CONNECTING SPEEDS, DIRECTIONS AND ARRIVAL TIMES OF 22 CORONAL MASS EJECTIONS FROM THE SUN TO 1 AU

Storms from the Sun, known as coronal mass ejections (CMEs), are massive, quickly expanding expulsions of plasma threaded by magnetic fields, originating from both quiescent and active regions in the Sun's corona. Over a distance of a few solar radii, they may accelerate up to speeds of 3000 km s⁻¹ in rare cases, and they subsequently propagate through the solar wind away from the Sun. CMEs are able to reach 1 AU in half a day in the most extreme cases, and they are the source of the strongest disturbances in the Earth's magnetosphere (e.g., Zhang et al. 2007).

Forecasting their general properties, such as propagation direction and speed close to the Sun and in the interplanetary (IP) medium, as well as their arrival time and arrival speed at a given planet or spacecraft, is a major issue in the field of heliophysics. Moreover, the science that underlies our ability to predict CME arrival times and speeds with high precision, which is at the heart of a reliable, real-time space weather forecast, is still not well understood, with average errors of the order of 0.5 to 1 day and several 100 km s⁻¹, respectively (e.g., Gopalswamy et al. 2001). Recent advances in analyzing multi-point imaging data have improved these classic values for a few CME events by roughly a factor of two (Mishra & Srivastava 2013; Colaninno et al. 2013). While this is clearly of greatest interest for the location of the Earth, predictions and parameters of CMEs impacting Mercury, Venus, Mars, Jupiter, and Saturn are also essential for studying their interaction with other planetary environments (e.g., Baker et al. 2013).

The Solar TErrestrial RElations Observatory (STEREO; Kaiser et al. 2008), launched in late 2006, consists of two spacecraft, one ahead (STEREO-A) and one behind the Earth (STEREO-B) in orbits around the Sun. Each year, each spacecraft separates from the Earth by about 22° in heliocentric longitude. Its SECCHI instruments seamlessly image CMEs from the Sun to 1 AU and beyond. We are able to extract CME speeds and directions from the images in order to pin down CME evolution and assess CME predictions (e.g., Möstl et al. 2009b; Wood et al. 2010; Liu et al. 2010a, 2013; Lugaz et al. 2010; Lynch et al. 2010; Savani et al. 2010; Davis et al. 2011; Liewer et al. 2011; Möstl et al. 2011; Savani et al. 2012; Rollett et al. 2012; Mishra & Srivastava 2013; Colaninno et al. 2013; Davies et al. 2013). Even numerical simulations have been employed to enhance our ability to derive the physics of solar wind structures from heliospheric imaging (e.g., Lugaz et al. 2009, 2011; Xiong et al. 2013a, 2013b; Rollett et al. 2013). A concerted campaign to analyze the series of CMEs launched by the Sun on 2010 August 1 has also revealed many details of CME propagation and their 3D evolution for interacting CMEs (Liu et al. 2012; Harrison et al. 2012; Möstl et al. 2012; Webb et al. 2013; Temmer et al. 2012).

A deceptively simple but persistent problem in the analysis of CMEs has been to find definite connections between the remote images of CMEs (Illing & Hundhausen 1985), taken by coronagraph or heliospheric imager instruments, and the signatures of CMEs in time series of plasma and magnetic field measurements taken directly (in situ) in the solar wind (Burlaga et al. 1981). Current space-based coronagraphs on three different spacecraft (STEREO-A/COR1/COR2, STEREO-B/COR1/COR2, and SOHO/LASCO) can image a CME in its entirety during its "birth" and early propagation phase (1–15 solar radii). These instruments provide white-light images of CMEs projected into the plane of the sky, i.e., the plane perpendicular to the Sun–spacecraft line. As the CME propagates farther away from the Sun, heliospheric imager (HI) instruments image, in white light, its integrated density signature around the so-called Thomson surface (Vourlidas & Howard 2006) or Thomson plateau (Howard & DeForest 2012b) at elongation angles of 4°–88° from the Sun (for STEREO/HI). Because of the wider viewing angle, the interpretation and analysis of HI data are more complex compared to coronagraphs and not yet fully understood (e.g., Rouillard 2011; Howard & DeForest 2012b).

When a CME hits a spacecraft with in situ instruments on board that are capable of characterizing the solar wind plasma and magnetic fields, it leads to distinct signatures in the time series of the measured parameters. Often, a shock is followed by a sheath region in front of a magnetic driver, which is either an irregular structure or a large-scale magnetic flux rope (e.g., Burlaga et al. 1981; Bothmer & Schwenn 1998; Lynch et al. 2003; Leitner et al. 2007; Möstl et al. 2009a; Richardson & Cane 2010; Isavnin et al. 2013; Al-Haddad et al. 2013). We call the interval including all of these signatures an "interplanetary CME" or "ICME." Throughout this paper, we use the term "CMEs" for events observed in images and "ICMEs" for ejecta identified from in situ measurements. However, these measurements of the in situ solar wind give a detailed but otherwise extremely limited and localized view of a CME at the position of the spacecraft near 1 AU. At this distance, a CME has already expanded into an enormous structure, covering up to around 100° in heliocentric longitude and several tenths of an AU along the radial direction to the Sun (Burlaga et al. 1981; Bothmer & Schwenn 1998; Liu et al. 2005; Richardson & Cane 2010; Wood et al. 2010; Möstl et al. 2012). Thus, progressing farther from the Sun leads to less and less information on the global structure of the CME, which is increasingly hard to interpret, providing a first explanation for the difficulties in linking the data sets.

As a background to our study, it needs to be understood that CMEs are almost never really single entities, but they react to their coronal and heliospheric environments (e.g., Temmer et al. 2011; Kilpua et al. 2012; Rollett et al. 2012). A possible general paradigm of CME propagation through the solar wind has recently emerged. Liu et al. (2013) state a picture of Sun-to-Earth propagation of fast CMEs, derived from a joint analysis using stereoscopic heliospheric images and radio and in situ observations of three CME events: fast CMEs impulsively accelerate close to the Sun, followed by a rapid deceleration out to about 0.4 AU, culminating in an almost constant speed propagation phase (see also, e.g., Gopalswamy et al. 2001, for earlier, similar ideas).

Our paper addresses the problem of seamlessly connecting CMEs from the Sun to 1 AU in two ways. First, we establish a list of suitable CME events from 2008 to 2012, using observations by coronagraphs, heliospheric imagers, and in situ instruments on board the STEREO and Wind spacecraft and model the imaging observations using single-spacecraft state-of-the-art "geometrical modeling" methods. Second, we use these connections to enhance our understanding of CME propagation and their prediction, focusing on the improvement of methods to extract CME parameters from heliospheric imager data. Our study builds on the results of Lugaz et al. (2012), who analyzed CMEs in STEREO/HI data that impacted the other STEREO spacecraft during the interval 2008–2010. This study established that predictions of speeds and arrival times for slow CMEs are roughly consistent with corresponding in situ parameters, and demonstrated the possibility for successfully predicting CMEs that propagate behind the limb or on the backside of the Sun as viewed from HI. However, our paper goes further along several, critical avenues: we included modeling with the new self-similar expansion fitting (SSEF) technique (Davies et al. 2012), which allows more flexibility for the CME width in the solar equatorial plane than previous models, which were either point-like (fixed-Φ, Sheeley et al. 1999; Rouillard et al. 2008) or extremely wide (harmonic mean, Lugaz et al. 2009, 2010). In addition, we now have STEREO data of very fast CMEs (>2000 km s⁻¹) available, and we mainly discuss Earth-directed events. The STEREO separation from Earth increased from 22° in early 2008 to 120° in mid-2012; thus, we include in our study backsided events (from the point of view of a STEREO spacecraft), similar to Lugaz et al. (2012).

Several lines of research have recently converged to make this work possible, apart from having available the remote STEREO observatories in conjunction with the Wind spacecraft (the latter at the Sun–Earth Lagrangian 1 or L1 point): (1) the existence of software packages (i.e., SATPLOT and croissant modeling) to easily extract and fit CMEs in STEREO/COR2 and HI data, (2) the development of mature models to obtain CME speeds and directions from heliospheric imagers, and (3) the rise of solar cycle 24, which culminated in several very fast CMEs. All this now gives us the opportunity to study the potentially most geoeffective events with multi-point in situ and imaging data (e.g., Liu et al. 2013; Davies et al. 2013).

The connections established in our paper may be used by other researchers to benchmark any empirical or numerical propagation model of CMEs. We need to emphasize that our paper focuses on establishing connections between the data sets, which means that we track CMEs as far as possible through the HI data, up to 30°–40° elongation from the Sun. For this reason the prediction lead times, which are the differences between the last data points used for extracting CME parameters and the actual in situ arrival times, are relatively short, of the order of one day. This should be kept in mind when discussing our results for the errors in CME speeds and arrival times. Shorter tracks in HI must be used in order to increase the prediction lead time to values suitable for real-time forecasting, namely, from more than 1 day for fast CMEs to several days for slow CMEs. Such an analysis was carried out by Möstl et al. (2011) for a case study and is the aim of future studies that will exploit our full data set, consisting of 22 CME events. The differences in speeds and arrival times that we derive from comparing the HI data to the in situ data thus show how well a HI system configured as on STEREO can perform for CME forecasting.

