/[MITgcm]/manual/s_overview/text/manual.tex
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revision 1.27 by jmc, Thu Jan 17 21:28:22 2008 UTC revision 1.30 by jmc, Wed May 11 18:45:43 2016 UTC
# Line 34  Line 34 
34    
35  % Section: Overview  % Section: Overview
36    
 % $Header$  
 % $Name$  
   
37  This document provides the reader with the information necessary to  This document provides the reader with the information necessary to
38  carry out numerical experiments using MITgcm. It gives a comprehensive  carry out numerical experiments using MITgcm. It gives a comprehensive
39  description of the continuous equations on which the model is based, the  description of the continuous equations on which the model is based, the
# Line 61  hydrodynamical kernel is used to drive f Line 58  hydrodynamical kernel is used to drive f
58  models - see fig \ref{fig:onemodel}  models - see fig \ref{fig:onemodel}
59    
60  %% CNHbegin  %% CNHbegin
61  \input{part1/one_model_figure}  \input{s_overview/text/one_model_figure}
62  %% CNHend  %% CNHend
63    
64  \item it has a non-hydrostatic capability and so can be used to study both  \item it has a non-hydrostatic capability and so can be used to study both
65  small-scale and large scale processes - see fig \ref{fig:all-scales}  small-scale and large scale processes - see fig \ref{fig:all-scales}
66    
67  %% CNHbegin  %% CNHbegin
68  \input{part1/all_scales_figure}  \input{s_overview/text/all_scales_figure}
69  %% CNHend  %% CNHend
70    
71  \item finite volume techniques are employed yielding an intuitive  \item finite volume techniques are employed yielding an intuitive
# Line 76  discretization and support for the treat Line 73  discretization and support for the treat
73  orthogonal curvilinear grids and shaved cells - see fig \ref{fig:finite-volumes}  orthogonal curvilinear grids and shaved cells - see fig \ref{fig:finite-volumes}
74    
75  %% CNHbegin  %% CNHbegin
76  \input{part1/fvol_figure}  \input{s_overview/text/fvol_figure}
77  %% CNHend  %% CNHend
78    
79  \item tangent linear and adjoint counterparts are automatically maintained  \item tangent linear and adjoint counterparts are automatically maintained
# Line 139  J. Geophysical Res., 104(C12), 29,529-29 Line 136  J. Geophysical Res., 104(C12), 29,529-29
136  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
137  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.
138    
 % $Header$  
 % $Name$  
   
