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A&A
Volume 689, September 2024
Article Number A187
Number of page(s) 16
Section The Sun and the Heliosphere
DOI https://doi.org/10.1051/0004-6361/202449530
Published online 12 September 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.

1. Introduction

Coronal mass ejections (CMEs) are remarkable transient events that affect the Solar System. They involve the substantial release of both magnetic field and plasma from the Sun’s corona, typically travelling with speeds ranging from 400 to 1000 km s−1, and occasionally exceeding 2000 km s−1 (Hundhausen et al. 1994; Dryer et al. 2012; Liou et al. 2014). Depending on their initial speed and that of the ambient solar wind, the majority of CMEs typically arrive at the orbital distance of the Earth within 1−4 days. Upon reaching our planet, CMEs can induce geomagnetic storms through interaction with the Earth’s magnetosphere. The severity of these storms depends on the internal magnetic field configuration and plasma properties of the CME (e.g. Schwenn 2006; Temmer 2021; Kilpua et al. 2017a; Koskinen et al. 2017). CMEs detected by a spacecraft in situ are also called interplanetary CMEs (ICMEs, e.g. Rodriguez et al. 2011; Kilpua et al. 2017b). ICMEs are characterised by specific signatures observed in the magnetic field and plasma data (Zurbuchen & Richardson 2006).

Halo CMEs refer to a specific type of CME observed in white-light coronagraph images, where the expanding structure appears as a halo around the occulting disc. This occurs when a CME travels either towards or away from the observer. When observed from Earth, these eruptive events are crucial for space weather predictions: their detection (for front-sided events, which are those seen coming towards Earth) indicates the potential propagation of the eruption along or in close proximity to the Sun–Earth line (Howard et al. 1982; Schwenn 2006; Rodriguez et al. 2009).

Historically, detection of halo CMEs along the Sun–Earth line relied heavily on instruments such as the Large Angle and Spectroscopic COronagraph (LASCO; Brueckner et al. 1995) on board the SOlar and Heliospheric Observatory (SOHO; Domingo et al. 1995) positioned at the Lagrange point L1 of the Sun–Earth system. Additional insights into associated signatures in the low corona, such as eruptive filaments, coronal dimmings, ‘EIT waves’, and post-eruption arcades, were gained through extreme-ultraviolet (EUV) observations (e.g. Zhukov 2007), notably from instruments such as the Extreme-ultraviolet Imaging Telescope (EIT; Delaboudinière et al. 1995).

However, the detection of CMEs improved with the launch of the Solar-TErrestial RElations Observatory (STEREO; Kaiser et al. 2008). The twin STEREO spacecraft provide a view from a location away from the Sun–Earth line by means of the COR coronagraphs and the Extreme Ultraviolet Imagers (EUVI) of the Sun–Earth Connection Coronal and Heliospheric Investigation instrument suites (SECCHI; Howard et al. 2008). When the STEREO spacecraft are positioned away from the Sun–Earth line, they enable tracking of Earth-directed CMEs based on side-view observations (e.g. Davies et al. 2009; Möstl et al. 2011; Rodriguez et al. 2020). This provides a very important viewpoint needed for early characterisation of Earth-directed CMEs, and in particular for determining the CME propagation direction, speed, and acceleration with minimal projection effects, therefore allowing a more accurate estimation of CME arrival times at Earth. This information, together with the knowledge of the internal magnetic field configuration of the CME, are of crucial importance for space weather forecasting.

The EUropean Heliospheric FORecasting Information Asset (EUHFORIA, Pomoell & Poedts 2018) is a space weather forecasting-targeted inner heliosphere physics-based model. It consists of two coupled domains, the coronal (which focuses on processes below 0.1 au) and the heliospheric (which focuses on the heliosphere starting at 0.1 au). The former uses synoptic magnetograms in order to compute magnetic field and plasma parameters at 0.1 au using an adaptation of the Wang-Sheeley-Arge empirical model (WSA, Arge et al. 2003), while the latter domain employs a model that takes the output from the former domain at 0.1 au as input and solves the three-dimensional (3D) time-dependent ideal magnetohydrodynamic (MHD) equations in the heliocentric Earth equatorial (HEEQ) system at a prescribed resolution. Finally, CMEs can then be incorporated into the heliospheric simulation of EUHFORIA using different CME models, such as the cone model (Xie et al. 2004), which does not prescribe an internal magnetic field configuration for the CME, and the more complex spheromak (Verbeke et al. 2019a; Scolini et al. 2019) flux rope CME model, which has a prescribed internal magnetic field configuration.

During the European Union Horizon 2020 project ‘EUHFORIA 2.0’, we carried out a validation of the cone and spheromak CME models, which we describe below. We evaluated the models both for the CME arrival time accuracy and for the possibility of predicting their geomagnetic impact based on the internal magnetic field profile and plasma parameters.

The present paper is organised as follows. Section 2 presents the selection of events for the two datasets used in our validation of the cone and spheromak CME models, and the collection of the necessary input data. Section 3 provides a brief overview of the models and the metrics used in this study. Then, in Section 4, we compare the results for arrival times and ICME internal characteristics – including geoeffectiveness – for the first dataset. In Section 5, using the second dataset, we present an evaluation of CME arrival predictions in EUHFORIA, specifically focusing on the accuracy of these predictions in terms of ICME arrivals at the L1 point. Finally, in Section 6, we summarise our results and provide conclusions.

2. Selection of events and collection of input data

In this section, we outline our approach to event selection and the data gathering essential for the study. We performed our validation of the cone and spheromak CME models using two distinct datasets: one containing 16 CMEs that arrived at Earth (Event list A), and another comprising all CMEs observed over a time period of 8 months within Solar Cycle 24, regardless of their Earth impact (Event list B). The reasoning for using two datasets is that we can study and validate different aspects. With the first dataset, we test how the CMEs simulated by EUHFORIA compare to in situ satellite data collected at the L1 point for the corresponding ICMEs. The second dataset allows us to evaluate the accuracy of EUHFORIA in predicting CME arrivals based on a scenario that more closely resembles that of a forecasting situation in real time, where all CMEs are considered.

2.1. Events list

2.1.1. Event list A: Selected events

This section describes the list of events (CME–ICME pairs) that are used for the first part of our study. The CMEs were chosen when coronagraphic observations from at least two out of three spacecraft (STEREO-A, STEREO-B, SOHO) were available, so that 3D-reconstructed geometric parameters could be used to drive EUHFORIA (Pomoell & Poedts 2018; Scolini et al. 2019). This requirement sets the start range of our possible CME candidates in 2007 (start of STEREO data availability). Furthermore, we required good availability of EUV and magnetic field data of the source region, which needs to be visible on-disc from the Earth’s point of view to ensure a clear characterisation of the CME source. We excluded events with interacting CMEs in order to reduce the complexities that could influence our analysis. Finally, the corresponding ICMEs were required to arrive at Earth so that simulation results could be compared with in situ data at the L1 point. We created a list of 16 events, which is shown in Table 1. This list is non-exhaustive; events were selected by visually inspecting the data and choosing clear cases for which the above-mentioned conditions were fulfilled.

