Can we accurately extract ocean tides from satellite altimeter records with substantial missing values in shallow bays?

Tidal dynamics in coastal areas remain poorly understood, primarily due to the complexity of local topography and the scarcity of observational data. Although satellite altimeters have proven to be a powerful tool for providing comprehensive and accurate sea level observations across the global ocean, their effectiveness is highly limited in coastal regions due to land interference. Classical harmonic analysis (CHA) model employs ordinary least square (OLS) to estimate tidal parameters from coastal satellite altimeter records, suffering from the problem of over-fitting when the number of unknown tidal parameters is comparable to or more than the number of valid observations. In this paper, two regularization methods (i.e. ridge and Lasso regression) are utilized to replace OLS in the CHA model to address the issue of over-fitting and the interleaved Topex/Poseidon-Jason1 series is analyzed with substantial missing values in Liaodong Bay, China. Practical experiments unequivocally demonstrate the superiority of Lasso regression to ridge regression and OLS. The spatially-averaged errors of OLS, ridge regression and Lasso regression are 5.43 cm, 3.99 cm and 2.84 cm, respectively. Moreover, tidal parameters obtained by OLS display significant unnatural spatial discontinuities along the satellite track, which are substantially diminished by Lasso regression. It is noteworthy that tidal constituents with small amplitudes obtained by Lasso regression may be unreliable due to residual over-fitting. Overall, CHA with Lasso regression is a method that can be widely applied to analyze various types of sea level records with substantial missing values in shallow bays.