# Fwd: Re: longitude again.

```Hi Penny:

(I am taking the liberty of posting to some mail groups that might be
interested in this topic).

First I need to make a few claims that may not be that useful to you.

A coordinate system can be thought of as an invertible mapping from indicial
space (I^n) onto a manifold embedded in R^n (see
http://www.unidata.ucar.edu/staff/caron/papers/CoordMath.htm for some
details). Netcdf 1-D coordinate variables are the simplest case of
coordinate systems, and the standard netcdf conventions have really only
dealt with coordinate variables and their use in mapping I^n -> R^n, in fact
limited to the case of products of 1D functions, eg (i, j, k ) -> (f(i),
g(j) ,h(k)). In this case the requirement that the mapping be invertible is
equivalent to the requirement of monotonicity on each coordinate variable.

Whew, thanks for letting me get that off my chest ;^]

More general coordinate systems are possible, and I hope we are ready to
start defining some general conventions on how to express these, of which
COARDS and CF are special versions.

In particular, I think what you actually have is a sequence of trajectories,
where a trajectory is a 1D sampling. (This should probably not be considered
a grid, which are usually thought of as tesselating, since the sequences of
trajectories may be too far apart to make interpolation useful.)

If you dont think of it as a grid, then you have a 1D trajectory embedded
into 3D space, so the coordinate system for one trajectory looks like
CS:(i) -> (x(i), y(i), z(i)).

If you do want to think of it as a grid, then you have a 2D manifold
embedded into 3D space, and the coordinate system looks like  CS:(i, j) ->
(x(i,j), y(i,j), z(i,j)).

In both these cases, all you need to be invertible is that the (x(i), y(i),
z(i)) points (or the (x(i,j), y(i,j), z(i,j) points) are unique. So the
sequence of lons in x(i) itself doesnt need to be monotonic. The underlying
reason is simple: the 1D or 2D sample is embedded in a higher (3D) space,
and you have a lot more freedom. The requirement of monotonicty only applies
to the case of mapping equal dimensioned spaces.

Ok, thats an argument for when monotonicity is needed and when its not, in a
theoretical sense.

Now what about in a practical sense where you actually want to use the data?
The problem is that a number of viewers and analysis programs only know
about / can process the simple case of netcdf coordinate variables. Its
possible you might be able to get more functionality out of these packages
by shoehorning your data into these older conventions that werent designed
for your data. If thats the case, you need to identify what applications you
need to use, and find out if its possible.

A better idea, if you can afford it, is to create a new, better convention,
and then help develop or extend applications to make use of those. I am
posting this message to the DODS tech group, because we have been discussing
some of these issues, and the netcdf group, who might be game for yet
another try, or might know of some existing conventions that are more
appropriate. In fact, it looks like you might be able to use CF "auxiliary
coordinate variables", but i'll have to look at those closer.

I will have a look at your files and post some specific ideas.

----- Original Message -----
Cc: <jimc@xxxxxxxxxxxxxxxx>
Sent: Monday, February 04, 2002 12:39 PM

> Dear John,
> Steve Hankin has suggested that I let you know the issues that we are
> dealing with for the final issue of the WOCE data set in netCDF, and
> I write with the hope that you might be able to advise us.
>
> You may already know that all the WOCE data are being distributed as
> netCDF files, and currently we are grappling with the issues of
> making the files as consistent as possible across all the diverse
> data streams, and at the same time following existing conventions
> where possible.
>
> We have been trying to follow the conventions set by COARDS and CF,
> but have a problem with longitude in particular.  We have files that
> may have a single value of latitude and longitude (eg a single CTD
> profile or a sea-level station) but also files that have a range of
> lat/lon (eg a float trajectory, or ADCP data along a ship track).  At
> present our "WOCE convention" is for lat and lon to be variables (not
> global attributes) and to specify longitude as -180 to 180, degrees_E
> positive.  However one of our members is arguing that this is not
> COARDS compliant and that we should make it so.  However I'm not sure
> that COARDS provides a convention that suits all our files and so I
> am left wondering how best to treat our dataset as a whole over this
> thorny issue.