Table 1.

CME–ICME pairs and simulation results.

2.1.2. Event list B – CMEs over eight months

We used a second dataset to assess the performance of EUHFORIA in predicting the arrival or non-arrival of the targeted CMEs. In this second dataset, we do not require an ICME counterpart at the Earth for the observed CMEs. Rather, we used all the CMEs observed over eight full months. Four months were taken during solar minimum (June–September 2010) and the other four during solar maximum (June–September 2012). For the former period (2010), we originally found 357 events, taken from the SOHO/LASCO CME catalogue (Gopalswamy et al. 2009)1. After excluding events with data gaps, events only visible to one spacecraft, and faint events with uncollectable input parameters, and after implementing thresholds for velocity (we selected only CMEs faster than 350 km s−1) and angular width (only CMEs wider than 60° were considered), the list was reduced to 24 events. From those cases, 12 are front-sided events and were simulated with EUHFORIA. As we are considering the ability of EUHFORIA to predict the arrival (hit) or non-arrival (miss) at Earth’s position, we do not include backsided events (i.e. those events seen to be moving away from Earth). For the period in 2012 (solar maximum), 857 events were originally collected; after removing events with gaps and applying the same velocity and angular width constraints as those applied during solar minimum, 191 events remained. Of those, 36 frontsided events were simulated with EUHFORIA.

2.2. Collection of input data

Knowledge of realistic CME intrinsic parameters is crucial for space weather forecasting using first-principle heliospheric models and semi-empirical CME models (e.g. Kilpua et al. 2019, and references therein). Regarding EUHFORIA, we need to constrain the geometry and kinematics of CMEs using the cone and spheromak CME models. Furthermore, spheromak CME models require magnetic field parameters as input. Below, we describe how input parameters were collected for Event list A, comprising selected events. For Event list B, which contains CMEs observed over 8 months, only cone CME runs were used. Information about the magnetic field configuration was not needed for this part of the study, the primarily aim of which is to assess the model’s performance in forecasting CME hits and misses. Input parameters for these EUHFORIA simulations were gathered using the StereoCat tool2, which is better suited for data analysis in a real-time forecasting environment.

2.2.1. Geometric and kinematic reconstruction of CMEs

We used the graduated cylindrical shell (GCS) model (Thernisien et al. 2009; Thernisien 2011) to determine the 3D morphology and the propagation direction of the CMEs in Event list A. The GCS model consists of a tubular section forming the main body of the structure attached to two cones that correspond to the ‘legs’ of the CME. As the model consists of a single geometric surface, it does not provide a description of the internal structure of the CME.

The model fits the geometrical structure of the CME as observed by white-light coronagraphs such as SOHO/LASCO and STEREO/COR2. The fitting can be performed from single or multiple spacecraft data. However, the results are more reliable when multiple and well-separated vantage points are used (e.g. Rodriguez et al. 2011). The following parameters can be obtained:

  • propagation longitude (ϕ),

  • propagation latitude (θ),

  • half-angular width (α),

  • aspect ratio (κ), that is the rate of expansion versus the height of the CME,

  • tilt angle (γ) with respect to the solar equator,

  • leading-edge height (h) of the CME.

For each CME, the fitting was performed for different consecutive moments in time in order to derive true 3D velocity vectors of the expanding structure. An example of a fit for the CME observed on 29 September 2013 is shown in Figure 1. The GCS fitting is shown as the green wireframe overlaid on the coronagraph images at each of the three spacecraft.

thumbnail Fig. 1.

GCS reconstruction of the CME observed at 23:54 UT on 29 September 2013. The fit can be seen in the bottom row. The images shown are from COR2-B (left panel), LASCO-C3 (middle panel), and COR2-A (right panel).

We note that due to the symmetry of the model, the fit is not perfect in the case of complex CMEs. Thernisien et al. (2006) mentioned several sources of error in the model; among them, there are errors intrinsic to the fitting method, and errors arising from the subjectivity of the observer. Regarding the intrinsic errors, it is important to note that different parameters may fit the same CME well (i.e. the solution may not be unique). This is especially true when fitting single-spacecraft data, which provide a single 2D projection of a 3D structure. Thernisien et al. (2009) estimated the errors for the GCS model using a sensitivity analysis method. For the 26 events studied, these authors found a mean value of ±4.3° (with a maximum value of 16.6°) in longitude, and ±1.8° degrees (max value of 3.7°) in latitude. Verbeke et al. (2023) estimated that the largest errors are found when only one viewpoint is available, with errors reducing significantly when two or more are used. Kay & Palmerio (2024) recently carried out a thorough analysis of the errors arising from the use of different catalogues and the subjectivity of the observer, finding that the typical difference between two independent reconstructions of the same event is 4° in latitude and 8° in longitude.

The results for all CMEs studied here are presented in Table 2. These CMEs were fast, with speeds of around 1000 km s−1 or higher. Their longitude is concentrated near the central meridian as seen from Earth, except for events 3, 4, and 13, which are closer to the limb. The majority of the events were also propagating close to the ecliptic plane, all within 30° of it. The speeds shown in the table are those used for the cone and spheromak models. For the cone model, the speed is obtained directly from the GCS fitting, whereas for the spheromak model we used the reduced radial speeds, as derived in Scolini et al. (2019). Regarding the CME half width (HW) used in the cone model, it is calculated as:

HW = α + arcsin κ . $$ \begin{aligned} \mathrm{HW} = \alpha + \arcsin {\kappa }. \end{aligned} $$(1)

Table 2.

Three-dimensional CME parameters as derived from the GCS fitting.

The spheromak model requires the radius at 0.1 au, which is derived as follows:

r spheromak = 21.5 · sin ( HW ) . $$ \begin{aligned} r_{\rm spheromak} = 21.5 \cdot \sin {\mathrm{(HW)}}. \end{aligned} $$(2)

2.2.2. Determination of CME input magnetic parameters

Knowledge of the magnetic parameters associated with the CMEs is a crucial input for constraining magnetised CME models in EUHFORIA. Using the near-Sun magnetic properties of a CME as initial inputs, EUHFORIA can simulate the Sun-to-Earth evolution of a CME and provide information on its magnetic properties at 1 au. However, it is difficult to obtain a direct estimation of the near-Sun magnetic properties of a CME, as the magnetic field of the solar corona cannot be reliably measured through remote-sensing observations. In this work, we use state-of-the-art observational proxies to estimate the different magnetic properties of CMEs for the 16 events studied in our Events list A in order to constrain the model inputs of EUHFORIA.

The three magnetic parameters required to constrain a force-free magnetic flux rope (FR) are its magnetic flux, its chirality, and the direction of axial magnetic field (e.g. Palmerio et al. 2017). The observational techniques to constrain these parameters are detailed below. The obtained magnetic parameters for the 16 events studied are provided in Table 3.

Table 3.

Magnetic parameters of CMEs.

