Standard names: *integrated ocean quantities*

[baylorfk]

Proposer's name Baylor Fox-Kemper

Date 24 OCT 2024

For each term please try to give the following:

- Term Proposed terms to appear in the vocabulary
existing term: integral_wrt_depth_of_sea_water_potential_temperature_expressed_as_heat_content.
new related terms:
integral_wrt_depth_of_sea_water_conservative_temperature_expressed_as_heat_content
integral_wrt_depth_of_sea_water_practical_salinity_expressed_as_salt_content
integral_wrt_depth_of_sea_water_preformed_salinity_expressed_as_salt_content
integral_wrt_depth_of_sea_water_absolute_salinity_expressed_as_salt_content

- Description A brief description to explain the meaning of the term

These new terms are for applications in comparison to observational syntheses and hybrid reconstructions (e.g., Domingues et al., 2008, updated; Levitus et al., 2012; Good et al., 2013; Cheng et al., 2017; Ishii et al., 2017; Zanna et al. 2019; Palmer et al. 2021), especially in the cases of integrated ocean heat content and integrated ocean salt content over the layers commonly used in these observational syntheses (which are related to the different technologies over time, e.g., XBT, Argo, etc.). Because they are for comparison to properties which are organized into layers delineated by hydrostatic pressure instruments and then connected to depth ranges, we specify them in pressure integrals rather than depth ranges (which also has implications for conversion from complex model vertical coordinate choices). Here are the specifications needed for the definite integration levels:

0-300m layer (0 to 30.3 bar)
300-700m layer (30.3 bar to 70.7 bar)
700-2000m layer (70.7 bar to 202.5 bar)
2000m to bottom (202.5 bar to the local maximum pressure at seafloor)

These integrated dimensions should have the following variables defined. The rationale for doing the integrals in advance is that modeling centers are using a variety of vertical coordinates which make these integrals hard to do or imprecise offline.

integral_wrt_depth_of_sea_water_potential_temperature_expressed_as_heat_content
(This variable is already defined, is ideal for using in non-TEOS-10 models and for comparison to traditional observations formulated in terms of potential temperature, with thetao=0C as the 0 kiloJoule reference temperature, in units of kilojoules m^-2 to aid with precision).

New variables:
integral_wrt_depth_of_sea_water_conservative_temperature_expressed_as_heat_content (for TEOS-10 models and comparison to observations utilizing TEOS-10, with bigthetao=0C as the 0 kiloJoule reference temperature, in units of kilojoules m^-2 to aid with precision)

integral_wrt_depth_of_sea_water_practical_salinity_expressed_as_salt_content. (for non-TEOS-10 models, in units of kg m^-2)
This variable is the equivalent to potential temperature heat content, but for column-integrated salt anomalies.

integral_wrt_depth_of_sea_water_preformed_salinity_expressed_as_salt_content (for TEOS-10 models, in units of kg m^-2)
This variable is the equivalent to conservative temperature heat content, but for column-integrated salt anomalies excluding the effects of biogeochemistry on salt. This may be relevant to observations using TEOS-10, but with conductivity conversion to salinity based on

integral_wrt_depth_of_sea_water_preformed_salinity_expressed_as_salt_content (for TEOS-10 models, in units of kg m^-2)
This variable is the equivalent to conservative temperature heat content, but for column-integrated salt anomalies including the effects of biogeochemistry on salt.

- Units
kilojoules m^-2 for the column integrated heat content variables, expressed gridpoint-by-gridpoint
kilograms m^-2 for the column integrated salt content variables, expressed gridpoint-by-gridpoint

[github-actions]

Thank you for your proposal. These terms will be added to the cfeditor (http://cfeditor.ceda.ac.uk/proposals/1) shortly. Your proposal will then be reviewed and commented on by the community and Standard Names moderator.

[taylor13]

There is a mix of uses of "content" in the current standard names. Often different standard names are defined depending on whether the vertical integral is calculated through the entire extent of a particular medium (e.g. atmosphere, sea ice, or ocean) or calculated only through a portion of the column (i.e., within some layer specified by bounds on a vertical coordinate). As an example, contrast atmosphere_mass_content_of_water and mass_content_of_water_in_atmosphere_layer.

