_Discrete_grids.dox

/*! \page Discrete_Grids Discrete Horizontal and Vertical Grids

\section horizontal_grids Horizontal grids

The placement of model variables on the horizontal C-grid is illustrated here:

\image html Arakawa_C_grid.png "MOM6 uses an Arakawa C grid staggering of variables with a North-East indexing convention."

\image latex Arakawa_C_grid.png "MOM6 uses an Arakawa C grid staggering of variables with a North-East indexing convention."

Scalars are located at the \f$h\f$-points, velocities are staggered such that

\f$u\f$-points and \f$v\f$-points are not co-located, and vorticities

are located at \f$q\f$-points. The indexing for points (\f$i,j\f$) in

the logically-rectangular domain is such that \f$i\f$ increases in

the \f$x\f$ direction (eastward for spherical polar coordinates), and

\f$j\f$ increases in the \f$y\f$ direction (northward for spherical polar

coordinates). A \f$q\f$-point with indices (\f$i,j\f$) lies to the upper

right (northeast) of the \f$h\f$-point with the same indices. The index

for the vertical dimension \f$k\f$ increases with depth, although the

vertical coordinate \f$z\f$, measured from the mean surface level \f$z =

0\f$, decreases with depth.

When the horizontal grid is generated, it is actually computed on the

\"supergrid\" at twice the nominal resolution of the model. The grid file

contains the grid metrics and the areas of this fine grid. The model

then decomposes it into the four staggered grids, along with computing

the grid metrics as shown here:

\image html Grid_metrics.png "The grid metrics around both \f$h\f$-points and \f$q\f$-points."

\imagelatex{Grid_metrics.png,The grid metrics around both $h$-points and $q$-points.,\includegraphics[width=\textwidth\,height=\textheight/2\,keepaspectratio=true]}

The model carries both the metrics as well as their inverses, for instance,

IdyT = 1/dyT. There are also the areas and the inverse areas for all four grid

locations. areaT and areaBu are the sum of the four areas from the supergrid

surrounding each h-point and each q-point, respectively. The velocity faces can be

partially blocked and their areas are adjusted accordingly, where \f$dy\_Cu\f$ and

\f$dx\_Cv\f$ are the blocked distances at \f$u\f$ and \f$v\f$ points, respectively.

\f{eqnarray}

\mbox{areaCu}_{i,j} &= dxCu_{i,j} * dy\_Cu_{i,j} \\

\mbox{areaCv}_{i,j} &= dx\_Cv_{i,j} * dyCv_{i,j} \\

\mbox{IareaCu}_{i,j} &= 1 / \mbox{areaCu}_{i,j} \\

\mbox{IareaCv}_{i,j} &= 1 / \mbox{areaCv}_{i,j}

\f}

The horizontal grids can be spherical, tripole, regional, or cubed sphere.

The default is for grids to be re-entrant in the \f$x\f$-direction; this needs

to be turned off for regional grids.

\section vertical_grids Vertical grids

The placement of model variables in the vertical is illustrated here:

\image html cell_3d.png "The MOM6 interfaces are at vertical location \f$e\f$ which are separated by the layer thicknesses \f$h\f$."

\imagelatex{cell_3d.png,The MOM6 interfaces are at vertical location $e$ which are separated by the layer thicknesses $h$.,\includegraphics[width=\textwidth\,height=\textheight/2\,keepaspectratio=true]}

The vertical coordinate is Lagrangian in that the interfaces between the layers are

free to move up and down with time. The interfaces have target depths or target

densities, depending on the desired vertical coordinate system. They can even have

target sigma values for terrain-following coordinates or you can design a hybrid

coordinate in which different interfaces have differing behavior. In any case, the

interfaces move with the fluid during the dynamic timesteps and then get reset during a

remapping operation. See section \ref ALE_Timestep for details.

*/