New Zealand Statistical Association 2024 Conference

Daniel Wrench

Victoria University of Wellington

Poster display: Quantifying the effect of data gaps on structure functions of turbulent time series: are the biases remediable?

This is joint work with Tulasi Parashar

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 characterise 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 generalise well to data from a solar wind regime elsewhere in the heliosphere. Given this success, we apply the correction to 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 analysis of future studies of fragmented solar wind time series, as well as sparsely-sampled astrophysical and geophysical processes more generally.