/[MITgcm]/manual/s_overview/text/manual.tex
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revision 1.18 by afe, Tue Mar 23 15:29:39 2004 UTC revision 1.24 by edhill, Wed Apr 5 02:27:32 2006 UTC
# Line 49  also presented. Line 49  also presented.
49    
50  \section{Introduction}  \section{Introduction}
51  \begin{rawhtml}  \begin{rawhtml}
52  <!-- CMIREDIR:innovations -->  <!-- CMIREDIR:innovations: -->
53  \end{rawhtml}  \end{rawhtml}
54    
55    
# Line 88  computational platforms. Line 88  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}:  \cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99,adcroft:04a,adcroft:04b,marshall:04}:
92    
93  \begin{verbatim}  \begin{verbatim}
94  Hill, C. and J. Marshall, (1995)  Hill, C. and J. Marshall, (1995)
# Line 142  give a feel for the wide range of proble Line 142  give a feel for the wide range of proble
142    
143  \section{Illustrations of the model in action}  \section{Illustrations of the model in action}
144    
145  The MITgcm has been designed and used to model a wide range of phenomena,  MITgcm has been designed and used to model a wide range of phenomena,
146  from convection on the scale of meters in the ocean to the global pattern of  from convection on the scale of meters in the ocean to the global pattern of
147  atmospheric winds - see figure \ref{fig:all-scales}. To give a flavor of the  atmospheric winds - see figure \ref{fig:all-scales}. To give a flavor of the
148  kinds of problems the model has been used to study, we briefly describe some  kinds of problems the model has been used to study, we briefly describe some
# Line 155  described in detail in the documentation Line 155  described in detail in the documentation
155    
156  \subsection{Global atmosphere: `Held-Suarez' benchmark}  \subsection{Global atmosphere: `Held-Suarez' benchmark}
157  \begin{rawhtml}  \begin{rawhtml}
158  <!-- CMIREDIR:atmospheric_example -->  <!-- CMIREDIR:atmospheric_example: -->
159  \end{rawhtml}  \end{rawhtml}
160    
161    
# Line 196  latitude-longitude grid. Both grids are Line 196  latitude-longitude grid. Both grids are
196    
197  \subsection{Ocean gyres}  \subsection{Ocean gyres}
198  \begin{rawhtml}  \begin{rawhtml}
199  <!-- CMIREDIR:oceanic_example -->  <!-- CMIREDIR:oceanic_example: -->
200  \end{rawhtml}  \end{rawhtml}
201  \begin{rawhtml}  \begin{rawhtml}
202  <!-- CMIREDIR:ocean_gyres -->  <!-- CMIREDIR:ocean_gyres: -->
203  \end{rawhtml}  \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
# Line 228  visible. Line 228  visible.
228    
229  \subsection{Global ocean circulation}  \subsection{Global ocean circulation}
230  \begin{rawhtml}  \begin{rawhtml}
231  <!-- CMIREDIR:global_ocean_circulation -->  <!-- CMIREDIR:global_ocean_circulation: -->
232  \end{rawhtml}  \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
# Line 249  circulation of the global ocean in Sverd Line 249  circulation of the global ocean in Sverd
249    
250  \subsection{Convection and mixing over topography}  \subsection{Convection and mixing over topography}
251  \begin{rawhtml}  \begin{rawhtml}
252  <!-- CMIREDIR:mixing_over_topography -->  <!-- CMIREDIR:mixing_over_topography: -->
253  \end{rawhtml}  \end{rawhtml}
254    
255    
# Line 272  instability of the along-slope current. Line 272  instability of the along-slope current.
272    
273  \subsection{Boundary forced internal waves}  \subsection{Boundary forced internal waves}
274  \begin{rawhtml}  \begin{rawhtml}
275  <!-- CMIREDIR:boundary_forced_internal_waves -->  <!-- CMIREDIR:boundary_forced_internal_waves: -->
276  \end{rawhtml}  \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
# Line 294  nonhydrostatic dynamics. Line 294  nonhydrostatic dynamics.
294    
295  \subsection{Parameter sensitivity using the adjoint of MITgcm}  \subsection{Parameter sensitivity using the adjoint of MITgcm}
296  \begin{rawhtml}  \begin{rawhtml}
297  <!-- CMIREDIR:parameter_sensitivity -->  <!-- CMIREDIR:parameter_sensitivity: -->
298  \end{rawhtml}  \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
# Line 317  yields sensitivities to all other model Line 317  yields sensitivities to all other model
317    
318  \subsection{Global state estimation of the ocean}  \subsection{Global state estimation of the ocean}
319  \begin{rawhtml}  \begin{rawhtml}
320  <!-- CMIREDIR:global_state_estimation -->  <!-- CMIREDIR:global_state_estimation: -->
321  \end{rawhtml}  \end{rawhtml}
322    
323    
# Line 338  consistency with altimetric and in-situ Line 338  consistency with altimetric and in-situ
338    
339  \subsection{Ocean biogeochemical cycles}  \subsection{Ocean biogeochemical cycles}
340  \begin{rawhtml}  \begin{rawhtml}
341  <!-- CMIREDIR:ocean_biogeo_cycles -->  <!-- CMIREDIR:ocean_biogeo_cycles: -->
