Seasonal and diurnal variation of geomagnetic activity: Russell‐McPherron effect during different IMF polarity and/or extreme solar wind conditions

Abstract

[1] The Russell‐McPherron (R‐M) effect is one of the most prevailing hypotheses accounting for semiannual variation of geomagnetic activity. To validate the R‐M effect and investigate the difference of geomagnetic activity variation under different interplanetary magnetic field (IMF) polarity and during extreme solar wind conditions (interplanetary shock), we have analyzed 42 years interplanetary magnetic field and geomagnetic indices data and 1270 SSC (storm sudden commencement) events from the year 1968 to 2010 by defining the R‐M effect with positive/negative IMF polarity (IMF away/toward the Sun). The results obtained in this study have shown that the response of geomagnetic activity to the R‐M effect with positive/negative IMF polarity are rather profound: the geomagnetic activity is much more intense around fall equinox when the direction of IMF is away the Sun, while much more intense around spring equinox when the direction of IMF is toward the Sun. The seasonal and diurnal variation of geomagnetic activity after SSCs can be attributed to both R‐M effect and the equinoctial hypothesis; the R‐M effect explains most part of variance of southward IMF, while the equinoctial hypothesis explains similar variance of ring current injection and geomagnetic indices as the R‐M effect. However, the R‐M effect with positive/negative IMF polarity explains the difference between SSCs with positive/negative IMFB_yaccurately, while the equinoctial hypothesis cannot explain such difference at the spring and fall equinoxes. Thus, the R‐M effect with positive/negative IMF polarity is more reasonable to explain seasonal and diurnal variation of geomagnetic activity under extreme solar wind conditions.

1. Introduction

[2] The semiannual variation in geomagnetic activity has been recognized for a long period of time [Cortie, 1912], which shows the maximum appears around equinoxes while the minimum appears around solstices, e.g., geomagnetic storm annual distribution [Echer et al., 2011]. Over the decades, several explanations for this variation have been put forward, such as the axial hypothesis, the equinoctial hypothesis and the Russell‐McPherron effect [Cortie, 1912; Bartels, 1932; McIntosh, 1959; Svalgaard, 1977; Russell and McPherron, 1973].

[3] The axial hypothesis takes the varying heliographic latitude of the earth into consideration; the equinoctial hypothesis is based on the angle between Earth‐Sun line and the dipole axis of the Earth; the R‐M effect holds that the angle between Z axis in geocentric solar magnetospheric (GSM) coordinate system and Y axis in geocentric solar equatorial (GSEQ) coordinate system plays an important role.Figure 1a shows the semiannual and diurnal variation of the angle θbetween the Z axis in GSM coordinate system and the Y axis in GSEQ coordinate system, that is, the controlling parameter of the R‐M effect. According to the R‐M effect, the probability of southward IMF increases when the angleθ, which is smaller than 90 degrees, decreases, so that the dayside reconnection can be more efficient and more energy can be conveyed into the magnetosphere. Figure 1b shows the semiannual and diurnal variation of the angle ψbetween Earth‐Sun line and the dipole axis of the Earth, that is, the crucial parameter of the equinoctial hypothesis.Crooker and Siscoe [1986]suggest the field configuration in the Chapman‐Ferraro current plane may change and prevent the energy transfer as theψ angle changes; whereas Russell et al. [2003] demonstrate that the tilt of dipole axis controls the size of dayside reconnection region and thus the reconnection rate and geomagnetic activity.

Figure 1

The Russell‐McPherron effect and the equinoctial hypothesis. (a) Seasonal and diurnal variation ofθ angle between Z axis in GSM coordinate system and Y axis in GSEQ coordinate system. (b) Seasonal and diurnal variation of ψangle between Earth‐Sun line and the dipole axis of the Earth.

[4] Nowadays, the R‐M effect is one of the most prevailing hypotheses.Orlando et al. [1993]investigated the connection between semiannual variation of the geomagnetic activity and interplanetary magnetic field from 1965 to 1987 and verified the accuracy of R‐M effect which suggests the geomagnetic activity is modulated by southward IMFB_z. Siscoe and Crooker [1996]analyzed diurnal variation of Dst index for 13 years and found the R‐M effect predicts such an diurnal oscillation. Also,O'Brien and McPherron [2002]investigated the dynamics of Dst index and demonstrated the R‐M effect is indeed valid.

