Effects of Nearly Frontal and Highly Inclined Interplanetary Shocks on High‐Latitude Field‐Aligned Currents (FACs)

We present high‐latitude field‐aligned current (FAC) response to nearly frontal shocks (NFSs) and highly inclined shocks (HISs) through a superposed epoch analysis. The FACs are derived from magnetic perturbation data provided by the Active Magnetosphere and Planetary Electrodynamics Response Experiment program. Forty‐nine events for each group are used for the superposed epoch analysis. The 25%, 50%, and 75% quantiles of the FAC and total current distributions are studied. We found that NFSs are statistically stronger shocks in terms of solar wind parameters such as solar wind speed and interplanetary magnetic field.For the 50% quantiles, both groups of shocks produce rapid increases in total currents after shock arrival, but NFSs result in sharper increase in FACs and more intense FACs compared to HISs. At the 50% and 75% quantiles, NFSs trigger stronger auroral‐zone current disturbance for the first hour after shock arrival than do HISs. Spatially, the difference in FAC response is most notable in (1) the dayside noon region, (2) the duskside Region 2 current system, and (3) the dawnside prenoon Region 1 current system. Our results are consistent with previous numerical simulations that showed more symmetric and stronger compression of the magnetosphere for high‐speed and nearly frontal shocks. We observationally confirm the role of shock impact angle in controlling the subsequent shock geoeffectiveness for fast shocks. We assert that determining the shock impact angle via an upstream solar wind model could provide useful insight in forecasting the geoeffectiveness of a shock prior to its arrival at the magnetopause.


Introduction
Interplanetary (IP) shocks occur when the relative speed of solar wind perturbations with respect to the local solar wind speed is larger than the magnetosonic speed of the environment (Kennel et al., 1985;Oliveira & Samsonov, 2018). The most geoeffective IP shocks, those driven by coronal mass ejections, interact with the Earth's magnetosphere and cause various disturbances in magnetosphere, ionosphere, and thermosphere, such as energization of energetic charged particles and formation of new radiation belt (e.g., Hudson et al., 1997;Li et al., 1993;Sarris & Van Allen, 1974), dayside shock aurora and nightside substorms (e.g., Liou et al., 2002;Lyons et al., 2005;Zhou & Tsurutani, 1999, and enhancements of thermospheric density and nitric oxide emissions (e.g., Knipp et al., 2013;Knipp et al., 2017;Oliveira et al., 2017).
The geoeffectiveness of IP shocks was shown to be affected by a number of solar wind parameters such as solar wind speed, intensity of the IP magnetic field (IMF) (e.g., Meurant et al., 2004), IP dynamic pressure pulses (e.g., Chua et al., 2001), and the precondition of the magnetosphere (e.g., Meurant et al., 2004;Sun et al., 2011;Zhou & Tsurutani, 2001). However, another shock feature, the IP shock orientation, is also an important controlling factor of the shock geoeffectiveness (see review by Oliveira & Samsonov, 2018). The IP shock impact angle is defined in terms of the shock orientation relative to the Sun-Earth line (Oliveira & Samsonov, 2018).
The first clear connection between the rise time of the geomagnetic sudden commencement and shock orientation was provided by Takeuchi et al. (2002). Various statistical studies on the effect of shocks of different orientation have been conducted using SuperMAG data (Oliveira et al., 2016;Oliveira & Raeder, 2015) ©2019. The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. or focusing on the sudden impulse rise time (Rudd et al., 2019;Wang et al., 2006). Field-aligned currents response to IP shocks with different impact angles has been addressed through simulations in previous case studies (Guo et al., 2005;Oliveira & Raeder, 2014;Selvakumaran et al., 2017). Shocks with small impact angle are generally found to be more geoeffective in all these simulation studies. This work provides observational support of those findings.

