Dependence of great geomagnetic storm intensity ( Δ SYM-H ≤ -200 nT) on associated solar wind parameters
aa r X i v : . [ phy s i c s . s p ace - ph ] N ov Solar PhysicsDOI: 10.1007/ ••••• - ••• - ••• - •••• - • Dependence of great geomagnetic storm intensity(∆SYM-H ≤ -200 nT) on associated solar windparameters Ming-Xian Zhao · Gui-Ming Le · Qi Li · Gui-Ang Liu · Tian Mao © Springer ••••
Abstract
We use ∆SYM-H to capture the variation in the SYM-H index duringthe main phase of a geomagnetic storm. We define great geomagnetic storms asthose with ∆SYM-H ≤ -200 nT. After analyzing the data that were not obscuredby solar winds, we determined that 11 such storms occurred during solar cycle23. We calculated time integrals for the southward interplanetary magnetic fieldcomponent I(B s ), the solar wind electric field I(E y ), and a combination of E y and the solar wind dynamic pressure I(Q) during the main phase of a greatgeomagnetic storm. The strength of the correlation coefficient (CC) between∆SYM-H and each of the three integrals I(B s ) (CC = 0.74), I(E y ) (CC = 0.85),and I(Q) (CC = 0.94) suggests that Q, which encompasses both the solar windelectric field and the solar wind dynamic pressure, is the main driving factorthat determines the intensity of a great geomagnetic storm. The results alsosuggest that the impact of B s on the great geomagnetic storm intensity is muchmore significant than that of the solar wind speed and the dynamic pressureduring the main phase of associated great geomagnetic storm. How to estimatethe intensity of an extreme geomagnetic storm based on solar wind parametersis also discussed. Keywords:
Solar wind; Disturbances; Magnetosphere; Geomagnetic disturbances B G.-M. [email protected] Key Laboratory of Space Weather, National Center for Space Weather, ChinaMeteorological Administration, Beijing, 100081, P.R. China School of Physics Science and Technology, Lingnan Normal University, Zhanjiang,524048, P.R. China Institute of Geophysics, China Earthquake Administration, Beijing, 100081, P. R.China
SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 1 .-X. Zhao et al.
1. Introduction
A geomagnetic storm is the result of the sustained interaction between solarwinds with the southward magnetic field and Earth’s magnetic field. Previousworks have explored the effect of different solar wind parameters on the intensityof an associated geomagnetic storm by calculating the correlation coefficients(CCs) between the peak value of various solar wind parameters and the mini-mum Dst index for the associated geomagnetic storm (e.g. Echer, Gonzalez, andTsurutani, 2008; Echer et al., 2008; Choi et al., 2009; Kane, 2005; Kane, 2010;Ji et al., 2010; Richardson and Cane, 2011; Wu and Lepping, 2002, 2016; Meng,Tsurutani, and Mannucci, 2019; Lawrance, Moon, and Shanmugaraju, 2020).However, these CC values have no physical meaning (Le, Liu, and Zhao, 2020).Wang et al. (2003) proposed that the geomagnetic storm intensity is largelyunaffected by the solar wind density or the dynamic pressure, and that it isonly a function of the interplanetary dawn-dusk electric field (termed as thesolar wind electric field in this study). Echer, Gonzalez, and Tsurutani (2008)determined that the CC between the time integral of the solar wind electricfield during the main phase of the super geomagnetic storm intensity and theminimum of Dst index is equal to 0.62. Balan et al. (2014, 2017) explored therelationship between super geomagnetic storms, the sudden high enhancementin the solar wind speed, and the southward magnetic field at the leading edgeof the associated coronal mass ejection (CME). Based on the work of Burton,McPherron, and Russell (1975), Kumar et al. (2015) estimated the magnitude ofthe interplanetary electric fields responsible for historical geomagnetic storms.Liu et al. (2014b,a); Liu, Chen, and Zhao (2020) evaluated an extreme geomag-netic storm intensity only based on solar wind electric field, without consideringthe effect of the solar wind dynamic pressure on the extreme geomagnetic stormintensity. Xue et al. (2005) identified the interplanetary sources that were respon-sible for the great geomagnetic storms (Dst ≤ -200 nT) that occurred during thesolar maximum (2000 - 2001) and quantified the linear fit between Dst and boththe solar wind electric field and the storm duration with the solar wind dynamicpressure making little contribution to the storm intensity. These published worksprovide valuable insight into geomagnetic storms, but largely ignore the possiblecontributions made by the solar wind density or the solar wind dynamic pressure.Case studies (Kataoka et al., 2005; Cheng, Le, and Zhao, 2020), global MHDsimulations (Lopez et al., 2004), and an impulse response function model (Weigel,2010) suggest that the solar wind density is an important parameter that mod-ulating the transfer of solar wind energy to the magnetosphere during the mainphase of a storm.The development of a geomagnetic storm depends on the ring current injectionterm, Q, and the decay term. Q is either implemented as a linear function ofthe solar wind electric field (Burton, McPherron, and Russell, 1975; Fenrichand Luhmann, 1998; O’Brien and McPherron, 2000), or as a function of boththe solar wind electric field and the solar wind dynamic pressure Wang, Chao,and Lin (2003). A recent study has shown that it is more appropriate to applythe definition of Q that includes the solar wind dynamic pressure for majorgeomagnetic storms (Dst ≤ -100 nT) (Le, Liu, and Zhao, 2020). SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 2 ependence of great Geomagnetic storms on Solar Wind Parameters
Le, Liu, and Zhao (2020) found that the time integrals for the southwardinterplanetary magnetic field component I(B s ), the solar wind electric field I(E y ),and a combination of E y and the solar wind dynamic pressure I(Q) duringthe main phase of the major geomagnetic storm make small, moderate, andcrucial contributions to the intensity of the major geomagnetic storm, respec-tively. Great geomagnetic storms (∆SYM-H ≤ -200 nT) are much stronger thanmajor geomagnetic storms (Dst min ≤ -100 nT). To determine whether a similarstatistical trend exists for great geomagnetic storms, we calculated the CCsbetween ∆SYM-H and these three time integrals for great geomagnetic storms.The stronger the geomagnetic storm, the worse the space weather and thegreater the harm. How to estimate the intensity of an extreme geomagneticstorm? Researchers (e.g. Liu et al., 2014b,a; Liu, Chen, and Zhao, 2020) usuallyestimated the intensity of an extreme geomagnetic storm by using the empiricalformulas found by Burton, McPherron, and Russell (1975); Fenrich and Luh-mann (1998); O’Brien and McPherron (2000). However, the empirical formulafound by Wang, Zhao and Lin (2003) was seldom used to estimate the intensity ofan extreme geomagnetic storm. Which empirical formula is better to describe therelation between solar wind parameters and the intensity of an extreme storm?To answer the question, we will discuss which empirical formula is the betterone. The data analysis, discussion, and summary for this study are presented inSection 2, Section 3, and Section 4, respectively.
2. Data analysis
The SYM-H index was obtained from the World Data Center for Geomagnetismin Kyoto (http://wdc.kugi.kyoto-u.ac.jp/aeasy/index.html). In this study, ourdata set consists of solar wind data recorded by the Advanced Composition Ex-plorer (ACE) (ftp://mussel.srl.caltech.edu/pub/ace/level2/magswe) from 1998to 2006 with a time resolution of 64 seconds.
Seventeen geomagnetic storms with a minimum of Dst ≤ -200 nT occurred duringsolar cycle 23. However, the main phases of five of those great geomagnetic stormscoincided with a data gap caused by the solar wind. The SYM-H index can betreated as a high time resolution Dst index (Wanliss and Showalter, 2006), weused ∆SYM-H to represent the variation in SYM-H during the main phase of ageomagnetic storm. In this study, we define storms with ∆SYM-H ≤ -200 nT asgreat geomagnetic storms. The geomagnetic storm that occurred on November9 th and 10 th in 2004, with ∆SYM-H = -165 nT during the main phase of thegeomagnetic storm, does not meet the criteria for a great geomagnetic storm;as such, we do not include it in our data set. Because the variation in SYM-Hduring the main phase of the geomagnetic storm on September 25 th in 1998 isequal to -177 nT, this storm is also not included in our data set. The minimum SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 3 .-X. Zhao et al.
Dst value for a major geomagnetic storm that occurred on October 21 st I(B s ), I(E y ), and I(Q) represent the time integrals of the southward componentof interplanetary magnetic field (IMF), the solar wind electric field, and the ringcurrent injection term (Wang, Chao, and Lin, 2003) during the main phase ofthe associated great geomagnetic storm, respectively. These integrals are definedas I ( B s ) = Z t end t start B z d t (1) I ( E y ) = Z t end t start V sw B z d t (2) I ( Q ) = Z t end t start Q d t (3)where t start and t end are the start and the end times of the main phase of a greatgeomagnetic storm, respectively. The Q variable in Equation (3) was found byWang, Chao, and Lin (2003), which is defined as Q = (cid:26) V sw B s ≤ . mV /m − . V sw B s − .
49) ( P k / / V sw B s > . mV /m (4)where P k is the solar wind dynamic pressure.The geomagnetic storm main phase is defined as a period from the momentwhen SYM-H starts to decrease to the moment when SYM-H reaches its lowestvalue. The start time of the main phase of a geomagnetic storm corresponds tothe moment when z-component of interplanetary magnetic field starts to becomenegative. ∆SYM-H represents the difference in the storm magnitude between thebeginning and the end of the main phase of a great geomagnetic storm.According to Equation listed below,dDst ∗ / d t = Q(t) − Dst ∗ /τ, (5)Equation (5) can be written as below, Z tets d (SYM-H ∗ ) = Z tets ( Q(t) − SYM-H ∗ /τ ) dt . (6)Where t s and t e are the start and the end time of the main phase of the associatedstorm. Assuming that the time integral of injection term is much larger than the SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 4 ependence of great Geomagnetic storms on Solar Wind Parameters time integral of the decay term during the main phase of a great geomagneticstorm, then we have Z t e t s d (SYM-H ∗ ) ≃ Z t e t s Q(t)d t (7) (cid:16) . q P k | t s − . q P k | t e (cid:17) is much smaller than △ SYM-H for a great geo-magnetic storm. Finally, we get the formula listed bellow,∆SYM-H ≃ Z t e t s Q ( t )d t = I ( Q ) (8)After determining the start and the end times of the main phase of thegreat geomagnetic storm, we calculate ∆SYM-H, identify the interplanetarysource responsible for that ∆SYM-H, and calculate the corresponding solar windparameters I(B s ), I(E y ), and I(Q).After determining the start and the end times of the main phase of thegreat geomagnetic storm, we calculate ∆SYM-H, identify the interplanetarysource responsible for that ∆SYM-H, and calculate the corresponding solar windparameters I(B s ), I(E y ), and I(Q).For example, let us examine the great geomagnetic storm that occurred onMay 15 th in 2005 (Fig. 1). The ACE spacecraft recorded an interplanetary shockat 02:05 UT on May 15 th in 2005 (the first vertical dashed line in Fig. 1). Theshock reached the magnetosphere at 02:38 UT and caused a sudden storm (thefirst vertical solid red line in Fig. 1). The main phase of the storm, which isthe period between the second and third vertical solid red lines in Figure 1,has a ∆SYM-H value of -350 nT. Solar wind between the second and thirdvertical dashed lines in Figure 1 is the interplanetary source responsible forthe main phase of the storm. The I(B s ), I(E y ), and I(Q) values for the mainphase of the storm are -3723.95 nT · min, -3292.92 mV · m − · min, and -35045.2mV · m − · nPa · min, respectively.The calculations for a second storm, which occurred on October 21 st to 22 nd in1999, are shown in Figure 2. The main phase of the storm is the period betweenthe first and second vertical red lines, and it was caused by the solar windbetween the first and second vertical dashed lines in Figure 2. During the mainphase of the storm, ∆SYM-H = -269 nT, and the I(B s ), I(E y ), and I(Q) valuesare -9183.60 nT · min, -4647.12 mV · m − · min, and -24798.4 mV · m − · nPa · min,respectively. After determining the I(B s ), (I(E y ), I(Q), and ∆SYM-H values for each greatgeomagnetic storm, we calculated the CC values between ∆SYM-H and each ofthe three time integrals: CC(I(B s ), ∆SYM-H) = 0.74, CC(I(E y ), ∆SYM-H) =0.85, and CC(I(Q), ∆SYM-H) = 0.94. SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 5 .-X. Zhao et al. S peed k m / s -40-2002040 n T B z B t -40-20020 E y m V / m N p 1 / c m P k n P a SY M - H n T Figure 1.
