Super-Resolution of Non-Stationary Tides using Wavelets: Introduction to the CWT_Multi Code

Published In

Journal of Atmospheric and Oceanic Technology

Document Type

Citation

Publication Date

2023

Abstract

Tides are often non-stationary on multiple time-scales due to non-linear dynamical interactions. Investigating these interactions requires a tradeoff between separation of tidal constituents (long analysis windows) and resolution of time variations (short windows). Previous continuous wavelet transform (CWT) tidal methods have resolved only tidal species. Here, we introduce a Matlab code (CWT_Multi) that implements super-resolution (Munk & Hasselman, 1964) using the linearity and known frequency response of CWTs (the response coefficient method) and introduces a modified Munk-Hasselman constituent selection criterion. Our code separates species on a time scale of a few days, and three constituents per species on a fortnightly time-scale. It outputs absolute phases and admittances (relative to astronomical potential and/or a reference station). CWT_Multi 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-level records from the Columbia River Estuary and San Francisco Bay are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and Utide. The window length needed to resolve three constituents per tidal species is shorter using CWT_Multi than with Utide, with equivalent or superior precision. NS_Tide resolves more constituents (with lower time resolution), and is better for prediction. Overall, CWT_Multi improves resolution of major tidal constituents, and is particularly useful for reconstruction, detiding, and dynamical analyses. It improves tidal inference by using time-varying data properties rather than user-chosen constituent ratios; this dynamical inference allows closely spaced constituents (e.g., K1 and P1) to be separated on fortnightly time scales.

Persistent Identifier

https://archives.pdx.edu/ds/psu/40796

Share

COinS