Searching for Carrington-like events and their signatures and triggers

The Carrington storm in 1859 is considered to be the major geomagnetic disturbance related to solar activity. In a recent paper, Cid et al. (2015) discovered a geomagnetic disturbance case with a profile extraordinarily similar to the disturbance of the Carrington event at Colaba, but at a mid-latitude observatory, leading to a re- interpretation of the 1859 event. Based on those results, this paper performs a deep search for other 'Carrington-like' events and analyses interplanetary observations leading to the ground disturbances which emerged from the systematic analysis. The results of this study based on two Carrington-like events (1) reinforce the awareness about the possibility of missing hazardous space weather events as the large H-spike recorded at Colaba by using global geomagnetic indices, (2) argue against the role of the ring current as the major current involved in Carrington-like events, leaving field- aligned currents (FACs) as the main current involved, and (3) propose abrupt southward reversals of IMF along with high solar wind pressure as the interplanetary trigger of a Carrington-like event.


Introduction
The prevailing paradigm assumes that when a solar ejection turns the IMF southward, remaining southward for a prolonged period of time, results in a geomagnetic storm, one feature of which is a decrease in the surface magnetic field of the Earth [e.g. Burton et al., 1975;Tsurutani and Gonzalez, 1995]. On 2 September 1859, the Colaba observatory (10º MLat, 147º MLong) measured the most extreme geomagnetic disturbance ever recorded at low and mid latitudes, the so-called Carrington event (e.g. Cliver and Dietrich, 2013]). However, due to the absence of interplanetary data at that time the role of southward IMF B z in triggering the storm is unknown. As a result, a large amount of guesswork has been done concerning the Carrington storm (see as an example Tsurutani et al. [2003], [2005], Siscoe et al. [2006], and Manchester et al. [2006] concerning the identification of the interplanetary trigger). Cid et al. [2015] found that the profile of the horizontal component (H) of the terrestrial magnetic field measured in a two-day period extending from 16:00 MLT, 28 October 2003to 16:00 MLT, 30 October 2003 at Tihany magnetic observatory (in Hungary) was very similar to that recorded at Colaba during the same MLTs on 1-3 September 1859.
Although the intensity of the disturbance was just half of that recorded at Colaba, many other similarities between those events guided Cid et al. [2015] to label the event recorded at Tihany as a 'Carrington-like' event.
A detailed analysis of magnetic records at different locations during the event on 29 October 2003, when a large dataset was available from modern terrestrial surface observatories, provided very interesting results that, extrapolated to the Carrington event, led Cid et al. [2015] to conclude that the Dst or SYM-H indices might have missed the large H-spike recorded at Colaba and to suggest that field-aligned currents (FACs) played a major role in the H-spike in Carrington-like events. These conclusions shook some previous results on Carrington storm, which considered that the negative Hspike was a drop of Dst and therefore related to a ring current enhancement as a consequence of a long duration and intense southern B z , due to a magnetic cloud [Tsurutani et al., 2003;Li et al., 2006]. Besides the H-spike at Colaba for the 1859 event had also been suggested as not attributed to the ring current by some authors (e.g. Green and Boardsen [2006]), it should be noted that only extremely large IMF B z component has been associated with the terrestrial disturbance (e.g. Ngwira et al. [2014] and references therein).
The goal of this paper is to discover other 'Carrington-like' events in local magnetograms and, after analysing their interplanetary triggers, to extrapolate the results to the Carrington storm at Colaba. Section 2 shows the result of a deep search for other 'Carrington-like' events in the period when interplanetary data are available.
Section 3 describes geospace disturbances during the Carrington-like event on 21 January 2005. In Section 4 we analyse solar and interplanetary observations of the two Carrington-like events observed at mid latitude which emerged from the systematic analysis. Finally, Section 5 is dedicated to discussion and Section 6 to conclusions.

Searching for 'Carrington-like' events in local magnetic records
We have implemented a pattern recognition algorithm [Theodoridis et al., 2010] as an automated search engine to identify Carrington-like storms which is labeled CLSE (Carrington Like Search Engine). The procedure let us quantify similarities between ground magnetic signatures of any event at any observatory with a previously established pattern or model. At this stage we have constrained the model pattern for similarity measure to the Carrington event (Model-C, 'Carrington').
