The harmonic constants of long-period tidal constituents are critical for simulating the tide process, obtaining theoretical datum sounding reduction, and conducting further ocean research. In this paper, the equidistant node orthogonal polynomial fitting (ENOPF) method is employed to fit the harmonic constants of the T/P satellite altimeter data and the gridded altimeter data from the Data Unification and Altimeter Combination System (DUACS) to obtain the full-field harmonic constants of the long-period tidal constituents (S_a and S_sa) in the Bohai Sea, Yellow Sea, and East China Sea (BYECS). To verify the validity of the ENOPF method, the long-period tidal harmonic constants of the ENOPF method, the Finite Element Solutions 2014 (FES2014) model, the Empirical Ocean Tide 20 (EOT20) model, and the DUACS data were compared with the observations of the X-TRACK products and the tide gauges. In addition, the root-mean-square errors (RMSEs), amplitude differences ($\Delta \mathrm{H}$), and phase-lag differences ($\Delta \mathrm{G}$) of the comparison results were calculated. According to the error analysis and the cotidal charts, the ENOPF method is better than the other three methods or models for comparing tide gauges (6.19 cm, 5.85 cm, 25.44°; 1.10 cm, 0.72 cm, 59.09°, respectively. The cotidal charts obtained by the ENOPF method are smoother and have better consistency with the actual track data. The results indicate that, due to the polynomial fitting method adopted in ENOPF method, which has the characteristics of improving the resolution infinitely, it is easier to obtain the harmonic constant of full field than with other models or methods. This study proves that the ENOPF method is a reasonable and simple tool in extracting the harmonic constants of the BYECS.

This study employs the two-dimensional Legendre polynomial fitting (2-D LPF) method to fit M2 tidal harmonic constants from satellite altimetry data within the region of 53°E–131°E, 34°S–6°N, extracting internal tide signals acting on the sea surface. The M2 tidal harmonic constants are derived from the sea surface height (SSH) data of the TOPEX/Poseidon (T/P), Jason-1, Jason-2, and Jason-3 satellites via t-tide analysis. We validate the 2-D LPF method against the 300 km moving average (300 km smooth) method and the one-dimensional Legendre polynomial fitting (1-D LPF) method. Through cross-validation across 42 orbits, the optimal polynomial orders are determined to be seven for 1-D LPF, and eight and seven for the longitudinal and latitudinal directions in 2-D LPF, respectively. The 2-D LPF method demonstrated superior spatial continuity and smoothness of internal tide signals. Further single-orbit correlation analysis confirmed generally higher correlation with topographic and density perturbations (correlation coefficients: 0.502, 0.620, 0.245; 0.420, 0.273, −0.101), underscoring its accuracy. Overall, the 2-D LPF method can use all regional data points, overcoming the limitations of single-orbit approaches and proving its effectiveness in extracting internal tide signals acting on the sea surface.

F_TIDE has been proven to be effective in obtaining the time-varying harmonic parameters of nonstationary tidal signals, and the results near the two endpoints of the analyzed time series are more accurate than those obtained by S_TIDE, which provides good conditions for the prediction of future sea levels. In this paper, F_TIDE is used for the short-term prediction of nonstationary tides in Nome (Alaska) and South Beach (Oregon). The significance of each standard parameter of F_TIDE is quantified by calculating its signal-to-noise ratio to determine the appropriate parameters that can be used for prediction. F_TIDE performs well in forecasting the sea level for three weeks at the Nome gauge and one week at the South Beach gauge. F_TIDE causes 30.1% and 42.0% decreases in the mean absolute errors between the forecasts and the observations compared to T_TIDE. F_TIDE is applied to the original signal at the Nome gauge, and the results show a strong correlation between the variation in M₂ amplitude and the variation in the mean sea level. A potential mechanism is speculated in that changes in tides are affected by the changes in water depth on different time scales, which the sea level pressure, wind, sea ice, and other marine motions may contribute to.