The latitude and longitude coordinates of a horizontal grid that was not defined as a Cartesian product of latitude and longitude axes, can sometimes be represented using two-dimensional coordinate variables. These variables are identified as coordinates by use of the coordinates attribute.

dimensions:
  xc = 128 ;
  yc = 64 ;
  lev = 18 ;
variables:
  float T(lev,yc,xc) ;
    T:long_name = "temperature" ;
    T:units = "K" ;
    T:coordinates = "lon lat" ;
  float xc(xc) ;
    xc:axis = "X" ;
    xc:long_name = "x-coordinate in Cartesian system" ;
    xc:units = "m" ;
  float yc(yc) ;
    yc:axis = "Y" ;
    yc:long_name = "y-coordinate in Cartesian system" ;
    yc:units = "m" ;
  float lev(lev) ;
    lev:long_name = "pressure level" ;
    lev:units = "hPa" ;
  float lon(yc,xc) ;
    lon:long_name = "longitude" ;
    lon:units = "degrees_east" ;
  float lat(yc,xc) ;
    lat:long_name = "latitude" ;
    lat:units = "degrees_north" ;
      

T(k,j,i) is associated with the coordinate values lon(j,i), lat(j,i), and lev(k). The vertical coordinate is represented by the coordinate variable lev(lev) and the latitude and longitude coordinates are represented by the auxiliary coordinate variables lat(yc,xc) and lon(yc,xc) which are identified by the coordinates attribute.

Note that coordinate variables are also defined for the xc and yc dimensions. This faciliates processing of this data by generic applications that don't recognize the multidimensional latitude and longitude coordinates.