Filling the gap in the IERS C01 polar motion series in 1858.9-1860.9

The C01 Earth orientation parameters (EOP) series provided by the International Earth Rotation and Reference Systems Service (IERS) is the longest reliable record of the Earth's rotation.

In particular, the polar motion (PM) series beginning from 1846 provides a basis for investigation of the long-term PM variations.

However, the pole coordinate $Y_p$ in the IERS C01 PM series has a 2-year gap, which makes this series not completely evenly spaced.

This paper presents the results of the first attempt to overcome this problem and discusses some ways to fill this gap.

Two novel approaches were considered for this purpose: parametric astronomical model consisting of the bias and the Chandler and annual wobbles with linearly changing amplitudes, and data-driven model based on Singular Spectrum Analysis (SSA).

Both methods were tested with various options to ensure robust and reliable results.

The results obtained by the two methods generally agree within the $Y_p$ errors in the IERS C01 series, but the results obtained by the SSA approach can be considered preferable because it is based on a more complete PM model.

;Comment: Revised version submitted to the Journal of Geodesy