Assessing Tidal Harmonic Constituents Using Sparse and Continuous Dictionary

Tidal signals are classically reconstructed using harmonic constituents whose amplitudes and phases evolve over time due to various factors. Traditional Fourier-based decomposition methods are widely used to estimate tidal constituents but suffer from limitations related to noise, resolution, and sampling constraints. High-resolution spectral estimation methods, particularly those based on compressed sensing, offer an alternative by exploiting the sparsity of tidal constituents. However, these approaches are highly sensitive to the resolution of the solution space, which is critical for accurately distinguishing closely spaced constituents, such as those in the semi-diurnal band. To address this challenge, we propose an experimental method that uses a sparse and continuous dictionary of tidal harmonic constituents on the sea-level time series of Socoa (SW France) characterized by periods of non-recording and gaps in the series linked to siltation problems. This study shows that sparse estimation can offer accurate spectral estimation and can support more usual approaches when data resolution is downgraded.