Since standard statistical techniques generally assume that time series are stationary, identification of intermittent phenomena is challenging. Methods such as wavelets may be used to provide tools for analyzing nonstationary signals, but interpretation of the resulting pictures is difficult unless signal-to-noise ratios are large and the phenomenology is well understood. To address these issues, the authors earlier developed the Coherent Structure Detector (CSD). This technique clearly defines an incoherent signal, and provides a statistically rigorous detection algorithm for coherent structures. The CSD is intended to detect single events in relatively short time series.
In this paper, we address the issue of estimating intermittency rates of localized phenomena using wavelets. The statistical problem is different than detecting single events, in which the false alarm rate must be controlled for the entire time series. Our new statistical technique controls the false alarm rate for each scale at each time sample, thereby controlling the total false alarm intermittency rate. This is done with a scale-dependent threshold for the wavelet coefficients, which allows two conclusions: that a signal contains intermittent localized phenomena, and that these phenomena are localized to specific time intervals in the signal. The algorithm is statistically rigorous and appropriate for long time series. Intermittent turbulence in near-ground wind fields is examined using the new approach.