A tentative study for the prediction of the CME related geomagnetic storm intensity and its transit time

Transcription

1 648 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No A tentative study for the prediction of the CME related geomagnetic storm intensity and its transit time ZHAO Xinhua 1,2 & FENG Xueshang 1,3 1. SIGMA Weather Group, Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing , China; 2. Graduate School of the Chinese Academy of Sciences, Beijing , China; 3. School of Geophysics and Geoinformation Systems, China University of Geosciences, Beijing , China Correspondence should be addressed to Feng Xueshang ( fengx@spaceweather.ac.cn) Received February 24, 2005 Abstract Using 80 CME-ICME events during , based on the eruptive source locations of CMEs and solar magnetic field observation at the photosphere, a current sheet magnetic coordinate (CMC) system is established in order to study the propagation of CME and its geoeffectiveness. In context of this coordinate system, the effect of the eruptive source location and the form of heliospheric current sheet (HCS) at the eruptive time of CME on the geomagnetic storm intensity caused by CME and the CME s transit time at the Earth is investigated in detail. Our preliminary conclusions are: 1) The geomagnetic disturbances caused by CMEs tend to have the so-called same side-opposite side effect, i.e. CMEs erupt from the same side of the HCS as the earth would be more likely to arrive at the earth and the geomagnetic disturbances associated with them tend to be of larger magnitude, while CMEs erupting from the opposite side would arrive at the earth with less probability and the corresponding geomagnetic disturbance magnitudes would be relatively weaker. 2) The angular separation between the earth and the HCS affect the corresponding disturbance intensity. That is, when our earth is located near the HCS, adverse space weather events occur most probably. 3) The erupting location of the CME and its nearby form of HCS will also affect its arrival time at the earth. According to these conclusions, in this context of CMC coordinate we arrive at new prediction method for estimating the geomagnetic storm intensity (Dst min ) caused by CMEs and their transit times. The application of the empirical model for 80 CME-ICME events shows that the relative error of Dst is within 30% for 59% events with Dst min 50 nt, while the averaged absolute error of transit time is lower than 10 h for all events. Keywords: coronal mass ejections, current sheet magnetic coordinate system, geomagnetic storm intensity, transit time, prediction method. DOI: /03ye0240

2 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 649 Coronal mass ejections (CMEs), which refer to large-scale magnetized plasma structures expelled from the sun into the heliosphere, are a kind of eruptive phenomenon in solar atmosphere usually associated with flares or eruptive prominences. The earth directed coronal mass ejections are often accompanied with intense geomagnetic storms, interplanetary shocks and energetic particle events and all these are adverse conditions for space weather. Shortly after its discovery in the 1970s of last century [1,2], CME was found to correlate well with the occurrence of a geomagnetic storm [3,4]. In earlier days, it was thought that solar flares and their associated interplanetary shocks were responsible for geomagnetic storms. However, recently, more evidences show that CMEs are the major cause for non-recurrent geomagnetic storms [5 7] and much attention has been paid to the studies on CMEs. Especially, how to predict the CME related geomagnetic storm intensity and the Sun-Earth transit time of the CME become two important aspects in space weather forecast. Wei et al. [8,9] established a flare-heliospheric current sheet coordinate system to investigate the propagation of flares-interplanetary shocks and their associated geomagnetic disturbances. There are two characteristic reference planes in this coordinate, one is the ideal heliospheric current sheet outspread by the real HCS near the flare source and the other is defined to be the plane perpendicular to the former as well as passing through the flare source. For different locations of the flares or different shape of the HCS, the corresponding coordinates established are also different. Therefore, it is convenient to see the influence of the HCS near the Sun on the propagation of solar transient disturbances in the heliosphere under this coordinate. Wei et al. [8,9] studied 277 flare-shock events and draw some innovative conclusions: 1) For events with sources located on the same side of the HCS as the Earth, the shocks are stronger and the levels of the corresponding geomagnetic disturbances are higher. While for events with sources located on the opposite side, both the shocks and the corresponding geomagnetic disturbances are of weaker magnitude. 2) The number of the same side events is larger than that of the opposite side events. 3) Interplanetary shocks prefer to propagate towards the HCS. This study indicates that the transient disturbances caused by solar activities will deflect towards the HCS in their traveling to the Earth through the interplanetary medium regardless of the discrimination that the solar sources are located on the north or south hemisphere. The idea of Wei et al. [8,9] has been demonstrated and applied by others [10 12]. Therefore, we can see that the HCS near the sun is an important characteristic plane for studying the propagation of solar transient disturbances and their related geomagnetic storms. In virtue of Wei s idea, this paper establishes a new coordinate system, i.e., current sheet magnetic coordinate (CMC) system, to study the propagation of CMEs and their associated geomagnetic storms by analyzing 80 CME-ICME events during under this new coordinate system. This paper is organized as follows: In section 1, we present the establishment of this kind of coordinate system. In section 2, we study

