A comparison of methods for analysis of tidal records containing multi-scale non-tidal background energy

Abstract

Many tidal phenomena, including river tides, estuarine currents, and shelf and fjord internal tides, are non-stationary. These tidal processes are poorly understood and largely beyond the realm of practical prediction, even when the perturbing phenomenon causing the non-stationary behavior is itself fairly predictable. Our inadequate understanding of these phenomena has been exacerbated by an absence of a self-consistent procedure for analysis of the entire spectrum of non-stationary motions, tidal and non-tidal. The most difficult methodological situation occurs when the disturbing non-tidal signal is stronger than the tidal one and has an event-like character. Such sharp changes in forcing are multi-scale, containing energy at tidal frequencies, as well as at larger sales. Because of the distinct response of different parts of the tidal spectrum to non-tidal perturbations, multi-scale forcing events have the potential to provide a valuable new generation of tests of tidal dynamics models. This paper compares three techniques for the analysis of such signals, using artificial tidal records of known frequency content to ascertain which method most accurately represents evolving frequency content. The methods are: (a) conventional least-squares, short-term harmonic analysis (STHA); (b) a modified STHA (or mSTHA) that uses a smoothing window and augments the frequency structure of the analysis wave; and (c) linear convolution analysis in the form of continuous wavelet transforms (CWT). Results show that STHA and mSTHA lack a definable frequency response and mix energy between tidal and non-tidal signals in an unpredictable manner. STHA also effectively imposes a boxcar window on the data, the effects of which can be serve for short records. In general, STHA and mSTHA results using short windows will be least reliable in the circumstances where short windows are most desired—when the signal is highly non-stationary. There is, moreover, no simple way to set a minimum window length for STHA/mSTHA that will produce stable results, except to make the window too long to capture the fluctuating variance being sought. In contrast, CWT correctly recovers both tidal and non-tidal variance, as long as resolution limits set by the Heisenberg uncertainty principle are respected. Whatever method is chosen, use of window lengths less than ∼4–6 d requires great care, unless diurnal and subtidal energy are insignificant.