Variables representing dimensional height or depth axes must always explicitly include the units attribute; there is no default value.

The direction of positive (i.e., the direction in which the coordinate values are increasing), whether up or down, cannot in all cases be inferred from the units. The direction of positive is useful for applications displaying the data. For this reason the attribute positive as defined in the COARDS standard is required if the vertical axis units are not a valid unit of pressure (a determination which can be made using the udunits routine, utScan) -- otherwise its inclusion is optional. The positive attribute may have the value up or down (case insensitive). This attribute may be applied to either coordinate variables or auxillary coordinate variables that contain vertical coordinate data.

For example, if an oceanographic netCDF file encodes the depth of the surface as 0 and the depth of 1000 meters as 1000 then the axis would use attributes as follows:

axis_name:units = "meters" ; 
axis_name:positive = "down" ; 	

If, on the other hand, the depth of 1000 meters were represented as -1000 then the value of the positive attribute would have been up. If the units attribute value is a valid pressure unit the default value of the positive attribute is down.

A vertical coordinate will be identifiable by:

Optionally, the vertical type may be indicated additionally by providing the standard_name attribute with an appropriate value, and/or the axis attribute with the value Z.

4.3.1. Dimensional Vertical Coordinate

The units attribute for dimensional coordinates will be a string formatted as per the udunits.dat file. The acceptable units for vertical (depth or height) coordinate variables are:

  • units of pressure as listed in the file udunits.dat. For vertical axes the most commonly used of these include include bar, millibar, decibar, atmosphere (atm), pascal (Pa), and hPa.

  • units of length as listed in the file udunits.dat. For vertical axes the most commonly used of these include meter (metre, m), and kilometer (km).

  • other units listed in the file udunits.dat that may under certain circumstances reference vertical position such as units of density or temperature.

Plural forms are also acceptable.

4.3.2. Dimensionless Vertical Coordinate

The units attribute is not required for dimensionless coordinates. For backwards compatibility with COARDS we continue to allow the units attribute to take one of the values: level, layer, or sigma_level. These values are not recognized by the Udunits package, and are considered a deprecated feature in the CF standard.

For dimensionless vertical coordinates we extend the COARDS standard by making use of the standard_name attribute to associate a coordinate with its definition from Appendix D, Dimensionless Vertical Coordinates. The definition provides a mapping between the dimensionless coordinate values and dimensional values that can positively and uniquely indicate the location of the data. A new attribute, formula_terms, is used to associate terms in the definitions with variables in a netCDF file. To maintain backwards compatibility with COARDS the use of these attributes is not required, but is strongly recommended.

Example 4.3. Atmosphere sigma coordinate

float lev(lev) ;
  lev:long_name = "sigma at layer midpoints" ;
  lev:positive = "down" ;
  lev:standard_name = "atmosphere_sigma_coordinate" ;
  lev:formula_terms = "sigma: lev ps: PS ptop: PTOP" ;

In this example the standard_name value atmosphere_sigma_coordinate identifies the following definition from Appendix D, Dimensionless Vertical Coordinates which specifies how to compute pressure at gridpoint (n,k,j,i) where j and i are horizontal indices, k is a vertical index, and n is a time index:

p(n,k,j,i) = ptop + sigma(k)*(ps(n,j,i)-ptop)

The formula_terms attribute associates the variable lev with the term sigma, the variable PS with the term ps, and the variable PTOP with the term ptop. Thus the pressure at gridpoint (n,k,j,i) would be calculated by

p(n,k,j,i) = PTOP + lev(k)*(PS(n,j,i)-PTOP)