Sometimes, however, the same standard name applies to both the entire column or only a portion. In this case, the interpretation by default is that the integral is over the entire column, but if bounds on a vertical coordinate are specified, then it is confined to a layer. For example, the names sea_water_potential_temperature_expressed_as_heat_content and sea_ice_temperature_expressed_as_heat_content include in the descriptions:

If used for a layer heat content, coordinate bounds should be used to define the extent of the layers. If no 
coordinate bounds are specified, it is assumed that the integral is calculated over the entire vertical extent 
of the medium, e.g, if the medium is sea water the integral is assumed to be calculated over the full depth 
of the ocean.

A similar approach is used for integral_wrt_depth_of_sea_water_temperature.

Of possible relevance are also these existing names:
integral_wrt_depth_of_product_of_conservative_temperature_and_sea_water_density kg degree_C m-2
integral_wrt_depth_of_product_of_salinity_and_sea_water_density 1e-3 kg m-2
integral_wrt_depth_of_sea_water_practical_salinity m
tendency_of_sea_water_salinity_expressed_as_salt_content kg m-2 s-1

Given the existing names and discussion above, I wonder if the following names might not be better:

sea_water_conservative_temperature_expressed_as_heat_content (J m-2) instead of integral_wrt_depth_of_sea_water_conservative_temperature_expressed_as_heat_content . I think the integral wrt depth is implied by "content".

sea_water_practical_salinity_expressed_as_mass_content_of_salt (kg m-2) instead of integral_wrt_depth_of_sea_water_practical_salinity_expressed_as_salt_content.

sea_water_preformed_salinity_expressed_as_mass_content_of_salt (kg m-2) instead of integral_wrt_depth_of_sea_water_preformed_salinity_expressed_as_salt_content

sea_water_absolute_salinity_expressed_as_mass_content_of_salt (kg m-2) instead of integral_wrt_depth_of_sea_water_absolute_salinity_expressed_as_salt_content

[JonathanGregory]

Thanks for your proposal, Baylor @baylorfk.

The background and motivation is useful, but for the description in the standard name table the text should be a short explanation of the quantity and the name, like the description of e.g. sea_water_potential_temperature_expressed_as_heat_content, which is

The phrase "expressed_as_heat_content" means that this quantity is calculated as the specific heat capacity times density of sea water multiplied by the potential temperature of the sea water in the grid cell and integrated over depth. If used for a layer heat content, coordinate bounds should be used to define the extent of the layers. If no coordinate bounds are specified, it is assumed that the integral is calculated over the entire vertical extent of the medium, e.g, if the medium is sea water the integral is assumed to be calculated over the full depth of the ocean. Potential temperature is the temperature a parcel of air or sea water would have if moved adiabatically to sea level pressure.

I think your clarification of the zero is useful to include. We ought to include that point in the above as well.

Karl has pointed out an inconsistency in the existing standard names. On the one hand, we have

kg degree_C m-2   integral_wrt_depth_of_product_of_conservative_temperature_and_sea_water_density
degree_C m-2      integral_wrt_depth_of_product_of_potential_temperature_and_sea_water_density
1e-3 kg m-2       integral_wrt_depth_of_product_of_salinity_and_sea_water_density
m                 integral_wrt_depth_of_sea_water_practical_salinity
K m               integral_wrt_depth_of_sea_water_temperature

and you have used this pattern for your proposed new ones

J m-2              integral_wrt_depth_of_sea_water_conservative_temperature_expressed_as_heat_content
kg m-2             integral_wrt_depth_of_sea_water_practical_salinity_expressed_as_salt_content
kg m-2             integral_wrt_depth_of_sea_water_preformed_salinity_expressed_as_salt_content
kg m-2             integral_wrt_depth_of_sea_water_absolute_salinity_expressed_as_salt_content

On the other hand we also have existing standard names (which below I call Group A)

J m-2              sea_water_potential_temperature_expressed_as_heat_content
W m-2              tendency_of_sea_water_conservative_temperature_expressed_as_heat_content
W m-2              tendency_of_sea_water_potential_temperature_expressed_as_heat_content
kg m-2 s-1         tendency_of_sea_water_salinity_expressed_as_salt_content

and several standard names of the form tendency_of_of_sea_water_{conservative|potential}_temperature_expressed_as_heat_content_due_to_X and tendency_of_sea_water_salinity_expressed_as_salt_content_due_to_X, where X is a process. I notice that there is an alias indicating that sea_water_potential_temperature_expressed_as_heat_content was formerly called integral_of_sea_water_temperature_wrt_depth_expressed_as_heat_content.

