Dear Alejandro,

The two CMIP variables which I'm talking about are cfadDbze94 currently defined 
as "CFAD (Cloud Frequency Altitude Diagrams) are joint height - radar 
reflectivity (or lidar scattering ratio) distributions." and cfadLidarsr532, 
which has the same definition. If they are not joint distributions we clearly 
have a problem with these definitions.

>From your reply I understand now that these are univariate distributions 
>giving the frequency of different radar reflectivities in different height 
>bands. Coming from radar/lidar instruments (or an emulator of these 
>instruments), there are multiple observations in each GCM-scale height band. 
>Presumably, there are also multiple profiles in the GCM-scale grid square, so 
>that we have a frequency distribution over sub-grid scale variability in the 
>vertical and the horizontal? Or is it actually evaluated at a spatial point?

If this is the case, you are right and we just need to correct the definitions 
in the CMIP tables (though there is still a case for introducing a 
frequencs_distribution for other variables, but that should ne another thread). 
I would favour a slightly more verbose and explicit definition, e.g.
"CFAD (Cloud Frequency Altitude Diagrams) are frequency distributions of radar 
reflectivity (or lidar scattering ratio) as a function of altitude. cfadDbze94 
is defined as the simulated relative frequency of radar reflectivity in 
sampling volumes defined by altitude bins and model grid cells."

Note that I'm using "altitude" rather than "height" to match the standard 
names: in the CF Convention, "altitude" means height above the geoid, and 
"height" means height above the surface.

Is that an accurate definition?


Dear Martin,

Thanks for your detailed explanation. I'd like to add a bit more information. 
These variables are not joint distributions, they are 1D distributions for 
different ranges of Z. The question is, does "histogram_of_X[_over_Z]" mean 
that the Z coordinate has to be completely collapsed? It is not clear to that 
the current definition implies that. If Z is not completely collapsed, you can 
then end up with a function of the form frequency(lat,lon,X,Z2), where the 
coordinate Z is only partially collapsed into bins described by Z2. I'm using 
here Z2 to explicitly show when the Z coordinate represents bins. This would 
look like a joint histogram, but it is not. I think that your proposal of 
dropping "_over_Z" from the standard name works for a joint distribution, but 
not for a collection of 1D distributions along Z, unless there is a way of 
distinguishing between both cases with the use of attributes.

Another detail is that these histograms provide relative frequencies (values 
between 0 and 1, not counts), not absolute frequencies. Is that inconsistent 
with the current definition of histogram in CF?



> -----Original Message-----
> From: martin.juckes at 
> [mailto:martin.juckes at 
> Sent: 12 October 2016 19:05
> To: cf-metadata at 
> Cc: Bodas-Salcedo, Alejandro
> Subject: Usage of histogram_of_X_over_Z
> Hello,
> There are two standard names of the form histogram_of_..... in the CF Standard
> Name list (at version 36):
> histogram_of_backscattering_ratio_over_height_above_reference_ellipsoid and
> histogram_of_equivalent_reflectivity_factor_over_height_above_reference_ellipsoid
> . Both of these where used in CMIP5 and set to be used in CMIP6, but the usage
> does not appear to match the standard name desecriptions.
> The possible confusion is over the role of different coordinates. The CF 
> definitions
> say ''"histogram_of_X[_over_Z]" means histogram (i.e. number of counts for 
> each
> range of X) of variations (over Z) of X.' This implies to me that you start 
> with a
> function of Z and possibly other coordinates and end up with a function of X 
> and the
> other coordinates. E.g. if the source data is X(lat,lon,Z), then the 
> histogram data will
> be of the form frequency(lat,lon,X).
> In the two CMIP5/CMIP6 draft variables (cfadLidarsr532, cfadDbze94) using 
> these
> standard names the "Z" coordinate  which is included in the standard name
> ("height_above_reference_ellipsoid") is one of the coordinates of the 
> histogram data
> variable. Both these variables appear to be joint distributions (frequency of 
> X and Y
> values) over sub-grid variability as a function of latitude, longitude and 
> time.
> I've been reviewing these existing definitions in some detail because there 
> are some
> new distribution variables in the request and I'd like to make sure that we 
> have a
> consistent approach.
> If we need to described a variable which carries a joint distribution of X 
> and Y, then
> the variable will have to use X and Y as coordinates, so perhaps we can 
> simplify the
> process by leaving them out of the standard name. Similarly the "over_Z" part 
> of the
> name would be better expressed as a cell_methods construct. This line of 
> reasoning
> suggests using a new standard name such as "frequency_distribution" (units 
> "1").
> The only difficulty is that the frequency distribution might be a function of 
> the
> quantities X and Y (scattering ratio and cloud top height for cfadLidarsr532) 
> and also
> of latitude, longitude and time. There should be some way of distinguishing 
> the
> different roles of these 5 coordinates: is is the distribution of X and Y as 
> a function of
> latitude, longitude and time. I think this could be done conveniently by 
> introducing a
> single new attribute, e.g. "bin_coords: X Y".
> "frequency_distribution" could be used for single or joint distributions.
> My questions to the list are:
> (1) am I missing something in my interpretation of the existing 
> histogram_of_...
> names?
> (2) if not, is the adoption of a "frequency_distribution" standard name an 
> appropriate
> way forward?
> regards,
> Martin
> regards,
> Martin

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