[Paper Review] A New Free Core Nutation Model with Variable Amplitude and Period

Zinovy Malkin|arXiv (Cornell University)|Jul 30, 2004

Geophysics and Gravity Measurements6 references3 citations

TL;DR

This paper presents a new empirical model for the Free Core Nutation (FCN) with variable amplitude and period, derived from three long VLBI nutation series (GSF, IAA, USN). By modeling the FCN as a time-varying oscillation using continuous amplitude and phase functions, the model reduces residuals between observed nutation and the IAU2000A model to approximately 100 μas, significantly improving celestial pole offset accuracy beyond the MHB2000 model.

ABSTRACT

Three most long and dense VLBI nutation series obtained at the Goddard Space Flight Center, Institute of Applied Astronomy, and U.S. Naval Observatory were used for investigation of the Free Core Nutation (FCN) contribution to the celestial pole offset. Some recent studies have showed that the FCN period or/and phase does not remain constant, but varies in a rather wide range of about 410--490 days (for equivalent period). To implement this result in the practice, a new FCN model with variable amplitude and period (phase) is developed. Comparison of this model with observations shows better agreement than existing one. After correction of the differences between observed VLBI nutation series and the IAU2000A model, they decreased to a level about 100 microarcseconds.

Motivation & Objective

• To develop a more accurate empirical model for the Free Core Nutation (FCN) that accounts for observed variability in amplitude and period.
• To reduce the discrepancy between observed VLBI nutation series and the IAU2000A model, which currently exhibits residuals of ~160 μas due to unmodeled FCN effects.
• To enable reliable prediction of FCN contributions beyond the 2001.4 cutoff of the MHB2000 model by using continuous, non-inflecting functions for amplitude and phase.
• To provide a practical, empirically derived FCN model suitable for routine use in VLBI data processing.

Proposed method

• The model uses three long, dense VLBI nutation series (GSF, IAA, USN) spanning 1979–2003, which were aligned to the IAU2000A reference frame and combined after error scaling.
• Band-pass Gaussian filtering with a transfer function of 0.988 was applied to the combined series to isolate the FCN signal, preserving the 410–490-day oscillation band.
• The FCN amplitude A(t) was computed as A(t) = √(dX_c(t)² + dY_c(t)²), assuming all residual differences stem from FCN.
• The FCN phase Φ(t) was computed via integration: Φ(t) = ∫(2π/P(t))dt + φ₀, where P(t) is the time-varying period derived from wavelet analysis.
• The model uses the form dX_c = A(t)sin(Φ(t)), dY_c = A(t)cos(Φ(t)) to compute the FCN contribution to celestial pole offset.
• Prediction of future FCN behavior was achieved using ARMA modeling on A(t) and Φ(t), enabling extrapolation beyond 2001.4.

Experimental results

Research questions

• RQ1 Can a time-varying FCN model with variable amplitude and period better reduce residuals between observed VLBI nutation series and the IAU2000A model than the MHB2000 model?
• RQ2 What is the true nature of FCN period and phase variability over the 1979–2003 interval, as revealed by wavelet and Short-time Periodogram analysis?
• RQ3 To what extent does the new model improve the accuracy of celestial pole offset computation, especially for post-2001.4 observations where MHB2000 degrades?
• RQ4 Can continuous, non-inflecting functions for A(t) and Φ(t) be used to reliably predict future FCN contributions?

Key findings

• The new FCN model reduces the weighted root mean square (WRMS) of differences between observed nutation series and the IAU2000A model to approximately 100 μas, down from ~156 μas with no FCN model.
• For the 2002–2003 period, the new model achieves a WRMS of 97 μas (mean), significantly lower than the 146 μas achieved with the MHB2000 model, which was not designed for this epoch.
• The model's performance is superior to MHB2000, especially after 2001.4, where MHB2000 residuals increase due to its limited validity period.
• The FCN amplitude and phase variations derived from wavelet analysis show consistent behavior with the MHB2000 model, but the new model provides smoother, continuous, and more predictable functions.
• The model successfully eliminates the dominant peak in the power spectrum of residuals, confirming that the FCN signal is fully accounted for.
• The model is now routinely used in VLBI processing at the Institute of Applied Astronomy since September 2003, indicating operational viability.