ACE spacecraft observations on May 15 th , 2005. From top to bottom, the panelsrepresent the solar wind speed, the total IMF (B t ) (blue line) and the z-component of theIMF (B z ) (red line), the solar wind electric field (E y ), the proton density (N p ), the solar winddynamic pressure (P k ), and the SYM-H values. The two horizontal dashed lines in the secondpanel denote 0 nT and -10 nT, respectively. The horizontal dashed line in the fifth paneldenotes 3 nPa. S peed k m / s -30-20-100102030 n T B z B t -15-10-505 E y m V / m N p 1 / c m P k n P a SY M - H n T Figure 2.
ACE spacecraft observations on October 21 st and 22 nd in 1999. The panels andlines are identical to those shown in Figure 1. SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 6 ependence of great Geomagnetic storms on Solar Wind Parameters -16000 -14000 -12000 -10000 -8000 -6000 -4000 -2000 0-450-400-350-300-250-200-150 S Y M - H I(B s )CC=0.76 -10000 -8000 -6000 -4000 -2000-500-450-400-350-300-250-200 S Y M - H I(E y )CC=0.85 (a) (b) -70000 -60000 -50000 -40000 -30000 -20000 -10000-500-450-400-350-300-250-200 S Y M - H I(Q)CC=0.94 (c)
Figure 3.
Statistical analyses of the relationships between ∆SYM-H and (a) I(B s ), (b) I(E y ),and (c) I(Q).
3. Discussion
A previous estimation of CC(I(E y ), Dstmin) = 0.62 (Echer, Gonzalez, and Tsu-rutani, 2008) for super geomagnetic storms (Dstmin ≤ -250 nT) is much lowerthan our CC(I(E y ), ∆SYM-H) value of 0.85 for great geomagnetic storms. Thedifference in these values arises due to the difficulty in determining the startand end time of a geomagnetic storm precisely using the Dst index. The timeresolution of the Dst index is one hour; the SYM-H index has a much finer timeresolution, which allows for more exact determination of the start and end timeof the main phase of a geomagnetic storm, and then the interplanetary sourceresponsible for the geomagnetic storm main phase can be determined exactly.SYM-Hmin is not equal to ∆SYM-H for some storms. For example, SYM-Hminfor the geomagnetic storm on 9-10, November 2004 is -214 nT, while ∆SYM-His -165 nT, which is much higher than SYM-Hmin. Equation (8) tell us thatCC(I(Q), ∆SYM-H) is more reasonable than CC(I(Q), SYM-Hmin). CC(I(E y ),∆SYM-H) is also more reasonable than CC(I(E y ), SYMmin). These should bealso the reason why CC(I(E y ), ∆SYM-H) in the present study is larger thanCC(I(E y ), Dstmin) in the article by Echer, Gonzalez, and Tsurutani (2008). SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 7 .-X. Zhao et al.
