Abstract
The geoeffectiveness of some coupling functions for the Solar Wind-Magnetosphere Interaction had been studied. 58 storms with peak Dst < −100 nT were used. The result showed that the interplanetary magnetic field appeared to be more relevant with the magnetic field (which agreed with previous results). However, both the (solar wind flow speed) and factors in the interplanetary dawn-dusk electric field () are effective in the generation of very intense storms (peak Dst < −250 nT) while “intense” storms (−250 nT ≤ peak Dst < −100 nT) are mostly enhanced by the factor alone (in most cases). The southward duration seems to be more relevant for Dst < −250 nT class of storms and invariably determines the recovery phase duration. Most of the storms were observed to occur at midnight hours (i.e., 2100–0400 UT), having a 41.2% incidence rate, with high frequency between 2300 UT and 0000 UT. 62% of the events were generated as a result of Magnetic Cloud (MC), while 38% were generated by complex ejecta. The - relation for the magnetic cloud attained a correlation coefficient of 0.8922, while it is 0.7608 for the latter. Conclusively, appears to be the most geoeffective factor, and geoeffectiveness should be a factor that depends on methods of event identification and classification as well as the direction of event correlation.
1. Introduction
Magnetic storm occurs at periods during which the global magnetic field, as measured by low-latitude ground magnetometers, significantly decreases. The intensity of the storm is characterized by the minimum peak Dst index [1], such that during intense storms the global field decreases at least a hundred nT (out of about 30,000 nT ground field at the equator). The interplanetary causes of such long-duration global magnetic field disturbances have been related to an intense and long-lasting southward IMF associated with the duskward interplanetary electric field (IEF) that is the main driver of global convection in the magnetosphere. For instance, Gonzalez and Tsurutani [2] define a southward IMF of at least −10 nT for more than 3 hours as a sufficient condition for the development of an intense magnetic storm. They further associate these long-duration and intense IEF enhancements either with high-speed streams or with solar wind density enhancement events, presumably known as coronal mass ejections (CMEs). These are large plasma clouds ejected from the Sun and which are characterized by intense flux-rope-like magnetic fields and low dynamic pressures. As the CMEs often travel faster than the ambient solar wind, a shock front develops in front of the CME. The interplanetary manifestation of a CME is called an interplanetary CME (ICME). However, Gosling et al. [3] had suggested that CMEs, particularly those associated with a shock, are regarded as the most important drivers of strong global geomagnetic activity.
According to Lu et al. [4], the interaction between the solar wind and the Earth’s magnetosphere produces a system of plasma circulation in the magnetosphere and high latitude ionosphere. The ionospheric convection configuration therefore provides important information of the solar wind-magnetosphere coupling. However, to predict the occurrence of a magnetic storm, according to Gonzalez et al. [5], one needs to be able to predict three interplanetary parameters: southward turning , flow speed , and the southward duration of (i.e., ). Moreover, Gonzalez et al. [1] gave a summary of some of the most commonly used coupling functions for the Solar Wind-Magnetosphere Interaction amongst which are [6, 7], [8, 9], [10], and [11].
In the work of Adebesin [12], while studying the probable roles of interplanetary and geomagnetic parameters in the generation of “intense” and “very intense” magnetic storms as well as the correlation between magnetic field intensity with flow speed , southward turning of (), and duration , a total of 18 storm events were observed (8 intense storms (−250 nT ≤ peak Dst < −100 nT) and 10 “very intense” (peak Dst < −250 nT) ones), from where it was observed that generally for the storms, the flow speed is the most correlated and hence the most geoeffective. These agree in part with the results of Gosling et al. [3] and Taylor et al. [13], who have shown statistically that out of all the variety of ejecta fields, the ones that are most effective in creating magnetic storms are events that are fast, with speeds exceeding the ambient wind speed by the magnetosonic wave speed, thereby causing a fast forward shock, The result of Adebesin [12] further showed that “very intense” storms present a negligible correlation between the flow speed and the magnetic field intensity whereas “intense” storms have 0.587 correlation between the two parameters. The present work is presented to ascertain whether the result would follow the same pattern for larger database of magnetic activities, as well as the validation of other “indicators” used in the coupling functions for the Solar Wind-Magnetosphere Interaction, as mentioned in the second paragraph. The choice of the magnetic field intensity is because for fast ICMEs, the solar ejecta and their upstream sheaths (behind the shocks) contain intense magnetic fields giving them a statistically higher probability of the right conditions to generate magnetic storms [14].
