[CF-metadata] axis attribute

Jim Biard jbiard at cicsnc.org
Fri Apr 14 16:11:44 MDT 2017


We've got no great options available. The axis attribute ought to be an 
indicator of an independent coordinate axis. Because of possible 
backward compatibility issues, I think we need to demote the axis 
attribute to being a plotting hint. I'm at a loss for a word to use for 
a new attribute, but overloading axis with the different meanings seems 
too confusing.

The existing convention for identifying 1D coordinate variables 
(variable name = dimension name) works well for identifying independent 
axes as far as that goes, so what are we missing with a fuzzy or demoted 
axis attribute? It seems to me that we lack a clean way to identify the 
x/y/z/t/etc relationships between the different independent axes, and we 
lack a way to clearly identify a 1-D variable as an independent axis if 
it doesn't conform to the variable name = dimension name convention.

I'm not sure what's the cleanest way to go about it, but I'll suggest a 
name for an attribute that would fill some portion of these purposes. 
How about basis (or bases)?

Grace and peace,


On 4/11/17 10:36 AM, Jonathan Gregory wrote:
> Dear David and Sebastien
> In a given model the level numbers are meaningful indeed, but there's no
> universal convention for them. Maybe some atmosphere models number them from
> the TOA downwards, for instance. Nothing would prohibit that, and the
> standard_name of model_level_number doesn't prescribe any convention for it.
> There is likewise no universal convention for how to number the gridboxes in
> x and y, but in any given model there is a convention for it. Thus I think
> it's the same. The standard name identifies a conventional concept, but not a
> convention for the numbers themselves.
> As for the axis attribute itself, maybe we could distinguish the two meanings
> of "axis" and avoid backwards compatibility by removing the restriction in
> chapter 5 that it is not permissible for a data variable to have both a
> coordinate variable and an auxiliary coordinate variable having an axis
> attribute with any given value. That is, at present you can't have both a 1D
> x-coordinate variable with axis="X" and a 2D longitude auxiliary coordinate
> variable with axis="X". But we could allow them both, with different meanings.
> We could say that the axis attribute of 1D coordinate variables labels the
> index dimensions of the data variable, while the axis attribute of multi-
> dimensional auxiliary coordinate variables labels them as spatiotemporal
> dimensions, as a hint for plotting.
> Best wishes
> Jonathan
> ----- Forwarded message from David Hassell <david.hassell at ncas.ac.uk> -----
>> Date: Tue, 11 Apr 2017 08:41:34 +0100
>> From: David Hassell <david.hassell at ncas.ac.uk>
>> To: Jonathan Gregory <j.m.gregory at reading.ac.uk>
>> CC: CF Metadata <cf-metadata at cgd.ucar.edu>
>> Subject: Re: [CF-metadata] axis attribute
>> Hello all,
>> I am still uncomfortable with creating a coordinate variable with arbitrary
>> values. The analogy with model_level_number is not quite there, I think, as
>> the model_level_number values are not arbitrary. For example, a value of 6
>> means (in one model I know) that this is the first level above the boundary
>> layer. That value and meaning is relevant however the data may have been
>> subspaced/sliced.
>> Perhaps an auxiliary coordinate variable could be used with missing data in
>> all of its values, an axis attribute (of "X" or "Y") and *no* standard
>> name? In the absence of a coordinate variable for that dimension, the axis
>> attribute of the auxiliary coordinate variable would give meaning to the
>> dimension.
>> This is still not ideal, though ...
>> All the best,
>> David
>> On 10 April 2017 at 18:25, Jonathan Gregory <j.m.gregory at reading.ac.uk>
>> wrote:
>>> Dear Sébastien
>>> Yes, you're right, we can't have an axis without coordinates. This is
>>> because
>>> CF is a netCDF convention, and there's no way to attach attributes to a
>>> dimension other than by creating a coordinate variable. Similarly we don't
>>> have data variables with just dimensions but no data. We could have
>>> conventions
>>> for these concepts in CF-netCDF but it hasn't been proposed.
>>> However it seems pretty good to me to do as you suggest and create a
>>> coordinate variable with the gridbox indices in it, for which (as
>>> discussed)
>>> we could define a standard name. This is analogous to model_level_number,
>>> which is already a standard name and could be a vertical coordinate
>>> variable.