There isn't one pattern which fits all these cases, but for the ones with expressed_as_heat_content and expressed_as_salt_content we ought to be consistent. Is it clearer to say "temperature expressed as heat content" or "integral wrt depth of temperature expressed as heat content" for a quantity in J m-2? - that's the question.

If we adopt the form "temperature expressed as heat content" the new names would be

sea_water_conservative_temperature_expressed_as_heat_content
sea_water_practical_salinity_expressed_as_salt_content
sea_water_preformed_salinity_expressed_as_salt_content
sea_water_absolute_salinity_expressed_as_salt_content

This would be consistent with existing names. If we adopt the form "integral wrt depth of temperature expressed as heat content", the new names would be as proposed by Baylor, but we should change the existing Group A for consistency to

integral_wrt_depth_of_sea_water_potential_temperature_expressed_as_heat_content
tendency_of_integral_wrt_depth_of_sea_water_conservative_temperature_expressed_as_heat_content
tendency_of_integral_wrt_depth_of_sea_water_potential_temperature_expressed_as_heat_content
tendency_of_integral_wrt_depth_of_sea_water_salinity_expressed_as_salt_content

and likewise with the tendencies due_to_X.

The latter is more complicated, but which is better?

Karl has implied another suggestion, that we should have expressed_as_mass_content_of_salt in the new names instead of expressed_as_salt_content. If we adopt that suggestion, we should also correspondingly change the seven existing standard names containing tendency_of_sea_water_salinity_expressed_as_salt_content. On the other hand, if we stick with salt_content, we ought to change the existing sea_ice_mass_content_of_salt in kg m-2 to sea_ice_salt_content. In either case, we have to change some existing names. Again, either is possible, but which is better?

Best wishes

Jonathan

[baylorfk]

Hi Both,
Thanks for the detailed suggestions. I think that emphasizing the integral in the name is key, as we are specifying integral layer definitions at the same time into the CMIP data request, specifically to address this point. I personally find sea_water_conservative_temperature_expressed_as_heat_content to be unclear if it is a vertical grid-cell integral (in J m-2) or an intensive quantity (in J m-3).
So, I prefer the
integral_wrt_depth_of_sea_water_potential_temperature_expressed_as_heat_content
versions, but I agree that consistency would be desired across the whole bunch.

[baylorfk]

I don't see a value in having non-energy units for e.g.,

kg degree_C m-2 integral_wrt_depth_of_product_of_conservative_temperature_and_sea_water_density

I just find that to be confusing. The Griffies et al. paper and the one supporting the data request are addressing these points precisely. The modeling centers should be converting to energy units based on these suggestions.

[JonathanGregory]

Dear @baylorfk

Certainly you can propose that modelling centres should convert their data from kg degree_C m-2 to J m-2 (by multiplying by specific heat capacity), but that makes a different geophysical quantity as far as CF is concerned. As you say, integral_wrt_depth_of_product_of_conservative_temperature_and_sea_water_density has units of kg degree_C m-2. Multiplying it by specific heat capacity gives integral_wrt_depth_of_sea_water_conservative_temperature_expressed_as_heat_content in J m-2, the quantity you propose. CF provides metadata (in this case standard names) for data-writers to describe the quantities they want to store, but CF doesn't have an opinion on what quantities they should store. CMIP has an opinion on that, of course, which is fine.

Cheers

Jonathan

[baylorfk]

Yes, @JonathanGregory, understood. I was just attempting to point out that we do not need to add other intermediate quantities involved in either the tendency or the content, e.g.,

integral_wrt_depth_of_product_of_potential_temperature_and_sea_water_density
integral_wrt_depth_of_product_of_preformed_salinity_and_sea_water_density
...

And so on...

[JonathanGregory]

Thanks, Baylor. Yes, I agree. J