This section illustrates the observations and models we used to extract CME parameters from various imaging and in situ data. We chose the events in our list by the criteria that each CME has (1) clear in situ signatures and (2) a clear track in J maps from one STEREO/HI instrument. We then tracked back the CME in the HI J map to the coronagraph images to find the corresponding CME observations in the corona. We do not attempt to provide a full list of all CMEs directed toward Earth and STEREO during the time between 2008 April and 2012 July. However, some of the brightest, fastest, and best-studied events in this time range show up in our list. A well-observed, Earth-directed CME that left the Sun on 2012 July 12 and arrived at Earth on 2012 July 14 serves to demonstrate our data pipeline.

2.1. Croissant Modeling

The so-called croissant model, also known as the "Graduated Cylindrical Shell" model, is a very well tested tool, available in the IDL SolarSoft package, for deriving the initial directions and speeds of CMEs in the fields of view of the STEREO/COR2 coronagraph, covering 2.5–15.6 R_☉ (Thernisien et al. 2006, 2009). At least two viewpoints are needed. Sometimes, the additional viewpoint of the SOHO/LASCO C2 and C3 coronagraphs at the near-Earth L1 point is used, to either give the second view or to provide a third. C2 and C3, combined, cover a distance of 1.5–30 R_☉ (Brueckner et al. 1995). The model has also been recently extended for the fields of view of heliospheric imaging (Colaninno et al. 2013), but we will use it in the classic way for analyzing coronagraph images only. Essentially, the model approximates the CME shape as a bent tube that is reminiscent of a croissant, with the mass distributed uniformly on its surface. This shape was chosen to be consistent with a geometry of the CME internal magnetic field as a bent, cylindrical magnetic flux rope. The application of the model consists of manually adjusting parameters that define the CME shape and direction to best fit images of the CME provided by coronagraphs. The major advantage of using this model is that it provides reliable results for the initial 3D propagation direction and initial speed of a CME, free of projection effects. The downside is that not every CME can be approximated by the shape of a croissant, and often CMEs occur within a few hours of each other, making it difficult to distinguish the different physical parts of each CME. Nevertheless, Vourlidas et al. (2013) found that close to the Sun, at least 40% of CMEs possessed a flux-rope-like structure. We refer the reader to an extensive discussion on the morphology of CMEs in coronagraphs that is provided by those authors.

As an example, the top row in Figure 1 shows images of the 2012 July 12 17:24 UT CME, and the bottom row a green grid of the croissant model overlaid on the same images. It can be seen that the croissant represents the shape of the CME well in all three viewpoints. It becomes clear that this CME is roughly directed toward the Earth, appearing as a full halo in SOHO/LASCO, and being directed to solar west from STEREO-B and to solar east from STEREO-A. To get the CME initial speed V_init, we linearly fit height-time measurements for the croissant's apex over a few data points (e.g., Colaninno et al. 2013). Thus, V_init is an average speed between 2.5 and 15.6 R_☉. The initial CME direction is similarly obtained by adjusting the wire-grid model to the images, and averages over a few data points define the initial CME direction in heliocentric longitude (Φ_{init; Earth}) in the solar equatorial plane, with the Earth as a reference point at 0° longitude.

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Common errors associated with croissant modeling are ±10° in heliocentric longitude for the CME propagation direction and ±10% of the average CME speed (e.g., Thernisien et al. 2009; Temmer et al. 2012). In Table 1, all results derived with the croissant model are summarized in Columns 2–4, including the time t_COR2 of the first observation in STEREO-A/COR2 images, the initial direction with respect to Earth (Φ_{init; Earth}), and the initial speed (V_init). For events 16 to 24 in Table 1, we have used three viewpoints (STEREO-A/B and SOHO), and for the other events the two viewpoints as provided by STEREO-A/B. For Earth-directed CMEs, which appear symmetric in STEREO-A/B, an additional viewpoint provides more reliable results (Vourlidas et al. 2011).

Table 1. Imaging: Croissant and Geometrical Modeling (SSEF) Results

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
CME	tCOR2	Φinit; Earth	Vinit	ΦIP; Earth	ΦIP; HI	VIP	VIPo	ta	Spacecraft
1	2008 Apr 26 14:53	−20	523	−45	−70	656	611	2008 Apr 29 13:21	STEREO-B
2	2008 Jun 1 21:23	−37	260	−15	−44	384	375	2008 Jun 6 22:34	STEREO-B
3	2008 Jun 2 02:07	...a	...	−44	−73	398	369	2008 Jun 7 12:39	STEREO-B
4	2008 Dec 12 07:37	8	497	10	55	421	414	2008 Dec 16 11:01	Wind
5	2008 Dec 27 05:23	−32	405	−79	−122	603	452	2008 Dec 31 05:01	STEREO-B
6	2009 Feb 13 06:37	...b	...	−75	−119	396	329	2009 Feb 18 11:11	Wind
7	2010 Apr 3 09:54	4	829	−19	−86	991	915	2010 Apr 5 06:35	Wind
8	2010 Apr 8 03:54	3	511	−34	−102	555	407	2010 Apr 12 07:19	Wind
9	2010 May 23 17:39	10	381	8	−63	440	433	2010 May 27 17:02	Wind
10	2010 Jun 16 11:24	−16	297	13	−62	376	364	2010 Jun 21 08:00	Wind
11	2010 Aug 1 08:24	−28	1160	−43	−122	980	808	2010 Aug 3 13:18	STEREO-B
12	2010 Aug 1 08:24	−28	1160	−43	−122	980	525	2010 Aug 4 14:34	Wind
13	2011 Feb 15 02:09	23	557	−40	−127	867	536	2011 Feb 18 04:21	Wind
14	2011 Aug 2 06:39	−29	1050	−25	−125	714	617	2011 Aug 5 00:14	Wind
15	2011 Sep 6 22:39	34	1160	−24	−127	838	731	2011 Sep 9 08:11	Wind
16	2011 Oct 22 01:09	19	692	−15	−120	813	772	2011 Oct 24 07:52	Wind
17	2012 Jan 19 15:09	−37	1335	−36	−144	1097	767	2012 Jan 21 19:03	Wind
18	2012 Jan 23 03:09	21	1708	−33	−141	2181	1644	2012 Jan 24 03:54	Wind
19	2012 Mar 5 04:09	−53	974	−41	−150	1347	807	2012 Mar 7 06:37	Wind
20	2012 Mar 7 01:39c	−35	2585	−42	−151	2202	1265	2012 Mar 8 08:34	Wind
21	2012 Mar 10 17:54	27	1265	−6	−116	1297	1286	2012 Mar 12 00:44	Wind
22	2012 Apr 19 16:24	−26	639	−20	−133	785	713	2012 Apr 22 01:46	Wind
23	2012 Jun 14 14:09	0	1102	−28	−145	1453	1205	2012 Jun 16 00:02	Wind
24	2012 Jul 12 16:54	−1	1277	−22	−142	1486	1336	2012 Jul 13 23:50	Wind

Notes. Explanation of parameters: (1) Number of CME event. (2) Date and time (UT) of the first image in COR2A when the CME is observed. (3) The initial direction (in degrees) in heliocentric longitude (Heliocentric Earth Equatorial or HEEQ coordinates) of the CME from croissant modeling (2.5–15.6 R_☉). Earth is at 0° longitude; angles >0° correspond to solar west. (4) The initial speed of the CME from croissant modeling, in km s⁻¹. (5) The IP direction (in degrees) of the CME in heliocentric longitude (close to but not exactly in the solar equatorial plane; see Section 2.2), from geometrical SSEF modeling with 45° half-width (Earth at 0°). (6) The IP direction of the CME apex in degrees, measured from the HI observer (at 0°). (7) The CME IP propagation speed, for the apex of the front (for the SSEF model), in km s⁻¹. (8) The speed of the point along the CME front that travels toward the in situ spacecraft (for the SSEF model), in km s⁻¹. (9) Date and time (UT) of the predicted arrival at the in situ spacecraft, from SSEF modeling. (10) Name of the in situ spacecraft for which the predicted arrival time t_a is calculated. ^aThis event is the core or trailing part of the CME on June 1, so it is not fitted with the croissant model. ^bThis CME was too faint to be fitted with the croissant model. ^cThis is the second CME of a double eruption of the same active region, with another CME first observed at 00:39 UT in COR2A. We quote the croissant results for the second event because it is mainly directed in the ecliptic plane and thus more likely to impact Earth, whereas the first CME is directed mainly northward.

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2.2. Geometrical Modeling

Figure 2 is a summary of the application and the results of the geometrical modeling techniques. Figure 2(a) shows an elongation versus time plot or J map (e.g., Sheeley et al. 1999; Rouillard et al. 2008; Davis et al. 2009; Liu et al. 2010b) for STEREO-A on 2012 July 12–15. In this plot, a stripe of a combined STEREO/COR2/HI1/HI2 image is extracted along a given position angle (P.A.), indicating the solar latitude that is presented. The stripes are then put together vertically one after another to form a J map (with a 30 minute time interval). The P.A. is measured from solar north (0°) to east (90°), south (180°), and west (270°). Consequently, when using STEREO-A(B) images, a P.A. of around 90° (270°) should be chosen to obtain measurements in the solar equatorial plane, which is also close to the ecliptic plane where the in situ observations are made.