>>> It can do what you want, and I agree it makes sense to label these
>>> coordinate
>>> variables as X and Y. That indicates that they are the horizontal
>>> dimensions.
>>> It's probably less important which is X and which Y. That's a plotting
>>> issue.
>>> I think the confusion probably arises because we didn't define what we mean
>>> by "axis". We used the word as an "obvious" concept, but there is an
>>> ambiguity
>>> about whether it corresponds to a dimension of a data variable, or a
>>> physical
>>> variable (not necessarily spatiotemporal) which could be an independent
>>> variable on which the data depends. Latitude might be an axis in the second
>>> sense even if it's not an axis in the first sense. I prefer the first
>>> sense,
>>> which is the one the axis attribute originally had.
>>> Best wishes
>>> Jonathan
>>> ----- Forwarded message from Sebastien Villaume <
>>> sebastien.villaume at ecmwf.int> -----
>>>> Date: Fri, 7 Apr 2017 09:10:09 +0000
>>>> From: Sebastien Villaume <sebastien.villaume at ecmwf.int>
>>>> To: David Hassell <david.hassell at ncas.ac.uk>
>>>> CC: CF Metadata <cf-metadata at cgd.ucar.edu>, Jonathan Gregory
>>>>        <j.m.gregory at reading.ac.uk>
>>>> Subject: Re: [CF-metadata] axis attribute
>>>> X-Mailer: Zimbra 8.6.0_GA_1200 (ZimbraWebClient - FF50
>>> (Linux)/8.6.0_GA_1200)
>>>> Dear David,
>>>> I see your point and you are probably right that a plotting routine will
>>> probably sort this out.
>>>> However this is not what I am after, I am more interested in metadata
>>> discovery and indexing.
>>>> I need to discover what I have in a file without plotting it, without
>>> having a human looking at it to confirm what it is and that it has been
>>> plotted correctly.
>>>> I also would like to use these metadata informations to perform actions
>>> like merging netCDF files, slicing, cropping, aggregating, interpolating,
>>> comparing data in different grids and representations, etc.
>>>> I understand that implicit is fine and that explicit is not required for
>>> some applications. I have no issue with this.
>>>> My personal point of view is that explicit is better than implicit: I
>>> tend to prefer "mandatory" over "optional".
>>>> Being implicit means that the assumptions made need to be valid 100% of
>>> the time to avoid accidents or corner cases.
>>>> I would like to be explicit so I need all the proper mechanisms
>>> (variables, semantics, etc.) in place so I can use them.
>>>> Right now it feels that I am missing some functionality.
>>>> Let me copy below few bits of the terminology section in the CF 1.7
>>> draft document (very similar to 1.6). Please read it keeping in mind what
>>> is really an axis, a coordinate, a spatio-temporal dimension and an an
>>> array dimension. Each time you read "coordinate2, "dimension" or
>>> "dimensional", ask yourself what is implied and if it is not ambiguous:
>>>> ------------------------
>>>> variables
>>>> ------------------------
>>>> auxiliary coordinate variable
>>>>      Any netCDF variable that contains coordinate data, but is not a
>>> coordinate variable (in the sense of that term defined by the NUG and used
>>> by this standard - see below). Unlike coordinate variables, there is no
>>> relationship between the name of an auxiliary coordinate variable and the
>>> name(s) of its dimension(s).
>>>> coordinate variable
>>>>      We use this term precisely as it is defined in section 2.3.1 of the
>>> NUG . It is a one-dimensional variable with the same name as its dimension
>>> [e.g., time(time) ], and it is defined as a numeric data type with values
>>> that are ordered monotonically. Missing values are not allowed in
>>> coordinate variables.
>>>> grid mapping variable
>>>>      A variable used as a container for attributes that define a specific
>>> grid mapping. The type of the variable is arbitrary since it contains no
>>> data.
>>>> multidimensional coordinate variable
>>>>      An auxiliary coordinate variable that is multidimensional.