3 650 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No CME-ICME events under this coordinate system and draw the conclusion that the geomagnetic disturbances caused by CMEs tend to have the same side-opposite side effect, and then a new method to predict the corresponding geomagnetic storm intensity is proposed. In section 3, we present a new method to predict when the ICME arrives at the Earth in context of the CMC system. Conclusions and discussions are given in section 4. 1 Current sheet magnetic coordinate system 1.1 Establishment of the CMC system We consider the erupting location of the CME and the large-scale shape of the HCS near the Sun in the establishment of the CMC system. When a CME erupts, it leaves behind hot post-eruption arcades or flare loops that mark the source location of the eruption on the surface of the Sun. This coordinate is a rectangular coordinate system whose origin is at the center of the Sun as shown in Fig. 1(a). The curved surface labeled as HCS in Fig. 1(a) is the real heliospheric current sheet. S is the subpoint of the CME source location at 2.5 solar radii. The direction ON, defined as the normal of the CME eruption, is the vector from the center of the Sun to the source location of the CME. And point P, located on the HCS, is the foot of the perpendicular of S. The vector OP gives the x-axis. We select a local segment of the real HCS near the foot P and extend it to a plane xoy passing through the center of the Sun. We call this plane the ideal HCS labeled as ICS in Fig. 1(a). The x-axis and the CME normal ON constitute the plane xoz that is considered to be the symmetrical plane for coronal mass ejections. These two characteristic and orthogonal planes constitute the peculiar coordinate system in this paper Current sheet Magnetic Coordinate (CMC) system. And the basis vectors x, y, and z complete a right-handed triad. Besides x, y and z, we define the latitude λ and longitude η to describe the position of the Earth in this coordinate. Here, λ stands for the angle between the Sun-Earth line and its projection on the plane xoy. That is to say, λ stands for the angular separation between the Earth and the HCS. And η stands for the angular distance from the x-axis to the projection of the Sun-Earth line on the plane xoy. These two angles are defined to be perpendicular, i.e., z λ = arctan x + y 2 2, y η = arctan. x One thing to be explained here is that we outspread the local HCS near CME source to a plane (called ideal HCS) and the established coordinate system is static. While in fact, the real HCS is very complex and rotating with the Sun with a period of about 27 d. The theoretical basis for these approximations is as follows: It takes CME only 5 9 h to pass through the inner heliosphere (18 20 Rs) where magnetic field controls the motion of plasma. Then the real HCS rotates with the angle of only about 3 5 within this short interval. The influence of magnetic field on plasma motion decreases rapidly when

4 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 651 CME propagates into the heliosphere beyond the Alfven point. Then the influence of the HCS beyond the Alfven point on CME propagation is regarded as inessential and could be neglected as an approximation. What is more, as P is the foot of the perpendicular of CME source on the real HCS, the latitude of the CME source in CMC (seen in sec. 1.3) represents the true angular distance from the CME source to the real HCS. In this paper, we try to predict the geomagnetic storm intensity caused by the CME and its transit time using parameters at CME erupting time. So we use the position of the Earth when CME erupts and not the one when the corresponding ICME arrives at the near Earth space. In fact, the interval between the erupting of CME and the arrival of the corresponding ICME at the Earth is within 3 5 d. The Earth rotates with the angle of only about 3 5 within this short interval under this static coordinate system. Therefore, this approximation is reasonable and acceptable. Fig. 1. The 3-dimensional sketch map of the CMC system (a) and its spread on solar magnetic field synoptic chart (b). In (a), O is the center of the Sun, S is CME erupting source, N is the normal of CME, HCS stands for the real heliospheric current sheet, P is the foot of the perpendicular of S on the HCS and ICS stands for the ideal HCS. In (b), line 1 represents the HCS; line 2 represents the ideal HCS; line 3 represents the ecliptic plane, S and P as in (a), E is the sub-earth point at CME erupting time, A and B are the points of intersection for the ecliptic plane and the ideal HCS. 1.2 The spread of the CMC system on solar magnetic field synoptic chart As an example, Fig. 1(b) demonstrates the spread of the CMC system on the contour

5 652 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No of solar source surface magnetic field on CR 1925 located at 2.5 solar radii from the Wilcox Solar Observatory ( The neutral line in this chart is the HCS at 2.5 Rs (line 1). There was a CME event erupting from N45E21 at 04:45 UT on 30 July In Fig. 1(b) we find S standing for the source location of this CME event according to the erupting location and the erupting date & time of this event. Line 2 stands for the ideal HCS that is extended by the local real HCS centered about the foot P. E stands for the sub-earth position when this CME erupted and line 3 stands for the ecliptic plane. A and B are points of intersection for the ecliptic plane and the ideal HCS. 1.3 The coordinates of the earth and CME source in the CMC system The coordinates of the earth in the CMC system can be derived from three angles, i.e. γ, ξ and ω. Here, γ denotes the angle between the ecliptic plane and the ideal HCS (or the angle between their normals). ξ denotes the angle between P and A relative to the center of the sun. And ω denotes the angle between E and A relative to the center of the sun. n1xn2x + n1yn2y + n1zn2z γ = arccos, ( n1x + n1y + n1z) i ( n2x + n2y + n2z) ( ) ξ = arccos cos( φ φ ) cos( ψ ψ ), A P A P ( ) ω = arccos cos( φ φ ) cos( ψ ψ ), A E A E where and n denote the normals of the ideal HCS and the ecliptic plane in the n1 2 solar equator coordinate system respectively. φ ψ,, A, A φ P P ψ and, φ E E ψ denote the longitudes and latitudes of A, P and E in solar magnetic filed synoptic chart respectively. If the values of γ, ξ and ω are known, then the coordinates of the Earth in the CMC system could be obtained: x = cos( ξ ) cos( ω) + sin( ξ) cos( γ) sin( ω ), (1a) E y = sin( ξ ) cos( ω) + cos( ξ) cos( γ) sin( ω ), (1b) E z = sin( γ ) sin( ω), (1c) E where x E, ye and z E are in units of AU. Then, λ E = arctan x z E 2 2 E + ye ye, ηe = arctan. (2) xe While the coordinates of CME source in the CMC system are

