[CF-metadata] CF-1.0-beta5: curvilinear bounds "contiguous"attribute

From: Jonathan Gregory <jonathan.gregory>
Date: Wed, 19 Mar 2003 11:34:08 +0000

Dear All

Here are some more points about boundary coordinates.

I accept the argument that it is nice to be able to tell from (n+1) boundaries
that the cells are contiguous. This is of course an advantage, and another
advantage is that this method has been commonly used. However, COARDS didn't
standardise any method for boundaries so whatever we do will present problems
for some existing data.

Generic applications: As I've said, the reason I'm unhappy about supporting
both (n+1) and (n,2) boundaries is that it makes the standard more
complicated. I am worried in particular that writers of generic applications or
data-users writing their own ad-hoc analysis code may not implement (n,2) if
(n+1) is used more commonly. That would mean we would have to wait longer for
full CF support, and that some programs would have problems with some
data. Bounds are a pretty basic requirement so this would be a nuisance.

Writing data: Even if we require (n+1) to be used for contiguous cells, writers
of data might use (n,2) when it is more convenient. For example, if you are
making a 3D variable (time,lat,lon) by concatenating separate (lat,lon)
variables, each with its own 2-element time bounds, it is convenient to produce
a (n,2) time boundary variable. To require (n+1) to be used means the
data-writer has to do a contiguousness check and write data in two different
formats according to the results. If we want to encourage people to write
CF-compliant data, we don't want to make it more difficult for them to do
so. On the other hand, if contiguous cells may be written in (2,n) format,
applications reading data cannot make any assumptions and have to be able to
check for themselves, just as if we did not support (n+1), so nothing has been
gained by complicating the standard.

Record dimension: This problem has already been raised. Doesn't it mean that
(n+1) can't be used for the unlimited dimension? Wouldn't that imply, again,
that applications need to be able to check (n,2) for contiguousness?

Wrap-round axis: A longitude axis spanning the whole world has only (n)
boundaries. Even if written in (n+1) form it must contain extreme boundaries
which are equal under modulo 360; it is not possible to avoid having to check
for contiguousness in order to determine whether it is a wrap-round axis.

1D case: In an earlier posting I said that you couldn't depend on the order of
the boundaries in (n,2). Obviously we could adopt one. For instance, we could
say that the sequence bound(i,0), point(i), bound(i,1), bound(i+1,0), ... must
be monotonic. In that case the extrema are bound(0,0) and bound(n-1,1), and
contiguousness is tested by comparing bound(i,1) with bound(i+1,0) e.g. if
(abs(bound(i+1,0)-bound(i,1)).lt.1e-5*abs(point(i+1)-point(i))) i.e. the
boundaries between adjacent cells are much closer together - even if not
exactly coincident because of numerical imprecision - than the grid
points. This convention is easy to implement and check for correctness because
it depends on numerical comparison.

2D case: I think we ought to distinguish between the polygon case and the
quadrilateral case. The bounds for the former cannot be decomposed into two
separate dimensions. Any number of vertices may be needed. The cells themselves
may not be in a 2D array. Contiguousness is complicated to test. In the
quadrilateral case, however, the bounds arrays can be dimensioned
bounds(n,m,2,2), as Steve says. If we adopt the above 1D convention for
ordering, we then know which 2D bounds to compare for contiguousness of any
pair of adjacent cells. This has the same purpose as saying the four points
must be ordered clockwise or anticlockwise. (The reason I am worried about
(anti)clockwise ordering is that I fear people might sometimes get confused
about whether they were considering index space or real space to decide the
sign convention.) Two notes on this:

* bounds(n,m,2,2) can be equivalenced/reformed to bounds(n,m,4) if users prefer
to view them that way. The points would be arranged as a Z rather than as going
round the perimeter.

* In the quadrilateral case, the 2D bounds are on auxiliary coordinate
variables. If the 1D coordinate variables have bounds as well, these can be
checked for contiguousness, which is easier.

I am sorry this is rather long. I hope it makes sense.

Jonathan
Received on Wed Mar 19 2003 - 04:34:08 GMT