Poloidal flux. Several studies have shown that the azimuthal (i.e. poloidal) flux of magnetic FRs formed due to reconnection is approximately equal to the low-coronal reconnection flux, which can be obtained either from the photospheric magnetic flux underlying the area swept out by the flare ribbons (Longcope et al. 2007; Qiu et al. 2007) or the magnetic flux underlying the post-eruption arcades (PEAs; Gopalswamy et al. 2017). The flux can be calculated using PEA analysis based on either the line-of-sight or vector magnetograms (Kilpua et al. 2019). There is also an existing catalogue by Kazachenko et al. (2015, 2017) that lists flare-ribbon fluxes for every flare of GOES class C1.0 and greater within 45° from the central meridian, from 2010 April until 2016 April. Magnetic field measurements are not reliable if the source location of the flaring event lies beyond 45° from the central meridian. In such cases, the empirical relation between soft X-ray peak flux and reconnection flux can be used to estimate the poloidal flux of the associated CME (Tschernitz et al. 2018; Scolini et al. 2020). To run the spheromak model, we need to convert the poloidal flux to toroidal flux. First, the FRED technique (Gopalswamy et al. 2018) is applied at 21.5 R⊙ to obtain the axial magnetic field strength (B0) from observations (assuming a Lunquist geometry of the magnetic cloud). The observed B0 is then equated to the field strength at the magnetic axis of the spheromak model (at 21.5 R⊙–rspheromak) (Sarkar et al. 2020, 2024). The toroidal flux can then be obtained by substituting B0 in Equation (7) of Verbeke et al. (2019a).

Chirality. One of the important properties of any FR is its helicity sign (chirality), which determines the winding direction of the poloidal flux. In order to determine this parameter, one may apply the hemispheric helicity rule to the source active region of the CME as a first-order approximation (Pevtsov et al. 1995; Bothmer & Schwenn 1998). This rule states that FRs from the northern hemisphere will show predominantly negative helicity, whereas those in the southern hemisphere will have predominantly positive helicity. However, statistical studies show that the ratio of the preferred helicity sign is correct only in about 60% of cases (Liu et al. 2014). Therefore, in order to confirm the chirality of the FRs, one can use further observations of preflare sigmoidal structures (Rust & Kumar 1996), J-shaped flare ribbons (Janvier et al. 2014), coronal dimmings (Webb et al. 2000; Gopalswamy et al. 2018), coronal cells (Sheeley 2013), or filament orientations (Hanaoka & Sakurai 2017).

Direction of axial magnetic field. The orientation of the axial magnetic field of a FR can be determined by knowing the magnetic polarities of its two anchoring foot points. By analysing the locations of the two core dimming regions or the two ends of the preflare sigmoidal structure, one can identify the locations of the two foot points of the FR. Thereafter, the locations of the FR foot points can be overlaid on the line-of-sight magnetogram to determine the magnetic polarities in which the FR is rooted (Palmerio et al. 2017).

Multi-wavelength observations of one example event (Event no. 12) are shown in Figure 2. This is an illustration of the observational techniques that we used to determine the magnetic parameters associated with each eruption.

thumbnail Fig. 2.

Multi-wavelength observations of the source region of Event no. 12. Panel a Depicts the filament channel as indicated by the yellow dashed line in AIA (Lemen et al. 2012) 304 Å image. The red dashed boundary line in panel b marks the PEA as observed in AIA 193 Å image. Panel c Illustrates the line-of-sight component of the HMI (Scherrer et al. 2012) magnetic field. The red dashed boundary and the yellow dashed line in (c) are the over-plotted PEA region and filament channel, respectively. The two ends of the reverse S-shaped filament channel are marked by the green circles and the underlying magnetic polarities are shown, which indicate a northward-pointing left-handed flux-rope.

3. Overview of EUHFORIA and metrics adopted

3.1. Overview of EUHFORIA

The spatial domain of EUHFORIA is divided into the coronal and the heliospheric domain. The former extends from the photosphere to 0.1 au, and the latter starts at 0.1 au and typically extends up to 2 au. The division is done at 0.1 au because beyond this distance, the solar wind plasma is supersonic and super-Alfvénic, which means that no information is traveling towards the Sun, as all MHD characteristic curves are outgoing (Pomoell & Poedts 2018). Both models are in principle independent of each other, and different models could be used as long as the correct coupling is assured. An adaptation of the WSA model (WSA, Arge et al. 2003) is used for the coronal part. The heliospheric model of EUHFORIA is a 3D time-dependent MHD simulation that solves the ideal MHD equations and self-consistently models the propagation, evolution, and interaction of solar wind and CMEs.

A synoptic magnetogram is the only input needed to produce a solar wind simulation. When CMEs are inserted into the model, the CME input parameters are then also needed; these will depend on the CME model used. As output of its heliospheric model, EUHFORIA provides plasma and magnetic field quantities at any location of its domain. An example of this output is shown in Figure 3, where a view from above the ecliptic plane and a meridional cut are shown for the simulation of Event 8 from Table 1.

thumbnail Fig. 3.

Equatorial and meridional slices for cone (top panel) and spheromak (bottom panel) models for Event 8.

Before launching the CME into EUHFORIA’s heliospheric domain, the background solar wind can be optimised in order to reproduce the correct ambient solar wind in which the CME will be injected. For this purpose, EUHFORIA is run with different global oscillation network group (GONG) magnetograms3 close to the CME launch time. The one that best reproduces the observed solar wind at 1 au before the ICME arrival is used. To pick the best magnetogram for modelling the solar wind before an ICME arrival, we carefully searched through available options. We started with the closest magnetogram to the CME launch time and ran simulations. If the initial magnetogram failed to yield satisfactory results, we systematically reviewed others at 6 hour intervals until finding the most suitable one. Most of the magnetograms were selected within three days of the CME (with a few within up to six days). This method ensures that the chosen magnetogram drives EUHFORIA to accurately represent the solar wind conditions, enabling realistic ICME propagation simulations. This is an optional optimisation; here it was done for our Event list A, and the selected magnetogram for each of the runs can be found in Table 1. The CMEs are then inserted into EUHFORIA at 0.1 au using the cone and spheromak models. Additionally, CMEs occurring in the days preceding Events 5, 6, and 14 were included in the simulation in order to create more realistic conditions for the main CMEs. Further details on these events can be found in Appendix A. For Event list B, we always used the magnetogram taken six hours before the CME, because this would be the situation most similar to a real-time CME forecasting scenario.

3.1.1. The cone CME model

The cone CME model treats the ejecta as a hydrodynamic (velocity and density) pulse injected at the inner radial boundary of the simulation domain. It is characterised by a self-similar expanding geometry (Xie et al. 2004; Odstrčil & Pizzo 1999), and does not contain a prescribed internal magnetic field. This does not mean that the internal magnetic field of the ICME will be zero; the pulse is injected into the solar wind and will interact with its magnetic field. Due to its simplicity, the cone CME model has been widely used in 3D MHD simulations in recent decades. Figure 4 presents a graphic representation of the cone model, together with the parameters normally required as input for EUHFORIA (derived from coronagraphic observations; Section 2.2.1); it shows a CME that propagates radially outward from the Sun and expands while maintaining constant angular width. The cone CME run for Event 8 is shown in the top panel of Figure 3.

thumbnail Fig. 4.

Schematics of the cone model, adapted from Dewey et al. (2015).

3.1.2. The spheromak model

The linear force-free spheromak CME model was implemented in EUHFORIA (Verbeke et al. 2019a) in order to allow the possibility of inserting CMEs into the heliospheric domain that contain a structured internal magnetic field, with a toroidal-like flux rope structure in this case. Figure 5 presents a visualisation of the magnetic field structure of the model from Verbeke et al. (2019a). In this case, on top of the geometric parameters, a set of magnetic parameters is needed (Section 2.2.2). The CME in this model is considered to be a sphere upon the time of its injection; it is launched outward following the latitude and longitude directions specified as input. The magnetic field structure is defined in a local spherical coordinate system, with origin at the centre of the spheromak and symmetry in the azimuthal direction. The spheromak CME run for Event 8 is shown in the bottom panel of Figure 3.

thumbnail Fig. 5.

Magnetic field lines depicting the structure of the spheromak CME model. The grey plane shows the meridional HEEQ y = 0–plane. From Verbeke et al. (2019a).

3.2. Metrics description

This section describes the list of metrics used for the comparison of EUHFORIA output with the in situ data at 1 au. Within the field of space weather forecasting, it is crucial to assess the reliability and accuracy of predictive models. A widely employed tool for this purpose is the contingency table; see for example Verbeke et al. (2019b). Events are categorised into four classes: hits (indicating correct prediction of space weather event), misses (representing instances where the model fails to predict a space weather event), false alarms (signifying predictions of the space weather event that does not occur), and correct rejections (denoting correct prediction of a quiet period). This analysis can also be conducted using different time intervals – which are needed to specify the maximum time allowed for the hit to occur (e.g. 24 hours) – between observed and predicted space weather events.

Based on the contingency table, some classic metrics can be calculated, such as the probability of detection (POD), the success ratio (SR), the bias score (BS), the critical success index (CSI), the accuracy (Ac), the probability of false detection (POFD), and the Hanssen and Kuipers discriminant. These metrics are listed in Table 4 and are complementary to each other. These metrics can be visualised in a single figure for clarity, known as the performance diagram (e.g. see Verbeke et al. 2019b).

Table 4.

Skill scores based on Verbeke et al. (2019b).

In addition to the previously mentioned metrics, we also employ a set of metrics specifically calculated within the ICME interval, focusing on the cases where the arrival of an ICME is predicted by EUHFORIA and is observed (hit events). The metrics applied in this case were the mean error (ME), the mean absolute error (MAE), the mean square error (MSE), the standard deviation (SD), and the root-mean-square error (RMSE). These metrics are computed based on key parameters such as the CME arrival time and Kp index. Further details regarding the computation and interpretation of these metrics can be found in Verbeke et al. (2019b).

4. Results – Event list A: Selected events

4.1. Comparison of arrival times between simulated and real CMEs

The arrival times for each simulation output of the Events list A are shown in Table 1. The arrival time estimates are compared with the observed arrival times, while the estimates of the ICME properties from the simulations are compared with measured in situ data obtained from the OMNI database. In particular, we focused on comparison of the solar wind bulk speed and magnetic field. The geomagnetic impact is estimated using the Kp index. In Appendix B, we provide plots of each event, including observations and results from simulations.

Figure 6 displays a histogram of the difference between the observed and simulated ICME arrival time for cone and spheromak runs. Cone CMEs tend to arrive earlier than spheromak ones. EUHFORIA correctly predicts that all 16 events arrived at the Earth. All the ICMEs arrive within 24 hours – with RMSE values of around 9 hours – for both cone and spheromak. This is a good result, close to the values of 10 or 12 hours for Enlil (Odstrcil 2003) observed in previous studies (Mays et al. 2015; Riley et al. 2018; Riley & Ben-Nun 2021; Wold et al. 2018). If we use ±12 h as a limit for evaluating the probability of detection of the model, we find that the cone model (14 hits out of 16 events) scores slightly higher than the spheromak model (12 hits out of 16 events). Table 5 shows the RMSE and SD for both cone and spheromak arrival times for the CMEs that arrive within a 12 hour time frame and those that arrive within 24 hours (all ICMEs), as well as the real observed times. All values in this table are below 10 hours. 100% of the ICMEs arrived within 24 hours, and 93% within 18 hours.

thumbnail Fig. 6.

Histogram of the difference between observed and simulated arrival time for the cone (pink) and spheromak (blue) models. Overlapping instances are represented in purple.

Table 5.

Cone and spheromak models root-mean-square error and standard deviation in arrival time, measured in hours.

4.2. Comparison of speed and geomagnetic impact between simulated and real CMEs

We evaluated correlation factors for the maximum value of speed between observed and simulated ICMEs in Events list A. Results are shown in Figure 7 for the cone and spheromak runs. Both cone and spheromak runs show a positive linear correlation between the observed and simulated maximum value of ICME speed as expected. The spheromak model shows a better performance when predicting the maximum speed. It is noteworthy, however, that there remains a significant spread in values; for example, an in situ speed of ∼800 km s−1 may correspond to predictions ranging from 400 to 1000 km s−1.

thumbnail Fig. 7.

Correlation between the maximum value of OMNI speed and the maximum value of cone (top) and spheromak (bottom) speed. The 68%, 95%, and 99% confidence bands are marked in yellow, green, and red, respectively.

The impact of a CME on Earth can be estimated using geomagnetic indices. Here, we use the Kp index that measures global geomagnetic activity. In its current version, EUHFORIA uses the simulation output in the solar wind upstream of the Earth’s magnetosphere to calculate the Kp-index based on Eq. (3), as provided by Newell et al. (2008):

K p = 0.05 + 2.244 × 10 − 4 d Φ MP dt + 2.844 · 10 − 6 n 1 / 2 V 2 . $$ \begin{aligned} K_p = 0.05 + 2.244 \times 10^{-4} \frac{d \Phi _{\rm MP}}{d t} + 2.844 \cdot 10^{-6} n^{1/2} V^2. \end{aligned} $$(3)

Here, dΦMP/dt is the rate at which magnetic flux is opened at the magnetopause, and is defined as

d Φ MP dt = V 4 / 3 B 2 / 3 sin 8 / 3 ( θ c / 2 ) , $$ \begin{aligned} \frac{d \Phi _{\rm MP}}{d t} = V^{4/3} B^{2/3} \sin ^{8/3} (\theta _{\rm c}/2), \end{aligned} $$

where V is solar wind speed, n is density, B is the magnetic field magnitude, and θc = arctan(By/Bz). We compared Kp indices calculated for cone (Kp, cone) and spheromak (Kp, spheromak) models with the corresponding observed Kp values (Kp, observed). We also computed the Kp values using Eq. (3) based on observed solar wind parameters from the OMNI database (Kp, calculated). In this way, in addition to comparing Kp, cone and Kp, spheromak with Kp, observed, we can also compare Kp, cone and Kp, spheromak with Kp, calculated, which gives us a better way of comparing the impact of the different CME models, and one that is independent of the empirical Kp formula used.

