"area: mean where type1 over type2" question

[taylor13]

In the conventions document, the explanation of the phrase "mean where type1 over type2" is:

"A cell_methods attribute with a string of the form "mean where type1 over type2" indicates the 
mean is calculated by summing over the type1 portion of the cell and dividing by the area of the 
type2 portion. [...] If "over type2" is omitted, the mean is calculated by summing over the type1 
portion of the cell and dividing by the area of this portion."

I wonder if in the above, "summing" should be replaced by "integrating".

Consider, for example, computing the area mean from multiple grid cells. If the cells are of different size, then most commonly the mean would be computed as:

mean of f = sum-over-cells(f_i * A_i) / sum-over-cells(A_i)

where A_i is the area of each cell and f is the variable that we're averaging. The above represents an area-weighted mean of f.

Note that if the size of the cells goes to zero, this would be represented as

mean of f = integral(f*dA)/integral(dA)

So, I think "summing" should be replaced by "integrating" (or the section needs rewording to indicate that the sums are not simple sums, but area-weighted sums).

[JonathanGregory]

Yes, I agree that "integrating" is the intended meaning. This could be changed as a defect issue in the conventions repo. Thanks, Karl @taylor13