Impact of solar cycle on the non-linearity of the relationship between the solar wind parameters and geomagnetic conditions

Abstract. Solar wind and its transients drive the dynamics of Earth’s magnetosphere. Interplanetary coronal mass ejections (ICMEs) induce the largest variations in the near-Earth space, but significant geomagnetic activity can also be driven by high-speed streams (HSSs) and stream interaction regions (SIRs). Solar wind – magnetosphere interaction may lead to fluctuations in the inner magnetosphere and, hence, impact the electrons in the outer radiation belt. In this study, we use mutual information from information theory to study the change in the statistical dependence between solar wind parameters and inner magnetospheric indices including ultra low frequency (ULF) waves in the Pc5 range and electrons in the outer radiation belt during solar cycle 23 (1998–2008). Unlike Pearson correlation coefficient, mutual information can be used to investigate non-linear statistical dependencies between different parameters. We calculate linear and non-linear correlation coefficients separately for each year during solar cycle 23 and define the non-linearity with the ratio between the linear and non-linear correlation coefficients. We find that the non-linearity between solar wind speed and electron flux index is higher during solar maximum when most of the geomagnetic activity is driven by ICMEs, while the non-linearity decreases during the declining phase, when a larger portion of the geomagnetic activity is driven by HSSs and SIRs. On the other hand, IMF B_z and solar wind electric field E_y = V_swB_z have smaller non-linearity with the geomagnetic indices during time periods of stronger geomagnetic activity. To investigate further if the change of the ratio of ICMEs and SIRs/HSSs as the driver of geomagnetic activity is the possible cause of the changes in the non-linearity during the solar cycle, we calculate the correlation coefficients separately during ICMEs, HSSs/SIRs and quiet solar wind. We find that non-linearity for solar wind speed and inner magnetospheric electron flux and ULF wave indices is smallest and correlations (both linear and non-linear) highest and therefore, the non-linearity is the lowest during the quiet time, while other studied solar wind parameters correlate better either during HSSs or ICMEs. These results show that the selected time period (phase of the solar cycle, dominant driver of the geomagnetic activity during the selected time) for the correlation analysis can significantly impact the results. Results also indicate that during ICMEs the solar wind – magnetosphere coupling becomes more non-linear for the majority of the studied solar wind–magnetospheric index parameter pairs (velocity, density, dynamic pressure) but IMF B_z and solar wind electric field E_y = V_swB_z have smaller non-linearity during time periods of stronger geomagnetic activity.