RESEARCH ARTICLE
High-latitude FACs are derived from the Iridium magnetic perturbation observations made available through the NSF-funded Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) program (Anderson et al., 2000). The AMPERE FACs have been used for various studies, such as case studies for geomagnetic storms and substorms (e.g., Murphy et al., 2013;Wilder et al., 2012); effects of solar wind drivers, mainly the IMF clock angle dependence (e.g., Anderson et al., 2008;Green et al., 2009); spatial and temporal studies on Region 0, Region 1 (R1), and Region 2 (R2) currents (e.g., Clausen et al., 2013;Coxon et al., 2014;Milan et al., 2015), and seasonal and IMF dependence of FACs (e.g., Green et al., 2009). However, a study that links IP shock impact angle to the subsequently observed high-latitude FAC responses has not yet been undertaken. This is the goal of this work.
We provide a statistical analysis of the response of high-latitude FACs to the impact of nearly frontal shocks (NFSs) and highly inclined shocks (HISs). We select 49 NFS events and 49 HIS events between October 2009 and September 2017 from the shock list provided by  where the zero-epoch time is the shock/compression onset time. Derived FAC distributions and total currents during the hour before and after the zero-epoch time are determined and used in superposed epoch analysis.

NFS and HIS Shock Events
IP shock impact angle θxn is defined in terms of the shock normal orientation relative to the geocentric solar ecliptic Sun-Earth line as described in Oliveira and Samsonov (2018) and Rudd et al. (2019). Here θxn ranges from 0°to 180°where θxn = 180°is associated with a purely frontal shock, while the smaller θxn, the more inclined the shock. The shock list provided by  is used in this study to identify NFS and HIS events. The list provides the shock arrival time as the positive jump in sudden impulse onset, shock impact angle, shock speed, and the maximum worldwide horizontal component of the ground magnetometer dB/dt measurements. Forty-nine NFS events with θxn ≥ 160°were found based on the IP shock list during October 2009 and September 2017, for which there exist raw AMPERE magnetic perturbation data available online. Forty-nine HIS events with θxn < 160°were chosen to match the number of NFS events. Figure 1 shows the histogram of the events used in this study. Since there are more NFS events in the first half of the year in total, more events in the first half of the year for HIS events were randomly chosen to match the distribution and minimize possible seasonal effects in the FACs. The list of events used in this study is provided in the supporting information.

Reconstructed High-latitude Magnetic Potential and FACs
Magnetic field perturbation data are provided by the AMPERE program using the engineering-graded magnetometer measurements from the Iridium constellation satellites. The measurements come from 66 satellites in six orbital planes with a revisit time of 9 min, providing a relatively global coverage with a cadence of 19.44 s under normal operation and 2.16 s under high-rate mode .
High-latitude toroidal magnetic potential and FACs are estimated from the AMPERE magnetic perturbation data following the optimal interpolation (OI) method in Matsuo et al. (2015) with a set of 244 modified polarcap spherical harmonics Ψ (Richmond & Kamide, 1988) and a coefficient vector x.
where x b is the background mean of the coefficient vector x, C b is the background model error covariance, C r is the observational error covariance, H is a linear forward model that maps x to the observation, y are all the 10.1029/2019SW002367 Space Weather magnetic perturbation data for ±2 min at the time point, and x a is the estimated coefficient vector for magnetic potential. FACs are then calculated as the curl of the estimated magnetic potential.
The vectors x b are C b are calculated from~100 days of magnetic perturbation data using the empirical orthogonal function analysis method described in Matsuo et al. (2015) and Cousins et al. (2015). C r is calculated from the data uncertainty provided by AMPERE. H is evaluated in Modified Apex coordinates following Richmond (1995).
We apply this procedure simultaneously in both hemispheres to estimate toroidal magnetic potential and FACs with a 2-min cadence to study the response to shocks in this study.

