What is sea_ice_area_fraction, really ?

[TomLav]

Question

Dear community,

Sea-ice concentration is the area fraction of an ocean surface that is covered by sea ice. This is the well accepted "geophysical" definition, adopted by all providers of satellite-based observation data.

In the CF world, sea-ice concentration is encoded with standard_name sea_ice_area_fraction. The definition of this term has evolved throughout the years.

In the first standard name table (April 2002) it was:

"X_area_fraction" means the fraction of horizontal area occupied by X. Sea ice area fraction is area of the sea surface occupied by sea ice. It is also called "sea ice concentration".

In version 66 (May 2019) it became:

"Area fraction" is the fraction of a grid cell's horizontal area that has some characteristic of interest. It is evaluated as the area of interest divided by the grid cell area. It may be expressed as a fraction, a percentage, or any other dimensionless representation of a fraction. Sea ice area fraction is area of the sea surface occupied by sea ice. It is also called "sea ice concentration". "Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs.

Today (version 89, January 2025) it is:

"Area fraction" is the fraction of a grid cell's horizontal area that has some characteristic of interest. It is evaluated as the area of interest divided by the grid cell area, or if the cell_methods restricts the evaluation to some portion of that grid cell (e.g. "where sea_ice"), then it is the area of interest divided by the area of the identified portion. It may be expressed as a fraction, a percentage, or any other dimensionless representation of a fraction. Sea ice area fraction is area of the sea surface occupied by sea ice. It is also called "sea ice concentration". "Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs.

Now imagine a coastal grid cell with partial ocean cover: 70% of the grid is over the ocean, 30% over land. Imagine the ocean is fully covered by sea ice. What sea-ice concentration should be reported for that grid cell?

If we follow the geophysical definition the correct answer is 100%: the entirety of the (coastal) ocean is covered.

In the CF-world (v66), there is an ambiguity. Should the sea_ice_area_fraction be reported as 100% (Sea ice area fraction is area of the sea surface occupied by sea ice.) or rather 70% ("Area fraction" is the fraction of a grid cell's horizontal area that has some characteristic of interest. It is evaluated as the area of interest divided by the grid cell area) ?

Going further, the latest definition of sea_ice_area_fraction mentions the option of using cell_methods to "restrict the evaluation to some portion of that grid cell".

If I understand this correctly, it would mean that:

float siconc(time, lat, lon) ;
	siconc:standard_name = "sea_ice_area_fraction" ;
	siconc:units = "%" ;
        siconc:cell_methods = "time: mean"

would report a value of 70% for the coastal grid cell introduced above, while

float siconc(time, lat, lon) ;
	siconc:standard_name = "sea_ice_area_fraction" ;
	siconc:units = "%" ;
	siconc:cell_methods = "area: mean where sea time: mean" ;

would report a value of 100% for the same coastal grid cell.

Obviously, the difference above is only a problem for grid cells with a non-zero land fraction. For cells farther from land, the ocean and grid cell areas are the same numbers.

Going back to the evolution of the standard_name definition, it strikes me how the sentences : Sea ice area fraction is area of the sea surface occupied by sea ice. It is also called "sea ice concentration". , that correspond to the geophysical definition of sea-ice concentration, have been there from the start. I would argue that the first definition (table v1) was leaning towards the geophysical definition, then version 66 was ambiguous, then today's version opens for the two options.

I find it sub-optimal that the definition of sea_ice_area_fraction does not hold a clear guidance that if one wants to follow the geophysical definition, one must use cell_methods with "area: mean where sea".

I also find it puzzling that reporting the sea-surface temperature for the same coastal grid cell would be un-problematic and would not require a cell_methods attribute.

float sst(time, lat, lon) ;
	sst:standard_name = "sea_surface_temperature" ;
	sst:units = "K" ;
	sst:cell_methods = "area: mean where sea time: mean" ;

would have the same values whether the cell_methods was present or not. This is puzzling because SIC, like SST, is only defined over the ocean (geophysical sense), why are they treated differently by CF?

Here comes the time for some questions:

• Do we agree that the definition of sea_ice_area_fraction opens for two interpretations of what values to report in coastal grid cells?
• Have I understood correctly how to use cell_methods to specify what flavour of sea-ice concentration one reports in a CF file?
• Should we more clearly state (in the standard_name definition of sea_ice_area_fraction) that the geophysical definition requires "area: mean where sea" in cell_methods?

And bonus questions:

• Can cell_measures be used to provide the area of ocean in each cell (as opposed to the total area of the cell), and how?

Sorry if the above was difficult to follow. I hope this discussion can help bring awareness on this ambiguity, and hopefully improve the situation for the future.

[TomLav]

@taylor13 @mohntorte, fyi

[taylor13]

I'm not an authority by any means on this, but here's my understanding:

Do we agree that the definition of sea_ice_area_fraction opens for two interpretations of what values to report in coastal grid cells?

Yes, sea_ice_area_fraction is different from the term ("sea ice concentration") that is apparently commonly used to describe how much sea ice there is. And sea_ice_area_fraction is defined consistently with other similar properties (e.g. area_fraction, cloud_area_fraction, sea_area_fraction) which all indicate the fraction of a grid cell occupied by some property of interest. Note there are other fractions besides the 2 you mention that can be recorded under the conventions. For example, you could report the sea ice area fraction "where cloud". In that case you would consider portions of the grid cell with cloud cover and report the fraction of that area also occupied by sea ice.

Have I understood correctly how to use cell_methods to specify what flavour of sea-ice concentration one reports in a CF file?

Yes, I think you have. In particular if you want to report the fraction of the sea portion of a cell occupied by sea ice, you should use the standard_name sea_ice_area_fraction and specify in the cell_methods that the evaluation is restricted to the portion of the cell "where sea".

Should we more clearly state (in the standard_name definition of sea_ice_area_fraction) that the geophysical definition requires "area: mean where sea" in cell_methods?

If "sea ice concentration" (as distinct from sea ice area fraction) is commonly of interest, we probably should include in the description something like: "To report sea ice concentration, which is the fraction of sea area in a grid cell covered by sea ice, use this standard name but include in the cell_methods the text area: mean where sea. "

Note that when "where sea" appears in cell_methods, the sea_ice_area_fraction will be undefined except for grid cells including at least some sea area. If "where sea" is omitted from the cell_methods, then sea_ice_area_fraction is defined everywhere but is equal to 0 where there is no sea.

Also, careful data providers will include in cell_methods for a sea_surface_temperature variable the "where sea" directive to explicitly exclude anywhere not occupied by sea. This was done, for example, for CMIP model output. CF does not formally require this, but it certainly would be recommended.

I'm surprised you were able to track down historical versions of the standard names. For another purpose, I would also be interested in looking at earlier versions. Where did you find them?

[TomLav]

I'm surprised you were able to track down historical versions of the standard names. For another purpose, I would also be interested in looking at earlier versions. Where did you find them?

It was not obvious, but the url to the standard name table has a version number. So https://cfconventions.org/Data/cf-standard-names/66/build/cf-standard-name-table.html refers to version 66, while https://cfconventions.org/Data/cf-standard-names/current/build/cf-standard-name-table.html is the latest.

It is for another discussion, but I wonder if diffs of the standard name table are accessible (like we can explore diffs of the convention). Also justifications and discussions that lead to changes. I suspect the standard name team is too small to keep track of everything, but in this case it would have been handy to see a trace of why changes were made (and of the discussion that led to that change).

[ChrisBarker-NOAA]

Thanks for bringing this up -- what a lot of confusion!

My thoughts:

I liked the 2002 definition:

"X_area_fraction" means the fraction of horizontal area occupied by X. Sea ice area fraction is area of the sea surface occupied by sea ice. It is also called "sea ice concentration".

This seems pretty straightforward, and consistent with the idea behind standard names -- they represent a particular physical quantity.

But then, in 2019, this was added:

"Area fraction" is the fraction of a grid cell's horizontal area that has some characteristic of interest. It is evaluated as the area of interest divided by the grid cell area. "

I understand that that's standard text, which is a great idea for standard names in general, but I wonder -- why introduce the "grid cell" concept here? fraction of a grid cell is not a physical quantity -- fraction of an area is - regardless of how that area is defined -- In this case, it's area_of_ice / total_area (unitless), and could be defined at a point, or at any area defined any way.

If it IS the average concentration over a cell, wouldn't that be specified by the cell method?

Is it really any different, from a what physical quantity is it? point of view than, say sea_ice_surface_temperature, as Tom points out?

I would argue that this can be used both for model output, or results of, e.g. remote sensing analysis. In remote sensing, "fraction of the cell's area" makes sense, but in the model case, it's not really a "fraction of the cell" -- it's the value that the model computes, and depending on the algorithm, could be a point measure or, the average of the cell, or ... really not that different than any other physical quantity, like temperature.