6 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 653 where φ S, λs = arccos(cos( φs φp) cos( ψs ψp)), η S = 0, (3) ψ S and φ P, ψ P denote the longitudes and latitudes of S and P in solar magnetic filed synoptic chart respectively. We can see from Fig. 1(a) that the z-axis of the CMC system is ensured to point to the direction of the normal of the CME eruption. Then λ S computed from our formulas is always positive for CMEs that erupt from either north hemisphere or south hemisphere. While λ E is positive for the same side events and negative for the opposite side events. Therefore, we can judge a CME to be the same side or opposite side event only by the sign of λ E in our CMC system. In context of this coordinate system mentioned above, we can calculate the parameters for the CME event erupting at 04:45 UT on 30 July 1997: λ S = 31.54, η S = 0 ; λ E = 5.39, η E = We draw the conclusion that this CME event erupted from the opposite side of the HCS as the Earth from the negative sign of λ E. Fig. 1(b) also displays this fact. 2 CMEs and their geoeffectiveness We have collected 80 CME-ICME events during For each event, we need the following observations of the CME: time of the first appearance in LASCO/C2, projected speed, the erupting location, the arrival time of the corresponding ICME at the near Earth spacecraft and the related geomagnetic storm intensity. These parameters are taken from the recognized results in the published papers [13 17] together with these websites ftp://ftp.ngdc.noaa.gov/stp/geomagnetic_data/indices/dst/. For those events that the erupting locations of the CME and/or the arrival time of the ICME are recognized to be evidently different in different papers and also the events that we cannot get the clear locations of the CME eruption are excluded from our samples of events. As for each event in our samples, we draw the solar magnetic field synoptic chart of the Carrington Rotation during which the CME erupted according to the observations of the Wilcox Solar Observatory ( establish the CMC system and then calculate the coordinates of the Earth and the CME erupting source in this coordinate. 2.1 The same side-opposite side effect of the geomagnetic disturbances caused by CMEs The plot of the geomagnetic storm intensity ( Dst min ) versus the angular distance between the HCS and the Earth is given in Fig. 2. In order to reveal the new distribution characteristics by dividing the total events into the same side-opposite side events, in Fig. 2(a) we select λ E in the CMC system and set the sign renewedly: if the Earth lies to north of the HCS (labeled as N), then the latitude is positive, on the contrary (labeled as

7 654 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No S) the latitude is negative. This definition is consistent with the solar equator coordinate system and different from our CMC system. We can see from this figure that the geomagnetic storm intensity is symmetrically distributed under two circumstances. The number of positive latitude events is 38 and accounts for 48% of the total events, while the number of negative latitude events is 42 and accounts for 52% of the total. The intense geomagnetic storms ( Dst < 100 nt) appear in both cases. min Fig. 2. The geomagnetic storm intensity plotted against the angular distance between the Earth and the HCS. (a) Without considering the same side-opposite side effect; (b) considering the same side-opposite side effect. We also see that the distribution of Dst is approximately symmetrical relative to the HCS: on one hand, there are more events appearing when the Earth is located near the HCS which may indicates that the propagation of the CME-ICME has the preponderance to deflect towards the HCS; on the other hand, the levels of the geomagnetic storms caused by ICMEs are larger when the Earth is located near the HCS. What s more, the geomagnetic storm intensity has the tendency to decrease with the increase of the angular separation between the Earth and the HCS. In Fig. 2(b) the x coordinate is λ E in the CMC system, i.e., positive when the Earth and the source location of the CME lie on the same side of the HCS (same side event)

8 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 655 and negative when the Earth and the source location of the CME lie on the opposite side (opposite side event). From this figure we can see that: (1) There is a distinct asymmetry in the distribution of the events. There are 56 same side events that account for 70% of all events, while there are only 24 opposite side events accounting for 30% of the total. (2) For 25 intense geomagnetic storms ( Dst min < 100 nt), 17 of them are same side events and only 8 of them are opposite side events. (3) For 12 geomagnetic storms with Dst min < 150 nt, 11 of them are same side events and only one is the opposite side event. (4) All the geomagnetic storms with Dst min < 200 nt appear as same side events. (5) For the same side events, the maximum angular separation between the Earth and the HCS is 76, while all the angular separations for the opposite side events are within 30. The above results indicate that there is a so-called here same side-opposite side effect in the geomagnetic disturbances caused by CMEs: when the source of the CME eruption locates on the same side of the HCS as the Earth, then the CME is more prone to arrive at the Earth and likely to cause more intense geomagnetic storm; the ideal HCS is a useful reference plane for studying CME-ICME-geomagnetic disturbances. This is consistent with the result obtained by Wei et al. [8,9] in the study of flare-shock events. 2.2 The prediction of geomagnetic storm intensity Geomagnetic storms are due to the enhancement of ring current at the Earth s equator. Dst, computed from mid-latitude ground magnetograms, is one of the important indices in evaluating the level of geomagnetic storm intensity. According to Gonzalez et al. [18], geomagnetic storms can be categorized in terms of their intensity by Dst as follows: (1) weak storms with Dst min falling between 30 and 50 nt; (2) moderate storms with Dst min falling between 50 and 100 nt; (3) intense storms with Dst min of 100 nt or less. Burton et al. [19] presented an algorithm for predicting the Dst index from a knowledge of the velocity and density of the solar wind and the north-south component of interplanetary magnetic field. Following Burton et al. [19], others have attempted to improve the prediction either by modifying the driver and decay terms [18,20] or by using other new methods such as neural networks [21] or other techniques [22], and the prediction error of Dst can be controlled within 10 nt (RMS error). The mostly accepted result indicates that the north-south component of interplanetary magnetic field and solar wind speed are two important factors in determining the intensity of geomagnetic storms. When the interplanetary magnetic field turns southward and lasts for an interval, then the southward magnetic field will interconnect with the Earth s magnetic field and allow solar wind energy transport into the Earth s magnetosphere and result in geomagnetic