Superposed Epoch Analysis (SEA)
An analysis of magnetic potential and FACs is performed for the two groups of events. The shock arrival time determined by the list is set as the zero-epoch time for each Superposed Epoch Analysis event.
Magnetic potential and FAC maps are reconstructed each 2 min in the two hemispheres for the ±1-hr interval around the shock arrival time. The maps are plotted from 60°to 90°latitude with a resolution of 10°in longitude and 1.67°in latitude. Finally, total FACs are calculated from the FAC patterns as the sum of the area of each grid bin multiplied by the FAC in each grid bin.

Total Upward and Downward Currents
To illustrate the change in total currents due to shock impact, the mean of the total upward and downward current for the 3 hr before shock arrival is first calculated and set as the quiet time baseline for the analysis. The ratio between the total upward and downward current at each time point and the quiet time baseline during the ±1-hr interval is then calculated. The time profiles of the normalized 25%, 50% (median), and 75% quantiles for total upward and downward currents between 60°and 90°latitude in both hemispheres are plotted in Figure 2. The northern hemisphere is shown in the top row and the southern hemisphere in the bottom row. Upward currents are shown on the left and downward currents on the right. Red lines are for NFSs, and blue lines are for HISs. For the NFS and HIS 75% quantiles, the shaded areas represent the uncertainties determined by the empirical cumulative distribution function using Greenwood's (1926) formula. (Note: The 10% and 90% quantiles are plotted in Figure S1 to show the range of response of FACs between the two groups of shocks. Those quantiles show similar trend to the 25% and 75% quantiles.) Table 1 summarizes the pre-and post-shock statistics for total current where we calculate the NFS/HIS ratio for total upward and downward current in both hemispheres and calculate the average ratio, as well as the percentage of time with higher total current for NFS compared to HIS.

Space Weather
An increase in total upward and downward currents after zero-epoch time is the clear shock response in high-latitude FACs. Most of the increase occurs in the first half hour after shock arrival. Before shock arrival, the median ratio of NFS/HIS total current is 1.05 but with NFS showing higher total currents more often; after shock arrival, the NFS/HIS ratio rises for all quantiles, and NFS total currents are higher than HIS currents for more than 90% of the time. From the total current quantile plots in Figure 2, we see that the NFSs produce higher total currents and more rapid increase after shock arrival for all quantiles in both hemispheres. The 75% quantiles appear to show the largest difference between the two groups of shocks.
In Figure 2, the 75% quantile curves for NFSs and HFSs appear distinct, but the uncertainties for the NFS and HIS 75% quantiles show some overlap. Thus, for this small sample size, we cannot be confident that the two quantile curves are entirely separated. (Note: For clarity, the uncertainties for 25% and 50% quantiles are not plotted in the figure.) However, all three total current quantiles for the NFS and HIS pairs are tested using Wilcoxon (1945) signed-rank test to determine whether the two samples selected are from the same distribution. The p values for the tests for each quantile level are all on the order of 10 −6 or less. Thus, the NFS and HIS time series at each quantile level are not from the same distribution.

Magnetic Potential and FAC Patterns-75% Quantile Patterns
To further explore the different behavior in total current response for the two groups of shocks, we show the magnetic potential and FAC patterns in Figure 3. The difference between NFS and HIS total current increases with higher quantiles; therefore, we mainly focus on the 75% quantiles in this section. Comparing Figures 3a and 3b with 3c-3f, FACs are enhanced for both HISs and NFSs after the shock arrival. The NFSs result in larger maximum and minimum values in both magnetic potential and FACs. The NFSs respond more vigorously in terms of near-noon, polar cap (Region 0) FACs. NFS R2 currents also show a general broadening and intensification relative to HIS R2 currents. The NFS and HIS maximum and minimum FAC values are higher in the northern hemisphere than the southern hemisphere; this may be due to the seasonal bias in event distribution. Figures 4a and 4b show, as a measure of variability, the 75% quantile of standard deviation in magnetic potential and FACs for the hour before shock arrival for the NFSs as an example of quiet time background. The standard deviation for the first hour after shock arrival for HISs and NFSs are in Figures 4c and 4d and Figures 4e and 4f, respectively. Standard deviation for each grid point within the hour before or after shock arrival is calculated for each event, and the 75% quantiles are plotted in Figure 4. The variation is enhanced for both NFSs and HISs after shock arrival compared to before shock arrival with similar asymmetries discussed above. Comparing NFS and HIS variations in FACs, the NFSs show more variability after shock arrival: (1) on the dayside around noon, (2) on the dawnside in the prenoon region, and (3) on the duskside in the premidnight region

