# Title
Correction to the definition of "ocean sigma over z coordinate" in Appendix D
# Moderator
None yet
# Moderator Status Review [last updated: YYYY-MM-DD]
None yet
# Technical Proposal Summary
The convention for this parametric vertical coordinate appears to be defective
in its design. Correcting it cannot be treated as a remedy for a defect,
because the intention isn't clear, but a remedy is needed because at the moment
there is no definition of what the coordinate variable should contain.
# Associated pull request
None yet
# Detailed Proposal
With the ocean sigma over z coordinate, above depth `depth_c` there are
`nsigma` layers and below this depth the levels are surfaces of constant height
`zlev` (positive upwards) relative to the horizontal datum. The vertical
coordinate `z` for level `k` at time `n` and point `(j,i)` is
for k <= nsigma:
z(n,k,j,i) = eta(n,j,i) + sigma(k)*(min(depth_c,depth(j,i))+eta(n,j,i))
for k > nsigma:
z(n,k,j,i) = zlev(k)
where `z(n,k,j,i)` is height (positive upwards) relative to the datum (e.g.
mean sea level) at gridpoint `(n,k,j,i)`, `eta(n,j,i)` is the height of the sea
surface (positive upwards) relative to the datum at gridpoint `(n,j,i)`,
`sigma(k)` is the dimensionless coordinate at vertical gridpoint `(k)` for `k
<= nsigma`, and `depth(j,i)` is the distance (a positive value) from the datum
to the sea floor at horizontal gridpoint `(j,i)`.
In the above, "`sigma(k)` is the dimensionless coordinate for `k <= nsigma`"
means that `sigma` is the value that appears for level `k` in the vertical
coordinate variable, whose standard name is `ocean_sigma_z_coordinate`.
However, `sigma` is not defined for `k>nsigma`, so it cannot supply the
vertical coordinate value at these lower levels. I think this must be an
oversight in the convention as it stands. The convention is therefore faulty in
not defining a monotonic set of values for the vertical coordinate variable.
I propose that we should *delete* the statement "`sigma(k)` is the
dimensionless coordinate for `k <= nsigma`", and add the following:
> The vertical coordinate variable with standard name
> `ocean_sigma_z_coordinate` should contain `sigma(k)*depth_c` for `k <=
> nsigma` and `zlev(k)` for `k>nsigma`, with `units` of length. These comprise
> a set of indicative values, monotonically increasing with `k`, for the depths
> of the levels below the datum.
We should also add "The `standard_name` for `sigma` is
`ocean_sigma_coordinate`" at the end of the entry, where the other standard
names are defined.
It would be particularly useful to have comments from anyone who uses this
vertical coordinate variable.
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