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

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-revision 1.21 by edhill,
Sat Oct 16 03:40:12 2004 UTC
+revision 1.26 by edhill,
Wed Jun 28 15:22:13 2006 UTC
 Line 88 
 computational platforms.
  \end{itemize}
  Key publications reporting on and charting the development of the model are
- \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}:
  \begin{verbatim}
  Hill, C. and J. Marshall, (1995)
 Line 142 
 give a feel for the wide range of proble
  \section{Illustrations of the model in action}
- 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,
  from convection on the scale of meters in the ocean to the global pattern of
  atmospheric winds - see figure \ref{fig:all-scales}. To give a flavor of the
  kinds of problems the model has been used to study, we briefly describe some
 Line 165 
 both atmospheric and oceanographic flows
  Figure \ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$
  temperature field obtained using the atmospheric isomorph of MITgcm run at
-.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
  (blue) and warm air along an equatorial band (red). Fully developed
  baroclinic eddies spawned in the northern hemisphere storm track are
  evident. There are no mountains or land-sea contrast in this calculation,
 Line 210 
 diffusive patterns of ocean currents. Bu
  increased until the baroclinic instability process is resolved, numerical
  solutions of a different and much more realistic kind, can be obtained.
- Figure \ref{fig:ocean-gyres} shows the surface temperature and velocity
+ Figure \ref{fig:ocean-gyres} shows the surface temperature and
- field obtained from MITgcm run at $\frac{1}{6}^{\circ }$ horizontal
+ velocity field obtained from MITgcm run at $\frac{1}{6}^{\circ }$
- resolution on a $lat-lon$
+ horizontal resolution on a \textit{lat-lon} grid in which the pole has
- grid in which the pole has been rotated by 90$^{\circ }$ on to the equator
+ been rotated by $90^{\circ }$ on to the equator (to avoid the
- (to avoid the converging of meridian in northern latitudes). 21 vertical
+ converging of meridian in northern latitudes). 21 vertical levels are
- levels are used in the vertical with a `lopped cell' representation of
+ used in the vertical with a `lopped cell' representation of
- topography. The development and propagation of anomalously warm and cold
+ topography. The development and propagation of anomalously warm and
- eddies can be clearly seen in the Gulf Stream region. The transport of
+ cold eddies can be clearly seen in the Gulf Stream region. The
- warm water northward by the mean flow of the Gulf Stream is also clearly
+ transport of warm water northward by the mean flow of the Gulf Stream
- visible.
+ is also clearly visible.
  %% CNHbegin
  \input{part1/atl6_figure}
 Line 231 
 visible.
  <!-- CMIREDIR:global_ocean_circulation: -->
  \end{rawhtml}
- 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
- the surface of a 4$^{\circ }$
+ currents at the surface of a $4^{\circ }$ global ocean model run with
- global ocean model run with 15 vertical levels. Lopped cells are used to
+vertical levels. Lopped cells are used to represent topography on a
- represent topography on a regular $lat-lon$ grid extending from 70$^{\circ
+ regular \textit{lat-lon} grid extending from $70^{\circ }N$ to
- }N $ to 70$^{\circ }S$. The model is driven using monthly-mean winds with
+ $70^{\circ }S$. The model is driven using monthly-mean winds with
- mixed boundary conditions on temperature and salinity at the surface. The
+ mixed boundary conditions on temperature and salinity at the surface.
- transfer properties of ocean eddies, convection and mixing is parameterized
+ The transfer properties of ocean eddies, convection and mixing is
- in this model.
+ parameterized in this model.
  Figure \ref{fig:large-scale-circ} (bottom) shows the meridional overturning
  circulation of the global ocean in Sverdrups.
 Line 301 
 Forward and tangent linear counterparts
  `automatic adjoint compiler'. These can be used in parameter sensitivity and
  data assimilation studies.
- As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity}
+ As one example of application of the MITgcm adjoint, Figure
- maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude
+ \ref{fig:hf-sensitivity} maps the gradient $\frac{\partial J}{\partial
- of the overturning stream-function shown in figure \ref{fig:large-scale-circ}
+   \mathcal{H}}$where $J$ is the magnitude of the overturning
- at 60$^{\circ }$N and $
+ stream-function shown in figure \ref{fig:large-scale-circ} at
- \mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over
+ $60^{\circ }N$ and $ \mathcal{H}(\lambda,\varphi)$ is the mean, local
- a 100 year period. We see that $J$ is
+ air-sea heat flux over a 100 year period. We see that $J$ is sensitive
- sensitive to heat fluxes over the Labrador Sea, one of the important sources
+ to heat fluxes over the Labrador Sea, one of the important sources of
- of deep water for the thermohaline circulations. This calculation also
+ deep water for the thermohaline circulations. This calculation also
  yields sensitivities to all other model parameters.
