[CF-metadata] dimensionless vertical coordinates

From: Jonathan Gregory <j.m.gregory>
Date: Mon, 10 Aug 2009 20:11:24 +0100

Dear Yilmaz

> 1) "s(k) is the dimensionless coordinate at vertical gridpoint (k)"
> Does this variable refer to itself, i.e. whose "formula_terms" attribute
> is being parsed? If this is the case, why do we still include this element
> in the "formula_terms" attribute?

Yes, it does refer to itself. The idea is that the formula identifies all the
variables which are needed to compute the dimensional vertical coordinate. It
happens that s is one of the terms in the formula, not all kinds of vertical
coordinate include themselves as one of the terms.

>
> 2) do variables which correspond to "depth" and "eta" need to have the same
> units? That is, can one of them be in meters and the other in centimeters?
> If they can be different, then doesn't the variable which
> corresponds to "depth_c"
> also need to have a unit? Do we need to expect a unit for it?

The standard does not make this clear, but I agree, they all need units, and
generic software should do appropriate units conversion.

> Because since it is
> a scalar variable, it is not required to have one according to CF
> conventions(?).

I think that's a confusion of the two meanings of "dimensionless". One sense
of "dimensionless" means a pure number, without units. Quantities like that,
such as sea-ice area fraction, do not need units. That's a different meaning
of "dimensionless" meaning zero-dimensional i.e. scalar. Scalar quantities
with physical dimensions do need units.

> 3) We know that a dimensional coordinate variable is either
> monotonically increasing
> or decreasing. Will it be the case for dimensionless ones after
> the formula is applied?
> That is, do these formulas and associated variable contents
> guarantee that, when the
P
> formula is applied, we will obtain a vector of pressure or height
> values, which are monotonically
> increasing or decreasing? (I would expect so since they are levels
> of depth or pressure)

I don't think that is guaranteed, though I agree it would be physically
sensible to arrange it. But it's not a requirement of CF.

> 4) "level", "layer", and "sigma_level" are deprecated according to CF
> conventions, however, still
> allowed. So how would it be possible for a generic application to
> interpret them?

They should all be interpreted as dimensionless, equivalent to 1.

> 5) And finally, under section "2.4 Dimensions" it says that
> "dimensions other than those of space
> and time may be included". If this is the case, is it still possible
> for a generic application to work
> without being able to interpret those additional dimensions? That is,
> how a could a generic application
> decide on which index value to pass for that dimension without recognizing it?

I don't really understand that question. The dimensions correspond to the array
subscripts. You can subscript an array without knowing the physical meaning of
the dimensions, can't you. Non-spatiotemporal dimensions should be identified
by standard name, although that is not a requirement of CF.

Cheers

Jonathan
Received on Mon Aug 10 2009 - 13:11:24 BST