Determination of Harmonic Parameters with Temporal Variations: An Enhanced Harmonic Analysis Algorithm and Application to Internal Tidal Currents in the South China Sea

We presented an enhanced harmonic analysis (EHA) algorithm that obtains harmonic parameters with continuous temporal variations. The whole process of methodology for this algorithm is derived based on the independent point scheme (IPS) and cubic spline interpolation method. Using numerical examples, the accuracy of EHA is verified. It has the ability to reveal the continuous and smooth temporal variations of harmonic parameters for different tidal constituents of the prescribed current data. The mean difference between EHA and segment harmonic analysis lies in the fact that the former is using the data from the entire record to determine the harmonic parameters at any particular point with the spline coupling included. Then it is applied to a 14-month current data from a mooring located at the continental shelf of northeastern South China Sea. Different IPSs lead to different harmonic results. We determine the optimal IPS for time series by evaluating the misfits between the tidal predictions and the simulated data as well as the consistency among different IPSs. Similar with classical harmonic analysis (CHA), EHA is carried out without the consideration of the dynamics of internal tides, assuming only the candidate tidal constituents. The advantage is to allow post facto analysis on the dynamics without any dynamic assumptions into the harmonic analysis. As a result, this approach may not be entirely adequate for strongly non-stationary or dynamically complex issues like internal solitary waves. In summary, EHA is a new viewpoint and a more precise method than CHA to view the temporal variations of harmonic parameters for internal tides (currents). While this method is applied here to a scalar time series of currents, it could be applied to any scalar time series such as elevation, temperature or salinity. Hopefully, this algorithm might present a brand-new view for researchers to investigate the irregular temporal motions of internal tides. Future works should be done to solve the automatic selection of the IPS and apply this method to observing data at different locations of the world oceans.