The events subject to be compared with the model appear as a result of a systematic analysis of a subset of data obtained from the INTERMAGNET database. The subset includes data on the period from 1991 to 2009 from nine observatories (each of them representing a latitude and longitude in a three by three worldwide sector grid): ABG, KAK, and SJG for low latitude; THY, BSL, and SPT for mid latitude; and ABK, FCC, and NAQ for high latitude (see Table 1 for geographical and magnetic coordinates of the observatories).
As described above, Model-C is the Carrington geomagnetic event at Colaba observatory recorded in 1859 (hereafter C59) and it is used as the model pattern input for the comparison in the CLSE. The first task to be done is to prepare Model-C data with the same temporal resolution as the events to be compared, i.e., to get C59 1-min resolution data to be compared to other 1-min resolution data from the INTERMAGNET database. Therefore in order to get C59 data ready for the algorithm we first digitized data from Figure 3 of Tsurutani et al. [2003] (which displays data for a two-day interval (1 September 16 h to 3 September 16 h Bombay local time), and then an interpolation was done to obtain 1-min resolution data of the two-days data sample.
The second step in the procedure was to obtain the event list to be compared to Model-C. For this purpose, the CLSE checks every 48-h time window (same interval as available for Model-C) from the subset database searching for a minimum at that time window at the same time as the Model-C minimum. This means that in that temporal window from 0 to 48 hours, the peak (minimum) value is detected at 18 hours and 43 minutes from the beginning. If this footprint is found, data of that 48h-window are saved as an event, otherwise another 48h-window (shifted 1 minute from the previous one) is checked until the complete subset database has been checked. It can be noticed that in this procedure, the time before and the time after the peak value in the 48hwindow are the conditions that define the events detected by the algorithm. No other condition is imposed to select the events. For example, the intensity of the event, the UT or the MLT of occurrence of the peak value are not taken into account.
Due to the large difference between the range of values of every geomagnetic event and Model-C, normalization is required before comparison. The scaling consists in a subtraction of the maximum value in the data set and then dividing by the total range of the window as shown in Equation 1.
where H is the value of the horizontal component of the geomagnetic field and Ĥ is the normalised value obtained. This normalization is applied to all geomagnetic events and to Model-C, so that absolute values will be lost but the profile of the events will remain.
A score value is obtained by normalizing the measure of the distance between the event and the model, dividing by 2880 (the number of minutes in two days) and subtracting from unity as shown in Equation 2. The highest score values obtained are highly dependent on latitude. Figure 1 shows histograms of score frequency at three observatories, FCC, THY and ABG, as representatives of high, mid and low latitudes, respectively. The total number of events emerged at each observatory is 3166 events for FCC, 3286 for THY and 2149 for ABG.
The histograms show the frequency distribution with a peak value which is clearly skewed when decreasing in latitude, indicating that the probability of finding a profile like the Carrington storm (Model-C) is larger at higher latitudes.
In each latitude range, we have analysed some of the highest score events (i.e. the disturbances most similar to the Carrington storm). We find that the onset of the highlatitude events took place close to local midnight, therefore indicating substorm activity, When comparing all panels in Figure 2 it can be noticed that a score as large as 0.87 can be obtained for an event (18 June 2003 at KAK) where the H-spike, both its decrease and recovering, is not as sharp as that of the Carrington event at Colaba. Even more, when the fast recovery of Colaba has been also pointed out as a relevant feature to explain FACs as the cause [Cid et al., 2015]. The uniqueness of the Colaba record relative to other typical storms shall be evidenced before following on, since a large score value seems to be not enough to label a storm as "Carrington-like". Therefore a threshold should be defined and any choice would be questionable. What is the minimum score value that indicates similarity?
This problem can be solved with cluster analysis (or clustering). It is a main task of exploratory data mining used in many fields, which consists in grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar to each other than to those in other groups (clusters). The task can be achieved by various algorithms, including groups with small distances among the cluster members, and the appropriate clustering algorithm and parameter settings (including the distance function to use and the threshold) depend on the individual data set and applications.
