# Calibrating the WSA Model in EUHFORIA Based on Parker Solar Probe Observations

E. Samara, C. N. Arge, R. F. Pinto, J. Magdalenić, N. Wijsen, M. L. Stevens, L. Rodriguez, S. Poedts

► To cite this version:

E. Samara, C. N. Arge, R. F. Pinto, J. Magdalenić, N. Wijsen, et al. Calibrating the WSA Model in EUHFORIA Based on Parker Solar Probe Observations. The Astrophysical Journal, 2024, 971, 10.3847/1538-4357/ad53c6. insu-04833958

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# Calibrating the WSA Model in EUHFORIA Based on Parker Solar Probe Observations

E. Samara¹, C. N. Arge¹, R. F. Pinto²,³, J. Magdalenic⁴,⁵, N. Wijsen⁵, M. L. Stevens⁶, L. Rodriguez⁴, and S. Poedts⁵,⁷

¹NASA Goddard Space Flight Center, Greenbelt, MD, USA; evangelia.samara@nasa.gov

²IRAP, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France

³InforMarty, Toulouse, France

⁴Solar-Terrestrial Centre of Excellence—SIDC, Royal Observatory of Belgium, Brussels, Belgium

⁵CmPA/Department of Mathematics, KU Leuven, Leuven, Belgium

⁶Smithsonian Astrophysical Observatory, Cambridge, MA, USA

⁷Institute of Physics, University of Maria Curie-Skłodowska, Lublin, Poland

Received 2023 October 25; revised 2024 May 19; accepted 2024 May 31; published 2024 August 7

## Abstract

We employ Parker Solar Probe (PSP) observations during the latest solar minimum period (years 2018–2021) to calibrate the version of the Wang–Sheeley–Arge (WSA) coronal model used in the European Heliospheric Forecasting Information Asset (EUHFORIA). WSA provides a set of boundary conditions at 0.1 au necessary to initiate the heliospheric part of EUHFORIA, namely, the domain extending beyond the solar Alfvénic point. To calibrate WSA, we observationally constrain four constants in the WSA semiempirical formula based on PSP observations. We show how the updated (after the calibration) WSA boundary conditions at 0.1 au are compared to PSP observations at similar distances, and we further propagate these conditions in the heliosphere according to EUHFORIA’s magnetohydrodynamic (MHD) approach. We assess the predictions at Earth based on the dynamic time-warping technique. Our findings suggest that, for the period of interest, the WSA configurations that resembled optimally the PSP observations close to the Sun were different from the ones needed to provide better predictions at Earth. One reason for this discrepancy can be attributed to the scarcity of fast solar wind velocities recorded by PSP. The calibration of the model was performed based on unexpectedly slow velocities that did not allow us to achieve generally and globally improved solar wind predictions compared to older studies. Other reasons can be attributed to missing physical processes from the heliospheric part of EUHFORIA but also the fact that the currently employed WSA relationship, as coupled to the heliospheric MHD domain, may need a global reformulation beyond that of just updating the four constant factors that were taken into account in this study.

Unified Astronomy Thesaurus concepts: Solar wind (1534); Magnetohydrodynamics (1964); Heliosphere (711); Space weather (2037)

## 1. Introduction

Validation of space weather forecasting models is crucial for accurately predicting space weather conditions in the heliosphere. This is necessary to mitigate possibly destructive consequences of extreme space weather on technological infrastructure at Earth or at any point in the heliosphere where man-made technologies exist (Hapgood 2011; Green & Baker 2015; Schrijver et al. 2015). However, the pace at which space weather forecasting tools evolve has outstripped the pace of improvements in the quality of the input data they employ (MacNeice et al. 2018). Minimization of uncertainties in those data is one way to advance our prediction capabilities. Calibration of models with observations is another. Both directions require the advent of novel missions with cutting-edge instrumentation that will not only provide data we never had before but also help improve the existing observations that are used to drive and validate models.

The Parker Solar Probe (PSP) is one of such novel missions launched only a few years ago (Fox et al. 2016; Szabo 2018; Parker 2020). In an effort to address a number of physical questions that the solar community has been struggling to answer for the past decades, e.g., how the solar corona is heated or how the fast solar wind and coronal mass ejections (CMEs)

are accelerated, PSP approaches the Sun unprecedentedly closely (eventually as close as $\approx 9.9 R_\odot$). This provides a unique opportunity to study the in situ conditions at close proximity to the Sun, as well as to take wide-field images of solar structures and outflows. In situ observations at this region can be very useful for the calibration of models employed to reconstruct solar wind conditions close to the Sun. Such models, usually called coronal models, reconstruct the global 3D structure of the magnetic corona up to the Alfvénic point and provide the boundary conditions that heliospheric models need as input to initiate and propagate the solar wind in the inner heliosphere.

In this paper, we aim to calibrate the implementation of the Wang–Sheeley–Arge (WSA) coronal model (Arge et al. 2003, 2004) used in the European Heliospheric Forecasting Information Asset (EUHFORIA; Pomoell & Poedts 2018) by employing PSP observations. We note that the version of WSA in EUHFORIA is different from the original WSA model (see the differences between Pomoell & Poedts 2018 and Arge et al. 2003, 2004). WSA has been routinely used for many years to reconstruct the solar wind conditions at close-to-the-Sun distances and predict solar wind velocities and magnetic field polarities in the heliosphere based on a 1D kinematic code. In the frame of this study, we only use the first (or coronal) part of WSA. The boundary conditions it generates are used to initiate the heliospheric part of EUHFORIA at 0.1 au (Pomoell & Poedts 2018). The degree of EUHFORIA’s success to reliably forecast space weather conditions throughout the heliosphere

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
depends on many factors, one of the most important being the quality of the boundary conditions from WSA. Until recently, it was not possible to validate them by employing in situ observations. However, this is currently possible thanks to the unique observations from PSP, which is the first spacecraft to cross the boundary of 0.1 au. Therefore, the aim is to investigate how much we can improve solar wind modeling in the heliosphere by undertaking the task to calibrate the WSA version used in EUHFORIA based on PSP data.

## 2. The WSA Model in EUHFORIA

To initiate the heliospheric part of EUHFORIA, a set of solar wind boundary conditions are needed at the inner boundary of the heliospheric domain (0.1 au). The first of them, the radial velocity ($v_r$), is provided by the WSA model based on the following equation:

$$v_r(f, d) = V_0 + \frac{V_1}{(1+f)^\alpha} \left[ 1 - 0.8 \exp\left(-\left(\frac{d}{w}\right)^\beta\right) \right]^3. \quad (1)$$

The constants used by default in EUHFORIA are $V_0 = 240 \text{ km s}^{-1}$, $V_1 = 675 \text{ km s}^{-1}$, $\alpha = 0.222$, $\beta = 1.25$, and $w = 0.02 \text{ rad}$ (see Pomoell & Poedts 2018 for more details). The parameter $f$ denotes the flux-tube expansion factor and is defined as

$$f = \left(\frac{R_{\odot}}{R_b}\right)^2 \frac{B_r(R_{\odot}, \theta, \phi)}{B_b(R_b, \theta_b, \phi_b)}, \quad (2)$$

where $R_b = 0.1 \text{ au}$, while $B_r$ and $B_b$ are the radial magnetic fields at the photosphere and at 0.1 au, respectively. For the purposes of this study, we revised this definition by taking $R_b = 2.5 R_{\odot}$ and $B_b$ at $2.5 R_{\odot}$, according to the original Wang-Sheeley prescription (see, e.g., Wang & Sheeley 1997). The parameter $d$ is the minimum angular distance of a magnetic flux-tube footpoint to the closest coronal hole (CH) boundary, otherwise known as the “distance to the CH boundary.” Both $f$ and $d$ are calculated based on the geometry of the magnetic flux tubes after the reconstruction of the 3D solar corona based on the potential field source surface (PFSS; Altschuler & Newkirk 1969; Schatten et al. 1969; Wiegelmann et al. 2017) and the Schatten current sheet (Schatten 1971) models.

With Equation (1) used to specify solar wind velocities at 0.1 au, the remaining parameters needed to initiate the heliospheric part of EUHFORIA (i.e., number density $n$, temperature $T$, and radial magnetic field $B_r$) are calculated as follows:

$$n = n_{\text{fsw}} \cdot (v_{\text{fsw}}/v_r)^2, \quad (3)$$

$$T = T_{\text{fsw}} \cdot (\rho_{\text{fsw}}/\rho), \quad (4)$$

and

$$B_r = \operatorname{sgn}(B_{\text{corona}}) \cdot B_{\text{fsw}} \cdot (v_r/v_{\text{fsw}}), \quad (5)$$

where $v_{\text{fsw}} = 675 \text{ km s}^{-1}$ is the velocity of the fast solar wind that carries a magnetic field of $B_{\text{fsw}} = 300 \text{ nT}$ at 0.1 au. The plasma number density of the fast solar wind at the same radius is $n_{\text{fsw}} = 300 \text{ cm}^{-3}$, while $\operatorname{sgn}(B_{\text{corona}})$ is the sign of the magnetic field as given by the coronal model. Also, the plasma thermal pressure is constant at the boundary and equal to $P = 3.3 \text{ nPa}$, corresponding to a temperature of $T_{\text{fsw}} = 0.8 \text{ MK}$ in the fast solar wind (see Pomoell & Poedts 2018 for more

details). The parameter $\rho$ denotes the mass density with $\rho_{\text{fsw}} = 0.5 n_{\text{fsw}} m_p$, where $m_p$ is the proton mass.

Equation (1) is of utmost importance since it provides velocities at 0.1 au, based on which all other plasma and magnetic parameters are calculated. However, it is interesting to understand how this semiempirical formula was first derived. If we go back to the literature (Arge et al. 2003, 2004; van der Holst et al. 2010), we see that Equation (1) was formulated after ballistically mapping the solar wind from L1 back to 0.1 au and searching for patterns between speeds and a number of photospheric/coronal parameters. A large number of test functions and values of constants were tried in Equation (1) until a good comparison with observations at 1 au was achieved, after propagating the WSA velocities ballistically to Earth using a simple 1D kinematic model and a specific type of magnetogram (originally Mount Wilson Solar Observatory maps and, more recently, Global Oscillation Network Group (GONG) and Vector Spectromagnetograph (VSM) maps). However, a kinematic model is different from a magnetohydrodynamic (MHD) polytropic model (as EUHFORIA) in the following ways. First, the velocity of the solar wind in the kinematic model is radial and does not change with distance except to conserve mass and mass flux at the stream interaction regions (Kim et al. 2014). No acceleration of the solar wind takes place as it propagates outward, only decelerations at the stream-interaction regions. On the other hand, an MHD polytropic model accelerates the supersonic and super-Alfvénic solar wind due to polytropic expansion, and it takes into account much more complex stream-interaction dynamics. Therefore, it is apparent that Equation (1) does not seem to be consistent when used to produce boundary conditions for 3D MHD polytropic models.

To account for this inconsistency, a number of ad hoc assumptions were adopted in EUHFORIA (and in other models similar to it, such as Enlil; see McGregor et al. 2008 and Owens et al. 2008 for more details). First, $50 \text{ km s}^{-1}$ are subtracted from the velocities at 0.1 au to account for the acceleration caused by the MHD heliospheric model when it propagates velocities in the interplanetary space (Pomoell & Poedts 2018). Second, velocities at 0.1 au are capped between a range of usually [275, 625] km s$^{-1}$. The reason of these constraints has not been clearly justified throughout the literature. The main argument behind the upper limit is that velocities above $625 \text{ km s}^{-1}$ tend to overestimate the fast solar wind at Earth. On the other hand, the reasoning behind the lower limit is that velocities below $275 \text{ km s}^{-1}$ could be sub-Alfvénic, something that it is not handled correctly by the MHD code. Even though these assumptions help us reconstruct the large-scale structure of the solar wind at Earth, we often miss the precise prediction of, e.g., well-defined high-speed streams (HSSs; see, for example, Hinterreiter et al. 2019; Samara et al. 2021). Moreover, the dynamics between the slow and the fast solar wind are generally poorly reproduced (see, e.g., Samara et al. 2022). However, it will be unfair to claim that the not fully accurate performance of EUHFORIA (and similar models) is solely caused because of this discrepancy. The problem of improving solar wind modeling is a multivariable problem that depends on a number of parameters, such as the magnetograms used, the kind of model used and the assumptions made in it, and the phase of the solar cycle, etc. In the framework of this paper, we will only focus on dealing with the discrepancy discussed above.
<figure><img src="image_4.png" /><figcaption>**Figure 1.** The lowest velocities observed by PSP between 0.1 and 0.4 au during the first eight encounters. The velocity range is restricted between 100 and 240 km s⁻¹. The points that were averaged for the calculation of the lowest velocity that PSP recorded (V₀), are circled in magenta (see the text for more details).</figcaption></figure>