139  \section{Illustrations of the model in action}  \section{Illustrations of the model in action}
140    
141  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,
# Line 177  in Held and Suarez; 1994 designed to tes Line 171  in Held and Suarez; 1994 designed to tes
171  there are no mountains or land-sea contrast.  there are no mountains or land-sea contrast.
172    
173  %% CNHbegin  %% CNHbegin
174  \input{part1/cubic_eddies_figure}  \input{s_overview/text/cubic_eddies_figure}
175  %% CNHend  %% CNHend
176    
177  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
# Line 193  cube-sphere grid and the flow calculated Line 187  cube-sphere grid and the flow calculated
187  latitude-longitude grid. Both grids are supported within the model.  latitude-longitude grid. Both grids are supported within the model.
188    
189  %% CNHbegin  %% CNHbegin
190  \input{part1/hs_zave_u_figure}  \input{s_overview/text/hs_zave_u_figure}
191  %% CNHend  %% CNHend
192    
193  \subsection{Ocean gyres}  \subsection{Ocean gyres}
# Line 224  transport of warm water northward by the Line 218  transport of warm water northward by the
218  is also clearly visible.  is also clearly visible.
219    
220  %% CNHbegin  %% CNHbegin
221  \input{part1/atl6_figure}  \input{s_overview/text/atl6_figure}
222  %% CNHend  %% CNHend
223    
224    
# Line 246  Figure \ref{fig:large-scale-circ} (botto Line 240  Figure \ref{fig:large-scale-circ} (botto
240  circulation of the global ocean in Sverdrups.  circulation of the global ocean in Sverdrups.
241    
242  %%CNHbegin  %%CNHbegin
243  \input{part1/global_circ_figure}  \input{s_overview/text/global_circ_figure}
244  %%CNHend  %%CNHend
245    
246  \subsection{Convection and mixing over topography}  \subsection{Convection and mixing over topography}
# Line 269  strong, and replaced by lateral entrainm Line 263  strong, and replaced by lateral entrainm
263  instability of the along-slope current.  instability of the along-slope current.
264    
265  %%CNHbegin  %%CNHbegin
266  \input{part1/convect_and_topo}  \input{s_overview/text/convect_and_topo}
267  %%CNHend  %%CNHend
268    
269  \subsection{Boundary forced internal waves}  \subsection{Boundary forced internal waves}
# Line 291  using MITgcm's finite volume spatial dis Line 285  using MITgcm's finite volume spatial dis
285  nonhydrostatic dynamics.  nonhydrostatic dynamics.
286    
287  %%CNHbegin  %%CNHbegin
288  \input{part1/boundary_forced_waves}  \input{s_overview/text/boundary_forced_waves}
289  %%CNHend  %%CNHend
290    
291  \subsection{Parameter sensitivity using the adjoint of MITgcm}  \subsection{Parameter sensitivity using the adjoint of MITgcm}
# Line 314  deep water for the thermohaline circulat Line 308  deep water for the thermohaline circulat
308  yields sensitivities to all other model parameters.  yields sensitivities to all other model parameters.
309    
310  %%CNHbegin  %%CNHbegin
311  \input{part1/adj_hf_ocean_figure}  \input{s_overview/text/adj_hf_ocean_figure}
312  %%CNHend  %%CNHend
313    
314  \subsection{Global state estimation of the ocean}  \subsection{Global state estimation of the ocean}
# Line 335  consistency with altimetric and in-situ Line 329  consistency with altimetric and in-situ
329  1992-1997.  1992-1997.
330    
331  %% CNHbegin  %% CNHbegin
332  \input{part1/assim_figure}  \input{s_overview/text/assim_figure}
333  %% CNHend  %% CNHend
334    
335  \subsection{Ocean biogeochemical cycles}  \subsection{Ocean biogeochemical cycles}
# Line 355  $\frac{1}{3}^{\circ}\times\frac{1}{3}^{\ Line 349  $\frac{1}{3}^{\circ}\times\frac{1}{3}^{\
349  shown).  shown).
350    
351  %%CNHbegin  %%CNHbegin
352  \input{part1/biogeo_figure}  \input{s_overview/text/biogeo_figure}
353  %%CNHend  %%CNHend
354    
355  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
# Line 373  arrested by its instability in a process Line 367  arrested by its instability in a process
367  stratification of the ACC.  stratification of the ACC.
368    
369  %%CNHbegin  %%CNHbegin
370  \input{part1/lab_figure}  \input{s_overview/text/lab_figure}
371  %%CNHend  %%CNHend
372    
 % $Header$  
 % $Name$  
   
373  \section{Continuous equations in `r' coordinates}  \section{Continuous equations in `r' coordinates}
374  \begin{rawhtml}  \begin{rawhtml}
375  <!-- CMIREDIR:z-p_isomorphism: -->  <!-- CMIREDIR:z-p_isomorphism: -->
# Line 396  and height, $z$, if we are modeling the Line 387  and height, $z$, if we are modeling the
387  \ref{fig:isomorphic-equations}).  \ref{fig:isomorphic-equations}).
388    
389  %%CNHbegin  %%CNHbegin
390  \input{part1/zandpcoord_figure.tex}  \input{s_overview/text/zandpcoord_figure.tex}
391  %%CNHend  %%CNHend
392    
393  The state of the fluid at any time is characterized by the distribution of  The state of the fluid at any time is characterized by the distribution of
# Line 410  kinematic boundary conditions can be app Line 401  kinematic boundary conditions can be app
401  see figure \ref{fig:zandp-vert-coord}.  see figure \ref{fig:zandp-vert-coord}.
402    
403  %%CNHbegin  %%CNHbegin
404  \input{part1/vertcoord_figure.tex}  \input{s_overview/text/vertcoord_figure.tex}
405  %%CNHend  %%CNHend
406    
407  \begin{equation}  \begin{equation}
# Line 661  which, for convenience, are written out Line 652  which, for convenience, are written out
652    
653  \subsection{Hydrostatic, Quasi-hydrostatic, Quasi-nonhydrostatic and  \subsection{Hydrostatic, Quasi-hydrostatic, Quasi-nonhydrostatic and
654  Non-hydrostatic forms}  Non-hydrostatic forms}
655    \label{sec:all_hydrostatic_forms}
656  \begin{rawhtml}  \begin{rawhtml}
657  <!-- CMIREDIR:non_hydrostatic: -->  <!-- CMIREDIR:non_hydrostatic: -->
658  \end{rawhtml}  \end{rawhtml}
# Line 769  Grad and div operators in spherical coor Line 761  Grad and div operators in spherical coor
761  OPERATORS.  OPERATORS.
762    
763  %%CNHbegin  %%CNHbegin
764  \input{part1/sphere_coord_figure.tex}  \input{s_overview/text/sphere_coord_figure.tex}
765  %%CNHend  %%CNHend
766    
767  \subsubsection{Shallow atmosphere approximation}  \subsubsection{Shallow atmosphere approximation}
# Line 890  stepping forward the horizontal momentum Line 882  stepping forward the horizontal momentum
882  stepping forward the vertical momentum equation.  stepping forward the vertical momentum equation.
883    
884  %%CNHbegin  %%CNHbegin
885  \input{part1/solution_strategy_figure.tex}  \input{s_overview/text/solution_strategy_figure.tex}
886  %%CNHend  %%CNHend
887    
888  There is no penalty in implementing \textbf{QH} over \textbf{HPE} except, of  There is no penalty in implementing \textbf{QH} over \textbf{HPE} except, of
# Line 1128  to discretize the model. Line 1120  to discretize the model.
1120  Tangent linear and adjoint counterparts of the forward model are described  Tangent linear and adjoint counterparts of the forward model are described
1121  in Chapter 5.  in Chapter 5.
1122    
 % $Header$  
 % $Name$  
   
