Directed Network of Substorms Using SuperMAG Ground-Based Magnetometer Data
DDirected Network of Substorms Using SuperMAGGround-Based Magnetometer Data
L. Orr , S. C. Chapman , and J. W. Gjerloev Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, UK, Applied Physics Laboratory-JohnHopkins University, Laurel, MD, USA, Birkeland Centre, University of Bergen, Bergen, Norway
Abstract
We quantify the spatiotemporal evolution of the substorm ionospheric current systemutilizing the SuperMAG + magnetometers. We construct dynamical directed networks from this datafor the first time. If the canonical cross-correlation between vector magnetic field perturbations observedat two magnetometer stations exceeds a threshold, they form a network connection. The time lag at whichcanonical cross-correlation is maximal determines the direction of propagation or expansion of thestructure captured by the network connection. If spatial correlation reflects ionospheric current patterns,network properties can test different models for the evolving substorm current system. We select 86isolated substorms based on nightside ground station coverage. We find, and obtain the timings for, aconsistent picture in which the classic substorm current wedge forms. A current system is seenpremidnight following the substorm current wedge westward expansion. Later, there is a weaker signal ofeastward expansion. Finally, there is evidence of substorm-enhanced convection. Plain Language Summary
Space weather makes beautiful auroral displays (the northern andsouthern lights), but with these come large-scale electrical currents in the ionosphere, which generatedisturbances of magnetic fields on the ground. These are observed by >
100 magnetometer stations onthe ground, and the challenge is to extract the important information from these many observations andpresent it as a few key parameters that indicate how severe the ground impact will be. Networks are now acommon analysis tool in societal data, where people are linked based on various social relationships. Otherexamples of networks include the world wide web, where websites are connected via hyperlinks, or maps,where places are linked via roads. We have constructed networks from the magnetometer observationsof space weather events (geomagnetic substorms), where magnetometers are linked if there is significantcorrelation between the observations. There has been considerable debate as to how the ionosphericpattern evolves during a geomagnetic substorm. We are able to use the networks to resolve some of thesecontroversies.
1. Introduction
Substorms, their associated current systems, and the corresponding geomagnetic displacements seen atEarth have been the subject of longstanding interest (Pulkkinen, 2015). The fundamental morphology, stagesof development, and their timings are well established (Akasofu, 1964). The classic scenario is that of theformation of a substorm current wedge (SCW; McPherron et al., 1973), a rapidly appearing, intense west-ward electrojet that follows disruption to the cross-tail current system. This corresponds to the DP1 patternof magnetic perturbations in the nightside auroral zone, which appears in addition to the DP2 geomagneticcounterpart associated with the convective system in the dawn and dusk auroral zones (Nishida, 1968).However, there have been several important variants of this picture. Kamide and Kokubun (1996) proposeda two component auroral electrojet, and Sergeev et al. (2011) argued that their computational wedge modelis more consistent with observations, if an additional region two polarity field-aligned current is added tothe classic SCW cartoon. Gjerloev and Hoffman (2014) proposed a two-wedge current system, comprisedof a bulge and an oval current wedge, in their empirical model of the ionospheric equivalent current sys-tem, during an auroral substorm. Recently, it was proposed, by Liu et al. (2018), that there is no large-scalewestward electrojet but rather many small, individual segments. These proposed models point to the out-standing question: What is the average substorm current system morphology that we can quantify andresolve uniquely from the full set of available ground-based magnetometer observations? The goal of this
RESEARCH LETTER
Key Points: • The first dynamical networkanalysis of substorm current systemsis directed, hence quantifying bothformation and expansion• Both the 100+ SuperMAGground-based magnetometers andPolar VIS are utilized to obtain thefull spatiotemporal pattern fromisolated substorms• We identified timings of aconsistent sequence in which theclassic substorm current wedgeforms
Supporting Information: • Supporting Information S1• Table S1
Correspondence to:
L. Orr,[email protected]
Citation:
Orr, L., Chapman, S. C., &Gjerloev, J. W. (2019). Directednetwork of substorms usingSuperMAG ground-basedmagnetometer data.