>>>> scalar coordinate variable
>>>>      A scalar variable (i.e. one with no dimensions) that contains
>>> coordinate data. Depending on context, it may be functionally equivalent
>>> either to a size-one coordinate variable (Section 5.7, "Scalar Coordinate
>>> Variables") or to a size-one auxiliary coordinate variable (Section 6.1,
>>> "Labels" and Section 9.2, "Collections, instances, and elements").
>>>> ------------------------
>>>> dimensions
>>>> ------------------------
>>>> latitude dimension
>>>>      A dimension of a netCDF variable that has an associated latitude
>>> coordinate variable.
>>>> longitude dimension
>>>>      A dimension of a netCDF variable that has an associated longitude
>>> coordinate variable.
>>>> spatiotemporal dimension
>>>>      A dimension of a netCDF variable that is used to identify a location
>>> in time and/or space.
>>>> time dimension
>>>>      A dimension of a netCDF variable that has an associated time
>>> coordinate variable.
>>>> vertical dimension
>>>>      A dimension of a netCDF variable that has an associated vertical
>>> coordinate variable.
>>>> ------------------------
>>>> So according to this terminology, I have in my file, 2 auxiliary
>>> coordinates variables, but no "real" coordinates variables (according to
>>> the NUG) so my auxiliary coordinates are auxiliary to what?
>>>> What is a "multidimensional coordinate"? if dimension means
>>> spatio-temporal dimension it is a non sense because a coordinate can only
>>> reference 1 spatio-temporal dimension, if it is meant to be
>>> array-dimensions it is not clear...
>>>> What are my 2D array latitude and longitude then? are they latitude and
>>> longitude dimension defined in the terminology? not really.... because
>>> there are no such things as latitude and longitude dimension: you can
>>> define latitude and longitude coordinates, associated with 2 axis that
>>> themselves define 2 spatial dimensions... but the coordinates can be
>>> defined in whatever n-D array.
>>>> I like the definition of "grid mapping variable", I could use a similar
>>> variable to be a container for attributes for my "axis variable" with no
>>> data!
>>>> I know that in the day-to-day life and discussions we don't make the
>>> effort to be precise (I don't) and that it is easy to overload the meaning
>>> of things but I think that the CF document needs to be very precise, non
>>> ambiguous and can not mix axes, coordinates, spatio-temporal and array
>>> dimensions.
>>>> /Sébastien
>>>> ----- Original Message -----
>>>> From: "David Hassell" <david.hassell at ncas.ac.uk>
>>>> To: "Sebastien Villaume" <sebastien.villaume at ecmwf.int>
>>>> Cc: "CF Metadata" <cf-metadata at cgd.ucar.edu>, "Jonathan Gregory" <
>>> j.m.gregory at reading.ac.uk>
>>>> Sent: Friday, 7 April, 2017 08:37:20
>>>> Subject: Re: [CF-metadata] axis attribute
>>>> Dear Sébastien,
>>>> Please bear with me when I ask to right back to the beginning! I am not
>>>> sure what the benefit is in labelling the dimensions as X or Y. In the
>>>> original tripolar case we have:
>>>> dimensions:
>>>>      i = 96 ;
>>>>      j = 73 ;
>>>> variables:
>>>>      float latitude(j, i) ;
>>>>          latitude:units = "degrees_north" ;
>>>>      float longitude(j, i) ;
>>>>          longitude:units = "degrees_east" ;
>>>>      float sit(j, i) ;
>>>>          sit:units = "m" ;
>>>>          sit:standard_name = "sea_ice_thickness" ;
>>>>          sit:coordinates = "latitude longitude" ;
>>>> There is nothing stopping anything from seeing that this is 2-d array of
>>>> size i*j, and there is nothing stopping software subpacing the data by i
>>>> and j indices.
>>>> I don't think a plotting routine would benefit from knowing that the i
>>>> dimension was "X", because there are no 1-d coordinates it can use along
>>>> that dimension.
>>>> Many thanks and all the best,
>>>> David
>>>> On 6 April 2017 at 22:45, Sebastien Villaume <
>>> sebastien.villaume at ecmwf.int>
>>>> wrote:
>>>>> Dear Mark and Jonathan,
>>>>> thank you for your comments.
>>>>> @Mark:
>>>>> the short answer: you can put in principle whatever you want in that
>>>>> variable because in this case it is a dummy variable only there to
>>> hold the
>>>>> axis attribute. But please read the long explanation!
