Disentangling Nonlinear and Nonstationary River-Tide Dynamics with CWT_Multi

That tides are nonlinear and non-stationary is both a source of dynamical understanding and a methodological challenge. The spacing of some major tidal frequencies is only 1-2 cy yr^-1, coastal processes have time scales of days to weeks, and non-astronomical frequencies are introduced by nontidal forcing and nonlinear interactions. Thus, it is difficult to extract detailed frequency content on the relevant time-scales. What is needed is a systematic way to cheat the Heisenberg uncertainty principle, which provides an apparent limit on simultaneous time-frequency resolution for wave processes. This can be done if the tidal frequencies are known, and this knowledge is systematically used. We here examine river-tides, perhaps the best understood non-stationary tidal process, using a new wavelet tidal analysis tool, CWT_Multi. CWT_Multi uses wavelet filter linearity, the astronomical tidal potential, and wavelet filters of about 1 and 6 mo length at each frequency. Constituent ratios from the 6-mo analyses are applied to the 1-mo filters (dynamical inference) to disentangle tidal constituents separated by 1-2 cy/yr on the 1-mo time scale. Energy levels at the red end of the tidal spectrum and amplitude ratio between the 1 and 6-mo filters are used to determine which constituents are valid. CWT_Multi has been validated using artificial data, by comparison to other tidal analysis tools, and by comparisons between stations. Applied to river-tides, it is evident that M2 responds more strongly to river flow variations than other constituents in the D2 band, and that river flow modulates O1-K1-M2 triad interactions. Given the characteristics of the 1-mo filters, CWT_Multi’s effective time resolution is 15 d, not rapid enough to capture all flow-induced variability, but still much better than suggested by the Heisenberg principle or provided by other tidal analysis tools. CWT_Multi will fail if frequencies are strongly Doppler shifted (Heisenberg’s revenge).