GeophysicalResearch Letters , , 6268–6278.https://doi.org/10.1029/2019GL082824Received 13 MAR 2019Accepted 3 JUN 2019Accepted article online 10 JUN 2019Published online 25 JUN 2019©2019. The Authors.This is an open access article under theterms of the Creative CommonsAttribution License, which permitsuse, distribution and reproduction inany medium, provided the originalwork is properly cited. ORR ET AL. 6268 eophysical Research Letters paper is to construct a method that quantifies the time-evolving spatial pattern seen across all 100+ mag-netometers, in a manner that allows systematic averaging across may substorm events. This will provide aquantitative benchmark to test against model predictions. Key aspects of many of the above models, whilebeing physically distinctive, are qualitative. Our results place these qualitative predictions in direct contactwith the observations and can thus drive forward the formation of quantitative hypotheses that will allowthese models to be distinguished.The SuperMAG initiative (Gjerloev, 2012) makes the full set of + ground-based magnetometer observa-tions routinely available, with a standardized coordinate system and a common baseline, supporting bothsingle event and comparative statistical studies. In this form the data are now amenable to analysis method-ologies designed to quantify spatiotemporal pattern in sets of multiple, spatially distributed observations.Complex network methodology has recently grown in popularity as a useful mathematical tool and hasbeen used to analyze complex systems from a variety of disciplines ranging from social sciences (Albert &Barabási, 2002; Newman, 2003; Watts & Strogatz, 1998) to geophysical data (Boccaletti et al., 2006; Malik etal., 2012; McGranaghan et al., 2017; Stolbova et al., 2014; Wiedermann et al., 2016). Crucially, unlike otherdata assimilative methods, including the assimilative mapping of ionospheric electrodynamics, Assimila-tive mapping of ionospheric electrodynamics (AMIE) (Richmond & Kamide, 1988), network analysis doesnot introduce spatial correlation. Furthermore, our network analysis does not require any a priori assump-tions for variation in ground conductivity since we normalize for this using solely the data to determine thetime- and station-dependent network threshold.Dods et al. (2015) recently demonstrated, on a small set of events, that a network methodology could beapplied to the full set of magnetometers for single isolated substorms to yield a characteristic network sig-nature of substorm onset. The networks are time-dependent, hence contain information on the timings ofsubstorm evolution (Dods et al., 2017). Canonical correlation is used to study correlations between multivari-ate data sets (Reinsel, 2003). If we have two vector time series, canonical correlation analysis will determinethe linear combination of the two, which are maximally cross-correlated. The cross-correlation betweenthese linear combinations is the (first) canonical cross-correlation (CCC) component. The key elements ofthis network analysis are (i) to calculate the CCC of the vector magnetic field time series between each pair ofmagnetometers and (ii) to apply a station and event specific threshold to this CCC, which is obtained directlyfrom the data. The station pairs that have CCC above the threshold then form a time-varying network.The analysis of Dods et al. (2015) only examined the undirected network (zero-lag CCC). This was sufficientto reveal the initial formation of the SCW at substorm onset but without directional information could notcapture the full spatiotemporal evolution of the current system. In this paper we construct the networksbased on the (often nonzero) time lags at which the CCC between each pair of stations is maximal, to formthe substorm directed network, which captures the direction of information propagation between networknodes (magnetometers). Looking across a range of CCC lags captures the full pattern of spatial correlationand how it evolves in time. Nonzero CCC lags indicate the timescale for propagation or expansion of a coher-ent structure and the sign of the lag gives the direction of propagation or expansion. We construct specificsubnetworks to test the hypotheses of different proposed models for how the ionospheric current systemevolves. The subnetworks isolate different spatial regions and allow us to test for connections between them.We will focus on spatially well-sampled isolated substorm events and establish network parameters thatcharacterize how the magnetometers collectively respond to the SCW. We have identified 86 events thatmeet the sampling requirements (this is a subset of the substorm list used in the series of papers by; Gjerloev& Hoffman, 2014, and Gjerloev et al., 2007). We find timings for a pattern in the magnetic field perturba-tions consistent with the SCW formation at onset, which then expands westward to form a coherent currentsystem in the premidnight sector. There is additional weaker, eastward expansion of the SCW, followed bycoherent correlation patterns spanning the entire nightside.The organization of the paper is as follows. In section 2 we describe the methods and the data used to obtainthe directed networks. In section 3 we highlight a case study of one substorm and present a statistical survey86 events, which reveals how on average the spatial pattern of correlation evolves as the substorm progresses.We conclude in section 4.ORR ET AL. 6269 eophysical Research Letters