On the practicalities:
As a user of sea ice concentration from ice-ocean models:
(Tom's example):

float siconc(time, lat, lon) ;
	siconc:standard_name = "sea_ice_area_fraction" ;
	siconc:units = "%" ;
        siconc:cell_methods = "time: mean"

would report a value of 70% for the coastal grid cell introduced above...

Please, please, please do not support this meaning! that is painfully difficult to for me to process on the other end, and feel completely unnecessary -- when would anyone want that definition?

I want to know what the concentration of sea ice is in a cell -- and in my case, I WANT a point value, which I would get by interpolating (or applying the same value to the whole cell) -- I absolutely want 100% in that case.

And trying to back-calculate from a reported 70% to 100% by looking at the fraction that is land would be really, really painful.

My thought is to remove the "fraction of the cell" language altogether, if possible.

Question: in the remote sensing case, if a cell (pixel?) did have 30% land, and 70% full coverage of sea ice, what would it report?

[taylor13]

Regarding

I want to know what the concentration of sea ice is in a cell -- and in my case, I WANT a point value, which I would get by interpolating (or applying the same value to the whole cell) -- I absolutely want 100% in that case.

For gridded data when cells are partly ocean and partly land, and you interpolated to each point within the cell (including the points on land) do you really want sea ice cover to be 100% everywhere? I would think you would ideally want it to be 100% for ocean points and 0% for land points. Especially for areas with very small fractions of sea. Do you want sea ice fraction to be 100% when most of the area is in fact land?

I think using cell_methods to distinguish between values calculated "where sea" or calculated over the entire cell seems like it should be very clear.

Question: in the remote sensing case, if a cell (pixel?) did have 30% land, and 70% full coverage of sea ice, what would it report?

This is one for the satellite folks. If they accurately sense an area fraction of sea ice independent of the underlying surface type, then I suppose they would find that the pixel was 70% sea-ice coverd (assuming 100% sea ice where sea). Their cell_methods would omit the phrase "where sea".

[TomLav]

Question: in the remote sensing case, if a cell (pixel?) did have 30% land, and 70% full coverage of sea ice, what would it report?

This is one for the satellite folks. If they accurately sense an area fraction of sea ice independent of the underlying surface type, then I suppose they would find that the pixel was 70% sea-ice covered (assuming 100% sea ice where sea). Their cell_methods would omit the phrase "where sea".

Speaking for myself, we are aware that some of our coastal grid cells have partial land cover, and we report 100% sea-ice cover when the ocean is fully ice cover. Lower sea-ice concentration at the coast tracks a "real" physical phenomenon, e.g. a polynya.

Our coastal grid cells can have up to 30% land cover. If there is more than 30% land cover, we consider there is too much land for doing a good retrieval, and mark the sea-ice concentration as undefined. But using other satellites with higher spatial resolution or fidelity could allow us to report sea-ice cover in grid cells with higher land percentage in the future. We would still report 100% (the geophysical definition).

At present we use sea_ice_area_fraction without cell_methods because I had not the ambiguity in mind when we first created those netCDF files (back in 2008/09!) (and I would argue like @ChrisBarker-NOAA that the pre-2019 definition supported this interpretation). We will probably want to add cell_methods = "area: mean where sea time: mean" in future versions of our files to clarify.

[ChrisBarker-NOAA]

For gridded data when cells are partly ocean and partly land, and you interpolated to each point within the cell (including the points on land) do you really want sea ice cover to be 100% everywhere? I would think you would ideally want it to be 100% for ocean points and 0% for land points. Especially for areas with very small fractions of sea. Do you want sea ice fraction to be 100% when most of the area is in fact land?

Sure: whether the point is on land or at sea is a different question than what the sea ice coverage is: sea ice fraction is undefined on land -- it really doesn't matter what value I get there.

To be honest, this is pretty hypothetical -- all the models I've ever dealt with son't have fraction-land cells, so I don't think my code would do the right thing anyway.

But I can't see the use case for define a sea-ice-fraction that isn't, well, the sea-ice fraction.

Maybe the way I think of it is that sea-ice-fraction is:

area_of_sea_ice / area_of_sea

or area_of_sea_ice / (area_of_open_water + area_of_sea_ice)

where area_of_land fits in to that I have no idea.

Again, I guess the idea is that I think if it not in terms of area but in terms of infinitesimal area -- units of (area/area), rather than an measurement over the finite size of the cell.

Consider continuity -- if you have one cell that's all sea, and next to it one with a fraction of land, and the sea ice conditions are the same in both, you really want to have a different value associated with those two cells?

