Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi

Journal Article · Tue Oct 01 00:00:00 EDT 2024 · Journal of Atmospheric and Oceanic Technology

DOI:https://doi.org/10.1175/JTECH-D-23-0144.1· OSTI ID:2472670

Lobo, Matthew ^[1]; Jay, David A. ^[2]; Innocenti, Silvia ^[3]; Talke, Stefan A. ^[4]; Dykstra, Steven L. ^[5]; Matte, Pascal ^[3]

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1. a Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, New Jersey, b Department of Civil and Environmental Engineering, Portland State University, Portland, Oregon
2. b Department of Civil and Environmental Engineering, Portland State University, Portland, Oregon
3. c Environment and Climate Change Canada, Meteorological Research Division, Québec City, Québec, Canada
4. d Civil and Environmental Engineering, California Polytechnic State University, San Luis Obispo, California
5. e School of the Earth, Ocean and Environment, University of South Carolina, Columbia, South Carolina, f College of Fisheries and Ocean Science, University of Alaska Fairbanks, Fairbanks, Alaska

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 CWT_Multi, 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. 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 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. CWT_Multi also helps quantify the 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 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, CWT_Multi, 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. CWT_Multi 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.

• Sponsoring Organization: USDOE
• OSTI ID: 2472670
• Journal Information: Journal of Atmospheric and Oceanic Technology, Journal Name: Journal of Atmospheric and Oceanic Technology Journal Issue: 10 Vol. 41; ISSN 0739-0572
• Publisher: American Meteorological Society
• Country of Publication: United States
• Language: English