Hit or Miss, Arrival Time, and B z Orientation Predictions of BATS-R-US CME Simulations at 1 AU
aa r X i v : . [ phy s i c s . s p ace - ph ] M a y SPACE WEATHER, VOL. ???, XXXX, DOI:10.1029/,
Hit or Miss, Arrival Time, and B z OrientationPredictions of BATS-R-US CME Simulations at 1 AU
J. M. Schmidt and Iver H. Cairns Corresponding author: J. M. Schmidt, School of Physics, University of Sydney, NSW 2006,Australia. ([email protected]) School of Physics, University of Sydney,NSW 2006, Australia.
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Abstract.
Using a refined setup process, we simulated the propagationof six observed Coronal Mass Ejections (CMEs) with the 2012 Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme (BATS-R-US) code from the Sun to theEarth or STEREO A and compared the outputs with observations. A lin-ear relation between the average CME speed below 6 solar radii and the fluxrope current is demonstrated and used to tune the simulations. The simu-lations correctly predict if and when an observable CME shock reaches oneastronomical unit (AU). The arrival time predictions of the CME shocks at1 AU have an accuracy of 0.9 ± Gopalswamyet al. [2000]. The approach shows promise for predicting the sense of the pre-dominant shock-associated change in the magnetic field component B z . How-ever, the magnetic fields and plasma conditions in the solar wind and CMEare not predicted well quantitatively. D R A F T May 23, 2019, 1:35am D R A F T
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1. Introduction
Coronal Mass Ejections (CMEs) hitting Earth’s magnetosphere can trigger spaceweather events and major geomagnetic storms that lead to major disruptions in ground-and space-based electrical systems and devices [see, e.g.,
Schrijver et al. , 2015]. The miti-gation of impacts requires forecasting if and when a CME will hit the Earth, and what theplasma and magnetic field variations will be. A widely used tool for such forecasting is theENLIL code developed at the Space Weather Prediction Center (SWPC) of the NationalOceanic and Atmospheric Administration (NOAA), USA. This code numerically simu-lates a CME launched at the Sun and propagating through the interplanetary space toone astronomical unit (AU) and beyond, including planets and spacecraft of interest. TheSun - CME system is usually described with Magneto HydroDynamics (MHD). However,in the ENLIL code the magnetic fields of the CME are either neglected or included as ateardrop shaped spheromak that has radial instead of azimuthal magnetic fields at thefront of the CME [see, e.g.,
Odstrcil , 2015;
Odstrcil et al. , 2018]. This makes the numericalcalculations fast, but leads to significant differences from the observations. Specifically,the predicted arrival time of the CME at Earth differs from that observed by 10 ± Wold et al. , 2018;
Verbeke et al. , 2018;
Riley et al. , 2018]. Even so, theENLIL code is the default approach internationally for simulating the motion of CMEs.Another sophisticated simulation code for a Sun - CME system that includes full MHDis the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme (BATS-R-US) code and itssubsequent Space Weather Modeling Framework (SWMF) extension developed at theUniversity of Michigan [
Powell et al. , 1999;
Roussev et al. , 2003, 2004;
Cohen et al. , D R A F T May 23, 2019, 1:35am D R A F T - 4
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Tˆoth et al. , 2012]. Considerable efforts have been made to simulate realisticCMEs with this code [see, e.g.,
Manchester et al. , 2008, 2012].Our major focus in this paper is on operational users who need to be able to accuratelypredict whether and when a CME will reach Earth and only then address the detailedproperties of the CME (e.g., B z ). For this purpose we developed a refined event-specificsimulation setup approach for the 2012 BATS-R-US code and simulated six CMEs thatwere launched towards the Earth or STEREO A. The simulation setup is such that thetime needed to set up and carry out such a simulation is smaller ( < ≈ Schmidt et al. , 2013;
Schmidt and Cairns ,2014;
Cairns and Schmidt , 2015;
Schmidt and Cairns , 2016;
Schmidt et al. , 2016]. Crucialsimulation outputs are whether or not the CME reaches Earth, the arrival time of a CMEat 1 AU, and the north-south component B z with respect to the ecliptic plane before,during, and after the CME’s arrival at 1 AU. Reliable prediction of the CME’s motionand arrival time at 1 AU enables the forecasting of if and when the CME can drive a spaceweather event at Earth. The correct prediction of the orientation of B z during the eventenables the forecast of whether an incident CME should trigger a space weather eventor not. If B z is oriented southward, then magnetic reconnection may occur at Earth’smagnetopause and magnetotail, triggering geomagnetic storms and other disruptions inthe magnetosphere. D R A F T May 23, 2019, 1:35am D R A F T
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In section 2 of this paper we describe a refined setup to simulate the propagation ofCMEs with the 2012 version of the BATS-R-US code from the Sun to 1 AU. We demon-strate that a linear relation exists between the average CME speed below 6 R s and theflux rope current for each event-specific setup and use this to tune the simulations to theobserved CME. We correctly predict if and when an observable CME shock reaches 1 AU(section 3). The approach also shows promise in predicting the sense of the predominantshock-associated change B z , but, in common with many other codes and reports does notadequately model the background solar wind or CMEs.
