Applications of Information Theory in Solar and Space Physics

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 (J_e) is anticorrelated with solar wind density (n_sw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed mainly to the J_e(t + 2 days) correlation with solar wind velocity (V_sw)(t) and n_sw(t + 1 day) anticorrelation with V_sw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (V_sw, n_sw) anticorrelation. Using CMI to remove the effects of V_sw, the response of J_e to n_sw is 30% smaller and has a lag time <24 h, suggesting that the loss mechanism due to n_sw 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 J_e(t + 2 days) vs. V_sw(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.