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In reality, CMEs often propagate away from the solar equatorial plane (e.g., Kilpua et al. 2009), and their signature is too faint around P.A. = 90°. For such CME events we choose a P.A. between 77° and 95°, depending on at which P.A. we were able to capture the CME front clearly. For the J map in Figure 2(a), P.A. = 80°, using data taken within D = ±3° of this P.A. This is also the reason that we will not further distinguish between measurements in the solar equatorial plane (valid for the croissant results) and ecliptic plane (valid for in situ results), because the HI data connecting the solar to in situ measurements are not exactly taken in either of these planes. This does not affect our conclusions because the resulting systematic error in heliocentric longitude of a few degrees is much lower than the differences between CME directions given by the different HI models, of the order of >10°.

Figure 2(a) was created with the SATPLOT software package, freely available in IDL SolarSoft. With this tool, a user can produce J maps and movies from data from both STEREO/HI instruments and interactively extract time-elongation (t) functions of dense solar wind structures by clicking in the J map (see the online manual for more information on the SATPLOT package). In our study, these are measurements of the CME leading edge, which is the front of a gray or white trace in the J maps indicating enhanced solar wind densities. This signal arises for an HI observer due to Thomson scattering of photospheric light off solar wind electrons, over a range of distances along the line of sight (Vourlidas & Howard 2006; Howard & DeForest 2012b).

Figure 2(b) shows the result of fitting the extracted (t) track using the SSEF model (Davies et al. 2012; Möstl & Davies 2013). This provides, for the time and elongation range of the HI observations, an average CME speed and its direction, as well as its arrival time at Earth and the other STEREO spacecraft. This fitting procedure works autonomously and takes only a few seconds. We also use two other models, the fixed-Φ fitting (FPF; Sheeley et al. 1999; Rouillard et al. 2008) and harmonic mean fitting (HMF; Lugaz 2010; Möstl et al. 2011) techniques, which are both available in SATPLOT. It is important to emphasize that these methods are all used for a single-spacecraft HI observer. Essentially, all of these models are based on purely geometrical considerations and use the concept that deceptive acceleration and deceleration arises in (t), depending on the speed and direction of the CME with respect to the HI observer (see, for example, extensive descriptions in Lugaz 2010; Möstl et al. 2011; Davies et al. 2012; Lugaz & Kintner 2013). We appropriately call them "geometrical models." All methods share the same assumptions of constant CME speed and direction, but differ on the description of the global shape of the CME front.

Figure 2(c) shows the resulting CME directions for the 2012 July 12–14 CME event in the IP medium and also serves as an illustration of the different geometries. The FPF model assumes a point-like CME without any extension in heliocentric longitude (the dot-dashed red line). The HMF model is shown as a very wide blue circle, with λ = 90°, where λ is the CME half-width (e.g., Davies et al. 2012; Möstl & Davies 2013). The SSEF model can be seen as a generalization of the FPF and HMF models, because λ can vary anywhere between 0° and 90°, which correspond to FPF and HMF, respectively. In our analysis, every result for the SSEF model uses a half-width of λ = 45°, as this forms the average value between the other two models. It is illustrated by the green circle in Figure 2(c).

For the longitudinally extended HMF and SSEF models, the speed to be compared to the in situ speed is not the apex speed from the geometrical model (V_IP), but a different speed calculated for the point on the CME model front that is directed toward the in situ observatory. We call it V_IPo, for IP speed toward the observer (o). In Figure 2(c), this point is the intersection of the green SSEF circle with the Sun–Earth line, close to Earth. For the FPF model a point-like CME shape is assumed, and it is not possible to differentiate between the two speeds. The speeds V_IPo can be calculated by knowing the apex speed and the difference in heliocentric longitude between the CME apex in the model and the position of the in situ spacecraft. The corresponding formulas are derived and summarized by Möstl & Davies (2013).

There is an error associated with manual measurements of CME fronts in J maps, which is on the order of ±05 in elongation angle (t) (Williams et al. 2009; Liu et al. 2010a; Möstl et al. 2011). Depending on the length of the (t) track, this error will propagate into the results of the geometrical models. In general, we tracked each CME to about 35° elongation from the Sun, because this is a range for which the fitting methods are known to give relatively well constrained results (Williams et al. 2009; Lugaz et al. 2011; Möstl et al. 2011). Because the tracks need to cover a large range in elongation for the fitting techniques to work, the methods cannot be applied to coronagraph measurements.

Concerning ICME directions, ±05 in (t) translates to an error of < ± 5° for CMEs tracked further than 30° elongation from the Sun (Williams et al. 2009; Lugaz et al. 2011; Möstl et al. 2011). Thus, we choose ±5° as the error bar on all plots including directions from geometrical modeling. For the IP speeds V_IP, we experimented with extracting several tracks of a ≈1000 km s⁻¹ CME in J maps created with SATPLOT and found a conservatively chosen error of ±10% in V_IP, which we use on all plots that show IP speeds. A similar range was found by Lugaz et al. (2011) through numerical testing. Our experiment showed systematic errors in the arrival times of a maximum of ±10% of the total CME transit time.

Table 1 presents a summary of results from geometrical modeling. We state, for simplicity, the results from SSEF only (with λ = 45°). The speeds and directions from SSEF are in between those from the extreme models FPF and HMF; thus, the SSEF results form a good average of these parameters. Columns 5–10 of this table show the ICME direction (heliocentric longitude) Φ_{IP; Earth} with respect to Earth and with respect to the HI observer, Φ_{IP; HI}, as well as the speed of the model apex, V_IP, and the speed of the front in the direction of the in situ observatory, V_IPo. Finally, t_a is the predicted arrival time of the CME leading edge at the spacecraft stated in the last column.

2.3. In Situ Solar Wind Data

Figure 3 presents an overview of the near-Earth (L1) in situ solar wind data of proton bulk parameters and magnetic field components from 2012 July 13–18. We show data from the Solar Wind Experiment (SWE; Ogilvie et al. 1995) and the Magnetic Field Investigation (MFI; Lepping et al. 1995) on the Wind spacecraft, at a 1 minute time resolution. For 5 of the 24 in situ ICME arrivals in our study we use magnetic fields and proton data from the IMPACT (Luhmann et al. 2008) and PLASTIC (Galvin et al. 2008) instruments on the STEREO-B spacecraft.

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In Figure 3, we can see the signatures of an ICME in the near-Earth solar wind. A clear shock is seen on 2012 July 14 1738 UT, signaled by sudden jumps in magnetic field, speed, density, and temperature, delimited by the first solid vertical line on the left. Behind the shock follows the sheath region of high-density and high-temperature solar wind and variable magnetic field. Around 2012 July 15 0600 UT, at the second solid vertical line, this region ends and the interval of a magnetic cloud (Burlaga et al. 1981) begins, which extends about 48 hr up to early July 17, where a third vertical line signals the end of the cloud. This region is an example of a clean magnetic structure passing the spacecraft and is characterized by strong magnetic field strength, a smooth rotation of the magnetic field vector, which is shown in Geocentric Solar Ecliptic (GSE) coordinates, and low proton temperature. Such observations are usually interpreted as a magnetic flux rope, extending tube-like from the Sun with a helical magnetic field geometry (e.g., Al-Haddad et al. 2013; Janvier et al. 2013). We do not discuss magnetic cloud geometry further in this paper, but, for completeness, in this case the field rotates from solar east (B_Y > 0) to south of the ecliptic (B_Z < 0) to solar west (B_Y < 0). This cloud is of the east–south–west type (Bothmer & Schwenn 1998; Mulligan et al. 1998), and its axis is consequently roughly normal to the ecliptic plane pointing southward. Also shown are the results for arrival times and speeds by the geometrical modeling methods ("SSEF corr." will be explained in Section 3.2). The fact that they are accurate to within a few hours of the observed arrival time at the location of Earth establishes the connection from the remote HI data to the in situ data near 1 AU.

In Table 2, Columns 5–9, we present in situ results for every ICME event in our data set, derived from similar plots. These parameters are as follows: (Column 5) the arrival time t_insitu of the shock, or, if no shock is present, the arrival time of a significant jump in proton density; (Column 6) the average proton bulk speed V_sheath inside the sheath region, and its standard deviation; (Column 7) the average proton density N_sheath inside the sheath, and its standard deviation; (Column 8) the maximum magnetic field B_max in the full ICME interval (consisting of shock, sheath, and any magnetic structure); and (Column 9) the minimum value of the southward component of the magnetic field (min B_Z) in the full ICME interval. Some of these parameters act as an independent check on the validity of the results of the HI models and highlight differences between the data sets when connecting CME observations from the Sun to 1 AU.

Table 2. In Situ ICME Parameters

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
CME	Spacecraft	di	ΦIP; insitu	tinsitu	Vsheath	Nsheath	Bmax	min Bz	min Dst
1	STEREO-B	1.0280	21	2008 Apr 29 14:10	430 ± 11	16 ± 6	14.0	−9.5	...
2	STEREO-B	1.0542	−11	2008 Jun 6 15:35	403 ± 16	15 ± 7	14.6	−8.6	...
3	STEREO-B	1.0548	19	2008 Jun 7 12:07	384 ± 17	13 ± 7	12.5	−11.3	...
4	Wind	0.9840	−10	2008 Dec 16 06:36	355 ± 9	16 ± 4	10.0	−7.6	...
5	STEREO-B	1.0263	34	2008 Dec 31 01:45	447 ± 10	7 ± 3	9.5	−6.7	...
6	Wind	1.0023	28	2009 Feb 18 10:00	350 ± 8	22 ± 4	12.3	−9.4	...
7	Wind	1.0004	19	2010 Apr 5 07:58	735 ± 18	10 ± 2	21.5	−14.6	−81
8	Wind	1.0021	34	2010 Apr 11 12:14	431 ± 18	10 ± 1	12.7	−8.6	−51
9	Wind	1.0132	−8	2010 May 28 01:52	370 ± 10	19 ± 4	13.7	−12.9	−85
10	Wind	1.0161	−13	2010 Jun 20 23:02	400 ± 6	8 ± 3	8.6	−2.8	...
11	STEREO-B	1.0604	−28	2010 Aug 3 05:00	632 ± 47	4 ± 4	33.2	−30,2	...
12	Wind	1.0146	43	2010 Aug 3 17:05	581 ± 16	10 ± 2	19.2	−11.2	−67
13	Wind	0.9881	40	2011 Feb 18 00:48	497 ± 27	25 ± 11	31.8	−24.3	...
14	Wind	1.0145	25	2011 Aug 4 21:18	413 ± 12	6 ± 1	10.1	−8.1	−107
15	Wind	1.0072	24	2011 Sep 9 11:46	489 ± 47	12 ± 14	23.3	−21.4	−69
16	Wind	0.9946	15	2011 Oct 24 17:38	503 ± 15	26 ± 4	24.3	−22.1	−132
17	Wind	0.9841	36	2012 Jan 22 05:28	415 ± 18	26 ± 17	30.8	−27.9	−69
18	Wind	0.9844	33	2012 Jan 24 14:36	638 ± 34	8 ± 2	30.5	−15.7	−73
19	Wind	0.9924	41	2012 Mar 7 03:28	501 ± 65	14 ± 5	18.8	−18.2	−74
20	Wind	0.9927	42	2012 Mar 8 10:24	679 ± 44	12 ± 4	30.4	−18.4	−131
21	Wind	0.9938	6	2012 Mar 12 08:28	489 ± 23	24 ± 9	29.2	−23.6	−50
22	Wind	1.0055	20	2012 Apr 23 02:14	383 ± 8	24 ± 7	15.9	−15.3	−108
23	Wind	1.0160	28	2012 Jun 16 19:34	494 ± 29	50 ± 24	41.0	−21.0	−71
24	Wind	1.0165	22	2012 Jul 14 17:38	617 ± 39	16 ± 6	27.7	−18.3	−127

Notes. Explanation of parameters: (1) Number of CME event. (2) The spacecraft that detected the ICME, using data from the PLASTIC (plasma) and IMPACT (magnetic field) instruments on STEREO-B, and SWE (plasma) and MFI (magnetic field) on Wind. (3) Heliocentric distance of the in situ spacecraft at ICME arrival, in AU. (4) Difference between the ICME direction (heliocentric longitude, from the SSEF model) and the HEEQ longitude of the in situ spacecraft, in degrees (Earth at 0°). Small angles indicate central hits, larger angles flank hits. For angles >0° (<0°), the in situ observer is west (east) of the CME apex derived from SSEF. (5) The date and time (UT) of the in situ detection of the shock, or a significant increase in density ahead of a magnetic structure, if no shock is present. (6) The mean proton bulk speed in the ICME sheath region, and its standard deviation, in km s⁻¹. (7) The mean proton density in the sheath region, and its standard deviation, in cm⁻³. (8) The maximum magnetic field (nT) in the ICME, including the sheath and ejecta intervals. (9) The minimum value of B_Z (nT) in the ICME, the component of the magnetic field normal to the ecliptic plane (for Wind) or the solar equatorial plane (for STEREO-B). (10) The minimum value of the Dst index (nT), provided by Kyoto, during the geomagnetic storm following the arrival of the ICME at Earth. Values > − 50 nT and events directed toward STEREO-B are ignored.

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For this comparison, most relevant are the average proton bulk speed inside the ICME sheath region and the arrival time of the shock. The reason that we choose these parameters is that previous research has shown that the density, which is mapped by the HI instrument, and which shows up as a high-density "track" in J maps, corresponds to the region of enhanced plasma density in the ICME sheath (e.g., Rouillard et al. 2009; Möstl et al. 2009b, 2010; Lynch et al. 2010; Liu et al. 2011; Howard & DeForest 2012a). Thus, tracking the leading edge of a CME in a J map essentially means tracking the front of the sheath region, which is the location of the shock. Hence, the predicted arrival time from geometrical modeling corresponds to the shock arrival time observed in situ, and V_IPo corresponds to V_sheath.

These in situ parameters are excellently suitable to act as target values for understanding the performance and limitations of the geometrical models, because they are very well defined and have very small intrinsic errors. The arrival time of the shock can be pinpointed usually to within a few minutes accuracy, which is negligible when compared to the several-hour error in arrival time prediction. For very slow (≈400 km s⁻¹) CMEs, where no shock is usually present, the in situ arrival time can be defined by the start of a high-density region in front of the magnetic structure, to an uncertainty of ±5 hr. This definition was necessary only for the events with numbers 4 and 10 in our list. The speed V_sheath (Column 6 in Table 2) has an average standard deviation of ±23 km s⁻¹. This is only 5% of the average sheath speed of 485 km s⁻¹, so it is also a well-constrained quantity.

In this section, we discuss the results from an analysis of all the parameters that we described in the previous section for the full set of 22 different CME events. For the 2008 June 1–7 CME, there are two tracks in HI, one for the leading and one for the trailing edge, enveloping a magnetic flux rope (Möstl et al. 2009b; Lynch et al. 2010); thus, we have two HI/in situ comparisons for a single CME. Additionally, for the CME on 2010 August 1–4, in situ data are available from the Wind and STEREO-B spacecraft, which observed different parts of the same shock front associated with the fastest and largest of several CMEs launched on the Sun on 2010 August 1 (Liu et al. 2012; Harrison et al. 2012; Möstl et al. 2012; Webb et al. 2013). In total, we end up with 24 different comparisons of imaging to in situ data. To track CMEs in HI data, we use STEREO-A for 21 events and STEREO-B for 1 event because of the slightly higher image quality for STEREO-A and some data gaps for STEREO-B. The imaging parameters are summarized in Table 1, and the in situ parameters are given in Table 2.

3.1. Connecting Coronagraph to HI Data

In this section, we discuss the comparison between CME parameters derived from the different imaging methods of croissant and geometrical modeling (Table 1). Essentially, we look for consistency between the CME speed and direction in the outer corona (<15 R_☉ or 0.07 AU) and in the IP medium (roughly up to 0.85 AU; see Section 3.2.2 for details on the distance range). The initial directions and speeds of the CMEs are very well defined in the corona, as they are constrained by multi-viewpoint imaging; this serves as a point of reference.

3.1.1. CME Directions

Figure 4(a) shows the initial directions Φ_{init; Earth} in the solar equatorial plane of all CMEs in our data set, with the length of the arrow referring to the initial speed, both derived from the croissant model. In the time between the first event in 2008 April and the last event in 2012 July, STEREO-A separated itself from Earth from 25° to 120°. It can be seen that for our specific set of events, the fastest CMEs tended to be launched about 30° east and west of Earth, and only a few events were initially directed centrally toward Earth.

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Figure 4(b) illustrates the IP directions from SSEF modeling (Φ_{IP; HI}), relative to the HI observer, which is at the fixed longitude of 0°. The length of the arrow corresponds to the IP speed of the SSEF circle's apex (V_IP). This figure demonstrates the important point that the fastest CMEs in our data set were all backsided from the vantage point of the HI observer, and that the slow events were mainly frontsided. This is simply a consequence of the weak solar cycle 24, which resulted in CMEs that had well over 1000 km s⁻¹ only after the end of 2011. By this time, the two STEREO spacecraft had already reached a mutual separation greater than 180°.

Figure 5 compares the CME directions from croissant modeling, Φ_{init; Earth}, to those from each geometrical model, Φ_{IP; Earth}. Each panel presents an angular histogram of ΔΦ = Φ_{IP; Earth} − Φ_{init; Earth} with bins of 15° width; Φ_{init; Earth} is at 0° longitude. The black arrow is the average 〈ΔΦ〉. There is considerable scatter; as an example, 90% of IP directions given by FPF are within ±35° of the croissant direction.

