Status of the update of the Earth's rotation theory and precession-nutation models
Authors: Ferrándiz José M. , Huang Cheng-li , Escapa Alberto , Karbon Maria , Belda Santiago , Baenas Tomás 
Published: March 2024

In last years, the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) have organized successive joint working groups (JWG) aimed at studying in depth the current theories and models of the Earth's rotation. Their activity resulted in IAU and IAG resolutions encouraging the improvement of such theories and models. in terms of accuracy and consistency. Let us note in passing that, although many times when talking about theories of the Earth's rotation one thinks only of precession and nutation (PN) theories, the reality is not so simple. The Earth Orientation Parameters (EOP) constitute a redundant set of variables and the PN pair is closely linked to the polar motion one, their definitions depending on assigning them properties difficult to express by mathematical constraints usable in the analysis of observations.
In any case, improving the consistency of EOPs requires that all equations refer to the same reference systems and frames, use the same basic Earth parameters, and that the auxiliary geophysical models used in theoretical developments and observational data analyses are compatible; in contrast, current PN theories use parameters and models more than 20 years old that differ from current standards. Worse still is the fact that PN theories are inconsistent even in some of their fundamentals; for example, the former uses a dynamical ellipticity H that is assumed to be a linear function of time while nutation theory was derived assuming H to be a constant, the value of which needs revision and updating.
In terms of accuracy, several works performed in the framework of the past IAU/IAG JWG ITMER showed that the unexplained variance of the PN variables, measured in terms of WRMS of the observed celestial pole offsets (CPO), can be significantly reduced by empirical corrections, fitted to the observations, of the precession linear terms and of the theoretical amplitudes of a few lunisolar and planetary nutation terms. The inclusion of such corrections also allows the derivation of alternative CPO series with lower WRMS when analyzing VLBI data. To give an idea of the magnitude of the reductions, for well-known benchmark series such as usn2023b, gsf2023a, and ivs19q4X, the percentage WRMS reductions of (dX,dY) after correcting for precession are (21%,6%), (23%,8%), and (11%,8%), respectively, while correcting also for nutation the respective total decreases are (31%,27%), (31%,17%), and (32%,19%).
However, the use of empirical nutation models is only a temporary solution and has strong limitations because many periods whose corrections should be non-negligible are too close to each other to be numerically separable; improving accuracy and consistency as much as possible makes it necessary to derive complete theories with analytical formulas that provide amplitudes as a function of general Earth parameters. The latter is one of the most important tasks of the JWG on Consistent Improvement of the Theory of Earth Rotation (CITER) that is currently being set up.
Acknowledgment. This research was supported partially by Spanish Projects PID2020-119383GB-I00 funded by Ministerio de Ciencia e Innovaci&#243;n (MCIN/AEI/10.13039/501100011033); PROMETEO/2021/030 and SEJIGENT/2021/001, funded by Generalitat Valenciana; and the European Union&#8212;NextGenerationEU (ZAMBRANO 21-04).