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.