9 656 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No storms [18]. It has been pointed out that magnetic clouds are usually major sources of strong southward interplanetary magnetic field and the resulting magnetic storms [3,23]. Wu and Lepping [24] found that the intensity of geomagnetic storms (Dst min ) are strongly related to the magnitude of solar wind parameters (Bz, VBs) within magnetic cloud complexes (including upstream sheath regions), and the correlation coefficient increases when the maximum solar wind speed within the entire cloud complex increased [25]. Wu and Lepping [26] presented empirical formulas to predict the intensity of geomagnetic storms using solar wind parameters within magnetic cloud complexes Dst min = and Dst = ( VBs), and the prediction relative error Bz min min max is less than 10% when Bz min or (VBs) max is observed by a spacecraft for a magnetic cloud. Although these methods are relatively precise, the lead time of the application of them to space weather is limited because the inputs to them are measurements in the near Earth interplanetary space. The delay time from the moment when the spacecraft at L1 point detects a magnetic cloud to the moment when Dst reaches its peak value is often about 1 h [27]. With the development of space weather and increase of space activities, people want to give the prediction much time in advance. As a working hypothesis, magnetic clouds (MCs) are one of the counterparts of coronal mass ejections in the interplanetary space (ICMEs). Therefore, looking for the observational characteristics of CMEs near the Sun by coronagraphs as the solar sources for geomagnetic storms will considerably advance the prediction of geomagnetic storms. Lindsay et al. [28] pointed out that there was a correlation between the CME speed and the magnitude of the interplanetary magnetic field within the associated ICME. Srivastava and Venkatakrishnan [29] studied a set of geoeffective halo CMEs and showed that the strength of the geomagnetic storm at the Earth is well correlated with the speed of the halo. Srivastava and Venkatakrishnan [30] selected 64 geoeffective CMEs during the period of that were found to produce intense geomagnetic storms with Dst min < 100 nt and found that the correlation coefficient between the initial speed of the CME and the Dst index is 0.66, only less than the correlation coefficient between Bz and Dst (0.77). And this displayed further the potential of the CME speed for forecasting Dst. Gonzalez et al. [31] started ddst Dst from the original formula = Qt () and made a series of approximations, dt τ then they got an empirical formula p 4 2 ve D (nt) = [0.22 (km/s) + 340] to pre- dict the peak value of Dst of the geomagnetic storms caused by magnetic clouds, based on the associated halo CME expansion speeds. They applied this formula to 13 halo CME events and found the correlation index was Therefore, it can be seen that the initial speed of CME is an important parameter concerning the prediction of geomagnetic storm intensities caused by CMEs. Owing to the monitoring of the SOHO/LASCO coronagraph on CMEs near the Sun, we can easily get the initial speeds of CMEs (projected on the sky plane), and this will make it possible to give the prediction of geo-

10 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 657 magnetic storm intensities more time in advance. Fig. 3 gives the plot of geomagnetic storm intensity speeds ( V p ) ( Dst min ) versus the projected of CMEs for 80 samples of events in this paper. Asterisks in this figure denote the same side events, while diamonds denote the opposite side events. The thick solid line represents a third order polynomial fit to the data points Dst min = Vp V Vp p. And the correlation index is 0.58 for these 80 events. Therefore, we come up with the conclusion that Dst depends on the CME initial speed to a great extent. Here, we use correlation index to describe the non-linear correlation of two variables, while we use correlation coefficient to describe the linear correlation of them and these two definitions are similar. Fig. 3. The geomagnetic storm intensity plotted against the projected speeds of CMEs. According to sec. 2.1, there is same side-opposite side effect in the geomagnetic disturbances caused by CMEs. What is more, the angular separation between the Earth and the HCS also influences the geomagnetic storm intensity. That is to say, when the HCS is located near the Earth in the interplanetary space, then the geomagnetic storm would likely be relatively stronger; otherwise, the geomagnetic storm would likely be relatively weaker. Henning et al. [32] pointed out that the angular distance between the flare position and the sub-earth position has a strong effect on the magnitude of disturbances. A larger angular disturbance tends to result in a smaller level disturbance. As far as our 80 events are concerned, the angular distance between the eruption position of the CME and the sub-earth position (marked AD in this paper) can be conveniently obtained from their coordinates in the CMC system, i.e., AD = arccos(cos( λ λ ) cos( η )). E S E In order to investigate the influence of AD on Dst, we must get rid of the contribution of CME speed firstly. Therefore, we plot Dstmin (observation minus prediction by the solid line in Fig. 3) versus AD as shown in Fig. 4(a). The linear correlation coefficient between them is As a contrast, Fig. 4(b) gives the plot of the same Dstmin verwww.scichina.com

