Hi Bob,
I agree that CF describes the types of 2D horizontal grids that you
outlined. Since the grid_mapping attribute will be optional using it to
identify grids has the same problems as depending on boundary attributes.
I believe that the CF metadata currently contains enough information to
identify these grids. Do you agree?
Brian
On Mon, 24 Jun 2002, Bob Drach wrote:
> Dear Jonathan,
>
> > I think you are setting yourself a hard task to distinguish such a tiling of
> > the whole surface from an irregular set of scattered points.
>
> I'm really trying to pin down the definition of 'grid' in a sense that will be
> useful to application writers. It is certainly difficult, but given that the term
> is used frequently in CF I hope the effort is worth it.
>
> > This is getting
> > outside the bounds of a purely technical question into the area of scientific
> > interpretation. Structurally the two are identical because functionally they
> > are really quite similar. For example, suppose you have a reduced grid covering
> > the whole Earth i.e. no gaps between its boxes. Then omit a single gridbox. Is
> > this now a reduced grid with a box missing, or is it a set of scattered points
> > each with an associated box surrounding it? Or, starting from the other end, it
> > might be the case that a small set of scattered station data spread over the
> > world really might be being used to estimate a global average quantity. Sea
> > level change is estimated from tide gauges in this kind of way. In this
> > case the user would actually or notionally have associated some kind of
> > region with each station, so it is not obvious that it would be inappropriate
> > to guess at the gridbox boundaries.
> >
> > However, the grid_mapping attribute we have been discussing may help. I suppose
> > that if there is a grid_mapping, it means that the whole world (or the portion
> > of it being considered) has been systematically covered in some kind of way.
> > The application may not understand how the grid_mapping works, but perhaps the
> > presence of this attribute would be sufficient to decide that the data was a
> > set of boxes covering the surface, rather than a set of irregularly scattered
> > points.
>
> Part of the question is whether there are any georeferenced data in CF that are
> not gridded (!). My sense is that the notion of'irregularly scattered points' lies
> outside the range of what is commonly called gridded, but that data with an
> associated tiling, or nonoverlapping convex cells (gridboxes) - particularly if
> the tiling covers the surface - could reasonably be called gridded. A tiling that
> covers a contiguous region carries the added notion of connectivity. But I agree
> with Brian that you can have a grid without explicitly defined gridboxes, e.g.,
> the example of spectral data translated to a T42 grid.
>
> Let me try to distill the discussion into a working definition of horizontal grid:
>
> Conceptually, a horizontal grid represents a discretization and
> structuring/ordering of lat-lon space. More formally, a (horizontal) grid is the
> discretization of a 1-1 mapping from a two-dimensional index space into lat-lon
> space. A grid may or may not have associated boundary information, representing
> the decomposition of lat-lon space into nonoverlapping cells, such that each point
> of the grid is contained in the corresponding cell.
>
> If in addition to being 1-1 the grid mapping function is a discretization of a
> continuous function, then the grid is considered to carry connectivity
> information, in the sense that for a given i,j, the neighboring grid points of
> point (i,j) are (i+/-1,j) and (i,j+/-1). Similarly, if boundary information is
> specified, and cells P, Q share an edge, then their corresponding grid points are
> neighbors.
>
> In CF the grid information is represented by coordinate variables and/or auxiliary
> coordinate variables [and/or a grid_mapping definition?], and the optional
> boundary information by boundary variables associated with the coordinate
> variables. CF stipulates the representation for three types of horizontal grids:
> independent lat/lon coordinate variables, dependent lat/lon coordinate variables,
> and reduced grids:
>
> Independent lat-lon variables: The grid mapping g(i,j) == <lat(i,j), lon(i,j)> is
> represented by g(i,j) = <lat(i), lon(j)>. The stronger definition of grid applies
> here, reflected in the requirement that lat and lon are monotonic. It is in this
> sense that a grid mapping imposes an ordering.
>
> Dependent lat-lon variables: g(i,j) = <lat(i,j), lon(i,j)> such that g is 1-1. The
> stronger sense of continuity applies to this case.
>
> Reduced grid: g(i,j) = <lat(i), lon(i,j)> such that g is 1-1, and lat(i) is
> monotonic.
>
>
>
> Best regards,
>
> Bob
>
>
> _______________________________________________
> CF-metadata mailing list
> CF-metadata at cgd.ucar.edu
> http://www.cgd.ucar.edu/mailman/listinfo/cf-metadata
>
-----------------------------------------------------------------
Brian Eaton | email: eaton at ucar.edu
Climate Modeling Section |
National Center for Atmospheric Research |
P.O. Box 3000, Boulder, CO 80307 |
Received on Tue Jun 25 2002 - 20:25:17 BST
