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

作　　者：ZHANG ZhiHua John C Moore 

机构地区：[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

出　　处：《Advances in Polar Science》2011年第3期192-198,共7页极地科学进展（英文版）

基　　金：partially supported by the National Key Science Program for Global Change Research (Grant no.2010CB950504);the National High-Technology Research & Development Program of China (863 Program,Grant no.2010AA012305);the National Natural Science Foundation of China(Grant no.41076125);the Fundamental Research Funds for the Central Universities (Key Program);the Polar Climate and Environment Key Laboratory

摘　　要：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.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.

关 键 词：Wavelet power spectrum significance testing Greenland winter temperature Baltic sea ice 

分 类 号：O211.61[理学—概率论与数理统计] TN959.1[理学—数学]