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.Plain Language Summary Based on the independent point scheme and cubic spline interpolation, a new approach, enhanced harmonic analysis, was developed to deal with nonstationary tides. Enhanced harmonic analysis is realized by a MATLAB toolbox, S_TIDE, which is developed from the widely used T_TIDE. S_TIDE assumes only known tidal frequencies and theoretically can be applied to all kinds of nonstationary tides and stationary tides. In this study, S_TIDE is applied to analyzing records of river rides that is one of the simplest kinds of nonstationary tides for which ample data are available. The method is compared with other methods to show its efficiency.

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.

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