Evaluation of CME Arrival Prediction Using Ensemble Modeling Based on Heliospheric Imaging Observations
Tanja Amerstorfer, Jürgen Hinterreiter, Martin A. Reiss, Christian Möstl, Jackie A. Davies, Rachel L. Bailey, Andreas J. Weiss, Mateja Dumbović, Maike Bauer, Ute V. Amerstorfer, Richard A. Harrison
mmanuscript submitted to
Space Weather
CME arrival prediction using ensemble modeling basedon heliospheric imaging observations
Tanja Amerstorfer , J¨urgen Hinterreiter , , Martin A. Reiss , , ChristianM¨ostl , , Jackie A. Davies , Rachel L. Bailey , , Andreas J. Weiss , , , MatejaDumbovi´c , Maike Bauer , , Ute V. Amerstorfer , Richard A. Harrison Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 26, 8042 Graz, Austria Institute of Physics, University of Graz, Universit¨atsplatz 5/II, 8010 Graz, Austria Institute of Geodesy, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria RAL Space, Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, UK Conrad Observatory, Zentralanstalt f¨ur Meteorologie und Geodynamik, Vienna, Austria Hvar Observatory, Faculty of Geodesy, University of Zagreb, Zagreb, Croatia
Key Points: • CME prediction tool ELEvoHI is ready to be used in real time, based onSTEREO-A/HI beacon data • Different model set-ups and inputs lead to large differences of the predictionaccuracies • Accurate modeling of the ambient solar wind is of particular importance toimprove CME predictions
Corresponding author: Tanja Amerstorfer, [email protected] –1– a r X i v : . [ phy s i c s . s p ace - ph ] A ug anuscript submitted to Space Weather
Abstract
In this study, we evaluate a coronal mass ejection (CME) arrival prediction tool thatutilizes the wide-angle observations made by STEREO’s heliospheric imagers (HI). Theunsurpassable advantage of these imagers is the possibility to observe the evolutionand propagation of a CME from close to the Sun out to 1 AU and beyond. We believethat by exploiting this capability, instead of relying on coronagraph observations only,it is possible to improve today’s CME arrival time predictions. The ELlipse Evolutionmodel based on HI observations (ELEvoHI) assumes that the CME frontal shapewithin the ecliptic plane is an ellipse, and allows the CME to adjust to the ambient solarwind speed, i.e. it is drag-based. ELEvoHI is used to perform ensemble simulations byvarying the CME frontal shape within given boundary conditions that are consistentwith the observations made by HI. In this work, we evaluate different set-ups of themodel by performing hindcasts for 15 well-defined isolated CMEs that occurred whenSTEREO was near L4/5, between the end of 2008 and the beginning of 2011. In thisway, we find a mean absolute error of between 6 . ± . . ±
13 h depending onthe model set-up used. ELEvoHI is specified for using data from future space weathermissions carrying HIs located at L5 or L1. It can also be used with near real-timeSTEREO-A HI beacon data to provide CME arrival predictions during the next ∼ As the main drivers of space weather events, coronal mass ejections (CMEs)are one of the most important subjects to be investigated as part of current solar-terrestrial research. CMEs are impulsive outbursts of the solar corona, consisting ofa magnetic flux rope that impounds coronal material and solar wind particles duringits propagation through the interplanetary medium. Fast CMEs can reach speeds ofup to 3000 km s − and, depending on their speeds and the characteristics of theirintrinsic magnetic fields, can cause, for example, severe issues for satellites and disrup-tive geomagnetic disturbances at Earth (Farrugia et al., 2006; Gopalswamy, Akiyama,Yashiro, Michalek, & Lepping, 2008; Huttunen, Schwenn, Bothmer, & Koskinen, 2005;Tsurutani, Gonzalez, Tang, Akasofu, & Smith, 1988; Wilson, 1987). One of the mostdifficult CME properties to predict is the orientation of the magnetic field inside theCME, which is, at the same time, the most critical parameter due to the fact that alarge southward magnetic field component facilitates the strongest geomagnetic storms.A large number of studies are currently tackling this task by developing new modelsthat try to predict the orientation of the magnetic field at 1 AU (e.g. Kay, Gopal-swamy, Reinard, & Opher, 2017; Kubicka et al., 2016; M¨ostl et al., 2018; Palmerioet al., 2017; Savani et al., 2015; Shiota & Kataoka, 2016; Singh, Yalim, Pogorelov, &Gopalswamy, 2020; Verbeke, Pomoell, & Poedts, 2019).Besides the magnetic field, the arrival speed of the CME plays an importantrole as high impact speeds, including those of the shock-front driven by the CME,can intensify a geomagnetic disturbance (Gosling, McComas, Phillips, & Bame, 1991;Oliveira et al., 2018; Yue et al., 2010). Generally, geoeffectiveness is related to thedawn-to-dusk electric field and therefore to the flow speed (O’Brien & McPherron,2000). While prediction of the orientation of the magnetic field within a CME isparticularly difficult—especially due to the lack of magnetic field measurements inthe corona—the prediction of the CME arrival time and speed can be carried outusing different kinds of data and numerous prediction models. In particular, accurateprediction of the shock arrival time at Earth is crucial in order to be able to reactaccordingly to an expected disturbance. However, the timing and the probability ofarrival at Earth are both still hard to predict. Wold et al. (2018) analyzed the real-time predictions performed at the Community Coordinated Modeling Center (CCMC)using the WSA-ENLIL+Cone model between the years 2010 and 2016. They found –2–anuscript submitted to Space Weather that the success ratio, reflecting the fraction of correct predictions, to be 0.4 and thefalse alarm ratio to be 0.6. This demonstrates the necessity of improving arrival timeand probability prediction of CMEs.Most prediction models rely on images from coronagraphs that observe the solarcorona out to a maximum plane-of-sky distance of 30 R (cid:12) (e.g. Dumbovi´c et al., 2018;Kay, Mays, & Verbeke, 2020; Pluta, Mrotzek, Vourlidas, Bothmer, & Savani, 2019;Singh, Yalim, & Pogorelov, 2018). The big advantages of these observations are theiravailability in real-time and their relatively simple interpretation. In coronagraph im-ages, the inferred distances can be directly used without any consideration of Thomsonscattering effects, which is commonly known as the plane-of-sky assumption. Addi-tionally, the integration of the scattered photospheric light along the line-of-sight canbe neglected, since the extent of a CME is rather small close to the Sun. The bigdrawback is the small field of view that corresponds to a maximum one seventh of theSun-Earth distance. Riley et al. (2018) analyzed the accuracy of models contributingto the CME scoreboard , a platform that is used by scientists and model developersto test their models in real-time. It was found that the model with the best perfor-mance (WSA-ENLIL+Cone run at NOAA/SPWC) achieved a mean absolute arrivaltime error of 13 h with a standard deviation of ±