2. Methods
For each substorm we first construct the full dynamical directed network before dividing it into subnet-works that flag spatial correlation within and between specific spatial regions. These regions are selectedto test different proposed models of substorm current patterns. The term “dynamical” is used here as inthe networks literature (Jost, 2007). Our analysis cannot resolve short-range fine structures that are smallerthan, or of the order of, the intermagnetometer spacings but can test whether long-range spatially correlatedpatterns exist. The method for forming a network, at zero lag, is detailed in Dods et al. (2015). The magne-tometer stations form the nodes of the network and a given pair of nodes are connected if the CCC of theirvector magnetic field perturbation time series exceeds an event and station specific threshold, as specifiedin Dods et al. (2015). In summary, the CCC is calculated over a 128-min running window of the magneticfield perturbations observed by magnetometer pairs. The data are at minute resolution, giving a 128-pointCCC for each station pair, every minute. The 128-min sliding window is chosen to give sufficient accuracyin the computed cross-correlation function while also capturing the large-scale spatial and temporal behav-ior of the SCW. Dods et al. (2017) previously demonstrated using model time series that this window lengthresolves changes on timescales much shorter than that of the window, specifically capturing onset wherethere is a sharp ramp in activity in time as the SCW forms. A network is calculated for every minute, and alltimes, t , will refer to the leading edge of the window, that is, the last time point spanned by the window (i.e.,a window spanning time interval [ T , T + ] will have network properties plotted at time t = T + ). Eachwindowed, three-component vector magnetic field time series is (1) linearly detrended, and (2) the CCC iscalculated for each station pair; then (3) if the correlation between magnetometers i and j exceeds the maxi-mum of the two station thresholds, then they are connected and are part of the network. For a network with M active magnetometers, an M × M adjacency matrix, A , is formed, which has A ij = , if i and j are con-nected, and A ij = , otherwise. The station specific threshold for each magnetometer station is determinedsuch that the station will be connected to the network for % of the month (28 days) surrounding the event.This ensures that all stations have the same likelihood of being connected to the network, independent oftheir individual sensitivities to an overhead current perturbation, which in turn depends on the individualinstrument characteristics and the local time and season-dependent ground conductivity.Dods et al. (2015) constructed the network using just the CCC at zero lag. Here, we form the directed networkby considering the lag at which the CCC is maximal, 𝜏 c , up to a lag of ± min. The value of the CCC value atlag 𝜏 c is used to determine if the stations are connected (exceeds the threshold) and each connection then alsohas a direction and timescale of propagation of the observed signal, which is spatially coherent between thetwo stations. This potentially corresponds to the coherent pattern of time-varying ionospheric currents. Theadjacency matrix, A , is not symmetric and the sign of 𝜏 cij determines the signal propagation direction for A ij .If the CCC between magnetometer i and j is above the threshold (they are connected), but with 𝜏 c < , wecan infer that the signal originates at j and propagates toward i , j → i . If 𝜏 c > the propagation is i → j .Gjerloev (2012) found that the probability distributions of differences between SuperMAG baselines andofficial quiet days rarely exceed 20 nT. For consistency we also exclude magnetometers from the networkwhose time series of magnetic field perturbations never exceed this noise level. We analyze vector magnetometer time series at 1-min time resolution for the full set of magnetometer sta-tions available from the SuperMAG database. These data are processed as in Gjerloev (2012), such that theground magnetic field perturbations are in the same coordinate system and have had a common baselineremoved. A set of isolated substorm events, occurring between 1997 and 2000, has been previously identi-fied in Gjerloev et al. (2007). These events have been selected such that (i) they are isolated single eventsoptically and magnetically; (ii) the onset location is spatially defined; (iii) bulge-type auroral events; (iv)there is a single expansion and recovery phase (or the end of the event is at the time of a new expansion); (v)the entire bulge region is in darkness to eliminate any terminator effects; and (vi) they are not during mag-netic storms ( | Dst | < nT) or prolonged magnetic activity. The requirement for darkness creates biases asthe events with the majority of the nightside in darkness are in the months around winter solstice. Exclud-ing daylit stations does however avoid large differences in ground conductivity between the stations, whichwould otherwise dominate the CCC analysis. We also require that activity levels are low for a full windowof 128 min before the substorm onset. Together these selection criteria, along with the requirement for aORR ET AL. 6270 eophysical Research Letters Figure 1.
