Articles | Volume 29, issue 1
Research article
10 Jan 2022
Research article |  | 10 Jan 2022

A waveform skewness index for measuring time series nonlinearity and its applications to the ENSO–Indian monsoon relationship

Justin Schulte, Frederick Policelli, and Benjamin Zaitchik

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Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Cited articles

An, S.-I.: A review of interdecadal changes in the nonlinearity of the El Nino–Southern Oscillation. Theor. Appl. Climatol., 97, 29–40,, 2009. 
An, S.-I and Jin, F.-F.: Nonlinearity and asymmetry of ENSO, J. Climate, 17, 2399–2412,<2399:NAAOE>2.0.CO;2, 2004. 
An, S.-L.: Interdecadal changes in the El Niño-La Niña symmetry, Geophys. Res. Lett., 31, L23210,, 2004. 
Ashok, K., Guan, Z., Saji, N. H., and Yamagata, T.: Individual and combined influences of ENSO and the Indian Ocean dipole on the Indian summer monsoon, J. Climate, 17, 3141–3155, 2004. 
Ashok, K., Guan, Z., and Yamagata, T.: Impact on the Indian Ocean dipole on the relationship between the Indian monsoon rainfall and ENSO, Geophys. Res. Lett., 28, 4499–4502, 2001. 
Short summary
The skewness of a time series is commonly used to quantify the extent to which positive (negative) deviations from the mean are larger than negative (positive) ones. However, in some cases, traditional skewness may not provide reliable information about time series skewness, motivating the development of a waveform skewness index in this paper. The waveform skewness index is used to show that changes in the relationship strength between climate time series could arise from changes in skewness.