Determining Undersampled Coastal Tidal Harmonics Using Regularized Least Squares

Satellite altimetry, which measures water level with global coverage and high resolution, provides an unprecedented opportunity for a wide and refined understanding of the changing tides in the coastal area. But its sampling frequency is too low to satisfy the Nyquist frequency requirement and too few data points per year are available to recognize a sufficient number of tidal constituents to capture the trend of tidal changes on a yearly basis. To address these issues, a novel regularized least‐square approach is developed to relax the sampling interval limit to the range of 9–11 days, reaching the revisit time of the existing satellites. In this method, the prior information of the regional tidal amplitudes is used to support a least square analysis to obtain the amplitudes of the tidal constituents for water elevation time series of different lengths and time intervals. Synthetic data experiments performed in Delaware Bay and Galveston Bay showed that the proposed method can determine the tidal amplitudes with high accuracy and the sampling interval can be extended to the application level of major altimetry satellites. The proposed algorithm was further validated using the data of the altimetry mission, Jason‐3, to show its applicability to irregular and noisy data. The new method could help identify the changing tides with sea‐level rise and anthropogenic activities in coastal areas, informing coastal flooding risk assessment and ecosystem health analysis. Plain Language Summary Using satellite data to directly measure the difference from high tide to low tide is a long‐lasting challenge because the interval between satellite visits to the same location is too long and there are too few data points per year that can be used. We developed a new algorithm to enable the direct measurement of coastal tidal activities. The method is validated using observations. The tests showed that the new algorithm outperforms its peers and meets the application requirements. The new algorithm paves a way to understand the global changes in tidal motion, which could help governments and coastal communities analyze the changing risk of coastal flooding and ecosystems and support informed decisions to prepare for and mitigate the impacts. Key Points A new algorithm is developed to determine tidal amplitudes with undersampled elevation data Synthetic data experiments and a real case study validate the new algorithm The new method to determine tidal amplitudes achieves a hi