I would think you would ideally want it to be 100% for ocean points and 0% for land points
Sure -- but the example here was having it be 70% on the whole cell, because only 70% of the cell is sea.

I think using cell_methods to distinguish between values calculated "where sea" or calculated over the entire cell seems like it should be very clear.

It may be clear, but it's not easy to detect and calculate.

Back to the example, if we take Tom's interpretation, then not having a cell_method, or ignoring it would lead to the "wrong" answer.

Though maybe there's a reasonable use case for the sea_ice_area_fraction to mean "fraction of cell" rather than "fraction of sea surface", I think the default, easy to process definition should be the "fraction of sea surface" one.

And "fraction of sea surface" is a physical quantity -- which we aim to represent with standard_names -- "fraction of cell area" isn't really a physical quantity -- as it depends on the the cell itself.

Use case:

In my oil spill model, the fraction of sea ice cover at a point influences the behavior of the oil. So we need to know it, and we have code that understands a wide variety or grid types, etc, and can interpolate to points within cells by various algorithms.

But we have no way to look at the cell method, and then go and adjust the value in a cell based on a whole other concept of what fraction of that cell is water vs land.

And that would be very ugly code to write.

[ChrisBarker-NOAA]

Also justifications and discussions that lead to changes.

if it's recent, it's all in gitHub discussions / issues -- maybe a bit hard to find, but it should be there.

[taylor13]

It was not obvious, but the url to the standard name table has a version number. So https://cfconventions.org/Data/cf-standard-names/66/build/cf-standard-name-table.html refers to version 66, while https://cfconventions.org/Data/cf-standard-names/current/build/cf-standard-name-table.html is the latest.

Thanks for that. I'm having a hard time seeing all the available versions. Can I get to the directory that lists them? this link returns a 404. I'm sure I'm doing something stupid here.
thanks,
Karl

[taylor13]

Chris, regarding https://github.com/orgs/cf-convention/discussions/407#discussioncomment-12409485, I think we all agree that the current definition of area_fraction is to take the area occupied by some area-type of interest and divide it by the entire area considered. An area fraction can therefore be calculated for any domain on earth. When area_fraction is reported on a grid of cells, then it represents the fraction of a cell area occupied by an area of interest and it can be defined for every cell; for example, the area_fraction of area-type "vegetation" would be 0 for all grid cells with land_area_fraction=0.

If you want the area_fraction occupied by "sea_ice", but you want it reported only for cells at least partly occupied by "sea", and you want it to represent the fraction of the sea area contained in the cell, then the CF conventions requires that you include in cell_methods the directive "where sea". We could define a new standard_name that specifically referred to this kind of fraction (e.g. "sea_ice_area_fraction_where_sea" or "sea_ice_concentration" or "fraction_of_sea_surface_with_sea_ice"), but that would need to be proposed and discussed. If adopted, it would provide an entirely duplicative way of representing the same quantity in two different ways--the current way and the new way.

By the way, your use case is helpful. As I understand it, your code will only give correct answers if cells are either wholly occupied by sea or not; grid cells with both land and ocean portions included would be problematic. It turns out for your data, including "where sea" for sea_ ice_area_fraction doesn't affect ocean values, but land values would be "undefined" or "0", depending on whether or not "where sea" were included. Maybe that's o.k. with the data you're dealing with, but much of the multi-petabyte archive of CMIP data comprises datasets that have been regridded with grid cells that are may be partially occupied by both land and sea. In CMIP analysis of oceans, we ask that the sea_ice_area_fraction be reported "where sea", so we do get the sea ice concentration and values should be undefined over land (where the area appearing in the divisor, the sea area, is 0).

[TomLav]

I think we all agree on the definition of _area_fraction in CF. And area_fraction, seconded by cell_methods, is indeed quite a powerful tool.

The issue is not that the CMIP data correctly add "where sea" to specify that the sea_ice_area_fraction is reported for the water part of the cell (good on you and the CMIP community).

The issues I have are:

• sea_ice_area_fraction does not define a single physical quantity, and partly contradicts itself (we must improve the definition);
• the "default" use of sea_ice_area_fraction (default = without cell_methods) points at an interpretation that very few people want (even CMIP made the choice of "where sea" for the main sea-ice concentration variable). There are thousands data files out there without cell_methods that actually store sea-ice concentration.
• sea_ice_area_fraction has a different behaviour than other sea_surface quantities (e.g. sea_surface_temperature) for partial cells. this is really not intuitive.