CC(I(B s ), ∆SYM-H) for great geomagnetic storms is 0.74, while CC(I(B s ),SYM-Hmin) for major geomagnetic storms is o.33 (Le, Liu, and Zhao, 2020),indicating that there is a big difference between the CC(I(B s ), ∆SYM-H) forgreat geomagnetic storms and CC(I(B s ), Dstmin) for major geomagnetic storms.We attribute this differences to the fact that the B s value for a great geo-magnetic storm is much larger than that of a major geomagnetic storm, andCC(I(B s ), ∆SYM-H) is more reasonable than CC(I(B s ), SYM-Hmin). BecauseEy = VswBs, CC(I(B s ), ∆SYM-H) and CC(I(E y ), ∆SYM-H) are 0.74 and 0.85respectively, indicating that the contribution to the great geomagnetic intensitymade by the solar wind speed is much smaller than southward component of IMF.The comparison between CC(I(B s ), ∆SYM-H) and CC(I(Q), ∆SYM-H) impliesthat the contributions to the great geomagnetic intensity made by the solar windspeed and dynamic pressure are much lower than southward component of IMF.Based on our CC values, we infer that B s contribution to the great geomagneticstorm intensity is much more significant than those of the solar wind speed andthe dynamic pressure.CC(I(Q), ∆SYM-H) is larger than CC(I(E y ), ∆SYM-H), suggesting that thering current injection term Q that includes both the solar wind electric field andthe solar wind dynamic pressure is more accurate than the Q definition thatonly depends on the solar wind electric field for great geomagnetic storms.For Q defined in Equation (4), Ey should be much larger than 0.49 mV/mduring the main phase of a great geomagnetic storm. As such, Q can be writtenas Q = − . E y − . P k / / (9)The averaged P k for the great geomagnetic storms ranged from 5.3 nPa to26.5 nPa, indicating that 1.2 < ( P k / / < y for greatgeomagnetic storms ranged from 7 mV/m to 26 mV/m, much larger than that ofaveraged ( P k / / . According to Equation (9), the impact of E y on Q is muchlarger than ( P k / / . This should be the reason why CC(I(Q), ∆SYM-H) isslightly larger than CC(I(E y ), ∆SYM-H), namely that the difference betweenI(Q) and I(E y ) is small for the great geomagnetic storms. If I(Q) is very closeto I(E y ) for extreme geomagnetic storm, then the intensity of an extreme geo-magnetic storm can be estimated by I(E y ). However, what is the real situation?Here, we give a real case. The solar wind dynamic pressure during the somepart of the main phase of the extreme geomagnetic storm shown in Figure4 of the article by Liu, Chen, and Zhao (2020) exceeded 700 nPa. The solarwind dynamic pressure is very big and should have a significant effect on theassociated extreme storm intensity according to Equation (9), implying that theextreme magnetic storm intensity shown in Figure 4 of the article by Liu, Chen,and Zhao (2020) was greatly underestimated. Anyway, CC(I(Q), ∆SYM-H) isalways larger than CC(I(E y ), ∆SYM-H) for great geomagnetic storms and evenstronger geomagnetic storms, implying that it is more accurate to estimate theintensity of an extreme geomagnetic storm by I(Q) than by I(E y ). SOLA: solphy2020.tex; 10 November 2020; 3:41; p. 8 ependence of great Geomagnetic storms on Solar Wind Parameters
4. Summary
Our CC values that capture the statistical relationship between ∆SYM-H andI(B s ), I(E y ), and I(Q), where Q is a combination of E y and the solar winddynamic pressure, for great geomagnetic storms (∆SYM-H ≤ -200 nT) are equalto 0.74, 0.85, and 0.94, respectively. With the strength of the correlation between∆SYM-H and I(Q), we infer that Q is the most important solar wind parameterin the determination of the intensity of a great geomagnetic storm. Furthermore,our results imply that it is more accurate to use the ring current injection termdefinition proposed by Wang, Chao, and Lin (2003) than it is to define Q asa linear function of the solar wind electric field when it comes to assessing theintensity of a great geomagnetic storm and even stronger geomagnetic storm.The statistical results also suggest that B s makes much more contribution tothe intensities of great geomagnetic storms that happened in Solar Cycle 23than solar wind speed and dynamic pressure. Acknowledgments
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