Modified SLEVE parametric vertical coordinate

[taylor13]

Question

I received a question regarding how in CF one should store data stored on a "modified" SLEVE parametric coordinate. It has apparently been modified by checking whether layers become thinner than a critical depth (leading to numerical instabilities). It doesn't appear that the algorithm that adjusts the layers is easily described. This leads to the following question:

Consider 3-d data stored on N levels in the atmosphere, but with the heights of these levels varying with horizontal position. The heights of the levels cannot be (easily) represented by a parametric formula. What is the CF-compliant way to store this data? Presumably, the height coordinate must be recorded: H(x,y,k), where k is the vertical index. But how is that related to the variable of interest which is also a function of (x,y,k).

[pvanlaake]

The simple answer is: use an ancillary variable. The parametric vertical coordinates are then stored as a regular data variable and the scientific variable of interest has an ancillary_variables attribute pointing to the parametric vertical coordinates.

The problem arises from identifying the ancillary variable as vertical coordinates. In the standard case, the scientific variable has a standard_name attribute that identifies it as one of nine defined parametric formulations and an additional formula_terms attribute giving the arguments to the algorithm to compute the parametric coordinates. There is no alternative way to communicate that an ancillary variable should be used instead, insofar as I am aware.

Perhaps this is something that should be added to the conventions? There is a corollary in the form of the latitude and longitude coordinates of a horizontal grid that was not defined as a Cartesian product of latitude and longitude: supply a grid mapping variable or include two-dimensional grids for latitude and longitude coordinates.

I have also come across a variant of "atmosphere_hybrid_sigma_pressure_coordinate", whereby top and bottom coordinates are specified, rather than the CF-standard mid-point possibly with boundary coordinates. This would also benefit from a including an ancillary variable rather than the formulaic representation.

[davidhassell]

The grid cell heights should be stored as a 3-d auxiliary coordinate variable, referenced by the data variable's coordinates attributes.
Cheers,
David

[taylor13]

So we've had two options suggested: store as a variable pointed to either by an ancillary_variables attribute or by a coordinates attribute. I would think that the coordinates attribute option is preferred. Anyone disagree?