SuperMAG polar plot indicating the spatial regions A, B, and C for which we obtain subnetworks. All dataare from stations between 60 ◦ and 75 ◦ magnetic latitude, within the nightside. The local time boundaries between A,B, and C are different for each event and are determined from Polar VIS images; they are separated by the east and westboundaries of the bulge at the time of maximum expansion (dashed lines). The magnetic latitude and local time ofonset (again from Polar VIS) for each event are indicated by the yellow star. sufficient number of stations in the spatial region around onset (described below), give 86 suitably isolatedsubstorms (listed in the supporting information). It is well established that substorms vary in duration (Kullen & Karlsson, 2004; Tanskanen et al., 2002). Inorder to perform an average across many events, we need to map each event onto a single normalized timebase such that, once normalized, all substorms share a common onset time and take the same length of timeto evolve from onset to the peak of activity. Following Gjerloev et al. (2007), the observed event time, t , isrelated to the normalized time, t ′ , by t ′ = T E × ( t − t onset ) t peak − t onset , (1)where T E = min, approximately the average length of a substorm expansion phase. The onset time isthen at t ′ = and the time of peak expansion t ′ = . The critical timings for this normalization, t onset and t peak , can be unambiguously identified in these isolated substorm events. We construct time-varying directed subnetworks that quantify correlation within and between specific spa-tial regions in the nightside. These spatial regions are selected for each event as shown in Figure 1. Thenetwork is constructed using stations located between 60 ◦ and 75 ◦ magnetic latitude and within the night-side. Gjerloev and Hoffman individually determined the timings and positions of onset and the east andwest ends of the bulge portion of the aurora using polar VIS images (Gjerloev et al., 2007). The LT of thebulge edges at the time of maximum expansion ( t ′ = ) has been used to define the boundaries of regionB. The study was repeated using the east and west boundaries of the bulge 15 normalized minutes before,and after, the maximum expansion phase ( t ′ = and t ′ = ); results are presented in the supporting infor-mation. This gives slight differences, but the overall results and conclusions are unchanged. The SCW istypically 6 hr of local time in extent (Gjerloev et al., 2007), which corresponds to region B; regions A and Care westward and eastward of the SCW, respectively.We will present a detailed study of the subnetworks for a single event and then will compare it to the averagesubnetwork behavior seen across all 86 isolated substorms. An event was identified that has ≥ t ′ = ). For the averaged study over 86 events we require atORR ET AL. 6271 eophysical Research Letters Figure 2.
The normalized number of connections, 𝛼 ( t ′ , 𝜏 c ) , is binned by the lag of maximal canonical cross-correlation, | 𝜏 c | . Each panel stacks vertically (one above the other) 𝛼 ( t ′ , 𝜏 c ) versus normalized time, t ′ , for | 𝜏 c | ≤ . | 𝜏 c | isindicated by color (see color bar). Panel 1 plots the SuperMAG electrojet index, SME. Panels 2–10 plot 𝛼 for connectionswithin and between each of the regions A, B, and C (identified in Figure 1). The left columns plot a single event,whereas the right plots the average of 86 events (containing subnetworks with ≥ t ′ = , and the maximum of the expansion phase (purple dashed line) is at t ′ = . least three magnetometers in a spatial region for its subnetwork to be included in the study. For example,a substorm in which there were ≥ < ≥ ≥ ∼ eophysical Research Letters vary. This will not affect the properties of the computed network provided regions A, B, and C continue to bewell sampled with stations. However, the number of stations within each region can change. We thereforeinclude a normalization to the number of possible connections to define the parameter that we will use toquantify the network, the normalized number of connections: 𝛼 ( t ) = N ( t ) ∑ i ≠ 𝑗 N ( t ) ∑ 𝑗 ≠ i A i 𝑗 N ( t )( N ( t ) − ) , (2)where A is the adjacency matrix and N ( t ) is the number of active magnetometers.
