[CF-metadata] Usage of histogram_of_X_over_Z

[m***@stfc.ac.uk]

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

[Bodas-Salcedo, Alejandro]

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?

Regards,

Alejandro

-----Original Message-----
Sent: 12 October 2016 19:05
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
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.
(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

[m***@stfc.ac.uk]

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?

regards,
Martin


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?

Regards,

Alejandro

-----Original Message-----
From: martin.juckes at stfc.ac.uk<http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata> [mailto:martin.juckes at stfc.ac.uk<http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata>]
Sent: 12 October 2016 19:05
To: cf-metadata at cgd.ucar.edu<http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata>
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
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.
(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

[Bodas-Salcedo, Alejandro]

Dear Martin,

You are right, those definitions are not correct.

Post by m***@stfc.ac.uk
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?

There is a sub-grid distribution of vertical profiles from which they are constructed.

The definition that you propose seems accurate to me. Thanks again for your time spent clarifying this.

Regards,

Alejandro

Post by m***@stfc.ac.uk
-----Original Message-----
Sent: 13 October 2016 13:05
Subject: [CF-metadata] Usage of histogram_of_X_over_Z
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?
regards,
Martin
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?
Regards,
Alejandro

-----Original Message-----
From: martin.juckes at

stfc.ac.uk<http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata>
[mailto:martin.juckes at stfc.ac.uk<http://mailman.cgd.ucar.edu/mailman/listinfo/cf-
metadata>]

Sent: 12 October 2016 19:05
To: cf-metadata at cgd.ucar.edu<http://mailman.cgd.ucar.edu/mailman/listinfo/cf-

metadata>

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
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.
(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

_______________________________________________
CF-metadata mailing list
http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata

[Jonathan Gregory]

Dear Martin and Alejandro (following off-list discussions)

Post by m***@stfc.ac.uk
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.'

Yes, that's in the guidelines for construction of standard names, and there
are only two of them at present, as you say. The simplest case is when you
have some quantity Q depending on only one dimension, Q(Z). Then the histogram
H(Q) is the number of values of Q which fall into each interval of Q,
considering variation over Z. In general there could be more than one
dimension retained, and more than one removed. If the original field was
Q(P,Y,Z,T), we might construct a histogram H(Q,Z,T), for instance, containing
the frequencies of values of Q falling into joint intervals of Q, Z and T, for
variation over P and Y. Following the guideline above, we would call this a
histogram of Q over P and Y, I think.

It is not necessary to indicate in the standard name the dimensions which
the histogram depends on (Z and T in my example) because the coordinate
variables (of Z and T) make that clear. Martin suggests that by this argument
we could also omit Q from the standard name, and just call it a histogram
(or frequency distribution) rather than a histogram of Q, where Q is air
temperature, precipitation amount, backscattering ratio, etc. I think there
are two reasons why we include Q in the standard name,

* I think a histogram of air temperature is not the same geophysical quantity
as a histogram of precipitation amount, for instance, so they should be
distinguished by standard name.

* Although histograms are pure numbers, and so are probabilities, probability
densities are not. Histograms, probability distributions and probability
density functions are all related ways of expressing the same information.
In the guidelines, we foresee that we might need names for all of them (though
so far we have only histograms) and it would make sense to give them consistent
names. The probability density function of air temperature has units of K-1,
and of precipitation amount kg-1 m2, for instance. Because they have different
canonical units, they must have different standard names, so Q needs to be
included in the standard name.

Cell methods describe how the values represent variation within the cells.
The transformation from the values of a quantity to a histogram of the
quantity makes the original quantity into a dimension. This seems more of
a radical transformation than computing a mean or a standard deviation, which
doesn't change the dimensions of the variable, but just reduces their size
(to unity if completely collapsed). A frequency distribution of Q is
regarded as a different geophysical quantity from Q itself, so we have not
used cell methods to describe the relationship. Of course, this is a bit
arbitrary (like everything else in the CF convention!).

I agree with Martin that we could omit the "over" part of the standard name for
histograms, probabilities and probability densities. It is useful to retain the
collapsed dimensions as size-1 dimensions, so that their original range can
be recorded. They could be assigned cell_method of "sum", the default for
extensive quantities, because the histogram applies to their entire range.
The same applies to the variable with has been histogrammed and is now a
dimension; the histogram is a sum for each of its cells.

For example, in the 1D case, suppose the original field is air_temperature
as a function of time only. Then the histogram variable is
float hair(tair);
hair:standard_name="histogram_of_air_temperature";
hair:units="1";
hair:cell_methods="time: sum tair: sum";
hair:coordinates="time";
float time; // scalar coordinate variable with bounds
float tair(tair);
tair:units="K";

As a multidimensional example, suppose the original field is
float tair(time,altitude,latitude,longitude);
tair:units="K";
tair:standard_name="air_temperature";
tair:cell_methods="altitude: mean area: mean time: mean";
from which we might construct
float pair(tair,time,altitude);
pair:standard_name="probability_density_function_of_air_temperature";
pair:units="K-1";
pair:cell_methods="altitude: mean time: mean area: sum tair: mean";
pair:coordinates="latitude longitude"; // to record the ranges
Here, I suggest that the cell_method for area is "sum", because the PDF
applies to the whole area, which is an extensive quantity. For air temperature
it seems more sense to interpret a PDF as a mean within cells, since a PDF is
an intensive quantity - you can interpolate it, for example - but not a point
quantity if it's calculated from a histogram with finite bin-widths.

Best wishes

Jonathan

Post by m***@stfc.ac.uk
Date: Wed, 12 Oct 2016 18:05:06 +0000
Subject: [CF-metadata] 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.
(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
_______________________________________________
CF-metadata mailing list
http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata

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