[CF-metadata] bounds

From: Jonathan Gregory <jonathan.gregory>
Date: Wed, 28 May 2003 15:13:53 +0100

I think I was wrong in the previous posting about the ordering of 2D vertices.
If we adopt (y,x,2,2) for 2D bounds, the natural convention (I feel) for the
size-2 trailing dimensions is the same as for 1D, that 0 indicates the side of
cell which faces in the direction of smaller cell index and 1 the direction of
larger index. With this convention, you know the "adjacencies" of the grid i.e.
which vertices should be coincident, so you can check for contiguousness. But
you don't know how to go round the square anticlockwise or clockwise unless you
have also inspected the handedness of the x-y-upward coordinate system. There
are four possibilities for how it looks in lat-lon, depending on the sign
conventions of x and y:

     1,0 < 1,1 1,1 > 1,0 0,0 > 0,1 0,1 < 0,0
      v ^ ^ v ^ v v ^
     0,0 > 0,1 0,1 < 0,0 1,0 < 1,1 1,1 > 1,0

On the other hand, with the (y,x,4) convention, you can specify the sense of
circulation in lat-lon, but then the adjacencies are more complicated. It
seems to be a choice (unless I am confused now - quite possible). Here are
the proposals again, modified to reflect this:

(1) For a 1D coordinate variable with bounds (x,2), define an ordering for the
2nd index, namely that the bounds should be ordered in the same sense as the
coordinates, so that the 0-bound of cell i is on the side that faces cell i-1
and the 1-bound on the side facing cell i+1. [At present, there is no ordering
defined for 1D bounds.]

(2) If 1D cells i and i+1 are contiguous, bound (i,1) should exactly equal
bound (i+1,0). The data-writer should ensure that this is so. [At present, the
standard does not state how contiguousness should be tested.]

(3) In the 2D rectilinear case, the bounds should be dimensioned (y,x,2,2),
where the first trailing index corresponds to the y dimension and the second to
the x. The trailing indexes have the same convention as for 1D points, so that
the 0-bound in either x or y is on the side which faces the cell with the next
smallest index in that dimension, the 1-bound on the side facing the cell with
the next largest index. If the coordinate system x-y-upward is right-handed
(like lon-lat-upward), the elements (j,i,0,0), (j,i,0,1), (j,i,1,1), (j,i,1,0)
in that order traverse the vertices of cell (j,i) anticlockwise in the lon-lat
plane as viewed from above. If the coordinate system is left-handed, this
sequence of elements traverse the vertices clockwise. [This dimensioning of the
2D vertices is new.]

(4) In the 2D rectilinear case, if cells (j,i) and (j,i+1) are contiguous in x,
bound(j,i,q,1) should exactly equal bound(j,i+1,q,0) for q=0 and q=1. If cells
(j,i) and (j+1,i) are contiguous in y, bound(j,i,1,p) should exactly equal
bound(j+1,i,0,p) for p=0 and p=1. Since a continuous grid mapping in 2D will
not affect contiguousness, it is sufficient to check the bounds for any single
value of j and q for contiguousness in x, i and p for contiguousness in y.

(5) In the non-rectilinear case, the bounds should be dimensioned
(...,n,p). The vertices must be traversed anticlockwise in the lon-lat plane as
viewed from above. The starting vertex is not specified by the standard. [At
present, the standard does not state any ordering.]

Jonathan
Received on Wed May 28 2003 - 08:13:53 BST