3. Results
We now present (in Figure 2) the directed network for the individual substorm identified above (left column)and the average of all 86 selected substorms (right column). Substorm evolution is not necessarily linear,but the individual substorm is plotted as an example to highlight that the multievent mean is a reasonableaverage. Having obtained the subnetworks for each region (identified in Figure 1), we have the normalizednumber of connections, 𝛼 ( t ′ , 𝜏 c ) (equation (2)) within (panels 2–4) or between the regions A, B, and C (panels5–10). Looking at connected magnetometers within each region provides timings of the emergence of coher-ent spatial patterns of correlation in the magnetic field perturbations (at ground level), while connectionsbetween regions provide information on how these patterns are propagating and/or expanding through outthe substorm; any interregion dependencies will also be flagged. If all possible magnetometer connectionsare present, then 𝛼 = . Since the connections between regions (e.g., A → C and C → A) are plotted separately(e.g., panels 7 and 8), then if these were fully connected, the sum over the two plots would be 1. Hence, therange of values for the y axes for connections between regions (panels 5–10) are half the size of that withinthe regions (panels 2–4).As the networks are constructed using the time delay/lag at which the CCC between each pair of mag-netometer stations is maximal, each connection has an associated signed lag, 𝜏 c . We bin the number ofconnections ( 𝛼 ) into ranges of the magnitude of this lag ( 𝜏 c ). Connections that are at zero lag have no timedelay, that is, 𝜏 c = (gray), and connections with an associated direction of propagation/expansion, fromone magnetometer to another, have a range of delays, that is, lags from 1–15 min (blue-red). The sign ofthe lag indicates a direction of propagation or expansion from one magnetometer location to another; thisinformation is combined with the physical geographical locations of the magnetometers to determine if thepropagation/expansion is eastward or westward. The connections are separated into different panels foreach direction and then binned by the magnitude of the lag. For example, between regions A and C, panel7 plots the A → C propagation/expansion, eastward, from region A into region C while panel 8 plots C → Apropagation/expansion, westward, from region C into region A. Connections with a lag 𝜏 c = (indicated ingray) are plotted on both panels 7 and 8 (A → C and C → A), as they simply indicate instantaneous correla-tion between regions A and C, which have no associated direction, and thus, by definition the gray bars areidentical on the two plots.Figure 2 stacks the time series of the normalized number of connections, 𝛼 ( t ′ , 𝜏 c ) , so that the value of 𝛼 foreach range of | 𝜏 c | is plotted one above the other for increasing | 𝜏 c | . The stacking is such that each indepen-dent 𝛼 ( t ′ , 𝜏 c ) is visible. The envelope is then the total (normalized) number of connections over all lags, thatis, all | 𝜏 c | ≤ . For example, during the individual substorm (left column), we see mostly instantaneous(gray) correlation within A (panel 2) with an additional low level of lagged correlation later in the substorm.On the other hand within B (panel 3), at the time of peak expansion (purple dashed line), the network ismade up of ∼
10% instantaneous correlation, ∼
80% with ≤ | 𝜏 c | ≤ (fast propagating or expanding),and <
10% of connections have | 𝜏 c | ≥ (slow expansion or propagation). The plot covers the time interval − ≤ t ′ ≤ normalized minutes where the times of onset, peak expansion, and the 10-min intervalsin-between are indicated with vertical dashed lines. The figure presents a summary of time-varying spatialcorrelation for each subnetwork for the duration of the substorm. The full networks for the individual sub-storm are plotted in the supporting information. The SuperMAG electrojet index for the individual event,and its multievent average, is plotted in panel 1 of Figure 2. We can see that although the events are on anormalized time base, the multievent average is more smooth and responds less sharply to onset than theindividual event.ORR ET AL. 6273 eophysical Research Letters Prior to onset, the multievent average shows some spatially coherent connections within each of regions Aand C (panels 2 and 4). These connections are mostly instantaneous ( | 𝜏 c | = , gray shading) or with 1-minlag ( | 𝜏 c | = , dark blue shading). Importantly, these regions are not correlated with each other, so that thenumber of A → C and C → A connections is small (panels 7 and 8). At onset, in both the individual event andthe statistical average, (panel 3) we see that the subnetwork within region B has the most prompt and largestresponse, that is, increase in spatial correlation. For the individual substorm we see a sharp increase in thenumber of correlated pairs, beginning at onset ( t ′ = ) and increasing to ∼ t ′ ∼ . Likewise, the multievent average number of correlated magnetometerpairs within the B subnetwork begins to increase at onset, but it is smoother and reaches a peak slightlylater than in the individual event; in this case, correlation maximizes with ∼
