# Correcting Projection Effects in CMEs using GCS-based Large Statistics of
Multi-viewpoint Observations

###### Abstract

This study addresses the limitations of single-viewpoint observations of
Coronal Mass Ejections (CMEs) by presenting results from a 3D catalog of 360
CMEs during solar cycle 24, fitted using the GCS model. The dataset combines
326 previously analyzed CMEs and 34 newly examined events, categorized by
their source regions into active region (AR) eruptions, active prominence (AP)
eruptions, and prominence eruptions (PE). Estimates of errors are made using a
bootstrapping approach. The findings highlight that the average 3D speed of
CMEs is $\sim$1.3 times greater than the 2D speed. PE CMEs tend to be slow,
with an average speed of 432 km $s^{-1}$. AR and AP speeds are higher, at 723
km $s^{-1}$ and 813 km $s^{-1}$, respectively, with the latter having fewer
slow CMEs. The distinctive behavior of AP CMEs is attributed to factors like
overlying magnetic field distribution or geometric complexities leading to
less accurate GCS fits. A linear fit of projected speed to width gives a
gradient of $\sim$2 km $s^{-1}\deg^{-1}$, which increases to 5 km
$s^{-1}\deg^{-1}$ when the GCS-fitted ‘true’ parameters are used. Notably, AR
CMEs exhibit a high gradient of 7 km $s^{-1}\deg^{-1}$, while AP CMEs show a
gradient of 4 km $s^{-1}\deg^{-1}$. PE CMEs, however, lack a significant
speed-width relationship. We show that fitting multi-viewpoint CME images to a
geometrical model such as GCS is important to study the statistical properties
of CMEs, and can lead to a deeper insight into CME behavior that is essential
for improving future space weather forecasting.

Space Weather

Department of Physics, Aberystwyth University, Aberystwyth, Wales, UK
Southwest Research Institute, 1050 Walnut Street Suite 300, Boulder CO, USA
Aryabhatta Research Institute of Observational Sciences, Nainital, India
Austrian Space Weather Office, GeoSphere Austria, Graz, Austria Indian
Institute of Astrophysics, 2nd Block Koramangala, Bangalore, India Center of
Excellence in Space Sciences, IISER, Kolkata, India Heliophysics Science
Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Department of Physics and Astronomy, George Mason University, Fairfax, VA
22030, USA

Harshita<EMAIL_ADDRESS>
Presents a large multi-viewpoint dataset containing 3D (true) speeds, 3D
(true) widths, locations, and source regions of 360 CMEs observed during the
solar cycle 24

Statistical analysis of true speed and width of CMEs with and without source
region separation is compared to the projected values

Corrected speed and width to be used as initial conditions in space weather
forecasting models for better arrival time predictions at Earth

## Plain Language Summary

Space weather refers to the changing conditions in space, largely influenced
by massive eruptions from the Sun. We call these eruptions ’Coronal mass
ejections’ or ’CMEs’. Earth-directed CMEs produce geomagnetic storms that
affect our satellites, communication systems, and power grids, causing
disruptions in our technology and infrastructure. Hence, how fast CMEs move
and how wide they are in 3D space is crucial to predicting their arrival on
Earth. To trace these eruptions in 3D, we use a geometrical model on a large
set of CMEs during low and high solar activity from different angles, like
figuring out the path of a flying bird from different angles. Derived 3D
characteristics such as speed and width (size) compared to the values obtained
from one angle (like watching the bird from only one spot) gives us a better
idea of how fast they are going. Some eruptions were slow, while others were
faster. The bigger the eruption, the faster it tends to be. Our results
highlight that the 3D aspect of CMEs is crucial for issuing timely warnings
and taking necessary precautions to safeguard our technology and prevent
potential damages caused by space weather events.

##  1 Introduction

###  1.1 Background and Previous Works

Coronal mass ejections (CMEs) (Hundhausen, 1997) are large-scale structures of
plasma and magnetic fields erupting from the Sun at speeds of up to several
thousand kilometers per second (DF. Webb Howard, 2012). CMEs are significant
drivers of space weather events on Earth, including geomagnetic storms,
auroras, and solar energetic particles (SEPs) (Luhman, 1997; Baker, 1998;
Gopalswamy, 2009). Auroras are a notable outcome of space weather phenomena,
which manifest as luminous displays in the Earth’s atmosphere. However, it is
important to note that solar energetic particles (SEPs) and geomagnetic storms
can lead to substantial disturbances in both terrestrial and space-based
equipments (St. Cyr ., 2000; D. Webb ., 2000; Wang ., 2002; Zhang ., 2003; Kim
., 2005; Michalek ., 2007), therefore, a crucial component of forecasting CME
events at Earth is to understand their kinematics (Taktakishvili ., 2009;
Thernisien ., 2006; Hutton Morgan, 2017) from both a solar (Temmer, 2021) and
a terrestrial perspective (Pulkkinen, 2007).

The first CME event was recorded on 14 December 1971 by a coronagraph aboard
NASA’s Seventh Orbiting Solar Observatory (OSO-7) (Tousey ., 1973), and led to
the realization of the importance of studying CME properties, including their
kinematics, based on coronagraph imagery (R. MacQueen ., 1974; Sheeley Jr .,
1980; RM. MacQueen ., 1980). The Solar and Heliospheric Observatory (SOHO)
(Domingo ., 1995) was launched in 1995, and had a suite of three coronagraphs,
called the Large Angle and Spectrometric Coronagraph Experiment (LASCO C1, C2,
and C3) (Brueckner ., 1995), providing a field of view (FOV) from 1.1 to 30
$R_{\odot}$. LASCO has provided us with more than two decades of data and has
significantly bolstered our scientific understanding of CMEs. Since 2006, we
have had a stereoscopic picture of CMEs thanks to the advent of the Solar
Terrestrial Relations Observatory (STEREO) (Kaiser ., 2008) and its two
coronagraphs (COR1: FOV of 1.1-4 $R_{\odot}$ and COR2: FOV of 2-15
$R_{\odot}$)(RA. Howard ., 2008).

Coronagraphs give single-vantage point 2-dimensional images of the Thomson-
scattered photospheric light from coronal electrons, integrated along a line
of sight through the optically thin corona onto an image plane (Burkepile .,
2004). Within coronagraph images, CMEs appear as structures that travel
outward through the coronagraph FOV (Gosling ., 1974; Hundhausen, 1993;
Manchester ., 2017). They have large variations in size, brightness and
shapes. Among different CME morphologies, one such morphology is a three-part
structure (R. Howard ., 1985) comprised of a bright leading loop, a dark low-
density cavity, and a high-density core (Hundhausen, 1993). This appearance is
interpreted as a large magnetic flux rope structure in the corona (Vourlidas,
2014; Hutton Morgan, 2015).