[5] However, there are also many studies on the semiannual variation which argued that the R‐M effect fails to explain the diurnal variation of the geomagnetic activity and can only explain a small part of seasonal variation of the geomagnetic activity.Cliver et al. [2000]argued that the R‐M effect can only predict part of semiannual variation, while the equinoctial hypothesis, which is based on the variation of the angleψbetween the Earth‐Sun line and the dipole axis of the Earth, accounts for a large part of semiannual variation of geomagnetic activity.Cliver et al. [2001]investigated the semiannual variation of Dst index for about 40 years and found the equinoctial hypothesis dominates the storm component of the variation of Dst index and the R‐M effect predicts little variance. The similar conclusion has been derived from the analysis of aa index, too [Cliver et al., 2002]. Moreover, Svalgaard et al. [2002] analyzed the largest geomagnetic storms from 1868 to 1998 and indicated the most difference of occurrence frequency between equinoxes and solstices arises from an equinoctial effect. Li et al. [2001] used the models of MeV electron at geostationary orbit and the Dst index to examine the cause of semiannual variation and found the equinoctial hypothesis contributes the largest part to semiannual variation of Dst index and MeV electrons in the inner magnetosphere. Furthermore, Mursula [2011] have studied seasonal variation of substorms and geomagnetic index Ap between 1993 and 2008 and showed that semiannual variation is mainly due to the artifact of annual maximum alternating from spring to fall; however, Svalgaard [2011]disprove this conclusion by showing the well‐established UT variation of geomagnetic activity and lack of organized annual variations of the solar driver, and confirm that the semiannual variation is not overestimated nor an artifact.

[6] On the other hand, the contribution of solar wind, especially during extreme solar wind conditions, like interplanetary shocks, to seasonal and diurnal variation of geomagnetic activity has been rare studied although it may play significant role.

[7] SSCs indicate the arrival of the interplanetary discontinuities/shocks [Gonzalez et al., 1994]. A SSC is a sudden increase in the H component of geomagnetic field preceding a geomagnetic storm. It differs from a sudden impulse (SI), which is physically the same phenomenon but without following a geomagnetic storm [Siscoe et al., 1968; Joselyn and Tsurutani, 1990; Araki, 1994; Echer et al., 2005]. MHD discontinuities have four types: rotational discontinuities, tangential discontinuities, contact discontinuities, and shocks. Shocks also have three different types, that is, fast, intermediate and slow. Either shocks or tangential discontinuities which have different densities across them can cause SIs or SSCs. Interplanetary shocks have a great impact on the Earth's magnetosphere. Fast shocks, which are most likely to cause a SSC or SI, can also lead to particle energization [Zong et al., 2009], dayside aurora, creation of new radiation belts, and substorms [Colburn and Sonett, 1966; Tsurutani et al., 2011]. Through the study of SSCs and shocks between 1978 and 1980, Smith et al. [1986] found that 80–90% of SSCs were associated with interplanetary shocks. Wang et al. [2006] observed 278 SSCs from January 1995 to December 2004 and found 225 of them were associated with interplanetary shocks, that is, the probability that a SSC is associated with a interplanetary shock is 0.75.

[8] Interplanetary shocks can cause intense geomagnetic storms. Jurac et al. [2002] found, 40% of forward shocks with shock normals perpendicular to the IMF cause intense storms(Dst < −100 nT), while 10–15% of shocks without normals perpendicular to the IMF lead to intense storms. Also, Echer and Gonzalez [2004] reported 57% of interplanetary shocks are followed by moderate and intense geomagnetic storms(Dst ≤ −50 nT). Interplanetary shocks can also trigger substorms [Zhou and Tsurutani, 2001; Tsurutani and Zhou, 2003]. The upstream IMF of shocks strongly affect auroral responses: southward IMF can lead to substorm expansion phase triggerings, nearly zero IMF leads to pseudobreakup events, and northward IMF for quiescent events. Yue et al. [2010] investigated 106 interplanetary shocks during 1997–2007 and found that IMF B_z keep southward or northward before the shock arrival and turns out to be more negative or positive after the arrival of the shock.

[9] In this study, we have examined the validity and precision of the R‐M effect and interplanetary shock related R‐M effect by analyzing a large amount of the data of magnetic field and geomagnetic indices from 1968 to 2010 and 1270 SSC (storm sudden commencement) events under different IMF polarity. We showed that the IMF polarity is one of the most important parameters when investigating seasonal and diurnal variation of geomagnetic activity. Geomagnetic activity are rather strong at spring and fall equinoxes with different IMF orientations: the geomagnetic activity is much more intense around fall equinox when the direction of IMF is away the Sun, while much more intense around spring equinox when the direction of IMF is toward the Sun, which is identical with the R‐M effect under different IMF polarity. This feature also exists before and after SSCs.

2. Seasonal and Diurnal Variation of Geomagnetic Activity: The R‐M Effect With Positive/Negative IMF Polarity

[10] Since the R‐M effect was first put forward in 1973, it becomes the most prevailing hypothesis accounting for the semiannual variation of geomagnetic activity. The R‐M effect explains the semiannual variation of geomagnetic activity by the varying probability of IMF southward component in GSM coordinate system, which is caused by the varying orientation of the GSM coordinate system relative to GSEQ coordinate system. The IMF southward component is widely believed to be the controlling factor of geomagnetic activity. The Earth rotation axis tilts ∼23.5° from Z axis in geocentric solar ecliptic (GSE) coordinate system, causes the seasonal variation of the projection of IMF onto Z axis in GSM, and thus causes the seasonal variation of the probability of southward IMF in GSM. The dipole axis inclines ∼11.5° from the rotation axis and leads to the diurnal variation of the southward IMF projection.

[11] There are three main assumptions in the R‐M effect: the IMF is always along the Parker spiral direction and its magnitude is constant; the IMF is either away or toward the Sun with equal possibility; and the northward IMF has no effect on the geomagnetic activity. Since different directions of IMF can have different effects on the magnetosphere, we study the R‐M effect under different IMF polarity, that is, away the Sun (positive polarity, IMFB_y > 0 in GSE coordinate system), we define it as “the R‐M effect with positive IMF polarity”, and toward the Sun (negative polarity, IMFB_y < 0), defined as “the R‐M effect with negative IMF polarity”.

[12] Figure 2shows the R‐M effect with positive/negative IMF polarity, namely, the contour plot of IMFB_z southward component in GSM coordinate system under the situation that IMF is away/toward the Sun, assuming IMF B_y of 1 γin GSEQ coordinate system, and the schematic diagram of the R‐M effect under different IMF polarity.

Figure 2

The schematic diagram of the R‐M effect with positive/negative IMF polarity. At spring equinox, IMF toward the Sun projects onto Z axis of GSM coordinate system and converts into an effective southward component; at fall equinox, IMF away the Sun projects onto Z axis with a southward projection. The R‐M effect with positive/negative IMF polarity shows the semiannual variation of IMFB_z southward component in GSM coordinate system due to IMF B_y in GSEQ coordinate system of 1 γ.

[13] At spring equinox, the Earth rotation axis is pointed ∼23.5° away from Z axis toward Y axis in GSE coordinate system, so that the IMF toward the Sun makes a negative projection onto the direction of Z axis of GSM coordinate system, which can increase the efficiency of dayside reconnection and enhance the geomagnetic activity, and the IMF away the Sun makes a positive projection onto the direction of Z axis, which has no effect on the geomagnetic activity according to assumptions in the R‐M effect. At fall equinox, the angle from the Earth rotation axis to Y axis in GSE coordinate is ∼113.5°, so that the IMF away the Sun projects onto the direction of Z axis in GSM coordinate system with a negative projection, and the IMF toward the Sun projects onto the Z axis with a positive projection.Figure 2shows that when IMF is away the Sun, corresponding to the R‐M effect with positive IMF polarity, the maximum of possibility of southwardB_zappears around fall equinox, and when IMF is toward the Sun, corresponding to the R‐M effect with negative IMF polarity, the maximum appears around spring equinox.

[14] To confirm the prospective R‐M effect with positive/negative IMF polarity, we have used the data set with 1 hour resolution from Omniweb (http://omniweb.gsfc.nasa.gov/) from 1968 to 2010 to analyze the contours of vB_s, defined as −vB_z in GSM coordinate system when IMF is southward, and defined to be zero when IMF is northward, in a 24 × 24 lattice of day of year and UT hour, under different polarity of IMF. Here we divide UT and day of year to 24 bins respectively, with a bin of 1 hour × 15.25 days, and calculate the probability of vB_s > 1 mV/m within each bin under different IMF polarity.

[15] Figure 3 shows the contour plots of the probability of vB_s > 1 mV/m with IMF B_y positive/negative. The patterns of variation showed in Figure 3are generally identical with the R‐M effect with positive/negative IMF polarity, as the maximum appears at about UT 23:00 at spring equinox when IMFB_y < 0, as well as the maximum appears around UT 10:00 at fall equinox when IMF B_y > 0. The correlation coefficient between the probability of vB_s > 1 mV/m under positive IMF B_y and IMF B_zsouthward component in GSM indicated by the R‐M effect with positive IMF polarity (asFigure 2 shows) is 0.91, while the coefficient between the probability of vB_s > 1 mV/m under negative IMF B_y and IMF B_zindicated by the R‐M effect with negative IMF polarity is 0.90. The results indicate the R‐M effect with positive/negative IMF polarity can predict the seasonal and diurnal variation ofvB_s with positive/negative IMF B_y precisely.

Figure 3

The seasonal and diurnal variation of probability of vB_s > 1 mV/m with positive/negative IMF B_y and southward IMF B_z, calculated in a 24 × 24 lattice and smoothed by a 3 × 3 average.

[16] In order to investigate the seasonal and diurnal variation of variation of ring current injection, we derive the ring current injection function Q from the Burton from the Burton equations [Burton et al., 1975]:

where Q is assumed as a function of vB_s, Dst* is the pressure‐correctedDst index, τ is the decay time of ring current, P is the solar wind dynamic pressure, and bis the pressure‐correction coefficient.O'Brien and McPherron [2000] gave Q(vB_s) = − 4.4(VB_s − E_c) when VB_s > E_c, Q = 0 when VBs < E_c. Here E_c is the ring current injection cutoff and E_c = 0.49 mV/m; τ = 2.40e^{9.74/(4.69+VBs)}, and b = 7.26.

[17] Then, we divide day of year and UT into a 24 × 24 lattice and plot contours of the probability of Q < −10 nT/h with positive/negative IMF B_y. The contours are shown in Figure 4. It is evident that the pattern of variation of ring current injection with positive/negative IMF B_yfits well with R‐M effect with positive/negative IMF polarity, with maximum at spring equinox when IMFB_y < 0 and at fall equinox when IMF B_y > 0. The correlation coefficients of situations during positive and negative B_ywith the R‐M effect with positive/negative IMF polarity are 0.69 and 0.72 respectively.

Figure 4

The seasonal and diurnal variation of probability of Q < −10 nT/h with positive/negative IMF B_y and southward IMF B_z, calculated as Figure 3.

[18] On the other hand, to examine whether the R‐M effect with positive/negative IMF polarity predicts the geomagnetic activity at low as well as high latitudes accurately, we perform the contour plots of variation of Dst index and AE index with different orientations of IMFB_y and B_z in a 24 × 24 lattice, too.

[19] The hourly Dst index, calculated from the magnetic field disturbances measured by midlatitude geomagnetic stations, is a widely accepted indicator of ring current intensity. AE index describes the global auroral electrojet activity so that it can be used as a proxy of geomagnetic activity at high latitude [Rostoker, 1972]. Figures 5 and 6 show the seasonal and diurnal variation of Dst and AE indices under different situations of IMF B_y and B_z, respectively.

Figure 5

The seasonal and diurnal variation of Dst index with positive/negative IMF B_y and southward/northward IMF B_z, calculated as Figure 3.

Figure 6

The seasonal and diurnal variation of AE index with positive/negative IMF B_y and southward/northward IMF B_z, calculated as Figure 3.

[20] From both figures we can find the pattern of semiannual variation with positive IMF B_yis consistent with the R‐M effect with positive IMF polarity, which shows the maximum at fall equinox, while the pattern with negative IMFB_yfits well with the R‐M effect with negative IMF polarity, as the maximum appears at spring equinox. The diurnal variation of Dst index, on the other hand, is not as clear as the seasonal variation, butFigures 5a and 5bstill reveal some UT variation pattern which is consistent with the R‐M effect with positive/negative IMF polarity.

[21] Also, compared contours of Dst and AE indices with southward/northward IMF B_z, we can find that the average value of geomagnetic indices is much higher when IMF B_z is southward than northward, which indicates much more intense geomagnetic activity resulting from more efficient dayside reconnection.

[22] Furthermore, by comparing Figures 5a and 5b, we can see that the average value of Dst index is much larger with positive IMF B_y, which indicates that the R‐M effect with positive IMF polarity can further enhance the geomagnetic activity. On the other hand,Figure 3 doesn't show much difference in IMF B_s under positive/negative IMF polarity, which suggests the enhanced geomagnetic activity under positive IMF B_y is more likely caused by the enhanced dayside reconnection rate.

[23] The correlation coefficients of Figures 5a, 5b, 5c, and 5dwith corresponding R‐M effect are −0.68, −0.66, −0.67 and −0.72 respectively, and forFigures 6a, 6b, 6c, and 6d, the correlation coefficients are 0.59, 0.58, 0.72 and 0.68 respectively. The correlation coefficients are summarized in Table 1.

Table 1. Summarization of Correlation Coefficients of Contours During Positive/Negative IMF B_y and Southward/Northward B_zWith Corresponding R‐M Effect With Positive/Negative IMF Polarity

	By > 0, Bz < 0 and R‐M Effect (+IMF)	By < 0, Bz < 0 and R‐M Effect (−IMF)	By > 0, Bz > 0 and R‐M Effect (+IMF)	By < 0, Bz > 0 and R‐M Effect (−IMF)
vBs	0.91	0.90
Q	0.69	0.72
Dst index	−0.68	−0.66	−0.67	−0.72
AE index	0.59	0.58	0.72	0.68

3. Seasonal and Diurnal Variation of Geomagnetic Activity Under Extreme Solar Wind Conditions

3.1. Seasonal and Diurnal Variation of Geomagnetic Activity Before and After SSC Events With Different Orientation of IMF B_z

[24] To examine seasonal and diurnal variation of geomagnetic activity before and after SSCs, we use vB_sfrom OMNI database to demonstrate the R‐M effect is present before and after SSCs. We divide UT and the day of year into 12 bins respectively, with each bin of 2 hours × 30.5 days, and calculate the probability ofvB_s > 1 mV/m before and after SSCs respectively in each bin. Here we use the SSC list from IAGA Bulletin and analyze 1270 SSCs between 1968 and 2010.

[25] According to Zhang et al. [2008], the duration of a CME preceding shock sheath is generally shorter than 24 hours, so we choose a time period of 12 hours before and after each SSC event respectively to perform contour plots before and after SSCs. In order to examine the effect of the orientation of IMF B_zon the R‐M effect, we perform the contour plots under southward and northward IMFB_z.

[26] Figure 7 shows the seasonal and diurnal variation of the probability of vB_s > 1 mV/m before and after SSCs respectively under southward IMF B_z. It's worth mentioning that the scales of two panels' color bars are different. From Figure 7, we find that the pattern of vB_svariation after SSCs is quite similar with the R‐M effect. It shows higher probability of southward IMFB_z at the equinoxes and lower at the solstices, as well as higher probability at midnight around spring equinox while at noon around autumn equinox. Before SSCs, the probability of vB_s > 1 mV/mis much smaller than after SSCs, however, the pattern doesn't well fit the R‐M effect. The correlation coefficient between the probability ofvB_s > 1 mV/m before/after SSCs and the angle θ, the controlling parameter of the R‐M effect, is −0.11/−0.60.

Figure 7

Seasonal and diurnal variation of the probability of VB_s > 1 mV/m before and after SSCs under southward IMF B_z.

[27] To compare with the R‐M effect, we also calculate the correlation coefficient between the probability ofvB_s > 1 mV/m and the angle ψ, which is the dominant parameter in the equinoctial hypothesis. The correlation coefficient before/after SSCs is 0.02/0.39 respectively. It indicates that the R‐M effect can explain the probability of southward IMFB_z after SSCs more precisely, while the equinoctial hypothesis can hardly explain the semiannual variation of vB_s clearly.

[28] We also calculate the probability of Q < −10 nT/h in a 12 × 12 lattice. The results are showed in Figure 8. Figure 8 shows the probability of Q < −10 nT/h before and after SSCs under southward IMF, which reveals prominent semiannual variation as higher at the equinoxes and lower at the solstices. The correlation coefficient of the probability of Q < −10 nT/h before/after SSCs and the angle θ is −0.30/−0.57, while for the angle ψ the correlation coefficient is 0.15/0.62. The correlation coefficients show that both θ and ψ can explain part of seasonal and diurnal variations of large ring current injection. And also, before SSCs both hypotheses explain less variations of ring current injections than after SSCs.

Figure 8

Seasonal and diurnal variation of the probability of Q < −10 nT/h before and after SSCs under southward IMF B_z.

[29] Moreover, in order to show the seasonal and diurnal variation of geomagnetic activity under extreme solar wind conditions, we perform the contour plots of Dst index before and after SSCs in a 12 × 12 lattice, and compare the contour plots with the R‐M effect as well as the equinoctial hypothesis to examine whether these two hypotheses account for variation of Dst index before and after SSCs.

[30] Figure 9 shows the seasonal and diurnal variation of Dst index before and after SSCs under southward and northward IMF B_z conditions, respectively. From Figure 9, we find that the semiannual variation with equinoxes maximum is evident, but the diurnal variation cannot be well explained by both hypotheses. The correlation coefficient of Dst variation before/after SSCs under southward IMF conditions (Figures 9a and 9b) with the θ angle is 0.42/0.51; as to the ψ angle the correlation coefficient is −0.13/−0.52; under northward IMF conditions (Figures 9c and 9d), the correlation coefficient of Dst variation before/after SSCs with the θ is 0.27/0.26, while for ψ is −0.01/−0.48.

Figure 9

Seasonal and diurnal variation of Dst index before and after SSCs under different IMF B_z conditions.

[31] It shows that both hypotheses predict part of the variation of Dst index after SSCs; however, as for the situation before SSCs, both hypotheses, especially the equinoctial hypothesis, cannot predict the variation of Dst index. Compared with different IMF orientations, we find that with southward IMF B_z, the absolute value of Dst index is much higher than another two cases, which indicates more energy transfer and larger geomagnetic storms.

[32] Moreover, by distinguishing different orientations of IMF B_y, we can derive higher correlation coefficients between the R‐M effect with positive/negative IMF polarity and variation of geomagnetic activity, which can be seen in the following section. The correlation coefficients of each situation with the angleθ and ψ are summarized in Table 2.

Table 2. Summarization of Correlation Coefficients Between Geomagnetic Activity Variation Before and After SSCs With Different IMF B_z Conditions and Two Hypotheses

	Time Period	IMF Bz Direction	The θ Angle	The ψ Angle
The probability of vBs > 1 mV/m	before SSCs	IMF Bz southward	−0.11	0.02
	after SSCs	IMF Bz southward	−0.60	0.39
The probability of Q < −10 nT/h	before SSCs	IMF Bz southward	−0.30	0.15
	after SSCs	IMF Bz southward	−0.57	0.62
The Dst index	before SSCs	IMF Bz southward	0.42	−0.13
		IMF Bz northward	0.27	−0.01
	after SSCs	IMF Bz southward	0.51	−0.52
		IMF Bz northward	0.26	−0.48

3.2. Seasonal and Diurnal Variation of Geomagnetic Activity Before and After SSCs With Positive/Negative IMF B_y

[33] The R‐M effect explains semiannual variation of geomagnetic activity using the changing IMF southward component, which is caused by the changing of GSM coordinate system relative to GSEQ coordinate system. To confirm the R‐M effect is indeed present before and after SSC events and has a great influence on the geomagnetic activity, we perform the contour plots under different IMFB_y orientations, that is, positive and negative. The contour plots of semiannual variation of the probability of vB_s > 1 mV/m, the probability of Q < −10 nT/h and the Dst index before/after SSCs with different IMF B_y are showed in Figures 10, 11, and 12. From these figures, we can find that as to the situation that IMF B_y is negative, the geomagnetic activity is more intense at spring equinox and relatively weak at fall equinox; when IMF B_yis positive, the geomagnetic activity around fall equinox is much more intense and less intense at the spring equinox, which is consistent with the R‐M effect with positive/negative IMF polarity.

Figure 10

Seasonal and diurnal variation of the probability of VB_s > 1 mV/m before and after SSCs under different IMF B_y conditions.

Figure 11

Seasonal and diurnal variation of the probability of Q < −10 nT/h before and after SSCs under different IMF B_y conditions.

Figure 12

Seasonal and diurnal variation of the Dst index before and after SSCs under different IMF B_y conditions.

[34] Meanwhile, we perform contour plots of AE index before/after SSCs under different IMF B_y conditions, as shown in Figure 13c, 13d, 13e, and 13f. As a comparison, we also perform contour plots of AE index before/after SSCs under all circumstances (Figures 13a and 13b). The variation of AE index before and after SSCs don't show clear feature of semiannual variation and UT variation as the R‐M effect or the equinoctial hypothesis suggested, which is likely caused by the equatorward expansion of the auroral electrojets and the longitudinal station gaps [Ahn et al., 2000]. However, even the seasonal and diurnal variation of AE index is quite distinctive, AE variation with positive/negative IMF B_ystill shows identical feature as the R‐M effect with positive/negative IMF polarity: when IMFB_y is negative, AE index is higher around the spring equinox and relatively lower around the fall equinox; when IMF B_y is positive, it is higher around the fall equinox and lower around the spring equinox.

Figure 13

Comparison between seasonal and diurnal variation of the AE index before and after SSCs with different IMF B_y orientations.

[35] The correlation coefficients of the variation before/after SSCs with positive/negative IMF B_yand corresponding R‐M effect are given inTable 3. For vB_swe can find that the R‐M effect with positive/negative IMF polarity can explain a large part of seasonal and diurnal variation ofvB_s, and the correlation coefficients are up to 0.90, which has been improved significantly compared to the R‐M effect without distinguishing IMF polarity. For Q and Dst, the correlation coefficients are also improved a lot. AE index, which doesn't show clear semiannual variation and the correlation coefficient of AE variation and the R‐M effect before/after SSCs is only 0.0003/0.21, indeed show features identical with the R‐M effect with positive/negative IMF polarity when distinguishing the polarity of IMFB_y, and the correlation coefficients are increased up to 0.65.

Table 3. Summarization of Correlation Coefficients Between Geomagnetic Activity Variation Before and After SSCs With Different IMF B_y Orientations and Two Hypotheses

	Time Period	+/− IMF By	The R‐M Effect With +/− IMF Polarity	The Equinoctial Hypothesis
The probability of vBs > 1 mV/m	before SSCs	By > 0	0.84	−010
		By < 0	087	0.04
	after SSCs	By > 0	0.93	0.12
		By < 0	0.92	0.05
The probability of Q < −10 nT/h	before SSCs	By > 0	0.67	0.13
		By < 0	−0.30	0.12
	after SSCs	By > 0	0.61	0.59
		By < 0	0.62	0.35
The Dst index	before SSCs	By > 0	−0.58	−0.01
		By < 0	−0.60	−0.06
	after SSCs	By > 0	−0.60	−0.38
		By < 0	−0.61	−0.45
The AE index	before SSCs	By > 0	0.61	−0.002
		By < 0	0.61	0.07
	after SSCs	By > 0	0.65	0.20
		By < 0	0.64	0.17

[36] The results confirm that the R‐M effect is indeed present before and after SSCs and can predict southward IMF accurately as well as a large part of geomagnetic activity. Also, it shows the IMF polarity is an important parameter when investigating semiannual variation as well as the R‐M effect. To compare the R‐M effect with the equinoctial hypothesis, we also calculate the correlation coefficients of the variation with theψ angle, which are also shown in Table 3.

