Multi-HSA detection of long-period sea-level variability: application to the quasi-60-yr geodynamic oscillation

While long-period signals in sea-level records are increasingly recognized as critical components of coastal dynamics, their precise reconstruction, quantification, and geophysical attribution remain elusive. This study introduces an extended multivariate Hankel spectral analysis (MHSA) framework that incorporates a stacked Hankel z-pole algorithm, achieving the enhanced spectral resolution and precision signal decomposition for the detection of long-term sea-level oscillation. By applying this methodology to global tide gauge {TG} and global mean sea-level (GMSL) records, we resolve a persistent 64.2 ± 0.8-yr oscillation (low-degree spherical harmonic (SH) mode, the variance explained >30% of long-term residuals) that may differ from previously documented periods and phases of climate-driven datasets. Three findings emerge: (1) A common variable mode detector specifying this signal’s prominent spatiotemporal coherence (strip-shaped SH distribution) across most coastal tide gauges is developed. (2) Monte Carlo simulation reveals that this SH-mode oscillation induces non-negligible deviations in sea-level trajectory models. For example, it minimally affects linear trends (2.1 ± 0.3 mm/yr) but can amplify acceleration budgets by >50% in short-scale (e.g. sub-cyclical records) tide gauge datasets. Furthermore, a 17.8 ± 2.3 mm in recent 30-yr altimetry sea-level projections is introduced. (3) MHSA approach reveals sea-level variations waveform- and phase-locked with the Earth’s rotation and magnetic field while asynchronous with possible climate-driven changes and activity. These results (SH distribution and waveform consistency of geophysical processes) imply an internal (core–mantle) origin rather than climatic forcing. Therefore, the MHSA methodology offers an effective tool for exploring long-period sea-level variations, which is benefit for the future sea-level projections and coastal-risk evaluation.