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Monitoring the global evolution of the storm ring current and storm indices from confined ground geomagnetic observatories
Journal of Atmospheric and Solar–Terrestrial Physics 191 (2019) 105049
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Monitoring the global evolution of the storm ring current and storm indices from confined ground geomagnetic observatories G. Zeng a, C. Shen a, *, Z.J. Rong b, c, X. Li d, T. Chen e, Z.Q. Chen e, Y.H. Ma a, f a
School of Science, Harbin Institute of Technology, Shenzhen, 518055, China Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China c Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China d Laboratory for Atmosphere and Space Physics, University of Colorado, Boulder, USA e State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China f Key Laboratory of Lunar and Deep Space Exploration, Chinese Academy of Sciences, Beijing, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Magnetic storms Substorms Ring current Gradient of magnetic field Multipoint data analysis method Storm indices
For the first time, the global structure of the geomagnetic disturbance field around the Earth as well as the magnetic storm indices have been deduced from magnetic field measurements by ground observatories in a confined range of longitude. The spatial gradient of the H component of the geomagnetic disturbance field was obtained from ground geomagnetic observatories only in the Eastern Hemisphere, provided the geomagnetic disturbance field varies approximately linearly in space. Furthermore, the storm symmetric and asymmetric indices were derived and the spatial distribution and temporal evolution of the storm ring current was inves tigated. It was found that the storm indices derived from observatories in the Eastern Hemisphere are consistent with the officially published Kyoto standard indices which are derived from six globally distributed observa tories. We also calculated the storm indices for 1941–1956 by using data from three observatories (HER, KAK and SJG). The correlation coefficient between the symmetric index deduced from three observatories and the one from the global six observatories is 0.98, and the correlation coefficient between the two kind of asymmetric indices is 0.79. Those results suggest that our approach is reasonable and significant when global ground ob servatories are not readily available.
1. Introduction The Dst index is one of the most important geomagnetic indices and has been used to describe the development and intensity of the magnetic storms [Dessler and Parker, 1959; Sckopke, 1966; Gonzalez et al., 1994]. During magnetic storms, particles in the near earth plasma sheet are injected into the inner magnetosphere, experience acceleration, and undergo drift motions, so as to lead to the formation of a ring current around the Earth, which causes a decrease of the H component of the geomagnetic field on the surface of the Earth [Akasofu and Chapman, 1961; Siscoe and Crooker, 1974; Gonzalez et al., 1994; Fok et al., 1996; Jordanova et al., 1997; De Michelis et al., 1997; Shen et al., 2002; Vallat et al., 2005; Chen et al., 2006; Daglis, 2006]. The decay of the ring current is mainly due to charge exchange between the ring current en ergetic ions and the cold atoms in the exosphere of the Earth [Jorgensen et al., 1997; Pollock et al., 2001; Brandt et al., 2004; Kozyra and
Liemohn, 2003; Perez et al., 2004]. The hourly Dst index was put for ward to depict the geomagnetic disturbance field during magnetic storms [Akasofu and Chapman, 1961; Sugiura, 1964; Sugiura and Kamei, 1991]. It is calculated by using data from four ground geomag netic observatories at low and middle latitude [Sugiura and Kamei, 1991]. Besides the symmetric ring current, other magnetospheric cur rents contribute to the Dst index, such as the partial ring current [Lie mohn et al., 2001; Liemohn, 2003], the dayside magnetopause current [Burton et al., 1975; Feldstein et al., 2006; O’Brien and McPherron, 2000], the magnetotail current [Burton et al., 1975; Alexeev et al., 1996; Feldstein et al., 2006; Turner et al., 2000], and the substorm current wedge [Friedrich et al., 1999; Munsami, 2000]. The Dst index can also be accurately predicted based on upstream solar wind conditions [Bur ton et al., 1975; O’Brien and McPherron, 2000; Temerin and Li, 2002, 2006, 2015]. In contrast to the hourly Dst index, the symmetric (SYM-H) and
* Corresponding author. E-mail address: [email protected] (C. Shen). https://doi.org/10.1016/j.jastp.2019.05.013 Received 15 December 2018; Received in revised form 7 April 2019; Accepted 27 May 2019 Available online 30 May 2019 1364-6826/© 2019 Elsevier Ltd. All rights reserved.
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105049
asymmetric (ASY-H) storm indices were developed at the 1 min time resolution [Iyemori, 1990]. Essentially, the SYM-H index is the same as the Dst index [Wanliss and Showalter, 2006; Love and Gammon, 2009; Gannon and Love, 2011], except that data from a different set of stations and a slightly different coordinate system are used (available at http ://wdc.kugi.kyoto-u.ac.jp/aeasy/asy.pdf). Clauer and Mcpherron (1974) created a local time-universal time contour map of the deviation of the X (geographic north) component of the geomagnetic field to study the development of magnetospheric substorms by using measurements of mid-latitude geomagnetic obser vatories. Iyemori (1990) has investigated the local time distribution of both the D and H components of geomagnetic disturbance field at mid-latitude geomagnetic observatories. With data from 98 mid- and low-latitude geomagnetic observatories, Newell and Gjerloev (2012) introduced four partial ring current indices to investigate ring current development. It is worth noting that a global distribution of geomag netic observatories is necessary in the works mentioned above. Six sta tions are used for the derivation of the Kyoto SYM-H (available at http ://wdc.kugi.kyoto-u.ac.jp/aeasy/asy.pdf), and four stations for the Kyoto Dst [Sugiura and Kamei, 1991]. Both sets of stations are almost distributed evenly in longitude. In the early 20th century, there were not enough geomagnetic observatories to cover the whole world. In this work, we will calculate storm indices and investigate ring current development using only data from eastern hemisphere geomagnetic observatories. In our previous work [Shen et al., 2015], a new method was devel oped to redefine the storm symmetric and asymmetric indices and to study the evolution of the storm ring current. The gradient of the cor rected H component of the disturbance field was calculated from ground geomagnetic observatories, and the storm symmetric and asymmetric indices were deduced. Calculations confirmed that this new approach is reasonable and can be applied to investigate the evolution of the storm ring current. In this study, the same method has been used to deduce the spatial gradient of the H component of the geomagnetic disturbance field from ground geomagnetic observatories in eastern hemisphere, then the storm symmetric and asymmetric indices are obtained, and the spatial distribution and temporal evolution of the storm ring current are deduced. The data and method are presented in section 2. The properties of the ring current and the newly defined storm indices are illustrated in section 3. In section 4, the storm symmetric and asymmetric indices are calculated before the year 1957. Finally, we present the summary and conclusions in section 5.
