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revision 1.6 by cnh, Wed Oct 24 15:21:27 2001 UTC revision 1.7 by cnh, Thu Oct 25 12:06:56 2001 UTC
# Line 54  MITgcm has a number of novel aspects: Line 54  MITgcm has a number of novel aspects:
54  \begin{itemize}  \begin{itemize}
55  \item it can be used to study both atmospheric and oceanic phenomena; one  \item it can be used to study both atmospheric and oceanic phenomena; one
56  hydrodynamical kernel is used to drive forward both atmospheric and oceanic  hydrodynamical kernel is used to drive forward both atmospheric and oceanic
57  models - see fig  models - see fig \ref{fig:onemodel}
 \marginpar{  
 Fig.1 One model}\ref{fig:onemodel}  
58    
59  %% CNHbegin  %% CNHbegin
60  \input{part1/one_model_figure}  \input{part1/one_model_figure}
61  %% CNHend  %% CNHend
62    
63  \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
64  small-scale and large scale processes - see fig  small-scale and large scale processes - see fig \ref{fig:all-scales}
 \marginpar{  
 Fig.2 All scales}\ref{fig:all-scales}  
65    
66  %% CNHbegin  %% CNHbegin
67  \input{part1/all_scales_figure}  \input{part1/all_scales_figure}
# Line 73  Fig.2 All scales}\ref{fig:all-scales} Line 69  Fig.2 All scales}\ref{fig:all-scales}
69    
70  \item finite volume techniques are employed yielding an intuitive  \item finite volume techniques are employed yielding an intuitive
71  discretization and support for the treatment of irregular geometries using  discretization and support for the treatment of irregular geometries using
72  orthogonal curvilinear grids and shaved cells - see fig  orthogonal curvilinear grids and shaved cells - see fig \ref{fig:finite-volumes}
 \marginpar{  
 Fig.3 Finite volumes}\ref{fig:finite-volumes}  
73    
74  %% CNHbegin  %% CNHbegin
75  \input{part1/fvol_figure}  \input{part1/fvol_figure}
# Line 102  give a feel for the wide range of proble Line 96  give a feel for the wide range of proble
96    
97  The MITgcm has been designed and used to model a wide range of phenomena,  The MITgcm has been designed and used to model a wide range of phenomena,
98  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
99  atmospheric winds - see fig.2\ref{fig:all-scales}. To give a flavor of the  atmospheric winds - see figure \ref{fig:all-scales}. To give a flavor of the
100  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
101  of them here. A more detailed description of the underlying formulation,  of them here. A more detailed description of the underlying formulation,
102  numerical algorithm and implementation that lie behind these calculations is  numerical algorithm and implementation that lie behind these calculations is
# Line 113  described in detail in the documentation Line 107  described in detail in the documentation
107    
108  \subsection{Global atmosphere: `Held-Suarez' benchmark}  \subsection{Global atmosphere: `Held-Suarez' benchmark}
109    
110  A novel feature of MITgcm is its ability to simulate both atmospheric and  A novel feature of MITgcm is its ability to simulate, using one basic algorithm,
111  oceanographic flows at both small and large scales.  both atmospheric and oceanographic flows at both small and large scales.
112    
113  Fig.E1a.\ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$  Figure \ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$
114  temperature field obtained using the atmospheric isomorph of MITgcm run at  temperature field obtained using the atmospheric isomorph of MITgcm run at
115  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
116  (blue) and warm air along an equatorial band (red). Fully developed  (blue) and warm air along an equatorial band (red). Fully developed
# Line 132  there are no mountains or land-sea contr Line 126  there are no mountains or land-sea contr
126  %% CNHend  %% CNHend
127    
128  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
129  globe permitting a uniform gridding and obviated the need to fourier filter.  globe permitting a uniform gridding and obviated the need to Fourier filter.
130  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear  The `vector-invariant' form of MITgcm supports any orthogonal curvilinear
131  grid, of which the cubed sphere is just one of many choices.  grid, of which the cubed sphere is just one of many choices.
132    
133  Fig.E1b shows the 5-year mean, zonally averaged potential temperature, zonal  Figure \ref{fig:hs_zave_u} shows the 5-year mean, zonally averaged zonal
134  wind and meridional overturning streamfunction from a 20-level version of  wind from a 20-level configuration of
135  the model. It compares favorable with more conventional spatial  the model. It compares favorable with more conventional spatial
136  discretization approaches.  discretization approaches. The two plots show the field calculated using the
137    cube-sphere grid and the flow calculated using a regular, spherical polar
138  A regular spherical lat-lon grid can also be used.  latitude-longitude grid. Both grids are supported within the model.