Comparisons for Magnetic Local Time Sectors
To investigate in detail the difference in spatial distribution of FACs resulting from NFSs and HISs, we checked the total currents by sector: (1) noon sector from 10 MLT to 14 MLT, (2) duskside from 14 MLT to 22 MLT, (3) an additional prenoon section from 08 MLT to 10 MLT, (4) midnight from 22 MLT to 02 MLT, and (5) dawnside from 02 MLT to 10 MLT. The NFS/HIS total current ratio and % time NFS/HIS ratio > 1 after shock arrival for 75% quantiles for different sections are listed in Table 2.
The largest total current response difference between NFS and HIS is in the noon region where the NFS total current is higher than HIS 100% of the time with average NFS/HIS ratio being 1.33 after shock arrival for 75% quantiles as shown in Figures 5a-5d (same format as Figure 2). More intense dayside FAC response is also consistent with Figure 4 where we see high variation around noon for NFSs. Similar tables for 25% and 50% quantiles are provided in the supporting information.
The FACs in the dusk region and prenoon region also show high difference for NFSs in Figure 4 and 4. Discussion

Comparisons for IP Parameters and Geophysical Indices
To expand on the results in Figures 2-5, we provide statistics of the relevant solar wind plasma and IMF parameters for NFSs and HISs, respectively. The 50% (solid lines) and 25% and 75% (dashed lines) quantiles of the (a) IMF magnitude, (b) solar wind speed, and (c) dynamic pressure for the NFSs (red) and HISs (blue) are plotted in Figure 6 as an indication of the energy input from the solar wind (Akasofu & Chao, 1980) and the strength of IP shocks. IMF magnetic field and solar wind speed data are obtained The IMF magnitudes for the two groups before shock arrival are similar. As for IMF B z direction, the median value for B z is close to zero before shock arrival and slightly negative around −1 nT for both groups of shocks after shock arrival, consistent with earlier findings with more shock events (e.g., panel (b) Figure 7 of Oliveira et al., 2017). IMF B y also show median values around zero for both groups of shocks. The 25%, 50%, and 75% quantiles for IMF B z and B y are plotted in the same format as Figure 6 in Figures S6 and S7. This suggests that there is little bias in IMF direction and preconditioning is not a significant factor in the differences reported here. A possible preconditioning element is solar wind speed where NFS solar wind speed is on average 6% higher than HIS for the 1 hr before shock arrival, possibly resulting in the higher total current for NFSs before shock arrival as shown in Table 1. Solar wind dynamic pressure also shows similar pre-shock condition but higher values for all quantiles for NFSs, with a similar to the trend of IMF magnitude.
The solar wind parameters indicate that NFSs are more likely to be stronger shocks in terms of solar wind forcing (see Figure 4 of . One possible reason for the difference is that stronger discontinuities in solar wind such as field deflection, shock propagation speed, plasma compression, and heating occur at the nose of shocks compared to at the flanks along the shock front (Bemporad et al., 2014). NFSs are more likely to be at the nose of shocks and therefore associated with stronger IP shocks, while HISs are more likely to be at the flanks of shocks and therefore weaker IP shocks.
In addition to the effect of IP shocks, Kilpua et al. (2019) report that the sheaths following the IP shocks of fast ejecta have on average high solar wind speeds, magnetic (B) field magnitudes, and fluctuations and generate efficiently strong out-of-ecliptic fields. Thus, for the top events in our study (75% quantile), a combination of factors including fast ejecta, NFSs association with the shock nose structure, and subsequent sheath features may play a role in post shock geoeffectiveness.
To compare the effect of different shock impact angles under similar shock strength conditions, the events are separated into two groups with respect to shock speeds: high-speed events with shock speeds higher than 450 km/s and low-speed events with shock speeds lower than 450 km/s. The choice of this threshold shock speed is based on the approximate average shock speed found by Rudd et al. (2019) for a sample with more than 500 IP shocks. This shock group distinction is based on earlier correlation analysis studies showing that high speed and NFSs were found to be more geoeffective, while low speed and HISs were found to be less geoeffective (Wang et al., 2006;Oliveira & Raeder, 2015;Oliveira et al., 2016l Selvakumaran et al., 2017Rudd et al., 2019). Figure 7 shows the 50% quantiles of (a) IMF magnitude, (b) solar wind speed, and (c) solar wind dynamic pressure for fast (solid lines) and slow (dashed lines) NFS (red) and HIS (blue) events. The solar wind conditions appear to be more similar for NFSs and HISs when separated by shock speeds. Figure 8 shows the 50% quantiles of total (a and c) upward and (b and d) downward currents for fast (solid lines) and slow (dashed lines) NFS (red) and HIS (blue) events. We see that the slow event NFS and HIS total currents show very similar trends and the average ratio of NFS/HIS total current is around 1.01. On the other hand, the fast event NFS total currents are much higher than the HIS total currents with an average ratio of NFS/HIS around 1.57, much higher than the ratio shown in Table 1. This indicates that NFSs result in much stronger FACs compared to HISs when the solar wind speed is high, but not so much when the speed is low, consistent with earlier findings.
The different total current response for the first hour between the two groups of shocks supports the argument of Raeder (2014, 2015) that symmetric compression on the magnetosphere from frontal shocks may trigger nightside geomagnetic activity more effectively than for inclined shocks that lack such symmetry. Figure 9 shows the 75% quantiles for AE index in solid lines, AU index in dash-dot lines, and AL index in dashed lines for NFS in red and HIS in blue as indication of auroral-zone current disturbance. For both groups, the AL index decreases after shock arrival, indicating enhanced westward electrojet, but

