Determining Undersampled Coastal Tidal Harmonics using Regularized Least Squares

High-accuracy tidal-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 tidal gauges. Satellite altimetry, which measures water level with global coverage and high resolution, provides an unprecedented opportunity to address the issue but two technical challenges prevent such satellite-based tidal harmonic analysis: a) sampling frequency requirement: data sampling/acquisition frequency must be at least two times of the major tidal frequency to avoid the aliasing issue dictated by the Nyquist theorem but satellite revisit frequency is well below the required Nyquist frequency, and b) data length requirement: a minimum length of sampled observation data is required to recognize a sufficient number of tidal constituents according to the Rayleigh criterion theorem. To address these issues, a novel Regularized Least-Square approach is developed to substantially relax the limitation. In this method, the prior information of the regional tidal amplitudes is used to support a least square analysis to obtain the amplitudes and phases of the tidal constituents for water elevation time series of different lengths and time intervals. A numerical experiment showed that the proposed method can determine the tidal amplitudes to a high accuracy and the sampling interval can be extended to the application level of major altimetry satellites. The proposed algorithm was validated using the data of the altimetry mission, Jason-3. The new method could help identify the changing tides with sea-level rise and anthropogenic activities in coastal areas.