> @taylor13  I haven't been following this, but what about tripolar grids, 
> which are often used in ocean models?
> @zklaus How are they represented in CF right now? As far as I know only by 2d 
> coordinates (which doesn't codify the iso-coordinate lines).

>From our specific experience : Most ocean models use the so-called ORCA grids.
These are not "just" a tripolar coordinate grid but use irregular sampling in 
various places.

Most importantly : ***a grid is not a projection***

So, a grid like ORCA has 2D latitude and longitude values for cell corners (and 
centres).  So that might *appear* to be like a coordinate-like space described 
by the grid indices.  But this is misleading, because a projection would be a 
smooth, reversible, total function  :  Instead ...
  1. you cannot define a point on the globe for an "interpolated" point in 
index-space like "ix=100.5, iy=101.3".  The relationship is entirely defined by 
the (2d) X and Y values, there is no smooth function from (ix, iy) to (lat, 
lon).
  1. there is no reverse mapping : you can't ask "where in the grid" a given 
point on the globe is.  Only which cells it may fall within... 
  1. in fact not all parts of the globe are covered at all.  The bottom of the 
space can be distorted to give extra detail in the Southern ocean, and does not 
cover the South pole.   Also, some model cells actually *overlap* along the top 
seam, referred to as a 'north fold'.  Thus...
  1. ... returning to the 'reversal' question, a given global location can be 
in several gridcells, or none.

In practice ORCA grids are particularly extreme case, in that the standard 
grids are defined _entirely_ by the provided 2D arrays of latitudes + 
longitudes, and there is no provided equation defining those numbers, as far as 
I can determine.

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