Extracting tidal frequencies using multivariate harmonic analysis of sea level height time series

This contribution is seen as a first attempt to extract the tidal frequencies using a multivariate spectral analysis method applied to multiple time series of tide-gauge records. The existing methods are either physics-based in which the ephemeris of Moon, Sun and other planets are used, or are observation-based in which univariate analysis methods-Fourier and wavelet for instance-are applied to tidal observations. The existence of many long tide-gauge records around the world allows one to use tidal observations and extract the main tidal constituents for which efficient multivariate methods are to be developed. This contribution applies the multivariate least-squares harmonic estimation (LS-HE) to the tidal time series of the UK tide-gauge stations. The first 413 harmonics of the tidal constituents and their nonlinear components are provided using the multivariate LS-HE. A few observations of the research are highlighted: (1) the multivariate analysis takes information of multiple time series into account in an optimal least- squares sense, and thus the tidal frequencies have higher detection power compared to the univariate analysis. (2) Dominant tidal frequencies range from the long-term signals to the sixth-diurnal species interval. Higher frequencies have negligible effects. (3) The most important tidal constituents (the first 50 frequencies) ordered from their amplitudes range from 212 cm (M2) to 1 cm (OQ2) for the data set considered. There are signals in this list that are not available in the 145 main tidal frequencies of the literature. (4) Tide predictions using different lists of tidal frequencies on five different data sets around the world are compared. The prediction results using the first significant 50 constituents provided promising results on these locations of the world.