Various automatic and manual techniques have been created to detect and track
CMEs in a series of coronagraph images (Gosling ., 1974; Harrison, 1994;
Balmaceda ., 2018; Munro ., 1979; R. MacQueen Fisher, 1983; R. Howard ., 1985;
Sheeley Jr ., 1986; Hundhausen, 1993; Burkepile St Cyr, 1993; Hundhausen .,
1994; St. Cyr ., 1999, 2000; Yashiro ., 2004; JP. Byrne ., 2012), and their
fundamental characteristics, such as location, speed, angular width, and mass,
have been recorded and stored in the catalogs. The most widely used SOHO/LASCO
and STEREO/SECCHI CME catalogs are the Coordinated Data Analysis Workshop
(CDAW) LASCO CME catalog (1996-present) (Yashiro ., 2004), the Computer Aided
CME Tracking (CACTus) LASCO (1997-present) (Robbrecht Berghmans, 2004), and
STEREO (2007 - 2014 for SECCHI-B and 2007-present for SECCHI-A) CME catalogs,
the Solar Eruptive Event Detection System (SEEDS), Automatic Recognition of
Transient Events and Marseille Inventory from Synoptic maps (ARTEMIS)
(Boursier ., 2009), the CORIMP LASCO CME catalog (JP. Byrne ., 2012), and
CIISCO (Patel ., 2021). These catalogs only include projected 2D properties.
This is a major drawback to investigating the kinematic evolution of CMEs. For
example, the projected speed and mass are, in general, a lower approximation
of the true speed and mass. For many scientific and operational purposes, such
2D studies are inadequate (Vršnak ., 2004; Zhang ., 2004; Yashiro ., 2003;
Gopalswamy ., 2003; Gopalswamy, 2006; Yashiro ., 2008; Gopalswamy ., 2009).
Various authors have aimed to overcome these effects by looking at CME
properties estimated for events that occur close to the plane of the sky
(i.e., over the solar limb), where projection effects are at their minimum
(Michałek ., 2003; Dal Lago ., 2003; Michalek ., 2009; Vasanth Umapathy,
2013).

CME observations from multiple viewpoints have the potential to give a more
accurate and comprehensive understanding of CME kinematics. In the pre-STEREO
era, CME reconstruction techniques like forward modeling, polarimetric,
spectroscopic, and direct inversion have been extensively used to reconstruct
3D CME morphology. Crifo . (1983) initiated the direct reconstruction of CMEs,
using polarization analysis to deduce that CMEs resembled 3D bubbles more than
planar loops. Subsequent studies, such as Jackson Froehling (1995), using
solar wind background models, confirmed this shape further in the heliosphere.
This finding aligns with the observed 3-part CME structure, characterized by a
bright front, a darker cavity, and a bright core, as described by Illing
Hundhausen (1985). By 1996, with the start of the SOHO mission, the earlier
concept of planar, loop-like CMEs was largely replaced by understanding CMEs
as 3D structures, particularly for events with this 3-part configuration.
Frazin . (2009) has determined CME density structures with only three
viewpoints using image processing methods. Thernisien . (2011) reviews the
pre-STEREO efforts in 3D CME reconstruction and compares them with the post-
STEREO results. In summary, the multi-viewpoint vantage provided by both SOHO
and STEREO has prompted various techniques to investigate the 3D geometrical
and kinematical information of CMEs (J. Chen ., 1997; Wood ., 1997; Michałek
., 2003; Zhang ., 2003; Xie ., 2004; Schwenn ., 2005; Gopalswamy ., 2009;
Mierla ., 2008; Moran ., 2010; Feng ., 2013; Aschwanden, 2009; Wood ., 2009;
Xie ., 2009). More recently, flux rope models have been utilized effectively
and suggested by many authors (A. Chen ., 2006; Vourlidas ., 2000; Cremades
Bothmer, 2004) to generate CME morphology (J. Chen ., 1997) and to investigate
their properties (Vourlidas ., 2000; Krall, 2006). An effective tool for the
3D reconstruction of CMEs, the Graduated Cylindrical Shell (GCS) model,
developed by Thernisien . (2006, 2009) was originally implemented to
simultaneously fit COR1 and COR2 images (Thernisien, 2011) and later to
LASCO-C2/C3 images (Shen ., 2013, 2014; Colaninno ., 2013), as well as to the
ground-based K-Cor (Majumdar ., 2022) images. The model consists of a main
structure with a tubular cross-section with a radius increasing with height
and two cones attached to its ends, separated by twice the half angle
$\alpha$. By fitting an observed CME image to the GCS model, we are assuming
that the CME has an axisymmetrical flux-tube geometry that is expanding with
distance from the Sun. This is a reasonable assumption that gives CME
properties that are closer to the true CME properties compared to a simple 2D
analysis. Recently, catalogs like the Coronal Mass Ejection Kinematic Database
(KINCAT) and Coronal Mass Ejection Database (CMEDB) are based on 3D CME
parameters estimated from using the GCS model.

It is known that CME kinematics in the corona differ depending on their source
location and eruption type (Hundhausen, 1993). CMEs associated with different
source region types have been extensively studied and are broadly classified
into active regions (ARs), prominences (PEs), and active prominences (APs) (R.
Howard ., 1986; Munro ., 1979; Subramanian Dere, 2001; Moon ., 2002; Majumdar
., 2020). AR-CMEs are mostly impulsive and fast with a stronger magnetic
field, whereas PE-CMEs are gradual and slow with a weaker magnetic field (R.
MacQueen Fisher, 1983; Sheeley Jr ., 1999). Historically, prominences have
been classified based on their morphology and activity e.g., the active,
eruptive, sunspot, tornado, and quiescent prominences of Pettit (1925); McMath
Pettit (1938); Pettit (1943). More recently, prominences have commonly been
placed into two categories: active region and quiescent (Gilbert ., 2000). AP
CMEs are associated with prominences with either or both of their footpoints
within an active region. Pettit (1925) describes active prominences as when
material flows into nearby active regions, altering the magnetic topology of
the constraining magnetic environment. The one exception to this
categorization may be some stealth CMEs which are thought to form higher in
the solar atmosphere (e.g. Alzate Morgan, 2017). The effect of various source
locations on the width distribution of CMEs was recently reported by Pant .
(2021), who found that the widths of CMEs followed power law distributions,
with some interesting differences in power law exponent according to the CME
source region type. To determine whether or not the source regions have a
measurable effect on CMEs, such big statistical studies are needed to examine
the speed and width of CMEs in the outer corona based on their source region
type. Unfortunately, Pant . (2021) was necessarily restricted to 2D projected
widths only, although some mitigation was provided through the selection of
limb events. Larger statistics of CMEs fitted to a 3D geometry are rare. Jang
. (2016) used the Stereoscopic CME analysis tool (StereoCAT) to calculate 3D
parameters, compared the 2D and 3D properties of 306 Halo CMEs, and found that
2D speeds underestimate 3D speeds by 20 %. They give estimates of average 3D
speed and average 3D width and compare 3D speed-width relationship to their
corresponding 2D relation. Previous research has made valuable contributions
to our understanding of CMEs and their kinematics. However, studies utilizing
the GCS technique are limited to a smaller number of cases and do not
investigate the relationships between CME speed, width, and different types of
CME source regions from a comprehensive statistical perspective. This study
addresses these gaps in the literature.

This work analyses 360 CMEs fitted using the GCS technique. The sample is
separated into three groups according to their source regions to find
statistical differences between the groups, and 3D (‘true’) and 2D projected
CME parameters are compared. The datasets and methodology are described in
sections 2 and 3. Section 4 presents the primary findings with discussion,
while Section 5 offers summary and conclusions.

##  2 Data Anaylsis

###  2.1 Data Selection and Preparation

First, we present a description of the chosen datasets and a justification for
the decisions made throughout this research. We then go on to detail the
subsequent preprocessing methods for the data. Note that in this section and
elsewhere, that the 3D fitted CME parameters are referred to as ‘true’,
although this is, of course, subject to the assumption that the GCS
geometrical model is the correct choice of geometry for all CMEs.

