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.

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.

Topographic Rossby waves (TRWs) in the abyssal South China Sea (SCS) are investigated using observations and high-resolution numerical simulations. These energetic waves can account for over 40% of the kinetic energy (KE) variability in the deep western boundary current and seamount region in the central SCS. This proportion can even reach 70% over slopes in the northern and southern SCS. The TRW-induced currents exhibit columnar (i.e., in-phase) structure in which the speed increases downward. Wave properties such as the period (5–60 days), wavelength (100–500 km), and vertical trapping scale (102–103 m) vary significantly depending on environmental parameters of the SCS. The TRW energy propagates along steep topography with phase propagation offshore. TRWs with high frequencies exhibit a stronger climbing effect than low-frequency ones and hence can move further upslope. For TRWs with a certain frequency, the wavelength and trapping scale are dominated by the topographic beta, whereas the group velocity is more sensitive to the internal Rossby deformation radius. Background circulation with horizontal shear can change the wavelength and direction of TRWs if the flow velocity is comparable to the group velocity, particularly in the central, southern, and eastern SCS. A case study suggests two possible energy sources for TRWs: mesoscale perturbation in the upper layer and large-scale background circulation in the deep layer. The former provides KE by pressure work, whereas the latter transfers the available potential energy (APE) through baroclinic instability.