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Geometric and Topological Approaches to Significance Testing in Wavelet Analysis : Volume 22, Issue 2 (10/03/2015)

By Schulte, J. A.

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Book Id: WPLBN0004017156
Format Type: PDF Article :
File Size: Pages 18
Reproduction Date: 2015

Title: Geometric and Topological Approaches to Significance Testing in Wavelet Analysis : Volume 22, Issue 2 (10/03/2015)  
Author: Schulte, J. A.
Volume: Vol. 22, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Duffy, C., Najjar, R. G., & Schulte, J. A. (2015). Geometric and Topological Approaches to Significance Testing in Wavelet Analysis : Volume 22, Issue 2 (10/03/2015). Retrieved from

Description: Department of Meteorology, Pennsylvania State University, University Park, Pennsylvania, USA. 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.

Geometric and topological approaches to significance testing in wavelet analysis

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