Tidal Analysis Using Time-Frequency Signal Processing and Information Clustering

Geophysical time series have a complex nature that poses challenges to reaching assertive conclusions, and require advanced mathematical and computational tools to unravel embedded information. In this paper, time-frequency methods and hierarchical clustering (HC) techniques are combined for processing and visualizing tidal information. In a first phase, the raw data are pre-processed for estimating missing values and obtaining dimensionless reliable time series. In a second phase, the Jensen-Shannon divergence is adopted for measuring dissimilarities between data collected at several stations. The signals are compared in the frequency and time-frequency domains, and the HC is applied to visualize hidden relationships. In a third phase, the long-range behavior of tides is studied by means of power law functions. Numerical examples demonstrate the effectiveness of the approach when dealing with a large volume of real-world data.