Why are methane spectroscopic parameters harder to determine and relatively poorly known, compared to other Earth trace gases?
A good explanation is found at the University of Bourgogne site MODELING THE ABSORPTION SPECTRUM OF METHANE.


  Although it is a small and simple molecule, its rovibrational spectroscopy is very complicated. This is mainly due to the high symmetry of this tetrahedral system (which leads to the existence of many degeneracies) and to its intricated vibrational structure. 


Vibrational and Rotational-vibrational energy level diagrams are available at the site.