[CF-metadata] Need for a new vertical coordinate definition: "Ocean generalized sigma coordinate"

[Jonathan Gregory]

Dear Rich

If sigma is a function of position (j,i) as well as level k, it will no longer
trace out levels at a fixed fraction of the distance between the surface and
the floor. In that case, what is the point of it as a sigma coordinate?
Obviously we could generalise its definition in the way you suggest, but this
is apparently equivalent to

z(n,k,j,i) = A(n,j,i)*eta(n,j,i) + B(k,j,i)

i.e. you specify the gridpoint vertical coordinates as the sum of a time-
invariant set of depths B, plus some fraction A of the time-variation of the
surface height. I wouldn't call that a sigma coordinate. This kind of
construction doesn't seem to have any surfaces at all, unless there is some
constraint on the smoothness of B(k,j,i) for each k. How do they construct
their grid, in fact?

Cheers

Jonathan