Predicting the Time-of-Arrival of Coronal Mass Ejections at Earth From Heliospheric Imaging Observations
Carlos Roberto Braga, Angelos Vourlidas, Guillermo Stenborg, Alisson Dal Lago, Rafael Rodrigues Souza de Mendonça, Ezequiel Echer
mmanuscript submitted to
JGR: Space Physics
Predicting the Time-of-Arrival of Coronal MassEjections at Earth From Heliospheric ImagingObservations
Carlos Roberto Braga , , Angelos Vourlidas , Guillermo Stenborg , AlissonDal Lago , Rafael Rodrigues Souza de Mendon¸ca , Ezequiel Echer George Mason University, 4400 University Drive, Fairfax, VA, 22030, USA The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA Space Science Division, U.S. Naval Research Laboratory, 4555 Overlook Ave. SW Washington, DC20375, USA National Institute for Space Research, Av. dos Astronautas, 1758, S˜ao Jos´e dos Campos, 12227-010, SP,Brazil
Key Points: • We study CME propagation relying on simultaneous observations of Earth-directed CMEs from the inner Heliospheric Imagers onboard STEREO • We adopt an elliptical front-fitting approach to the two HI-1 viewpoints and usea drag model to simulate the CME propagation in the heliosphere • We derive a CME Time-of-Arrival and Speed-on-Arrival mean absolute errorsof 6 . ± . ±
102 km/s for a set of 14 events
Corresponding author: Carlos Roberto Braga, [email protected] –1– a r X i v : . [ a s t r o - ph . S R ] A ug anuscript submitted to JGR: Space Physics
Abstract
The Time-of-Arrival (ToA) of coronal mass ejections (CME) at Earth is a key parameterdue to the space weather phenomena associated with the CME arrival, such as intense geo-magnetic storms. Despite the incremental use of new instrumentation and the developmentof novel methodologies, ToA estimated errors remain above 10 hours on average. Here, weinvestigate the prediction of the ToA of CMEs using observations from heliospheric imagers,i.e., from heliocentric distances higher than those covered by the existent coronagraphs. Inorder to perform this work we analyse 14 CMEs observed by the heliospheric imagers HI-1onboard the twin STEREO spacecraft to determine their front location and speed. Thekinematic parameters are derived with a new technique based on the Elliptical Conver-sion (ElCon) method, which uses simultaneous observations from the two viewpoints fromSTEREO. Outside the field of view of the instruments, we assume that the dynamics of theCME evolution is controlled by aerodynamic drag, i.e., a force resulting from the interactionwith particles from the background solar wind. To model the drag force we use a physicalmodel that allows us to derive its parameters without the need to rely on drag coefficientsderived empirically. We found a CME ToA mean error of 1 . ± . . ± . Coronal mass ejections (CMEs) have been tracked with space-based coronagraphs formore than 40 years. Thousands of events have been studied and catalogued (Tousey, 1973;Gosling et al., 1974; Howard et al., 1985; Webb & Howard, 1994; Gopalswamy, 2004;Robbrecht & Berghmans, 2004; Yashiro, 2004; Gopalswamy et al., 2009; Gopalswamy,2016; Vourlidas et al., 2017; Lamy et al., 2019). One of the key open issues about CMEs isunderstanding their propagation in the heliosphere, especially for events directed to Earth.CMEs are the main drivers of intense geomagnetic storms (Gosling, 1993) and one ofthe most basic variables from a Space Weather perspective is the Time-of-Arrival (ToA) ofa given CME in the Earth’s vicinity. Not surprisingly, the ToA has been studied for a longtime. An extensive review of methods to estimate the ToA and their results can be foundin Zhao and Dryer (2014) and Vourlidas et al. (2019).The methods applied to ToA estimation include empirical approaches (Gopalswamyet al., 2001; Schwenn et al., 2005; Kilpua et al., 2012; Mkel et al., 2016; M¨ostl et al.,2017), magneto-hydrodynamic (MHD) modeling (Wold et al., 2018; Mays et al., 2015),CME three dimensional (3D) reconstruction, and CME propagation analysis based on drag-based models (Vrˇsnak et al., 2014; Shi et al., 2015; Napoletano et al., 2018), just to namea few (see, e.g., Zhao & Dryer, 2014). In spite of the insight gained with the dual view-point provided by the Solar Terrestrial Relations Observatory (STEREO) mission (Kaiseret al., 2007) since 2007, the uncertainty of the CME ToA persist. According to a reviewfrom Vourlidas et al. (2019), the CME ToA mean absolute error (MAE) is 9 . ± –2–anuscript submitted to JGR: Space Physics by comparing the estimated SoA with the CME speed measured in situ, one can determinethe SoA error. This error has been investigated in a limited number of studies in theSTEREO era. This is evident in a recent review from Vourlidas et al. (2019). Among 24studies including ToA error analysis, only 5 included SoA errors. Now, we briefly introducethese 5 studies along with their median SoA errors. Using several methods to determine thefront, such as fixed-phi, harmonic mean and self-similar expansion fitting (described latterin this section) for a set of 22 CMEs, M¨ostl et al. (2014) found median SoA errors in the200-300 km/s range, depending on the method used. Corona-Romero et al. (2017) estimatedthe SoA using a theoretical piston shock model combined with an empirical relationship for40 fast CMEs, which are typically preceded by shock waves. The median SoA error theyfound is 95 ± km/s . Probably the most extensive study including SoA errors is M¨ostlet al. (2017), which includes more than 50 events in each STEREO viewpoint. The medianSoA error found using self-similar expansion fitting is 191 ± km/s for STEREO-A eventsand 245 ± km/s for STEREO-B. Other studies cover fewer CME events and find smallererrors. Hess and Zhang (2015) used a flux rope geometrical model (A. F. R. Thernisien etal., 2006; A. Thernisien, 2011) for the CME front and a prolate spheroid bubble model(Kwon et al., 2014) for the sheath front associated with the CME. Combining both modelswith the drag force, the average SoA error found was 24 . km/s for their set of 7 events.One of the lowest SoA median errors was found by Rollett et al. (2016) using an ellipticalCME front model: for a set of 21 events, the median error is lower than 20 km/s.Thanks to the Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI)suite onboard STEREO, CMEs can be observed further into the inner heliosphere by theheliospheric imagers (HI-1 and HI-2), typically up to heliocentric distances between 0 . au and 1 au . Details about SECCHI are described in R. A. Howard et al. (2008). Nevertheless,a quick check of the literature reveals that the use of the imaging products of the heliosphericimagers is limited compared to those of the coronagraphs (Vourlidas et al., 2019; Zhao &Dryer, 2014; Harrison et al., 2017).In the heliospheric imagers FOV, the position of the CME can be derived only underassumptions about the CME trajectory. Widely-used methods include the Fixed- φ (f- φ )(Sheeley et al., 1999; Kahler & Webb, 2007; Rouillard et al., 2008) and harmonic mean(HM) methodology (Lugaz et al., 2009). The former considers the CME as a point-likestructure moving radially away from the Sun with constant speed to determine the directionof propagation and CME position. The HM considers a circular structure centered in theSun with half-width of 90 ◦ propagating at constant speed. A third method is the self-similarexpansion fitting (SSEF), which also assumes a circular front with half-width constant overtime but adjustable to each CME (Lugaz, 2010; Davies et al., 2012; M¨ostl & Davies, 2013).The f- φ , HM and SSEFs methodologies allow us to determine the CME front po-sition using a single viewpoint. These methods have been extensively applied to CMEsobserved in the STEREO-era and the results are publicly available in the HELCATS (He-liospheric Cataloguing, Analysis and Techniques Service) project ( ).Many other catalogs are part of this project, such as the HELCATS Heliospheric Imager Ge-ometrical Catalogue (HIGeoCAT), which reports kinematic properties derived using single-spacecraft observations of CMEs observed by the HI-1 and HI-2 instruments, includingtheir speeds, propagation directions, and launch times (M¨ostl et al., 2017; Barnes et al.,2019). Another list of CME kinematic parameters based on HI-1 observations is available in . Some studies also compare the resultsof multiple CME kinematics and ToA derived using the different methodologies mentionedabove (M¨ostl et al., 2014).Triangulation is yet another methodology to derive the CME kinematics. In this case,co-temporal observations are needed, e.g., from the twin heliospheric imagers or corona-graphs onboard STEREO (e.g., Y. Liu et al., 2010, 2011; Liewer et al., 2011; Braga et al.,2017). This methodology normally requires selection and tracking of particular point-like –3–anuscript submitted to JGR: Space Physics features in each viewpoint. It uses epipolar geometry, which allows the use of multipleviewpoints, and it normally requires assumptions about the structure under study.To properly locate and track the CME fronts, and hence kinematically characterize theCME evolution in heliospheric images, further analysis is required (as compared to coro-nagraph observations) beyond the assumptions discussed above. The relative contributionof the electron corona signal (i.e., the K-corona) to the total signal recorded by the HIinstruments for elongations greater than about 8 ◦ ( ∼ R (cid:12) ) is well below that recordedby coronagraphs. Therefore, to help reveal the CME boundaries and inner structure duringtheir evolution across the HI instrument field-of-view (FOV), it is necessary to remove thedominant signal coming from the F-corona, i.e., photospheric light scattered by the dustparticles in orbit around the Sun (Leinert et al., 1998).In addition, at the solar elongation covered by the heliospheric imagers, the emissionproperties of the coronal electrons change due to Thomson Scattering (Minnaert, 1930).The maximum brightness contribution along the line of sight is