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Testing the Empirical Shock Arrival Model Using Quadrature Observations SPACE WEATHER, VOL. 11, 661–669, doi:10.1002/2013SW000945, 2013 Testing the empirical shock arrival model using quadrature observations N. Gopalswamy,1 P. Mäkelä,1,2 H. Xie,1,2 and S. Yashiro1,2 Received 17 May 2013; revised 9 October 2013; accepted 26 October 2013; published 20 November 2013. [1] The empirical shock arrival (ESA) model was developed based on quadrature data from Helios (in situ) and P-78 (remote sensing) to predict the Sun-Earth travel time of coronal mass ejections (CMEs). The ESA model requires earthward CME speed as input, which is not directly measurable from coronagraphs along the Sun-Earth line. The Solar Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory (SOHO) were in quadrature during 2010–2012, so the speeds of Earth-directed CMEs were observed with minimal projection effects. We identified a set of 20 full halo CMEs in the field of view of SOHO that were also observed in quadrature by STEREO. We used the earthward speed from STEREO measurements as input to the ESA model and compared the resulting travel times with the observed ones from L1 monitors. We find that the model predicts the CME travel time within about 7.3 h, which is similar to the predictions by the ENLIL model. We also find that CME-CME and CME-coronal hole interaction can lead to large deviations from model predictions. Citation: Gopalswamy, N., P. Mäkelä, H. Xie, and S. Yashiro (2013), Testing the empirical shock arrival model using quadrature observations, Space Weather, 11, 661–669, doi:10.1002/2013SW000945. 1. Introduction acceleration of CMEs using Solwind coronagraph data and Helios in situ observations reported in Lindsay et al. [2] Coronal mass ejections (CMEs) are the cause of the [1999]. The IP acceleration was more accurate than the severest of geomagnetic storms and large energetic particle one derived from coronagraphic images obtained by the events [see Gopalswamy, 2009, and references therein]. Solar and Heliospheric Observatory (SOHO) and in situ CMEs appearing close to the disk center of the Sun often measurements from the Wind spacecraft because both appear as halo CMEs [Howard et al., 1982; Gopalswamy Wind and SOHO were located along the Sun-Earth line. et al., 2010a] and are highly likely to intersect Earth. The IP acceleration derived by Gopalswamy et al. [2001] is Unfortunately, it is difficult to measure the nose part of of the form the CMEs arriving at Earth by coronagraphs located along the Sun-Earth line because of the occulting disk. The nose a ¼ –0:0054 ðÞu–uc ; (1) part can be directly measured only by the in situ instru- where u is the initial speed of the CME in coronagraph field ments in the solar wind. On the other hand, the nose part of view (FOV) and u = 406 km/s, identified as the average of the CME can be observed by both remote sensing and c solar wind speed. The acceleration can be positive or in situ observations if the observing spacecraft are in quad- negative depending on whether the CME speed is smaller rature. For example, the Solwind coronagraph on board or greater than the solar wind speed. The acceleration in P-78 mission located in Earth orbit observed limb CMEs equation 1 provides a simple means to predict the CME heading toward the Helios spacecraft that detected the travel time to Earth using simple kinematic relations CMEs in situ [Lindsay et al., 1999]. The combined in situ [Gopalswamy et al., 2001]. Note that the acceleration has also and coronagraphic observations were useful in deriving been modeled to have a quadratic dependence CME rela- the interplanetary (IP) acceleration of CMEs, free from tive speed (for details, see Vršnak et al. [2013]). By reducing projection effects. Gopalswamy et al. [2000] obtained the IP the CME travel time by the average shock standoff time at 1 AU, Gopalswamy et al. [2005a] derived the empirical shock 1Goddard Space Flight