11institutetext:  Predictive Science Inc., San Diego, CA 92121, USA
11email<EMAIL_ADDRESS>22institutetext: Space Sciences Laboratory,
University of California–Berkeley, Berkeley, CA 94720, USA 33institutetext:
Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA 44institutetext: Department of Astronomy, University of Maryland,
College Park, MD 20742, USA 55institutetext: University of Houston, Houston,
TX 77204, USA 66institutetext: KBR, Inc., Houston, TX 77002, USA
77institutetext: School of Physics and Astronomy, University of Leicester,
Leicester, LE1 7RH, UK 88institutetext: Department of Mathematics/Centre for
Mathematical Plasma Astrophysics, KU Leuven, B-3001 Leuven, Belgium
99institutetext: Laboratório de Instrumentação e Física Experimental de
Partículas, 1649-003 Lisbon, Portugal 1010institutetext: Instituto Superior
Técnico, University of Lisbon, 1049-001 Lisbon, Portugal 1111institutetext:
European Space Research and Technology Centre, European Space Agency, 2201 AZ
Noordwijk, The Netherlands 1212institutetext: Institut für Geophysik und
extraterrestrische Physik, TU Braunschweig, D-38106 Braunschweig, Germany
1313institutetext: Space Research Institute, Austrian Academy of Sciences,
A-8042 Graz, Austria

# Improved modelling of SEP event onset within the WSA–Enlil–SEPMOD framework

Erika Palmerio 11 Janet G. Luhmann 22 M. Leila Mays 33 Ronald M. Caplan 11
David Lario 33 Ian G. Richardson 3344 Kathryn Whitman 5566 Christina O. Lee 22
Beatriz Sánchez-Cano 77 Nicolas Wijsen 88 Yan Li 22 Carlota Cardoso 991010
Marco Pinto 111199 Daniel Heyner 1212 Daniel Schmid 1313 Hans-Ulrich Auster
1212 David Fischer 1313

###### Abstract

Multi-spacecraft observations of solar energetic particle (SEP) events not
only enable a deeper understanding and development of particle acceleration
and transport theories, but also provide important constraints for model
validation efforts. However, because of computational limitations, a given
physics-based SEP model is usually best-suited to capture a particular phase
of an SEP event, rather than its whole development from onset through decay.
For example, magnetohydrodynamic (MHD) models of the heliosphere often
incorporate solar transients only at the outer boundary of their so-called
coronal domain—usually set at a heliocentric distance of 20–30 $R_{\odot}$.
This means that particle acceleration at CME-driven shocks is also computed
from this boundary onwards, leading to simulated SEP event onsets that can be
many hours later than observed, since shock waves can form much lower in the
solar corona. In this work, we aim to improve the modelled onset of SEP events
by inserting a “fixed source” of particle injection at the outer boundary of
the coronal domain of the coupled WSA–Enlil 3D MHD model of the heliosphere.
The SEP model that we employ for this effort is SEPMOD, a physics-based test-
particle code based on a field line tracer and adiabatic invariant
conservation. We apply our initial tests and results of SEPMOD’s fixed-source
option to the 2021 October 9 SEP event, which was detected at five well-
separated locations in the inner heliosphere—Parker Solar Probe, STEREO-A,
Solar Orbiter, BepiColombo, and near-Earth spacecraft.

###### keywords:

solar eruptions – solar energetic particles – coronal mass ejections –
heliospheric modelling – particle transport

##  1 Introduction

Solar energetic particle (SEP) events can display a wide variation in their
properties such as intensity, fluence, composition, temporal profile, energy
spectrum, and spatial extent. Traditionally, their acceleration sites have
been distinguished between solar flares, giving rise to impulsive SEP events
(e.g., Lin, 2011), and coronal mass ejection (CME)-driven shocks, thus
generating gradual SEP events (e.g., Desai and Giacalone, 2016). Whilst
impulsive SEP events are characterised by a prompt onset and a rapid decay,
resulting in a short duration (order of a few hours), gradual ones tend to
feature variable profiles (depending on the observer’s location with respect
to the shock nose), can last up to a few days, and may include a local
energetic storm particle (ESP) event in the vicinity of the CME-driven shock
passage. Nowadays, this dichotomy has become more blurred, as both flares and
CMEs have been shown to be able to contribute to SEP acceleration within a
single event (e.g., Cane et al., 2010; Trottet et al., 2015). Significant
progress in understanding SEP acceleration and transport has been achieved
owing to multi-point measurements, which have allowed the study of, e.g., the
broad longitudinal distribution of so-called widespread events (e.g., Lario et
al., 2014; Xie et al., 2017; Kollhoff et al., 2021; Dresing et al., 2023), how
the local heliospheric conditions may facilitate or hinder the transport of
particles up to a given location (e.g., Richardson and Cane, 1996; Lario and
Karelitz, 2014; Bain et al., 2016; Palmerio et al., 2021), as well as the
longitudinal and/or radial variation of SEP profiles and properties (e.g.,
Rouillard et al., 2012; Cohen et al., 2014; Lario et al., 2016; Wellbrock et
al., 2022). In addition to providing a wealth of data for the development and
refinement of theories of particle acceleration and transport, multi-point
observations of SEPs are also crucial for validating modelling efforts, since
they conveniently provide results at multiple locations that can test the
predictions of a single simulation run.

The current status of SEP modelling has been recently reviewed by Whitman et
al. (2023), who highlighted that the models that are presently existing or in
development employ a wide variety of approaches and have different goals. For
example, empirical models are based on correlations found between
observational parameters and the properties of the subsequent SEP event that
may be related to one or more underlying physical processes (e.g., Posner,
2007; Anastasiadis et al., 2017; Bruno and Richardson, 2021). They are able to
provide rapid forecasts, often in the form of an “all clear” or “not all
clear” prediction, representing e.g. the confidence level that an SEP event of
a certain magnitude will be observed at a given location. A somewhat similar
approach is undertaken by more recently-developed machine learning models
(e.g., Aminalragia-Giamini et al., 2021; Lavasa et al., 2021; Kasapis et al.,
2022), which are usually trained with large data sets and thus aim to provide
prompt forecasts with improved accuracy, and as a consequence by “hybrid”
models that combine empirical and machine learning characteristics (e.g.,
Núñez et al., 2017; Laurenza et al., 2018). Another class of SEP models is
represented by physics-based ones, which make use of our current understanding
of particle acceleration and transport to simulate the full distribution of
SEPs from a certain event in 2D or 3D space (e.g., Schwadron et al., 2010;
Zhang and Zhao, 2017; Tenishev et al., 2021). Some of these models can be
coupled to magnetohydrodynamic (MHD) models of the corona and/or heliosphere,
yielding thus a self-consistent description of particle acceleration at e.g. a
CME-driven shock as it propagates away from the Sun (e.g., Sokolov et al.,
2004; Linker et al., 2019; Li et al., 2021). Despite their generally more
realistic representation of the physics at play, most physics-based models are
computationally intensive and may require estimates of physical parameters
that are poorly determined from observations or theory, and thus may not be
best suited for real-time forecasts with current high-performance computing
capabilities and/or costs.

Another issue found when coupling physics-based SEP transport and MHD
heliospheric models is that, because of computational constraints, MHD models
are usually separated into two spatial domains: A coronal one (generally
extending up to 20–30 $R_{\odot}$) and a heliospheric one (typically covering
the region from 20–30 $R_{\odot}$ to 1 au and beyond). In most cases, the
coronal and heliospheric domains are characterised not only by different
spatial scales, but also slightly different physical assumptions. A subset of
these models, in particular, circumvent the complex modelling of coronal
dynamics by inserting solar transients (such as CMEs) only at the heliospheric
inner boundary. This simplified (and faster) approach has been shown to be
adequate when simulating, e.g., CME arrival time (e.g., Lee et al., 2015; Wold
et al., 2018), flux rope properties (e.g., Scolini et al., 2019; Maharana et
al., 2022), and/or ESP events (e.g., Ding et al., 2022; Wijsen et al., 2022)
in interplanetary space. However, neglecting solar transients below the
heliospheric inner boundary inevitably results in missing the critical early
acceleration phase of SEPs (e.g., Palmerio et al., 2022), since both solar
flares and CME-driven shocks are able to produce and release energetic
particles at much lower coronal heights (e.g., Kozarev et al., 2015; Masson et
al., 2019; Young et al., 2021).

In this work, we aim to mitigate this issue by “artificially” inserting
sources that inject SEPs at the inner heliospheric boundary of one such 3D MHD
model. The modelling suite that we employ consists of the coronal
Wang–Sheeley–Arge (WSA; Arge and Pizzo, 2000; Arge et al., 2004), the
heliospheric Enlil (Odstrcil, 2003; Odstrcil et al., 2004), and the Solar
Energetic Particle MODel (SEPMOD; Luhmann et al., 2007, 2010) codes. We apply
the model architecture to the 2021 October 9 SEP event, which was observed at
five locations in the inner heliosphere that were relatively well connected to
the eruption’s source region (see Figure 1). Several studies have addressed
some aspects of this event. For example, Lario et al. (2022) analysed the
large-scale structure of the interplanetary context and studied its influence
on the transport of SEPs to each observer. Yang et al. (2023) investigated the
evolution of the CME associated with the SEP event and its interaction with
the structured solar wind. Jebaraj et al. (2023) examined the acceleration of
electrons by both the solar flare temporally associated with the parent solar
eruption and by the shock driven by the corresponding CME. Finally, Wijsen et
al. (2023) simulated the propagation of the CME-driven shock and the ESP event
at two of the five observers using the European Heliospheric FORecasting
Information Asset (EUHFORIA; Pomoell and Poedts, 2018) and PArticle Radiation
Asset Directed at Interplanetary Space Exploration (PARADISE; Wijsen et al.,
2019) models.

Figure 1: Position of planets and spacecraft within 1 AU from the Sun on 2021
October 9 at 06:30 UT. The source region of the CME eruption associated with
an M1.6-class flare is indicated with a triangle symbol on the surface of the
Sun. Earth and the spacecraft have been connected to the Sun through the
nominal Parker spiral for a solar wind speed of 400 km$\cdot$s-1. The same
spiral connects the source region of the eruption to the heliosphere. The
orbits of Mercury, Venus, and Earth are also shown.

After providing an overview of the 2021 October 9 eruption (Section 2), we
first show modelling results with WSA–Enlil–SEPMOD in their “default” settings
and compare them with interplanetary magnetic field, solar wind plasma, and
particle data as supplied by the spacecraft at the five locations (Section
3.1). We then detail the implementation of the so-called “fixed-source” option
in SEPMOD (Section 3.2) by simulating two different particle acceleration
sites: one connected to the active region from which the eruption originated
(“solar flare source”) and the other related to the CME-driven shock in the
corona (“coronal shock source”). We compare results from both fixed-source
options with SEP measurements at the five observers (Section 4), expecting to
find improvements in the simulated event onset time(s) with respect to the
default model architecture. Finally, we discuss our results in the context of
space weather predictions of SEP events (Section 5) and provide concluding
thoughts as well as recommendations for future improvements in physics-based
particle modelling (Section 6).

##  2 Overview of the 2021 October 9 eruption

The event that we focus on in this work commenced on 2021 October 9 around
06:30 UT. It originated from NOAA active region (AR) 12882, located at N18E08
(in Stonyhurst coordinates) at the time of the eruption and highlighted in
Figure 2(a), which displays data from the Atmospheric Imaging Assembly (AIA;
Lemen et al., 2012) telescope onboard the Earth-orbiting Solar Dynamics
Observatory (SDO; Pesnell et al., 2012). The eruption was associated with a
CME, seen to move slightly to the northwest of its source region in SDO/AIA
imagery, an extreme ultra-violet (EUV) wave (described in detail by Lario et
al., 2022), and an M1.6-class flare with start time 06:19 UT, peak time 06:38
UT, and end time 06:53 UT as observed by the Geostationary Operational
Environmental Satellite (GOES). The northwesterly motion of the CME and
associated EUV wave may be due to the presence of coronal holes to the south
of AR 12882, as shown in Figure 2(a).

Figure 2: Overview of the 2021 October 9 CME eruption from remote-sensing
imagery. (a) Image in the 211 Å channel taken by SDO/AIA showing AR 12882
erupting. (b) Coronagraph difference image from SOHO/LASCO/C3, shown in (c)
with the GCS wireframe overlaid. (d) Coronagraph difference image from
STEREO/SECCHI/COR2-A, shown in (e) with the GCS wireframe overlaid.

The CME propagation through the solar corona was observed in white light from
two perspectives, namely the Solar and Heliospheric Observatory (SOHO; Domingo
et al., 1995), placed at the Sun–Earth L1 point, and the Solar Terrestrial
Relations Observatory Ahead (STEREO-A; Kaiser et al., 2008) spacecraft,
located ${\sim}$40∘ east of Earth and about 1 au from the Sun at the time of
the event. Coronagraph imagery from these two observers is shown in Figure
2(b)–(e), which displays data from the C3 telescope of the Large Angle and
Spectrometric Coronagraph (LASCO; Brueckner et al., 1995) onboard SOHO and the
COR2 telescope of the Sun Earth Connection Coronal and Heliospheric
Investigation (SECCHI; Howard et al., 2008) onboard STEREO-A. It is clear from
these data that the CME appeared as a full halo from Earth’s perspective,
whilst its angular width from the STEREO-A viewpoint was ${\sim}$130∘. These
observations suggest that the 2021 October 9 CME was Earth-directed, with the
possibility of a flank encounter at most at STEREO-A.

To obtain a more quantitative estimate of the CME size, trajectory, and speed
(especially useful for the heliospheric modelling described in Section 3), we
perform reconstructions of the eruption in the corona using the Graduated
Cylindrical Shell (GCS; Thernisien, 2011) model applied to nearly-simultaneous
SOHO/LASCO and STEREO/SECCHI images. An example of the GCS wireframe—basically
a hollow croissant-like shell described by six free parameters—is projected
onto coronagraph data in Figure 2(c) (SOHO) and Figure 2(e) (STEREO-A).
According to our reconstruction(s), the CME nose propagated in the direction
($\theta$, $\phi$) = (9∘, 5∘) in Stonyhurst coordinates, and its axis was
tilted by $\gamma$ = 40∘ counterclockwise to the western direction at the
solar equator. We obtain the CME angular extent both along its axis and in the
direction perpendicular to it by calculating the semi-angular widths of the
projection of the GCS wireframe as seen “from its top” (approximately, the
ellipse that is visible in Figure 2(c); see also Verbeke et al., 2023),
resulting in ($R_{\mathrm{maj}}$, $R_{\mathrm{min}}$) = (49∘, 28∘). The CME
speed is estimated by performing two GCS reconstructions at times separated by
one hour and by considering the radial distance travelled by the CME nose in
between, resulting in $V$ = 770 km$\cdot$s-1 (calculated when the CME had
reached heights in the range ${\sim}$12–17 $R_{\odot}$). Thus, through the
solar corona, the 2021 October 9 CME travelled close to the Sun–Earth line,
spanned ${\sim}$100∘ along its axis, and was characterised by a moderate
speed.

##  3 Modelling the 2021 October 9 CME and SEP event

Here, we focus on modelling the 2021 October 9 CME and SEP event using the
combined WSA–Enlil–SEPMOD architecture. WSA is a model that operates within
the simulation’s coronal domain, i.e. in the range 1–21.5 $R_{\odot}$ from the
centre of the Sun. It employs photospheric magnetic field maps of the full Sun
to generate solar wind and interplanetary magnetic field conditions up to 21.5
$R_{\odot}$ (or 0.1 au), corresponding to the WSA outer boundary and also the
Enlil inner boundary. Enlil then uses the WSA output as input to model the
conditions within the simulation’s heliospheric domain (from 0.1 au onwards)
by solving the MHD equations via a flux-corrected-transport algorithm. In this
work, we set the outer boundary of the simulation to 2 au. CMEs are directly
inserted at the Enlil inner boundary of 0.1 au as hydrodynamic pulses, i.e.
without an internal magnetic field. Enlil results are then read by the SEPMOD
code to generate SEP fluxes (typically, for protons) at the observer(s) of
interest. Specifically, it forward-models the transport of SEPs along field
lines that connect a CME-driven shock to a specific observer, using shock-
source injections followed by a constant-energy, guiding-center transport
approximation—it follows that the transport of particles is assumed to be
scatter-free, i.e. diffusive propagation is neglected. In this section, we
first describe the modelling set up using the default WSA–Enlil–SEPMOD
architecture (Section 3.1), and then we illustrate the implementation of the
fixed-source option in SEPMOD to emulate the early-acceleration phase of SEP
events (Section 3.2).

###  3.1 Using the default WSA–Enlil–SEPMOD architecture

The first step in our modelling efforts consists of setting up the
WSA–Enlil–SEPMOD simulation run that only uses CME-driven shock information in
the heliospheric domain to produce particles—we will refer to this default set
up as the “interplanetary shock source” for SEPMOD. This run is performed at
NASA’s Community Coordinated Modeling Center (CCMC). As input conditions for
WSA, we use time-dependent (hourly) National Solar Observatory (NSO) Global
Oscillation Network Group (GONG; Harvey et al., 1996) zero-point-corrected
magnetogram synoptic maps. The CME input parameters are derived directly from
the GCS reconstructions presented in Section 2, and the time of injection into
Enlil is derived from the CME speed calculated as far into the COR2-A field of
view as possible and propagated to 21.5 $R_{\odot}$ under the assumption of
constant velocity. This results in the CME being injected into the
heliospheric domain at $t_{0}$ = 2021-10-09T11:03, with nose trajectory
($\theta$, $\phi$) = (9∘, 5∘) in Stonyhurst coordinates, tilt $\gamma$ = 40∘
(defined positive for counterclockwise rotations from the west direction),
half-angular widths ($R_{\mathrm{maj}}$, $R_{\mathrm{min}}$) = (49∘, 28∘), and
initial speed $V$ = 770 km$\cdot$s-1. Note that these input parameters result
in a CME morphology that consists of a tilted ellipsoid rather than the
classic (spherical) ice-cream cone (see also Mays et al., 2015). An overview
of the WSA–Enlil simulation, with the CME being inserted at the 21.5
$R_{\odot}$ boundary and its propagation through the inner heliosphere, is
shown in Figure 3.

Figure 3: Overview of the WSA–Enlil simulation of the 2021 October 9 CME. (a)
Radial slice of the solar wind radial speed at the Enlil inner boundary of
21.5 $R_{\odot}$, showing the injection of the CME at its point of maximum
width. (b) Same as (a), but for the solar wind number density. (c) View on the
ecliptic plane of the solar wind radial speed within the simulation’s
heliospheric domain (0.1–2.0 au), showing the CME approaching Earth. (d) Same
as (c), but for the normalised solar wind number density. The CME ejecta is
traced from its injection based on the density enhancement with respect to the
background solar wind (initially set to 4 times the ambient density), and is
outlined with a black contour in panels (c) and (d).

Once the WSA–Enlil run is complete, SEPMOD uses shock and connectivity
information from Enlil to model SEP fluxes at the observers of interest. In
Enlil, shocks are defined as increases in the solar wind speed by ${\geq}$20
km$\cdot$s-1 with respect to the corresponding ambient simulation (i.e., the
run without CMEs), and the shock speed is computed as a time-derivative of the
shock position. In SEPMOD, the particle source at the interplanetary shock is
described by a time sequence of point sources on each observer-connected field
line where a shock is found. The Enlil-derived shock parameters (generally
speed, density and speed jumps, as well as shock location) are used, together
with the observer-connected field lines, to model the injection of protons at
the time of each connection. Their subsequent trajectories along the field
line are traced under the guiding-centre approximation, integrating as the
observer passes from field line to field line to obtain the “observed” event
flux time profile. The default energy distribution of each proton injection is
an inverse power-law whose spectral index ($\alpha$) depends on the Enlil
shock compression ratio at the point that is magnetically connected to the
observer, according to the standard formula for diffusive shock acceleration
(e.g., Jones and Ellison, 1991):

$\alpha=-\frac{1}{2}\frac{J_{n}+2}{J_{n}-1}\,,$ (1)

where $J_{n}$ is the density jump at the shock, whilst its intensity at a
certain energy is determined by the velocity jump using empirical results from
Lario et al. (1998). The default injected pitch angle distribution is assumed
to be isotropic.

###  3.2 Introducing the fixed-source option in SEPMOD

The fixed-source option in SEPMOD aims to mitigate the lack of simulated solar
transients—and, thus, of CME-driven shocks and SEP injection regions—within
the coronal domain of models such as WSA–Enlil. The scheme is realised by
setting a predefined source of particles at the coronal–heliospheric model
boundary and by regulating the corresponding injection by means of properties
such as width of the source, timing of the injection, energy spectrum, and
decay profile. A preliminary version of this concept was described by Luhmann
et al. (2012), who employed ad-hoc values to model the early onset of a series
of SEP events in 2010 August. In this work, we expand upon the initial
implementation of Luhmann et al. (2012) to use insights from more recent work
to describe the fixed source, as well as to combine the resulting SEP fluxes
with those that emerge later on from the interplanetary shock source once the
CME has been inserted at the heliospheric inner boundary of the simulation.
Furthermore, here we consider two separate fixed-source descriptions, to
emulate the two possible particle acceleration sites (e.g., Reames, 1999):

  * •

Solar flare source: This source is directly related to the active region where
an eruption originates from and approximates the flare acceleration site—very
close to the solar surface—that gives rise to so-called impulsive SEP events.

  * •

Coronal shock source: This source is directly related to the early propagation
of the corresponding CME and approximates the low-coronal shock acceleration
site that gives rise to so-called gradual SEP events—as the CME travels away
from the Sun, this source naturally morphs into the interplanetary shock
source.

The criteria that we define for each of the two fixed-source descriptions are
summarised in Table 1, and further details are provided throughout the rest of
this section. The solar flare source option uses separate Potential Field
Source Surface (PFSS; Wang and Sheeley, 1992) mapping of the flare site to the
source surface to infer the location and area of the fixed source at 21.5
$R_{\odot}$, where it assumes protons are injected with an initial peak flux
weighted by an empirical factor depending on the 1–8 Å X-ray intensity and
that falls exponentially with a decay constant that is scaled with the
corresponding flare class. In contrast, the coronal shock source is assumed to
be located on the 21.5 $R_{\odot}$ Enlil inner boundary at the location of the
cone CME insertion, where it assumes injection of protons over the area of the
cone CME with an initial rollover spectrum (with rollover energy set to 10
MeV) that evolves to a power law with spectral index $\alpha=-$2\. The assumed
exponential decay time constant for this source is currently the transit time
out to 21.5 $R_{\odot}$ based on the CME speed in the corona.

Table 1: Criteria used to define the solar flare and coronal shock SEP
sources.

|  Solar Flare Source | Coronal Shock Source
---|---|---
Spatial location | AR open field at 2.5 $R_{\odot}$ | Maximum CME width at ${\sim}$10–15 $R_{\odot}$
Injection time | X-ray flare peak | Type II onset
Energy spectrum | Steep/soft power law | Rollover spectrum
Maximum intensity | Scaled with flare class | Scaled with CME speed
Temporal profile | Exponential decay from flare time | Exponential decay from Type Il time
Decay constant | Scaled by flare magnitude | Based on CME transit time to 21.5 $R_{\odot}$

  * •

_Notes._ See the text in Section 3.2 for further details.

An overview of the spatial locations and extents of the two fixed sources
selected for the 2021 October 9 event is presented in Figure 4. The extent of
the solar flare source (Figure 4(a)) is obtained from the GONG magnetogram
that is closest to the eruption time from the series of input maps used for
WSA (see Section 3.1), i.e. the one for October 9 at 06:04 UT. After
processing the magnetogram via interpolation, flux balancing, and smoothing,
we perform on it a PFSS extrapolation using the POT3D (Caplan et al., 2021)
tool. We then select a mask of AR 12882 (by thresholding it to ${\pm}$10 G)
and trace field lines from it onto the 2.5 $R_{\odot}$ PFSS source surface
(represented with a red contour in Figure 4(a)). Finally, we select a circular
area encompassing the mapped AR to represent the solar flare source—shown in
yellow in Figure 4(a)—resulting in a patch centred at ($\theta$, $\phi$) =
($10^{\circ}$, $-8^{\circ}$) in Stonyhurst coordinates and with a $14^{\circ}$
radius. The extent of the coronal shock source (Figure 4(b)) is obtained from
the GCS-derived (see Figure 2) CME dimensions that are used as input for Enlil
(see Section 3.1). Specifically, we construct a circle around the CME’s
elliptical cross-section to account for the fact that, whilst CMEs are usually
assumed to be croissant-shaped, the shocks driven by them are generally
interpreted as spheroids (e.g., Liu et al., 2019a; Dumbović et al., 2020).
This results in a patch centred at ($\theta$, $\phi$) = ($9^{\circ}$,
$5^{\circ}$) in Stonyhurst coordinates (i.e., the propagation direction of the
CME nose derived from white-light observations) and with a $49^{\circ}$
radius. To approximate either the solar flare or coronal shock source in
SEPMOD, SEPs are introduced into the Enlil simulation volume at the 21.5
$R_{\odot}$ inner boundary. These are injected over a circular area centered
on the coordinates of either the PFSS-mapped flare field line(s) described
above, or the cone CME in the case of the coronal shock source. Their spatial
concentrations over the circular source area are described in each case by a
normalised Gaussian whose half-width is based on the radius of the area. We
note that the coronal source option is particularly amenable to real-time
modelling because it uses the same CME source parameters employed to run the
WSA–Enlil model.

Figure 4: Overview of the selected fixed sources for the 2021 October 9 event.
(a) Solar flare source. The panel shows the smoothed GONG zero-point-corrected
magnetogram for 2021-10-09 at 06:04 UT (saturated at ${\pm}$50 G), the PFSS-
derived location of the heliospheric current sheet at 2.5 $R_{\odot}$ (lime
contour), the mapping of AR 12882 onto the 2.5 $R_{\odot}$ PFSS source surface
(red contour), and the selected fixed-source area to employ for SEP injection
(yellow contour). (b) Coronal shock source. The panel shows the solar wind
radial speed at the Enlil inner boundary of 21.5 $R_{\odot}$ at the point of
maximum width of the CME insertion (2021-10-09 at 15:39 UT, same as Figure
3(a)), the location of the modelled heliospheric current sheet (black
contour), the selected fixed-source area to employ for SEP injection (white
contour), and the projected Enlil-modelled field lines connecting each of the
five observers to the 21.5 $R_{\odot}$ sphere.

Next, we need to define the SEP injection times and temporal profiles,
together with their fluxes and energy spectra. For the solar flare source, we
use as the SEP injection time the peak time of the associated GOES X-ray
emission, i.e. 06:38 UT (we note that Jebaraj et al., 2023, reported a radio
Type III emission starting at 06:31 UT, which could be used as an alternative
constraint), and employ an exponential decay time that is scaled with the
flare class, under the assumption that this parameter is related to the
duration of the X-ray emission—e.g., Kahler and Ling (2022) showed that
stronger flares tend to decay over longer time scales, possibly due to the
longer duration of the related reconnection processes. For the coronal shock
source, we use the onset time of the corresponding radio Type II emission
(considered a signature of a formed CME-driven shock; e.g., Vršnak and Cliver,
2008; Magdalenić et al., 2010), i.e. 06:33 UT according to the analysis
performed by Jebaraj et al. (2023) employing ground-based observations. In
this case we also use an exponential decay time profile, but with a time
constant calculated from the transit time of the CME through the corona to the
Enlil inner boundary—we remark that this choice has no physical basis, but
allows for a smooth transition from the coronal shock source to the default
interplanetary one. For the injected energy spectrum in the solar flare source
we use a soft power law consistent with observed flare events with index
$\alpha=-4.0$, while for the coronal shock source we use a time-dependent
‘rollover spectrum’ with a rollover energy of 10 MeV (see, e.g., Desai and
Giacalone, 2016) that starts with sharply diminished low energy fluxes and
evolves over the time it would take the CME to arrive at 21.5 $R_{\odot}$ to a
power law with index $\alpha=-2.0$.

To scale the intensities of the particles injected with either the solar flare
or the coronal shock sources, we use empirical relations based on SEP events
detected at Earth between December 2006 and February 2018 (see Balch, 1999,
2008, for a similar approach used in operational SEP forecasting). The list of
events that we use to do so is taken (and expanded) from Richardson et al.
(2014), who catalogued all the $>$25 MeV proton events observed by the twin
STEREO spacecraft and/or Earth. These relations are used to scale the SEP
intensity to the GOES flare class for the solar flare source and to the CME
plane-of-sky speed in LASCO (taken, in our case, from the LASCO CME catalogue
of Gopalswamy et al., 2009) for the coronal shock source. We first select all
the events that were observed at Earth, irrespective of their detection at
either STEREO probe. We then consider their peak 25 MeV flux against the
corresponding GOES X-ray peak flux and LASCO CME plane-of-sky speed, and
ultimately derive linear fits for both cases, shown in Figure 5. Note that the
data points shown in the figure include both near- and far-sided events, but
near-sided events only were used to obtain the linear fitting curves. The
relation that we obtain for the solar flare source option (scaled with the
GOES X-ray peak flux) is

$F=e^{6.133}\cdot
X^{1.005}\;\;\;\mathrm{or}\;\;\;\log(F)=1.005\log(X)+2.664\,,$ (2)

where $F$ is the 25 MeV proton flux and $X$ is the X-ray flux. For the coronal
shock source option (scaled with the LASCO plane-of-sky CME speed), we obtain

$F=e^{0.004V-9.071}\;\;\;\mathrm{or}\;\;\;\log(F)=\frac{V}{{\color[rgb]{0,0,0}576}}-3.94\,,$
(3)

where $V$ is the CME speed. The resulting correlation coefficients (also
reported in Figure 5) are 0.563 for the flare class and 0.685 for the CME
speed. We remark, nevertheless, that observational comparisons of SEP fluxes
with flare class and/or CME speed like the ones we use here are not
necessarily representing strictly flare-accelerated and shock-accelerated
particles, respectively, but may instead present contributions from both
acceleration mechanisms within a single event.

Figure 5: Empirical relationships between the maximum proton flux at 25 MeV
and (left) the GOES X-ray flux as well as (right) the LASCO plane-of-sky CME
speed for SEP events detected at Earth between December 2006 and February
2018. The plot distinguishes between near-sided (red) and far-sided (blue)
events. The best fit curves shown in green are applied to the near-sided data
only. The top left corner of both panels shows the corresponding equation for
the best fit curve and the Pearson correlation coefficient.

##  4 Modelling results and comparison with observations

In this section, we compare modelling results using the various
WSA–Enlil–SEPMOD setups described in Section 3 with in-situ observations at
the five locations depicted in Figure 1, i.e. Earth as well as the BepiColombo
(Bepi; Benkhoff et al., 2021), Solar Orbiter (SolO; Müller et al., 2020),
Parker Solar Probe (PSP; Fox et al., 2016), and STEREO-A spacecraft. These
four probes were respectively located at approximately 0.33, 0.68, 0.77, and
0.96 au from the Sun at the time of the 2021 October 9 event, and their
longitudinal separations from Earth were respectively 2∘, 15∘, 48∘, and 39∘
towards the east. At Bepi, we use magnetic field data from the Mercury
Planetary Orbiter Magnetometer (MPO-MAG; Heyner et al., 2021) and particle
data from the BepiColombo Environment Radiation Monitor (BERM; Pinto et al.,
2022)—the plasma instruments are not operational during cruise phase. At SolO,
we use magnetic field data from the Magnetometer (MAG; Horbury et al., 2020),
plasma data from the Proton and Alpha Sensor (PAS) of the Solar Wind Analyser
(SWA; Owen et al., 2020), and particle data from the Energetic Particle
Detector (EPD; Rodríguez-Pacheco et al., 2020). At PSP, we use magnetic field
data from FIELDS (Bale et al., 2016), plasma data 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, and particle data from the Integrated
Science Investigation of the Sun (IS$\odot$IS; McComas et al., 2016). At
STEREO-A, we use magnetic field data from the Magnetic Field Experiment (MFE;
Acuña et al., 2008) part of the In situ Measurements of Particles And CME
Transients (IMPACT; Luhmann et al., 2008) suite, plasma data from the Plasma
and Suprathermal Ion Composition investigation (PLASTIC; Galvin et al., 2008),
and particle data from the Low Energy Telescope (LET; Mewaldt et al., 2008)
and High Energy Telescope (HET; von Rosenvinge et al., 2008) part of IMPACT.
Finally, for Earth we employ measurements from two probes that are located at
the Sun–Earth Lagrange L1 point, i.e. Wind (Ogilvie and Desch, 1997) and SOHO.
We use magnetic field data from the Magnetic Field Investigation (MFI; Lepping
et al., 1995) as well as plasma data from the Solar Wind Experiment (SWE;
Ogilvie et al., 1995), both onboard Wind, and particle data from the
Comprehensive Suprathermal and Energetic Particle Analyser (COSTEP; Müller-
Mellin et al., 1995) onboard SOHO.

###  4.1 The baseline: The interplanetary shock source

Before we can evaluate the possible improvements in modelling the onset time
of SEP events with the WSA–Enlil–SEPMOD architecture, we shall explore the
results obtained with the default simulation setup, i.e. using uniquely the
interplanetary shock source (see Section 3.1). An overview of magnetic field,
plasma, and particle data compared to the modelling output at each of the five
available observers is presented in Figure 6 (also, see Figure 3 for a
visualisation of the configuration of the various spacecraft with respect to
the CME). Regarding the CME impacts at the different locations, we note that
all encounters are correctly predicted, albeit with more or less significant
errors in arrival time. At Bepi (Figure 6(a)), a shock is detected in the
WSA–Enlil simulation ${\sim}$2 hours later than observed. At SolO (Figure
6(b)), the shock passage takes place in the model ${\sim}$5 hours earlier than
in the data. At PSP (Figure 6(c)), there is no clear indication of a CME
impact in the model, in agreement with the in-situ measurements. At STEREO-A
(Figure 6(d)), a glancing encounter with the eastern flank of the shock is
simulated ${\sim}$6 hours later than observed. Finally, at Earth (Figure
6(e)), the modelled CME-driven shock makes an impact ${\sim}$7 hours earlier
than in the in-situ observations. Nevertheless, we remark that all impact
times fall within the typical CME arrival time uncertainties, which are of the
order of ${\sim}$10 hours (e.g., Riley et al., 2018; Wold et al., 2018;
Paouris et al., 2021).

Figure 6: Results of the default WSA–Enlil–SEPMOD simulation run (i.e., using
the interplanetary shock source only) compared with observations of the 2021
October 9 CME and SEP event at five locations in the inner heliosphere—(a)
Bepi, (b) SolO, (c) PSP, (d) STEREO-A, and (e) Earth. Each plot shows, from
top to bottom: Magnetic field magntitude, solar wind bulk speed, proton
density, proton temperature, and proton/ion fluxes. Magnetic field and plasma
data are shown in solid black, whilst the corresponding simulated quantities
are shown in solid magenta—the related ambient run (i.e., without CME) is
shown in dashed magenta. Energetic particle data are shown with solid lines,
whilst the corresponding simulated fluxes are shown with dashed lines. The
(observed) arrival of the CME-driven shock is marked with a vertical grey
line, where applicable. The heliocentric distances reported for each observer
refer to the eruption time of the 2021 October 9 event.

Regarding the simulated SEPs at each location of interest, we note that both
the intensity values and the intensity–time profiles are generally well
reproduced. Despite the discrepancy in the onset times, there is a remarkable
qualitative agreement between the observed and modelled SEP time series at
SolO, PSP, and STEREO-A. At Bepi, the simulated fluxes are higher in magnitude
than the measured ones, but the shapes of the SEP enhancements are overall
well-behaved. At Earth, in addition to predicting higher fluxes during the
first half of the event, SEPMOD features less steep profiles than observed,
especially at higher energies—this is not surprising, since Earth is the
location with the poorest magnetic connectivity to the eruption’s source (see
Figure 1). Despite the predominantly encouraging agreement between simulation
and observations, it is clear that the onset of the SEP event is entirely
missed at every location, with delays ranging from ${\sim}6$ hours (Bepi) to
${\sim}11$ hours (Earth). This issue is addressed in the following sections
via the fixed-source option of SEPMOD.

###  4.2 Additional SEP injection: The solar flare source

The first fixed-source option that we explore is the solar flare one. Figure 7
(shown in the same format as Figure 6) displays the modelled SEP fluxes that
we obtain by including, alongside the “default” interplanetary shock source,
the additional particle injection at the Enlil inner boundary using the patch
shown in Figure 4(a). It is clear that at all locations except Earth, the
onset time of the SEP event is greatly improved overall, but we note a stark
“dip” marking the decay of the solar flare source and the takeover of the
interplanetary shock source. This is a result of the assumption that the
particle intensity decay is loosely based on the short lifetime of the
observed 2021 October 9 flare (beginning around 06:30 UT and lasting
${\sim}$3.5 hours in total) compared to the injection time of the CME itself
into the Enlil heliospheric domain beginning at 21.5 $R_{\odot}$ (set to
around 11:00 UT in the simulation run described in Section 3.1).

Figure 7: Results of the WSA–Enlil–SEPMOD simulation run that includes the
solar flare source compared with observations of the 2021 October 9 CME and
SEP event at five locations in the inner heliosphere—(a) Bepi, (b) SolO, (c)
PSP, (d) STEREO-A, and (e) Earth. All panels are shown in the same format as
Figure 6.

At Bepi (Figure 7(a)), the simulated SEP profiles show a better onset time
compared to the default SEPMOD version, but the peak fluxes—already higher-
than-observed when using the interplanetary shock source only—are
significantly stronger than in the corresponding measurements (even by two
orders of magnitude). At SolO (Figure 7(b)), the modelled SEP fluxes reach
their peak a couple of hours earlier than observed, and the offset between the
measured and simulated flux values shortly after onset is seen to increase
with increasing energy. At PSP (Figure 7(c)), the short-lived, quick-rising
SEPMOD profiles feature a remarkably similar behaviour to the correponding
measurements, although the peak fluxes at the different energy channels are
more “spread out” in intensity than observed. At STEREO-A (Figure 7(d)), the
modelled SEPs peak in flux earlier than observed (as in the SolO case), and
the dip between the solar flare and interplanetary shock contributions is
especially prominent. Finally, at Earth (Figure 7(e)), the fixed-source
component of the simulated SEP profiles is extremely minor—only lower-energy
particles exceed the instrument background—and can virtually be considered
negligible.

###  4.3 Additional SEP injection: The coronal shock source

We now investigate how results change when considering the coronal shock
source. Figure 8 (shown in the same format as Figure 6) displays the modelled
SEP fluxes that we obtain by including, alongside the “default” interplanetary
shock source, the additional particle injection at the Enlil inner boundary
using the patch shown in Figure 4(b). Again, the onset time of the SEP event
appears greatly improved overall, and this time we note a significantly
smoother transition between the coronal and interplanetary shock sources,
resulting in a more realistic time series. This is likely due to the fact that
the coronal shock source is based on the same CME input parameters that are
employed for Enlil, and its decay time profile is scaled with the CME transit
time to 21.5 $R_{\odot}$.

Figure 8: Results of the WSA–Enlil–SEPMOD simulation run that includes the
coronal shock source compared with observations of the 2021 October 9 CME and
SEP event at five locations in the inner heliosphere—(a) Bepi, (b) SolO, (c)
PSP, (d) STEREO-A, and (e) Earth. All panels are shown in the same format as
Figure 6.

At Bepi (Figure 8(a)), the modelled SEP profiles display a similar trend to
the measured ones, but all the magnitudes are higher in all cases (as in the
previous two simulation runs). At SolO (Figure 8(b)), PSP (Figure 8(c)), and
STEREO-A (Figure 8(d)), the modelled fluxes appear remarkably similar to the
observed ones, in terms of both the shapes of the SEP enhancements and in the
peak intensities at the different energy levels. The SEPMOD fluxes drop below
the corresponding instrumental backgrounds earlier than in the spacecraft data
in a few cases, including the two lowest energy ranges at PSP (5.70–6.70 MeV
and 13.5–16.0 MeV) as well as the two mid energy levels at STEREO-A (15.0–17.1
MeV and 29.6–33.4 MeV). Finally, at Earth (Figure 8(e)), SEPMOD simulates a
significantly more abrupt onset of the SEP event than observed, and with
generally higher fluxes at all energy ranges.

##  5 Discussion

The results presented in Section 4 show that the SEPMOD fixed-source option
that we have implemented and tested on the 2021 October 9 SEP event yields
overall earlier onset times—generally closer to the observed ones—as well as
greater peak fluxes over different energy ranges—often more similar to the
corresponding measurements, but significantly higher in a few instances. Here,
we discuss such results (especially in terms of the heliospheric context) and
attempt to quantify the level of improvement of both the solar flare and
coronal shock sources over the default interplanetary shock source.

First of all, we note that the solar flare source, despite producing overall
more accurate onset times than the default model and partially better peak
fluxes, yields SEP profiles that are characterised by an abrupt, short-lived
peak followed by a dip and, only after, by the default interplanetary shock
contribution. As mentioned in Section 4.2, this is due to the short SEP
injection time that is scaled to the corresponding X-ray flare emission. An
exception is found, in part, at PSP, where an initial short-lived
peak—without, however, a prominent dip following—is present in the spacecraft
data as well. This is, in fact, the location that is best connected to the
eruption’s source region (see Figure 1). It is possible that PSP observed the
SEP event with both a flare and a CME-driven shock contribution (e.g., Cane et
al., 2010; Anastasiadis et al., 2019). The coronal shock source, on the other
hand, produces better onset times and more realistic profiles overall. As
mentioned in Section 4.3, this is likely due to the fact that this source is
scaled to the CME parameters used for the Enlil run—and from which SEPMOD
derives its default interplanetary shock source—thus yielding a more seamless
transition between the two SEP injection modes. An exception is found at
Earth, where the coronal shock contribution results in a more rapid onset and
higher peak fluxes. This is the location characterised by the poorest
connectivity to the eruption’s source region (see Figure 1). It is likely that
the patch selected for the coronal shock SEP injection was too large at the
beginning of the event, since CME-driven shocks are usually formed in the
lower corona and tend to expand rapidly during their early propagation (e.g.,
Kwon et al., 2014; Liu et al., 2019b). Future improvements to the SEPMOD
coronal shock source will consider a linearly-growing patch from the first CME
observation time in coronagraphs until its “maximum” size used as input for
Enlil.

Table 2: Differences in the SEPMOD modelled onset times of the 2021 October 9
SEP event at the various observers using the default code and the two fixed-
source options.

|  Observed |  Default |  \+ Solar Flare | \+ Coronal Shock
---|---|---|---|---
Bepi | 08:00 UT | +6.0 h |  $-$1.5 h |  $-$1.5 h
SolO | 07:30 UT | +6.5 h |  $-$1.0 h |  $-$1.0 h
PSP | 07:00 UT | +7.5 h |  $-$0.5 h |  $-$0.5 h
STEREO-A | 07:30 UT | +6.5 h |  $-$1.0 h |  $-$1.0 h
Earth | 13:00 UT | +11.0 h | +11.0 h |  $-$6.5 h

  * •

_Notes._ The first column shows the approximate (to the nearest half-hour)
observed SEP event onset times at each spacecraft, whilst the remaining
columns report the corresponding differences in the simulated onset times for
different versions of SEPMOD. Positive (negative) offsets indicate that the
predicted onset took place later (earlier) than observed. For each time
estimate, we have referred mainly to the orange SEP time series in Figures 6,
7, and 8, with energy ranges of 5.9–9.1 MeV at Bepi, 14.6–15.7 MeV at SolO,
13.5–16.0 MeV at PSP, 15.0–17.1 MeV at STEREO-A, and 7.8–25 MeV at SOHO.

Table 2 provides an overview of the different SEP onset times modelled by
SEPMOD compared to their corresponding observations. For each observer, we
report the actual event onset times (approximated to the nearest half-hour) as
well as the deviation from those for each of the SEPMOD runs employed in this
work. It is clear that the default (interplanetary shock source) version
yields times that are delayed at least by a few hours in all cases, as
mentioned in Section 3.1. Both fixed-source options, on the other hand, bring
overall significant improvements, with onset times that are 30 to 60 minutes
earlier than observed at all locations but Earth. The fact that these SEP
events start earlier than in the corresponding spacecraft data may be due to
either a larger path length along the interplanetary magnetic field than that
modelled by Enlil, or an SEP injection that was set to commence too soon in
SEPMOD (note that we used here the flare peak time for the solar flare source
and the onset of the Type II radio emission for the coronal shock source). At
Earth, the solar flare source produces no significant changes when compared to
the default simulation run—likely due to the source patch being too small for
particles to reach this location—whilst the coronal shock source yields an
onset time that is significantly earlier than observed—likely due to the
source patch being too large during the early phases of SEP acceleration, as
mentioned above.

Table 3 provides an overview of the different SEP peak fluxes modelled by
SEPMOD compared to their corresponding observations. For each observer, we
report the measured SEP intensity peak in one of the energy channels shown in
Figures 6, 7, and 8 as well as the corresponding value for each of the SEPMOD
runs employed in this work. It is clear that at SolO, PSP, and STEREO-A, the
default version of SEPMOD tends to significantly underestimate the peak
fluxes. This is not surprising, since for well-connected observers an SEP
event usually reaches its highest intensities close to onset. The solar flare
source, however, shows still rather low fluxes at SolO and STEREO-A, whilst at
PSP intensities are overestimated by approximately a factor of two. The
coronal shock source, on the other hand, produces SEP peak fluxes at these
three observers that are no worse than ${\sim}$0.6 times the measured ones. At
Bepi and Earth, all three SEPMOD simulation runs produce fluxes that are
higher than observed. Whilst at Bepi this could be due to the packed
configuration of the instrument during its cruise phase, implying that the
spacecraft itself may screen some particles (see also Appendix A in Palmerio
et al., 2022), it is clear that at Earth this is owing to either a too-large
SEP injection patch or the specific heliospheric context—Lario et al. (2022)
and Wijsen et al. (2023), in fact, showed that there was a solar wind high-
speed stream flowing between the CME source region and Earth’s location, which
may have resulted in particles being partially occulted and/or delayed.

Table 3: Differences in the SEPMOD modelled peak intensities of the 2021
October 9 SEP event at the various observers using the default code and the
two fixed-source options.

|  Observed |  Default |  \+ Solar Flare | \+ Coronal Shock
---|---|---|---|---
Bepi | 2.232 | 19.123 (857%) | 32.308 (1447%) | 21.487 (963%)
SolO | 1.734 | 0.245 (14%) | 0.371 (21%) | 1.069 (62%)
PSP | 1.963 | 0.116 (6%) | 4.159 (212%) | 1.202 (61%)
STEREO-A | 1.471 | 0.081 (6%) | 0.289 (20%) | 0.862 (59%)
Earth | 0.047 | 0.184 (391%) | 0.184 (391%) | 0.411 (874%)

  * •

_Notes._ The reported fluxes refer to the orange SEP time series in Figures 6,
7, and 8, with energy ranges of 5.9–9.1 MeV at Bepi, 14.6–15.7 MeV at SolO,
13.5–16.0 MeV at PSP, 15.0–17.1 MeV at STEREO-A, and 7.8–25 MeV at SOHO. The
units are [cm${}^{2}\cdot$sr$\cdot$s$\cdot$MeV]-1 for all reported values. The
percentages in parentheses for the SEPMOD runs are calculated with respect to
the corresponding observed fluxes.

Finally, to provide a comparison of the different modelled SEP fluxes versus
their corresponding spacecraft data as a whole, we employ the Dynamic Time
Warping (DTW; Bellman and Kalaba, 1959) technique, which is an algorithm
useful for measuring similarity between two time series. In DTW, an optimal
comparison (more specifically, alignment) between two data sequences is found
by stretching and/or compressing one series onto the other, and the resulting
DTW distance is a measure of their similarity—the lower the distance, the
higher the correlation. The technique has found applications in many fields of
science and technology, including more recently in heliophysics (e.g., Laperre
et al., 2020; Samara et al., 2022). To apply the DTW method to our data sets,
we first ensure that any pair of time series covers the same temporal
interval, and successively linearly interpolate any data gaps that may be
present in the spacecraft measurements. Table 4 shows the DTW distances
resulting from comparing observations of the 2021 October 9 SEP event with
each of the three SEPMOD runs considered in this work. Note that the values
reported in the table are not normalised, i.e., they should not be compared
across the different in-situ observers for each SEPMOD running mode, but only
across the different SEPMOD runs for each spacecraft. It is clear that for
SolO, PSP, and STEREO-A, the coronal shock source is characterised by a
significantly lower (by at least a factor of two or three) DTW distance than
the remaining two, indicating a better match to observations. For all these
three observers, the solar flare source also displays consistently lower
values than the default (interplanetary shock only) option. In the case of
Bepi, the default run provides the smallest DTW distance, followed by the
coronal shock and then by the solar flare sources—we note, nevertheless, that
the best and worst values differ by less than a factor of two. At Earth, the
interplanetary shock and the solar flare sources display equal results, whilst
the coronal shock source features a DTW distance that is ${\sim}$2.5 times
higher. When considering all these results as a whole, it appears that the
coronal shock source (and, to a lesser extent, the solar flare one) represents
overall an improvement over the default SEPMOD running mode, which neglects
SEP acceleration below heliocentric heights of 21.5 $R_{\odot}$.

Table 4: DTW distances between spacecraft data and SEPMOD profiles of the 2021
October 9 SEP event at the various observers using the default code and the
two fixed-source options.

|  Default |  \+ Solar Flare | \+ Coronal Shock
---|---|---|---
Bepi | 26.931 | 43.597 | 35.714
SolO | 4.593 | 4.003 | 1.451
PSP | 3.357 | 3.303 | 0.891
STEREO-A | 6.301 | 4.917 | 1.853
Earth | 0.282 | 0.282 | 0.682

  * •

_Notes._ The calculated DTW distances refer to the orange SEP time series in
Figures 6, 7, and 8, with energy ranges of 5.9–9.1 MeV at Bepi, 14.6–15.7 MeV
at SolO, 13.5–16.0 MeV at PSP, 15.0–17.1 MeV at STEREO-A, and 7.8–25 MeV at
SOHO. The units are [cm${}^{2}\cdot$sr$\cdot$s$\cdot$MeV]-1 for all reported
values.

##  6 Summary and conclusions

In this work, we have implemented the so-called fixed-source option in the SEP
transport code SEPMOD, and applied it within the framework of MHD heliospheric
modelling using the WSA–Enlil–SEPMOD architecture. The reasoning behind this
effort is to improve modelling of the onset and early evolution of SEP events,
which often cannot be reproduced in models that include CME transients only in
their heliospheric domain (often set at 21.5 $R_{\odot}$ or 0.1 au). We have
employed two separate fixed SEP sources, namely a solar flare (with SEP
properties modulated by the corresponding flare characteristics) and a coronal
shock (with SEP properties modulated by the corresponding CME
characteristics), aimed at emulating the two sites where particle acceleration
may occur. We have tested both these sources on the 2021 October 9 SEP event,
which was triggered by an eruption characterised by an M1.6-class flare and a
moderate-speed (${\sim}$770 km$\cdot$s-1) CME, and found a series of
improvements over the default SEPMOD running mode, which only includes
particle acceleration at the CME-driven interplanetary shock above 21.5
$R_{\odot}$.

Overall, results obtained with the coronal shock source appeared to match
observations better than the other two simulation modes in terms of event
onset timing, peak fluxes, and similarity with the corresponding spacecraft
measurements. This is not surprising, given that the 2021 October 9 event was
characterised indeed by a strong shock-accelerated component (see Wijsen et
al., 2023, for details on the corresponding ESP event, showing that the shock
was still accelerating particles by the time it reached 1 au), hence the solar
flare source option may not have been particularly appropriate for this case.
In the context of real-time space weather forecasting, the coronal shock
source may be in general a simpler option to implement, since it uses directly
the CME parameters employed for the related MHD simulation of the solar wind
and interplanetary magnetic field (in this case, with WSA–Enlil), whilst the
solar flare source requires the additional step of performing a PFSS
extrapolation of the nearby open fields. Additionally, the properties of the
flare source that are relevant for characterizing the SEP event are generally
less clear. For example, we have assumed that the particle intensity rate is
loosely dependent on the X-ray flare decay time, which may not be correct,
used a soft SEP spectrum based on small flare events that may not be well-
suited for these more energetic events, and assumed that the flare-accelerated
particles are released over a small region of open fields based on a PFSS
extrapolation, which may not be appropriate where the field configuration is
strongly evolving during the eruption of a CME. Flare acceleration by
reconnection may also occur over a wider region beneath the CME assumed for
the PFSS extrapolation. Another caveat that holds true for either fixed-source
option is that, as mentioned in Section 3, SEPMOD neglects cross-field SEP
transport (at least in its current implementation), hence these assumptions
and results may be generally applicable only to events for which each location
of interest is relatively well-connected to the eruption’s source region
and/or the CME-driven shock, as was the case for the 2021 October 9 event
explored here.

With these caveats in mind, in future work we will consider more stricly-
impulsive SEP events accompanied e.g. by jets or narrow/slow CMEs (e.g., Nitta
et al., 2006; Papaioannou et al., 2016) and test the solar flare source option
further. Additional future efforts will consider employing a linearly growing
source patch for the coronal shock source, to emulate the expanding behaviour
of CME-driven shocks in the corona (and to avoid SEPs reaching poorly-
connected observers too early, as was the case for Earth in this work). In
fact, the implementation of a time-dependent coronal shock source could be
combined with the solar flare source description introduced here to obtain
realistic-looking SEP profiles that are characterised by both a flare- and a
shock-accelerated component (as was likely the case for PSP in this work)—such
an option shall also be explored in the future. Additionally, we note that
these developments to the SEPMOD code were tested and applied thoroughly
uniquely on the event showcased in this work. A more systematic survey of many
more events observed by multiple spacecraft in the inner heliosphere is
underway and will reveal the applicability of the fixed-source description
presented here for any given SEP-producing eruption.

Nevertheless, we remark that SEPMOD is a simplified-physics model that assumes
scatter-free propagation of SEPs along magnetic field lines, whilst neglecting
additional particle transport processes (e.g., Giacalone and Jokipii, 2001;
Qin et al., 2004). In fact, effects such as diffusive/perpendicular transport
(e.g., Zhang et al., 2003; Zank et al., 2015), which have been shown to often
play a significant role in the spread of SEPs (e.g., Laitinen et al., 2013;
Dresing et al., 2014), are not included in the current implementation of
SEPMOD. We have described in this section a set of potential improvements to
our semi-empirical treatment of the flare and/or coronal shock sources, but
additional avenues to pursue could include the incorporation of cross-field
transport to yield a more realistic description of the spread of particles in
the heliosphere. Since one of the major strengths of SEPMOD is its
computational efficiency, which makes the model particularly well-suited for
real-time applications111See, e.g., the SEP Scoreboard hosted at NASA’s
Community Coordinated Modeling Center (CCMC), available at
https://ccmc.gsfc.nasa.gov/scoreboards/sep, which regularly includes SEPMOD
predictions in real-time applications., one of the greatest challenges in this
regard is the attainment of an optimal balance between physics-based
formulations and semi-empirical approximations that can provide sufficient
physical insight whilst maintaining simulation runs executable over short time
scales.

Finally, it is worth keeping in mind that simulating the acceleration and
transport of SEPs with architectures such as the one employed in this work
will necessarily involve inherent uncertainties that go beyond the mere
treatment of particles and are related to various aspects of the full Sun-to-
heliosphere modelling chain. These include uncertainties in the photospheric
magnetic field measurements (e.g., Bertello et al., 2014; Riley et al., 2014),
in the reconstructed coronal fields (e.g., Caplan et al., 2021; Parenti et
al., 2021), in the modelled ambient solar wind (e.g., Gressl et al., 2014;
Jian et al., 2015), and in the estimation of CME input parameters (e.g., Singh
et al., 2022; Verbeke et al., 2023). In other words, the parameter space of
the simulation has a large number of poorly-constrained degrees of freedom,
thus making generalisation of the method for space weather forecasting
applications particularly challenging. Extensive efforts dedicated to
quantitative comparisons and performance benchmarking for each of these pieces
of the modelling chain (e.g., Reiss et al., 2023a, b; Temmer et al., 2023;
Whitman et al., 2023) will be increasingly important for model refinement and
development and advancing our space weather prediction capabilities.

###### Acknowledgements.

EP and RMC acknowledge support from NASA’s PSP-GI (no. 80NSSC22K0349), O2R
(no. 80NSSC20K0285), LWS (no. 80NSSC19K0067), and LWS-SC (no. 80NSSC22K0893)
programmes. DL and IGR acknowlege support from NASA programmes
NNH19ZDA001N-LWS and NNH19ZDA001N-HSR. IGR also acknowledges support from the
STEREO mission. COL acknowledges support from NASA LWS grant 80NSSC21K1325.
BS-C acknowledges support through STFC Ernest Rutherford Fellowship
ST/V004115/1 and STFC grant ST/Y000439/1. NW acknowledges funding from the
Research Foundation – Flanders (FWO – Vlaanderen, fellowship no. 1184319N). DH
is supported by the German Ministerium für Wirtschaft und Klimaschutz and the
German Zentrum für Luft- und Raumfahrt under contract 50QW2202. The authors
thank NASA’s Community Coordinated Modeling Center (CCMC;
https://ccmc.gsfc.nasa.gov) for supporting the simulation efforts presented in
this work (run id: Erika_Palmerio_111522_SH_1). The WSA model was developed by
C. N. Arge (currently at NASA Goddard Space Flight Center), the Enlil model
was developed by D. Odstrcil (currently at George Mason University), and the
SEPMOD model was developed by J. G. Luhmann (currently at University of
California–Berkeley).

## References

  * Acuña et al. (2008) Acuña, M. H., D. Curtis, J. L. Scheifele, C. T. Russell, P. Schroeder, A. Szabo, and J. G. Luhmann, 2008.  The STEREO/IMPACT Magnetic Field Experiment.  _Space Sci. Rev._ , 136(1-4), 203–226.  10.1007/s11214-007-9259-2.
  * Aminalragia-Giamini et al. (2021) Aminalragia-Giamini, S., S. Raptis, A. Anastasiadis, A. Tsigkanos, I. Sandberg, A. Papaioannou, C. Papadimitriou, P. Jiggens, A. Aran, and I. A. Daglis, 2021.  Solar Energetic Particle Event occurrence prediction using Solar Flare Soft X-ray measurements and Machine Learning.  _J. Space Weather Space Clim._ , 11, 59.  10.1051/swsc/2021043.
  * Anastasiadis et al. (2019) Anastasiadis, A., D. Lario, A. Papaioannou, A. Kouloumvakos, and A. Vourlidas, 2019.  Solar energetic particles in the inner heliosphere: status and open questions.  _Phil. Trans. R. Soc. London Ser. A_ , 377(2148), 20180,100.  10.1098/rsta.2018.0100.
  * Anastasiadis et al. (2017) Anastasiadis, A., A. Papaioannou, I. Sandberg, M. Georgoulis, K. Tziotziou, A. Kouloumvakos, and P. Jiggens, 2017.  Predicting Flares and Solar Energetic Particle Events: The FORSPEF Tool.  _Sol. Phys._ , 292(9), 134.  10.1007/s11207-017-1163-7.
  * Arge et al. (2004) Arge, C. N., J. G. Luhmann, D. Odstrcil, C. J. Schrijver, and Y. Li, 2004\.  Stream structure and coronal sources of the solar wind during the May 12th, 1997 CME.  _J. Atmos. Solar-Terr. Phys._ , 66(15-16), 1295–1309.  10.1016/j.jastp.2004.03.018.
  * Arge and Pizzo (2000) Arge, C. N., and V. J. Pizzo, 2000.  Improvement in the prediction of solar wind conditions using near-real time solar magnetic field updates.  _J. Geophys. Res._ , 105(A5), 10,465–10,480.  10.1029/1999JA000262.
  * Bain et al. (2016) Bain, H. M., M. L. Mays, J. G. Luhmann, Y. Li, L. K. Jian, and D. Odstrcil, 2016.  Shock Connectivity in the August 2010 and July 2012 Solar Energetic Particle Events Inferred from Observations and ENLIL Modeling.  _ApJ_ , 825(1), 1.  10.3847/0004-637X/825/1/1.
  * Balch (1999) Balch, C. C., 1999.  SEC proton prediction model: verification and analysis.  _Radiat. Meas._ , 30(3), 231–250.  10.1016/S1350-4487(99)00052-9.
  * Balch (2008) Balch, C. C., 2008.  Updated verification of the Space Weather Prediction Center’s solar energetic particle prediction model.  _Space Weather_ , 6(1), S01001.  10.1029/2007SW000337.
  * Bale et al. (2016) Bale, S. D., K. Goetz, P. R. Harvey, P. Turin, J. W. Bonnell, et al., 2016\.  The FIELDS Instrument Suite for Solar Probe Plus. Measuring the Coronal Plasma and Magnetic Field, Plasma Waves and Turbulence, and Radio Signatures of Solar Transients.  _Space Sci. Rev._ , 204(1-4), 49–82.  10.1007/s11214-016-0244-5.
  * Bellman and Kalaba (1959) Bellman, R., and R. Kalaba, 1959.  On adaptive control processes.  _IEEE Trans. Automat. Contr._ , 4(2), 1–9.  10.1109/TAC.1959.1104847.
  * Benkhoff et al. (2021) Benkhoff, J., G. Murakami, W. Baumjohann, S. Besse, E. Bunce, et al., 2021\.  BepiColombo - Mission Overview and Science Goals.  _Space Sci. Rev._ , 217(8), 90.  10.1007/s11214-021-00861-4.
  * Bertello et al. (2014) Bertello, L., A. A. Pevtsov, G. J. D. Petrie, and D. Keys, 2014.  Uncertainties in Solar Synoptic Magnetic Flux Maps.  _Sol. Phys._ , 289(7), 2419–2431.  10.1007/s11207-014-0480-3, 1312.0509.
  * Brueckner et al. (1995) Brueckner, G. E., R. A. Howard, M. J. Koomen, C. M. Korendyke, D. J. Michels, et al., 1995.  The Large Angle Spectroscopic Coronagraph (LASCO).  _Sol. Phys._ , 162(1-2), 357–402.  10.1007/BF00733434.
  * Bruno and Richardson (2021) Bruno, A., and I. G. Richardson, 2021.  Empirical Model of 10 - 130 MeV Solar Energetic Particle Spectra at 1 AU Based on Coronal Mass Ejection Speed and Direction.  _Sol. Phys._ , 296(2), 36.  10.1007/s11207-021-01779-4, 2101.04234.
  * Cane et al. (2010) Cane, H. V., I. G. Richardson, and T. T. von Rosenvinge, 2010.  A study of solar energetic particle events of 1997-2006: Their composition and associations.  _J. Geophys. Res._ , 115(A8), A08101.  10.1029/2009JA014848.
  * Caplan et al. (2021) Caplan, R. M., C. Downs, J. A. Linker, and Z. Mikic, 2021.  Variations in Finite-difference Potential Fields.  _ApJ_ , 915(1), 44.  10.3847/1538-4357/abfd2f, 2102.05618.
  * Case et al. (2020) Case, A. W., J. C. Kasper, M. L. Stevens, K. E. Korreck, K. Paulson, et al., 2020.  The Solar Probe Cup on the Parker Solar Probe.  _ApJS_ , 246(2), 43.  10.3847/1538-4365/ab5a7b, 1912.02581.
  * Cohen et al. (2014) Cohen, C. M. S., G. M. Mason, R. A. Mewaldt, and M. E. Wiedenbeck, 2014\.  The Longitudinal Dependence of Heavy-ion Composition in the 2013 April 11 Solar Energetic Particle Event.  _ApJ_ , 793(1), 35.  10.1088/0004-637X/793/1/35.
  * Desai and Giacalone (2016) Desai, M., and J. Giacalone, 2016.  Large gradual solar energetic particle events.  _Living Rev. Sol. Phys._ , 13(1), 3.  10.1007/s41116-016-0002-5.
  * Ding et al. (2022) Ding, Z., N. Wijsen, G. Li, and S. Poedts, 2022.  Modeling the 2020 November 29 solar energetic particle event using EUHFORIA and iPATH models.  _A &A_, 668, A71.  10.1051/0004-6361/202244732, 2210.16967.
  * Domingo et al. (1995) Domingo, V., B. Fleck, and A. I. Poland, 1995.  The SOHO Mission: an Overview.  _Sol. Phys._ , 162(1-2), 1–37.  10.1007/BF00733425.
  * Dresing et al. (2014) Dresing, N., R. Gómez-Herrero, B. Heber, A. Klassen, O. Malandraki, W. Dröge, and Y. Kartavykh, 2014.  Statistical survey of widely spread out solar electron events observed with STEREO and ACE with special attention to anisotropies.  _A &A_, 567, A27.  10.1051/0004-6361/201423789.
  * Dresing et al. (2023) Dresing, N., L. Rodríguez-García, I. C. Jebaraj, A. Warmuth, S. Wallace, et al., 2023.  The 17 April 2021 widespread solar energetic particle event.  _A &A_, 674, A105.  10.1051/0004-6361/202345938, 2303.10969.
  * Dumbović et al. (2020) Dumbović, M., B. Vršnak, J. Guo, B. Heber, K. Dissauer, et al., 2020.  Evolution of Coronal Mass Ejections and the Corresponding Forbush Decreases: Modeling vs. Multi-Spacecraft Observations.  _Sol. Phys._ , 295(7), 104.  10.1007/s11207-020-01671-7, 2006.02253.
  * Fox et al. (2016) Fox, N. J., M. C. Velli, S. D. Bale, R. Decker, A. Driesman, et al., 2016\.  The Solar Probe Plus Mission: Humanity’s First Visit to Our Star.  _Space Sci. Rev._ , 204(1-4), 7–48.  10.1007/s11214-015-0211-6.
  * Galvin et al. (2008) Galvin, A. B., L. M. Kistler, M. A. Popecki, C. J. Farrugia, K. D. C. Simunac, et al., 2008.  The Plasma and Suprathermal Ion Composition (PLASTIC) Investigation on the STEREO Observatories.  _Space Sci. Rev._ , 136(1-4), 437–486.  10.1007/s11214-007-9296-x.
  * Giacalone and Jokipii (2001) Giacalone, J., and J. R. Jokipii, 2001.  The transport of energetic particles and cosmic rays in the heliosphere.  _Adv. Space Res._ , 27(3), 461–469.  10.1016/S0273-1177(01)00075-8.
  * Gopalswamy et al. (2009) Gopalswamy, N., S. Yashiro, G. Michalek, G. Stenborg, A. Vourlidas, S. Freeland, and R. Howard, 2009.  The SOHO/LASCO CME Catalog.  _Earth Moon Planets_ , 104(1-4), 295–313.  10.1007/s11038-008-9282-7.
  * Gressl et al. (2014) Gressl, C., A. M. Veronig, M. Temmer, D. Odstrčil, J. A. Linker, Z. Mikić, and P. Riley, 2014.  Comparative Study of MHD Modeling of the Background Solar Wind.  _Sol. Phys._ , 289(5), 1783–1801.  10.1007/s11207-013-0421-6, 1312.1220.
  * Harvey et al. (1996) Harvey, J. W., F. Hill, R. P. Hubbard, J. R. Kennedy, J. W. Leibacher, et al., 1996.  The Global Oscillation Network Group (GONG) Project.  _Science_ , 272(5266), 1284–1286.  10.1126/science.272.5266.1284.
  * Heyner et al. (2021) Heyner, D., H. U. Auster, K. H. Fornaçon, C. Carr, I. Richter, et al., 2021.  The BepiColombo Planetary Magnetometer MPO-MAG: What Can We Learn from the Hermean Magnetic Field?  _Space Sci. Rev._ , 217(4), 52.  10.1007/s11214-021-00822-x.
  * Horbury et al. (2020) Horbury, T. S., H. O’Brien, I. Carrasco Blazquez, M. Bendyk, P. Brown, et al., 2020.  The Solar Orbiter magnetometer.  _A &A_, 642, A9.  10.1051/0004-6361/201937257.
  * Howard et al. (2008) Howard, R. A., J. D. Moses, A. Vourlidas, J. S. Newmark, D. G. Socker, et al., 2008.  Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI).  _Space Sci. Rev._ , 136(1-4), 67–115.  10.1007/s11214-008-9341-4.
  * Jebaraj et al. (2023) Jebaraj, I. C., A. Kouloumvakos, N. Dresing, A. Warmuth, N. Wijsen, et al., 2023.  Multiple injections of energetic electrons associated with the flare and CME event on 9 October 2021.  _A &A_, 675, A27.  10.1051/0004-6361/202245716, 2301.03650.
  * Jian et al. (2015) Jian, L. K., P. J. MacNeice, A. Taktakishvili, D. Odstrcil, B. Jackson, H. S. Yu, P. Riley, I. V. Sokolov, and R. M. Evans, 2015\.  Validation for solar wind prediction at Earth: Comparison of coronal and heliospheric models installed at the CCMC.  _Space Weather_ , 13(5), 316–338.  10.1002/2015SW001174.
  * Jones and Ellison (1991) Jones, F. C., and D. C. Ellison, 1991.  The plasma physics of shock acceleration.  _Space Sci. Rev._ , 58(1), 259–346.  10.1007/BF01206003.
  * Kahler and Ling (2022) Kahler, S. W., and A. G. Ling, 2022.  A Comparison of Solar X-Ray Flare Timescales and Peak Temperatures with Associated Coronal Mass Ejections.  _ApJ_ , 934(2), 175.  10.3847/1538-4357/ac7e56.
  * Kaiser et al. (2008) Kaiser, M. L., T. A. Kucera, J. M. Davila, O. C. St. Cyr, M. Guhathakurta, and E. Christian, 2008.  The STEREO Mission: An Introduction.  _Space Sci. Rev._ , 136(1-4), 5–16.  10.1007/s11214-007-9277-0.
  * Kasapis et al. (2022) Kasapis, S., L. Zhao, Y. Chen, X. Wang, M. Bobra, and T. Gombosi, 2022\.  Interpretable Machine Learning to Forecast SEP Events for Solar Cycle 23.  _Space Weather_ , 20(2), e2021SW002842.  10.1029/2021SW002842.
  * Kasper et al. (2016) Kasper, J. C., R. Abiad, G. Austin, M. Balat-Pichelin, S. D. Bale, et al., 2016.  Solar Wind Electrons Alphas and Protons (SWEAP) Investigation: Design of the Solar Wind and Coronal Plasma Instrument Suite for Solar Probe Plus.  _Space Sci. Rev._ , 204(1-4), 131–186.  10.1007/s11214-015-0206-3.
  * Kollhoff et al. (2021) Kollhoff, A., A. Kouloumvakos, D. Lario, N. Dresing, R. Gómez-Herrero, et al., 2021.  The first widespread solar energetic particle event observed by Solar Orbiter on 2020 November 29.  _A &A_, 656, A20.  10.1051/0004-6361/202140937.
  * Kozarev et al. (2015) Kozarev, K. A., J. C. Raymond, V. V. Lobzin, and M. Hammer, 2015.  Properties of a Coronal Shock Wave as a Driver of Early SEP Acceleration.  _ApJ_ , 799(2), 167.  10.1088/0004-637X/799/2/167, 1406.2363.
  * Kwon et al. (2014) Kwon, R.-Y., J. Zhang, and O. Olmedo, 2014.  New Insights into the Physical Nature of Coronal Mass Ejections and Associated Shock Waves within the Framework of the Three-dimensional Structure.  _ApJ_ , 794(2), 148.  10.1088/0004-637X/794/2/148.
  * Laitinen et al. (2013) Laitinen, T., S. Dalla, and M. S. Marsh, 2013.  Energetic Particle Cross-field Propagation Early in a Solar Event.  _ApJ_ , 773(2), L29.  10.1088/2041-8205/773/2/L29, 1307.6362.
  * Laperre et al. (2020) Laperre, B., J. Amaya, and G. Lapenta, 2020.  Dynamic Time Warping as a New Evaluation for Dst Forecast with Machine Learning.  _Front. Astron. Space Sci._ , 7, 39.  10.3389/fspas.2020.00039, 2006.04667.
  * Lario and Karelitz (2014) Lario, D., and A. Karelitz, 2014.  Influence of interplanetary coronal mass ejections on the peak intensity of solar energetic particle events.  _J. Geophys. Res. Space Phys._ , 119(6), 4185–4209.  10.1002/2014JA019771.
  * Lario et al. (2016) Lario, D., R. Y. Kwon, A. Vourlidas, N. E. Raouafi, D. K. Haggerty, et al., 2016.  Longitudinal Properties of a Widespread Solar Energetic Particle Event on 2014 February 25: Evolution of the Associated CME Shock.  _ApJ_ , 819(1), 72.  10.3847/0004-637X/819/1/72.
  * Lario et al. (2014) Lario, D., N. E. Raouafi, R. Y. Kwon, J. Zhang, R. Gómez-Herrero, N. Dresing, and P. Riley, 2014.  The Solar Energetic Particle Event on 2013 April 11: An Investigation of its Solar Origin and Longitudinal Spread.  _ApJ_ , 797(1), 8.  10.1088/0004-637X/797/1/8, 1410.5490.
  * Lario et al. (1998) Lario, D., B. Sanahuja, and A. M. Heras, 1998.  Energetic Particle Events: Efficiency of Interplanetary Shocks as 50 keV $<$ E $<$ 100 MeV Proton Accelerators.  _ApJ_ , 509(1), 415–434.  10.1086/306461.
  * Lario et al. (2022) Lario, D., N. Wijsen, R. Y. Kwon, B. Sánchez-Cano, I. G. Richardson, et al., 2022.  Influence of Large-scale Interplanetary Structures on the Propagation of Solar Energetic Particles: The Multispacecraft Event on 2021 October 9.  _ApJ_ , 934(1), 55.  10.3847/1538-4357/ac6efd.
  * Laurenza et al. (2018) Laurenza, M., T. Alberti, and E. W. Cliver, 2018.  A Short-term ESPERTA-based Forecast Tool for Moderate-to-extreme Solar Proton Events.  _ApJ_ , 857(2), 107.  10.3847/1538-4357/aab712.
  * Lavasa et al. (2021) Lavasa, E., G. Giannopoulos, A. Papaioannou, A. Anastasiadis, I. A. Daglis, A. Aran, D. Pacheco, and B. Sanahuja, 2021.  Assessing the Predictability of Solar Energetic Particles with the Use of Machine Learning Techniques.  _Sol. Phys._ , 296(7), 107.  10.1007/s11207-021-01837-x.
  * Lee et al. (2015) Lee, C. O., C. N. Arge, D. Odstrcil, G. Millward, V. Pizzo, and N. Lugaz, 2015.  Ensemble Modeling of Successive Halo CMEs: A Case Study.  _Sol. Phys._ , 290(4), 1207–1229.  10.1007/s11207-015-0667-2.
  * Lemen et al. (2012) Lemen, J. R., A. M. Title, D. J. Akin, P. F. Boerner, C. Chou, et al., 2012.  The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO).  _Sol. Phys._ , 275(1-2), 17–40.  10.1007/s11207-011-9776-8.
  * Lepping et al. (1995) Lepping, R. P., M. H. Acũna, L. F. Burlaga, W. M. Farrell, J. A. Slavin, et al., 1995.  The Wind Magnetic Field Investigation.  _Space Sci. Rev._ , 71(1-4), 207–229.  10.1007/BF00751330.
  * Li et al. (2021) Li, G., M. Jin, Z. Ding, A. Bruno, G. A. de Nolfo, B. M. Randol, L. Mays, J. Ryan, and D. Lario, 2021.  Modeling the 2012 May 17 Solar Energetic Particle Event Using the AWSoM and iPATH Models.  _ApJ_ , 919(2), 146.  10.3847/1538-4357/ac0db9.
  * Lin (2011) Lin, R. P., 2011.  Energy Release and Particle Acceleration in Flares: Summary and Future Prospects.  _Space Sci. Rev._ , 159(1-4), 421–445.  10.1007/s11214-011-9801-0, 1110.1805.
  * Linker et al. (2019) Linker, J. A., R. M. Caplan, N. Schwadron, M. Gorby, C. Downs, T. Torok, R. Lionello, and J. Wijaya, 2019.  Coupled MHD-Focused Transport Simulations for Modeling Solar Particle Events.  _J. Phys. Conf. Ser._ , 1225, 012007.  10.1088/1742-6596/1225/1/012007, 1905.05299.
  * Liu et al. (2019a) Liu, Y. D., X. Zhao, H. Hu, A. Vourlidas, and B. Zhu, 2019a.  A Comparative Study of 2017 July and 2012 July Complex Eruptions: Are Solar Superstorms “Perfect Storms” in Nature?  _ApJS_ , 241(2), 15.  10.3847/1538-4365/ab0649, 1902.03416.
  * Liu et al. (2019b) Liu, Y. D., B. Zhu, and X. Zhao, 2019b.  Geometry, Kinematics, and Heliospheric Impact of a Large CME-driven Shock in 2017 September.  _ApJ_ , 871(1), 8.  10.3847/1538-4357/aaf425, 1811.10162.
  * Luhmann et al. (2008) Luhmann, J. G., D. W. Curtis, P. Schroeder, J. McCauley, R. P. Lin, et al., 2008.  STEREO IMPACT Investigation Goals, Measurements, and Data Products Overview.  _Space Sci. Rev._ , 136(1-4), 117–184.  10.1007/s11214-007-9170-x.
  * Luhmann et al. (2007) Luhmann, J. G., S. A. Ledvina, D. Krauss-Varban, D. Odstrcil, and P. Riley, 2007.  A heliospheric simulation-based approach to SEP source and transport modeling.  _Adv. Space Res._ , 40(3), 295–303.  10.1016/j.asr.2007.03.089.
  * Luhmann et al. (2010) Luhmann, J. G., S. A. Ledvina, D. Odstrcil, M. J. Owens, X. P. Zhao, Y. Liu, and P. Riley, 2010.  Cone model-based SEP event calculations for applications to multipoint observations.  _Adv. Space Res._ , 46(1), 1–21.  10.1016/j.asr.2010.03.011.
  * Luhmann et al. (2012) Luhmann, J. G., Y. Li, D. J. Bercik, L. Wang, and D. Odstrcil, 2012.  Issues in heliospheric field mapping to flare SEP sources.  In Q. Hu, G. Li, G. P. Zank, X. Ao, O. Verkhoglyadova, and J. H. Adams, eds., Space Weather: the Space Radiation Environment: 11th Annual International AstroPhysics Conference, vol. 1500 of _American Institute of Physics Conference Series_ , 3–13.  10.1063/1.4768737.
  * Magdalenić et al. (2010) Magdalenić, J., C. Marqué, A. N. Zhukov, B. Vršnak, and T. Žic, 2010.  Origin of Coronal Shock Waves Associated with Slow Coronal Mass Ejections.  _ApJ_ , 718(1), 266–278.  10.1088/0004-637X/718/1/266.
  * Maharana et al. (2022) Maharana, A., A. Isavnin, C. Scolini, N. Wijsen, L. Rodriguez, M. Mierla, J. Magdalenić, and S. Poedts, 2022.  Implementation and validation of the FRi3D flux rope model in EUHFORIA.  _Adv. Space Res._ , 70(6), 1641–1662.  10.1016/j.asr.2022.05.056, 2207.06707.
  * Masson et al. (2019) Masson, S., S. K. Antiochos, and C. R. DeVore, 2019.  Escape of Flare-accelerated Particles in Solar Eruptive Events.  _ApJ_ , 884(2), 143.  10.3847/1538-4357/ab4515, 1909.13578.
  * Mays et al. (2015) Mays, M. L., B. J. Thompson, L. K. Jian, R. C. Colaninno, D. Odstrcil, et al., 2015.  Propagation of the 7 January 2014 CME and Resulting Geomagnetic Non-event.  _ApJ_ , 812(2), 145.  10.1088/0004-637X/812/2/145, 1509.06477.
  * McComas et al. (2016) McComas, D. J., N. Alexander, N. Angold, S. Bale, C. Beebe, et al., 2016\.  Integrated Science Investigation of the Sun (ISIS): Design of the Energetic Particle Investigation.  _Space Sci. Rev._ , 204(1-4), 187–256.  10.1007/s11214-014-0059-1.
  * Mewaldt et al. (2008) Mewaldt, R. A., C. M. S. Cohen, W. R. Cook, A. C. Cummings, A. J. Davis, et al., 2008.  The Low-Energy Telescope (LET) and SEP Central Electronics for the STEREO Mission.  _Space Sci. Rev._ , 136(1-4), 285–362.  10.1007/s11214-007-9288-x.
  * Müller et al. (2020) Müller, D., O. C. St. Cyr, I. Zouganelis, H. R. Gilbert, R. Marsden, et al., 2020.  The Solar Orbiter mission. Science overview.  _A &A_, 642, A1.  10.1051/0004-6361/202038467, 2009.00861.
  * Müller-Mellin et al. (1995) Müller-Mellin, R., H. Kunow, V. Fleißner, E. Pehlke, E. Rode, et al., 1995.  COSTEP - Comprehensive Suprathermal and Energetic Particle Analyser.  _Sol. Phys._ , 162(1-2), 483–504.  10.1007/BF00733437.
  * Nitta et al. (2006) Nitta, N. V., D. V. Reames, M. L. De Rosa, Y. Liu, S. Yashiro, and N. Gopalswamy, 2006.  Solar Sources of Impulsive Solar Energetic Particle Events and Their Magnetic Field Connection to the Earth.  _ApJ_ , 650(1), 438–450.  10.1086/507442.
  * Núñez et al. (2017) Núñez, M., P. J. Reyes-Santiago, and O. E. Malandraki, 2017.  Real-time prediction of the occurrence of GLE events.  _Space Weather_ , 15(7), 861–873.  10.1002/2017SW001605.
  * Odstrcil (2003) Odstrcil, D., 2003.  Modeling 3-D solar wind structure.  _Adv. Space Res._ , 32(4), 497–506.  10.1016/S0273-1177(03)00332-6.
  * Odstrcil et al. (2004) Odstrcil, D., P. Riley, and X. P. Zhao, 2004.  Numerical simulation of the 12 May 1997 interplanetary CME event.  _J. Geophys. Res._ , 109(A2), A02116.  10.1029/2003JA010135.
  * Ogilvie et al. (1995) Ogilvie, K. W., D. J. Chornay, R. J. Fritzenreiter, F. Hunsaker, J. Keller, et al., 1995.  SWE, A Comprehensive Plasma Instrument for the Wind Spacecraft.  _Space Sci. Rev._ , 71(1-4), 55–77.  10.1007/BF00751326.
  * Ogilvie and Desch (1997) Ogilvie, K. W., and M. D. Desch, 1997.  The wind spacecraft and its early scientific results.  _Adv. Space Res._ , 20(4-5), 559–568.  10.1016/S0273-1177(97)00439-0.
  * Owen et al. (2020) Owen, C. J., R. Bruno, S. Livi, P. Louarn, K. Al Janabi, et al., 2020\.  The Solar Orbiter Solar Wind Analyser (SWA) suite.  _A &A_, 642, A16.  10.1051/0004-6361/201937259.
  * Palmerio et al. (2021) Palmerio, E., E. K. J. Kilpua, O. Witasse, D. Barnes, B. Sánchez-Cano, et al., 2021.  CME Magnetic Structure and IMF Preconditioning Affecting SEP Transport.  _Space Weather_ , 19(4), e2020SW002654.  10.1029/2020SW002654, 2102.05514.
  * Palmerio et al. (2022) Palmerio, E., C. O. Lee, M. L. Mays, J. G. Luhmann, D. Lario, et al., 2022\.  CMEs and SEPs During November-December 2020: A Challenge for Real-Time Space Weather Forecasting.  _Space Weather_ , 20(5), e2021SW002993.  10.1029/2021SW002993, 2203.16433.
  * Paouris et al. (2021) Paouris, E., J. Čalogović, M. Dumbović, M. L. Mays, A. Vourlidas, A. Papaioannou, A. Anastasiadis, and G. Balasis, 2021.  Propagating Conditions and the Time of ICME Arrival: A Comparison of the Effective Acceleration Model with ENLIL and DBEM Models.  _Sol. Phys._ , 296(1), 12.  10.1007/s11207-020-01747-4, 2012.05857.
  * Papaioannou et al. (2016) Papaioannou, A., I. Sandberg, A. Anastasiadis, A. Kouloumvakos, M. K. Georgoulis, K. Tziotziou, G. Tsiropoula, P. Jiggens, and A. Hilgers, 2016.  Solar flares, coronal mass ejections and solar energetic particle event characteristics.  _J. Space Weather Space Clim._ , 6, A42.  10.1051/swsc/2016035.
  * Parenti et al. (2021) Parenti, S., I. Chifu, G. Del Zanna, J. Edmondson, A. Giunta, et al., 2021\.  Linking the Sun to the Heliosphere Using Composition Data and Modelling.  _Space Sci. Rev._ , 217(8), 78.  10.1007/s11214-021-00856-1, 2110.06111.
  * Pesnell et al. (2012) Pesnell, W. D., B. J. Thompson, and P. C. Chamberlin, 2012.  The Solar Dynamics Observatory (SDO).  _Sol. Phys._ , 275(1-2), 3–15.  10.1007/s11207-011-9841-3.
  * Pinto et al. (2022) Pinto, M., B. Sanchez-Cano, R. Moissl, J. Benkhoff, C. Cardoso, et al., 2022.  The BepiColombo Environment Radiation Monitor, BERM.  _Space Sci. Rev._ , 218(7), 54.  10.1007/s11214-022-00922-2.
  * Pomoell and Poedts (2018) Pomoell, J., and S. Poedts, 2018.  EUHFORIA: European heliospheric forecasting information asset.  _J. Space Weather Space Clim._ , 8, A35.  10.1051/swsc/2018020.
  * Posner (2007) Posner, A., 2007.  Up to 1-hour forecasting of radiation hazards from solar energetic ion events with relativistic electrons.  _Space Weather_ , 5(5), 05001.  10.1029/2006SW000268.
  * Qin et al. (2004) Qin, G., M. Zhang, J. R. Dwyer, and H. K. Rassoul, 2004.  Interplanetary Transport Mechanisms of Solar Energetic Particles.  _ApJ_ , 609(2), 1076–1081.  10.1086/421101.
  * Reames (1999) Reames, D. V., 1999.  Particle acceleration at the Sun and in the heliosphere.  _Space Sci. Rev._ , 90, 413–491.  10.1023/A:1005105831781.
  * Reiss et al. (2023a) Reiss, M. A., C. N. Arge, C. J. Henney, J. A. Klimchuk, J. A. Linker, K. Muglach, A. A. Pevtsov, R. F. Pinto, and S. J. Schonfeld, 2023a.  Progress and challenges in understanding the ambient solar magnetic field, heating, and spectral irradiance.  _Adv. Space Res._ , in press.  10.1016/j.asr.2023.08.039.
  * Reiss et al. (2023b) Reiss, M. A., K. Muglach, R. Mullinix, M. M. Kuznetsova, C. Wiegand, et al., 2023b.  Unifying the validation of ambient solar wind models.  _Adv. Space Res._ , 72(12), 5275–5286.  10.1016/j.asr.2022.05.026, 2201.13447.
  * Richardson and Cane (1996) Richardson, I. G., and H. V. Cane, 1996.  Particle flows observed in ejecta during solar event onsets and their implication for the magnetic field topology.  _J. Geophys. Res._ , 101(A12), 27,521–27,532.  10.1029/96JA02643.
  * Richardson et al. (2014) Richardson, I. G., T. T. von Rosenvinge, H. V. Cane, E. R. Christian, C. M. S. Cohen, A. W. Labrador, R. A. Leske, R. A. Mewaldt, M. E. Wiedenbeck, and E. C. Stone, 2014.  $>$ 25 MeV Proton Events Observed by the High Energy Telescopes on the STEREO A and B Spacecraft and/or at Earth During the First $\sim$ Seven Years of the STEREO Mission.  _Sol. Phys._ , 289(8), 3059–3107.  10.1007/s11207-014-0524-8.
  * Riley et al. (2014) Riley, P., M. Ben-Nun, J. A. Linker, Z. Mikic, L. Svalgaard, J. Harvey, L. Bertello, T. Hoeksema, Y. Liu, and R. Ulrich, 2014.  A Multi-Observatory Inter-Comparison of Line-of-Sight Synoptic Solar Magnetograms.  _Sol. Phys._ , 289(3), 769–792.  10.1007/s11207-013-0353-1.
  * Riley et al. (2018) Riley, P., M. L. Mays, J. Andries, T. Amerstorfer, D. Biesecker, et al., 2018.  Forecasting the Arrival Time of Coronal Mass Ejections: Analysis of the CCMC CME Scoreboard.  _Space Weather_ , 16(9), 1245–1260.  10.1029/2018SW001962, 1810.07289.
  * Rodríguez-Pacheco et al. (2020) Rodríguez-Pacheco, J., R. F. Wimmer-Schweingruber, G. M. Mason, G. C. Ho, S. Sánchez-Prieto, et al., 2020.  The Energetic Particle Detector. Energetic particle instrument suite for the Solar Orbiter mission.  _A &A_, 642, A7.  10.1051/0004-6361/201935287.
  * Rouillard et al. (2012) Rouillard, A. P., N. R. Sheeley, A. Tylka, A. Vourlidas, C. K. Ng, et al., 2012.  The Longitudinal Properties of a Solar Energetic Particle Event Investigated Using Modern Solar Imaging.  _ApJ_ , 752(1), 44.  10.1088/0004-637X/752/1/44.
  * Samara et al. (2022) Samara, E., B. Laperre, R. Kieokaew, M. Temmer, C. Verbeke, L. Rodriguez, J. Magdalenić, and S. Poedts, 2022.  Dynamic Time Warping as a Means of Assessing Solar Wind Time Series.  _ApJ_ , 927(2), 187.  10.3847/1538-4357/ac4af6, 2109.07873.
  * Schwadron et al. (2010) Schwadron, N. A., L. Townsend, K. Kozarev, M. A. Dayeh, F. Cucinotta, et al., 2010.  Earth-Moon-Mars Radiation Environment Module framework.  _Space Weather_ , 8(10), S00E02.  10.1029/2009SW000523.
  * Scolini et al. (2019) Scolini, C., L. Rodriguez, M. Mierla, J. Pomoell, and S. Poedts, 2019\.  Observation-based modelling of magnetised coronal mass ejections with EUHFORIA.  _A &A_, 626, A122.  10.1051/0004-6361/201935053, 1904.07059.
  * Singh et al. (2022) Singh, T., T. K. Kim, N. V. Pogorelov, and C. N. Arge, 2022.  Ensemble Simulations of the 2012 July 12 Coronal Mass Ejection with the Constant-turn Flux Rope Model.  _ApJ_ , 933(2), 123.  10.3847/1538-4357/ac73f3, 2205.13009.
  * Sokolov et al. (2004) Sokolov, I. V., I. I. Roussev, T. I. Gombosi, M. A. Lee, J. Kóta, T. G. Forbes, W. B. Manchester, and J. I. Sakai, 2004.  A New Field Line Advection Model for Solar Particle Acceleration.  _ApJ_ , 616(2), L171–L174.  10.1086/426812.
  * Temmer et al. (2023) Temmer, M., C. Scolini, I. G. Richardson, S. G. Heinemann, E. Paouris, et al., 2023.  CME Propagation Through the Heliosphere: Status and Future of Observations and Model Development.  _Adv. Space Res._ , in press.  10.1016/j.asr.2023.07.003, 2308.04851.
  * Tenishev et al. (2021) Tenishev, V., Y. Shou, D. Borovikov, Y. Lee, N. Fougere, A. Michael, and M. R. Combi, 2021.  Application of the Monte Carlo Method in Modeling Dusty Gas, Dust in Plasma, and Energetic Ions in Planetary, Magnetospheric, and Heliospheric Environments.  _J. Geophys. Res. Space Phys._ , 126(2), e28242.  10.1029/2020JA028242.
  * Thernisien (2011) Thernisien, A., 2011.  Implementation of the Graduated Cylindrical Shell Model for the Three-dimensional Reconstruction of Coronal Mass Ejections.  _ApJS_ , 194(2), 33.  10.1088/0067-0049/194/2/33.
  * Trottet et al. (2015) Trottet, G., S. Samwel, K. L. Klein, T. Dudok de Wit, and R. Miteva, 2015\.  Statistical Evidence for Contributions of Flares and Coronal Mass Ejections to Major Solar Energetic Particle Events.  _Sol. Phys._ , 290(3), 819–839.  10.1007/s11207-014-0628-1, 1411.4133.
  * Verbeke et al. (2023) Verbeke, C., M. L. Mays, C. Kay, P. Riley, E. Palmerio, et al., 2023.  Quantifying errors in 3D CME parameters derived from synthetic data using white-light reconstruction techniques.  _Adv. Space Res._ , 72(12), 5243–5262.  10.1016/j.asr.2022.08.056, 2302.00531.
  * von Rosenvinge et al. (2008) von Rosenvinge, T. T., D. V. Reames, R. Baker, J. Hawk, J. T. Nolan, et al., 2008.  The High Energy Telescope for STEREO.  _Space Sci. Rev._ , 136(1-4), 391–435.  10.1007/s11214-007-9300-5.
  * Vršnak and Cliver (2008) Vršnak, B., and E. W. Cliver, 2008.  Origin of Coronal Shock Waves. Invited Review.  _Sol. Phys._ , 253(1-2), 215.  10.1007/s11207-008-9241-5.
  * Wang and Sheeley (1992) Wang, Y. M., and J. Sheeley, N. R., 1992.  On Potential Field Models of the Solar Corona.  _ApJ_ , 392, 310.  10.1086/171430.
  * Wellbrock et al. (2022) Wellbrock, A., G. H. Jones, N. Dresing, A. J. Coates, C. Simon Wedlund, et al., 2022.  Observations of a Solar Energetic Particle Event From Inside and Outside the Coma of Comet 67P.  _J. Geophys. Res. Space Phys._ , 127(12), e2022JA030398.  10.1029/2022JA030398.
  * Whitman et al. (2023) Whitman, K., R. Egeland, I. G. Richardson, C. Allison, P. Quinn, et al., 2023.  Review of Solar Energetic Particle Prediction Models.  _Adv. Space Res._ , 72(12), 5161–5242.  10.1016/j.asr.2022.08.006.
  * Wijsen et al. (2019) Wijsen, N., A. Aran, J. Pomoell, and S. Poedts, 2019.  Modelling three-dimensional transport of solar energetic protons in a corotating interaction region generated with EUHFORIA.  _A &A_, 622, A28.  10.1051/0004-6361/201833958, 1901.09596.
  * Wijsen et al. (2022) Wijsen, N., A. Aran, C. Scolini, D. Lario, A. Afanasiev, R. Vainio, B. Sanahuja, J. Pomoell, and S. Poedts, 2022.  Observation-based modelling of the energetic storm particle event of 14 July 2012.  _A &A_, 659, A187.  10.1051/0004-6361/202142698, 2201.06454.
  * Wijsen et al. (2023) Wijsen, N., D. Lario, B. Sánchez-Cano, I. C. Jebaraj, N. Dresing, et al., 2023.  The Effect of the Ambient Solar Wind Medium on a CME-driven Shock and the Associated Gradual Solar Energetic Particle Event.  _ApJ_ , 950(2), 172.  10.3847/1538-4357/acd1ed, 2305.09525.
  * Wold et al. (2018) Wold, A. M., M. L. Mays, A. Taktakishvili, L. K. Jian, D. Odstrcil, and P. MacNeice, 2018.  Verification of real-time WSA-ENLIL+Cone simulations of CME arrival-time at the CCMC from 2010 to 2016.  _J. Space Weather Space Clim._ , 8, A17.  10.1051/swsc/2018005, 1801.07818.
  * Xie et al. (2017) Xie, H., P. Mäkelä, O. C. St. Cyr, and N. Gopalswamy, 2017.  Comparison of the coronal mass ejection shock acceleration of three widespread SEP events during solar cycle 24.  _J. Geophys. Res. Space Phys._ , 122(7), 7021–7041.  10.1002/2017JA024218.
  * Yang et al. (2023) Yang, L., C. Hou, X. Feng, J. He, M. Xiong, et al., 2023.  Global Morphology Distortion of the 2021 October 9 Coronal Mass Ejection from an Ellipsoid to a Concave Shape.  _ApJ_ , 942(2), 65.  10.3847/1538-4357/aca52d.
  * Young et al. (2021) Young, M. A., N. A. Schwadron, M. Gorby, J. Linker, R. M. Caplan, et al., 2021.  Energetic Proton Propagation and Acceleration Simulated for the Bastille Day Event of 2000 July 14.  _ApJ_ , 909(2), 160.  10.3847/1538-4357/abdf5f, 2012.09078.
  * Zank et al. (2015) Zank, G. P., P. Hunana, P. Mostafavi, J. A. Le Roux, G. Li, G. M. Webb, O. Khabarova, A. Cummings, E. Stone, and R. Decker, 2015.  Diffusive Shock Acceleration and Reconnection Acceleration Processes.  _ApJ_ , 814(2), 137.  10.1088/0004-637X/814/2/137.
  * Zhang et al. (2003) Zhang, M., J. R. Jokipii, and R. B. McKibben, 2003.  Perpendicular Transport of Solar Energetic Particles in Heliospheric Magnetic Fields.  _ApJ_ , 595(1), 493–499.  10.1086/377301.
  * Zhang and Zhao (2017) Zhang, M., and L. Zhao, 2017.  Precipitation and Release of Solar Energetic Particles from the Solar Coronal Magnetic Field.  _ApJ_ , 846(2), 107.  10.3847/1538-4357/aa86a8.