Estimating intermittency significance by means of surrogate data: implications for stationarity

Intermittency is a property of turbulent astrophysical plasmas, such as the solar wind, that implies non-uniformity in the transfer rate of energy carried by non-linear structures from large to small scales. We evaluate the intermittency level of the turbulent magnetic field measured by the Parker Solar Probe in the slow solar wind in the proximity of the Sun, at about 0.17 AU, during the probe’s first encounter. A quantitative measure of the intermittency of a time-series can be deduced based on the normalized forth order moment of the probability distribution functions, the flatness parameter. We observe that when dividing the data into contiguous samples of various lengths, from three to twenty-four hours, flatness differs significantly from sample to sample, suggestive of alternating intermittency-free time intervals with highly intermittent samples. In order to describe this variability, we apply an elaborate statistical test tailored to identify nonlinear dynamics in a time series which involves the construction of surrogate data that eliminate all nonlinear correlations contained in the dynamics of the signal but are otherwise consistent with an “underlying” linear process, i.e. the null hypothesis that we want to falsify. If a discriminating statistic for the original signal, such as the flatness parameter, is found to be significantly different than that of the ensemble of surrogates, then the null hypothesis is not valid, and we can conclude that the computed flatness reliably reflects the intermittency level of the underlying non-linear processes. We determine that non-stationarity of the time-series strongly influences the flatness of both the data and surrogates and the null hypothesis cannot be falsified. The intermittency level detected in such cases reflects the effects of isolated and, maybe, statistically not meaningful events, consequently, we stress upon the importance of careful data selection and evaluating the significance of the evaluated discriminating statistic.