Dear Alison,

Thank you, that is a good summary. I agree that it makes sense to treat 
"covariance" and "correlation" in the same way as "product".


Although these two terms appear in the guidelines, they don't yet appear in the 
standard name table itself, so the usage 
"covariance_over_longitude_of_northward_wind_and_air_temperature" will be a 
first for "covariance". Can we include a sentence in the description saying 
that "Covariance refers to the sample covariance rather than the population 
covariance"? I don't think it is likely that we will need to deal with 
population covariances in the CF standard name list, but, if we do, it would 
make sense to have a separate term for them.


Jonathan asked whether it would make better sense to use "covariance_wrt_..." 
rather than "convariance_over_". I think this would be an improvement: the 
covariance is an integral of a product and so using the same syntax as used for 
integrals makes sense here.


regards,

Martin


________________________________
From: CF-metadata <cf-metadata-boun...@cgd.ucar.edu> on behalf of Alison 
Pamment - UKRI STFC <alison.pamm...@stfc.ac.uk>
Sent: 30 May 2019 14:12
To: cf-metadata@cgd.ucar.edu
Subject: Re: [CF-metadata] order of product in standard name

Dear Jonathan and Martin,

I would like to make sure that we have fully resolved this issue as it affects 
names that are currently under discussion in two threads:
covariance_over_longitude_of_northward_wind_and_air_temperature (latest 
comment: http://mailman.cgd.ucar.edu/pipermail/cf-metadata/2019/020922.html);
also:
  *   product_of_eastward_wind_and_lagrangian_tendency_of_air_pressure
  *   product_of_northward_wind_and_lagrangian_tendency_of_air_pressure
  *   product_of_lagrangian_tendency_of_air_pressure_and_specific_humidity
  *   product_of_lagrangian_tendency_of_air_pressure_and_air_temperature
  *   product_of_lagrangian_tendency_of_air_pressure_and_geopotential_height
(latest comment 
http://mailman.cgd.ucar.edu/pipermail/cf-metadata/2019/020927.html).

I agree with Jonathan that for covariance and correlation names it is better to 
have covariance_over_Z_of_X_and_Y, (rather than putting over_Z at the end as 
stated in the current guidelines). This is consistent with the way we now write 
integrals as integral_wrt_X_of_Y.

The current guidelines for correlation and covariance say simply that X and Y 
should be ordered alphabetically, whereas for product we have additional 
guidance: 'If X and Y are both scalars or both components of vectors, they are 
put in alphabetical order. If one of them is the component of a vector, it is 
put first i.e. the vector component is X, the scalar is Y.'

I think we are agreed that the same guidelines should apply to the ordering of 
X and Y in standard names for all commutative properties such as product, 
covariance, correlation, etc.

The rule about putting vector components first means that the covariance name 
as written above is in the correct order.

Regarding the lagrangian tendency names, I agree with Martin's argument that 
lagrangian_tendency_of_air_pressure should be regarded as a vertical component 
of the air velocity vector, rather than a scalar. Therefore it is correct to 
write the specific_humidity, air_temperature and geopotential_height names as 
above (this is the opposite way round to what was originally proposed).

I also agree with Martin's suggestion of ordering vector components as 
X=horizontal and Y=vertical when horizontal and vertical components are the 
operands. This is a useful general convention and gets around the problem of 
having product_of_eastward_wind_and_lagrangian_tendency_of_air_pressure and 
product_of_lagrangian_tendency_of_air_pressure_and_northward_wind which would 
arise from the alphabetical rule. (Of course if we are combining two horizontal 
or two vertical vector components we would still need to fall back on the 
alphabetical rule).

It is on my 'To Do' list in the next couple of months to conduct a thorough 
review of the standard names Guidelines document and the sections of the 
Conventions document covering standard names and units. They are all somewhat 
out of date. If we can agree these changes they can be included as part of that 
process.

Best wishes,
Alison

-----------------------------------------------------------------------------------------------------------
Alison Pamment                                                         Tel: +44 
1235 778065
NCAS/Centre for Environmental Data Analysis    Email: alison.pamm...@stfc.ac.uk
STFC Rutherford Appleton Laboratory
R25, 2.22
Harwell Oxford, Didcot, OX11 0QX, U.K.


-----Original Message-----
From: CF-metadata <cf-metadata-boun...@cgd.ucar.edu> On Behalf Of Jonathan 
Gregory
Sent: 10 May 2019 15:08
To: cf-metadata@cgd.ucar.edu
Subject: [CF-metadata] order of product in standard name

Dear all

I should have noticed that we already have a guideline about 
product_of_X_and_Y, which should also apply to covariance, correlation, and any 
other commutative function of X and Y:

 If X and Y are both scalars or both components of vectors, they  are put in 
alphabetical order. If one of them is the component  of a vector, it is put 
first i.e. the vector component is X, the  scalar is Y.

Cheers

Jonathan
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