Our comprehensive database of 360 CMEs includes the original CME data (cdaw
date, first C2 appearance time, position angle, projected speed, and projected
width from automated and manual methods) and the corrected speed, width, and
source region type from 2007-2021, covering the rising and declining phase of
solar cycle 24. There is a data gap from October 2014 to November 2015 when
STEREO A went behind the Sun. We select only those CMEs with a clear three-
part morphology, which appear bright and well-structured in the SECCHI/COR2
field of view. In line with this, we have combed through archival papers and
catalogs to compile a list of CME features that meet the aforementioned
criteria. Given the manual and subjective nature of fitting the GCS model to
CMEs, we developed a selection criterion for CME events to reduce subjective
biases. Our approach focused on including events already documented in
existing catalogs, such as KINCAT and CMEDB, and those discussed in research
papers where the GCS model fitting was systematically applied to multiple CME
events. In contrast, we deliberately omitted isolated case studies like the
September 2017 event, which is extensively covered in various studies (e.g.,
(Gopalswamy ., 2018; Shen ., 2018; Werner ., 2019; Wu ., 2019; Scolini .,
2019, 2020)) to maintain consistency and minimize individual biases in our
analysis. This was complemented by adding these events to our own dataset. As
listed in Table 1, information on most of the 360 CMEs in this study is gained
from the KINCAT and CMEDB. Other CMEs are extracted from published papers, as
listed in Table 1, and 29 from the Data Research and More in Space Physics
(DREAMS) catalog (Shen ., 2013, 2014). A further 34 other CMEs are fitted by
ourselves, as described in section 3.1. These 34 CMEs were not available in
the other existing catalogs. There are no duplicate events in the set of 360
CMEs in this study. The kinematic properties of the CMEs, such as speed and
angular width, were directly available and recorded for our study.

No. | No. of CMEs | 3D Catalogs/past studies | 2D Catalogs used for comparison
---|---|---|---
1 | 119 | CME Kinematic Database KINCAT | Automated catalogs [CACTus (No. of events = 342)
2 | 79 | CME Database | and SEEDs (No. of events = 18)
3 | 50 | Majumdar . (2020) | from STEREO-A viewpoint ]
4 | 07 | Cremades . (2020) |
5 | 29 | DREAMS | and
6 | 23 | Pal . (2018) |
7 | 19 | Lee . (2015) | Manual Catalog [CDAW (No. of events = 355)
8 | 34 | This study | from LASCO viewpoint]

Table 1: Collection of CMEs and associated catalogs, containing 34 CMEs fitted
during this study and 360 CMEs studied in total.

The definition of parameters relating to CME size (or angular width) differs
between the various studies and catalogs, however, we were able to use the
parameters such as half-angle and aspect ratio to determine a consistent
angular width. The GCS fitting procedure has been conducted on 360 events
using coronagraph images from two viewpoints, namely STEREO-A and STEREO-B for
events from 2007 until 2014 October, and STEREO-A and LASCO for events
occurring after 2015. Our selection criteria for 2D catalogs aimed to ensure
that the catalogs contained detections in one of the coronagraph images:
LASCO, STEREO-A, STEREO-B, or all three. Automated catalog CACTus detects CMEs
in STEREO and LASCO whereas manual catalog like CDAW only detects CMEs in
LASCO. We made a list of STEREO/SECCHI-COR2 projected parameters from the
widely used automatic catalogs CACTus and SEEDS and LASCO projected parameters
from CDAW while keeping in mind that any catalog, whether automatic or manual,
would have computational and human biases, with detections affected by
projection effects (Yashiro ., 2008) . Hence, by using pre-existing 2D CME
databases, we conducted a statistical analysis to compare the actual kinematic
qualities with the expected kinematic features.

CACTus was the reference catalog for projected parameters for 342 events,
whereas 18 events not cataloged in CACTus were taken from SEEDS. However, both
CACTus (Robbrecht ., 2009) and SEEDS (Olmedo ., 2009) are automated catalogs;
they detect and track the front of CMEs in running difference images
differently to provide an estimation of the CME projected parameters. Hess
Colaninno (2017) compares similarities and differences between SEEDS and
CACTus and shows a strong correlation between these detection techniques and
datasets when comparing them across LASCO and SECCHI. When we compare
estimated speeds calculated automatically using CACTus or SEEDs to those
derived by visual observation, we find substantial differences (Braga .,
2013). Sometimes, CMEs can drive shocks in the solar wind and can have
significant implications when cataloging and measuring the properties of CMEs
(Kahler Gopalswamy, 2009), especially the angular width. In instances where a
shock front is closely aligned with a CME, the effective width observed may
indeed be an amalgamation of both features, and the brightness enhancement
could be seen extending beyond the actual boundary of the CME ejecta.
Automated algorithms like CACTus identify CMEs by detecting transient changes
in brightness in coronagraph images (Figure 1 shows two CMEs fitted with
CACTus).

Figure 1: (a) CME of 2016/04/04 at 08:54 UT fiited by CACTus in COR2A (b) CME
of 2016/10/14 at 20:24 UT fitted by CACTus in COR2A.

Consequently, CACTus may overestimate the width of the CME by including the
shock in its measurement. On the other hand, manual fitting methods like the
GCS model focus on capturing the three-dimensional structure of the CME by
focusing on the core of the CME with a flux rope structure, potentially
neglecting the shock structure. As a result, the GCS model’s width may
underestimate the event’s total spatial extent as observed in a coronagraph.
Some bias will always be involved regardless of the fitting methods, such as
subjectivity from human inspections or misjudgment based on image processing
thresholds in automated methods. Hence, both automated and manual methods can
be affected by the presence of shocks associated with CMEs, leading to
potential inaccuracies in the determined widths. Hence, in this context, using
either of the projected sets of parameters is valid as both methods yielded
similar correlations for speed-width distributions.

###  2.2 Source region determination

CMEs were divided into three categories based on their source region type:
active regions, prominences, and active prominences. Data from the Solar
Dynamics Observatory’s Atmospheric Imaging Assembly (AIA; Lemen . (2012)), the
Extreme Ultraviolet Imaging Telescope (EIT; Delaboudiniere . (1995)) on board
SOHO and SECCHI EUVI were used to identify the source locations of CMEs
emerging from the Sun’s surface. JHelioviewer https://www.jhelioviewer.org/
(Muller ., 2009; Müller ., 2017), a visualization software for solar image
data was used to access the data. To identify the source region (SR) for
frontside CMEs in the low corona, EIT observations in 195 Å and 304 Å from
2007 to 2009, and AIA observations in the 171Å 193 Å and 304Å channels
post-2009 were examined for pre- and post-eruptive signatures of CMEs, such as
the outward motion of coronal material in the form of loops (Figure 2 shows
loops after CME eruption from AR12673) or eruptive prominences (D. Webb
Hundhausen, 1987) and post-eruptive loops/arcades (Sterling ., 2000; Cremades
Bothmer, 2004) whereas SECCHI EUVI 195 Å and 304 Å channels were used to
identify source region signatures for the backside CMEs with respect to the
Earth.

Figure 2: A source region AR12673 that erupted 2017/09/04 CME is shown in AIA
171A with post eruptive loops.

For a comprehensive explanation of the identification process for source
regions, see Majumdar . (2020) and (Majumdar ., 2023). As shown in Figure 3,
170 (47.2%) of the cataloged events fall into the AR category, 90 (25%) fall
into the AP category, and 100 (27.8%) fall into the PE category.

Figure 3: CME’s source region classification into types active region, active
prominence, and prominence eruption.