11 658 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No sus λ E in the CMC system, which represents the angular separation between the Earth and the HCS, and this time the linear correlation coefficient is Fig. 4. The geomagnetic storm intensity corrected by the CME speed (a) plotted against AD & (b) plotted against λ E. Comparing Fig. 4(a) with 4(b), we can find that the geomagnetic storm intensity correlates well with not the angular distance between the eruption position of CME and the Earth (AD), but the angular separation between the Earth and the HCS. We make the statistical test about this correlation coefficient, and select the confidence level α = According to the tabulation on the critical values of the correlation coefficient, for N = 80, N 2 = 78, then = As 0.36 > =r (78), then this correlation r 0.01 (78) 0.01 coefficient is not rejected with confidence level α = Here, a small value of α indicates a significant correlation or anticorrelation. So it is evident that the angular separation between the Earth and the HCS, i.e. λ E in the CMC system, surely contributes to the geomagnetic storm intensity. In fact, early studies showed that the HCS is a characteristic reference surface for the organization of solar wind plasma. The solar wind speed and temperature are the lowest in the vicinity of the HCS, while the plasma den-

12 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 659 sity is the highest. And the solar wind speed and temperature increase with the angular distance from the HCS, while the density decreases [33,34]. Then different angular separations of the Earth from the HCS actually represent different background solar wind parameters in the near Earth space. The closer the Earth is to the HCS, the lower the background solar wind speed near the Earth would be, then the stronger the disturbance would be for the same disturbance propagation speed (i.e., ICME speed), and the corresponding geomagnetic disturbance would be more intense. Fig. 4(b) reflects this tendency to a certain extent. In a word, we combine CME speed with the angular separation between the Earth and the HCS that are contributing to the geomagnetic storm intensity and give a prediction method for the geomagnetic storm intensity caused by CMEs. Considering the same side-opposite side effect of geomagnetic disturbances, we deal with the same side and opposite side events respectively. That is, for same side events: p p p Dstmin = V V V λE, (4a) for opposite side events: Here min p Dstmin = V p 2.893λE. (4b) Dst, V and λ E are in units of nt, km/s and degrees respectively. For same side events, we use the third order polynomial form of form of λ E as the expression of samples of events (only 24 events), the linear form of V p combined with the linear Dst min. While for opposite side events, due to lack of Vp and λ E is adopted. Fig. 5(a) demonstrates the predictions of Dst min using this method comparing with the observations of them for these 80 events. The mean absolute error of this formula is 35 nt for 80 events, and the relative error 10% for 16% of all events, 30% for 43% and 50% for 64%. While for the moderate and intense storm events ( Dstmin 50 nt), the relative error 10% for 23% of them, 30% for 59% and 50% for 86%. We can see that this method is more applicable for the prediction of moderate and intense geomagnetic storms, but not too suitable for the prediction of weak geomagnetic storms because the relative errors for these are too large. Owing to the fact that moderate and intense geomagnetic storms are major causes for atrocious space weather, therefore our method can give prediction of intensity for this kind of geomagnetic storm with relatively little error. As the inputs to this method are the observational characteristics of CMEs near the Sun, it can give prediction 1 5 days earlier which greatly advances the prediction giving time for atrocious space weather.

13 660 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No Fig. 5. (a) The prediction of geomagnetic storm intensity compared with the observation; (b) the predicted geomagnetic storm intensity plotted against the initial speeds of CMEs ( λ taken as 20.5 ). One thing to explain here is that formulas (4a) and (4b) are based on 54 same side events and 24 opposite side events respectively. Due to the limited number of events and different distribution characteristics for the same side and opposite side events, there are some limiting ranges for the applicability of the formulas. That is: 100 km/s V p 1800 km/s and 0 λ E 76 for the same side events formula (4a); 100 km/s V p 1500 km/s and 25 λ E < 0 for the opposite side events formula (4b). We believe that the CME initial speed together with λ E in the CMC system determines the corresponding geomagnetic storm intensity. In order to review the same side-opposite side effect of the formulas, we have to compare the geomagnetic storm intensity severally predicted by formulas (4a) and (4b) with the same and. Therefore, we contrast the varia- tions of Vp Dst versus V in formula (4a) with that in (4b) with fixed min compute the mean value p λ E (4a) and (4b), then we draw the variations of λ E E λ E. We = 20.5 for these 80 events, and take it into formulas Dst versus as shown in Fig. 5(b). The solid curve in this figure refers to formula (4a), while the dashed line refers to for- min V p

