Correlating the interplanetary factors to distinguish extreme and major geomagnetic storms

We investigate the correlation between Disturbance Storm Time (Dst) characteristics and solar wind conditions for the main phase of geomagnetic storms, seeking possible factors that distinguish extreme storms (minimum Dst <−250 nT) and major storms (minimum Dst <−100 nT). In our analysis of 170 storms, there is a marked correlation between the average rate of change of Dst during a storm's main phase (ΔDst/Δt) and the storm's minimum Dst, indicating a faster ΔDst/Δt as storm intensity increases. Extreme events add a new regime to ΔDst/Δt, the hourly time derivative of Dst (dDst/dt), and sustained periods of large amplitudes for southward interplanetary magnetic field Bz and solar wind convection electric field Ey. We find that Ey is a less efficient driver of dDst/dt for extreme storms compared to major storms, even after incorporating the effects of solar wind pressure and ring current decay. When minimum Dst is correlated with minimum Bz, we observe a similar divergence, with extreme storms tending to have more negative Dst than the trend predicted on the basis of major storms. Our results enable further improvements in existing models for storm predictions, including extreme events, based on interplanetary measurements.


Introduction
The modern definition of the geomagnetic storm is characterized by a prolonged depression in the horizontal component of the Earth's low-latitude magnetic field (Rostoker et al., 1997). This depression is caused by the ring current encircling the Earth in a westward direction (Kamide et al., 1998;Daglis et al., 1999). The Dst (Disturbance Storm Time) index is used to gauge the intensity of geomagnetic storms by measuring this overall ring current intensity (Iyemori, 1990) at low-latitude observatories.
The critical importance of the time derivative of Dst is manifested in part in its use for reconstructing global geomagnetic fields. The measurement of symmetric disturbances for the Horizontal geomagnetic field (SYM-H) is a de facto higher resolution Dst (Wanliss and Showalter, 2006) commonly utilized by the geospace model-ing community to further the understanding of geomagnetic field dynamics. In Sitnov et al., (2008), the application of SYM-H and its time-related derivative were fundamental within their Nearest-Neighbor (NN) approach to spatially reconstruct the magnetosphere and identify storm phases. More recently, Stephens et al., (2019) built upon the NN approach, using SYM-H and its time derivative with the addition of the Auroral Electrojet Index Amplitude Lower (AL) and the AL time derivative to create 3-D models of magnetospheric stretching and dipolarization processes during substorm disturbances. Given the lengthy history of Dst usage, the focus of this paper is on the Dst metric over SYM-H, which was introduced in 1981, to ensure continuity and consistency across our storm analyses.
Two interplanetary factors that are widely thought to help drive the occurrence of geomagnetic storms are the solar wind convection electric field E y and the southward component of the Interplanetary Magnetic Field (IMF) B z (e.g., Yokoyama and Kamide, 1997), in the Geocentric Solar Magnetospheric (GSM) coordinate system. A southward B z component indicates beneficial conditions for the process of magnetic reconnection to occur at the magnetopause, with subsequent storage of energy in the magnetotail. The release of this stored magnetic energy due to magnetotail reconnection results in particle injections that form the ring current around the Earth, which in turn causes the depression in the horizontal component of Earth's magnetic field (Lakhina and Tsurutani, 2017).
Many studies have investigated the empirical relationships between Dst and interplanetary factors, by using a basic form: where Dst * = Dst-(a and b are constants) is correcting for solar wind dynamic pressure (P) since this pressure affects the magnetopause location and its associated current. Q represents the driving term, and Dst*/ represents the decay of the ring current primarily due to charge exchange between ions and neutral atoms. Burton et al., (1975) first laid the foundation for this empirical analysis, where Q(t) depends on the solar wind electric field under southward IMF. O'Brien and McPherron (2000) modified the coefficients in the formula for Dst* and redetermined . Wang CB et al., (2003) took into account the effect of the solar wind pressure in Q. In the Temerin and Li (2006) model, Dst depends on both the present and past solar wind conditions. Thanks to these studies, the Dst prediction has been much improved, for example, as demonstrated in Ji et al., (2012) where various Dst models are compared. We expand upon the previously studied regimes by analyzing 7 additional extreme storms to establish a positive and nonlinear correlation between the interplanetary electric field E y and dDst/dt, showing that E y is a less efficient driver of dDst/dt for extreme storms.
The effect of IMF B z on storms has long been recognized. The strength of a geomagnetic storm and its main phase duration were found to be directly proportional to the strength and duration of the IMF B z component (Vichare et al., 2005;Alex et al., 2006;Rawat et al., 2007Rawat et al., , 2010. Gonzalez and Echer (2005) completed an extensive study with the conclusion that the driving B z component at the Lagrange L1 location tends to reach its peak value about 2 hours before the peak minimum Dst, corresponding to about 1 hour for the solar wind conditions to propagate to the Earth and an additional hour for the magnetosphere to respond. Li et al., (2011) conducted a statistical analysis of 89 storms with minimum Dst ranging from −100 nT to −422 nT, between 1996−2008. In this analysis, they noted a close correlative relationship between the amplitudes of the peak B z and peak Dst, before and after removing the solar wind dynamic pressure effect. In this paper, we build upon these earlier findings extending the analysis to include more recent events.
Despite great improvements in Dst models and investigations of solar wind conditions, there is a lack of understanding whether extreme storms differ qualitatively from major storms in Dst characteristics and interplanetary driving conditions. In this study, we analyze the relationships among minimum Dst, the time derivative of Dst, the time duration of the main phase, the solar wind electric field, and IMF B z , to elucidate features that distinguish extreme storms (minimum Dst < −250 nT) from major storms (−250 nT < minimum Dst < −100 nT).