##  3 Methodology

###  3.1 3D Reconstruction and Estimation of Geometric Parameters

The 34 CMEs we fitted using the GCS model were chosen to improve the
statistical sample size. The data used for this sample are taken from the
STEREO COR-2A coronagraphs, the STEREO Extreme UltraViolet Imager (EUVI), and
LASCO/SOHO C2/C3. The level 0.5 data of EUVI and COR-2 were reduced to level
1.0 using the secchi_prep.pro routine in the Solarsoft library of the
Interactive Data Language (IDL), and for LASCO, we used level 1 data
(corrected for instrumental effects and solar north and calibrated to physical
units of brightness) (Majumdar ., 2020). Further, they were processed with the
Simple Radial Gradient Filter (SiRGraF: Patel ., 2022) utilizing the full
daily images to create the necessary backgrounds. The processed SiRGraF images
were then used to fit the CMEs to the GCS geometrical model. To capture
evolution in the outer corona, the model is fitted simultaneously to the COR-2
(FOV of 2.5–15 $R_{\odot}$) and C2/C3 (FOV of 2.2–30 $R_{\odot}$) images. The
GCS fitting for two limb CMEs at 2016/04/04 06:24 UT and 2013/03/05 07:54 UT
and a halo CME at 2017/09/04 20:24 UT is shown in figure 4. As a result,
fitting parameters (see Table 2) such as height, aspect ratio, half-angle,
tilt-angle, latitude, and longitude were recorded. Since three–vantage point
observations are not available since STEREO-B stopped functioning in 2014,
some model parameters (Latitude, Longitude, tilt-angle) were fixed according
to their source region location, while the height, half-angle, and aspect
ratio were fitted to the time series of images. The fitting procedure was
carried out according to the descriptions of Thernisien . (2006, 2009) and
Majumdar . (2020). The fitted geometrical parameters are listed in Table 2
with CME speed and width derived from GCS and projected parameters taken from
automated and manual catalogs for comparison.

Figure 4: Fittings of the GCS flux rope to the COR-2A (left) and C2 (right)
images for three CMEs. Panels (a) and (b): CME of 2016/04/04 at 06:24 UT.
Panels (c) and (d): Halo CME of 2017/09/04 at 20:24 UT. Panels (e) and (f):
CME of 2013/04/05 at 07:47UT

###  3.2 Estimation of 3D Kinematic properties

Following the GCS geometrical fitting, the average speed of the 34 CMEs is
estimated using height-time information, and as shown in 5b, linear regression
is used to fit the data. To maintain consistency in the speed estimates for
all 360 CMEs, a simple linear relationship of distance to time is maintained.
Since GCS is a manual technique for fitting CMEs, there is a possibility of
human bias being included in the parameters that are modeled. Using a range of
possible values for each fitting parameter helps to confine better the
estimations like the speed and width of the CME. This could be done by
performing the fitting procedure multiple times to lower the degree of
uncertainty and increase confidence in the fitting parameters or by employing
a resampling method instead to carry out the same tasks. Keeping this in mind,
we used a resampling technique called bootstrapping. First introduced by Efron
Tibshirani (1986) and more recently described in Efron Tibshirani (1994);
Chernick (1988) and J. Byrne . (2013), the method works by resampling the
original dataset thousands of times with randomly-ordered residuals to
generate simulated datasets. In the case of CMEs, bootstrapping techniques can
be beneficial for estimating the uncertainty in speed. Here, we have utilized
the IDL BootXYFIT procedure on height and time measurements, which aims to
perform a linear fit to the data with errors in both $X$ (time) and $Y$
(height) where measurement errors are unavailable. A histogram of the speed
sample estimated by BOOT_XYFIT is shown in figure 5a, where the 95% confidence
interval is shown as dotted red lines. This range defines the speed error,
shown as the grey shaded region in figure 5b. Since we do not know the exact
kinematic form a CME should take nor the true uncertainty due to possible
unknown sources of error, a bootstrapping technique allows an appropriate
confidence interval to be assigned to the kinematic parameters. Table 2 lists
the GCS fitting parameters along with GCS speed and width for all 34 CMEs.

Figure 5: (a) Distribution of speed estimates arising from a bootstrapping
resampling method (see text), with 95% confidence intervals (CI) between the
dotted red lines. (b) An example of a height-time plot for a CME occurred at
01:25 UT on 2017-07-23. The red line shows the linear fit, and the shaded area
indicates the 95% uncertainty arising from the bootstrap distribution.

##  4 Results and Discussion

Table 2 summarises the parameters for the 34 CMEs fitted during this study.
Listed in columns 1 through 6 is the total number of CME occurrences, the
dates and times when CMEs were first detected in LASCO FOV, their SR type, and
the latitudes and longitudes of the SR locations. The other columns list the
GCS parameters. True width ($W_{GCS}$) in column 10 is calculated using the
formula (2$\alpha$+2$\delta$) where $\delta$ = $\arcsin$($\kappa$) and
$\alpha$ and $\kappa$ are the GCS half-angle and aspect-ratio shown in columns
8 and 9. Columns 10 and 11 show true width and speed estimated from GCS with
uncertainty calculated using Bootstrap. Projected width and projected speed
from automated and manual methods are listed in columns 10 to 15.

No. | Date | Time [UT] | SR | Lat($\theta)$ | Long($\phi)$ | Tilt($\gamma$) | aspect-ratio($\kappa$) | half-angle($\alpha$) |  $W_{GCS}$(∘) |  $V_{GCS}$(km-1s) |  $V_{CACTus}$(km-1s) |  $W_{CACTus}$(∘) |  $V_{CDAW}$(km-1s) |  $W_{CDAW}$(∘)
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 2013-04-05 | 06:36 | PE | 2 | 243 | 65 | 0.24 | 30 | 88 | 575(15) | 543 | 137 | 588 | 228
2 | 2013-04-08 | 08:36 | PE | -28 | 120 | -45 | 0.23 | 10 | 52 | 555(18) | 413 | 52 | 529 | 85
3 | 2013-04-08 | 13:25 | AR | -17 | 120 | 50 | 0.20 | 10 | 42 | 395(12) | 427 | 55 | 393 | 89
4 | 2016-01-01 | 23:24 | AP | -26 | 320 | 50 | 0.25 | 20 | 69 | 1580(25) | 1562 | 328 | 1730 | 360
5 | 2016-01-04 | 23:36 | PE | 54 | 279 | -12 | 0.25 | 10 | 78 | 236(21) | 431 | 62 | 250 | 164
6 | 2016-01-06 | 14:00 | PE | -19 | 284 | 45 | 0.24 | 12 | 52 | 370(13) | 353 | 63 | 969 | 360
7 | 2016-01-29 | 21:15 | AR | -22 | 110 | -27 | 0.32 | 18 | 73 | 925(53) | 657 | 76 | 901 | 118
8 | 2016-02-20 | 14:24 | AP | 6 | 139 | 90 | 0.36 | 26 | 94 | 660(20) | 446 | 170 | 491 | 360
9 | 2016-04-04 | 03:24 | PE | 10 | 232 | 60 | 0.22 | 12 | 50 | 518(47) | 446 | 74 | 444 | 129
10 | 2016-05-10 | 23:36 | AR | -36 | 268 | 29 | 0.23 | 10 | 45 | 368(30) | 347 | 76 | 327 | 36
11 | 2016-05-15 | 15:12 | AR | 15 | 60 | 54 | 0.56 | 14 | 96 | 962(45) | 892 | 146 | 1118 | 176
12 | 2016-06-25 | 02:48 | AP | 20 | 285 | 67 | 0.32 | 14 | 65 | 489(17) | 378 | 96 | 540 | 128
13 | 2016-09-06 | 08:36 | AP | -20 | 114 | 33 | 0.25 | 33 | 95 | 688(44) | 694 | 70 | 650 | 101
14 | 2016-10-14 | 09:48 | AP | -20 | 270 | 37 | 0.37 | 12 | 67 | 511(20) | 510 | 100 | 375 | 75
15 | 2016-10-14 | 16:48 | AR | -15 | 273 | 42 | 0.29 | 12 | 58 | 646(52) | 510 | 100 | 540 | 104
16 | 2016-12-12 | 06:48 | PE | 28 | 151 | 25 | 0.22 | 13 | 51 | 622(78) | 595 | 52 | 424 | 152
17 | 2016-12-21 | 20:00 | AR | 1.6 | 302 | -69 | 0.28 | 12 | 57 | 202(12) | 211 | 58 | 207 | 93
18 | 2017-03-13 | 20:12 | AP | 15 | 140 | -61 | 0.21 | 22 | 69 | 465(35) | 341 | 106 | 668 | 221
19 | 2017-04-18 | 19:48 | AR | 18 | 285 | 70 | 0.25 | 30 | 88 | 906(46) | 892 | 154 | 926 | 360
20 | 2017-07-14 | 01:25 | AR | -10.6 | 35.8 | -31 | 0.68 | 41 | 167 | 1460(25) | 892 | 202 | 1200 | 360
21 | 2017-07-17 | 16:36 | AR | -6 | 71 | 83 | 0.19 | 25 | 72 | 512(37) | 337 | 90 | 376 | 122
22 | 2017-07-20 | 18:12 | AR | 1 | 125 | 58 | 0.30 | 22 | 79 | 686(63) | 500 | 82 | 590 | 95
23 | 2017-07-23 | 01:25 | AR | -5 | 146 | -52 | 0.70 | 35 | 66 | 1002(52 | 756 | 190 | 654 | 144)
24 | 2017-07-23 | 04:48 | AR | -5 | 146 | 63 | 0.19 | 22 | 160 | 2039(569) | 1388 | 352 | 1848 | 360
25 | 2017-09-04 | 20:36 | AR | -10 | 12 | -24 | 0.48 | 18 | 92 | 997(99) | 462 | 274 | 1418 | 360
26 | 2017-09-06 | 12:24 | AR | -8 | 36 | 26 | 0.65 | 19 | 119 | 1591(114) | 735 | 352 | 1571 | 360
27 | 2017-09-09 | 16:24 | AR | -8 | 105 | 45 | 0.24 | 18 | 64 | 609(144) | 403 | 72 | 473 | 95
28 | 2017-09-10 | 16:00 | AR | -11 | 91 | 80 | 0.54 | 35 | 135 | 2320(150) | 1785 | 352 | 3163 | 360
29 | 2017-09-17 | 12:00 | AP | -6 | 189 | -39 | 0.55 | 22 | 110 | 1910(250) | 1250 | 166 | 1385 | 360
30 | 2017-10-18 | 05:48 | AP | -13 | 260 | -52 | 0.61 | 17 | 109 | 1530(163) | 600 | 126 | 1576 | 360
31 | 2019-04-30 | 14:48 | AP | -5 | 192 | 17 | 0.43 | 37 | 125 | 1040(85) | 781 | 94 | 665 | 360
32 | 2020-12-07 | 16:24 | AP | -22 | 7 | 58 | 0.41 | 24 | 95 | 1560(45) | 584 | 359 | 1407 | 360
33 | 2021-10-09 | 07:12 | AR | 19 | 5 | 45 | 0.32 | 22 | 81 | 1589(33) | 781 | 152 | 712 | 360
34 | 2021-10-28 | 15:48 | AR | -27 | 1 | 8 | 0.60 | 40 | 153 | 1369(23) | 924 | 121 | 1519 | 360

Table 2: The GCS Model Parameters of the 34 CMEs that were fitted during this
work, together with their true width (column 9), average true speed (column
10), and speed calculated via bootstrap with errors (column 11).

A summary of average CME properties with and without SR segregation, before
and after correcting projection effects, is provided in Table 3. This table
presents a comprehensive overview of the observed properties of CMEs
classified by different source regions. It includes aggregated statistical
parameters for all CMEs under study (360 events) and subsets categorized by
source regions: ’170 AR’ (Active Region), ’90 AP’ (Average Prominence), and
’100 PE’ (Prominence Eruption) CMEs. For each category, the table lists the
mean and median values of the 3D Angular Width, 3D Speed, 2D Angular Width,
and 2D Speed. Additionally, the slope and associated error of the speed-width
relation, along with the 95% confidence intervals for both the 3D and 2D
slopes, are provided. These intervals offer insights into the reliability and
variability of the slope estimates. The data indicate notable differences
across categories, reflecting the inherent diversity in CME dynamics. TA.
Howard Tappin (2008) shows a similar table with the mean in average apparent
and corrected speeds.

CME Property | ALL (360) CMEs | 170 ”AR” CMEs | 90 ”AP” CMEs | 100 ”PE” CMEs
---|---|---|---|---
GCS Angular Width (mean, median in ∘) | 77, 72 | 79, 74 | 85, 80 | 66, 62
GCS Speed (mean, median in km s-1) | 665, 561 | 723, 642 | 813, 690 | 432, 388
CACTus Angular Width (mean, median in ∘) | 112, 93 | 122, 100 | 133, 117 | 75, 69
CACTus Speed (mean, median in km s-1) | 499, 446 | 534, 491 | 592, 531 | 358, 337
CDAW Angular Width(mean, median in ∘) | 189, 153 | 202, 169 | 234, 221 | 123, 109
CDAW Speed(mean, median in km s-1) | 613, 527 | 656, 553 | 782, 650 | 390, 347
slope, error in slope and cc of GCS speed-width | 5.81, 0.63, 0.44 | 7.80, 0.97, 0.52 | 4.57, 1.20, 0.37 | -0.78, 0.71, -0.10
95% confidence interval for GCS slope | (4.57, 7.05) | (5.88, 9.72) | (2.18, 6.96) | (-2.20, 0.63)
slope, error in slope and cc of CACTus speed-width | 2.19, 0.15, 0.61 | 2.07, 0.20, 0.62 | 2.07, 0.20, 0.50 | 1.47, 0.37, 0.36
95% confidence interval in slope | (1.89, 2.49) | (1.67, 2.47) | (1.23, 2.63) | (0.73, 2.23)
slope, error in slope and cc of CDAW speed-width | 2.14, 0.14, 0.60 | 2.27, 0.23, 0.59 | 1.83, 0.34, 0.49 | 0.97, 0.19, 0.45
95% confidence interval in slope | (1.85, 2.42) | (1.80, 2.73) | (1.15, 2.51) | (0.58,1.37)

Table 3: Shows the statistical parameters, including mean and median values
for angular width and speed, slope errors, and 95% confidence intervals for
the slope estimates, segregated into overall, AR-CMEs, AP-CMEs, and PE-CMEs
groups before and after correction.

###  4.1 Comparing Speed and Width Distributions before and after correction

Figure 6 shows the distributions of apparent speeds (2D) of CMEs (left panel)
and the true speeds (3D) of CMEs using GCS (right panel). The distributions
are not symmetrical, with the maximum number of CMEs with speeds peaking
around 300-500 km s-1 in both cases as expected. The range of true radial
speeds (figure b) is much higher (100-2900 km s-1) than the projected speeds
(figure a), ranging from 100-1900 km s-1. The figure demonstrates that after
correcting the projection effects, the high-speed tail of the distribution is
significantly boosted. In contrast, the low-speed tail is significantly
suppressed, with the number of CMEs with speeds between 100-300 km s-1 reduced
by half. The average speed of a CME is 500 km s-1 before the correction;
however, the GCS approach produces an average speed of 665 km s-1 showing that
2D speed tends to be about 30% underestimated compared to the 3D ones. The 3D
distribution has a higher median speed (561 km s-1) compared to the 2D
distribution (446 km s-1), indicating that the corrected speeds tend to be
higher overall.

Figure 6: Speed distributions of 360 CMEs, represented by vertical bars,
before correction (left panel), and after correction using the GCS approach
(right panel), together with the average speed of the CMEs. The bin size is
200 km $s^{-1}$.

There is a more significant spread of speeds in the 3D distribution, as
evidenced by a larger standard deviation (415 km s-1 vs. 255 km s-1) and a
wider interquartile range (493 km s-1 vs. 306 km s-1). This implies that the
corrected data have a broader range of values and potentially more variability
or dispersion around the median. A large number of studies [for example,
Burkepile . (2004); Vršnak . (2007); T. Howard . (2008); TA. Howard Tappin
(2008); Yeh . (2005); Xie . (2009); Shen . (2013); Jang . (2016)] have looked
at the distribution of kinematics of CMEs, with and without projection
effects. T. Howard . (2008) compared apparent and true speed histograms from
1996 - 2005 on a yearly basis and showed that the magnitude of corrected
measurements differs significantly from the projected plane-of-sky
measurements with average speeds ranging from 625-900 km $s^{-1}$ (true) and
270-435 km $s^{-1}$ (apparent) which closely matches the average speeds in our
study. Shen . (2013) showed using GCS that the true speeds of halo CMEs vary
from 274 km $s^{-1}$ to 2016 km $s^{-1}$ with an average speed of 985 km
$s^{-1}$. The most extensive study to date, conducted by Jang . (2016), used
StereoCAT to estimate 3D parameters of 306 front-side halo CMEs during the
rising phase of the solar cycle 24 and demonstrated that the 2D speed
underestimates the 3D speed by approximately 20%. Their result shows that the
average speed of halo CMEs changes from 733 km $s^{-1}$ to 896 km $s^{-1}$
after correcting for projection effects. Prior studies have drawn similar
conclusions when comparing 2D speeds with 3D speeds using methods such as
triangulation [(Pizzo Biesecker, 2004);(Mierla ., 2008);(Temmer ., 2009)],
STEREO-CAT [http://ccmc.gsfc.nasa.gov/analysis/stereo/manual.pdf], etc.
Therefore, the results presented in this study not only support prior findings
but also validate the effectiveness of various methodologies employed in
reconstructing CMEs using multi-viewpoint images.

Figure 7: Width distributions of 360 CMEs, represented by vertical bars,
before correction (left panel), and after correction using the GCS approach
(right panel), together with the average width of the CMEs. The bin size is 30
∘.

The relationship between the apparent and true angular width of a CME, in
general, is complicated (St. Cyr ., 2000; Yashiro ., 2004; T. Howard ., 2008;
DF. Webb Howard, 2012; Pant ., 2021). The apparent angular width of a CME
measured in the projected plane tends to be broader or narrower than the
actual one. This could be due to the orientation and appearance (viewed edge-
on or face-on) of CME in coronagraph FOV and the central longitude/latitude
location of CME relative to the observer. The frequency distribution of the
projected and true width is shown in Figure. 7 as histograms with bins of 30∘,
showing how the CME angular width spreads out before (left panel) and after
(right panel) the correction. It can be seen that following the correction,
the number of CME events that have wide angular spans (apparent width $>$
180∘) drops to zero, while the number of events that have narrow angular spans
shows a significant increase. The maximum frequency lies in the range 75∘ to
105∘ in both histograms, with an average true width of 77∘ and the average
projected width of 112∘. Studies that have compared 2D widths to 3D widths
using techniques like triangulation and STEREO-CAT have also reached similar
conclusions. These results not only corroborate those of previous research,
but they also demonstrate the validity and difficulties associated with using
different approaches to estimating the width of CMEs.

The projected/apparent average angular widths observed in previous studies
vary widely, for example, the average width detected by the Solwind instrument
between 1979 and 1981 was 45∘, and 24∘ between 1984 and 1985 (R. Howard .,
1985; Sheeley Jr ., 1986). The average width for the 1300 CMEs recorded by the
SMM instrument between 1984-1989 was 47∘ (Hundhausen, 1993), while the average
width for the 240 CMEs recorded by the ground-based coronagraph MK3 between
1980 and 1989 was 37∘. (St. Cyr ., 1999). Also, St. Cyr . (2000) found that
the average apparent width for 841 LASCO CMEs between January 1996 and June
1998 was 72∘.Yashiro . (2003) calculated the yearly averaged width for LASCO
CMEs from 1996 to 2001, and the results varied from 51∘ to 66∘. Yeh . (2005)
shows that the average width of a CME changes from 77∘ (apparent) to
58∘(corrected). Jang . (2016) found that the average width of partial and full
halo CMEs changes from 227∘ to 83∘ after correcting the projection effects.

Compared to the values above, we find a higher apparent average angular width
in our case which overestimates the true average width by 30%. In particular,
the distribution of CME widths is considerably narrower than that of apparent
widths. The overall shape of the distribution seen in Figure 7 (a) and (b) is
consistent with that of prior studies (R. Howard ., 1985, 1986; Hundhausen,
1993; St. Cyr ., 1999; Gopalswamy ., 2003; Yeh ., 2005; Jang ., 2016), being
somewhat skewed to the right, but displaced towards higher values. Yashiro .
(2004) found that a log-normal distribution well describes the CME speed
distribution, and the CME width distribution is also broad and skewed.
Gopalswamy (2006) studied the speed and width distributions of CMEs observed
between 1996 and 2004 and found that the speed distribution is broad and
skewed, with a long tail toward higher speeds, and that the width distribution
is also broad and skewed, with a peak at around 100 degrees. Our results
emphasize that CME parameters must be cautiously handled, particularly when
physical quantities such as CME speed and width are considered.

###  4.2 Effect of Source Region on the Speed and Width Distributions

The kinematics of CMEs are heavily influenced by the source region from which
they erupt (Burlaga ., 1981; D. Webb ., 2000; Subramanian Dere, 2001; Mishra
., 2005; Zhao ., 2017; Pal ., 2018). Here, we demonstrate how the speed and
width distributions (Figures 6 and 7) of CMEs change when they are separated
into three broad categories: active region eruption (Pal ., 2018; Majumdar .,
2021), prominence eruption (Sheeley Jr ., 1980; Munro ., 1979; R. Howard .,
1985; D. Webb Hundhausen, 1987; St. Cyr ., 1999), and active prominence
eruption (Gilbert ., 2000). The source region segregated distributions are
shown in Figure 8 (speed) and Figure 9 (width).

Figure 8: Histograms of the apparent/projected (left) and true (right) speed
of CMEs based on source region segregation: AR CMEs (shown in red), PE CMEs
(shown in blue), and AP CMEs (shown in green) with their corresponding average
values.

Figure 8 compares the speed distributions of AR, PE, and AP-CMEs before (left
panel) and after (right panel) correcting for projection effects. The CME
speeds from AR have the most right-skewed distribution (shown in red),
covering a broader range of speeds with 3D speeds ranging from 200-2800 km
$s^{-1}$ (higher than corresponding 2D values) with an average speed of 723 km
$s^{-1}$ as compared to the average 2D speed that is 534 km $s^{-1}$. The CMEs
that originate from PE regions (shown in blue), on the other hand, cover a
small range of speeds with an average 2D speed of 358 km $s^{-1}$ and an
average 3D speed of 432 km $s^{-1}$. The distribution (shown in green) of CME
speeds from the AP region differs significantly from AR and PE distributions,
with the highest average 2D speed of 592 km $s^{-1}$ and the highest average
3D speed of 813 km $s^{-1}$. The results in 2D and 3D show that CMEs from PE
regions are slow and gradual eruptions as expected. AR distribution has the
widest range and very high speeds but with the most probable slow CMEs. APs
have a far reduced number of slow CMEs with the highest average speed,
suggesting that either the reconnection mechanisms or magnetic environment
surrounding the APs are inducive to more impulsive, faster CMEs since
footpoints of the eruption are within the region of strong magnetic field, yet
the confining magnetic environment may be weaker compared to the active
region. It could also be due to such CMEs having a tendency to have a
different geometry, perhaps asymmetry, that is poorly modeled by GCS.

Source regions have an effect not only on the speed of CMEs but also on their
angular width (Zhao ., 2017; Pant ., 2021). Figure 9 shows the distribution of
width influenced by different source region types, before and after
correction. Figure 9 (b) shows that the width distribution of CMEs coming from
AR and AP regions are quite similar, with most CMEs of width 90∘ with average
widths of 78∘ and 84∘ respectively. CMEs from PE region have an average width
of 66∘, peaking at 60∘. This shows that AR and AP-based CMEs are wider than PE
CMEs. When compared to their corresponding projected distributions (left panel
of Figure 9), the average widths are found to be higher in all three cases
(effects of projections).

Figure 9: Histograms of the width of CMEs before correction (left) and after
correction (right) based on source region segregation: AR CMEs (shown in red),
PE CMEs (shown in blue), and AP CMEs (shown in green) with their corresponding
average values.

###  4.3 CME Speed versus CME Width

Wider CMEs tend to be faster than narrower CMEs. This phenomenon has been
described in previous studies by Gopalswamy . (2001); Yashiro . (2004);
Burkepile . (2004); Yeh . (2005); Vršnak . (2007); T. Howard . (2008). These
authors demonstrated a weak but positive correlation of $\sim$0.4 between
projected speed and width and that the correlation completely disappears after
the correction for the projection effect. Note that the parameters used to
discover the association in the above studies are projected in the plane-of-
sky. With the data sample collected for this paper, the correlation is
reexamined. The scatter plots of apparent and true speed plotted as a function
of apparent and true width are depicted in figure 10. We find that the 3D
speed-width plot has a weaker correlation (cc = 0.40 and p$<$0.001) and a
steeper slope of 5.26 km $s^{-1}\deg^{-1}$ in comparison to their 2D plot,
which has cc = 0.60 and a slope of 2.19 km $s^{-1}\deg^{-1}$.

Figure 10: Scatterplots between CME speed (V) and angular width (W) before
correction (left panel) and after the correction (right panel). The regression
line and the correlation coefficients are indicated on the plot.

Jang . (2016) conducted a comparison between the 3D and 2D statistical
properties of both full and partial halo CMEs. They observed a correlation
coefficient of 0.54 between 3D speed and width, which is marginally higher
than the correlation found in our study. They noted that the slope in 3D is
about five times greater than in 2D when all types of CMEs are considered.
However, this increase in slope is approximately 2.5 times for partial halo
CMEs alone. This finding aligns with the slope derived from AR CMEs in our
study, considering that most halo CMEs originate from AR. Richardson . (2015)
and Shen . (2013) found a cc = 0.47 and cc = 0.48, which is a little higher
than ours (cc = 0.4). A similar correlation can be found in Vršnak . (2007)
where the projected plane-of-sky velocity and angular width of non-halo CMEs
are compared. These differences may be due to the criteria for selecting
events. For example, Jang . (2016) selected CMEs with apparent widths larger
than 180, while we selected CMEs ranging in apparent width from 30 to 360.
Besides this, we investigated the correlation coefficient and the slope of the
speed-width plot before and after correction by looking at their trends from
different source regions. Figures 11 (a) and (b) show the variation of speed
with width for CMEs originating from AR, AP, and PE regions. We found that the
slope of the 3D values is almost $\sim$3 times that of their 2D slope in the
case of AR-CMEs, and $\sim$2 times in the case of AP-CMEs, implying that wider
CMEs originating from ARs tend to be faster as compared to the CMEs of same
width but originating from APs. A clear difference can be spotted in the slope
for PE-CMEs before and after correction, with a slope of 1.47 (former) and
-0.70 (latter), implying almost anticorrelation between the speed and width of
CMEs originating from prominences. This relation needs examination with a
bigger dataset.

Figure 11: Scatterplots between CME speed (V) and angular width (W) after SR
segregation, before and after correction. The regression lines (black for AR-
CMEs, red for AP-CMEs, and blue for PE-CMEs) and their correlation
coefficients for AR, AP, and PE CMEs are indicated on the plot.

###  4.4 True Speed versus Projected Speed

Figure 12: Scatter plot of True speed versus Projected speed. Blue points show
2D speeds in LASCO from manual catalog CDAW, whereas red points show 2D speeds
in STEREO-A extracted from automated catalogs CACTus and SEEDs. A strong
correlation can be seen in both cases. A dashed line is where the true speed
matches the projected speed

Figure 12 shows a scatterplot between true speed (on the y-axis), estimated
from GCS, and their corresponding projected speed (on the x-axis), taken from
CACTus. When the effects of projection are taken into account, the true speeds
of all CMEs should ideally be greater than the 2D speeds; however, our
findings for a small number of CMEs indicate some inconsistency in this
assumption. A linear fitting performed on the two data sets (blue points
correspond to projected speeds in STEREO-A, whereas red data points correspond
to the projected speed in LASCO FOV) gives a slope of 1.33 and 1.37, which
indicates that the true speed varies by a factor of $\sim$1.3 regardless of
the coronagraphs that were used to determine the projected speeds. The dashed
line is where projected and true speeds are the same.

TA. Howard Tappin (2008) found that the average corrected speed tends to be a
factor of 1.7 higher than their projected values. Similar behavior in 3D
versus 2D plots can be seen in Majumdar . (2020) and Jang . (2016). A
statistical correlation analysis between the corrected and apparent speeds
from CACTus and CDAW generated a Pearson’s linear correlation coefficient of
cc = 0.82 and 0.87 , showing a strong and positive correlation. Studies (for
example TA. Howard Tappin (2008); Richardson . (2015); Jang . (2016)) found
the correlation between the 3D and 2D speed to be cc = 0.71, 0.68, and 0.94.