139    
140  %% CNHbegin  %% CNHbegin
141  \input{part1/hs_zave_u_figure}  \input{part1/hs_zave_u_figure}
# Line 157  diffusive patterns of ocean currents. Bu Line 151  diffusive patterns of ocean currents. Bu
151  increased until the baroclinic instability process is resolved, numerical  increased until the baroclinic instability process is resolved, numerical
152  solutions of a different and much more realistic kind, can be obtained.  solutions of a different and much more realistic kind, can be obtained.
153    
154  Fig. ?.? shows the surface temperature and velocity field obtained from  Figure \ref{fig:ocean-gyres} shows the surface temperature and velocity
155  MITgcm run at $\frac{1}{6}^{\circ }$ horizontal resolution on a $lat-lon$  field obtained from MITgcm run at $\frac{1}{6}^{\circ }$ horizontal
156    resolution on a $lat-lon$
157  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
158  (to avoid the converging of meridian in northern latitudes). 21 vertical  (to avoid the converging of meridian in northern latitudes). 21 vertical
159  levels are used in the vertical with a `lopped cell' representation of  levels are used in the vertical with a `lopped cell' representation of
160  topography. The development and propagation of anomalously warm and cold  topography. The development and propagation of anomalously warm and cold
161  eddies can be clearly been seen in the Gulf Stream region. The transport of  eddies can be clearly seen in the Gulf Stream region. The transport of
162  warm water northward by the mean flow of the Gulf Stream is also clearly  warm water northward by the mean flow of the Gulf Stream is also clearly
163  visible.  visible.
164    
# Line 174  visible. Line 169  visible.
169    
170  \subsection{Global ocean circulation}  \subsection{Global ocean circulation}
171    
172  Fig.E2a shows the pattern of ocean currents at the surface of a 4$^{\circ }$  Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean currents at
173    the surface of a 4$^{\circ }$
174  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
175  represent topography on a regular $lat-lon$ grid extending from 70$^{\circ  represent topography on a regular $lat-lon$ grid extending from 70$^{\circ
176  }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
# Line 182  mixed boundary conditions on temperature Line 178  mixed boundary conditions on temperature
178  transfer properties of ocean eddies, convection and mixing is parameterized  transfer properties of ocean eddies, convection and mixing is parameterized
179  in this model.  in this model.
180    
181  Fig.E2b shows the meridional overturning circulation of the global ocean in  Figure \ref{fig:large-scale-circ} (bottom) shows the meridional overturning
182  Sverdrups.  circulation of the global ocean in Sverdrups.
183    
184  %%CNHbegin  %%CNHbegin
185  \input{part1/global_circ_figure}  \input{part1/global_circ_figure}
# Line 195  Dense plumes generated by localized cool Line 191  Dense plumes generated by localized cool
191  ocean may be influenced by rotation when the deformation radius is smaller  ocean may be influenced by rotation when the deformation radius is smaller
192  than the width of the cooling region. Rather than gravity plumes, the  than the width of the cooling region. Rather than gravity plumes, the
193  mechanism for moving dense fluid down the shelf is then through geostrophic  mechanism for moving dense fluid down the shelf is then through geostrophic
194  eddies. The simulation shown in the figure (blue is cold dense fluid, red is  eddies. The simulation shown in the figure \ref{fig::convect-and-topo}
195    (blue is cold dense fluid, red is
196  warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to  warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to
197  trigger convection by surface cooling. The cold, dense water falls down the  trigger convection by surface cooling. The cold, dense water falls down the
198  slope but is deflected along the slope by rotation. It is found that  slope but is deflected along the slope by rotation. It is found that
# Line 214  presence of complex geometry makes it an Line 211  presence of complex geometry makes it an
211  dynamics and mixing in oceanic canyons and ridges driven by large amplitude  dynamics and mixing in oceanic canyons and ridges driven by large amplitude
212  barotropic tidal currents imposed through open boundary conditions.  barotropic tidal currents imposed through open boundary conditions.
213    
214  Fig. ?.? shows the influence of cross-slope topographic variations on  Fig. \ref{fig:boundary-forced-wave} shows the influence of cross-slope
215    topographic variations on
216  internal wave breaking - the cross-slope velocity is in color, the density  internal wave breaking - the cross-slope velocity is in color, the density
217  contoured. The internal waves are excited by application of open boundary  contoured. The internal waves are excited by application of open boundary
218  conditions on the left.\ They propagate to the sloping boundary (represented  conditions on the left. They propagate to the sloping boundary (represented
219  using MITgcm's finite volume spatial discretization) where they break under  using MITgcm's finite volume spatial discretization) where they break under
220  nonhydrostatic dynamics.  nonhydrostatic dynamics.