This work is inspired by the study of McGregor et al. (2011) who calibrated the WSA equation in Enlil. Their study relied on Helios data to perform the calibration since Helios was the only mission before PSP to have approached the Sun closer than any other mission had ever done before (up to 0.3 au). Their calibrated solar wind results proved to better reconstruct the solar wind velocities at Earth. They also proved to better reconstruct the Ulysses measurements. Now, the proximity of PSP close to the Sun gives us the unprecedented chance to use more accurate data to calibrate our model and improve solar wind predictions by applying the method of McGregor et al. (2011).

# 3. Calibrating the WSA Equation

## 3.1. Data Sets

In EUHFORIA, the WSA velocities at the boundary are typically produced with 2° resolution in both longitude and latitude on a 3D sphere of a radius equal to 0.1 au. For a proper calibration of those velocities, we would ideally need observations at exactly 0.1 au for all the latitudes and longitudes of that sphere. This is, of course, not possible since (a) the orbit of PSP is elliptical in the ecliptic plane, so it only records data within a very restricted latitudinal zone (≈±5° around the solar equator), and (b) PSP only stays shortly close to 0.1 au due to Kepler's second law.

To compare the WSA velocities with PSP data and perform the calibration, we first removed the influence of CMEs from the PSP observations based on the HELIO4CAST interplanetary CME catalog (Möstl et al. 2017, 2020). Then, we made the assumption that WSA velocities within the latitudinal zone of ±5° should resemble PSP velocities between 0.1 and 0.4 au. The reason we chose to compare our modeled data with measurements from an extended radial zone is twofold: first, because PSP measurements very close to 0.1 au are statistically poor (there are not so many data points to perform a proper comparison and calibration); second, because McGregor et al. (2011) had relied on Helios measurements between 0.3 and 0.4 au to perform the calibration of the WSA velocities in Enlil. Due to lack of observations at close-to-the-Sun distances, this was the best they could do. Therefore, we decided to retain McGregor's radial range and extend it downward to 0.1 au with PSP data. The longitudes of the WSA velocities taken into account were also in accordance with the longitudinal PSP

passage for the periods of interest. The calibration was performed based on level-3 10 minute cadence data from the Solar Probe Cup (Case et al. 2020) and Solar Probe ANalyzer (Whittlesey et al. 2020) instruments on board PSP for the first eight encounters that took place during 2018–2021 (invalid data have been discarded). These years are around the minimum phase of solar cycle 24/25, and the data selection was restricted to those in order to have minimal influence from transient solar phenomena (such as CMEs) that contaminate the solar wind measurements.

## 3.2. Calibration of V₀

The terms subject to calibration in Equation (1) are four: V₀, V₁, β, and w. For a global calibration of the WSA formula, all constant parameters should be calibrated. Nevertheless, we chose to focus on the aforementioned four because they can be fine-tuned based on PSP observations and past studies (McGregor et al. 2011). We first discuss V₀, which should reflect the lowest velocity close to the 0.1 au boundary. Its default value is currently 240 km s⁻¹ (see Equation (1)), and it represents the lowest solar wind velocity typically seen at the vicinity of Earth. To understand what is the best value to update V₀, we plot in Figure 1 the velocities up to 240 km s⁻¹ recorded by PSP between 0.1 and 0.4 au during the first eight encounters. Based on this figure, V₀ should be replaced by ≈177 km s⁻¹ since this is the lowest velocity recorded at ≈0.11 au. However, this value is not representative of the velocities seen close to the boundary, i.e., it only characterizes two to three PSP measurements. To be more consistent with the overall velocities that the spacecraft measured, we took their average in the range 100 km s⁻¹ to 240 km s⁻¹ between 0.10 and 0.11 au. This resulted in the value of 207 km s⁻¹, which will be the updated V₀ from now on.