The above could be considered a defect rather than a feature (addendum: ...a defect in the context of wanting to report sea-ice concentration. Not a defect of the area fraction mechanism, this works great in general, but not for sea-ice concentration).

But before that I'll try (future posts) to explore the differences in workflows (e.g. remapping to another grid, or computing the sea-ice area) between the two flavors of sea_ice_area_fraction variables.

For most of those workflows we will need a way to store sea_area in the netCDF file alongside the siconc variable (or in an external file). I am not sure the convention currently supports this.

[ChrisBarker-NOAA]

Thanks @TomLav:

That's exactly what I was trying to say -- but far less clearly!

The above could be considered a defect rather than a feature (addendum: ...a defect in the context of wanting to report sea-ice concentration. Not a defect of the area fraction mechanism, this works great in general, but not for sea-ice concentration).

Bingo! I very much consider this a defect -- at least for my use cases.

NOTE: I'm little wary of the focus on CMIP here -- I know it's a big driver of CF, and we want CF to support that use case -- but it's only one use-case -- we do need to keep all the others in mind.

To add a bit more "flesh" to Tom's points -- while I focus on reading the data ('cause that's what I need) -- thinking about this a bit more, it seems defining sea-ice fraction in this way (i.e. fraction of the cell, rather than a differential quantity) makes it harder to write the data as well -- as I think that the ice fraction / concentration is measured somehow only on the sea part -- so to properly write the data, you'd need to re-calculate the value based on the size of the cell and it's fraction that is the sea.

I presume that's what CMIP is doing now?

I have to wonder if that was the intention when the name was updated ?

[TomLav]

To add a bit more "flesh" to Tom's points -- while I focus on reading the data ('cause that's what I need) -- thinking about this a bit more, it seems defining sea-ice fraction in this way (i.e. fraction of the cell, rather than a differential quantity) makes it harder to write the data as well -- as I think that the ice fraction / concentration is measured somehow only on the sea part -- so to properly write the data, you'd need to re-calculate the value based on the size of the cell and it's fraction that is the sea.

If you are the writer of the file, you can (you must) add :cell_methods = "area: mean where sea" when you write sea-ice concentration. Or you could transform your sea-ice concentration to sea-ice area fraction and omit the "where sea". But why would you?

I have to wonder if that was the intention when the name was updated ?

History is history. We will probably never know if the incompatibility between sea_ice_area_fraction and sea-ice concentration (in partial ocean cells) was already there in the first version of the standard_name table, or if it follows from when when _area_fraction was set to relate to grid cells (as opposed to any area) around version 66 (see the definitions in my first post).

[TomLav]

Credits where they are due, this topic was already brought by @Bruce-T-T-Calvert in cf-vocabulary issue 66.

[Bruce-T-T-Calvert]

As I mentioned in the older thread referenced by @TomLav, my view is that introducing a new standard name of sea_ice_concentration could be useful. Although, I understand the reasons for not doing this.

From the perspective of working with global instrumental temperature datasets, which often rely on sea ice information when infilling temperatures of polar sea regions, sometimes you need to use both definitions of sea ice area fraction (both sea ice concentration and sea ice fraction of grid cell area). Since different sea ice datasets may use different and inconsistent land masks, infilling missing sea ice information using sea ice concentrations may make sense. On the other hand, sea ice fraction of grid cell area is ultimately what matters when infilling temperatures.

Instrumental temperature datasets that use sea ice information include HadCRU_MLE & DCENT_MLE (my two datasets), HadCRUT5 Analysis, GloSAT (not yet made publicly available), Berkeley Earth, NASA GISTEMPv4, and COBE-STEMP3. The observational sea ice datasets typically used (HadISST2, COBE-SST3, G10010v2, G02202v4, OSI SAF GBL SICO CDR R3, etc.) often do not clarify (either in the netcdf file, peer reviewed papers, or user guides) which definition of sea ice area fraction is being used, although there is a tendency to avoid grid cells with non-integer land fractions, which helps avoid ambiguity. Reanalysis datasets like ERA5 and JRA-3Q also rely on these somewhat ambiguous sea ice datasets. Sadly, the broader community generally hasn't adopted the CF Conventions guidelines of clarifying the calculation using cell_methods.

The ambiguous definition of sea ice fraction is a bit of a hassle when writing papers. In my most recent paper, I had to clarify at the beginning of the document that I was using sea ice fraction to refer to the fraction of grid cell area, while I would use sea ice concentration for the other definition. It would be convenient if the scientific community, beyond the context of CF Convention guidelines, could adopt clearer standard definitions.