15 h. The predictions evaluated weremade in real-time over a time range of almost 6 years, i.e. the numbers in that studyreflect the state of the art better than any of the other studies that covered only asmall number of selected events.Other instruments that enable CMEs to be observed in white-light are the he-liospheric imagers (HI; Eyles et al., 2009) on-board the Solar TErrestrial RElationsObservatory (STEREO; Kaiser et al., 2008). These wide-angle cameras image thespace between the Sun and 1 AU and beyond. Due to their large field of view, line-of-sight integration is an important factor when interpreting these images and theplane-of-sky assumption is not valid for HI. Therefore, it is necessary to assume a cer-tain longitudinal extent of the CME frontal shape, as well as being aware that it is notpossible to follow the same part of the CME front during its propagation through theentire field of view of HI. One of the drawbacks of STEREO/HI data is that the nearreal-time beacon data suffer from low time and spatial resolution and from data gaps,i.e. it is expected that real-time predictions based on HI beacon data cannot achievethe same accuracy as predictions based on HI science data (Tucker-Hood et al., 2015).Now that STEREO-A is again observing the space between Sun and Earth from anoptimal vantage point, predictions using HI beacon data will no doubt be contributedto the CME scoreboard in the future. ESA is currently planning a space weathermission to the observationally advantageous Lagrange point 5 (L5) of the Sun-Earthsystem, located around 60 ◦ behind the Sun-Earth line (Gibney, 2017). This mission isdedicated to space weather prediction and will, if funded, carry HI cameras providingreal-time data with quality comparable to STEREO/HI science data. This could bean important step forward to improving CME arrival time and speed prediction.With regard to this and other possible future space weather monitoring missionscarrying heliospheric imagers, we present a detailed evaluation of different model pa-rameters and inputs to the ELlipse Evolution model based on single spacecraft HIobservations (ELEvoHI; Amerstorfer et al., 2018; Rollett et al., 2016). ELEvoHI isdesigned to be operational in real-time as soon as HI real-time data are available withsufficient quality to be used by this model. We have found that small changes withinthe model, its parameters or inputs, can lead to a large difference in the CME arrivalprediction. In the following sections, we investigate different ways of using ELEvoHItogether with HI science data and compare these approaches to each other in order to https://kauai.ccmc.gsfc.nasa.gov/CMEscoreboard –3–anuscript submitted to Space Weather identify the optimal model set-up leading to the smallest prediction errors in time andspeed.
We use a list of 15 well-observed (remotely and in situ) non-interacting Earth-directed CMEs within the time range extending from the end of 2008 until the begin-ning of 2011 (Table 1). During this time, STEREO was in an ideal location (between45 and 90 ◦ east and west of Earth) to observe Earth-directed events. Unfortunately,due to low solar activity during these years, the number of fast CMEs in this interval isvery small, i.e. only one event arrived at Earth with a speed of more than 700 km s − ,while most of the events in the list were detected in situ with a speed of less than 400km s − .Parts of this study use coronagraph images provided by (1) the SOHO mission,with LASCO C2 and C3 (Brueckner et al., 1995), which observe the space aroundthe Sun between 2 and 30 R (cid:12) in the plane of sky, and by (2) STEREO from twodifferent vantage points, with COR2 (R. A. Howard et al., 2008) having a field of viewextending from 2 to 15 R (cid:12) . For parts of this study, we use coronagraph observationsfrom all three vantage points together to get an estimate of the CME shape. Themost important data source for this study and the ELEvoHI model are provided bythe heliospheric imagers on-board STEREO. The HI instrument on each spacecraftconsists of two white-light wide-angle cameras: HI1 having an angular field of view inthe ecliptic of 4–24 ◦ from Sun-center and HI2 having an angular field of view, againin the ecliptic, of 18–88 ◦ , roughly corresponding to a heliocentric distance of 1 AU.For this study, we used HI science data, having a time-cadence of 40 minutes (HI1)and 2 hours (HI2). Three events in the list (n ◦ were used. Thiscatalog lists, among those for other spacecraft, the interplanetary CME (ICME) shockarrivals detected by the Wind spacecraft (Lepping et al., 1995; Ogilvie et al., 1995)located at L1. Parts of this study rely on information about the solar wind speed at1 AU detected by the Wind spacecraft, that is used as approximation for the ambientsolar wind speed influencing the CME during its propagation (Section 4.2). The ELlipse Evolution model based on Heliospheric Imager data (ELEvoHI) wasfirst presented by Rollett et al. (2016) as a single-run model, where it was shownthat including solar wind drag leads to an improvement of CME arrival time andspeed predictions over the common HI prediction methods, such as Fixed-Phi (Kahler& Webb, 2007; Rouillard et al., 2008), Harmonic Mean (T. A. Howard & Tappin,2009; Lugaz, Vourlidas, & Roussev, 2009) or Self-similar Expansion fitting (Davies etal., 2012; M¨ostl & Davies, 2013). Allowing the CME to adjust its kinematics to theambient solar wind flow particularly improves the arrival speed predictions, which hasdirect relevance to accurately predicting geomagnetic storm strength (Rollett et al.,2016). –4–anuscript submitted to Space Weather
Table 1.