In this paper, the algorithm to group storm events in two different clusters will use the distance function given by Equation 1. The two groups correspond to Model-C (C59 described above) and Model-B ('Basic'), which is conceived as a typical geomagnetic storm, where the three phases can be easily identified, as sudden commencement (SC), main and recovery phase [Gonzalez et al., 1994]. Figure 3 shows a sketch of the procedure.
We chose to represent Model-B as the disturbance registered at Tihany observatory (THY) on 20 November 2003 due to its smooth and easily identifiable phases.
Moreover, this is also one of the most intense storms (-422 nT as seen by Dst index) whose interplanetary trigger is well identified: a magnetic cloud, preceded by a sheath, with a large and long-duration B z [Zhang et al., 2007]. Data for Model-B are 1-min resolution data from the INTERMAGNET database (no interpolation or smoothing is performed) from 20 November 2003 01:12 UT to 22 November 2003 01:11 UT. Model-B is obtained after scaling the sample following the same feature scaling procedure described above for Model-C. Figure 4 shows the 48 h-window which represents the normalised profile of magnetic disturbance labeled Model-B (green line). Model-C (red dot line) has been over plotted in Figure 4 for comparison purposes and to understand better the difference between both profiles (and as a result between being member of group B or C).
The distance function of Equation 1 between Model-B and Model-C, equal to 0.85, is a useful parameter which allows us to establish a threshold to classify an event in group B or C. However, scoring more than 0.85 is not enough to belong to a certain group. We will come back to this issue later. In any case, it is important to notice that this parameter will change if a different storm profile is considered as Model-B.
Once we have established Models-B and -C, the CLSE is applied to the same subset database (records from 1991-2009 from nine INTERMAGNET observatories, see above). The geomagnetic events are obtained, processed and evaluated to obtain B-and C-scores. Therefore, similarity measures are computed twice for every event detected by CLSE, one for Model-B and another for Model-C.
Classification of the events is done by comparing both scores. A scatter plot of score C versus score B for all geomagnetic events enables us to classify the events as group C (or group B) whether it is above (or below) the line of equal similarity. The farther away from that line the greater its membership to one group and not to the other. Furthermore, due to similarity between both model events, there is a limit on how much one score can differ from the other. This limit is the score that we obtain when comparing both models (equal to 0.85, see above). Therefore, we use this value as a lower threshold for the minimum score required for an event to belong to group B or C, that is, we can properly assign an event to group C when C-score > 0.85 and B-score < 0.85. When applying this criterion, the group C has 1443 elements at high-, 16 at mid-and 0 at low latitude.
In the same way, an event is properly assigned to group B when B-score > 0.85 and Cscore < 0.85. It is important to note that an event with C-score > 0.85 and B-score > 0.85 cannot be assigned to any group, as the event is too similar to both Models. In this way, it is worth noticing that a large score value does not always mean belonging to a certain group: the larger the difference of scores (and not the larger score) the more definite the belonging to a certain group.
Regarding the observatory data, some considerations have to be noted: there are some missing data periods of one year in the INTERMAGNET database for some observatories analysed; events with data gaps were not considered, as they may raise the score giving false information, and events with spikes were also discarded for similar reasons.
The results from this analysis appear in Figure  Hereafter these events at these locations will be named as C03 and C05, respectively.
The event on 29 October 2003 at FCC has also been highlighted as C03 in Figure 5c, to note that it corresponds to the same date and time. A light blue circle in Figure 5c indicates the position of the event on 21 January 2005. At high latitudes the event appears at FFC observatory but with a very poor and comparable C-(0.63) and B-(0.68) scores.
We have performed an equivalent analysis using other storms as Model-B. No other event in the sample analysed, but C03 and C05, can be properly assigned to group C.
This fact allows us to consider common features of these events as signatures of a "Carrington-like" event and the events as representative of this group.

Geospace disturbances during the event on 21 January 2005
Geospace disturbances during C03 event were analysed by Cid et al. [2015]. In this paper, we perform a similar analysis for C05 in order to identify whether there are more similarities between both 'Carrington-like' events than a local geomagnetic record.   Figure 6). Vertical lines showing S1 and S2 timings have been also added in Figure 6a keeping the same label. Vertical lines with labels T1 and T2 included in Figure 6 are explained below.