As an aside, I am co-authoring a large community science paper on assessing 1.5°C of warming. A small part of this paper discusses historic sea ice concentration estimates. The scientific community really needs to move away from relying on HadISST2 as that dataset has significant issues for the Antarctic prior to the satellite era (as discussed in the upcoming paper).

[TomLav]

As I mentioned in the older thread referenced by @TomLav, my view is that introducing a new standard name of sea_ice_concentration could be useful. Although, I understand the reasons for not doing this.

Let's see where this goes. My priority for (re)opening the topic is to bring larger attention, then fix the current definition of sea_ice_area_fraction. We could later propose a new standard name.

Since different sea ice datasets may use different and inconsistent land masks, infilling missing sea ice information using sea ice concentrations may make sense. On the other hand, sea ice fraction of grid cell area is ultimately what matters when infilling temperatures.

Could you elaborate on why the sea ice fraction of grid cell area is what matters? is it because you are working with air temperature (defined over the whole grid cell) and not sea temperature (defined only over the sea fraction)?

The ambiguous definition of sea ice fraction is a bit of a hassle when writing papers. In my most recent paper, I had to clarify at the beginning of the document that I was using sea ice fraction to refer to the fraction of grid cell area, while I would use sea ice concentration for the other definition.

Ha! Thank you for linking to your paper here. Until I read your paper I had no doubt that sea_ice_area_fraction was sea-ice concentration. Reading your paper, I thought "no way, he is wrong". And now here we are :)

It would be convenient if the scientific community, beyond the context of CF Convention guidelines, could adopt clearer standard definitions.

To clarify: the sea-ice community is clear in its (geophysical) definition of sea-ice concentration (that I recall at the beginning of the threads). This goes for the different glossaries you can find around, the WMO definitions, including the GCOS ECV. People in the field and doing satellite products always talk of sea-ice concentration. The translation of sea-ice concentration into gridded fields is where we (community) must be very clear.

As an aside, I am co-authoring a large community science paper on assessing 1.5°C of warming. A small part of this paper discusses historic sea ice concentration estimates. The scientific community really needs to move away from relying on HadISST2 as that dataset has significant issues for the Antarctic prior to the satellite era (as discussed in the upcoming paper).

HadISST2 has explored different routes (than most other datasets) when it comes to sea ice. Also for the satellite era. The collection of sea-ice area dataset by the University of Hamburg is a good starting point if one wants access to a curated dataset from multiple providers.

[Bruce-T-T-Calvert]

Could you elaborate on why the sea ice fraction of grid cell area is what matters? is it because you are working with air temperature (defined over the whole grid cell) and not sea temperature (defined only over the sea fraction)?

Most global instrumental temperature datasets statistically infill land surface air temperatures over regions of sea ice rather than extend sea surface temperature or marine air temperature observations over these regions. This is because land surface air temperature is considered a better proxy for air temperature over sea ice. Although, there are a few exceptions to this such as the direct use of ice buoy air temperature observations by NOAAGlobalTempv6. Therefore, when estimating the temperature anomaly over a 5° by 5° grid cell, the fraction of the grid cell covered by land or ice matters when calculating a weighted-average temperature anomaly.

HadISST2 has explored different routes (than most other datasets) when it comes to sea ice. Also for the satellite era. The collection of sea-ice area dataset by the University of Hamburg is a good starting point if one wants access to a curated dataset from multiple providers.

Thanks for the link. I have worked with most of these datasets in the past. This includes the OSI-450a/OSI-430a data (I cited one of your papers in the supporting information of my recent paper). Unfortunately, while I tried last year to append OSI-450a/OSI-430a data to HadISST2 to deal with missing data after August 2020, I did not have enough time to account for the adjustments applied by HadISST2 to OSI SAF data. So, I ended up not appending with the OSI-450a/OSI-430a data for my main results to avoid large discontinuities in sea ice concentrations.

[taylor13]

For most of those workflows we will need a way to store sea_area in the netCDF file alongside the siconc variable (or in an external file).

I agree that if you report "sea_ice_area_fraction, area: mean where sea" and if some of your grid cells are partly land and partly sea, then you should also provide the sea_area_fraction. This allows you to calculate, for example, the total area of sea ice over a cell or a region: seaIceArea=seaiceFraction(where sea) x seaFraction x gridCellArea. Also for this case, sea_ice_area_fraction is "undefined" or "missing" over cells entirely occupied by land because (seaIceArea)/(seaArea) is undefined for those cells.

