Improved significance testing of wavelet power spectrum near data boundaries as applied to polar research

ZHANG ZhiHua; & John C Moore

doi:10.3724/SP.J.1085.2011.00192

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RESEARCH-ARTICLE

Improved significance testing of wavelet power spectrum near data boundaries as applied to polar research

ZHANG ZhiHua Correspondence author

, 1, & John C Moore Correspondence author

, 2, 3, 4

Correspondence: zhangzh@bnu.edu.cn john.moore@bnu.edu.cn ORCID:

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Vol. 22, Issue 3, pp. 192-198 (2011) • DOI

First published at: Jan 25, 2011

Abstract

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Abstract

When one applies the wavelet transform to analyze finite-length time series, discontinuities at the data boundaries will distort its wavelet power spectrum in some regions which are defined as a wavelength-dependent cone of influence (COI). In the COI, significance tests are unreliable. At the same time, as many time series are short and noisy, the COI is a serious limitation in wavelet analysis of time series. In this paper, we will give a method to reduce boundary effects and discover significant frequencies in the COI. After that, we will apply our method to analyze Greenland winter temperature and Baltic sea ice. The new method makes use of line removal and odd extension of the time series. This causes the derivative of the series to be continuous (unlike the case for other padding methods). This will give the most reasonable padding methodology if the time series being analyzed has red noise characteristics.

Keywords

Wavelet power spectrum; significance testing; Greenland winter temperature; Baltic sea ice

Author Address:

1. College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China;
2. State Key Laboratory of Earth Surface Processes and Resource Ecology/College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China;;
3. Arctic Centre, University of Lapland, Rovaniemi, Finland;
4. Department of Earth Sciences, Uppsala University, Sweden

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