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Seasonal and diurnal variation of geomagnetic activity:

Russell-McPherron effect during different IMF polarity

and/or extreme solar wind conditions

H. Zhao

1,2

and Q.-G. Zong

1,3

Received 23 April 2012; revised 1 October 2012; accepted 2 October 2012; published 29 November 2012.

[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 IMF B

y

accurately, 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.

Citation: Zhao, H., and Q.-G. Zong (2012), Seasonal and diurnal variation of geomagnetic activity: Russell-McPherron effect

during different IMF polarity and/or extreme solar wind conditions, J. Geophys. Res.,117, A11222, doi:10.1029/2012JA017845.

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 qbetween 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 angle q, 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 y

between Earth-Sun line and the dipole axis of the Earth, that

is, the crucial parameter of the equinoctial hypothesis.

1

Institute of Space Physics and Applied Technology, Peking University,

Beijing, China.

2

Laboratory for Atmospheric and Space Physics, Department of

Aerospace Engineering Sciences, University of Colorado Boulder, Boulder,

Colorado, USA.

3

Center for Atmospheric Research, University of Massachusetts Lowell,

Lowell, Massachusetts, USA.

Corresponding author: Q.-G. Zong, Institute of Space Physics

and Applied Technology, Peking University, Beijing 100871, China.

(qgzong@gmail.com)

©2012. American Geophysical Union. All Rights Reserved.

0148-0227/12/2012JA017845

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, A11222, doi:10.1029/2012JA017845, 2012

A11222 1of15

Crooker and Siscoe [1986] suggest the field configuration in

the Chapman-Ferraro current plane may change and prevent

the energy transfer as the yangle changes; whereas Russell

et al. [2003] demonstrate that the tilt of dipole axis controls

the size of dayside reconnection region and thus the recon-

nection rate and geomagnetic activity.

[4] Nowadays, the R-M effect is one of the most prevailing

hypotheses. Orlando et al. [1993] investigated the connec-

tion 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 IMF B

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 geo-

magnetic 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 angle ybetween the Earth-Sun line and the dipole axis

of the Earth, accounts for a large part of semiannual varia-

tion 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 geo-

magnetic 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 semian-

nual 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 inter-

planetary shocks, to seasonal and diurnal variation of geo-

magnetic 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: rota-

tional discontinuities, tangential discontinuities, contact dis-

continuities, 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

Figure 1. The Russell-McPherron effect and the equinoctial hypothesis. (a) Seasonal and diurnal variation

of qangle between Z axis in GSM coordinate system and Y axis in GSEQ coordinate system. (b) Seasonal

and diurnal variation of yangle between Earth-Sun line and the dipole axis of the Earth.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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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 inter-

planetary 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 south-

ward 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 com-

ponent 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 23.5from 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 prob-

ability of southward IMF in GSM. The dipole axis inclines

11.5from the rotation axis and leads to the diurnal varia-

tion 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, IMF B

y

> 0 in GSE coor-

dinate system), we define it as “the R-M effect with positive

IMF polarity”, and toward the Sun (negative polarity, IMF

B

y

< 0), defined as “the R-M effect with negative IMF

polarity”.

[12] Figure 2 shows the R-M effect with positive/negative

IMF polarity, namely, the contour plot of IMF B

z

southward

component in GSM coordinate system under the situation

that IMF is away/toward the Sun, assuming IMF B

y

of 1 g

in GSEQ coordinate system, and the schematic diagram of

the R-M effect under different IMF polarity.

[13] At spring equinox, the Earth rotation axis is pointed

23.5away 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 recon-

nection 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 pro-

jects 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 2

shows that when IMF is away the Sun, corresponding to

the R-M effect with positive IMF polarity, the maximum of

possibility of southward B

z

appears 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 calcu-

late the probability of vB

s

>1mV/mwithin each bin under

different IMF polarity.

[15] Figure 3 shows the contour plots of the probability of

vB

s

>1mV/mwith IMF B

y

positive/negative. The patterns of

variation showed in Figure 3 are 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 IMF B

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

>1mV/munder

positive IMF B

y

and IMF B

z

southward component in

GSM indicated by the R-M effect with positive IMF polarity

(as Figure 2 shows) is 0.91, while the coefficient between the

probability of vB

s

>1mV/munder negative IMF B

y

and IMF

B

z

indicated by the R-M effect with negative IMF polarity is

0.90. The results indicate the R-M effect with positive/

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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negative IMF polarity can predict the seasonal and diurnal

variation of vB

s

with positive/negative IMF B

y

precisely.