2. Simulation setup
In the BATS-R-US code the solar coronal magnetic fields are reconstructed with atruncated spherical harmonic series expansion of the magnetic fields measured with theWilcox Solar Observatory [see, e.g., wso.stanford.edu]. The analytic coefficients of thisseries are listed in a file for each Carrington rotation of the Sun and stored in an archiveat the Wilcox Solar Observatory. The BATS-R-US code reads the specific coefficient fileduring a simulation run of a specific CME.The reconstruction of the solar wind magnetic field, speed, and density to 1 AU and be-yond in the 2012 version of BATS-R-US is based on the model of
Cohen et al. [2007, 2008].This uses (1) a modified Wang, Sheeley and Arge model [
Arge and Pizzo , 2000] in orderto obtain initial estimates for magnetic field, speed, and density profiles, and (2) Bernoulliintegrations along the magnetic field lines in order to estimate the ratio of specific heatsfor the plasma and so improved estimates for the solar wind speeds and densities.The CME is then introduced into the reconstructed solar wind as an analytic
Titovand D´emoulin [1999] flux rope, which is launched by cutting the magnetic field lines that
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SCHMIDT AND CAIRNS: SPACE WEATHER RELEVANT FEATURES anchor the flux rope to the Sun. This analytic flux rope is dimensioned with parametersderived from observations of the initial CME. We determined these parameters with arefined version of the CME Analysis Tool (CAT) in SolarSoft [see, e.g.,
Millward et al. ,2013]. This refined tool reads STEREO A/COR2, STEREO B/COR2, SOHO/LASCOC2, and/or SOHO/LASCO C3 coronagraph images of the CME and adjusts a cone in-teractively to fit the CME. Each CME fit assumes an aspect ratio of 0.8 for the flux ropecross section.By applying the cone fit to successive images of a specific CME, a height-time diagramof the erupting CME is created with CAT. The averaged slope of that height-time diagrambelow 6 solar radii ( R s ) is a measure of the CME’s initial velocity. In the simulation, theCME’s outflow velocity is a function of a solar subsurface current that generates the CMEflux rope and the strength of the reconstructed surrounding solar magnetic fields. For thesetup of each CME we varied the subsurface current and determined the resulting CMEspeed as the slope of the CME’s height-time diagram below 6 R s .A crucial result, illustrated in Fig. 1 for the six simulated events, is a closely linearrelationship between the subsurface current and the average CME speed below 6 R s .The lines that connect the diamonds belong to simulations with an initial level 5 gridresolution, and the lines that connect the stars belong to simulations with an initial level2 grid resolution. Note that both the level 2 and level 5 simulations show linear relationsbetween current and CME velocity, differing substantially in slope between level 2 andlevel 5 runs but being very similar between events with the same initial grid refinementlevel. The linear relationship for each specific event and a given grid refinement level wasthen used to tune the subsurface current required to match the observed CME speed, D R A F T May 23, 2019, 1:35am D R A F T
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X - 7 which was evaluated using the CAT tool. No other tuning was performed. Note that only3 runs are thus required to simulate a given event; 2 to define the linear relation and 1for the fine-tuned run.Another important refinement was to increase the number of grid cells in the simulationto about 16 million cells from the default of about 32,000 cells, corresponding to increasingthe initial grid refinement level from two to five and an average spatial grid resolution ofabout 1 R s (or 1 hour convection time) at 1AU. This reduces the numerical dispersionof the code and allows simulation of sharp CME-driven shocks that define precise arrivaltimes at 1 AU.Importantly, the increased grid resolution leads to a decreased initial CME accelerationwith the CME launcher inbuilt in the code. This requires the subsurface current thatgenerates the CME magnetic fields to be increased in order to obtain the observed initialCME outflow speed, as shown in Fig. 1. Typical currents in our refined simulations areabout 3 × A, which are larger than the currents of 2 . × A - 6 × A in
Manchester et al. [2008, 2012].
