Tidal analysis and prediction based on the Fourier basis pursuit spectrum

The high-precision prediction of ocean tides is important for coastal management. Traditional harmonic analysis (HA) regards tides as the cumulative motion of multiple trigonometric functions, ignoring the time-varying characteristics of harmonic constants. Although the time-frequency transformation method can reconstruct the time-varying characteristics of tides, there are problems with tidal component coupling and edge effects. Therefore, we propose a method of reconstructing tidal components based on Fourier basis pursuit (FBP) spectral bandpass filtering (FBPBPF) by combining the Fourier dictionary and the basis pursuit algorithm and apply this method to four tide stations in the Gulf of Maine and Hong Kong station to try to solve the above two problems. The results show that the FBP spectrum can effectively identify and separate the main coupling tidal components. In the Gulf of Maine, FBPBPF can use shorter tide data to obtain better or equivalent prediction results than HA. Especially within 30 days, the prediction accuracy of FBPBPF at the four sites can be improved by 53.5% on average compared with that of HA. At Hong Kong station, FBPBPF has higher prediction accuracy than HA and Inaction Method (IM) in 4 months, but its long-term accuracy is gradually reduced (including all stations). We believe that the frequency resolution is the key factor leading to the divergence of long-term prediction errors.