Table 1 Coordinates of the observatories. Observatory
Geographic
AAA ABG ASP BMT CTA GUI HBK HER KAK KDU KNY LRM LZH MBO MMB QSB TAM TSU
Geomagnetic
Latitude ( )
Longitude ( )
Latitude (� )
longitude (� )
43.25 18.63 23.76 40.06 20.08 28.32 25.88 34.43 36.23 12.69 31.42 22.22 36.1 14.38 43.9 33.87 22.79 19.2
76.92 72.87 133.88 116.18 146.25 16.43 27.71 19.23 140.18 132.47 130.88 114.1 103.84 16.97 144.2 35.64 5.52 17.58
34.3 10.2 32.9 30.1 28 33.8 27.1 34 27.4 22 21.9 32.4 25.9 20.1 35.4 30.3 24.7 18.8
152.7 146.2 208.2 187 221 60.6 94.4 84 208.8 205.6 200.8 186.5 176.1 57.5 211.3 113.5 81.8 85.9
�
�
the corrected horizontal components of these observatories. The for mulas are as follows: SYM
H¼
ASY
H¼
N 1 X Hα ; N α¼1 cosφα
� H �� cos φ�max
� H �� ; cos φ�min
(1) (2)
where N is the number of the observatories, and the superscript α refers to the αth observatory. H represents the horizontal component of the geomagnetic disturbance field, which is obtained by subtracting the main and Sq field from the original data. φ is the geomagnetic latitude of the observatory. The formula H=cos φ is a latitudinal correction of the horizontal component for each individual observatory. It is noted that the latitudinal corrections in equations (1) and (2) are slightly different from those in the original definitions of Kyoto SYM-H and ASY-H. In this research, the latitudinal correction of the H component is made for each observatory, which is similar to the method described by Mursula et al. (2008) and Love and Gammon (2009). Assuming the geomagnetic disturbance varies linearly in space, the two observatories with maximum and minimum disturbances will be located at the Earth’s magnetic equator, and the distance between them is the Earth’s diameter (2RE). The first order gradient of the corrected H component in magnetic equatorial plane can be expressed as,
2. Data and method To produce the Kyoto SYM-H and ASY-H, six geomagnetic observa tories are used. Their locations are distributed in the mid- and lowlatitudes, evenly in longitude (available at http://wdc.kugi.kyoto-u.ac. jp/aeasy/asy.pdf). In this work, we seek to get the SYM-H and ASY-H indices from geomagnetic measurements confined to the eastern hemisphere. We select 18 geomagnetic observatories in the eastern hemisphere (hereafter called “eastern stations”). The geomagnetic latitude of the observatories range between 10� to 40� both in northern and southern hemisphere. The geographic and geomagnetic coordinates of the 18 observatories are given in Table 1. Their distribution is shown in Fig. 1. It should be noted that, for some particular months, there are long data gaps in a few observatories. In our previous work [Shen et al., 2015], a new method was devel oped to redefine the storm symmetric and asymmetric indices and to study the evolution of the storm ring current, which is introduced briefly below. In this work, the same method has been used except with different observatories. Traditionally, the SYM-H index is defined as the average value of the corrected horizontal components of the observatories, and the ASY-H index is calculated by subtracting the minimum from the maximum of
� � �req Hc� ¼ Hcmax Hcmin ; 2RE
(3)
where Hc ¼ H=cos φ is the corrected H component, and the superscript eq refers to the gradient in the geomagnetic equatorial plane. It is noted that the direction of geomagnetic disturbance is opposite to that of geomagnetic main field, and geomagnetic disturbance value is positive. The gradient of Hc is in the direction of maximum value of Hc which represents the minimum disturbance. In other words, the opposite di rection of gradient of Hc points to the peak of partial ring current. Consequently, a new definition of the storm index Asy-H can be written as, � � Asy H ¼ 2RE �req Hc�: (4) The arithmetic mean of the corrected H components for the SYM-H index describes the disturbance at the barycenter of the ground obser vatories. But we prefer to represent the storm symmetric index by the disturbance at the dipole center of the Earth. The Earth’s dipole center does not coincide with the barycenter of ground observatories in 2
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105049
Fig. 1. Distribution of observatories in geographic coordinates. The black dots represent the observatories. The black solid line denotes the magnetic equator.
general. Thus, there is a difference between disturbance at the Earth’s dipole center and that at the barycenter of ground observatories. We add the difference by a first order linear correction term on the arithmetic mean term, and that is N 1 X H ¼ Hcðr ¼ rCD Þ ¼ Hcα þ rCD ⋅rHc; N α¼1
Sym
qα ¼
N 1 X rα rα N α¼1
(5)
3. Results 3.1. Intense storm on 4–8 October 2000 We first analyze the intense storm event on 4–8 October 2000. A sawtooth event composed of a series of substorms occurs during the main phase of this storm [Huang et al., 2003; Reeves et al., 2003; Spencer et al., 2007; Troshichev et al., 2011]. Fig. 2a–c shows the evolutions of the IMF, solar wind velocity and AE index. The black curves in Fig. 2d and e are the Kyoto SYM-H and ASY-H indices. As shown in Fig. 2a, the IMF Bz turns southward at around 0530UT on 4 October 2000, and re mains at around 10 nT until 0330UT on 5 October. Subsequently, it reaches 27 nT at around 0530UT with a sudden decrease, then turns northward by a rapid increase between 0530UT and 0700UT. The solar wind velocity is 400–500 km/s (Fig. 2b). While the IMF Bz remains southward, there are continuous quasi-periodic oscillations of AE index as shown in Fig. 2c. Fig. 2d shows that the storm main phase commences as the IMF Bz turns southward. The SYM-H index drops to a minimum ( 185 nT) as the IMF Bz reaches a minimum value. Afterwards, the SYM-H index attains another minimum ( 184 nT) as the IMF Bz turns southward again with a sudden decrease. Shen et al. (2015) used six global stations to calculate storm Sym-H and Asy-H indices and the MLT positions of the peaks of the ring current, which are represented by blue in Fig. 2d–f. Red represent results ac quired from only eastern stations. As shown in Fig. 2d, the storm Sym-H index derived from the eastern stations is in good agreement with that from global stations and with the Kyoto SYM-H index. Fig. 2e shows that there is little difference in the values of the three storm asymmetric
(6)
where rα is the position vector of the α th ground observatories in the geography coordinates. The volumetric tensor has three nonnegative b ð1Þ , eigenvalues ω1 , ω2 and ω3 , and three corresponding eigenvectors k b ð2Þ and k b ð3Þ . k Based on the multipoint analysis method [Shen et al., 2012], the gradient of Hc can be deduced as N X
Hcα qα
rHc ¼
(8)
ðlÞ where ~rαl ¼ rα ⋅ b k is the lth component of rα .
where the superscript α refers to the αth observatory. The direction of the position vector rCD is from the barycenter of the observatories to the dipole center of the Earth, and the length is the distance between them. The method described by Fraser-Smith (1987) is used to calculate the position of the eccentric dipole. It may be mentioned that the anti-direction of the gradient of Hc points to the peak of the ring current. The gradient of Hc can be deduced from measurements of ground geomagnetic observatories with the multipoint data analysis method [Harvey, 1998; Shen et al., 2012] applied. The spatial gradient can be determined by a volumetric tensor [Harvey, 1998], which is defined as R¼
3 X ðlÞ 1 ~rαl b k N ωl l¼1
(7)
α¼1
where 3
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Fig. 2. A comparison between results acquired from global stations and only eastern stations for the 4–8 October 2000 storm. (a) The total magnitude and the three components of the interplanetary magnetic field (IMF) in GSE coordinate; (b) The three components of the velocity of the solar wind in GSE coordinate; (c) The AE index; (d) The storm symmetric index which is derived from our new method (Hcðr ¼ rCD Þ) by eastern stations (red) and global stations (blue), and the standard � � Kyoto SYM-H index (black); (e) The storm asymmetric index which is derived from our new method (�req Hc�⋅2RE ) by eastern stations (red) and global stations (blue), and the standard Kyoto ASY-H index (black); (f) The magnetic local time of the anti-direction of the equatorial gradient of Hc (req Hc), which indicates the position of the peak of the ring current. The red pluses represent the result deduced from eastern stations, and the blue dots represent that from global stations. The locations of the ABG station, which is approximately the center station of the Eastern stations in Fig. 1, are marked by the green dots.
the ring current deduced from eastern stations are near local dusk, which correspond to results from global six stations. This supports our method of only using eastern hemisphere stations.
indices. The variation trends of those curves are also similar. Fig. 2f shows that, during the main phase and initial recovery phase, the po sitions of the peak of the ring current are near local dusk, which agree well with the positions deduced from global stations. It is indicated that our new method works well when only eastern hemisphere stations are available.
3.3. Super storm on 7–11 November 2004 Fig. 4 illustrates a super storm on 7–11 November 2004, which is driven by an interplanetary magnetic cloud. A shock passes the magnetosphere at around 1930UT on 7 November as shown in Fig. 4a. Meanwhile, the solar wind velocity increases to ~650 km/s, and the storm main phase commences. At around 1930UT 9 November another shock passes over the magnetosphere and again causes a decrease of the SYM-H index. Fig. 4c shows continuous AE activity with a peak of ~3500 nT. From Fig. 4d, there is a big difference between the Sym-H and Kyoto SYM-H index around the minimum value, but they are in good agreement outside that difference band. Fig. 4e shows good con sistency between the Asy-H index derived from the eastern stations and the Kyoto ASY-H index. The positions of the peak of ring current deduced from the eastern stations are consistent with those from the global stations as shown in Fig. 4f.
