Applications of Information Theory in Solar and Space Physics

Abstract

Characterizing and modeling processes at the sun and space plasma in our solar system are difficult because the underlying physics is often complex, nonlinear, and not well understood. The drivers of a system are often nonlinearly correlated with one another, which makes it a challenge to understand the relative effects caused by each driver. However, entropy-based information theory can be a valuable tool that can be used to determine the information flow among various parameters, causalities, untangle the drivers, and provide observational constraints that can help guide the development of the theories and physics-based models. We review two examples of the applications of the information theoretic tools at the Sun and near-Earth space environment. In the first example, the solar wind drivers of radiation belt electrons are investigated using mutual information (MI), conditional mutual information (CMI), and transfer entropy (TE). As previously reported, radiation belt electron flux (Je) is anticorrelated with solar wind density (nsw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed mainly to the Je(t + 2 days) correlation with solar wind velocity (Vsw)(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time <24 h, suggesting that the loss mechanism due to nsw or solar wind dynamic pressure has to start operating in <24 h. Nonstationarity in the system dynamics is investigated using windowed TE. The triangle distribution in Je(t + 2 days) vs. Vsw(t) can be better understood with TE. In the second example, the previously identified causal parameters of the solar cycle in the Babcock–Leighton type model such as the solar polar field, meridional flow, polar faculae (proxy for polar field), and flux emergence are investigated using TE. The transfer of information from the polar field to the sunspot number (SSN) peaks at lag times of 3–4 years. Both the flux emergence and the meridional flow contribute to the polar field, but at different time scales. The polar fields from at least the last 3 cycles contain information about SSN.

Systematic Analysis of Machine Learning and Feature Selection Techniques for Prediction of the Kp Index

“…There are several ways in which this can be done, and this is currently an active area of research (Ali et al, ; Gao et al, ; Jiang & Wang, , e.g.). One way is to bin variables uniformly using bins of a predefined size for each variable (e.g.,Wing et al, ; Wing & Johnson, ). Sturges () proposed that the optimal bin size for a normal distribution is and bin width w = range / n b , where n is the total number of measurements in the data set and range is the maximum‐minimum value of a variable.…”

“…A more detailed description of MI and other concepts of information theory and their application in space physics can be found in Wing and Johnson (). Below, two methods based on the MI that are used in this work are described.…”

Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

“…, M, are assumed to be equal its mean value (ϕ i ) = 0, µ i s (t) ≡ µ s (t), 1 ≤ s ≤ 4, moreover, taking into account stochastic representations of log-skew elliptical random vectors [39], the expressions for univariate and multivariate Shannon entropies (measured in nats) take the following forms [40]: σ 22 ,α 3 ,β 3 ,γ 3 ,σ 33 ,α 4 ,β 4 ,γ 4 ,σ 44 ,σ 12 ,σ 13 ,σ 14 ,σ 23 ,σ 24 ,σ 34 As we can see from Equation 45, the mutual information, I, is calculated directly by summing the individual entropies and subtracting the joint entropy. Mutual information, I, between two random variables, X s and X u , compares the uncertainty of measuring variables jointly with the uncertainty of measuring the two variables independently, identifies nonlinear dependence between two variables [41][42][43], and is non-negative and symmetrical. A generalization of bivariate mutual information to more than two variables have been analyzed in few different scenarios [20,21,[41][42][43].…”

“…Mutual information, I, between two random variables, X s and X u , compares the uncertainty of measuring variables jointly with the uncertainty of measuring the two variables independently, identifies nonlinear dependence between two variables [41][42][43], and is non-negative and symmetrical. A generalization of bivariate mutual information to more than two variables have been analyzed in few different scenarios [20,21,[41][42][43]. A direct multivariate extension of bivariate mutual information expressed by Equation 45to n variables X 1 , X 2 , and X n is named as the multi-information [44,45], also known as total correlation, and is defined by:…”

Analyzing changes in the complexity of climate in the last four decades using MERRA-2 radiation data

“…Here, we keep our work within the Information Theory domain and present an analysis of causality based on Transfer Entropy 33 , another measure which allows us to determine the causality between two series of data without being restricted to an underlying linear dynamics. This technique, which has been applied to different fields from biochemistry 34 to Earth 35 and Space sciences 36 , allows us to capture the exchange of information between two systems and the directionality of the flux, determining the influence of one variable into the other. While autoregressive models are limited to linear relations, Transfer Entropy is a general technique which can be used to analyze any system, being equivalent to Granger causality for Gaussian variables 37 .…”