60% connectivity at t ′ ∼ . TheJanuary substorm onset is mainly characterized by fast propagating (0- to 6-min lag) connections while inthe multievent mean subnetwork ∼
80% of connections are propagating (nonzero peak lag) throughout. Thisis consistent with a pattern that is both coherent and propagating and/or expanding. The timings of regionB growth are consistent across the majority of substorms observed.About 10 normalized minutes after onset we can see in panel 6 westward propagation and/or expansionfrom region B (around onset) into region A (westward of onset), B → A. This coincides with an increase inspatial correlation within region A (panel 2). For both the individual and the multievent average, the B → Atime series (panel 6), that is, the relative increase in the number of connections at different lags, resemblesthat of the network located wholly within region B (panel 3), except that it occurs ∼
10 normalized minuteslater and has about half the magnitude. Within region A (panel 2), ∼
50% of magnetometers become highlycorrelated at < t ′ < . For the individual substorm most of the connections between magnetometers areinstantaneous, but for the multievent average ∼ of the increase in the number of connections is at nonzerolag. We have found some variation between individual substorms as to how spatial correlation betweenmagnetometers within region A develops from − ≤ t ′ ≤ , with some substorms having no obviousresponse to onset. The A → B (panel 5) propagation and/or expansion develops on similar timescales to B → A (panel 6), but there are significantly fewer connections (20–30% of magnetometers correlated at peak, t ′ = ) within the multievent average, with ∼ of these connections being instantaneous (zero lag, nodirection).The subnetwork for region C (panel 4, east of the SCW) has the smallest response to substorm onset ofany region. The January substorm remains moderately connected ( ∼ < t ′ < , and the region is maximallycorrelated after peak expansion, t ′ > with ∼ % of magnetometer pairs being connected; this patternof correlation is consistent long into the recovery phase. This is consistent with many of the individual sub-storms showing little/no response to onset. In panel 9 we see that region B becomes correlated with region Cwith eastward propagation and/or expansion (B → C) ∼ ∼
20% magnetometer pairs correlated at t ′ > . In panel 10, we can see that for the individual event < → B, with this small increase only occurring ∼
25 normalized min-utes after onset. Correlation increases by ∼
15% for the multievent average between t ′ ∼ and t ′ ∼ .Thus, the response within region C simply tracks that of the propagation or expansion from B → C, and anypropagation from C → B occurs subsequently.Finally, ∼ t ′ ∼ , long after the time of peak expansion. There is slightly more eastward propaga-tion (A → C, >
20% of magnetometers) than westward propagation (C → A, ∼
10% and ∼
18% of magnetometerpairs for the individual and multievent average, respectively). Again, the lagged correlation originating in Cis very small (and mostly instantaneous) for the individual event.
If we can interpret coherent patterns of spatial correlation across the distributed SuperMAG magnetometersas the emergence of current systems, the above time-dependent network provides an evolution sequence,with timings, for the substorm current system in the nightside. Our analysis then provides a quantitativemeasure of spatial coherence as well as the timescales on which evolution occurs. By separating the nightsideinto three regions, we have attempted to isolate the components that have been proposed. To use the termi-nology of Kamide and Kokubun (1996), we have (A) eastward electrojet; (B) substorm unloading componentORR ET AL. 6274 eophysical Research Letters (SCW), and (C) westward electrojet. Whereas B is associated with the SCW, or DP1 perturbations, A and Ccan be related to the general magnetospheric convective system, DP2 (Nishida, 1968), which is enhancedduring substorm growth and expansion phases (Milan et al., 2017). To summarize the above results, weidentify key time ranges, before and after onset: ≤ t ′ < , ≤ t ′ < , ≤ t ′ < and t ′ ≥ in terms of normalized time, t ′ . Relating these intervals to substorm evolution t ′ is following onset, t ′ isexpansion phase, t ′ is near substorm peak, and t ′ is the early recovery phase. The timings are as follows:• Before onset, the premidnight and postmidnight regions A and C each have a relatively weak coherentpattern consistent with convection (DP2); notably, A and C are not coherent with each other.• In t ′ we first see the formation of a SCW (SCW/DP1) around onset (correlation within B), whichapproaches maximum in t ′ .• In t ′ there is westward propagation and/or expansion of the SCW west toward the premidnight region (A).We see connections (B → A) and at the same time a signature of a coherent current system within region A(correlation within A). This is shortly followed by weaker correlation from A → B, indicating that the entireA-B system is now correlated. These all approach a maximum at t ′ .