221    
# Line 231  Forward and tangent linear counterparts Line 229  Forward and tangent linear counterparts
229  `automatic adjoint compiler'. These can be used in parameter sensitivity and  `automatic adjoint compiler'. These can be used in parameter sensitivity and
230  data assimilation studies.  data assimilation studies.
231    
232  As one example of application of the MITgcm adjoint, Fig.E4 maps the  As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity}
233  gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude  maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude
234  of the overturning streamfunction shown in fig?.? at 40$^{\circ }$N and $  of the overturning streamfunction shown in figure \ref{fig:large-scale-circ}
235  \mathcal{H}$ is the air-sea heat flux 100 years before. We see that $J$ is  at 60$^{\circ }$N and $
236    \mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over
237    a 100 year period. 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
240  yields sensitivities to all other model parameters.  yields sensitivities to all other model parameters.
# Line 250  ocean circulation. An appropriately defi Line 250  ocean circulation. An appropriately defi
250  the departure of the model from observations (both remotely sensed and  the departure of the model from observations (both remotely sensed and
251  insitu) over an interval of time, is minimized by adjusting `control  insitu) over an interval of time, is minimized by adjusting `control
252  parameters' such as air-sea fluxes, the wind field, the initial conditions  parameters' such as air-sea fluxes, the wind field, the initial conditions
253  etc. Figure ?.? shows an estimate of the time-mean surface elevation of the  etc. Figure \ref{fig:assimilated-globes} shows an estimate of the time-mean
254  ocean obtained by bringing the model in to consistency with altimetric and  surface elevation of the ocean obtained by bringing the model in to
255  in-situ observations over the period 1992-1997.  consistency with altimetric and in-situ observations over the period
256    1992-1997. {\bf CHANGE THIS TEXT - FIG FROM PATRICK/CARL/DETLEF}
257    
258  %% CNHbegin  %% CNHbegin
259  \input{part1/globes_figure}  \input{part1/globes_figure}
# Line 263  in-situ observations over the period 199 Line 264  in-situ observations over the period 199
264  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
265  example one can study the effects of interannual changes in meteorological  example one can study the effects of interannual changes in meteorological
266  forcing and upper ocean circulation on the fluxes of carbon dioxide and  forcing and upper ocean circulation on the fluxes of carbon dioxide and
267  oxygen between the ocean and atmosphere. The figure shows the annual air-sea  oxygen between the ocean and atmosphere. Figure \ref{fig:biogeo} shows
268  flux of oxygen and its relation to density outcrops in the southern oceans  the annual air-sea flux of oxygen and its relation to density outcrops in
269  from a single year of a global, interannually varying simulation.  the southern oceans from a single year of a global, interannually varying
270    simulation. The simulation is run at $1^{\circ}\times1^{\circ}$ resolution
271    telescoping to $\frac{1}{3}^{\circ}\times\frac{1}{3}^{\circ}$ in the tropics (not shown).
272    
273  %%CNHbegin  %%CNHbegin
274  \input{part1/biogeo_figure}  \input{part1/biogeo_figure}
# Line 273  from a single year of a global, interann Line 276  from a single year of a global, interann
276    
277  \subsection{Simulations of laboratory experiments}  \subsection{Simulations of laboratory experiments}
278    
279  Figure ?.? shows MITgcm being used to simulate a laboratory experiment  Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a
280  enquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An  laboratory experiment enquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An
281  initially homogeneous tank of water ($1m$ in diameter) is driven from its  initially homogeneous tank of water ($1m$ in diameter) is driven from its
282  free surface by a rotating heated disk. The combined action of mechanical  free surface by a rotating heated disk. The combined action of mechanical
283  and thermal forcing creates a lens of fluid which becomes baroclinically  and thermal forcing creates a lens of fluid which becomes baroclinically
284  unstable. The stratification and depth of penetration of the lens is  unstable. The stratification and depth of penetration of the lens is
285  arrested by its instability in a process analogous to that whic sets the  arrested by its instability in a process analogous to that which sets the
286  stratification of the ACC.  stratification of the ACC.
287    
288  %%CNHbegin  %%CNHbegin
# Line 293  stratification of the ACC. Line 296  stratification of the ACC.
296    
297  To render atmosphere and ocean models from one dynamical core we exploit  To render atmosphere and ocean models from one dynamical core we exploit
298  `isomorphisms' between equation sets that govern the evolution of the  `isomorphisms' between equation sets that govern the evolution of the
299  respective fluids - see fig.4  respective fluids - see figure \ref{fig:isomorphic-equations}.
