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.

An improved independent point (IP) scheme was proposed to estimate the open boundary conditions (OBCs) for a 3D internal tidal model through assimilating the TOPEX/Poseidon (T/P) altimeter data. Under the assumption that the OBCs were spatially and smoothly varying, values at a set of independent points along the open boundary were inverted using the adjoint method and values at other points were interpolated by the spline method. The scheme was calibrated through idealized experiments where the M₂ tidal constituent in the northern South China Sea was simulated. The OBCs can be successfully inverted with the improved scheme and were better in spatial smoothness than the results obtained with the Cressman interpolation when embedded in the IP scheme. Simulations in realistic domains showed that the errors between simulations and observations were smaller when the spline interpolation was employed instead of the Cressman interpolation. Three boundary conditions of spline interpolation were used in simulations in realistic domains, and the result of the periodic boundary condition had the smallest error compared with the first and second boundary conditions.