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The black arrow on each histogram shows that, on average, the croissant direction is consistent with FPF modeling to within a few degrees, whereas for the SSEF and HMF models, there is a bias in direction that increases with larger CME width. It results in an average difference in 30° longitude between croissant and HMF directions. Because almost all events are observed by STEREO-A, which is positioned to the west of Earth and looks toward solar east, the resulting direction bias is toward solar east or angles <0°. This means that the SSEF and HMF methods place the CME apex farther away from the HI observer. Lugaz & Kintner (2013) showed theoretically that this behavior ultimately results from the constant speed assumption of the models, because the real deceleration of a fast CME in the IP medium is interpreted by the models as geometrical deceleration, which means a change in direction as compared to a CME that is not decelerating. Lugaz & Kintner (2013) argued that the FPF model is in this way superior to the others, because the error resulting from neglecting deceleration is cancelled by neglecting the CME width.

We confirm this relationship from the observations in our data set in Figure 6, where we plot the IP speed V_IP against the difference in direction from the two extreme models FPF and HMF: $\Delta \Phi ^{\prime }_{\mathrm{IP}}=\Phi _{\mathrm{IP; FPF}}-\Phi _{\mathrm{IP;HMF}}$. Higher IP speeds are clearly correlated with larger differences in direction. We also quote linear relationships on the plot from which the resulting FPF–HMF direction difference $\Delta \Phi ^{\prime }_{\mathrm{IP}}$ can be estimated, if V_IP is already known from one of the geometrical models.

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We can take away from this section that connecting CME directions from the corona to the IP medium works to within 30° in heliocentric longitude. However, the models that feature an extended CME width (SSEF and HMF) and that are at first glance more mature than the point-like FPF model produce systematically biased directions for fast CMEs.

3.1.2. CME Speeds and Launch Times

Figure 7 plots the relationship between the initial (V_init) and the IP (V_IP) CME speed of the model apex. For each V_init, the three different speeds by the geometrical models are shown. The black dashed line indicates where V_init = V_IP. We linearly fitted the data for each geometrical model separately. These linear fits work well for this relationship, and they allow one speed to be estimated if the other is known. They result in

$$\begin{equation} V^{\prime }_{\mathrm{IP}}=0.595 \; V_{\mathrm{init}}+277,\quad (\rm{FPF\ model}) \end{equation} \tag{ 1 }$$

$$\begin{equation} V^{\prime }_{\mathrm{IP}}=1.073 \; V_{\mathrm{init}}+100,\quad (\rm{HMF\ model}) \end{equation} \tag{ 2 }$$

$$\begin{equation} V^{\prime }_{\mathrm{IP}}=0.861 \; V_{\mathrm{init}}+188,\quad (\rm{SSEF\ model}) \end{equation} \tag{ 3 }$$

with both speeds in km s⁻¹.

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The FPF method yields a deceleration between the corona and the IP medium, with the slope of the linear fit indicating V_IP∝0.6V_init. When using SSEF, the deceleration is less (V_IP∝0.86V_init), and for HMF, the speed remains approximately constant, V_IP∝1.07V_init. Here, again, our physical interpretation depends highly on which models we use, and thus these relationships are most useful for understanding the biases inherent in the different techniques. Nevertheless, taking these results at face value and knowing from theoretical considerations (Lugaz & Kintner 2013) that FPF should give more accurate results for fast CMEs, a deceleration of CMEs from the corona to the IP medium seems to be the most realistic conclusion.

Furthermore, concerning another quantitative link between the COR2 and HI data sets, we checked whether the launch time t₀ resulting from the geometrical models is consistent with the time t_COR2 (see Table 1) of the first image of the CME in COR2. The launch time is defined as the time when the fitting function (t₀) = 0 (Möstl et al. 2011). The average difference 〈|t_COR2 − t₀|〉 = 1.7 hr, and for 92% of all events it is <3 hr. This means that the launch time is an excellent proxy for linking a CME track, which was extracted and from HI J maps and modeled, to its coronal counterpart, provided that only one CME is launched during this time window.

3.2. Connecting HI to In Situ Data

In this section, we discuss the link between the ICME in situ data and the speeds and arrival times derived from the HI observations. The CME direction cannot be compared to in situ because there is no simple way to derive the principal direction of an ICME from in situ data. This might be possible with deeper investigations on orientations of the shocks and flux ropes inside the ICMEs (e.g., Liu et al. 2010b; Möstl et al. 2012; Isavnin et al. 2013), but this is beyond the scope of the current study.

3.2.1. CME and ICME Speeds

We first focus on a comparison of speeds. For the heliospheric imager data, these are the speeds toward the in situ observer (V_IPo) derived from the three geometrical models (FPF, HMF, SSEF). For the in situ ICME data, these are the average proton bulk speeds in the ICME sheath regions (V_sheath).

Figure 8 shows the difference ΔV = V_IPo − V_sheath for each event included in our study. Note that the speed V_IPo already includes a correction to account for which part of the CME front impacts the spacecraft. It is clearly seen that for most slow CMEs in the sample, until late 2011, there is a relatively good consistency. For FPF, in 42% of events the absolute difference |ΔV| < 200 km s⁻¹ (SSEF: 54%; HMF: 50%). This means that for about half of the events there is a reasonable match between the imaging and in situ speeds.

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However, most IP speeds exceed the in situ ones. For FPF, 87% of events are faster in the IP medium than when observed in situ (SSEF: 75%, HMF 83%). This is most evident for the fast CMEs in our sample, those with initial speeds >1000 km s⁻¹, for which the predicted in situ speeds are strongly overestimated (consistent with Lugaz & Kintner 2013), on the order of 500–1000 km s⁻¹. These are the events on the right side of Figure 8. The geometrical models yield an average IP propagation speed of a CME. Especially for very fast CMEs, these speeds will not match the speeds measured in situ at 1 AU because of the CME deceleration that occurs up to 1 AU (e.g., Gopalswamy et al. 2001; Vršnak et al. 2013). In essence, the assumption of constant speed in the geometrical models is at the root of this discrepancy.

Table 3 summarizes the |ΔV| obtained with the different methods. On average, 〈|ΔV|〉 is 303 km s⁻¹(FPF), 267 km s⁻¹(SSEF), and 282 km s⁻¹(HMF). Taking the average over these values gives 284 km s⁻¹. We can also see that the differences between the geometrical models are only about 40 km s⁻¹, which makes it impossible to state which one performs best. In Table 3 we also state the results of a comparison |ΔV| = |V_IP − V_sheath|, which means that we just use the CME model apex speed without a correction for the position of the in situ observer. This results in an average difference over all models of 431 km s⁻¹. Consequently, correcting for apex or flank encounters strongly enhances the consistency with in situ data, for the present set of events on average by ≈150 km s⁻¹. However, this is likely caused by the effect that a flank speed is invariably lower than the apex speed, simulating to some degree the effect of real CME deceleration. However, even when using V_IPo, the average difference to the in situ speeds is still too large, almost 300 km s⁻¹. It becomes clear that we need to introduce some kind of correction to the IP speeds to be able to better predict the in situ speed from heliospheric images.

Table 3. Performance of HI Geometrical Models in Connecting Remote Observations of CMEs to In Situ Data at 1 AU

Method	Variable	Unit	FPF	SSEF	HMF	Average
Speed of model apex	ΔV	km s−1	298 ± 296	443 ± 445	541 ± 567	427 ± 455
Speed in direction of in situ observatory	ΔV	km s−1	298 ± 296	252 ± 302	274 ± 304	275 ± 297
Speed with empirical correction	ΔV	km s−1	0 ± 69	0 ± 79	0 ± 74	0 ± 73
Speed of model apex	|ΔV|	km s−1	303 ± 290	446 ± 442	544 ± 564	431 ± 451
Speed in direction of in situ observatory	|ΔV|	km s−1	303 ± 290	267 ± 289	282 ± 296	284 ± 288
Speed with empirical correction	|ΔV|	km s−1	50 ± 47	57 ± 53	53 ± 51	53 ± 50
Arrival time in direction of in situ observatory	Δt	hours	−6.7 ± 7.6	−1.4 ± 11.1	−3.3 ± 9.5	−3.8 ± 9.6
Arrival time with empirical correction (=version 1)	Δt	hours	0.0 ± 7.0	0.0 ± 9.2	0.0 ± 7.8	0.0 ± 7.9
Arrival time with transit time relationship (=version 2)	Δt	hours	−1.9 ± 6.6	1.2 ± 9.8	−2.0 ± 8.3	−0.9 ± 8.4
Arrival time in direction of in situ observatory	|Δt|	hours	8.5 ± 5.4	8.4 ± 7.2	7.5 ± 6.6	8.1 ± 6.3
Arrival time with empirical correction (=version 1)	|Δt|	hours	5.6 ± 4.1	6.8 ± 6.0	5.9 ± 4.9	6.1 ± 5.0
Arrival time with transit time relationship (=version 2)	|Δt|	hours	5.7 ± 3.8	7.7 ± 6.1	6.6 ± 5.3	6.6 ± 5.1

Notes. Explanation: for each method, the differences C − O (calculated − observed) between the parameters from geometrical modeling and the corresponding in situ parameters are given. The speed and arrival time from geometrical modeling are compared to the average proton bulk speed of the ICME sheath region and the in situ arrival time of a shock or significant density jump, respectively. The numbers in the table correspond to the variables ΔV and Δt in the text, and errors quoted correspond to ±1 standard deviation.

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Figure 9 presents the IP speed (V_IPo) in the direction of the in situ observatory against the ICME sheath region speed (V_sheath). Separate linear fits for each geometrical model are shown in corresponding colors. These fits are very similar to each other. With the coefficients from these fits, we can apply an empirical correction to the speed V_IPo for each model, to get a better proxy for the speed of the in situ sheath region, which we call $V^{\prime }_{\mathrm{sheath}}$ or a "corrected" speed:

$$\begin{equation} V^{\prime }_{\mathrm{sheath}}=0.227 V_{\mathrm{IPo}}+307,\quad (\rm{FPF\ model})\ \ \end{equation} \tag{ 4 }$$

$$\begin{equation} V^{\prime }_{\mathrm{sheath}}=0.213 V_{\mathrm{IPo}}+323,\quad (\rm{HMF\ model}) \end{equation} \tag{ 5 }$$

$$\begin{equation} V^{\prime }_{\mathrm{sheath}}=0.205 V_{\mathrm{IPo}}+334,\quad (\rm{SSEF\ model}) \end{equation} \tag{ 6 }$$

with both speeds given in km s⁻¹. We use this formula to obtain corrected sheath speeds based on V_IPo, and compare them again to the in situ observed V_sheath.

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Returning to Figure 8, the pink bars show the comparison $\Delta V=V^{\prime }_{\mathrm{sheath}}-V_{\mathrm{sheath}}$, for the SSEF method only. It can be seen that the consistency with V_sheath greatly improves, for both slow and fast CMEs. On average, 〈|ΔV|〉 = 50 km s⁻¹(FPF), 53 km s⁻¹(SSEF), and 57 km s⁻¹(HMF); see again Table 3 for a summary. For the whole data set, for FPF, the absolute difference |ΔV| < 100 km s⁻¹ in 92% of cases (SSEF: 83%; HMF: 88%). This is an improvement over more than 200 km s⁻¹ compared to geometrical modeling without this empirical correction. Clearly, the caveat of this correction is that we derived it from the current set of events, and the results will change for a different set of CMEs. Nevertheless, it definitely results in an improvement in the prediction capability compared to using the geometrical models alone, and it should also be used in future studies.

In summary, the average differences between CME speeds predicted from geometrical modeling to in situ ICME sheath region speeds are, for all methods, as follows: using V_IP, 〈|ΔV|〉 = 431 km s⁻¹; using V_IPo, 〈|ΔV|〉 = 284 km s⁻¹; and using $V^{\prime }_{\mathrm{sheath}}$, 〈|ΔV|〉 = 53 km s⁻¹. The differences between the different geometrical models are negligible, so none can be claimed as performing significantly better than the other.

3.2.2. Interplanetary Distance Ranges

Before we move on to discuss similar comparisons of ICME arrival times, we first need to clearly state the range of distances in the IP medium that are covered by the STEREO/HI observations. Using J maps created by the SATPLOT software, we tracked every CME event out to about 30°–40° elongation from the Sun. Rather than elongation, we need to know the corresponding distance range in AU to see how far from the Sun we have actually tracked the front of each CME. The average elongation value of the last HI data point of each CME is 349  ±  71. The corresponding distance to the maximum elongation is calculated by d_p = (t_p − t₀) × V_IP. This means that we propagate the CME away from the Sun with the IP speed of the model apex, from the launch time to the last time of HI observation (t_p). For simplicity, we state the result as a mean and standard deviation for all CMEs for the SSEF model only, because it is intermediate between the FPF and HMF models. The average maximum distance of the CME apex from the Sun, over all CMEs, is 〈d_p〉 = 0.855 ± 0.276 AU (SSEF). The maximum value is 1.41 AU, and the minimum 0.48 AU. The maximum apex distance for some events is >1 AU, especially for those cases where the CME flank hits the in situ spacecraft, which is situated near 1 AU.

3.2.3. Prediction Lead Times

We focus on connecting CMEs in different data sets, so we track the CMEs in the HI data for as long as possible. However, we can also ask ourselves how useful the results will be for forecasting the in situ parameters. For this it is necessary to place the parameters that we have calculated from remote images, and their comparison to in situ observations, into the context of space weather prediction.

A very important parameter in this respect is the prediction lead time (t_lead). This is the difference between the actual in situ arrival time of the ICME and the time (t_p) when a prediction for its arrival was issued. In our study, the latter is again the last point at which the event was observed by HI (i.e., the last point clicked in a J map); of course, here we are not discussing real-time predictions but artificial "predictions" made long after the events have happened, derived from a preexisting data set. We define t_lead = t_p − t_insitu, where t_insitu is the actual ICME arrival time. With this definition, prediction times earlier than the actual arrival give a t_lead < 0, as desirable when really "predicting" CMEs. Over our data set, on average, 〈t_lead〉 = −26.4 ± 15.3 hr, with a minimum t_lead for any individual event of −53.6 hr (>2 days), and a maximum of +0.28 hr. For the latter, t_p was already later than the in situ arrival time. Hence, the results that we state for arrival times and speeds are valid for a prediction lead time of the order of one day, albeit with considerable scatter around this value. We also need to point out that we have used HI science data, which are of better quality than those available from STEREO in real time.

3.2.4. Arrival Times

Figure 10 is a bar chart showing, for all CMEs, the difference Δt = t_a − t_insitu between predicted CME arrival time and the observed ICME arrival time taken from the in situ measurements. Here t_a is the predicted arrival time from heliospheric imaging, derived by the following expression (similar to Möstl et al. 2011; Möstl & Davies 2013):

$$\begin{equation} t_\mathrm{a}=t_0+\frac{d_\mathrm{i}}{V_{\mathrm{IPo}}}, \end{equation} \tag{ 7 }$$

where t₀ is the launch time, as discussed above, d_i is the heliocentric distance of the in situ spacecraft, and V_IPo is the (assumed constant) CME speed in the direction of the in situ observatory.

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In Figure 10, values of Δt < 0 refer to the situation where the predicted arrival time is before the in situ arrival time. This is the case in particular for the events after 2011 October, on the right-hand side of Figure 10, which are all backsided events, from the HI observer point of view, as determined by the SSEF direction. Even so, the fastest CMEs after 2011 October have a reasonable |Δt| < 10 hr, but this is mainly due to the fact that fast CMEs have a transit time of the order of 20–40 hr, compared to around 100 hr for slower events. In general, we find that Δt is of the order of 10% of the total CME transit time. However, all three methods predict arrival times that are 1 day early for slow and backsided CMEs (e.g., 2012 April 19 with V_init = 639 km s⁻¹), consistent with theoretical expectations (Lugaz & Kintner 2013).

There is considerable scatter around Δt ≈ 0, and for a specific event, different methods can give quite different arrival times. The maximum and minimum values of Δt are about ±1 day, while the average absolute values of 〈|Δt|〉 = 8.5  ±  5.4 hr for the FPF model (SSEF: 8.4 ± 7.2 hr; HMF: 7.5  ±  6.6 hr; 8.1 ± 6.3 hr over all methods). Results are summarized in Table 3, including averages of signed values of 〈Δt〉.

We have derived corrections to the arrival times, using a similar approach as for correcting the speed predictions, but independent of the results for the speeds. Figure 11 is a scatter plot of the IP speed V_IPo versus Δt, for each CME and for all three methods. Faster IP speeds tend to be correlated with lower values of Δt, attributable again to the constant speed assumption used in geometrical modeling. Faster CMEs are predicted to arrive before they actually do, because modeling a fast and decelerating CME assuming a constant speed results in a much higher speed than the final in situ speed, as we have shown in the previous section. Similar to what was done in Figure 9, we fit the data points in Figure 11 for each model independently with a simple, linear relationship. The results of these fits are

$$\begin{eqnarray} &&\Delta t^{\prime }=-0.0078 V_{\mathrm{IPo}} - 0.52\quad (\rm{FPF\ model}), \end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray} &&\Delta t^{\prime }=-0.0144 V_{\mathrm{IPo}} +7.64\quad (\rm{HMF\ model}), \end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray} &&\Delta t^{\prime }=-0.0169 V_{\mathrm{IPo}} +11.04\quad (\rm{SSEF\ model}), \end{eqnarray} \tag{ 10 }$$

with Δt' in hr and V_IPo in km s⁻¹. This allows us to make an empirical correction (that we call "version 1") to the arrival time from our knowledge of V_IPo alone. To this end, we calculate a corrected arrival time by

$$\begin{equation} t_{\mathrm{a;{\rm corr};v1}}=t_\mathrm{a}-\Delta t^{\prime }, \end{equation} \tag{ 11 }$$

using Δt' from the fit for the corresponding geometrical model. The result of such a calculation for the SSEF model is shown using pink bars in Figure 10. On average, it improves the prediction performance by 2 hr. Comparing corrected arrival times to in situ arrival times results in 〈|Δt|〉 = 5.6 ± 4.1 hr for the FPF model (SSEF: 6.8 ± 6.0 hr; HMF: 5.9 ± 4.9 hr). The average over all models is 6.1 ± 5.0 hr, compared to 8.1 hr without the empirical correction (see Table 3).

