Temporal Structure of the Southern Oscillation as Revealed by Waveform and Wavelet Analysis

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Abstract
Wavelet transforms (WLT) and waveform transforms (WFT) are effective tools that reveal temporal structure of nonstationary time series. The authors discuss principles and practical aspects of their geophysical applications. The WLT can display variance as a continuous function of time and frequency, but the frequency (time) locality reduces at the high (low) frequency bands. The WFT, on the other hand, provides a sharp view of the locality in both time and frequency, but presents variance by discrete base functions. The two techniques are complementary. The authors use both Morlet WLT and Gabor WFT to analyze temporal structure of the Southern Oscillation (50). The principal period of the SO has experienced two rapid changes since 1872, one in the early 1910s and the other in the mid-1960s. The dominant period was 3–4 years in the earliest four decades (1872–1910), 5–7 years in the ensuing five decades (1911–1960. except the 1920s), and about 5 years in the last two decades (1970–1992). Ale SO al... Abstract Wavelet transforms (WLT) and waveform transforms (WFT) are effective tools that reveal temporal structure of nonstationary time series. The authors discuss principles and practical aspects of their geophysical applications. The WLT can display variance as a continuous function of time and frequency, but the frequency (time) locality reduces at the high (low) frequency bands. The WFT, on the other hand, provides a sharp view of the locality in both time and frequency, but presents variance by discrete base functions. The two techniques are complementary. The authors use both Morlet WLT and Gabor WFT to analyze temporal structure of the Southern Oscillation (50). The principal period of the SO has experienced two rapid changes since 1872, one in the early 1910s and the other in the mid-1960s. The dominant period was 3–4 years in the earliest four decades (1872–1910), 5–7 years in the ensuing five decades (1911–1960. except the 1920s), and about 5 years in the last two decades (1970–1992). Ale SO al...

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