In order to evaluate how well EUHFORIA predicts the geoeffectiveness of ICMEs, we classified our events into three groups, depending on their Kp-index

  • No storm observed, Kp ≤ 4;

  • Moderate to strong storm, 5 ≤ Kp ≤ 7;

  • Severe or extreme storm Kp ≥ 8.

The correctness of the prediction of the Kp-index by EUHFORIA is assessed using the following criteria: a prediction from the cone and spheromak models is considered a hit if the maximum predicted Kp value falls within the same interval as Kp, observed (or Kp, calculated), a false alarm if it overestimates the geoeffectiveness of the storm (higher Kp than observed), and a miss if it underestimates it (lower Kp than observed). There is no correct rejection in this case. The maximum value of Kp for each of the selected events can be found in Table 6. Furthermore, Table 7 provides metrics based on the POD, the SR, the SD, and the RMSE.

Table 6.

Maximum values of Kp-indices.

Table 7.

Performance metrics for Kp – indices.

If we first compare the Kp, observed and the Kp, calculated using the measured solar wind parameters in Eq. (3) (i.e. without using the predictions from the EUHFORIA CME models), we can see that they fall within the same Kp interval for ten events. For the remaining six cases, the Kp, calculated overestimates the CME impact at Earth (events 4, 6, 8, 10, 14, and 15; success ratio = 0.63). The Kp, calculated has a RMSE of 1.31 when compared to the observed one, with SD = 0.96 (Table 7).

The cone model correctly predicted the observed geomagnetic impact of the CMEs for eight events (POD = 0.88), overestimated the impact for seven events (3, 6, 8, 10, 13, 14, and 15), and underestimated it for event 2. The RMSE amounts to 2.8, with a SD = 2.20. If we now compare the Kp, cone with the Kp, calculated (instead of the Kp, observed), then the correct predictions increase to 11 events, with an underestimation for 2 events (2, 4) and overestimation for 3 events (3, 13, 15). The RMSE is then improved to 2.40, with SD = 2.25.

The spheromak model shows a poorer performance than the cone model in predicting the level of Kp activity; it predicts a Kp index within the correct interval (compared to Kp, observed) for five events, underestimates it for seven events (2, 4, 5, 6, 9, 12, and 16), and overestimates it for four events (8, 10, 14, and 15), with an SD = 2.18 and RMSE = 2.30. However, comparison of the Kp, calculated shows better results; the spheromak model estimated the correct geomagnetic storm level for eight events, and underestimated for eight events (1, 2, 4, 5, 6, 9, 12, 16) with an SD = 1.93, RMSE = 2.54. These numbers show that the cases where the Kp, spheromak is overestimated are mainly caused by overestimation in the Kp formula (all overestimated cases disappear when we compare with the calculated Kp).

The results of the comparison of simulated versus Kp, calculated for cone and spheromak models are shown in Figure 8. For three events (5, 9, and 12), the spheromak model underestimates the Kp index while the cone model predicts the value in the correct range. The opposite occurs for two events (3, 13), where the cone model overestimates the value, while the spheromak model captures it correctly. This can be explained by the simulated solar wind speed and density in the cone model having higher values than for the spheromak model for these cases, overcompensating the lower magnetic fields encountered by the cone model. For events 3 and 13, the cone model overestimates the speed and density by a great extent, hence abnormally overestimating the Kp index. Another possible reason for the cases where the cone performs better than the spheromak is that, for the latter, even when correctly determining the speed at arrival, an incorrect rotation of the Bz field can influence the resulting Kp.

thumbnail Fig. 8.

Comparison of simulated Kp-index value with Kp, calculated for cone and spheromak models.

5. Results – Event list B: Evaluation of CME arrival forecast

In order to validate the capability of EUHFORIA in forecasting the correct arrival at the Earth, we employed Events list B and the contingency tables approach, as described in Section 3.2. In this case, events for which a CME arrival is both predicted and detected by instruments are considered as hits; a false alarm is considered to be when a CME arrival is predicted, but the ICME is not observed to arrive; a miss is considered as a case where a CME arrives despite lacking a prior prediction; and finally a correct rejection is a case where a CME is neither predicted to arrive nor observed.

A complete summary, including all the classic metrics, is given in Table 8. Figure 9 shows some of the metrics used in this study in a graphical way. EUHFORIA performs well, with a 75% POD in a 12 hour time window (with 4 hours RMSE and SD) and a 100% POD in a 24 hour time window (with 9 hours RMSE and 7.6 hours SD). The bias score (BS) is balanced at unity for 12 hours and shows a slight prevalence of false alarms over misses in the 24 hour time window. The critical success index (CSI) improves when moving from a 12 to a 24 hour time window, as the number of correctly forecasted events increases. The accuracy (Ac) is very high in both time windows, as this metric depends mostly on the correct rejections, where EUHFORIA demonstrates a very good performance. The POFD remains very low for both time windows. The Hanssen and Kuipers discriminant is very close to the POD (as the POFD is very small for both time windows). In summary, the classic metrics show that EUHFORIA is very good at correctly predicting the arrival of ICMEs.

thumbnail Fig. 9.

Performance diagram for the events in Section 2.1.2. The dashed diagonal lines correspond to lines of equal BS, while the blue contours correspond to equal CSI. The coloured dots are used to mark different time intervals allowed for the ICME to arrive. The shortest interval is 1 hour (no ICME arrivals) and the largest one is 24 hours (for which all the ICMEs arrive).

Table 8.

Metrics for the set of CMEs in 2010 and 2012.

6. Conclusions

In this paper, we present a detailed analysis of the validation of the cone and spheromak CME models in the framework of EUHFORIA. We used two datasets to validate the geoeffectiveness and arrival-time predictions respectively. The first dataset is composed of 16 CMEs with an ICME counterpart that arrives at Earth. In this way, we can compare the in situ solar wind and magnetic field parameters as measured at the L1 point. Furthermore, we compared their geomagnetic impact by means of the Kp-index. Input parameters for all the CMEs were constrained from observations and used to run EUHFORIA.

Results show that cone CMEs tend to arrive earlier than spheromak ones. All the ICMEs arrive within 24 hours. The RMSE value is 9 hours for both cone and spheromak. These values are comparable to the 10 hours found by Mays et al. (2015), Riley & Ben-Nun (2021), and Wold et al. (2018) for similar MHD models. If we focus on the 12 h time frame, the probability of detection of the CME for cone numerical simulations is slightly higher than for spheromak runs, with 14 events out of 16 arriving, compared to 12 events for spheromak runs. Regarding the obtained ICME speeds, both cone and spheromak runs indicate a positive correlation between the observed and simulated maximum value of ICME speed as expected, with a large spread. The spheromak model shows higher accuracy when predicting the maximum speed.

We estimated the impact of an ICME at Earth by means of the Kp-index. We compared Kp indices calculated for cone (Kp, cone) and spheromak (Kp, spheromak) models, both with the observed Kp values (Kp, observed) and with the calculated Kp values using Eq. (3) based on observed solar wind parameters from the OMNI database (Kp, calculated). The comparison between the Kp, calculated and Kp, observed has an RMSE of 1.31. The cone model correctly forecasts the Kp, calculated range for 11 out of 16 events (69%) with an RMSE of 2.4. If we instead use the Kp, observed, the correct forecast reduces to 8 out of 16 events (50%) and the RMSE value reaches 2.8. The spheromak model forecasts Kp within the correct interval for only five events (31%) when compared with Kp, observed, with an RMSE value of 2.3. However, comparison with Kp, calculated increases the correct forecast to eight events (50%) with a RMSE of 2.54. The cases where the Kp, spheromak is overestimated are caused by an overestimation introduced by the Kp formula. In principle, one would have expected the spheromak model to provide a better estimation of Kp, but this was not the case here. This could be due to edge encounters. Because of its compact spherical shape and lack of CME legs, the spheromak has difficulty in modelling the events when ICMEs impact Earth with their flanks. One more possible reason for the cases where the cone performs better than the spheromak is that for the latter, even when correctly determining the speed at arrival, an incorrect rotation of the Bz field can influence the Kp result. In the case of the cone model, there is no prescribed internal magnetic field within the CMEs. Nevertheless, a magnetic field is present there, as everywhere else in the EUHFORIA simulation domain. This magnetic field is affected by the CME plasma dynamics (e.g. compression), creating a magnetic field inside the ICME that can be distinguished from the background solar wind. New CME flux rope models are currently being tested with EUHFORIA, and an improvement in regards to this important aspect is expected in the future. Recent developments in flux rope CME models include the implementation of the flux rope in 3D (FRI3D) model (Maharana et al. 2022) and a toroidal CME model (Linan et al. 2024) in EUHFORIA.

In order to evaluate EUHFORIA forecasts in terms of arrival (hits or misses) of CMEs, we used a second (larger) dataset of CMEs for which their arrival at Earth is not a condition. We took all front-sided CMEs wider than 60° and faster than 350 km s−1 over a time period of eight months. Four months were taken during solar minimum (June–September 2010) and the other four during solar maximum (June–September 2012). The final dataset contains 48 CMEs; these were simulated with the EUHFORIA cone model in order to predict Earth arrivals or misses. The spheromak model was not used in this study, as we are mainly interested in evaluating the arrival of ICMEs and not their internal magnetic field configuration. EUHFORIA showed a 75% probability of detection in a 12 hour time window (with 4 hours RMSE) and 100% probability of detection in a 24 hours time window (with 9 hours RMSE). In this dataset, the events were not carefully selected as in the dataset of 16 CME–ICME pairs, and our findings therefore show that EUHFORIA can perform well even when CMEs are not handpicked.

These results validate the use of cone and spheromak CME models in forecasting space weather in real time. EUHFORIA is currently being used for such purposes by the space weather forecast team at the Royal Observatory of Belgium.

Acknowledgments

EUHFORIA was created as a joint effort between KU Leuven and the University of Helsinki and was developed further by the the project EUHFORIA 2.0, a European Union’s Horizon 2020 research and innovation programs under grant agreement No. 870405. These results were also obtained in the framework of the projects C14/19/089 (C1 project Internal Funds KU Leuven), G.0D07.19N and G.0B58.23N (FWO-Vlaanderen), 4000134474 SIDC Data Exploitation (ESA Prodex-12), and BELSPO projects BR/165/A2/CCSOM and B2/191/P1/SWiM. The Royal Observatory of Belgium team thanks the Belgian Federal Science Policy Office (BELSPO) for the provision of financial support in the framework of the PRODEX Programme of the European Space Agency (ESA) under contract numbers 4000134088, 4000112292, 4000134474, and 4000136424. The OMNI data were obtained from the GSFC/SPDF OMNIWeb interface at https://omniweb.gsfc.nasa.gov. SOHO LASCO CME catalog is generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. SOHO is a project of international cooperation between ESA and NASA. RS acknowledges support from the Academy of Finland Grant 350015. EA acknowledges support from the Academy of Finland/Research Council of Finland (Postdoctoral Researcher grant number 322455 and Academy Research Fellow grant number 355659). JP acknowledges support from the Academy of Finland project SWATCH (343581). ES research was supported by an appointment to the NASA Postdoctoral Program at the NASA Goddard Space Flight Center, administered by Oak Ridge Associated Universities under contract with NASA. We acknowledge the Community Coordinated Modeling Center (CCMC) at Goddard Space Flight Center for the use of StereoCAT, https://ccmc.gsfc.nasa.gov/analysis/stereo

References

  1. Arge, C. N., Odstrcil, D., Pizzo, V. J., & Mayer, L. R. 2003, AIP Conf. Ser., 679, 190 [Google Scholar]
  2. Bothmer, V., & Schwenn, R. 1998, Ann. Geophys., 16, 1 [Google Scholar]
  3. Brueckner, G. E., Howard, R. A., Koomen, M. J., et al. 1995, Sol. Phys., 162, 357 [NASA ADS] [CrossRef] [Google Scholar]
  4. Cliver, E. W., Kahler, S. W., Kazachenko, M., & Shimojo, M. 2019, ApJ, 877, 11 [NASA ADS] [CrossRef] [Google Scholar]
  5. Davies, J. A., Harrison, R. A., Rouillard, A. P., et al. 2009, Geophys. Res. Lett., 36, L02102 [Google Scholar]
  6. Delaboudinière, J.-P., Artzner, G. E., Brunaud, J., et al. 1995, Sol. Phys., 162, 291 [CrossRef] [Google Scholar]
  7. Dewey, R. M., Baker, D. N., Anderson, B. J., et al. 2015, J. Geophys. Res.: Space Phys., 120, 5667 [NASA ADS] [CrossRef] [Google Scholar]
  8. Domingo, V., Fleck, B., & Poland, A. I. 1995, Sol. Phys., 162, 1 [Google Scholar]
  9. Dryer, M., Liou, K., Wu, C., et al. 2012, AGU Fall Meeting Abstracts, 2012, SH44B–04 [Google Scholar]
  10. Gopalswamy, N., Yashiro, S., Michalek, G., et al. 2009, Earth Moon Planets, 104, 295 [NASA ADS] [CrossRef] [Google Scholar]
  11. Gopalswamy, N., Yashiro, S., Akiyama, S., & Xie, H. 2017, Sol. Phys., 292, 65 [NASA ADS] [CrossRef] [Google Scholar]
  12. Gopalswamy, N., Akiyama, S., Yashiro, S., & Xie, H. 2018, IAU Symp., 335, 258 [NASA ADS] [Google Scholar]
  13. Hanaoka, Y., & Sakurai, T. 2017, ApJ, 851, 130 [NASA ADS] [CrossRef] [Google Scholar]
  14. Howard, R. A., Michels, D. J., Sheeley, N. R., & Koomen, M. J. 1982, ApJ, 263, L101 [NASA ADS] [CrossRef] [Google Scholar]
  15. Howard, R. A., Moses, J. D., Vourlidas, A., et al. 2008, Space Sci. Rev., 136, 67 [NASA ADS] [CrossRef] [Google Scholar]
  16. Hundhausen, A. J., Burkepile, J. T., & St. Cyr, O. C. 1994, J. Geophys. Res., 99, 6543 [NASA ADS] [CrossRef] [Google Scholar]
  17. Janvier, M., Aulanier, G., Bommier, V., et al. 2014, ApJ, 788, 60 [Google Scholar]
  18. Kaiser, M. L., Kucera, T. A., Davila, J. M., et al. 2008, Space Sci. Rev., 136, 5 [Google Scholar]
  19. Kay, C., & Palmerio, E. 2024, Space Weather, 22, e2023SW003796 [NASA ADS] [CrossRef] [Google Scholar]
  20. Kazachenko, M. D., Fisher, G. H., Welsch, B. T., Liu, Y., & Sun, X. 2015, ApJ, 811, 16 [NASA ADS] [CrossRef] [Google Scholar]
  21. Kazachenko, M. D., Lynch, B. J., Welsch, B. T., & Sun, X. 2017, ApJ, 845, 49 [NASA ADS] [CrossRef] [Google Scholar]
  22. Kilpua, E. K. J., Balogh, A., von Steiger, R., & Liu, Y. D. 2017a, Space Sci. Rev., 212, 1271 [CrossRef] [Google Scholar]
  23. Kilpua, E., Koskinen, H. E. J., & Pulkkinen, T. I. 2017b, Liv. Rev. Sol. Phys., 14, 5 [Google Scholar]
  24. Kilpua, E. K. J., Lugaz, N., Mays, M. L., & Temmer, M. 2019, Space Weather, 17, 498 [NASA ADS] [CrossRef] [Google Scholar]
  25. Koskinen, H. E. J., Baker, D. N., Balogh, A., et al. 2017, Space Sci. Rev., 212, 1137 [Google Scholar]
  26. Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, Sol. Phys., 275, 17 [Google Scholar]
  27. Linan, L., Maharana, A., Poedts, S., Schmieder, B., & Keppens, R. 2024, A&A, 681, A103 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  28. Liou, K., Wu, C.-C., Dryer, M., et al. 2014, J. Atmos. Sol. Terr. Phys., 121, 32 [NASA ADS] [CrossRef] [Google Scholar]
  29. Liu, Y., Hoeksema, J. T., Bobra, M., et al. 2014, ApJ, 785, 13 [NASA ADS] [CrossRef] [Google Scholar]
  30. Longcope, D., Beveridge, C., Qiu, J., et al. 2007, Sol. Phys., 244, 45 [Google Scholar]
  31. Maharana, A., Isavnin, A., Scolini, C., et al. 2022, Adv. Space Res., 70, 1641 [NASA ADS] [CrossRef] [Google Scholar]
  32. Mays, M. L., Taktakishvili, A., Pulkkinen, A., et al. 2015, Sol. Phys., 290, 1775 [CrossRef] [Google Scholar]
  33. Möstl, C., Rollett, T., Lugaz, N., et al. 2011, ApJ, 741, 34 [CrossRef] [Google Scholar]
  34. Newell, P. T., Sotirelis, T., Liou, K., & Rich, F. J. 2008, J. Geophys. Res.: Space Phys., 113, A04218 [NASA ADS] [CrossRef] [Google Scholar]
  35. Odstrcil, D. 2003, Adv. Space Res., 32, 497 [CrossRef] [Google Scholar]
  36. Odstrčil, D., & Pizzo, V. J. 1999, J. Geophys. Res., 104, 483 [CrossRef] [Google Scholar]
  37. Palmerio, E., Kilpua, E. K. J., James, A. W., et al. 2017, Sol. Phys., 292, 39 [Google Scholar]
  38. Pevtsov, A. A., Canfield, R. C., & Metcalf, T. R. 1995, ApJ, 440, L109 [NASA ADS] [CrossRef] [Google Scholar]
  39. Pomoell, J., & Poedts, S. 2018, J. Space Weather Space Clim., 8, A35 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  40. Qiu, J., Hu, Q., Howard, T. A., & Yurchyshyn, V. B. 2007, ApJ, 659, 758 [Google Scholar]
  41. Riley, P., & Ben-Nun, M. 2021, Space Weather, 19, e02775 [CrossRef] [Google Scholar]
  42. Riley, P., Mays, M. L., Andries, J., et al. 2018, Space Weather, 16, 1245 [NASA ADS] [CrossRef] [Google Scholar]
  43. Rodriguez, L., Zhukov, A. N., Cid, C., et al. 2009, Space Weather, 7, S06003 [NASA ADS] [CrossRef] [Google Scholar]
  44. Rodriguez, L., Mierla, M., Zhukov, A. N., West, M., & Kilpua, E. 2011, Sol. Phys., 270, 561 [CrossRef] [Google Scholar]
  45. Rodriguez, L., Scolini, C., Mierla, M., Zhukov, A. N., & West, M. J. 2020, Space Weather, 18, e02533 [NASA ADS] [CrossRef] [Google Scholar]
  46. Rust, D. M., & Kumar, A. 1996, ApJ, 464, L199 [NASA ADS] [CrossRef] [Google Scholar]
  47. Sarkar, R., Gopalswamy, N., & Srivastava, N. 2020, ApJ, 888, 121 [NASA ADS] [CrossRef] [Google Scholar]
  48. Sarkar, R., Pomoell, J., Kilpua, E., et al. 2024, ApJS, 270, 18 [NASA ADS] [CrossRef] [Google Scholar]
  49. Scherrer, P. H., Schou, J., Bush, R. I., et al. 2012, Sol. Phys., 275, 207 [Google Scholar]
  50. Schwenn, R. 2006, Liv. Rev. Sol. Phys., 3, 2 [Google Scholar]
  51. Scolini, C., Rodriguez, L., Mierla, M., Pomoell, J., & Poedts, S. 2019, A&A, 626, A122 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  52. Scolini, C., Chané, E., Temmer, M., et al. 2020, ApJS, 247, 21 [Google Scholar]
  53. Sheeley, N. R. Jr., Martin, S. F., Panasenco, O., & Warren, H. P., 2013, ApJ, 772, 88 [NASA ADS] [CrossRef] [Google Scholar]
  54. Temmer, M. 2021, Liv. Rev. Sol. Phys., 18, 4 [NASA ADS] [CrossRef] [Google Scholar]
  55. Thernisien, A. 2011, ApJS, 194, 33 [Google Scholar]
  56. Thernisien, A. F. R., Howard, R. A., & Vourlidas, A. 2006, ApJ, 652, 763 [Google Scholar]
  57. Thernisien, A., Vourlidas, A., & Howard, R. A. 2009, Sol. Phys., 256, 111 [Google Scholar]
  58. Tschernitz, J., Veronig, A. M., Thalmann, J. K., Hinterreiter, J., & Pötzi, W. 2018, ApJ, 853, 41 [NASA ADS] [CrossRef] [Google Scholar]
  59. Verbeke, C., Pomoell, J., & Poedts, S. 2019a, A&A, 627, A111 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Verbeke, C., Mays, M. L., Temmer, M., et al. 2019b, Space Weather, 17, 6 [CrossRef] [Google Scholar]
  61. Verbeke, C., Mays, M. L., Kay, C., et al. 2023, Adv. Space Res., 72, 5243 [Google Scholar]
  62. Webb, D. F., Lepping, R. P., Burlaga, L. F., et al. 2000, J. Geophys. Res., 105, 27251 [NASA ADS] [CrossRef] [Google Scholar]
  63. Wold, A. M., Mays, M. L., Taktakishvili, A., et al. 2018, J. Space Weather Space Clim., 8, A17 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  64. Xie, H., Ofman, L., & Lawrence, G. 2004, J. Geophys. Res.: Space Phys., 109, A03109 [NASA ADS] [Google Scholar]
  65. Zhukov, A. N. 2007, Astrophys. Space Sci. Lib., 344, 5 [NASA ADS] [CrossRef] [Google Scholar]
  66. Zurbuchen, T. H., & Richardson, I. G. 2006, Space Sci. Rev., 123, 31 [Google Scholar]

Appendix A: Supplementary events for improving background solar wind modeling

Table A.1 provides detailed information on the additional events that occurred in the days preceding Runs 5, 6, and 14. These events were included in the simulation in order to create more realistic conditions for the main CMEs. It is important to note that the CMEs listed in the supplementary Table A.1 are not considered to interact with the CMEs from the main list in Table 1, but occurred before them. The main characteristics of these CMEs, as presented in the table, were obtained through StereoCat fitting.

Table A.1.

List of CMEs that were not initially part of the study, but were added to the runs to create more realistic solar wind conditions. StereoCat was used to collect CME parameters.

Appendix B: EUHFORIA runs - visualisation of selected events

In this Appendix, a series of plots is provided for each of the selected events. These plots combine observational data obtained from OMNI with the results of EUHFORIA simulations for both cone and spheromak models. Each line in the plots is colour coded for clarity: purple lines represent cone simulation results, green lines depict spheromak simulation with a standard setup density of 1e-18. Observational data are represented by black lines. To aid interpretation, vertical lines of corresponding colours indicate the arrival time of the ICME within each plot. The Kp value for all scenarios is determined using Eq. 3 of Newell et al. (2008).

thumbnail Fig. B.1.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 1.

thumbnail Fig. B.2.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 2.

thumbnail Fig. B.3.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 3.

thumbnail Fig. B.4.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 4.

thumbnail Fig. B.5.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 5.

thumbnail Fig. B.6.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 6.

thumbnail Fig. B.7.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 7.

thumbnail Fig. B.8.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 8.

thumbnail Fig. B.9.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 9.

thumbnail Fig. B.10.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 10.

thumbnail Fig. B.11.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 11.

thumbnail Fig. B.12.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 12.

thumbnail Fig. B.13.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 13.

thumbnail Fig. B.14.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 14.

thumbnail Fig. B.15.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 15.

thumbnail Fig. B.16.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 16.

All Tables

Table 1.

CME–ICME pairs and simulation results.

In the text
Table 2.

Three-dimensional CME parameters as derived from the GCS fitting.

In the text
Table 3.

Magnetic parameters of CMEs.

In the text
Table 4.

Skill scores based on Verbeke et al. (2019b).

In the text
Table 5.

Cone and spheromak models root-mean-square error and standard deviation in arrival time, measured in hours.

In the text
Table 6.

Maximum values of Kp-indices.

In the text
Table 7.

Performance metrics for Kp – indices.

In the text
Table 8.

Metrics for the set of CMEs in 2010 and 2012.

In the text
Table A.1.

List of CMEs that were not initially part of the study, but were added to the runs to create more realistic solar wind conditions. StereoCat was used to collect CME parameters.

In the text

All Figures

thumbnail Fig. 1.

GCS reconstruction of the CME observed at 23:54 UT on 29 September 2013. The fit can be seen in the bottom row. The images shown are from COR2-B (left panel), LASCO-C3 (middle panel), and COR2-A (right panel).
In the text
thumbnail Fig. 2.

Multi-wavelength observations of the source region of Event no. 12. Panel a Depicts the filament channel as indicated by the yellow dashed line in AIA (Lemen et al. 2012) 304 Å image. The red dashed boundary line in panel b marks the PEA as observed in AIA 193 Å image. Panel c Illustrates the line-of-sight component of the HMI (Scherrer et al. 2012) magnetic field. The red dashed boundary and the yellow dashed line in (c) are the over-plotted PEA region and filament channel, respectively. The two ends of the reverse S-shaped filament channel are marked by the green circles and the underlying magnetic polarities are shown, which indicate a northward-pointing left-handed flux-rope.
In the text
thumbnail Fig. 3.

Equatorial and meridional slices for cone (top panel) and spheromak (bottom panel) models for Event 8.
In the text
thumbnail Fig. 4.

Schematics of the cone model, adapted from Dewey et al. (2015).
In the text
thumbnail Fig. 5.

Magnetic field lines depicting the structure of the spheromak CME model. The grey plane shows the meridional HEEQ y = 0–plane. From Verbeke et al. (2019a).
In the text
thumbnail Fig. 6.

Histogram of the difference between observed and simulated arrival time for the cone (pink) and spheromak (blue) models. Overlapping instances are represented in purple.
In the text
thumbnail Fig. 7.

Correlation between the maximum value of OMNI speed and the maximum value of cone (top) and spheromak (bottom) speed. The 68%, 95%, and 99% confidence bands are marked in yellow, green, and red, respectively.
In the text
thumbnail Fig. 8.

Comparison of simulated Kp-index value with Kp, calculated for cone and spheromak models.
In the text
thumbnail Fig. 9.

Performance diagram for the events in Section 2.1.2. The dashed diagonal lines correspond to lines of equal BS, while the blue contours correspond to equal CSI. The coloured dots are used to mark different time intervals allowed for the ICME to arrive. The shortest interval is 1 hour (no ICME arrivals) and the largest one is 24 hours (for which all the ICMEs arrive).
In the text
thumbnail Fig. B.1.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 1.
In the text
thumbnail Fig. B.2.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 2.
In the text
thumbnail Fig. B.3.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 3.
In the text
thumbnail Fig. B.4.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 4.
In the text
thumbnail Fig. B.5.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 5.
In the text
thumbnail Fig. B.6.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 6.
In the text
thumbnail Fig. B.7.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 7.
In the text
thumbnail Fig. B.8.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 8.
In the text
thumbnail Fig. B.9.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 9.
In the text
thumbnail Fig. B.10.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 10.
In the text
thumbnail Fig. B.11.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 11.
In the text
thumbnail Fig. B.12.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 12.
In the text
thumbnail Fig. B.13.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 13.
In the text
thumbnail Fig. B.14.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 14.
In the text
thumbnail Fig. B.15.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 15.
In the text
thumbnail Fig. B.16.

Comparison of real data with EUHFORIA cone and spheromak runs for Event 16.
In the text

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