Center, NASA, Greenbelt, Maryland, USA. arrival (ESA) model. For initial CME speeds > 450 km/s, 2 Department of Physics, The Catholic University of America, the ESA model travel time T (in h) can be approximated Washington, District of Columbia, USA. by the formula, Corresponding author: N. Gopalswamy, Goddard Space Flight ¼ u þ ; Center, NASA, Bldg. 21, Rm. 170, Code 671, Greenbelt, MD 20771, T AB C (2) USA. ([email protected]) with A = 151.002, B = 0.998625, and C = 11.5981 [Gopalswamy ©2013. American Geophysical Union. All Rights Reserved. et al., 2005b]. The ESA model has been tested using sky- 1542-7390/13/10.1002/2013SW000945 plane speed from SOHO correcting for projection effects 661 GOPALSWAMY ET AL.: EMPIRICAL SHOCK ARRIVAL MODEL Table 1. List of Shocks Detected at L1 and the Corresponding Halo CMEs Observed by SOHO Shock Date Vsw To Limb Vsp (km/s) d Δ Δ Δ Time (km/s) CME Time Location (A, B) Deg S/C VE (km/s) tESA (h) tobs (h) t (h) VE1 (km/s) tESA1 (h) t1 (h) t2 (h) 2010/02/15 17:28 300 02/12 13:31 N26E11 À14,À30b 867 B 765 64.3 76.0 À11.7 756 65.0 À11.0 ---- 2010/04/11 12:18 360 04/08 04:30 N24E16 À6,À35 771c A 677 71.1 79.8 À8.7 630 75.1 À4.7 À3.3 2010/08/03 16:51 425 08/01 08:24 N20E36 23,À54 1031c A 784 62.9 56.5 +6.4 1257 38.4 À18.1 À6.9 2011/02/18 00:40 325 02/15 02:36 S12W18 À21, 22 945 A 879 56.7 70.1 À13.4 864 57.6 À12.5 À9.8 2011/03/10 05:45 300 03/07 14:48 N11E21 19,À16 691 B 633 74.8 63.0 +11.8 738 66.3 +3.3 1.8 2011/06/23 02:18 600 06/21 03:16 N16W08 À2, 11 986 A 939 53.1 47.0 +6.1 812 61.0 +14.0 +9.6 2011/08/04 21:10 350 08/02 06:36 N14W15 À5, 18 1015 A 951 52.4 62.6 À10.2 883 56.4 À6.2 ---- 2011/08/05 17:23 350 08/03 13:17 N22W30 À20, 33 1322 A 1062 46.6 52.1 À5.5 1161 42.2 À9.9 À0.4 2011/08/05 18:32 395 08/04 03:40 N19W36 À26, 39 1709 A 1307 36.6 38.9 À2.3 1945 22.0 À16.9 ---- 2011/09/09 11:49 340 09/06 02:24 N14W07 6, 12 513 A 494 88.1 81.4 +6.7 521 85.3 +3.9 5.2 2011/09/17 03:05 350 09/14 00:00 N22W03 10, 9 577 B 534 84.0 75.1 +8.9 467 91.0 +15.9 À5.9 2011/11/12 05:10 350 11/09 13:36 N22E44 41,À12 1366 B 911 54.7 63.6 À8.9 1210 40.2 À23.4 À3.5 2012/01/22 05:18 312 01/19 14:25 N32E22 40, 1 1153 B 907 54.9 62.9 À8.0 674 71.3 +8.4 ---- 2012/01/24 14:33 400 01/23 03:38 N29W20 À2, 44 2002 A 1645 27.3 34.9 À7.6 1245 38.8 +3.9 À0.5 2012/02/26 21:07 350 02/24 03:46 N25E28 47,À1 779 B 623 75.7 65.3 +10.4 678 71.0 +5.7 À1.0 2012/03/08 10:53 475 03/07 01:24 N17E27 47, 1 2190c B 1866 23.2 33.3 À10.3 2190 19.0 À14.5 À0.8 2012/03/11 12:52 400 03/09 04:14 N17W03 17, 31 861 B 822 60.3 56.6 +3.7 1176 41.5 À15.1 ---- 2012/03/12 08:45 400 03/10 17:40 N17W24 À4, 52 1558 A 1361 34.8 39.1 À4.3 1081 45.7 +6.6 14.3 2012/06/16 08:52 300 06/14 14:36a S17E06 33, 20 1207 B 1148 42.7 42.3 +0.4 1317 36.3 À6.0 10.0 2012/07/14 17:27 350 07/12 16:49 S14W01 36, 19 1548 B 1502 30.7 48.6 À17.9 1210 40.2 À8.4 À5.5 aThe halo CME announcement incorrectly listed the CME onset time as 12:36 UT. bSTA had a data gap for this event, so STB is used for measurement. cNew space speed measurements from STEREO/COR2. dDates are formatted as year/month/day. using a cone model [Xie et al., 2006]. Quadrature observa- originated from N32E22 in Earth view. On that day, STB tions became available in 2010 from SOHO and the twin was at E113. Therefore, STB viewed the solar source as spacecraft of the Solar Terrestrial Relations Observatory W91 (just a degree behind the limb) and hence was in (STEREO) [Kaiser et al., 2008] mission, allowing us to quadrature with SOHO. On the other hand, STA was at directly obtain the earthward speed of CMEs without W108 and viewed the source at E130, which was 40° behind modeling. Making use of the SOHO-STEREO quadrature the limb in the STA view. The measurements of this CME observations, we report on the performance of the ESA made from STB had minimal projection effects, so we used model for a set of 20 full halo CMEs, whose space speed the STB measurements for this event.
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