[16] In order to investigate the seasonal and diurnal varia-

tion 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]:

dDst*

dt ¼QtðÞDst*

tð1Þ

Dst* ¼Dst b

ﬃﬃﬃ

P

pþcð2Þ

where Q is assumed as a function of vB

s

,Dst* is the

pressure-corrected Dst index, tis the decay time of ring

current, Pis 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;t= 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/hwith

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

y

fits well with R-M

effect with positive/negative IMF polarity, with maximum at

spring equinox when IMF B

y

< 0 and at fall equinox when

IMF B

y

> 0. The correlation coefficients of situations during

positive and negative B

y

with the R-M effect with positive/

negative IMF polarity are 0.69 and 0.72 respectively.

[18] On the other hand, to examine whether the R-M effect

with positive/negative IMF polarity predicts the geomag-

netic 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 IMF B

y

and B

z

in a

24 24 lattice, too.

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 IMF B

z

southward component

in GSM coordinate system due to IMF B

y

in GSEQ coordinate system of 1 g.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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[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.

[20] From both figures we can find the pattern of semi-

annual variation with positive IMF B

y

is consistent with the

R-M effect with positive IMF polarity, which shows the

maximum at fall equinox, while the pattern with negative

IMF B

y

fits 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, but Figures 5a and 5b still

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

5d with corresponding R-M effect are 0.68, 0.66, 0.67

and 0.72 respectively, and for Figures 6a, 6b, 6c, and 6d,

the correlation coefficients are 0.59, 0.58, 0.72 and 0.68

Figure 3. The seasonal and diurnal variation of probability of vB

s

>1mV/mwith positive/negative IMF

B

y

and southward IMF B

z

, calculated in a 24 24 lattice and smoothed by a 3 3 average.

Figure 4. The seasonal and diurnal variation of probability of Q<10 nT/hwith positive/negative IMF

B

y

and southward IMF B

z

, calculated as Figure 3.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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respectively. The correlation coefficients are summarized in

Table 1.

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 geo-

magnetic activity before and after SSCs, we use vB

s

from

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 of vB

s

>1mV/mbefore 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

z

on the R-M effect, we perform the

contour plots under southward and northward IMF B

z

.

[26] Figure 7 shows the seasonal and diurnal variation of

the probability of vB

s

>1mV/mbefore 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

s

variation after SSCs

is quite similar with the R-M effect. It shows higher proba-

bility of southward IMF B

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

>1mV/mis much

smaller than after SSCs, however, the pattern doesn’t well fit

the R-M effect. The correlation coefficient between the

probability of vB

s

>1mV/mbefore/after SSCs and the

angle q, the controlling parameter of the R-M effect, is

0.11/0.60.

[27] To compare with the R-M effect, we also calculate

the correlation coefficient between the probability of

vB

s

>1mV/mand the angle y, which is the dominant

parameter in the equinoctial hypothesis. The correlation

coefficient before/after SSCs is 0.02/0.39 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.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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It indicates that the R-M effect can explain the probability of

southward IMF B

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/hin

a1212 lattice. The results are showed in Figure 8.

Figure 8 shows the probability of Q<10 nT/hbefore 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/hbefore/after SSCs and the angle qis 0.30/

0.57, while for the angle ythe correlation coefficient is

0.15/0.62. The correlation coefficients show that both qand

ycan 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.

[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.

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.

Table 1. Summarization of Correlation Coefficients of Contours During Positive/Negative IMF B

y

and Southward/Northward B

z

With Corresponding R-M Effect With Positive/Negative IMF Polarity

B

y

>0,B

z

<0 B

y

<0,B

z

<0 B

y

>0,B

z

>0 B

y

<0,B

z

>0

and R-M Effect (+IMF) and R-M Effect (IMF) and R-M Effect (+IMF) and R-M Effect (IMF)

vB

s

0.91 0.90

Q0.69 0.72

Dst index 0.68 0.66 0.67 0.72

AE index 0.59 0.58 0.72 0.68

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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[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 maxi-

mum 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 con-

ditions (Figures 9a and 9b) with the qangle is 0.42/0.51; as

to the yangle 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 qis 0.27/0.26, while for yis 0.01/0.48.

[31] It shows that both hypotheses predict part of the

variation of Dst index after SSCs; however, as for the situ-

ation before SSCs, both hypotheses, especially the equi-

noctial 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 angle qand yare summarized in Table 2.

