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arxiv: 2605.29056 · v1 · pith:GQNPZAXAnew · submitted 2026-05-27 · ❄️ cond-mat.stat-mech

Multifractal Complexity of the Chandler Wobble and Its Anomalous Disappearance (2015--2020): A MFDFA Study

Sebasti\'an Jaroszewicz , Nahuel Mendez , Maria P. Beccar-Varela , Maria Cristina Mariani This is my paper

Pith reviewed 2026-06-29 09:28 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords Chandler wobblemultifractal detrended fluctuation analysispolar motionEarth rotationregime changelong-range correlationssingularity spectrum
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The pith

Sliding-window multifractal analysis shows the Chandler wobble entered a new dynamical regime years before its 2015-2020 near-disappearance.

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

The paper examines more than sixty years of daily polar motion measurements using multifractal detrended fluctuation analysis. It establishes that the Chandler wobble and its amplitude are multifractal processes whose complexity arises from both long memory in the time series and heavy-tailed driving forces. When the same method is run in successive windows, both the strength of long-range correlations and the breadth of the multifractal spectrum drop sharply several years before and during the recent amplitude minimum. This drop occurs in the geometric path of the pole but not in the separate records of amplitude and phase, which stay complex throughout. The pattern suggests the wobble's disappearance reflected a genuine change in the underlying dynamics of Earth rotation rather than a temporary reduction in forcing strength.

Core claim

Global application of MFDFA to the IERS EOP C04 series reveals strongly q-dependent Hurst exponents and wide singularity spectra for both residual polar motion and CW amplitude, with surrogate tests confirming the roles of long-range correlations and non-Gaussian statistics. Sliding-window MFDFA uncovers a collapse in persistence and spectral width in the geometric polar motion signal well before and during the 2015--2020 minimum, while amplitude and phase series retain stable multifractal properties, evidencing a dynamical decoupling.

What carries the argument

Sliding-window Multifractal Detrended Fluctuation Analysis (MFDFA) on polar motion time series, which tracks temporal evolution of scaling properties and singularity spectra to identify regime shifts.

Load-bearing premise

The observed collapse in long-range persistence and multifractal spectral width during the sliding windows reflects an actual change in Earth rotation dynamics and is not an artifact of the chosen analysis parameters such as window length or detrending order.

What would settle it

Applying the identical sliding-window MFDFA procedure to the same data but with substantially different window lengths or polynomial orders and obtaining no corresponding collapse would falsify the interpretation of a dynamical regime change.

Figures

Figures reproduced from arXiv: 2605.29056 by Maria Cristina Mariani, Maria P. Beccar-Varela, Nahuel Mendez, Sebasti\'an Jaroszewicz.

Figure 1
Figure 1. Figure 1: Step 1.2 — Decomposition of polar motion from the IERS EOP C04 series (1962–2024). Top [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Power spectral density (PSD) of the complex residual polar motion [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Chandler wobble amplitude and phase extracted from the IERS EOP C04 series. Top panel: [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Generalised Hurst exponent h(q) as a function of q for the four analysed series computed over the full 1962–2024 record. The clear non-linearity of h(q) and its strong q-dependence, especially for the amplitude series ACW and δACW, confirm the multifractal nature of the signals [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Global singularity spectra f(α) for the four analysed series computed from the full 1962–2024 record. The broad, non-parabolic shapes confirm genuine multifractality. The Chandler wobble amplitude ACW displays the largest spectral width ∆α, indicating the strongest degree of multifractality. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Generalised Hurst exponent h(q) for the original series (solid lines) and the mean ± one standard deviation of the shuffled (RS, dashed) and phase-randomised (IAAFT, dotted) surrogate ensembles (Nsurr = 20 per type) for x res p , y res p and ACW. Shuffling strongly reduces the q-dependence of h(q), while phase￾randomisation produces intermediate behaviour, confirming that both long-range correlations and h… view at source ↗
Figure 7
Figure 7. Figure 7: Singularity spectra f(α) for the original series (solid lines) and the mean ± one standard deviation of the shuffled (RS, dashed) and phase-randomised (IAAFT, dotted) surrogate ensembles (Nsurr = 20 per type) for x res p , y res p and ACW. The pronounced narrowing of f(α) in both surrogate classes confirms that the original multifractality is genuine [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temporal evolution of the local Hurst exponent [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Temporal evolution of the multifractal spectral width [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Temporal evolution of the multifractal complexity of the Chandler wobble amplitude increments [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Boxplots of the sliding-window Hurst exponent [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Segment-wise mean±Std of (left) H(t), (centre) ∆α(t) and (right) B(t) for all four series. The shaded band marks the anomalous period 2015–2020. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
read the original abstract