## 3.3. Calibration of V₁

V₁ should reflect the maximum speed range that solar wind can vary above V₀. As suggested by McGregor et al. (2011), to calibrate this value we rely on (a) the work of Riley et al. (2003), (b) the work of Schwadron et al. (2005), and (c) Figure 2. In their study, Riley et al. (2003) ballistically mapped Ulysses solar wind measurements from 12 different Carrington

<footnote n="8">⁸ Velocities recorded by PSP below 100 km s⁻¹ are not assumed reliable for science and should be ignored.</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Flux-tube expansion factor ($f$) as a function of the distance to the CH boundary ($d$) during the first eight PSP encounters around the Sun. The points have been produced based on the default WSA model in EUHFORIA. The two vertical black lines signify the regime that velocities between 600 and 740 km s⁻¹ originate from, based on the study of Schwadron et al. (2005).</figcaption></figure>

rotations to the outer boundary of a coronal MHD model. Then, they mapped the velocities to their source regions in the photosphere and showed that velocities below 600 km s⁻¹ come from regions up to 6° from the CH boundary. Two years later, Schwadron et al. (2005) showed that speeds in the range 600–740 km s⁻¹ originate from a region between 6° and 10° from the CH boundary. This is the range that is restricted by the two vertical black lines in Figure 2. More specifically, Figure 2 shows the flux-tube expansion factor ($f$) as a function of the distance to the CH boundary ($d$) based on the default WSA model in EUHFORIA for the first eight encounters of PSP. Following McGregor et al. (2011), we adjusted $V_1$ so that $v_r$ in Equation (1) gives the value 600 km s⁻¹ for $f=15$, assuming an asymptotically large $d$ and the updated value of $V_0$. Based on the aforementioned assumptions $V_1$ is 725 km s⁻¹, namely, 50 km s⁻¹ higher than the default $V_1$.

### 3.4. Calibration of w and β

The parameters $w$ and $\beta$ define the influence of the distance to the CH boundary ($d$) in Equation (1). They reflect where the transition from slow to fast solar wind takes place from the CH boundary and how abrupt this transition is, respectively. The best choice of $w$ and $\beta$ defines the dynamics between the fast and slow solar wind in the predicted solar wind time series, something that we want to improve in the model. Figure 3 depicts how the WSA radial velocity ($v_r$) at 0.1 au changes for different $w$ values (when keeping $\beta$ fixed) and for different $\beta$ values (when keeping $w$ fixed). The flux-tube expansion factor ($f$) is color coded. It is important to notice that the difference among Figures 3(a)–(c) is the angular distance ($d$) from the CH boundary at which the transition between the slow and fast solar wind takes place—in other words, how quickly from (or how far inside in) the CH boundary the transition occurs. As $w$ grows bigger, the transition migrates to larger values of $d$, namely, it takes place deeper into the CH. The deeper it is, the more slow solar wind we get before the transition, with the transition to intermediate solar wind speeds occurring deeper in the CHs. That leaves a more restricted range of fast solar wind

velocities after the transition zone, which can only be obtained if the CH is big enough. On the other hand, in Figures 3(d)–(f) the distance from the CH boundary stays approximately the same, but the slope of the transition changes. For lower $\beta$ values, the transition is more gradual, while for larger $\beta$ values, slow wind changes abruptly to fast wind within only a fraction of the degree.

In order to find the best [$w, \beta$] combination, we performed a parametric study of these values, keeping $V_0$ and $V_1$ fixed at their updated values. More specifically, for each PSP encounter we selected one GONG ADAPT global photospheric magnetic field map. The date of each map was taken at the time that PSP was the closest to the solar central meridian as seen from Earth at the heliocentric Earth equatorial frame. For each encounter, we tested the following values for $w$: 0.017, 0.020, 0.026, 0.031, and 0.035 rad. This range was decided after conducting many runs to understand the extreme cases of the modeled output. Then, for every value of $w$, we varied $\beta$ in the range [0.50, 3] with a step of 0.5. Additional values of 0.25, 0.75, and 1.25 were considered. Therefore, for each $w$ value, we ran the WSA model nine times. Taking into account all $w$ and $\beta$ values and all encounters, the total number of WSA runs for this parametric study was 360.