now located on the “curved”Thomson sphere rather than the flat “sky-plane” (Vourlidas and Howard (2006) and refer-ences therein). This effect complicates the visualization of the event boundaries, as CMEsmove away from the Sun.A motivation for this work is the application of a similar methodology to CME obser-vations in the inner heliosphere from upcoming and planned missions, such as the recentlyselected PUNCH or L5-mission concepts (Vourlidas, 2015). Future observations can be usedin combination with a second spacecraft observing the same region, such as STEREO-A.To carry out the investigation, we apply a customized version of the technique developedby Stenborg and Howard (2017) to remove the background signal in the HI-1 FOV on a set of14 Earth-directed CME events spread over the rise and maximum of Cycle 24 (2010-2013).Co-temporal HI-1 observations from two viewpoints are used to construct an elliptical modelof the CME fronts and hence estimate their locations in the solar corona. Beyond the HI-1FOV, we apply a drag force model to propagate the CME up to 1 au. We finally compare theCME ToA errors computed with this approach to those calculated using mainly observationsfrom SECCHI coronagraphs.This article is organized as follows. In Section 2.1 we describe the events studied.From Section 2.2 to Section 2.8, we describe the methodology applied to calculate the CMEkinematics in the HI-1 FOV and extrapolate them in the remaining trajectory toward theEarth. The results (the calculated CME travel time, final speed, etc.) and a comparisonwith the actual observations are shown in Section 3. Finally, we summarize the results inSection 5. We devised a methodology to estimate the CME ToA by combining a geometric frontreconstruction model with a CME propagation model. To obtain the CME propagationdirection, we fit the CME front in the ecliptic plane with an ellipse (see Section 2.5). Todetermine the CME kinematics, we use an aerodynamic drag force model (see Section 2.6).The elliptical front allows us to estimate the initial position and the speed, which are thenused as input parameters for the drag force estimation. As a final result, we derive the CMEspeed and ToA at 1 au . Our starting point is the list of CME events analyzed by Sachdeva et al. (2017), whichincludes 38 well-observed events between March 2010 and March 2013. This list includesonly events with continuous observations in all STEREO SECCHI instruments, includingthe coronagraphs and heliospheric imagers, as well as from the Large Angle Spectromet- –4–anuscript submitted to
JGR: Space Physics ric Coronagraph (LASCO; Brueckner et al., 1995) C2 instrument onboard the Solar andHeliopheric Observatory (SOHO; Domingo et al., 1995). Since our study targets only obser-vations from heliospheric imagers, we do not use the kinematic parameters and height-timeprofiles derived by Sachdeva et al. (2017) because they were obtained using observationsfrom coronagraphs (SECCHI and LASCO) and heliospheric imagers. We consider only thetiming of each event in the list to identify the corresponding observations on the HI-1 FOV.Moreover, Sachdeva et al. (2017) did not identify the CME counterparts in the Earth’s vicin-ity (the so-called interplanetary coronal mass ejections - ICMEs); therefore, we undertakethis task for each event.In order to perform this task, we use the ICME list compiled from WIND missionobservations from Nieves-Chinchilla et al. (2018), which is available online at https://wind.nasa.gov/ICMEindex.php . Our criterion to associate a given ICME to its correspondingCME counterpart is based on the time elapsed ( t el ) between the ICME in situ observationtime and the time of the first coronagraph observation of the CME counterpart candidate.The CME travel time considered was taken from an extensive study of CME-ICMEs pairsby Richardson and Cane (2010). We consider it a match when 0.5 days < t el < ∅ in column “Remark”). In these cases, either the corresponding ICME was not includedin the ICME list possibly due to data gaps or poor data quality, or the CME reported onSachdeva et al. (2017) missed the WIND spacecraft.In two other cases ( (cid:107) in column “Remarks” ofTable 1. When CME-CME interaction takes places, a detailed study would be necessarybecause additional forces need to be taken into account in the CME propagation to estimatetheir travel times (see, e.g., Y. D. Liu et al. (2012); Colaninno et al. (2013); Temmer et al.(2012), just to mention some recent studies). Case studies of CME interaction are beyondthe scope of the present manuscript. Notice that our criteria do not remove a given eventfrom our list if CME interaction takes place below the HI-1 FOV or if one of the CMEs liessignificantly northward or southward from the ecliptic plane.Therefore, from the original list of 38 events, 20 were left after the application of allcriteria mentioned in the paragraphs above. The final list studied here has 14 events because –5–anuscript submitted to JGR: Space Physics
Table 1.
List of CMEs and corresponding ICMEs. The symbols (cid:107) indicate the events removedfrom the list due to observation of another CMEs in close timing. Events associated to multipleICMEs, without any ICME associated, or whose time elapsed between the CME and correspondingICME observation falls outside our criteria are indicated by Π, ∅ and ∆, respectively. We couldnot apply the F-corona background removal methodology (see Section 2.2) to events indicated by † and they were removed from the analysis. The final list of 14 events that match all the criteriaexplained in Section 2.1 and that could be processed as explained in Section 2.2 are indicated by astar. ID Remark Date Realistic timing Unique ICME ICME start date1 † (cid:63) (cid:63) (cid:107) † † ∅ (cid:63) ∅ (cid:63) ∅ (cid:63) ∅ ∅ ∅ (cid:63) (cid:107) (cid:107) (cid:107) ∅ ∅ † (cid:63) (cid:63) (cid:63) (cid:63) (cid:63) (cid:63) (cid:107) (cid:63) (cid:63) † † –6–anuscript submitted to JGR: Space Physics additional 6 events are eliminated when applying the methodology to remove the backgroundF-corona, as explained in Section 2.2.It is worth mentioning here how our list of events compares to the total number of eventsavailable during the entire period of two-viewpoint observations from STEREO. Althoughhundreds of Earth-directed CMEs were observed in the period here selected (see, e.g., Barneset al., 2019), we expect that our strict selection criteria would eliminate the majority ofthem, hence reducing the number of events significantly. As an illustration, the numberof ICMEs available from 2007 to 2014 is 138 according to the Wind ICME catalog. Afterremoving ICMEs observed in close timing (one of our criteria requirements), 118 are left.Moreover, each of these ICMEs need to be associated to a unique CME observed on both HI-1 instruments (i.e, on STEREO-A and on STEREO-B). Continuous observations recordingthe passage of the event across the FOV in both instruments is the next requirement, alongwith the absence of another event prior or after the case under study in a time period of afew hours. A precise number of the remaining events would require an extensive case-by-casestudy to check our selection criteria, which is outside the scope of the present study.Briefly, from the list of 38 events used in the manuscript with corresponding ICMEs,we ended up with 14 events, i.e., the number of events is reduced to less than half afterapplying our selection criteria. Therefore, if we assume that the ratio of events selected tothe sample size is kept, then the list of 138 ICMEs would have resulted in approximately50 events. So, we estimate that the event list studied here corresponds to approximatelyone forth of the events that follow our criteria in the entire two-viewpoint STEREO period(2007-2014).
The HI-1 observations include a background scene that must be removed to allow theCME event tracking and characterization. This background scene is dominated by thescattering from dust particles in orbit around the Sun, the so-called F-corona (the F letterstands for Fraunhofer). The F-corona intensity overtakes the K-corona above approximately5 R (cid:12) (Koutchmy & Lamy, 1985), well below the inner edge of the HI-1 instrument, whichis about 16 R (cid:12) .Experience from observations of the corona over the last 40 years suggests that theF-corona is constant over timescales of days or weeks while the K-corona is highly dynamicand can change significantly in a matter of hours. For this reason, empirical models of the F-corona are usually constructed by computing the minimum of the daily median images overan extended period of time (normally a solar rotation), centered on the day of observation(Morrill et al., 2006).Stenborg and Howard (2017) showed that at the larger elongations covered by the HI-1instruments, the use of background models obtained considering extended periods of timeleads to the introduction of artifacts. This occurs due to the subtle changes resulting fromdifferent viewpoints (Stenborg et al., 2018). Therefore, to remove the background contri-bution from the F-corona from each individual HI-1 observation, we created its respectivebackground model following Stenborg and Howard (2017).An example of a processed HI-1 observation pair, highlighting CME feature, is shown inFigure 1. The images reveal the often-seen (in coronagraphs) faint-bright front pair (shockor wave followed by the flux rope and a cavity, see Vourlidas et al. (2013) for details), aswell as more complex internal structure without the known artifacts that result from theuse of the running difference scheme generally adopted by the solar physics community. Inthis scheme, each image is subtracted from a base image, which is typically taken a fewtime-steps behind. Background structures, such as streamers, that change over the courseof hours, result in artifacts in the final image. These artifacts normally prevent us from –7–anuscript submitted to JGR: Space Physics
Figure 1.
Example of CME identifying internal structures of the CME such as core and void, and, depending or theirsize or relative brightness, the apex of a given CME (Stenborg & Howard, 2017).In the current study, we focused on the selection of the CME furthermost point visiblein the HI-1 FOV at each time-instance and at a position angle close to the ecliptic plane.Since we are interested in the arrival of the transient at the Earth, we did not take anymeasurement of their internal structure (e.g., the core of the events) but we also did notdifferentiate between shock and CME front, which may add some error in our ToA estimates.As mentioned above, for some events in Table 1, the corresponding observations couldnot be properly processed (i.e., the background brightness model could not be determined)due to the presence of extended bright objects in the FOV of the instruments (e.g., theMilky Way), saturated objects (e.g., a bright planet) and/or instrumental artifacts (e.g.,ghost features). We kept only events with simultaneous observation in HI-1 both on-boardSTEREO-A and STEREO-B that allowed proper identification of the CME front in at leastpart of the FOV in each spacecraft. Due to these reasons, the following 6 events wereremoved from our analysis:
To analyze the kinematic evolution of the events, we need to identify their correspondingfronts in the processed images and construct elongation-time maps of a given part of eachfront. The spatial location can then be derived under some assumptions for translatingangular positions to heliocentric distances (Sheeley et al., 2008b, 2008a; Rouillard et al.,2008; Rouillard, Savani, et al., 2009; Rouillard, Davies, et al., 2009).Given a set of sequential images observed by HI-1, we selected a position angle (PA)close to the ecliptic plane to construct the time-elongation profiles, frequently called J-maps(Davies et al., 2009). We use the PA of 90 ◦ for STEREO-A and 270 ◦ for STEREO-B, aregion that nearly corresponds to the central height of the image. The PA is kept constantfor a given CME event in each viewpoint, i.e., it is set to be the same at all instances. –8–anuscript submitted to JGR: Space Physics
Figure 2.
Example of J-map of CME
Each time-elongation profile constructed in this way shows at least one bright feature thatlooks like an inclined line. This corresponds to the brighter points along the selected PAin the images, i.e., to the apex of the CME projected onto the plane of the sky at thatparticular PA. An example of a J-map created for event (cid:15) med [ t ], (cid:15) min [ t ], (cid:15) max [ t ]). A quick look at some events indicate that at the first time-instance t we have (cid:15) max [ t ] - (cid:15) min [ t ] ≈ . ◦ and in the latest t f we get (cid:15) max [ t f ] - (cid:15) min [ t f ] ≈ . ◦ .These 3 elongation versus time profiles are all used to estimate the CME Time-of-Arrival(ToA) at Earth, as described in Section 2.5 and Section 3.In a few events, the J-maps produced at the PA mentioned (90 ◦ for STEREO-A and270 ◦ for STEREO-B) were not clear and we used PA shifted by up to 3 degrees instead.This happened due to the presence of artifacts in the background at a given elongation,such as a bright planet. This negatively affected the CME front tracking in the J-map atthat particular PA due to the excessive brightness of this feature as compared to that ofboth the background and the CME front. From our assessment using a few test CMEs,we understood that the shifted position angle within the range mentioned here producesdifferences that are within the error range between (from (cid:15) min to (cid:15) max ). Typically for aone degree PA shift, the elongation is changed by 0 . ◦ in the latest time-instance studied,generally lying in the range from 15 ◦ − ◦ . Therefore, these shifts are not expected to affectsignificantly the results found here. –9–anuscript submitted to JGR: Space Physics
Figure 3.
Diagram explaining the CME’s Time-of-Arrival (ToA) and Speed-on-Arrival (SoA)determinations. The left half illustrates the determination of CME front as a function of time fromobservation in the HI-1 FOV. The right half explains the application of the drag model, that isused only after the last position observed on HI-1 FOV. The boxes in white indicate inputs forthe models and their outputs are shown in gray. The blue boxes indicate the range (along theSun-Earth line) where each methodology is applied.
We calculate the travel time and Speed-on-Arrival of the CME using the drag model(Section 2.6) and kinematic parameters derived from HI-1 observations from both spacecraft.The delineation of the procedure followed is depicted in the diagram in Figure 3. Briefly,we first extract the elongation of the CME front at a given PA as a function of time in-dependently for each telescope. Then, a geometric model (Section 2.5) called EllipticalConversion (ElCon) is used to derive the CME front position at each time instance, as wellas its direction of propagation and its speed. These parameters are then used to calculatethe CME acceleration at each point (in steps of 0 .
01 au along the Sun-Earth line) afterits last observation on HI-1 (typically from tenths of solar radii) to the L1 point (around215 R (cid:12) ) using the aerodynamic drag model (Section 2.6).We have not considered other forces, such as the Lorentz force in this model, becausethis force is considered to be important only closer to the Sun, typically below 50 R (cid:12) (theend of the HI-1 FOV is at about 96 R (cid:12) ), especially for fast CMEs (Bein et al., 2011;Sachdeva et al., 2015, 2017). To derive the CME position in the HI-1 FOV, we adopt the Elliptical Conversion(ElCon) model as described in M¨ostl et al. (2015) and Rollett et al. (2016). This modelconsiders an elliptically shaped CME front on the ecliptic plane. Its position and speed canthen be derived at any location in space using just geometrical arguments, provided the –10–anuscript submitted to
JGR: Space Physics
Figure 4.
The elliptical front model used in this study to derive the CME front position (dashedblack line). The parameters of the model (CME half width in the ecliptic plane λ , aspect ratio ofelliptical front f = b/a , central position angle in the ecliptic plane α ) are derived by a best-fit of asequence of time-instances observed simultaneously by HI-1-A and HI-1-B. For each time-instancewe derive the position of the CME front point along the Sun-Earth line ( r is ) and along the centralaxis of the CME ( r el ). time evolution of the front’s elongation is known and a set of given parameters of the CMEfront (e.g., angular width, direction of propagation, aspect ratio, etc.) are defined. Themodel adds an extra degree of freedom when compared to circular CME fronts, which is theaspect ratio. Since the CMEs can have various shapes, the elliptical front is a more generalfit allowing more CMEs to be fit. This model and its parameters are shown in Figure 4.In this study, we derive the parameters of the model (CME half width in the eclipticplane λ , aspect ratio of elliptical front f , central position angle in the ecliptic plane α ,speed) by doing a best-fit of a sequence of n time-instances observed simultaneously byHI-1-A and HI-1-B. In previous studies these parameters were fixed for a given set of CMEsfor simplicity (M¨ostl et al., 2015; Rollett et al., 2016). The residual σ was calculated fromthe following expression: σ = (cid:80) nt =1 ( | r is ( t ) A − r is ( t ) B | + | r el ( t ) A − r el ( t ) B | ) /n where r is ( t ) is the position of the CME front point along the Sun-Earth line on theecliptic plane as a function of time, t , derived using observations from a given spacecraft; r el ( t ) denotes the position of the central axis on the CME front. The angle between r is and r el corresponds to α . Positive values of α indicate that the CME propagates towardsSTEREO-A. The superscripts A and B indicate values from STEREO-A and STEREO-Bobservations, respectively. –11–anuscript submitted to JGR: Space Physics
Table 2.
Parameters of the CMEs elliptical front derived using the ElCon model: linear speeds( v med , v min and v max ), CME half width in the ecliptic plane ( λ ), aspect ratio of the front ( f )and the CME central position angle on the ecliptic plane ( α , positive ahead of the Earth). Otherparameters shown are the residual ( σ ) and the position of the last point that the CME was trackedsimultaneously on both viewpoints ( s ). ID last tracked time (UT) s v med v min v max f λ σ α (UT) [au] [km/s] [km/s] [km/s] [ ◦ ] [au] [ ◦ ]2 03-Apr-2010 20:29:21 0.22 846 866 876 0.5 80 0.0047 -173 09-Apr-2010 00:39:22 0.28 490 448 491 0.6 60 0.0021 129 15-Feb-2011 18:29:34 0.26 465 456 475 0.5 65 0.0028 -1211 26-Mar-2011 07:59:25 0.20 448 446 427 0.5 50 0.0033 -1113 14-Jun-2011 23:49:28 0.28 769 765 775 0.5 70 0.0081 -1917 14-Sep-2011 10:29:53 0.14 605 584 568 0.5 80 0.0093 6325 20-Apr-2012 10:29:25 0.25 446 446 453 0.5 80 0.0079 -3226 15-Jun-2012 03:19:22 0.27 741 755 776 0.5 80 0.0051 -727 13-Jul-2012 07:59:27 0.31 743 732 780 0.9 80 0.0475 2028 28-Sep-2012 08:29:50 0.18 740 721 739 0.6 20 0.0056 2029 06-Oct-2012 01:49:52 0.36 692 686 712 0.5 30 0.0075 1530 28-Oct-2012 11:59:57 0.21 431 422 441 0.5 20 0.0097 1133 15-Mar-2013 15:59:43 0.19 765 703 737 0.6 80 0.0030 134 11-Apr-2013 15:49:33 0.18 764 780 667 0.5 65 0.0042 -1The list of parameters derived using the ElCon model is shown in Table 2. As alreadymentioned, from the list of 38 events shown in Table 1, only 14 are used with the ElConmodel. The rest were removed due to the reasons described in Section 2.1 and 2.2.We fitted the elliptical model three times for each event: one using the median elon-gation extracted at each time instance (cid:15) med [ t ], a second with minimum elongation (cid:15) min [ t ]and a third time using the maximum (cid:15) max [ t ]. In each case, a set of parameters λ , f , α isderived and r is at each time instance t is calculated as the average of r Ais and r Bis . v med , v min , v max are the linear speeds calculated from the parameters of the ElConderived using (cid:15) med [ t ], (cid:15) min [ t ] and (cid:15) max [ t ], respectively. All three speeds considered here arecalculated along the Sun-Earth line, i.e., using r is . The differences between the 3 values(typically well below 50 km/s ) give us an idea of the error introduced in the CME speeddue to differences in the identification of the CME front in the J-maps. The 3 speeds areused for the calculation of the CME travel time and ToA error, as described in Section 3. InSection 3.2, we compare speeds derived in this work with previous studies. The remainingparameters shown in Table 2 ( f , λ , σ and α ) are calculated using the median elongationprofile.The elliptical fronts we derived correspond to wide CMEs in most cases: 11 of the 14events have λ ≥ ◦ . The CMEs aspect ratio ranges from 0 . . .
