De-Biasing Structure Function Estimates From Sparse Time Series of the Solar Wind: A Data-Driven Approach

TL;DR

This paper develops a data-driven correction method for structure function estimates from sparse solar wind time series, improving analysis accuracy of turbulence properties in fragmented datasets from spacecraft observations.

Contribution

It introduces an empirical correction factor learned from data to de-bias structure function estimates affected by gaps, applicable across different solar wind regimes.

Findings

The correction reduces errors in structure function estimates for missing data fractions over 25%.

Application to Voyager data yields spectral indices consistent with previous research.

The method generalizes well to various spacecraft datasets and astrophysical time series.

Abstract

Structure functions, which represent the moments of the increments of a stochastic process, are essential complementary statistics to power spectra for analysing the self-similar behaviour of a time series. However, many real-world environmental datasets, such as those collected by spacecraft monitoring the solar wind, contain gaps, which inevitably corrupt the statistics. The nature of this corruption for structure functions remains poorly understood - indeed, often overlooked. Here we simulate gaps in a large set of magnetic field intervals from Parker Solar Probe in order to characterize the behaviour of the structure function of a sparse time series of solar wind turbulence. We quantify the resultant error with regards to the overall shape of the structure function, and its slope in the inertial range. Noting the consistent underestimation of the true curve when using linear interpolation, we demonstrate the ability of an empirical correction factor to de-bias these estimates. This correction, "learnt" from the data from a single spacecraft, is shown to generalize well to data from a solar wind regime elsewhere in the heliosphere, producing smaller errors, on average, for missing fractions >25%. Given this success, we apply the correction to gap-affected Voyager intervals from the inner heliosheath and local interstellar medium, obtaining spectral indices similar to those from previous studies. This work provides a tool for future studies of fragmented solar wind time series, such as those from Voyager, MAVEN, and OMNI, as well as sparsely-sampled astrophysical and geophysical processes more generally.