The results of the parametric study are summarized in the box-whisker plot of Figure 4. Every box represents a velocity distribution from all eight PSP encounters with a median value shown in red, and the first and third quartiles are shown by the lower and upper box edges, respectively. The black legs extending above and below the boxes show the maximum and minimum velocity values of those distributions, respectively. The first (green) box in Figure 4 corresponds to the distribution of the PSP velocities between 0.1 and 0.4 au during the first eight encounters. The second (blue) box depicts the velocities from the default WSA model at 0.1 au without the ad hoc assumptions of subtracting 50 km s⁻¹ and capping the velocities between [275, 625] km s⁻¹ at the boundary (from now on, stated as “noadhoc” in the plots). All other boxes reflect the WSA velocity distributions obtained after the parametric study of $w$ and $\beta$, having included the updated values for $V_0$ and $V_1$.

Figure 4 shows that the default WSA distribution (blue box) does not resemble the PSP distribution (green box). It seems that the default WSA setup generally overestimates the measured PSP velocities. To understand if any other box better approximates the green distribution, we extended the lines of the median (red) and first and third quartiles (green) of the PSP box throughout the whole figure for a better comparison with the rest of the distributions. The WSA configuration that resembles the green PSP distribution the closest is circled in magenta and corresponds to the [$w, \beta$] combination [0.031 rad, 0.50]. As a second and third optimal choice, we further selected the combinations [0.035 rad, 0.50] and [0.026 rad, 0.50], respectively.

To obtain a better idea how the selected distributions look and compare to the PSP one, we present in Figure 5 the histograms of velocities from the PSP- and WSA-modeled output close to the Sun. The red distributions of Figures 5(a)–(d) correspond to the blue box and the three optimal WSA configurations (circled in magenta) of Figure 4. We notice that the optimal WSA configurations selected in Figure 4 better resemble the PSP distribution compared to the default WSA setup (see, e.g., the comparison between Figures 5(b)–(d) and (a)). The question
<figure><img src="image_6.png" /><figcaption>Figure 3. Radial velocity at the boundary ($v_r$) as a function of the distance to the CH boundary ($d$). From panels (a) to (c), $w$ increases while $\beta$ stays fixed. From panels (d) to (e), $\beta$ increases as $w$ stays fixed. The flux-tube expansion factor ($f$) is color coded.</figcaption></figure>

now is does this better agreement between the WSA boundary conditions and the PSP data close to the Sun lead to better solar wind forecasts in the inner heliosphere? To see if this is the case, we ran the heliospheric part of EUHFORIA. The heliospheric predictions arising from the optimal WSA configurations are presented and discussed in Section 4.

## 4. Solar Wind Predictions at PSP and Earth

The solar wind velocity predictions resulting from the three optimal WSA configurations of Figure 4 are presented in Figures 6 and 7 for the PSP and Earth position, respectively. Comparisons with in situ data and predictions based on the default WSA configuration are also shown. In Figure 6 we notice that for some time intervals solar wind velocity is reconstructed better from the default WSA setup (blue line; see, e.g., the last HSSs at the end of encounter 1, the HSSs at the beginning of encounter 3, or the HSSs at the beginning and end of encounter 7). On the other hand, other time intervals seem to be modeled better when using one of the three optimized configurations of Figure 4 (red, green, or magenta line; see, e.g., the slow solar wind at the beginning of encounter 1 or the dynamics between the slow and fast solar wind during parts of encounters 5, 6, and 7). From Figure 7 we conclude that the solar wind forecasts from the optimized configurations of Figure 4 (red, green, and magenta lines) generally underpredict observations at Earth. It is, overall, the default WSA set up that provides the best predictions, even though these predictions still have a lot of room for improvement.

To accurately quantify the performance of our modeled output compared to the observations and see if the aforementioned “by-eye” conclusions are true, we applied the dynamic time warping method (DTW; Samara et al. 2022). This method

was applied only for the time series at Earth as PSP observations are characterized by big data gaps. Based on DTW, we can define a skill score called sequence similarity factor (SSF):

$$ \text{SSF} = \frac{\text{DTW}_{\text{score}}(O, M)}{\text{DTW}_{\text{score}}(O, R)}, \quad \text{SSF} \in [0, \infty), \quad (6) $$

this being a number that provides a quantification of how good the forecast is compared to the ideal and reference prediction scenarios. In Equation (6), the DTW score is a distance measure between the modeled and observed series. More specifically, the numerator is the DTW score between the observed ($O$) and modeled ($M$) time series. The denominator is the DTW score between the observed time series and a reference case scenario that, for the purposes of this study, corresponds to the average value of observations per encounter (mean model). For DTW score = 0, we have perfect agreement between the predictions and observations. Therefore, SSF equal to zero indicates the perfect forecast, while SSF equal to one shows that the forecast performs the same as our reference model. For SSF values higher than one, the model’s predictions are worse than the predictions from the reference model. The closer the SSF is to zero, the better the forecast is.

## 5. Results

### 5.1. Evaluation of Predictions at Earth According to DTW

The results from the evaluation of the solar wind velocity predictions at Earth based on the default and the three optimal WSA setups identified in Figure 4 are summarized in Table 1. From there we conclude that the default WSA configuration is
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Box-whisker plot of velocities distributions. Green box: velocity values recorded by PSP between 0.1 and 0.4 au for all the first eight encounters. Blue box: WSA velocities at 0.1 au without the ad hoc modifications. All other boxes reflect the WSA velocity distributions resulted out of the parametric study of [*w*, *β*]. The median value of each distribution is shown in red, while the first and third quartiles are represented by the lower and upper box edges, respectively. The black legs extending above and below the boxes show the maximum and minimum velocity values of those distributions. Distributions circled in magenta resemble the PSP (green) distribution the best.</figcaption></figure>
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 5.** Histograms of PSP (white) and WSA (red) velocities for the first eight PSP encounters while the spacecraft was between 0.1 and 0.4 au. Panel (a): comparison between PSP observations and the default WSA model without the ad hoc modifications. Panel (b): comparison between PSP observations and the WSA model with [$V_0, \beta$] = [0.026 rad, 0.50] corresponding to the first circled distribution of Figure 4. Panel (c): same as (b) but for the WSA modeling setup of [$w, \beta$] = [0.031 rad, 0.50] corresponding to the second circled distribution of Figure 4. Panel (d): same as (b) but for the WSA modeling setup of [$w, \beta$] = [0.035 rad, 0.50] corresponding to the third circled distribution of Figure 4.</figcaption></figure>

the best to reconstruct the solar wind velocities at Earth for all cases except encounter 5. During the latter encounter, the WSA setup of [$w, \beta$] = [0.026 rad, 0.50] (red line in Figure 7(e)) performs the best compared to all other configurations. We also notice that for all other encounters, the second-best WSA configuration is [$w, \beta$] = [0.026 rad, 0.50], which always performs better compared to [$w, \beta$] = [0.031 rad, 0.50] and [$w, \beta$] = [0.035 rad, 0.50].

For a more global assessment of our results, we present in the table of Figure 8 the complete array of DTW evaluation results at Earth for all performed runs and encounters. We then ask the opposite question to before, namely, for which pair of [$w, \beta$] do we get the best results at Earth? Is it any of the pairs we selected from Figure 4 based on the calibration close to the Sun, or is it a different one? The first thing we notice is that the default WSA setup performs optimally for five out of eight

encounters (from now on the encounters are abbreviated as “E”), namely, for E1, E3, E6, E7, and E8 (i.e., the SSF factor is the lowest among all performed runs; see the circled numbers in Figure 8). For the three remaining encounters, the best results are given from the combination [$w, \beta$] = [0.017 rad, 0.50] for E2 and E4 and [$w, \beta$] = [0.020 rad, 0.25] for E5. We also notice that as we move to regions of higher *w* (right part of the table in Figure 8), the performance of the time series becomes generally worse (higher SSF) for all encounters except E5. This is because, for the same $\beta$, the solar wind becomes increasingly slower. A comparison of time series of different *w* and same $\beta$ is presented in Figure 13 for E1. There, we notice a systematic shift toward lower velocities as *w* grows. This finding is directly associated to the discussion in Section 3.4, in which Figures 3(a)–(c) show that as *w* grows bigger, the transition from slow to fast solar wind migrates
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 6.** Comparison between PSP time series (black) and modeled output from WSA+EUHFORIA (colorful lines). The blue time series correspond to runs made with the default WSA configuration. The red, green and magenta time series correspond to runs made with the optimized configurations of Figure 4. ICMEs have been removed from observations according to the HELIO4CAST ICME catalog (see Möstl et al. 2017, 2020 for more details).</figcaption></figure>

