Using Regularized Least Squares to Break the Data Requirements of Tidal Harmonics Analysis

Recent observation reveals a stunning fact that the coastal tides are experiencing a rapid change in the last century at several places in the world. High-accuracy tide level data is needed to achieve a wide and refined understanding of the phenomenon. In-situ measurements - the traditional and main data source to support tidal harmonic analysis - are often sparse and limited to fixed locations, which are insufficient to provide information about the spatiotemporal variability of tidal processes beyond the tidal gauges. Satellite altimetry may fundamentally change the situation. This technology measures water level with much wider spatial coverage and higher resolution, but it has not been used in tidal analysis due to two major limitations in the harmonic analysis: a) a minimum length of sampled observed data is required to recognize a sufficient number of tidal constituents according to the Rayleigh criterion and b) data sampling/acquisition frequency must be at least two times the major tidal frequencies to avoid the aliasing issue dictated by the Nyquist theorem. To address these issues, a novel Regularized Least-Square approach is proposed to break the limitations. In this method, the prior information of the regional tidal amplitudes is used to support a least square algorithm to obtain the amplitudes and phases of the tidal constituents for data series with different lengths and time intervals. A numerical experiment showed that the proposed method can determine the tidal amplitudes with a low level of error and the sampling interval can be relaxed to the application level equal to altimetry satellite revisit intervals. The proposed algorithm was also tested using the data of the altimetry mission, Jason-3, and the performance was excellent. The potential use of this method could help identify the changing tides with climate change and anthropogenic activities in the coastal area.