Exploring Complexity Measures for Analysis of Solar Wind Structures and Streams

TL;DR

This study applies information-theoretic and network-based measures to Wind/MFI solar wind time series across four structures (fast/slow streams, sheaths, magnetic clouds) to quantify fluctuations at multiple scales. It combines permutation-entropy-based Jensen-Shannon complexity with Fisher-Shannon information planes, using both permutation PDFs and HVG degree distributions, and augments with HVG-tail analyses via the exponential parameter $\lambda$. The results show that most solar wind fluctuations are stochastic, but magnetic clouds consistently display distinctive global structure (low entropy with higher complexity or higher FIM), especially in the magnetic-field magnitude, and that larger time lags improve type separation. Collectively, the methods provide a robust, complementary toolkit for identifying solar wind structures and shedding light on their origins and formation processes, with potential implications for space-weather interpretation.

Abstract

In this paper we use statistical complexity and information theory metrics to study structure within solar wind time series. We explore this using entropy-complexity and information planes, where the measure for entropy is formed using either permutation entropy or the degree distribution of a horizontal visibility graph (HVG). The entropy is then compared to the Jensen complexity (Jensen-Shannon complexity plane) and Fisher information measure (Fisher-Shannon information plane), formed both from permutations and the HVG approach. Additionally we characterise the solar wind time series by studying the properties of the HVG degree distribution. Four types of solar wind intervals have been analysed, namely fast streams, slow streams, magnetic clouds and sheath regions, all of which have distinct origins and interplanetary characteristics. Our results show that, overall, different metrics give similar results but Fisher-Shannon, which gives a more local measure of complexity, leads to a larger spread of values in the entropy-complexity plane. Magnetic cloud intervals stood out in all approaches, in particular when analysing the magnetic field magnitude. Differences between solar wind types (except for magnetic clouds) were typically more distinct for larger time lags, suggesting universality in fluctuations for small scales. The fluctuations within the solar wind time series were generally found to be stochastic, in agreement with previous studies. The use of information theory tools in the analysis of solar wind time series can help to identify structures and provide insight into their origin and formation.

Figures (10)

• Figure 1: The Jensen-Shannon complexity plane showing the placement of data points calculated for different solar wind types (fast, slow, sheath and magnetic cloud). The data points that are calculated for subsampling rate $r=300$ are surrounded by grey circles and those without the surrounding circle are calculated for $r=20$. The maximum and minimum curves are given for $r=300$.
• Figure 2: A zoom-in to the bottom right corner of the Jensen-Shannon complexity-entropy plane. The symbols and curves are the same as in Figure \ref{['Jensen_Shannon_figure']}.
• Figure 3: The Fisher-Shannon information plane. The solar wind events not marked with a grey circle have $r=20$, and those marked with the circle are calculated for $r=300$.
• Figure 4: A zoomed-in section of the Fisher-Shannon plane. The top dotted curve is the fBm curve with $r=300$, and the lower curve is the fBm curve with $r=300$.
• Figure 5: The Fisher-Shannon information plane formed from the HVG degree distribution.