection{Boundary forced internal waves}
274    \begin{rawhtml}
275    <!-- CMIREDIR:boundary_forced_internal_waves: -->
276    \end{rawhtml}
277    
278  The unique ability of MITgcm to treat non-hydrostatic dynamics in the  The unique ability of MITgcm to treat non-hydrostatic dynamics in the
279  presence of complex geometry makes it an ideal tool to study internal wave  presence of complex geometry makes it an ideal tool to study internal wave
# Line 269  nonhydrostatic dynamics. Line 293  nonhydrostatic dynamics.
293  %%CNHend  %%CNHend
294    
295  \subsection{Parameter sensitivity using the adjoint of MITgcm}  \subsection{Parameter sensitivity using the adjoint of MITgcm}
296    \begin{rawhtml}
297    <!-- CMIREDIR:parameter_sensitivity: -->
298    \end{rawhtml}
299    
300  Forward and tangent linear counterparts of MITgcm are supported using an  Forward and tangent linear counterparts of MITgcm are supported using an
301  `automatic adjoint compiler'. These can be used in parameter sensitivity and  `automatic adjoint compiler'. These can be used in parameter sensitivity and
# Line 289  yields sensitivities to all other model Line 316  yields sensitivities to all other model
316  %%CNHend  %%CNHend
317    
318  \subsection{Global state estimation of the ocean}  \subsection{Global state estimation of the ocean}
319    \begin{rawhtml}
320    <!-- CMIREDIR:global_state_estimation: -->
321    \end{rawhtml}
322    
323    
324  An important application of MITgcm is in state estimation of the global  An important application of MITgcm is in state estimation of the global
325  ocean circulation. An appropriately defined `cost function', which measures  ocean circulation. An appropriately defined `cost function', which measures
# Line 306  consistency with altimetric and in-situ Line 337  consistency with altimetric and in-situ
337  %% CNHend  %% CNHend
338    
339  \subsection{Ocean biogeochemical cycles}  \subsection{Ocean biogeochemical cycles}
340    \begin{rawhtml}
341    <!-- CMIREDIR:ocean_biogeo_cycles: -->
342    \end{rawhtml}
343    
344  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
345  example one can study the effects of interannual changes in meteorological  example one can study the effects of interannual changes in meteorological
# Line 321  telescoping to $\frac{1}{3}^{\circ}\time Line 355  telescoping to $\frac{1}{3}^{\circ}\time
355  %%CNHend  %%CNHend
356    
357  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
358    \begin{rawhtml}
359    <!-- CMIREDIR:classroom_exp: -->
360    \end{rawhtml}
361    
362  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a
363  laboratory experiment inquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An  laboratory experiment inquiring into the dynamics of the Antarctic Circumpolar Current (ACC). An
364  initially homogeneous tank of water ($1m$ in diameter) is driven from its  initially homogeneous tank of water ($1m$ in diameter) is driven from its
365  free surface by a rotating heated disk. The combined action of mechanical  free surface by a rotating heated disk. The combined action of mechanical
366  and thermal forcing creates a lens of fluid which becomes baroclinically  and thermal forcing creates a lens of fluid which becomes baroclinically
# Line 339  stratification of the ACC. Line 376  stratification of the ACC.
376  % $Name$  % $Name$
377    
378  \section{Continuous equations in `r' coordinates}  \section{Continuous equations in `r' coordinates}
379    \begin{rawhtml}
380    <!-- CMIREDIR:z-p_isomorphism: -->
381    \end{rawhtml}
382    
383  To render atmosphere and ocean models from one dynamical core we exploit  To render atmosphere and ocean models from one dynamical core we exploit
384  `isomorphisms' between equation sets that govern the evolution of the  `isomorphisms' between equation sets that govern the evolution of the
# Line 347  One system of hydrodynamical equations i Line 387  One system of hydrodynamical equations i
387  and encoded. The model variables have different interpretations depending on  and encoded. The model variables have different interpretations depending on
388  whether the atmosphere or ocean is being studied. Thus, for example, the  whether the atmosphere or ocean is being studied. Thus, for example, the
389  vertical coordinate `$r$' is interpreted as pressure, $p$, if we are  vertical coordinate `$r$' is interpreted as pressure, $p$, if we are
390  modeling the atmosphere (left hand side of figure \ref{fig:isomorphic-equations})  modeling the atmosphere (right hand side of figure \ref{fig:isomorphic-equations})
391  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
392  \ref{fig:isomorphic-equations}).  \ref{fig:isomorphic-equations}).
393    
394  %%CNHbegin  %%CNHbegin
# Line 369  see figure \ref{fig:zandp-vert-coord}. Line 409  see figure \ref{fig:zandp-vert-coord}.
409  \input{part1/vertcoord_figure.tex}  \input{part1/vertcoord_figure.tex}
410  %%CNHend  %%CNHend
411    
412  \begin{equation*}  \begin{equation}
413  \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}}
414  \right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}}  \right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}}
415  \text{ horizontal mtm} \label{eq:horizontal_mtm}  \text{ horizontal mtm} \label{eq:horizontal_mtm}
416  \end{equation*}  \end{equation}
417    
418  \begin{equation}  \begin{equation}
419  \frac{D\dot{r}}{Dt}+\widehat{k}\cdot \left( 2\vec{\Omega}\times \vec{\mathbf{  \frac{D\dot{r}}{Dt}+\widehat{k}\cdot \left( 2\vec{\Omega}\times \vec{\mathbf{