• A weaker signal of eastward propagation and/or expansion of the SCW toward the postmidnight regionstarts in t ′ and reaches its maximum in t ′ . We see connections (B → C) and on a similar timescale asignature of a coherent current system within region C (correlation within C), with additional weakercorrelation from C → B. The correlation in region C is relatively low.• The regions eastward and westward of onset (A and C) each have a coherent pattern consistent withenhanced magnetospheric convection (DP2). Later in the substorm there is coherence between regions Aand C, beginning well after onset, in t ′ , and reaching maximum correlation in t ′ ; that is, only after regionB has become correlated with all other regions. This can either reflect direct correlation between A and C,or could simply imply that both A and C are correlated with B.We can then consider what support these results provide for proposed models for substorm current systems,specifically, models with a single westward electrojet segment (Kamide & Kokubun, 1996; McPherron et al.,1973), a westward, and a lower (but still in the auroral zones) latitude eastward electrojet segment (Ritter& Lühr, 2008; Sergeev et al., 2011, 2014); two unconnected westward electrojet segments premidnight andpostmidnight (Gjerloev & Hoffman, 2014; Rostoker, 1996); and finally, many small individual segments (Liuet al., 2018). Importantly, any method for quantifying spatial correlation cannot distinguish between directcorrelation (here, A → C) and indirect correlation (here, A → B → C); this indirect correlation may enhancethe number of A → C connections relative to B → C. Therefore, our results are not inconsistent with multipleseparate current systems provided that they are either spatially correlated with each other, or on spatialscales smaller than that of the magnetometer spacing.The coherent patterns of eastward and westward expansion are in agreement with previous work usingsynchronous space- and ground-based magnetometers (Nagai, 1982, 1991). However, we have not founddefinitive support for two, or more, distinct and uncorrelated substorm current systems. A lag, | 𝜏 c | > , forB → C connections, implies that C is delayed with respect to B, consistent with a propagation from B to C.Interpreting these results in terms of current components suggests two scenarios for this propagation: (i) asingle current segment, which is expanding from B to C, or (ii) a current segment in B and another in C,where the segment in C is correlated with that in B but is developing with some delay. There is no interpre-tation of our results, which would suggest a scenario where regions B and C are uncorrelated, independentcurrent systems.If they are associated entirely with general magnetospheric convection (DP2 system), the premidnight andpostmidnight (A and C) are directly driven by the solar wind and must enhance on similar timescales,although the magnitudes may differ (Kamide & Kokubun, 1996). We have found that preonset, the regionsA and C each have coherent, but relatively small, signatures of correlation with little CCC between them.Postonset, in both the individual event and the average over 86 substorms, the long range east to west (A → C)correlation patterns only emerge after the growth of the SCW (region B). The growth of spatially coherentpatterns appears first in B (the SCW, at onset) followed by A (with correlation between B and A) and later,in C. This suggests that following onset, A and C are not solely attributable to enhanced convection, and thepresence of contemporaneous B → C and B → A connections suggests that there may be a combination ofcontributions from convection enhancement and SCW expansion. Importantly, this does not require that acurrent segment in A expands or propagates into C.ORR ET AL. 6275 eophysical Research Letters
Finally, if instead of a large-scale SCW there were only many small, uncorrelated, individual segments (Liuet al., 2018), we would not expect to find the long-range correlations (A to C) seen here (also supportinginformation; Figure 1). Since we calculate CCC on minute resolution time series, each connection in thenetwork is derived from a 128-min time window. Thus, we cannot resolve short-timescale events such as alarge number of small wedgelets each associated with a bursty bulk flow in the plasma sheet, which havelifetimes of some 10 min. In addition, we cannot resolve structures that are on smaller spatial scales thanthe intermagnetometer spacing. If multiple wedgelets are present, their spatial aggregate would give anoverall large-scale magnetic amplitude signature mainly at the edges of the region containing the wedgelets,regardless of whether or not the wedglets are spatiotemporally correlated. Here, both spatial and temporalinformation is used to obtain the cross-correlation so that temporally uncorrelated wedgelets would giveno spatially coherent signature