>>>>> the long, boring explanation:
>>>>> As I understand it, the CF convention does not recognize axis as a
>>> valid
>>>>> object on its own like for "dimensions" and the various type of
>>> "variables"
>>>>> and the convention seems to make it mandatory to attach to it a
>>> variable
>>>>> that becomes a "coordinate" variable. Note that I say that it is the
>>>>> coordinate variable that is attached to the axis and not the opposite.
>>>>>  From a mathematical point of view, it is perfectly possible to define
>>> an
>>>>> axis without a coordinate on it (arguably it is not that useful). The
>>>>> common case is that a 1-D array defines positions on that axis (the
>>>>> coordinate). Then your 1-D data points are positioned with the help of
>>> the
>>>>> coordinate, itself attached to the axis.
>>>>> If you have one more axis, you can define a new coordinate on it. This
>>>>> creates a 2-D space. Now you have the choice on how you represent your
>>> 2-D
>>>>> data points:
>>>>> if the dataset is totally irregular you will have a 1-D array of "n"
>>> data
>>>>> points associated with a 1-D array of "n" positions for the first
>>> dimension
>>>>> and a 1-D array of "n" positions for the second dimension. It works,
>>> it is
>>>>> still a 2-D dataset stored in a long one dimensional vector.
>>>>> Imagine that you realize that your dataset is not as irregular as you
>>>>> thought, it is in fact a regular grid! you identify that you only have
>>> i
>>>>> possible values of the first coordinate and j possible values for the
>>>>> second coordinate, you also notice that i*j=n. Great you can now
>>> represent
>>>>> your dataset with 2 coordinates of length i and j respectively, each of
>>>>> them associated with 2 axes x and y and your data is now a 2-D array of
>>>>> size (i,j). you can position your data using the coordinates, it is
>>> mapped
>>>>> using the indices within each coordinate array. Now you have a 2-D
>>> spatial
>>>>> dataset sored in a 2-D array with 2 supporting 1-D spatial coordinates
>>>>> stored in one dimensional vectors.
>>>>> Lets say now that you take this regular grid and you distort it... your
>>>>> regular grid is gone you can no longer use i and j for partitioning!
>>>>> really? well no, nobody says that you can not slice your "n" long
>>> vectors
>>>>> into i*j arrays! you could choose whatever you want for i and j as
>>> long as
>>>>> i*j=n. Of course if you choose (2)*(n/2) or (n/2)*(2), it is a bit
>>> useless,
>>>>> but you can also choose meaningful i and j because even if your grid
>>> became
>>>>> irregular, it is not random points, it is still a grid of size i*j .
>>> This
>>>>> is exactly my use case! And in that situation your coordinates can be
>>>>> arranged in arrays of size i*j. What I need is 2 axes and 2
>>> coordinates of
>>>>> dimension 2 with lengths i and j. The catch here is that I have 2-D
>>> arrays
>>>>> to store one "spatial" dimension! It is another case of overlapped
>>>>> concepts, dimension is used transparently for the dimension of arrays,
>>>>> dimension of the geometrical space, and sometimes for the size of one
>>> of
>>>>> the dimensions of an array!!
>>>>> Anyway, I should be able to define my axes like this:
>>>>> int x;
>>>>>      x:axis = "X";
>>>>>      x:standard_name = "x_axis" ; // no standard name exists...
>>>>>      x:units = "1" ; // no units, it will come with the coordinate
>>>>> int y;
>>>>>      y:axis = "Y";
>>>>>      y:standard_name = "y_axis" ; // no standard name exists...
>>>>>      y:units = "1" ; // no units, it will come with the coordinate
>>>>> float longitude(j,i);
>>>>>      longitude:standard_name = "longitude" ;
>>>>>      longitude:units = "degrees" ;
>>>>>      longitude:positive = "east" ;
>>>>>      longitude:long_name = "longitude" ;
>>>>>      longitude:axis_mapping = "X" ;
>>>>> float latitude(j,i);
>>>>>      latitude:standard_name = "latitude" ;
>>>>>      latitude:units = "degrees" ;
>>>>>      latitude:positive = "north" ;
>>>>>      latitude:long_name = "latitude" ;
>>>>>      latitude:axis_mapping = "Y" ;
>>>>> float sit(j, i) ;
>>>>>      sit:units = "m" ;
>>>>>      sit:standard_name = "sea_ice_thickness" ;
>>>>>      sit:long_name = "Ice thickness" ;
>>>>>      sit:coordinates = "latitude longitude" ;
>>>>> several comments:
>>>>> notice how one could tell on which axis the coordinate should go using
>>> for
>>>>> instance a "axis_mapping" attribute. Not a "coordinate" attribute,
>>> this one
>>>>> should be used to tell the coordinates of my data variable!
