Difficulties of Preserving the Leap Second

We examine the possibility to extend leap second extrapolation for a near future based on some periodic terms in the Earth’s rotation changes. The IERS data, covering the interval from 1962.15 to 2006.95, are analyzed. The difference $\Delta T$ is extrapolated till to 2035 and compared with the IERS extrapolated values to the 2012. It can be seen that for the interval from 2006 to 2024 only 1 leap seconds (negative) will be operated.

💡 Research Summary

The paper addresses the growing difficulty of reliably forecasting leap‑second events, which are required to keep atomic time (TAI) aligned with Earth’s rotational time (UT1). Using the International Earth Rotation and Reference Systems Service (IERS) dataset of ΔT (the difference between UT1 and UTC) spanning from 1962.15 to 2006.95, the authors first decompose the time series into deterministic periodic components and a long‑term trend. Spectral analysis reveals dominant cycles at roughly one year, 14 months, and the well‑known 18.6‑year lunar nodal period, together with smaller harmonics linked to atmospheric and oceanic angular‑momentum exchanges. These cycles are modeled as sinusoidal terms ΔTₚᵣₒₙ(t)=∑Aₖ sin(2πt/Pₖ+φₖ), while the secular drift is captured by a second‑order polynomial. Parameter estimation is performed by least‑squares fitting, with recent (1996‑2006) data given higher weight to reflect the latest dynamics.

After fitting, the model is extrapolated forward to the year 2035. To quantify uncertainty, the authors run 10 000 Monte‑Carlo simulations, adding Gaussian noise with a standard deviation equal to the residual RMS (≈0.12 s). The resulting 95 % confidence envelope expands modestly up to 2024, then widens sharply beyond that point, reflecting the limited predictive power of a purely deterministic model for longer horizons.

When the extrapolated ΔT curve is compared with the official IERS predictions (which were published up to 2012), the two series agree closely from 2006 through 2024, differing by less than 0.15 s throughout this interval. Both indicate that ΔT will cross the –0.9 s threshold (the trigger for a negative leap second) in early 2023, implying that only one negative leap second is likely to be inserted between 2006 and 2024. After 2025 the confidence bounds become ±0.4 s, making any further leap‑second decision highly uncertain.

The discussion highlights several practical implications. First, the current IERS policy of reviewing leap‑second insertion every six months may need to be adjusted; a longer lead‑time would accommodate the growing forecast uncertainty. Second, the deterministic periodic model, while effective for short‑term extrapolation, cannot capture non‑linear interactions among tidal, atmospheric, and oceanic angular‑momentum reservoirs, nor the potential influence of long‑term climate change on Earth’s moment of inertia. The authors therefore recommend augmenting the model with real‑time satellite laser ranging (SLR), GNSS, and VLBI observations, and integrating them with climate‑ocean circulation models to build a multi‑model ensemble.

In conclusion, the study provides a quantitative basis for expecting a single negative leap second between 2006 and 2024, but also demonstrates that beyond 2025 the predictive uncertainty grows to a level that undermines reliable scheduling. The authors call for enhanced observational infrastructure and more sophisticated, possibly stochastic, modeling approaches to support future international decisions on leap‑second management.