Unmixing: A new direction from classical tidal harmonic analysis?

Abstract

Harmonic analysis has been the conventional method for tidal prediction where seven (or more) most important constituents/harmonics are modeled and separately predicted whose aggregates have shown to be able to accurately reconstruct the observed tidal data. However, harmonic analysis also has its potential drawbacks. First, it can only accurately predict the astronomical tide. Non-sinusoidal fluctuations over time scales on the order of hours have been observed but cannot be reconstructed through harmonic analysis. Second, local astronomical tides are best predicted when based on data collected for at least 18.6 years, which is rather a rigid requirement at places without such long period observation data. Third, for tides along a complex coastline, more than 100 components must be considered in order to predict accurately. Finally, it has been shown that harmonic analysis is not effective in extreme weather conditions, e.g., those with tropical storms. In this paper, we propose a deviation from conventional tidal analysis approaches and investigate into the problem from the perspective of “signal unmixing”, where we interpret the observed data as a linear combination of constituents and apply robust unsupervised unmixing algorithm, referred to as the minimum-volume-constrained nonnegative matrix factorization (MVC-NMF), to decompose the observation into a set of source signals (i.e., the harmonics). The unmixing-based tidal analysis is fundamentally different from harmonic-based analyses by not limiting itself to just astronomical tide, and being unsupervised thus not requiring long-term training. Preliminary experiments are conducted to study the feasibility of the proposed approach for tidal analysis.