The choice of solar wind flow speed , southward turning of , and duration () could also be attributed to their roles in previous works. For instance, from the work of Dal Lago et al. ([15], and references therein), 5 great geomagnetic storms with Dst < −250 nT, observed in the period of 1978-1979, were studied, and it was found that two types of interplanetary cause were present. First was the shock compressed magnetic field, and the other was the magnetic cloud field. The first is due to a shock wave propagating in the solar wind, probably driven by a CME-related structure (ejecta), which compresses the existing solar wind magnetic field, that by chance can be pointing antiparallel to the Earth’s magnetic field (i.e., negative direction), and the second believed to be the ejected material from the CMEs, similar to interplanetary magnetic clouds. Ballatore [16] however observed that high solar wind speeds the processes responsible for the energy transfer between the interplanetary medium and the magnetosphere saturate. In addition, the influence of internal magnetospheric plasma physics on the geomagnetic activity may be larger for the faster solar wind intervals and concluded that an order in the interplanetary-magnetosphere coupling is significant only until a certain threshold of solar wind speed (~550 km/s).
Dal Lago et al. [15] also studied the solar and interplanetary causes of the 9 great geomagnetic storms (Dst < −200 nT) observed from January 1997 to April 2001 and found out that the sources of the interplanetary southward magnetic field , responsible for the occurrence of the storms, were related to either (i) the intensified shock/sheath field, (ii) interplanetary magnetic clouds field, or (iii) the combination of sheath-cloud or sheath-ejecta field. One of the events was related to a slow CME, with CME expansion speed not greater than 550 km/s. Gonzalez et al. ([5], and references therein), in an analysis of more than 1200 magnetic storms, showed that double/triple-step storms are caused by two IMF southward field events of approximately equal strength. However, a likely explanation is that the first event was caused by sheath southward IMFs (shocked, slow solar wind plasma and fields) and the second was from the remnants of the ICME itself (magnetic cloud). However, a plot of peak values of magnetic field intensity (nT) and the solar wind speed for the magnetic cloud events shows that the faster the cloud moves, the higher is the core magnetic field.
Huang et al. [18] in their studies of the magnetic storm of October 29–31, 2003, often referred to as the Halloween storm, reported that the storm is characterized by extremely high solar wind speeds and three southward IMF turnings within the interval. Moreover, Vieira et al. [19] have shown that about 15% of intense storms caused by magnetic clouds can be of the triple-step type, especially when large amplitude density waves/discontinuities exist within the cloud, thus causing an additional Bs structure.
2. Data and Methods
In the present study, a total of 58 storm events were presented. 40 of the storms were intense (i.e., −250 nT ≤ peak Dst < −100 nT) and the remaining 18 were “very intense” or severe (i.e., peak Dst < −250 nT). It should be noted that very intense storms are not so common, hence the reason for the limited number of events when compared to the intense ones. For instance, no intense geomagnetic activity was recorded between December 18, 2006 and July 2011. The one that occurred on August 8, 2011 does not have the required parameters for this study. Moreover, Table 1 also supported the argument that very-intense storms are not so common like the other ones. The table highlighted the basic classification of magnetic storms on the basis of the Dst index using the 1957–1993 measurements (according to [17]). It was shown that very-intense (i.e., Severe and Great) storms take just about 5% of the list. Weak (44%), moderate (32%), and strong (i.e., intense) storms take 19%.