14 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 661 mula (4b). In the same way we can draw the variations of Dst min versus V p with λ E fixed at any other meaningful values. All the results indicate that the solid curve is beneath the dashed line regardless of the value at which λ E is fixed. That is to say, the geomagnetic storm intensity of the same side event is more intense than that of the opposite side event with the same CME speed and, the angular separation between the Earth and the HCS. This reveals the same side-opposite side effect further. 3 The prediction of CME s transit time Since CMEs are major causes for non-recurrent geomagnetic storms, the prediction of CME s arrival time at the Earth is another aspect in space weather forecast. Unfortunately, our current knowledge on CMEs mainly comes from two spatial domains: the near-sun region remote-sensed by coronagraphs and the near-earth space and beyond where in situ observations are made by spacecrafts. So people usually rely on empirical models to predict the 1 AU arrival time of CMEs. Brueckner et al. [35] found that the travel time for most of CMEs during solar minimum is nearly 80 h. Wang et al. [36] studied 15 CME events that were associated with severe storms (K p > 7) and found that the transit time of CMEs can be predicted by the formula λ E T = / Vp, where V(km/s) is the CME projected speed and T(h) is the transit time of CME defined as the interval from CME s first appearance in C2 to the time of K p maximum. Srivastava and Venkatakrishnan [30] determined an empirical relation between the transit time and the initial speed from 64 CME events in their paper T = V p, here T(h) is the difference in the timings of CME start and geomagnetic storm onset marked by the decrease in Dst, while V(km/s) is also the CME projected speed. The commonly used method in the prediction of CME arrival is the ECA (Empirical CME Arrival) model developed by Gopalswamy et al. [37,15]. In this model CMEs are believed to undergo an interplanetary acceleration that depends linearly on the CME initial speed until propagation to the cessation distance d1 4 a = α β u; 1 2 S = ut + at, 2 here a and u stand for the CME acceleration and initial speed, α and β are positive constants, t is the time for CMEs to propagate to the distance S. And CMEs propagate freely beyond this cessation distance to 1 AU, 2 = 1 AU d. Then the arrival time of the ICME at the Earth can be expressed as d 1 t = t1 + t 2, where

15 662 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No t = [( u + 2 ad ) u]/ a, t = d /( u + 2 ad ). Gopalswamy et al. [15] studied 47 CME-ICME events during and found α = 2.193, β = while the typical value of is 0.76 AU. The mean absolute error of this model is 10.7 h for those 47 events. It must be pointed out that different authors considered different samples of CME events and they adopted different definitions for the transit time, then the formulas they provided are also discrepant. But all their studies showed that the transit time of CME depends on its initial speed to a great extent. Unfortunately, what people get conveniently is the projected speed of CME s space speed on the sky plane (perpendicular to the Sun-Earth line) near the Sun, and it cannot stand for the propagation speed of CME to the Earth. However, just as Gopalswamy et al. [15] pointed out, the projection effects may be somehow compensated for by the initial expansion of CME. Then the sky plane speed seems to be a reasonable representation of CME s initial speed. In this paper, we define the transit time (TT) of CME to be the difference in the timings of the appearance of CME remote-sensed by the LASCO/C2 coronagraph and the time of arrival of the corresponding ICME in situ observed by spacecrafts at L1 point. The scatter plot of the transit times of CMEs and their projected speeds ( ) for 80 events is given in Fig. 6. The solid line in this figure is the second order polynomial fit to the data points that gives the mean absolute error of 10.9 h for these 80 events. d TT = V p Vp, (5) V p where TT is the transit time of CME in hours and V p is its projected speed in km/s. Fig. 6. The transit times of CMEs plotted against their projected speeds. Except for its initial speed, the transit time of CME also depends on the propagation of the ICME in the interplanetary space and the direction of the CME eruption. Macqueen et al. [38] pointed out that the propagation of CME transients in the inner corona is

16 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time 663 tilted toward the solar equator and this may be the results of the nonradial force acting upon the CME material by the background coronal magnetic and flow patterns. Since the HCS is a characteristic reference surface for the organization of solar wind plasma, then the studies on the influence of the HCS on the propagation of solar disturbances in interplanetary space have attracted a lot of people s attention. Wei and Dryer [39] analyzed 149 flare-shock wave events based on interplanetary scintillation (IPS) observational data and found that the flare-associated shock waves, deviating from the flare normal, tend to propagate toward the low latitude region. Also, the fastest propagation directions tend toward the heliospheric current sheet near 1 AU and the meridional shape of the typical shock wave is roughly symmetrical relative to the heliospheric current sheet. Smith et al. [40] performed a 2.5-dimensional MHD parametric study to explore the effect of the HCS and HPS (heliospheric plasma sheet) on the shock propagation and arrived at the conclusion that both the shock travel time to 1 AU and the shock properties at 1 AU are affected when the shock crosses the HPS in which the HCS is embedded. Leau and Chao 1) used the HAF code to simulate four CME events and showed that the ejected plasma and its driven interplanetary shocks can not permeate the sector boundary (HCS), but they will interact with the sector boundary and change the shape of the sector boundary. Then the arrival times at the Earth of the shocks also change as a result. Since in earlier days it was thought that solar flares and their associated interplanetary shocks were responsible for geomagnetic storms, therefore the studies mainly lay emphasis on the effect of the HCS on the propagation of shocks. Nowadays more and more evidences show that interplanetary shocks are driven by interplanetary CMEs. Then the effect of the HCS on the propagation of interplanetary shocks can be attributed to the influence of the HCS on the propagation of CMEs. The location of the CME s eruption relative to the HCS is naturally one of the factors to depict this effect quantitatively. As a summary, both the eruption location of CME and the shape of the HCS in the vicinity of the eruption region are contributed to the transit time of CME. Here and (, ) E E ( λ S,0) λ η are locations of the CME eruption source and the Earth in the CMC system respectively. While λs λe and 0 ηe denote their angular separations perpendicular to and parallel to the ideal HCS, and these two angles are perpendicular to each other. So we give an empirical formula for the prediction of the transit time of CME based on Vp, λs λe and η E : 5 2 p p S E TT = V V 85.2 cos(0.77( λ λ )) cos( ηe). (6) In this formula TT and and V are in units of hours and km/s respectively, while, p λ S λ E η E are in units of degrees. The applicability range of this formula is 100 km V p 1) Leau, W. K., Chao, J. K., Interaction between the solar coronal mass ejections and heliospheric sector boundary, Graduation thesis for master degree of Institute of Space Science National Center University,