In Figure 6a we compare the measurements from a set of magnetic observatories at similar geomagnetic latitude (40º) and spread in longitude, keeping our attention in the first two hours after the SC, i.e., approximately the time interval corresponding to S1 and S2 labels. The magnetic trace for SPT and SUA, located in the dusk sector, shows an increase in H-component ranging from 50 nT to almost 100 nT at SC onset.
However, larger enhancements of 150 nT appear at IRT, which is located in the midnight sector. FRN and BSL, located in the pre-noon sector, show a negative change.
Instead of a positive disturbance, a fast decrease takes place in both observatories leading to a negative depression similar to the Carrington event. However, a difference appears in this event: the magnetic trace in FRN shows a two-pulse structure with two negative H-spikes comparable in intensity.
At low latitudes, the SC appears at the four magnetic observatories involved in the computation of the Dst index. For these four observatories, as in the event on 29 October 2003, the disturbance of the two first hours following the SC depends strongly

Solar and interplanetary observations leading to 'Carrington-like'
disturbances.

The triggers of the C03 event
The Similarly to the Carrington event, a magnetic crochet coincided with the solar flare on 28 October 2003 [Villante and Regi, 2008]. The size of the magnetic crochet recorded on the Greenwich and Kew geomagnetograms was used to estimate the flare soft X-ray peak intensity ranging from no less than X10 and more than X48 [Cliver and Svalgaard, 2004].  [Smith et al., 1998] are fully available for the event.

The triggers of the C05 event
A GOES X7.1-class flare at 06:40 UT on 20 January 2005 and a halo CME observed on just one uncontaminated LASCO image at 06:54 UT are the observations of the main solar activity related to the C05 event. In this case, the intensity of the X-flare was not enough to produce a magnetic crochet as in the C03 and C59 events and the active region (NOAA 10720) was not a very complex active region. Nevertheless, AR10720 presented large flaring activity and produced several fast halo CMEs in the previous days. The fastest CME of cycle 23, which may have reached a speed of ~3000 km s -1 close to the Sun [Pohjolainen et al., 2007], originated in this active region.
At the time of C05 event, the Dst index was already disturbed after a moderate geomagnetic storm that happened two days before. Interaction between two CMEs and a high speed stream associated with a coronal hole characterized the interplanetary event.  The arrival of the S1 shock is followed by a secondary front discontinuity (solid vertical line S2) at 18:21 UT. While the interval after S1 shows very high temperature (7×10 5 K) and densities of about 15 cm -3 , after S2 the plasma is cooler and the density is highly enhanced, peaking at 60 cm -3 . After S1, the has also been plotted in this panel although it will not be discussed in this section (we will come back to this figure in the next Section).
Our analysis of the two first hours after S1 reveals two sharp southward turnings of B z (shown as vertical dashed lines in Figure 8, labeled as T1 and T2) changing from northward to southward of about 30 nT in 2 minutes at 16:54 UT and at 17:52 UT (these times correspond to the mid-point of the time interval time of the sharp turning).

Discussion
When performing a systematic search for 'Carrington-like' profiles in the horizontal component recorded at mid-and low-latitude observatories spread in longitude, only two events arise whose temporal profiles during two days are extraordinarily similar to the one recorded at Colaba in 1859 (C59): the event on 29 October 2003 (C03) and the event on 21 January 2005 (C05). The similarities between the C03 event and the C59 event were first discovered by Cid et al. [2015]. Their results showed that although recorded magnetic field variations at one of the observatories (THY) closely resembled the profile recorded at Colaba during the Carrington event, a large asymmetry appeared in the disturbance when moving in longitude for C03. As a result, the disturbance of C03 in SYM-H and Dst indices was missed when averaging local disturbances.