Overview of events used in this study. The columns state the event number, the timeand date when the CME was first visible in HI1, the observing STEREO spacecraft, the HEElongitude (i.e. the separation of the observing spacecraft from Earth), the in situ arrival time andspeed detected at Earth. This information was taken from the HELCATS project website. n ◦ First observed by HI1 [UT] HI observer HEE longitude [ ◦ ] Arrival time [UT] Arrival speed [km s − ]1 2008-12-12 15:29 A 42.3 2008-12-17 03:35 3552 2009-01-30 20:09 B -46.1 2009-02-03 19:11 3603 2009-09-03 23:29 A 59.6 2009-09-10 10:19 3064 2010-02-03 14:49 A 64.7 2010-02-07 18:04 4065 2010-02-03 20:49 B -70.7 2010-02-07 18:04 4066 2010-03-19 20:09 B -71.4 2010-03-23 22:33 2927 2010-04-03 12:09 A 67.5 2010-04-05 07:55 7348 2010-04-08 06:49 A 67.8 2010-04-11 12:28 4329 2010-05-23 22:09 A 71.6 2010-05-28 02:23 37010 2010-05-24 00:09 B -70.0 2010-05-28 02:23 37011 2010-06-16 23:29 B -69.8 2010-06-21 03:35 40112 2010-10-26 16:10 B -80.6 2010-10-31 02:09 36613 2010-12-15 21:29 A 85.2 2010-12-19 20:23 38114 2011-01-30 20:09 A 86.2 2011-02-04 01:55 37615 2011-01-30 18:49 B -93.0 2011-02-04 01:55 376Amerstorfer et al. (2018) introduced the ELEvoHI ensemble approach and testedit using a case study, in which a CME was detected in situ by two radially alignedspacecraft at 0.48 and 1.08 AU. The authors showed that it is possible to predict CMEarrival at the observing spacecraft itself, i.e. it is possible to predict a halo CME,supporting the idea of having an HI instrument positioned at L1.ELEvoHI is a combination of three main modules that derive parameters fromobservations to serve as input to the next module. Figure 1 presents the predictionscheme based on ELEvoHI ensemble modeling used in this paper. The left columnshows different inputs (gray boxes) to the three main modules of ELEvoHI (blue el-lipses), resulting in the modeling and prediction results (red box). The green boxes onthe right show the different data that can be used to drive the model, while only datafrom heliospheric imagers is mandatory and all other data are optional. The middlepart of the figure (yellow boxes) presents the three groups of inputs that this studyinvestigates in order to identify their best combination (in terms of CME geometry,ambient solar wind speed, and DBM fitting). In the following paragraphs, the indi-vidual steps within ELEvoHI (blue circles in Figure 1) in its ensemble approach arebriefly described:The starting point is the CME time-elongation track, (cid:15) ( t ), acquired from HI ob-servations, usually from a time-elongation map at fixed position angle. This track isconverted from angular units to units of radial distance by ELEvoHI’s built-in proce-dure ELlipse Conversion (ELCon), based on an ensemble of assumed front shapes andpropagation directions (see below). Detailed information on the ELCon conversionmethod can be found in Rollett et al. (2016).In the next step, each ensemble member time-distance track for the CME is fittedusing a equation of motion based on the drag-based model (DBM) given in Vrˇsnak etal. (2013): –5–anuscript submitted to Space Weather (cid:15) ( t ) φ, f, λ ELConambient solar windspeedDBM fittingELEvo
CME evolution & arrival time and speed prediction FPFSSEFEAGELWSA-HUXstatisticscurrently @ 1AUall residualslast 3 residuals heliospheric imagescoronagraphobservationsmagnetic field mapsin situsolar wind speedmandatoryoptional
ELEvoHI CME Modeling
Figure 1.
Schematic illustration of all parts contributing to an ELEvoHI ensemble prediction.The green boxes are the possible data used, the blue boxes are the three main modules buildingELEvoHI. The gray boxes are all input parameters needed. The yellow boxes show the possiblesources of these input parameters grouped into three different parts that are tested in this study.The red box is the model output, i.e. kinematical profiles and arrival time and speed predictionsat the target of interest. R ( t ) = ± /γ ln[1 ± γ ( v init − w ) t ] + wt + r init , (1)where r init is the initial distance and v init the initial speed. The sign ± is positivewhen the CME is accelerating ( v init < w ) and negative when it is decelerating ( v init >w ) due to the drag-force exerted by the ambient solar wind. The drag parameter, γ = C D A CME ρ sw m CME , is the parameter that results from least-square fitting of the time-distance track within the DBM fitting routine implemented in ELEvoHI. C D is thedrag-coefficient assumed to equal 1, A CME is the CME cross section that the drag isacting on, m CME is the CME mass, and ρ sw is the solar wind density. Within the DBMfitting procedure, t init , the initial time of the fit, is defined manually by the user oncefor each event. Subsequently, r init and v init are derived separately for each ensemblemember from the output of ELCon.The procedure of defining the ambient solar wind speed, w , is described in Section4.2. Figure 2 demonstrates the approach of ELCon and the following DBM fitting for –6–anuscript submitted to Space Weather one example CME (CME n ◦ λ , andinverse ellipse aspect ratio, f ) and propagation direction, φ . Each of these threeparameters is varied within a certain range to build an ensemble of different CMEshapes, from each of which a prediction is made. Depending on the assumed angularwidth, aspect ratio and direction of the tracked feature, the derived kinematics differfor each ensemble member. The lower panel shows the interplanetary speed profilesof the CME apex derived by ELCon from each of the time-distance profiles. The redvertical lines mark the start and the end point of the HI data used for DBM fitting(fits are not shown) and for making the CME arrival prediction.The parameters obtained by DBM fitting serve as input for the ELlipse Evolutionmodel (ELEvo; M¨ostl et al., 2015) that produces the arrival prediction. ELEvo runsthe DBM by propagating the previously-defined elliptical CME frontal shape in thealso previously defined direction, which is different for each ensemble member, andpredicts its arrival at any target of interest based on the drag parameter and ambientsolar wind speed derived from DBM fitting. Figure 2.