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3.2.5. Transit Times

There is another way to calculate CME arrival times that performs slightly better than the straightforward arrival time calculation using geometrical modeling, as stated in Equation (7). We have applied this new method, which we call "version 2," which also depends only on V_IPo, to our list of events. We define a CME's transit time (TT) as the time difference between its first appearance in coronagraph images (t_COR2) and its actual in situ arrival time t_insitu. This definition of TT covers a distance range from 2.5 R_☉, which is the inner boundary of STEREO/COR2, to 1 AU or ≈215 R_☉.

Figure 12 shows a relationship between TT and IP speeds (V_IPo) for all CMEs in our data set. For each geometrical model, we fit a power law to the data, quoting the results on the plot. For SSEF, the resulting power law is

$$\begin{equation} \rm{TT}^{\prime }=9537 \times V_{\mathrm{IPo}}^{ -0.76}\quad (\rm{SSEF\ model}), \end{equation} \tag{ 12 }$$

with V_IPo given in km s⁻¹ and TT' in hr. Similar relationships have been shown, for example, by Schwenn et al. (2005) and Vršnak & Žic (2007), but using CME coronagraph speeds, whereas we show IP speeds. They include to some extent the CME propagation through the background solar wind. The average transit time in our data set is around 72 hr (or 3 days), which compares well to the classic Brueckner et al. (1998) 80 hr rule for average CME transit times. These power laws allow us to predict the arrival time, based solely on the IP speed in direction of the in situ observatory V_IPo, by

$$\begin{equation} t_{\mathrm{a;{\rm corr};v2}}=t_{0} + \rm{TT}^{\prime }. \end{equation} \tag{ 13 }$$

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For simplicity, we do not show resulting arrival time differences Δt for each event, but only summarize the resulting values. For this method, the difference between predicted and in situ arrival times is 〈|Δt|〉 = 5.7 ± 3.8 hr for the FPF model (SSEF: 7.7 ± 6.1 hr; HMF: 6.6 ± 5.3 hr). The average for all models is 6.6 ± 5.1 hr, almost as good as for the empirically corrected arrival times (6.1 hr).

3.2.6. CME Speed and ICME Magnetic Field

The last step in our analysis concerns the relationship between the maximum magnetic field B_max in the full ICME interval (Column 8 in Table 2), consisting of shock, sheath, and ejecta parts, and the IP speed V_IPo in the direction of the in situ observatory, as derived from HI geometrical modeling. CMEs that have higher speeds close to the Sun are known to be correlated with stronger magnetic fields at in situ spacecraft (e.g., Lindsay et al. 1999; Yurchyshyn et al. 2005). This is thought to arise from the role played by magnetic reconnection during CME eruption, namely, through a possible formation of their interior magnetic flux rope (e.g., Qiu & Yurchyshyn 2005; Qiu et al. 2007; Möstl et al. 2009c). Another explanation is that faster CMEs lead to stronger compression of the ambient solar wind, which results in a higher magnetic field strength in the ICME sheath region (Liu et al. 2008). Around half of the ICMEs in our data set reach their B_max in the sheath and the other half in their interior magnetic ejecta, so both effects can be expected to play a role in our analysis. In the same way as we have done for the transit times above, we can extend such previously found relationships by comparing IP rather than coronal CME speeds to the in situ magnetic field magnitude.

Figure 13 shows, as a scatter plot, that stronger ICME maximum magnetic fields are correlated with faster ICME speeds. Again, we perform independent, linear fits for each model, which, for SSEF, results in

$$\begin{equation} B^{\prime }_{\mathrm{max}}=0.0189 V_{\mathrm{IPo}}+6.73, \end{equation} \tag{ 14 }$$

with $B_{\mathrm{max}}^{\prime }$ in nT and V_IPo in km s⁻¹. The average, absolute difference $\Delta B=B^{\prime }_{\mathrm{max}}-B_{\mathrm{max}}$ between predicted and observed maximum magnetic fields, based on the speeds from FPF, is 〈|ΔB|〉 = 4.8 nT (SSEF: 4.7 nT; HMF: 4.4 nT). Use of the resulting linear fits for $B_{{\rm max}}^{\prime }$ for each model results in a successful prediction of B_max to within ±5 nT for 58% of events with the FPF method (SSEF: 67%; HMF 71%). The same numbers for predictions within ±10 nT are 88% for FPF (SSEF: 88%; HMF 92%). In summary, for around two out of three events in our sample, the maximum magnetic field in the ICME interval could be predicted within a precision of 5 nT, solely based on the ICME speed.

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We have presented a study in which we have connected white light to in situ observations of a set of 22 near-equatorial CMEs. Their parameters cover a wide range of initial and propagation speeds (260–2715 km s⁻¹) and a variety of principal CME directions with respect to the HI observer (40°–170° in heliocentric longitude). This is the first study to do such an analysis of such a large and diverse set of events. Here we summarize our results and their implication for space weather prediction and the evolution of CMEs between the Sun and 1 AU separately, emphasizing our main conclusions in italics.

First, concerning space weather prediction, we have mainly tested methods for predicting CME directions, speeds, and arrival times based on J maps produced using observations from a single-spacecraft heliospheric imager instrument. These data were provided by HI on STEREO-A/B, which, for the CMEs under study, were positioned well outside the Sun–Earth line, on heliocentric longitudes between 30° and 120° away from the Earth.

• 1.  
  Event selection. We have selected CME events with clear ICME signatures (shock, sheath, and ejecta) in Wind and STEREO-B in situ observations near 1 AU, and which we could easily track in the HI J maps. This set of CMEs covers a wide range of initial speeds, so it is suitable for statistical analysis, although there are actually many more CMEs in the data during this time range. The events in our list occurred during the rise of solar cycle 24, between 2008 and 2012, and STEREO progressed toward and beyond opposition during this time. Therefore, our data set contains mostly slow frontsided and fast backsided CMEs. Our results must be considered carefully with this in mind and are likely to be different for different data sets.
• 2.  
  Tracking CMEs and prediction lead times. We tracked CMEs as far as possible in the J maps, resulting in an average track length of 349 ± 71 elongation. Depending on the CME speed, its direction, and the model applied, this corresponds to different distances each CME has traveled away from the Sun at the time of the last HI observation. This distance is on average 0.86 ± 0.28 AU; thus, we have tracked most CMEs almost up to 1 AU. The prediction lead times also depend on several of the aforementioned parameters and are on average −26 ± 15 hr, about −1day. This is considerably longer than those provided by a solar wind monitor at L1 (on the order of 1 hr, e.g., the current ACE mission), but definitely shorter than lead times using coronagraphs only (on the order of CME transit times of a few days, e.g., Kilpua et al. 2012). The work presented here should rather be seen as an attempt to establish connections between CME-related phenomena detected in different data sets (coronagraph, heliosphere, in situ), which is strongly desirable for benchmarking various empirical or numerical CME prediction models.
• 3.  
  CME directions. The three different geometrical models used in this study do not provide consistent CME directions, with differences of up to 50° in heliocentric longitude for fast CMEs. For this reason, we derived the direction from multi-viewpoint applications of the croissant model to coronagraph images as a well-constrained reference for the initial CME direction. The FPF direction was shown to be, on average, consistent to within a few degrees with the croissant direction. This means that if CMEs propagate radially away from the Sun above 15 solar radii, the FPF method is superior over the others in deriving the CME principal direction. However, there is also considerable scatter, of the order of ±30° heliocentric longitude around the average direction. The directions provided by the SSEF and HMF models, which assume an extended CME front, differ by about 30° from the croissant direction. These methods show a bias in the direction to values farther away from the HI observer, with larger differences for faster CMEs, confirming theoretical predictions by Lugaz & Kintner (2013).
• 4.  
  CME arrival time and speed predictions. Using geometrical modeling to predict CME speed and arrival time, with a lead time of roughly 1 day, results in average absolute differences from observed ICME sheath speeds and arrival times of |ΔV| = 284 ± 288 km s⁻¹ and |Δt| = 8.1 ± 6.3 hr, respectively, averaged over all three methods. The arrival time difference given by the rms method is Δt_rms = 10.3 hr. Conserving the sign of the differences, similar numbers for calculated minus observed speeds and arrival times are ΔV = 275 ± 297 km s⁻¹ and Δt = −3.8 ± 9.6 hr, respectively. In summary, predicted ICME speeds at 1 AU are, on average, overestimated, and consequently, predicted arrival times are too early compared with the in situ observations. Correlating the ICME speed in the direction of the in situ observatory with the in situ speeds and, independently, with the differences in observed and predicted arrival times, we obtained new empirical relationships between these variables, based on linear fits. These allow us to predict the CME speed and arrival time with better accuracy for, at least, the present data set. Applying these empirical corrections in the prediction of CME speeds and arrival times, |ΔV| = 53  ±  50 km s⁻¹(ΔV = 0  ±  73 km s⁻¹), and |Δt| = 6.1  ±  5.0 hr (Δt = 0.0  ±  7.9 hr, Δt_rms = 7.9 hr), averaged over all events and methods. More specifically, 88% (or roughly 9 out of 10) of all in situ ICME sheath region speeds in our data set were predicted to within |ΔV| < 100 km s⁻¹. In 71% of cases (or roughly three out of four), ICME arrival times are predicted within |Δt| < 8 hr. Moreover, we quantified the relationship between the maximum magnetic field B_max in the ICME and the IP propagation speed, which lets us predict B_max to within ±5 nT in two out of three cases.
• 5.  
  Comparison to stereoscopic modeling. Colaninno et al. (2013) found similar results for CME arrival time and speed prediction using the results of methods applied to two heliospheric imager instruments, such as fitting the stereoscopic croissant model to STEREO/COR2/HI1/HI2 and SOHO/LASCO images, for heliocentric distances up to about 0.9 AU. Similar to our study, they also applied corrections for the apex and flank parts of the CMEs impacting the in situ observatory. They found that for 78% of cases, Δt < 6 hr, and for 55% of CMEs, ΔV < 100 km s⁻¹, although for all events ΔV < 140 km s⁻¹. Colaninno et al. (2013) fitted the height-time data in several different ways, and they found a linear fit between 50 R_☉ (0.23 AU) and 1 AU and thus assuming a constant speed to produce the best predictions, even though they also concluded that CMEs clearly decelerate. It is interesting to note that an equivalent assumption of constant speed between 0.07 and 0.85 AU in our geometrical modeling methods yields a similar level of predictive performance.