##  5 Summary and Conclusion

In prior research, the GCS model has been frequently applied to fit CMEs. The
primary catalogs available, KINCAT and CMEDB, extend only up to 2014, halting
just as STEREO-A began its transit behind the Sun. As a result, these catalogs
mainly capture the ascent of solar cycle 24 and include a restricted number of
CMEs evaluated by other scholars. Our dataset is distinct, with no CMEs
duplicated and ensuring no redundancy. In our study, we have assembled data on
360 unique CMEs identified by SOHO and STEREO from 2007 to 2021, spanning
varied stages of solar cycle 24 with the data gap from October to December in
2014 and January to November in 2015, a period when STEREO-A transitioned
behind the Sun. This compilation encompasses 326 GCS-modeled CMEs, assessed by
various authors between 2007 and 2014 during the rising phase of solar cycle
24. Our work introduces 34 CMEs that transpired during the declining phase of
solar cycle 24 and is a significant addition to the existing datasets.
However, we acknowledge the inherent challenges in fully validating the
accuracy of these reconstructions, given the current limitations in directly
measuring the true properties of CMEs. Combining CME properties from different
catalogs could impact the overall results due to the slight variations in the
reconstructions of the same CME. These variations often arise because
different observers choose different features to fit. A recent paper by Kay
Palmerio (2023) provides a comprehensive database and gives a detailed
discussion on the limitations of variations in the reconstructed parameters
across multiple studies. They illustrate a potential variation of up to 19% in
speed and 27% in angular width in CME reconstructions. Similarly, Majumdar .
(2020) showed a 15% error in the speed estimation. The uncertainty in speed
calculated using the bootstrapping technique for the 34 CMEs fitted during
this work falls within these estimated variations. We examined the
distributions of speed and width and their interrelationship, which were then
associated with their SR type, segregated into three broad categories: ARs,
PEs, and APs. Subsequently, these distributions were compared with the 2D
automated parameters cataloged by CACTus (primary catalog) and SEEDS (fill in
the missing data) and with the 2D manual parameters cataloged by CDAW to
assess the impact of projection. Cactus and SEEDS are the only 2D catalogs
that detect CMEs in STEREO images. They often include anomalous and high CME
speeds at the position angles adjacent to the flanks, resulting in erroneous
CME speed and width measurements. To mitigate these discrepancies, we
meticulously reviewed the CACTus catalog and looked at associated movies to
obtain the most precise CME speeds. We have also compared the true and
projected values acquired via LASCO from the CDAW for 360 events. Both methods
yielded similar correlation coefficients (cc) for speed-width distributions
(cc=0.60 in the case of CDAW and cc = 0.61 in the case of CACTus). Table 3
summarizes statistical parameters using GCS, CACTus, and CDAW. The main
results from this work are:

  1. 1.

Speed distributions of CMEs before and after correction (see Fig. 6) varies
significantly, with true speeds ranging from 200-2800 km $s^{-1}$ with an
average speed of 665 km $s^{-1}$ as compared to the projected speeds ranging
from 200-1800 km $s^{-1}$ with an average speed of 500 km $s^{-1}$, implying
that 2D speeds are underestimated by approximately 30% when compared to 3D
ones hence showing a significant amount of projection effects in the 2D
estimates.

  2. 2.

Comparison of CME width distributions before and after correction (see Fig. 7)
reveals that 2D widths are greatly overestimated due to projection effects
compared to their 3D parameters. Following the correction, the number of CME
events with wide angular spans (apparent width $>$ 180) drops to zero, while
the number of events with narrow angular spans increases significantly. In
both histograms, the maximum frequency range peaks around 90∘, with an average
true width of 77 and an average projected width of 112∘.

  3. 3.

True speed and width distributions of CMEs associated with AR, AP, and PE are
examined and compared to their apparent distributions (see Fig. 8 and 9). As
expected, CMEs associated with prominences are slow, gradual, and narrower,
with an average true speed of 432 km $s^{-1}$ and average true width of 66∘,
whereas CMEs associated with ARs have higher speeds with an average true speed
of 723 km $s^{-1}$ and average width of 78∘, with slower CMEs most likely in
both cases (slightly more in PE-CMEs than AR-CMEs).

  4. 4.

APs have a much smaller number of slow CMEs with the highest average true
speed of 813 km $s^{-1}$ and the highest average width of 84∘, respectively.
The values are higher than the average values obtained for CMEs from ARs due
to the low number of slow CMEs. This could be due to the reconnection
mechanisms or the magnetic environment around the APs causing more sudden,
faster CMEs as the footpoints of the eruption are in a region with a stronger
magnetic field, yet the confining magnetic field may be weaker compared to an
active region.

  5. 5.

3D Speed versus width relation (shown in Fig. 10) has a weak but positive
correlation cc = 0.40 and p$<$0.001) with wider CMEs having higher speeds with
a slope of 5.26 km $s^{-1}\deg^{-1}$. The exact relation in 2D shows a slope
of 2.19 km $s^{-1}\deg^{-1}$ with a cc = 0.60. This implies that the
correlation between speed and width decreases with the removal of projection
effects and that the true behaviour of CMEs is much more complicated when it
comes to studying the effect of width on speed. A similar correlation between
GCS speed and width is found in a study by Shen . (2013).

  6. 6.

The relationship between speed and width (shown in Fig. 11) for different SRs
has not been extensively studied in earlier studies. A linear fit to CMEs
(shown in black and red) follows a trend with a slope of 7.22 (AR) and 3.88
(AP). Almost an anticorrelation is found between speed and width for PE CMEs.
Hence, we show that kinematics of CMEs changes significantly when they are
associated with different SR types.

  7. 7.

True and projected speeds are compared (see Fig. 12) for 360 CMEs with
projected speeds taken from CACTus and CDAW separately. A slope of $\sim$1.3
in both cases implies the true speed is higher than the projected speed
regardless of the single viewpoint values. However, a small fraction of CMEs
were found to have projected speeds higher than true speeds. A strong and
positive correlation of cc = 0.82 and cc = 0.87 can be seen while comparing
true speeds with automated and manual projected speeds.

In conclusion, our results show that removing projection effects in CMEs is
crucial for accurately understanding their kinematic properties and physical
parameters. Several studies have been conducted to investigate the impact of
projection effects on CME properties and to develop methods to correct them.
In general, eliminating projection effects in CMEs is a crucial step towards
gaining an improved understanding of their physical processes and their
influence on space weather. However, further research is still needed to
improve the existing methods and investigate the impact of CME orientation and
width on the speed. Due to the subjectivity of these studies, machine learning
techniques such as convolutional neural networks to fit CMEs autonomously in
multi-view coronagraph images could be a major step to improve the accuracy of
CME speed and width measurements by avoiding the manual bias and reducing the
fitting time.

## Open Research Section

The data used to make the plots in the paper can be found at Harshita (2024)

###### Acknowledgements.

HG is supported by an STFC studentship at Aberystwyth University. HM’s
contribution is supported by Leverhulme grant RPG-2019-361. We acknowledge
SECCHI/STEREO consortium for providing data. The SECCHI data used here were
produced by an international consortium of the Naval Research Laboratory
(USA), Lockheed Martin Solar and Astrophysics Lab (USA), NASA Goddard Space
Flight Center (USA), Rutherford Appleton Laboratory (UK), University of
Birmingham (UK), Max-Planck-Institut for Solar System Research (Germany),
Centre Spatiale de Li$\grave{e}$ge (Belgium), Institut d’Optique
Th$\acute{e}$orique et Appliqu$\acute{e}$e (France), Institut d’Astrophysique
Spatiale (France). We also thank NASA for making SOHO/LASCO data publicly
available. SOHO is a project of international cooperation between ESA and
NASA. The STEREO/SECCHI/COR2 CME catalog is generated and maintained at the
Institute for Astrophysics of the University of Goettingen, supported by the
German Space Agency DLR and the European Union in collaboration with the U.S.
Naval Research Laboratory, Washington. The authors acknowledge the use of
computing resources provided by ARIES and Aberystwyth University.

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