ON NONLINEAR-ANALYSIS OF TIDAL OBSERVATIONS

Synthetic series, denoting a simple tidal record, and 1 year of real sea level record of Ingeniero White, Argentina (38-degrees 47'S, 62-degrees 16'W) are analyzed by classical methods of time series analysis, with adequate linear spectral estimators and by methods of bispectral analysis. The tidal synthetic series is used to verify, in a simple way, the accuracy of the methodology to assess the nonlinear spectral energy. It is shown that classical spectral estimators fail to differentiate linear from non-linear energy. The proposed methodology estimates the linear and non-linear constituents separately. This is done by using Capon or Pisarenko's spectral predictors and subtracting them (the linear spectra) from the total spectra obtained via Fast Fourier Transform (FFT). The use of bispectral estimators, on the other hand, allows the identification of the non-linear interactions. The application of the bispectral analysis in the identification of non-linear constituents is made by studying the bispectra of the seasonal sea level data. Results show that maximum non-linear energy due to second order interactions occurs in the terdiurnal bands among all seasons. Three main groups of non-linear tidal interactions can be identified: the low frequency group, including the mean sea level and the diurnal bands, the mean frequency group that include the semidiurnal and the terdiurnal bands, and the high frequency group that embraces the fourth diurnal and the higher order bands. The most common non-linear tidal constituent interactions occur among themselves, producing non-linear tidal constituents with frequency double of the original periodicities. The mean sea level shows significant non-linear tidal energy, also a link with different tidal bands.