Melrose [2017] states that the typical current for a fluxrope in an active region driving a flare is 1 × A, but he also states that this current canbe much larger.
Titov and D´emoulin [1999] and
Savcheva et al. [2012] fitted observed fluxropes in an active region with a current of 7 × A and 2 × A, respectively. Thus,the electric currents in our refined simulations are in the observed range. Interestingly,the currents in our level 2 runs are a factor of ≈
10 smaller than for the level 5 runs(Fig. 1). The values are in the range 1 − × A. D R A F T May 23, 2019, 1:35am D R A F T - 8
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A final refinement, of lesser importance here, is that before releasing the CME we ranthe code in time-independent mode for 1000 steps (rather than the default 300) in orderto obtain a more settled plasma-field system out to 1 AU.
3. Simulation results
The six CME events we simulated started on 4 Sep 2017 at 19:12 UT, 6 Sep 2017 at12:30 UT, 7 Sep 2017 at 10:36 UT, 7 Sep 2017 at 15:24 UT, 12 Feb 2018 at 2:00 UT, and 29Nov 2013 at 20:00 UT, based on CACTUS detections. The first five of these were launchedclose to the Sun-Earth direction, while the 29 Nov 2013 event headed toward STEREO A.In Fig. 2 we show colour-coded snapshots of the simulated magnetic field strength in theecliptic plane at a specific elapsed time for each event. The yellow-bounded red featuresin each panel of Fig. 2 show the propagating CME and its driven shock. Clearly, the firstfive CMEs are predicted to hit the Earth and the sixth CME to hit STEREO A.Figures 3(a) and (b) show the observed (solid lines) and simulated (stars) magneticfield strengths at the position of the Earth as functions of time for the two 7 Sep 2017events. While the simulated CMEs do reach Earth, the simulated fields are always andusually well below the observed fields for the first and second events, respectively. This isconsistent with the observations not showing any signatures of a shock wave. The otherMHD variables also show no observable shock or CME signatures.Fig. 4 presents the simulated and observed arrival times of the CME-driven shocksfor the 4 Sep 2017, 6 Sep 2017, and 12 Feb 2018 CMEs at Earth (events 1 to 3) andat STEREO A for the 29 Nov 2013 CME (event four), defined as the temporal positionhalfway up the CME-driven shock ramp. In each case the difference between the simulatedand observed shock arrival times is less than 2 hours. The average of the absolute value of
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X - 9 the difference is 0.9 ± ± ± Wold et al. , 2018]. We interpret the increased prediction accuracy of CME arrival timesat 1 AU for our approach as a consequence of (a) demonstration of a linear relationshipbetween the solar subsurface current and the average CME speed below 6 R s , which allowsus to fine-tune precisely the solar subsurface current to the CME outflow speed observedbelow 6 R s , and (b) increasing the initial grid resolution by three levels, leading to sharperCME-driven shocks, less numerical dispersion (and viscosity), and changed propagationspeeds. This type of linear relation likely exists for other simulation codes, suggestingthat our approach for fine-tuning is likely widely applicable.Fig. 5 overplots the initial speeds and average accelerations for the CME events ontoFigure 2 of Gopalswamy et al. [2000], which shows observational data and a fitted linearmodel between the observed initial CME speeds and average accelerations. We determinedthese parameters as the slope and curvature of CME height-time diagrams measured inthe simulation box. We find that the simulation results are very close to the
Gopalswamyet al. [2000] model and associated data. Thus, the CMEs simulated with the BATS-R-UScode appear to have very similar dynamical properties to observed CMEs.An issue with our level 5 simulations is that, as a consequence of the large flux ropecurrents, the simulated CME magnetic fields near 1 AU are about ten times larger thanthe observed fields. Also, the present approach does not accurately predict the ambientsolar wind plasma and field parameters in the ecliptic near 1 AU, as also found in many
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SCHMIDT AND CAIRNS: SPACE WEATHER RELEVANT FEATURES other papers for multiple simulation codes [e.g.,
Cohen et al. , 2008;
Jian et al. , 2011;
Gressl et al. , 2012;
Shen et al. , 2018;
Den et al. , 2018;
T¨or¨ok et al. , 2018]. From anoperational point of view such imprecisions in CME fields and solar wind properties areof lesser concern, compared with the gain in prediction accuracy of the CME arrival timeat 1 AU demonstrated below for our simulations. Our opinion is that the greater priorityfor the space weather community is a tool to predict these arrival times more accurately,as described above.Turning now to the B z predictions, Fig. 6 shows the simulated (stars) and observed(solid line) B z magnetic field as a function of time at Earth for the 4 Sep 2017, 6 Sep2017, and 12 Feb 2018 CME events and at STEREO A for the 29 Nov 2013 CME event.For the 4 Sep 2017 CME event in Fig. 6(a) the simulated B z turns abruptly negative atthe shock arrival time (hour 11.5 ± < -15 nT until after hour 25. Theobserved B z component is highly disturbed just before and after the CME-driven shock: B z turns positive near hour 11, has two large oscillations, then turns strongly negativewith large oscillations around hour 13.5, and remains predominantly negative until hour23. The BATS-R-US simulation is not able to predict the major oscillations of B z beforeor after the shock transition. However, the simulated change in B z onsets within 2 hoursof the right time and is predominantly negative. Thus, ignoring the oscillations in B z , thepolarity of the change in B z appears to be predicted correctly, suggesting that this CMEevent should be geoeffective. An increase of the Kp index to 5 on 6 Sep 2017 8:00 UTwas indeed observed.Similar patterns are found for the other events. For the 6 Sep 2017 CME event astrongly negative change in B z is predicted at the shock transition. This negative change D R A F T May 23, 2019, 1:35am D R A F T
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X - 11 coincides well with the observed change in B z , which however shows major oscillationsand becomes positive 3 hours later. Thus, the onset of a trigger for space weather ispredicted reasonably well for the 6 Sep 2017 event.The simulated B z component for the 12 Feb 2018 CME event also becomes stronglynegative after the shock transition and remains there. The location of the large negativechange in B z is very close to the onset of the observed CME-driven shock, after whichthe observed B z starts to oscillate substantially. The observed oscillations in B z are notcaptured in the simulation.Finally, the simulation for the 29 Nov 2013 CME event correctly predicts the onset andmagnitude of a large negative change in B z shortly after the shock arrival, which is latercompletely obscured by very strong oscillations observed in B z . If STEREO A were atEarth, it would be reasonable to predict a space weather event.Noting that resolving a change reliably requires at least 3 radial cells and so a convec-tion time of ≈ R s /v sw ≈ B z on timescales of 1-2 hpurs. More-over, given the large amplitude of these oscillations in the observed B z time series, it isunclear how well B z is modelled behind the shock. In detail, while the 6 Sep 2017 and29 Nov 2013 events show the predicted change in B z directly behind the shock, the 4 Sep2017 and 12 Feb 2018 events are obscured by large oscillations in B z . Accordingly, no firmconclusion can be reached at this time whether the sign of B z is adequately predicted inour simulations. D R A F T May 23, 2019, 1:35am D R A F T - 12
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4. Discussion and conclusions
We have simulated the propagation of six observed CMEs from the Sun to either Earthor STEREO A with the 2012 BATS-R-US code and examined the implications for spaceweather predictions. We developed a refined approach that determines the CME parame-ters using CAT and coronagraph data, and implements (and shows the necessity of) muchhigher initial grid refinement levels and numbers of simulation cells to reduce numericaldispersion and attain (relatively) sharp shocks, fine-tunes the CME launch using a newlinear relationship between flux rope current and initial average CME speed below 6 R s ,and uses a more settled plasma-field system out to 1 AU. This approach for 6 eventsresults in the greatly improved and accurate (error of 1 ± Gopalswamy et al. [2000]. It also showspromise in predicting the dominant sign of B z after shock arrival, although the trendin B z is obscured and made less reliable by large oscillations observed in the B z data.Therefore, our approach appears to predict well the onset of triggers for possible spaceweather events.However, the BATS-R-US code does not simulate the large oscillations observed in B z in the solar wind or after the CME-driven shock arrival, although for stronger CME events(the 6 Sep 2017 and 29 Nov 2013 events) the simulated and observed negative changesin B z are in better quantitative agreement. Of more general concern, there are majorquantitative differences between the simulated and observed magnetic fields and plasmaparameters. These issues require further work. D R A F T May 23, 2019, 1:35am D R A F T
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Having steeper and more realistic CME-driven shocks in the simulation requires 5th levelinitial grid refinement and 16 million simulation cells. In order to make the simulationoperational, where the sum of the setup, simulation, and analysis times is much less thanthe propagation time of the CME from the Sun to 1 AU, requires use of a large parallelcomputer. For our cases, with 96 processors, these times were ≈ ≈ ≈ B z upon arrival, it appears that this code and refined setupapproach are appropriate for space weather predictions and should be explored further. Acknowledgments.
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Figure 1.
Simulated CME outflow speeds (diamonds) as a function of the solar subsurfacecurrent for the six CME simulations with level 5 grid refinement. The relationship is closelylinear. The stars are for runs with level 2 grid refinement, and ’X’ denotes the fine-tuned valuefor the 29 Nov 2013 event.
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Figure 2.
Simulated magnetic fields in the ecliptic plane for the CME events of (a) 4 Sep 201719:12, (b) 6 Sep 2017 12:30, (c) 7 Sep 2017 10:36, (d) 7 Sep 2017 15:24, (e) 12 Feb 2018 2:00, and(f) 29 Nov 2013 20:00, propagating toward the Earth (a)-(e) and STEREO A (f). The centralblue dot in each panel is a sphere of 20 R s surrounding the Sun. The red circle is the orbit ofthe Earth with a red dot labelled E marking Earth. In Fig. 2(f) the red dot denotes the positionof STEREO A. D R A F T May 23, 2019, 1:35am D R A F T - 20
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Figure 3.
Simulated magnetic field (stars) and ACE data (solid lines) at Earth’s orbit for the(a) 7 Sep 2017 10:36 and (b) 7 Sep 2017 15:24 CME events. The simulated field remains belowor near the observed background, which shows no signature of a shock arrival.
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Figure 4.
Observed (simulated) arrival times of the shock at 1 AU as diamonds (stars for level5 grid refinement and squares for level 2 grid refinement) in order for the 4 Sep 2017 CME (event1), the 6 Sep 2017 CME, the 12 Feb 2018 CME, and the 29 Nov 2013 CME (event four). Theobserved and simulated arrival times for level 5 grid refinement match each other very well. Thepredictions for level 2 grid refinement are less accurate because of much broader shock fronts.
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Figure 5.
Simulation results for the initial shock speed and average acceleration for the 4Sep 2017, 6 Sep 2017, 12 Feb 2018, and 29 Nov 2013 CME events, as derived from height -time measurements in the simulation box, are superposed onto Figure 2 of
Gopalswamy et al. [2000]. Crosses are for level 5 grid refinement simulations and stars for level 2 grid refinementsimulations. The simulation results agree well with the empirical models of
Gopalswamy et al. [2000] (dashed and solid lines) and associated data (diamond and plus symbols).
D R A F T May 23, 2019, 1:35am D R A F T
CHMIDT AND CAIRNS: SPACE WEATHER RELEVANT FEATURES
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Figure 6.
Simulated variations in B z (stars) at 1 AU for the (a) 4 Sep 2017, (b) 6 Sep 2017, (c)12 Feb 2018, and (d) 29 Nov 2013 CME events. The solid lines are ACE (a)-(c) and STEREOA (d) B z measurements. Vertical lines denote the observed shock transition.measurements. Vertical lines denote the observed shock transition.