Second, we summarize our results in terms of the physical evolution of CMEs between the Sun and 1 AU. In general, we find that, using single-spacecraft HI observations, it is much more difficult to generalize the behavior of CMEs in terms of such properties as propagation direction, speed variation, and global shape evolution when compared to the use of stereoscopic HI measurements (e.g., Liu et al. 2010a, 2011, 2013; Lugaz et al. 2010; Colaninno et al. 2013; Mishra & Srivastava 2013; Davies et al. 2013).

• 1.  
  CME radial propagation. A major unsolved question is whether CMEs propagate radially away from the Sun, or undergo any significant change of direction as they travel through the IP medium. CMEs are known to be deflected in the corona by coronal holes (Gopalswamy et al. 2009) and possibly through CME–CME interaction in IP space (Lugaz et al. 2012). Liu et al. (2013) and Davies et al. (2013) showed the CME direction for a few events to stay within about ±15° (heliocentric longitude) from the corona to the IP medium. This can still be considered as consistent with a radial propagation. With our own data set, CME deflections are difficult to assess without further analysis. As discussed above, the HI methods can give very different answers for a single event—CME principal directions are not well defined using single-spacecraft HI methods. Note also that we assume constant direction in IP space in contrast to the stereoscopic methods, so we can only assess deflections by comparing directions derived from coronagraph and HI measurements. However, there is considerable scatter between these initial and IP directions (of the order of ±30°, about twice the level derived from stereoscopic methods), pointing indeed to the possibility that some CMEs may significantly change in direction between the corona and the IP medium. While the croissant model constrains the CME direction well close to the Sun, there is no straightforward way to constrain the CME direction using single-spacecraft in situ data, and thus we leave further analysis for future work.Our results on CME direction in IP space clearly point out that its calculation is always influenced by the strongly idealized shapes of the CME front, which we assume in the first place. The geometrical definitions we use make it possible to describe CME front shapes analytically and form very useful tools. However, our study casts some doubts on their use in defining a CME's central propagation direction in the IP medium, because its calculation depends so strongly on the assumption of its frontal geometry. Consequently, we propose that future work should quote ranges of heliocentric longitude that will be affected by a CME, rather than a central direction. This would be especially helpful when describing distorted or asymmetric CME front shapes (e.g., Savani et al. 2010; Möstl et al. 2012).
• 2.  
  CME speed profiles. CMEs are well known to decelerate in the solar wind out to 1 AU, mainly due to a force equivalent to aerodynamic drag (e.g., Gopalswamy et al. 2001; Kilpua et al. 2012; Vršnak et al. 2013; Liu et al. 2013), and we can see this clearly in our data. We can compare stepwise a CME initial speed (<15 R_☉, or <0.07 AU) to its average IP propagation speed (from ≈0.07 to 0.86 ± 0.28 AU), and to the speed of the ICME sheath region observed in situ near 1 AU. FPF and SSEF suggest that CMEs decelerate from the corona to IP space, while HMF yields a constant speed. CMEs are clearly slower when observed in situ near 1 AU than in IP space, and the in situ sheath region speeds can be reasonably well predicted by multiplying the IP speeds with ≈0.2 and adding 320 km s⁻¹, which is independent of the model used. The speed of 320 km s⁻¹ is reminiscent of the slow solar wind, and this relationship is also consistent with early work by Lindsay et al. (1999). However, we cannot definitely say where most of the deceleration occurs, because of our assumption of constant IP speed. Recent analyses with stereoscopic methods by Liu et al. (2013) showed much of the deceleration of fast CMEs occurring up to about 80 solar radii (0.37 AU), but there is probably no general distance by which the deceleration ceases, as a case has been found where a CME almost does not decelerate out to 1 AU (Möstl et al. 2010).
• 3.  
  Evolution of the global CME shape. We expected that there would be clear differences concerning the prediction performance of different geometrical models, giving us hints as to which one better describes the CME front shape in the plane perpendicular to the HI images. In particular, we expected the SSEF model, as it is the most mature, with a well-defined CME width, to perform best. However, surprisingly, we did not find any significant difference in its performance for predicting CMEs compared to the other models. We think that this is caused by their assumptions of constant speed and constant direction, as well as their high sensitivity to a violation of these assumptions (Lugaz & Kintner 2013). In summary, the current state of the art of geometrical modeling of CMEs with single-spacecraft instruments (i.e., fitting methods) in comparison to single-spacecraft in situ data precludes inferences to be made regarding the large-scale geometry of CME fronts in planes perpendicular to the HI images, such as the ecliptic plane.

We conclude that predicting CME speeds and arrival times with heliospheric images gives more accurate results than using projected initial speeds from coronagraph measurements. These improvements are on the order of 12 hr for the arrival times (Colaninno et al. 2013), and our results are consistent with those found with other space weather models in the STEREO era (see also Gopalswamy et al. 2013; Mishra & Srivastava 2013; Mishra et al. 2014). Independent of the specific methods used, we can derive an average of the CME IP propagation speed when we track a CME out to 1 AU. This average speed includes to some extent the background solar wind, which is known to play a significant role in modulating CME propagation (e.g., Gopalswamy et al. 2001; Vršnak & Žic 2007; Temmer et al. 2011; Kilpua et al. 2012). The same is true for interacting CMEs, although it can be very difficult to differentiate and decipher different density tracks in HI when CMEs are launched close together in time and space (Harrison et al. 2012; Webb et al. 2013).

It is clear that the information contained in heliospheric images does indeed improve space weather prediction. However, the compromise between prediction accuracy (Δt) and prediction lead times (t_lead) needs to be better studied. Future modeling should thus focus on modeling CME tracks in J maps for elongations from the Sun of <35°, which will result in longer prediction lead times than 1 day in the current study. It needs to be assessed how the predictions for speed and arrival time become less accurate as the prediction lead time is increased, and the best balance for space weather prediction purposes needs to be found.

Another possibility for future work is to actually include deceleration into the geometrical fitting methods for single-spacecraft HI instruments. This is expected to further improve the accuracy of predicting CME arrival times and speeds through use of a more realistic approach than the current assumption of constant speed. Such an approach, applied to the different model geometries, could provide clues to the CME global front shape, in particular when constrained by multi-point in situ measurements.

Another solution would be to send a mission equipped with a heliospheric imager in a polar orbit around the Sun to look down onto the ecliptic plane (Liewer et al. 2008). In this way, information on the global shape of a CME in the ecliptic, as it approaches Earth, would be revealed, and the CME propagation characteristics could be provided by the geometrical models as used in our paper. However, for effectively predicting geo-effectiveness it is also necessary to know the components of the IP magnetic field, which cannot be derived from white-light images and require new ideas like the Faraday-rotation technique (e.g., Xiong et al. 2013b). Moreover, the Solar Orbiter (e.g., Müller et al. 2013) and Solar Probe Plus missions are currently under development and will approach the Sun closer than ever before by the end of the decade. The results and methods presented in this paper may provide both the scientific background and tools for analyzing the data from these exciting future missions.

This research was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme. C.M. and T.R. thank the Austrian Science Fund (FWF): [P26174-N27]. M.T. was also supported by the Austrian Science Fund (FWF): V195-N16. The presented work has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreements No. 263252 [COMESEP], No. 284461 [eHEROES] and No. 606692 [HELCATS]. T.R. gratefully acknowledges the JungforscherInnenfonds of the Council of the University Graz. Work at the University of California, Berkeley, was supported from STEREO grant NAS5-03131. The work of K.A., J.R.H., P.C.L., and E.M.D. was conducted at the Jet Propulsion Laboratory, California Institute of Technology under a contract from NASA. N.L. was supported by AGS-1239704. It is also supported by NASA grant NNX13AP39G and NASA STEREO grant to U.N.H. We acknowledge the use of Wind data provided by the magnetometer and the solar wind experiment teams at NASA/GSFC, and we thank the center for geomagnetism in Kyoto for providing the Dst indices. We also thank the "International study of earth affecting transients" (ISEST) team lead by Jie Zhang.