# Modeling a Coronal Mass Ejection from an Extended Filament Channel.
II. Interplanetary Propagation to 1 au

Erika Palmerio Predictive Science Inc., San Diego, CA 92121, USA  Anwesha
Maharana Centre for mathematical Plasma Astrophysics (CmPA), KU Leuven, 3001
Leuven, Belgium  Solar–Terrestrial Centre of Excellence—SIDC, Royal
Observatory of Belgium, 1180 Brussels, Belgium  Benjamin J. Lynch Space
Sciences Laboratory, University of California–Berkeley, Berkeley, CA 94720,
USA  Camilla Scolini Space Science Center, University of New Hampshire,
Durham, NH 03824, USA  Simon W. Good Department of Physics, University of
Helsinki, FI-00014 Helsinki, Finland  Jens Pomoell Department of Physics,
University of Helsinki, FI-00014 Helsinki, Finland  Alexey Isavnin Rays of
Space Oy, FI-00750 Helsinki, Finland  Emilia K. J. Kilpua Department of
Physics, University of Helsinki, FI-00014 Helsinki, Finland

(Received July 28, 2023; Revised September 18, 2023; Accepted October 9, 2023)

###### Abstract

We present observations and modeling results of the propagation and impact at
Earth of a high-latitude, extended filament channel eruption that commenced on
2015 July 9. The coronal mass ejection (CME) that resulted from the filament
eruption was associated with a moderate disturbance at Earth. This event could
be classified as a so-called “problem storm” because it lacked the usual solar
signatures that are characteristic of large, energetic, Earth-directed CMEs
that often result in significant geoeffective impacts. We use solar
observations to constrain the initial parameters and therefore to model the
propagation of the 2015 July 9 eruption from the solar corona up to Earth
using 3D magnetohydrodynamic heliospheric simulations with three different
configurations of the modeled CME. We find the best match between observed and
modeled arrival at Earth for the simulation run that features a toroidal flux
rope structure of the CME ejecta, but caution that different approaches may be
more or less useful depending on the CME–observer geometry when evaluating the
space weather impact of eruptions that are extreme in terms of their large
size and high degree of asymmetry.

Quiet Sun (1322); Solar filament eruptions (1981); Solar coronal mass
ejections (310); Magnetohydrodynamical simulations (1966); Interplanetary
magnetic fields (824); Solar-terrestrial interactions (1473); Space weather
(2037)

††journal: ApJ††facilities: ACE (SWICS); BBSO (H$\alpha$); GONG (Magnetogram);
SOHO (LASCO); SDO (AIA, HMI); Wind (MFI, SWE)††software: ARMS (DeVore &
Antiochos, 2008); AstroPy (Astropy Collaboration et al., 2022); EUHFORIA
(Pomoell & Poedts, 2018); SolarSoft (Freeland & Handy, 1998); SunPy (SunPy
Community et al., 2020)

##  1 Introduction

Geoeffective interplanetary coronal mass ejections (ICMEs) that have no clear
solar counterpart or that are associated with ambiguous or negligible solar
activity are usually referred to as “problem storms.” The concept was first
introduced by Dodson & Hedeman (1964), who surveyed a large number of
geomagnetic storms and could not always find a preceding solar event to
account for the disturbances at Earth. It should be noted, however, that in
the 1960s the sources of the largest geomagnetic disturbances used to be
searched uniquely in solar flares (Gosling, 1993). With the first detections
of coronal mass ejections (CMEs) in the 1970s using coronagraph observations,
the role of solar eruptions in causing geomagnetic activity at Earth became
increasingly evident. Alongside flares, it was noted that possible low-coronal
signatures that indicate the occurrence of a CME eruption include post-
eruption arcades, coronal dimmings, and disappearing filaments (e.g., Hudson &
Cliver, 2001). Nevertheless, the problem storm issue still survives to this
day (e.g., Nitta et al., 2021).

What makes a CME “problematic”? In principle, any geomagnetic storm that is
(fully or mostly) unexpected can be defined as a problem storm. Besides the
well-known, current issues in space weather forecasting, related e.g. to CME
evolution and interactions in interplanetary space (e.g., Kilpua et al., 2019;
Vourlidas et al., 2019), additional complexity may arise from CMEs that lack
low-coronal signatures (so-called “stealth CMEs;” e.g., Robbrecht et al.,
2009b; Nitta & Mulligan, 2017), that are not visible in coronagraph imagery
(e.g., Howard & Simnett, 2008; Palmerio et al., 2019), and/or that do not
present obvious Earth-directed components (e.g., Schwenn et al., 2005; Kilpua
et al., 2014). Such CMEs may feature diverse characteristics, but what makes
them problematic is that their potential geoeffectiveness usually goes
unnoticed when formulating space weather forecasts.

One interesting class of CMEs in this regard is that of streamer-blowout CMEs
(e.g., Sheeley et al., 1982; Vourlidas & Webb, 2018), which are large-scale,
gradual events that originate from the quiet Sun and that are followed by wide
and slow CMEs. Streamer blowouts are not accompanied by flares because of
their gradual and slow nature, as well as their usual initiation sites higher
up in the corona, thus they are generally not considered as potentially
geoeffective as the more impulsive active-region CMEs. An excellent example of
a geoeffective streamer-blowout CME, however, was presented by McAllister et
al. (1996), who reported a CME with a large source region (spanning
${\sim}150^{\circ}$ in longitude and ${\sim}35^{\circ}$ in latitude) that
could be identified only because of the appearance of an extended post-
eruption arcade in soft X-ray data. The lack of an associated flare or
filament disappearance made the following severe geomagnetic storm largely
unexpected.

In this paper, we build upon the work of Lynch et al. (2021), hereafter Paper
I, to analyze the propagation of an extended, high-latitude filament eruption
up to Earth. The event that we focus on commenced on 2015 July 9 and is in
several aspects analogous to the CME reported by McAllister et al. (1996) in
the sense that, despite affecting a significant portion of the solar southern
hemisphere upon eruption, both events were characterized by faint, non-
impulsive on-disk signatures, characteristic of a streamer-blowout CME.
Furthermore, both CMEs caused problem storms at Earth, although with different
magnitudes (Dst${}_{\text{min}}$ = $-203$ nT for the McAllister et al., 1996,
event and Dst${}_{\text{min}}$ = $-68$ nT for the event described in this
paper).

While the effort of Paper I was centered on modeling the eruption and initial
evolution (up to 30 $R_{\odot}$) of the CME, in this work we focus on modeling
the propagation of the CME from the solar corona (21.5 $R_{\odot}$ or 0.1 au)
up to Earth’s orbit (1 au) using magnetohydrodynamic (MHD) simulations. Due to
the intrinsic complexity of simulating such a large-scale structure, we
initialize our CME inputs using three different configurations of the modeled
ejecta: a hydrodynamic pulse, a spheromak, and a toroidal flux rope. Our aim
is to investigate the impact that the CME’s internal magnetic structure and
configuration has on the ejecta’s heliospheric evolution and synthetic in-situ
profiles, in order to best inform future space weather forecasting and
modeling.

This paper is organized as follows. Section 2 provides an observational
overview of the 2015 July 9 CME from the Sun to Earth, starting from the
eruption itself analyzed in detail in Paper I ($\S$2.1), following the CME
propagation through the solar corona ($\S$2.2), and finally observing the
corresponding ICME at Earth’s Lagrange L1 point ($\S$2.3). Section 3 presents
the modeling setup for the three simulations, first in terms of the solar wind
background ($\S$3.1) and then in terms of the CME input parameters for the
three different ejecta configurations ($\S$3.2). Section 4 shows our modeling
results aimed at connecting the CME structure in the corona to its associated
ICME near Earth, including a comparison of the resulting CMEs in the
heliosphere with the simulated CME in the corona from Paper I ($\S$4.1) and
the corresponding time series at Earth ($\S$4.2). In Section 5 we discuss our
results in the context of predicting the space weather effects of large and
slow CMEs. Finally, in Section 6 we summarize the results and present our
conclusions.

##  2 Overview of the Observations

The onset and eruption of the 2015 July 9 CME was analyzed and modeled in
detail in Paper I, hence we provide only a brief review in Section 2.1. We
discuss the evolution of the CME through the solar corona based on corongraph
observations in Section 2.2. Finally, we present the measurements and analysis
of the corresponding ICME near Earth in Section 2.3.

###  2.1 CME Eruption at the Sun

Figure 1: Pre-eruptive configuration of the filament. (a) H$\alpha$ image from
BBSO, with left-bearing filament barbs (signatures of a right-handed filament)
indicated by arrows. (b) SDO/HMI magnetogram with the global PILs marked in
orange. The approximate locations of the positive and negative filament
footpoints with respect to the PIL involved in the eruption are marked with
$\oplus$ and $\ominus$ symbols, respectively.

The eruption of the CME analyzed in this work initiated on 2015 July 9 around
19:00 UT. Solar extreme ultra-violet (EUV) observations from the Atmospheric
Imaging Assembly (AIA; Lemen et al., 2012) instrument on board the Solar
Dynamics Observatory (SDO; Pesnell et al., 2012) reveal a large southern-
hemisphere filament spanning the whole Earth-facing disk in longitude and
slowly erupting asymmetrically from its eastern leg toward its western one.
The whole eruption occurred over large time scales, taking approximately 12 hr
for the filament to completely disappear from the AIA field of view (see
Figure 1 and the accompanying animation in Paper I).

To estimate the magnetic properties of the CME at the time of the eruption, or
intrinsic flux rope type (see Palmerio et al., 2017, and references therein),
we combine chromospheric observations of the pre-eruptive filament with
photospheric measurements of the solar magnetic field, both shown in Figure 1.
Respectively, we use data from the Big Bear Solar Observatory (BBSO) full-disk
H$\alpha$ telescope (Denker et al., 1999) and the Helioseismic and Magnetic
Imager (HMI; Scherrer et al., 2012) on board SDO. In the case of large quiet-
Sun filaments, such as the one involved in this eruption, the study of
filament barbs, fine structures seen along the sides of filament spines, is an
excellent method for determining the corresponding magnetic helicity sign or
chirality (e.g., Martin, 2003). The filament shown in Figure 1(a) is
characterized by left-bearing barbs, a signature of sinistral filaments and
thus indicating a right-handed flux rope. The magnetogram data shown in Figure
1(b) confirm that the source of the eruption corresponds to an extended quiet-
Sun filament channel, and the assumption of right-handed chirality implies
that the filament’s eastern (western) footpoint is rooted in the positive
(negative) polarity on either side of the underlying polarity inversion line
(PIL), . Then, the flux rope axial field is simply expected to run from the
positive polarity to the negative one, i.e. toward the west in the case of
this event.

From the analysis of the pre-eruptive structure based on the data shown in
Figure 1, we can conclude that the 2015 July 9 CME flux rope was characterized
by a right-handed chirality (or positive helicity), as well as that its axis
had a low inclination to the solar equator (note how both the filament and the
underlying PIL span the solar disk in the east–west direction, with an
inclination of ${\sim}20^{\circ}$ to the equatorial plane) and was directed
toward the west. This suggests a south–west–north (SWN) flux rope type at the
time of the eruption, following the nomenclature of Bothmer & Schwenn (1998)
and Mulligan et al. (1998).

###  2.2 CME Evolution in the Corona

After its eruption from the Sun, we follow the initial propagation of the 2015
July 9 CME in the corona using the C2 and C3 telescopes, which are part of the
Large Angle and Spectrometric Coronagraph (LASCO; Brueckner et al., 1995) on
board the Solar and Heliospheric Observatory (SOHO; Domingo et al., 1995). The
east-to-west asymmetry that can be seen in EUV observations (see Section 2.1)
is well reflected in white-light ones. The CME is first observed in the
LASCO/C2 field of view around 20:00 UT on July 9 as a relatively narrow
streamer blowout to the southeast of the solar disk. A few hours later, around
03:00 UT on July 10, this structure is followed by an extended loop-like
feature that sweeps the whole southern hemisphere in an asymmetric way, from
east to west. Finally, around 14:30 UT on July 10, the loop is followed by a
structure to the southwest that is reminiscent of a three-part CME cavity. The
same features (streamer blowout to the southeast, large loop structure to the
south, three-part cavity to the southwest) can also be discerned in LASCO/C3
imagery, starting around 02:00 UT on July 10. Overall, the passage of the
whole 2015 July 9 CME through the two coronagraphs’ fields of view takes place
over $\sim$1.5 days, largely due to the multi-part structure of the eruption
and to the ejecta’s slow propagation speed (see Figure 2 and the accompanying
animation in Paper I).

We note that in the Computer Aided CME Tracking (CACTus; Robbrecht &
Berghmans, 2004; Robbrecht et al., 2009a) catalog, the eruption under study is
reported as two separate CMEs, the first appearing on 2015 July 9 at 20:00 UT
(corresponding to the initial streamer blowout) and the second appearing on
2015 July 10 at 02:48 UT (corresponding to the loop-like ejected material). In
the SOHO/LASCO CME catalog (Yashiro et al., 2004; Gopalswamy et al., 2009),
the CME is also reported as two separate partial halos, one starting on 2015
July 9 at 19:00 UT and the second starting on 2015 July 10 at 02:24 UT. We
remark that the CACTus catalog is algorithm-generated (i.e., without human
supervision) while the SOHO/LASCO one is manually generated, hence these
results highlight the complexity of the event under study.

Figure 2: GCS reconstructions of the three different sub-parts—(a) streamer
blowout, (b) large loop, and (c) three-part cavity—of the complex 2015 July 9
CME using the single LASCO/C3 viewpoint. The panels to the left show 2-hour
difference images and the panels to the right display the corresponding GCS
wireframe projection overlaid.

To obtain an estimate of the CME’s geometric and kinematic parameters, we
perform reconstructions of its structure based on coronagraph images using the
Graduated Cylindrical Shell (GCS; Thernisien, 2011) model, which consists of a
parameterized shell (described by six parameters) that is meant to reproduce
the morphology of CMEs in the corona. By projecting the GCS wireframe onto the
plane of sky of coronagraph imagery, a user can adjust the six free parameters
until the obtained shell visually matches the CME’s appearance. Forward
modeling with the GCS technique is often performed to derive CME input
parameters for , but in the case of the 2015 July 9 event there are two
factors that make the analysis more complex than usual. First, the Solar
Terrestrial Relations Observatory Ahead (STEREO-A) spacecraft was in superior
conjunction with Earth, meaning that most of its instruments were not
operational and only the SOHO (Earth) vantage point is available. Although
forward modeling with the GCS is usually performed with simultaneous
coronagraph images from two or three viewpoints (Thernisien et al., 2009), the
technique was initially developed and tested using uniquely the SOHO/LASCO
perspective (Thernisien et al., 2006). One caveat to keep in mind, however, is
that the uncertainties stemming from a single viewpoint will be inevitably
larger (Verbeke et al., 2022). Second, the strongly-asymmetric and slow nature
of the 2015 July 9 event results in the CME never appearing in its entirety in
a single coronagraph image. Thus, to take all the different sub-parts of the
erupting CME into account, we perform three separate GCS fits for the streamer
blowout, the large loop structure, and the three-part cavity, respectively.

Table 1: GCS parameters for each of the three sub-parts of the 2015 July 9 CME shown in Figure 2. Latitude and longitude are reported in Stonyhurst coordinates. The tilt is measured from the solar west direction and is defined positive for counterclockwise rotations. The half-width is the half-angular distance between the axes of the CME legs. The aspect ratio is the ratio of the CME size at two orthogonal directions.  GCS parameter | Part 1 | Part 2 | Part 3
---|---|---|---
Latitude ($\theta$) | $-33^{\circ}$ | $-40^{\circ}$ | $-35^{\circ}$
Longitude ($\phi$) | $-32^{\circ}$ | $-22^{\circ}$ | $40^{\circ}$
Axial tilt ($\gamma$) | $90^{\circ}$ | $23^{\circ}$ | $70^{\circ}$
Nose height ($H$) | $21.5\,R_{\odot}$ | $21.5\,R_{\odot}$ | $21.5\,R_{\odot}$
Half-width ($\alpha$) | $6^{\circ}$ | $43^{\circ}$ | $10^{\circ}$
Apect ratio ($\kappa$) | 0.33 | 0.43 | 0.30

Snapshots of the different CME features through the SOHO/LASCO/C3 field of
view together with the corresponding GCS fits are shown in Figure 2, and the
GCS parameters obtained for each reconstruction are presented in Table 1. It
is clear from these results that all sub-parts of the 2015 July 9 CME
propagate strongly toward the south, with latitudinal directions of the apexes
lying around $-35^{\circ}$. It is also evident that so-called ‘Part 1’ and
‘Part 3’ of the event are directed away from the Sun–Earth line, while from
‘Part 2’ it is possible to expect a grazing encounter at Earth with the CME’s
northern flank.

###  2.3 CME Measurements at Earth

Figure 3: The 2015 July 9 CME observed in situ by the Wind and ACE spacecraft,
together with its geomagnetic response. The panels show: (a) magnetic field
magnitude, (b) Cartesian components of the magnetic field, (c) latitudinal and
(d) longitudinal angles of the magnetic field, (e) solar wind speed, (f)
proton density, (g) proton temperature, (h) plasma beta, (i) total pressure
(proton and electron gas pressure plus magnetic pressure), (j) pitch-angle
spectrogram of suprathermal 265 eV electrons, (k) oxygen charge state ratio,
(l) average iron charge state, and (m) Dst index. The gray vertical line
indicates the arrival of the shock-like disturbance, while the gray-shaded
areas highlight the ICME ejecta (dark gray) and the magnetic cloud interval
(light gray) within it. A Lundquist flux rope fitting has been plotted in pink
over the magnetic cloud interval.

Despite propagating considerably toward the south (as shown from the GCS
estimates presented in Section 2.2), the 2015 July 9 CME impacted Earth on
July 13. Figure 3 shows measurements taken from Earth’s Lagrange L1 point by
the Wind (Ogilvie & Desch, 1997) and Advanced Composition Explorer (ACE; Stone
et al., 1998) spacecraft, together with Dst index values, during the days
following the July 9 eruption. The spacecraft data are provided by the
Magnetic Field Investigation (MFI; Lepping et al., 1995), Solar Wind
Experiment (SWE; Ogilvie et al., 1995), and Three-Dimensional Plasma and
Energetic Particle Investigation (3DP; Lin et al., 1995) instruments on board
Wind as well as the Solar Wind Ion Composition Spectrometer (SWICS; Gloeckler
et al., 1998) on board ACE. The final Dst index is supplied by the World Data
Center (WDC) for Geomagnetism, Kyoto.

The sequence of disturbances commences with a shock-like feature around 01:00
UT on 2015 July 13. This structure cannot be defined as a fully developed
shock, since a clear jump is observed only in the magnetic field magnitude,
plasma density, and total pressure, although the solar wind bulk speed
experiences a small enhancement. Nevertheless, this feature marks the arrival
of the CME-driven sheath region, and a full shock is likely not formed because
the CME is traveling in a stream of fast solar wind—the plasma speed lies
around 600 km$\cdot$s-1 before the arrival of the disturbance. Starting around
08:00 UT on July 13, the ICME ejecta is seen to pass by the observing
spacecraft. The ejecta shows clear ICME signatures (e.g., Zurbuchen &
Richardson, 2006), including a declining speed profile (indicating expansion)
and bidirectional electrons (indicating a structure that is still connected to
the Sun from both legs). Additionally, the ejecta features magnetic cloud
signatures (e.g., Burlaga et al., 1981), including an elevated magnetic field
magnitude, smoothly rotating magnetic field vectors, as well as a low
temperature and plasma beta. The ICME ejecta boundaries, however, seem to
extend beyond the magnetic cloud boundaries, leading to a five-part ICME
(Kilpua et al., 2013) that includes a shock, a sheath region, an ICME front
region, a magnetic cloud, and an ICME rear region.

This aspect is also evident from charge state data, which display more
elevated values inside the magnetic cloud region than within the extended ICME
ejecta region. Finally, as mentioned in the Introduction, this event reached
Dst${}_{\text{min}}$ = $-68$ nT, corresponding to a moderate geomagnetic
storm, possibly induced by the turbulent sheath region and the initial portion
of ejecta material, since the index peaked approximately at the of the
magnetic cloud interval.

Another interesting feature of this in-situ event is the magnetic field
magnitude (and total pressure) profile, which peaks at the very front and very
rear of the whole ICME structure. This trend appears remarkably similar to a
series of CMEs observed in situ by Ulysses at ${\sim}3.5$ au and
${\sim}60^{\circ}$ latitude and described by Gosling et al. (1994). The ICMEs
detected by Ulysses were bounded by a forward–reverse shock pair, possibly
driven by CME overexpansion in interplanetary space rather than by an
intrinsic high radial speed. Interestingly, one of these Ulysses ICMEs was the
interplanetary counterpart of the large, high-latitude filament eruption
reported by McAllister et al. (1996). In the case of the event investigated
here, we note that the discontinuity at the end of the structure cannot be
defined as a reverse shock, since the temperature profile features an increase
rather than a decrease. It is possible that the structure encountered in 2015
July was not characterized by a forward–reverse shock pair because it was
detected at 1 au rather than at ${\sim}3.5$ au and along the ecliptic plane
(yielding a flank encounter) rather than at high latitudes (resulting in a
more central impact). Alternatively, the compression observed toward the rear
of the ICME ejecta may be uniquely due to the faster solar wind following it,
suggesting that the CME was embedded in a high-speed stream from either side—a
rather unusual occurrence that has been, nevertheless, reported in the
literature (e.g., Heinemann et al., 2019). SDO/AIA observations in the 211 Å
channel (not shown), in fact, reveal the presence of a single coronal hole
that could have been responsible for the fast solar wind measured at Earth
(located along the solar equator and with a longitude of ${\sim}35^{\circ}$
west on 2015 July 9).

To evaluate the flux rope properties of the 2015 July 9 ICME, we perform a
Lundquist force-free flux rope fitting (Lundquist, 1950; Burlaga, 1988;
Lepping et al., 1990), using the procedure described in Good et al. (2019),
over the interval that we identified as a magnetic cloud (i.e., the light-gray
shaded area in Figure 3). The method yields a right-handed flux rope with
normalized impact parameter $p=0.64$ and axis orientation ($\vartheta_{0}$,
$\varphi_{0}$) = ($-12^{\circ}$, $269^{\circ}$). Additionally, a Lundquist
fitting performed over the whole interval that we identified as ICME ejecta
(i.e., including the dark-gray shaded areas in Figure 3) reports a right-
handed flux rope as well, with $p=0.70$ and ($\vartheta_{0}$, $\varphi_{0}$) =
($-11^{\circ}$, $264^{\circ}$). Thus, different fitting boundaries
consistently yield a right-handed, low-inclination flux rope with a westward
axis that is encountered fairly far from its center. This is consistent with
the hypothesis of the 2015 July 9 CME propagating mainly toward the south and
encountering Earth only through its northern edge.

##  3 Modeling Setup

In this work, we model the interplanetary propagation of the 2015 July 9 CME
using the EUropean Heliospheric FORecasting Information Asset (EUHFORIA;
Pomoell & Poedts, 2018) MHD code. Here, we first introduce the inputs and
settings necessary to model the solar wind background in Section 3.1. Then, in
Section 3.2 we list the CME input parameters that we derive and set up for
running three different EUHFORIA simulations that differ by the
configuration—and thus physics—of the modeled ejecta.

###  3.1 Solar Wind Background

The EUHFORIA architecture consists of two modules, namely a coronal domain
(1–21.5 $R_{\odot}$) and a heliospheric one (0.1–2 au)—note that 21.5
$R_{\odot}$ equals 0.1 au. The coronal domain employs the semi-empirical
Wang–Sheeley–Arge (WSA; Arge et al., 2004) model, which uses synoptic maps of
the line-of-sight photospheric magnetic field to compute a background solar
wind solution at 21.5 $R_{\odot}$. Specifically, the WSA model extrapolates
the solar magnetic field using the Potential Field Source Surface (PFSS;
Altschuler & Newkirk, 1969) model up to 2.6 $R_{\odot}$ and the Schatten
Current Sheet (SCS; Schatten et al., 1969) model in the range 2.3–21.5
$R_{\odot}$.

In principle, the ambient solar wind is modeled using a magnetogram from a
time before or very close to the CME eruption. For this event, the eruption
begins on July 9 around 19:00 UT, and slowly evolves in the low corona to
reach 21.5 $R_{\odot}$ on July 10 after $\sim$08:00 UT as per our forward
modeling estimates using GCS (see Figure 2 and Table 1). Since the filament
eruption took place over an extended time period, we consider updating the
solar wind conditions around the time the CME reaches the EUHFORIA inner
heliospheric boundary of 0.1 au. Therefore, in this work, we employ a
magnetogram from July 10 at 00:00 UT to generate the background solar wind. We
use a synoptic standard photospheric map from the Global Oscillation Network
Group (GONG; Harvey et al., 1996) of ground-based telescopes.

###  3.2 CME Input Parameters

While keeping the ambient medium described in the previous section fixed, the
three EUHFORIA simulation runs that we set up to model the interplanetary
propagation of the 2015 July 9 CME differ significantly in the geometric and
magnetic configuration of the ejecta. The full list of input parameters used
for each run is presented in Table 2, and a detailed description of the CME
ejecta properties in each run is provided throughout this section.

Table 2: List of the input parameters used to inject each CME in the three different EUHFORIA runs. Latitudes and longitudes are reported in Stonyhurst coordinates. The tilt is measured from the solar west direction and is defined as positive for counterclockwise rotations. Note that for the EUHFORIA+Spheroid run, the 2015 July 9 event is initialized in three parts (see Section 3.2.1 for details).  Model version $\rightarrow$ | EUHFORIA+Spheroid | EUHFORIA+Spheromak | EUHFORIA+FRi3D
---|---|---|---
$\downarrow$ Input | Part 1 | Part 2 | Part 3 |  |
Injection day | 2015-07-10 | 2015-07-10 | 2015-07-10 | 2015-07-10 | 2015-07-10
Time at 21.5 $R_{\odot}$ ($t_{0}$) | 08:30 | 12:54 | 20:18 | 12:54 | 12:54
Latitude ($\theta$) | $-33^{\circ}$ | $-35^{\circ}$ | $-35^{\circ}$ | $-35^{\circ}$ | $-38^{\circ}$
Longitude ($\phi$) | $-32^{\circ}$ | $-18^{\circ}$ | $40^{\circ}$ | $-18^{\circ}$ | $-25^{\circ}$
Axial tilt ($\gamma$) | $90^{\circ}$ | $22^{\circ}$ | $70^{\circ}$ | $22^{\circ}$ | $10^{\circ}$
Nose speed ($V_{0}$) | 560 km$\cdot$s-1 | 425 km$\cdot$s-1 | 600 km$\cdot$s-1 | 425 km$\cdot$s-1 | 425 km$\cdot$s-1
Semi-major width ($R_{\mathrm{maj}}$) | $23^{\circ}$ | $43^{\circ}$ | $25^{\circ}$ | — | $50^{\circ}$
Semi-minor width ($R_{\mathrm{min}}$) | $18^{\circ}$ | $23^{\circ}$ | $17^{\circ}$ | — | $26^{\circ}$
Radius ($R_{0}$) | — | — | — | 18.7 $R_{\odot}$ | —
Toroidal height ($h_{T}$) | — | — | — | — | 15.0 $R_{\odot}$
Mass density ($\rho$) |  $10^{-18}$ kg$\cdot$m-3 |  $10^{-18}$ kg$\cdot$m-3 |  $10^{-18}$ kg$\cdot$m-3 |  $10^{-18}$ kg$\cdot$m-3 |  $10^{-17}$ kg$\cdot$m-3
Temperature ($T$) |  $8\times 10^{5}$ K |  $8\times 10^{5}$ K |  $8\times 10^{5}$ K |  $8\times 10^{5}$ K |  $8\times 10^{5}$ K
Chirality ($\chi$) | — | — | — | +1 | +1
Total flux ($\Phi_{B}$) | — | — | — |  $2.0\times 10^{13}$ Wb |  $2.0\times 10^{13}$ Wb
Polarity ($\Xi$) | — | — | — | — | EW
Pancaking ($\zeta$) | — | — | — | — | 0.5
Flattening ($\eta$) | — | — | — | — | 0.5
Skew ($\psi$) | — | — | — | — | $30^{\circ}$
Twist ($\tau$) | — | — | — | — | 1.2

####  3.2.1 EUHFORIA+Spheroid

Our first simulation run employs the EUHFORIA+Spheroid (Scolini & Palmerio,
2023) model, which is an extension of the “original” EUHFORIA+Cone (Pomoell &
Poedts, 2018) model in that it generalizes the geometry of the CME ejecta
front from the ice-cream cone of Fisher & Munro (1984)—with a circular cross-
section—to that of a spheroid—thus, with an elliptical cross-section. In both
these EUHFORIA versions, CMEs are modeled as hydrodynamic pulses, with a
uniform density distribution across their volume and no internal magnetic
field. This means that it is possible to simulate the CME arrival time and
speed, but not its magnetic configuration. This approach, albeit simplified,
allows us to emulate the highly asymmetric and slow nature of the 2015 July 9
event by injecting the CME into the EUHFORIA heliospheric domain as three
separate parts, i.e. those identified in the GCS reconstructions showcased in
Figure 2—corresponding to the streamer blowout, the large loop structure, and
the three-part cavity (see Section 2.2). Therefore, the full CME eruption from
an extended filament channel that spans almost the entire solar disk is
modeled as simply the superposition of the three separate spheroid eruptions
staggered in both longitudinal position and time. This approach is well-suited
for the spheroid hydrodynamic pulses because of their lack of an internal
magnetic structure, i.e. there is no possibility for distinct CME flux systems
to interact via e.g. collisions and/or reconnection.

The input parameters used for each CME portion inserted in the
EUHFORIA+Spheroid simulation run are reported in Table 2. The CME injection
time ($t_{0}$), latitude ($\theta$), longitude ($\phi$), and tilt ($\gamma$)
are taken directly from the GCS fitting results reported in Table 1. The
dimensions of the spheroid, i.e. the semi-major ($R_{\mathrm{maj}}$) and semi-
minor ($R_{\mathrm{min}}$) angular widths of its elliptical cross-section, are
derived from the GCS fits by extracting the projection of the 3D structure
along the plane perpendicular to the radial direction of the CME nose at its
point of maximum breadth (the full details of this procedure are outlined in
Appendix A). The CME injection speed ($V_{0}$) is determined by performing
additional GCS fits 1 hour before the times at which each CME part is
estimated to have reached 21.5 $R_{\odot}$, and thus by calculating the
velocity needed for the CME front(s) to travel the difference in radial
distance (or nose height) between the two sets of reconstructions.

####  3.2.2 EUHFORIA+Spheromak

Our second simulation run employs the EUHFORIA+Spheromak (Verbeke et al.,
2019) model, which describes the CME ejecta as a linear force-free spheromak
(Vandas et al., 1997). Since in this version of EUHFORIA CMEs are magnetized,
it is possible to model not only the arrival time of the CME-driven
disturbance but also the magnetic structure of the following ejecta. On the
other hand, the spherical geometry limits the ability to cover the entire
eruption in the case of the large, asymmetric 2015 July 9 event, and the
presence of internal fields no longer allows a convenient “superposition” of
multiple ejecta because of the expected interactions between distinct CME flux
systems. Since in this work we are primarily interested in modeling the
arrival of the CME at Earth, we resolve to focus our modeling efforts on the
portion of the eruption that encompasses Earth’s longitude, i.e. that
corresponding to the loop-like structure shown in Figure 2(b), or “Part 2” in
the EUHFORIA+Spheroid simulation.

The input parameters used for the EUHFORIA+Spheromak simulation run are
reported in Table 2. Since the geometric and kinematic properties of the CME
are based on the GCS reconstruction of “Part 2” in Table 1, parameters such as
the CME injection time ($t_{0}$), latitude ($\theta$), longitude ($\phi$),
tilt ($\gamma$), and nose speed ($V_{0}$) are identical to those in the
corresponding portion of CME in the EUHFORIA+Spheroid run. The intrinsic
spherical morphology of the spheromak only allows for the set up of a single
radius. Given the high latitude of the CME apex as inferred from coronagraph
observations, we construct our spheromak around the major axis of the GCS-
fitted CME (more information is provided in Appendix B). Furthermore, the set
of input parameters for the EUHFORIA+Spheromak run include two additional
properties that are needed to model the magnetic structure of the embedded
flux rope. The first of these is the chirality ($\chi$), set to right-handed
based on the analysis presented in Section 2.1. The second of these is the
total magnetic flux ($\Phi_{B}$) embedded in the CME, for which we use the
reconnection flux of the 2015 July 9 event derived in Paper I using the flare
ribbon masking method of Kazachenko et al. (2017), i.e. $2.0{\times}10^{13}$
Wb. We remark that the 2015 July 9 filament eruption, due to its slow and
gradual nature, was not characterized by classic flare ribbons signatures, and
the reconnection flux was estimated based on EUV emissions more suggestive of
post-eruption arcades—the reader can refer to Appendix B of Paper I for
further details. Finally, we note that the EUHFORIA implementation of the
Spheromak CME employed in this work does not take the CME nose speed and total
flux as inputs, but rather the radial speed and axial flux. We have chosen to
display, nevertheless, $V_{0}$ and $\Phi_{B}$ for uniformity across all the
runs shown in Table 2—more information on the equations employed to determine
instead the Spheromak-required input parameters is outlined in Appendix B.

####  3.2.3 EUHFORIA+FRi3D

Finally, our third simulation run employs the Flux Rope in 3D (FRi3D; Isavnin,
2016) model to describe the CME ejecta, thus yielding the EUHFORIA+FRi3D
(Maharana et al., 2022) architecture. As in the spheromak case, this ejecta is
magnetized, but the overall geometry of the CME—at least at insertion time—is
croissant-like (analogous to the GCS morphology) instead of spherical.
Furthermore, FRi3D allows for global deformations of the structure due to
pancaking (a direct consequence of the radial propagation of CMEs; e.g., Riley
& Crooker, 2004), front-flattening (due to the drag exerted by the background
solar wind; e.g., Vršnak et al., 2013), and rotational skew (due to the
east–west asymmetry resulting from interaction with a spiral-shaped solar
wind; e.g., Luhmann et al., 2020). Despite these additional free parameters,
it is not possible to reproduce the full extent of the large 2015 July 9 CME
with the FRi3D model, especially considering that the three sub-parts
identified in white-light data never appear simultaneously in the
coronagraph’s field of view (see Figure 2). Hence, we employ a similar
approach as in the spheromak case, i.e. we focus on the loop-like structure
that encompasses Earth’s longitude (“Part 2” in the EUHFORIA+Spheroid run).
For this simulation, our CME input parameters are not derived from the GCS
reconstructions in Figure 2, but from FRi3D’s own white-light CME fitting
tool—more information is provided in Appendix C, and a comparison of the GCS
and FRi3D reconstructions is shown in Figure 8.

The input parameters used for the EUHFORIA+FRi3D simulation run are reported
in Table 2. With respect to the Spheromak run, there are a few additional
properties that describe the CME: the toroidal height ($h_{T}$; i.e., the
heliocentric distance of the apex of the flux rope axis), the polarity ($\Xi$;
i.e., the direction of the flux rope axial field), the deformation parameters
described above, i.e., pancaking ($\zeta$), flattening ($\eta$), and skew
($\psi$), as well as the flux rope twist ($\tau$). We set the flux rope
polarity from east to west (EW), based on the remote-sensing analysis
presented in Section 2.1 (see, in particular, Figure 1(b)). For the flux rope
twist, which is not possible to determine from solar disc imagery without
performing magnetic field extrapolations, we set a value of 1.2 turns based on
the statistical analysis of Wang et al. (2016), who found that the most
probable estimate for $\tau$ (from leg to leg) is between 0.8 and 1.6 turns.
As in the case of the Spheromak run, we use for the total flux $\Phi_{B}$ =
$2.0{\times}10^{13}$ Wb based on the results of Paper I. The remaining
parameters (i.e., $h_{T}$, $\zeta$, $\eta$, and $\psi$) are direct outputs of
the FRi3D white-light fitting tool.

##  4 Modeling the CME Propagation

In this section, we present our modeling results in terms of both the large-
scale structure of the simulated CMEs through the inner heliosphere and the
corresponding (hindcast) predictions at Earth. In Section 4.1, we compare the
structure(s) of the CMEs that are injected in EUHFORIA to the structure of the
CME in the solar corona that resulted from the modeling efforts (of the
filament’s eruption and early evolution) presented in Paper I. In Section 4.2,
we compare the synthetic time series at Earth from the three EUHFORIA
runs—alongside the so-called ambient run of the steady-state background—with
in-situ observations from the Wind spacecraft.

###  4.1 Large-Scale Structure of the CME

Figure 4: Overall modeling results of the 2015 July 9 CME. The figure shows
the three heliospheric simulations performed with EUHFORIA compared with each
other and with the Paper I coronal simulation modeled with ARMS+STITCH. (a)
ARMS+STITCH simulation. (b) EUHFORIA+Spheroid simulation. (c)
EUHFORIA+Spheromak simulation. (d) EUHFORIA+FRi3D simulation. Each panel shows
(left) the $-20^{\circ}$ latitude plane and (right) the $0^{\circ}$ longitude
plane in Stonyhurst coordinates. The latitudinal plane shows the radial
velocity $V_{r}$ and the longitudinal plane shows the $B_{z}$ component of the
magnetic field. Representative magnetic field lines are shown in the
simulations with magnetized CME ejecta and the black contours in panel (b)
highlight the merged density enhancement of the non-magnetized spheroid CMEs.

First of all, our main focus is to evaluate the large-scale structure and
morphology of the modeled event in each of the three EUHFORIA simulation runs,
especially to assess similarities and differences. Additionally, we are
interested in comparing the EUHFORIA heliospheric results with the coronal
ones obtained in Paper I. The simulation presented and described in Paper I
was performed using the Adaptively Refined MHD Solver (ARMS; DeVore &
Antiochos, 2008) code, which solves the equations of ideal MHD on a 3D
spherical grid with solution-adaptive mesh refinement implemented via the
PARAMESH (MacNeice et al., 2000) toolkit. In Paper I, the pre-eruption corona
was modeled with a low-order spherical harmonic expansion based on the GONG
synoptic map for Carrington Rotation 2165 with an isothermal Parker (1958)
solar wind for $T=1.4$ MK. The extended filament channel was energized with
the STatistical InjecTion of Condensed Helicity (STITCH; Dahlin et al., 2022)
procedure to introduce sheared horizontal flux along the PIL. The filament
eruption begins from the eastern limb and progresses towards the western limb,
resulting in a skewed, asymmetric CME flux rope structure, propagating
approximately $30^{\circ}$ south of the ecliptic plane but expanding
significantly in latitude, in agreement with remote-sensing observations of
the solar disk and corona.

Figure 4 presents an overview of the 2015 July 9 CME modeled with the four
different simulations in the planes of (left) $-20^{\circ}$ latitude and
(right) $0^{\circ}$ longitude (in Stonyhurst coordinates). Within each run,
the left panel shows the radial solar wind velocity ($V_{r}$) and the right
panels show the north–south component of the magnetic field ($B_{z}$). The
choice to display an inclined, constant-latitude plane rather than the
equatorial (or ecliptic) one is motivated by the fact that, as shown in Paper
I and in the remote-sensing analysis part of Section 2, the bulk of the CME
propagated toward the south. A plane inclined by $20^{\circ}$ to the equator
allows us to more readily compare the full longitudinal extent of the modeled
ejecta, while keeping our viewpoint reasonably close to Earth’s latitude.

From the $V_{r}$ panels, it is possible to note that there are significant
differences arising between the four runs. In the ARMS+STITCH simulation
(Figure 4(a)), there is a clear east–west asymmetry that reflects the observed
evolution of the eruption in remote-sensing data, i.e. with the east limb
portion of the extended filament erupting first, and the rest of the energized
filament channel field structure following suit via the well-known zipper
effect associated with reconnection above extended PILs (e.g., Priest &
Longcope, 2017). This feature of the coronal simulation, i.e. the eastern
flank/leg of the erupting structure leading with the western one trailing, is
not maintained in the heliospheric domain of any of the three EUHFORIA runs
(Figure 4(b–d)). In fact, the western leg is now the leading portion of the
ejecta, with the degree of asymmetry depending on the specific run. This holds
true even in the case of the EUHFORIA+FRi3D simulation (Figure 4(d)), in which
the CME was injected with an initial morphology that more closely resembled
that of the eruption modeled in the corona with ARMS, i.e. with a skew of its
toroidal axis toward eastern heliolongitudes. In all cases, we can attribute
this apparent “counter-skewing” in interplanetary space to a fast solar wind
stream rooted on the western hemisphere of the Sun—and visible in all the
EUHFORIA runs, since they all used the same ambient medium as input. As a
consequence, the western flank of the CME propagates faster than the eastern
one, thus becoming the leading portion of the overall structure. We also note
that interaction with the faster solar wind flow leads to greater acceleration
of the ejecta in the EUHFORIA+FRi3D run than in the remaining two. This is
likely due to the specific geometry and magnetic description of each of the
CME ejecta, which may in turn yield different interaction outcomes. For
example, in the EUHFORIA+Spheroid run (Figure 4(b)), the lack of a magnetized
ejecta is not expected to result in a realistic interaction process (see also
Palmerio et al., 2022a), but rather in a CME-like disturbance propagating more
or less straightforwardly through a background wind. In the EUHFORIA+Spheromak
run (Figure 4(c)), the lack of CME legs may represent less of an “obstacle” to
the ambient solar wind, which in turn may be able to flow about the ejecta
with minimal interaction of the two flux systems.

From the $B_{z}$ panels, it is obvious (as expected) that the CME propagates
mostly south of the Sun–Earth line. Additionally, the ARMS and EUHFORIA
runs—excluding the Spheroid one, which does not include CME internal
fields—all display a leading (trailing) negative (positive) $B_{z}$, in
agreement with the SWN flux rope type inferred from remote-sensing
observations (see Section 2.1) and, thus, indicating that no dramatic
rotations of the ejecta have taken place in the simulation(s). Overall, the
EUHFORIA runs display a flatter front than the ARMS one, which is to be
expected since the drag exerted by the background solar wind builds up as a
CME travels away from the Sun, i.e., its effects are more noticeable in
interplanetary space than in the corona. Finally, it appears that the CME in
the FRi3D run intercepts the Sun–Earth line with a larger portion than in the
remaining two EUHFORIA runs, i.e., its overall trajectory is more comparable
to that of the ARMS CME. Again, this may be due to more realistic CME
interactions with the ambient wind resulting from the initial configuration of
the ejecta magnetic fields.

###  4.2 Modeled Time Series at Earth

After evaluating the global structure of the 2015 July 9 CME modeled with
EUHFORIA, we analyze the corresponding time series at Earth’s location and
compare them with in-situ measurements taken by the Wind spacecraft (and
described in detail in Section 2.3). The collective of in-situ profiles,
together with the ambient run (of the background wind with no CMEs), is shown
in Figure 5(a). First of all, we note that the arrival time and speed of the
fast solar wind stream preceding the CME—and that leads to the interaction
discussed in Section 4.1—are reproduced fairly well by EUHFORIA. The
compression of solar wind material at the stream interaction region is largely
underestimated, which is on the other hand a well-known issue of heliospheric
MHD models (e.g., Pahud et al., 2012; Riley et al., 2012).

Figure 5: Simulated magnetic field and plasma time series for (a) all EUHFORIA
simulations and (b) the EUHFORIA+FRi3D simulation, shown against the
corresponding measurements taken by the Wind spacecraft. The panels show, from
top to bottom: Magnetic field magnitude, magnetic field components in
Cartesian coordinates, solar wind bulk speed, proton density, proton
temperature, plasma beta, . The solid vertical lines mark the arrival of the
shock-like disturbance, while the dashed vertical lines mark the leading of
the ICME ejecta (i.e., the beginning of the gray shaded area in Figure 3). The
results in (a) show the simulated time series at Earth only, while the results
in (b) show simulation outputs at Earth as well as in the ${\pm}5^{\circ}$ and
${\pm}10^{\circ}$ latitudinal and longitudinal offsets around Earth.

Regarding the arrival of the CME itself, we note clear differences among the
three EUHFORIA runs. The Spheroid simulation, in particular, is hardly
distinguishable from the ambient one—the two curves begin separating around
16:00 UT on July 13 (visible especially in the speed, density, and beta
profiles), but their offset is so modest that it can be considered negligible.
In practice, this event would have been effectively considered a “miss” at
Earth in terms of space weather predictions using the spheroid model. The
Spheromak simulation, on the other hand, features a somewhat clearer impact
around 02:00 UT on July 14, i.e. approximately one day later than observed
(the CME-related disturbance was determined to have commenced around 01:00 UT
on July 13 in Section 2.3). Furthermore, the CME-induced enhancements in the
magnetic field and plasma parameters are substantially less prominent than
observed—in practical terms, this prediction would have likely been considered
an “almost-miss” given its weak impact. Finally, the FRi3D simulation displays
an arrival time at Earth that is just about 2 hr earlier than detected by
Wind, i.e. around 23:00 UT on July 12. Both the plasma structure and magnetic
field configuration of the ICME ejecta are generally well captured by the
model, but the magnetic field magnitude, as well as the intensity of the
$B_{z}$ component, are moderately underestimated. One possible cause for this
is that the trailing portion of the fast solar wind stream in which the CME is
embedded does not appear in the EUHFORIA simulation(s), leading to a lack of
compression at the back of the ejecta. Hinterreiter et al. (2019), in a study
aimed at assessing the performance of EUHFORIA in modeling the ambient
background, found that coronal hole areas are generally underestimated, often
yielding narrower flows of fast wind than observed in in-situ data.

A zoomed-in view of the CME arrival in the FRi3D simulation is shown in Figure
5(b) alongside results at virtual spacecraft surrounding Earth with offsets of
${\pm}5^{\circ}$ and ${\pm}10^{\circ}$ in both latitude and longitude. As
discussed in Scolini et al. (2019), considering outputs around the specific
location of interest is an adequate way to account for the typical
uncertainties associated with estimates of CME size and/or trajectory based on
remote-sensing imagery (which become even more prominent when employing a
single viewpoint; see Verbeke et al., 2022). Across the whole range of virtual
spacecraft, the CME arrival times are clustered ${\pm}8$ hr around the
observed one (well within the known typical uncertainties; e.g., Riley et al.,
2018; Wold et al., 2018). The largest spreads in predictions of the ICME
ejecta are found in the magnetic field magnitude and $B_{y}$ component, with
values in the range [2, 8] nT and [$-$8, 2] nT, respectively. On the other
hand, we find no significant differences in the $B_{z}$ component, i.e., no
synthetic time series reaches the minimum observed values of $-$9 nT. Thus,
although an encounter with the northern flank of the ICME ejecta as well as
its overall magnetic configuration are correctly predicted, the intensity of
the (moderate) geomagnetic storm that ensued would have been somewhat
underestimated.

##  5 Discussion

From the results presented in Section 4, it is evident that the EUHFORIA+FRi3D
run performed significantly better than the remaining two in terms of
capturing the arrival and magnetic field configuration of the 2015 July 9 CME.
Nevertheless, it is important to scrutinize these findings in the context of
extreme events in terms of their spatial and temporal extent. The CME analyzed
here erupted over a prolonged amount of time and covered a wide range of
heliolongitudes (basically encompassing almost the full Earth-facing solar
disk). Therefore, a number of assumptions and approximations had to be made in
order to accommodate the heliospheric modeling of such a peculiar event. To
emulate the highly asymmetric and slow coronal evolution of the eruption, we
divided the whole CME structure into three parts (based on its appearance in
white light) in the simulation that did not include internal ejecta magnetic
fields (EUHFORIA+Spheroid run, see Section 3.2.1). For the simulations that
featured magnetized ejecta, on the other hand, we resolved to select a
“portion of interest” to model, as to avoid spurious interactions arising from
simulating three separate CME flux systems. The first of them
(EUHFORIA+Spheromak run, see Section 3.2.2) simplified the Earth-directed
portion of the event as a magnetized sphere, while the second (EUHFORIA+FRi3D
run, see Section 3.2.3) approximated the structure as an asymmetric croissant
that was however significantly less extended in longitude than observed in
coronagraph imagery.

The 2015 July 9 CME was encountered at Earth only through its northern edge,
but the impact was still relatively close to its nose (under the assumption
that the axis of the embedded flux rope was approximately east–west oriented).
Had the encounter taken place closer to the apex in latitude, but farther from
it in longitude, then the Spheromak run may have yielded more accurate
results. This is because the CME would have likely encountered Earth through
its leg in the FRi3D run even though the full event extended beyond the
boundary of the FRi3D flux rope geometry, whereas the Spheromak configuration
lacks any CME leg features (see also Maharana et al., 2023). Hence, the
simplified Spheromak magnetic structure may be a more convenient modeling
strategy when simulating only a portion of a particular CME, depending on the
in-situ observer’s location. On the other hand, had we been interested in
predicting the CME arrival at several observers in the inner heliosphere
spread across broad longitudes, then the Spheroid ejecta would have likely
been a more fitting option. In fact, the superposition of multiple
hydrodynamic pulses launched with different trajectories and at different
times results in a more asymmetric and wider “global” ejecta, which is more
suitable for comparisons with multi-point measurements. Thus, the Spheroid (or
Cone) ejecta seems to be currently the most feasible tool to model extended
and asymmetric CMEs as a whole. However, the advantages of this approach may
be somewhat limited to periods of relatively simple ambient conditions, e.g.
without significant CME interactions with the structured solar wind that would
require a more complete ejecta description to model accurately. Therefore, we
caution against extrapolating conclusions that are contingent on the
particular event analyzed in this work and remark on the importance of
carefully selecting the modeling strategy that best fits the specific research
(or operational) goal(s).

Our interest in the 2015 July 9 CME was driven in particular by the moderate
problem geomagnetic storm that followed upon its impact at Earth. While this
work showcases some of the difficulties associated with this particular class
of events, the CME studied here featured some specific characteristics that
made it “problematic”: It was exceptionally extended as well as highly
asymmetric (and, thus, difficult to model in its entirety), it was slow, and
had no significant Earth-directed component (at least according to estimates
from remote-sensing imagery). Furthermore, its related space weather effects
were likely intensified by the fact that it traveled through a flow of high-
speed solar wind—that CME interaction with fast streams can lead to enhanced
geoeffectiveness has been shown both via observational (e.g., Nitta et al.,
2021; Palmerio et al., 2022b) and modeling (e.g., Kay et al., 2022) studies.
Our work demonstrated two viable ways as to how to model cases in which the
“problematic” status can be attributed to an extended and/or asymmetric
structure of the CME, i.e., either via modeling only the Earth-directed (or
observer-of-interest-directed) component or via constructing the whole CME
from separate parts. This also raises interesting questions regarding the
physics and coherence of more extended CMEs. For example, are CMEs truly
composed of distinct sections or simply appear complex in coronagraph images
due to local distortions and/or projection effects, and to what extent do they
maintain their integrity while they propagate in the structured solar wind?
Multi-spacecraft heliospheric observations over broad longitudes and short
radial distances (e.g., Lugaz et al., 2022) may provide further insight into
these issues.

Nevertheless, problem geomagnetic storms can feature different characteristics
of their solar counterparts that grant their “problematicness,” including the
weakness or total absence of remote-sensing signatures (e.g., Nitta &
Mulligan, 2017; Palmerio et al., 2021b). While attempts at modeling such
events have been performed (e.g., Lynch et al., 2016; Palmerio et al., 2021a),
these CMEs are mostly analyzed in hindcast mode, as they often escape the eyes
in real-time applications. In the case of the 2015 July CME investigated here,
on the other hand, the problematic nature of the event in terms of real-time
predictions was given by the fact that the CME appeared as three separate
eruptions in white-light imagery, and a detailed analysis of the corresponding
solar disk observations was necessary to gain a deeper insight into its onset
and early evolution. In the future, improvements in resolution and sensitivity
for EUV and white-light imaging, as well as the availability of remote-sensing
observers from multiple viewpoints (see, e.g., Gibson et al., 2018; Howard et
al., 2023; Palmerio et al., 2023) will significantly advance our ability to
identify and include these different types of problematic CMEs in space
weather forecasting applications.

##  6 Summary and Conclusions

In this work, we have simulated the interplanetary propagation and arrival at
Earth of the large, slow, and highly asymmetric CME that erupted on 2015 July
9. Starting from estimates of the CME geometry and kinematics based on white-
light coronagraph observations, we have adopted three different approaches to
represent the ejecta within the EUHFORIA model. In the first
(EUHFORIA+Spheroid, lacking an internal ejecta magnetic field) we modeled the
event in three separate parts to emulate the wide spread in longitude and slow
temporal evolution of the CME. In the remaining two (EUHFORIA+Spheromak and
EUHFORIA+FRi3D, both featuring magnetized ejecta but with different
morphologies) we selected the Earth-directed portion of the exceptionally
large CME for heliospheric modeling of its propagation. We found that the
FRi3D simulation run yielded the best results at Earth in terms of CME arrival
time and magnetic configuration upon impact, but remarked that the remaining
two ejecta descriptions may represent better modeling choices in different
situations, especially in the case of forecasting the properties of problem
geomagnetic storms.

One major challenge in interplanetary CME modeling—and especially evident in
the case of the 2015 July 9 event—is represented by adapting complex CME
morphologies to the simplified flux rope models that are implemented in
existing heliospheric simulations. While flux rope models of increasingly
higher complexity are being developed (e.g., Weiss et al., 2022; Nieves-
Chinchilla et al., 2023), their inclusion within global MHD simulations is
still a considerable challenge from a computational standpoint. Alternative,
but more complex approaches, include full Sun-to-heliosphere simulations
(e.g., Jin et al., 2017; Török et al., 2018)—in our case, this would translate
into propagating the 2015 July 9 CME as modeled with ARMS in Paper I
seamlessly from the coronal domain into the heliosphere. However, such
simulation runs are computationally expensive and, thus, less suitable for
real-time space weather predictions at least for the time being. The approach
undertaken in this work represents a practical way to circumnavigate these
current limitations and to provide, in the meanwhile, a strategy toward
modeling more problematic events.

## Acknowledgments

E.P. acknowledges support from NASA’s HTMS (grant no. 80NSSC20K1274) and LWS-
SC (grant no. 80NSSC22K0893) programs as well as NSF’s PREEVENTS (grant no.
ICER-1854790) program. A.M. acknowledges support from projects C14/19/089 (C1
project Internal Funds KU Leuven), G.0025.23N (WEAVE FWO-Vlaanderen), SIDC
Data Exploitation (ESA Prodex-12), and Belspo project B2/191/P1/SWiM. B.J.L.
acknowledges NSF AGS-2147399, NASA 80NSSC22K0674, and NASA 80NSSC21K1325. C.S.
acknowledges support from the Research Foundation – Flanders (FWO strategic
base PhD fellowship 1S42817N) and NASA grants 80NSSC19K0914, 80NSSC20K0197,
and 80NSSC20K0700. S.W.G. was supported by Academy of Finland Fellowship
grants 338486 and 346612 (INERTUM), and Project grant 310445 (SMASH). S.W.G.,
J.P., and E.K.J.K. acknowledge the European Research Council (ERC) under the
European Union’s Horizon 2020 Research and Innovation Programme Project SolMAG
(grant agreement no. 724391) and the Finnish Centre of Excellence in Research
of Sustainable Space (Academy of Finland grants no. 312390 and no. 336807).
EUHFORIA is developed as a joint effort between the University of Helsinki and
KU Leuven. Simulations were carried out at KU Leuven and the Flemish
Supercomputer Center (VSC), funded by the Hercules foundation and the Flemish
Government, Department of Economy, Science and Innovation (EWI). The CACTus
CME catalog (http://sidc.oma.be/cactus/) is generated and maintained by the
SIDC at the Royal Observatory of Belgium. The SOHO/LASCO CME catalog
(https://cdaw.gsfc.nasa.gov/CME_list/) is generated and maintained at the CDAW
Data Center by NASA and The Catholic University of America in cooperation with
the Naval Research Laboratory. We thank the WDC for Geomagnetism, Kyoto
(http://wdc.kugi.kyoto-u.ac.jp), and the geomagnetic observatories for their
cooperation to make the final Dst indices available. E.P. thanks the Croom
team for fruitful discussions and collaborations. We also thank Dr. Daria
Shukhobodskaia (Royal Observatory of Belgium, Brussels) for developing the
user-friendly GUI application used in this work to fit the FRi3D model to
white-light images.

##  Appendix A Derivation of the CME Angular Widths from GCS Fits

In the following, we refer to the formulation of Thernisien (2011), who
provides an overview of the GCS croissant geometry and all its parameters,
summarized in Figure 6. Given the croissant-like geometry of the GCS model, it
follows that the projection of the 3D wireframe on the plane perpendicular to
the radial direction of the CME nose at its maximum extent corresponds to an
ellipse of semi-major axis $R_{\mathrm{maj}}$ and semi-minor axis
$R_{\mathrm{min}}$ (highlighted in Figure 6), corresponding to the face-on and
edge-on angular widths, respectively.

Figure 6: Overview of the GCS geometry in the (left) face-on and (right) edge-
on projections, adapted from Thernisien (2011). The half-angular face-on
($R_{\mathrm{maj}}$) and edge-on ($R_{\mathrm{min}}$) widths of the croissant
are highlighted in magenta.

Considering that the GCS aspect ratio parameter is defined as
$\kappa=\sin\delta$, one obtains the half-angular width of the edge-on cross
section ($R_{\mathrm{min}}$) from Equations (28) and (29) in Thernisien
(2011), as well as the relation $\tan{R_{\mathrm{min}}}=R(\beta=\pi/2)/OC_{1}$
(right panel of Figure 6), which gives

$R_{\mathrm{min}}=\arctan{\kappa}\,.$ (A1)

Thernisien (2011) outlined the procedure for the numerical calculation of the
face-on half-width $R_{\mathrm{maj}}$ by noting that it corresponds to the
maximum of the $x$-coordinate of $\overrightarrow{BP}$. Thus,
$R_{\mathrm{maj}}$ is estimated by finding the value of the angle $\beta$ such
that $\partial(\overrightarrow{BP}\cdot\hat{x})/\partial\beta=0$. Given that
$\overrightarrow{BP}\cdot\hat{x}=\left(X_{0}+R\right)\cos{\beta}$ using the
Thernisien (2011) definitions

$X_{0}=\frac{\rho+b\kappa^{2}\sin{\beta}}{1-\kappa^{2}}\;\;\;\;\text{and}\;\;\;\;R=\left[X_{0}^{2}+\frac{b^{2}\kappa^{2}-\rho^{2}}{1-\kappa^{2}}\right]^{1/2}\;,$
(A2)

setting this derivative to zero yields

$\displaystyle\frac{\partial}{\partial\beta}\left(\overrightarrow{BP}\cdot\hat{x}\right)$
$\displaystyle=$ $\displaystyle\frac{\partial}{\partial\beta}f(\beta)$ (A3)
$\displaystyle=$
$\displaystyle\frac{\partial}{\partial\beta}\left[\left(\frac{\rho+b\kappa^{2}\sin{\beta}}{1-\kappa^{2}}\right)\cos{\beta}+\left(\left(\frac{\rho+b\kappa^{2}\sin{\beta}}{1-\kappa^{2}}\right)^{2}+\frac{b^{2}\kappa^{2}-\rho^{2}}{1-\kappa^{2}}\right)^{1/2}\cos{\beta}\right]=0\;.$

We note that with the substitution of the additional GCS geometric parameter
definitions $b=h/\cos{\alpha}$ and $\rho=h\tan{\alpha}$, the expression for
the derivative is now solely a function of the parameters $(\alpha,\kappa,h)$.
Since $h$ describes the full height of the cone under self-similar expansion
($OD$ in Figure 6), it does not affect the angular dependence. We have solved
Equation A3 numerically to obtain values of $\beta_{0}$ such that $\partial
f(\beta_{0})/\partial\beta=0$ for a $300\times 300$ input array of
$(\alpha,\kappa)$ with $\alpha\in[0^{\circ},90^{\circ}]$ and $\kappa\in[0,1]$.
This yields a 2D distribution of $R_{\mathrm{maj}}(\alpha,\kappa)$ given by

$R_{\mathrm{maj}}(\alpha,\kappa)=\arcsin{\left[\frac{|\overrightarrow{BP}|\cos\beta_{0}}{\sqrt{b^{2}+|\overrightarrow{BP}|^{2}+2b|\overrightarrow{BP}|\sin\beta_{0}}}\right]}\;,$
(A4)

where $|\overrightarrow{BP}|=X_{0}(\beta_{0})+R(\beta_{0})$. Figure 7(a) shows
the numerical $R_{\mathrm{maj}}(\alpha,\kappa)$ results. Since this procedure
can be somewhat cumbersome, we have also constructed an empirical
approximation, $\widehat{R}_{\mathrm{maj}}(\alpha,\kappa)$, as a 2nd-order, 2D
polynominal fit to the numerical $R_{\mathrm{maj}}$,

$\displaystyle\widehat{R}_{\mathrm{maj}}(\alpha,\kappa)=\sum_{i,j=0}^{2}c_{ij}\,\alpha^{i}\,\kappa^{j}$
$\displaystyle=\begin{bmatrix}\alpha^{0}&\alpha^{1}&\alpha^{2}\end{bmatrix}\begin{bmatrix}-9.17{\rm
E}{-02}&+1.08{\rm E}{+00}&-6.53{\rm E}{-03}\\\ +6.38{\rm E}{+01}&-1.04{\rm
E}{+00}&+6.13{\rm E}{-03}\\\ -1.87{\rm E}{+01}&+2.98{\rm E}{-01}&-1.52{\rm
E}{-03}\end{bmatrix}\begin{bmatrix}\kappa^{0}\\\ \kappa^{1}\\\ \kappa^{2}\\\
\end{bmatrix}\;.$ (A5)

Figure 7: Dependence of the GCS face-on width $R_{\mathrm{maj}}$ on model
parameters $\alpha$ and $\kappa$. (a) $R_{\mathrm{maj}}$ computed numerically
via Equation A4 using the procedure outlined in Thernisien (2011). (b) The
empirical fit $\widehat{R}_{\mathrm{maj}}$ given by Equation A5. (c) The
residual $(R_{\mathrm{maj}}-\widehat{R}_{\mathrm{maj}})$ between the numerical
(a) and empirical (b) formulations.

Figure 7(b) shows this empirical estimate
$\widehat{R}_{\mathrm{maj}}(\alpha,\kappa)$, and Figure 7(c) plots the
residual $R_{\mathrm{maj}}-\widehat{R}_{\mathrm{maj}}$. The magnitude of the
residual is always ${\lesssim}0.6^{\circ}$, which is significantly less than
the inherent uncertainty associated with the GCS geometry parameters due to
both the model’s sensitivity (Thernisien et al., 2009) and the user’s
subjectivity (Verbeke et al., 2022).

##  Appendix B Derivation of Spheromak-Specific Input Parameters

The GCS model usually features an elongated (croissant-like) morphology,
unless $\alpha=0$, for which $R_{\mathrm{maj}}=R_{\mathrm{min}}$ and the so-
called cone model is retrieved. When adapting GCS parameters to the spheromak
morphology, a single radius has to be derived, usually from the half-width
$\alpha$ and/or the aspect ratio $\kappa$, for cases in which $\alpha\neq 0$.
In this work, we employ for the spheromak run the “maximum” (face-on) radius
derived from GCS parameters as defined by Asvestari et al. (2021),

$R_{0}=21.5\,R_{\odot}\sin\left(\frac{\omega_{\mathrm{FO}}}{2}\right)\;,$ (B1)

where $\omega_{\mathrm{FO}}=2(\alpha+\delta)=2(\alpha+\arcsin{\kappa})$
indicates the full face-on width of the croissant (see Figure 6).

The spheromak radial speed ($V_{\mathrm{rad}}$) is derived from the CME nose
speed ($V_{0}$) using the formula in Scolini et al. (2019), who derived that
the total (nose) speed of a CME front can be decomposed into its radial speed
(i.e., the speed of the CME center) and its expansion speed (i.e., the rate of
growth of its cross-section). In GCS quantities, this converts to

$V_{0}=V_{\mathrm{rad}}+V_{\mathrm{exp}}=\frac{1}{1+\kappa}\diff{H}{t}+\frac{\kappa}{1+\kappa}\diff{H}{t}\;,$
(B2)

where $\kappa$ is again the GCS aspect ratio, and $H$ is the height of the CME
nose ($OH$ in Figure 6).

Another parameter that has to be adapted to the spheromak implementation of
EUHFORIA is the axial (or toroidal) magnetic flux ($\Phi_{T}$) of the CME. To
do so, we start from the total reconnection flux ($\Phi_{B}$) estimated in
Paper I and use the formulation of Scolini et al. (2019) under the assumption
that all the reconnected flux goes into the poloidal magnetic flux of the
erupted flux rope (Qiu et al., 2007) to obtain the toroidal flux as:

$\Phi_{T}=\frac{2B_{0}}{a^{2}}\left[-\sin(x_{01})+\int_{0}^{x_{01}}\frac{\sin
x}{x}dx\right]\;,$ (B3)

where $\alpha$ is the force-free parameter and $x_{01}=\alpha R_{0}=4.4934$ is
the first zero of the Bessel function $J_{1}$. $B_{0}$ is the axial field
strength of the spheromak flux rope, defined as

$B_{0}=\frac{\alpha^{3}}{2\pi}\frac{\Phi_{P}(R_{\star})R_{\star}}{\left[\sin(\alpha
R_{\star})-\alpha R_{\star}\cos(\alpha R_{\star})\right]}\;,$ (B4)

where $R_{\star}$ is the distance from the center of the spheromak where the
magnetic field becomes completely axial.

##  Appendix C Comparison of the GCS and FRi3D White-Light Fitting Tools

Both the GCS and FRi3D models can be used to visually fit a parameterized CME
morphology to white-light coronagraph images from one or more viewpoints. The
difference between the two methods resides in the number of free parameters
that describe the CME shell—six for GCS and nine for FRi3D. The six GCS
properties are: latitude, longitude, axial tilt, nose height, half-width, and
aspect ratio (see also Table 1). The nine FRi3D properties, on the other hand,
are: latitude, longitude, axial tilt, nose height, half-width, half-height,
flattening, pancaking, and skew. It follows that the FRi3D model allows for
much greater control and fine-tuning of the overall flux rope geometry, which
is particularly useful in the case of strongly distorted and/or asymmetric
CMEs.

Figure 8 shows a comparison of the GCS and FRi3D fits to the central portion
of the extended 2015 July 9 CME—i.e., that displayed in Figure 2(b) and
corresponding to Part 2 in Table 1. It is evident that there are stark
differences between the two models: The FRi3D reconstruction allows for a
lower latitude of the flux rope axis, a tilt that is closer to the equatorial
plane, and a clearer separation of the CME legs, while maintaining the overall
appearance of east–west asymmetry (cf. also the EUHFORIA input parameters in
Table 2 resulting from the two sets of fitting procedures).

Figure 8: Comparison of a (b) GCS versus a (c) FRi3D fitting of the 2017 July
9 CME applied to (a) SOHO/LASCO/C3 imagery from July 10 at 12:54 UT.

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