Range of HI kinematics (upper panel: time-distance profiles, lower panel: time-speed profiles) resulting from the input parameters corresponding to different CME frontalshapes and directions. The red vertical lines mark the start and end times of the HI data usedfor CME arrival prediction, the gray shaded area in the lower panel illustrates the range of theambient solar wind speed resulting from drag-based fitting to the HI kinematics.
In the following, we describe the different methods used to derive input parame-ters for ELEvoHI, such as information on the CME frontal shape, propagation directionand the ambient solar wind speed. All of them are optional and can be replaced by abasic statistical estimation or a simple assumption. –7–anuscript submitted to
Space Weather
Besides the time-elongation track measured from HI observations, ELEvoHIneeds information on the frontal shape, i.e. f and λ , and the direction of motionof the CME. The latter can either be gained from HI observations or from corona-graph observations, which additionally provide the possibility to estimate the angularwidth. The first potential method to provide φ and λ parameters used by ELEvoHI isbased on the Graduated Cylindrical Shell fitting method (GCS fitting; A. Thernisien,2011; A. Thernisien, Vourlidas, & Howard, 2009; A. F. R. Thernisien, Howard, &Vourlidas, 2006). GCS fitting (implemented within SolarSoft, rtsccguicloud.pro )enables the manual fitting of a croissant-shaped CME body to simultaneous imagesfrom coronagraphs observing from different vantage points. In our study, we use imagesfrom STEREO/COR2 from both sides, as well as LASCO/C2 and/or C3 images.Several shape-related CME parameters can be adjusted within a widget tool until thebest match with the CME visible within the coronagraph images is achieved. For ourpurposes, GCS is run as a part of the so-called EAGEL (Ecliptic cut Angles from GCSfor ELEvoHI) tool, which is described below.Within EAGEL the download and pre-processing of the coronagraph data isincluded in such a way that a CME is clearly recognizable in the images. Based onthese images, GCS fitting of a CME is performed. EAGEL then creates an eclipticcut of the wire-frame of the fitted CME and calculates λ and φ with respect to Earth,STEREO-A and STEREO-B. ELEvoHI is operated in an ensemble mode, in which theinput values of shape and direction are varied within a pre-defined range. In the casethat inputs from EAGEL are used, λ and φ are each varied within ± ◦ . This rangeis chosen based on a previous study by Mierla et al. (2010), who cite this as the errorrange of these parameters when different observers manually fit the same CME usingGCS. Panels a)–c) in Figure 3 show a GCS fit to one of the CMEs under study (n ◦ ≈ − ◦ ), the eclipticcut conducted by the EAGEL tool corresponds to a very narrow structure as shownin panel d). Because of the ± ◦ in λ and φ used in the ELEvoHI ensemble mode, thewhole ensemble appears to be relatively wide compared to the input ecliptic cut. Tobuild the ensemble, these inputs are varied using a step size of ∆ φ = 2 ◦ and ∆ λ = 5 ◦ .The parameter f , which is related to the curvature of the front, is not obtained fromthe ecliptic cut but is, instead, varied between 0.8 (flat elliptical frontal shape) and 1(circular frontal shape). In the study predicting CME arrival times and speeds using ELEvoHI performedby Rollett et al. (2016), the propagation direction was obtained from FPF and the sameangular half-width, namely 35 ◦ , was used for every CME in the list. Although thisis a quick and easy approach with no additional need for coronagraph data, it doesnot provide information about the true angular half-width of the CME. With suchinformation as input, we might be able to improve ELEvoHI’s prediction accuracy. Inthe study by Amerstorfer et al. (2018), the information on the CME frontal shape wastaken from an intersection of the GCS shape with the ecliptic plane (as discussed inSection 4.1.1). That case study resulted in a prediction with very high precision.To test the effect of assuming a finite CME width, we use the direction of motionfrom Fixed-Phi Fitting (FPF; Kahler & Webb, 2007; Rouillard et al., 2008) as well as –8–anuscript submitted to Space Weather a) c)b) d)
Figure 3.
