Should we find out new mathematical strategies to model the Free Core Nutation?

Consideration of the Free Core Nutation (FCN) is required to improve the modelling of the Celestial Pole Offsets (CPO) since it is the major source of inaccuracy or unexplained time variability with respect to the current IAU2000 nutation theory. The FCN is a free mode related to the non-alignment of the rotation axis of the core and of the mantle. It can only be measured/detected by Very Long Baseline Interferometry (VLBI). IERS Conventions (2010) recommends an empirical FCN model of Lambert (2007). However, other alternative models are available today (e.g. Krásná et al. 2013; Malkin 2013; Belda 2016). All these models are based on the sliding window least-squares fit method, assuming a constant period of about -430 solar days.

In our previous studies, we evidenced that the period of the FCN could vary with time. Due to this FCN period variability, the conventional empirical FCN models would not be completely correct. Therefore, should we find out new mathematical approaches/strategies to model the FCN?

In this study, a new mathematical strategy is examined. We utilized the Whittaker smoother to extract the desired signal from the CPO series obtained from VLBI. This technique tends to behave as highly adaptive and versatile fitting algorithms and can thus replace conventional FCN models. Apart from that, it is extremely fast, gives continuous control over smoothness with only one parameter (lambda), interpolates automatically, and allows fast leave-one-out cross-validation. The preliminary assessment using the observed nutations derived from VLBI analysis demonstrated the potential of Whitaker smoother as an optimum algorithm to successfully reconstruct the FCN signal with more efficient performance to retrieve reliable patterns. This analysis could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS).