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| Titel |
Geometric and topological approaches to significance testing in wavelet analysis |
| VerfasserIn |
J. A. Schulte, C. Duffy, R. G. Najjar |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 22, no. 2 ; Nr. 22, no. 2 (2015-03-10), S.139-156 |
| Datensatznummer |
250120969
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| Publikation (Nr.) |
 copernicus.org/npg-22-139-2015.pdf |
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| Zusammenfassung |
| Geometric and topological methods are applied to significance testing in the
wavelet domain. A geometric test was developed for assigning significance to
pointwise significance patches in local wavelet spectra, i.e., contiguous regions
of significant wavelet power coefficients with respect to some noise model.
This geometric significance test was found to produce results similar to an
existing areawise significance test while being more computationally
flexible and efficient. The geometric significance test can be readily
applied to pointwise significance patches at various pointwise significance
levels in wavelet power and coherence spectra. The geometric test determined
that features in wavelet power of the North Atlantic Oscillation (NAO) are
indistinguishable from a red-noise background, suggesting that the NAO is a
stochastic, unpredictable process, which could render difficult the future
projections of the NAO under a changing global system. The geometric test
did, however, identify features in the wavelet power spectrum of an El
Niño index (Niño 3.4) as distinguishable from a red-noise
background. A topological analysis of pointwise significance patches
determined that holes, deficits in pointwise significance embedded in
significance patches, are capable of identifying important structures, some
of which are undetected by the geometric and areawise tests. The application
of the topological methods to ideal time series and to the time series of
the Niño 3.4 and NAO indices showed that the areawise and geometric
tests perform similarly in ideal and geophysical settings, while the
topological methods showed that the Niño 3.4 time series contains
numerous phase-coherent oscillations that could be interacting nonlinearly. |
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