A practical guide to wavelet analysis
Bulletin of the American Meteorological Society, 79 (1):
61--78 (January 1998)Abstract
A practical step-by-step guide to wavelet analysis is given, with
examples taken from time series of the El Nino-Southern Oscillation
(ENSO). The guide includes a comparison to the windowed Fourier transform,
the choice of an appropriate wavelet basis function, edge effects
due to finite-length time series, and the relationship between wavelet
scale and Fourier frequency. New statistical significance tests for
wavelet power spectra are developed by deriving theoretical wavelet
spectra for white and red noise processes and using these to establish
significance levels and confidence intervals. It is shown that smoothing
in time or scale can be used to increase the confidence of the wavelet
spectrum. Empirical formulas are given for the effect of smoothing
on significance levels and confidence intervals. Extensions to wavelet
analysis such as filtering, the power Hovmoller, cross-wavelet spectra,
and coherence are described. The statistical significance tests are
used to give a quantitative measure of changes in ENSO variance on
interdecadal timescales. Using new datasets that extend back to 1871,
the Nino3 sea surface temperature and the Southern Oscillation index
show significantly higher power during 1880-1920 and 1960-90, and
lower power during 1920-60, as well as a possible 15-yr modulation
of variance. The power Hovmoller of sea level pressure shows significant
variations in 2-8-yr wavelet power in both longitude and time.
