Transfer entropy and cumulant-based cost as measures of nonlinear causal relationships in space plasmas: applications to <i>D</i><sub>st</sub>
Journal Article
Abstract. It is well known that the magnetospheric response to the solar wind is; nonlinear. Information theoretical tools such as mutual information, transfer; entropy, and cumulant-based analysis are able to characterize the; nonlinearities in the system. Using cumulant-based cost, we show that; nonlinear significance of Dst peaks at 3–12 h lags that can be; attributed to VBs, which also exhibits similar behavior.; However, the nonlinear significance that peaks at lags 25, 50, and 90 h can; be attributed to internal dynamics, which may be related to the relaxation of; the ring current. These peaks are absent in the linear and nonlinear; self-significance of VBs. Our analysis with mutual; information and transfer entropy shows that both methods can establish that; there are strong correlations and transfer of information from; Vsw to Dst at a timescale that is consistent with; that obtained from the cumulant-based analysis. However, mutual information; also shows that there is a strong correlation in the backward direction, from; Dst to Vsw, which is counterintuitive. In contrast,; transfer entropy shows that there is no or little transfer of information; from Dst to Vsw, as expected because it is the solar; wind that drives the magnetosphere, not the other way around. Our case study; demonstrates that these information theoretical tools are quite useful for; space physics studies because these tools can uncover nonlinear dynamics that; cannot be seen with the traditional analyses and models that assume linear; relationships.;