Example of a CME (event n ◦
12) having a large inclination relative to the eclipticplane. Panels a)—c) show the GCS reconstruction of the CME shape overlaid on STEREO-A/COR2, SOHO/C3 and STEREO-B/COR2 difference images. Panel d) shows the ecliptic cutresulting from the EAGEL tool, with the blue arrow pointing towards Earth, the green and redlines defining the outer edges of the CME and the yellow arrow pointing along the direction ofmotion used as input to ELEvoHI. from Self-Similar Expansion Fitting (SSEF; Davies et al., 2012; M¨ostl & Davies, 2013).These methods are analogous except that, in the latter, the CME is not assumed tobe a point and one has to assume an angular half-width for the circular shaped CMEfront. FPF and SSEF both perform a numerical fit to the time-elongation profile of theCME track measured from HI observations, hence they are based on the same inputas ELEvoHI. Both methods assume a constant propagation direction and, in contrastto ELEvoHI, a constant propagation speed. We derive the propagation direction usingSSEF assuming a half-width of 45 ◦ . The propagation directions from both HI fittingmethods were then used together with a range of 30 – 50 ◦ (and a step size of 5 ◦ ) forthe angular half-width within ELEvoHI.As a check, we compared the propagation directions resulting from FPF, SSEFand EAGEL for the 15 CMEs under study, and found that the mean absolute differ-ence between the directions derived from the EAGEL approach and those from theHI fitting methods was around 14 ◦ and, between the two HI fitting methods, it wasaround 9 ◦ . Figure 4 shows the derived directions of motion derived using the threemethods (EAGEL: green dot, FPF: blue circle, SSEF: orange triangle) for each eventstudied. For events 2 and 3, no GCS fit could be performed due to the faint natureof the CME structure within the coronagraph images. Therefore, for these events,we have no prediction based on model set-ups using information from the EAGELmethod. It is expected that the direction of motion and the angular half-width con-tribute significantly to the prediction accuracy. Amerstorfer et al. (2018) performed asensitivity study that showed that, indeed, for the halo CME under study, the direc-tion of motion had the biggest influence on the predicted transit time. However, thiscould be different for a side-on view of a CME or for different events. It is importantto emphasize that λ and φ are the only parameters in our model that dictate if Earth(or any other target) is hit by the CME or not.For the ELEvoHI model set-up test, as discussed in this section, we use thefollowing inputs for the CME direction and angular half width:1. EAGEL direction and half-width,2. FPF direction and predefined angular half-width from 30 − ◦ ,3. SSEF direction and predefined angular half-width from 30 − ◦ . –9–anuscript submitted to Space Weather
Event number f r o m S un - S T E R E O li ne [] Direction of CME Motion
FPFSSEFEAGEL
Figure 4.
Absolute propagation directions relative to the Sun-STEREO line derived fromEAGEL (green), FPF (blue) and SSEF (orange). For two events GCS fitting was not possible.The mean absolute difference of the resulting directions is around 12.7 ◦ . In its current version, ELEvoHI accepts only a constant (in space and time)background solar wind input. Rollett et al. (2016) and Amerstorfer et al. (2018)assumed that the ambient solar wind at 1 AU is the same that influences the CMEthroughout its evolution, i.e. the solar wind speed at 1 AU was used as input toELEvoHI. Note that a background solar wind speed prescribed in this way is not trulyrepresentative of the actual background wind through which the CME propagates.In that approach, the minimum and maximum solar wind speed values over the timerange of the HI data (either from STEREO-A or B) are used for making the prediction,and three values in between those minimum and maximum values, as the basis for theDBM fitting. Hence, five DBM fits are performed, and the optimal fit (defined below)gives us the background speed, which is further used to perform the prediction.
In order to find a better method, we investigate whether the DBM fit is ableto ‘decide’ for itself which solar wind speed best fits the CME kinematics. To thisend, we calculated the mean solar wind speed in OMNI data between the years 2004and 2018 to be 425 km s − with a standard deviation of 100 km s − . We use thesevalues to define the speed range utilized for DBM fitting as the mean value ± twice thestandard deviation. For each ensemble member, we perform 17 DBM fits corresponding –10–anuscript submitted to Space Weather to speeds from 225 to 625 km s − in steps of 25 km s − ; the optimal DBM fit thenyields the background solar wind speed.This approach allows the model to select from a wide range of possible back-ground solar wind speeds for itself. This is possible because the HI kinematics are notcompatible with every possible solar wind speed. Depending on the CME speed andits evolution, i.e. whether the CME is decelerating, accelerating or propagating with aconstant speed, only some candidate solar wind speeds will result in a converging DBMfit. Due to the wide range of ensemble members, each having different kinematics (seegray area in the lower panel of Figure 2, the selected solar wind speed can be differentfor each ensemble member. As a third approach to deriving the background solar wind speed for input toELEvoHI, we test the usage of the Wang-Sheeley-Arge and Heliospheric Upwind eX-trapolation models (WSA-HUX). More specifically, we use magnetic maps of the pho-tospheric field from the Global Oscillation Network Group (GONG) of the NationalSolar Observatory (NSO) as input to magnetic models of the solar corona. Usingthe Potential Field Source Surface model (PFSS; Altschuler & Newkirk, 1969; Schat-ten, Wilcox, & Ness, 1969) and the Schatten Current Sheet model (SCS; Schatten,1971), we compute the global coronal magnetic field topology. While the PFSS modelattempts to find the potential magnetic field solution in the corona with an outerboundary condition stating that the field is radial at the source surface at 2.5 R (cid:12) ,the SCS model accounts for the latitudinal invariance of the radial magnetic field inthe region between 2.5 and 5 R (cid:12) as observed in Ulysses field measurements (Wang &Sheeley, 1995). From the global magnetic field topology, we calculate the solar windconditions near the Sun using the Wang-Sheeley-Arge model (WSA; Arge, Odstrcil,Pizzo, & Mayer, 2003). To map the solar wind solutions from near Sun to Earth, we usethe Heliospheric Upwind eXtrapolation model (HUX; Riley & Lionello, 2011), whichsimplifies the fluid momentum equation as much as possible. The HUX model solu-tions match the dynamic evolution predicted by global heliospheric MHD codes fairlywell while having low processing power requirements. More details on the numericalframework can be found in Reiss et al. (2019).Figure 5 presents the modeled ambient solar wind for one event under study. Forthis method, we consider only that radial range of the heliosphere where the DBM fit isperformed, i.e. between the two red vertical lines indicated in Figure 2 (approximately30–100 R (cid:12) ). In longitude, we use a range φ ± λ to define the area in which the solarwind is acting on a certain CME ensemble member. The median value of the solarwind speed within this sector is calculated and a range of ±
100 km s − is assumed.Over this range of ambient solar wind speeds, in steps of 25 km s − , 9 DBMfits areperformed.To test the ELEvoHI model set-up, we use the three previously discussed methodsto provide the source for the ambient solar wind speed, i.e.1. in situ data from 1 AU,2. speed range derived from statistics,3. modeled by WSA-HUX model. In the current version of ELEvoHI, the optimal DBM fit (out of several fitsperformed based on a range of input ambient solar wind speeds, as discussed in theprevious section) is defined as the fit with the smallest mean residual to the time- –11–anuscript submitted to
Space Weather
Figure 5.