17 664 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No km/s, λs λe 50 and ηe 45. Fig. 7(a) demonstrates the predictions for the transit times of these 80 events in this method comparing with the observations of them. Fig. 7. (a) Comparison between predicted and observed transit times; (b) estimated error of the predictions. Fig. 7(b) shows the computed error of this prediction (observation minus prediction). From Fig. 7, we can see that the mean absolute error of this method is 9.8 h for 80 samples of events and this is 1.1 h less than that predicted by formula (5). The results of the prediction test show the relative errors 10% for 49% of all events, 20% for 75%, and only 9% of all events with relative errors >30%. According to formula (6), the transit time of CME depends on both the projected speed of CME and the parameters in the CMC system. In order to compare our method to the ECA model developed by Gopalswamy et al. [37,15] in the prediction for these 80 events in this paper, we adopt the mean value cos(0.77( λ λ )cos( η ) = 0.91, and rewrite formula (6) as follows: S E E

18 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time p TT = V V (7) p Fig. 8 presents the transit times of the CMEs plotted against their projected speeds, together with the prediction curves given by our formula (7) and the ECA model. The solid and dashed curve in this figure represent our formula (7) and the ECA model respectively. Fig. 8. Comparison between our formula (7) and the ECA model for our events. The solid curve denotes formula (7), while the dashed curve denotes the ECA model. We can see from this figure that our formula (7) accords with most of these 80 events fairly well. Also, the mean absolute error given by the ECA model for our 80 events is 15.3 h larger than 9.8 h predicted by our method of formula (6). As for the formulas given by Wang et al. [36] and Srivastava and Venkatakrishnan [30], since the definitions of CME s transit time in their papers are different from ours, no comparison would be made in this paper. 4 Conclusions and discussions We have studied 80 CME-ICME events during under the CMC system, a new established coordinate system in this paper, and arrived at the conclusion of the same side-opposite side effect for the geomagnetic disturbances caused by CMEs, i.e. CMEs erupting from the same side of the HCS as the Earth are more likely to arrive at the Earth and more likely to cause intense geomagnetic storms. Based on this conclusion, we give an empirical method to predict the geomagnetic storm intensity caused by CMEs using the projected speed of CME and the latitude of the Earth in the CMC system. The relative error for the storm intensity of this method is not larger than 30% for 59% of the moderate and intense geomagnetic storm events (Dst min 50 nt). Also, we consider the CME eruption location together with the shape of the HCS near the CME source and give a new method to predict the CME transit time to the Earth. And the resulting relative error of transit time is less than 30% for more than 90% of all the events. As the inputs to these methods in this paper are the observational characteristics of

19 666 Science in China Ser. E Engineering and Materials Science 2005 Vol.48 No CMEs near the Sun, so we can give the predictions 1 5 d earlier. The results show that the methods given here are applicable for the prediction of arrival time of CME and the corresponding geomagnetic storm intensity with errors acceptable. However, there are still some problems to be analyzed further, including: (1) The three-dimensional structure of the real HCS is very complex, while the CMC is a static coordinate system. In the establishment of the CMC system, we only consider the influence of large-scale solar magnetic structures on the propagation of interplanetary disturbances, and neglect the rotation of the Sun and the influence of other segments of the HCS far away from the CME eruption region etc. Therefore our model is an approximation to a certain extent. (2) Previous studies show that southward interplanetary magnetic fields play an important role in producing geomagnetic storms. Thus, how to predict the interplanetary magnetic field southern component within the ICME need further study. (3) The influences of other background solar wind parameters (such as solar wind speed and background interplanetary magnetic field) on the propagation of CME and the relevant geomagnetic disturbance is not addressed here. Acknowledgements We are grateful to Dr. Chen Yao at University of Science and Technology of China for providing valuable comments on the improvement of the manuscript. Thanks also go to the relevant free data websites: ftp://ftp.ngdc.noaa.gov/stp/geomagnetic_data/in- DICES/DST/; This CME catalog is generated and maintained by NASA and the Catholic University of America in cooperation with the Naval Research Laboratory. SOHO is a project of international cooperation between ESA and NASA. This work was jointly supported by the National Natural Science Foundation of China (Grant Nos , ), the One-hundred Talent Program of the Chinese Academy of Sciences and the National Key Basic Research Science Foundation (Grant No. G ), and also by the International Collaboration Research Team Program of the Chinese Academy of Sciences. References 1. MacQueen, R. M., Eddy, J. A., Gosling, J. T. et al., The outer solar corona as observed from skylab: preliminary results, Astrophys. J., 1974, 187: L85 L Gosling, J. T., Hildner, E., Macqueen, R. M. et al., Mass ejections from the sun a view from skylab, Astrophys. J., 1974, 79: Burlaga, L. F., Sittler, E., Mariani, F. et al., Magnetic loop behind an interplanetary shock Voyager, Helios, and IMP 8 observations, J. Geophys. Res., 1981, 86(A8): Wilson, R. M., Hilder, E., Are interplanetary magnetic clouds manifestations of coronal transients at 1 AU? Solar Phys., 1984, 91: Sheeley, Jr. N. R., Howard, R. A., Koomen, M. J. et al., Coronal mass ejections and interplanetary shocks, J. Geophys. Res., 1985, 90(A1): Gosling, J. T., McComas, D. J., Phillips, J. L. et al., Geomagnetic activity associated with earth passage of interplanetary shock disturbances and coronal mass ejections, J. Geophys. Res., 1991, 96: Gosling, J. T., The solar flare myth, J. Geophys. Res., 1993, 98(A11): Wei, F. S., Zhang, J. H., Huang, S. P., Study of the propagation characteristics of flare-associated interplanetary shock waves in the flare-heliospheric current sheet coordinate system, Acta Geophysica Sinica, 1990, 33:

