On the corrections to precession and nutation models that can be implemented to reduce their uncertainties at the short term

The precession-nutation (PN) angles give the location of the so-called celestial intermediate pole, an axis defined so that it has no short period harmonic components in the space frame. Their variations are the largest among the Earth orientation parameters and can be quite well approximated by the conventional PN models IAU2006 and IAU2000, respectively, since the magnitude of the deviations or Celestial pole offsets (CPO) has a WRMS ranging typically around 200-300 micro arcseconds.

Regarding precession, it has become clear from the work reported by different research groups that revising the rates and offsets of the observed CPO is an urgent need to reduce the WRMS of all kinds of CPO time series. Therefore, it must be one of the issues considered in the ongoing update of the IERS Conventions Chapter 5. In practice, this correction can be implemented independently of revising a part of the theory, namely the values of some second-order components of IAU2006 which affects the estimated ellipticity H_d and thus indirectly the nutations amplitudes of IAU2000 to a non-negligible extent. As the linear model for the J₂ variation adopted in the development of IAU2006 is no longer valid, the challenge of updating the precession theory to a more realistic model arose, which would require modifying coefficients beyond the linear ones. Liu and Huang (2025) have published such an update of IAU2006 model named as IAU20006_J2, which allows a larger WRMS reduction and helps to reduce the observed upwards curvature of dX in recent years according to the assessment performed so far.

Regarding nutations, there is strong evidence in favour of no longer neglecting the non-rigid contributions that have been ignored so far in the planetary ones. The simplest way to implement this is to use the available corrections arising from an analytical solution, which can be enhanced with around five empirical corrections to increase the WRMS reduction. However, replacing the whole block of rigid planetary nutations with non-rigid ones would is also an option not more difficult to implement but offering better consistency.

As for the lunisolar nutations, it has been shown that the direct fit of corrections to the amplitudes of a few periods allows reducing the WRMS of VLBI solutions in a significantly larger amount than other approaches such as indirect fits of selected basic earth parameters, which suffers from the incomplete derivation of certain higher-order theoretical and geophysical corrections.

Based on the tests performed so far, applying all the previous corrections to the current PN models would enable the definition of modified CPOs, with a noticeable lesser WRMS across the entire VLBI determined series. Finally, using convenient free core nutation (FCN) models would largely reduce their yet unexplained or unmodelled variability.

Acknowledgments.- This work has been partially supported by the Spanish projects PID2020-119383GB-I00 funded by Ministerio de Ciencia e Innovación and SEJIGENT/2021/001 funded by Generalitat Valenciana