An Introduction to Wavelet Analysis in Oceanography and Meteorology: With Application to the Dispersion of Yanai Waves

TLDR

Wavelet analysis provides instantaneous amplitude and phase estimates for each harmonic, offering a local, time‑ or space‑dependent alternative to Fourier’s average‑amplitude approach. The study aims to use wavelet analysis to investigate nonstationary signal characteristics and to demonstrate its utility by examining Yanai wave dispersion in a reduced‑gravity equatorial model. The authors apply the wavelet transform to Yanai wave data, compare preprocessing methods, and measure group velocity across wavenumbers by tracking the transform’s temporal evolution. The measured group velocity matches linear theory at high wavenumbers but is reduced at low wavenumbers, likely due to basin‑boundary interactions.

Abstract

Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an “instantaneous” estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumber, possibly due to interaction with the basin boundaries.