/[MITgcm]/manual/s_overview/text/manual_fromjm.tex
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revision 1.3 by adcroft, Mon Oct 15 19:34:28 2001 UTC revision 1.5 by edhill, Sat Apr 8 01:50:49 2006 UTC
# Line 100  give a feel for the wide range of proble Line 100  give a feel for the wide range of proble
100    
101  \section{Illustrations of the model in action}  \section{Illustrations of the model in action}
102    
103  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,
104  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
105  atmospheric winds - see fig.2\ref{fig:all-scales}. To give a flavor of the  atmospheric winds - see fig.2\ref{fig:all-scales}. To give a flavor of the
106  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 118  oceanographic flows at both small and la Line 118  oceanographic flows at both small and la
118    
119  Fig.E1a.\ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$  Fig.E1a.\ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$
120  temperature field obtained using the atmospheric isomorph of MITgcm run at  temperature field obtained using the atmospheric isomorph of MITgcm run at
121  2.8$^{\circ }$ resolution on the cubed sphere. We see cold air over the pole  $2.8^{\circ }$ resolution on the cubed sphere. We see cold air over the pole
122  (blue) and warm air along an equatorial band (red). Fully developed  (blue) and warm air along an equatorial band (red). Fully developed
123  baroclinic eddies spawned in the northern hemisphere storm track are  baroclinic eddies spawned in the northern hemisphere storm track are
124  evident. There are no mountains or land-sea contrast in this calculation,  evident. There are no mountains or land-sea contrast in this calculation,
# Line 158  increased until the baroclinic instabili Line 158  increased until the baroclinic instabili
158  solutions of a different and much more realistic kind, can be obtained.  solutions of a different and much more realistic kind, can be obtained.
159    
160  Fig. ?.? shows the surface temperature and velocity field obtained from  Fig. ?.? shows the surface temperature and velocity field obtained from
161  MITgcm run at $\frac{1}{6}^{\circ }$ horizontal resolution on a $lat-lon$  MITgcm run at $\frac{1}{6}^{\circ }$ horizontal resolution on a \textit{lat-lon}
162  grid in which the pole has been rotated by 90$^{\circ }$ on to the equator  grid in which the pole has been rotated by $90^{\circ }$ on to the equator
163  (to avoid the converging of meridian in northern latitudes). 21 vertical  (to avoid the converging of meridian in northern latitudes). 21 vertical
164  levels are used in the vertical with a `lopped cell' representation of  levels are used in the vertical with a `lopped cell' representation of
165  topography. The development and propagation of anomalously warm and cold  topography. The development and propagation of anomalously warm and cold
# Line 174  visible. Line 174  visible.
174    
175  \subsection{Global ocean circulation}  \subsection{Global ocean circulation}
176    
177  Fig.E2a shows the pattern of ocean currents at the surface of a 4$^{\circ }$  Fig.E2a shows the pattern of ocean currents at the surface of a $4^{\circ }$
178  global ocean model run with 15 vertical levels. Lopped cells are used to  global ocean model run with 15 vertical levels. Lopped cells are used to
179  represent topography on a regular $lat-lon$ grid extending from 70$^{\circ  represent topography on a regular \textit{lat-lon} grid extending from $70^{\circ
180  }N $ to 70$^{\circ }S$. The model is driven using monthly-mean winds with  }N $ to $70^{\circ }S$. The model is driven using monthly-mean winds with
181  mixed boundary conditions on temperature and salinity at the surface. The  mixed boundary conditions on temperature and salinity at the surface. The
182  transfer properties of ocean eddies, convection and mixing is parameterized  transfer properties of ocean eddies, convection and mixing is parameterized
183  in this model.  in this model.
# Line 233  data assimilation studies. Line 233  data assimilation studies.
233    
234  As one example of application of the MITgcm adjoint, Fig.E4 maps the  As one example of application of the MITgcm adjoint, Fig.E4 maps the
235  gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude  gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude
236  of the overturning streamfunction shown in fig?.? at 40$^{\circ }$N and $  of the overturning streamfunction shown in fig?.? at $40^{\circ }N$ and $
237  \mathcal{H}$ is the air-sea heat flux 100 years before. We see that $J$ is  \mathcal{H}$ is the air-sea heat flux 100 years before. We see that $J$ is
238  sensitive to heat fluxes over the Labrador Sea, one of the important sources  sensitive to heat fluxes over the Labrador Sea, one of the important sources
239  of deep water for the thermohaline circulations. This calculation also  of deep water for the thermohaline circulations. This calculation also
# Line 656  $\underline{\underline{\mathcal{F}_{\dot Line 656  $\underline{\underline{\mathcal{F}_{\dot
656  \end{equation}  \end{equation}
657  \qquad \qquad \qquad \qquad \qquad  \qquad \qquad \qquad \qquad \qquad
658    
659  In the above `${r}$' is the distance from the center of the earth and `$lat$  In the above `${r}$' is the distance from the center of the earth and
660  ' is latitude.  `\textit{lat}' is latitude.
661    
662  Grad and div operators in spherical coordinates are defined in appendix  Grad and div operators in spherical coordinates are defined in appendix
663  OPERATORS.  OPERATORS.
# Line 674  Most models are based on the `hydrostati Line 674  Most models are based on the `hydrostati
674  which the vertical momentum equation is reduced to a statement of  which the vertical momentum equation is reduced to a statement of
675  hydrostatic balance and the `traditional approximation' is made in which the  hydrostatic balance and the `traditional approximation' is made in which the
676  Coriolis force is treated approximately and the shallow atmosphere  Coriolis force is treated approximately and the shallow atmosphere
677  approximation is made.\ The MITgcm need not make the `traditional  approximation is made.  MITgcm need not make the `traditional
678  approximation'. To be able to support consistent non-hydrostatic forms the  approximation'. To be able to support consistent non-hydrostatic forms the
679  shallow atmosphere approximation can be relaxed - when dividing through by $  shallow atmosphere approximation can be relaxed - when dividing through by $
680  r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$,  r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$,
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