Currently the dimensionality of a FITS WCS is assumed to match the dimensionality of the image raster as specified by the NAXIS keyword. If the WCS is of a higher dimensionality than the image the current recommendation is to add dummy image dimensions. This is done by setting NAXIS to the higher dimensionality of the WCS and adding NAXISn keywords with a value of 1 for the extra dimensions.
This proposal defines the WCS dimensionality to be the maximum of the image dimensionality, as specified by NAXIS, and the highest index of the CTYPEn keywords. Thus, if NAXIS is 2 but there is a CTYPE3 keyword then the WCS dimensionality would be 3. To evaluate the WCS, pixel coordinates of one would be used for the higher dimensions.
Software that deals with FITS files where the WCS dimensionality indicated by the CTYPE keywords is higher than NAXIS may chose to internally represent the image as a raster with the higher dimensionality and axes lengths of 1 or treat the image raster with the dimensionality specified by NAXIS but evaluate coordinates with dummy pixel coordinates of 1 for the extra dimensions of the WCS.
This proposal follows the basic FITS principle that existing FITS files using the the extra raster dimensions of length 1 still be valid. New files created using this proposal will require reading software to adopt one of the easy to implement options described here.
In earlier data there was the possibility that no CTYPE keywords might be present. This proposal continues to support this possibility. However, in order to define a WCS dimensionality higher than the image dimensionality given by NAXIS requires that CTYPE keywords be used (technically only the one for the highest dimensionality is needed though that would be bad form). Not including CTYPE keywords is a practice which is discouraged.
The examples given in the documents "Functional Corrections and Axes Coupling in FITS WCS" and "Spectral WCS Conventions" below make use of this dimensionality proposal.