Madsen and Holme reanalysed cleaned LOD records from the International Earth Rotation and Reference Systems Service (IERS) for 1962 to 2025 using cubic B-splines and penalized least-squares splines to recover smooth trends and their time derivatives. This time-domain approach emphasises transient, non-stationary events that standard Fourier methods can smear or miss.
The authors removed tidal, atmospheric and oceanic contributions before fitting the splines, then isolated intradecadal residuals and examined first and second derivatives to reveal coherent oscillatory periods. Their spline methods allow direct estimation of derivatives from the basis functions, reducing artefacts introduced by numerical differentiation.
Using a least-squares spline with equispaced knots they removed the long-period behaviour and fit the residual with pure cosines while testing for non-stationarity. Separately, an over-parameterized penalized spline captured subtle features in the first and second derivatives that highlight the 6-year and an 8.5-year component.
The fits consistently show a dominant 5.9-year oscillation up to 2010, a brief shortening around 2010 to 2014, and a return to the 6-year rhythm after 2014. These findings are robust to alternative binning, outlier-handling strategies and comparison with lunar-occultation derived LOD series.
The anomaly between 2010 and 2014
From the cleaned IERS LOD series, the authors extract a 5.9-year oscillation that dominates the intradecadal residual through 2010. Between 2010 and 2014 the expected peak-to-peak interval shortens, with a one-off separation of roughly 4.7 years, before the 6-year timing re-establishes itself after 2014.
This disruption is visible both in the residual to the long-period spline fit and more clearly in the negative second time derivative of the spline, which amplifies intradecadal signals and aligns extrema with the suspected event. The effect is not a slow amplitude modulation but a discontinuous change in timing that a stationary spectral analysis would struggle to capture.
The authors checked whether a low quality-factor damped oscillator could produce such a shortening and found synthetic low-Q models did not reproduce the abrupt 4-year interval, arguing the feature is unlikely an intrinsic statistical artefact.
Contemporaneous geomagnetic and flow-model indicators show similar timing. Independent magnetic-field analyses and core-flow reconstructions display intradecadal variability with local maxima at 2010, 2014 and 2020, matching the LOD extrema.
Looking back with lunar occultations
To test whether the 2010 event was unique, Madsen and Holme used the lunar occultation catalogue (Herald and Gault), which compiles occultation timings from 1623 onward, to build a T (time integral of LOD) series and derive LOD reliably from around 1830. Their processing used Huber-weighted binning and iterative outlier removal before spline-based smoothing and differentiation.
The occultation-derived LOD reproduces the modern IERS behaviour over the 20th century and shows a generally persistent 6-year oscillation throughout the 19th and 20th centuries. However, it also reveals an earlier interruption between 1916 and 1920, where the 6-year rhythm briefly shortens to roughly 4.2 years, a near-analogue of the 2010 to 2014 event.
Because occultation data are sparser and noisier before about 1900, the authors restrict detailed intradecadal analysis to 1830 onward, using 30-year sliding windows to track time-varying best-fit periods. This rolling window approach shows persistent 6-year power except for the short 1916 to 1920 anomaly and the modern 2010 to 2014 anomaly.
That both modern instrumental records and historical occultations show qualitatively similar disruptions strengthens the conclusion that these are real core-linked events and not purely observational or processing artefacts.
Magnetic fingerprints inside Earth’s core
Multiple independent lines of evidence point to a core origin. Core-surface flow inversions and secular variation models, including CHAOS family geomagnetic field models, show changes in flow patterns and magnetic variability beneath the Pacific and Indonesian sectors around 2010 to 2014.
Principal-component and multivariate analyses of core-field variability identify components with near-6-year periods and show peaks in 2010, 2014 and 2020, the same cadence seen in the LOD residuals. These coincidences imply a common deep-Earth driver, not a surface fluid origin.
Seismological studies and inner-core seismic signatures have also been reported to change in the same general interval, suggesting a chain of events that might couple inner-core processes, outer-core fluid dynamics and the geomagnetic field.
The authors propose plausible mechanisms. Mass or density anomalies near the inner-outer core boundary could trigger Alfvén or magneto-Coriolis waves, disturb gravitational coupling of the inner core with the mantle, and thereby alter the normal-mode timing that produces the 6-year oscillation. This qualitative hypothesis sits within current dynamo and core-flow modelling frameworks.
Why the 8-year cycle stayed stable
The analysis also isolates an 8.5-year component, stronger in time derivatives than in the residual, that appears largely unaffected during the 2010 to 2014 disruption. That relative immunity suggests different physical origins for the two signals.
The prevailing interpretation is that the 6-year oscillation links to inner-core and mantle gravitational eigenmodes or gravitational coupling of the solid inner core, whereas the 8-year component more directly reflects fluid outer-core dynamics, such as torsional oscillations or magneto-Coriolis waves.
If true, the selective disturbance of the 6-year timing during discrete core events implies changes that preferentially perturb inner-core coupling, for example sudden density redistribution at the inner boundary, while leaving outer-core fluid mode timing relatively intact.
Why rare interruptions matter
Millisecond-scale LOD shifts encode information about the geodynamo and core–mantle coupling over decades. The 1916 to 1920 and 2010 to 2014 events act as natural experiments that constrain how fast and how strongly the inner core and outer core can interact.
The study highlights the value of time-domain methods, such as splines and derivatives, alongside spectral approaches. Non-stationary or discontinuous events will be under-represented in frequency-domain averages. Complementary methods are essential to detect and interpret sudden changes in core behaviour.
Future work should refine the temporal alignment between LOD extrema, geomagnetic jerks and seismic inner-core indicators, test dynamo simulations that include impulsive inner-core boundary events, and extend the occultation-based LOD record where possible to probe earlier centuries.
Implications for core dynamics
Time-domain spline analysis of modern IERS LOD data and a historical occultation LOD series reveals that the usually stable 6-year LOD oscillation was briefly interrupted in 2010 to 2014, a phenomenon mirrored in 1916 to 1920.
The timing matches independent changes in geomagnetic secular variation and core-flow models, pointing to a transient internal core process that briefly altered the Earth’s rotational normal-mode timing.
References:
1 A recent interruption in the 6-year oscillation in length-of-day – Frederik Dahl Madsen et al. – Geophysical Journal International – August 28, 2025 – https://doi.org/10.1093/gji/ggaf337 – OPEN ACCESS