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

[Rich Signell]

        I was helping

The collaborators of the Mediterranean Forecast System are trying to get 
their model output into CF conventions, but they cannot, because they 
have a generalized sigma coordinate that varies spatially on their 
lon/lat grid.   They need the following definition, which is basically 
the same as ocean_sigma_coordinate, except that we specify sigma (k,j,i) 
instead of just sigma(k):

------------------------------------------------------------------------------------------------------


        Ocean generalized sigma coordinate

standard_name = "ocean_generalized_sigma_coordinate"

/Definition:/

z(n,k,j,i) = eta(n,j,i) + sigma(k,j,i)*(depth(j,i)+eta(n,j,i))

where z(n,k,j,i) is height, positive upwards, relative to ocean datum 
(e.g. mean sea level) at gridpoint (n,k,j,i), eta(n,j,i) is the height 
of the ocean surface, positive upwards, relative to ocean datum at 
gridpoint (n,j,i), sigma(k,j,i) is the dimensionless coordinate at 
vertical gridpoints (k,j,i), and depth(j,i) is the distance from ocean 
datum to sea floor (positive value) at horizontal gridpoint (j,i).

The format for the formula_terms attribute is:

formula_terms = "sigma: var1 eta: var2 depth: var3"


        --------------------------------------------------------------------------------------------------------

This would also allow people who use "S-coordinate" models that are more general than the specific functional form adopted in the CF 1.0 "ocean_s_coordinate" to specify their vertical coordinate. 

-- 
Richard P. Signell           rsignell at usgs.gov
U.S. Geological Survey       Phone: (508) 457-2229
384 Woods Hole Road          Fax:   (508) 457-2310
Woods Hole, MA  02543-1598