For "sea_ice_area_fraction, area: mean", you should always provide the sea_area_fraction because otherwise it would be impossible to calculate sea ice concentration, which in this case equals seaiceFraction/seaFraction. Note that for this case, sea_ice_area_fraction is defined everywhere and is equal to 0 in regions underlain by land.

[TomLav]

Good that we agree (ref the obs4MIPS discussion)!

But how do we do that the CF(*) way?

For the purpose of computing sea-ice area/extent, I would naturally provide sea_area [units m²], rather than the area fraction of sea. That way, the user or application does not need to find or compute the area of the grid cell.

The standard name table has "sea_area": "X_area" means the horizontal area occupied by X within the grid cell. The extent of an individual grid cell is defined by the horizontal coordinates and any associated coordinate bounds or by a string valued auxiliary coordinate variable with a standard name of "region".

And I guess (I hope), a user or application can follow the thread from "area: mean where sea" to looking for a variable whose standard_name is sea_area.

I know CF has the concept of cell_measures, but I do not see how it would help here, since:

• the discussion around cell_measures seems to be only concerned with full cell, not partial area/volume inside a cell;
• the mechanism outlined above with standard_name should work just fine (for sea and other official area_types).

I know cell_measures offers the external_variables mechanism, but for this to be useful in my case (and externalize the variable with sea_area), we would first need to clarify that cell_measures can be used for partial cell area/volume.

(*) I suspect we can find a quicker route for obs4MIPS / CMIP. It seems to me that obs4MIPS / CMIP is much more based on variable names (siconc, areacello, sftof) than CF, where links have to be established via standard_name.

[ChrisBarker-NOAA]

introducing a new standard name of sea_ice_concentration

+1 on this, because:

the sea-ice community is clear in its (geophysical) definition of sea-ice concentration

And at least some of us want to know (and report?) what the sea ice concentration is at a given point -- I'm having a really hard time understanding why it would be helpful to convert concentration to "fraction over a grid cell". I'm sure I'm missing (maybe many) use cases, but if one wanted, for instance, to know what the total area of sea ice was in a cell, then the "fraction over a grid cell" would be helpful, obviously, but is that useful without knowing what the rest of the cell has in it? how much open water? how much land how much land with ice/snow/??.

In that case, you'd need to do a lot more computation anyway ....

In short -- these various quantities can be derived from each other, and as a rule, we prefer in CF to define only one -- but in this case, it seems we are storing the derived quantity, which seems off to me.

But we have what we have, so adding a "sea_ice_concentration" name might be the best way forward.

In a sense, they ARE different things.

A concentration is unitless, "differential" quantity: area/area. It can ( at least in theory) vary over a region of any size, like most other location-dependent quantities.

Whereas when you define it as:

"Area fraction": the fraction of a grid cell's horizontal area

Then it is, by definition, a discrete quantity, dependent on the cell size, that does not vary over the cell. So a different thing.

But I do agree with @TomLav: first, clarify the definition for what we already have.

[TomLav]

Here is the current definition of sea_ice_area_fraction:

"Area fraction" is the fraction of a grid cell's horizontal area that has some characteristic of interest. It is evaluated as the area of interest divided by the grid cell area, or if the cell_methods restricts the evaluation to some portion of that grid cell (e.g. "where sea_ice"), then it is the area of interest divided by the area of the identified portion. It may be expressed as a fraction, a percentage, or any other dimensionless representation of a fraction. Sea ice area fraction is area of the sea surface occupied by sea ice. It is also called "sea ice concentration". "Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs.

I suggest a new text along the lines of:

By default, a variable with this standard name holds the fraction of a grid cell covered by sea ice. It may be expressed as a fraction, a percentage, or any other dimensionless representation of a fraction. "Area fraction" is the fraction of a grid cell's horizontal area that has some characteristic of interest. It is evaluated as the area of interest divided by the grid cell area, or if the cell_methods restricts the evaluation to some portion of that grid cell (e.g. "where sea_ice"), then it is the area of interest divided by the area of the identified portion. Consequently, a variable with a standard name of sea_ice_area_fraction and an attribute cell_methods that includes "area:mean over sea", holds the sea-ice concentration : the area fraction of ocean surface that is covered by sea ice. The two quantities (the sea ice area fraction of a grid cell, and the sea-ice concentration) differ in grid cells that are partly sea, e.g. in coastal grid cells. "Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs.