  %%CNHbegin
 Line 341 
 consistency with altimetric and in-situ
  <!-- CMIREDIR:ocean_biogeo_cycles: -->
  \end{rawhtml}
- MITgcm is being used to study global biogeochemical cycles in the ocean. For
+ MITgcm is being used to study global biogeochemical cycles in the
- example one can study the effects of interannual changes in meteorological
+ ocean. For example one can study the effects of interannual changes in
- forcing and upper ocean circulation on the fluxes of carbon dioxide and
+ meteorological forcing and upper ocean circulation on the fluxes of
- oxygen between the ocean and atmosphere. Figure \ref{fig:biogeo} shows
+ carbon dioxide and oxygen between the ocean and atmosphere. Figure
- the annual air-sea flux of oxygen and its relation to density outcrops in
+ \ref{fig:biogeo} shows the annual air-sea flux of oxygen and its
- the southern oceans from a single year of a global, interannually varying
+ relation to density outcrops in the southern oceans from a single year
- simulation. The simulation is run at $1^{\circ}\times1^{\circ}$ resolution
+ of a global, interannually varying simulation. The simulation is run
- telescoping to $\frac{1}{3}^{\circ}\times\frac{1}{3}^{\circ}$ in the tropics (not shown).
+ at $1^{\circ}\times1^{\circ}$ resolution telescoping to
+ $\frac{1}{3}^{\circ}\times\frac{1}{3}^{\circ}$ in the tropics (not
+ shown).
  %%CNHbegin
  \input{part1/biogeo_figure}
-Line 770 
 OPERATORS.
+Line 772 
 OPERATORS.
  \subsubsection{Shallow atmosphere approximation}
- Most models are based on the `hydrostatic primitive equations' (HPE's) in
+ Most models are based on the `hydrostatic primitive equations' (HPE's)
- which the vertical momentum equation is reduced to a statement of
+ in which the vertical momentum equation is reduced to a statement of
- hydrostatic balance and the `traditional approximation' is made in which the
+ hydrostatic balance and the `traditional approximation' is made in
- Coriolis force is treated approximately and the shallow atmosphere
+ which the Coriolis force is treated approximately and the shallow
- approximation is made.\ The MITgcm need not make the `traditional
+ atmosphere approximation is made.  MITgcm need not make the
- approximation'. To be able to support consistent non-hydrostatic forms the
+ `traditional approximation'. To be able to support consistent
- shallow atmosphere approximation can be relaxed - when dividing through by $
+ non-hydrostatic forms the shallow atmosphere approximation can be
- r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$,
+ relaxed - when dividing through by $ r $ in, for example,
- the radius of the earth.
+ (\ref{eq:gu-speherical}), we do not replace $r$ by $a$, the radius of
+ the earth.
  \subsubsection{Hydrostatic and quasi-hydrostatic forms}
  \label{sec:hydrostatic_and_quasi-hydrostatic_forms}
-Line 815 
 et.al., 1997a. As in \textbf{HPE }only a
+Line 818 
 et.al., 1997a. As in \textbf{HPE }only a
  \subsubsection{Non-hydrostatic and quasi-nonhydrostatic forms}
- The MIT model presently supports a full non-hydrostatic ocean isomorph, but
+ MITgcm presently supports a full non-hydrostatic ocean isomorph, but
  only a quasi-non-hydrostatic atmospheric isomorph.
  \paragraph{Non-hydrostatic Ocean}
-Line 1074 
 friction. These coefficients are the sam
+Line 1077 
 friction. These coefficients are the sam
  The mixing terms for the temperature and salinity equations have a similar
  form to that of momentum except that the diffusion tensor can be
- non-diagonal and have varying coefficients. $\qquad $
+ non-diagonal and have varying coefficients.
  \begin{equation}
  D_{T,S}=\nabla .[\underline{\underline{K}}\nabla (T,S)]+K_{4}\nabla
  _{h}^{4}(T,S)  \label{eq:diffusion}
-Line 1213 
 In $p$-coordinates, the upper boundary a
+Line 1216 
 In $p$-coordinates, the upper boundary a
  surface ($\phi $ is imposed and $\omega \neq 0$).
  \subsubsection{Splitting the geo-potential}
+ \label{sec:hpe-p-geo-potential-split}
  For the purposes of initialization and reducing round-off errors, the model
  deals with perturbations from reference (or ``standard'') profiles. For
-Line 1485 
 u=r\cos \varphi \frac{D\lambda }{Dt}
+Line 1489 
 u=r\cos \varphi \frac{D\lambda }{Dt}
  \end{equation*}
  \begin{equation*}
- v=r\frac{D\varphi }{Dt}\qquad
+ v=r\frac{D\varphi }{Dt}
  \end{equation*}
- $\qquad \qquad \qquad \qquad $
  \begin{equation*}
  \dot{r}=\frac{Dr}{Dt}
-Line 1497 
 Here $\varphi $ is the latitude, $\lambd
+Line 1500 
 Here $\varphi $ is the latitude, $\lambd
  distance of the particle from the center of the earth, $\Omega $ is the
  angular speed of rotation of the Earth and $D/Dt$ is the total derivative.
- The `grad' ($\nabla $) and `div' ($\nabla $.) operators are defined by, in
+ The `grad' ($\nabla $) and `div' ($\nabla\cdot$) operators are defined by, in
  spherical coordinates:
  \begin{equation*}
-Line 1507 
 spherical coordinates:
+Line 1510 
 spherical coordinates:
  \end{equation*}
  \begin{equation*}
- \nabla .v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial
+ \nabla\cdot v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial
  \lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\}
  +\frac{1}{r^{2}}\frac{\partial \left( r^{2}\dot{r}\right) }{\partial r}
  \end{equation*}

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