Debiasing Structure Function Estimates from Sparse Time Series of the Solar Wind: A Data-driven Approach - Daniel Wrench; Tulasi N. Parashar (The Astrophysical Journal, 2025)
Structure functions (SFs), which quantify the moments of increments of a stochastic process, are essential complementary statistics to power spectra for analyzing the self-similar behavior of a time series. However, many real-world data sets, such as those from spacecraft monitoring the solar wind, contain gaps, which inevitably corrupt the statistics. The nature of this corruption for SFs remains poorly understood—indeed, often overlooked. In this study, we simulate gaps in a large set of Parker Solar Probe magnetic field intervals to characterize how missing data affect SFs of solar wind turbulence. We find that linear interpolation systematically underestimates the true SF, and we introduce a simple, empirically derived correction factor to address this bias. Learned from data from a single spacecraft, the correction generalizes well to solar wind measured elsewhere in the heliosphere. Compared to conventional gap-handling methods, our approach reduces the mean error for missing data fractions above 20%, and the overall error is reduced by nearly 50% when averaged across all missing fractions tested. We apply the correction to Voyager intervals from the inner heliosheath and local interstellar medium (60%–85% missing) and recover spectral indices consistent with previous studies. The correction factor is released as an open-source Python package, enabling more accurate analysis of scaling in gapped solar wind data sets.