As should be clear from the above, the new text clarifies what sea_ice_area_fraction can be, it does not change its meaning in either way.

[taylor13]

Tom's text is a definite improvement. We should hear from those familiar with how the standard name "descriptions" are constructed to guide us with the wording. In general, names are supposed to indicate a property or quantity independent of how it is reported. So, I think we should first describe it in general terms without reference to grid cells. Also, if a term appears in multiple standard names, then the description of that term is usually stated separately and consistently across all variables, so any change in the description of the termarea_fraction should be applied to other standard_names, as well.

I've suggested some edits here:

By default, a variable with this standard name represents the fractional area of some region of earth's surface covered by sea ice. It may be expressed as a fraction, a percentage, or any other dimensionless representation of a fraction. In general, an area fraction representative of grid cells is evaluated as the area of interest in the cell divided by the grid cell area, or if the cell_methods restricts the evaluation to some portion of that grid cell (e.g. "where land"), then it is the area of interest divided by the area of the identified portion. Consequently, a variable with a standard name of sea_ice_area_fraction and a cell_methods attribute that includes "area:mean over sea" represents what is defined as the "sea-ice concentration": the area fraction of the sea surface that is covered by sea ice. The sea ice area fraction of a grid cell, and the sea-ice concentration will differ in grid cells that are partly sea, e.g. in coastal grid cells, except when the concentration is 0. "Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs.

I'm sure further tweaks of the above could improve it.

[TomLav]

Tom's text is a definite improvement. We should hear from those familiar with how the standard name "descriptions"

Thanks. Yes, I will open a discussion at the vocabularies repo during the week. I wanted to check we were roughly on the same page.

You suggest to change my first sentence:

By default, a variable with this standard name holds the fraction of a grid cell covered by sea ice.

to:

By default, a variable with this standard name represents the fractional area of some region of earth's surface covered by sea ice.

This is quite a change. To me, a substantial part of the issue we are discussing is because the area_fraction standard name calls for "grid cells", not "some region of earth's surface". Thus, by default (in the meaning of not being modified by additional information), sea_ice_area_fraction is computed wrt to the total area of the grid cell. Hence my opening sentence.

This is the definition of area_fraction:

"Area fraction" is the fraction of a grid cell's horizontal area that has some characteristic of interest. It is evaluated as the area of interest divided by the grid cell area, or if the cell_methods restricts the evaluation to some portion of that grid cell (e.g. "where sea_ice"), then it is the area of interest divided by the area of the identified portion. It may be expressed as a fraction, a percentage, or any other dimensionless representation of a fraction. To specify which area is quantified by a variable with standard name area_fraction, provide a coordinate variable or scalar coordinate variable with standard name area_type. Alternatively, if one is defined, use a more specific standard name of X_area_fraction for the fraction of horizontal area occupied by X.

If the area_fraction standard name can actually be interpreted outside the realm of grid cells, then this discussion and its conclusion, would have been quite different. Maybe it is the definition of area_fraction that must be revised?

[TomLav]

After a good night sleep, I'd like to come back on this:

If the area_fraction standard name can actually be interpreted outside the realm of grid cells, then this discussion and its conclusion, would have been quite different.

Actually I don't think the main conclusion would have been different. We would still want to encourage producers to add "area: mean where sea" to their cell_methods attribute in case their reference area (a cell, a region, a zonal band, a hemisphere, the globe, etc.) has other surfaces than "sea". And in that case, the presence or absence of "area: mean where sea" does change the values.

But I do support (as @taylor13 below) that the definition text for _area_fraction is revised to be less cell-centric.

[taylor13]

I wonder if we should say just before the last sentence in my description:

The sea ice concentration is undefined where there is no sea because the denominator in the area fraction calculation is zero there.

[TomLav]

Maybe. We can discuss it further at the future vocabularies issue. This is not specific to sea_ice_area_fraction- though, so it sounds like something that should go in all such standard names, or in the convention document.

[taylor13]

Yes, please move it to a vocabularies issue. And I agree that all area_fraction descriptions should be reworded without (initial) reference to the.bounds of the area represented by the fraction. The area could be a cell, a region, a pixel, a zonal band, a hemisphere, the globe, etc. For example, the global land_area_fraction, as I recall, is about 30%, so there is no need to mention "cell". This is similar to "surface_temperature", for which the name is independent of the area it represents. It might apply to individual grid cells or the globe, for example.

[JonathanGregory]

The answer is being pursued in vocabularies issue 254, opened by @TomLav. Thanks.