>
> Can you suggest a longitude convention that might suit the whole of
> our diverse dataset and that is an existing convention.... or should
> we accept that we may have to treat different data streams in the
> WOCE data resource slightly differently?
>
> Below is the recent discussion I have had with Steve Hankin on this
subject.
>
> Best regards,
> Penny
>
>
> >Date: Mon, 4 Feb 2002 19:25:38 +0000
> >To: Steve Hankin <hankin@xxxxxxxxxxxxx>
> >From: Penny Holliday <nph@xxxxxxxxxxxxxxxxxxxx>
> >Subject: Re: longitude again.
> >Cc: jimc@xxxxxxxxxxxxxxxx
> >Bcc:
> >X-Attachments:
> >
> >Hi Steve,
> >
> >>Hi Penny,
> >>
> >>COARDS was a standard designed to deal with grids. For a globe
encircling
> >>grid, COARDS specifies that the coordinates of a grid as encoded must be
> >>monotonic -- i.e. that the branch point, at which the coordinates have a
> >>360 degree discontinuity, is always at the edge of the grid.
> >>
> >>Am I correct in assuming that the WOCE data in question is a single
> >>profile per file?
> >
> >not always... we have shipboard ADCP and Met data which are underway
> >surface data that may span the dateline in one file (perhaps one
> >days-worth, or a single file per cruise).  Also drifter and float
> >tracks that may  wander across the dateline.  It sounds to me as
> >though they would not be compliant.... but then if we chose 0 to 360
> >then we would have the same problem in the Atlantic.
> >
> >>The single-point longitude axis contained in each file
> >>is then by definition COARDS-like (monotonic in a degenerate sense). But
> >>the data collection taken as a whole has a discontinuity somewhere ...
> >>unavoidably.
> >>
> >>So if I have interpreted your question correctly, the answer is
> >>
> >>   1. COARDS supplies an answer on a per-file basis, only, and your
> >>      encoding sounds fine
> >>   2. for the collection as a whole, the important thing is that all
> >>      individual files share the same convention about where the branch
> >>      point is located.
> >>
> >>There is no existing COARDS-like standard that deals with a collection
of
> >>netCDF files viewed as a whole.  It might be worth contacting John Caron
> >>of Unidata/netCDF (caron@xxxxxxxx) to make him aware of the question
that
> >>WOCE faces.  John is involved in the "THREDDS" project, which is
defining
> >>methodologies for handling large file collections through XML catalogs.
> >
> >I think I will do that since from your answer the COARDS convention
> >doesnt quite provide a solution for us.
> >
> >>     Has this helped at all? - steve
> >
> >Yes I think it has - we may not have solved our dilemma quite yet,
> >but I do understand a bit more about the thinking behind the COARDS
> >convention.
> >
> >Thank you again for replying so quickly,
> >Penny
> >
> >>
> >>==========================================================
> >>
> >>Penny Holliday wrote:
> >>
> >>  > Hi Steve, another question about longitude.  I'd like to check with
> >>  > you that our "WOCE convention" on longitude is CF/COARDS compliant.
> >>  > We have specified that it should be written as -180 to 180 with
> >>  > positive values east.  However Bernie Kilonsky says this is not
> >>  > compliant because the COARDS requires the sequence of values in a
> >>  > single file to be "monotonic in a non-modulo sense".  I confess to
> >>  > not knowing what the phrase "non-modulo sense" means, but does this
> >>  > mean that a file with longitudes in the Pacific that might range
from
> >>  > -160 to 160 would not be compliant since it goes from -179 to 179 at
> >>  > one point?
> >>  > Thanks,
> >>  > Penny
>
> ---------------------------------------------------------------
> Dr. N. Penny Holliday
> Deacon Hydrobiology Team and WOCE International Project Office
>
> Southampton Oceanography Centre
> Waterfront Campus, European Way
> SOUTHAMPTON, SO14 3ZH, UK
> Tel:+44-(0)23-80596206   Fax:+44-(0)23-80596204
>
> email:nph@xxxxxxxxxxxxxxx
> http://www.soc.soton.ac.uk/GDD/hydro/
> http://www.woce.org/ipo.html
> ---------------------------------------------------------------
>

```
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