Consistency problems associated to the improvement of precession-nutation theories

The complexity of the modelling of the rotational motion of the Earth in space has produced that no single theory has been adopted to describe it in full. Hence, it is customary using at least a theory for precession and another one for nutation. The classic approach proceeds by deriving some of the fundamentals parameters from the precession theory at hand, like, e.g. the dynamical ellipticity H, and then using that valuesin the nutation theory. The former IAU1976 precession and IAU1980 nutation theories followed that scheme. Along with the improvement of the accuracy of the determination of EOP (Earth orientation parameters), IAU1980 was superseded by IAU2000, based on the application of the MHB2000 (Mathews et al 2002) transfer function to the previous rigid earth analytical theory REN2000 (Souchay et al 1999). The latter was derived while the precession model IAU1976 was still in force therefore it used the corresponding values for some of the fundamental parameters, as the precession rate, associated to the dynamical ellipticity, and the obliquity of the ecliptic at the reference epoch. The new precession model P03 was adopted as IAU2006. That change introduced some inconsistency since P03 used different values for some of the fundamental parameters that MHB2000 inherited from REN2000. Besides, the derivation of the basic earth parameters of MHB2000 itself comprised a fitted variation of the dynamical ellipticity adopted in the background rigid theory. Due to the strict requirements of accuracy of the present and coming times, the magnitude of the inconsistencies originated by this two-fold approach is no longer negligible as earlier. Some corrections have been proposed by Capitaine et al (2005) and Escapa et al (2014) in order to reach a better level of consistency between precession and nutation theories and parameters. In this presentation we revisit the problem taking into account some of the advances in precession theory not accounted for yet, stemming from the non-rigid nature of the Earth. Special attention is paid to the assessment of the level of consistency between the current IAU precession and nutation models and its impact on the adopted reference values. We suggest potential corrections and possibilities to incorporate theoretical advances and improve accuracy while being compliant with IAU resolutions.