>>>>> I find this approach clearer and more flexible as it can probably cater
>>>>> for any situation of axes, coordinates, etc.
>>>>> But because in CF one cannot create bare axis, I follow the rules and
>>>>> creates:
>>>>> double x(i);
>>>>>      x:axis = "X";
>>>>>      x:standard_name = "..." ; // not an axis anymore, give me a
>>> standard
>>>>> name
>>>>>      x:units = "1" ;
>>>>>      y:long_name = "i-index of mesh grid" ;
>>>>> double y(j);
>>>>>      y:axis = "Y";
>>>>>      y:standard_name = "..." ; // not an axis anymore, give me a
>>> standard
>>>>> name
>>>>>      y:units = "1" ;
>>>>>      y:long_name = "j-index of mesh grid" ;
>>>>> and I have the choice of what I put in those arrays since it is somehow
>>>>> artificial.
>>>>> I could populate the "primary" coordinates with 1 to i and 1 to j which
>>>>> would represent the indices and if I subset the grid, I then retain the
>>>>> information that the domain has been cropped because the indices left
>>> will
>>>>> not be 1 to i/j but n to m.
>>>>> I don' t really like this but what can I do?
>>>>> If we follow this idea, it means introducing a clear concept from
>>> "axis"
>>>>> besides the other types of variables, defining new attribute to
>>> "attach"
>>>>> coordinates to axes, etc.
>>>>> Another solution, much less disturbing, would be to heavily modify the
>>>>> proper chapters in the CF document to:
>>>>> - completely decouple the concepts of "axis" and "coordinate": a
>>>>> coordinate is not an axis and vice versa.
>>>>> - completely decouple the concepts of spatio temporal dimension from
>>> array
>>>>> dimension from the size the array dimension
>>>>> - continue to use the "axis" attribute  but on n-D array coordinates:
>>> the
>>>>> array has n-D dimensions but the coordinate map to 1 axis/spatial
>>> dimension
>>>>> only!
>>>>> - Whatever the dimensions of the array for the coordinate, all the
>>> values
>>>>> contained in the array must be mapped on one given axis, the one
>>> defined in
>>>>> axis attribute. For instance, a 2-D latitude only contains values that
>>> are
>>>>> latitudes and will only map on one axis.
>>>>> - In principle one could have in the same file several coordinates of
>>>>> possibly different "array" dimensions, different sizes and different
>>> units
>>>>> defined for one axis. This means that the attribute "axis=z" for
>>> instance
>>>>> can appears more than once in the file. The only restriction I see is
>>> that
>>>>> 2 data variables can be only plotted simultaneously if all their
>>>>> coordinates share the same units (the coordinate mapped on one axis of
>>> the
>>>>> first data variable must have the same units than the coordinate
>>> mapped on
>>>>> the same axis for the other data variable). This allow 2 data variables
>>>>> defined on two different grid sharing the same units to be in the same
>>> file
>>>>> and plotted together.
>>>>> - X and Y should be clearly decoupled from longitude and latitude. X
>>> and Y
>>>>> are the axes, longitude and latitude are the coordinates!
>>>>> @Jonathan:
>>>>> I think the whole confusion here comes from the overlapping of
>>> concepts:
>>>>> axes and coordinates on one hand and dimension of arrays and spatial
>>>>> dimensions on the other hand. If the relevant chapters are rewritten
>>>>> carefully to separate axes from coordinates and array dimensions from
>>>>> spatio-temporal dimensions we are good.  think
>>>>> @all: Reading more through the Trac tickets system, I noticed the nice
>>>>> Trac ticket 117 about "multiple" time axis. This is a nice example of
>>>>> mixing axes, coordinates, dimensions of arrays, the time dimension,
>>> etc!