Methodology
The hourly averaged Dst data used in this study were acquired from the World Data Center for Geomagnetism, WDC-Kyoto. The hourly average solar wind parameters were acquired from the OMNI database for all except three extreme storms, where Advanced Composition Explorer (ACE) satellite data is substituted (shifted to the bow shock nose, according to the measured solar wind speed).
The primary period of interest for our analysis is from January 1967-August 2018, when solar wind data are available. We designated major storms as minimum −250 nT < Dst < −100 nT and extreme storms as minimum Dst < −250 nT, and selected 130 storms that fit into either of the two categories. An additional 40 geomagnetic storms during January 1957-May 1992 were used only for Dst-related calculations to further improve the statistical significance for extreme storms. In some events, Dst was found to exhibit two minima before returning to a quiet level. If there was marked separation and recovery between the relative minima, they were considered to be two storms. If the two Dst minima do not have a clear separation or recovery period, the storm is treated as a single event, which is classified as a Type 2 storm in Kamide et al., (1998).
All geomagnetic storm events were analyzed during their main phases, from the maximum Dst value before a significant decline to the absolute minimum of their Dst profiles. Storms that were separated into two events essentially were considered as two separate main phases. The interplanetary factors were analyzed during this same main-phase time frame, designated by using the Dst profiles.

