Minding the Gaps in Solar Wind Data

Spacecraft scattered throughout the solar system keep tabs on the solar wind, but the measurements are dotted with data gaps. How can scientists prevent these gaps from biasing their studies of the solar wind?

Sampling the Solar Wind

The solar wind is a tenuous, fast-moving, turbulent plasma that constantly streams out from the Sun. Studying the solar wind is important for understanding how potentially damaging space weather events like coronal mass ejections travel through the solar system. Solar wind studies also have far-reaching implications, since solar-wind-like plasmas exist throughout the universe, such as in the sparse medium between galaxies in a cluster.

Luckily, there are many spacecraft that sample the solar wind from various locations within our solar system. Unluckily, many of these spacecraft do not continuously monitor the solar wind. For example, when a spacecraft orbiting a planet dips into the planet’s atmosphere, this detour creates an hours-long gap in solar wind monitoring.

The Impact of Data Gaps

How do these data gaps affect studies of the solar wind? In a recent research article, Daniel Wrench and Tulasi Parashar (Victoria University of Wellington) approached this question in terms of how gaps affect the structure function: a mathematical description of how the solar wind fluctuates over different length or time scales.

Wrench and Parashar introduced random artificial gaps into data from the Parker Solar Probe, which monitors the solar wind continuously, and compared the structure functions calculated from the continuous and interrupted data sets. They used the difference between the true structure function — calculated from the continuous data set — and the structure functions from the artificially gapped data sets to develop a correction factor.

The team then tested their correction factor using data from the Wind spacecraft, which continuously monitors the solar wind from the L₁ Lagrange point. The team calculated the structure function from 1) the continuous data set, 2) the artificially gapped data, 3) the gapped data with linear interpolation used to fill the gaps, and 4) the gapped data with the correction factor applied. This test showed that the correction factor performs better than other commonly used gap-handling methods, such as linear interpolation, which can systematically underestimate the structure function. Using the correction factor, the error in the structure function remained below 50% even when 95% of the data were missing.

Correcting Voyager 1

Finally, the authors applied their validated method to data from Voyager 1. Data from the two Voyager spacecraft are extremely scientifically valuable — no other spacecraft have ventured as far from the Sun and can measure the solar wind at such large distances. The data are also extremely sparse; one segment used in this work was missing 85% of the data. This means that an effective method of correcting these data has potentially huge scientific significance.

Wrench and Parashar applied their correction factor to the Voyager 1 data, showing that this method handily removes artifacts while avoiding the underestimation introduced by linear interpolation. While the authors saved the interpretation of the newly corrected Voyager 1 data for future research, this study makes it clear that even large data gaps needn’t hinder studies of the solar wind.

Citation

“Debiasing Structure Function Estimates from Sparse Time Series of the Solar Wind: A Data-Driven Approach,” Daniel Wrench and Tulasi N. Parashar 2025 ApJ 987 28. doi:10.3847/1538-4357/addc6a