10.1029/2019SW002367
Space Weather who used a modified version of the AE index to investigate nightside auroral power response to IP shock impacts with different orientations.

Global and Sector FACs 4.2.1. Global
For the 50% quantile, the total-current comparison (Figure 2) during the post-shock interval shows sharper increase in FACs and higher total current for NFSs with average NFS/HIS total current ratio of 1.17. This indicates that on average, NFSs result in faster rise and more intense FACs in the high-latitude region. Oliveira and Raeder (2014) studied FAC response to frontal shocks and inclined shocks. Using MHD simulations and assuming the same plasma parameters except for the impact angle, they found frontal shocks to be more geoeffective than inclined shock in terms of FACs. The data and plots in Figures 2-4 provide the observational support of their findings. Note that their simulations used only southward IMF after the shock. We believe our results are more general, since we include both signs of IMF vertical component in the shock selection.

Sectors and Local
In Figure 5, we emphasized three sectors that show particularly strong response to NFS: noon, dusk, and prenoon. (Total current plots for the other four sectors are provided in the supporting information.) Here we provide additional discussion about the regions showing enhanced sensitivity to NFSs.
The largest total current response difference between NFS and HIS is in the noon region as shown in the Figures 3c-3f and 5a-5d. The noon region is found in various earlier simulation and event studies to be the first location to see FAC response under shock impact (Fujita et al., 2003;Guo & Hu, 2007;Ridley et al., 2006;Samsonov et al., 2010;Shi et al., 2017;Sun et al., 2015). A similar result was found in simulations of Oliveira and Raeder (2014) where dayside FAC enhancement is found to be much more intense for frontal shocks while nightside FAC enhancement is qualitatively similar for different shock impact angles.
Related to the high NFS/HIS, the dusk R2 current ratio at 1.31, the R2 currents in the ionosphere are believed to be closely related to the ring current (Ganushkina et al., 2018, and references within) which is often asymmetric and shows stronger currents on the duskside during storms (e.g., Liu et al., 2006). Shi et al. (2006) reported that stronger solar wind dynamic pressure enhancement intensified the asymmetry in the ring current. NFSs being stronger shocks and having more symmetric compression on the magnetosphere compared to HISs likely produce strong spatial differences in the duskside R2 currents.
Regarding the high NFS/HIS prenoon Region R1 current at 1.27, Ohtani et al. (2018) noticed similar enhancements of dawnside R1 current and strong dawnside current wedge during several intense storms. Our results suggest that this kind of strong dawnside current can happen at times other than during intense storms and maybe a feature of NFS response.
Earlier studies stated that the difference in geoeffectiveness between NFSs and HISs can be seen in lower-latitude regions (e.g., Rudd et al., 2019;Selvakumaran et al., 2017;Wang et al., 2006). For future research, we would like to investigate other indices for a measure of currents in lower-latitude regions such as SYM/H or SMR index derived from SuperMAG (Newell & Gjerloev, 2012) for the events used in this study. It will likely provide more information on the comparison between high-latitude and low-latitude responses to shocks with different impact angles and strengths.
