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arxiv: 2412.07868 · v3 · submitted 2024-12-10 · ⚛️ physics.geo-ph · astro-ph.IM· physics.data-an

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

Zinovy Malkin , Nina Golyandina , Roman Olenev This is my paper

Pith reviewed 2026-05-23 07:29 UTC · model grok-4.3

classification ⚛️ physics.geo-ph astro-ph.IMphysics.data-an
keywords polar motionIERS C01gap fillingsingular spectrum analysisEarth orientation parametersChandler wobbleannual wobble
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The pith

The 2-year gap in the IERS C01 polar motion series can be filled using either a parametric model or singular spectrum analysis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The IERS C01 series is the longest reliable record of Earth's polar motion. It has a gap in the Y_p coordinate from 1858.9-1860.9 that prevents even spacing. Two methods were tested to fill it: a parametric astronomical model with bias and wobbles of varying amplitudes, and singular spectrum analysis. The methods agree within errors, but SSA is preferred for using a fuller model of polar motion.

Core claim

The gap in the Y_p series of the IERS C01 polar motion data can be filled reliably by both a parametric model consisting of bias plus Chandler and annual wobbles with linear amplitude changes and singular spectrum analysis. The results from both methods agree within the uncertainties of the original series, but the SSA-based filling is preferable because it rests on a more complete description of polar motion behavior.

What carries the argument

Singular Spectrum Analysis (SSA) applied as a data-driven reconstruction of polar motion signals across the data gap

If this is right

  • The completed series provides an evenly spaced record suitable for studies of long-term polar motion variations.
  • Both filling methods produce values consistent with each other within the reported errors of the IERS C01 series.
  • SSA incorporates additional periodic components of polar motion beyond the basic Chandler and annual terms used in the parametric model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • SSA reconstruction could be tested on other gaps or incomplete geophysical time series to check consistency.
  • Comparison against any newly uncovered astronomical observations from the gap years would directly test the filled values.
  • Extending SSA to the entire C01 series might expose additional low-amplitude signals not captured by standard parametric models.

Load-bearing premise

That the parametric components and SSA decomposition capture the true polar motion behavior inside the gap without systematic bias from unmodeled signals or data selection effects.

What would settle it

Independent historical measurements of pole position from 1858.9-1860.9 that lie outside the uncertainty range of either set of filled values.

Figures

Figures reproduced from arXiv: 2412.07868 by Nina Golyandina, Roman Olenev, Zinovy Malkin.

Figure 1
Figure 1. Figure 1: The Xp component (top panel) and Y p component (bottom panel) of the IERS C01 series. in the framework of several programs for determination of absolute declinations of stars at three observatories: Greenwich, Pulkovo, and Washington. The Greenwich latitude variations were taken from Chandler (1894b) (years 1836.0–1851.0) and Thackeray (1893) (years 1851.0–1891.5). The Pulkovo latitude variations were take… view at source ↗
Figure 2
Figure 2. Figure 2: Generalized Lomb-Scargle periodogram of the IERS C01 PM [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: 3 Parametric model It is not possible to use a straightforward model consisting of two components, CW and AW, because their amplitudes do not remain constant over time in the date range around the gap (Ko laczek and Kosek, 1999; Yatskiv, 2000; Guo et al., 2005; Miller, 2011; Lopes et al., 2022; Zotov et al., 2022). However, these two inde￾pendent analyses of the IERS C01 series showed that the CW amplitude… view at source ↗
Figure 3
Figure 3. Figure 3: IERS C01 Yp series with filled missed data between 1858.9 and 1860.9 using the BCA model (upper panel) and BCA2 (bottom panel). Plot titles show date intervals used to fit the Yp data to the model. To evaluate the real accuracy of the PM series approximation by the parametric models, we computed the differences between the modeled and observed PM values for each of seven variants for the epochs before and … view at source ↗
Figure 4
Figure 4. Figure 4: IERS C01 Yp series with filled missed data between 1858.9 and 1860.9 computed using the CSSA model with the seven models providing the minimal approximation error. Comparison of the data presented in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The Y components of CSSA solution with r=6 (in arcseconds) and their Lomb-Scargle periodograms (except the trend component, arbitrary units). The period of the most powerful oscillation and the contribution of the component to the total signal are shown on the right. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The Y components of CSSA solution with r=9 (in arcseconds) and their Lomb-Scargle periodograms (except the trend component, arbitrary units). The period of the most powerful oscillation and the contribution of the component to the total signal are shown on the right. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: IERS C01 Yp series with filled missed data between 1858.9 and 1860.9 using the average values for both BCA and SSA models. wavelet technique, etc., have modifications for processing unevenly spaced data. Many examples of application of such analyses to study PM series can be found in the literature, e. g., Gaposchkin (1972); Ko laczek and Kosek (1999); Gambis (2000); Guo et al. (2005); Zotov and Bizouard (… view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper presents the first attempt to fill a 2-year gap (1858.9-1860.9) in the Y_p component of the IERS C01 polar motion series using two approaches: a parametric model consisting of bias plus Chandler and annual wobbles with linearly changing amplitudes, and a data-driven Singular Spectrum Analysis (SSA) decomposition. Both methods produce filled values that lie within the published C01 uncertainties, with the authors concluding that the SSA results are preferable because they rest on a more complete PM model.

Significance. A reliably filled gap would yield a fully even-spaced long-term PM record useful for studies of secular variations. The significance is reduced by the absence of any quantitative validation, error propagation, or external checks, so it remains unclear whether the filled values improve or degrade the series for downstream analyses.

major comments (3)
  1. [Abstract] Abstract: the claim that SSA results 'can be considered preferable because it is based on a more complete PM model' is not accompanied by any quantitative comparison (RMS difference, cross-validation score, or recovery metric) or falsification test; without such evidence the preference cannot be justified over the deliberately restricted parametric model.
  2. [Methods / Results] No section describes a synthetic-gap recovery experiment, hold-out interval test, or comparison against independent historical proxies for 1858.9-1860.9; such a test is required to show that the additional SSA modes are unbiased physical signals rather than edge or embedding artifacts.
  3. [Abstract / Results] The manuscript states that 'multiple options were tested and results agree within errors' but supplies no numerical validation metrics, error-propagation formulas, or uncertainty estimates for the filled Y_p values themselves.
minor comments (2)
  1. [Methods] Notation for the parametric model components (bias, Chandler amplitude trend, annual amplitude trend) should be defined explicitly with equations rather than described only in prose.
  2. [Methods] The embedding dimension and window length chosen for SSA should be stated together with a brief justification or sensitivity check.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments highlighting the need for stronger quantitative validation. We respond to each major comment below and will revise the manuscript accordingly where feasible.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that SSA results 'can be considered preferable because it is based on a more complete PM model' is not accompanied by any quantitative comparison (RMS difference, cross-validation score, or recovery metric) or falsification test; without such evidence the preference cannot be justified over the deliberately restricted parametric model.

    Authors: We accept the point that the preference requires quantitative support. The SSA approach is based on a data-driven decomposition that captures the full observed PM spectrum (including any additional low-frequency or irregular components) rather than restricting to pre-specified Chandler and annual terms with linear amplitude trends. In revision we will add explicit RMS differences between the two filled series, the fraction of variance explained by extra SSA modes, and a synthetic recovery test to provide the requested metrics. revision: yes

  2. Referee: [Methods / Results] No section describes a synthetic-gap recovery experiment, hold-out interval test, or comparison against independent historical proxies for 1858.9-1860.9; such a test is required to show that the additional SSA modes are unbiased physical signals rather than edge or embedding artifacts.

    Authors: We agree a synthetic-gap recovery test is needed and will add one by creating artificial gaps in adjacent well-sampled intervals, recovering them with both methods, and reporting recovery statistics and mode stability. No independent historical proxies for polar motion exist for the specific 1858.9-1860.9 gap interval; this is the documented observational gap in the primary series. revision: partial

  3. Referee: [Abstract / Results] The manuscript states that 'multiple options were tested and results agree within errors' but supplies no numerical validation metrics, error-propagation formulas, or uncertainty estimates for the filled Y_p values themselves.

    Authors: We agree that numerical metrics and uncertainty estimates should be supplied. The revised manuscript will include tables of RMS agreement values between methods and options, explicit formulas for propagating the original C01 uncertainties into the filled values, and per-epoch uncertainty estimates for the SSA-filled Y_p series. revision: yes

standing simulated objections not resolved
  • Comparison against independent historical proxies for 1858.9-1860.9, as no such proxies are known to exist.

Circularity Check

0 steps flagged

No circularity: gap fill derived from external data only

full rationale

The paper applies both the parametric model (bias plus linear-amplitude Chandler and annual terms) and SSA to the C01 series outside the 1858.9-1860.9 gap, then uses the fitted models to generate values inside the gap. The filled values are therefore model outputs, not inputs that define the models. The stated preference for SSA rests on the modeling assumption of greater completeness rather than any equation that reduces the result to its own fitted parameters or to a self-citation chain. No self-definitional, fitted-input-called-prediction, or ansatz-smuggling steps are present in the described derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work rests on the domain assumption that polar motion is adequately described by bias plus Chandler and annual terms (parametric) or by the dominant singular vectors extracted from surrounding data (SSA). No new entities are postulated.

free parameters (1)
  • linear amplitude trends
    Amplitudes of Chandler and annual wobbles are allowed to vary linearly and are adjusted to surrounding data.
axioms (2)
  • domain assumption Polar motion consists of bias plus Chandler and annual wobbles whose amplitudes may change linearly
    Invoked to construct the parametric model for gap filling.
  • domain assumption Singular spectrum analysis extracts the dominant components of polar motion from the observed series
    Basis for the data-driven SSA filling method.

pith-pipeline@v0.9.0 · 5742 in / 1160 out tokens · 19433 ms · 2026-05-23T07:29:58.198638+00:00 · methodology

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Reference graph

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    ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all ...

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    write newline

    " write newline "" before.all 'output.state := FUNCTION add.period duplicate empty 'skip "." * add.blank if FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION ...

    work page