300  \marginpar{  One system of hydrodynamical equations is written down
 Fig.4. Isomorphisms}. One system of hydrodynamical equations is written down  
301  and encoded. The model variables have different interpretations depending on  and encoded. The model variables have different interpretations depending on
302  whether the atmosphere or ocean is being studied. Thus, for example, the  whether the atmosphere or ocean is being studied. Thus, for example, the
303  vertical coordinate `$r$' is interpreted as pressure, $p$, if we are  vertical coordinate `$r$' is interpreted as pressure, $p$, if we are
304  modeling the atmosphere and height, $z$, if we are modeling the ocean.  modeling the atmosphere (left hand side of figure \ref{fig:isomorphic-equations})
305    and height, $z$, if we are modeling the ocean (right hand side of figure
306    \ref{fig:isomorphic-equations}).
307    
308  %%CNHbegin  %%CNHbegin
309  \input{part1/zandpcoord_figure.tex}  \input{part1/zandpcoord_figure.tex}
# Line 311  velocity $\vec{\mathbf{v}}$, active trac Line 315  velocity $\vec{\mathbf{v}}$, active trac
315  depend on $\theta $, $S$, and $p$. The equations that govern the evolution  depend on $\theta $, $S$, and $p$. The equations that govern the evolution
316  of these fields, obtained by applying the laws of classical mechanics and  of these fields, obtained by applying the laws of classical mechanics and
317  thermodynamics to a Boussinesq, Navier-Stokes fluid are, written in terms of  thermodynamics to a Boussinesq, Navier-Stokes fluid are, written in terms of
318  a generic vertical coordinate, $r$, see fig.5  a generic vertical coordinate, $r$, so that the appropriate
319  \marginpar{  kinematic boundary conditions can be applied isomorphically
320  Fig.5 The vertical coordinate of model}:  see figure \ref{fig:zandp-vert-coord}.
321    
322  %%CNHbegin  %%CNHbegin
323  \input{part1/vertcoord_figure.tex}  \input{part1/vertcoord_figure.tex}
# Line 410  S\text{ is specific humidity in the atmo Line 414  S\text{ is specific humidity in the atmo
414  \end{equation*}  \end{equation*}
415    
416  The $\mathcal{F}^{\prime }s$ and $\mathcal{Q}^{\prime }s$ are provided by  The $\mathcal{F}^{\prime }s$ and $\mathcal{Q}^{\prime }s$ are provided by
417  extensive `physics' packages for atmosphere and ocean described in Chapter 6.  `physics' and forcing packages for atmosphere and ocean. These are described
418    in later chapters.
419    
420  \subsection{Kinematic Boundary conditions}  \subsection{Kinematic Boundary conditions}
421    
422  \subsubsection{vertical}  \subsubsection{vertical}
423    
424  at fixed and moving $r$ surfaces we set (see fig.5):  at fixed and moving $r$ surfaces we set (see figure \ref{fig:zandp-vert-coord}):
425    
426  \begin{equation}  \begin{equation}
427  \dot{r}=0atr=R_{fixed}(x,y)\text{ (ocean bottom, top of the atmosphere)}  \dot{r}=0atr=R_{fixed}(x,y)\text{ (ocean bottom, top of the atmosphere)}
# Line 447  where $\vec{\mathbf{n}}$ is the normal t Line 452  where $\vec{\mathbf{n}}$ is the normal t
452    
453  \subsection{Atmosphere}  \subsection{Atmosphere}
454    
455  In the atmosphere, see fig.5, we interpret:  In the atmosphere, (see figure \ref{fig:zandp-vert-coord}), we interpret:
456    
457  \begin{equation}  \begin{equation}
458  r=p\text{ is the pressure}  \label{eq:atmos-r}  r=p\text{ is the pressure}  \label{eq:atmos-r}
# Line 681  r $ in, for example, (\ref{eq:gu-speheri Line 686  r $ in, for example, (\ref{eq:gu-speheri
686  the radius of the earth.  the radius of the earth.
687    
688  \subsubsection{Hydrostatic and quasi-hydrostatic forms}  \subsubsection{Hydrostatic and quasi-hydrostatic forms}
689    \label{sec:hydrostatic_and_quasi-hydrostatic_forms}
690    
691  These are discussed at length in Marshall et al (1997a).  These are discussed at length in Marshall et al (1997a).
692    
# Line 799  Marshall et al, 1997) resulting in a non Line 805  Marshall et al, 1997) resulting in a non
805  hydrostatic limit, is as computationally economic as the \textbf{HPEs}.  hydrostatic limit, is as computationally economic as the \textbf{HPEs}.
806    
807  \subsection{Finding the pressure field}  \subsection{Finding the pressure field}
808    \label{sec:finding_the_pressure_field}
809    
810  Unlike the prognostic variables $u$, $v$, $w$, $\theta $ and $S$, the  Unlike the prognostic variables $u$, $v$, $w$, $\theta $ and $S$, the
811  pressure field must be obtained diagnostically. We proceed, as before, by  pressure field must be obtained diagnostically. We proceed, as before, by
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