Example of the ambient solar wind speed for one event under study, observed bySTEREO-A and STEREO-B (event n ◦ ◦
10 in Table 1). The region of interest is ex-tracted and averaged and serves as input to the ELEvoHI ensemble model. distance profile along the whole extent of the fitted curve. The ambient solar windspeed associated with the best DBM fit is then used for further modeling. Usually,the DBM fit is performed over a radial distance of around 30 to 100 R (cid:12) . Sometimeswe find that the DBM best fit does not actually agree very well with the last fitteddata points, which can have a significant influence on the prediction. Therefore, it istested if using only the mean residual of the last three fitted points leads to a betterprediction than considering the residuals of the whole fit. Note that, in both cases,the total number of data points that are fitted stays the same, i.e. the track is fittedbetween the two end points that are manually chosen (vertical red lines in Figure 8).Only the evaluation of the residual differs in these two approaches.For testing the ELEvoHI model set-up, we use the two previously discussedmethods for evaluating the DBM fit and choosing the most suitable background solarwind speed, i.e. –12–anuscript submitted to
Space Weather
1. the smallest mean residual along the whole extent of the fit,2. the smallest mean residual of the last three fitted points.
In order to compare the results of the different ELEvoHI ensemble runs to a well-established but simple prediction method that relies on HI data only, we use Fixed-Phifitting (FPF; Kahler & Webb, 2007; Rouillard et al., 2008). The FPF method is thesimplest of all such techniques based on HI data. It reduces the CME front to a point-like feature and assumes a radial propagation direction at a constant propagationspeed. The best-fit equation of motion to the time-elongation profile extracted fromHI data provides an estimate of the arrival time and speed at the target of interest.We apply FPF to the same time-elongation profiles as ELEvoHI and limit the tracklength to the start and end points between which the DBM fit is performed (red lines inFigure 2), i.e. the same number of data points is used. Although the method is simple,its predictions are not significantly worse than the predictions from more sophisticatedmethods (M¨ostl et al., 2014). Using results from a benchmark model as a comparisonprovides the possibility to prove whether ELEvoHI is able to increase the predictionaccuracy compared to the simple FPF method.
We perform 18 ensemble runs for each CME in our list of 15 events by combiningthree different approaches related to the ambient solar wind speed, three different waysof gaining the CME frontal shape/direction and two different methods of defining thebest DBM fit. Every ensemble run consists of 220 ensemble members (resulting fromvarying λ , f and φ input parameters within certain ranges), i.e. for each event, weperform 3960 predictions with 59400 predictions in total. We calculate the median,the mean and the standard deviation of the distribution of predictions of the arrivaltime at Earth for each of the 18 ensembles and for each of the 15 CMEs. Figure 6shows four different time steps of the ELEvoHI simulation result for one example event(n ◦ . ± . . . t , and speed, v , for each of the 18 different model set-ups. Negative values correspond to an under-estimated transit time, hence the event was predicted to arrive earlier than it actuallydid. In the case of the arrival speed prediction, negative values correspond to an un-derestimated arrival speed. The results are ordered from smallest to largest MAE inarrival time, revealing that the six set-ups using the WSA-HUX output as input for theambient solar wind estimate lead to the most accurate predictions. The benchmarkFPF technique leads to an MAE of 7.8 h with an MSTD of 10.5 h and an ME of 2.6h, which means that FPF has a tendency to overestimate the transit time. Consid-ering the underlying geometry assumed by FPF, this is not surprising. FPF reduces –13–anuscript submitted to Space Weather a)c) d)b)a)c) d)b)
Figure 6.
Four different time steps during ELEvoHI CME modeling for one example event(event n ◦ https://doi.org/10.6084/m9.figshare.12333173.v1 . the CME front to a single point and assumes this point is tracked throughout theCME’s propagation. Being conscious of the fact that CMEs can be extremely large-scale structures, it is clear that this is an oversimplification. Additionally, our CMEsample almost exclusively consists of slow CMEs for which the assumption of constantpropagation speed is usually close to reality. The faster the CME and hence the largerits likely deceleration, the larger the error due to a constant speed assumption (Lugaz,Roussev, & Gombosi, 2011). However, we cannot dismiss the result that FPF per-forms as well as ELEvoHI (when averaging over all model set-ups) for the chosen setof CMEs. Again, it can be shown that a more sophisticated method is no guarant ofa better prediction as already demonstrated by Vrˇsnak et al. (2014), who comparedthe performance of the DBM and the WSA-Enlil+Cone model based on a list of 50CMEs. The authors found that the two methods predicted the CME arrival time withan MAE of 14.8 and 14.1 h, respectively (for real-time predictions). Fortunately, thisdoes not mean that we have already reached the best possible prediction accuracy;improving a method can still reap rewards. As Table 2 shows, ELEvoHI based onphi from FPF can outperform the benchmark FPF when part of a more sophisticatedmodel set-up, e.g. when coupled with WSA-HUX as the source of the solar wind. –14–anuscript submitted to Space Weather
WSA+HUX statistics L1 EAGEL FPF SSEF all last three a) ELEvoHI MAE (arrival time) as a function of input sources | t | WSA+HUX statistics L1 EAGEL FPF SSEF all last three | v | b) ELEvoHI MAE (arrival speed) as a function of input sources
Figure 7.
