Numerous tidal phenomena, including river tides, internal tides, and tides in ice‐covered bay, are nonstationary, which pose a great challenge for traditional tidal analysis methods. Based on the independent point scheme and cubic spline interpolation, a new approach, namely the enhanced harmonic analysis, is developed to deal with nonstationary tides. A MATLAB toolbox, S_TIDE, developed from the widely used T_TIDE, is used to realize the approach. The efficiency of S_TIDE is validated by analyzing a set of hourly water level observations from stations on the lower Columbia River. In all stations, the hindcast of S_TIDE is more accurate than NS_TIDE that is a powerful nonstationary tidal analysis tool adapted to river tides. The changing mean water level and tidal constituent properties obtained by S_TIDE are similar to those obtained by NS_TIDE, continuous wavelet transform, and empirical mode decomposition and highly consistent with theory on river tides. Moreover, different from NS_TIDE that only can be applied to river tides, enhanced harmonic analysis is free of dynamic content, assuming only known tidal frequencies. Therefore, S_TIDE can be applied to all kinds of nonstationary tides theoretically. Though powerful, S_TIDE also has some limitations: S_TIDE cannot be used for prediction and too many independent points in S_TIDE may induce computational memory overflow and unrealistic results.

Due to the strong nonlinear interaction with river discharge, tides in estuaries are characterised as nonstationary and their mechanisms are yet to be fully understood. It remains highly challenging to accurately predict estuarine water levels. Machine learning methods, which offer a unique ability to simulate the unknown relationships between variables, have been increasingly used in a large number of research areas. This study applies the LightGBM model to predicting the water levels along the lower reach of the Columbia River. The model inputs consist of the discharges from two upstream rivers (Columbia and Willamette Rivers) and the tide characteristics, including the tide range at the estuary mouth (Astoria) and tide constituents. The model is optimized with the selected parameters. The results show that the LightGBM model can achieve high prediction accuracy, with the root-mean-square-error values of water level being reduced to 0.14 m and the correlation coefficient and skill score being in the ranges of 0.975–0.987 and 0.941–0.972, respectively, which are statistically better than those obtained from physics-based models such as the nonstationary tidal harmonic analysis model (NS_TIDE). The importance of subtide constituents in interacting with the river discharge in the estuary is clearly revealed from the model results.

The seasonal variation of tides plays a significant role in water level changes in coastal regions. In this study, seasonal variations of four principal tidal constituents, M₂, S₂, K₁, and O₁, in the Bohai Sea, China, were studied by applying an enhanced harmonic analysis method to two time series: 1-year sea level observations at a mooring station (named E2) located in the western Bohai Sea and 17-year sea level observations at Dalian. At E2, the M₂ amplitude and phase lag have annual frequencies, with large values in summer and small values in winter, while the frequencies of S₂ and K₁ amplitudes are also nearly annual. In contrast, the O₁ amplitude increases constantly from winter to autumn. The maxima of phase lags appear twice in 1 year for S₂, K₁, and O₁, taking place near winter and summer. The seasonal variation trends estimated by the enhanced harmonic analysis at Dalian are different from those at E2, except for the M₂ phase lag. The M₂ and S₂ amplitudes show semi-annual and annual cycles, respectively, which are relatively significant at Dalian. The results of numerical experiments indicate that the seasonality of vertical eddy viscosity induces seasonal variations of the principal tidal constituents at E2. However, the tested mechanisms, including seasonally varying stratification, vertical eddy viscosity, and mean sea level, do not adequately explain the observed seasonal variations of tidal constituents at Dalian.

As an effective tool to distinguish different tidal components, classical tidal current harmonic analysis has been widely used to obtain harmonic parameters of internal tidal currents. However, harmonic parameters cannot exactly reveal the motion of internal tides, as the irregular temporal variations for internal tides are significant in many regions of the world’s oceans. An enhanced harmonic analysis (EHA) algorithm based on the independent point scheme and cubic spline interpolation is presented in this paper to obtain harmonic parameters with temporal variations for different tidal constituents of internal tides. Moreover, this algorithm is applied to analyze 14 months of current data obtained from a mooring located on the continental shelf in the northeastern region of the South China Sea. The obvious irregular temporal variations for the four principal constituents—M₂, K₁, S₂, and O₁—of internal tides in this region are indicated. It is hoped that this algorithm might present a brand-new view for researchers to investigate the irregular temporal motions of internal tides.

A lot of tidal phenomena, including river tides, tides in ice-covered bays, and internal tides in fjords, are nonstationary. These tidal processes present a severe challenge for the conventional tidal analysis method. The empirical mode decomposition (EMD) method is useful for nonstationary and nonlinear time series and has been used for different geophysical data. However, application of EMD to nonstationary tides is rare. This paper is meant to demonstrate a new tidal analysis tool that can help study nonstationary tides, in this case river tides. EMD is applied to a set of hourly water level records on the lower Columbia River, where the tides are greatly influenced by the fluctuating river flow. The results show that the averaged period of any EMD mode almost exactly doubles that of the previous one, suggesting that EMD is a dyadic filter. The highest and second highest frequency modes of EMD represent the semidiurnal (D₂) and diurnal (D₁) tides, respectively. The sum of the EMD modes except for the first two is the mean water level (MWL). The study finds that the EMD method successfully captured the nonstationary characteristics of the D₁ tides, the D₂ tides, and the MWL induced by river flow.