Seasonal and nodal variations of predominant tidal constituents in the global oceanS

Tides are one of the basic types of ocean water motions. Previous studies have reported that the M-2 constituent exhibits seasonal variations (annual cycles) in some regions. However, based on the newly proposed method of modified two-step harmonic analysis (HA) and its application at 240 global tide gauges, we find that the M-2 constituent as well as the S-2 and K-1 do not have significant seasonal variations at these tide gauges. The seasonal variations of the M-2 constituent reported in previous studies are caused by its satellites, the H-1 and H-2 constituents, which are not resolved in these studies due to the short time window (one month or three months) used in HA. Because the frequency of the H-1 (H-2) constituent is equal to that of the M-2 minus (plus) the frequency of annual cycles, the superposition of the M-2, H-1 and H-2 constituents with constant amplitudes is equivalent to the M-2 constituent with seasonally varying amplitudes. Compared with the new method, some adaptations to traditional HA aiming to capture variations in amplitudes and phase lags of constituents have some limitations, because they either neglect some satellites of the major constitutes or introduce spurious fluctuations resulting from an unreasonably large number of independent points. The nodal modulations of predominant constituents are also explored in this study. On the global scale, the nodal modulations of the M-2, K-1 and O-1 constituents agree with the theoretical predictions, except a cold spot region with reduced nodal modulation in the Gulf of Maine and a hot spot region with enhanced nodal modulation in the South China Sea for the M-2. Nodal modulation is also found for the S-2 constituent (in theory, the S-2 has no nodal modulation), which is 0.8% averaged at 164 tide gauges where the S-2 is not too weak.