Preprints
https://doi.org/10.5194/npg-2020-48
https://doi.org/10.5194/npg-2020-48

  17 Dec 2020

17 Dec 2020

Review status: this preprint is currently under review for the journal NPG.

A Waveform Skewness Index for Measuring Time Series Nonlinearity and its Applications to the ENSO-Indian Monsoon Relationship

Justin Schulte1, Frederick Policelli2, and Benjamin Zaitchik3 Justin Schulte et al.
  • 1Science Systems and Applications, Inc.
  • 2NASA Goddard Space Flight Center
  • 3Johns Hopkins University, Department of Earth and Planetary Sciences

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 to quantify 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 Monsson 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.

Justin Schulte et al.

 
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Justin Schulte et al.

Justin Schulte et al.

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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.