9. This means that all CME fronts are elongated perpendicular to thepropagation direction.There is limited literature to compare the elliptical front geometries derived here (Rollettet al., 2016; M¨ostl et al., 2015). In Rollett et al. (2016) both f and λ were set to fixed valuesfor all CMEs in their set of 21 events to test their methodology. The aspect ratios ( f )derived here are typically lower than values assumed on Rollett et al. (2016), which are f = 0 . f = 1 . f = 1 .
2. It is interesting to note that their results suggest that amongthe 3 values of f used, f = 0 . –12–anuscript submitted to JGR: Space Physics average aspect ratio found in our study ( f = 0 . ± km/s ( f = 0 . ± km/s ( f = 1) and 38 ± km/s ( f = 1 . f = 1 . . ± . h ).Using f = 0 .
8, the error is approximately 1 hour higher (6 . ± . h ). Since the objective ofRollett et al. (2016) work was to introduce the methodology and assess its reliability, theyset the half-width of all events under study to 35 ◦ to simplify their analysis. Thus, it isimpossible to derive conclusions by comparing our results with theirs. M¨ostl et al. (2015)considered a single CME event observed on January 7, 2014, which is not in our list. Dueto specific reasons associated to this event, including the in situ observations that providesome constraints on the CME geometry, the half-width calculated is in the range from 35 ◦ to 60 ◦ and the front ratio f ranges from 0 .
55 to 1 .
0. The results in M¨ostl et al. (2015) arein the same range as ours. Overall, the elliptical front geometries we derived are consistentwith previous studies.
The aerodynamic drag results from the interaction of the CME with the solar wind.There are many works that apply such kind of force, most of them relying on empirically-derived drag coefficients (Cargill, 2004; Vrˇsnak, 2006; T. A. Howard et al., 2007; Borgazzi etal., 2009; Byrne et al., 2010; Maloney & Gallagher, 2010; Vrˇsnak et al., 2010, 2013; Mishra& Srivastava, 2013; Dolei et al., 2014; Iju et al., 2014; Temmer & Nitta, 2015).Among these works, many authors have used a constant drag coefficient for a givenCME in its path from the Sun to the Earth so that the drag could only be a function ofthe (i) difference between the CME and solar wind speed, (ii) CME mass, (iii) solar winddensity, and (iv) cross section area of the CME (Vrˇsnak et al., 2013; Temmer & Nitta, 2015;Mishra & Srivastava, 2013). Only a few works have used a drag coefficient as a functionof the Reynolds number, which in turn depends on the viscosity of the solar wind plasma(Subramanian et al., 2012; Sachdeva et al., 2015).The drag force description using the Reynolds number was found to work quite wellfor CMEs analyzed in Subramanian et al. (2012). We believe that this method based on aphysical description of the plasma is a better solution than using either ad hoc or empiricalparameters, which are normally derived using a set of CMEs. As background solar windconditions are dramatically different from case to case, some events may not have theirparticularities represented in the set of events used to define the empirical parameters and,therefore, they may not be appropriately described.Following Sachdeva et al. (2015), we consider the drag force description given by: F drag [ s ] = − m CME γ [ s ] ( v CME [ s ] − v SW [ s ]) | v CME [ s ] − v SW [ s ] | , where v CME is the CME speed and v SW is the background solar wind speed and γ isthe drag parameter. Both speeds are a function of CME position s along the Sun-Earthline. For a CME propagating towards the Earth, s increases as time passes. m CME isthe CME mass taken from the CDAW CME catalog (Yashiro, 2004). If not available, weconsider m CME = 1 . × g , the median value reported on Vourlidas et al. (2010) forCMEs observed between 1996 and 2009.The drag force adopted here, which is proportional to the square of difference betweenthe CME speed and the solar wind speed, is also used in several studies involving obser-vations from STEREO (see, e.g., Sachdeva et al., 2015, 2017; Maloney & Gallagher, 2010;Mishra & Srivastava, 2013; Temmer et al., 2012; Mishra et al., 2014; Salman et al., 2020;Hess & Zhang, 2015).The drag force can also be described as proportional to ( v CME − v SW ) β with β set toone, two or determined empirically. Considering the ToA, Vrnak and Gopalswamy (2002)found smaller errors with β = 1 for events observed by LASCO while Shanmugaraju and –13–anuscript submitted to JGR: Space Physics
Vrˇsnak (2014) found the smaller errors with β = 2 for a set of CMEs observed by STEREO.Byrne et al. (2010) empirically found β = 2 .
27. Shi et al. (2015) found that β = 2 results in abetter CME ToA prediction than the linear one for a set of 21 CMEs observed by STEREO.Shi et al. (2015) also considered a hybrid model that combines both β = 1 and β = 2descriptions and found that the latter has a larger contribution in the ToA determination.Here we adopt the description of the drag based on a physical model of the viscositymechanism, as was done by Subramanian et al. (2012), Sachdeva et al. (2015) and Sachdevaet al. (2017). The drag that is proportional to v CME − v SW is normally used in studies thatare focused on empirical descriptions of the dynamics of the CME based on the observedCME speed profiles. Our objective here is not following an empirical description of the dragmodel and, for this reason, we adopt the description of the drag force proportional to thesquare of the CME speed.Here we consider that γ is given by: γ [ s ] = C D [ s ] n SW [ s ] m P A CME [ s ] m CME where C D is the dimensionless drag coefficient, n SW is the solar wind proton numberdensity, m P is the proton mass, A CME is the CME cross section area (explained in thenext paragraphs) and m CME is the CME mass. Typically γ has values ranging from 1 × − km − to 2 × − km − , see, e.g. Temmer and Nitta (2015) and Vrˇsnak et al. (2013).In several previous studies, C D was empirically determined and considered to be con-stant (see, e.g. Cargill (2004); Vrˇsnak et al. (2010); Mishra and Srivastava (2013); Temmerand Nitta (2015), and references therein). In these studies, C D typically ranges from 0 . .
4. In this study, on the other hand, we determine the value of C D using a set of equationsbased on a physical definition of the CME aerodynamic drag introduced by Subramanianet al. (2012) and previously studied by Sachdeva et al. (2015, 2017). Here we describe C D using the following expression determined experimentally by Achenbach (1972): C D [ s ] = 0 . − . × ( Re [ s ]) − + 9 . × − Re [ s ] .This equation for C D is a fit to data observed on a solid metal sphere immersed ina flow with high Reynolds number Re . We considered that this result is suitable for theinteraction of the CME with the background solar wind because (i) the equation of the dragforce considers a solid-like body immersed on a high-Reynolds number and (ii) typically theboundaries of magnetic clouds (and therefore, CMEs) are over-pressured structures, i.e.,they have a substantial jump in their total pressure (magnetic plus plasma) in the regionclose to their boundaries (Jian et al., 2006).The Reynolds number depends on the macroscopic lengthscale of the CME, its velocityrelative to the background solar wind particles and the viscosity of the solar wind. For moredetails, the reader is referred to Sachdeva et al. (2017).The CME cross section area A CME is calculated as: A CME [ s ] = π × R CME [ s ] × w/ w is the width of the CME (in degrees, as determined by the CME CDAWcatalog) and R CME is the radius of the CME that was taken to be 0 . s . This expression of R CME was experimentally chosen in this study as a good solution to reduce the ToA errorfor the set of CME events studied here among different values of the coefficient lower thanthe unit. –14–anuscript submitted to
JGR: Space Physics
As described in previous section, the solar wind speed v SW at any point along theSun-Earth is required to calculate the drag. Close to 1 au, the solar wind conditions arecontinuously observed by instrumentation at the Lagrangian point L1, such as by the SolarWind Electron, Proton, and Alpha Monitor (SWEPAM) instrument (McComas et al., 1998)onboard Advanced Composition Explorer (ACE) mission (Stone et al., 1998) and by theSolar Wind Electron (SWE) instrument (Ogilvie et al., 1995) onboard Wind spacecraft(King, 2005). In the remaining points of the trajectory, on the other hand, v SW needs tobe calculated using empirical models or simulation.In this study, we use an empirical expression to extrapolate the solar wind speed atany position along the Sun-Earth line using observation at 1 au ( v SW @1 au ). FollowingN. R. Sheeley et al. (1997) and Sheeley et al. (1999), the solar wind speed along the Sun-Earth line ( v sw [ s ]) is considered to be: v SW [ s ] = v SW @1 au [1 − e − ( s − r ) /r a ]where s is a given position along the Sun-Earth line, r = 1 . R (cid:12) is the distance fromthe Sun where the solar wind is taken to be zero and r a = 50 R (cid:12) is the distance over whichthe asymptotic speed is reached. According to this model, the solar wind speed increasesmore significantly close to the Sun, typically up to approximately 100 R (cid:12) , and then it isalmost constant up to 1 au .In this work, we considered that v SW @1 au is the average observed value in the timeperiod from 48 up to 24 hours before the CME is first observed on the LASCO/C2 FOV.We chose this time period taking into account the typical travel time for a solar wind parcelto travel from the solar corona to 1 au. Besides the solar wind speed, the solar wind density along the CME trajectory is alsorequired for calculating the drag force as described in Section 2.6. Again, the observationsare limited to 1 au and the density evolution must be derived via a model. The solar windproton density n SW as a function of position s is given by Leblanc et al. (1998): n SW [ s ] = (cid:0) n SW @1 au . (cid:1) (cid:0) . × s − + 4 . × s − + 8 × s − (cid:1) where n SW @1 au is the solar wind density observed in the L1 Lagrangian Point (closeto 1 au). Here we use the model of electron density from Leblanc et al. (1998) assumingthat the electron and proton densities are equal. The term between parentheses considersthe difference of the density at 1 au from the original value of 7 . cm − used on the model. n SW @1 au was assumed to be the average observation value from 48 up to 24 hours beforethe CME first observation on LASCO C2.In the density equation, s − is the dominant term in the outer corona and inner helio-sphere. We, nevertheless, retain the full expression for completeness. Now we explain and exemplify the application of the drag force to derive the CMEspeeds and profiles as a function of position (Section 3.1). Then, we compare the speeds wederived with previous studies that include some CMEs studied here (Section 3.2) and onecatalog based on observations from HI-1 (Section 3.3). Finally, we show results from theToA and SoA errors in Section 3.4 and 3.5. –15–anuscript submitted to
JGR: Space Physics
To calculate the drag coefficient, we use the last HI-1 observation position for whichthe CME front is visible and the linear speed of the portion of the CME front along theSun-Earth line ( v med , v min , v max ). Some geometric parameters derived using ElCon (suchas the angular width and angle) are not used explicitly in the drag force model, but theyare indirectly taken into account in the derivation of r is at each time-instance.We start the application of the drag model at the last HI-1 observation position ( s ). Insome cases, the brightness of the CME front is similar to that of the background (speciallyin the outer half of the FOV). In these cases, the CME front cannot be resolved. Thus, the s position changes from event to event ( s is indicated in the second column of Table 2).Typically, the last height-time observation ranges between 20 and 80 solar radii.An example of the application of the drag model is shown in Figure 5. In each panel,the horizontal axis shows the distance from the Sun (in solar radii). In the top left panel,the black line denotes the acceleration based on the initial speed v med . Acceleration profilesbased on v min and v max are indicated by the red and blue lines, respectively. The CMEspeed derived using v med as initial speed is shown in the second panel, from top to bottom.The speed of the background solar wind speed ( v sw ) is indicated by the green line. Theremaining lines represent speeds calculated using v min and v max . The background solar windproton density is represented on the third panel, from top to bottom. Other parametersshown are the drag coefficient (fourth panel, from top to bottom), the Reynolds number(fifth panel) and the viscosity (lower panel).For all analyzed events, C D has a decreasing profile from the Sun to 1 au, typicallywith steeper slope close to the Sun, as shown in Figure 5. The variations for the differentcases arise from differences between the CME and background solar wind speed and density,and the CME area and mass. Close to the Sun, C D ranges from 0 .
36 to 0 .
19 while at L1its values ranges from 0 .
16 to 0 .
28. Values of C D in any position mentioned above lie in thesame range than previous studies that adopted a single drag coefficient for a set of events,which have values typically chosen between 0 . . n sw ) decreases (from values typically around50 cm − to 5 cm − and/or (ii) the Reynolds number ( Re ) decreases thus reducing the dragcoefficient C D .All 14 CMEs in our sample decelerate since all have v CME > v SW . The decelerationrate is higher close to the Sun (values up to 3 . m/s ) and decreases as the CME propagatestoward 1 au . We now compare the speeds we derived here with past works. Several CMEs in ourlist were analyzed elsewhere (M¨ostl et al., 2014; Rollett et al., 2016; Barnard et al., 2017;Colaninno et al., 2013; Wood et al., 2017). However, most of these studies consideredcoronagraph observations alone or coronagraph observations combined with heliosphericimages. Thus, the speed derived by them is typically at an earlier stage of the CMEpropagation than done here. Only Rollett et al. (2016) used observations exclusively fromheliospheric imagers.Table 3 compares the speed measurements across the various studies. The first columnrefers to the event number in this manuscript (Tables 1 and 2). The second column liststhe reference and event ID in that reference. The references for each event vary since eachstudy used its own criteria for CME selection. The speeds are listed in the third column –16–anuscript submitted to
JGR: Space Physics
Figure 5.
The application of the drag force to a sample CME that is decelerated from thesolar corona to 1 au. In the panels with multiple lines, the black ones indicate the CME kinematicparameters calculated using v med and the red and blue lines indicate CME parameters calculatedusing v min and v max , respectively. The green line on the second panel (from top to bottom)indicates the background solar wind speed. –17–anuscript submitted to JGR: Space Physics and the fourth column contains some remarks about the particularities of the speed derivedin each case.M¨ostl et al. (2014) has 8 CMEs in common with our study. They use the averagespeed between 2 . . R ◦ based on Graduated Cylindrical Shell (GCS) model fits(A. F. Thernisien & Howard, 2006; A. Thernisien et al., 2009; A. Thernisien, 2011). Thederived speeds are not necessarily on the ecliptic plane, which is where our speeds arederived. Another difference is that we track the CMEs in the HI-1 FOV while M¨ostl et al.(2014) considers only the coronagraph FOV. We see that fast CMEs have higher speeds inM¨ostl et al. (2014). This is not surprising since their speeds are derived lower in the coronaand CMEs tend to decelerate away from the Sun (see the review from Manchester et al.,2017, and references therein). So, the speed differences between the two works likely reflectdeceleration rather than any measurement discrepancies.Sachdeva et al. (2017) also derived the CME kinematics with the GCS fitting techniquebut using observations from both the coronagraphs (including LASCO) and heliosphericimagers. Although we are using the same events, we derive the CME initial speed froma third-degree polynomial fit to the height-time observations of the CME leading edge.Another difference is that the CME speed derived on Sachdeva et al. (2017) is not necessarilyon the ecliptic plane; in some cases the GCS model can be more than 30 ◦ away in Carringtonlatitude. We identified a significant difference in the speeds for events km/s or less, considering the typical difference between CMEspeed derived by different methods (see, e.g., Mierla et al., 2010). In the other 4 cases, ourspeeds are significantly lower than those obtained by Sachdeva et al. (2017). The differencemay be due to the height where those speeds refer to. Sachdeva et al. (2017) derives theinitial speed at less 10 R ◦ (see remarks in the third column of Table 3) while our speeds arethe average speeds in the HI-1 FOV only, typically up to 40 − R ◦ . CMEs with speedsexceeding 1000 km/s (as is the case for events φ method to derive some parameters of the ElCon model, such asdirection of propagation. Another difference is that their speeds are derived at positionscloser to the Sun than ours. Many speeds from Rollett et al. (2016) mentioned in Table3 are derived doing a fit of the drag-based model to the initial point in the trajectory ofthe CME studied. In some events, this point is below 10 R ◦ . This difference can partiallyexplain why the speeds derived by Rollett et al. (2016) are higher than ours for the fastestCMEs.Barnard et al. (2017) estimated the speed of CME R ◦ in thisparticular case). However, the difference in the two speeds is only 6 km/s .Gopalswamy et al. (2013) measured the speeds on the STEREO/COR2 coronagraph(i.e., up to about 15 R (cid:12) ) in the ecliptic plane. Therefore, speeds from this reference arelocated much closer to the Sun than our speeds. Gopalswamy et al. (2013) consider theirspeeds to be unprojected because they were measured when the STEREO spacecraft positionwere within 30 ◦ from quadrature. In each event, they selected the STEREO spacecraft(Table 3) with CME observations closer to the limb. We have 4 common CMEs ( km/s ) than in Gopalswamy et al. (2013). We believe that the same explanation holds forthese discrepancies; namely, the faster CME decelerate as they travel away from the Sun. –18–anuscript submitted to JGR: Space Physics
To summarize, the speed comparisons with our method suggest that the height wherespeeds are measured plays a very big role, particularly for faster CMEs. Our speeds arelower than the works in Table 3 because we measure the CME kinematics at a later stagein their propagation, when they have undergone deceleration.