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 IMF

B

y

orientations, that is, positive and negative. The contour

plots of semiannual variation of the probability of

vB

s

>1mV/m, the probability of Q<10 nT/hand the Dst

Figure 7. Seasonal and diurnal variation of the probability of VB

s

>1mV/mbefore and after SSCs under

southward IMF B

z

.

Figure 8. Seasonal and diurnal variation of the probability of Q<10 nT/hbefore and after SSCs under

southward IMF B

z

.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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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

y

is positive, the geo-

magnetic 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.

[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 elec-

trojets 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

y

still shows identical feature as the R-M effect with

positive/negative IMF polarity: when IMF B

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

Figure 9. Seasonal and diurnal variation of Dst index before and after SSCs under different IMF B

z

conditions.

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 qAngle The yAngle

The probability of vB

s

>1mV/mbefore SSCs IMF B

z

southward 0.11 0.02

after SSCs IMF B

z

southward 0.60 0.39

The probability of Q<10 nT/hbefore SSCs IMF B

z

southward 0.30 0.15

after SSCs IMF B

z

southward 0.57 0.62

The Dst index before SSCs IMF B

z

southward 0.42 0.13

IMF B

z

northward 0.27 0.01

after SSCs IMF B

z

southward 0.51 0.52

IMF B

z

northward 0.26 0.48

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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higher around the fall equinox and lower around the spring

equinox.

[35] The correlation coefficients of the variation before/

after SSCs with positive/negative IMF B

y

and corresponding

R-M effect are given in Table 3. For vB

s

we can find that the

R-M effect with positive/negative IMF polarity can explain a

large part of seasonal and diurnal variation of vB

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 IMF B

y

, and the corre-

lation coefficients are increased up to 0.65.

[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 the yangle, 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 IMF B

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 IMF B

z

southward component in GSM coordinate system at fall

equinox, which indicates more efficient dayside reconnec-

tion 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 var-

iation of probability of vB

s

>1mV/m, probability of large

ring current injection Q<10 nT/h, geomagnetic indices

Figure 10. Seasonal and diurnal variation of the probability of VB

s

>1mV/mbefore and after SSCs

under different IMF B

y

conditions.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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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

y

is 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 of vB

s

with

the R-M effect with positive/negative IMF polarity in our

paper is 0.91/0.90, and the correlation coefficient of Qwith

the R-M effect with positive/negative IMF polarity is 0.69/

0.72, while O’Brien and McPherron [2002] derived the rank

order correlation coefficient of 0.55 0.03 between

possibility of vB

s

>1mV/mwith angle q, which is the

controlling parameter of the R-M effect, and the corre-

lation coefficient of 0.44 0.04 between possibility of

Q<10 nT/hand q. 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

z

is

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 geo-

magnetic 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 by Russell 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 IMF B

z

more 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

Figure 11. Seasonal and diurnal variation of the probability of Q<10 nT/hbefore and after SSCs

under different IMF B

y

conditions.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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shown in Figures 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

with Cliver et al. [2000], which believes the equinoctial

hypothesis contributes to the semiannual variation of geo-

magnetic 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 IMF B

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

>1mV/mand

Q<10 nT/has 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 geo-

magnetic 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 com-

pression 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 with O’Brien and McPherron [2002], we find

that the probability of vB

s

>1nT as well as Q<10 nT/hof

our study are higher than O’Brien and McPherron’s, and

the correlation coefficients of variation and the angle qas

well as the angle yof 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, as Crooker 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 nega-

tive IMF B

y

respectively, 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/

Figure 12. Seasonal and diurnal variation of the Dst index before and after SSCs under different IMF B

y

conditions.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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negative IMF polarity can explain difference of variance

of geomagnetic activity with different IMF B

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 IMF

Figure 13. Comparison between seasonal and diurnal variation of the AE index before and after SSCs

with different IMF B

y

orientations.

ZHAO AND ZONG: SEMIANNUAL VARIATION A11222A11222

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B

z

is 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 qangle,

the controlling parameter of the R-M effect, is 0.60, while

the correlation coefficient between vB

s

and yangle, 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 hypoth-

esis. 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

y

and

corresponding R-M effect are improved significantly: for vB

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

y

are much lower than the R-M effect with positive/negative

IMF polarity. These results indicate that equinoctial hypoth-

esis 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 polar-

ity and extreme solar wind conditions.

[55]Acknowledgments. 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 Omni-

Web for providing the Omni database.

[56]Masaki Fujimoto thanks the reviewers for their assistance in

evaluating this paper.

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Time Period +/IMF B

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