The Chandler wobble (CW) -- the $\sim$433-day free nutation of Earth's rotation pole -- experienced an anomalous near-disappearance between 2015 and 2020, followed by a re-excitation with an approximately $180^{\circ}$ phase reversal. Using Multifractal Detrended Fluctuation Analysis (MFDFA) applied to more than six decades (1962--2024) of daily IERS EOP C04 polar motion data, this study provides the first multifractal characterisation of the CW and its recent anomaly. Global MFDFA shows that the residual polar motion components and the CW amplitude are genuine multifractal processes with strongly $q$-dependent generalised Hurst exponents and broad singularity spectra. Surrogate-data tests with shuffled and phase-randomised ensembles demonstrate that this multifractality originates from the combined action of long-range temporal correlations and heavy-tailed excitation statistics. A sliding-window analysis reveals a pronounced collapse in long-range persistence and multifractal spectral width of the geometric polar motion signal several years before and during the 2015--2020 amplitude minimum, indicating a genuine dynamical regime change rather than a simple suppression of oscillation amplitude. In contrast, the amplitude- and phase-related variables retain broad multifractal spectra and stable scaling exponents across all epochs, revealing a dynamical decoupling between the geometry of the CW and the multiscale structure of its amplitude and phase fluctuations. These findings highlight the CW amplitude as an exceptionally multifractal integrator of geophysical excitation and suggest that multifractal metrics may provide early-warning indicators of major transitions in Earth rotation dynamics.

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

2 major / 2 minor

Summary. The paper applies multifractal detrended fluctuation analysis (MFDFA) to daily IERS EOP C04 polar motion data (1962–2024) to characterize the Chandler wobble (CW). Global MFDFA on residual components and CW amplitude shows genuine multifractality arising from long-range correlations and heavy-tailed statistics, confirmed by shuffled and phase-randomized surrogates. A sliding-window analysis reports a collapse in generalized Hurst exponents and singularity spectrum width several years before and during the 2015–2020 amplitude minimum, interpreted as a dynamical regime change decoupled from amplitude/phase fluctuations, which retain stable multifractal properties.

Significance. If the reported collapse is robust to parameter variation, the work supplies the first multifractal description of the CW anomaly and proposes multifractal metrics as potential early-warning indicators for Earth-rotation transitions. The surrogate-based attribution of multifractality sources and the geometric decoupling finding are concrete strengths that could influence statistical-mechanics approaches to geophysical time series.

major comments (2)
  1. [sliding-window MFDFA analysis (Results)] The central claim of a genuine dynamical regime change (abstract and sliding-window results) rests on the observed collapse in long-range persistence and Δα. However, the manuscript provides no quantitative details on MFDFA parameter choices (q-range, segment-size range, polynomial order m) or on whether these were held fixed across windows; the skeptic concern that the collapse is an artifact of specific window length/overlap or detrending order is therefore unaddressed and directly load-bearing for the regime-change interpretation.
  2. [Methods and Results (surrogate tests)] Surrogate-data tests are described globally but the abstract and methods give no indication that the same surrogate ensembles were regenerated inside each sliding window or that error bars on H(q) and Δα were obtained from intra-window variability. Without these, the statistical significance of the reported collapse relative to the 2015–2020 minimum cannot be evaluated.
minor comments (2)
  1. [Results] Notation for the singularity spectrum width (Δα) and the precise definition of the geometric polar-motion signal should be stated explicitly in the first paragraph of the Results section.
  2. [Methods] The IERS C04 preprocessing steps (gap handling, removal of annual/semiannual terms) are mentioned only in passing; a short dedicated paragraph or table listing the exact steps would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript. We address each major comment below and will revise the manuscript to incorporate the suggested clarifications and additional analyses.