As in C03, the magnetic disturbance of C05 is also missed by the SYM-H and Dst indices. When analysing at mid-latitude local magnetic records during the C05 event, a large asymmetry appears also in the disturbance when moving in longitude. As in the C03 event, in C05 the disturbance depends strongly on the magnetic local time. Even more, in both events similar profiles correspond to similar MLTs, being negative in the dayside and positive in the nightside: peaking at dawn-noon sector and almost unnoticed in the noon-dusk sector. In both events less-than-one-hour local depressions (H-spikes) happened simultaneously with auroral effects, with auroral displays observed at locations up to 10º away in latitude from the stations that recorded the maximum magnetic disturbance. This scenario, where a clear day-night asymmetry appears when moving in longitude, is indicative of a disturbance caused by R1 FAC [Yu et al., 2010].
Indeed, according to the Biot-Savart's law, the horizontal geomagnetic field grounddisturbance (H) at mid latitude due to R1 FACs is negative in the dayside and positive in the nightside, in line with what is observed in both C03 and C05 events. Moreover, the only available record at low latitude for C59, which fits to C03 and C05 patterns at the same MLT, supports that FACs are the main magnetospheric current system involved in Carrington-like disturbances, as previously suggested by Cid et al. [2015].
On the other hand, when applying the Biot-Savart's law to an enhanced ring current, a depression in H is expected at any longitude, and as a result at any MLT, making lowlatitude global indices such as Dst or SYM-H appropriate to study magnetic disturbances related to a symmetric ring current enhancement, but making them unsuitable when large asymmetries (positive and negative disturbances) appear in longitude. Indeed, the ASY-H index was introduced to describe the longitudinally asymmetric geomagnetic disturbance field at mid latitude due to a partial ring current enhancement, which results in a dawn-dusk asymmetry. In the case of R1 FACs, due to the day-night asymmetry at mid and low latitude, those indices are unsuitable to quantify the disturbance.
To reinforce the hypothesis of FACs as the main magnetospheric current system involved in Carrington-like disturbances, a deeper analysis has been carried out with the subsets of events from Figure 5 with membership to group C (C-score > 0.85 and B-score < 0.85) and with those assigned to group B (C-score < 0.85 and B-score > 0.85). Figure 9 shows a scatter plot of score versus MLT for each subset (group-C events appear as red crosses and group-B ones in green) for high-, mid-and low-latitude ground geomagnetic stations.
Looking at the bottom panels (a) and (b) in Figure 9, the distribution in longitude of group B events at low and mid latitude shows a clear dawn-dusk asymmetry. Indeed, H < 0 appears almost at any MLT (indicative of a ring current enhancement), with the largest scores peaking at dusk sector as indicative of the major role of the partial ring current in the initial phase of typical geomagnetic storms.
On the other hand, in panels of Figure 9c, a day-night asymmetry in the distribution of events (with most of the events at night sector) appears at high latitude for both group B and group C, as indicative of the significant occurrence of substorms of the tail current system at latitudes close to the auroral electrojet. It should be also noticed the highest score values correspond to group C at high latitude.
A day-night asymmetry appears again at mid latitude for group C, but in this case the Hspike of Carrington-like events concentrate in day-time, departing from the substorms affinity with night-time. Despite the small number of events in the plot, the large difference to the equivalent figure at mid latitude for group B is enough to suggest another current as cause responsible for the magnetic disturbance.
The MLT distribution of the highest C-score events at mid latitude points out to R1 FACs as the most probable cause of C-events. Nevertheless, the analysis of the evolution of the magnetic disturbance in longitude for every event is essential to conclude the direct effect through the Biot-Savart's law of R1 FACs as the cause of the H-spike disturbances for the Carrington-like events.
Searching for the interplanetary trigger of C03 and C05, we find out that in both events the drop of the H-spike (S and T in Figure 7, T1 and T2 in Figure 8) took place when southward incursions of the IMF larger than 10 nT/min under high dynamic pressure (note that the horizontal axes in bottom panel in Figures 7 and 8 are shifted 14 min for C03 and 25 min for C05 in order to make coincident the interplanetary shock and the SC). Indeed southward abrupt reversals have been identified as the cause of prompt electric field penetration [Othani et al., 2013], which is favoured by high solar wind density/pressure [Lopez et al., 2004;Fiori et al., 2014]. The end of each drop in H (the peak of the spike) is well correlated to a northward IMF turning as well. These results suggest that the disturbances recorded during C03 and C05 were controlled by the magnetic reconnection process. Similar results were obtained by Wei et al. [2008] when analysing a long-lasting penetration event observed during 11-16 November 2003.