>>>>> /Sébastien
>>>>> ----- Original Message -----
>>>>> From: "Jonathan Gregory" <j.m.gregory at reading.ac.uk>
>>>>> To: cf-metadata at cgd.ucar.edu
>>>>> Sent: Thursday, 6 April, 2017 16:49:56
>>>>> Subject: Re: [CF-metadata] axis attribute
>>>>> Dear Jim and Sebastien
>>>>> The original intention of axis was to label the independent variables
>>> as 1D
>>>>> xyzt axes of the data variables.  This can be deduced from other
>>>>> attributes,
>>>>> but it's more effort. It's partly a plotting hint, but also it's
>>> because
>>>>> you
>>>>> might reasonable want to tell software, "give me the z-axis
>>> coordinates",
>>>>> or
>>>>> "calculate a mean over the x-direction". The latter is often a zonal
>>> mean,
>>>>> but
>>>>> it isn't with a rotated-pole or tripolar grid, yet the operation is
>>> still
>>>>> performed sometimes.
>>>>> It's useful that you've pointed out the confusion of purpose. If it
>>> were
>>>>> regarded as an acceptable backwards-incompatibility, which I'm nervous
>>>>> about,
>>>>> I'd be happy if we returned "axis" to its original purpose of
>>> identifying
>>>>> 1D
>>>>> axes, and also for scalar coordinate variables (which are equivalent to
>>>>> axes
>>>>> of size one), and provided another attribute to label aux coords as
>>>>> horizontal.
>>>>> I agree that if we have 1D x and y, with 2D lat and lon, the 1D
>>> variables
>>>>> are
>>>>> the axes. That's consistent with the original purpose of the axis
>>>>> attribute.
>>>>>> I also find the units of latitude and longitude confusing: it looks
>>> like
>>>>> it was a way to squeeze the direction of the coordinate inside the
>>> units. I
>>>>> have the same observation for the time coordinate that has its origin
>>> in
>>>>> the units!
>>>>> This convention was kept in CF for backwards-compatibility with
>>>>> does
>>>>> not use units in any other case to identify the quantity or sense.
>>>>>> It was done correctly for z coordinate using "units" and "positive",
>>>>> probably because there are many types of z coordinates with various
>>> origin
>>>>> and directions, and no real consensus. I note however that often the
>>> origin
>>>>> is not always clearly defined.
>>>>> The positive attribute was also kept for backwards-compatibility with
>>>>> COARDS.
>>>>> It has the advantage of being useful to identify the vertical axis, but
>>>>> this
>>>>> can also be done with axis="Z". CF standard names provide information
>>> which
>>>>> indicates the sign convention.
>>>>> If coordinate_index is confusing, I think standard_names containing
>>> x_index
>>>>> or y_index would be OK, provided we change the existing standard names
>>>>>    magnitude_of_derivative_of_position_wrt_x_coordinate_index
>>>>>    magnitude_of_derivative_of_position_wrt_y_coordinate_index
>>>>> to remove "_coordinate".
>>>>> Best wishes
>>>>> Jonathan
>>>>> _______________________________________________
>>>>> CF-metadata mailing list
>>>>> CF-metadata at cgd.ucar.edu
>>>>> http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata
>>>>> _______________________________________________
>>>>> CF-metadata mailing list
>>>>> CF-metadata at cgd.ucar.edu
>>>>> http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata
>>>> --
>>>> David Hassell
>>>> National Centre for Atmospheric Science
>>>> Department of Meteorology, University of Reading,
>>>> Earley Gate, PO Box 243, Reading RG6 6BB
>>>> Tel: +44 118 378 5613
>>>> http://www.met.reading.ac.uk/
>>> ----- End forwarded message -----
>>> _______________________________________________
>>> CF-metadata mailing list
>>> CF-metadata at cgd.ucar.edu
>>> http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata
>> -- 
>> David Hassell
>> National Centre for Atmospheric Science
>> Department of Meteorology, University of Reading,
>> Earley Gate, PO Box 243, Reading RG6 6BB
>> Tel: +44 118 378 5613
>> http://www.met.reading.ac.uk/
> ----- End forwarded message -----
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