# Line 472  in later chapters. Line 512  in later chapters.
512  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}):
513    
514  \begin{equation}  \begin{equation}
515  \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)}
516  \label{eq:fixedbc}  \label{eq:fixedbc}
517  \end{equation}  \end{equation}
518    
519  \begin{equation}  \begin{equation}
520  \dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \  \dot{r}=\frac{Dr}{Dt} \text{\ at\ } r=R_{moving}\text{ \
521  (ocean surface,bottom of the atmosphere)}  \label{eq:movingbc}  (ocean surface,bottom of the atmosphere)}  \label{eq:movingbc}
522  \end{equation}  \end{equation}
523    
# Line 571  The boundary conditions at top and botto Line 611  The boundary conditions at top and botto
611  atmosphere)}  \label{eq:moving-bc-atmos}  atmosphere)}  \label{eq:moving-bc-atmos}
612  \end{eqnarray}  \end{eqnarray}
613    
614  Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt})  Then the (hydrostatic form of) equations
615  yields a consistent set of atmospheric equations which, for convenience, are written out in $p$  (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yields a consistent
616  coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).  set of atmospheric equations which, for convenience, are written out
617    in $p$ coordinates in Appendix Atmosphere - see
618    eqs(\ref{eq:atmos-prime}).
619    
620  \subsection{Ocean}  \subsection{Ocean}
621    
# Line 615  which, for convenience, are written out Line 657  which, for convenience, are written out
657    
658  \subsection{Hydrostatic, Quasi-hydrostatic, Quasi-nonhydrostatic and  \subsection{Hydrostatic, Quasi-hydrostatic, Quasi-nonhydrostatic and
659  Non-hydrostatic forms}  Non-hydrostatic forms}
660    \begin{rawhtml}
661    <!-- CMIREDIR:non_hydrostatic: -->
662    \end{rawhtml}
663    
664    
665  Let us separate $\phi $ in to surface, hydrostatic and non-hydrostatic terms:  Let us separate $\phi $ in to surface, hydrostatic and non-hydrostatic terms:
666    
# Line 622  Let us separate $\phi $ in to surface, h Line 668  Let us separate $\phi $ in to surface, h
668  \phi (x,y,r)=\phi _{s}(x,y)+\phi _{hyd}(x,y,r)+\phi _{nh}(x,y,r)  \phi (x,y,r)=\phi _{s}(x,y)+\phi _{hyd}(x,y,r)+\phi _{nh}(x,y,r)
669  \label{eq:phi-split}  \label{eq:phi-split}
670  \end{equation}  \end{equation}
671  and write eq(\ref{eq:incompressible}) in the form:  %and write eq(\ref{eq:incompressible}) in the form:
672    %                  ^- this eq is missing (jmc) ; replaced with:
673    and write eq( \ref{eq:horizontal_mtm}) in the form:
674    
675  \begin{equation}  \begin{equation}
676  \frac{\partial \vec{\mathbf{v}_{h}}}{\partial t}+\mathbf{\nabla }_{h}\phi  \frac{\partial \vec{\mathbf{v}_{h}}}{\partial t}+\mathbf{\nabla }_{h}\phi
# Line 1052  salinity ... ). Line 1100  salinity ... ).
1100    
1101  \subsection{Vector invariant form}  \subsection{Vector invariant form}
1102    
1103  For some purposes it is advantageous to write momentum advection in eq(\ref  For some purposes it is advantageous to write momentum advection in
1104  {eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the (so-called) `vector invariant' form:  eq(\ref {eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the
1105    (so-called) `vector invariant' form:
1106    
1107  \begin{equation}  \begin{equation}
1108  \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t}  \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t}
# Line 1164  In $p$-coordinates, the upper boundary a Line 1213  In $p$-coordinates, the upper boundary a
1213  surface ($\phi $ is imposed and $\omega \neq 0$).  surface ($\phi $ is imposed and $\omega \neq 0$).
1214    
1215  \subsubsection{Splitting the geo-potential}  \subsubsection{Splitting the geo-potential}
1216    \label{sec:hpe-p-geo-potential-split}
1217    
1218  For the purposes of initialization and reducing round-off errors, the model  For the purposes of initialization and reducing round-off errors, the model
1219  deals with perturbations from reference (or ``standard'') profiles. For  deals with perturbations from reference (or ``standard'') profiles. For
# Line 1193  _{o}(p_{o})=g~Z_{topo}$, defined: Line 1243  _{o}(p_{o})=g~Z_{topo}$, defined:
1243  The final form of the HPE's in p coordinates is then:  The final form of the HPE's in p coordinates is then:
1244  \begin{eqnarray}  \begin{eqnarray}
1245  \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}  \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}
1246  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \label{eq:atmos-prime} \\  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}}
1247    \label{eq:atmos-prime} \\
1248  \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\  \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\
1249  \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{  \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{
1250  \partial p} &=&0 \\  \partial p} &=&0 \\
# Line 1239  _{\theta ,p}\frac{DS}{Dt}+\left. \frac{\ Line 1290  _{\theta ,p}\frac{DS}{Dt}+\left. \frac{\
1290  _{\theta ,S}\frac{Dp}{Dt}  \label{EOSexpansion}  _{\theta ,S}\frac{Dp}{Dt}  \label{EOSexpansion}
1291  \end{equation}  \end{equation}
1292    
1293  Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is the  Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is
1294  reciprocal of the sound speed ($c_{s}$) squared. Substituting into \ref{eq-zns-cont} gives:  the reciprocal of the sound speed ($c_{s}$) squared. Substituting into
1295    \ref{eq-zns-cont} gives:
1296  \begin{equation}  \begin{equation}
1297  \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{  \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{
1298  v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}  v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}
Legend:
Removed from v.1.15  
changed lines
  Added in v.1.22
  ViewVC Help
Powered by ViewVC 1.1.22