20 A tentative study for prediction of CME related geomagnetic storm intensity & its transit time Wei, F. S., Liu, S. Q., Zhang, J. H., Study of distribution characteristics of the geomagnetic disturbances corresponding to the flare-associated interplanetary shock waves in the flare-heliospheric current sheet coordinate system, Acta Geophysica Sinica, 1991, 34: Dryer, M., Interplanetary studies: propagation of disturbances between the sun and the magnetosphere, Space Sci. Rev., 1994, 67: [DOI] 11. Odstrcil, D., Dryer, M., Smith, Z., Propagation of an interplanetary shock along the heliospheric plasma sheet, J. Geophys. Res., 1996, 101(A9): (doi: /96JA00479)[DOI] 12. Tokumaru, M., Kojima, M., Fujiki, K. et al., Three-dimensional propagation of interplanetary disturbances detected with raio scintillation measurements at 327 MHz, J. Geophys. Res., 2000, 105(A5): (doi: /2000JA900001) [DOI] 13. Manoharan, P. K., Gopalswamy, N., Yashiro, S. et al., Influence of coronal mass ejection interaction on propagation of interplanetary shocks, J. Geophys. Res., 2004, 109: A (doi: /2003JA010300) [DOI] 14. Michalek, G., Gopalswamy, N., Yashiro, S., A new method for estimating widths, velocities, and source location of halo coronal mass ejections, Astrophys. J., 2003, 584: [DOI] 15. Gopalswamy, N., Lara, A., Yashiro, S. et al., Predicting the 1-AU arrival times of coronal mass ejections, J. Geophys. Res., 2001, 106(A12): (doi: /2001JA000177) [DOI] 16. Webb, D. F., Cliver, E. W., Crooker, N. U. et al., Relationship of halo coronal mass ejections, magnetic clouds, and magnetic storms, J. Geophys. Res., 2000, 105(A4): (doi: /1999JA000275) [DOI] 17. Cane, H. V., Richardson, I. G., Interplanetary coronal mass ejections in the near-earth solar wind during , J. Geophys. Res., 2003, 108(A4): (doi: /2002JA009817) [DOI] 18. Gonzalez, W. D., Joselyn, J. A., Kamide, Y. et al., What is a geomagnetic storm? J. Geophys. Res., 1994, 99(A4): (doi: /93JA02867) [DOI] 19. Burton, R. K., McPherron, R. L., Russell, C. T., An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 1975, 80(31): O Brien, T. P., McPherron, R. L., An empirical phase space analysis of ring current dynamics: Solar wind control of injection and decay, J. Geophys. Res., 2000, 105(A4): (doi: /1998JA000437) [DOI] 21. Wu, J. G., Lundstedt, H., Neural network modeling of solar wind-magnetosphere interaction, J. Geophys. Res., 1997, 102(A7): (doi: /97JA01081) [DOI] 22. Temerin, M., Li, X., A new model for the prediction of Dst on the basis of the solar wind, J. Geophys. Res., 2002, 107(A12): (doi: /2001JA007532) [DOI] 23. Wilson, R. M., On the behavior of the Dst geomagnetic index in the vicinity of magnetic cloud passages at Earth, J. Geophys. Res., 1990, 95(A1): Wu, C. C., Lepping, R. P., Effects of magnetic clouds on the occurrences of geomagnetic storms: the first 4 years of wind, J. Geophys. Res., 2002a, 107(A10): (doi: /2001JA000161) [DOI] 25. Wu, C. C., Lepping, R. P., Effect of solar wind velocity on magnetic cloud-associated magnetic storm intensity, J. Geophys. Res., 2002b, 107(A11): (doi: /2002JA009396) [DOI] 26. Wu, C. C., Lepping, R. P., Relationships for predicting magnetic cloud-associated geomagnetic storms intensity, J. Atmos. and Terr. Phys., 2004, 67: (doi: /j.jastp ) [DOI] 27. Wang, Y. M., Shen, C. L., Wang, S. et al., An empirical formula relating the geomagnetic storm s intensity to the interplanetary parameters: VBz and t, Geophys. Res. Lett., 2003, 30(20): (doi: /2003GL017901) [DOI] 28. Lindsay, G. M., Luhmann, J. G., Russell, C. T. et al., Relationship between coronal mass ejection speeds from coronagraph images and interplanetary characteristics of associated interplanetary coronal mass ejections, J. Geophys. Res., 1999, 104(A6): (doi: /1999JA900051) [DOI] 29. Srivastava, N., Venkatakrishnan, P., Relationship between CME speed and geomagnetic storm intensity, Geophys. Res. Lett., 2002, 29(9): (doi: /2001GL013597) [DOI]