of cross-correlation at all, whereas if the same wedgelets were temporallycorrelated, we would find a signature of spatial cross-correlation.Potential limitations to the technique include sensitivity to the location of the east and west bulge bound-aries, which are static and therefore may not fully represent fast changes in the time-varying current system.There may also be a spatial coarse-graining effect due to the geographic location of the finite number ofmagnetometers; there are few near the eastward SWC boundary during the January substorm. To test this,we present the same plots for this event, but with the east and west boundaries of the bulge at t ′ = and t ′ = in the supporting information. These show little change from the results shown in Figure 2. Addi-tionally, the detailed network maps of the individual event, for the times represented by the vertical dashedlines in Figure 2, onset-peak, are provided in the supporting information. They highlight the importance ofthe spatial coverage and geographical locations of the highly correlated magnetometer pairs.Also, in the analysis and by the organization of data into three regions, A, B, and C, we are quantifying thecoherence over these regions. This is over a range in both latitude (60–75 ◦ ) and local time (typically region Bis ∼
4. Conclusions
We used the full set of SuperMAG ground-based magnetometer observations of isolated substorms to quan-tify the time evolution of patterns of spatial correlation. If the observed pattern of spatial correlation betweenmagnetometer observations captures ionospheric current patterns, then we can directly test different modelsfor substorm ionospheric current systems. We have obtained the first directed networks for isolated sub-storms. Each connection in the network indicates when the maximum CCC between the vector magneticfield perturbations seen at each pair of magnetometers exceeds an event and station specific threshold. Themaximum of the CCC corresponding to each connection in the network can occur at a nonzero time lag.The resulting directed network then contains information, not only on the formation of coherent patternsseen by multiple magnetometers but also on the propagation and/or expansion of these spatially coherentstructures.To gain insight on the ionospheric current system during a substorm, we obtained specific time-varyingsubnetworks from the data that isolate specific physical regions. These regions are west (A), within (B), andeast (C) of the bulge boundaries for each substorm (obtained from polar VIS images at the time of peakexpansion). We presented both a study of an individual event, which has at least seven magnetometers ineach of these regions for the duration of the substorm, as well as the average of the network properties of 86substorm events. If the observed pattern of spatial correlation between magnetometer observations capturesionospheric current patterns, we find the following sequence of events in terms of key time ranges afteronset: ≤ t ′ < , ≤ t ′ < , ≤ t ′ < and t ′ ≥ ( t ′ is normalized time Gjerloev et al., 2007):• Preonset, the premidnight and postmidnight regions A and C each have a relatively weak coherent patternconsistent with general magnetospheric convection (DP2) and are not coherent with each other.• A dominant SCW forming around the onset location (within region B) at the time of onset, t , whichreaches maximum spatial correlation at t , half way through the expansion phase.• This is followed by a westward expansion of this SCW (starting at t , with peak at t ) contemporaneous toand coherent with a current system in the premidnight region (within A).ORR ET AL. 6276 eophysical Research Letters • An additional weaker eastward expansion of the SCW (starting slowly at t with peak at t ). The signal ofa self-contained current postmidnight (region C) is relatively weaker and occurs late in the substorm. Theenhancement of C is delayed with respect to that of A.• Following the SCW expansion, A and C are coherent with each other, but at the same time are coherentwith the SCW. This is consistent with a combination of convection and expansion of the SCW.These conclusions are drawn from the averaged network over 86 isolated substorms. Although the over-all spatiotemporal timings revealed by this network analysis are reasonably consistent between individualevents and the 86 event average for the formation of a SCW around onset (B) and its expansion both east(B → C) and west (B → A), the exact timings of the current system evolution vary. Variability between eventscould be intrinsic or could relate to the observing conditions, such as differing magnetometer spatial cover-age or the static choice of location for region boundaries. Future work will quantify event-by-event variabilityacross multiple events and extend the analysis to multiple, compound events. So far in our analysis we havenot utilized the direction of the (vector) maximal CCC. In principle this could resolve the direction of theelectojet (eastward/westward).
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