[37] We find that the correlation coefficients of the variation and the R‐M effect with positive/negative IMF polarity are much higher than that of the equinoctial hypothesis, which can demonstrate the R‐M effect can predict the geomagnetic activity more efficiently when we distinguish positive/negative IMFB_y; although the equinoctial hypothesis also explains part of the variation, it cannot explain the difference between the semiannual variation with positive IMF B_y and negative IMF B_y.

4. Discussion and Conclusions

[38] By defining the R‐M effect with positive/negative IMF polarity according to the IMF polarity, that is, away/toward the Sun, we find that the patterns of semiannual variation predicted by them are totally different. The R‐M effect with positive IMF polarity predicts larger IMFB_zsouthward component in GSM coordinate system at fall equinox, which indicates more efficient dayside reconnection and energy input leading to more intense geomagnetic activity, while the R‐M effect with negative IMF polarity shows the maximum at spring equinox.

[39] To confirm the validity of the R‐M effect with positive/negative IMF polarity, we plot contours of semiannual variation of probability ofvB_s > 1 mV/m, probability of large ring current injection Q < −10 nT/h, geomagnetic indices Dst and AE under different conditions of IMF B_y, and find the results are identical with the R‐M effect with positive/negative IMF polarity. It indicates that the R‐M effect predicts the semiannual variation of geomagnetic activity more accurately, while other hypotheses cannot explain such difference at equinoxes between different IMF polarity.

[40] Also, the contours show the pattern of diurnal variation with positive/negative IMF B_yis similar to the R‐M effect with positive/negative IMF polarity, which indicates that the R‐M effect can also predict part of diurnal variation. Compared to previous studies [O'Brien and McPherron, 2002; Cliver et al., 2000], the correlation coefficients between contours of geomagnetic activity and the R‐M effect are improved a lot. The correlation coefficient ofvB_swith the R‐M effect with positive/negative IMF polarity in our paper is 0.91/0.90, and the correlation coefficient ofQwith the R‐M effect with positive/negative IMF polarity is 0.69/0.72, whileO'Brien and McPherron [2002] derived the rank order correlation coefficient of −0.55 ± 0.03 between possibility of vB_s > 1 mV/m with angle θ, which is the controlling parameter of the R‐M effect, and the correlation coefficient of −0.44 ± 0.04 between possibility ofQ < −10 nT/h and θ. Cliver et al. [2000]calculated the correlation coefficient between Dst index and R‐M angle and obtained 0.45, and the seasonal and diurnal variation of AE index in their paper doesn't show a pattern of the R‐M effect clearly, while our correlation coefficients with Dst index are much higher and the semiannual variation of AE index with positive/negative IMF polarity also fits the R‐M effect with positive/negative IMF polarity well. The results show that the R‐M effect with positive/negative IMF polarity explains semiannual variation of geomagnetic activity more precisely.

[41] From Figure 5, we find that the average value of Dst index is much larger with positive IMF B_y when IMF B_zis southward, which indicates that compared to the R‐M effect with negative IMF polarity, the R‐M effect with positive IMF polarity can further enhance the geomagnetic activity.

[42] Also, our results indicate that unlike the R‐M effect which assumes the northward IMF has no effect on the geomagnetic activity, the northward IMF can also have effects on the magnetosphere. This is consistent with recent research, although it is much weaker than southward IMF situation. Thus the assumption made byRussell and McPherron [1973]may introduce some errors in the R‐M effect.

[43] For the seasonal and diurnal variation of geomagnetic activity before and after SSCs, from Figure 7, we find that the R‐M effect predicts the seasonal and diurnal variation of southward IMFB_zmore precisely than the equinoctial hypothesis after SSCs. But when it comes to ring current injections as well as Dst index, the equinoctial hypothesis explains similar amount of variance as the R‐M effect, as shown inFigures 8 and 9. It indicates that the R‐M effect predicts southward IMF precisely and explains part of semiannual variation of geomagnetic activity, while the equinoctial hypothesis also explains part of variance of geomagnetic activity after SSCs. Our result is consistent withCliver et al. [2000], which believes the equinoctial hypothesis contributes to the semiannual variation of geomagnetic activity by reducing the coupling efficiency of dayside reconnection at solstices, as well as O'Brien and McPherron [2002]. On the other hand, we also find both the R‐M effect and the equinoctial hypothesis can explain seasonal and diurnal variation of geomagnetic activity more accurately after SSCs than before SSCs. This may be because before SSCs IMFB_z component is too small to show clear seasonal and diurnal features.

