An introduction to wavelet transform tidal analysis methods

Continuous wavelet transforms (CWTs) provide an approach to understanding t he numerous tidal phenomena that deviate markedly from an assumed statistic al stationarity or exact periodicity inherent in traditional tidal methods. Use of wavelets allows determination of the degree of non-stationarity pre sent 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-st ationary tides. We summarize basic notions of the wavelet transform, also k nown as a perfect reconstruction filter bank or a multire solution analysis , contrast them with those of harmonic analysis and Fourier transforms, con struct a continuous wavelet transform basis with a scale selection especial ly 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 typic al of coastal stations, this paper analyses processes that are in part tida lly 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, l inear analysis of tidal and non-tidal variance and reveals features that ha rmonic analysis on a Fourier transform approach could not elucidate. (C) 20 00 Academic Press.