Southward turnings instead of long-lasting and intense southward IMF B z were considered as better solar-wind precursors of large variations of Dst . Skoug et al. [2004] also pointed out that large alternating northward and southward IMF contributed to extreme geomagnetic storms as 4 August 1972, 15 July 2000, and 31 March 2001. Tsurutani et al. [2003] proposed that the most likely driver for the H-spike in C59 (what they called the main phase of the Carrington storm) would be a magnetic cloud due to its long duration and intense southern B z , but no interplanetary data were available at that time to check this hypothesis. Following this hypothesis, the Carrington event was associated with very extreme solar wind and IMF conditions in order to reproduce a Dst value of -1600 nT [Li et al., 2006] or a ground-magnetic disturbance of the same value at one location, i.e. Colaba [Ngwira et al., 2014]. Their models yielded an extremely large IMF B z component (> -200 nT for 2.5 hours) and an equally large density (400-800 cm -3 ) and velocity ( 2000 km s -1 ). Although coronagraph images show CMEs travelling at speeds like that one assumed by Ngwira et al. [2014] however the magnetic field and the solar wind density proposed are unprecedented: the strongest absolute field strengths reported at 1AU are 60-80 nT (less than one third) and the largest observed density is below 200 cm -3 .
In the cases of C03 and C05, the driver was the sheath downstream of the interplanetary shock, where the abrupt reversals of IMF B z are combined with a high dynamic pressure. Solar wind pressure has been pointed out above as a factor which favours prompt electric field penetration, as it produces a larger compression of the magnetosphere, which results in larger FACs and as a consequence, in a larger peak at the spike in the pre-noon sector.
In spite of the lack of solar wind data in some of the events studied in this paper, the time of transit of all of them is well established: 17.5 h for C59 [Tsurutani, 2014], 19 h for C03 [Skoug et al., 2004] and 34 h for C05 [Pohjolainen et al., 2007]. A smaller transit time is equivalent to a larger solar wind velocity and therefore larger dynamical pressure will be expected. The observed peak values at the H-spike in the three Carrington-like events (C59, C03 and C05) agree with these expectations.
Even more, assuming by extrapolation that the trigger of C59 was also an abrupt reversal of IMF B z, combined with a high dynamic pressure, a linear extrapolation can be performed to estimate solar wind conditions preceding the Carrington event. As the intensity of the H-spike in C59 is 2.3 times that of C03, this factor let us estimate a solar wind density close to 230 cm -3 , an abrupt southward reversal of IMF B z, of about 135 nT/min and later on a southward turning with a long-lasting B z value of about -50 nT for about 7 hours. Similar values are obtained by extrapolation of solar wind data conditions during C05. According to historical solar wind data records, these values are much more reasonable than those previously considered in simulations. Nevertheless, the profile of the disturbance resulting at ground level is expected to be highly dependent on longitude (as in C03 and C05), contrary to the results shown in Figure 9 from Ngwira et al. [2014] where a similar pattern appears at low-latitude ground locations at different longitudes.

Conclusions
We 1) As previously suggested by Cid et al. [2015] for C03 and C59, our analyses based on ground-magnetometers records of C05 at low-and mid-latitude observatories, and on the similarity of the temporal profiles observed for these events at different MLTs, support the suggestion of Cid et al. [2015] that FACs play a major role in the large Hspike of C05 and for all Carrington-like events observed at mid latitude, discarding the role of the ring current as the major current involved in this kind of disturbance.
2) As observed in C03, also in C05 the H-spike is missed in indices such as Dst or SYM-H. This fact arises due to the large differences appearing among the local magnetic disturbances from observatories spread in longitude (positive in some and negative in others) and averaged out. Besides the large differences in local magnetic records at the same magnetic latitude in every event, similar profiles are recorded for C03 and C05 at The editor thanks Mauro Regi and an anonymous referee for their assistance in evaluating this paper.         Interplanetary magnetic field (same panel distribution as 4 top panels of Figure 5) and solar wind parameters, Vsw, N, T, in the next 3 panels, measured at ACE location.