cdm/src/main/java/ucar/nc2/wmo/Util.java
public static boolean isUnitless(String unit) {
    if (unit == null) return true;
    String munge = unit.toLowerCase().trim();
    munge = StringUtil2.remove(munge, '(');
    return munge.length()  == 0 ||
        munge.startsWith("numeric") || munge.startsWith("non-dim") || munge.startsWith("see") ||
        munge.startsWith("proportion") || munge.startsWith("code") || munge.startsWith("0=") ||
        munge.equals("1") ;
  }
public static boolean isUnitless(String unit) {
    if (unit == null) return true;
    String munge = unit.toLowerCase().trim();
    munge = StringUtil2.remove(munge, '(');
    return munge.length()  == 0 ||
        munge.startsWith("numeric") || munge.startsWith("non-dim") || munge.startsWith("see") ||
        munge.startsWith("proportion") || munge.startsWith("code") || munge.startsWith("0=") ||
        munge.equals("1") ;
  }
The given unit is "unitless".