The authors decided to divide the storms into these 2 categories (i.e., “intense” and “very-intense”) so as to be able to understand the storms behavior at peak Dst < −250 nT, and not just generally at −250 nT ≤ peak Dst < −100 nT condition alone. The NSSDC’s OMNI database (http://nssdc.gsfc.nasa.gov/omniweb/) provided the hourly values of the low latitude magnetic index Dst (nT), the solar wind flow speed (km/s), the imbedded magnetic field intensity (nT), and the southward Interplanetary magnetic field (nT)—in GSM. was thereafter calculated from . Presented in Tables 2 and 3, respectively, are the lists of storm dates with corresponding peak values of Dst, magnetic field intensity , IMF , southward turning interval , and solar wind flow speed , within the storm interval, as well as the calculated values for some coupling functions for the Solar Wind-Magnetosphere Interaction for “intense” and “very intense” conditions. The hourly peak values of , , and taken are generally near Dst hourly maximum depression. The only exception to this condition is the event of 13 March 1989 (in which the Cliver values were used, i.e., km/s). It is assumed that the intensity of the storm makes the measurement of the other parameters to be impossible at Dst maximum depression.
All the , , and values are approximate with a possible uncertainty of ~5%. This is because the respective peak values of the three parameters may differ from their values at Dst maximum depression by around 5% or less. Thereafter, the Regression fit was plotted and the correlation coefficients were computed.
3. Results
Figures 1, 2, and 3 present the Regression plots of (a) versus , (b) versus , and (c) versus for intense, very intense, and all storms, respectively. However, the generated corresponding correlation coefficients for these plots were highlighted in Table 4. From the table, versus ratio recorded the highest correlation coefficient of 0.868, 0.819, and 0.885 for intense, very-intense, and all storms, respectively. The correlation between the magnetic field intensity and the flow speed is low (0.252) for intense storms, 0.439 for very-intense, and 0.489 for all storms. Moreover, versus (i.e., the southward duration) is rather low for both intense and all storms (~0.250), while it is 0.474 for very-intense ones.
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Furthermore, highlighted in Figures 4, 5, and 6 are the regression plots of with some commonly used coupling functions for the Solar Wind-Magnetosphere Interaction for intense, very-intense, and all storms, respectively: (a) (b) , (c) , (d) . Table 5 however presents the correlation coefficient between , , and (according to [1]) as well as the self-derived ,, and with magnetic field intensity . Observe from the table that for all the storms, versus recorded the highest correlation (0.857), followed by , , , and , in that order (all above 75% range). Note that the - relationship is negligible (i.e., 0.085). The ratio is introduced as a function connecting the three parameters used, and it could be seen as yielding good result with (i.e., 0.750). Moreover, the factor used also yielded good correlation strength. However, increasing the power of any further (i.e., , ) reduces the - value.
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4. Discussion
On the average, had the highest correlation percentage with , irrespective of whether the storm is intense or very-intense (i.e., above 80%), but as long as the peak Dst ≤ −100 nT condition is satisfied. For the flow speed , the correlation is approximately 49% for all the 58 storms considered, but rather too low for intense storms alone. The southward duration’s () correlation is very weak in all, but a little below average (47%) for very-intense storms. It follows therefore from these results that the interplanetary dawn dusk electric field, given by , is enhanced only by for intense (i.e., −250 nT ≤ peak Dst < −100 nT) and by both factors ( and ) for “very intense” (i.e., peak Dst ≤ −250 nT) storms. The latter statement points to the fact that the resulting magnetospheric energization as a result of the electric field becomes more effective for magnetic storm occurrence. The very-intense storm empirical relationship between and (0.439) may likely be due to the Corona mass ejection (CME) release and acceleration mechanism occurring near the Sun. Moreover, seems to be more relevant with for peak Dst ≤ −250 nT.
