Implementing Super-Resolution of Non-Stationary Tides with Wavelets: An Introduction to CWT_Multi

Abstract

Abstract Tides are often non-stationary due to non-astronomical influences. Investigating variable tidal properties implies a tradeoff between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a Matlab code that: a) uses CWT linearity (via the “Response Coefficient Method”) to implement super-resolution (Munk and Hasselman 1964); b) provides a Munk-Hasselman constituent-selection criterion; and c) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time-scales of days and multiple constituents per species with fortnightly filters. It outputs astronomical phase-lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s) and reconstruction(s), confidence limits, and signal-to-noise ratios. Artificial data and water-levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time-resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K1, S1, and P1) on fortnightly time scales, quantifying impacts of diel power-peaking (with a 24-hour period, like S1) on water levels in the LCRE. CWT_Multi also helps quantify impacts of high flows and a salt-barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to non-stationary data.