caa a22 4500 606166165 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10440-014-9979-8 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9979-8 Modulated Haar Wavelet Analysis of Climatic Background Noise [Elektronische Daten] [Zhihua Zhang, Palle Jorgensen] We model background noise in time series of climate data as AR(1) red noise. To extract significant features of these time series, we use comparisons of wavelet power spectrum time series with that of AR(1) red noise. We improve on earlier work which has so far only relied on empirical formulas for the distribution of AR(1) red noise in Morlet wavelet power spectrum; see Torrence and Compo (Bull. Am. Meteorol. Soc. 79:61-78, 1998). Although wavelet phase distributions do play an important role in analysis of causal relations in climate time series, up to now, the wavelet phase distribution of AR(1) red noise has not been rigorously established for wavelet transforms. In this paper, we derive the formulas for both the wavelet power spectrum distribution, and the wavelet phase distribution of modulated Haar wavelet background noise. We give rigorous proofs. Springer Science+Business Media Dordrecht, 2014 Climatic background noise nationallicence Wavelet power spectrum nationallicence Wavelet phase nationallicence Haar wavelet nationallicence Zhang Zhihua College of Global Change and Earth System Science, Beijing Normal University, 100875, Beijing, China aut Jorgensen Palle Department of Mathematics, University of Iowa, 52242, Iowa City, IA, USA aut Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 71-93 0167-8019 140:1<71 2015 140 10440 https://doi.org/10.1007/s10440-014-9979-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9979-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Zhihua College of Global Change and Earth System Science, Beijing Normal University, 100875, Beijing, China aut NATIONALLICENCE 700 1- Jorgensen Palle Department of Mathematics, University of Iowa, 52242, Iowa City, IA, USA aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 71-93 0167-8019 140:1<71 2015 140 10440