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

Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWTMulti, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i. e. , resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWTMulti 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 CWTMulti and compare it to harmonic analysis programs NSTide and UTide. CWTMulti provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1, S 1, and P 1) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1) on water levels in the LCRE. CWTMulti also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWTMulti does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWTMulti, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWTMulti is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.