ELEvoHI MAE of a) arrival time and b) speed prediction corresponding to eachsource of input parameter. The left set of bars correspond to the three different sources of am-bient solar wind input, the middle set of bars correspond to the three different sources of propa-gation direction (and CME frontal shape in case of EAGEL), and the right set of bars show theresults that correspond to the two different ways of defining the best DBM fit. The error barsmark the standard deviation of the predictions. The horizontal dashed lines represent the MAEof the benchmark model, FPF.
Figure 7 shows the performance of the different model set-ups, grouped by theinput type. The left/middle/right bars show the MAE and the MSTD of predictionsbased on different kinds of solar wind input/frontal shape/direction/best DBM fit.For all runs that use WSA-HUX, we find an MAE of 7 . ± . . ± . . ± . –15–anuscript submitted to Space Weather T a b l e . A cc u r a c y o f e a c h m o d e l s e t - up , s o r t e db y t h e m e a n a b s o l u t ee rr o r ( M A E ) . M A E , t h e m e a n e rr o r ( M E ) , t h e r oo t m e a n s q u a r ee rr o r ( R M S E ) a nd t h e m e a n s t a nd a r dd e v i a t i o n o f t h e a rr i v a l t i m e (t) a nd s p ee d ( v ) p r e d i c t i o n a r e g i v e n . T h e l a s t c o l u m n li s t s t h e c o rr e s p o nd i n g m o d e l s e t - up i nd i c a t i n g t h e i npu t s f o r d i r e c t i o n ( a nd s h a p e i n c a s e o f E A G E L ) , s o l a r w i nd a nd t h e w a y o f d e fin i n g t h e b e s t D B M fi t . M A E (t) [ h ] M E (t) [ h ] R M S E (t) [ h ] M S T D (t) [ h ] M A E ( v ) [ k m s − ] M E ( v ) [ k m s − ] R M S E ( v ) [ k m s − ] M S T D ( v ) [ k m s − ] m o d e l s e t - up . . . . . . . . F P F W S A - HUX a ll . - . . . . . . . F P F W S A - HUX l a s t . . . . . . . . SS E F W S A - HUX a ll . - . . . . . . . E A G E L W S A - HUX a ll . . . . . . . . SS E F W S A - HUX l a s t . - . . . . . . . E A G E L W S A - HUX l a s t . - . . . . . . . E A G E L s t a t s a ll . - . . . . . . . E A G E L s t a t s l a s t . - . . . . . . . E A G E LL ll . - . . . . . . . E A G E LL l a s t . . . . . . . . F P F s t a t s a ll . . . . . . . . F P F s t a t s l a s t . . . . . . . . SS E F s t a t s a ll . . . . . . . . SS E F s t a t s l a s t . . . . . . . . F P F L ll . . . . . . . . F P F L l a s t . . . . . . . . SS E F L ll . . . . . . . . SS E F L l a s t T h e b e n c h m a r k m o d e l F P F r e s u l t s f o r t h e a rr i v a l t i m e p r e d i c t i o n i n a n M A E o f . h , a n M E o f . h , a n M S T D o f . h a nd a R M S E o f . h . F o r t h e a rr i v a l s p ee dp r e d i c t i o n F P F r e s u l t s i n a n M A E o f X h , a n M E o f X h , a n M S T D o f X h a nd a R M S E o f h . –16–anuscript submitted to Space Weather
Comparing the predictions based on different sources of CME frontal shape/directioninput, we find that the input from the EAGEL tool leads to an MAE of 7 . ± . . ± . . ± . . ± . . ± . ±
50 km s − (L1: 58 ±
52 km s − , statistical background wind:53 ±
53 km s − ). Using input from EAGEL yields an MAE of 63 ±
69 km s − (FPF:44 ±
43 km s − , SSEF: 53 ±
43 km s − ). Judging the best DBM fit by the residuals ofthe whole fit gives 68 ±
52 km s − (last three residuals: 66 ±
52 km s − ). In case ofthe CME arrival speed prediction, the set-up used appears to make little difference.Figure 8 a) shows an overview of the performance of all of the different modelset-ups as box and whiskers plots, based on the difference between predicted and actualarrival time for all events and all runs ( ∼ t ) is 11 h and the MAE( t ) is 8 . ± . v ) is 66 km s − and the MAE( v ) is 53 km s − . Figure 8 b) showsthe analogous plot for arrival speed. Overall, ELEvoHI provides an MAE in the arrivalspeed prediction of 53 ±
51 km s − , an RMSE of 66 km s − , and ME of 23 km s − . Thelatter means that ELEvoHI is not biased towards producing arrival speed predictionsthat are either too fast or too slow.Some of the events under study (n ◦ ◦
14 in Table 1) are shown and panel b) presentsthe predictions based on STEREO-B/HI data (n ◦
15 in Table 1). Interestingly, theresults are highly dependent on the model set-up used. For the view from STEREO-A,EAGEL+WSA-HUX input seems to be the best choice compared to the predictionsbased on the two HI fitting methods that lead to an error between 30 and 40 h. Thecombination of SSEF/FPF and WSA-HUX was not possible for this event from thevantage point of STEREO-A because the ambient solar wind speed range providedby WSA-HUX did not agree with the HI kinematics. Contrariwise, from the vantagepoint of STEREO-B, the EAGEL+WSA-HUX set-up leads to an error of more than10 hours, while the predictions based on input directions derived from SSEF almostexactly match the in situ arrival time. A more detailed analysis on CMEs observed –17–anuscript submitted to
Space Weather a)b)
Figure 8.