Global simulations comparing NSFs and HISs have predicted higher total FACS in the post fast and NFS regime. Our results confirm this. Further, as shown in this study, there is a sharper and stronger response in the AE index in the NFS post-shock regime. The latter result suggests immediately stronger auroral-zone currents in the NSF post-shock regime. These new results should guide future forecasts of shock response. We have also identified specific regions where the NFS FAC response is stronger than HIS FAC response.  Of particular interest is possible post dawn current system (e.g., Ohtani et al., 2018) subsequent to NFSs. This may be a region to watch for geomagnetically induced currents effects just after the impact of the most extreme shocks.

Conclusion
In this paper, we investigated the effect of IP shock impact angle on high-latitude FAC response. Forty-nine NFSs and 49 HISs are used in a superposed epoch analysis. A ±1-hr interval of magnetic potential and FAC patterns are reconstructed for each event with an OI method using AMPERE magnetic field perturbation data with a 2-min cadence around the shock arrival time and studied for each event. Total currents are calculated from the FAC patterns. Quantiles of total currents and FAC patterns are discussed here as the indication of FAC response to the two groups of shocks with following main findings: 1. Using global FAC patterns derived from magnetic perturbations at low Earth orbit, we provide observational verification that NFSs are more geoeffective than HISs, particularly for the category of high-speed (strong) shocks. 2. NFSs and HISs show rapid increase in FACs after shock arrival, but NFSs show sharper and stronger increase in general. This is likely due to stronger auroral-zone current disturbance resulting from more symmetric compression on the magnetosphere for NFSs (e.g., Oliveira & Samsonov, 2018). 3. NFSs are stronger IP shocks in terms of solar wind parameters (IMG magnitude, solar wind speed, and solar wind dynamic pressure) and have a higher, 1-hr-ahead solar wind speed by about 5%. 4. NFSs result in stronger FACs compared to HISs for fast shocks but similar FACs for slow shocks. 5. NFSs produce a sharper and stronger response in the AE and AL indices within 15 min of shock arrival. 6. NFSs produce enhanced response in magnetic potential and FAC patterns (75% quantiles), at (1) noon currents, (2) duskside R2 currents, and (3) prenoon R1 current.
Our observational and OI results show that NFSs are more geoeffective in terms of high-latitude FACs, consistent with earlier predictions through numerical simulations (e.g., Guo et al., 2005;Oliveira & Raeder, 2014;Selvakumaran et al., 2017). In addition, we show that NFSs are statistically stronger IP shocks and are more likely to result in more intense auroral-zone current disturbance and in more intense regional currents at prenoon, noon, and dusk. Further research on the geoeffectiveness of shocks with different impact angles in terms of FACs can be beneficial for various space weather applications.