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.

SUMMARY A three‐dimensional internal tidal model involving the adjoint method is constructed based on the nonlinear, time‐dependent, free‐surface hydrodynamic equations in spherical coordinates horizontally, and isopycnic coordinates vertically, subject to the hydrostatic approximations. This model consists of two submodels: the forward model is used for the simulation of internal tides, while the adjoint model is used for optimization of modal parameters. Mode splitting technique is employed in both forward and adjoint models. In this model, the adjoint method is employed to estimate model parameters by assimilating the interior observations. As a preliminary feasibility study, a set of ideal experiments with the model‐generated pseudo‐observations of surface currents are performed to invert the open boundary conditions (OBCs). In the ideal experiments, 14 kinds of bottom topographies and six kinds of predetermined distributions of OBCs are considered to examine their influence on experiment results. The inversion obtained satisfying results and all the predetermined distributions were successfully inverted. Analysis of results suggests the following: in the case where the spatial variation of the OBC distribution is great or the open boundary is close to a rough topography, the results will be comparatively poor, but still satisfactory; both the tidal elevations and currents can be simulated very accurately with the surface currents at several observation points; the assimilation precision could be reliable and able to reflect both of the inversion and simulation results in the whole field. The performance and results of ideal experiments give a preliminary indication that the construction of this model is successful. Copyright © 2011 John Wiley & Sons, Ltd.

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The adjoint tidal model based on the theory of inverse problem has been applied to investigate the effect of bottom friction coefficient (BFC) on the tidal simulation. Using different schemes of BFC containing the constant, different constant in different subdomain, depth-dependent form, and spatial distribution obtained from data assimilation, the M2constituent in the Bohai, Yellow, and East China Sea (BYECS) is simulated by assimilating TOPEX/Poseidon altimeter data, respectively. The simulated result with spatially varying BFC obtained from data assimilation is better than others. Results and analysis of BFC in BYECS indicate that spatially varying BFC obtained from data assimilation is the best fitted one; meanwhile it could improve the accuracy in the simulation of M2constituent. Through the analysis of the best fitted one, new empirical formulas of BFC in BYECS are developed with which the commendable simulated results of M2constituent in BYECS are obtained.

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A new method for the inversion of bottom friction coefficients (BFCs) in a two-dimensional tidal model is proposed in this study. In this method, the field of BFCs is constructed by interpolating values at independent points using a surface spline. The surface spline interpolation has an advantage: that the constructed surface is smoother than the surface constructed by the traditionally used linear interpolation, which has unrealistic extrema. The method is validated in twin experiments where the prescribed nonlinear distribution of BFCs are better inverted with the surface spline interpolation. In practical experiments, the BFCs are inverted and the M2 tide in the Bohai Sea is simulated by assimilating the TOPEX/Poseidon (T/P) data. The small errors between the simulation results and the observations, as well as the accurate cotidal charts, demonstrate the feasibility of the new method in practical application.

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.

Open boundary conditions (OBCs) of the M2 tidal constituent in the Bohai and Yellow Seas (BYS) were inverted successfully through assimilation of TOPEX/Poseidon (T/P) altimeter data. An improved independent points (IPs) scheme was employed in the inversion. Under the assumption that the OBC was spatially varying, values at a set of IPs along the open boundary were inverted using the adjoint method and those at other points were calculated by the spline interpolation. The OBC inverted with the improved scheme was closer to reality in terms of smoothness than that inverted with the Cressman interpolation. The scheme was calibrated in twin experiments. Practical experiments showed that the misfits between simulated results and observations were smaller when the spline interpolation was used.