Overview of the prediction accuracy for every model set-up tested. Figure a)presents the prediction accuracy for the arrival time, figure b) for the arrival speed. The verticallines within the boxes correspond to the median values, the boxes are delimited by the first andthe third quartile, and the whiskers correspond to 1.5 times the interquartile range; the diamondsrepresent outliers. stereoscopically and modeled by ELEvoHI will be presented in a study by Hinterreiteret al. (in preparation for Space Weather).This comparison shows that the current assumptions within ELEvoHI, i.e. con-stant ambient solar wind speed and elliptical CME frontal shape, are not correct forevery event. When the CME is observed and predicted from the two different van-tage points, the results can differ significantly; with the correct assumptions in placefor a specific CME, this should not be the case. Therefore, including a deformableshape within ELEvoHI to simulate CME interaction with structures in the ambientsolar wind might lead to an improvement of the predictions. Indeed, observations frommore than one vantage point could be used to help constrain the shape and kinemat- –18–anuscript submitted to
Space Weather
Figure 9.
Comparison of ELEvoHI predictions for one example event (n ◦
14 and 15 in Ta-ble 1) performed separately for the two different vantage points, i.e. from STEREO-A and B,respectively. The dashed red line shows the result of the benchmark model. ics of the CME leading to such an improvement in the arrival prediction accuracies.This finding supports the benefit of having HI observations from two separate vantagepoints, e.g. L1 and L5.
By far the fastest and according to our findings in this study, a relatively satisfy-ing way to set-up ELEvoHI, is using a combination of FPF and the statistical ambientsolar wind approach. FPF uses the same data as needed by ELEvoHI, i.e. the HI time-elongation track. The FPF fitting method yields the propagation direction needed byELEvoHI, while the half-width within the ecliptic plane can be assumed to be between30 and 50 ◦ (it can be assumed, indeed, to be any other value). The statistical solarwind approach is directly implemented within the ELEvoHI model. As shown above,this set-up leads to an MAE in arrival time of 8.6 h and an ME of 2.7 h. However,if an ambient solar wind solution is available in real-time (e.g. the WSA-HUX orsimilar), ELEvoHI can achieve an MAE of 6.2 h with an ME of 0.1 h—still withoutthe necessity for additional coronagraph data or the need for manual fitting to theseimages. Of course, we always need to keep in mind that these values are derived from apre-defined set of very well-observed, and isolated, events and from HI science qualitydata that is currently not available in real-time. However, HI beacon data is availablein near real-time and can serve as input to ELEvoHI since STEREO-A/HI is alreadyclose to L5 and is observing the space between the Sun and Earth—hopefully until2027, when it will be around L4. An additional possibility for having HI real-time dataavailable in the future might be provided by the Polarimeter to Unify the Corona andHeliosphere (PUNCH) mission. PUNCH will be launched in 2023 and will operate inlow Earth orbit. –19–anuscript submitted to Space Weather
For real-time predictions, it is of the utmost importance to be able to include anestimate of the arrival probability with a CME prediction. Currently, ELEvoHI simplycalculates this as the ratio of the number of ensemble members that are predicted tohit the target to the total ensemble size. This is going to be updated in the near future,to give predicted flank hits a lower weighting. In addition, we have noticed that forflank hits, the arrival time error tends to be larger than expected and the transit timeis overestimated. This could be due to the elliptical shape of the front resulting inhighly curved flanks. In the future, we will examine if we can find a suitable approachto deal with these strongly bent flanks to avoid such extreme delays when predictinga flank encounter.
In this work we studied 18 different combinations of inputs to run the HI-basedensemble CME arrival prediction model, ELEvoHI, in order to ascertain the set-upleading to the most accurate arrival time and speed predictions. As input for theambient solar wind that influences the drag-based propagation of the modeled CMEwe used 1) the WSA-HUX background solar wind model, 2) an approach of simplyproviding a range of possible solar wind speeds (225–625 km s − ) derived from 14years of observations at L1, and 3) the solar wind speed measured in situ at L1 duringthe evolution of the CME. We found that having a more accurate ambient solar windas input leads to significantly better arrival time prediction. Using input from WSA-HUX improves the MAE by an hour, compared to simply providing a range for solarwind speeds, and leads to almost two hours improvement on MAE over the usage ofL1 solar wind speed.To analyze the influence of the CME frontal shape/propagation direction onELEvoHI predictions, we compared three different sources of λ and φ : 1) Coronagraphimages were used to perform a GCS-fit to derive the 3D shape of the CME. Theintersection of this 3D front with the ecliptic plane provides a 2D structure from whichthe measured angular half-width and direction were input to ELEvoHI. 2) The FPFand 3) the SSEF HI fitting methods, which only provide the direction of motion. Inthese cases, we had to assume a half-width (we chose a range between 30 and 50 ◦ ). Inall cases we had to assume f to vary between 0 . –20–anuscript submitted to Space Weather
In the future, an interesting advancement might be to include a range of values for thesolar wind to contribute to the ensemble instead of deriving only a single value pershape/direction set-up. Another logical next step would be to release ELEvoHI fromits rigid elliptical shape and to allow deformation due to the influence of the ambientsolar wind. In any case, with ELEvoHI, we are prepared for real-time CME arrivalpredictions, once a new HI observer is delivering high quality data in real-time.
Data
STEREO/HI:
STEREO/COR2 and SoHO/LASCO: https://sdac.virtualsolar.org/cgi/search
NSO/GONG: https://gong.nso.edu/data/magmap/
Model
ELEvoHI is available on github under https://github.com/tamerstorfer/ELEvoHI/releases/tag/v1.0.0.0 . Results
The visualization of each prediction result, i.e. movies and figures, can be downloadedfrom https://doi.org/10.6084/m9.figshare.12333173.v1 . Acknowledgments
T.A., J.H., M.B., M.R., C.M., A.J.W., R.L.B, and U.V.A. thank the Austrian ScienceFund (FWF): P31265-N27, J4160-N27, P31659-N27, P31521-N27. M.D. acknowledgessupport by the Croatian Science Foundation under the project 7549 (MSOC).
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