1123  \section{Appendix ATMOSPHERE}  \section{Appendix ATMOSPHERE}
1124    
1125  \subsection{Hydrostatic Primitive Equations for the Atmosphere in pressure  \subsection{Hydrostatic Primitive Equations for the Atmosphere in pressure
# Line 1150  p\alpha &=&RT  \label{eq:atmos-eos} \\ Line 1139  p\alpha &=&RT  \label{eq:atmos-eos} \\
1139  c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q}  \label{eq:atmos-heat}  c_{v}\frac{DT}{Dt}+p\frac{D\alpha }{Dt} &=&\mathcal{Q}  \label{eq:atmos-heat}
1140  \end{eqnarray}  \end{eqnarray}
1141  where $\vec{\mathbf{v}}_{h}=(u,v,0)$ is the `horizontal' (on pressure  where $\vec{\mathbf{v}}_{h}=(u,v,0)$ is the `horizontal' (on pressure
1142  surfaces) component of velocity,$\frac{D}{Dt}=\vec{\mathbf{v}}_{h}\cdot  surfaces) component of velocity, $\frac{D}{Dt}=\frac{\partial}{\partial t}
1143  \mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$ is the total  +\vec{\mathbf{v}}_{h}\cdot \mathbf{\nabla }_{p}+\omega \frac{\partial }{\partial p}$
1144  derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter, $\phi =gz$ is  is the total derivative, $f=2\Omega \sin \varphi$ is the Coriolis parameter,
1145  the geopotential, $\alpha =1/\rho $ is the specific volume, $\omega =\frac{Dp  $\phi =gz$ is the geopotential, $\alpha =1/\rho $ is the specific volume,
1146  }{Dt}$ is the vertical velocity in the $p-$coordinate. Equation(\ref  $\omega =\frac{Dp }{Dt}$ is the vertical velocity in the $p-$coordinate.
1147  {eq:atmos-heat}) is the first law of thermodynamics where internal energy $  Equation(\ref {eq:atmos-heat}) is the first law of thermodynamics where internal
1148  e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass and $  energy $e=c_{v}T$, $T$ is temperature, $Q$ is the rate of heating per unit mass
1149  p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing.  and $p\frac{D\alpha }{Dt}$ is the work done by the fluid in compressing.
1150    
1151  It is convenient to cast the heat equation in terms of potential temperature  It is convenient to cast the heat equation in terms of potential temperature
1152  $\theta $ so that it looks more like a generic conservation law.  $\theta $ so that it looks more like a generic conservation law.
# Line 1257  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime } Line 1246  _{h}+\mathbf{\nabla }_{p}\phi ^{\prime }
1246  \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi }  \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi }
1247  \end{eqnarray}  \end{eqnarray}
1248    
 % $Header$  
 % $Name$  
   
1249  \section{Appendix OCEAN}  \section{Appendix OCEAN}
1250    
1251  \subsection{Equations of motion for the ocean}  \subsection{Equations of motion for the ocean}
# Line 1474  the perturbation density. Nevertheless, Line 1460  the perturbation density. Nevertheless,
1460  _{nh}=0$ form of these equations that are used throughout the ocean modeling  _{nh}=0$ form of these equations that are used throughout the ocean modeling
1461  community and referred to as the primitive equations (HPE).  community and referred to as the primitive equations (HPE).
1462    
 % $Header$  
 % $Name$  
   
1463  \section{Appendix:OPERATORS}  \section{Appendix:OPERATORS}
1464    
1465  \subsection{Coordinate systems}  \subsection{Coordinate systems}
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