3.2. Moderate storm on 25–28 October 2007 The moderate storm on 25–28 October 2007 was generated by a corotating interaction region (CIR) event [Balogh et al., 1999; Smith and Wolfe, 1976; Tsurutani et al., 1995; Tsurutani et al., 2006; Turner et al., 2006]. As shown in Fig. 3a–d, there was a rapidly varying IMF Bz as the storm begins at around 1200 UT on 25 October, and the maximum Bz reaches ~20 nT. During the main phase, the AE index reaches maximum at ~1200 nT. In the high speed stream region that is sunward of CIRs (from 20 UT day 25 Oct until the end of the interval in Fig. 3), the stream is filled with large amplitude Alfven waves [Belcher and Davis, 1971]. When the Alfven wave with southward component magnetic field im pinges onto the Earth’s magnetosphere, magnetic reconnection occurs [Dungey, 1961], and energy is injected into the nightside magneto sphere [Tsurutani and Gonzalez, 1987]. A series of sub storms/convection events take place, which is called a High-Intensity, Long-Duration, Continuous AE Activity (HILDCAA) event. The energy is injected only to L > 4 [Søraas et al., 2003], so only the outer ring current is affected. A review for interested readers can be found in the work of Tsurutani et al. (2006). As illustrated in Fig. 3d and e, the storm indices derived from the eastern stations are in agreement with those from the global six stations and Kyoto storm indices. As shown in Fig. 3f, the positions of the peak of
4. Storm indices before 1957 The Kyoto standard Dst index has been calculated since the year 1957. Karinen and Mursula (2005) reconstructed the Dst index before 1957 by using geomagnetic data, using a formula quite similar to the original standard one. In this section, we will calculate the storm sym metric and asymmetric indices before 1957 by our new method. The geomagnetic data we use are from three of the four low-latitude ob servatories which contribute data to calculate the standard Dst index. 4
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Fig. 3. A comparison between the results acquired from global stations and only eastern stations for the 25–28 October 2007 storm. The format of the figure is the same as that of Fig. 2.
Fig. 4. A comparison between the results acquired from global stations and only eastern stations for the 7–11 November 2004 storm. The format of the figure is the same as that of Fig. 2.
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some minority of cases. All of the cases were divided between stormtime (Sym-H-6 <¼ 30 nT) and quite-time (Sym-H-6 > 30 nT), and the correlations between Asy-H-3 and Asy-H-6 are investigated sepa rately. The result shows that the correlation coefficient was 0.78 in the storm-time cases and 0.66 in the quite-time cases. The correlation for quite-times is not better than for storm-times. The particle injection in storm-time may not be a possible mechanism that violates the linearity, but more strong evidence is needed. In order to investigate the nonlinearity systematically, we will deduce the second-order gradient in future work. The approach to assessing the skill of forecasting binary events [Jolliffe and Stephenson, 2003] is also used to evaluate the correspon dence between the storm indices deduced from the three stations and those from the global six stations. Three measures were chosen to quantify the performance of the storm indices deduced from the three stations in the final analyses. The three measures are the probability of detection (POD), the probability of false detection (POFD) and the Heidke skill score (HSS) [Doswell et al., 1990; Ganushkina et al., 2015; Lopez et al., 2007; Pulkkinen et al., 2013]. These measures can be defined as a function of the number of (a) hits, (b) false alarms, (c) misses, and (d) correct rejections. A hit represents a threshold crossing event which was both forecasted and observed. A false alarm represents a threshold crossing event which was forecasted but not observed. A miss represents a threshold crossing event which was not forecasted but observed. A correct rejection represents a threshold crossing event which was neither forecasted nor observed. The probability of detection (POD) is defined as
The four standard observatories are Hermanus (HER, 34.40� S, 19.22� E), Honolulu (HON, 21.30� N, 158.10� W), Kakioka (KAK, 36.23� N, 140.18� E), and San Juan (SJG, 18.38� N, 66.12� W) [Sugiura and Kamei, 1991], where the values in the parentheses are geographic latitude and longitude of the observatories. The three observatories we use are HER, KAK and SJG whose distribution is shown in Fig. 5. Fig. 6 depicts the storm symmetric index deduced from these three observatories in 1941–1956 by our method. This period is from the end of solar cycle 17 to the beginning of the solar cycle 19. Fig. 7 depicts the storm asymmetric index deduced from these three observatories. In order to evaluate the indices deduced from these three observatories, we compare the Sym-H-3 (or Asy-H-3) index (3 refer to three observatories) to the Sym-H-6 (or Asy-H-6) index (the storm symmetry or asymmetry index deduced from global six observatories which here are ABG, HER, HON, KAK, SJG and TUC. The distribution is shown in Fig. 5). Fig. 8a shows the frequency distribution histograms of the Sym-H-3 and Sym-H-6 index for 1941–1956. The bin size is 2 nT. The mean and standard deviation of the Sym-H-3 index are 16.44 nT and 24.84 nT, respectively. The mean and standard deviation of the Sym-H-6 index are 16.11 nT and 23.64 nT, which are closely similar to those of the SymH-3 index. To measure the differences between the values of the Sym-H-3 and Sym-H-6 indices, we calculated the root-mean-square deviation (RMSD) or root-mean-square error (RMSE). The RMSD between the Sym-H-3 and Sym-H-6 indices is 4.99 nT. Fig. 8b shows the plot of the Sym-H-3 index versus the Sym-H-6 index. The line is a linear fit. The correlation coefficient between them is 0.98. Fig. 8c shows the histogram frequency distributions of the Asy-H-3 and Asy-H-6 indices. The bin size is 2 nT. The mean and standard devi ation of the Asy-H-3 index are 19.36 nT and 18.57 nT which are close to those for the Asy-H-6 index (23.22 nT for the mean and 19.94 nT for the standard deviation). And the RMSD between the Asy-H-3 and Asy-H-6 indices is 13.21 nT. Fig. 8d shows a plot of the Asy-H-3 index versus the Asy-H-6 index. The line is a linear fit. The correlation coefficient be tween them is 0.79. It means the linear assumption does not apply to
POD ¼
a : aþc
(9)
POD is the ratio of correct forecasts to the number of observed threshold crossings. It ranges from 0 to 1 with 1 being a perfect score. The probability of false detection (POFD) is defined as
Fig. 5. Distribution of the three observatories and the global six observatories in geographic coordinate, which are used to calculate the storm indices before 1957. The pentagrams represent the three observatories, and the dots represent the global six observatories. The black solid line denotes the magnetic equator. 6
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Fig. 6. The storm symmetry indices deduced from the three observatories for 1941–1956 with the formula Sym
POFD ¼
b : bþd
H ¼ Hcðr ¼ rCD Þ.
The Heidke skill score (HSS) is defined as [Doswell et al., 1990]
(10)
HSS ¼
POFD is the ratio of false forecasts to the number of observed no threshold crossings. It ranges from 0 to 1 with 0 being a perfect score. 7
ða þ dÞ e ; n e
(11)
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Fig. 7. The storm asymmetry indices deduced from the three observatories for 1941–1956 with the formula Asy
8
� � H ¼ 2RE �req Hc�.
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Fig. 8. (a) The frequency distribution histograms of the Sym-H indices with 2 nT bin size for 1941–1956. (b) The plot of the Sym-H-3 index versus the Sym-H-6 index and the linear fit line. (c) The frequency distribution histograms of the Asy-H indices with 2 nT bin size for 1941–1956. (d) The plot of the Asy-H-3 index versus the Asy-H-6 index and the linear fit line.
where n is the total number of events (aþbþcþd) and e is the expected number of correct forecasts due purely to random chance. The e is computed as e¼
ða þ bÞða þ cÞ þ ðb þ dÞðc þ dÞ : aþbþcþd
Asy-H greater than 100, 200, 300 nT are summarized in Table 2, respectively. For symmetric storm indices deduced from three stations (Sym-H-3), the PODs, POFDs and HSSs are both perfectly reasonable at all three thresholds. For asymmetric storm indices deduced from three stations (Asy-H-3), the HSSs are a little small but reasonable. The POFDs are close to zero, and the PODs are around 0.6. It shows that nearly half of the Asy-H-3 indices didn’t cross the threshold while the Asy-H-6 indices did. In other words, several Asy-H-3 indices are smaller compared to the Asy-H-6 indices, especially with weak geomagnetic activity.
(12)
The range of HSS is from 1 to 1. A perfect forecast receives HSS ¼ 1, while a forecast equivalent to random chance receives HSS ¼ 0. Nega tive values of HSS indicate that the forecast is worse than a random chance. In the final analyses, we considered the storm indices deduced from three stations as forecast events, and the storm indices from the global six stations as observed events. In view of the hourly data resolution, we treat the data in each 1 h window as an event. The thresholds which we selected for Sym-H are 50, 100, 250 nT, and for Asy-H are 100, 200, 300 nT. The probability of detections, probability of false detections and Heidke skill scores for Sym-H smaller than 50, 100, 250 nT and for
5. Summary and conclusions In this study, we presented a capability to deduce the geomagnetic disturbance field around the Earth and the magnetic storm indices from geomagnetic measurements from ground observatories confined in longitude for the first time. The methods developed in our previous work [Shen et al., 2015] have been used, which have been further developed to calculate the gradient of the corrected H component of the geomag netic disturbance field, redefine the storm symmetric and asymmetric indices, and investigate the evolution of the storm ring current. In this research, 18 ground geomagnetic observatories located in the eastern hemisphere have been chosen for analysis. The results were compared with those obtained from the six global observatories in our previous work [Shen et al., 2015] and with the Kyoto standard storm indices. Furthermore, storm indices were calculated in 1941–1956 using data from three of the four standard low-latitude observatories used for the
Table 2 PODs, POFDs and HSSs for the storm indices at different threshold. Threshold (nT) Sym-H Asy-H
50 100 250 100 200 300
POD
POFD
HSS
0.926 0.940 0.875 0.543 0.569 0.667
0.014 0.002 0.00009 0.002 0.0002 0.00002
0.866 0.879 0.832 0.620 0.554 0.706
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105049
Kyoto Dst index. For the super (Dst < 250 nT), intense ( 250 nT < Dst < 100 nT) and moderate ( 100 nT < Dst < 50 nT) storms, the storm indices derived from the eastern stations are consistent with those from the global stations and with the Kyoto Dst index. On the assumption that the anti-direction of the gradient of the H component indicates the peak location of the ring current, for intense and moderate storms, the peak of the ring current is near local dusk during the storm main and early re covery phase, which is the same as the result deduced from the global six stations. For super storms, the position of the peak of the ring current deduced from the eastern stations is also consistent with that from the global stations. These results are also consistent with the statistical spatial distribution of the storm ring current as shown by Le et al. (2004) and Yang et al. (2016). In view of the above results, it is noted that this new method which only uses eastern stations is still applicable when a full global complement is not available. We also calculated the storm indices for 1941–1956 using data from three of the four low-latitude observatories which contribute data to calculate the standard Dst index. The correlation coefficient between the symmetric index deduced from three observatories and the one from global six observatories is 0.98, and the correlation coefficient between the two kind of asymmetric indices is 0.79. At different thresholds, both symmetric and asymmetric indices deduced from three observatories have reasonable HSSs. Our results indicate that accurate storm indices can be obtained in earlier years when there was a lack of globally distributed ground geomagnetic observatories. In conclusion we believe that we are able to obtain magnetic storm indices and investigate the evolution of the storm ring current with ground observatories confined in longitude, which has great significance when global ground observatories are not readily available. However, the spatial gradient of the geomagnetic disturbance in the equatorial plane cannot be obtained with one or two points magnetic measure ments. It is absolutely necessary to calculate the storm indices from at least three observations.
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Acknowledgments This work was supported by the National Natural Science Foundation of China Grant No. 41874190 and 41231066 (Chao Shen), 41374180 (Zhaojin Rong), 41204117 (Zhiqing Chen) and 41704168 (Yonghui Ma), the Strategic Priority Research Program of Chinese Academy of Sciences Grant No. XDA17010301 (Tao Chen), the Specialized Research Fund for State Key Laboratories of the CAS (Zhiqing Chen), the Shenzhen Tech nology Project JCYJ20160505175406823 (Yonghui Ma) and the CAS Key Laboratory of Lunar and Deep Space Exploration through grant 16080271 (Yonghui Ma). We thank Dr. M. Temerin for Englishproofreading of the final manuscript. We also thank the INTER MAGNET (http://www.intermagnet.org) for providing the geomagnetic data, the World Data Center for Geomagnetism (Edinburgh) (http: //www.wdc.bgs.ac.uk) for providing the geomagnetic data before the year 1957, the World Data Center for Geomagnetism (Kyoto) (htt p://wdc.kugi.kyoto-u.ac.jp) for publishing the ASY-H, SYM-H and AE indices, which are calculated by Kyoto University, and the OMNIweb (http://omniweb.gsfc.nasa.gov) for releasing the IMF and solar wind speed data. References Akasofu, S.I., Chapman, S., 1961. The ring current, geomagnetic disturbance, and the Van Allen belts. J. Geophys. Res. 66, 1321–1350. https://doi.org/10.1029/ JZ066i005p01321. Alexeev, I.I., Belenkaya, E.S., Kalegaev, V.V., Feldstein, Y.I., Grafe, A., 1996. Magnetic storms and magnetotail currents. J. Geophys. Res. 101 (A4), 7737–7747. https://doi. org/10.1029/95JA03509. Corotating interaction regions. In: Balogh, A., Gosling, J.T., Jokipii, J.R., Kallenbach, R., Kunow, H. (Eds.), Space Sci. Rev. 89 (1–2).
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Munsami, V., 2000. Determination of the effects of substorms on the storm-time ring current using neural networks. J. Geophys. Res. 105 (A12), 27. https://doi.org/ 10.1029/2000JA000041, 833–27,840. Mursula, K., Holappa, L., Karinen, A., 2008. Corrent normalization of the Dst index. Astrophys. Space Sci. Trans. 4, 41–45. https://doi.org/10.5194/astra-4-41-2008. Newell, P.T., Gjerloev, J.W., 2012. SuperMAG-based partial ring current indices. J. Geophys. Res. 117, A05215. https://doi.org/10.1029/2012JA017586. O’Brien, T.P., Mcpherron, R.L., 2000. An empirical phase space analysis of ring current dynamics: solar wind control of injection and decay. J. Geophys. Res. 105 (A4), 7707–7719. https://doi.org/10.1029/1998JA000437. Perez, J.D., Zhang, X.-X., son Brandt, P.C., Mitchell, D.G., Jahn, J.-M., Pollock, C.J., 2004. Dynamics of ring current ions as obtained from IMAGE HENA and MENA ENA images. J. Geophys. Res. 109, A05208. https://doi.org/10.1029/2003JA010164. Pollock, C.J., et al., 2001. First medium energy neutral atom (MENA) images of Earth’s magnetosphere during substorm and storm time. Geophys. Res. Lett. 28, 1147. https://doi.org/10.1029/2000GL012641. Pulkkinen, A., et al., 2013. Community-wide validation of geospace model ground magnetic field perturbation predictions to support model transition to operations. Space Weather 11 (6), 369–385. https://doi.org/10.1002/swe.20056. Reeves, G.D., et al., 2003. IMAGE, POLAR, and geosynchronous observations of substorm and ring current ion injection. In: Sharma, A.S., Kamide, Y., Lakhina, G.S. (Eds.), Disturbances in Geospace: the Storm-Substorm Relationship. American Geophysical Union, Washington, D. C.. https://doi.org/10.1029/142GM09 Sckopke, N., 1966. A general relation between the energy of trapped particles and the disturbance field near the Earth. J. Geophys. Res. 71 (13), 3125–3130. https://doi. org/10.1029/JZ071i013p03125. Siscoe, G.L., Crooker, N.U., 1974. A theoretical relation between Dst and the solar wind merging electric field. Geophys. Res. Lett. 1 (1), 17–19. https://doi.org/10.1029/ GL001i001p00017. Smith, E.J., Wolfe, J.H., 1976. Observations of interaction regions and corotating shocks between one and five AU: pioneers 10 and 11. Geophys. Res. Lett. 3, 137–140. https://doi.org/10.1029/GL003i003p00137. Shen, C., et al., 2012. Spatial gradients from irregular, multiple-point spacecraft configurations. J. Geophys. Res. 117, A11207. https://doi.org/10.1029/ 2012JA018075. Shen, C., Zeng, G., Li, X., Rong, Z.J., 2015. Evolution of the storm magnetic field disturbance around Earth’s surface and the associated ring current as deduced from multiple ground observatories. J. Geophys. Res. Space Phys. 120 https://doi.org/ 10.1002/2014JA020562. Shen, C., Liu, Z.X., Kamei, T., 2002. A physics based study of the Dst-AL relationship. J. Geophys. Res. 107 (A1) https://doi.org/10.1029/2001JA900121. Søraas, F., Oksavik, K., Aarsnes, K., Evans, D.S., Greer, M.S., 2003. Storm time equatorial belt – an “image” of RC behavior. Geophys. Res. Lett. 30 (2), 1052. https://doi.org/ 10.1029/2002GL015636. Spencer, E., Horton, W., Mays, M.L., Doxas, I., Kozyra, J., 2007. Analysis of the 3–7 October 2000 and 15–24 April 2002 geomagnetic storms with an optimized
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Monitoring the global evolution of the storm ring current and storm indices from confined ground geomagnetic observatories G. Zeng a, C. Shen a, *, Z.J. Rong b, c, X. Li d, T. Chen e, Z.Q. Chen e, Y.H. Ma a, f a
School of Science, Harbin Institute of Technology, Shenzhen, 518055, China Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China c Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China d Laboratory for Atmosphere and Space Physics, University of Colorado, Boulder, USA e State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China f Key Laboratory of Lunar and Deep Space Exploration, Chinese Academy of Sciences, Beijing, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Magnetic storms Substorms Ring current Gradient of magnetic field Multipoint data analysis method Storm indices
For the first time, the global structure of the geomagnetic disturbance field around the Earth as well as the magnetic storm indices have been deduced from magnetic field measurements by ground observatories in a confined range of longitude. The spatial gradient of the H component of the geomagnetic disturbance field was obtained from ground geomagnetic observatories only in the Eastern Hemisphere, provided the geomagnetic disturbance field varies approximately linearly in space. Furthermore, the storm symmetric and asymmetric indices were derived and the spatial distribution and temporal evolution of the storm ring current was inves tigated. It was found that the storm indices derived from observatories in the Eastern Hemisphere are consistent with the officially published Kyoto standard indices which are derived from six globally distributed observa tories. We also calculated the storm indices for 1941–1956 by using data from three observatories (HER, KAK and SJG). The correlation coefficient between the symmetric index deduced from three observatories and the one from the global six observatories is 0.98, and the correlation coefficient between the two kind of asymmetric indices is 0.79. Those results suggest that our approach is reasonable and significant when global ground ob servatories are not readily available.
1. Introduction The Dst index is one of the most important geomagnetic indices and has been used to describe the development and intensity of the magnetic storms [Dessler and Parker, 1959; Sckopke, 1966; Gonzalez et al., 1994]. During magnetic storms, particles in the near earth plasma sheet are injected into the inner magnetosphere, experience acceleration, and undergo drift motions, so as to lead to the formation of a ring current around the Earth, which causes a decrease of the H component of the geomagnetic field on the surface of the Earth [Akasofu and Chapman, 1961; Siscoe and Crooker, 1974; Gonzalez et al., 1994; Fok et al., 1996; Jordanova et al., 1997; De Michelis et al., 1997; Shen et al., 2002; Vallat et al., 2005; Chen et al., 2006; Daglis, 2006]. The decay of the ring current is mainly due to charge exchange between the ring current en ergetic ions and the cold atoms in the exosphere of the Earth [Jorgensen et al., 1997; Pollock et al., 2001; Brandt et al., 2004; Kozyra and
Liemohn, 2003; Perez et al., 2004]. The hourly Dst index was put for ward to depict the geomagnetic disturbance field during magnetic storms [Akasofu and Chapman, 1961; Sugiura, 1964; Sugiura and Kamei, 1991]. It is calculated by using data from four ground geomag netic observatories at low and middle latitude [Sugiura and Kamei, 1991]. Besides the symmetric ring current, other magnetospheric cur rents contribute to the Dst index, such as the partial ring current [Lie mohn et al., 2001; Liemohn, 2003], the dayside magnetopause current [Burton et al., 1975; Feldstein et al., 2006; O’Brien and McPherron, 2000], the magnetotail current [Burton et al., 1975; Alexeev et al., 1996; Feldstein et al., 2006; Turner et al., 2000], and the substorm current wedge [Friedrich et al., 1999; Munsami, 2000]. The Dst index can also be accurately predicted based on upstream solar wind conditions [Bur ton et al., 1975; O’Brien and McPherron, 2000; Temerin and Li, 2002, 2006, 2015]. In contrast to the hourly Dst index, the symmetric (SYM-H) and
* Corresponding author. E-mail address: [email protected] (C. Shen). https://doi.org/10.1016/j.jastp.2019.05.013 Received 15 December 2018; Received in revised form 7 April 2019; Accepted 27 May 2019 Available online 30 May 2019 1364-6826/© 2019 Elsevier Ltd. All rights reserved.
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105049
asymmetric (ASY-H) storm indices were developed at the 1 min time resolution [Iyemori, 1990]. Essentially, the SYM-H index is the same as the Dst index [Wanliss and Showalter, 2006; Love and Gammon, 2009; Gannon and Love, 2011], except that data from a different set of stations and a slightly different coordinate system are used (available at http ://wdc.kugi.kyoto-u.ac.jp/aeasy/asy.pdf). Clauer and Mcpherron (1974) created a local time-universal time contour map of the deviation of the X (geographic north) component of the geomagnetic field to study the development of magnetospheric substorms by using measurements of mid-latitude geomagnetic obser vatories. Iyemori (1990) has investigated the local time distribution of both the D and H components of geomagnetic disturbance field at mid-latitude geomagnetic observatories. With data from 98 mid- and low-latitude geomagnetic observatories, Newell and Gjerloev (2012) introduced four partial ring current indices to investigate ring current development. It is worth noting that a global distribution of geomag netic observatories is necessary in the works mentioned above. Six sta tions are used for the derivation of the Kyoto SYM-H (available at http ://wdc.kugi.kyoto-u.ac.jp/aeasy/asy.pdf), and four stations for the Kyoto Dst [Sugiura and Kamei, 1991]. Both sets of stations are almost distributed evenly in longitude. In the early 20th century, there were not enough geomagnetic observatories to cover the whole world. In this work, we will calculate storm indices and investigate ring current development using only data from eastern hemisphere geomagnetic observatories. In our previous work [Shen et al., 2015], a new method was devel oped to redefine the storm symmetric and asymmetric indices and to study the evolution of the storm ring current. The gradient of the cor rected H component of the disturbance field was calculated from ground geomagnetic observatories, and the storm symmetric and asymmetric indices were deduced. Calculations confirmed that this new approach is reasonable and can be applied to investigate the evolution of the storm ring current. In this study, the same method has been used to deduce the spatial gradient of the H component of the geomagnetic disturbance field from ground geomagnetic observatories in eastern hemisphere, then the storm symmetric and asymmetric indices are obtained, and the spatial distribution and temporal evolution of the storm ring current are deduced. The data and method are presented in section 2. The properties of the ring current and the newly defined storm indices are illustrated in section 3. In section 4, the storm symmetric and asymmetric indices are calculated before the year 1957. Finally, we present the summary and conclusions in section 5.
Table 1 Coordinates of the observatories. Observatory
Geographic
AAA ABG ASP BMT CTA GUI HBK HER KAK KDU KNY LRM LZH MBO MMB QSB TAM TSU
Geomagnetic
Latitude ( )
Longitude ( )
Latitude (� )
longitude (� )
43.25 18.63 23.76 40.06 20.08 28.32 25.88 34.43 36.23 12.69 31.42 22.22 36.1 14.38 43.9 33.87 22.79 19.2
76.92 72.87 133.88 116.18 146.25 16.43 27.71 19.23 140.18 132.47 130.88 114.1 103.84 16.97 144.2 35.64 5.52 17.58
34.3 10.2 32.9 30.1 28 33.8 27.1 34 27.4 22 21.9 32.4 25.9 20.1 35.4 30.3 24.7 18.8
152.7 146.2 208.2 187 221 60.6 94.4 84 208.8 205.6 200.8 186.5 176.1 57.5 211.3 113.5 81.8 85.9
�
�
the corrected horizontal components of these observatories. The for mulas are as follows: SYM
H¼
ASY
H¼
N 1 X Hα ; N α¼1 cosφα
� H �� cos φ�max
� H �� ; cos φ�min
(1) (2)
where N is the number of the observatories, and the superscript α refers to the αth observatory. H represents the horizontal component of the geomagnetic disturbance field, which is obtained by subtracting the main and Sq field from the original data. φ is the geomagnetic latitude of the observatory. The formula H=cos φ is a latitudinal correction of the horizontal component for each individual observatory. It is noted that the latitudinal corrections in equations (1) and (2) are slightly different from those in the original definitions of Kyoto SYM-H and ASY-H. In this research, the latitudinal correction of the H component is made for each observatory, which is similar to the method described by Mursula et al. (2008) and Love and Gammon (2009). Assuming the geomagnetic disturbance varies linearly in space, the two observatories with maximum and minimum disturbances will be located at the Earth’s magnetic equator, and the distance between them is the Earth’s diameter (2RE). The first order gradient of the corrected H component in magnetic equatorial plane can be expressed as,
2. Data and method To produce the Kyoto SYM-H and ASY-H, six geomagnetic observa tories are used. Their locations are distributed in the mid- and lowlatitudes, evenly in longitude (available at http://wdc.kugi.kyoto-u.ac. jp/aeasy/asy.pdf). In this work, we seek to get the SYM-H and ASY-H indices from geomagnetic measurements confined to the eastern hemisphere. We select 18 geomagnetic observatories in the eastern hemisphere (hereafter called “eastern stations”). The geomagnetic latitude of the observatories range between 10� to 40� both in northern and southern hemisphere. The geographic and geomagnetic coordinates of the 18 observatories are given in Table 1. Their distribution is shown in Fig. 1. It should be noted that, for some particular months, there are long data gaps in a few observatories. In our previous work [Shen et al., 2015], a new method was devel oped to redefine the storm symmetric and asymmetric indices and to study the evolution of the storm ring current, which is introduced briefly below. In this work, the same method has been used except with different observatories. Traditionally, the SYM-H index is defined as the average value of the corrected horizontal components of the observatories, and the ASY-H index is calculated by subtracting the minimum from the maximum of
� � �req Hc� ¼ Hcmax Hcmin ; 2RE
(3)
where Hc ¼ H=cos φ is the corrected H component, and the superscript eq refers to the gradient in the geomagnetic equatorial plane. It is noted that the direction of geomagnetic disturbance is opposite to that of geomagnetic main field, and geomagnetic disturbance value is positive. The gradient of Hc is in the direction of maximum value of Hc which represents the minimum disturbance. In other words, the opposite di rection of gradient of Hc points to the peak of partial ring current. Consequently, a new definition of the storm index Asy-H can be written as, � � Asy H ¼ 2RE �req Hc�: (4) The arithmetic mean of the corrected H components for the SYM-H index describes the disturbance at the barycenter of the ground obser vatories. But we prefer to represent the storm symmetric index by the disturbance at the dipole center of the Earth. The Earth’s dipole center does not coincide with the barycenter of ground observatories in 2
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Fig. 1. Distribution of observatories in geographic coordinates. The black dots represent the observatories. The black solid line denotes the magnetic equator.
general. Thus, there is a difference between disturbance at the Earth’s dipole center and that at the barycenter of ground observatories. We add the difference by a first order linear correction term on the arithmetic mean term, and that is N 1 X H ¼ Hcðr ¼ rCD Þ ¼ Hcα þ rCD ⋅rHc; N α¼1
Sym
qα ¼
N 1 X rα rα N α¼1
(5)
3. Results 3.1. Intense storm on 4–8 October 2000 We first analyze the intense storm event on 4–8 October 2000. A sawtooth event composed of a series of substorms occurs during the main phase of this storm [Huang et al., 2003; Reeves et al., 2003; Spencer et al., 2007; Troshichev et al., 2011]. Fig. 2a–c shows the evolutions of the IMF, solar wind velocity and AE index. The black curves in Fig. 2d and e are the Kyoto SYM-H and ASY-H indices. As shown in Fig. 2a, the IMF Bz turns southward at around 0530UT on 4 October 2000, and re mains at around 10 nT until 0330UT on 5 October. Subsequently, it reaches 27 nT at around 0530UT with a sudden decrease, then turns northward by a rapid increase between 0530UT and 0700UT. The solar wind velocity is 400–500 km/s (Fig. 2b). While the IMF Bz remains southward, there are continuous quasi-periodic oscillations of AE index as shown in Fig. 2c. Fig. 2d shows that the storm main phase commences as the IMF Bz turns southward. The SYM-H index drops to a minimum ( 185 nT) as the IMF Bz reaches a minimum value. Afterwards, the SYM-H index attains another minimum ( 184 nT) as the IMF Bz turns southward again with a sudden decrease. Shen et al. (2015) used six global stations to calculate storm Sym-H and Asy-H indices and the MLT positions of the peaks of the ring current, which are represented by blue in Fig. 2d–f. Red represent results ac quired from only eastern stations. As shown in Fig. 2d, the storm Sym-H index derived from the eastern stations is in good agreement with that from global stations and with the Kyoto SYM-H index. Fig. 2e shows that there is little difference in the values of the three storm asymmetric
(6)
where rα is the position vector of the α th ground observatories in the geography coordinates. The volumetric tensor has three nonnegative b ð1Þ , eigenvalues ω1 , ω2 and ω3 , and three corresponding eigenvectors k b ð2Þ and k b ð3Þ . k Based on the multipoint analysis method [Shen et al., 2012], the gradient of Hc can be deduced as N X
Hcα qα
rHc ¼
(8)
ðlÞ where ~rαl ¼ rα ⋅ b k is the lth component of rα .