The HELCATS Heliospheric Imager Geometrical Catalogue (HIGeoCAT) (Barnes etal., 2019) reports speeds derived from STEREO/HI observations without considering obser-vations from coronagraphs. Since this catalog covers most events studied here, we compareits results with those derived here.As introduced in Section 1, the reported speeds in the HIGeoCAT catalog are derivedusing three single-spacecraft geometric models, namely f- φ , HM, and SEEF. By comparingthe timing of each event in HIGeoCAT with our height-time points, we identify the HIGeo-CAT event that corresponds to our event. This was done for both viewpoints (STEREO-Aand STEREO-B). We did not find any CME in HIGeoCAT STEREO-A event list corre-sponding to our event v med (mentioned in Table 2). Given the 3 fits and the two viewpoints available, eachCME speed derived here can be compared to 6 different speeds from HIGeoCAT. Theseresults are all summarized in Table 4.Significant agreement between HIGeoCAT reported speeds and ours is not expected.First, HIGeoCAT speeds are calculated using both HI-1 and HI-2 observations while we onlyuse HI-1. This catalog reports linear speeds derived over both heliospheric imagers FOVsand CMEs can be accelerated or decelerated while within HI-2 FOV. Second, we derive theCME speed in the ecliptic plane while the HIGeoCAT speeds are not necessarily measuredin the ecliptic plane; the speeds are derived at the position angle of the CME apex. Forexample, for the event ◦ above the ecliptic. Third,the HIGeoCAT speeds are calculated independently for each viewpoint while our speeds areobtained considering both. (Although HIGeoCAT does associate the observations of eachevent from both STEREO viewpoints, there is no reported speed obtained considering thecombined dual-viewpoint.)As a result of using the viewpoints independently from one another, the reported speedvalues are different for any given event (see Table 4). For example, the speeds reportedfor event ±
24 km/s from STEREO-A and1368 ± km/s from STEREO-B. Among the 13 events compared here, the median absolutedifference between the speeds derived using HM for the two STEREO viewpoints is 140 km/s with standard deviation of 256 km/s . The differences are similar for the derived speedsbased on f- φ and SSEF. The median absolute difference between v med and the speed derivedusing f- φ on STEREO-A (STEREO-B) is 53 ± km/s (68 ± km/s ). Comparing theresults derived using f- φ with observations from STEREO-A and those from STEREO-B, the median absolute difference found is 96 ± km/s . We understand that thesedifferences are acceptable considering the several differences between the assumptions behindour methodology and those from the f- φ method.Some events, though, exhibit much larger differences depending on the methodologyused, both between the different fittings used on HIGeoCAT and between our speeds andthe HIGeoCAT speeds. This is the case for events km/s . For the remaining events, the differences are mostly below 100 km/s .The reason for this large difference is not obvious and needs to be investigated. –19–anuscript submitted to JGR: Space Physics
Table 3.
Comparison of speeds derived for CMEs studied here with previous studies.
CME km/s up to 47 R ◦ M¨ostl et al. (2014), km/s initial speedRollett et al. (2016), km/s . R ◦ , f = 1Wood et al. (2017), km/s peak speedWood et al. (2017), km/s terminal speedSachdeva et al. (2017), km/s . R ◦ km/s up to 60 R ◦ M¨ostl et al. (2014), km/s initial speedRollett et al. (2016), km/s . R ◦ f = 1Sachdeva et al. (2017), km/s . R ◦ km/s up to 56 R ◦ M¨ostl et al. (2014), km/s initial speedRollett et al. (2016), km/s . R ◦ f = 1Wood et al. (2017), km/s peak speedWood et al. (2017), km/s terminal speedGopalswamy et al. (2013), km/s COR2, STEREO ASachdeva et al. (2017), km/s . R ◦
11 this study 448 km/s up to 43 R ◦ Wood et al. (2017), km/s peak speedWood et al. (2017), km/s terminal speedSachdeva et al. (2017), km/s . R ◦
13 this study 769 km/s up to 60 R ◦ Wood et al. (2017), km/s peak speedWood et al. (2017), km/s terminal speedSachdeva et al. (2017), km/s . R ◦
17 this study 605 km/s up to 30 R ◦ Wood et al. (2017), km/s peak speedWood et al. (2017), km/s terminal speedGopalswamy et al. (2013), km/s
COR2, STEREO BSachdeva et al. (2017), km/s . R ◦
25 this study 446 km/s up to 54 R ◦ M¨ostl et al. (2014), km/s initial speedRollett et al. (2016), km/s . R ◦ f = 1Sachdeva et al. (2017), km/s initial speed at 23 . R ◦
26 this study 741 km/s up to 58 R ◦ M¨ostl et al. (2014), km/s initial speedRollett et al. (2016), km/s . R ◦ f = 1Wood et al. (2017), km/s peak speedWood et al. (2017), km/s terminal speedGopalswamy et al. (2013), km/s COR2, STEREO BSachdeva et al. (2017) , km/s initial speed at 6 . R ◦
27 this study 743 km/s up to 67 R ◦ M¨ostl et al. (2014), km/s initial speedM¨ostl et al. (2014), km/s . R ◦ f = 1Gopalswamy et al. (2013), km/s COR2, STEREO BSachdeva et al. (2017), km/s initial speed at 4 . R ◦
28 this study 740 km/s up to 39 R ◦ Sachdeva et al. (2017), km/s initial speed at 6 . R ◦
29 this study 692 km/s up to 77 R ◦ Barnard et al. (2017), km/s
Sachdeva et al. (2017), km/s initial speed at 31 . R ◦
30 this study 431 km/s up to 45 R ◦ Sachdeva et al. (2017), km/s initial speed at 36 . R ◦
33 this study 765 km/s R ◦ Sachdeva et al. (2017), km/s initial speed at 5 . R ◦
34 this study 764 km/s R ◦ Sachdeva et al. (2017), km/s initial speed at 5 . R ◦ –20–anuscript submitted to JGR: Space Physics T a b l e . C o m p a r i s o n o f s p ee d s ( k m / s ) c a l c u l a t e d i n t h i ss t ud y ( v m e d s e c o nd c o l u m n ) w i t h H E L C A T s ( r d t o7 t h c o l u m n s , f r o m l e f tt o r i g h t) . “ A ”o r “ B ” b e f o r e t h e a c r o n y m o f e a c h m e t h o d t h e v i e w p o i n t u s e d ( S T E R E O - A o r S T E R E O - B , r e s p e c t i v e l y ) . T h e t h i r d c o l u m n , f r o m r i g h tt o l e f t ,i nd i c a t e s t h e d i ff e r e n c e b e t w ee n SS E F d e r i v e du s i n g S T E R E O - A a ndSS E F d e r i v e du s i n g S T E R E O - B . T h e r e m a i n i n g t w o c o l u m n s i nd i c a t e t h e d i ff e r e n c e b e t w ee nSS E F a nd v m e d . v m e d A f - φ A SS E F AH M B f - φ B SS E F B H M A SS E F - B SS E F A SS E F - v m e d B SS E F - v m e d ± ± ± ± ± ± - ± ± ± ± ± ± - ± ± ± ± ± ± - - ± ± ± ± ± ± - -
14 13769805 ± ± ± ± ± ± ± ± ± ± ± ± -
42 25446 --- ± ± ± --- ± ± ± ± ± ± - ± ± ± . ± ± ± ± ± ± ± ± ± -
12 29692620 ± ± ± ± ± ± - ± ± ± ± ± ± - - ± ± ± ± ± ± - ± ± ± ± ± ± - - –21–anuscript submitted to JGR: Space Physics
Figure 6.
The calculated and observed travel time (from the last observation on HI-1 FOV untilL1). The labels correspond to the CME IDs in Table 1. The line indicates the points where themodel and observed travel times are identical, i.e., the ToA error is zero ( δt = 0). In this section we compare the CME travel time from its last HI-1 observation point s up to 1 au calculated using the ElCon model and the aerodynamic drag model ( tt calc )with the actual travel time ( tt obse ). The latter is the time difference between the first ICMEobservation and the last CME observation at s . The results are shown in Figure 6.The instant of the CME arrival at Earth is clearly identified from in situ observations forall events studied here. All events are preceded by a clear discontinuity in the magnetic fieldand solar wind parameters (solar wind speed, density and temperature). For this reason,it is unlikely that the CME ToA errors found here are due to ambiguous determination ofICME arrival time. Since tt obse is not expected to be a source of errors, we focus this studyon sources of errors associated to tt calc . –22–anuscript submitted to JGR: Space Physics
For the 14 CME-ICMEs pairs studied here, the ToA error mean value is 1 . ± . . ± . tt calc and t obs is 0 . γ ratherthan from the model we adopted here); only one study adopted the ElCon model (althoughwithout using simultaneous observations from STEREO). The low MAE is probably notsurprising given our small sample size (only 14 CMEs). It does cover about a third of thetotal possible sample (see Section 2.1), over 4 out of the 8 years of STEREO-B, and over therise to solar maximum. Other studies using drag-based model included up to 34 events andother references about empirical methods have more than 200 CMEs in their sample. Themain reasons for the small data set are our rather strong selection criteria. As mentionedin Section 2.1, we require simultaneous observations from both HI-1s, events well-separatedin time/space and reliable CME-ICME identifications.The relatively low ToA error found here suggests that events observed in close timingwith others, which were discarded by our criteria, will likely increase ToA errors. The criteriaadopted here limit the use of this methodology on routine space weather applications thatthat can not perform event selection and need to measure all CMEs. Carefully selected andinvestigated event samples can help isolate physical effects during CME propagation fromanalysis errors (e.g. front identification) and hence help improve our physical understandingof these events and eventually space weather forecasting.Our results, along with the Colaninno et al. (2013) and Rollett et al. (2016) results,suggest that the estimation of the ToA using HI-1 measurements could result in a moreaccurate estimation (i.e., smaller error) than in those cases based on coronagraph observa-tions, at least for fast CME events. This conclusion is based on studies with a rather smalllist of event and is therefore subject to verification with more extensive data sets. In ad-dition, many of the methods rely on coronagraph measurements of CME width, mass, andother properties. Hence, it is more likely that approaches built upon as extensive height-timemeasurements as possible, will be more fruitful in reducing the errors of the ToA estimation. Here, we compare the CME SoA at 1 au derived from our drag-based model with thecorresponding in situ observed ICME speed ( v ICME ).The in situ ICME speed, v ICME , is derived here as the average proton speed observed insitu during the sheath period, not during the whole time period comprised by the passageof the ICME. The use of this time period is motivated by the higher proton density ofthe sheath feature (this density is a common physical parameter to both the in situ andimaging instruments). After the sheath, a region with lower density and smooth magneticfield (the magnetic cloud) is observed, which does not correspond to the front we identify onHI-1 observations. Heliospheric imagers identify the compression region (sheath) developedaround the ejecta, and not necessarily the magnetic cloud. The in situ data used here comesfrom the OMNI database and consists of merged observations from the ACE and the Windspacecraft (King, 2005).In this study, we calculated the SoA using 3 different initial speeds in the drag modelfor each CME ( v med , v min and v max ). The SoA derived are labelled v final , v − final and v + final , respectively (Table 5). The difference between v med , v min and v max comes from themultiple visual CME identification in the J-map . Due to the subjective CME identification,every visual inspection led to slightly different elongation-time profile since the specific pointidentified changes (see details in Section 2.3). We found that | v max − v min | is < km s − for all events, except for km s − ). The mean value of v + final − v − final is 27 km s − . –23–anuscript submitted to JGR: Space Physics T a b l e . C a l c u l a t e d a nd o b s e r v e d C M E t r a v e l t i m e a nd s p ee db e t w ee n e nd H I - F O V a nd L . I D fi r s t o b s e r v a t i o n l a s tt r a c k i n g A rr i v a l a t a u tt c a l c tt o b s e δ t v i n i t v f i n a l v + f i n a l v − f i n a l v I C M E v S W @ a u n S W @ a u ( U T )( U T )( U T ) [ h ][ h ][ h ][ k m / s ][ k m / s ][ k m / s ][ k m / s ][ k m / s ][ k m / s ][ c m − ] - A p r - : : - A p r - : : - A p r - : : - A p r - : : - A p r - : : - A p r - : : - F e b - : : - F e b - : : - F e b - : : - M a r - : : - M a r - : : - M a r - : : - - J un - : : - J un - : : - J un - : : - - S e p - : : - S e p - : : - S e p - : : - - A p r - : : - A p r - : : - A p r - : : - J un - : : - J un - : : - J un - : : - J u l - : : - J u l - : : - J u l - : : - S e p - : : - S e p - : : - S e p - : : - - O c t - : : - O c t - : : - O c t - : : - - O c t - : : - O c t - : : - O c t - : : - M a r - : : - M a r - : : - M a r - : : - A p r - : : - A p r - : : - A p r - : : - –24–anuscript submitted to JGR: Space Physics
Compared to the typical CME speed error of ≈ km s − found by Mierla et al. (2010)when comparing several methodologies with observations from SECCHI coronagraphs, theSoA uncertainty caused by multiple visual CME identification on J-maps is quite low.This result suggests that the difference in the visual selection of features on a J-map(which is responsible for the difference in the initial speed used on the drag model) leadto a minor differences in the SoA. An example of CME speeds as a function of positioncalculated using both v min and v max is shown in Figure 5 (second panel, from top). Theyare represented by the blue and red lines, respectively. In this example the difference between v − final and v + final is 31 km s − .The distribution of v final versus v ICME is shown in Figure 7. The error bars shownin the plot are defined by v + final and v − final . The CME SoA error ( δv = v final − v ICME )is 114 ± km s − and the SoA MAE is 117 ± km s − . It is clear that our SoA arehigher than the observed ICME speeds. The Pearson correlation coefficient between v final and v ICME is 0 .
53, lower than the correlation found comparing observed and calculatedtravel times (0 . v + final and v − final . Thisindicates that the error in the initial CME speed, estimated via multiple visual identificationson the J-maps, cannot explain the majority of the SoA error. We offer a few plausibleadditional sources of error below: • an error in the initial CME speed ( v init ) due to the ElCon model and its assumptions,such as linear speed and fixed direction of propagation. The goodness of the fit σ (Table 2) is quite low for most events ( < . au ), σ being higher for event σ or parameters from theelliptical model such as half-width λ nor aspect ratio f . However, we do not haveestimates of ElCon model contribution on the SoA error; • the v ICME does not correspond to the CME front speed precisely. This could happensbecause v ICME is measured in situ from observations of the solar wind particlesaround the observing spacecraft. It is widely known from in situ observations that thisspeed is highly variable over time and position, even within periods and dimensionsthat are typically associated to ICMEs (see, e.g., Richardson & Cane, 2010). On theother hand, v final is a parameter that describes the CME front as a whole, which hasspatial dimensions that are orders of magnitude larger than the region observed insitu by a spacecraft; • an incomplete or incorrect description of the forces that affect the CME propagationfrom s to 1 au . This can impact the CME dynamics in all along its propagationfrom the Sun to the Earth.The SoA MAE was compared with results from 5 other studies, as shown in Table 1 ofVourlidas et al. (2019). Our results are similar except the much smaller SoA in Rollett etal. (2016) (16 ± km s − ).We identified that 5 events studied here ( | δv | = | v final − v ICME | ) higher than 198 km s − while the remaining arelower than 95 km s − (this can be seen clearly in Figure 7). We tried to identify anytrend between the | δv | and input parameters used in the drag model, particularly those thatchange between events. We could not find, though, any trend between | δv | and CME mass,width, background solar wind speed in the corona and 1 au nor solar wind density at 1 au.One common point among events with higher | δv | is that the CME initial speed isbetween ∼ km s − and ∼ km s − . The opposite is not true, however. Some CMEswith initial speed in the same range have | δv | among the lowest values ( < km s − ). Thisresult suggests that the CME propagation modeling used here (ElCon and our drag forcedescription) do not lead to higher SoA error for any particular range of CME initial speeds. –25–anuscript submitted to JGR: Space Physics
Figure 7.
The CME speed calculated at 1 au using the drag model ( v final ) compared to the insitu ICME speed ( v ICME ). The labels correspond to the CME IDs in Table 1. The line representsthe region with δv = 0, i.e., the position a given event would be located if it had null SoA error.–26–anuscript submitted to JGR: Space Physics
In this Section, we focus on the ToA and SoA errors and their possible sources. Namely,we examine the influence of the background solar wind conditions (Section 4.1), the dragmodel assumptions (Section 4.2), and the effects of extending tracking further into theheliosphere (Section 4.4). We also investigate the ToA error when we completely remove thedrag force and consider a CME propagating with constant speed up to the Earth (Section4.3). Our findings are summarized in Table 6. The first column indicates, shortly, thepossible sources of error. Details about each case are explained in Sections 3.5 to 4.4. Thesecond column indicates the variable associated to the corresponding error source. In somecases, we compare the variable with the SoA and ToA to evaluate any correlation betweenthem. The last column (right) states whether the corresponding plausible sources of errorare likely to result in SoA and ToA errors comparable to those found in our work.
