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

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 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.

Three-Dimensional Dynamic Variations of Ground/Air Surface Temperatures and Their Correlation with Large-Scale Circulation Indexes in Southwest China (1980–2019)

“…We considered only the influence of elevation, latitude, and longitude on temperature; therefore, the effects of geomorphology, slope direction, wind direction, wind speed, airflow, and other factors should be considered in future studies. Furthermore, although WTC can be used to detect correlation between two time series in the frequency domain, if one of the time series has varying skewness, the correlation in the temporal domain would be weak [84]. Many geophysical time series are nonlinear [84][85][86] and exhibit skewness and kurtosis; thus, it is important to determine whether such characteristics also exist in GST, SAT, and SATD time series.…”

“…Furthermore, although WTC can be used to detect correlation between two time series in the frequency domain, if one of the time series has varying skewness, the correlation in the temporal domain would be weak [84]. Many geophysical time series are nonlinear [84][85][86] and exhibit skewness and kurtosis; thus, it is important to determine whether such characteristics also exist in GST, SAT, and SATD time series. Moreover, owing to large errors in GST before 1980, we selected the higher quality GST data of 1980-2019 and revealed the WTC between GST, SAT, SATD, and the large-scale indexes for the period 1980-2019.…”