# CMEs and SEPs During November–December 2020: A Challenge for Real-Time Space
Weather Forecasting

###### Abstract

Predictions of coronal mass ejections (CMEs) and solar energetic particles
(SEPs) are a central issue in space weather forecasting. In recent years,
interest in space weather predictions has expanded to include impacts at other
planets beyond Earth as well as spacecraft scattered throughout the
heliosphere. In this sense, the scope of space weather science now encompasses
the whole heliospheric system, and multi-point measurements of solar
transients can provide useful insights and validations for prediction models.
In this work, we aim to analyse the whole inner heliospheric context between
two eruptive flares that took place in late 2020, i.e. the M4.4 flare of
November 29 and the C7.4 flare of December 7. This period is especially
interesting because the STEREO-A spacecraft was located ${\sim}60^{\circ}$
east of the Sun–Earth line, giving us the opportunity to test the capabilities
of “predictions at $360^{\circ}$” using remote-sensing observations from the
Lagrange L1 and L5 points as input. We simulate the CMEs that were ejected
during our period of interest and the SEPs accelerated by their shocks using
the WSA–Enlil–SEPMOD modelling chain and four sets of input parameters,
forming a “mini-ensemble”. We validate our results using in-situ observations
at six locations, including Earth and Mars. We find that, despite some
limitations arising from the models’ architecture and assumptions, CMEs and
shock-accelerated SEPs can be reasonably studied and forecast in real time at
least out to several tens of degrees away from the eruption site using the
prediction tools employed here.

Space Weather

Space Sciences Laboratory, University of California–Berkeley, Berkeley, CA
94720, USA CPAESS, University Corporation for Atmospheric Research, Boulder,
CO 80301, USA Heliophysics Science Division, NASA Goddard Space Flight Center,
Greenbelt, MD 20771, USA School of Physics and Astronomy, University of
Leicester, Leicester, LE1 7RH, UK Department of Astronomy, University of
Maryland, College Park, MD 20742, USA Department of Physics and Astronomy,
University of Turku, FI-20014 Turku, Finland Harvard–Smithsonian Center for
Astrophysics, Cambridge, MA 02138, USA California Institute of Technology,
Pasadena, CA 91125, USA Swedish Institute of Space Physics, S-75121 Uppsala,
Sweden Department of Physics and Astronomy, Uppsala University, S-75120
Uppsala, Sweden Space Research Institute, Austrian Academy of Sciences, A-8042
Graz, Austria Institute of Physics, University of Graz, A-8010 Graz, Austria
Institut für Geophysik und extraterrestrische Physik, TU Braunschweig, D-38106
Braunschweig, Germany Physics Department, University of California–Berkeley,
Berkeley, CA 94720, USA Space Science Center, University of New Hampshire,
Durham, NH 03824, USA Swedish Institute of Space Physics, S-98192 Kiruna,
Sweden LESIA, Observatoire de Paris, Univ. PSL, CNRS, Sorbonne Univ., Univ.
Paris Diderot, F-92195 Meudon, France Institute for Space Research, RU-117997
Moscow, Russian Federation

E<EMAIL_ADDRESS>
We model the inner heliospheric context between the two eruptive flares of
2020 Nov 29 and Dec 7 using the WSA–Enlil–SEPMOD modelling chain

CME input parameters are obtained using remote-sensing observations from Earth
and STEREO-A, located near the L5 point

The modelling setup used in this work can provide useful CME and shock-
accelerated SEP predictions in real-time forecasts

Coronal mass ejections (CMEs) and solar energetic particles (SEPs) are
phenomena from the Sun that are able to cause significant disturbances at
Earth and other planets. Reliable predictions of these events and their
effects are amongst the major goals of space weather forecasts, which aim to
tackle all processes related to solar activity that can endanger human
technology and society. In recent years, the breadth of space weather science
has started to encompass other locations than Earth, ranging from all solar
system planets to spacecraft scattered throughout space. In this work, we test
our current capabilities in predicting space weather events in the inner solar
system (i.e., within the orbit of Mars) for a period in late 2020. We use a
chain of models that are able to simulate the background solar wind as well as
transient phenomena such as CMEs and SEPs, and compare our results with
spacecraft measurements from six well-separated locations, including Earth and
Mars. We find that our current forecasting tools, despite their limitations,
can successfully provide reasonable predictions of both CMEs and SEPs,
especially out to several tens of degrees around the corresponding eruption
source region on the Sun.

##  1 Introduction

Coronal mass ejections (CMEs; e.g., Webb and Howard, 2012) and solar energetic
particles (SEPs; e.g., Reames, 2021) are manifestations of the variable solar
activity and important drivers of space weather effects at Earth and other
planets (e.g., Eastwood et al., 2017; Koskinen et al., 2017; Temmer, 2021). A
CME impacting Earth’s magnetosphere may trigger a geomagnetic storm depending
on its kinematic and magnetic properties (e.g., Gonzalez et al., 1994; Zhang
et al., 2007). SEPs accelerated by solar flares and/or CME-driven shocks are
able to reach energies of tens of MeV/nuc or higher and may penetrate Earth’s
ionosphere (e.g., Klein and Dalla, 2017; Malandraki and Crosby, 2018) or even
produce secondary particles that reach the ground (causing a so-called ‘ground
level enhancement’ or GLE; e.g., Nitta et al., 2012; Shea and Smart, 2012).
These phenomena frequently occur in concert, especially in the case of large
and fast CMEs that are associated with strong flares and that are able to
accelerate particles at the shocks ahead of them, generating so-called
‘gradual’ SEP events (e.g., Desai and Giacalone, 2016). Amongst the active
areas of CME and SEP research, significant efforts are dedicated to improving
forecasts of their arrival and space weather impact at a given location in the
heliosphere. Recent reviews on the current status of space weather science
were compiled by Vourlidas et al. (2019) for CMEs and by Anastasiadis et al.
(2019) for SEPs.

The interplanetary propagation of CMEs has been addressed during the past
couple of decades by the development of a multitude of models, ranging from
numerical (based on magnetohydrodynamics or MHD equations, e.g., Odstrcil and
Pizzo, 1999; Pomoell and Poedts, 2018; Wu et al., 2007) to analytical (e.g.,
Corona-Romero et al., 2017; Hess and Zhang, 2015; Vršnak et al., 2013) to
empirical (e.g., Gopalswamy et al., 2001; Paouris and Mavromichalaki, 2017;
Vršnak and Žic, 2007). The plethora of existing prediction tools has drawn the
space weather community towards coordinated, international efforts (see, e.g.,
the CME Arrival Time and Impact Working Team:
https://ccmc.gsfc.nasa.gov/iswat/CME-Arrival-Time-Working-Team) focused on
benchmarking CME forecasts, especially in terms of hit/miss and arrival time
(e.g., Riley et al., 2018; Verbeke et al., 2019a; Wold et al., 2018; Zhao and
Dryer, 2014). These studies found out that, despite continued efforts, typical
uncertainties for arrival time are still of the order of ${\pm}10$ hours and
typical accuracies in determining a hit or a miss lie around 85%. Predictions
of the magnetic structure of CMEs, also known as $B_{Z}$ forecasts, are
currently even less advanced (e.g., Kilpua et al., 2019), although this issue
has gained significant momentum during recent years and is being tackled with
MHD (e.g., Jin et al., 2017; Shiota and Kataoka, 2016; Verbeke et al., 2019b),
analytical (e.g., Isavnin, 2016; Kay et al., 2022; Möstl et al., 2018), and
machine learning (e.g., Reiss et al., 2021) models.

Predictions of SEPs have also been explored with a number of physics-based
(e.g., Marsh et al., 2015; Schwadron et al., 2010; Zhang and Zhao, 2017),
empirical (e.g., Anastasiadis et al., 2017; Bruno and Richardson, 2021;
Posner, 2007; Richardson et al., 2018), and machine learning (e.g., Kasapis et
al., 2022; Lavasa et al., 2021; Stumpo et al., 2021) models, some of which can
additionally be coupled with coronal and/or heliospheric MHD simulations to
investigate time-dependent particle acceleration (e.g., Luhmann et al., 2017;
Wijsen et al., 2021; Young et al., 2021). International efforts (see, e.g.,
the SEP Validation Team: https://ccmc.gsfc.nasa.gov/iswat/SEP-Validation-Team)
are underway to assess the current status of SEP forecasting and to establish
community-wide metrics. Recently, Bain et al. (2021) assessed the performance
of the National Oceanic and Atmospheric Administration’s Space Weather
Prediction Center (NOAA/SWPC) proton event forecasts, finding for ${\geq}10$
MeV (${\geq}100$ MeV) proton warnings a probability of detection of 91% (53%)
and a false alarm ratio of 24% (38%), with a median lead time of 88 min (10
min). The authors suggested that these results may serve as a benchmark for
SEP models that can operate in a nowcast setting, and noted that a particular
challenge is to accurately predict the onset, peak, and end times and fluxes
of SEP events in different energy ranges.

In addition to dedicated efforts in the context of space weather, which are
traditionally focused on the Sun–Earth chain, the research community has also
taken advantage of data from multiple spacecraft forming part of the
Heliophysics System Observatory to perform multi-point studies of CMEs (e.g.,
Burlaga et al., 1981; Davies et al., 2020; Palmerio et al., 2021a; Witasse et
al., 2017) and SEPs (e.g., Bruno and Richardson, 2021; Lee et al., 2018;
Richardson et al., 2014; Rodríguez-García et al., 2021) at well-separated
locations in both longitude and heliocentric distance. Such works have
uncovered myriad characteristics and processes that may not be identified
based on single-viewpoint in-situ measurements or require statistical surveys
of large samples of events. These include the detection of longitudinal
variations in the shape of CME-driven shock fronts and/or the magnetic
structure of flux ropes within CMEs (e.g., Farrugia et al., 2011; Kilpua et
al., 2011; Mulligan et al., 2013), the characterisation of the radial
evolution of CMEs (e.g., Good et al., 2019; Salman et al., 2020; Vršnak et
al., 2019), the observation of unexpectedly large longitudinal spreads for
some SEP events (e.g., Dresing et al., 2012; Gómez-Herrero et al., 2015;
Palmerio et al., 2021b; Wiedenbeck et al., 2013), and the investigation of the
longitudinal variation of SEP profiles and properties (e.g., Cohen et al.,
2014; Lario et al., 2006, 2013, 2016; Rouillard et al., 2012). Furthermore,
multi-point data for a single event can provide useful constraints and
validation for CME and SEP propagation models.

An additional level of complexity is given by periods that are characterised
by several, successive eruptions (see Lugaz et al., 2017, for a review), which
can lead to solar wind as well as interplanetary magnetic field
preconditioning and thus result in altered (sometimes enhanced) CME
geoeffectiveness (e.g., Liu et al., 2014; Scolini et al., 2020) and higher SEP
fluxes (e.g., Lario and Karelitz, 2014; Richardson and Cane, 1996). In this
regard, studies that aim to analyse and/or model successive CME and SEP events
measured at different, well-separated locations in the inner heliosphere
(e.g., Bain et al., 2016; Dumbović et al., 2019; Luhmann et al., 2018; Möstl
et al., 2012; Palmerio et al., 2019) undertake the holistic approach necessary
to better understand the whole heliospheric context and the interplay of
complex processes. The recent years have seen the launch of three missions
(i.e., Parker Solar Probe, BepiColombo, and Solar Orbiter) that are currently
cruising and sampling the solar wind in the inner heliosphere. These “newer”
spacecraft, together with the “older” but still operational ones (i.e.,
STEREO-A and those near Earth and Mars), represent an excellent opportunity to
test, validate, and improve our current modelling capabilities and
understanding of the inner heliosphere “at $360^{\circ}$”.

Using this framework, the aim of this article is to use observations and
modelling to understand the heliospheric context (including CMEs and SEPs)
following two noteworthy eruptive flares that took place in late 2020, namely
the M4.4 flare of November 29 (originating from S25E96 in Stonyhurst
coordinates and peaking at 13:11 UT) and the C7.4 flare of December 7
(originating from S25W08 in Stonyhurst coordinates and peaking at 16:32
UT)—hereafter, Flare1 and Flare2. Both commenced from the same source region,
AR 12790, which was still behind the Earth-facing eastern limb at the time of
Flare1, indicating that its “true” X-ray class might have been even higher
than observed. The first of these eruptions has already gained significant
attention, since it was associated with the first widespread SEP event of
Solar Cycle 25 and with a CME detected in situ by the Parker Solar Probe and
STEREO-A spacecraft (e.g., Cohen et al., 2021; Giacalone et al., 2021;
Kollhoff et al., 2021; Kouloumvakos et al., 2022; Lario et al., 2021; Mason et
al., 2021; Mitchell et al., 2021; Möstl et al., 2022; Nieves-Chinchilla et
al., 2022). The configurations of planets and spacecraft within the orbit of
Mars on the days of the two flares are shown in Figure 1. An interesting
aspect is that STEREO-A was located ${\sim}60^{\circ}$ east of Earth, thus
providing the opportunity to test modelling and forecasting capabilities based
on observations from the Lagrange L1 (Earth) and L5 (STEREO-A) points. This
article is organised as follows: In Section 2, we provide an overview of the
spacecraft instrumentation and data sets employed in this study. In Section 3,
we describe the the simulation setup and the different sets of CME input
parameters used to generate a “mini-ensemble” of model runs of the inner
heliosphere. In Section 4, we present the simulation results and compare them
with in-situ solar wind and SEP observations from six locations. In Section 5
we discuss the implications of our results for space weather forecasting and
in Section 6 we summarise our study and draw our conclusions.

Figure 1: Position of planets and spacecraft in the inner heliosphere on (a)
2020 November 29 and (b) 2020 December 7. The orbits of all planets are also
indicated. The locations of (a) Flare1 and (b) Flare2 are marked with star
symbols on the surface of the Sun. Bepi = BepiColombo; PSP = Parker Solar
Probe; SolO = Solar Orbiter; ST-A = STEREO-A.

##  2 Spacecraft Data

The observations used in this study include remote-sensing observations from
two viewpoints (Earth and STEREO-A, representing views from L1 and L5,
respectively) and in-situ measurements from six locations (Parker Solar Probe,
STEREO-A, Mars, Earth, BepiColombo, and Solar Orbiter) as shown in Figure 1.
The corresponding heliocentric distances throughout the analysed period are
approximately: 0.79 AU for Parker Solar Probe, 0.96 AU for STEREO-A, 1.47 AU
for Mars, 0.99 AU for Earth, 0.83 AU for BepiColombo, and 0.86 AU for Solar
Orbiter. Remote-sensing observations include extreme ultra-violet (EUV) solar
disc and white-light (WL) coronagraph data, whilst in-situ measurements
include, where available, magnetic field, plasma, and energetic particle data.
In the following, we refer to SEPs of energy in the range ${\sim}1$–$10$ MeV
as “lower-energy particles” and those of energy ${\gtrsim}10$ MeV as “higher-
energy particles”. All particle data employed here refer to protons.

  * •

Remote-sensing observations: EUV images of the solar disc wavelengths are
provided by the Atmospheric Imaging Assembly (AIA; Lemen et al., 2012) onboard
the Solar Dynamics Observatory (SDO; Pesnell et al., 2012) orbiting Earth and
the Extreme UltraViolet Imager (EUVI) part of the Sun Earth Connection Coronal
and Heliospheric Investigation (SECCHI; Howard et al., 2008) suite onboard the
Solar Terrestrial Relations Observatory (STEREO; Kaiser et al., 2008) Ahead
(STEREO-A) spacecraft. WL coronagraph imagery is supplied by the C2 and C3
telescopes of the Large Angle and Spectrometric Coronagraph (LASCO; Brueckner
et al., 1995) onboard the Solar and Heliospheric Observatory (SOHO; Domingo et
al., 1995) at Earth’s Lagrange L1 point and the COR2 camera of SECCHI onboard
STEREO-A.

  * •

Parker Solar Probe: At the Parker Solar Probe (PSP; Fox et al., 2016)
spacecraft, we use magnetic field measurements from the fluxgate magnetometer
part of the FIELDS (Bale et al., 2016) investigation and 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) investigation. SEP
measurements come from the Energetic Particle Instrument-High (EPI-Hi;
Wiedenbeck et al., 2017) part of the Integrated Science Investigation of the
Sun (IS$\odot$IS; McComas et al., 2016): lower-energy particles are detected
by the Low Energy Telescope A (LETA), whereas higher-energy particles are
detected by the High Energy Telescope A (HETA).

  * •

STEREO-A: At the STEREO-A spacecraft, we use magnetic field measurements form
the Magnetic Field Experiment (MFE; Acuña et al., 2008), lower-energy particle
data from the Low Energy Telescope (LET; Mewaldt et al., 2008), and higher-
energy particle data from the High Energy Telescope (HET; von Rosenvinge et
al., 2008), all part of the In situ Measurements of Particles And CME
Transients (IMPACT; Luhmann et al., 2008) investigation. In-situ plasma data
come from the Plasma and Suprathermal Ion Composition (PLASTIC; Galvin et al.,
2008) instrument.

  * •

Mars: In-situ measurements from Mars orbit are provided by three spacecraft.
Plasma data come from the Analyzer of Space Plasmas and Energetic Atoms
(ASPERA-3; Barabash et al., 2006) onboard Mars Express (MEX; Chicarro et al.,
2004). Lower-energy particle data are supplied by the Solar Energetic Particle
(SEP; Larson et al., 2015) investigation onboard the Mars Atmosphere and
Volatile Evolution (MAVEN; Jakosky et al., 2015) spacecraft. Higher-energy
particles are not directly measured by the spacecraft orbiting Mars;
nevertheless, we use proxy data from the High Energy Neutron Detector (HEND)
part of the Gamma Ray Spectrometer (GRS; Boynton et al., 2004) suite onboard
2001 Mars Odyssey (MOdy; Saunders et al., 2004) as well as MAVEN/SEP. Magnetic
field measurements of the upstream solar wind from MAVEN are not available
during the period under study.

  * •

Earth: In-situ measurements from near Earth are provided by three spacecraft
located at Earth’s Lagrange L1 point. Magnetic field and plasma data are
supplied by the Magnetic Field Investigation (MFI; Lepping et al., 1995) and
Solar Wind Experiment (SWE; Ogilvie et al., 1995) instruments onboard Wind
(Ogilvie and Desch, 1997). Lower-energy particles are detected by the
Electron, Proton, and Alpha Monitor (EPAM; Gold et al., 1998) onboard the
Advanced Composition Explorer (ACE; Stone et al., 1998). Higher-energy
particles are measured by the Energetic and Relativistic Nuclei and Electron
(ERNE; Torsti et al., 1995) experiment onboard SOHO.

  * •

BepiColombo: The BepiColombo (Bepi; Benkhoff et al., 2010; Milillo et al.,
2020) spacecraft is currently in cruise phase before its planned Mercury orbit
insertion in 2025. Magnetic field measurements are provided by the Mercury
Planetary Orbiter (MPO) Magnetometer (MPO-MAG; Heyner et al., 2021). Data from
the particle spectrometer are not available during the period under study;
nevertheless, we use in our investigation proton counts over both lower and
higher SEP energy ranges from the Bepicolombo Environment Radiation Monitor
(BERM; Pinto et al., 2021). The plasma instrument from BepiColombo is not
operational during cruise phase.

  * •

Solar Orbiter: At the Solar Orbiter (SolO; Müller et al., 2020) spacecraft, we
use magnetic field data from the Magnetometer (MAG; Horbury et al., 2020) and
electron density measurements from the Radio and Plasma Waves (RPW; Maksimovic
et al., 2020) instrument (data from the instrument dedicated to solar wind
plasma are not available during the events investigated here). We also include
solar wind speed estimates based on MAG and RPW data using deHoffmann–Teller
analysis, the details of which are described in Steinvall et al. (2021). SEPs
are measured with the Energetic Particle Detector (EPD; Rodríguez-Pacheco et
al., 2020), specifically with the Electron Proton Telescope (EPT) for lower-
energy particles and the High Energy Telescope (HET) for higher-energy ones.

##  3 Simulation Setup

To model the heliospheric conditions during the period under analysis, we use
the Wang–Sheeley–Arge (WSA; Arge et al., 2004) coronal model coupled with the
3D MHD Enlil (Odstrcil, 2003; Odstrcil et al., 2004) heliospheric model,
henceforth WSA–Enlil. As input for WSA, we employ time-dependent National
Solar Observatory (NSO) Global Oscillation Network Group (GONG; Harvey et al.,
1996) zero-point-corrected magnetogram synoptic maps, used to generate solar
wind and interplanetary magnetic field conditions up to the Enlil inner
boundary, set at $21.5\,R_{\odot}$ or 0.1 AU. From there, Enlil uses WSA
output as input to model the heliospheric conditions by solving the MHD
equations using a flux-corrected-transport algorithm. Since we are interested
in modelling CME propagation and SEP transport up to the orbit of Mars, we set
the Enlil outer boundary to 3 AU. We then send the WSA–Enlil output data files
to the SEPMOD (Luhmann et al., 2007, 2010) SEP prediction code. SEPMOD uses
field line and shock description outputs from WSA–Enlil to forward model SEP
flux time series, typically for protons at energies from 1 to 100 MeV, along
sequential observer-connected field lines using shock-source injections
followed by a constant-energy, guiding-centre transport approximation. In our
WSA–Enlil–SEPMOD simulation runs, we use WSA version 5.2, Enlil version 2.8f,
and SEPMOD version 2. The runs are performed at NASA’s Community Coordinated
Modeling Center (CCMC).

CMEs are inserted in the model at the Enlil inner boundary as hydrodynamic,
high-pressure pulses that are able to drive shock waves if their speed is
sufficiently greater than that of the ambient solar wind. Because of the
inherent limits of the numerical simulation approach used in Enlil, this inner
boundary is set at $21.5\,R_{\odot}$. As a result, extrapolations of
magnetograph and coronagraph data are needed to drive the model on that
spherical “source surface”. For this reason, there are no coronal or solar
wind disturbances—and, thus, no modeled interplanetary shocks—below
$21.5\,R_{\odot}$. Note that since CMEs are inserted into the Enlil
heliospheric domain as hydrodynamic structures, they lack internal magnetic
fields. Hence, it is not possible to model their magnetic configuration, e.g.,
to predict the presence or absence of a flux rope structure in situ.

In order to model the heliospheric context and solar wind transients during
the time interval between Flare1 and Flare2, we selected all the CMEs
(excluding minor outflows and ’jet-like’ eruptions, according to the
definition of Vourlidas et al., 2013, 2017) observed between 2020 November 29
and December 7 via inspection of SOHO/LASCO and STEREO/SECCHI data. In
addition, Flare1 was preceded by a similarly-directed eruption that originated
late on 2020 November 26 (e.g., Lario et al., 2021; Nieves-Chinchilla et al.,
2022). We also include this event in our investigation, since it likely led to
preconditioning of the heliosphere, which may have affected the propagation
speed of the CME associated with Flare1 and the transport of associated SEPs.
In all, we selected five CMEs, shown in Figure 2 from the perspectives of both
SOHO and STEREO-A. CME2 and CME5 are associated with Flare1 and Flare2,
respectively.

Figure 2: The five CMEs modelled in this study as seen in coronagraph imagery
from (top row) SOHO/LASCO/C3 at L1 and (bottom row) STEREO/SECCHI/COR2-A close
to L5. Flare1 and Flare2 are associated with CME2 and CME5, respectively.

To explore how variations to CME input parameters affect shock arrival times,
as well as shock–observer connectivity and thus SEP access, we employ a “mini-
ensemble” approach. The advantages of ensemble modelling techniques, where the
outputs of a series of model runs with slightly different input conditions are
compared, for space weather forecasting were briefly reviewed by Knipp (2016)
and Murray (2018). Multiple studies have performed ensemble modelling of CME
propagation using WSA–Enlil (e.g., Cash et al., 2015; Emmons et al., 2013; Lee
et al., 2013, 2015; Mays et al., 2015a, b; Pizzo et al., 2015) as well as
other models (e.g., Amerstorfer et al., 2018, 2021; Dumbović et al., 2018; Kay
et al., 2020). In this work, we explore how outcomes such as CME arrival time,
interplanetary magnetic field connectivity, and SEPs spatial spread and peak
fluxes vary with respect to CME input parameters. Our WSA–Enlil–SEPMOD mini-
ensemble consists of four members, with the CME input parameters for each
shown in Table 1 and derived in the following way:

Table 1: CME Input Parameters for the WSA–Enlil–SEPMOD Simulation Runs.

(a) Run1—Real time CME | $t_{0}$ | $\theta$ | $\phi$ | $\gamma$ | $\psi_{1}$ | $\psi_{2}$ | $V$
---|---|---|---|---|---|---|---
# | UT | [∘] | [∘] | [∘] | [∘] | [∘] | [km$\cdot$s-1]
1 | 2020-11-27T03:43 | $6.0$ | $-100.0$ | $0.0$ | $32.00$ | $32.00$ | $550.0$
2 | 2020-11-29T16:00 | $-6.0$ | $-75.0$ | $0.0$ | $58.00$ | $58.00$ | $1336.0$
3 | 2020-12-01T10:59 | $8.0$ | $-45.0$ | $0.0$ | $35.00$ | $35.00$ | $774.0$
4 | 2020-12-03T22:40 | $-5.0$ | $-130.0$ | $0.0$ | $20.00$ | $20.00$ | $314.0$
5 | 2020-12-07T18:49 | $-21.0$ | $12.0$ | $0.0$ | $41.00$ | $41.00$ | $1383.0$

(b) Run2—Cone model CME | $t_{0}$ | $\theta$ | $\phi$ | $\gamma$ | $\psi_{1}$ | $\psi_{2}$ | $V$
---|---|---|---|---|---|---|---
# | UT | [∘] | [∘] | [∘] | [∘] | [∘] | [km$\cdot$s-1]
1 | 2020-11-27T04:59 | $4.0$ | $-98.0$ | $0.0$ | $22.95$ | $22.95$ | $425.1$
2 | 2020-11-29T15:25 | $-4.0$ | $-88.0$ | $0.0$ | $60.46$ | $60.46$ | $1661.9$
3 | 2020-12-01T12:51 | $18.0$ | $-40.0$ | $0.0$ | $36.87$ | $36.87$ | $811.6$
4 | 2020-12-03T23:05 | $-6.0$ | $-135.0$ | $0.0$ | $17.46$ | $17.46$ | $328.5$
5 | 2020-12-07T19:38 | $-22.0$ | $5.0$ | $0.0$ | $42.07$ | $42.07$ | $1120.9$

(c) Run3—Croissant model CME | $t_{0}$ | $\theta$ | $\phi$ | $\gamma$ | $\psi_{1}$ | $\psi_{2}$ | $V$
---|---|---|---|---|---|---|---
# | UT | [∘] | [∘] | [∘] | [∘] | [∘] | [km$\cdot$s-1]
1 | 2020-11-27T04:30 | $4.0$ | $-96.0$ | $-25.0$ | $39.67$ | $20.49$ | $521.8$
2 | 2020-11-29T15:27 | $-8.0$ | $-92.0$ | $-38.0$ | $58.75$ | $35.45$ | $1700.6$
3 | 2020-12-01T13:33 | $15.0$ | $-40.0$ | $-20.0$ | $50.33$ | $29.99$ | $599.1$
4 | 2020-12-03T19:52 | $-9.0$ | $-155.0$ | $5.0$ | $34.63$ | $15.07$ | $502.5$
5 | 2020-12-07T19:36 | $-22.0$ | $8.0$ | $20.0$ | $51.53$ | $31.33$ | $1120.9$

(d) Run4—A posteriori CME | $t_{0}$ | $\theta$ | $\phi$ | $\gamma$ | $\psi_{1}$ | $\psi_{2}$ | $V$
---|---|---|---|---|---|---|---
# | UT | [∘] | [∘] | [∘] | [∘] | [∘] | [km$\cdot$s-1]
1 | 2020-11-27T04:59 | $4.0$ | $-98.0$ | $0.0$ | $23.00$ | $23.00$ | $400.0$
2 | 2020-11-29T15:25 | $-4.0$ | $-96.0$ | $0.0$ | $50.00$ | $50.00$ | $2050.0$
3 | 2020-12-01T12:00 | $18.0$ | $-55.0$ | $0.0$ | $28.00$ | $28.00$ | $1350.0$
4 | 2020-12-03T23:05 | $-6.0$ | $-135.0$ | $0.0$ | $18.00$ | $18.00$ | $350.0$
5 | 2020-12-07T19:38 | $-22.0$ | $5.0$ | $0.0$ | $42.00$ | $42.00$ | $1380.0$

Note. Each block shows, from left to right: CME number, time ($t_{0}$) of
insertion of the CME at the Enlil inner boundary of $21\,R_{\odot}$ or 0.1 AU,
latitude ($\theta$) and longitude ($\phi$) of the CME apex in Stonyhurst
coordinates, tilt ($\gamma$) of the CME axis with respect to the solar equator
(defined positive for counterclockwise rotations), semi-major ($\psi_{1}$) and
semi-minor ($\psi_{2}$) axes of the CME cross-section (note that
$\psi_{1}\neq\psi_{2}$ only in Run3), and CME radial speed at $21\,R_{\odot}$
($V$).

  * •

Run1: For this run, we use CME input parameters derived in real time and
stored at the Space Weather Database Of Notifications, Knowledge, Information
(DONKI; https://kauai.ccmc.gsfc.nasa.gov/DONKI/), maintained by the Community
Coordinated Modeling Center (CCMC) at the NASA Goddard Space Flight Center.
The CMEs are analysed using the Space Weather Prediction Center CME Analysis
Tool (SWPC_CAT; Millward et al., 2013), in which a teardrop-shaped 3D
structure is visually fitted to coronagraph data so that it best matches
observations. Since DONKI runs are performed in real time, SOHO and STEREO-A
data are used simultaneously only if available at the time of the analysis,
otherwise single-spacecraft imagery is employed. We remark that STEREO-A data,
if available, are in the so-called “beacon” (Biesecker et al., 2008) format,
which is characterised by a lower processing level than science-level data.
Links to the DONKI CME analysis results for each of the eruptions under study
are provided in the Data Availability Statement section.

  * •

Run2: For this run, we derive CME input parameters by employing the cone model
(Fisher and Munro, 1984; Zhao et al., 2002), consisting of a 3D conical base
culminating in a spherical front, applied to simultaneous science-level data
from SOHO and STEREO-A. In order to do so, we use the Graduated Cylindrical
Shell (GCS; Thernisien et al., 2006, 2009) reconstruction technique, which
consists of a parameterised shell intended to reproduce the 3D morphology of
flux ropes (whose envelopes are closed coronal loops) that can be visually
fitted to coronagraph images. Its free parameters are latitude ($\theta$),
longitude ($\phi$), and height ($H$) of the CME apex, tilt ($\gamma$) of the
CME axis, angular distance ($\alpha$) between the CME legs, and aspect ratio
($\kappa$). The cone model geometry is achieved by setting $\alpha$ to zero,
and the value of $\gamma$ becomes irrelevant given the circular cross-section
of the structure.

  * •

Run3: For this run, we use the same methodology as in Run2, but allow the full
range of GCS parameters to be freely adjusted until they best match
simultaneous SOHO and STEREO-A coronagraph observations. The resulting CME
morphology is reminiscent of a croissant, with both legs connected to the Sun
and a toroidal axis. Furthermore, this is the only run in the mini-ensemble
that allows for an elliptical cross-section of the resulting CME to be
inserted in Enlil, often a more realistic representation (e.g., Cremades and
Bothmer, 2004; Krall and St. Cyr, 2006).

  * •

Run4: The CME parameters for this run are obtained by fine-tuning the inputs
of Run2 with the aim to match, to the best of our abilities, the observed CME-
driven shock arrivals and arrival times at the six available in-situ locations
described in Section 2. In other words, the CME input parameters are adjusted
in order to minimise the rate of incorrect hit/miss predictions and the
$\Delta{t}$ between observed and simulated arrival times derived from the
other runs—in particular, Run2. This “a posteriori” run sets the benchmark in
terms of what the present version of the coupled WSA–Enlil–SEPMOD models can
achieve for the period under study. For example, shock–observer connectivities
below $21\,R_{\odot}$ will be naturally missed because CMEs are not described
beneath the Enlil inner boundary. Hence, this run will aid in discriminating
between features that depend exclusively on the input parameters in the other
three runs and those that cannot be reproduced with the current model setup
even with optimal tuning.

For Run2 and Run3, the CME dimensions (with circular cross-section for Run2
and elliptical cross-section for Run3) are derived by “slicing” the image
fitting-derived 3D structures at their widest point (see Thernisien, 2011, for
additional notes and formulas on the model geometry), and the time of
injection at the Enlil inner boundary is derived by propagating the CMEs to
$21.5\,R_{\odot}$ from their final observation in the combined C3+COR2 field
of view under the assumption of constant speed (calculated between
reconstructions performed at the times shown in Figure 2 minus 60 minutes for
CME1, CME3, and CME4, minus 30 minutes for the faster CME2 and CME5). In this
respect, Run1 can be considered an actual forecast, Run2 and Run3 are
hindcasts, and Run4 corresponds to post-event analysis. Links to all
WSA–Enlil–SEPMOD runs can be found in the Data Availability Statement section.

##  4 Simulation Results

Simulation results for each of the six in-situ locations, including model–data
comparisons, are shown in Appendix A (Figures 7 to 12). Additionally,
successive snapshots of the ecliptic plane for each of the four mini-ensemble
runs are reported in Appendix B (Figures 13 to 16). According to in-situ
measurements, CME1 impacted PSP, CME2 impacted PSP and STEREO-A, CME3 impacted
STEREO-A, CME4 did not impact any observer, and CME5 impacted Earth and
possibly Mars (more discussion of this aspect can be found in Section 4.1).
Note that by “impact”, we refer exclusively to the arrival of CME-driven
shocks. None of the CMEs considered in this work impacted Bepi or SolO. SEPs
from CME2/Flare1 were observed at all in-situ locations except for Bepi,
whilst SEPs from CME5/Flare2 were detected at PSP, STEREO-A, Mars, and Earth,
with possible effects at Bepi and SolO (more discussion of this aspect can be
found in Section 4.3). Thus, particles from the first (second) SEP event
spread over at least $240^{\circ}$ ($100^{\circ}$) in longitude. In the
remainder of this section, we review and analyse the WSA–Enlil–SEPMOD
simulation results in terms of three main aspects: CME-driven shock arrivals
(Section 4.1), shock–observer connectivities (Section 4.2), and duration and
peak fluxes of SEP events (Section 4.3).

###  4.1 CME-driven Shock Arrival Time and Speed

As described in Section 3, the five CMEs modelled in this study are inserted
in the Enlil heliospheric domain as hydrodynamic structures that are able to
drive shocks in the heliosphere. Hence, the first step of our analysis is
centred on evaluating whether a CME-driven shock is correctly predicted to
impact each observing location by comparing the results of the different WSA-
Enlil runs with the corresponding in-situ observations (shown in Appendix A).
As briefly mentioned above, we identify six total shock arrivals, which could
be attributed to CME1 (at PSP), CME2 (at PSP and STEREO-A), CME3 (at
STEREO-A), and CME5 (at Earth and Mars). Whilst the first five impacts present
clear signatures of CME-driven shocks in in-situ measurements, the impact of a
shock driven by CME5 at Mars is more ambiguous (see Figure 9), in particular
because of the lack of upstream magnetic field data and the low cadence of
plasma data.

Table 2 shows contingency tables for each of the four mini-ensemble WSA–Enlil
runs, where ‘hit’ (H) means that a CME is correctly predicted to impact a
target, ‘correct rejection’ (R) indicates that a CME missed an observer in the
model as well as in actual observations, and ‘false alarm’ (F) denotes that a
CME forecast to impact a certain location was not detected in situ. A fourth
‘miss’ category is usually included in contingency tables, in this case
signifying that a CME is incorrectly predicted to avoid a target. However, we
have no instances of ‘miss’ in our mini-ensemble. Overall, the contingency
tables for the four runs are similar, as might be expected, but there are a
few differences. In particular, the only instances of inaccurate forecasts in
Table 2 correspond to ‘false alarms’ associated with CME1, CME2, and CME3.
Note that ‘false alarms’ at Mars for CME2 and CME3 are reported for all runs,
including Run4 that was tuned to reflect in-situ measurements in terms of
impacts and arrival times (see Section 3). However, we remark that any clear
deviation from the associated ‘ambient’ run (without CMEs, also shown in
Figures 7 to 12) is considered an impact here. Several are rather weak and
could be difficult to recognise in the corresponding in-situ measurements. As
for the other runs, Run1 was characterised by five ‘false alarms’, whilst Run2
and Run3 each reported four ‘false alarms’, indicating that these mini-
ensemble members performed largely comparably in this regard.

Table 2: Contingency Tables for Each WSA–Enlil Simulation Run.

(a) Run1 #CME | 1 | 2 | 3 | 4 | 5
---|---|---|---|---|---
PSP | H | H | R | R | R
ST-A | F | H | H | R | R
Mars | R | F | F | R | H
Earth | R | F | F | R | H
Bepi | R | R | R | R | R
SolO | R | R | R | R | R

(b) Run2 #CME | 1 | 2 | 3 | 4 | 5
---|---|---|---|---|---
PSP | H | H | R | R | R
ST-A | R | H | H | R | R
Mars | R | F | F | R | H
Earth | R | F | F | R | H
Bepi | R | R | R | R | R
SolO | R | R | R | R | R

(c) Run3 #CME | 1 | 2 | 3 | 4 | 5
---|---|---|---|---|---
PSP | H | H | R | R | R
ST-A | F | H | H | R | R
Mars | R | F | F | R | H
Earth | R | R | F | R | H
Bepi | R | R | R | R | R
SolO | R | R | R | R | R

(d) Run4 #CME | 1 | 2 | 3 | 4 | 5
---|---|---|---|---|---
PSP | H | H | R | R | R
ST-A | R | H | H | R | R
Mars | R | F | F | R | H
Earth | R | R | R | R | H
Bepi | R | R | R | R | R
SolO | R | R | R | R | R

Note. H = hit; R = correct rejection; F = false alarm. An additional category
usually employed in contingency tables is M = miss, with no occurrences in
this particular case.

Figure 3: Difference between simulated and in-situ arrival times (${\Delta}t$)
versus arrival speeds ($V_{\mathrm{arr}}$) shown for each location where a
CME-driven shock was detected and for each of the WSA–Enlil model runs.

An overview of the differences between the observed and predicted CME-driven
shock arrival times and speeds for the six ‘hit’ instances for the four runs
in the mini-ensemble is shown in Figure 3. Regarding the arrival times, apart
from Run4, in which errors were minimised by design, there is no run that
consistently performed best at all locations. Nevertheless, there are
differences in the cumulative error over the six impacts: 40.5 hours for Run1,
31.4 hours for Run2, 59.6 hours for Run3, and 3.2 hours for Run4. Thus, Run3
performed worst overall, which may seem surprising since the ellipsoidal
morphology included in this run was intended to correspond to a more realistic
CME representation (see Section 3). The poorer performance of Run1 compared
with Run2 may arise because two remote-sensing viewpoints were not always
available when the CME input parameters for Run1 were issued in real time (see
Section 3) and lower-quality STEREO-A beacon images were used. Nevertheless,
the difference between Run1 and Run2 in $\Delta t$ averages to only
${\sim}1.5$ hours per event (${\sim}9$ hours over six CME impacts), suggesting
that remote-sensing data available in real time may be sufficient for the
purpose of CME arrival time forecasting with Enlil—at least with the observing
spacecraft configuration explored in this work, i.e., L1+L5.

It is also important to critically consider these results in relation to the
background solar wind modelled by WSA–Enlil through which the CMEs are
propagating, which is reflected in both the modelled arrival times and speeds.
One clear example of this is CME5 at Earth (Figure 3(e)), where Run1 achieved
a more accurate arrival time than Run2 and Run3; nevertheless, the Enlil
ambient solar wind preceding the event was ${>}100$ km$\cdot$s-1 slower than
observed, indicating that the “true” CME speed was likely closer to that set
for the worse performing runs. A slower background wind also affects CME drag
and deceleration, resulting in this case in all the simulated arrival speeds
being significantly ($\Delta V>100$ km$\cdot$s-1) lower than observed. This
aspect may also explain why the general trend shown in Figure 3 is that all
runs tend to estimate a later CME arrival time: Most impacts are preceded by
slower ambient speeds modelled by Enlil (see Appendix A), suggesting that this
is due to an intrinsic underestimation of the background solar wind speed for
this particular time period rather than, e.g., systematic human error when
evaluating CME input parameters. In fact, 13 (72%) of the 18 arrival times for
the first three runs (i.e., excluding Run4) are characterised by $\Delta t\geq
3$ hours, only 2 (11%) feature $\Delta t\leq{-}3$ hours, and 3 (17%) result in
arrival times within 3 hours of the observed ones. At the same time, 14 (58%)
of the 24 total shock arrival speeds are lower than observed by at least 50
km$\cdot$s-1, and this is true even for Run4 in half of the cases
(CME2/STEREO-A, CME5/Earth, and CME5/Mars). In contrast, only 2 (8%) modelled
speeds are faster than observed by at least 50 km$\cdot$s-1, whilst the
remaining 8 (34%) impacts are within 50 km$\cdot$s-1 of the observed arrival
speeds.

###  4.2 Shock–Observer Connectivity

Another interesting aspect to analyse is the connectivity of the CME shocks to
the six in-situ locations with respect to each WSA–Enlil simulation run. This
is particularly important for SEPMOD, since this model requires connection to
a shock for accelerated particles to be detected at a particular location. In
Enlil, shocks are defined as ${\geq}20$ km$\cdot$s-1 increases in solar wind
speed with respect to the corresponding ambient simulation (without CMEs), and
the shock speed is derived separately as a time-derivative of the shock
position. Connectivity also directly affects the SEP intensity–time profiles
modelled by SEPMOD. Figure 4 shows the intervals of shock–observer
connectivity for each CME in terms of the shock radial distance along the
field line connected to the observer. In Enlil simulations, a shock may become
magnetically connected to an observer at any point within the simulation
domain, which in our runs corresponds to heliocentric distances between 0.1
and 3 AU. This means that a shock may first connect to an observer “from
behind”, when the shock is already beyond the radial distance of the observer
(indicated by the dashed lines in Figure 4). Several examples of connection
from behind are evident in the figure.

Figure 4: Shock–observer connectivity shown in terms of the shock radial
distance along the observer-connected field line. Connectivity is shown for
the five CMEs in this study with respect to each of the four mini-ensemble
simulation runs, at (a) PSP, (b) STEREO-A, (c) Mars, (d) Earth, (e) Bepi, and
(f) SolO. The dashed line in each panel indicates the time-dependent
heliocentric distance of the corresponding observer.

According to the modelling results shown in Figure 4, the shock driven by CME2
(corresponding to Flare1) connects with every observer at some point
throughout the temporal domain for each simulation run. However, connectivity
is established when the shock is still sunward of the spacecraft only at PSP
and STEREO-A, while Mars and Earth connect with the shock when it is at or
beyond their respective heliocentric distances in all cases except for Run1.
Bepi and SolO become magnetically linked to the CME2 shock only when it is
well beyond 2 AU, approximately 10 days after the eruption of Flare1. These
results are consistent with the locations of the various observers with
respect to Flare1 shown in Figure 1a. The second SEP-rich event, i.e. CME5
(associated with Flare2), becomes magnetically connected to all observers
except PSP. Connectivity is achieved “from the front” at STEREO-A, Mars, and
Earth, and “from behind” at Bepi and SolO. Again, these results are generally
as expected considering the spacecraft configuration relative to the location
of Flare2 shown in Figure 1b, with STEREO-A, Earth, and Mars favourably
positioned for early connection to the shock, whilst Bepi and SolO behind the
west limb connect to the shock once it has propagated well beyond 1 AU. The
absence of connectivity at PSP can be accounted for because the modelled CME
when sunward of the spacecraft is not sufficiently extended in longitude to
reach the field line connecting to PSP (see the figures in Appendix B), and
PSP is not suitably located to be connected to the shock from behind. The
connectivities for CME1, CME3, and CME4 are more dependent on the specific
simulation run. CME1 becomes connected to PSP and STEREO-A in all runs, but
connectivity with Earth and Mars is achieved only in Run1 and Run3. CME3
connects to all observers in Run1, Run2, and Run3, but misses SolO in Run4.
Finally, CME4 becomes briefly (for ${\sim}1$ hour) connected to PSP only in
Run3.

Overall, the connectivity curves shown in Figure 4 are largely similar for
each observer across the four simulation runs, apart from the few differences
discussed above. The major differences between the runs at any given observer
are in the times when connectivity to a shock is first achieved, with spreads
ranging from a few hours to ${\sim}2.5$ days. This indicates that the
connectivity to a shock modelled by Enlil is more sensitive to the CME input
parameters than the shock arrival time, which only shows a range of less than
24 hours across the four runs (see Section 4.1). As an example, for CME1 at
PSP, the spread in arrival times for the CME-driven shock is ${\sim}8$ hours,
whereas the spread in magnetic connection onset times is about ${\sim}27$
hours. This spread in the first connection times significantly affects the SEP
intensity–time profiles modelled by SEPMOD for each run, as explored in
greater detail in the next section. Moreover, we highlight the expected
sources of error related to the employed modelling methods. First of all,
connectivity cannot be modelled below 0.1 AU—the height of Enlil’s inner
boundary at which the modelled CMEs are inserted. Hence, early CME
acceleration and shock formation cannot be realistically described. In
addition, the lack of CME internal magnetic fields is expected to yield
intrinsic uncertainties in the resulting interplanetary magnetic field
preconditioning and, thus, in the modelled connectivities. This may hold true
especially in the case of CME2, which was launched shortly after and on a
similar trajectory to CME1.

###  4.3 SEP Event Duration and Flux

The figures in Appendix A show the SEP proton intensity–time profiles
generated by SEPMOD at three sample energies together with observations from
each spacecraft again in three proton energy ranges, which vary between
instruments. In order for particles to be detected by a spacecraft, SEPMOD
requires that the observer encounters a magnetic field line that at some time
was connected with the shock and therefore populated with energetic particles
injected by the shock. The intensity and energy spectrum of these particles
depend on the shock compression ratio and velocity jump, respectively, at the
point where the field line intersects the shock. The figures in Appendix A
show that the major SEP enhancements observed at the various locations were
associated with CME2/Flare1 and CME5/Flare2. All observers except Bepi
detected the first SEP event, whilst the second SEP event was detected at
least at PSP, STEREO-A, Mars, and Earth. Bepi and SolO recorded low-energy SEP
enhancements following the eruption of Flare2 (see panel (f) of Figures 11 and
12), but it is unclear whether these were associated with this event or with
the passage of a stream interaction region (SIR; e.g., Richardson, 2018) that
appears to corotate from Bepi to SolO. Although plasma observations are
incomplete, the Enlil results at Bepi show an SIR on December 8, associated
with an observed magnetic field enhancement and a sector crossing, that is
also evident at SolO on December 10. An additional complication is that Bepi
and SolO detected a minor SEP event with onset around 00:00 UT on 2020
December 11. This was likely related with a CME eruption late on December 10
from behind the west (east) limb as seen from Earth (STEREO-A) that was well
positioned for Bepi and SolO but was outside our CME analysis interval. There
is also a weak SEP event associated with CME1 observed at PSP (see Figure 7).

Table 3: Contingency Tables for Each WSA–Enlil–SEPMOD Simulation Run.

(a) Run1 #CME | 2 | 5
---|---|---
| lo-mi-hi | lo-mi-hi
PSP | H H H |  M M M
ST-A | H H H | H H h
Mars | H H H | H H F
Earth | H H h | H H H
Bepi | R R R | ? ? ?
SolO |  M M M | ? ? ?

(b) Run2 #CME | 2 | 5
---|---|---
| lo-mi-hi | lo-mi-hi
PSP | H H H |  M M M
ST-A | H H H | H H H
Mars | H H H | H H F
Earth | H H h | H H H
Bepi | R R R | ? ? ?
SolO |  M M M | ? ? ?

(c) Run3 #CME | 2 | 5
---|---|---
| lo-mi-hi | lo-mi-hi
PSP | H H H |  M M M
ST-A | H H H |  M M M
Mars | H H H | H H F
Earth | H H h | H H H
Bepi | R R R | ? ? ?
SolO |  M M M | ? ? ?

(d) Run4 #CME | 2 | 5
---|---|---
| lo-mi-hi | lo-mi-hi
PSP | H H H |  M M M
ST-A | H H H | H H H
Mars | h H H | H H F
Earth | H H M | H H H
Bepi | R R R | ? ? ?
SolO |  M M M | ? ? ?

Note. H = hit; R = correct rejection; M = miss, F = false alarm. A ‘h’ is used
for H instances for which the modelled SEP fluxes peaked barely above the
corresponding instrument’s background. The three values for each CME (‘lo’,
‘mi’, and ‘hi’) refer to the SEP low, mid, and high energies shown
respectively in panels (f), (g), and (h) of Figures 7 to 12.

Table 3 shows contingency tables for each of the SEPMOD runs in relation to
the SEP events driven by CME2 and CME5, in a similar fashion to Table 2. For
CME1 (not shown in Table 3), all runs predict a lower-energy particle
(${\sim}5$ MeV) enhancement that far exceeds the observed intensities that
rise just above the instrument noise level, whilst protons with energies
${\sim}25$ MeV are predicted only in Run1 and Run3. SEPs from CME2 are
predicted to reach all observers, including Bepi, which in reality missed the
event. However, the predicted arrival at Bepi and SolO is approximately 10
days after the eruption and occurs because of connection to the shock well
beyond the spacecraft (Figure 4(e–f)). In practical terms, these predictions
can be considered as ‘misses’ (or ‘correct rejections’). Due to the temporal
proximity of CME1, CME2, and CME3, potentially the particle fluxes at some
locations might have contributions from all three CMEs. Inspection of the
SEPMOD predicted fluxes for each CME separately suggests that these
contributions were likely to be negligible compared to that from the larger
and more energetic CME2. An exception is Run3 at Earth and Mars, where CME3
makes a significant contribution to the resulting predicted SEP profile,
though it is not clear from the observed fluxes that there was an actual
contribution from CME3. The observed SEPs from CME5 were not predicted at PSP,
or at STEREO-A for Run3 only, and were predicted to reach SolO and Bepi
${\sim}$5–8 days later, after the small particle enhancement (possibly
associated with an SIR) discussed above (note that, because of the dubious
association of the weak SEP event at Bepi and SolO, the corresponding values
in Table 3 are indicated with a question mark). All remaining SEPMOD SEP
predictions for both CME2 and CME5 can be classified as ‘hits’, whilst
predictions for CME4 are ‘correct rejections’ at all locations. Overall, all
runs performed largely comparably, with a slightly worse performance achieved
by Run3. We emphasise that the contingency tables in Table 3 are based
entirely on the model–data comparisons shown in Figures 7 to 12, hence they
are dependent on factors such as the instrumental background noise. For
example, in the case of the SEP event driven by CME2, Run1, Run2, and Run3
predict enhancements that are barely above the noise level (‘h’), whilst Run4
predicts an enhancement that is just below the background (‘M’). In reality,
the obseved SEP event itself was not significantly above background levels,
and all runs predicted fluxes within a factor 5 of the measurements.

Figure 5: Temporal extent of the SEP enhancements associated with (a)
CME2/Flare1 and (b) CME5/Flare2, at the six in-situ locations, showing data
(black) versus the mini-ensemble runs (colours). These are based on “mid-
energy particles” (panel (g) in Figures 7 to 12) measurements everywhere apart
from Bepi and SolO for CME5/Flare2, where the event was possibly observed only
at lower energies (panel (f) in Figures 11 and 12). The blue vertical lines
mark the injection times of the corresponding CMEs into the Enlil heliospheric
domain, which can be considered uniform across the four mini-ensemble runs in
the scale shown (see Table 1).

The temporal extents of the SEP enhancements associated with CME2/Flare1 and
CME5/Flare2 modelled by SEPMOD are compared with those observed in situ at
${\sim}25$ MeV (panel (g) in Figures 7 to 12) in Figure 5. In line with the
results shown in Table 3, the occurrence of an SEP event is successfully
predicted at most locations. However, the predicted onset times of these
events are later than observed in all cases, with delays ranging from a few
hours up to several days. The different event onset times for the four
simulation runs reflect the differences in shock–observer connectivity as
discussed in Section 4.2. In at least half of the cases, the observed particle
onset times occur before the CME injection time into Enlil (represented by a
vertical line in each panel), indicating that magnetic connectivity was likely
established when the shock was still below 21.5 $R_{\odot}$. In such cases, it
is impossible to predict the correct SEP onset time with the heliospheric
modelling setup used in this work. SEPMOD best predicts the temporal durations
of the SEP enhancements at PSP and STEREO-A for CME2, and at Mars and Earth
(and to some extent at STEREO-A) for CME5. These locations were closest in
terms of longitude to the respective CME source regions. Note that here we
consider the results for CME5/STEREO-A to be more successful than those for
CME2/Earth and CME2/Mars. This is because, in the former case, approximately
the first half of the event is captured, i.e. close to its peak, whilst
capturing the second half of an event corresponds to its declining phase, when
particle fluxes are generally lower. The least successful predictions are for
Bepi and SolO, for which the sources of both CMEs were at or behind the solar
limb from their viewpoints, and for PSP in the case of CME5/Flare2. Thus,
these results indicate that the SEP prediction performance declines with
longitudinal distance from the eruption site. In Figure 5(b), the small
particle enhancements observed at Bepi and SolO have been associated with CME5
even if their origin is not fully clear and they may be related to an SIR as
discussed above. In any case, the SEPMOD results at these two locations
suggest that the particle events would commence significantly later than
observed (almost a ‘miss’), or that they were simply a ‘false alarm’. Finally,
there are no significant differences across the four mini-ensemble members,
even including Run4 that was designed to match the observed CME arrival times
(see Section 3). This suggests that an improved CME-shock arrival forecast
will not automatically result in a better SEP forecast. The performance is
only slightly worse for Run3, which missed the SEP event driven by CME5 at
STEREO-A and predicted a larger contribution from CME3 in the SEP event driven
by CME2.

Figure 6: Maximum SEP flux associated with (a) CME2 or Flare1 and (b) CME5 or
Flare2, showing data (black) versus the mini-ensemble runs (colours). The
three energy levels (‘low’, ‘mid’, and ‘high’) correspond to those reported in
panels (f), (g), and (h) of Figures 7 to 12, respectively. The ‘data’ markers
are accompanied by a horizontal bar for clarity.

The maximum SEP fluxes predicted by SEPMOD in each run at every observing
location are compared with the maximum fluxes observed in situ in Figure 6.
The energy ranges, from left to right, correspond to those shown in panels
(f), (g), and (h) of Figures 7 to 12. Since the energy ranges differ for each
instrument, the fluxes should not be compared directly across the six
observers. It is clear that, apart from a few cases, SEPMOD generally tends to
underestimate the maximum fluxes. It is possible that the lack of a realistic
shock description below 21.5 $R_{\odot}$, where CMEs tend to travel faster and
accelerate higher-energy particles (before they are slowed down via solar wind
drag), together with delayed shock–observer connectivities, result in an
underestimation of particle acceleration and, thus, of peak fluxes. Of the 84
(21$\times$4) instances of available data–model comparisons shown in Figure 6,
41 (49%) cases underestimate and 10 (12%) overestimate the peak fluxes by a
factor ${\geq}$5, whilst 33 (39%) lie within a factor 5 of the measurements
(in either direction). If we consider a factor 3, these values become,
respectively, 49 (58%), 15 (18%), and 20 (24%). We note, however, that in the
case of CME2 at PSP, fluxes at low energies seem to be greatly overestimated,
but this is not likely to be the case since PSP data are accompanied by a
large data gap centred on the CME2 shock arrival, where the ${\sim}$4-MeV
particle intensity tends to peak. If we consider only the best-connected
observers—i.e., PSP (excluding the low energies) and STEREO-A for CME2, as
well as STEREO-A, Earth, and Mars for CME5—the percentages of
underestimated–overestimated–acceptable fluxes become 33%–13%–54% for a factor
5 and 44%–23%–33% for a factor 3. This suggests that SEP peak fluxes tend to
be better modelled for well-connected observers. Again, there is no mini-
ensemble member that performed consistently better than the others, the only
significant outlier being Run3 that predicted exceptionally low SEP fluxes at
STEREO-A for CME5 compared to the other runs (which translated into a ‘miss’
in Table 3). In particular, we note that Run4 often does not provide the best
results, again showing that improving CME arrival predictions may not lead to
improved SEP predictions.

##  5 Discussion

The results presented in Section 4 suggest a number of discussion points
relevant to both CME and SEP predictions. The four mini-ensemble runs employed
in this study provide an opportunity to analyse and review simulation outcomes
based on using real-time forecasts, science-level hindcasts (assuming circular
or elliptical cross-section CMEs), and post-event analysis. The input
parameters used for each run were discussed in Section 3.

First of all, all the mini-ensemble members correctly reported all the CME-
driven shock impacts that were detected in situ (i.e., no CME arrival was
missed). All the runs, however, were characterised by a few false alarms,
albeit with different degrees of importance—most were only weak flank
encounters. The worst-performing simulation run in terms of shock arrival time
was Run3, using hindcasts performed with elliptical cross-section CMEs. This
is rather unexpected, since a non-circular CME cross section is intended to
provide a more realistic CME morphology. We note however that Amerstorfer et
al. (2021) reached similar conclusions when deriving input parameters for
STEREO heliospheric imager-based CME propagation and forecasting models. They
reported that simply assuming the CME half-width to lie within a certain range
led to more accurate predictions than using GCS-derived values. The authors
speculated that this may be due to CME deflections and/or rotations taking
place beyond the coronagraphs’ field of view. We also conjecture that the
greater number of free parameters available when performing GCS
reconstructions with a croissant morphology may lead to additional
uncertainties and thus less precise estimates of the CME inputs for Run3. It
is possible that more “elongated”, non-circular, CME cross-sections provide
more realistic, and better performing, morphologies for CMEs that include
magnetic flux ropes, but if CME internal magnetic fields are not considered,
as in this study, then simply assuming a circular cross-section seems to yield
better results. We also note that Run2 (using hindcasts with a circular CME
cross-sections) performed slightly better than Run1 (using parameters from
real-time forecasts). The poorer performance of Run1 may be due to the lack of
data from one coronagraph (either SOHO or STEREO-A) at the time when the
prediction was issued (which is not always reported, hence we cannot draw
solid conclusions) and/or to the fact that real-time STEREO-A imagery is only
available as beacon data. Bauer et al. (2021) showed that beacon data tend to
perform worse (albeit not dramatically worse, as is the case in this study)
than science data for space weather forecasting based on the heliospheric
imaging cameras onboard STEREO. This work employs coronagraph rather than
heliospheric imagery, but it is reasonable to assume that similar issues
withstand.

Though not considered in the mini-ensemble used in this work, where just the
CME parameters are varied, CME arrival time predictions are also inevitably
affected by the solar wind background that is modelled by Enlil using a model-
generated coronal magnetic field input—in this case, from the WSA model. Since
WSA uses maps of the photospheric magnetic field as input, differences in the
input maps from specific ground- or space-based observatories and their
calibration are expected to affect the modelled background solar wind.
Therefore, an ensemble approach to modelling the background solar wind using
different magnetic field maps combined with ensemble CME modelling may lead to
more robust CME arrival forecasts. The influence of different input magnetic
field maps in the context of global MHD simulations of the heliosphere has
been explored by Jin et al. (2022), whilst more information on the impact of
inner heliospheric boundary conditions generated with different models can be
found in Gonzi et al. (2021). Additionally, it is important to consider the
uncertainties regarding the predicted shock arrival time that are intrinsic to
the choice of CME propagation model—in this case, Enlil. These have been
explored in several studies, either within a single model (e.g., Čalogović et
al., 2021; Dumbović et al., 2021; Wold et al., 2018) or by comparing results
from different models (e.g., Paouris et al., 2021; Riley et al., 2018, see
also CCMC’s CME Scoreboard: https://ccmc.gsfc.nasa.gov/scoreboards/cme). At
the time of the events studied, STEREO-A was approximately at the L5 point.
The fact that all the errors in the CME arrival time results described here
were similar to the “typical errors” in arrival time obtained in previous
studies (see Introduction), and no ‘misses’ occurred, suggests that remote-
sensing monitoring from the Lagrange L1 and L5 points can provide adequate
constraints on the propagation direction of CMEs.

Considering shock–observer connectivities, we found that the differences in
CME parameters amongst the four runs had a greater effect on the time at which
a location becomes first connected to the associated shock (differences across
the mini-ensemble members exceeded 2 days) than on the shock arrival time
(differences of less than 1 day). The connectivity of the various shocks to
each observer was largely similar across the four simulation runs. The
variation in the connectivity onset and duration suggests that an ensemble
approach may be able to provide a more robust range of possible outcomes.
However, two significant limitations of the connectivity modelling in this
study are that CMEs are introduced into Enlil at its heliospheric inner
boundary ($21.5\,R_{\odot}$ or 0.1 AU), resulting in delayed shock–observer
connectivity onsets and the absence of a realistic CME acceleration profile,
and that CMEs lack an internal magnetic field, resulting in a less realistic
description of interplanetary magnetic field preconditioning. We also note
that, in several cases, magnetic connection to the shock was established “from
behind”, when the shock front was beyond the observer’s heliocentric distance.
These instances take place in the model when an observer is well-separated in
longitude from the shock nose, and tend to result in even longer delays before
connection to the shock occurs. Nevertheless, as noted by Luhmann et al.
(2018), in SEPMOD, shock connections far from the Sun provide considerably
reduced SEP contributions compared to those near the Sun, since CME-driven
shocks tend to weaken with heliocentric distance. Bain et al. (2016) performed
a multi-point study of the Enlil shock–observer connectivity for two periods
characterised by several successive eruptions in a similar fashion to the ones
analysed here, and compared results with SEP measurements at Earth, STEREO-A,
and STEREO-B. They found that about two-thirds of the shock connections
identified in the simulations occurred within a few hours of an observed SEP
event, but also that a number of initial connections were missed due to the
modelled shocks being initiated at $21.5\,R_{\odot}$. Our results support
these conclusions.

Regarding SEP predictions, SEPMOD requires the existence of a shock–observer
magnetic field connection and the predicted SEP properties depend on the shock
parameters at the connection point. Here we consider the three main areas that
were identified by Bain et al. (2021) to be of high importance (see also the
Introduction), i.e. SEP onset time, event duration, and peak fluxes. We found
that the durations and peak fluxes of SEP events are generally well
reproduced, but these predictions tend to become less accurate with increasing
longitudinal distance from the CME eruption site. A likely reason in this
respect is that SEPMOD assumes scatter-free propagation along well-defined
field lines that are connected to a shock, whilst additional particle
transport effects (e.g., Qin et al., 2004) are neglected in the model. These
include, e.g., diffusive (e.g., Zank et al., 2015) and perpendicular (e.g.,
Zhang et al., 2003) transport, which are expected to play a more significant
role in widespread SEP events (Dresing et al., 2014, found that possible
reasons for SEPs spreading broadly in longitude are cross-field transport in
the interplanetary medium and/or particularly extended particle injection
regions close to the Sun). In fact, these additional transport mechanisms may
explain the two major ‘miss’ instances in the modelled SEP events, i.e. those
associated with CME2 at SolO and CME5 at PSP, which are characterised by
observers that are so far from the eruption site that connectivity to the
shock is either never achieved, or achieved only much later from behind.
Hence, it is natural to assume that SEPMOD results and predictions are more
accurate for well-connected observers, where scatter-free transport plays a
major role.

Interestingly, SEPMOD results from Run4 were not significantly better than
those from the other runs, even though the CME shock arrival times were
matched with observations by design. This may be due to the fact that, in
order to reduce the amount of ‘false alarms’ for shock arrivals from the
previous runs (see Section 4.1), the sizes of some CMEs were somewhat
diminished, thus delaying the time at which a well-separated observer becomes
first connected to a shock. The least successful predictions of the model runs
are for the SEP event onset times, which were delayed a few hours even in the
best-connected cases. The SEP events at Bepi and SolO were predicted to
commence several days later than the corresponding CME/flare eruption time,
due to connectivities reached from behind, and particles at PSP from CME5 were
entirely missed. However, as discussed in relation to shock connectivity, this
is entirely to be expected because shocks are not modelled below
$21.5\,R_{\odot}$, whereas it is well known that shocks associated with fast
CMEs can often form in the low corona, and some can even be observed in
coronagraph imagery (e.g., Vourlidas et al., 2013). Furthermore, SEP events
can clearly commence when shocks are much lower in the corona, as is evident
from the results in this work and many other studies (e.g., Agueda et al.,
2014; Gopalswamy et al., 2013). Additionally, it is possible that a SEP event
has contributions from both a flare source that remains rooted in the corona
and a CME-driven shock within the same eruptive event (e.g., Cane et al.,
2010). Thus, as noted earlier, the modelling setup used here may not be the
best option to predict SEP onset times. In addition, obtaining the CME
parameters usually requires the CME to be detected and tracked in coronagraph
images, at which point a SEP event may have already commenced, even if the
images were available in real time. It is also possible to initiate a
WSA–Enlil simulation based on real-time EUV imagery only, but the CME input
parameters will likely be significantly less accurate. The existing gap
between 1 and $21.5\,R_{\odot}$ could possibly be filled with MHD models that
are able to simulate CME propagation and particle acceleration in the corona
(e.g., Li et al., 2021; Young et al., 2021). An alternative approach may be to
take advantage of the ‘fixed-flare-source’ option in SEPMOD, demonstrated by
Luhmann et al. (2012). This assumes the presence of a source at the Enlil
inner boundary that is able to inject particles through the heliospheric
domain. This injection can be synchronised with the onset of a flare and
scaled according to its X-ray classification. Such potential improvements will
be explored further in the context of real-time space weather forecasts in
future work.

##  6 Summary and Conclusions

In this work, we have modelled the inner heliospheric context including CMEs
and SEPs for a time period including two notable eruptive events in late
November and early December 2020. We have employed the WSA–Enlil–SEPMOD
modelling chain to simulate the background solar wind and its transients using
four different sets of CME input parameters that provide a mini-ensemble
framework for predictions of CME arrival and SEP events. CME input parameters
were derived from coronagraph observations near Earth and at the STEREO-A
spacecraft (located ${\sim}60^{\circ}$ east of the Sun–Earth line),
representing observers from the Lagrange L1 and L5 points.

We have found that, despite limitations mostly related to the model’s
architecture and assumptions, reasonable predictions were obtained for both
shock arrivals and SEP event fluxes and durations, at least out to several
tens of degrees (${\sim}70^{\circ}$) away from the corresponding eruption
site. We noted that CME shock arrival time predictions using real-time
parameters (and STEREO beacon data) are only slightly worse than those
obtained in hindcasts with science-level data. The modelling setup used is not
able to correctly predict SEP event onsets, which may take place before the
corresponding CME is estimated to reach the 21.5 $R_{\odot}$ inner boundary of
Enlil. We noted that SEP predictions do not tend to be significantly better
for the model run in which the predicted shock arrival times are matched to
the observed ones, suggesting that a “perfect” CME shock arrival forecast may
not be necessary for obtaining reasonable SEP predictions. In fact, the
observed variation in the modelled event durations and peak fluxes suggests
that an ensemble approach (currently in use in several CME forecasting
settings by both NOAA and the UK MET Office; see Murray, 2018) may be
beneficial for SEP predictions as well. We conclude that our current real-time
forecasting tools can satisfactorily predict CME arrival times as well as SEP
peak fluxes and event durations (except the few hours following the event
onset) for well-connected observers. The strength of the modelling setup
employed here is that WSA–Enlil is already operational for real-time
forecasts, whilst SEPMOD is run as a computationally-efficient post-processing
procedure on the Enlil simulation output. In fact, SEP predictions from SEPMOD
driven in real time are currently displayed on the SEP Scoreboard at NASA’s
CCMC (https://ccmc.gsfc.nasa.gov/challenges/sep). Our results indicate that
coupling SEPMOD with the existing WSA–Enlil framework in operational settings
can provide useful information on the duration and peak fluxes of a gradual
SEP event.

We have also shown that a combination of remote-sensing observers placed at
the Lagrange L1 and L5 points (i.e., separated by ${\sim}60^{\circ}$) can
constrain a CME’s propagation direction even over a broad range of
heliolongitudes. However, such a configuration is already no longer available,
since the STEREO-A spacecraft is currently approaching Earth at a rate of
${\sim}20^{\circ}$ per year until reaching radial alignment in August 2023. By
then, the advantages of remote-sensing observations of the Sun from two well-
separated viewpoints will be lost at least for a while (we note that SolO is
equipped with a coronagraph and a heliospheric imager, but its rapidly-
changing heliocentric distance and longitudinal separation with Earth may not
be optimal for forecasting purposes). Dedicated missions to the Lagrange L4
and/or L5 points (e.g., Bemporad, 2021; Posner et al., 2021; Vourlidas, 2015)
may prove beneficial in this regard. This includes the European Space Agency
(ESA)’s Vigil (Pulkkinen et al., 2019) mission, which is currently in
development to place a spacecraft equipped with remote-sensing and in-situ
instruments at L5. As to in-situ measurements, it is clear that the
availability of multi-point observers at different radial distances and
heliolongitudes is crucial for analysing and validating modelling results
across the entire inner heliosphere. Given the presence of currently-
operational spacecraft at six independent locations (i.e., the ones explored
in this work), it is important to consider the future opportunities for
heliophysics and space weather science via multi-point studies and coordinated
observations (e.g., Hadid et al., 2021; Möstl et al., 2022; Velli et al.,
2020). In conclusion, the potential for significant progress in heliophysics
and space weather science will be realised as future studies increasingly
utilise the multi-spacecraft capabilities of the Heliophysics System
Observatory.

##  Appendix A WSA–Enlil–SEPMOD Runs

Results of each of the mini-ensemble WSA–Enlil–SEPMOD simulation runs are
shown against the corresponding in-situ data in Figures 7 to 12. Magnetic
field and plasma measurements are reported for each observer (where available)
and compared directly with Enlil data—including the so-called ‘ambient’ run,
which indicates the corresponding run of the solar wind background without
CMEs. In each figure, the dashed teal lines mark the peak times of Flare1 and
Flare2 (associated with CME2 and CME5, respectively), whilst the solid grey
lines mark the arrival in situ of a CME-driven shock (with the driving CME
indicated for each case). We remark that speed and density data at Mars
(Figure 9) as well as speed data at SolO (Figure 12) are derived rather than
directly measured, and are thus expected to be characterised by non-negligible
uncertainties. Particle measurements are shown at three illustrative energies
(roughly in the ranges 1–6 MeV, 20–25 MeV, and 40–60 MeV) and compared with
SEPMOD data that have been interpolated to the centre of each energy channel
(indicated to the top left of the corresponding panel). Note that, in each
panel, the lower end of the Y-axis has been cut immediately above the
corresponding instrument’s noise level (i.e., the instrumental background). At
PSP (Figure 7), STEREO-A (Figure 8), Earth (Figure 10), and SolO (Figure 12),
SEPMOD data are directly compared to the measured differential proton fluxes.
At Bepi (Figure 11), SEPMOD fluxes are shown against proton countrates at
well-defined energy channels, and the two datasets are arbitrarily normalised
with respect to each other. We also remark that Bepi/BERM is placed behind the
radiator pointing towards the $-{Y}$ direction, meaning that the instrument is
pointing in the anti-sunward direction. This aspect, together with the packed
configuration of Bepi during its cruise phase, could imply that the spacecraft
itself may screen some particles. Finally, we note that at the moment, only
uncalibrated “raw” BERM data are available, and a proper calibration is in
planning. At Mars (Figure 9), the data in the lowest energy channel are shown
in flux units, whilst the remaining two sets of measurements are shown in
countrates. The first comes from particles in the Foil–Thick–Open (FTO)
detector of MAVEN/SEP, which corresponds to approximately 12–78 MeV protons
(more information can be found in Larson et al., 2015; Lee et al., 2018), and
is shown against SEPMOD results at 45 MeV (centre of the 12–78 MeV range). The
second comes from MOdy/HEND counts that are sensitive to particles of energy
as low as 0.2 MeV (Sánchez-Cano et al., 2018) up to galactic cosmic rays, and
is shown arbitrarily agains SEPMOD results at 60 MeV.

Figure 7: WSA–Enlil–SEPMOD results at PSP shown against PSP data. The
parameters shown are: (a) magnetic field magnitude, (b) $\theta$ and (c)
$\phi$ angles of the magnetic field, (d) solar wind speed, (e) proton density,
and (f–h) particle measurements in three different energy channels. Figure 8:
WSA–Enlil–SEPMOD results at STEREO-A shown against STEREO-A data. The
parameters shown are: (a) magnetic field magnitude, (b) $\theta$ and (c)
$\phi$ angles of the magnetic field, (d) solar wind speed, (e) proton density,
and (f–h) particle measurements in three different energy channels. Figure 9:
WSA–Enlil–SEPMOD results at Mars shown against data from Mars orbit. The
parameters shown are: (a) magnetic field magnitude, (b) $\theta$ and (c)
$\phi$ angles of the magnetic field, (d) solar wind speed, (e) proton density,
and (f–h) particle measurements in three different energy channels. Figure 10:
WSA–Enlil–SEPMOD results at Earth shown against data taken at Earth’s Lagrange
L1 point. The parameters shown are: (a) magnetic field magnitude, (b) $\theta$
and (c) $\phi$ angles of the magnetic field, (d) solar wind speed, (e) proton
density, and (f–h) particle measurements in three different energy channels.
Figure 11: WSA–Enlil–SEPMOD results at Bepi shown against Bepi data. The
parameters shown are: (a) magnetic field magnitude, (b) $\theta$ and (c)
$\phi$ angles of the magnetic field, (d) solar wind speed, (e) proton density,
and (f–h) particle measurements in three different energy channels. Figure 12:
WSA–Enlil–SEPMOD results at SolO shown against SolO data. The parameters shown
are: (a) magnetic field magnitude, (b) $\theta$ and (c) $\phi$ angles of the
magnetic field, (d) solar wind speed, (e) proton density, and (f–h) particle
measurements in three different energy channels.

##  Appendix B Snapshots from WSA–Enlil

Snapshots from the WSA–Enlil simulation runs are shown in Figures 13 to 16.
Each figure shows the modelled radial solar wind speed on the ecliptic plane
at four different times. The five CMEs analysed in this study are labelled in
each panel.

Figure 13: Snapshots from the WSA–Enlil simulation for Run1 on the ecliptic
plane. The parameter shown is the radial solar wind speed ($V_{\mathrm{r}}$).
From https://ccmc.gsfc.nasa.gov/database_SH/Erika_Palmerio_082921_SH_1.php.
Figure 14: Snapshots from the WSA–Enlil simulation for Run2 on the ecliptic
plane. The parameter shown is the radial solar wind speed ($V_{\mathrm{r}}$).
From https://ccmc.gsfc.nasa.gov/database_SH/Erika_Palmerio_082921_SH_2.php.
Figure 15: Snapshots from the WSA–Enlil simulation for Run3 on the ecliptic
plane. The parameter shown is the radial solar wind speed ($V_{\mathrm{r}}$).
From https://ccmc.gsfc.nasa.gov/database_SH/Erika_Palmerio_082921_SH_3.php.
Figure 16: Snapshots from the WSA–Enlil simulation for Run4 on the ecliptic
plane. The parameter shown is the radial solar wind speed ($V_{\mathrm{r}}$).
From https://ccmc.gsfc.nasa.gov/database_SH/Erika_Palmerio_082921_SH_4.php.

## Data Availability Statement

Simulation results have been provided by the Community Coordinated Modeling
Center at Goddard Space Flight Center through their public Runs on Request
system (http://ccmc.gsfc.nasa.gov).

DONKI runs used in this study:

  * •

CME1: https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CMEAnalysis/16146/2

  * •

CME2: https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CMEAnalysis/16172/1

  * •

CME3: https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CMEAnalysis/16186/3

  * •

CME4: https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CMEAnalysis/16204/2

  * •

CME5: https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CMEAnalysis/16219/2

WSA–Enlil–SEPMOD runs performed in this study:

  * •

Run1:

    * –

Enlil:
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_082921_SH_1

    * –

SEPMOD (GOES-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_1

    * –

SEPMOD (IMP8-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_2

  * •

Run2:

    * –

Enlil:
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_082921_SH_2

    * –

SEPMOD (GOES-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_3

    * –

SEPMOD (IMP8-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_4

  * •

Run3:

    * –

Enlil:
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_082921_SH_3

    * –

SEPMOD (GOES-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_5

    * –

SEPMOD (IMP8-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_6

  * •

Run4:

    * –

Enlil:
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_082921_SH_4

    * –

SEPMOD (GOES-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_7

    * –

SEPMOD (IMP8-like):
https://ccmc.gsfc.nasa.gov/results/viewrun.php?domain=SH&runnumber=Erika_Palmerio_090121_SH_8

Remote-sensing data from SDO, SOHO, and STEREO are openly available at the
Virtual Solar Observatory (VSO; https://sdac.virtualsolar.org/). These data
were processed and analysed trough SunPy (SunPy Community et al., 2020), IDL
SolarSoft (Freeland and Handy, 1998), and the ESA JHelioviewer software
(Müller et al., 2017).

PSP, STEREO, Wind, and ACE in-situ data are publicly available at NASA’s
Coordinated Data Analysis Web (CDAWeb) database
(https://cdaweb.sci.gsfc.nasa.gov/index.html/). MAVEN data can be accessed at
the Planetary Plasma Interactions (PPI) Node of NASA’s Planetary Data System
(PDS; https://pds-ppi.igpp.ucla.edu). MEX data are stored at at ESA’s
Planetary Science Archive (PSA; https://archives.esac.esa.int/psa). MOdy data
are available at the Geosciences Node of the PDS (https://pds-
geosciences.wustl.edu/). SOHO particle data can be downloaded from the
SOHO/ERNE webpage (https://srl.utu.fi/projects/erne/). The Bepi data used in
this study are stored at https://doi.org/10.25392/leicester.data.16941040, and
the full mission data set will be released in the future at ESA’s PSA. SolO
data are openly available at ESA’s Solar Orbiter Archive
(http://soar.esac.esa.int/soar/).

###### Acknowledgements.

E. Palmerio’s research was supported by the NASA Living With a Star (LWS) Jack
Eddy Postdoctoral Fellowship Program, administered by UCAR’s Cooperative
Programs for the Advancement of Earth System Science (CPAESS) under award no.
NNX16AK22G. C. O. Lee acknowledges support from NASA MAVEN Project subcontract
via Grant no. NNH10CC04C, managed by the University of Colorado. C. O. Lee and
J. G. Luhmann acknowledge support from the STEREO Project via the
STEREO/IMPACT grant to UC Berkeley. D. Lario and I. G. Richardson acknowledge
support from NASA LWS programs NNH17ZDA001N-LWS and NNH19ZDA001N-LWS, as well
as the Goddard Space Flight Center Heliophysics Innovation Fund (HIF) program.
B. Sánchez-Cano acknowledges support through UK-STFC Ernest Rutherford
Fellowship ST/V004115/1 and STFC grants ST/S000429/1 and ST/V000209/1. K.
Steinvall and Y. V. Khotyaintsev acknowledge support from the Swedish Research
Council, grant 2016-05507, and the Swedish National Space Agency (SNSA), grant
20/136. C. Möstl and A. J. Weiss thank the Austrian Science Fund (FWF):
P31521-N27, P31659-N27. The WSA model was developed by C. N. Arge (currently
at NASA/GSFC), the Enlil model was developed by D. Odstrcil (currently at
GMU), and the SEPMOD model was developed by J. Luhmann (currently at UCB).
Finally, we thank the Mission Teams of all the spacecraft and instruments
employed in this study. This work was supported by NASA’s Parker Solar Probe
Mission, contract no. NNN06AA01C. Parker Solar Probe was designed, built, and
is now operated by the Johns Hopkins Applied Physics Laboratory as part of
NASA’s LWS program.

## References

  * Acuña et al. (2008) Acuña, M. H., Curtis, D., Scheifele, J. L., Russell, C. T., Schroeder, P., Szabo, A., and Luhmann, J. G. (2008), The STEREO/IMPACT Magnetic Field Experiment, Space Sci. Rev., 136(1-4), 203–226, 10.1007/s11214-007-9259-2.
  * Agueda et al. (2014) Agueda, N., Klein, K. L., Vilmer, N., Rodríguez-Gasén, R., Malandraki, O. E., Papaioannou, A., Subirà, M., Sanahuja, B., Valtonen, E., Dröge, W., Nindos, A., Heber, B., Braune, S., Usoskin, I. G., Heynderickx, D., Talew, E., and Vainio, R. (2014), Release timescales of solar energetic particles in the low corona, A&A, 570, A5, 10.1051/0004-6361/201423549.
  * Amerstorfer et al. (2018) Amerstorfer, T., Möstl, C., Hess, P., Temmer, M., Mays, M. L., Reiss, M. A., Lowrance, P., and Bourdin, P. A. (2018), Ensemble Prediction of a Halo Coronal Mass Ejection Using Heliospheric Imagers,  Space Weather, 16(7), 784–801, 10.1029/2017SW001786.
  * Amerstorfer et al. (2021) Amerstorfer, T., Hinterreiter, J., Reiss, M. A., Möstl, C., Davies, J. A., Bailey, R. L., Weiss, A. J., Dumbović, M., Bauer, M., Amerstorfer, U. V., and Harrison, R. A. (2021), Evaluation of CME Arrival Prediction Using Ensemble Modeling Based on Heliospheric Imaging Observations,  Space Weather, 19(1), e2020SW002553, 10.1029/2020SW002553.
  * Anastasiadis et al. (2017) Anastasiadis, A., Papaioannou, A., Sandberg, I., Georgoulis, M., Tziotziou, K., Kouloumvakos, A., and Jiggens, P. (2017), Predicting Flares and Solar Energetic Particle Events: The FORSPEF Tool, Sol. Phys., 292(9), 134, 10.1007/s11207-017-1163-7.
  * Anastasiadis et al. (2019) Anastasiadis, A., Lario, D., Papaioannou, A., Kouloumvakos, A., and Vourlidas, A. (2019), Solar energetic particles in the inner heliosphere: status and open questions,  Philosophical Transactions of the Royal Society of London Series A, 377(2148), 20180,100, 10.1098/rsta.2018.0100.
  * Arge et al. (2004) Arge, C. N., Luhmann, J. G., Odstrcil, D., Schrijver, C. J., and Li, Y. (2004), Stream structure and coronal sources of the solar wind during the May 12th, 1997 CME,  Journal of Atmospheric and Solar-Terrestrial Physics, 66(15-16), 1295–1309, 10.1016/j.jastp.2004.03.018.
  * Bain et al. (2016) Bain, H. M., Mays, M. L., Luhmann, J. G., Li, Y., Jian, L. K., and Odstrcil, D. (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.
  * Bain et al. (2021) Bain, H. M., Steenburgh, R. A., Onsager, T. G., and Stitely, E. M. (2021), A Summary of National Oceanic and Atmospheric Administration Space Weather Prediction Center Proton Event Forecast Performance and Skill,  Space Weather, 19(7), e2020SW002670, 10.1029/2020SW002670.
  * Bale et al. (2016) Bale, S. D., Goetz, K., Harvey, P. R., Turin, P., Bonnell, J. W., Dudok de Wit, T., Ergun, R. E., MacDowall, R. J., Pulupa, M., Andre, M., Bolton, M., Bougeret, J. L., Bowen, T. A., Burgess, D., Cattell, C. A., Chandran, B. D. G., Chaston, C. C., Chen, C. H. K., Choi, M. K., Connerney, J. E., Cranmer, S., Diaz-Aguado, M., Donakowski, W., Drake, J. F., Farrell, W. M., Fergeau, P., Fermin, J., Fischer, J., Fox, N., Glaser, D., Goldstein, M., Gordon, D., Hanson, E., Harris, S. E., Hayes, L. M., Hinze, J. J., Hollweg, J. V., Horbury, T. S., Howard, R. A., Hoxie, V., Jannet, G., Karlsson, M., Kasper, J. C., Kellogg, P. J., Kien, M., Klimchuk, J. A., Krasnoselskikh, V. V., Krucker, S., Lynch, J. J., Maksimovic, M., Malaspina, D. M., Marker, S., Martin, P., Martinez-Oliveros, J., McCauley, J., McComas, D. J., McDonald, T., Meyer-Vernet, N., Moncuquet, M., Monson, S. J., Mozer, F. S., Murphy, S. D., Odom, J., Oliverson, R., Olson, J., Parker, E. N., Pankow, D., Phan, T., Quataert, E., Quinn, T., Ruplin, S. W., Salem, C., Seitz, D., Sheppard, D. A., Siy, A., Stevens, K., Summers, D., Szabo, A., Timofeeva, M., Vaivads, A., Velli, M., Yehle, A., Werthimer, D., and Wygant, J. R. (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.
  * Barabash et al. (2006) Barabash, S., Lundin, R., Andersson, H., Brinkfeldt, K., Grigoriev, A., Gunell, H., Holmström, M., Yamauchi, M., Asamura, K., Bochsler, P., Wurz, P., Cerulli-Irelli, R., Mura, A., Milillo, A., Maggi, M., Orsini, S., Coates, A. J., Linder, D. R., Kataria, D. O., Curtis, C. C., Hsieh, K. C., Sandel, B. R., Frahm, R. A., Sharber, J. R., Winningham, J. D., Grande, M., Kallio, E., Koskinen, H., Riihelä, P., Schmidt, W., Säles, T., Kozyra, J. U., Krupp, N., Woch, J., Livi, S., Luhmann, J. G., McKenna-Lawlor, S., Roelof, E. C., Williams, D. J., Sauvaud, J.-A., Fedorov, A., and Thocaven, J.-J. (2006), The Analyzer of Space Plasmas and Energetic Atoms (ASPERA-3) for the Mars Express Mission, Space Sci. Rev., 126, 113–164, 10.1007/s11214-006-9124-8.
  * Bauer et al. (2021) Bauer, M., Amerstorfer, T., Hinterreiter, J., Weiss, A. J., Davies, J. A., Möstl, C., Amerstorfer, U. V., Reiss, M. A., and Harrison, R. A. (2021), Predicting CMEs Using ELEvoHI With STEREO-HI Beacon Data,  Space Weather, 19(12), e2021SW002873, 10.1029/2021SW002873.
  * Bemporad (2021) Bemporad, A. (2021), Possible advantages of a twin spacecraft Heliospheric mission at the Sun-Earth Lagrangian points L4 and L5,  Frontiers in Astronomy and Space Sciences, 8, 627576, 10.3389/fspas.2021.627576.
  * Benkhoff et al. (2010) Benkhoff, J., van Casteren, J., Hayakawa, H., Fujimoto, M., Laakso, H., Novara, M., Ferri, P., Middleton, H. R., and Ziethe, R. (2010), BepiColombo—Comprehensive exploration of Mercury: Mission overview and science goals, Planet. Space Sci., 58(1-2), 2–20, 10.1016/j.pss.2009.09.020.
  * Biesecker et al. (2008) Biesecker, D. A., Webb, D. F., and St. Cyr, O. C. (2008), STEREO Space Weather and the Space Weather Beacon, Space Sci. Rev., 136(1-4), 45–65, 10.1007/s11214-007-9165-7.
  * Boynton et al. (2004) Boynton, W. V., Feldman, W. C., Mitrofanov, I. G., Evans, L. G., Reedy, R. C., Squyres, S. W., Starr, R., Trombka, J. I., D’Uston, C., Arnold, J. R., Englert, P. A. J., Metzger, A. E., Wänke, H., Brückner, J., Drake, D. M., Shinohara, C., Fellows, C., Hamara, D. K., Harshman, K., Kerry, K., Turner, C., Ward, M., Barthe, H., Fuller, K. R., Storms, S. A., Thornton, G. W., Longmire, J. L., Litvak, M. L., and Ton’chev, A. K. (2004), The Mars Odyssey Gamma-Ray Spectrometer Instrument Suite, Space Sci. Rev., 110, 37–83, 10.1023/B:SPAC.0000021007.76126.15.
  * Brueckner et al. (1995) Brueckner, G. E., Howard, R. A., Koomen, M. J., Korendyke, C. M., Michels, D. J., Moses, J. D., Socker, D. G., Dere, K. P., Lamy, P. L., Llebaria, A., Bout, M. V., Schwenn, R., Simnett, G. M., Bedford, D. K., and Eyles, C. J. (1995), The Large Angle Spectroscopic Coronagraph (LASCO), Sol. Phys., 162(1-2), 357–402, 10.1007/BF00733434.
  * Bruno and Richardson (2021) Bruno, A., and Richardson, I. G. (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.
  * Burlaga et al. (1981) Burlaga, L., Sittler, E., Mariani, F., and Schwenn, R. (1981), Magnetic loop behind an interplanetary shock: Voyager, Helios, and IMP 8 observations, J. Geophys. Res., 86(A8), 6673–6684, 10.1029/JA086iA08p06673.
  * Cane et al. (2010) Cane, H. V., Richardson, I. G., and von Rosenvinge, T. T. (2010), A study of solar energetic particle events of 1997-2006: Their composition and associations, J. Geophys. Res., 115(A8), A08101, 10.1029/2009JA014848.
  * Case et al. (2020) Case, A. W., Kasper, J. C., Stevens, M. L., Korreck, K. E., Paulson, K., Daigneau, P., Caldwell, D., Freeman, M., Henry, T., Klingensmith, B., Bookbinder, J. A., Robinson, M., Berg, P., Tiu, C., Wright, J., K. H., Reinhart, M. J., Curtis, D., Ludlam, M., Larson, D., Whittlesey, P., Livi, R., Klein, K. G., and Martinović, M. M. (2020), The Solar Probe Cup on the Parker Solar Probe, ApJS, 246(2), 43, 10.3847/1538-4365/ab5a7b.
  * Cash et al. (2015) Cash, M. D., Biesecker, D. A., Pizzo, V., de Koning, C. A., Millward, G., Arge, C. N., Henney, C. J., and Odstrcil, D. (2015), Ensemble Modeling of the 23 July 2012 Coronal Mass Ejection,  Space Weather, 13(10), 611–625, 10.1002/2015SW001232.
  * Chicarro et al. (2004) Chicarro, A., Martin, P., and Trautner, R. (2004), The Mars Express mission: an overview, in Mars Express: the Scientific Payload, ESA Special Publication, vol. 1240, edited by A. Wilson and A. Chicarro, pp. 3–13.
  * Cohen et al. (2014) Cohen, C. M. S., Mason, G. M., Mewaldt, R. A., and Wiedenbeck, M. E. (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.
  * Cohen et al. (2021) Cohen, C. M. S., Christian, E. R., Cummings, A. C., Davis, A. J., Desai, M. I., de Nolfo, G. A., Giacalone, J., Hill, M. E., Joyce, C. J., Labrador, A. W., Leske, R. A., Matthaeus, W. H., McComas, D. J., McNutt, R. L., Mewaldt, R. A., Mitchell, D. G., Mitchell, J. G., Rankin, J. S., Roelof, E. C., Schwadron, N. A., Stone, E. C., Szalay, J. R., Wiedenbeck, M. E., Vourlidas, A., Bale, S. D., Pulupa, M., and MacDowall, R. J. (2021), PSP/IS$\odot$IS observations of the 29 November 2020 solar energetic particle event, A&A, 656, A29, 10.1051/0004-6361/202140967.
  * Corona-Romero et al. (2017) Corona-Romero, P., Gonzalez-Esparza, J. A., Perez-Alanis, C. A., Aguilar-Rodriguez, E., de-la-Luz, V., and Mejia-Ambriz, J. C. (2017), Calculating travel times and arrival speeds of CMEs to Earth: An analytic tool for space weather forecasting,  Space Weather, 15(3), 464–483, 10.1002/2016SW001489.
  * Cremades and Bothmer (2004) Cremades, H., and Bothmer, V. (2004), On the three-dimensional configuration of coronal mass ejections, A&A, 422, 307–322, 10.1051/0004-6361:20035776.
  * Davies et al. (2020) Davies, E. E., Forsyth, R. J., Good, S. W., and Kilpua, E. K. J. (2020), On the Radial and Longitudinal Variation of a Magnetic Cloud: ACE, Wind, ARTEMIS and Juno Observations, Sol. Phys., 295(11), 157, 10.1007/s11207-020-01714-z.
  * Desai and Giacalone (2016) Desai, M., and Giacalone, J. (2016), Large gradual solar energetic particle events,  Living Reviews in Solar Physics, 13, 3, 10.1007/s41116-016-0002-5.
  * Domingo et al. (1995) Domingo, V., Fleck, B., and Poland, A. I. (1995), The SOHO Mission: an Overview, Sol. Phys., 162(1-2), 1–37, 10.1007/BF00733425.
  * Dresing et al. (2012) Dresing, N., Gómez-Herrero, R., Klassen, A., Heber, B., Kartavykh, Y., and Dröge, W. (2012), The Large Longitudinal Spread of Solar Energetic Particles During the 17 January 2010 Solar Event, Sol. Phys., 281(1), 281–300, 10.1007/s11207-012-0049-y.
  * Dresing et al. (2014) Dresing, N., Gómez-Herrero, R., Heber, B., Klassen, A., Malandraki, O., Dröge, W., and Kartavykh, Y. (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.
  * Dumbović et al. (2018) Dumbović, M., Čalogović, J., Vršnak, B., Temmer, M., Mays, M. L., Veronig, A., and Piantschitsch, I. (2018), The Drag-based Ensemble Model (DBEM) for Coronal Mass Ejection Propagation, ApJ, 854(2), 180, 10.3847/1538-4357/aaaa66.
  * Dumbović et al. (2019) Dumbović, M., Guo, J., Temmer, M., Mays, M. L., Veronig, A., Heinemann, S. G., Dissauer, K., Hofmeister, S., Halekas, J., Möstl, C., Amerstorfer, T., Hinterreiter, J., Banjac, S., Herbst, K., Wang, Y., Holzknecht, L., Leitner, M., and Wimmer–Schweingruber, R. F. (2019), Unusual Plasma and Particle Signatures at Mars and STEREO-A Related to CME-CME Interaction, ApJ, 880(1), 18, 10.3847/1538-4357/ab27ca.
  * Dumbović et al. (2021) Dumbović, M., Čalogović, J., Martinić, K., Vršnak, B., Sudar, D., Temmer, M., and Veronig, A. (2021), Drag-based model (DBM) tools for forecast of coronal mass ejection arrival time and speed,  Frontiers in Astronomy and Space Sciences, 8, 639986, 10.3389/fspas.2021.639986.
  * Eastwood et al. (2017) Eastwood, J. P., Biffis, E., Hapgood, M. A., Green, L., Bisi, M. M., Bentley, R. D., Wicks, R., McKinnell, L. A., Gibbs, M., and Burnett, C. (2017), The Economic Impact of Space Weather: Where Do We Stand?,  Risk Analysis, 37(2), 206–218, 10.1111/risa.12765.
  * Emmons et al. (2013) Emmons, D., Acebal, A., Pulkkinen, A., Taktakishvili, A., MacNeice, P., and Odstrcil, D. (2013), Ensemble forecasting of coronal mass ejections using the WSA-ENLIL with CONED Model,  Space Weather, 11(3), 95–106, 10.1002/swe.20019.
  * Farrugia et al. (2011) Farrugia, C. J., Berdichevsky, D. B., Möstl, C., Galvin, A. B., Leitner, M., Popecki, M. A., Simunac, K. D. C., Opitz, A., Lavraud, B., Ogilvie, K. W., Veronig, A. M., Temmer, M., Luhmann, J. G., and Sauvaud, J. A. (2011), Multiple, distant (40°) in situ observations of a magnetic cloud and a corotating interaction region complex,  Journal of Atmospheric and Solar-Terrestrial Physics, 73(10), 1254–1269, 10.1016/j.jastp.2010.09.011.
  * Fisher and Munro (1984) Fisher, R. R., and Munro, R. H. (1984), Coronal transient geometry. I - The flare-associated event of 1981 March 25, ApJ, 280, 428–439, 10.1086/162009.
  * Fox et al. (2016) Fox, N. J., Velli, M. C., Bale, S. D., Decker, R., Driesman, A., Howard, R. A., Kasper, J. C., Kinnison, J., Kusterer, M., Lario, D., Lockwood, M. K., McComas, D. J., Raouafi, N. E., and Szabo, A. (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.
  * Freeland and Handy (1998) Freeland, S. L., and Handy, B. N. (1998), Data Analysis with the SolarSoft System, Sol. Phys., 182, 497–500, 10.1023/A:1005038224881.
  * Galvin et al. (2008) Galvin, A. B., Kistler, L. M., Popecki, M. A., Farrugia, C. J., Simunac, K. D. C., Ellis, L., Möbius, E., Lee, M. A., Boehm, M., Carroll, J., Crawshaw, A., Conti, M., Demaine, P., Ellis, S., Gaidos, J. A., Googins, J., Granoff, M., Gustafson, A., Heirtzler, D., King, B., Knauss, U., Levasseur, J., Longworth, S., Singer, K., Turco, S., Vachon, P., Vosbury, M., Widholm, M., Blush, L. M., Karrer, R., Bochsler, P., Daoudi, H., Etter, A., Fischer, J., Jost, J., Opitz, A., Sigrist, M., Wurz, P., Klecker, B., Ertl, M., Seidenschwang, E., Wimmer-Schweingruber, R. F., Koeten, M., Thompson, B., and Steinfeld, D. (2008), The Plasma and Suprathermal Ion Composition (PLASTIC) Investigation on the STEREO Observatories, Space Sci. Rev., 136, 437–486, 10.1007/s11214-007-9296-x.
  * Giacalone et al. (2021) Giacalone, J., Burgess, D., Bale, S. D., Desai, M. I., Mitchell, J. G., Lario, D., Chen, C. H. K., Christian, E. R., de Nolfo, G. A., Hill, M. E., Matthaeus, W. H., McComas, D. J., McNutt, R. L., Mitchell, D. G., Roelof, E. C., Schwadron, N. A., Getachew, T., and Joyce, C. J. (2021), Energetic Particles Associated with a Coronal Mass Ejection Shock Interacting with a Convected Magnetic Structure, ApJ, 921(2), 102, 10.3847/1538-4357/ac1ce1.
  * Gold et al. (1998) Gold, R. E., Krimigis, S. M., Hawkins, I., S. E., Haggerty, D. K., Lohr, D. A., Fiore, E., Armstrong, T. P., Holland, G., and Lanzerotti, L. J. (1998), Electron, Proton, and Alpha Monitor on the Advanced Composition Explorer spacecraft, Space Sci. Rev., 86, 541–562, 10.1023/A:1005088115759.
  * Gómez-Herrero et al. (2015) Gómez-Herrero, R., Dresing, N., Klassen, A., Heber, B., Lario, D., Agueda, N., Malandraki, O. E., Blanco, J. J., Rodríguez-Pacheco, J., and Banjac, S. (2015), Circumsolar Energetic Particle Distribution on 2011 November 3, ApJ, 799(1), 55, 10.1088/0004-637X/799/1/55.
  * Gonzalez et al. (1994) Gonzalez, W. D., Joselyn, J. A., Kamide, Y., Kroehl, H. W., Rostoker, G., Tsurutani, B. T., and Vasyliunas, V. M. (1994), What is a geomagnetic storm?, J. Geophys. Res., 99, 5771–5792, 10.1029/93JA02867.
  * Gonzi et al. (2021) Gonzi, S., Weinzierl, M., Bocquet, F. X., Bisi, M. M., Odstrcil, D., Jackson, B. V., Yeates, A. R., Jackson, D. R., Henney, C. J., and Nick Arge, C. (2021), Impact of Inner Heliospheric Boundary Conditions on Solar Wind Predictions at Earth,  Space Weather, 19(1), e2020SW002499, 10.1029/2020SW002499.
  * Good et al. (2019) Good, S. W., Kilpua, E. K. J., LaMoury, A. T., Forsyth, R. J., Eastwood, J. P., and Möstl, C. (2019), Self-Similarity of ICME Flux Ropes: Observations by Radially Aligned Spacecraft in the Inner Heliosphere,  Journal of Geophysical Research: Space Physics, 124(7), 4960–4982, 10.1029/2019JA026475.
  * Gopalswamy et al. (2001) Gopalswamy, N., Lara, A., Yashiro, S., Kaiser, M. L., and Howard, R. A. (2001), Predicting the 1-AU arrival times of coronal mass ejections, J. Geophys. Res., 106(A12), 29,207–29,218, 10.1029/2001JA000177.
  * Gopalswamy et al. (2013) Gopalswamy, N., Xie, H., Akiyama, S., Yashiro, S., Usoskin, I. G., and Davila, J. M. (2013), The First Ground Level Enhancement Event of Solar Cycle 24: Direct Observation of Shock Formation and Particle Release Heights, ApJ, 765(2), L30, 10.1088/2041-8205/765/2/L30.
  * Hadid et al. (2021) Hadid, L. Z., Génot, V., Aizawa, S., Milillo, A., Zender, J., Murakami, G., Benkhoff, J., Zouganelis, I., Alberti, T., André, N., Bebesi, Z., Califano, F., Dimmock, A. P., Dosa, M., Escoubet, C. P., Griton, L., Ho, G. C., Horbury, T. S., Iwai, K., Janvier, M., Kilpua, E., Lavraud, B., Madar, A., Miyoshi, Y., Müller, D., Pinto, R. F., Rouillard, A. P., Raines, J. M., Raouafi, N., Sahraoui, F., Sánchez-Cano, B., Shiota, D., Vainio, R., and Walsh, A. (2021), BepiColombo’s cruise phase: unique opportunity for synergistic observations,  Frontiers in Astronomy and Space Sciences, 8, 718024, 10.3389/fspas.2021.718024.
  * Harvey et al. (1996) Harvey, J. W., Hill, F., Hubbard, R. P., Kennedy, J. R., Leibacher, J. W., Pintar, J. A., Gilman, P. A., Noyes, R. W., Title, A. M., Toomre, J., Ulrich, R. K., Bhatnagar, A., Kennewell, J. A., Marquette, W., Patron, J., Saa, O., and Yasukawa, E. (1996), The Global Oscillation Network Group (GONG) Project,  Science, 272(5266), 1284–1286, 10.1126/science.272.5266.1284.
  * Hess and Zhang (2015) Hess, P., and Zhang, J. (2015), Predicting CME Ejecta and Sheath Front Arrival at L1 with a Data-constrained Physical Model, ApJ, 812(2), 144, 10.1088/0004-637X/812/2/144.
  * Heyner et al. (2021) Heyner, D., Auster, H. U., Fornaçon, K. H., Carr, C., Richter, I., Mieth, J. Z. D., Kolhey, P., Exner, W., Motschmann, U., Baumjohann, W., Matsuoka, A., Magnes, W., Berghofer, G., Fischer, D., Plaschke, F., Nakamura, R., Narita, Y., Delva, M., Volwerk, M., Balogh, A., Dougherty, M., Horbury, T., Langlais, B., Mandea, M., Masters, A., Oliveira, J. S., Sánchez-Cano, B., Slavin, J. A., Vennerstrøm, S., Vogt, J., Wicht, J., and Glassmeier, K. H. (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., O’Brien, H., Carrasco Blazquez, I., Bendyk, M., Brown, P., Hudson, R., Evans, V., Oddy, T. M., Carr, C. M., Beek, T. J., Cupido, E., Bhattacharya, S., Dominguez, J. A., Matthews, L., Myklebust, V. R., Whiteside, B., Bale, S. D., Baumjohann, W., Burgess, D., Carbone, V., Cargill, P., Eastwood, J., Erdös, G., Fletcher, L., Forsyth, R., Giacalone, J., Glassmeier, K. H., Goldstein, M. L., Hoeksema, T., Lockwood, M., Magnes, W., Maksimovic, M., Marsch, E., Matthaeus, W. H., Murphy, N., Nakariakov, V. M., Owen, C. J., Owens, M., Rodriguez-Pacheco, J., Richter, I., Riley, P., Russell, C. T., Schwartz, S., Vainio, R., Velli, M., Vennerstrom, S., Walsh, R., Wimmer-Schweingruber, R. F., Zank, G., Müller, D., Zouganelis, I., and Walsh, A. P. (2020), The Solar Orbiter magnetometer, A&A, 642, A9, 10.1051/0004-6361/201937257.
  * Howard et al. (2008) Howard, R. A., Moses, J. D., Vourlidas, A., Newmark, J. S., Socker, D. G., Plunkett, S. P., Korendyke, C. M., Cook, J. W., Hurley, A., Davila, J. M., Thompson, W. T., St Cyr, O. C., Mentzell, E., Mehalick, K., Lemen, J. R., Wuelser, J. P., Duncan, D. W., Tarbell, T. D., Wolfson, C. J., Moore, A., Harrison, R. A., Waltham, N. R., Lang, J., Davis, C. J., Eyles, C. J., Mapson-Menard, H., Simnett, G. M., Halain, J. P., Defise, J. M., Mazy, E., Rochus, P., Mercier, R., Ravet, M. F., Delmotte, F., Auchere, F., Delaboudiniere, J. P., Bothmer, V., Deutsch, W., Wang, D., Rich, N., Cooper, S., Stephens, V., Maahs, G., Baugh, R., McMullin, D., and Carter, T. (2008), Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI), Space Sci. Rev., 136(1-4), 67–115, 10.1007/s11214-008-9341-4.
  * Isavnin (2016) Isavnin, A. (2016), FRiED: A Novel Three-dimensional Model of Coronal Mass Ejections, ApJ, 833, 267, 10.3847/1538-4357/833/2/267.
  * Jakosky et al. (2015) Jakosky, B. M., Lin, R. P., Grebowsky, J. M., Luhmann, J. G., Mitchell, D. F., Beutelschies, G., Priser, T., Acuna, M., Andersson, L., Baird, D., Baker, D., Bartlett, R., Benna, M., Bougher, S., Brain, D., Carson, D., Cauffman, S., Chamberlin, P., Chaufray, J. Y., Cheatom, O., Clarke, J., Connerney, J., Cravens, T., Curtis, D., Delory, G., Demcak, S., DeWolfe, A., Eparvier, F., Ergun, R., Eriksson, A., Espley, J., Fang, X., Folta, D., Fox, J., Gomez-Rosa, C., Habenicht, S., Halekas, J., Holsclaw, G., Houghton, M., Howard, R., Jarosz, M., Jedrich, N., Johnson, M., Kasprzak, W., Kelley, M., King, T., Lankton, M., Larson, D., Leblanc, F., Lefevre, F., Lillis, R., Mahaffy, P., Mazelle, C., McClintock, W., McFadden, J., Mitchell, D. L., Montmessin, F., Morrissey, J., Peterson, W., Possel, W., Sauvaud, J. A., Schneider, N., Sidney, W., Sparacino, S., Stewart, A. I. F., Tolson, R., Toublanc, D., Waters, C., Woods, T., Yelle, R., and Zurek, R. (2015), The Mars Atmosphere and Volatile Evolution (MAVEN) Mission, Space Sci. Rev., 195(1-4), 3–48, 10.1007/s11214-015-0139-x.
  * Jin et al. (2017) Jin, M., Manchester, W. B., van der Holst, B., Sokolov, I., Tóth, G., Mullinix, R. E., Taktakishvili, A., Chulaki, A., and Gombosi, T. I. (2017), Data-constrained Coronal Mass Ejections in a Global Magnetohydrodynamics Model, ApJ, 834(2), 173, 10.3847/1538-4357/834/2/173.
  * Jin et al. (2022) Jin, M., Nitta, N. V., and Cohen, C. M. S. (2022), Assessing the Influence of Input Magnetic Maps on Global Modeling of the Solar Wind and CME-Driven Shock in the 2013 April 11 Event,  Space Weather, 20(3), e2021SW002894, 10.1029/2021SW002894.
  * Kaiser et al. (2008) Kaiser, M. L., Kucera, T. A., Davila, J. M., St. Cyr, O. C., Guhathakurta, M., and Christian, E. (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., Zhao, L., Chen, Y., Wang, X., Bobra, M., and Gombosi, T. (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., Abiad, R., Austin, G., Balat-Pichelin, M., Bale, S. D., Belcher, J. W., Berg, P., Bergner, H., Berthomier, M., Bookbinder, J., Brodu, E., Caldwell, D., Case, A. W., Chandran, B. D. G., Cheimets, P., Cirtain, J. W., Cranmer, S. R., Curtis, D. W., Daigneau, P., Dalton, G., Dasgupta, B., DeTomaso, D., Diaz-Aguado, M., Djordjevic, B., Donaskowski, B., Effinger, M., Florinski, V., Fox, N., Freeman, M., Gallagher, D., Gary, S. P., Gauron, T., Gates, R., Goldstein, M., Golub, L., Gordon, D. A., Gurnee, R., Guth, G., Halekas, J., Hatch, K., Heerikuisen, J., Ho, G., Hu, Q., Johnson, G., Jordan, S. P., Korreck, K. E., Larson, D., Lazarus, A. J., Li, G., Livi, R., Ludlam, M., Maksimovic, M., McFadden, J. P., Marchant, W., Maruca, B. A., McComas, D. J., Messina, L., Mercer, T., Park, S., Peddie, A. M., Pogorelov, N., Reinhart, M. J., Richardson, J. D., Robinson, M., Rosen, I., Skoug, R. M., Slagle, A., Steinberg, J. T., Stevens, M. L., Szabo, A., Taylor, E. R., Tiu, C., Turin, P., Velli, M., Webb, G., Whittlesey, P., Wright, K., Wu, S. T., and Zank, G. (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.
  * Kay et al. (2020) Kay, C., Mays, M. L., and Verbeke, C. (2020), Identifying Critical Input Parameters for Improving Drag-Based CME Arrival Time Predictions,  Space Weather, 18(1), e2019SW002382, 10.1029/2019SW002382.
  * Kay et al. (2022) Kay, C., Mays, M. L., and Collado-Vega, Y. M. (2022), OSPREI: A Coupled Approach to Modeling CME-Driven Space Weather with Automatically-Generated, User-Friendly Outputs,  Space Weather, 20(4), e2021SW002914, 10.1029/2021SW002914.
  * Kilpua et al. (2011) Kilpua, E. K. J., Jian, L. K., Li, Y., Luhmann, J. G., and Russell, C. T. (2011), Multipoint ICME encounters: Pre-STEREO and STEREO observations,  Journal of Atmospheric and Solar-Terrestrial Physics, 73, 1228–1241, 10.1016/j.jastp.2010.10.012.
  * Kilpua et al. (2019) Kilpua, E. K. J., Lugaz, N., Mays, M. L., and Temmer, M. (2019), Forecasting the Structure and Orientation of Earthbound Coronal Mass Ejections,  Space Weather, 17(4), 498–526, 10.1029/2018SW001944.
  * Klein and Dalla (2017) Klein, K.-L., and Dalla, S. (2017), Acceleration and Propagation of Solar Energetic Particles, Space Sci. Rev., 212, 1107–1136, 10.1007/s11214-017-0382-4.
  * Knipp (2016) Knipp, D. J. (2016), Advances in Space Weather Ensemble Forecasting,  Space Weather, 14(2), 52–53, 10.1002/2016SW001366.
  * Kollhoff et al. (2021) Kollhoff, A., Kouloumvakos, A., Lario, D., Dresing, N., Gómez-Herrero, R., Rodríguez-García, L., Malandraki, O. E., Richardson, I. G., Posner, A., Klein, K. L., Pacheco, D., Klassen, A., Heber, B., Cohen, C. M. S., Laitinen, T., Cernuda, I., Dalla, S., Espinosa Lara, F., Vainio, R., Köberle, M., Kühl, R., Xu, Z. G., Berger, L., Eldrum, S., Brüdern, M., Laurenza, M., Kilpua, E. J., Aran, A., Rouillard, A. P., Bučík, R., Wijsen, N., Pomoell, J., Wimmer-Schweingruber, R. F., Martin, C., Böttcher, S. I., Freiherr von Forstner, J. L., Terasa, J. C., Boden, S., Kulkarni, S. R., Ravanbakhsh, A., Yedla, M., Janitzek, N., Rodríguez-Pacheco, J., Prieto Mateo, M., Sánchez Prieto, S., Parra Espada, P., Rodríguez Polo, O., Martínez Hellín, A., Carcaboso, F., Mason, G. M., Ho, G. C., Allen, R. C., Bruce Andrews, G., Schlemm, C. E., Seifert, H., Tyagi, K., Lees, W. J., Hayes, J., Bale, S. D., Krupar, V., Horbury, T. S., Angelini, V., Evans, V., O’Brien, H., Maksimovic, M., Khotyaintsev, Y. V., Vecchio, A., Steinvall, K., and Asvestari, E. (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.
  * Koskinen et al. (2017) Koskinen, H. E. J., Baker, D. N., Balogh, A., Gombosi, T., Veronig, A., and von Steiger, R. (2017), Achievements and Challenges in the Science of Space Weather, Space Sci. Rev., 212(3-4), 1137–1157, 10.1007/s11214-017-0390-4.
  * Kouloumvakos et al. (2022) Kouloumvakos, A., Kwon, R. Y., Rodríguez-García, L., Lario, D., Dresing, N., Kilpua, E. K. J., Vainio, R., Török, T., Plotnikov, I., Rouillard, A. P., Downs, C., Linker, J. A., Malandraki, O. E., Pinto, R. F., Riley, P., and Allen, R. C. (2022), The first widespread solar energetic particle event of solar cycle 25 on 2020 November 29. Shock wave properties and the wide distribution of solar energetic particles, A&A, 660, A84, 10.1051/0004-6361/202142515.
  * Krall and St. Cyr (2006) Krall, J., and St. Cyr, O. C. (2006), Flux-Rope Coronal Mass Ejection Geometry and Its Relation to Observed Morphology, ApJ, 652(2), 1740–1746, 10.1086/508337.
  * Lario and Karelitz (2014) Lario, D., and Karelitz, A. (2014), Influence of interplanetary coronal mass ejections on the peak intensity of solar energetic particle events,  Journal of Geophysical Research: Space Physics, 119(6), 4185–4209, 10.1002/2014JA019771.
  * Lario et al. (2006) Lario, D., Kallenrode, M. B., Decker, R. B., Roelof, E. C., Krimigis, S. M., Aran, A., and Sanahuja, B. (2006), Radial and Longitudinal Dependence of Solar 4-13 MeV and 27-37 MeV Proton Peak Intensities and Fluences: Helios and IMP 8 Observations, ApJ, 653(2), 1531–1544, 10.1086/508982.
  * Lario et al. (2013) Lario, D., Aran, A., Gómez-Herrero, R., Dresing, N., Heber, B., Ho, G. C., Decker, R. B., and Roelof, E. C. (2013), Longitudinal and Radial Dependence of Solar Energetic Particle Peak Intensities: STEREO, ACE, SOHO, GOES, and MESSENGER Observations, ApJ, 767(1), 41, 10.1088/0004-637X/767/1/41.
  * Lario et al. (2016) Lario, D., Kwon, R. Y., Vourlidas, A., Raouafi, N. E., Haggerty, D. K., Ho, G. C., Anderson, B. J., Papaioannou, A., Gómez-Herrero, R., Dresing, N., and Riley, P. (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. (2021) Lario, D., Richardson, I. G., Palmerio, E., Lugaz, N., Bale, S. D., Stevens, M. L., Cohen, C. M. S., Giacalone, J., Mitchell, D. G., Szabo, A., Nieves-Chinchilla, T., Wilson, L. B., Christian, E. R., Hill, M. E., McComas, D. J., McNutt, R. L., Schwadron, N. A., and Wiedenbeck, M. E. (2021), Comparative Analysis of the 2020 November 29 Solar Energetic Particle Event Observed by Parker Solar Probe, ApJ, 920(2), 123, 10.3847/1538-4357/ac157f.
  * Larson et al. (2015) Larson, D. E., Lillis, R. J., Lee, C. O., Dunn, P. A., Hatch, K., Robinson, M., Glaser, D., Chen, J., Curtis, D., Tiu, C., Lin, R. P., Luhmann, J. G., and Jakosky, B. M. (2015), The MAVEN Solar Energetic Particle Investigation, Space Sci. Rev., 195(1-4), 153–172, 10.1007/s11214-015-0218-z.
  * Lavasa et al. (2021) Lavasa, E., Giannopoulos, G., Papaioannou, A., Anastasiadis, A., Daglis, I. A., Aran, A., Pacheco, D., and Sanahuja, B. (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. (2013) Lee, C. O., Arge, C. N., Odstrčil, D., Millward, G., Pizzo, V., Quinn, J. M., and Henney, C. J. (2013), Ensemble Modeling of CME Propagation, Sol. Phys., 285(1-2), 349–368, 10.1007/s11207-012-9980-1.
  * Lee et al. (2015) Lee, C. O., Arge, C. N., Odstrcil, D., Millward, G., Pizzo, V., and Lugaz, N. (2015), Ensemble Modeling of Successive Halo CMEs: A Case Study, Sol. Phys., 290(4), 1207–1229, 10.1007/s11207-015-0667-2.
  * Lee et al. (2018) Lee, C. O., Jakosky, B. M., Luhmann, J. G., Brain, D. A., Mays, M. L., Hassler, D. M., Holmström, M., Larson, D. E., Mitchell, D. L., Mazelle, C., and Halekas, J. S. (2018), Observations and Impacts of the 10 September 2017 Solar Events at Mars: An Overview and Synthesis of the Initial Results, Geophys. Res. Lett., 45, 8871–8885, 10.1029/2018GL079162.
  * Lemen et al. (2012) Lemen, J. R., Title, A. M., Akin, D. J., Boerner, P. F., Chou, C., Drake, J. F., Duncan, D. W., Edwards, C. G., Friedlaender, F. M., Heyman, G. F., Hurlburt, N. E., Katz, N. L., Kushner, G. D., Levay, M., Lindgren, R. W., Mathur, D. P., McFeaters, E. L., Mitchell, S., Rehse, R. A., Schrijver, C. J., Springer, L. A., Stern, R. A., Tarbell, T. D., Wuelser, J.-P., Wolfson, C. J., Yanari, C., Bookbinder, J. A., Cheimets, P. N., Caldwell, D., Deluca, E. E., Gates, R., Golub, L., Park, S., Podgorski, W. A., Bush, R. I., Scherrer, P. H., Gummin, M. A., Smith, P., Auker, G., Jerram, P., Pool, P., Soufli, R., Windt, D. L., Beardsley, S., Clapp, M., Lang, J., and Waltham, N. (2012), The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO), Sol. Phys., 275, 17–40, 10.1007/s11207-011-9776-8.
  * Lepping et al. (1995) Lepping, R. P., Acũna, M. H., Burlaga, L. F., Farrell, W. M., Slavin, J. A., Schatten, K. H., Mariani, F., Ness, N. F., Neubauer, F. M., Whang, Y. C., Byrnes, J. B., Kennon, R. S., Panetta, P. V., Scheifele, J., and Worley, E. M. (1995), The Wind Magnetic Field Investigation, Space Sci. Rev., 71, 207–229, 10.1007/BF00751330.
  * Li et al. (2021) Li, G., Jin, M., Ding, Z., Bruno, A., de Nolfo, G. A., Randol, B. M., Mays, L., Ryan, J., and Lario, D. (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.
  * Liu et al. (2014) Liu, Y. D., Luhmann, J. G., Kajdič, P., Kilpua, E. K. J., Lugaz, N., Nitta, N. V., Möstl, C., Lavraud, B., Bale, S. D., Farrugia, C. J., and Galvin, A. B. (2014), Observations of an extreme storm in interplanetary space caused by successive coronal mass ejections,  Nature Communications, 5, 3481, 10.1038/ncomms4481.
  * Lugaz et al. (2017) Lugaz, N., Temmer, M., Wang, Y., and Farrugia, C. J. (2017), The Interaction of Successive Coronal Mass Ejections: A Review, Sol. Phys., 292(4), 64, 10.1007/s11207-017-1091-6.
  * Luhmann et al. (2007) Luhmann, J. G., Ledvina, S. A., Krauss-Varban, D., Odstrcil, D., and Riley, P. (2007), A heliospheric simulation-based approach to SEP source and transport modeling,  Advances in Space Research, 40(3), 295–303, 10.1016/j.asr.2007.03.089.
  * Luhmann et al. (2008) Luhmann, J. G., Curtis, D. W., Schroeder, P., McCauley, J., Lin, R. P., Larson, D. E., Bale, S. D., Sauvaud, J. A., Aoustin, C., Mewaldt, R. A., Cummings, A. C., Stone, E. C., Davis, A. J., Cook, W. R., Kecman, B., Wiedenbeck, M. E., von Rosenvinge, T., Acuna, M. H., Reichenthal, L. S., Shuman, S., Wortman, K. A., Reames, D. V., Mueller-Mellin, R., Kunow, H., Mason, G. M., Walpole, P., Korth, A., Sanderson, T. R., Russell, C. T., and Gosling, J. T. (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. (2010) Luhmann, J. G., Ledvina, S. A., Odstrcil, D., Owens, M. J., Zhao, X. P., Liu, Y., and Riley, P. (2010), Cone model-based SEP event calculations for applications to multipoint observations,  Advances in Space Research, 46(1), 1–21, 10.1016/j.asr.2010.03.011.
  * Luhmann et al. (2012) Luhmann, J. G., Li, Y., Bercik, D. J., Wang, L., and Odstrcil, D. (2012), Issues in heliospheric field mapping to flare SEP sources, in Space Weather: the Space Radiation Environment: 11th Annual International AstroPhysics Conference, American Institute of Physics Conference Series, vol. 1500, edited by Q. Hu, G. Li, G. P. Zank, X. Ao, O. Verkhoglyadova, and J. H. Adams, pp. 3–13, 10.1063/1.4768737.
  * Luhmann et al. (2017) Luhmann, J. G., Mays, M. L., Odstrcil, D., Li, Y., Bain, H., Lee, C. O., Galvin, A. B., Mewaldt, R. A., Cohen, C. M. S., Leske, R. A., Larson, D., and Futaana, Y. (2017), Modeling solar energetic particle events using ENLIL heliosphere simulations,  Space Weather, 15(7), 934–954, 10.1002/2017SW001617.
  * Luhmann et al. (2018) Luhmann, J. G., Mays, M. L., Li, Y., Lee, C. O., Bain, H., Odstrcil, D., Mewaldt, R. A., Cohen, C. M. S., Larson, D., and Petrie, G. (2018), Shock Connectivity and the Late Cycle 24 Solar Energetic Particle Events in July and September 2017, Space Weather, 16(5), 557–568, 10.1029/2018SW001860.
  * Maksimovic et al. (2020) Maksimovic, M., Bale, S. D., Chust, T., Khotyaintsev, Y., Krasnoselskikh, V., Kretzschmar, M., Plettemeier, D., Rucker, H. O., Souček, J., Steller, M., Štverák, Š., Trávníček, P., Vaivads, A., Chaintreuil, S., Dekkali, M., Alexandrova, O., Astier, P. A., Barbary, G., Bérard, D., Bonnin, X., Boughedada, K., Cecconi, B., Chapron, F., Chariet, M., Collin, C., de Conchy, Y., Dias, D., Guéguen, L., Lamy, L., Leray, V., Lion, S., Malac-Allain, L. R., Matteini, L., Nguyen, Q. N., Pantellini, F., Parisot, J., Plasson, P., Thijs, S., Vecchio, A., Fratter, I., Bellouard, E., Lorfèvre, E., Danto, P., Julien, S., Guilhem, E., Fiachetti, C., Sanisidro, J., Laffaye, C., Gonzalez, F., Pontet, B., Quéruel, N., Jannet, G., Fergeau, P., Brochot, J. Y., Cassam-Chenai, G., Dudok de Wit, T., Timofeeva, M., Vincent, T., Agrapart, C., Delory, G. T., Turin, P., Jeandet, A., Leroy, P., Pellion, J. C., Bouzid, V., Katra, B., Piberne, R., Recart, W., Santolík, O., Kolmašová, I., Krupař, V., Krupařová, O., Píša, D., Uhlíř, L., Lán, R., Baše, J., Ahlèn, L., André, M., Bylander, L., Cripps, V., Cully, C., Eriksson, A., Jansson, S. E., Johansson, E. P. G., Karlsson, T., Puccio, W., Břínek, J., Öttacher, H., Panchenko, M., Berthomier, M., Goetz, K., Hellinger, P., Horbury, T. S., Issautier, K., Kontar, E., Krucker, S., Le Contel, O., Louarn, P., Martinović, M., Owen, C. J., Retino, A., Rodríguez-Pacheco, J., Sahraoui, F., Wimmer-Schweingruber, R. F., Zaslavsky, A., and Zouganelis, I. (2020), The Solar Orbiter Radio and Plasma Waves (RPW) instrument, A&A, 642, A12, 10.1051/0004-6361/201936214.
  * Malandraki and Crosby (2018) Malandraki, O. E., and Crosby, N. B. (2018), Solar Energetic Particles and Space Weather: Science and Applications, in Solar Particle Radiation Storms Forecasting and Analysis, vol. 444, edited by O. E. Malandraki and N. B. Crosby, pp. 1–26, 10.1007/978-3-319-60051-2_1.
  * Marsh et al. (2015) Marsh, M. S., Dalla, S., Dierckxsens, M., Laitinen, T., and Crosby, N. B. (2015), SPARX: A modeling system for Solar Energetic Particle Radiation Space Weather forecasting,  Space Weather, 13(6), 386–394, 10.1002/2014SW001120.
  * Mason et al. (2021) Mason, G. M., Cohen, C. M. S., Ho, G. C., Mitchell, D. G., Allen, R. C., Hill, M. E., Andrews, G. B., Berger, L., Boden, S., Böttcher, S., Cernuda, I., Christian, E. R., Cummings, A. C., Davis, A. J., Desai, M. I., de Nolfo, G. A., Eldrum, S., Elftmann, R., Kollhoff, A., Giacalone, J., Gómez-Herrero, R., Hayes, J., Janitzek, N. P., Joyce, C. J., Korth, A., Kühl, P., Kulkarni, S. R., Labrador, A. W., Espinosa Lara, F., Lees, W. J., Leske, R. A., Mall, U., Martin, C., Martínez Hellín, A., Matthaeus, W. H., McComas, D. J., McNutt, R. L., Mewaldt, R. A., Mitchell, J. G., Pacheco, D., Parra Espada, P., Prieto, M., Rankin, J. S., Ravanbakhsh, A., Rodríguez-Pacheco, J., Rodríguez Polo, O., Roelof, E. C., Sánchez-Prieto, S., Schlemm, C. E., Schwadron, N. A., Seifert, H., Stone, E. C., Szalay, J. R., Terasa, J. C., Tyagi, K., Freiherr von Forstner, J. L., Wiedenbeck, M. E., Wimmer-Schweingruber, R. F., Xu, Z. G., and Yedla, M. (2021), Solar energetic particle heavy ion properties in the widespread event of 2020 November 29, A&A, 656, L12, 10.1051/0004-6361/202141310.
  * Mays et al. (2015a) Mays, M. L., Taktakishvili, A., Pulkkinen, A., MacNeice, P. J., Rastätter, L., Odstrcil, D., Jian, L. K., Richardson, I. G., LaSota, J. A., Zheng, Y., and Kuznetsova, M. M. (2015a), Ensemble Modeling of CMEs Using the WSA-ENLIL+Cone Model, Sol. Phys., 290(6), 1775–1814, 10.1007/s11207-015-0692-1.
  * Mays et al. (2015b) Mays, M. L., Thompson, B. J., Jian, L. K., Colaninno, R. C., Odstrcil, D., Möstl, C., Temmer, M., Savani, N. P., Collinson, G., Taktakishvili, A., MacNeice, P. J., and Zheng, Y. (2015b), Propagation of the 7 January 2014 CME and Resulting Geomagnetic Non-event, ApJ, 812(2), 145, 10.1088/0004-637X/812/2/145.
  * McComas et al. (2016) McComas, D. J., Alexander, N., Angold, N., Bale, S., Beebe, C., Birdwell, B., Boyle, M., Burgum, J. M., Burnham, J. A., Christian, E. R., Cook, W. R., Cooper, S. A., Cummings, A. C., Davis, A. J., Desai, M. I., Dickinson, J., Dirks, G., Do, D. H., Fox, N., Giacalone, J., Gold, R. E., Gurnee, R. S., Hayes, J. R., Hill, M. E., Kasper, J. C., Kecman, B., Klemic, J., Krimigis, S. M., Labrador, A. W., Layman, R. S., Leske, R. A., Livi, S., Matthaeus, W. H., McNutt, R. L., Mewaldt, R. A., Mitchell, D. G., Nelson, K. S., Parker, C., Rankin, J. S., Roelof, E. C., Schwadron, N. A., Seifert, H., Shuman, S., Stokes, M. R., Stone, E. C., Vandegriff, J. D., Velli, M., von Rosenvinge, T. T., Weidner, S. E., Wiedenbeck, M. E., and Wilson, P. (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., Cohen, C. M. S., Cook, W. R., Cummings, A. C., Davis, A. J., Geier, S., Kecman, B., Klemic, J., Labrador, A. W., Leske, R. A., Miyasaka, H., Nguyen, V., Ogliore, R. C., Stone, E. C., Radocinski, R. G., Wiedenbeck, M. E., Hawk, J., Shuman, S., von Rosenvinge, T. T., and Wortman, K. (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.
  * Milillo et al. (2020) Milillo, A., Fujimoto, M., Murakami, G., Benkhoff, J., Zender, J., Aizawa, S., Dósa, M., Griton, L., Heyner, D., Ho, G., Imber, S. M., Jia, X., Karlsson, T., Killen, R. M., Laurenza, M., Lindsay, S. T., McKenna-Lawlor, S., Mura, A., Raines, J. M., Rothery, D. A., André, N., Baumjohann, W., Berezhnoy, A., Bourdin, P. A., Bunce, E. J., Califano, F., Deca, J., deÂ la Fuente, S., Dong, C., Grava, C., Fatemi, S., Henri, P., Ivanovski, S. L., Jackson, B. V., James, M., Kallio, E., Kasaba, Y., Kilpua, E., Kobayashi, M., Langlais, B., Leblanc, F., Lhotka, C., Mangano, V., Martindale, A., Massetti, S., Masters, A., Morooka, M., Narita, Y., Oliveira, J. S., Odstrcil, D., Orsini, S., Pelizzo, M. G., Plainaki, C., Plaschke, F., Sahraoui, F., Seki, K., Slavin, J. A., Vainio, R., Wurz, P., Barabash, S., Carr, C. M., Delcourt, D., Glassmeier, K. H., Grande, M., Hirahara, M., Huovelin, J., Korablev, O., Kojima, H., Lichtenegger, H., Livi, S., Matsuoka, A., Moissl, R., Moncuquet, M., Muinonen, K., Quèmerais, E., Saito, Y., Yagitani, S., Yoshikawa, I., and Wahlund, J. E. (2020), Investigating Mercury’s Environment with the Two-Spacecraft BepiColombo Mission, Space Sci. Rev., 216(5), 93, 10.1007/s11214-020-00712-8.
  * Millward et al. (2013) Millward, G., Biesecker, D., Pizzo, V., and de Koning, C. A. (2013), An operational software tool for the analysis of coronagraph images: Determining CME parameters for input into the WSA-Enlil heliospheric model,  Space Weather, 11(2), 57–68, 10.1002/swe.20024.