where the superscript α refers to the αth observatory. The direction of the position vector rCD is from the barycenter of the observatories to the dipole center of the Earth, and the length is the distance between them. The method described by Fraser-Smith (1987) is used to calculate the position of the eccentric dipole. It may be mentioned that the anti-direction of the gradient of Hc points to the peak of the ring current. The gradient of Hc can be deduced from measurements of ground geomagnetic observatories with the multipoint data analysis method [Harvey, 1998; Shen et al., 2012] applied. The spatial gradient can be determined by a volumetric tensor [Harvey, 1998], which is defined as R¼
3 X ðlÞ 1 ~rαl b k N ωl l¼1
(7)
α¼1
where 3
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Fig. 2. A comparison between results acquired from global stations and only eastern stations for the 4–8 October 2000 storm. (a) The total magnitude and the three components of the interplanetary magnetic field (IMF) in GSE coordinate; (b) The three components of the velocity of the solar wind in GSE coordinate; (c) The AE index; (d) The storm symmetric index which is derived from our new method (Hcðr ¼ rCD Þ) by eastern stations (red) and global stations (blue), and the standard � � Kyoto SYM-H index (black); (e) The storm asymmetric index which is derived from our new method (�req Hc�⋅2RE ) by eastern stations (red) and global stations (blue), and the standard Kyoto ASY-H index (black); (f) The magnetic local time of the anti-direction of the equatorial gradient of Hc (req Hc), which indicates the position of the peak of the ring current. The red pluses represent the result deduced from eastern stations, and the blue dots represent that from global stations. The locations of the ABG station, which is approximately the center station of the Eastern stations in Fig. 1, are marked by the green dots.
the ring current deduced from eastern stations are near local dusk, which correspond to results from global six stations. This supports our method of only using eastern hemisphere stations.
indices. The variation trends of those curves are also similar. Fig. 2f shows that, during the main phase and initial recovery phase, the po sitions of the peak of the ring current are near local dusk, which agree well with the positions deduced from global stations. It is indicated that our new method works well when only eastern hemisphere stations are available.
3.3. Super storm on 7–11 November 2004 Fig. 4 illustrates a super storm on 7–11 November 2004, which is driven by an interplanetary magnetic cloud. A shock passes the magnetosphere at around 1930UT on 7 November as shown in Fig. 4a. Meanwhile, the solar wind velocity increases to ~650 km/s, and the storm main phase commences. At around 1930UT 9 November another shock passes over the magnetosphere and again causes a decrease of the SYM-H index. Fig. 4c shows continuous AE activity with a peak of ~3500 nT. From Fig. 4d, there is a big difference between the Sym-H and Kyoto SYM-H index around the minimum value, but they are in good agreement outside that difference band. Fig. 4e shows good con sistency between the Asy-H index derived from the eastern stations and the Kyoto ASY-H index. The positions of the peak of ring current deduced from the eastern stations are consistent with those from the global stations as shown in Fig. 4f.
3.2. Moderate storm on 25–28 October 2007 The moderate storm on 25–28 October 2007 was generated by a corotating interaction region (CIR) event [Balogh et al., 1999; Smith and Wolfe, 1976; Tsurutani et al., 1995; Tsurutani et al., 2006; Turner et al., 2006]. As shown in Fig. 3a–d, there was a rapidly varying IMF Bz as the storm begins at around 1200 UT on 25 October, and the maximum Bz reaches ~20 nT. During the main phase, the AE index reaches maximum at ~1200 nT. In the high speed stream region that is sunward of CIRs (from 20 UT day 25 Oct until the end of the interval in Fig. 3), the stream is filled with large amplitude Alfven waves [Belcher and Davis, 1971]. When the Alfven wave with southward component magnetic field im pinges onto the Earth’s magnetosphere, magnetic reconnection occurs [Dungey, 1961], and energy is injected into the nightside magneto sphere [Tsurutani and Gonzalez, 1987]. A series of sub storms/convection events take place, which is called a High-Intensity, Long-Duration, Continuous AE Activity (HILDCAA) event. The energy is injected only to L > 4 [Søraas et al., 2003], so only the outer ring current is affected. A review for interested readers can be found in the work of Tsurutani et al. (2006). As illustrated in Fig. 3d and e, the storm indices derived from the eastern stations are in agreement with those from the global six stations and Kyoto storm indices. As shown in Fig. 3f, the positions of the peak of
4. Storm indices before 1957 The Kyoto standard Dst index has been calculated since the year 1957. Karinen and Mursula (2005) reconstructed the Dst index before 1957 by using geomagnetic data, using a formula quite similar to the original standard one. In this section, we will calculate the storm sym metric and asymmetric indices before 1957 by our new method. The geomagnetic data we use are from three of the four low-latitude ob servatories which contribute data to calculate the standard Dst index. 4
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Fig. 3. A comparison between the results acquired from global stations and only eastern stations for the 25–28 October 2007 storm. The format of the figure is the same as that of Fig. 2.
Fig. 4. A comparison between the results acquired from global stations and only eastern stations for the 7–11 November 2004 storm. The format of the figure is the same as that of Fig. 2.
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some minority of cases. All of the cases were divided between stormtime (Sym-H-6 <¼ 30 nT) and quite-time (Sym-H-6 > 30 nT), and the correlations between Asy-H-3 and Asy-H-6 are investigated sepa rately. The result shows that the correlation coefficient was 0.78 in the storm-time cases and 0.66 in the quite-time cases. The correlation for quite-times is not better than for storm-times. The particle injection in storm-time may not be a possible mechanism that violates the linearity, but more strong evidence is needed. In order to investigate the nonlinearity systematically, we will deduce the second-order gradient in future work. The approach to assessing the skill of forecasting binary events [Jolliffe and Stephenson, 2003] is also used to evaluate the correspon dence between the storm indices deduced from the three stations and those from the global six stations. Three measures were chosen to quantify the performance of the storm indices deduced from the three stations in the final analyses. The three measures are the probability of detection (POD), the probability of false detection (POFD) and the Heidke skill score (HSS) [Doswell et al., 1990; Ganushkina et al., 2015; Lopez et al., 2007; Pulkkinen et al., 2013]. These measures can be defined as a function of the number of (a) hits, (b) false alarms, (c) misses, and (d) correct rejections. A hit represents a threshold crossing event which was both forecasted and observed. A false alarm represents a threshold crossing event which was forecasted but not observed. A miss represents a threshold crossing event which was not forecasted but observed. A correct rejection represents a threshold crossing event which was neither forecasted nor observed. The probability of detection (POD) is defined as
The four standard observatories are Hermanus (HER, 34.40� S, 19.22� E), Honolulu (HON, 21.30� N, 158.10� W), Kakioka (KAK, 36.23� N, 140.18� E), and San Juan (SJG, 18.38� N, 66.12� W) [Sugiura and Kamei, 1991], where the values in the parentheses are geographic latitude and longitude of the observatories. The three observatories we use are HER, KAK and SJG whose distribution is shown in Fig. 5. Fig. 6 depicts the storm symmetric index deduced from these three observatories in 1941–1956 by our method. This period is from the end of solar cycle 17 to the beginning of the solar cycle 19. Fig. 7 depicts the storm asymmetric index deduced from these three observatories. In order to evaluate the indices deduced from these three observatories, we compare the Sym-H-3 (or Asy-H-3) index (3 refer to three observatories) to the Sym-H-6 (or Asy-H-6) index (the storm symmetry or asymmetry index deduced from global six observatories which here are ABG, HER, HON, KAK, SJG and TUC. The distribution is shown in Fig. 5). Fig. 8a shows the frequency distribution histograms of the Sym-H-3 and Sym-H-6 index for 1941–1956. The bin size is 2 nT. The mean and standard deviation of the Sym-H-3 index are 16.44 nT and 24.84 nT, respectively. The mean and standard deviation of the Sym-H-6 index are 16.11 nT and 23.64 nT, which are closely similar to those of the SymH-3 index. To measure the differences between the values of the Sym-H-3 and Sym-H-6 indices, we calculated the root-mean-square deviation (RMSD) or root-mean-square error (RMSE). The RMSD between the Sym-H-3 and Sym-H-6 indices is 4.99 nT. Fig. 8b shows the plot of the Sym-H-3 index versus the Sym-H-6 index. The line is a linear fit. The correlation coefficient between them is 0.98. Fig. 8c shows the histogram frequency distributions of the Asy-H-3 and Asy-H-6 indices. The bin size is 2 nT. The mean and standard devi ation of the Asy-H-3 index are 19.36 nT and 18.57 nT which are close to those for the Asy-H-6 index (23.22 nT for the mean and 19.94 nT for the standard deviation). And the RMSD between the Asy-H-3 and Asy-H-6 indices is 13.21 nT. Fig. 8d shows a plot of the Asy-H-3 index versus the Asy-H-6 index. The line is a linear fit. The correlation coefficient be tween them is 0.79. It means the linear assumption does not apply to
POD ¼
a : aþc
(9)
POD is the ratio of correct forecasts to the number of observed threshold crossings. It ranges from 0 to 1 with 1 being a perfect score. The probability of false detection (POFD) is defined as
Fig. 5. Distribution of the three observatories and the global six observatories in geographic coordinate, which are used to calculate the storm indices before 1957. The pentagrams represent the three observatories, and the dots represent the global six observatories. The black solid line denotes the magnetic equator. 6
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Fig. 6. The storm symmetry indices deduced from the three observatories for 1941–1956 with the formula Sym
POFD ¼
b : bþd
H ¼ Hcðr ¼ rCD Þ.
