# Drag-based CME modeling with heliospheric images incorporating frontal
deformation: ELEvoHI 2.0

###### Abstract

The evolution and propagation of coronal mass ejections (CMEs) in
interplanetary space is still not well understood. As a consequence, accurate
arrival time and arrival speed forecasts are an unsolved problem in space
weather research. In this study, we present the ELlipse Evolution model based
on HI observations (ELEvoHI) and introduce a deformable front to this model.
ELEvoHI relies on heliospheric imagers (HI) observations to obtain the
kinematics of a CME. With the newly developed deformable front, the model is
able to react to the ambient solar wind conditions during the entire
propagation and along the whole front of the CME. To get an estimate of the
ambient solar wind conditions, we make use of three different models:
Heliospheric Upwind eXtrapolation model (HUX), Heliospheric Upwind
eXtrapolation with time dependence model (HUXt), and EUropean Heliospheric
FORecasting Information Asset (EUHFORIA). We test the deformable front on a
CME first observed in STEREO-A/HI on February 3, 2010 14:49 UT. For this case
study, the deformable front provides better estimates of the arrival time and
arrival speed than the original version of ELEvoHI using an elliptical front.
The new implementation enables us to study the parameters influencing the
propagation of the CME not only for the apex, but for the entire front. The
evolution of the CME front, especially at the flanks, is highly dependent on
the ambient solar wind model used. An additional advantage of the new
implementation is given by the possibility to provide estimates of the CME
mass.

Space Weather

Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 6, 8042
Graz, Austria University of Graz, Institute of Physics, Universitätsplatz 5,
8010 Graz, Austria Department of Meteorology, University of Reading, Reading,
UK University of Helsinki, 00100 Helsinki, Finland

Jürgen<EMAIL_ADDRESS>
The implementation of a deformable front based on ELEvoHI for three different
ambient solar winds models is presented

The parameters influencing the propagation of the CME are studied in detail

An estimate of the CME mass is obtained depending on DBM fitting and the
cross-sectional area of the CME

##  1 Introduction

Coronal mass ejections (CMEs) are large clouds of energetic and magnetized
plasma erupting from the solar corona (Hundhausen ., 1994). They propagate in
the solar system and are responsible for the strongest space weather effects.
Earth directed CMEs can directly impact various systems including space
missions, power grids, navigation systems and oil pipelines. (e.g. Gosling .,
1990; Kilpua ., 2012; Richardson Cane, 2012; Cannon, 2013). Therefore,
predicting the arrivals of CMEs has become essential. To obtain accurate space
weather forecasting it is important to understand the behavior of CMEs in
interplanetary space. Furthermore, the properties of CMEs at the time of
impact determine the severity of geomagnetic storms (Pulkkinen, 2007). These
properties are the magnetic field, especially the $B_{z}$ component, but the
size and kinematics of CMEs are also important. It is necessary to understand
how CMEs evolve during their propagation in the heliosphere and how they
interact with the ambient solar wind to achieve accurate forecasts (e.g.
Manchester ., 2017; Kilpua ., 2019).

Our current real-time CME arrival predictions are not better than $\sim$ 10
$\pm$ 20 hours (Riley ., 2018). Today, a large number of CME arrival time and
speed forecasting models are available. Table 1 in Riley . (2018) lists most
of the available models, which exhibit various levels of complexity. For
example, the Effective Acceleration Model (EAM; Paouris Mavromichalaki, 2017),
uses an empirical relation for the acceleration as a function of the initial
speed of the CME. Other models consider physics-based equations and account
for drag, i.e. drag-based models, between the ambient solar wind and the CME
(e.g. DBM; Vršnak . 2013, DBEM; Dumbović . 2018, ANTEATR; Kay . 2020). Fixed-
phi fitting (FPF; Sheeley ., 1999; Rouillard ., 2008), harmonic mean fitting
(HMF; Lugaz, 2010; Möstl ., 2011), and self-similar-expansion fitting (SSEF;
Lugaz ., 2010; Davies ., 2012; Möstl Davies, 2013) are examples of CME arrival
prediction models using wide-angle white light observations from heliospheric
imagers (HI) that require techniques assuming certain shapes of the CME front
in the ecliptic plane. Furthermore, there are prediction models combining both
the drag-based approach and HI observations (e.g. DBM fitting; Žic . 2015,
Ellipse Evolution model based on HI observations, ELEvoHI; Rollett . 2016;
Amerstorfer . 2018). Numerical models solve magnetohydrodynamic (MHD)
equations, based on synoptic photospheric magnetic-field maps, and simulate
the ambient solar wind in the full heliosphere (e.g., ENLIL; Odstrcil . 2004,
EUHFORIA; Pomoell Poedts 2018). To provide CME arrival predictions at
different locations in the heliosphere, CMEs are injected in the ambient solar
wind.

However, none of these models were found to outperform all others (Riley .,
2018). Some questions arise: What are the main factors that lead to better CME
arrival predictions and can we improve forecasts by combining different model
approaches?

It has been shown that CMEs may be influenced by different phenomena in the
heliosphere, e.g. magnetic forces close to the Sun, other CMEs, or by high-
speed solar wind streams (Lugaz ., 2012; Kay Opher, 2015; Möstl ., 2015; Shen
., 2011; Gui ., 2011). The kinematic and morphological characteristics of CMEs
can additionally be affected by the ambient solar wind (e.g. Gosling ., 1990;
Gopalswamy ., 2000; Manoharan ., 2004; Temmer ., 2011; Y. Wang ., 2016; Zhuang
., 2017). CMEs propagating slower than the ambient solar wind speed are likely
to experience acceleration while fast CMEs may decelerate (Richardson Cane,
2010; Manoharan Mujiber Rahman, 2011). As a consequence, not only the
propagation direction but also the kinematics and shape of CMEs can be altered
(e.g. Savani ., 2010; Zuccarello ., 2012; Liu ., 2014; Rollett ., 2014;
Ruffenach ., 2015; Kay Nieves-Chinchilla, 2020).

HI-based prediction models typically assume a certain geometry for the
propagation in the heliosphere. In a series of three papers (Howard Tappin,
20091; Tappin Howard, 2009; Howard Tappin, 20092) the authors proposed a model
based on the Solar Mass Ejection Imager (SMEI) to constrain the CME frontal
shape at large distances from the Sun and to obtain the kinematics of CMEs.
The Tappin-Howard (TH) model was further updated to use STEREO data and Howard
Tappin (2010) showed the applicability for space weather forecasting. Rollett
. (2014) and Barnard . (2017) proposed to include a non-uniform evolution of a
CME in order to account for different ambient solar wind conditions. This
result is further supported in a statistical study by Hinterreiter . (2021).
The authors apply the ELEvoHI method, which assumes an elliptical shape of the
CME front and show that predictions for the same CME based on STEREO-A and
STEREO-B observations exhibit the largest differences in highly structured
ambient wind conditions.

In this study we present the next step in the ELEvoHI model development and
account for a time- and spatial dependent drag along the CME front and during
the entire propagation of the CME. With this approach, we aim to shed light
upon CME propagation in the interplanetary space by considering different
parameters crucial for the arrival time and speed at different locations in
the heliosphere.

In Section 2, we present the selected CME for this case study and list the
applied data from different spacecraft. Section 3 deals with ELEvoHI, its set-
up and the input data needed as well as the three ambient solar wind models
used. In Section 3.3, we explain the implementation of the deformable front
into ELEvoHI. Section 4 lists our results and compares the deformable front to
the elliptical front for one event based on the ambient solar wind models. We
summarize and discuss our results in Section 5.

##  2 Data

In this case study, we model the arrival time and arrival speed of the CME
that hit Earth on February 7, 2010 18:04 UT using ELEvoHI. To run the model we
make use of several data products. Most important are images from HI onboard
STEREO (Eyles ., 2009). The HI instrument on each STEREO spacecraft consists
of two white-light wide-angle imagers, HI1 and HI2. HI1 has a field-of-view
(FOV) extending from 4° – 24° elongation (angle from Sun center) in the
ecliptic and HI2 has an angular FOV extending from 18.8° – 88.8° elongation in
the ecliptic. The nominal cadence of the HI1 and HI2 science data is 40
minutes and 120 minutes, respectively. The science image bin size is 70 arc
sec for HI1 and 4 arc min for HI2. The studied CME was first observed in
STEREO-A/HI on February 3, 2010 14:49 UT. This time corresponds to the unique
identifier and time according to the HELCATS HICAT CME catalog (version 6).
The first observation in STEREO-B occurred six hours later on February 3, 2010
20:49 UT. The HELCATS catalog provides the initial speed of $\sim 350$ km s-1
based on self-similar expansion fitting. The CME fronts were tracked by the
authors from about 4° to 28° in STEREO-A and from about 6° to 27° in STEREO-B
HI observations using ecliptic time-elongation maps (Sheeley ., 1999; Davies
., 2009). To extract the time-elongation profiles, we use the SATPLOT tool
implemented in IDLTM SolarSoft, which allows any user to measure the
elongation at different latitudes. The time-elongation profiles are then
converted to time-distance profiles using the ELlipse Conversion (ELCon; a
derivation can be found in Rollett ., 2016) procedure. ELCon is similar to
other conversion methods (e.g. Fixed-Phi, Harmonic Mean, Self-similar
Expansion), but additionally to the propagation direction and longitudinal
extent also the shape of the modeled CME front is taken into account.

Figure 1 shows the in situ solar wind parameters measured by the Wind
spacecraft from February 6 – 9, 2010. Plotted from top to bottom are: the
magnetic field components with the total field, the solar wind speed, and
solar wind density. The identified interplanetary CME (ICME) in situ arrival
time is indicated by the vertical solid black line, while the vertical dashed
black line is the start date of the magnetic flux rope. The ICME in situ
signatures reveal a density enhancement but no shock about 1 hour ahead of a
magnetic flux rope (MFR). This density enhancement is used to define the
arrival time at Earth, on February 7, 2010 18:04 UT, with an arrival speed of
$406\pm 2$ km s-1. The ICME times and speeds are taken from the HELCATS
ICMECAT catalog (version 2.0; Möstl ., 2020, see also the links in the data
section), which gives an in situ arrival time of the ICME in question at the
Wind spacecraft located in a Lissajous orbit around Lagrange point 1.

Figure 1: In situ signatures of the studied CME. The vertical solid black line
indicates the defined arrival time of the CME, which is February 7, 2010 18:04
UT. The vertical dashed black lines define the start and the end time of the
magnetic flux rope. The top panel shows the total magnetic field and the
individual components. The middle and the lower panel show the solar wind
speed and density at Wind spacecraft, respectively.

To get the propagation direction and the half width of the CME we use the
Ecliptic cut Angles from GCS for ELEvoHI tool (EAGEL, Hinterreiter ., 2021),
which incorporates the Graduated Cylindrical Shell method (GCS, AFR.
Thernisien ., 2006; A. Thernisien ., 2009). Figure 2 shows STEREO-A
coronagraph images used to perform GCS fitting. STEREO/COR2 have a FOV from 2
– 15 R⊙ with a cadence of the coronagraph science images of about 15 minutes.
GCS fitting was performed based on COR2 images from both, STEREO-A and
STEREO-B spacecraft (no LASCO data available for this event), on February 3,
2010 15:54 UT. At this time, the CME front was clearly visible and already far
out in the coronagraph images. The GCS fitting parameters in Stonyhurst
coordintate system are: longitude 355°, latitude: $-$17°, tilt angle: $-$1°,
aspect ratio: 0.33, half angle: 30°. Based on the ecliptic cut, the half width
used in this study is 40°, and the CME propagation direction is set to 68°
with respect to STEREO-A, which corresponds to 4° East of Earth. These values
serve as initial input to ELEvoHI. The STEREO-A/COR2 images are further used
to get an estimate of the latitudinal extent of the CME (see Figure 2).

##  3 Methods

In the following paragraphs, we describe the ELEvoHI ensemble model and the
input data needed to obtain an estimate of the arrival time and speed at any
location in the heliosphere (Section 3.2). An essential input to the model is
the ambient solar wind speed in the ecliptic. We therefore employ three
different ambient solar wind models, introduced in Section 3.1. The
implementation of the deformable front in ELEvoHI not only requires the solar
wind bulk speed but also the solar wind mass density, both as a function of
radial distance and in the ecliptic plane (Section 3.3). For the CME, we
assume the longitudinal and latitudinal expansion to be constant as well as a
constant mass during the whole propagation in the heliosphere.

###  3.1 Ambient Solar Wind models

The three ambient solar wind models considered in this study are the
Heliospheric Upwind eXtrapolation model (HUX; Reiss ., 2019, 2020), the
Heliospheric Upwind eXtrapolation with time dependence model (HUXt; M. Owens
., 2020), and EUropean Heliospheric FORecasting Information Asset (EUHFORIA;
Pomoell Poedts, 2018), which exhibit some differences. HUX and HUXt are based
on the solution of the 1D incompressible hyrdrodynamics equations, whereas
EUHFORIA is based on the solution of the full 3D MHD equations. Additionally,
HUX and EUHFORIA provide a static solution of the ambient solar wind for a
full Carrington rotation, HUXt provides a map of the ambient solar wind speed
for each time step. Important for the deformable front is an estimate not only
for the ambient solar wind speed but also for the ambient solar wind density.
Contrary to the other two models, EUHFORIA self-consistently models the plasma
dynamics and thus also provides the ambient solar wind density, $n$. For HUX
and HUXt, we rely on an empirical relation proposed by Eyni Steinitz (1980):

$n(r,w)=1.3\times 10^{6}r^{-2.0}w^{-2.0},$ (1)

where $r$ [AU] is the radial distance and $w$ [km s-1] the solar wind speed.
Hence, $n$, [protons cm-3] is not only dependent on the radial distance to the
Sun but also on the ambient solar wind speed, leading to a structured ambient
solar wind density.

####  3.1.1 HUX

To model the physical conditions in the evolving ambient solar wind flow, we
use the numerical framework discussed in Reiss . (2019, 2020). We specifically
use magnetic maps of the photospheric magnetic field from the Global
Oscillation Network Group (GONG) provided by the National Solar Observatory
(NSO) as input to magnetic models of the corona. Using the Potential Field
Source Surface model (PFSS; Altschuler Newkirk, 1969; Schatten ., 1969) and
the Schatten current sheet model (SCS; Schatten, 1971) we compute the global
coronal magnetic field topology. While the PFSS model attempts to find the
potential magnetic field solution in the corona with an outer boundary
condition that the field is radial at the source surface at 2.5 R⊙, the SCS
model in the region between 2.5 and 5 R⊙ accounts for the latitudinal
invariance of the radial magnetic field as observed by Ulysses (YM. Wang
Sheeley, 1995). From the global magnetic field topology, we calculate the
solar wind conditions near the Sun using the established Wang-Sheeley-Arge
(WSA) relation YM. Wang Sheeley (1995); Arge . (2003); Riley Lionello (2011)
as described in Reiss . (2019). To evolve the solar wind solutions from near
the Sun to Earth, we use the Heliospheric Upwind eXtrapolation model (HUX)
Riley Lionello (2011). The HUX model simplifies the fluid momentum equation as
much as possible, by neglecting the pressure gradient and the gravitation term
in the fluid momentum equations as proposed by Riley Lionello (2011). The
model solutions match the dynamical evolution explored by global heliospheric
MHD codes fairly well while having low processor requirements.

HUX provides a static solution of the ambient solar wind for a full Carrington
rotation. The data spans from 5 to 430 R⊙ with a radial resolution of 1 R⊙
while the longitudinal resolution is 2°.

####  3.1.2 HUXt

HUXt is a solar wind numerical model that treats the solar wind as a 1D
incompressible, time-dependent hydrodynamic flow (M. Owens ., 2020). This
reduced physics approach enables very efficient computational solutions, which
are approximately 103 times faster than comparable 3D MHD solar wind
solutions. Nonetheless, HUXt can closely emulate the solar wind speed output
of full 3D MHD solar wind models (M. Owens ., 2020). Consequently, HUXt can be
a useful surrogate in situations where full 3D MHD solar wind simulations are
too computationally expensive - for example, large ensemble simulations
(Barnard ., 2020). The only boundary condition of HUXt is the solar wind speed
on the inner boundary, which is typically derived from the output of coronal
models.

For this study we use the HUXt model with the inner boundary conditions from
WSA, provided by the CCMC. HUXt data starts at 21.5 R⊙, corresponding the
outer boundary from the WSA, and reaches up to 300.5 R⊙ with a resolution of 1
R⊙. The longitudinal resolution is 0.7° while the temporal resolution is given
by 3.865 minutes.

####  3.1.3 EUHFORIA

As noted in the previous sections, EUHFORIA models the dynamical evolution of
the solar wind in the inner heliosphere by numerically solving the equations
of single-fluid magnetohydrodynamics (including gravity) in a three-
dimensional volume starting at a heliocentric distance of 0.1 AU. On the
sphere defining the inner radial boundary, the MHD quantities representing the
solar wind at that heliocentric distance need to be specified. This is most
often done by employing empirical relations that are based on magnetic field
models of the low and extended corona using the PFSS and SCS models,
respectively. For this study, as input to the coronal model, a synoptic
magnetogram constructed from SOHO/MDI observations for Carrington rotation
2093 as provided by the Joint Science Operations Center (JSOC) was used.

To arrive at a solution describing the heliospheric plasma conditions at a
given time, EUHFORIA solves the MHD equations in the HEEQ coordinate frame
until a steady-state solution in the co-rotating frame is achieved. Thus,
after this time, if the boundary conditions do not evolve in this frame, the
solution remains unchanged. Employing this assumption in this study, the solar
wind conditions like for HUX, are provided as a steady-state solution for a
full Carrington rotation. The model output spans from 20.56 to 324.43 R⊙ with
a resolution of 0.94 R⊙ while the longitudinal and latitudinal resolution is
1°. EUHFORIA not only provides the ambient solar wind speed but all MHD
quantities and therefore self-consistently provides the ambient solar wind
density. Note that for this study, from the model output a two-dimensional
slice of data representing the ecliptic plane is henceforth used in all the
analysis.

###  3.2 ELEvoHI ensemble modeling

ELEvoHI uses HI time-elongation profiles of CME fronts and assumes an
elliptical shape for those fronts to derive their interplanetary kinematics.
The model converts the resulting time-elongation profiles to time-distance
profiles, assuming an elliptic frontal shape using the ELEvoHI built-in
procedure ELCon. Furthermore, ELEvoHI accounts for the effect of the drag
force exerted by the ambient solar wind. The interaction of the CME with the
solar wind, that can effectively be described by introducing a drag term in
the equation of motion, is an essential factor influencing the dynamic
evolution of CMEs in the heliosphere. ELEvoHI incorporates a drag-based
equation of motion (DBM; Vršnak ., 2013) to fit the time-distance tracks.
Within these profiles, the user has to manually define the start- and end
point for the DBM fit. For this event they are set to around $30$ R⊙ and $65$
R⊙, respectively. In order to account for the de-/acceleration of the CME due
to drag, an estimate of the ambient solar wind speed is needed.

In a previous study by Amerstorfer . (2021), the authors applied different
approaches to get an estimate of the ambient solar wind speed used as input to
ELEvoHI. They tested 1) the ambient solar wind speed from the HUX model, 2) a
range of possible solar wind speeds (225 – 625 km s-1), and 3) solar wind
speed measured at L1 during the evolution of the CME, and found the best
results based on the HUX ambient solar wind conditions.

In this study we make use of three different ambient solar wind models: HUX,
HUXt, and EUHFORIA. The ambient solar wind speeds in the ecliptic plane for
each model can be seen in Figure 3, with snapshots of the ELEvoHI modeled CME
fronts. The estimate of the ambient solar wind speed used for DBM fitting is
obtained identically for each model. We only consider the region of the full
ambient solar wind speed data according to the start- and end-point selected
by the user, the CME propagation direction, and the half width for each
ensemble member. This corresponds to the radial extent used for DBM fitting
(see Section 3.3 in Hinterreiter ., 2021). From that region we take the median
of the solar wind speed and define the uncertainties to be $\pm$100 km s-1,
based on a study by Reiss . (2020), where the authors considered nine years
(mid 2006 to mid 2015) and report a mean absolute error of the HUX solar wind
speed prediction with respect to the in situ speed of 91 km s-1 (see Section
3.3 in Hinterreiter ., 2021, for more details). For consistency, we also apply
the same uncertainties for the obtained median solar wind speed for the HUXt
and the EUHFORIA ambient solar wind models. We then split the ambient solar
wind speed with its uncertainty into steps of 25 km s-1, leading to nine
different input speeds to ELEvoHI. For each of the nine input speeds DBM
fitting is performed. ELEvoHI then selects the combination of drag parameter
and ambient solar wind speed that best fits the time-distance profile for each
ensemble member (for a detailed description see Rollett ., 2016).

The selected drag parameter, $\gamma$, and solar wind speed, $w$, from DBM
fitting are assumed to be valid for the entire propagation of the apex, which
is defined by Equation 2 and Equation 3 (Vršnak ., 2013):

$v(t)=\frac{v_{0}-w}{1\pm\gamma(v_{0}-w)t}+w$ (2)
$r(t)=\pm\ln[1\pm\gamma(v_{0}-w)t]+wt+r_{0},$ (3)

with $v_{0}$ as the initial CME speed while $t$ defines the time of the CME
propagation. An important factor in these equations is the sign of $\gamma$.
It is defined so that the CME accelerates when the sign is negative while the
CME front decelerates when the sign of $\gamma$ is positive.

In order to get the shape and the propagation direction of the CME we make use
of the EAGEL tool (Hinterreiter ., 2021). It provides the propagation
direction with respect to the observer ($\phi$ = 68°, with respect to STA) and
half width ($\lambda$ = 40°). The inverse ellipse aspect ratio, $f$, defines
the shape of the assumed CME front in the ecliptic plane, where $f=1$
represents a circular front, while $f<1$ corresponds to an elliptical CME
front (with the semi-major axis perpendicular to the propagation direction).

ELEvoHI is operated in ensemble mode by varying $\phi$, $\lambda$, and $f$
(for a detailed description see Amerstorfer ., 2018). The parameters $\phi$
and $\lambda$ vary over a range of $\pm 10$° with a step size of $2$° and
$5$°, respectively. The range $\pm 10$° is based on a study by Mierla .
(2010), in which the authors report an uncertainty in the parameters when
different users manually perform GCS reconstruction. For $f$ we set a fixed
range from $0.7-1.0$ ($0.1$ step size). Thus we get a total of 220 ensemble
members for one event (i.e. 11 values of $\phi$, 5 values of $\lambda$ and 4
values of $f$). When running ELEvoHI in ensemble mode, we get a frequency
distribution from which we can calculate the median, mean and standard
deviation of the modeled CME arrival time and speed. In addition, we can give
a probability for whether a CME is likely to hit Earth or not. When all of the
220 ensemble members model an arrival at Earth, we assume the likelihood of an
Earth hit to be 100%.

###  3.3 Implementation of the deformable CME front

In the original version of ELEvoHI, i.e. for the elliptical front, the apex of
the CME propagates the whole way through the heliosphere according to the
ambient solar wind speed and drag parameter obtained from DBM fitting.

For the deformable front, however, $\gamma$ and $w$ from the DBM fit are not
considered for the entire propagation of the CME front, but only up to about
65 R⊙ (corresponding to the endcut of the DBM fit defined by the user). At
this distance we start a transition from the rigid elliptical front to a
deformable front. We define the front to consist of 101 points, leading to a
longitudinal resolution of about 1° when assuming a half width of 50°. With
decreasing $\lambda$ the longitudinal resolution increases. Each point of the
front can propagate individually according to the different ambient solar wind
conditions. We therefore need to know the parameters in Equation 2 and 3
($v_{0}$, $w$, $\gamma$) at each time and location in the heliosphere. The CME
frontal speed for each point, $v_{0}$, is obtained from the previous time
step, while the solar wind speed, $w$, for each time and location is taken
from the ambient solar wind models. To derive the drag parameter, $\gamma$,
for each time and location we have to make further assumptions. That is, the
longitudinal and latitudinal expansion as well as the mass, $M$, of the CME is
constant during the entire propagation.

In order to obtain an estimate of $M$, we use a similar approach as
Amerstorfer . (2018) and rearrange Equation 4 (Cargill, 2004):

$\gamma(r)=c_{d}\frac{A(r)n(r,w)}{M},$ (4)

where $\gamma$ is the drag parameter, $c_{d}$ is a dimensionless drag
coefficient and is set to 1 in this study. $A$ is the cross-sectional area of
the CME, $n$ is the ambient solar wind density. We get $\gamma$ and $w$ from
DBM fitting, i.e. the drag parameter and the ambient solar wind at the
transition from rigid to deformable front. Also the radial distance of the
front at this time is known, so $n(r,w)$ can be derived from Equation 1 and
$A(r)$ can be calculated (see below). Note that $n$ is provided by EUHFORIA
and can therefore directly be used within ELEvoHI. An estimate of the CME mass
can now be given based on DBM fitting. Furthermore, $\gamma$ can be expressed
by the radial distance and the solar wind density at any location in the
heliosphere, by assuming a constant mass.

To get an estimate of the cross-sectional area, $A$, at different time steps
of the model, we assume a constant expansion in longitude and latitude. The
longitudinal extent of the CME is obtained by EAGEL and is defined by
$\lambda$. For the latitudinal extent, we make use of STEREO coronagraph
images (see Figure 2). We first define the main latitudinal propagation
direction (red solid line in Figure 2c). Next, two parallel lines are added at
the maximum northern and southern extent of the CME (dashed red lines in
Figure 2c). The magenta line is orthogonal to the red lines and indicates the
CME front. The intercept of the magenta line with the dashed red lines
represents the maximum latitudinal extent of the CME. The blue solid lines
connect the two intercepts with the solar center and therefore provide an
angle ($\kappa$) for the latitudinal extent of the CME ($\kappa$ = 28° for
this event). As mentioned above, $\kappa$ is assumed to be constant during the
propagation. In good approximation, the cross-sectional area can be considered
as an ellipse ($A=ab\pi$). The semi major axis, $a$, is defined by $\lambda$
and can be calculated for each radial distance from the Sun. The same applies
for the semi minor axis, $b$, which is dependent on $\kappa/2$ and the radial
distance. As a consequence, $A$ can be expressed with regard to the radial
distance of the CME front to the Sun, i.e. $A=A(r)$.

Figure 2: STEREO-A coronagraph images for the CME on February 3, 2010. a) COR2
image at 15:54 UT. b) Same as a) with the GCS wireframe overplotted. c) COR2
image with the definition of the latitudinal extent of the CME. The red dashed
lines represent the maximum extent (north and south) of the CME as viewed from
the propagation direction in the latitude (solid red line). The solid magenta
line defines the CME front. The angle ($\kappa$) between the solid blue lines
represents the latitudinal extent of the CME.

With the assumptions mentioned previously, all the parameters in Equation 2
and 3 at any time and location in the heliosphere can be estimated. So, at
around 65 R⊙ we perform a transition from the rigid elliptical CME front to
the deformable front that is able to react to the different solar wind
conditions. We set this distance in agreement with MJ. Owens . (2017), who
found that at about 0.3 AU the majority of CMEs can no longer be considered as
coherent structures. We set the temporal resolution for the deformable front
to 15 minutes. Only for HUXt the temporal resolution is set to be 15.46
minutes, which corresponds to 4 times the temporal resolution of the model
output.

Note that the results for the rigid elliptical front are still generated,
allowing us to compare the modeled arrivals for the different implementations
of the ELEvoHI.

##  4 Results

Figure 3: Snapshots of the ELEvoHI model results. From top to bottom the CME
fronts based on HUX, HUXt, and EUHFORIA are shown. The green solid line
represents the elliptical CME front (for one individual ensemble member) and
the red lines represent the deformed fronts. The dark red line corresponds to
the same individual run as for the elliptical CME front (green line). Plotted
in black are the positions of the virtual spacecraft (VSC1 and VSC2), which
are located $\pm$30° East and West of Earth. The positions of additional
planets and spacecraft are indicated by the colored circles and squares,
respectively.

Figure 3 shows one ensemble member of the elliptical front (green) and all the
ensemble members of the deformed front (red) for the three different ambient
solar wind models used as input. The dark red deformed front corresponds to
the single ensemble member shown in green for the elliptical front. The
ELEvoHI input parameters for this ensemble member are: $\phi$ = 68° with
respect to STEREO-A (corresponding to 4° with respect to Earth), $\lambda$ =
40° and $f$ = 0.7. In Table 1 we list the modeled arrival times for the
elliptical and the deformed front for the three ambient solar wind models.
Note that all of the individual ensemble members estimate an arrival at Earth
giving a 100% chance of an Earth hit. Table 1 further lists the modeled
arrival times at two different predefined positions in the heliosphere, called
virtual spacecraft (VSC). VSC1 and VSC2 are located $\pm$30° East and West of
Earth, respectively. We include these two additional locations in order to
assess the CME propagation at the flanks. Furthermore, introducing VSC1 and
VSC2 allows us to point out the differences based on the three ambient solar
wind models at other longitudes. In contrast to the 100% chance of an arrival
at Earth, not all ensemble members are estimated to arrive at VSC1 and VSC2.
The reason can be found in the changing propagation direction and half width
for each of the ensemble members.

Table 1: Modeled arrival times for different ambient solar wind models and locations for the elliptical and the deformed CME front. Given are the median arrival times with the standard deviation as uncertainty. $\Delta_{\mathrm{insitu}}$ lists the difference to the in situ arrival time for both the elliptical and deformed front. $\Delta_{\mathrm{shape}}$ gives the difference between the two frontal shapes, where a positive value represents a later arrival of the deformed front. The in situ arrival time is defined to be February 7, 2010 18:04 UT. Location | ATellipse | $\Delta_{\mathrm{insitu}}$ | ATdeformed | $\Delta_{\mathrm{insitu}}$ | $\Delta_{\mathrm{shape}}$
---|---|---|---|---|---
| [UT $\pm$ h] | [h] | [UT $\pm$ h] | [h] | [h]
ELEvoHI/HUX |  |
Earth | 2010-02-07 10:54 $\pm$ 0.7 | -7.2 | 2010-02-07 16:21 $\pm$ 0.6 | -1.7 | 5.5
VSC1 | 2010-02-07 22:44 $\pm$ 10.2 | — | 2010-02-07 17:51 $\pm$ 3.0 | — | -4.9
VSC2 | 2010-02-08 05:24 $\pm$ 9.7 | — | 2010-02-08 04:06 $\pm$ 3.7 | — | -1.3
ELEvoHI/HUXt |  |
Earth | 2010-02-07 12:04 $\pm$ 0.6 | -6.0 | 2010-02-07 16:26 $\pm$ 0.5 | -1.6 | 4.4
VSC1 | 2010-02-08 00:04 $\pm$ 10.2 | — | 2010-02-08 02:14 $\pm$ 5.2 | — | 2.1
VSC2 | 2010-02-08 06:44 $\pm$ 10.2 | — | 2010-02-08 14:21 $\pm$ 6.0 | — | 7.6
ELEvoHI/EUHFORIA |  |
Earth | 2010-02-07 09:34 $\pm$ 1.1 | -8.5 | 2010-02-07 11:51 $\pm$ 0.6 | -6.2 | 2.3
VSC1 | 2010-02-07 20:39 $\pm$ 10.2 | — | 2010-02-07 22:29 $\pm$ 5.2 | — | 1.8
VSC2 | 2010-02-08 03:44 $\pm$ 9.2 | — | 2010-02-08 13:06 $\pm$ 9.0 | — | 9.4

###  4.1 Model results for the elliptical front

From Table 1 it can be seen that the elliptical fronts of all of the solar
wind models estimate the Earth arrival too early (in situ arrival time is
defined to be February 7, 2010 18:04 UT). The modeled arrival times are
February 7, 2010 10:54 UT $\pm$ 0.7 hours, February 7, 2010 12:04 UT $\pm$ 0.6
hours, and February 7, 2010 09:34 UT $\pm$ 1.1 hours for ELEvoHI/HUX,
ELEvoHI/HUXt, and ELEvoHI/EUHFORIA, respectively. The largest difference
within the ambient solar wind models is found for ELEvoHI/HUXt and
ELEvoHI/EUHFORIA with 2.5 hours. This leads to more than 8.5 hours difference
for the calculated arrival time based on ELEvoHI/EUHFORIA with respect to the
actual in situ arrival time. Also the modeled arrival times for the virtual
spacecraft, differ up to about 3.5 hours for VSC1 and 3 hours for VSC2.

To find the reasons for the differences, we check the median ambient solar
wind speed in the range corresponding to the start- and endcut of the DBM fit
of each model. From ELEvoHI/HUX we obtain $455$ km s-1, from ELEvoHI/HUXt it
is $421$ km s-1. For ELEvoHI/EUHFORIA the median ambient solar wind speed is
$561$ km s-1 (more than $100$ km s-1 faster than for the other two models).
The in situ solar wind speed is roughly $500$ km s-1 about 3.5 days prior to
the actual arrival and gradually decreases to about $350$ km s-1 (see Figure
7). When checking the speed from the best DBM fit, we find for ELEvoHI/HUX:
$555$ km s-1, for ELEvoHI/HUXt: $521$ km s-1, and for ELEvoHI/EUHFORIA: $661$
km s-1, indicating that ELEvoHI selects the fastest ambient solar wind
available. The drag parameters, $\gamma$, are $2.73\times 10^{-8}$ km-1 for
ELEvoHI/HUX, $4.20\times 10^{-8}$ km-1 for ELEvoHI/HUXt, and $1.07\times
10^{-8}$ km-1 for ELEvoHI/EUHFORIA. The $\gamma$ obtained for all the models
seems to be roughly in the same range of other studies (see, e.g. Vršnak .,
2013; Dumbović ., 2018; Rollett ., 2016). Even with the largest $\gamma$, in
this case the highest acceleration, the HUXt based model provides the latest
arrival at Earth.

###  4.2 Model results for the deformed front

Next, we compare the modeled arrival times for the deformed front based on the
three different ambient solar wind models. Here we find an almost identical
modeled arrival time for ELEvoHI/HUX and ELEvoHI/HUXt on February 7, 2010
16:21 UT and 16:26 UT, respectively (see Table 1). They are about two hours
too early with respect to the actual in situ arrival time, while
ELEvoHI/EUHFORIA models the arrival time more than 6 hours too early. The
calculated arrival times at VSC1 exhibit quite large differences of more than
8.5 hours for ELEvoHI/HUX and ELEvoHI/HUXt. At VSC2 location, the calculated
arrival times show even larger differences of more than $\sim$ 10 hours.

To find the reason for the arrival time variations based on the ambient solar
wind models, we check the input parameters to the deformable front right at
the transition from the elliptical to the deformed front. The CME speed at the
transition is similar based on all the three ambient solar wind models and
reaches $404$ km s-1, while a calculated cross-sectional area, $A$, of
$6.93\times 10^{14}$ km2 is obtained. $\gamma$ and $n$ are based on the DBM
fit and therefore lead to different values for each ambient solar wind model.
When expressing $M$ from Equation 4 we get $1.17\times 10^{15}$ g for
ELEvoHI/HUX, $1.61\times 10^{15}$ g for ELEvoHI/HUXt, and $3.92\times 10^{15}$
g for ELEvoHI/EUHFORIA, which is more than two times larger than for the other
two models. However, these values are in good agreement with the CME mass
estimated based on coronagraph images of $1.45\pm 0.15\times 10^{15}$ g. In
coronagraph images, the CME mass is defined via the excess brightness in the
white-light image. Assuming a composition of 90% hydrogen and 10% helium, the
brightness is converted into electron mass (see Billings 1966). A detailed
description of how the CME mass is estimated can be found in Colaninno
Vourlidas (2009) and Bein . (2013), while de Koning (2017) provides a
discussion regarding the uncertainties. In Figure 4 the calculated mass based
on the three different ambient solar wind models are shown. The red vertical
line indicates the input parameters for the individual run shown in dark red
in Figure 3. For all the input parameters from the ensemble mode to the
deformable front see the supplementary material .

Figure 4: Calculated masses for each individual ensemble member and the three
ambient solar wind models. The red vertical line represents the mass obtained
for the individual ensemble run plotted in dark red in Figure 3. The blue
vertical line indicates the CME mass with its uncertainty obtained from
coronagraph images.

###  4.3 Deformation measure

In Figure 3 the green solid line represents the ELEvoHI elliptical CME front,
while the dark red solid line is the deformed front for one ensemble member.
We further aim to find a measure to determine the deformation of the CME front
with regard to the elliptical front. To do so, we calculate the mean of the
absolute difference in radial coordinate ($\Delta F$) of each point from the
elliptical and the deformed CME front at the arrival time at Earth. This gives
a first indication on the difference between the elliptical and the deformed
front. However, this value is not just dependent on the deformation, but also
changes when the deformed front propagates faster or slower than the
elliptical front. Hence, we provide an additional parameter, $\sigma F$, which
is defined to be the standard deviation of the absolute differences for each
point on the CME front. A larger value of $\sigma F$ represents a more
deformed CME front. For the single ensemble member (dark red and green lines
shown in Figure 3) of ELEvoHI/HUX, we obtain $\Delta F=12.1$ R⊙ and $\sigma
F=7.3$ R⊙. The parameters for ELEvoHI/HUXt are $\Delta F=9.2$ R⊙ and $\sigma
F=4.2$ R⊙ and for ELEvoHI/EUHFORIA we obtain $\Delta F=11.5$ R⊙ and $\sigma
F=6.8$ R⊙. Based on the $\sigma F$ values for the different ambient solar wind
models, the ELEvoHI/HUX results show the largest deformation, followed by the
ELEvoHI/EUHFORIA and ELEvoHI/HUXt. To get an impression for these values, we
also calculate these measures only for the elliptical front on February 7,
2010 13:00 UT and 5 hours later (February 7, 2010 18:00 UT) for ELEvoHI/HUX.
We find $\Delta F=11.0$ R⊙ and $\sigma F=0.8$ R⊙, indicating that the CME
front shows almost no deformation but the absolute difference between the CME
points is comparable to the deformed front.

###  4.4 Behavior of the propagation parameters

Figure 5: Extracted parameters over distance in the heliosphere for the three
different ambient solar wind models. The positions are indicated by the
different colors, where black represents Earth direction, red represents VSC1,
and blue VSC2. ELEvoHI/HUX: panel a), b), c); ELEvoHI/HUXt: panel d), e), f);
ELEvoHI/EUHFORIA: panel f), h), i). In panel a), d), and g) the ambient solar
wind speed (faint colors) and the speed of the CME front (bold colors) are
shown. Panels b), e), h) show the drag parameter and panels c), f), i) the
ambient solar wind density.

Another interesting point is how the individual parameters develop during the
propagation of the CME front in the heliosphere. We therefore consider the
ambient solar wind speed, the CME frontal speed, the drag parameter, and the
ambient solar wind density. In Figure 5 these parameters are plotted for
ELEvoHI/HUX, ELEvoHI/HUXt, and ELEvoHI/EUHFORIA, respectively. The plots
further show the four parameters for three different propagation directions
along predefined longitudes: Earth, VSC1, and VSC2. Earth direction (black) is
the longitude corresponding to Earth location. VSC1 (red) and VSC2 (blue) are
virtual spacecraft located 30° East and West of Earth, respectively. For the
ELEvoHI/HUX Earth direction the ambient solar wind is in the range of $450$ km
s-1. The same applies for the ELEvoHI/HUXt Earth direction, while here the
ambient solar wind starts slightly below $450$ km s-1. The ambient solar wind
speed for ELEvoHI/EUHFORIA shows the largest variation starting from roughly
$500$ km s-1, rising to about $650$ km s-1 and coming back to about $500$ km
s-1.

A striking feature in Figure 5 is that the ambient solar wind speed shows
’jumps’ for ELEvoHI/HUX and ELEvoHI/EUHFORIA nearly throughout the entire
propagation and for almost every longitude plotted. The reason can be found in
the static solution of the ambient solar wind speed provided by these models
and the temporal resolution of ELEvoHI. In order to select the corresponding
ambient solar wind speed at a given time and location in the heliosphere, we
purely rotate the solar wind model output according to the correct time. The
small ’jumps’ in the plot arise from changing from one grid cell to the other
in the radial direction, while the large ’jumps’ are due to the change from
one longitude to the next. The ’jumps’ in $\gamma$ and $n$ are due to the
’jumps’ in the solar wind speed since these parameters are derived from the
solar wind speed. Even though the ELEvoHI/HUXt ambient solar wind model is
time dependent (with a resolution of 3.865 minutes) the speeds also exhibit
small ’jumps’. They occur, however, only in regions where the ambient solar
wind changes significantly during a short period of time (see VSC2 in the HUXt
panel in Figure 5).

For all of the ambient solar wind models the CME frontal speeds, at the three
predefined longitudes, do not reach the ambient solar wind speed leading to a
continuous acceleration of the front up to L1 distance (roughly 214 R⊙).
$\gamma$ is quite small for all the models and directions already in the
beginning, with the exception of VSC2 direction for ELEvoHI/HUXt. Furthermore,
$\gamma$ decreases due to the decreasing ambient solar wind density, $n$, when
the front is farther out in the heliosphere. Therefore, it is less likely that
the CME catches up with the ambient solar wind farther out in the heliosphere.
For ELEvoHI/EUHFORIA however, it can be seen that at about 320 R⊙ the CME
speed is higher than the ambient solar wind speed. This directly leads to
change in sign of $\gamma$ and corresponds to a deceleration of the CME front
within Earth direction.

The modeled arrival time for the deformed front shows the largest discrepancy
to the actual in situ arrival time for the ELEvoHI/EUHFORIA combination. We
believe that this mainly arises from the high ambient solar wind speed. While
the Earth-directed part for ELEvoHI/HUX and ELEvoHI/HUXt only slightly
accelerates, the modeled speed from ELEvoHI/EUHFORIA increases from about
$400$ km s-1 up to more than $475$ km s-1 at the end of the simulation,
resulting in an even earlier arrival than for ELEvoHI/HUX and ELEvoHI/HUXt.

###  4.5 Modeled CME arrival speed

Figure 6: CME front parameters at the modeled arrival time. Panels a), c), e):
Ambient solar wind speed (blue) and CME speed of the deformed front (red) of
each individual ensemble member and the different ambient solar wind models.
Panels b), d), f): Drag parameter for each ensemble member and ambient solar
wind models. The dark colors represent the values for one individual ensemble
member.

We are further interested in the CME frontal speed for the three different
ambient solar wind models. We therefore plot the speed of the ambient solar
wind and the frontal speed at the time when the front is estimated to arrive
at Earth (see Figure 6) with the drag parameter for the ambient solar wind
models. The CME frontal speed (red in the left panels in Figure 6) resembles
the shape of the CME front. Also the drag parameter seems to show the same
behavior as the ambient solar wind. The most striking feature is that the sign
of $\gamma$ changes for different longitudes. As mentioned before, we define a
negative sign of $\gamma$ to indicate an acceleration while a positive sign of
$\gamma$ leads to a deceleration for this certain part of the CME front. When
comparing the left and the right panels in Figure 6 it is obvious that only
such ensemble members show a change in sign of $\gamma$ for which the ambient
solar wind speed is lower than the CME frontal speed of this part. This is
most pronounced for the EUHFORIA based model results.

Figure 7: Solar wind speed profiles for Earth direction. The black line is the
in situ speed, while the blue line represents the modeled solar wind speed.
The vertical solid black line indicates the in situ arrival and the vertical
dashed black line is the start of the magnetic flux rope. The blue vertical
bar indicates the modeled arrival time with its uncertainty. Up to that time,
the speed is taken from the ambient solar wind models, afterwards the speed is
set to the calculated CME arrival speed. From top to bottom the results for
ELEvoHI/HUX, ELEvoHI/HUXt, and ELEvoHI/EUHFORIA are shown.

The actual in situ arrival speed is given by $406\pm 2$ km s-1. The modeled
arrival speeds are $413\pm 3$ km s-1 for ELEvoHI/HUX, $416\pm 3$ km s-1 for
ELEvoHI/HUXt and $469\pm 7$ km s-1 for ELEvoHI/EUHFORIA, where the speed
corresponds to the median of all the ensemble members and the uncertainty is
given by the standard deviation. The high overestimation of the calculated
arrival speed also explains the early arrival when using EUHFORIA speed maps.
However, the deformable front provides better speed results than for the
original version of ELEvoHI. The modeled arrival speeds for the elliptical
front are $474\pm 7$ km s-1 for ELEvoHI/HUX, $461\pm 4$ km s-1 for
ELEvoHI/HUXt and $492\pm 12$ km s-1 for ELEvoHI/EUHFORIA.

In Figure 7 the speed profiles for the three ambient solar wind models in
comparison to the in situ wind speed are shown. We indicate the modeled
arrival time by the vertical blue bar, where the uncertainty is given by the
standard deviation of all the ensemble members that are estimated to hit
Earth. Before the modeled arrival time the solar wind speed is taken from the
ambient solar wind models. After that time, the calculated CME arrival speed
is plotted for half a day. We can see that HUX already overestimates the
ambient solar wind speed about three days prior to the in situ arrival time.
The HUXt model seems to correctly model a small speed enhancement at around
February 6, 2010 04:00 UT. However from this time on, also HUXt overestimates
the in situ speed. EUHFORIA shows a good agreement with the in situ speed but
seems to be shifted roughly by one day. Also the speed after about February 7,
2010 06:00 UT is highly overestimated. From Figure 7 we see that all of the
models provide ambient solar wind speeds that are too fast compared to the
measurements. The figure further shows that the modeled arrival time and speed
match the actual in situ arrival quite well for ELEvoHI/HUX and ELEvoHI/HUXt.
For ELEvoHI/EUHFORIA the arrival is estimated too early and too fast.
Interestingly, the modeled speed profiles behave contrary to the measured
speed profiles. The in situ speed is slightly slower before the defined CME
arrival time and increases when the CME passes the Wind spacecraft. The
modeled wind profiles, however, show a decrease of solar wind speed at
arrival.

###  4.6 Shifting Earth

A different approach to get an estimate of the uncertainty of the modeled CME
arrival time is to artificially shift Earth position. This means that we do
not consider longitude 0° to be the location of Earth (see Figure 6) but shift
Earth to $\pm$10°. By doing so, we get a calculated arrival time for +10° of
February 07, 2010 16:07 UT $\pm$ 1.8 hours and for -10° February 07, 2010
18:07 UT $\pm$ 2.3 hours for ELEvoHI/HUX. The modeled arrival time based on
ELEvoHI/HUXt gives February 07, 2010 16:42 UT $\pm$ 2.0 hours for +10° and
February 07, 2010 16:42 UT $\pm$ 1.8 for -10° and ELEvoHI/EUHFORIA models an
arrival at February 07, 2010 21:07 UT $\pm$ 2.6 hours for +10° and February
07, 2010 12:07 UT $\pm$ 1.6 for -10°. The calculated arrival times for
ELEvoHI/HUX differ by 2 hours, with the -10° being almost spot on regarding
the in situ arrival time. ELEvoHI/HUXt provides exactly the same modeled
arrival time, which is still about 1.5 hours too early. A quite different
result is found ELEvoHI/EUHFORIA. For this ambient solar wind model we obtain
the largest differences of 9 hours. This result is not surprising when having
a look at Figure 6. It can be seen that the modeled speed is much slower for
the ELEvoHI/EUHFORIA ambient solar wind speed at +10° leading to a much later
calculated arrival time.

##  5 Discussion and Conclusions

In this study we present a new method for a deformable front based on ELEvoHI.
The original version of ELEvoHI accounts for the drag exerted by the ambient
solar wind. However, the kinematic of a CME obtained by DBM fitting is assumed
only for the apex of the CME. Furthermore, the drag parameter and the ambient
solar wind speed are assumed to be constant during the entire propagation in
the heliosphere. With the new approach of a deformable front, ELEvoHI is able
to adapt to the ambient solar wind conditions not only at the apex, but along
the whole CME front. The new version of ELEvoHI can handle three different
ambient solar wind models: HUX, HUXt, and EUHFORIA.

We test the deformable front by studying a CME first observed in STEREO-A/HI
on February 3, 2010 14:49 UT, which has a defined in situ arrival time on
Februray 7, 2010 18:04 UT and a measured speed of 406 $\pm$2 km s-1. In
addition to Earth direction, we also model the arrival times for two
additional locations in the heliosphere, defined to be $\pm$30° East and West
of Earth (VSC1 and VSC2). We compare the calculated arrival times based on the
three different ambient solar wind models for the original implementation of
ELEvoHI, i.e. the elliptical front. For Earth direction the modeled arrival
times differ at maximum 2.5 hours. However, the best model result
(ELEvoHI/HUXt) is still 6 hours too early with respect to the in situ arrival
time. For VSC1 and VSC2 the model results differ at maximum 3.5 and 3 hours,
respectively. Considering the deformable front, we find quite different
results. ELEvoHI/HUX and ELEvoHI/HUXt model an almost identical arrival time
(less than 2 hours too early with respect to the in situ arrival time), while
ELEvoHI/EUHFORIA models the arrival time 4.5 hours earlier compared the other
two ambient solar wind models. The differences are even bigger when comparing
the arrival times at the virtual spacecraft. At VSC1 the calculated arrival
times differ up to more than 8.5 hours, while for VSC2 the differences reach
even more than 10 hours for the three ambient solar wind models. For this case
study, the modeled arrival times at Earth with the deformable front provide
better results (at least 2.2 hours and 23 km s-1 for ELEvoHI/EUFHORIA) than
the elliptical front for all the three ambient solar wind models used.

With this new approach it is further possible to get an estimate of the CME
mass based on DBM fitting to the heliospheric imager data and an estimate of
the cross-sectional area. For this event it could be shown that the CME mass
is close to the results purely based on coronagraph images, which is in
agreement with Amerstorfer . (2018), who applied ELEvoHI to a halo CME event
and found similar results.

Additionally, all the parameters important for the propagation of the CME
front in the heliosphere can now be studied in detail at each time and
location (see Figure 5 for three distinct directions). The solar wind density,
$n$, decreases with increasing distance to the Sun, which also leads to a
decreasing drag parameter, $\gamma$. The CME continually adjusts to the
ambient solar wind speed the further out it propagates in the heliosphere.
Both, the modeled CME frontal speed and drag parameter, resemble the CME shape
quite well (see Figure 6). Also, most parts of the CME front show acceleration
while some parts (especially for ELEvoHI/EUHFORIA) are decelerated.

For the CME treated in this case study, we obtain almost perfect arrival
speeds for ELEvoHI/HUX and ELEvoHI/HUXt, while it is overestimated by about 60
km s-1 by ELEvoHI/EUHFORIA. Interestingly, all of the ambient solar wind
models overestimate the solar wind speed about one day before the actual in
situ arrival. This leads to a modeled speed profile that is contrary to the
measured speed profile. In the data we see an increase in solar wind speed up
to the in situ arrival time, while in the modeled profile the speed drops at
the calculated arrival time.

We also study the arrival time uncertainties by shifting Earth to different
locations (e.g. $\pm$10°, see Section 4.6). We find that for ambient solar
wind models, which exhibit more structured ambient solar wind conditions, the
uncertainties in the arrival time increases. In the case of ELEvoHI/EUHFORIA
the modeled arrival times differ up to more than 9 hours. This is again in the
range of our current forecast capabilities. It also shows that ELEvoHI is
highly dependent on accurate ambient solar wind models but those are known to
have substantial inherent uncertainties by themselves.

In this study we consider the CME arrival times and speed only in the ecliptic
plane, even though the ambient solar wind and CMEs are 3D phenomena.
Therefore, we do not provide any uncertainties regarding the modeled CME
arrival depending on the latitude. However, we expect the uncertainties to be
in the same range as when shifting the Earth to different longitudes.

In the previous version of ELEvoHI the CMEs are treated as coherent
structures, meaning that the frontal shape, once defined, does not change
during propagation. Hence, it assumes that the internal magnetic field and the
associated magnetic tension force prevents the CME from deformation. MJ. Owens
. (2017) showed that at about 0.3 AU the majority of CMEs do not behave as
coherent structures anymore. As a consequence the different flanks of a CME
are effectively independent from each other, while neighbouring parts of the
CME front are most likely to experience magnetic tension. In the current
implementation of ELEvoHI 2.0 each point of the CME front propagates
individually, i.e. no structural coherence is given. However, the results
obtained in this study indicate that the CME fronts do not show
discontinuities for the three ambient solar wind models used. The reason is
mainly due to the relatively small change of ambient solar wind speed from one
longitude to the next.

Recent studies (e.g. Barnard ., 2017; Kay Nieves-Chinchilla, 2021; Y. Wang .,
2016; Zhuang ., 2017) have shown the importance of deformation, but also
deflection and expansion of CMEs to obtain more accurate CME arrival time
predictions for drag-based models. Associated to that, an evaluation of the
drag parameter along the whole CME front is required. Also CME-CME interaction
is essential for arrival time prediction. However, such interactions are not
incorporated in the current version of ELEvoHI 2.0. A preceding CME leads to a
preconditioning of the ambient solar wind (e.g. Temmer ., 2017), which is so
far not implemented in the solar wind models used by our model. This study is
only a first step to a better understanding of the CME propagation behavior in
the heliosphere. Future work will include a broader test based on a larger
sample of events to detect and constrain the important factors influencing CME
arrival predictions.

##  6 Data Sources

Data

STEREO/HI: https://www.ukssdc.ac.uk/solar/stereo/data.html
STEREO/COR2: https://stereo-ssc.nascom.nasa.gov/data/
HELCATS: https://www.helcats-fp7.eu
ICMECAT: https://doi.org/10.6084/m9.figshare.6356420

Model

ELEvoHI 2.0 is available at https://doi.org/10.5281/zenodo.5045415

Results

The visualization of each model result, i.e. movies and figures, as well as
the results from the ambient solar wind models can be downloaded from
https://doi.org/10.6084/m9.figshare.14923032.v1.

Software

IDLTM Version 8.4
Python 3.7.6
SATPLOT:
https://hesperia.gsfc.nasa.gov/ssw/stereo/secchi/idl/jpl/satplot/SATPLOT_User_Guide.pdf

###### Acknowledgements.

J.H., T.A., M.A.R., A.J.W., C.M., M.B. and U.V.A. thank the Austrian Science
Fund (FWF): P31265-N27, P31659-N27, P31521-N27. STEREO/HI was developed by a
consortium comprising Rutherford Appleton Laboratory, and University of
Birmingham (UK), Centre Spatiale de Liége (Belgium), and the Naval Research
Laboratory (USA). The authors acknowledge the UK Solar System Data Centre for
provision of the STEREO/HI data. The STEREO/SECCHI data used here are produced
by an international consortium of the Naval Research Laboratory (USA),
Lockheed Martin Solar and Astrophysics Laboratory (USA), NASA Goddard Space
Flight Center (USA), Rutherford Appleton Laboratory (UK), University of
Birmingham (UK), Max-Planck-Institut für Sonnensystemforschung (Germany),
Centre Spatiale de Liège (Belgium), Institut d’Optique Théorique et Appliqué
(France), and Institut d’Astrophysique Spatiale (France).

## References

  * Altschuler Newkirk (1969) altschuler69Altschuler, MD. Newkirk, G.  196909\.  Magnetic Fields and the Structure of the Solar Corona. I: Methods of Calculating Coronal Fields Magnetic Fields and the Structure of the Solar Corona. I: Methods of Calculating Coronal Fields.  Sol. Phys.9131-149.  10.1007/BF00145734
  * Amerstorfer . (2021) Amerstorfer2021Amerstorfer, T., Hinterreiter, J., Reiss, MA., Möstl, C., Davies, JA., Bailey, RL.Harrison, RA.  2021\.  Evaluation of CME Arrival Prediction Using Ensemble Modeling Based on Heliospheric Imaging Observations Evaluation of cme arrival prediction using ensemble modeling based on heliospheric imaging observations.  Space Weather191e2020SW002553.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020SW002553 e2020SW002553 10.1029/2020SW002553  https://doi.org/10.1029/2020SW002553
  * Amerstorfer . (2018) Amerstorfer2018Amerstorfer, T., Möstl, C., Hess, P., Temmer, M., Mays, ML., Reiss, MA.Bourdin, PA.  201807\.  Ensemble Prediction of a Halo Coronal Mass Ejection Using Heliospheric Imagers Ensemble Prediction of a Halo Coronal Mass Ejection Using Heliospheric Imagers.  Space Weather167784-801.  10.1029/2017SW001786
  * Arge . (2003) arge03Arge, CN., Odstrcil, D., Pizzo, VJ. Mayer, LR.  200309\.  Improved Method for Specifying Solar Wind Speed Near the Sun Improved Method for Specifying Solar Wind Speed Near the Sun.  M. Velli, R. Bruno, F. Malara B. Bucci (), Solar Wind Ten Solar wind ten ( 679, 190-193).  10.1063/1.1618574
  * Barnard . (2020) Barnard2020Barnard, L., Owens, MJ., Scott, CJ. de Koning, CA.  2020\.  Ensemble CME Modeling Constrained by Heliospheric Imager Observations Ensemble cme modeling constrained by heliospheric imager observations.  AGU Advances13e2020AV000214.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020AV000214 e2020AV000214 10.1029/2020AV000214  10.1029/2020AV000214
  * Barnard . (2017) Barnard2017Barnard, LA., de Koning, CA., Scott, CJ., Owens, MJ., Wilkinson, J. Davies, JA.  201706\.  Testing the current paradigm for space weather prediction with heliospheric imagers Testing the current paradigm for space weather prediction with heliospheric imagers.  Space Weather156782-803.  10.1002/2017SW001609
  * Bein . (2013) Bein2013Bein, BM., Temmer, M., Vourlidas, A., Veronig, AM. Utz, D.  201305\.  The Height Evolution of the “True” Coronal Mass Ejection Mass derived from STEREO COR1 and COR2 Observations The Height Evolution of the “True” Coronal Mass Ejection Mass derived from STEREO COR1 and COR2 Observations.  ApJ768131.  10.1088/0004-637X/768/1/31
  * Billings (1966) Billings1966Billings, DE.  1966\.  A guide to the solar corona A guide to the solar corona.
  * Cannon (2013) Cannon2013Cannon, PS.  201304\.  Extreme Space Weather—A Report Published by the UK Royal Academy of Engineering Extreme Space Weather—A Report Published by the UK Royal Academy of Engineering.  Space Weather114138-139.  10.1002/swe.20032
  * Cargill (2004) Cargill2004Cargill, PJ.  200405\.  On the Aerodynamic Drag Force Acting on Interplanetary Coronal Mass Ejections On the Aerodynamic Drag Force Acting on Interplanetary Coronal Mass Ejections.  Sol. Phys.2211135-149.  10.1023/B:SOLA.0000033366.10725.a2
  * Colaninno Vourlidas (2009) Colaninno2009Colaninno, RC. Vourlidas, A.  200906\.  First Determination of the True Mass of Coronal Mass Ejections: A Novel Approach to Using the Two STEREO Viewpoints First Determination of the True Mass of Coronal Mass Ejections: A Novel Approach to Using the Two STEREO Viewpoints.  ApJ6981852-858.  10.1088/0004-637X/698/1/852
  * Davies . (2012) Davies2012Davies, JA., Harrison, RA., Perry, CH., Möstl, C., Lugaz, N., Rollett, T.Savani, NP.  201205\.  A Self-similar Expansion Model for Use in Solar Wind Transient Propagation Studies A Self-similar Expansion Model for Use in Solar Wind Transient Propagation Studies.  ApJ750123.  10.1088/0004-637X/750/1/23
  * Davies . (2009) Davies2009Davies, JA., Harrison, RA., Rouillard, AP., Sheeley, NR., Perry, CH., Bewsher, D.Brown, DS.  200901\.  A synoptic view of solar transient evolution in the inner heliosphere using the Heliospheric Imagers on STEREO A synoptic view of solar transient evolution in the inner heliosphere using the Heliospheric Imagers on STEREO.  Geophys. Res. Lett.362L02102.  10.1029/2008GL036182
  * de Koning (2017) DeKoning2017de Koning, CA.  201707\.  Lessons Learned from the Three-view Determination of CME Mass Lessons Learned from the Three-view Determination of CME Mass.  ApJ844161.  10.3847/1538-4357/aa7a09
  * Dumbović . (2018) Dumbovic2018Dumbović, M., Čalogović, J., Vršnak, B., Temmer, M., Mays, ML., Veronig, A. Piantschitsch, I.  201802\.  The Drag-based Ensemble Model (DBEM) for Coronal Mass Ejection Propagation The Drag-based Ensemble Model (DBEM) for Coronal Mass Ejection Propagation.  ApJ8542180.  10.3847/1538-4357/aaaa66
  * Eyles . (2009) Eyles2009Eyles, CJ., Harrison, RA., Davis, CJ., Waltham, NR., Shaughnessy, BM., Mapson-Menard, HCA.Rochus, P.  200902\.  The Heliospheric Imagers Onboard the STEREO Mission The Heliospheric Imagers Onboard the STEREO Mission.  Sol. Phys.2542387-445.  10.1007/s11207-008-9299-0
  * Eyni Steinitz (1980) EyniSteinitz1980Eyni, M. Steinitz, R.  198001\.  An empirical relation between density, flow velocity and heliocentric distance in the solar wind An empirical relation between density, flow velocity and heliocentric distance in the solar wind.  M. Dryer E. Tandberg-Hanssen (), Solar and Interplanetary Dynamics Solar and interplanetary dynamics ( 91, 147-149).
  * Gopalswamy . (2000) Gopalswamy2000Gopalswamy, N., Lara, A., Lepping, RP., Kaiser, ML., Berdichevsky, D. St. Cyr, OC.  200001\.  Interplanetary acceleration of coronal mass ejections Interplanetary acceleration of coronal mass ejections.  Geophys. Res. Lett.272145-148.  10.1029/1999GL003639
  * Gosling . (1990) Gosling1990Gosling, JT., Bame, SJ., McComas, DJ. Phillips, JL.  199006\.  Coronal mass ejections and large geomagnetic storms Coronal mass ejections and large geomagnetic storms.  Geophys. Res. Lett.177901-904.  10.1029/GL017i007p00901
  * Gui . (2011) GUI2011Gui, B., Shen, C., Wang, Y., Ye, P., Liu, J., Wang, S. Zhao, X.  201107\.  Quantitative Analysis of CME Deflections in the Corona Quantitative Analysis of CME Deflections in the Corona.  Sol. Phys.2711-2111-139.  10.1007/s11207-011-9791-9
  * Hinterreiter . (2021) Hinterreiter2021Hinterreiter, J., Amerstorfer, T., Reiss, MA., Möstl, C., Temmer, M., Bauer, M.Owens, MJ.  2021\.  Why are ELEvoHI CME Arrival Predictions Different if Based on STEREO-A or STEREO-B Heliospheric Imager Observations? Why are elevohi cme arrival predictions different if based on stereo-a or stereo-b heliospheric imager observations?  Space Weather193e2020SW002674.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020SW002674 e2020SW002674 2020SW002674  https://doi.org/10.1029/2020SW002674
  * Howard Tappin (20091) HowardTappin2009_1Howard, TA. Tappin, SJ.  2009110\.  Interplanetary Coronal Mass Ejections Observed in the Heliosphere: 1. Review of Theory Interplanetary Coronal Mass Ejections Observed in the Heliosphere: 1. Review of Theory.  Space Sci. Rev.1471-231-54.  10.1007/s11214-009-9542-5
  * Howard Tappin (20092) HowardTappin2009_3Howard, TA. Tappin, SJ.  2009210\.  Interplanetary Coronal Mass Ejections Observed in the Heliosphere: 3. Physical Implications Interplanetary Coronal Mass Ejections Observed in the Heliosphere: 3. Physical Implications.  Space Sci. Rev.1471-289-110.  10.1007/s11214-009-9577-7
  * Howard Tappin (2010) HowardTappin2010Howard, TA. Tappin, SJ.  201007\.  Application of a new phenomenological coronal mass ejection model to space weather forecasting Application of a new phenomenological coronal mass ejection model to space weather forecasting.  Space Weather87S07004.  10.1029/2009SW000531
  * Hundhausen . (1994) Hundhausen1994Hundhausen, AJ., Stanger, AL. Serbicki, SA.  199412\.  Mass and energy contents of coronal mass ejections: SMM results from 1980 and 1984-1988 Mass and energy contents of coronal mass ejections: SMM results from 1980 and 1984-1988.  JJ. Hunt (), Solar Dynamic Phenomena and Solar Wind Consequences, the Third SOHO Workshop Solar dynamic phenomena and solar wind consequences, the third soho workshop ( 373, 409).
  * Kay . (2020) Kay2020Kay, C., Mays, ML. Verbeke, C.  202001\.  Identifying Critical Input Parameters for Improving Drag-Based CME Arrival Time Predictions Identifying Critical Input Parameters for Improving Drag-Based CME Arrival Time Predictions.  Space Weather181e02382.  10.1029/2019SW002382
  * Kay Nieves-Chinchilla (2020) KayNievesChinchilla2020Kay, C. Nieves-Chinchilla, T.  202011\.  Modeling Interplanetary Expansion and Deformation of CMEs with ANTEATR-PARADE I: Relative Contribution of Different Forces Modeling Interplanetary Expansion and Deformation of CMEs with ANTEATR-PARADE I: Relative Contribution of Different Forces.  arXiv e-printsarXiv:2011.06030.
  * Kay Nieves-Chinchilla (2021) Kay2021Kay, C. Nieves-Chinchilla, T.  202105\.  Modeling Interplanetary Expansion and Deformation of CMEs With ANTEATR PARADE: 1. Relative Contribution of Different Forces Modeling Interplanetary Expansion and Deformation of CMEs With ANTEATR PARADE: 1. Relative Contribution of Different Forces.  Journal of Geophysical Research (Space Physics)1265e28911.  10.1029/2020JA028911
  * Kay Opher (2015) KayOpher2015Kay, C. Opher, M.  201510\.  The Heliocentric Distance where the Deflections and Rotations of Solar Coronal Mass Ejections Occur The Heliocentric Distance where the Deflections and Rotations of Solar Coronal Mass Ejections Occur.  ApJ8112L36.  10.1088/2041-8205/811/2/L36
  * Kilpua . (2012) Kilpua2012Kilpua, EKJ., Jian, LK., Li, Y., Luhmann, JG. Russell, CT.  201211\.  Observations of ICMEs and ICME-like Solar Wind Structures from 2007 - 2010 Using Near-Earth and STEREO Observations Observations of ICMEs and ICME-like Solar Wind Structures from 2007 - 2010 Using Near-Earth and STEREO Observations.  Sol. Phys.2811391-409.  10.1007/s11207-012-9957-0
  * Kilpua . (2019) Kilpua2019Kilpua, EKJ., Lugaz, N., Mays, ML. Temmer, M.  201904\.  Forecasting the Structure and Orientation of Earthbound Coronal Mass Ejections Forecasting the Structure and Orientation of Earthbound Coronal Mass Ejections.  Space Weather174498-526.  10.1029/2018SW001944
  * Liu . (2014) Liu2014Liu, YD., Luhmann, JG., Kajdič, P., Kilpua, EKJ., Lugaz, N., Nitta, NV.Galvin, AB.  201403\.  Observations of an extreme storm in interplanetary space caused by successive coronal mass ejections Observations of an extreme storm in interplanetary space caused by successive coronal mass ejections.  Nature Communications53481.  10.1038/ncomms4481
  * Lugaz (2010) Lugaz2010Lugaz, N.  201012\.  Accuracy and Limitations of Fitting and Stereoscopic Methods to Determine the Direction of Coronal Mass Ejections from Heliospheric Imagers Observations Accuracy and Limitations of Fitting and Stereoscopic Methods to Determine the Direction of Coronal Mass Ejections from Heliospheric Imagers Observations.  Sol. Phys.2672411-429.  10.1007/s11207-010-9654-9
  * Lugaz . (2012) Lugaz2012Lugaz, N., Farrugia, CJ., Davies, JA., Möstl, C., Davis, CJ., Roussev, II. Temmer, M.  201211\.  The Deflection of the Two Interacting Coronal Mass Ejections of 2010 May 23-24 as Revealed by Combined in Situ Measurements and Heliospheric Imaging The Deflection of the Two Interacting Coronal Mass Ejections of 2010 May 23-24 as Revealed by Combined in Situ Measurements and Heliospheric Imaging.  ApJ759168.  10.1088/0004-637X/759/1/68
  * Lugaz . (2010) LugazEtAl2010Lugaz, N., Hernandez-Charpak, JN., Roussev, II., Davis, CJ., Vourlidas, A. Davies, JA.  201005\.  Determining the Azimuthal Properties of Coronal Mass Ejections from Multi-Spacecraft Remote-Sensing Observations with STEREO SECCHI Determining the Azimuthal Properties of Coronal Mass Ejections from Multi-Spacecraft Remote-Sensing Observations with STEREO SECCHI.  ApJ7151493-499.  10.1088/0004-637X/715/1/493
  * Manchester . (2017) Manchester2017Manchester, W., Kilpua, EKJ., Liu, YD., Lugaz, N., Riley, P., Török, T. Vršnak, B.  201711\.  The Physical Processes of CME/ICME Evolution The Physical Processes of CME/ICME Evolution.  Space Sci. Rev.2123-41159-1219.  10.1007/s11214-017-0394-0
  * Manoharan . (2004) Manoharan2004Manoharan, PK., Gopalswamy, N., Yashiro, S., Lara, A., Michalek, G. Howard, RA.  200406\.  Influence of coronal mass ejection interaction on propagation of interplanetary shocks Influence of coronal mass ejection interaction on propagation of interplanetary shocks.  Journal of Geophysical Research (Space Physics)109A6A06109.  10.1029/2003JA010300
  * Manoharan Mujiber Rahman (2011) Manoharan2011Manoharan, PK. Mujiber Rahman, A.  201104\.  Coronal mass ejections—Propagation time and associated internal energy Coronal mass ejections—Propagation time and associated internal energy.  Journal of Atmospheric and Solar-Terrestrial Physics735-6671-677.  10.1016/j.jastp.2011.01.017
  * Mierla . (2010) Mierla2010Mierla, M., Inhester, B., Antunes, A., Boursier, Y., Byrne, JP., Colaninno, R.Zhukov, AN.  201001\.  On the 3-D reconstruction of Coronal Mass Ejections using coronagraph data On the 3-D reconstruction of Coronal Mass Ejections using coronagraph data.  Annales Geophysicae281203-215.  10.5194/angeo-28-203-2010
  * Möstl Davies (2013) MoestlDavies2013Möstl, C. Davies, JA.  201307\.  Speeds and Arrival Times of Solar Transients Approximated by Self-similar Expanding Circular Fronts Speeds and Arrival Times of Solar Transients Approximated by Self-similar Expanding Circular Fronts.  Sol. Phys.2851-2411-423.  10.1007/s11207-012-9978-8
  * Möstl . (2015) Moestl2015Möstl, C., Rollett, T., Frahm, RA., Liu, YD., Long, DM., Colaninno, RC.Vršnak, B.  201505\.  Strong coronal channelling and interplanetary evolution of a solar storm up to Earth and Mars Strong coronal channelling and interplanetary evolution of a solar storm up to Earth and Mars.  Nature Communications67135.  10.1038/ncomms8135
  * Möstl . (2011) Moestl2011Möstl, C., Rollett, T., Lugaz, N., Farrugia, CJ., Davies, JA., Temmer, M.Biernat, HK.  201111\.  Arrival Time Calculation for Interplanetary Coronal Mass Ejections with Circular Fronts and Application to STEREO Observations of the 2009 February 13 Eruption Arrival Time Calculation for Interplanetary Coronal Mass Ejections with Circular Fronts and Application to STEREO Observations of the 2009 February 13 Eruption.  ApJ741134.  10.1088/0004-637X/741/1/34
  * Möstl . (2020) Moestl2020Möstl, C., Weiss, AJ., Bailey, RL., Reiss, MA., Amerstorfer, UV., Amerstorfer, T.Stansby, D.  202007\.  Prediction of the in situ coronal mass ejection rate for solar cycle 25: Implications for Parker Solar Probe in situ observations Prediction of the in situ coronal mass ejection rate for solar cycle 25: Implications for Parker Solar Probe in situ observations.  arXiv e-printsarXiv:2007.14743.
  * Odstrcil . (2004) Odstrcil2004Odstrcil, D., Pizzo, VJ., Linker, JA., Riley, P., Lionello, R. Mikic, Z.  200410\.  Initial coupling of coronal and heliospheric numerical magnetohydrodynamic codes Initial coupling of coronal and heliospheric numerical magnetohydrodynamic codes.  Journal of Atmospheric and Solar-Terrestrial Physics6615-161311-1320.  10.1016/j.jastp.2004.04.007
  * M. Owens . (2020) Owens2020SoPhOwens, M., Lang, M., Barnard, L., Riley, P., Ben-Nun, M., Scott, CJ.Gonzi, S.  202003\.  A Computationally Efficient, Time-Dependent Model of the Solar Wind for Use as a Surrogate to Three-Dimensional Numerical Magnetohydrodynamic Simulations A Computationally Efficient, Time-Dependent Model of the Solar Wind for Use as a Surrogate to Three-Dimensional Numerical Magnetohydrodynamic Simulations.  Sol. Phys.295343.  10.1007/s11207-020-01605-3
  * MJ. Owens . (2017) Owens2017NatOwens, MJ., Lockwood, M. Barnard, LA.  201706\.  Coronal mass ejections are not coherent magnetohydrodynamic structures Coronal mass ejections are not coherent magnetohydrodynamic structures.  Scientific Reports74152.  10.1038/s41598-017-04546-3
  * Paouris Mavromichalaki (2017) Paouris2017Paouris, E. Mavromichalaki, H.  201712\.  Effective Acceleration Model for the Arrival Time of Interplanetary Shocks driven by Coronal Mass Ejections Effective Acceleration Model for the Arrival Time of Interplanetary Shocks driven by Coronal Mass Ejections.  Sol. Phys.29212180.  10.1007/s11207-017-1212-2
  * Pomoell Poedts (2018) Pomoell2018Pomoell, J. Poedts, S.  201806\.  EUHFORIA: European heliospheric forecasting information asset EUHFORIA: European heliospheric forecasting information asset.  Journal of Space Weather and Space Climate8A35.  10.1051/swsc/2018020
  * Pulkkinen (2007) Pulkkinen2007Pulkkinen, T.  200705\.  Space Weather: Terrestrial Perspective Space Weather: Terrestrial Perspective.  Living Reviews in Solar Physics411.  10.12942/lrsp-2007-1
  * Reiss . (2019) reiss19Reiss, MA., MacNeice, PJ., Mays, LM., Arge, CN., Möstl, C., Nikolic, L. Amerstorfer, T.  201902\.  Forecasting the Ambient Solar Wind with Numerical Models. I. On the Implementation of an Operational Framework Forecasting the Ambient Solar Wind with Numerical Models. I. On the Implementation of an Operational Framework.  ApJS24035.  10.3847/1538-4365/aaf8b3
  * Reiss . (2020) Reiss2020ApJReiss, MA., MacNeice, PJ., Muglach, K., Arge, CN., Möstl, C., Riley, P.Amerstorfer, U.  202003\.  Forecasting the Ambient Solar Wind with Numerical Models. II. An Adaptive Prediction System for Specifying Solar Wind Speed near the Sun Forecasting the Ambient Solar Wind with Numerical Models. II. An Adaptive Prediction System for Specifying Solar Wind Speed near the Sun.  ApJ8912165.  10.3847/1538-4357/ab78a0
  * Richardson Cane (2010) RichardsonCane2010Richardson, IG. Cane, HV.  2010Jun.  Near-Earth Interplanetary Coronal Mass Ejections During Solar Cycle 23 (1996 - 2009): Catalog and Summary of Properties Near-Earth Interplanetary Coronal Mass Ejections During Solar Cycle 23 (1996 - 2009): Catalog and Summary of Properties.  Sol. Phys.2641189-237.  10.1007/s11207-010-9568-6
  * Richardson Cane (2012) RichardsonCane2012Richardson, IG. Cane, HV.  201205\.  Near-earth solar wind flows and related geomagnetic activity during more than four solar cycles (1963-2011) Near-earth solar wind flows and related geomagnetic activity during more than four solar cycles (1963-2011).  Journal of Space Weather and Space Climate2A02.  10.1051/swsc/2012003
  * Riley Lionello (2011) riley11bRiley, P. Lionello, R.  201106\.  Mapping Solar Wind Streams from the Sun to 1 AU: A Comparison of Techniques Mapping Solar Wind Streams from the Sun to 1 AU: A Comparison of Techniques.  Sol. Phys.270575-592.  10.1007/s11207-011-9766-x
  * Riley . (2018) Riley2018Riley, P., Mays, ML., Andries, J., Amerstorfer, T., Biesecker, D., Delouille, V.Zhao, X.  201809\.  Forecasting the Arrival Time of Coronal Mass Ejections: Analysis of the CCMC CME Scoreboard Forecasting the Arrival Time of Coronal Mass Ejections: Analysis of the CCMC CME Scoreboard.  Space Weather1691245-1260.  10.1029/2018SW001962
  * Rollett . (2016) Rollett2016Rollett, T., Möstl, C., Isavnin, A., Davies, JA., Kubicka, M., Amerstorfer, UV. Harrison, RA.  2016Jun.  ElEvoHI: A Novel CME Prediction Tool for Heliospheric Imaging Combining an Elliptical Front with Drag-based Model Fitting ElEvoHI: A Novel CME Prediction Tool for Heliospheric Imaging Combining an Elliptical Front with Drag-based Model Fitting.  ApJ8242131.  10.3847/0004-637X/824/2/131
  * Rollett . (2014) Rollett2014Rollett, T., Möstl, C., Temmer, M., Frahm, RA., Davies, JA., Veronig, AM.Zhang, TL.  201407\.  Combined Multipoint Remote and in situ Observations of the Asymmetric Evolution of a Fast Solar Coronal Mass Ejection Combined Multipoint Remote and in situ Observations of the Asymmetric Evolution of a Fast Solar Coronal Mass Ejection.  ApJ7901L6.  10.1088/2041-8205/790/1/L6
  * Rouillard . (2008) Rouillard2008Rouillard, AP., Davies, JA., Forsyth, RJ., Rees, A., Davis, CJ., Harrison, RA.Perry, CH.  200805\.  First imaging of corotating interaction regions using the STEREO spacecraft First imaging of corotating interaction regions using the STEREO spacecraft.  Geophys. Res. Lett.3510L10110.  10.1029/2008GL033767
  * Ruffenach . (2015) Ruffenach2015Ruffenach, A., Lavraud, B., Farrugia, CJ., Démoulin, P., Dasso, S., Owens, MJ.Galvin, AB.  201501\.  Statistical study of magnetic cloud erosion by magnetic reconnection Statistical study of magnetic cloud erosion by magnetic reconnection.  Journal of Geophysical Research (Space Physics)120143-60.  10.1002/2014JA020628
  * Savani . (2010) Savani2010Savani, NP., Owens, MJ., Rouillard, AP., Forsyth, RJ. Davies, JA.  201005\.  Observational Evidence of a Coronal Mass Ejection Distortion Directly Attributable to a Structured Solar Wind Observational Evidence of a Coronal Mass Ejection Distortion Directly Attributable to a Structured Solar Wind.  ApJ7141L128-L132.  10.1088/2041-8205/714/1/L128
  * Schatten (1971) schatten71Schatten, KH.  1971\.  Current sheet magnetic model for the solar corona. Current sheet magnetic model for the solar corona.  Cosmic Electrodynamics2232-245.
  * Schatten . (1969) schatten69Schatten, KH., Wilcox, JM. Ness, NF.  196903\.  A model of interplanetary and coronal magnetic fields A model of interplanetary and coronal magnetic fields.  Sol. Phys.6442-455.  10.1007/BF00146478
  * Sheeley . (1999) Sheeley1999Sheeley, NR., Walters, JH., Wang, YM. Howard, RA.  199911\.  Continuous tracking of coronal outflows: Two kinds of coronal mass ejections Continuous tracking of coronal outflows: Two kinds of coronal mass ejections.  J. Geophys. Res.104A1124739-24768.  10.1029/1999JA900308
  * Shen . (2011) Shen2011Shen, C., Wang, Y., Gui, B., Ye, P. Wang, S.  201104\.  Kinematic Evolution of a Slow CME in Corona Viewed by STEREO-B on 8 October 2007 Kinematic Evolution of a Slow CME in Corona Viewed by STEREO-B on 8 October 2007.  Sol. Phys.2692389-400.  10.1007/s11207-011-9715-8
  * Tappin Howard (2009) TappinHoward2009_2Tappin, SJ. Howard, TA.  200910\.  Interplanetary Coronal Mass Ejections Observed in the Heliosphere: 2. Model and Data Comparison Interplanetary Coronal Mass Ejections Observed in the Heliosphere: 2. Model and Data Comparison.  Space Sci. Rev.1471-255-87.  10.1007/s11214-009-9550-5
  * Temmer . (2017) Temmer2017Temmer, M., Reiss, MA., Nikolic, L., Hofmeister, SJ. Veronig, AM.  201702\.  Preconditioning of Interplanetary Space Due to Transient CME Disturbances Preconditioning of Interplanetary Space Due to Transient CME Disturbances.  ApJ8352141.  10.3847/1538-4357/835/2/141
  * Temmer . (2011) temmer2011Temmer, M., Rollett, T., Möstl, C., Veronig, AM., Vršnak, B. Odstrčil, D.  201112\.  Influence of the Ambient Solar Wind Flow on the Propagation Behavior of Interplanetary Coronal Mass Ejections Influence of the Ambient Solar Wind Flow on the Propagation Behavior of Interplanetary Coronal Mass Ejections.  ApJ7432101.  10.1088/0004-637X/743/2/101
  * A. Thernisien . (2009) Thernisien2009Thernisien, A., Vourlidas, A. Howard, RA.  2009May.  Forward Modeling of Coronal Mass Ejections Using STEREO/SECCHI Data Forward Modeling of Coronal Mass Ejections Using STEREO/SECCHI Data.  Sol. Phys.2561-2111-130.  10.1007/s11207-009-9346-5
  * AFR. Thernisien . (2006) Thernisien2006Thernisien, AFR., Howard, RA. Vourlidas, A.  2006Nov.  Modeling of Flux Rope Coronal Mass Ejections Modeling of Flux Rope Coronal Mass Ejections.  ApJ6521763-773.  10.1086/508254
  * Vršnak . (2013) Vrsnak2013Vršnak, B., Žic, T., Vrbanec, D., Temmer, M., Rollett, T., Möstl, C.Shanmugaraju, A.  201307\.  Propagation of Interplanetary Coronal Mass Ejections: The Drag-Based Model Propagation of Interplanetary Coronal Mass Ejections: The Drag-Based Model.  Sol. Phys.2851-2295-315.  10.1007/s11207-012-0035-4
  * Žic . (2015) Zic2015Žic, T., Vršnak, B. Temmer, M.  201506\.  Heliospheric Propagation of Coronal Mass Ejections: Drag-based Model Fitting Heliospheric Propagation of Coronal Mass Ejections: Drag-based Model Fitting.  ApJS218232.  10.1088/0067-0049/218/2/32
  * Y. Wang . (2016) Wang2016Wang, Y., Zhang, Q., Liu, J., Shen, C., Shen, F., Yang, Z.Zhuang, B.  201608\.  On the propagation of a geoeffective coronal mass ejection during 15-17 March 2015 On the propagation of a geoeffective coronal mass ejection during 15-17 March 2015.  Journal of Geophysical Research (Space Physics)12187423-7434.  10.1002/2016JA022924
  * YM. Wang Sheeley (1995) wang95Wang, YM. Sheeley, NR., Jr.  199507\.  Solar Implications of ULYSSES Interplanetary Field Measurements Solar Implications of ULYSSES Interplanetary Field Measurements.  ApJ447L143.  10.1086/309578
  * Zhuang . (2017) Zhuang2017Zhuang, B., Wang, Y., Shen, C., Liu, S., Wang, J., Pan, Z.Liu, R.  201708\.  The Significance of the Influence of the CME Deflection in Interplanetary Space on the CME Arrival at Earth The Significance of the Influence of the CME Deflection in Interplanetary Space on the CME Arrival at Earth.  ApJ8452117.  10.3847/1538-4357/aa7fc0
  * Zuccarello . (2012) Zuccarello2012Zuccarello, FP., Bemporad, A., Jacobs, C., Mierla, M., Poedts, S. Zuccarello, F.  201201\.  The Role of Streamers in the Deflection of Coronal Mass Ejections: Comparison between STEREO Three-dimensional Reconstructions and Numerical Simulations The Role of Streamers in the Deflection of Coronal Mass Ejections: Comparison between STEREO Three-dimensional Reconstructions and Numerical Simulations.  ApJ744166.  10.1088/0004-637X/744/1/66


# Track 3 ICASSP 2023 LIMMITS Chalenge Submission for VANI:
Very-lightweight Accent-controllable TTS for Native and Non-native speakers
with Identity Preservation

##  1 Abstract

In this track, we present VANI, a very lightweight multi-lingual accent
controllable speech synthesis system. Our approach builds upon autoregressive
flow models and utilizes the same approach in Track $1$ to create a very
lightweight ($<5$ million parameters) multilingual speech model which can
generate speech with the proper native accent of the target language while
retaining a person’s voice without relying on parallel or bilingual training
with the person speaking in multiple languages. Our model supports explicit
control over accent, language, speaker and fine-grained $F_{0}$ and energy
features. We utilize augmentation to boost content and acoustic quality of our
model since the track requires dataset to be limited per speaker.

##  2 Data Setup

In this section, we describe the dataset for the Track3, our data cleaning and
preprocessing efforts.

###  2.1 Data Cleaning

The Track3 challenge requires us to use only 5 hours of data per speaker
(about 12.5% of the original dataset). As part of data cleaning, we remove any
empty audio files (we found 1 in Hindi-Male and 4 in Telugu-Female), duplicate
transcripts (16 in Hindi-Female and 138 in Telugu-Female), new-line characters
in transcripts and corrected the sentence separators (ASCII character 124 vs
2404 in hindi).

To select samples with clean speech, we first run the wav files through an ASR
(Automatic Speech Recognition) model111Hindi - Harveenchadha/vakyansh-
wav2vec2-hindi-him-4200
Marathi - tanmaylaud/wav2vec2-large-xlsr-hindi-marathi
Telugu - Harveenchadha/vakyansh-wav2vec2-telugu-tem-100 and generate
transcripts. We selected top 8000 datapoints per speaker with least character
error rate (CER) between ground truth transcript and generated transcript.

###  2.2 Data Selection

Since we have a hard requirement of using less than $5$ hours of data per
speaker, we have to further filter the cleaned dataset. Since one of our goals
is to do cross-lingual synthesis, its very important to disentangle speaker
from language/text. We believe, our model can benefit from a parallel dataset
with speakers of the same language speaking the same text tokens. Using our
cleaned set these 8000 datapoints per speaker, we identify parallel data for
each language by computing CER between transcripts for male and female speaker
of each language. We identify 3000 disjoint prompts with least character error
rate. These selected datapoints have the most overlap between speakers of the
same language which will help disentangle text from speakers.

Final selected data has been summarized in Table 1. Filelists including
fileIDs for ”parallel” section of our dataset can be found
here222shorturl.at/kvxZ6

Table 1: Summary of the dataset.

speaker | original dataset | parallel dataset
---|---|---
|  |  | train | val
| files | # hours | files | # hours | files | # hours
Hindi Female | 16512 | 40.28 | 2222 | 4.95 | 100 | 0.17
Hindi Male | 17798 | 40.48 | 2226 | 4.97 | 100 | 0.18
Marathi Female | 17874 | 42.83 | 2078 | 4.51 | 90 | 0.19
Marathi Male | 16747 | 41.2 | 2110 | 4.51 | 88 | 0.18
Telugu Female | 15933 | 41.08 | 1533 | 3.6 | 53 | 0.12
Telugu Male | 16939 | 42.03 | 2068 | 4.43 | 82 | 0.17

Table 2: Parameter count of different components of VANI.

accent_embedding weight | 12
---|---
attention key_proj | 44,800
attention query_proj | 57,920
context_lstm | 439,560
decoder flows | 1,391,424
duration predictor | 289,377
embedding weight | 106,240
encoder | 1424020
energy predictor | 169,313
f0 predictor | 572,001
speaker_embedding weight | 72
unvoiced_bias_module 0 | 261
voiced prediction | 71,025
Total | 4,969,025

Table 3: Mono-lingual Evaluation using Cosine Sim(speaker identity retention)
and CER(content quality) on resynthesis.

Model Hindi Female Hindi Male Marathi Female Marathi Male Telugu Female Telugu
Male Cosine Sim ($\uparrow$) CER ($\downarrow$) Cosine Sim ($\uparrow$) CER
($\downarrow$) Cosine Sim ($\uparrow$) CER ($\downarrow$) Cosine Sim
($\uparrow$) CER ($\downarrow$) Cosine Sim ($\uparrow$) CER ($\downarrow$)
Cosine Sim ($\uparrow$) CER ($\downarrow$) GT 1.0 0.035 1.0 0.015 1.0 0.089
1.0 0.094 1.0 0.049 1.0 0.049 Track1 (RADMMM + Aug + HiFiGAN) $0.865\pm 0.022$
0.045 $0.871\pm 0.022$ 0.015 $0.809\pm 0.045$ 0.096 $0.869\pm 0.016$ 0.127
$0.831\pm 0.056$ 0.056 $0.856\pm 0.027$ 0.047 Track2 (VANI-NP + Waveglow)
$0.853\pm 0.025$ 0.072 $0.773\pm 0.037$ 0.034 $0.757\pm 0.052$ 0.221 $0.785\pm
0.031$ 0.243 $0.770\pm 0.071$ 0.124 $0.758\pm 0.026$ 0.111 Track2 (VANI-NP +
HiFiGAN) $0.829\pm 0.027$ 0.079 $0.740\pm 0.028$ 0.036 $0.727\pm 0.052$ 0.211
$0.727\pm 0.036$ 0.242 $0.750\pm 0.041$ 0.112 $0.727\pm 0.076$ 0.148 Track3
(VANI-P + Aug + Waveglow) $0.842\pm 0.037$ 0.094 $0.782\pm 0.013$ 0.043
$0.740\pm 0.044$ 0.224 $0.760\pm 0.034$ 0.256 $0.767\pm 0.053$ 0.156 $0.706\pm
0.037$ 0.172 Track3 (VANI-P + Aug + HiFiGAN) $0.845\pm 0.018$ 0.067 $0.758\pm
0.052$ 0.045 $0.745\pm 0.031$ 0.229 $0.759\pm 0.042$ 0.233 $0.771\pm 0.032$
0.151 $0.701\pm 0.042$ 0.200

Table 4: Cross-Lingual Evaluation on 2 languages using Cosine Sim(speaker
identity retention) and CER(content quality).

Model Hindi Female Hindi Male Marathi Female Marathi Male Telugu Female Telugu
Male Cosine Sim ($\uparrow$) CER ($\downarrow$) Cosine Sim ($\uparrow$) CER
($\downarrow$) Cosine Sim ($\uparrow$) CER ($\downarrow$) Cosine Sim
($\uparrow$) CER ($\downarrow$) Cosine Sim ($\uparrow$) CER ($\downarrow$)
Cosine Sim ($\uparrow$) CER ($\downarrow$) Track1 (RADMMM + Aug + HiFiGAN)
$0.295\pm 0.060$ 0.041 $0.324\pm 0.100$ 0.016 $0.339\pm 0.117$ 0.138 $0.301\pm
0.071$ 0.160 $0.352\pm 0.105$ 0.06 $0.301\pm 0.076$ 0.048 Track2 (VANI-NP +
HiFiGAN) $0.273\pm 0.081$ 0.072 $0.294\pm 0.107$ 0.040 $0.330\pm 0.128$ 0.268
$0.305\pm 0.112$ 0.276 $0.313\pm 0.125$ 0.136 $0.299\pm 0.115$ 0.142 Track3
(VANI-P + Aug + HiFiGAN) $0.288\pm 0.072$ 0.071 $0.266\pm 0.104$ 0.045
$0.308\pm 0.142$ 0.255 $0.307\pm 0.150$ 0.265 $0.285\pm 0.139$ 0.203 $0.282\pm
0.142$ 0.218

###  2.3 Data Pre-processing

To further improve the audio quality, we perform volume normalization of each
speech sample. We further discovered that there are many starting and trailing
silences in the speech samples. We trim these silences by identifying non-
silent frames in a given audio using 50dB as threshold. We then identify the
boundaries of the audio and pad it with 0.2 seconds of silence at the
beginning and the end to have uniform beginning and trailing silences.

##  3 Model Setup

We build upon the strategies proposed in RADMMM [rad_tts, radpp] to develop a
lightweight multilingual TTS system. Our model synthesizes
mels($X\in\mathbb{R}^{C_{\mathit{mel}}\times F}$) using encoded
text($\Phi\in\mathbb{R}^{C_{\mathit{txt}}\times T}$),
accent($A\in\mathbb{R}^{D_{\mathit{accent}}}$),
speaker($S\in\mathbb{R}^{D_{\mathit{speaker}}}$), fundamental
frequency($F_{0}\in\mathbb{R}^{\mathit{1}\times F}$) and
energy($\xi\in\mathbb{R}^{\mathit{1}\times F}$) as conditioning variables
where $F$ is the number of mel frames, $T$ is the text length, and energy is
per-frame mel energy average. Although we believe attribute predictors can be
generative models, but we use deterministc attribute predictors where
$F_{0}^{h}$, $\mathcal{E}^{h}$ and $\Lambda^{h}$ are predicted pitch, energy
and durations conditioned on text $\Phi$, accent $A$ and speaker $S$:

$P_{vani}(X)=P_{mel}(X|\Phi,\Lambda^{h},A,S,F_{0}^{h},\mathcal{E}^{h})$ (1)

We leverage the text preprocessing, shared alphabet set and the accent-
conditioned alignment learning mechanism proposed in RADMMM to our setup. This
supports code-switching by default and allows for having a single model that
works with many languages. We consider language to be _implicit in the phoneme
sequence_ and the sequence of IPA tokens carry this information whereas the
information captured by accent variable $A$ should explain the fine-grained
differences between _how phonemes are pronounced in different languages_.

However, since our goal is to have very lightweight model, we use
autoregressive architecture for the mel decoder. Our architecture is very
similar to Flowtron[Flowtron] with 2 steps of flow running (one forward and
one backward). Each step of flow uses 3 LSTM layers and is conditioned on
text, accent, speaker and fine-grained $F_{0}$ and energy features as
described above. Our encoder, aligner and attribute prediction models are
borrowed from RADMMM. We use deterministic attribute predictors to predict
fine-grained features given text, accent and speaker. We call this model VANI.

As described in Sec 2, our dataset is limited to $5$ hours per speakers. Since
our dataset is very limited, we apply formant scaling augmentation suggested
in RADMMM[badlani2023multilingual] with the goals of improving the quality of
output and disentangling speaker $S$ and accent $A$ attributes. We apply
constant formant scales of $0.875$ and $1.1$ to speech samples to obtain 2
augmented samples and treat them as coming from 2 new speakers. This helps
reduce the dependence of speakers on text and accent by having the those
variables same for multiple speakers. We observed both a qualitative and
quantitative improvement as measured by CER (character error rate).

##  4 Vocoder Details

We use the flow-based Waveglow [prenger2019waveglow] as a vocoder to convert
mel-spectrograms synthesized by the mel spectrogram generator network into
time-domain waveforms. Waveglow is a generative model that learns the
distribution of the audio samples conditioned on mel-spectrograms. We trained
separate models for each speaker in the dataset. Each model was trained on the
preprocessed data at a constant learning rate of 1e-4 on 16 V100 GPUs. We use
a simple STFT based denoiser, with strength 0.001, to remove any unwanted
artifacts from the speech produced by Waveglow.

##  5 Results

In this section, we evaluate the performance of VANI on the challenge task in
terms of content quality, acoustic quality and speaker identity retention.

###  5.1 Synthesis Quality Evaluation

####  5.1.1 Character Error Rate:

We generate transcripts using the Huggingface ASR models provided to us by the
competition organizers. We calculate CER between the transcripts generated
from the synthesized speech and the ground truth transcripts from the dataset.
Lower the error rate, the better is the model in terms of content quality.

####  5.1.2 Speaker Embedding Cosine Similarity:

We use Titanet[titanet] to get speaker embeddings and compare the similarity
of synthesized sample by a model against ground truth samples for the same
speaker(ground truth mel spectograms passed through the vocoder to remove
vocoder differences). We call this metric as Cosine Sim. Higher scores mean
better speaker identity retention because the synthesized sample is closer to
original GT sample.

###  5.2 Analysis

Table 3 compares the Track1 model (RADMMM) against Track2 (VANI with non
parallel dataset) and Track3 (VANI with limited parallel dataset) on
resynthesis of speakers on 10 prompts in their own language. We observe that
even with limited dataset, the large parameter RADMMM model significantly
outperforms the small parameter models both in terms of speaker identity
retention (higher cosine similarity across all speakers) as well as content
quality (lower CER across all speakers). We notice that Track2 with larger
dataset retains identity and content quality better than Track2 with limited
data (under 5 hours per speaker). However, all tracks do reasonably well on
maintaining identity. There’s a drop in content quality as we go to lower
parameter models (Track2 and Track3). More analysis on cross-lingual
evaluation and effects of augmentation will be provided in final paper. Table
4 compares the Track1 model (RADMMM) against Track2 (VANI with non parallel
dataset) and Track3 (VANI with limited parallel dataset) on resynthesis of
speakers on 50 prompts outside in the 2 languages other than their own
language. We observe that on transfer, we’re able to achieve decent CER
comparable to resynthesis case, meaning our model preserves content on
transfering language of the speaker.

##  6 API Details

Per the submission guideline and example, we created an API for serving audio
given text and target speaker. This API is available on IP 52.14.182.205 and
port 12400. An example on how to make a request to the server is available
here.333 https://gist.github.com/aroraakshit/1d9b4c852fb2ec79e5dca770267294f9

##  7 Acknowledgements

The authors would like to thank Roman Korostik for discussions on spectogram
enhancement, Evelina Bakhturina for discussions on dataset cleanup and Sirisha
Rella for Telugu evaluation.