[44] However, as shown in Figures 10, 11, 12, and 13, before/after SSCs with positive or negative IMF B_y, the semiannual variation of the probability of vB_s > 1 mV/m and Q < −10 nT/h as well as the Dst and AE indices all reveal clear features as much higher at spring equinox when IMF B_y < 0, while much higher at fall equinox when IMF B_y > 0. We find that the R‐M effect with positive/negative IMF polarity can explain such difference perfectly, while the equinoctial hypothesis cannot.

[45] The results presented in this paper demonstrate before and after SSCs, the R‐M effect is actually present and accounts for a large part of semiannual variation of geomagnetic activity. It also shows that the IMF polarity, that is, positive/negative, is a very important parameter when examining semiannual variation of geomagnetic activity or the R‐M effect.

[46] Crooker et al. [1992]found that differential compression at the shock increases the Parker spiral angle and increases the projected IMF southward component, which results in the enhancement of the R‐M effect. Compared our results withO'Brien and McPherron [2002], we find that the probability of vB_s > 1 nT as well as Q < −10 nT/h of our study are higher than O'Brien and McPherron's, and the correlation coefficients of variation and the angle θ as well as the angle ψof our study are approximately equal to theirs. It indicates the differential compression at the interplanetary shock can result in the enhancement of the R‐M effect, asCrooker et al. [1992] show. And compared the results of the Dst and the AE index with Cliver et al. [2000], we can also derive the same conclusion.

[47] However, since we calculate the semiannual and diurnal variation before/after SSCs with positive and negative IMF B_yrespectively, and derive much higher correlation coefficients with the R‐M effect with positive/negative IMF polarity, we can demonstrate the presence of the R‐M effect under extreme solar wind conditions more evidently, and show before/after SSCs, the R‐M effect with positive/negative IMF polarity can explain difference of variance of geomagnetic activity with different IMFB_y conditions perfectly while the equinoctial hypothesis cannot.

[48] In summary, we have performed contour plots of parameters and calculated the correlation coefficients of each IMF condition with the R‐M effect with positive/negative IMF polarity and interplanetary shock related R‐M effect as well as the equinoctial hypothesis by analyzing a large amount of the data of magnetic field and geomagnetic indices from 1968 to 2010 and 1270 SSC (storm sudden commencement) events. The main results in this paper can be summarized as:

[49] 1. The polarity of IMF is one of controlling factors for the semiannual and diurnal variation of geomagnetic activity or the R‐M effect: the geomagnetic activity is much more intense around fall equinox when the direction of IMF is away the Sun, while much more intense around spring equinox when the direction of IMF is toward the Sun.

[50] 2. The average value of Dst index is much higher under the R‐M effect with positive IMF polarity when IMFB_zis southward, which indicates that the R‐M effect with positive IMF polarity can indeed enhance the geomagnetic activity.

[51] 3. After SSC events, the correlation coefficient between variation of vB_s under southward IMF and θangle, the controlling parameter of the R‐M effect, is −0.60, while the correlation coefficient betweenvB_s and ψangle, the controlling parameter of the equinoctial hypothesis, is only 0.39. It indicates the R‐M effect can explain more variation of IMF southward component than the equinoctial hypothesis. However, as for Q and Dst index, the equinoctial hypothesis explains similar amount of variance as the R‐M effect.

[52] 4. The semiannual and diurnal variations under extreme solar wind conditions with positive and negative IMF B_y are quite different: when B_y is positive, the maximum of geomagnetic activity appears around the fall equinox; when B_y is negative, the maximum appears at the spring equinox. The correlation coefficients between variance of geomagnetic activity before/after SSCs with positive/negative IMF B_yand corresponding R‐M effect are improved significantly: forvB_s, Q, Dst and AE, the correlation coefficients after SSCs with positive/negative IMF B_y are 0.93/0.92, 0.61/0.62, −0.60/−0.61 and 0.65/0.64 respectively.

[53] 5. As for the equinoctial hypothesis, the correlation coefficients before/after SSCs with positive/negative IMF B_yare much lower than the R‐M effect with positive/negative IMF polarity. These results indicate that equinoctial hypothesis cannot explain the difference between geomagnetic activity variation under positive IMF polarity and negative IMF polarity, and its prediction precision is much lower than the R‐M effect with positive/negative IMF polarity.

[54] Thus, the R‐M effect with positive/negative IMF polarity is more reasonable to explain seasonal and diurnal variation of geomagnetic activity under different IMF polarity and extreme solar wind conditions.

Acknowledgments

[55] This work was supported by Major Project of Chinese National Programs for Fundamental Research and Development (2012CB825603) and National Natural Science Foundation of China (40831061, 41074117 and 41050110440). We would like to thank OmniWeb for providing the Omni database.

[56] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper.