11institutetext:  Predictive Science Inc., San Diego, CA 92121, USA
11email<EMAIL_ADDRESS>22institutetext: Heliophysics Science Division,
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 33institutetext:
Department of Physics, The Catholic University of America, Washington, DC
20064, USA 44institutetext: Space Science Center, University of New Hampshire,
Durham, NH 03824, USA

# Modeling CME encounters at Parker Solar Probe with OSPREI: Dependence on
photospheric and coronal conditions

Vincent E. Ledvina now at Geophysical Institute, University of Alaska
Fairbanks, Fairbanks, AK 9709, USA11 Erika Palmerio 11 Christina Kay 2233 Nada
Al-Haddad 44 Pete Riley 11

(Received; accepted)

###### Abstract

Context. Coronal mass ejections (CMEs) are eruptions of plasma from the Sun
that travel through interplanetary space and may encounter Earth. CMEs often
enclose a magnetic flux rope (MFR), the orientation of which largely
determines the CME’s geoeffectiveness. Current operational CME models do not
model MFRs, but a number of research ones do, including the Open Solar Physics
Rapid Ensemble Information (OSPREI) model.

Aims. We report the sensitivity of OSPREI to a range of user-selected
photospheric and coronal conditions.

Methods. We model four separate CMEs observed in situ by Parker Solar Probe
(PSP). We vary the input photospheric conditions using four input magnetograms
(HMI Synchronic, HMI Synoptic, GONG Synoptic Zero-Point Corrected, and GONG
ADAPT). To vary the coronal field reconstruction, we employ the Potential-
Field Source-Surface (PFSS) model and we vary its source-surface height in the
range 1.5–3.0 R⊙ with 0.1 R⊙ increments.

Results. We find that both the input magnetogram and PFSS source surface often
affect the evolution of the CME as it propagates through the Sun’s corona into
interplanetary space, and therefore the accuracy of the MFR prediction
compared to in-situ data at PSP. There is no obvious best combination of input
magnetogram and PFSS source surface height.

Conclusions. The OSPREI model is moderately sensitive to the input
photospheric and coronal conditions. Based on where the source region of the
CME is located on the Sun, there may be best practices when selecting an input
magnetogram to use.

###### Key Words.:

Sun: coronal mass ejection — Sun: photosphere — Sun: magnetic fields — Sun:
CME modeling

##  1 Introduction

A coronal mass ejection (CME) is an eruption on the Sun that releases
significant amounts of plasma into interplanetary space (see more in Webb &
Howard, 2012). As plasma moves out from the Sun, the magnetic field becomes
‘frozen-in’ so that it remains fixed within the plasma parcels in which it is
embedded close to the Sun. Due to this frozen-in flux property of space
plasmas, CMEs carry with them an embedded magnetic field in the form of a flux
rope (e.g., Green et al., 2018). Occasionally, CMEs launched from the Sun will
be Earth-directed, and when they come in contact with Earth’s magnetic
environment, they may cause geomagnetic storms that damage power grids, cause
spacecraft charging, and create auroral displays (e.g., Pulkkinen, 2007). The
strength and type of interaction a CME produces has much to do with its speed,
ram pressure, and magnetic configuration. Current solar wind models used by
space weather forecasting offices to model CMEs can only predict their speeds,
densities, and arrival times operationally (Pizzo et al., 2011). Other CME
models that are presently used in research use alternative workflows to
predict not only speed, density, and arrival time, but also the configuration
of the magnetic flux rope (MFR) embedded inside the CME. Magnetohydrodynamic
(MHD) models are generally more realistic, but also complex and
computationally-expensive, and these include the Magnetohydrodynamic Algorithm
outside a Sphere (MAS; Mikić et al., 1999) code coupled with the modified
Titov–Démoulin flux rope (Török et al., 2018), the Alfvén Wave Solar Model
(AWSoM; Oran et al., 2013) coupled with the Gibson–Low flux rope (Jin et al.,
2017), and the European Heliospheric Forecasting Information Asset (EUHFORIA;
Pomoell & Poedts, 2018) coupled with the Spheromak (Verbeke et al., 2019) or
the FRi3D (Maharana et al., 2022) flux rope models. On the other hand,
analytical models are generally less realistic, but at the same time simpler
and computationally efficient. Such models include the Three‐Dimensional
Coronal ROpe Ejection (3DCORE; Möstl et al., 2018), the INterplanetary Flux
ROpe Simulator (INFROS; Sarkar et al., 2020), and the Open Solar Physics Rapid
Ensemble Information (OSPREI; Kay et al., 2022a). Most notably, analytical
models can achieve MFR predictions quickly with relatively easily-obtained
input parameters.

The orientation of the MFR inside a CME is correlated with how much energy is
transferred from the solar wind into Earth’s magnetic system and has a great
effect on what impacts are seen on Earth’s surface and in the near-Earth space
environment. An MFR with a long-duration negative Bz component is required for
strong geomagnetic storms, as it opens the subsolar magnetopause via magnetic
reconnection, allowing for the transfer of energy, plasma, and momentum from
the solar wind into Earth’s magnetosphere (e.g., Dungey, 1961). Predictions of
an MFR’s Bz component are important for understanding its impact at Earth, but
current forecasts are still unable to model CME MFRs, resulting in frequent
over and under-estimations of CME geoeffectiveness. For example, the strength
of the “St Patrick’s Day Storm” on 17 March 2015 (Kataoka et al., 2015; Wu et
al., 2016) was underestimated by the National Oceanic and Atmospheric
Administration’s Space Weather Prediction Center (NOAA/SWPC), which predicted
only maximum G1 geomagnetic storm conditions. The CME shock arrived 15 hours
ahead of forecasts and the MFR contained a large southward Bz component,
producing a G4-level geomagnetic storm. Conversely, one of the first notable
space weather events of solar cycle 25, a partial halo CME eruption on 28
March 2022, triggered a G3 geomagnetic storm watch from NOAA SWPC for 31 March
2022. While the arrival time of the CME was accurately forecasted, due to an
MFR with a strong positive Bz configuration, the CME only managed to create a
brief G1-level geomagnetic storm. These are only two examples of where best-
effort space weather forecasting simply does not do enough to account for the
contribution of a CME’s MFR.

Deflections of the CME propagating through the Sun’s corona may also affect
the orientation of the MFR and CME’s speed and trajectory, affecting the
accuracy of the forecast arrival time. In one example, Mays et al. (2015) and
Möstl et al. (2015) showed that the major CME of 7 January 2014 was not
forecast accurately due to rotations and deflections before propagating in the
solar wind. Improving the orientation and directionality of the CME through
more advanced modeling improved the forecast arrival time by over 18 hours at
Earth. While there are a host of models that can model MFRs and coronal
deflections of CMEs, for them to be operationally viable, they need to be
validated and their sensitivities to different input parameters assessed.

In this work, we investigate the OSPREI model and determine its sensitivity to
varying input photospheric and coronal conditions. We compare OSPREI model
results with Parker Solar Probe (PSP; Fox et al., 2016) in-situ solar wind
measurements. PSP is used as a ground truth instead of Earth so that we can
contextualize our results to space weather predictions at any point in the
heliosphere assuming that maps of the solar photospheric field are only
captured from Earth’s viewpoint. At the times of the CME events analyzed here,
PSP was located at heliocentric distances between ${\sim}$0.45 and
${\sim}$0.75 au, so one may expect forecasting uncertainties to decrease as
the spacecraft gets closer to the Sun. Nevertheless, in our investigation we
do not focus on CME arrival time, but rather on the MFR magnetic structure.
Although it has been shown that CMEs can deflect and rotate in interplanetary
space (e.g., Isavnin et al., 2014), it is well known that most changes in
trajectory and orientation take place in the solar corona (e.g., Kay & Opher,
2015). Hence, we can assume the impact of these contributions to decrease with
radial distance so rapidly to not significantly affect our results. The
findings of this work will be useful for incorporating OSPREI as a potential
future operational CME model.

The outline of this manuscript is as follows: We begin with an overview of
OSPREI and by detailing the modeling setup used for our analysis in Sect. 2.
In Sect. 3, we discuss the data sets used and our methodology to vary the
photospheric and coronal conditions as inputs into the OSPREI model. In Sect.
4 we describe the model’s reaction to our varying input parameters on the four
CMEs, and we discuss these results in Sect. 5. Finally, in Sect. 6 we
interpret our findings in the context of other CME models and make suggestions
as to how OSPREI may be used in real-time forecasting situations.

##  2 Modeling Setup

In this section, we describe the modeling setup used in this study: We provide
a brief overview of the OSPREI modeling suite (Sect. 2.1), and then follow
with a description of the different photospheric (Sect. 2.2) and coronal
(Sect. 2.3) inputs that we explore to test the model’s sensitivity.

###  2.1 Overview of OSPREI

OSPREI models Sun-to-Earth—or, more generally, Sun-to-heliosphere—CME behavior
beyond more traditional interplanetary propagation models, including internal
thermal and magnetic field properties of the CME. OSPREI has three components:
(1) the Forecasting a CME’s Altered Trajectory (ForeCAT; Kay et al., 2015)
module calculates the CME’s deflections and rotations as it propagates through
the solar corona; (2) the Another Type of Ensemble Arrival Time Results
(ANTEATR; Kay & Gopalswamy, 2018) module calculates the heliospheric
propagation and arrival time of the CME at a given point in interplanetary
space; and (3) the ForeCAT In situ Data Observer (FIDO; Kay & Gopalswamy,
2017) models the CME flux rope’s magnetic field as a time series at the
location of interest. We remark that all CME deflections and rotations take
place within the ForeCAT (coronal) domain, while in the ANTEATER
(interplanetary) one CMEs are assumed to maintain their trajectory. For more
information on these modules and OSPREI’s capabilities, see Kay et al.
(2022a).

In this work, we set the outer boundary of the ForeCAT (coronal) domain to 20
R⊙. Additionally, we use the Physics-driven Approach to Realistic Axis
Deformation and Expansion version of ANTEATR (ANTEATR-PARADE; Kay & Nieves-
Chinchilla, 2021a), which includes the Elliptic-Cylindrical (EC) analytical
flux rope model of Nieves-Chinchilla et al. (2018) and is able to model
physics-driven changes in the size and shape of the CME’s central axis as well
as cross-section during propagation. We note that the sensitivity of ANTEATR-
PARADE—and, as a consequence, of OSPREI—to CME input parameters has been
explored in Kay & Nieves-Chinchilla (2021b). Here, we focus instead on
OSPREI’s sensitivity to the initial photospheric and coronal conditions, while
maintaining the CME input parameters fixed.

###  2.2 Magnetogram Sources

OSPREI’s FORECAT module requires realistic modeling of the global solar corona
to compute deflections and rotations of the CME flux rope as it propagates
through the corona. Since direct measurements of the coronal magnetic field
are not performed routinely, models are usually employed to extrapolate the
global configuration of the solar corona using photospheric field measurements
as boundary condition (e.g., Wiegelmann et al., 2017). Hence, the first source
of uncertainty when modeling CME propagation through the solar corona concerns
the chosen input photospheric field map. Several studies have tested the
influence of input magnetograms on MHD modeling results of the ambient solar
wind and its transients (e.g., Riley & Ben-Nun, 2021; Jin et al., 2022) but,
to our knowledge, similar studies have not been performed in the context of
analytical CME modeling. In this section, we present the four types of
magnetograms that we use in this work to test OSPREI’s sensitivity to user-
selected input conditions: HMI Synchronic, HMI Synoptic, GONG Zero-Point
Corrected, and GONG ADAPT #10. We note that, in previous applications, OSPREI
has only employed the HMI Synchronic or Synoptic magnetograms in its ForeCAT
module.

####  2.2.1 HMI Synoptic

The Helioseismic and Magnetic Imager (HMI; Scherrer et al., 2012) on board the
Solar Dynamics Observatory (SDO; Pesnell et al., 2012) provides space-based,
full-disk photospheric vector magnetic field measurements with a 12-minute
cadence. We use synoptic maps made from the imputed radial component of the
magnetic field over the entire solar disk. Synoptic maps are generated using
20 magnetograms captured close to the time of the central meridian passage
(CMP) for that longitude, so the effective temporal width of the HMI synoptic
map contribution is about three hours. In general, these individual
magnetograms are all captured within ${\sim}2^{\circ}$ of the CMP. After a
full Carrington rotation, a full synoptic map is created representing
photospheric magnetic fields at all Carrington longitudes. Because the
standard synoptic map is constructed from data observed within $2^{\circ}$ of
the central meridian, each longitude is both a different physical location and
the field measured at a different time. While central meridian observations
provide the best observational quality and radial magnetic field calculations,
synoptic maps by nature poorly represent fast-evolving features such as active
regions.

####  2.2.2 HMI Synchronic

HMI synchronic maps involve the same instruments, observational methods, and
image processing routines as HMI synoptic maps, but are designed to provide a
full-Sun snapshot that better represents the magnetic conditions on the Earth-
facing solar disk. Synchronic (daily) maps replace a $120^{\circ}$ longitude
range of data centered around the central meridian from the original synoptic
map with data observed at a one synchronized time (see, e.g., Hayashi et al.,
2015).

####  2.2.3 GONG Zero-point Corrected

The Global Oscillations Network Group (GONG; Harvey et al., 1996) is a program
operated by the National Solar Observatory, whose six telescopes provide
24-hour coverage, low-noise, near-real-time, precise synoptic maps of the
photospheric magnetic field (Hill, 2018). The reliability, high cadence, and
spatial coverage of GONG magnetograms make them appealing for operationally-
oriented space weather applications, including the WSA–Enlil model employed at
NOAA/SWPC (Pizzo et al., 2011; Steenburgh et al., 2014) and the EUHFORIA model
employed at the ESA Virtual Space Weather Modelling Centre (Poedts et al.,
2020). One factor impacting the quality of the magnetogram observations from
the GONG network stems from non-uniformities and small imperfections in each
observatory’s magnetogram modulator. These can introduce uncertainties of
several Gauss in the zero point of the magnetograms, and these uncertainties
can be amplified when data are merged from multiple GONG sites. Areas of quiet
Sun are most affected by these zero-point errors since the surface magnetism
is sometimes on the order of tens of Gauss (e.g., Bellot Rubio & Orozco
Suárez, 2019). Thus, the current method of zero-point correction involves
fitting a low-order 2D polynomial surface to quiet-Sun regions, with careful
attention to exclude any contribution from active regions. The resulting
fitted surface is used as the zero point. These zero-point corrected synoptic
magnetograms are important for extrapolations of the solar corona using models
since open magnetic field lines are often rooted in regions of weaker magnetic
field.

####  2.2.4 GONG ADAPT Realization #10

The Air Force Data Assimilative Photospheric Flux Transport (ADAPT; Arge et
al., 2010, 2011, 2013) model is a modified version of the Worden & Harvey
(2000) model and accounts for differential rotation, meridional flow,
supergranular diffusion, and random flux emergence, thus, creating more
accurate estimates of magnetic flux distribution on the solar surface. GONG
ADAPT magnetograms combine photospheric magnetic field observations from the
GONG telescope network with the ADAPT flux transport model, producing 12
possible realizations of the photospheric magnetic field. The ADAPT
realizations are synchronic maps. For this study, we randomly select the ADAPT
realization #10.

###  2.3 Coronal Extrapolations

As mentioned in the previous section, models are needed to extrapolate the
coronal magnetic field from photospheric maps. Hence, the second source of
uncertainty when modeling CME propagation through the solar corona is related
to the coronal model assumptions and choice of input parameters. In this work,
we employ the widely-used Potential Field Source Surface (PFSS; Wang &
Sheeley, 1992) model, which neglects electric currents in the corona and
represents the global field using a scalar potential. Magnetic forces dominate
the low corona (i.e., the plasma beta is low), but at larger heights the
weaker fields are dragged out with the solar wind, becoming essentially
radial. To simulate this effect, the PFSS model sets the scalar potential to
be constant on a certain surface—the source surface (Schatten et al., 1969).
Above the PFSS source surface, the coronal field lines are forced to be
radial, modeling the effect on the field of the outflowing solar wind.

Historically and in most applications to this day, the PFSS source surface has
been set to be at Rss = 2.5 R⊙ (Altschuler & Newkirk, 1969)—and this is also
valid for previous simulations ran with OSPREI. The location of the
heliospheric current sheet (HCS) resulting from setting the PFSS source
surface at 2.5 R⊙ is shown for each of the input magnetograms in Figs. 2–5.
Nevertheless, a number of studies have questioned the use of a single, fixed
value for Rss, suggesting e.g. that it should be lowered to better represent
the interplanetary magnetic field during solar minimum (Lee et al., 2011), to
reconstruct the areas of coronal holes (Asvestari et al., 2019), or to (at
least partially) resolve the open flux problem (Riley et al., 2019). Arden et
al. (2014) proposed the use of a “breathing” source surface, with its height
changing with the phase of the solar cycle. Furthermore, the spherical shape
of the PFSS source surface is even questioned by some studies (e.g., Schulz et
al., 1978; Schulz, 1997; Levine et al., 1982; Riley et al., 2006; Kruse et
al., 2020). These works and others have tested Rss values approximately within
the range 1.2–3.5 R⊙. In our study, we vary Rss in the range 1.5–3.0 R⊙ with
0.1 R⊙ increments, i.e., we associate each of the four magnetograms presented
in Sect. 2.2 with 16 different PFSS extrapolations, yielding a total of 64
combinations of photospheric and coronal conditions to test for each event.

##  3 Event Selection and Analysis

In this section, we first provide an overview of the four CME events observed
in situ by PSP that we use to investigate the effect of input magnetogram and
PFSS source surface on OSPREI results (Sect. 3.1). Then, we describe our
analysis of the input magnetograms used for each event (Sect. 3.2) and the
OSPREI input parameters that we set for each CME (Sect. 3.3).

###  3.1 Events

In this parameter study, we model four CME events, with source regions placed
at very different locations with respect to Earth’s viewpoint (see Fig. 1).
The first CME event is a streamer blowout on 21 June 2020 that erupted from
close to the central meridian. The second CME event is a northwestern limb
eruption on 9 June 2021 originating from an active region just off the visible
solar disk. The third CME event occurred on 7 November 2021 from an active
region close to the northeastern limb of the Sun. Finally, the fourth CME
event occurred on 26 January 2022 from an active region on the far side of the
Sun. For each event, we provide an overview of the available remote-sensing
observations as Supplementary Movies. These observations come from two
viewpoints, namely Earth and the Solar Terrestrial Relations Observatory Ahead
(STEREO-A; Kaiser et al., 2008) spacecraft, orbiting the Sun from a
heliocentric distance of ${\sim}$1 au—with variable longitudinal separation
with respect to Earth. Earth-based observations come from the Atmospheric
Imaging Assembly (AIA; Lemen et al., 2012) on board SDO, imaging the solar
disk, as well as the C2 and C3 cameras 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), imaging the solar
corona. From STEREO-A, we use data from the Extreme Ultraviolet Imager (EUVI)
solar disk telescope and the COR2 coronagraph, both part of the Sun-Earth
Connection Coronal and Heliospheric Investigation (SECCHI; Howard et al.,
2008) suite.

Figure 1: Positions of PSP, Earth, and STEREO-A at the CME onset time for (a)
Event 1, (b) Event 2, (c) Event 3, and (d) Event 4. The arrow in each panel
indicates the source longitude of the corresponding CME. The longitudes shown
are in Carrington coordinates. The plots are made with the Solar MAgnetic
Connection HAUS (Solar-MACH; Gieseler et al., 2023) tool.

####  3.1.1 Event 1

The first CME that we analyze in this work is a streamer blowout initiated on
21 June 2020 around 18:00 UT from close to the central meridian of the Earth-
facing Sun (Fig. 1(a)). For full details related to this event, please see
Palmerio et al. (2021a) and Pal et al. (2022). An overview of the remote-
sensing observations associated with this event is shown in Movie 1. Notably,
this type of eruption is what is known as a “stealth CME.” A CME is stealth if
no distinct low-coronal signatures (such as coronal dimmings, coronal waves,
filament eruptions, flares, and post-eruptive arcades; Hudson & Cliver, 2001)
can be found on the solar disk—a “CME from nowhere” (Robbrecht et al., 2009;
Palmerio et al., 2021b). Thus, the magnetic fields of stealth CMEs are
particularly hard to model and forecast since it is often difficult to
determine a well-defined source region and flux rope configuration. Since
stealth CMEs can still drive major geomagnetic disturbances at Earth (Nitta &
Mulligan, 2017; Nitta et al., 2021), it bears merit to analyze this particular
event so that it may lead to better techniques for modeling stealth CMEs in
the heliosphere.

####  3.1.2 Event 2

The second CME that we analyze in this work occurred on 9 June 2021 around
12:00 UT. See Movie 2 for an overview of remote-sensing observations of this
event. Starting around 12:00 UT, a large eruption was seen by SDO/AIA. The
source of the eruption was an active region off the northwestern limb of the
solar disk ($\sim$23.5∘ latitude and $\sim$77∘ longitude in Carrington
coordinates, see Fig. 1(b)). The eruption evacuated the corona, generating a
blast wave that propagated eastward from the limb across the solar disk. A
flux rope structure was also seen leaving the corona off the Sun’s limb behind
the initial bright front of the CME. We examine coronagraph images from the
SOHO/LASCO C2 and C3 telescopes and find a well-defined three-part structure
(i.e., consisting of a bright front, a cavity, and a core; Illing &
Hundhausen, 1985; Vourlidas et al., 2013) with a flux rope visible in the
darker region as the CME propagated out of the C3 field of view. This event
was selected because at the eastern and western limbs, “stitching” occurs in
synchronic magnetogram maps that may create different coronal field
reconstructions when compared to diachronic magnetogram maps, thereby altering
the OSPREI model outputs.

####  3.1.3 Event 3

The third CME that we analyze in this work occurred on 7 November 2021 around
13:00 UT. See Movie 3 for an overview of remote-sensing observations of this
event. The source of the eruption was an active region on the northeastern
limb of the Sun as seen from SDO (Fig. 1(c)), with a position in Carrington
coordinates of $\sim$15∘ latitude and $\sim$78∘ longitude. As seen in Movie 3,
the source region of the event was also seen by STEREO/SECCHI/EUVI-A. In
coronagraph imagery, the CME is visible in the C2 and C3 telescopes on board
SOHO’s LASCO as a faint white-light plume extending away from the left-hand
side of the occulting disk. The STEREO-A spacecraft was nearly in quadrature
($\sim$90∘ east of the Sun-Earth line) with Earth, and therefore in the COR2
coronagraph on board SECCHI the CME was observed as a faint full-halo
signature, better identified in base-difference images (e.g., Attrill & Wills-
Davey, 2010). This event was selected because it represents an almost base-
case scenario for OSPREI: An eruption on the Earth-facing disk is optimal for
magnetogram reconstruction of the source region, and multiple space-based
coronagraph and low-coronal observations make other CME parameters (tilt,
speed, chirality, etc.) easier to determine. Moreover, this event originated
from ${\sim}60^{\circ}$ east of the central meridian of the Earth-facing Sun,
i.e., in the vicinity of where the “stitching” occurs in synchronic
magnetogram maps.

####  3.1.4 Event 4

The fourth and final CME that we analyze in this work is an eruption that took
place on 26 January 2022 around 21:00 UT. See Movie 4 for an overview of
remote-sensing observations of this event. The eruption initiated from an
active region on the Sun’s far side. SDO imagery shows no evidence of the CME
using AIA, but the EUVI instrument on board STEREO-A did capture post-eruptive
arcades (e.g., Tripathi et al., 2004) from an active region approaching the
eastern limb of the visible disk. Based on magnetograms rendered at the time
of the eruption showing an active region in this general location, we
determine that the CME initiated from an active region at $\sim$ -17∘ latitude
and $\sim$ 30∘ longitude in Carrington coordinates (Fig. 1(d)).
STEREO/SECCHI/COR2-A observed a faint CME, while in SOHO/LASCO the eruption is
more visible. This event was chosen because it can be used to test the
differences in model outputs for a far-sided event, where no “recent”
magnetograph observations are available, while the limb measurements from
STEREO-A give us confidence on the location from where the CME launched.

###  3.2 Magnetogram Analysis

Figure 2: The four magnetograms that we use as input photospheric conditions
for Event 1. Top left: HMI Synchronic; Top right: HMI Synoptic; Bottom left:
GONG Zero-point corrected; Bottom right: GONG ADAPT Realization #10. The green
vertical line indicates the Carrington longitude of the central meridian as
seen from Earth. The dotted circle marks the approximate location of the CME
source region. The gray curve marks the location of the heliospheric current
sheet at 2.5 R⊙. All maps are saturated to ${\pm}100$ G, with red (blue)
indicating positive (negative) polarity.

Figure 3: The four magnetograms that we use as input photospheric conditions
for Event 2. Top left: HMI Synchronic; Top right: HMI Synoptic; Bottom left:
GONG Zero-point corrected; Bottom right: GONG ADAPT Realization #10. The green
vertical line indicates the Carrington longitude of the central meridian as
seen from Earth. The dotted circle marks the approximate location of the CME
source region. The gray curve marks the location of the heliospheric current
sheet at 2.5 R⊙. All maps are saturated to ${\pm}100$ G, with red (blue)
indicating positive (negative) polarity.

Figure 4: The four magnetograms that we use as input photospheric conditions
for Event 3. Top left: HMI Synchronic; Top right: HMI Synoptic; Bottom left:
GONG Zero-point corrected; Bottom right: GONG ADAPT Realization #10. The green
vertical line indicates the Carrington longitude of the central meridian as
seen from Earth. The dotted circle marks the approximate location of the CME
source region. The gray curve marks the location of the heliospheric current
sheet at 2.5 R⊙. All maps are saturated to ${\pm}100$ G, with red (blue)
indicating positive (negative) polarity.

Figure 5: The four magnetograms that we use as input photospheric conditions
for Event 4. Top left: HMI Synchronic; Top right: HMI Synoptic; Bottom left:
GONG Zero-point corrected; Bottom right: GONG ADAPT Realization #10. The green
vertical line indicates the Carrington longitude of the central meridian as
seen from Earth. The dotted circle marks the approximate location of the CME
source region. The gray curve marks the location of the heliospheric current
sheet at 2.5 R⊙. All maps are saturated to ${\pm}100$ G, with red (blue)
indicating positive (negative) polarity.

In this section, we analyze the input magnetograms for each event and comment
on their differences (see Sect. 2.2 for a description of the different
datasets). Figs. 2, 3, 4, and 5 show the four magnetograms that associated
with Events 1 to 4, respectively. Across the four events, we notice that two
pairs of magnetograms feature magnetic features in their images that are more
consistent with each other: HMI Synchronic and GONG Adapt Realization #10 is
one pair, and HMI Synoptic and GONG Zero-point corrected is another pair. This
makes sense as these are pairs of synchronic and synoptic magnetograms,
respectively. The two GONG magnetograms also have a lower resolution than the
HMI magnetograms, with magnetic elements appearing larger and less defined. In
the HMI synchronic magnetograms, it is possible to notice the two lines that
mark where “stitching” occurs between the synchronic magnetogram snapshots and
the synoptic data. The GONG Adapt Realization does not have a similar
stitching line, since the photospheric field that does not face Earth is
modeled via flux transport algorithms.

We also note differences in synchronic vs. synoptic magnetograms when finding
active regions at the locations of the CME source regions. In Figs. 2–5 we
include a dotted circle as an indicator of the location from where each CME
launched. For Event 1, we use the Carrington coordinates provided in Palmerio
et al. (2021a), since the CME was stealthy and was not associated with low-
coronal signatures. For Events 2–4, we use remote-sensing extreme-ultraviolet
(EUV) measurements from SDO and/or STEREO-A to locate the source active
regions.

In Events 2 and 4, the identified source region matches the location of an
active region only in the synoptic magnetograms. Both synchronic magnetograms
do not show a source magnetic region in the vicinity of the CME’s real source
as determined from EUV images. In synchronic magnetograms, the area from the
left-hand border of the magnetogram (i.e., Carrington longitude of 0∘) up to
the “stitching” line includes magnetic field data from the previous Carrington
rotation. In other words, synchronic magnetograms cannot use “future” data,
since synoptic maps are made available once per Carrington rotation, while
synchronic magnetograms are updated daily. This affects magnetic elements that
may be on the “left side” of the stitching area, in particular new flux
emergence. Notably, the “stitching” area does not cover the entire Earth-
facing solar disk, but only ${\pm}60^{\circ}$ from the central meridian, hence
active regions close to the limb of the Earth-facing solar disk may be
misrepresented in synchronic magnetic maps.

###  3.3 OSPREI Input Parameters

Once the events to be investigated in this study and their source regions have
been identified, the next step is to set up the OSPREI input parameters that
describe each CME as well as the background solar wind through which they
propagate. Our aim is to use the same set of input parameters for each set of
64 ensemble model runs (combination of four magnetograms and 16 PFSS source
surface heights, see Sect. 2) and evaluate whether there are any significant
differences and/or emerging trends. While some parameters (such as source
region coordinates) are taken directly from remote-sensing and in-situ
observations, some others (such as solar wind drag coefficient) are inherently
less constrained by data. Since our goal in this work is not to perform
forecasts, but rather to explore the photospheric and coronal input parameter
space, we attempt to fine-tune these less-constrained parameters in order to
match the CME arrival time at PSP. When performing the fine-tuning, we use as
reference what we call the “baseline” run, i.e. the run that uses HMI
synchonic magnetograms and a PFSS source surface height of 2.5 R⊙—which is
considered to be the “standard” setup for OSPREI applications. Table 1,
similar to Table 1 in Kay et al. (2022a), shows the free parameters for all
four events that we adjust before running OSPREI. The set of input parameters
can be divided into CME and ambient medium ones, and are illustrated in more
detail below together with a description of how each quantity is
selected—using a combination of real measurements and best-guess
approximations.

OSPREI Input | Event 1 | Event 2 | Event 3 | Event 4 | Source
---|---|---|---|---|---
|  |  |  |  |
CME parameters |  |  |  |  |
Date | 21 June 2020 | 9 June 2021 | 7 November 2021 | 26 January 2022 |
Start time ($\mathrm{t_{0}}$) | 18:00 UT | 12:00 UT | 13:00 UT | 21:00 UT | EUV
Initial Carrington latitude ($\theta$) | $-18^{\circ}$ | 26∘ | 15∘ | $-17^{\circ}$ | Magnetogram
Initial Carrington longitude ($\phi$) | 340∘ | 77∘ | 78∘ | 30∘ | Magnetogram
Initial tilt ($\psi$) | 15∘ | 140∘ | 110∘ | 60∘ | Magnetogram
Flux rope handedness (H) | + | – | – | + | EUV/HHR
Initial nose height ($\mathrm{R_{0}}$) | 1.5 R⊙ | 1.1 R⊙ | 1.1 R⊙ | 1.1 R⊙ | EUV
Initial slow-rise velocity ($\mathrm{V_{R0}}$) | 30 km s-1 | 100 km s-1 | 30 km s-1 | 50 km s-1 | Estimated
Start of rapid acceleration ($\mathrm{R_{1}}$) | 4 R⊙ | 1.3 R⊙ | 4.8 R⊙ | 1.1 R⊙ | Estimated
Height of max coronal velocity ($\mathrm{R_{2}}$) | 20 R⊙ | 5 R⊙ | 8 R⊙ | 3 R⊙ | Estimated
Max coronal velocity ($\mathrm{V_{R2}}$) | 350 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | 600 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | 650 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | 500 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | GCS
Angular width (AW) | 30∘ | 35∘ | 30∘ | 45∘ | GCS
Perpendicular AW ($\mathrm{AW_{\perp}}$) | 10∘ | 15∘ | 15∘ | 20∘ | GCS
Flux rope initial magnetic field (B0) | 1200 nT | 4000 nT | 3200 nT | 2500 nT | Estimated
Flux rope initial temperature (T0) |  $2.11\times 10^{6}$ K |  $4.44\times 10^{6}$ K |  $2.75\times 10^{6}$ K |  $2.31\times 10^{6}$ K | Estimated
CME mass ($\mathrm{M_{CME}}$) | 2 $\mathrm{\times\leavevmode\nobreak\ 10^{15}\leavevmode\nobreak\ g}$ | 1 $\mathrm{\times\leavevmode\nobreak\ 10^{16}\leavevmode\nobreak\ g}$ | 7 $\mathrm{\times\leavevmode\nobreak\ 10^{15}\leavevmode\nobreak\ g}$ | 6 $\mathrm{\times\leavevmode\nobreak\ 10^{15}\leavevmode\nobreak\ g}$ | Estimated
Coronal axis aspect ratio ($\mathrm{\delta_{Ax}}$) | 0.6 | 0.6 | 0.6 | 0.7 | Fine-tuned
Coronal cross-section aspect ratio ($\mathrm{\delta_{CS}}$) | 1 | 1 | 1 | 1 | Default
Adiabatic index ($\mathrm{\gamma}$) | 1.66 | 1.33 | 1.5 | 1.66 | Fine-tuned
Interplanetary expansion factor ($\mathrm{f_{exp}}$) | 0.50 | 0.25 | 0.50 | 0.85 | Fine-tuned
|  |  |  |  |
Ambient medium parameters |  |  |  |  |
Drag coefficient (CD) | 0.9 | 0.8 | 1 | 1 | Fine-tuned
Solar wind speed (VSW) | 300 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | 350 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | 300 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | 350 $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | PSP data
Solar wind density (NSW) | 25 $\mathrm{cm^{-3}}$ | 25 $\mathrm{cm^{-3}}$ | 55 $\mathrm{cm^{-3}}$ | 20 $\mathrm{cm^{-3}}$ | PSP data
Solar wind magnetic field (BSW) | 10 nT | 5 nT | 20 nT | 5 nT | PSP data
Solar wind temperature (TSW) |  $2.5\times 10^{4}$ K |  $3.0\times 10^{4}$ K |  $7.0\times 10^{4}$ K |  $5.0\times 10^{4}$ K | PSP data
Initial s/c latitude (Carrington) | 2.0∘ | 3.4∘ | 3.8∘ | 3.8∘ | PSP ephemeris
Initial s/c longitude (Carrington) | 327.1∘ | 74.0∘ | 75.0∘ | 12.6∘ | PSP ephemeris
Initial s/c heliocentric distance | 96.8 R⊙ | 163.9 R⊙ | 96.6 R⊙ | 147.3 R⊙ | PSP ephemeris
Table 1: Full list of OSPREI free Parameters for the four CME events. For a
more robust explanation of each parameter, please see Kay et al. (2022a).
Latitudes and longitudes are expressed in Carrington coordinates. The “Source”
column indicates where the value/information was sourced from.

From EUV observations, we identify the source region and establish the CME
start time ($\mathrm{t_{0}}$), by evaluating the first signs of any associated
motion. Using the identified source and magnetogram data, we determine the CME
initial latitude and longitude ($\theta$ and $\phi$ respectively, i.e., the
Carrington coordinates of the corresponding source region), as well as the
tilt ($\psi$). The tilt is the angle that describes the direction of the flux
rope axis and is defined to move counterclockwise from the solar west
direction. We initially determine the tilt from the orientation of the local
polarity inversion line (e.g., Marubashi et al., 2015), and then we resolve
the $180^{\circ}$ ambiguity by means of the flux rope handedness (H, also
known as chirality), assuming that the MFR axial field points from the
positive magnetic field polarity to the negative one. The flux rope handedness
of each CME is determined from EUV observations (e.g., Palmerio et al., 2017),
where possible (Event 3), and with the hemispheric helicity rule (HHR; Pevtsov
et al., 2014), also known as the Bothmer–Schwenn scheme (from Bothmer &
Schwenn, 1998), otherwise (Events 1, 2, and 4). According to the HHR, which is
of statistical nature, CMEs from the northern (southern) hemisphere tend to be
characterized by a left- (right-) handed chirality. We note that for Event 3,
the handedness determined from remote-sensing observations is in agreement
with the HHR.

Another OSPREI parameter to define is the height of the CME nose at the start
of the run, $\mathrm{R_{0}}$. Event 1 is a streamer-blowout stealth CME that
was observed in STEREO/EUVI-A off-limb images to initiate high up in the
corona, at around 1.5 R⊙. Events 2, 3, and 4 were all active-region eruptions
with clear on-disk signatures, indicating that they originated much lower in
the corona. For these events, we use the OSPREI default value of 1.1 R⊙, which
allows for inclusion of low-coronal effects but is not so low as to be
sensitive to ringing effects that the PFSS model occasionally suffers near
high-intensity active regions. From the height of $\mathrm{R_{0}}$, CMEs in
OSPREI initially move at their slow-rise velocity ($\mathrm{V_{R0}}$) until
their reach a point ($\mathrm{R_{1}}$) from which they start their
acceleration phase. During the acceleration phase, the CME speed increases
linearly from $\mathrm{V_{R0}}$ up to $\mathrm{V_{R2}}$, i.e. the maximum
coronal velocity, which is attained at a height $\mathrm{R_{2}}$. After
$\mathrm{R_{2}}$, it is assumed that CMEs continue their coronal and
interplanetary propagation at a constant speed until the outer boundary of the
coronal domain (set in this work at 20 R⊙), when OSPREI begins to simulate
drag and other interplanetary processes that affect the CME speed. These steps
are meant to emulate the “classic” kinematic evolution of CMEs, consisting of
the an initiation phase, an impulsive acceleration phase, and a propagation
phase (e.g., Zhang et al., 2001). We select values for $\mathrm{V_{R0}}$,
$\mathrm{R_{1}}$, and $\mathrm{R_{2}}$ via rough estimates of the CME
kinematics as observed in (off-limb) EUV and coronagraph imagery.

The CME maximum coronal speed ($\mathrm{V_{R2}}$), on the other hand, together
with both angular-width parameters (AW and AW⟂), are determined using the
Graduated Cylindrical Shell (GCS; Thernisien, 2011) model applied to nearly-
simultaneous coronagraph images from SOHO and STEREO-A. The GCS geometry is
meant to represent the flux rope morphology of CMEs, resulting in a toroidal
body and two legs curving toward the Sun, reminiscent of a croissant. It
follows that this structure has an elliptical projection onto the plane
perpendicular to the radial direction at the CME nose, and the angular-width
parameters are represented by the semi-major (AW) and semi-minor (AW⟂) axes of
such an ellipse, corresponding to the CME face-on and edge-on angular widths,
respectively. The maximum coronal speed $\mathrm{V_{R2}}$ is simply derived
from the positions of the CME apex given by two GCS reconstructions separated
by 1 hour.

The CME initial magnetic field (B0) and temperature (T0) are loosely estimated
based on previous OSPREI work, under the assumption that these input
quantities tend to vary with the overall scale of the CME (e.g., size and
speed), with more extreme events being generally associated with higher
values. The CME mass ($\mathrm{M_{CME}}$) is estimated “by eye” based on the
brightness of each event in coronagraph imagery, using a lower-bound value of
$2\times 10^{15}$ g for Event 1, i.e. the faintest in our set (using the
estimate of Palmerio et al., 2021a) and an upper-bound value of $10^{16}$ g
for Event 2, i.e. the brightest in our set. In fact, Gopalswamy et al. (2005)
found in a study of all CMEs observed over almost a full month that the
distribution of masses tends to display a double peak at ${\sim}10^{15}$ g and
${\sim}10^{16}$ g, with extremely narrow (${\sim}10^{\circ}$ width) CMEs
featuring values of the order of $10^{14}$ g and extreme space weather events
(such as those associated with the 2003 Halloween storm) surpassing $10^{17}$
g. We note that precise determination of the last three input parameters (B0,
T0, and $\mathrm{M_{CME}}$) in the context of space weather forecasting is a
critical subject of ongoing studies (e.g., Vourlidas et al., 2019). For
example, existing works have attempted to estimate the CME magnetic field
strength from radio measurements (e.g., Carley et al., 2017), or the CME mass
from white-light coronagraph images (e.g., Colaninno & Vourlidas, 2009; Temmer
et al., 2021) and EUV dimmings (e.g., López et al., 2019).

The geometry of the MFR embedded in the modeled CMEs is described by the
coronal axis aspect ratio ($\mathrm{\delta_{Ax}}$) and cross-section aspect
ratio ($\mathrm{\delta_{CS}}$). As mentioned in Sect. 2.1, OSPREI uses the EC
analytical flux rope model of Nieves-Chinchilla et al. (2018), and the
implemented MFR geometry consists of a toroidal axis defined by an ellipse
with semi-major and semi-minor lengths L⟂ and Lr, and an elliptical cross-
section with semi-major and semi-minor lengths r⟂ and rr (more information can
be found in Kay & Nieves-Chinchilla, 2021a). The ratios mentioned above
correspond to $\mathrm{\delta_{Ax}}$ = Lr/L⟂ and $\mathrm{\delta_{CS}}$ =
rr/r⟂. In this work, we keep all inputs for $\mathrm{\delta_{CS}}$ to their
OSPREI default value of 1, corresponding to a circular cross-section of the
MFR, while for $\mathrm{\delta_{Ax}}$ we use values in the range 0.6–0.7,
which emulate the “classic” geometry of flux ropes that assumes an axis that
is elongated in one direction (e.g., Krall & St. Cyr, 2006).

The last two CME parameters, i.e. the adiabatic index ($\mathrm{\gamma}$) and
the interplanetary expansion factor ($\mathrm{f_{exp}}$), control the CME
propagation due to internal forces. The adiabatic index allows for the CME
thermal expansion to vary between isothermal ($\mathrm{\gamma}$ = 1) and
adiabatic ($\mathrm{\gamma}$ = 1.67), while the expansion factor describes the
CME initial velocity decomposition, or how the propagation speed translates
into expansion speed. For $\mathrm{f_{exp}}$ = 0, the CME experiences fully
self-similar behavior; for $\mathrm{f_{exp}}$ = 1, the CME undergoes fully
convective expansion. $\mathrm{f_{exp}}$ only sets the expansion speeds at the
beginning of the interplanetary portion, beyond this first step the expansion
evolves according to the interplanetary (drag, magnetic, and thermal) forces.
We set the values for $\mathrm{\gamma}$ and $\mathrm{f_{exp}}$ to explore
different propagation scenarios across the four events under study, with minor
adjustments to ultimately yield better CME arrival times for the baseline run.

Finally, we describe the ambient medium parameters used in OSPREI. The
(dimensionless) drag coefficient ($\mathrm{C_{D}}$) quantifies the external
drag exerted on the CME by the background solar wind (Cargill, 2004). We
initially use the default OSPREI value for $\mathrm{C_{D}}$ of 1, and we
slightly vary it in order to obtain a better CME arrival time for the baseline
run, where necessary. This results in $\mathrm{C_{D}}$ values of 0.9 and 0.8
for Events 1 and 2, respectively. We find the ambient velocity
($\mathrm{V_{SW}}$), density ($\mathrm{N_{SW}}$), magnetic field
($\mathrm{B_{SW}}$), and temperature ($\mathrm{T_{SW}}$) by examining the PSP
solar wind data for $\sim$1 day before the CME impact and by taking an average
value for each parameter. The only exception is the background speed for Event
3, which had no available data, and for which we use a slow solar wind speed
of 300 km s-1 based on the results of McGregor et al. (2011), who found that
the slow wind close to solar minimum peaks around this value at 0.3–0.4 au
(PSP was at ${\sim}$0.45 au during Event 3) and is generally slower than the
ambient speed at 1 au (which peaks at 350 km s-1). Table 1 also shows the
initial PSP latitude, longitude, and heliocentric distance, i.e. the position
of PSP at the CME eruption time. In addition to these values, we load onto
OSPREI the PSP ephemeris throughout the simulated period, meaning that the
synthetic trajectory through each CME encounter corresponds to the actual
time-dependent PSP orbit.

##  4 Results

After the ensemble OSPREI runs have been performed for each event, we compare
ForeCAT (coronal deflections and rotations until 20 R⊙) and FIDO (synthetic
in-situ profiles along the PSP trajectory) results to visualize the model’s
sensitivity to the different input magnetograms and PFSS source surface
heights. We compare the FIDO profiles with PSP data, specifically magnetic
field measurements from the fluxgate magnetometer part of the FIELDS (Bale et
al., 2016) investigation and plasma measurements from the Solar Probe Cup
(SPC; Case et al., 2020) part of the Solar Wind Electrons Alphas and Protons
(SWEAP; Kasper et al., 2016) suite. Summary plots for each CME are shown in
Figs. 6, 7, 8, and 9 for Events 1, 2, 3, and 4, respectively. In these
figures, each input magnetogram is represented by one color, with the thicker
line showcasing the corresponding $\mathrm{R_{ss}}=2.5$ R⊙ case and the
thinner lines representing results at all other PFSS source surface heights.

###  4.1 Event 1

In Event 1 (front-sided CME as seen from Earth, Fig. 6), there are relatively
small differences between the four magnetograms for fixed
$\mathrm{R_{ss}}=2.5$ R⊙ in the ForeCAT results. Different PFSS source surface
heights result in a wider spread in both CME deflections and rotations.
Latitude and longitude are more severely affected by the PFSS source surface
height: The latitudes at 20 R⊙ span a range of ${\sim}25^{\circ}$, while the
longitudes span a range of ${\sim}20^{\circ}$. The final tilts spread over a
smaller range (${\sim}12^{\circ}$) that is due to a few outliers, since the
majority of them are clustered around the corresponding $\mathrm{R_{ss}}=2.5$
R⊙ profiles.

Examining FIDO results, we note that all combinations of magnetograms and PFSS
source surface heights result in a more or less accurate representation of the
CME MFR, especially in the BT (rotating from negative to positive) and BN
(positive throughout the rope) components. The BR profiles feature larger
differences, with approximately half of the runs capturing its negative trend.
This is most likely a direct result of the different final latitudes in
ForeCAT: The runs that ended with a positive (negative) latitude in the corona
later crossed the CME below (above) its central axis in situ (we remark that
all runs featured a tilt at 20 R⊙ in the range 4–$16^{\circ}$, indicating a
low-inclination MFR with its axis nearly parallel to the solar equator). Most
notably, several runs do not result in an impact at PSP—specifically, all the
runs with $\mathrm{R_{ss}}=1.5$ R⊙, the HMI Synchronic and GONG ADAPT runs
with $\mathrm{R_{ss}}=1.6$ R⊙, and the GONG ADAPT runs with $\mathrm{R_{ss}}$
in the range 2.7–3.0 R⊙. Of these, the runs characterized by the smaller
source surface heights were those featuring the smallest latitudinal
deflections in ForeCAT, suggesting that the CME remained too south of PSP to
produce an impact. The GONG ADAPT runs with larger source surface heights, on
the other hand, were the ones featuring the most prominent longitudinal
deflections in the solar corona, up to ${>}15^{\circ}$ away from the CME
source region (we remark that the CME was set to have a half-angular width of
$30^{\circ}$ along its major axis, see Table 1). Finally, we do not note
significant differences in the modeled plasma parameters, i.e. solar wind
speed, density, and temperature.

Figure 6: ForeCAT and FIDO results for Event 1 plotted in panels (a) and (b),
respectively. The FIDO results are shown against PSP magnetic field and plasma
data. The thicker contours represent the model output using a PFSS with
$\mathrm{R_{ss}}=2.5$ R⊙. The thinner contours represent all other PFSS source
surface heights. The four different colors correspond to different input
magnetograms. If a given combination of input magnetogram and PFSS source
surface height resulted in a “miss” according to OSPREI, it was not included
in the FIDO plot (see text for details).

###  4.2 Event 2

In Event 2 (west-limb CME as seen from Earth, Fig. 7), there are minimal
variations in the ForeCAT results at 20 R⊙. The CME is modeled to experience
virtually no deflections regardless of the choice of input magnetogram and
PFSS source surface height, and the final latitudes and longitudes spread over
${<}2^{\circ}$ across all the 64 runs. The tilt values span a range of
${\sim}6^{\circ}$—due to three outliers, since the majority of them spread
over ${\sim}3^{\circ}$ only—and all indicate an MFR inclined by
${\sim}40^{\circ}$ with respect to the solar equator.

Regarding FIDO results, there are no major differences in the predicted MFR
configuration, even with the varying PFSS source surface height, and all 64
ensemble runs result in an impact at PSP. Interestingly, none of the magnetic
field components is modeled by OSPREI particularly well in the case of this
event, and the duration of the flux rope is also overestimated by almost 24
hours. The positive BR profile is PSP data is missed in all the runs, which
predicts a predominantly-negative radial field. Results are slightly better
for BT, where the negative sign is correctly captured, and for BN, in which
however the duration of the negative field is considerably underestimated.
Nevertheless, all the runs produce very similar results for each of the
magnetic field components. We also do not note significant differences in the
modeled plasma parameters, i.e. solar wind speed, density, and temperature.
Regardless of the accuracy of the model in predicting the CME magnetic
configuration, in the case of this event the MFR profiles appear to be
basically unaffected by the input photospheric and coronal magnetic fields.

Figure 7: ForeCAT and FIDO results for Event 2 plotted in panels (a) and (b),
respectively. The FIDO results are shown against PSP magnetic field and plasma
data. The thicker contours represent the model output using a PFSS with
$\mathrm{R_{ss}}=2.5$ R⊙. The thinner contours represent all other PFSS source
surface heights. The four different colors correspond to different input
magnetograms.

###  4.3 Event 3

In Event 3 (east-limb CME as seen from Earth, Fig. 8), we note a high
sensitivity to the input magnetogram and PFSS source surface height. In
ForeCAT, in the range 1.1–5 R⊙, the CME undergoes very different coronal
deflections depending on the input magnetogram and PFSS source surface height.
While the CME is seen to deflect southward in all runs, the latitudes at 20 R⊙
are spread over ${\sim}40^{\circ}$. Considering the $\mathrm{R_{ss}}=2.5$ R⊙
cases, we note that the GONG ADAPT run reaches a final latitude of
approximately $-20^{\circ}$, while the three remaining magnetograms result in
a ${\sim}0^{\circ}$ latitude. Significant differences are also seen in the
longitudes, with all the synoptic runs (regardless of source surface height)
experiencing minimal deflections, all the HMI Synchronic runs deflecting by
${\sim}20^{\circ}$ eastward, and the GONG ADAPT runs deflecting initially
eastward in all cases, but then resulting in either eastward or westward
deflections at 20 R⊙ depending on the PFSS source surface heigh. As for the
latitudes, the final longitudes are overall spread over ${\sim}40^{\circ}$.
Furthermore, with GONG ADAPT at $\mathrm{R_{ss}}=2.5$ R⊙, the CME rotates by
about ${\sim}30^{\circ}$, while the other magnetograms induce minimal tilt
changes—although there appears to be a large sensitivity to the PFSS source
surface height in the HMI Synchronic case. The final tilts at 20 R⊙ are spread
over ${\sim}60^{\circ}$ across all runs. Overall, ForeCAT is very sensitive to
both input magnetogram and PFSS surface height for this event, with a large
distribution of final latitudes, longitudes, and tilts.

Examining FIDO results (where all 64 runs produce an impact at PSP), it is
clear that the differences persist, as it is possible to observe clear changes
in the magnetic configuration of the modeled MFR. Starting with the total
field, Btot, we note that there is a wide range of maximum field strengths,
from 20 nT to almost 60 nT based on the input magnetogram and PFSS source
surface height being used. BR shows a similar spread of field strengths. The
BT profile is generally well reproduced by most runs, although the magnitude
of the negative dip is better captured by the synchronic magnetograms and by a
only a few of the remaining cases. The negative-to-positive trend of BN is
missed by most runs, although the profile is generally better captured in a
few HMI Synchronic and GONG ADAPT cases—these are the runs that were
associated with the largest counterclockwise deflections in ForeCAT. In terms
of flux rope duration, all combinations tend to produce overestimates by at
least six hours, with a subset of runs extending up to ${\sim}$24 hours beyond
the observed ejecta trailing edge. Unfortunately, there are no PSP solar wind
speed data available for this event, but we note that the modeled speed
profiles again depend on what magnetogram and PFSS source surface height were
input into OSPREI. Additionally, for some source surface heights, the velocity
exhibits a “stair-stepping” behavior towards the end of the CME, and some
combinations produce sharp velocity increases or decreases at the end of the
flux rope. We do not note significant differences in the modeled solar wind
density and temperature between magnetograms.

Figure 8: ForeCAT and FIDO results for Event 3 plotted in panels (a) and (b),
respectively. The FIDO results are shown against PSP magnetic field and plasma
data. The thicker contours represent the model output using a PFSS with
$\mathrm{R_{ss}}=2.5$ R⊙. The thinner contours represent all other PFSS source
surface heights. The four different colors correspond to different input
magnetograms.

###  4.4 Event 4

In Event 4 (far-sided CME as seen from Earth, Fig. 9), looking at ForeCAT
model results, there are more or less significant differences between the
input magnetograms with no particular pattern. While results at 20 R⊙ appear
rather sensitive to the input photospheric magnetic field—with final spreads
in latitude of ${\sim}25^{\circ}$, in longitude of ${\sim}15^{\circ}$, and in
tilt of ${\sim}30^{\circ}$—there are generally fewer differences within a
single magnetogram with respect to PFSS source surface height adjustments. The
only exception is GONG ADAPT, which shows larger deviations from the
“traditional” $\mathrm{R_{ss}}=2.5$ R⊙ case at other heights.

Examining FIDO (where all 64 runs produce an impact at PSP), the resulting
predicted MFR structure agrees relatively well with the PSP measurements for
all runs, with the largest differences observed in modeled Btot for the HMI
Synchronic runs, which underestimate the total field strength of the CME by
${\sim}10$ nT. Most combinations include an anomalous rotation in the magnetic
field components toward the end of the flux rope, although a few PFSS source
surface heights paired with the HMI Synchronic magnetogram do not display this
characteristic. Generally, all runs display a similar magnetic configuration
of the modeled flux rope, despite the more or less large differences in the
ForeCAT outputs. The MFR duration is overestimated by ${\sim}24$ hours in all
runs. Finally, we do not note significant differences in the modeled plasma
parameters, i.e. solar wind speed, density, and temperature.

Figure 9: ForeCAT and FIDO results for Event 4 plotted in panels (a) and (b),
respectively. The FIDO results are shown against PSP magnetic field and plasma
data. The thicker contours represent the model output using a PFSS with
$\mathrm{R_{ss}}=2.5$ R⊙. The thinner contours represent all other PFSS source
surface heights. The four different colors correspond to different input
magnetograms.

##  5 Discussion

The results presented in Sect. 4 show that there are moderate dependencies of
the OSPREI model to the input photospheric and coronal conditions. OSPREI has
been used and tested mostly in the case of Earth-impacting events, hence the
combination of HMI Synchronic magnetogram and a PFSS source surface height of
2.5 R⊙ (referred to as the baseline run in this work) has been the default
setup for describing the photospheric and coronal magnetic field properties
thus far. However, as shown in this investigation, results may vary more or
less dramatically depending on the choice of input conditions. Before
discussing trends and results for individual events and/or quantities, we
remark that the approach we took in this work is that of a “semi-hindcast”:
While CME input parameters that are well-constrained by observations (such as
the source region location or the CME speed and size in the corona) were
derived directly from remote-sensing or in-situ data, other less-constrained
parameters (such as the drag coefficient or the adiabatic index) were fine-
tuned to match the MFR arrival time in the baseline run. We then ran, for each
of the four events under study, 64 OSPREI simulations (16 different PFSS
source surfaces for each of the four magnetograms) using a fixed set of CME
and background solar wind input parameters. This allowed us to focus on
ensemble variations due uniquely to the choices of input magnetogram and PFSS
source surface height, rather than on the intrinsic success of a given
forecast.

The four events investigated in this study were selected to originate from
different locations on the Sun with respect to Earth’s viewpoint—roughly,
front side, west limb, east limb, and far side—and to range from the deep
Solar Cycle 24/25 minimum through the ascending phase of Solar Cycle 25.
Albeit far from being a comprehensive, statistical study, the results shown
here can be contextualized with respect to the CME source region location and
the representative global magnetic field configurations at different phases of
the solar cycle. For example, the case studied here that showed the greatest
dependency on the initial conditions is Event 1, for which 10 out of the 64
ensemble runs resulted in the MFR completely missing PSP. This may seem
surprising given that this CME was front-sided and originated from close to
the central meridian as seen from Earth (thus featuring the most up-to-date
magnetograms); however, this event took place during the deep solar minimum,
and its source region had no active regions in its vicinity (see Fig. 2). As a
result, there are no strong magnetic forces that are able to “channel” the CME
as it propagates through the solar corona (e.g., Shen et al., 2011). In such
cases, the polar field strengths and flux distributions—which dictate the
overall amount of closed and open magnetic flux and can significantly impact
the size and shape of the helmet streamer belt—are likely to be the dominant
factor for determining the large-scale gradients in magnetic pressure
responsible for CME deflections (see, e.g., Riley et al., 2014; Linker et al.,
2017; Li et al., 2021, for a comparison of different magnetogram sources).
This is likely reflected in Event 1’s estimated ForeCAT deflections being
distributed over ${\sim}25^{\circ}$ in latitude and ${\sim}20^{\circ}$ in
longitude.

Another case that displayed relatively major differences is Event 3, which
originated from close to the eastern limb as seen from Earth and took place
${\sim}1.5$ years after Event 1—as Solar Cycle 25 was ascending, which is also
clear from the presence of multiple active regions on the photosphere (see
Fig. 4). This CME also displayed a significant spread in ForeCAT deflections
(even more dramatically than Event 1), but the most striking result was
related to the MFR tilt angle, which showed differences up to
${\sim}60^{\circ}$ at 20 R⊙ across the ensemble. As a result, the runs that
feature a large counterclockwise rotation of the MFR are those that better
captured the large-scale magnetic configuration of the CME observed by PSP in
FIDO—due to the variety of ForeCAT rotations observed in this case, Event 3 is
the only event in our sample for which a fundamentally different magnetic
configuration of the CME would be predicted depending on the photospheric and
coronal input conditions. Events 2 (western limb as seen from Earth) and 4
(far side as seen from Earth), on the other hand, were characterized by the
least variance in ForeCAT results and by basically consistent FIDO predictions
across all the ensemble runs. Interestingly, for both these events the CME
source active region is entirely “missing” in two of the four magnetograms
(see Figs. 3 and 5)—i.e., HMI Synchronic and GONG ADAPT, which are released in
real time and thus contain no information on “future” Carrington longitudes.
Given the high level of agreement across the different OSPREI results, this
suggests that the magnetic environment surrounding a CME’s source region may
play a more important role than the source region itself in terms of coronal
deflections and rotations. In fact, for Event 3 the CME source region itself
is present in all the photospheric maps, but the surrounding environment is
fundamentally different across different magnetogram realizations.

A visualization of the differences in ForeCAT results across the different
runs for each of the events studied here is shown in Figure 10, which displays
the spreads in latitude, longitude, and tilt at 20 R⊙ with respect to the
baseline run—HMI Synchronic with R$\mathrm{{}_{ss}}=2.5$ R⊙. It is clear from
Figure 10 that the influence of the input magnetogram and PFSS source surface
height on coronal deflections and rotations varies from case to case, with
Event 3 showing significant spreads and Event 2 featuring virtually no
differences with respect to the baseline run. In the case of Event 1, the
distributions in latitude and longitude appear organized by the value of Rss,
with lower (higher) source surface heights leading to the CME being directed
more southward (northward) and westward (eastward). Given that this event took
place during deep solar minimum conditions, in the absence of strong active
region fields the location and height of the HCS cusp are likely to play a
major role in channeling a CME after its eruption. In Events 3 and 4, on the
other hand, the spreads appear generally less organized, possibly due to the
much more complex configuration of the photospheric magnetic field during the
ascending phase of the solar cycle. Overall, individual patterns in
deflections and rotations may emerge based on the balance of local magnetic
gradients due to active region fields and global magnetic gradients pointing
to the HCS. However, the lower the Rss value, the less time a CME spends under
the influence of such gradients, possibly leading to reduced deflections and
rotations with respect to higher Rss trajectories.

Figure 10: ForeCAT spreads at 20 R⊙ in (a) latitude, (b) longitude, and (c)
tilt. Events are listed on the x-axis with four columns for each event
corresponding to the four magnetograms used, from left to right: HMI
Synchronic, HMI Synoptic, GONG Zero, and GONG ADAPT. The columns are color-
coded according to the PFSS source surface height and the deflection/rotation
values are normalized according to the OSPREI “standard” setup of HMI
Synchronic with Rss=2.5 R⊙ for each event (represented as a black scatter
point).

Regarding FIDO results, it is clear that the input photospheric and coronal
conditions have a much more substantial impact on the modeled magnetic field
parameters rather than the plasma quantities—in particular, proton density and
temperature appear unchanged across the ensembles, while minor differences can
be observed for the solar wind speed (with Event 3 only displaying a larger
spread of results). This is to be expected, since the choice of magnetogram
and Rss only affects the location/orientation of the CME and not its internal
properties or bulk speed. Alongside differences and similarities across
different input magnetograms, it is clear the choice of PFSS source surface
height may affect the MFR structure predicted by OSPREI, with some events
showing large distributions in results with varying Rss (e.g., FIDO output of
Events 1 and 3) and some showing almost no change (e.g., FIDO output for
Events 2 and 4). We also note that the CME arrival time is mostly unaffected
by the choice of photospheric and coronal magnetic fields, the only
differences (resulting in spreads of a couple of hours at most) being related
to which part of the MFR is being crossed by the spacecraft. This is also to
be expected, since we used in this work a version of OSPREI that includes a
simple 1D, time-independent empirical model for the ambient solar wind. Future
developments to OSPREI that allow for a time-dependent, variable ambient wind
(see Kay et al., 2022b, for initial reports on the inclusion of any 1D profile
for the background wind) will likely result in the input photospheric and
coronal conditions having an effect also on the CME propagation module of the
model, i.e. ANTEATR. Additionally, the inclusion of solar wind high-speed
streams in OSPREI will also allow for better estimates of the CME passage time
at a spacecraft—in most of the events modeled here (i.e., all but Event 1),
the MFR was followed by the fast solar wind, resulting in compression and/or
inhibited expansion and, thus, in overestimation of the CME duration by
OSPREI.

Finally, it is worth considering the results presented in this work in the
context of operational CME models in space weather forecasting offices. The
events we selected represent a few unique scenarios for forecasters: Event 1
is a stealth CME, Event 2 is a limb eruption as seen by SDO, Event 3 is close
to the limb but seen by both SDO and STEREO-A, and Event 4 is completely on
the Sun’s far side. Analyzing case studies from a variety of sources with
respect to Earth’s viewpoint (while assuming that observations of the
photospheric magnetic field are only available from Earth) is extremely
beneficial for future CME predictions across the whole heliosphere (e.g.,
Shiota et al., 2014; Palmerio et al., 2022a)—considering, e.g., the increasing
interest in space weather at Mars (e.g., Lee et al., 2017; Luhmann et al.,
2017; Palmerio et al., 2022b), it is not unreasonable to expect that forecasts
over the next decade(s) will include information for other planets and/or for
crews on deep-space travel. As we have shown in this study, in the OSPREI
model, the type of magnetogram and PFSS source surface height the end-user
chooses will affect both the coronal deflection/rotation and MFR prediction of
the CME in a more or less significant way. We do not report what combination
of input conditions results in the most accurate prediction of the MFR
configuration—this will be detailed in a follow-on study. In fact, in future
studies, we hope to statistically determine the best input magnetogram and
PFSS source surface height for a variety of CME case scenarios. For example,
while this study only focuses on four events, in a larger study, many CMEs
spread across a few different scenarios (e.g., far side versus on-disk
eruptions, as well as solar minimum versus solar maximum ones) may provide
enough results to draw correlations between properties such as the PFSS source
surface height and the MFR magnetic field magnitude as modeled by OSPREI.
Additionally, another future research direction could be to extend the ANTEATR
module of OSPREI to include other coherent but specifically non-MFR types of
CME ejecta profiles for events that may not be well-described by an MFR
topology (Al-Haddad et al., 2011, 2019b, 2019a). In this study, our “semi-
hindcast” approach to fine-tuning OSPREI to each CME allowed us to easily
compare the model results to PSP magnetic field and plasma data. In
operational use cases, a forecaster does not have readily available in-situ
data of the CME to fine-tune OSPREI’s input parameters, hence in future
studies we will test OSPREI using only remote-sensing observations available
in real time and default input parameters. Multi-spacecraft validations and
comparisons to modeled-versus-observed space weather responses at different
locations will also be a valuable addition to future OSPREI investigations. In
fact, recent analyses of MHD simulation data have shown that internal CME
structures can yield substantially different in-situ profiles depending on the
observational sampling trajectories and radial distances (e.g., Scolini et
al., 2021; Lynch et al., 2022), thus highlighting the need for multi-
spacecraft observations that can provide the larger-scale heliospheric CME
context and/or additional modeling constraints.

##  6 Summary and Conclusions

In this work, we have explored the sensitivity of the OSPREI CME analytical
model to the input photospheric and coronal conditions. We have considered
four events that were observed in situ by PSP, with source regions located at
variable positions with respect to Earth’s viewpoint. We have used four
different magnetogram maps and 16 PFSS source surface heights to realize 64
ensemble runs for each of the events while keeping CME and background solar
wind input parameters fixed. We found that the influence of the input
photospheric and coronal fields on the “final” CME magnetic field predictions
tends to vary from event to event: For Event 1, a subset of simulation runs
resulted in the CME missing PSP altogether, Event 2 and Event 4 showed
generally less disagreement between predictions, and for Event 3 different
combinations of input photospheric and coronal conditions led to different MFR
configuration estimates in situ.

We found no overall pattern in the way the chosen magnetogram or PFSS source
surface height affect the output of ForeCAT or FIDO, but we suggest that
results tend to vary more or less dramatically with respect to the input
conditions depending on the phase of the solar cycle (affecting the presence
of active regions on the photosphere) and the CME source region location with
respect to Earth’s viewpoint (affecting how “old” its photospheric
observations are). Our study showed that OSPREI is moderately sensitive to the
input magnetogram and PFSS model used to reconstruct the photospheric and
coronal magnetic environment from which the CME propagates. This realization,
as well as follow-up work, will help pinpoint possible limitations of the
model, but more importantly, will establish context for space weather
forecasters looking to use architectures such as OSPREI—thus predicting the
MFR configuration of CMEs—operationally.

###### Acknowledgements.

This work was supported by NASA’s Parker Solar Probe Guest Investigator (PSP-
GI) program (grant no. 80NSSC22K0349). E.P. also acknowledges support from
NASA’s HTMS program (grant no. 80NSSC20K1274). N.A. acknowledges support from
NSF AGS-1954983 and NASA ECIP 80NSSC21K0463. P.R. acknowledges support from
NASA’s HSO-C program (80NSSC20K1285) and R2O program (80NSSC20K1403). Solar
disk and coronagraph imagery related to the events studied in this work has
been inspected and analyzed via the JHelioviewer (Müller et al., 2017)
software.

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