Dear Ken

Yes, the `standard_error` modifier is not in `cell_methods` because it doesn't 
relate to a particular dimension. But considering (as I said above) that the 
statistical standard error of a quantity is 1/sqrt(N) times the standard 
deviation over an imaginary `realization` dimension which indexes the 
observations of the quantity, I think it's very similar to a cell method.

My suggestion above is to define `standard_error` as a new cell method, and 
introduce a special keyword of `uncertainty` which would go in place of the 
dimension, indicating a statistic calculated over a set of realisations, thus 
making `cell_methods="uncertainty: standard_error"`. There would be no need to 
use the `standard_error` modifier.

I think some of the comments in the previous email discussion, as well as yours 
and @larsbarring's, may be partly addressed by keeping in mind that the 
`standard_name` is __not__ the entire description of the quantity. The 
`cell_methods` is often a very important qualifier. For example, 
`standard_name="air_temperature"` with `cell_methods="time: mean longitude: 
maximum"` means the zonal maximum of the time-mean air temperature. I 
appreciate the point that a standard deviation "feels" a bit different from a 
mean, and a variance even more so because of its different units, but I can't 
see a clear justification for treating these two differently from mean, median, 
mode or other cell methods - they are all statistics which characterise 
variation of a single quantity over its dimensions.

I agree that what I sketched above is insufficient to deal with your more 
complex description of uncertainty computations. I didn't write any more 
because I'd already written quite a lot! I agree that some further attributes 
may be needed to provide information about how the uncertainty is derived.

Best wishes

Jonathan


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