Common solar wind drivers behind magnetic storm-magnetospheric substorm dependency

Abstract

The dynamical relationship between magnetic storms and magnetospheric substorms is one of the most controversial issues of contemporary space research. Here, we address this issue through a causal inference approach to two corresponding indices in conjunction with several relevant solar wind variables. We find that the vertical component of the interplanetary magnetic field is the strongest and common driver of both storms and substorms. Further, our results suggest, at least based on the analyzed indices, that there is no statistical evidence for a direct or indirect dependency between substorms and storms and their statistical association can be explained by the common solar drivers. Given the powerful statistical tests we performed (by simultaneously taking into account time series of indices and solar wind variables), a physical mechanism through which substorms directly or indirectly drive storms or vice versa is, therefore, unlikely.

Figure 1

Time series of solar and magnetospheric variables for 2001. Time points with missing values in any of the variables are excluded from the analysis, taking lags into account. Clearly, there is strong solar and magnetospheric activity, in Supplementary Table S1 we classify storms into moderate, intense, and super-storm events.

Figure 2

Example of causal interactions in a three-variable process. (a) Time series graph which encodes the spatio-temporal dependencies. The set of parents ${\mathcal{P}}_{Y_t}$ (blue boxes) separates Y_t from the past of the whole process ${\mathbf{X}}_t^{-}\backslash {\mathcal{P}}_{Y_t}$, which implies conditional independence (Markov property) and is used in the algorithm to estimate the graph^,. (b) Process graph, which aggregates the information in the time series graph for better visualization (labels denote the lags, link and node colors denote the cross- and auto-coupling strength).

Figure 3

Lag functions of information-transfer measures. The lag functions were estimated with nearest-neighbor CMI estimation parameter k = 50^,. For example, the panel B_Z → AL shows the lag function $I(B_{Z,t-\tau };{\mathrm{AL}}_t|\dots )$ of MI (Eq. (1), gray), bivTE excluding the past lag of AL (Eq. (2), black), and the multivariate ITY (Eq. (3), blue) conditioning out the influence also of other variables with the parents $\mathcal{P}$ given in Table 1. All (C)MI values have been rescaled to the (partial) correlation scale via $I\to \sqrt{1-e^{-2I}}\in [0,1]$. For ITY, the solid line marks the significance threshold. MI and bivTE are clearly significant for a large range of lags. Confidence intervals (errorbars) are mostly smaller than the dots. MI and bivTE with their broad peaks clearly provide no precise information about relevant drivers and coupling delays. On the other hand, ITY features large values only at few selected lags. In Supplementary Fig. S1 we show that these results are robust for further method parameters and storm indices.

Figure 4

Graph based on significant ITY values at the 95% level in Fig. 3. Edges correspond to directional lagged links, and the labels indicate their lags. If more than one lag is significant, they are listed in the order of their strength. The edge color and width indicate the value at the lag with the largest ITY. The node color depicts the strength of the lag-1 auto-dependency for AL and SYM-H. Note that the weak ITY value in B_Z → SYM-H is likely due to B_Z occurring with two neighboring lags in the parents of SYM-H, which reduces the information transfer of either of them. In Supplementary Fig. S2 we show the robustness of these results using a different CMI estimation parameter and another substorm index.