Dear Jonathan and Martin,

Thank you both for your comments.

I think the product names are now agreed. I withheld them from the May update 
due to the continuation of the discussion but will now mark them as accepted 
and add them in the June update:
*   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.

I think we are now agreed on 
covariance_over_longitude_of_northward_wind_and_air_temperature (Canonical 
units: K m s-1). I agree with Martin's suggestion to include 'Covariance refers 
to the sample covariance rather than the population covariance' in the 
definition. Putting this together with other comments in the discussion, plus 
our usual text for some of the terms, I suggest the following:
'Covariance refers to the sample covariance rather than the population 
covariance. The quantity with standard name 
covariance_over_longitude_of_northward_wind_and_air_temperature is the 
covariance of the deviations of meridional air velocity and air temperature 
about their respective zonal mean values. The data variable must be accompanied 
by a vertical coordinate variable or scalar coordinate variable and is 
calculated on an isosurface of that vertical coordinate. "Northward" indicates 
a vector component which is positive when directed northward (negative 
southward). Wind is defined as a two-dimensional (horizontal) air velocity 
vector, with no vertical component. (Vertical motion in the atmosphere has the 
standard name "upward_air_velocity"). Air temperature is the bulk temperature 
of the air, not the surface (skin) temperature.'

Is that okay?

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: 30 May 2019 22:49
To: cf-metadata@cgd.ucar.edu
Subject: Re: [CF-metadata] order of product in standard name

Dear Alison

I agree with all this and support Martin's suggestions that you have enacted.
I agree that omega is like w and it's normal to write wT.

Best wishes and thanks

Jonathan

----- Forwarded message from Alison Pamment - UKRI STFC 
<alison.pamm...@stfc.ac.uk> -----

> Date: Thu, 30 May 2019 13:12:10 +0000
> From: Alison Pamment - UKRI STFC <alison.pamm...@stfc.ac.uk>
> To: "cf-metadata@cgd.ucar.edu" <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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----- End forwarded message -----
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