342  \end{rawhtml}  \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
# Line 356  telescoping to $\frac{1}{3}^{\circ}\time Line 356  telescoping to $\frac{1}{3}^{\circ}\time
356    
357  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
358  \begin{rawhtml}  \begin{rawhtml}
359  <!-- CMIREDIR:classroom_exp -->  <!-- CMIREDIR:classroom_exp: -->
360  \end{rawhtml}  \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
# Line 377  stratification of the ACC. Line 377  stratification of the ACC.
377    
378  \section{Continuous equations in `r' coordinates}  \section{Continuous equations in `r' coordinates}
379  \begin{rawhtml}  \begin{rawhtml}
380  <!-- CMIREDIR:z-p_isomorphism -->  <!-- CMIREDIR:z-p_isomorphism: -->
381  \end{rawhtml}  \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
# Line 409  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 611  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 656  which, for convenience, are written out Line 658  which, for convenience, are written out
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}  \begin{rawhtml}
661  <!-- CMIREDIR:non_hydrostatic -->  <!-- CMIREDIR:non_hydrostatic: -->
662  \end{rawhtml}  \end{rawhtml}
663    
664    
# Line 666  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 766  OPERATORS. Line 770  OPERATORS.
770    
771  \subsubsection{Shallow atmosphere approximation}  \subsubsection{Shallow atmosphere approximation}
772    
773  Most models are based on the `hydrostatic primitive equations' (HPE's) in  Most models are based on the `hydrostatic primitive equations' (HPE's)
774  which the vertical momentum equation is reduced to a statement of  in which the vertical momentum equation is reduced to a statement of
775  hydrostatic balance and the `traditional approximation' is made in which the  hydrostatic balance and the `traditional approximation' is made in
776  Coriolis force is treated approximately and the shallow atmosphere  which the Coriolis force is treated approximately and the shallow
777  approximation is made.\ The MITgcm need not make the `traditional  atmosphere approximation is made.  MITgcm need not make the
778  approximation'. To be able to support consistent non-hydrostatic forms the  `traditional approximation'. To be able to support consistent
779  shallow atmosphere approximation can be relaxed - when dividing through by $  non-hydrostatic forms the shallow atmosphere approximation can be
780  r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$,  relaxed - when dividing through by $ r $ in, for example,
781  the radius of the earth.  (\ref{eq:gu-speherical}), we do not replace $r$ by $a$, the radius of
782    the earth.
783    
784  \subsubsection{Hydrostatic and quasi-hydrostatic forms}  \subsubsection{Hydrostatic and quasi-hydrostatic forms}
785  \label{sec:hydrostatic_and_quasi-hydrostatic_forms}  \label{sec:hydrostatic_and_quasi-hydrostatic_forms}
# Line 811  et.al., 1997a. As in \textbf{HPE }only a Line 816  et.al., 1997a. As in \textbf{HPE }only a
816    
817  \subsubsection{Non-hydrostatic and quasi-nonhydrostatic forms}  \subsubsection{Non-hydrostatic and quasi-nonhydrostatic forms}
818    
819  The MIT model presently supports a full non-hydrostatic ocean isomorph, but  MITgcm presently supports a full non-hydrostatic ocean isomorph, but
820  only a quasi-non-hydrostatic atmospheric isomorph.  only a quasi-non-hydrostatic atmospheric isomorph.
821    
822  \paragraph{Non-hydrostatic Ocean}  \paragraph{Non-hydrostatic Ocean}
# Line 1096  salinity ... ). Line 1101  salinity ... ).
1101    
1102  \subsection{Vector invariant form}  \subsection{Vector invariant form}
1103    
1104  For some purposes it is advantageous to write momentum advection in eq(\ref  For some purposes it is advantageous to write momentum advection in
1105  {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
1106    (so-called) `vector invariant' form:
1107    
1108  \begin{equation}  \begin{equation}
1109  \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 1208  In $p$-coordinates, the upper boundary a Line 1214  In $p$-coordinates, the upper boundary a
1214  surface ($\phi $ is imposed and $\omega \neq 0$).  surface ($\phi $ is imposed and $\omega \neq 0$).
1215    
1216  \subsubsection{Splitting the geo-potential}  \subsubsection{Splitting the geo-potential}
1217    \label{sec:hpe-p-geo-potential-split}
1218    
1219  For the purposes of initialization and reducing round-off errors, the model  For the purposes of initialization and reducing round-off errors, the model
1220  deals with perturbations from reference (or ``standard'') profiles. For  deals with perturbations from reference (or ``standard'') profiles. For
# Line 1237  _{o}(p_{o})=g~Z_{topo}$, defined: Line 1244  _{o}(p_{o})=g~Z_{topo}$, defined:
1244  The final form of the HPE's in p coordinates is then:  The final form of the HPE's in p coordinates is then:
1245  \begin{eqnarray}  \begin{eqnarray}
1246  \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}}
1247  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \label{eq:atmos-prime} \\  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}}
1248    \label{eq:atmos-prime} \\
1249  \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\  \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\
1250  \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{  \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{
1251  \partial p} &=&0 \\  \partial p} &=&0 \\
# Line 1283  _{\theta ,p}\frac{DS}{Dt}+\left. \frac{\ Line 1291  _{\theta ,p}\frac{DS}{Dt}+\left. \frac{\
1291  _{\theta ,S}\frac{Dp}{Dt}  \label{EOSexpansion}  _{\theta ,S}\frac{Dp}{Dt}  \label{EOSexpansion}
1292  \end{equation}  \end{equation}
1293    
1294  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
1295  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
1296    \ref{eq-zns-cont} gives:
1297  \begin{equation}  \begin{equation}
1298  \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{
1299  v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}  v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}
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