Now we examine the effects of the background solar wind conditions, such as protondensity or speed, on the drag model and by extension on ToA and SoA.The drag force depends on the difference between CME and background solar windspeed. Our events occur over a diverse range of 1 au solar wind speeds, v sw @1 au , as listedin the second column of Table 5, from right to left. Since v sw @1 au is used to extrapolate thesolar wind speed to s , it affects the drag force used in the model.For all our events, v sw is lower than v CME at the first height of application of the dragforce ( s ) and, as a result, the drag force produces deceleration. In 11 of the 14 events v sw @1 au was lower than 500 km/s . The highest value of v sw @1 au was observed in CME km/s . In some events (such as v sw @1 au = 279 km/s . We do not find any trend between v sw @1 au and ToA or SoA errors.This can be due to either the drag force description we use is insensitive to background solarwind speed or the δt and δv originate from sources other than the drag force, such as errorsin the determination of initial CME speed, direction of propagation or position.Another solar wind parameter of the drag model is the background solar wind densityat 1 au , which is used in the drag force calculation to estimate the solar wind density alongthe CME path. For only two events ( n SW @1 au = 5 cm − ). Again, wefind no trend between the background solar wind density and δt or δv . This result suggeststhat the drag model estimates are insensitive to the details of the background solar winddensity, at least, for the range of values used here.However, we note that the background solar wind density and speeds considered hereare just model-based values. The actual heliospheric conditions may be very different due,for example, to the existence of transients such as, other CMEs or stream interaction regions(SIRs). Although we tried to exclude periods with multiple CMEs in the HI-1 FOV (seeSection 2.1), we did not check for the existence of upstream CMEs or SIRs.In particular, we notice that at least one of the events studied here ( δt = − h found for this event. The CME speed variation (∆ v = v final − v init ) in the entire range we applied the dragforce (from s up to 1 au ) is > km s − for event v > km s − for thefollowing events: < ∆ v < km s − . –27–anuscript submitted to JGR: Space Physics T a b l e . Su mm a r y p a r a m e t e r s u s e d o n t h e d r ag f o r c ee s t i m a t i o n a nd t h e i r e x p e c t e d c o n t r i bu t i o n o n T o A a ndS o A e rr o r s . P o ss i b l e s o u r ce o f e rr o r V a r i a b l e C o rr e l a t i o n w i t h S o A a nd T o A e rr o r s M ag n i t ud e l a r g ee n o u g h t o e x p l a i nS o A a nd T o A e rr o r s f o undh e r e Sp ee d e rr o r du e t o v i s u a l C M E i d e n t i fi c a t i o n o n J - m a p s | ( v m a x − v m i n ) | N o N o R e s i du e o f t h ee lli p t i c a l f r o n t d e t e r m i n a t i o n σ N o U n k n o w n B a c k g r o und s o l a r w i ndd e n s i t y a t a u n S W @ A U N o N o B a c k g r o und s o l a r w i nd s p ee d a t a u v S W @ A U N o N o P o s i t i o n o f l a s t C M E o b s e r v a t i o n o n H I - F O V s T o A ( l o w ) U n k n o w n C M E c r o sss ec t i o n a r e a A C M E N o Y e s C M E m a ss m C M E N o Y e s I n c o m p l e t e o r i n c o rr ec t f o r ce d e s c r i p t i o n a U n k n o w n U n k n o w n –28–anuscript submitted to JGR: Space Physics
Since the typical error of CME speed in coronagraph observations is around 100 km s − (Mierla et al., 2010), we conclude that the contribution of drag on the SoA is small andwithin the error range of the CME speed observations, at least for the events considered here.Our results agree with Sachdeva et al. (2015) who found that the drag force is minimumat distances above 15-50 solar radii for slow CMEs since they propagate almost at constantspeeds after that range.A second point is that all events with ∆ v > km s − have v init > km s − but some events with v init > km s − ( , v < km s − .This result illustrates that although the drag force absolute value is frequently higher forhigh-speed CMEs, factors other than the CME initial speed strongly affect some events. To assess the effect of drag in the estimation of the ToA, we repeated the ToA calculationwithout the drag force. This corresponds to a very simplified model consisting of a CMEpropagating from s to 1 au with constant speed, which equals v init .The ToA mean error considering no drag force is − . ± . h and ToA mean absoluteerror is 6 . ± . h . Comparing these values to the results found using the drag force, we cansee that they are identical within the error range. Therefore, the contribution of the dragforce is at most at the same level of magnitude than other unknown reasons that drive theToA error. As discussed in Section 4.2, results from previous studies using the same dragforce model suggest that the effect of this force is not very significant at the heliocentricdistances range where s typically lies.This does not mean that drag is negligible for CME propagation studies. The dragforce is likely stronger closer to the Sun than at the locations studied here ( s ) because thesolar wind speed is lower and, at least for fast CMEs, the CME speed is higher. The drag model does not start at the same position for all 14 events. Each CME istracked until s , which is the last point where it is clearly observed in HI-1 FOV. Then,drag is applied from this point up to 1 au , as explained in Section 2.4. CMEs with lower s have their speed, direction of propagation and morphological parameters (such as angularwidth in the ecliptic plane and elliptical aspect ratio) derived closer to the Sun.Within our limited 14-event sample, there is no correlation between the SoA absoluteerror | δv | = | v final − v ICME | and s (the Pearson correlation coefficient is 0 . s exhibit, however, a tendency toward higher absolute ToA errors | δt | (in thiscase the correlation coefficient is 0 . s , beyond that point we use ElCon toderive the CME parameters. Beyond s , a free parameter for acceleration is included butthe direction propagation is still assumed to be constant.The last consideration to explain the trend observed for higher | δt | is also pointed outon Barnard et al. (2017). The authors observed unrealistic acceleration in regions close tothe outer side of the HI-1 FOV, mainly after typical values of s . The same study also foundunrealistic accelerations when other methods with constraints in the direction of propagationwere used, such as harmonic mean and self-similar expansion. In this way, the results from –29–anuscript submitted to JGR: Space Physics
Barnard et al. (2017) seem to support hypothesis (ii) as the explanation for a tendencytoward a higher | δt | for the events studied here with higher s . From an initial list of 38 Earth-directed CMEs in 2010-2013 compiled by Sachdeva et al.(2017), we selected 14 events by applying three rather strict criteria: simultaneous observa-tions from both STERO/HI-1 instruments, a clear CME-ICME counterpart identification,and events separated in time to avoid CME-CME interactions. Our objective was to min-imize as much as possible the source of errors in the measurements of the CME kinematicparameters and ToA. The arrival time of all 14 events could be unambiguously determinedfrom in-situ observation thanks to a discontinuity clearly observed in both magnetic fieldand solar wind plasma parameters.We extracted the kinematics of the events using observations from HI-1, modeled theirfront using ElCon, and extrapolated both their time-of- and their speed-on- arrival using adrag force model. The modeled CME speed at 1 au was typically higher than the observedICME speed. This was the case for all events analyzed but one ( km/s for 5 events ( km/s for the remaining 8 events. This suggests that either the actual initial CME speed was lowerthan what our measurements suggested or that the deceleration magnitude calculated usingthe drag-based model studied here was lower than the actual one. The latter seems to be amore likely explanation since excess SoA is a common result in many studies (Vourlidas etal., 2019).The resulting ToA absolute errors are below 12 hours when considering all 14 events.Our MAE compares favorably against past studies and is encouraging regarding our ap-proach. However, the results are based on a small number of events and the methodologymay not necessarily lead to lower ToA when applied to more CMEs. We plan to pursue thisfurther by addressing the various issues we identified below.Sources of ToA and SoA errors can arise in drag force calculation or in the presence ofother unaccounted for forces, such as the Lorentz force. Another source of error may be theassumption of the elliptical conversion model used for the determination of the CME radialposition from its elongation, such as fixed direction of propagation and constant speed.Finally, errors on the front identification arise towards the outer FOV of HI-1 as the CMEfront becomes fainter.The drag force calculation at any point in the CME trajectory depends on the ambi-ent solar wind density and speed. These conditions can change significantly during CMEpropagation and unfortunately in-situ observations were available only close to the Earthfor the CMEs under study. In this study, both solar wind density and speed were extrap-olated using empirical expressions. For this reason, the drag force should be understoodas an approximation rather than a precise calculation. More realistic solar wind conditionsderived using simulation are out of the scope of the present manuscript and could be partof a future study.The amplitude of the drag force is stronger close to the Sun when compared to condi-tions close to the Earth. The reason is twofold: (i) the difference between the solar windand the CME speeds and (ii) the density profile of the solar wind, which is higher close tothe Sun (typically by one order of magnitude at 50 solar radii when compared to L1).Deceleration was observed in all 14 events since all had initial speeds higher than thesolar wind speed at the starting point of the drag force application. This deceleration ismore intense close to the Sun, where the background solar wind speed is also lower. Thedeceleration reaches values up to − . m s − close to the Sun and − . m s − close to theEarth. –30–anuscript submitted to JGR: Space Physics
Despite the difficulties to track CMEs in the HI-1 FOV due to the presence of theF-corona and reduced CME brightness, the results suggest that the ToA error is similar tomany studies based on coronagraph observations, at least for the events discussed here.The recently (2018) launched Parker Solar Probe (PSP) Mission (Fox et al., 2015) hasan imager instrument with comparable elongation range to the HI-1 used. This imager is theWide-field Imager for Solar PRobe (WISPR) (Vourlidas et al., 2016). Similar observationswill also be performed by the Solar Orbiter Heliospheric Imager (SoloHI) (R. A. Howard etal., 2019), onboard the upcoming Solar Orbiter (SO) mission (M¨uller et al., 2013). In thissense, the present study, which relies mostly on observations from heliospheric imagers (usingonly masses and width derived from coronagraph observations), can be used as a guidelinefor future studies with the PSP and SO targeted on CME ToA or SoA estimations. Wehope the results of CME ToA errors estimated could motivate future studies with similarobjectives using observations from WISPR and SoloHI.
Acknowledgments
C.R.B. acknowledges grants .The SOHO LASCO CME catalog is generated and maintained at the CDAW DataCenter by NASA and The Catholic University of America in cooperation with the Naval Re-search Laboratory. This catalog is available at https://cdaw.gsfc.nasa.gov/CME list/ .The Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) was pro-duced by an international consortium of the Naval Research Laboratory (USA), LockheedMartin Solar nd Astrophysics Lab (USA), NASA Goddard Space Flight Center (USA),Rutherford Appleton Laboratory (UK), University of Birmingham (UK), Max Planck In-stitute for Solar System Research (Germany), Centre Spatiale de Lige (Belgium), InstitutdOptique Theorique et Applique (France), and Institut d’Astrophysique Spatiale (France).STEREO data are available for download at https://secchi.nrl.navy.mil/ .This research has made use of the Solar Wind Experiment (SWE) and Magnetic FieldInvestigations (MFI) instrument’s data onboard WIND. We thank to the Wind team andthe NASA/GSFC’s Space Physics Data Facility’s CDAWeb service to make the data avail-able. Wind data are available from https://cdaweb.sci.gsfc.nasa.gov . The ICMElist compiled from WIND mission observations can be found at https://wind.nasa.gov/ICMEindex.php . The OMNI data were obtained from the GSFC/SPDF OMNIWeb interfaceat https://omniweb.gsfc.nasa.gov . –31–anuscript submitted to JGR: Space Physics
The HELCATS catalogs are available from the HELCATS website ( ), HIGeoCat ( https://doi.org/10.6084/m9.figshare.5803176.v1 ) and HIJoin-Cat ( ).The codes and script created to perform this study are available in the following repos-itory: https://doi.org/10.7910/DVN/J7SYTO . References
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