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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 36, issue 4 | Copyright
Ann. Geophys., 36, 945-952, 2018
https://doi.org/10.5194/angeo-36-945-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

ANGEO Communicates 02 Jul 2018

ANGEO Communicates | 02 Jul 2018

Transfer entropy and cumulant-based cost as measures of nonlinear causal relationships in space plasmas: applications to Dst

Jay R. Johnson1, Simon Wing2, and Enrico Camporeale3 Jay R. Johnson et al.
  • 1Andrews University, Berrien Springs, MI, USA
  • 2The Johns Hopkins University, Applied Physics Laboratory, Laurel, MD, USA
  • 3Center for Mathematics and Computer Science (CWI), Amsterdam, the Netherlands

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 3–12h lags that can be attributed to VBs, which also exhibits similar behavior. However, the nonlinear significance that peaks at lags 25, 50, and 90h 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.

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The magnetospheric response to the solar wind is nonlinear. Information theoretical tools are able to characterize the nonlinearities in the system. We show that nonlinear significance of Dst peaks at lags of 3–12 hours which can be attributed to VBs, which also exhibits similar behavior. However, the nonlinear significance that peaks at lags of 25, 50, and 90 hours can be attributed to internal dynamics, which may be related to the relaxation of the ring current.
The magnetospheric response to the solar wind is nonlinear. Information theoretical tools are...
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