The results from other “indicators” used in the coupling functions for the Solar Wind-Magnetosphere Interaction showed that all the indicators agreed with earlier results, (e.g., [1, 5, 16, 20] and references therein) with a correlation percentage of above 70%. The only exception is the - relationship. The strong cross-magnetospheric convection electric fields with associated field-aligned potentials which are also a significance effect of magnetic reconnection and strong magnetic field distortions may be one of the factors responsible for the high correlation value between and (0.857). The plots in Figure 7 also showed that is the most driving factor for the interplanetary dawn-to-dusk electric field. Here, a correlation plot of (a) against gives a value of 0.901, (b) against flow speed yields 0.709, and (c) against recorded an apparently low value of 0.391. The result of (b) shows the relevance of the flow speed in the parameter as well but only points to the fact that it is not as geoeffective as as far as generation of intense storms is concerned. The result of (c) implies that both and are not necessarily dependent of each other, or that their dependency is low. It should be noted that parallel electric fields above the ionosphere may lead to downward acceleration of electrons to energies of 1–10 keV.
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The high correlation value of versus tends to disagree with the work of Adebesin [12], where it was observed that for all storms (i.e., intense and very-intense), the flow speed is the most correlated with (correlation = 0.509) and hence the most geoeffective, in which case versus value is as low as 0.219. This can be explained on the following basis. According to Y. I. Yermolaev and M. Y. Yermolaev [21], based on various clarifications, there are six main large-scale types of interplanetary occurrences, namely, (i) fast solar wind from coronal holes, (ii) slow solar wind from coronal streamers, (iii) heliospheric current sheet, (iv) decompressed streams of solar wind, (v) complex ejecta, that is, compressed streams of solar wind (corotating interaction region, CIR, and sheath, streams ahead magnetic clouds, MC), and (vi) magnetic clouds. However, among the six, it is only the last two types that are geoeffctive, just because they can contain long Interplanetary Magnetic Field southward component [22–24]. It is most likely that one or more of the other first four classifications may be the main driver of most of the 18 storms considered by Adebesin [12]. If this is so, then the flow speed will invariably be more correlated with than with , since it does not involve long southward . Another factor that may contribute to the result may be the limited number of investigated storms (i.e., 18). Another factor may be that most of the storms could have been associated with multiple halo CMEs that may have been intermingling, and such interactions are more likely near maximum and could explain some of the compositional anomalies of ICMEs [25].
From earlier results by different authors, it has been shown that quite a lot of strong magnetic storms (i.e., events of March 31, 2001, Dst peak value of −387 nT; April 11, 2001, Dst = −271 nT [26]; November 20, 2003, Dst = −472 nT [27]; October 29-30, 2003, Dst = −363 nT [28]; November 8–10, 2004, Dst = −373 nT [29]) have been generated as a result of multiple interacting magnetic clouds. However, according to Farrugia et al. [30], it was observed that a significant number of our large events (6 out of 16) consisted of ICMEs/magnetic clouds interacting with each other forming complex ejecta. In like manner, Xie et al. [31] studied 37 long-lived geomagnetic storms with Dst < −100 nT and the associated CMEs which occurred between 1998 and 2002 and found that 24 of 37 events (~65%) were caused by successive CMEs and number of interacting magnetic clouds was observed from 2 up to 4.
In light of the above, we went further to investigate for the percentage of storms generated by either the magnetic cloud or complex ejecta. Figures 8 and 9 revealed the correlation plots of Magnetic field with (a) , (b) , and (c) Dst for magnetic cloud and complex ejecta events, respectively. It was observed from Figure 8 that there are better plotted points for (a) and (c), while that of (b) was dispersed. Figure 9 also revealed a dispersed plot for (b) and (c). However, the summary of the results was highlighted in Table 6. 62% of the events were as a result of magnetic cloud (MC), while 38% were generated by complex ejecta. The - relation attained a correlation coefficient of 0.8922, a little above B versus Dst (0.8304), while - recorded 0.4970. For the complex ejecta, the versus correlation is 0.7608. The values are presumably low for the other two parameters. The overall respective high correlation values of the parameters with during magnetic cloud events over the complex ejecta events seem to suggest that though both classes can cause intense storm, but the former is more geoeffective than the latter.
