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.

中文翻译：

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测量时间序列非线性的波形偏度指数及其在ENSO-印度季风关系中的应用

摘要。许多地球物理时间序列具有非线性特征，这些特征反映了时间序列描述的现象的基本物理性质。时间序列的非线性特性会随时间变化，因此在不假设平稳性的情况下量化时间序列的非线性非常重要。量化时间序列非线性时间演化的一种常用方法是计算滑动偏斜时间序列，但此处显示，当时间序列包含周期性时，这种方法可能会产生误导。为了弥补这种偏度的不足，提出了一种新的波形偏度指数，用于量化嵌入在时间序列中的局部非线性。提出了波形偏斜度频谱，用于确定有助于时序波形偏斜度的频率分量。将该新方法应用于厄尔尼诺/南方涛动（ENSO）和印度季风，以检验最近提出的假设，该假设指出ENSO-印度蒙松关系的变化与ENSO非线性有关。我们表明，在高ENSO波形偏斜期间，ENSO-印度降水关系减弱。两种不同分析的结果表明，在高ENSO波形偏斜时间段内ENSO-印度季风关系的破裂与强太平洋中部厄尔尼诺事件的频繁发生有关，支持了ENSO-印度降雨变化的论点关系不仅与噪音有关。我们表明，在高ENSO波形偏斜期间，ENSO-印度降水关系减弱。两种不同分析的结果表明，在高ENSO波形偏斜时间段内ENSO-印度季风关系的破裂与强太平洋中部厄尔尼诺事件的频繁发生有关，支持了ENSO-印度降雨变化的论点关系不仅与噪音有关。我们表明，在高ENSO波形偏斜期间，ENSO-印度降水关系减弱。两种不同分析的结果表明，在高ENSO波形偏斜时间段内ENSO-印度季风关系的破裂与强太平洋中部厄尔尼诺事件的频繁发生有关，支持了ENSO-印度降雨变化的论点关系不仅与噪音有关。