Opened 3 years ago

# Time mean over area fractions which vary with time — at Version 2

Reported by: Owned by: martin.juckes cf-conventions@… medium cf-conventions

Following a discussion on the mailing list, I'd like to propose adding a new example to the CF Convention document to illustrate the use of cell_methods to specify different mean quantities when using a mask which is time varying (e.g. sea_ice). The qualifier where has been introduced into the cell_methods to specify masked spatial operations, e.g. area: mean where sea_ice to represent a spatial mean over sea ice. The current convention does not explicitly comment on whether the where construct can be used with other dimensions. For the CMIP6 data request there is a requirement to specify the temporal mean of quantities averaged over sea ice, and the spatial extent of the sea ice is generally varying in time.

The proposal is to make it clear that use of where for non-spatial dimensions is allowed by adding examples in section 7. It is also necessary to provide these examples to clarify the subtle differences implied by different formulations of the cell_methods statement.

## New example for time-varying area fractions

The following new example and explanatry text should be added in section 7.3.3:

Example 7.8: Time mean over area fractions which vary with time

```float simple_mean(lat,lon):
simple_mean:cell_methods: area: mean where sea_ice time: mean

float weighted_mean(lat,lon):
weighted_mean:cell_methods: area: time: mean where sea_ice

float partial_mean(lat,lon):
partial_mean:cell_methods: area: mean where sea_ice over sea time: mean
```

When the area fraction is varying with time, there are several different ways in which a time mean can be formulated. Three of these are illustrated in this example. Suppose, for instance, we are averaging over three time steps and the data at one grid point is -10, -6, -2 with area fractions .75, .50, .25. The values of the simple_mean, weighted_mean and partial mean are, respectively, (-10 -6 -2)/3 = -6, (-10*.75 - 6*.5 -2*.25)/(.75+.5+.25) = -7.33 , and (-10*.75 - 6*.5 -2*.25)/3 = -3.667. The partial mean provides the contribution to the mean over the entire grid from a specified area type. The simple mean is weighting each time period equally, while the weighted mean provides equal weighting to each unit area of sea_ice.

In example 7.8, time could be replaced by any other coordinate over which an average is taken, such as an ensemble index.

### comment:1 Changed 3 years ago by jonathan

Dear Martin

Thank you for making this proposal, which I support. Is the text following the example to be included in the standard document as explanation? I suppose it should be.

I think that this proposal should also include some modification to the first paragraph of 7.3.3, which at the moment refers explicitly to "horizontal area". For instance, this could be changed to "extent in the dimension(s) concerned" or something, and in the parenthesis you could add "or over the time-interval when sea-ice is present". Possibly the next paragraph might need some minor tweaking for generality as well.

Best wishes

Jonathan

### comment:2 Changed 3 years ago by martin.juckes

• Description modified (diff)

Hello Jonathan,

The answer to the first question is yes, and I've modified the layout to make it a bit clearer.

On the 2nd point, I'm not sure. What I'm proposing is clarifying the usage with time-varying area fractions, or, in principle, area fractions which vary with any other coordinate dimension (e.g. an ensemble index). At the moment the construct is still dependent on the standard name area_fraction, so it can only apply to horizonal areas.

I've added a sentence to the proposed insert to clarify that time can be replaced by another dimension.

regards, Martin

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