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

Many tidal phenomena, including river tides, estuarine currents, and shelf and fjord internal tides, are non-stationary. These tidal processes are poo rly understood and largely beyond the realm of practical prediction, even w hen the perturbing phenomenon causing the non-stationary behavior is itself fairly predictable. Our inadequate understanding of these phenomena has be en exacerbated by an absence of a self-consistent procedure for analysis of the entire spectrum of non-stationary motions, tidal and non-tidal. The mo st 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 frequ encies, as well as at larger sales. Because of the distinct response of dif ferent parts of the tidal spectrum to non-tidal perturbations, multi-scale forcing events have the potential to provide a valuable new generation of t ests of tidal dynamics models. This paper compares three techniques for the analysis of such signals, using artificial tidal records of known frequenc y content to ascertain which method most accurately represents evolving fre quency content. The methods are: (a) conventional least-squares, short-term harmonic analysis (STHA); (b) a modified STHA (or mSTHA) that uses a smoot hing window and augments the frequency structure of the analysis wave; and (c) linear convolution analysis in the form of continuous wavelet transform s (CWT). Results show that STHA and mSTHA lack a definable frequency respon se and mix energy between tidal and non-tidal signals in an unpredictable m anner. STHA also effectively imposes a boxcar window on the data, the effec ts of which can be serve for short records. In general, STHA and mSTHA resu lts using short windows will be least reliable in the circumstances where s hort windows are most desired-when the signal is highly non-stationary. The re is, moreover, no simple way to set a minimum window length for STHA/mSTH A that will produce stable results, except to make the window too long to c apture the fluctuating variance being sought. In contrast, CWT correctly re covers both tidal and non-tidal variance, as long as resolution limits set by the Heisenberg uncertainty principle are respected. Whatever method is c hosen. use of window lengths less than similar to 4-6 d requires great carl , unless diurnal and subtidal energy are insignifcant. (C) 1999 Elsevier Sc ience Ltd. All rights reserved.