The Heidke skill score (HSS) is defined as [Doswell et al., 1990]
(10)
HSS ¼
POFD is the ratio of false forecasts to the number of observed no threshold crossings. It ranges from 0 to 1 with 0 being a perfect score. 7
ða þ dÞ e ; n e
(11)
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Fig. 7. The storm asymmetry indices deduced from the three observatories for 1941–1956 with the formula Asy
8
� � H ¼ 2RE �req Hc�.
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Fig. 8. (a) The frequency distribution histograms of the Sym-H indices with 2 nT bin size for 1941–1956. (b) The plot of the Sym-H-3 index versus the Sym-H-6 index and the linear fit line. (c) The frequency distribution histograms of the Asy-H indices with 2 nT bin size for 1941–1956. (d) The plot of the Asy-H-3 index versus the Asy-H-6 index and the linear fit line.
where n is the total number of events (aþbþcþd) and e is the expected number of correct forecasts due purely to random chance. The e is computed as e¼
ða þ bÞða þ cÞ þ ðb þ dÞðc þ dÞ : aþbþcþd
Asy-H greater than 100, 200, 300 nT are summarized in Table 2, respectively. For symmetric storm indices deduced from three stations (Sym-H-3), the PODs, POFDs and HSSs are both perfectly reasonable at all three thresholds. For asymmetric storm indices deduced from three stations (Asy-H-3), the HSSs are a little small but reasonable. The POFDs are close to zero, and the PODs are around 0.6. It shows that nearly half of the Asy-H-3 indices didn’t cross the threshold while the Asy-H-6 indices did. In other words, several Asy-H-3 indices are smaller compared to the Asy-H-6 indices, especially with weak geomagnetic activity.
(12)
The range of HSS is from 1 to 1. A perfect forecast receives HSS ¼ 1, while a forecast equivalent to random chance receives HSS ¼ 0. Nega tive values of HSS indicate that the forecast is worse than a random chance. In the final analyses, we considered the storm indices deduced from three stations as forecast events, and the storm indices from the global six stations as observed events. In view of the hourly data resolution, we treat the data in each 1 h window as an event. The thresholds which we selected for Sym-H are 50, 100, 250 nT, and for Asy-H are 100, 200, 300 nT. The probability of detections, probability of false detections and Heidke skill scores for Sym-H smaller than 50, 100, 250 nT and for
5. Summary and conclusions In this study, we presented a capability to deduce the geomagnetic disturbance field around the Earth and the magnetic storm indices from geomagnetic measurements from ground observatories confined in longitude for the first time. The methods developed in our previous work [Shen et al., 2015] have been used, which have been further developed to calculate the gradient of the corrected H component of the geomag netic disturbance field, redefine the storm symmetric and asymmetric indices, and investigate the evolution of the storm ring current. In this research, 18 ground geomagnetic observatories located in the eastern hemisphere have been chosen for analysis. The results were compared with those obtained from the six global observatories in our previous work [Shen et al., 2015] and with the Kyoto standard storm indices. Furthermore, storm indices were calculated in 1941–1956 using data from three of the four standard low-latitude observatories used for the
Table 2 PODs, POFDs and HSSs for the storm indices at different threshold. Threshold (nT) Sym-H Asy-H
50 100 250 100 200 300
POD
POFD
HSS
0.926 0.940 0.875 0.543 0.569 0.667
0.014 0.002 0.00009 0.002 0.0002 0.00002
0.866 0.879 0.832 0.620 0.554 0.706
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Kyoto Dst index. For the super (Dst < 250 nT), intense ( 250 nT < Dst < 100 nT) and moderate ( 100 nT < Dst < 50 nT) storms, the storm indices derived from the eastern stations are consistent with those from the global stations and with the Kyoto Dst index. On the assumption that the anti-direction of the gradient of the H component indicates the peak location of the ring current, for intense and moderate storms, the peak of the ring current is near local dusk during the storm main and early re covery phase, which is the same as the result deduced from the global six stations. For super storms, the position of the peak of the ring current deduced from the eastern stations is also consistent with that from the global stations. These results are also consistent with the statistical spatial distribution of the storm ring current as shown by Le et al. (2004) and Yang et al. (2016). In view of the above results, it is noted that this new method which only uses eastern stations is still applicable when a full global complement is not available. We also calculated the storm indices for 1941–1956 using data from three of the four low-latitude observatories which contribute data to calculate the standard Dst index. The correlation coefficient between the symmetric index deduced from three observatories and the one from global six observatories is 0.98, and the correlation coefficient between the two kind of asymmetric indices is 0.79. At different thresholds, both symmetric and asymmetric indices deduced from three observatories have reasonable HSSs. Our results indicate that accurate storm indices can be obtained in earlier years when there was a lack of globally distributed ground geomagnetic observatories. In conclusion we believe that we are able to obtain magnetic storm indices and investigate the evolution of the storm ring current with ground observatories confined in longitude, which has great significance when global ground observatories are not readily available. However, the spatial gradient of the geomagnetic disturbance in the equatorial plane cannot be obtained with one or two points magnetic measure ments. It is absolutely necessary to calculate the storm indices from at least three observations.
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Acknowledgments This work was supported by the National Natural Science Foundation of China Grant No. 41874190 and 41231066 (Chao Shen), 41374180 (Zhaojin Rong), 41204117 (Zhiqing Chen) and 41704168 (Yonghui Ma), the Strategic Priority Research Program of Chinese Academy of Sciences Grant No. XDA17010301 (Tao Chen), the Specialized Research Fund for State Key Laboratories of the CAS (Zhiqing Chen), the Shenzhen Tech nology Project JCYJ20160505175406823 (Yonghui Ma) and the CAS Key Laboratory of Lunar and Deep Space Exploration through grant 16080271 (Yonghui Ma). We thank Dr. M. Temerin for Englishproofreading of the final manuscript. We also thank the INTER MAGNET (http://www.intermagnet.org) for providing the geomagnetic data, the World Data Center for Geomagnetism (Edinburgh) (http: //www.wdc.bgs.ac.uk) for providing the geomagnetic data before the year 1957, the World Data Center for Geomagnetism (Kyoto) (htt p://wdc.kugi.kyoto-u.ac.jp) for publishing the ASY-H, SYM-H and AE indices, which are calculated by Kyoto University, and the OMNIweb (http://omniweb.gsfc.nasa.gov) for releasing the IMF and solar wind speed data. References Akasofu, S.I., Chapman, S., 1961. The ring current, geomagnetic disturbance, and the Van Allen belts. J. Geophys. Res. 66, 1321–1350. https://doi.org/10.1029/ JZ066i005p01321. Alexeev, I.I., Belenkaya, E.S., Kalegaev, V.V., Feldstein, Y.I., Grafe, A., 1996. Magnetic storms and magnetotail currents. J. Geophys. Res. 101 (A4), 7737–7747. https://doi. org/10.1029/95JA03509. Corotating interaction regions. In: Balogh, A., Gosling, J.T., Jokipii, J.R., Kallenbach, R., Kunow, H. (Eds.), Space Sci. Rev. 89 (1–2).
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