Hansen, J.M.; Aagaard, T., and Kuijpers, A., 2015. Sea-level forcing by synchronization of 56- and 74-year oscillations with the Moon's nodal tide on the northwest European Shelf (eastern North Sea to central Baltic Sea).

The North Sea and Baltic Sea long-term records reveal a strong correlation (0.997) between sea-level changes and the sum of identified harmonic oscillations, corresponding to the lunar nodal period and four multiples of it. We developed a transparent method for iterative least residual sine regression that is capable of identifying harmonic sea-level oscillations, e.g., gravitational sea-level effects of the lunar nodal oscillation. Three relatively large harmonic sea-level oscillations with period lengths of 18.6 (18.6), 60.5 (55.8), and 76.1 (74.4) years correspond well to factors 1, 3, and 4 of the 18.6-year lunar nodal period (multiple periods in parentheses). The sum of these oscillations leaves small residuals that can be resolved into two further, statistically less significant oscillations with apparent period lengths of 28.1 (27.9) and 111.1 (111.7) years, corresponding to factors 1½ and 6 of the lunar nodal period. Periods and amplitudes expose strong entrainment, i.e. phase synchronization at rational ratios of the identified oscillations' periods as well as amplitude locking at reciprocal rational ratios of 1/2, 1/3, and 2/3 of the three largest oscillations. On top of the region's general sea-level rise (1.18 mm/y), strong quasi-oscillations occur when the two largest oscillations are in phase. Thus, a large quasi-oscillation commenced in 1971 adding a 40-year sea-level rise of 1.0–1.2 mm/y to the region's general sea-level rise. If our theory is correct, the ongoing quasi-oscillation should culminate in 2011, and the suggestion may be tested after completion of the ongoing 18.6-year nodal oscillation, i.e. in 2020–21. A purely mathematical extension of the oscillation parameters identified by the applied method suggests that the sum of harmonic oscillations produces 223-year pulses of quasi-oscillations, which can be divided into 158-year periods (e.g., 1747–1905 and after 1970) with large oscillations (60–65 mm), followed by 65-year periods (e.g., 1905–70) with much smaller oscillations (2–16 mm).