In discussing auxiliary information, it may be useful to keep in mind a particular example of such information: the uncertainty in a measurement. Uncertainty generally does not stand alone on its own merits as a variable in its own right, so it does not belong in the data. On the other hand, it is too important to be left to local processing codes (not to mention that fact that, if it varies enough over the data, it could use up a considerable amount of disk space if put into the processing codes, since for every PROCVAL there must be a PROCFORM.) Hence, the existence of a separate group of metadata: auxiliary information.
Note that the auxiliary information can refer not only to the data, but to the dimensions as well. For example, temperatures (data) may have uncertainties attached, but so can the altitudes (dimension) at which those temperatures were taken. Therefore, the auxiliary information refers to one set of dimensions (including Level 0 dimensions if it refers to the data), and it will at the same time apply to another set of dimensions-that is, it may vary over a range of those other dimensions.
If the uncertainties in the temperatures in our example vary from day to day, then we must specify not only the dimensions to which the auxiliary information refers, but also the dimension (time) over which it varies, and we must include in the auxiliary values a set of uncertainties applicable for each day. The auxiliary information, then, is said to apply over the time dimension.
These two concepts (reference and application) can be summarized by stating that the reference dimensions tell what the auxiliary information is about; the application dimensions tell how it varies over the data field.
The quantity code associated with auxiliary information may be a quantity such as ``error'' or ``uncertainty,'' in which case the quantity or quantities of the data or dimensions to which it refers are the actual physical quantities involved. In addition, auxiliary information may carry its own units. If it is marked as having no units, either there are no units for the auxiliary information or the units are to be taken from the variables being referred to.
The auxiliary information itself is contained in an array, and some correspondence must then be established between the elements of that array and the data and its dimensions. To do this, two fields are defined: APPLEV and APPNDEX, lists of dimensional levels and dimensional indices, respectively, whose elements correspond to the associated dimensions of the auxiliary array.
Thus, the number of application dimensions determines the number of
dimensions of the auxiliary information array. The size of the
auxiliary array (i.e., the number of grid points in each of its dimensions)
is determined by the START-END indices associated with the Auxgroup.
Thus, to determine the size of the 
'th dimension of the auxiliary
array, one would look at the 'th element of the application dimension
list, obtain the level and index of the data dimension to which the array
dimension corresponds, and use that level and index to look into the
START and END lists for the beginning and ending data dimension grid points
over which the Auxgroup applies. The number of grid points is then the
same as the size of the auxiliary array along that array dimension.
A similar mechanism exists to indicate which data dimensions the Auxgroup refers to. Again, two fields are defined: REFLEV and REFNDEX, which contain the levels and indices of the data dimensions referred to by the auxiliary information. The order of the elements of these two lists is unimportant. The extent of a dimension over which the Auxgroup refers is specified by the Auxgroup's START and END fields. A reference dimension may also appear in the application dimensions' list; this indicates that the auxiliary information not only refers to that dimension, but applies to it as well (i.e., varies over its grid points as well). If a reference dimension is not repeated in the application dimensions' list, then all of the auxiliary information refers to each grid point in that reference dimension (as bounded by its START and END points).