Abstract
Abstract. Many geophysical time series possess nonlinear characteristics that reflect the underlying physics of the phenomena the time series describe. The nonlinear character of times series can change with time, so it is important to quantify time series nonlinearity without assuming stationarity. A common way of quantifying the time evolution of time series nonlinearity is to compute sliding skewness time series, but it is shown here that such an approach can be misleading when time series contain periodicities. To remedy this deficiency of skewness, a new waveform skewness index is proposed for quantifying local nonlinearities embedded in time series. A waveform skewness spectrum is proposed for determining the frequency components that are contributing to time series waveform skewness. The new methods are applied to the El Niño–Southern Oscillation (ENSO) and the Indian monsoon to test a recently proposed hypothesis that states that changes in the ENSO–Indian monsoon relationship are related to ENSO nonlinearity. We show that the ENSO–Indian rainfall relationship weakens during time periods of high ENSO waveform skewness. The results from two different analyses suggest that the breakdown of the ENSO–Indian monsoon relationship during time periods of high ENSO waveform skewness is related to the more frequent occurrence of strong central Pacific El Niño events, supporting arguments that changes in the ENSO–Indian rainfall relationship are not solely related to noise.
Highlights
Many geophysical time series such as the solar cycle (Rusu, 2007), Quasi-biennial Oscillation (QBO; Hamilton and Hsieh, 2002; Lu et al, 2009), and El Niño–Southern Oscillation (ENSO; Timmermann, 2003) are nonlinear
In the case of ENSO, the tendency for El Niño events to be stronger than La Niña events (i.e., ENSO asymmetry) is related to the propagation characteristics of equatorial Pacific SST anomalies and nonlinear dynamical heating (NDH; An and Jin, 2004; Santoso et al, 2013), where strong El Niño events are associated with eastward-propagating SST anomalies and enhanced NDH
The above experiment shows that phase synchronization among frequency modes produces positive waveform skewness. In another example shown in the Supplement, we showed that large waveform skewness can arise if there is covariance between amplitude and phase, a finding consistent with how nonlinearity can arise from such covariance (Pires and Hannachi, 2021)
Summary
Many geophysical time series such as the solar cycle (Rusu, 2007), Quasi-biennial Oscillation (QBO; Hamilton and Hsieh, 2002; Lu et al, 2009), and El Niño–Southern Oscillation (ENSO; Timmermann, 2003) are nonlinear. The second caveat is that the index can only be applied to ENSO and not to arbitrary geophysical time series Given these deficiencies, there is a clear need to construct a quantity that can measure the skewness of individual time series events regardless of the chosen study topic. There is a clear need to construct a quantity that can measure the skewness of individual time series events regardless of the chosen study topic Another approach to quantifying time series nonlinearity is Fourier or wavelet-based higher-order spectral analysis. They found that interacting Fourier components of the Niño 3.4 index on typical ENSO timescales of 2 to 7 years contribute to the overall skewness of the Niño 3.4 index While these approaches can quantify time series nonlinearity, they cannot measure the nonlinearity of individual time series events like the other methods mentioned above. An early (JJ) monsoon season and late monsoon (August–September) season time series were constructed in the same way as they were created for the ENSO time series
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