Results
We first examine how the average rate of Dst change during the main phase (ΔDst/Δt) varies as a function of storm strength ( Figure 1a). The calculation of ΔDst/Δt was performed by taking the difference of the minimum Dst and relative maximum at the start of the main phase and dividing it by the time difference between the two points.  Figure 1 are the strong initial pulse of Dst during the storms' sudden commencement. With the initial positive Dst at the start of the main phase, the minimum Dst tends toward less negative values. We have confirmed this explanation by examining ΔDst/Δt as a function of the difference between the initial and minimum Dst, which indeed has a stronger correlation without significant deviations (data not shown).
In order to qualitatively understand further differences between extreme and major storms, the time duration of the storm main phase was compared with minimum Dst values. Notably, the time duration of storms is a critical factor in their impact on thermosphere heating and satellite drag (Oliveira et al., 2020). In Figure 1b, we provide the context needed to not only understand potential differences between extreme and major storms on thermosphere heating and satellite drag, but also elucidates the broader implications of Figure 1a. Despite the variation in the main phase duration for weak storms, overall the duration is around 10 hours. The uniformity of the main phase duration is the underlying reason for the correlation between ΔDst/Δt and minimum Dst.
Next, we investigate the relationship between dDst/dt and solar wind conditions. In Figure 2, we show the scatter plot for dDst/dt and the solar wind electric field, where the hourly dDst/dt(t = ) = (Dst( + )−Dst( − ))/ (2 ), and is 1 hour. The analysis includes 124 events since 1967 with available solar wind paramet-ers, primarily from the OMNI database except for three cases, in which we used ACE. The trend indicated by this figure points to higher amplitude E field as the amplitude of dDst/dt increases. It also indicates a threshold for nonlinear behavior for higher E field values: the more extreme storms in red are skewed towards the lower half of the graph in a manner that departs from the linear trend. Data are divided into six subgroups according to dDst/dt. The edges of each bin are marked by dashed vertical lines, and the black crosses indicate the medians for each bin. At the black cross shown in the bottom left of Figure 2, there is a marked deviation that again supports the presence of some bias among the more extreme storms.
The existing studies about Dst have suggested that the solar wind dynamic pressure (P) and the ring current decay have effects on dDst/dt (e.g., O'Brien and McPherron, 2000;Wang CB et al., 2003), as shown in Equation (1). In order to account for these effects, we follow the model by Wang CB et al., (2003): here, P is the solar wind dynamic pressure in nanopascals (nPa). set. Still, across both figures, the driving E components are much stronger for extreme storms, departing from the linear trend line.
Due to the solar wind E-field's role as a main driver of dDst/dt, we further examine the relationship between the integral of E (int E) during the storm main phase and the minimum Dst. In Figure 4, we illustrate a moderate correlation between the two parameters, though many of the extreme storms depart from the trend line's predicted values.
The interplanetary magnetic field B z component is a major parameter of interest for storms and has long been associated with the initiation of the storm main phase (Kokubun, 1972;Gonzalez and Tsurutani, 1987). In Figure 5, we present a correlative picture of minimum B z vs. minimum Dst, including six additional geomagnetic storms with accessible B z data to form a dataset of 130 storms. In the weaker range of storms (> −250Dst) within Figure 5, the majority of data points are closely surrounding the linear trend line, however the extreme storms fall further from the trend line. Since the linear coefficient is fairly high, it is evident that there is a trend towards lower minimum B z components as geomagnetic storms increase in strength. The results in Figures 4 and 5 are consistent with those presented in Gonzalez and Echer (2005). We include such analyses to emphasize the importance of sustained large values of solar wind E y and southward IMF B z in producing strong storms, and contrast the differences between these interplanetary measures for extreme and major storms that fall outside the scope of Gonzalez and Echer (2005). Based on the aforementioned graphical results, it is clear that extreme events tend to have more nonlinear correlations, pushing towards farreaching values.

Discussion and Conclusions
In this paper, we examined the statistical relationships between driving interplanetary factors and Dst variations to differentiate the characteristics of extreme and major geomagnetic storms during the main phase. While strong correlations were observed in this study, extreme geomagnetic storms distinguish themselves in every factor of interest. In the case of ΔDst/Δt in relation to minimum Dst, extreme storms tend to exhibit much higher rates during their main phase than their major storm counterparts. For the relation of solar wind E and dDst/dt, driving E is much stronger than the linearly predicted E for extreme storms even after adjusting for pressure and decay rates, indicating that the solar wind electric field is less efficient in driving dDst/dt for extreme storms. The minimum Dst is correlated with the integral of E and the minimum B z ; however, the extreme storms tend to have more negative Dst than the trend for major storms.
Our results indicate that during storms with major to extreme strengths, the magnetosphere response as an integrated system must be better understood to obtain more accurate storm predictions. In previous studies such as Wang CB et al., (2003), a uniform relationship between dDst/dt and solar wind conditions was obtained for all storms, whereas our study points out the necessity   to consider qualitative differences between major and extreme storms. For example, our finding that the solar wind electric field is less efficient in driving dDst/dt for extreme storms can have important bearing on how the magnetosphere handles the increased energy input during extreme storms. The solar wind energy input to the magnetosphere is mainly through dayside reconnection, while the polar cap potential associated with the dayside reconnection rate tends to exhibit saturations at large values of the solar wind electric field, possibly related to the effects of ionosphere outflow (e.g., Borovsky and Birn, 2014;Dorelli, 2019). In other words, the increasing rate of energy input through dayside reconnection could be regulated in part by the ionosphere and consequently affect ring current variations. One of the key implications is that the extreme-storm impact on the polar ionosphere is immediate and should be better quantified as part of the magnetosphere's response to extreme solar driving, in addition to Dst. Table S1. List of extreme and major storms analyzed in the paper.