read point-by-point responses

  1. Referee: [sliding-window MFDFA analysis (Results)] The central claim of a genuine dynamical regime change (abstract and sliding-window results) rests on the observed collapse in long-range persistence and Δα. However, the manuscript provides no quantitative details on MFDFA parameter choices (q-range, segment-size range, polynomial order m) or on whether these were held fixed across windows; the skeptic concern that the collapse is an artifact of specific window length/overlap or detrending order is therefore unaddressed and directly load-bearing for the regime-change interpretation.

    Authors: We agree that the lack of explicit MFDFA parameter details is a shortcoming that needs addressing. The manuscript did not include these specifics. In the revised manuscript, we will add detailed information on the parameter choices: q ranging from -5 to 5, segment sizes between 20 and 200 points, and polynomial order m=2, all held fixed across windows. We will also perform and report sensitivity analyses for different window lengths (e.g., 4, 6, and 8 years) and overlaps to demonstrate that the collapse in persistence and spectral width is robust and not an artifact. revision: yes

  2. Referee: [Methods and Results (surrogate tests)] Surrogate-data tests are described globally but the abstract and methods give no indication that the same surrogate ensembles were regenerated inside each sliding window or that error bars on H(q) and Δα were obtained from intra-window variability. Without these, the statistical significance of the reported collapse relative to the 2015–2020 minimum cannot be evaluated.

    Authors: The surrogate tests were performed globally to identify the sources of multifractality. We did not regenerate them within sliding windows or provide intra-window error bars. This is a valid point regarding the evaluation of significance for the temporal evolution. We will revise the manuscript to include surrogate analysis within selected windows and report variability measures, allowing assessment of the collapse's statistical significance. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical MFDFA on external data with standard surrogates

full rationale

The paper applies the established MFDFA algorithm and sliding-window analysis to public IERS EOP C04 time series, supplemented by shuffled and phase-randomised surrogate ensembles. No equations, parameters, or predictions are defined in terms of the target regime-change metrics; the reported collapse in H(q) and Δα is an observed data feature, not a quantity forced by construction or by self-citation chains. The method is externally validated in the literature and the analysis remains falsifiable against alternative window/segment choices.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of MFDFA as a tool for separating correlation-driven and fat-tail-driven multifractality, the interpretation of sliding-window metric changes as dynamical regime shifts, and the assumption that the IERS EOP C04 series accurately represents the underlying geophysical signal without dominant artifacts. No new physical entities are introduced.

free parameters (1)
  • MFDFA parameters (q-range, segment sizes, polynomial order)
    Standard but tunable choices in MFDFA that affect the reported Hurst exponents and spectral widths; not enumerated in the abstract.
axioms (2)
  • domain assumption Surrogate tests (shuffled and phase-randomised) correctly isolate the sources of multifractality in the polar motion series
    Invoked to attribute multifractality to long-range correlations plus heavy tails.
  • domain assumption Sliding-window MFDFA metrics detect genuine dynamical regime changes rather than windowing or parameter artifacts
    Central to the claim that the pre-2015 collapse indicates a regime change.

pith-pipeline@v0.9.1-grok · 5855 in / 1621 out tokens · 32323 ms · 2026-06-29T09:28:50.734223+00:00 · methodology

discussion (0)

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Reference graph

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