/[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 1.23 by jmc, Mon Jul 11 13:49:28 2005 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 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 1096  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 1208  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 1237  _{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 1283  _{\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}
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