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| Titel |
Significance tests for the wavelet cross spectrum and wavelet linear coherence |
| VerfasserIn |
Z. Ge |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
0992-7689
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| Digitales Dokument |
URL |
| Erschienen |
In: Annales Geophysicae ; 26, no. 12 ; Nr. 26, no. 12 (2008-12-02), S.3819-3829 |
| Datensatznummer |
250016312
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| Publikation (Nr.) |
 copernicus.org/angeo-26-3819-2008.pdf |
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| Zusammenfassung |
This work attempts to develop significance tests for the wavelet cross spectrum and the wavelet linear coherence
as a follow-up study on Ge (2007). Conventional approaches that are used by Torrence and Compo (1998) based on stationary
background noise time series were used here in estimating the sampling distributions of the wavelet cross spectrum
and the wavelet linear coherence. The sampling distributions are then
used for establishing significance levels for these two wavelet-based quantities. In addition to these two
wavelet quantities, properties of the phase angle of the wavelet cross spectrum of, or the phase difference
between, two Gaussian white noise series are discussed. It is found that the tangent of the principal part of the phase angle
approximately has a standard Cauchy distribution and the phase angle is uniformly distributed,
which makes it impossible to establish significance levels
for the phase angle. The simulated signals clearly show that, when there is no
linear relation between the two analysed signals, the phase angle disperses into
the entire range of [−π,π] with fairly high probabilities for values close to ±π to occur.
Conversely, when linear relations are present, the phase angle of the wavelet cross spectrum settles around an associated value
with considerably reduced fluctuations. When two signals are linearly coupled, their wavelet linear coherence
will attain values close to one. The significance test of the wavelet linear coherence can therefore be
used to complement the inspection of the phase angle of the wavelet cross spectrum.
The developed significance tests are also applied to actual data sets, simultaneously recorded wind speed and
wave elevation series measured from a NOAA buoy on Lake Michigan. Significance levels of the wavelet cross spectrum
and the wavelet linear coherence between the winds and the waves reasonably separated meaningful peaks from
those generated by randomness in the data set. As with simulated signals, nearly constant phase angles of
the wavelet cross spectrum are found to coincide with large values in the wavelet linear coherence between the winds
and the waves. Not limited to geophysics, the significance tests developed in the present work can also be applied
to many other quantitative studies using the continuous wavelet transform. |
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