An Introduction to Wavelet Transform Tidal Analysis Methods

Continuous wavelet transforms (CWTs) provide an approach to understanding the numerous tidal phenomena that deviate markedly from an assumed statistical stationarity or exact periodicity inherent in traditional tidal methods. Use of wavelets allows determination of the degree of non-stationarity present in time series, such as estuarine and shelf currents, usually treated as stationary. Wavelets also provide a consistent analysis of tidal and non-tidal variance, a feature often essential for dynamical analyses of non-stationary tides. We summarize basic notions of the wavelet transform, also known as a perfect reconstruction filter bank or a multire solution analysis, contrast them with those of harmonic analysis and Fourier transforms, construct a continuous wavelet transform basis with a scale selection especially adapted to tidal problems, describe possibilities for analysis of scalar and vector quantities, define a criterion for knowledge of independence of process between adjoining scales, and illustrate use of wavelet tools with several examples. In contrast to the nearly periodic barotropic tide typical of coastal stations, this paper analyses processes that are in part tidally driven but non-stationary, e.g. baroclinic tidal currents, river tides, continental shelf internal tides, and some kinds of biological activity in the coastal ocean. In all cases, wavelet analysis provides a consistent, linear analysis of tidal and non-tidal variance and reveals features that harmonic analysis on a Fourier transform approach could not elucidate.