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The frequency distribution of (i.e., the southward duration) for all the storms showed that 41.5% is in the range 3–9 hours, 35.8% (10–19 hours), 18.9% (20–29 hours), and 3.8% (≥30 hours). This shows that about 58.5% of extended beyond 10 hours of southward orientation. The implication of this is that with every southward field turning, there is a decrease in Dst; so the longer the is, the longer is the storm recovery phase (since only northward orientation of the interplanetary magnetic field would aid the recovery phase in most cases). The southward field turnings therefore cause magnetic reconnection and plasma injections into the nightside magnetosphere. However, these periods of continuous substorm activity are known as “high-intensity, long duration, continuous AE activities (HILDCAA)”. Therefore, the sporadic injection of plasma into the magnetosphere is the reason why the ring current does not appear to decay. However the interplanetary field fluctuations are as a result of Alfven waves present in the high-speed streams when the waves are compressed, leading, in most cases, to irregular shaped storm main phase. This may be responsible for the highest correlation value observed (0.885) for the - relationship.
According to Gonzalez and Tsurutani [2] and Gosling et al. [3], 90% of storms with intensities of peak Dst ≤ −100 nT are caused by southward magnetic fields within high-speed streams led by shocks.
Figure 10 illustrates the radial time distribution of peak Dst value (i.e., the exact hour of the day that Dst reaches its peak value) for all the 58 storms under investigation. The time was divided into four categories, namely, sunrise (0500–0900 UT), prenoon/postnoon (1000–1500 UT), sunset/late evening (1600–2000 UT), and midnight hours (2100–0400 UT). The figure revealed a 41.2% occurrence for midnight hours, followed by sunrise period with 29.3%. The prenoon/postnoon and the sunset episodes recorded 15.5% and 13.8%, respectively. Moreover, the hourly frequency distribution of peak Dst values was depicted in Figure 11. The figure revealed that the 0800 UT, 2300 UT and 0000 UT recorded the observed highest values. The explanation for this is still left open.
5. Summary and Conclusion
58 storms of different intensities were considered in this study. Previous works have shown that the southward interplanetary magnetic field is the most geoeffective factor in the solar wind-magnetosphere coupling function. However, the result of Adebesin [12] in which 18 storms were observed arrived at the conclusion that the flow speed is the most geoeffective. However, the result of the present study revealed the following.(i) shows to be more relevant with the magnetic field for all storms.(ii)The southward duration seems to be more relevant with for Dst < −250 nT (i.e., very intense storms).(iii)Both the and factors in the interplanetary dawn-dusk electric field which causes magnetosphere energization are effective in the occurrence of “very intense” storms while “intense” storms are mostly enhanced by the factor alone.(iv) determines the duration of the recovery phase of the storm.(v) and have little or no dependence on each other.(vi)In contrast to Adebesin [12], has high correlation with .(vii)The disagreement with the result of Adebesin [12] was suggested to be due to differences in the causative factors of the storms studied then, and those for the present study, as well as the number of storms considered.(viii)Observations on the coupling functions for the Solar Wind-Magnetosphere interaction parameters agree with earlier results with regards to , , and , as well as the derived ones (i.e., , , and ).(ix)Most of the storms were observed to occur at midnight hours, having a 41.2% incidence rate, followed by the sunrise hours (with 29.3%).(x)62% of the events were as a result of magnetic cloud (MC), while 38% were generated by complex ejecta. The - relation for the magnetic cloud attained a correlation coefficient of 0.8922. For the complex ejecta, the versus correlation is 0.7608.
We therefore can say from the above that the factor in the parameter (i.e., the interplanetary dawn-dusk electric field) is very geoeffective for both the −250 nT ≤ peak Dst < −100 nT and peak Dst < −250 nT class of storms, whereas the flow speed is only effective for the first class alone (in most cases).
Acknowledgment
The author would like to thank NSSDC’s OMNI database (http://nssdc.gsfc.nasa.gov/omniweb/) for their data support.