deeper into the CH, causing the intermediate solar wind velocities and transition to fast to occur deeper inside the CH. Another important piece of information that Figure 8 provides is that the best solar wind predictions for E1, E3, E6, and E7 based on the parametric study we performed (ignoring for a moment the default WSA configuration) are given by a WSA setup with the lowest *w* (0.017 rad) and high *β* values (e.g., mostly for *β* = 2.0, 2.5, 3.0). This is because, in these four

encounters, the arriving HSSs were characterized by very high amplitudes (see, e.g., Figures 7(a), (c), (f), (g)). Higher *β* values invoke sharper and bigger changes between slow and fast solar wind, and it would be necessary to capture more correctly the fast flows during these periods. To visualize the influence of *β* better, we present in Figure 14 how the predicted time series at Earth change for the same *w* but different *β* values during E1. We notice that the background level of slow solar wind remains
<figure><img src="image_20.png" /><figcaption>**Figure 7.** Same as Figure 6 but for time series at Earth.</figcaption></figure>

approximately the same; however, the changes between slow and fast solar wind are very different each time. Additional information from the table of Figure 8 includes the fact that the best-performed runs for encounters E2 and E4 originate from setups with the lowest *w* (0.017 rad) and quite low *β* (e.g., *β* = 0.50). This is because the peaks of HSSs are generally overestimated by the default WSA setup during these periods (see, e.g., Figures 7(b), (d)) so a smaller *β* would be needed to better capture the fast flows. For E8 the default WSA setup provides the best simulations at Earth, while the second best is

given by the combination [*w*, *β*] = [0.017 rad, 0.50]. Lastly, E5 is an exception among all other encounters because of the overall slower solar wind recorded. Only a few HSSs arrive at Earth during this period with amplitudes that do not exceed 500 km s⁻¹. The best WSA configuration for E5 is given by a different combination, i.e., [*w*, *β*] = [0.020 rad, 0.25]. It is interesting to point out that even if we had found an ideal [*w*, *β*] pair that would provide the best results for all other encounters, it would not describe well the solar wind velocities for E5 because of their much lower amplitudes. This result shows that
<figure><img src="image_21.png" /><figcaption>**Figure 8.** Summarized table of SSF skill scores as calculated by DTW. The x-axis represents all the different WSA configurations, while the y-axis shows the individual PSP encounters. The color bar extends from the best-possible prediction (SSF = 0; magenta) to the worst one that occurred in our data set (SSF = 3; yellow). For every encounter and WSA configuration, the exact SSF value appears in black at the center of each box. Circled boxes indicate the lowest SSF value that corresponds to the best prediction.</figcaption></figure>
<table><caption>**Table 1**
Evaluation of Solar Wind Velocity Time Series at Earth Based on the DTW Method for the Dates of Each PSP Encounter</caption><thead><tr><th>Encounter</th><th>SSF WSA Default</th><th>SSF WSA [0.026 rad, 0.50]</th><th>SSF WSA [0.031 rad, 0.50]</th><th>SSF WSA [0.035 rad, 0.50]</th></tr></thead><tbody><tr><td>1</td><td>0.63</td><td>1.19</td><td>1.42</td><td>1.56</td></tr><tr><td>2</td><td>1.44</td><td>1.49</td><td>1.72</td><td>1.92</td></tr><tr><td>3</td><td>0.88</td><td>1.79</td><td>2.01</td><td>2.16</td></tr><tr><td>4</td><td>0.68</td><td>0.98</td><td>1.25</td><td>1.44</td></tr><tr><td>5</td><td>2.50</td><td>1.65</td><td>1.75</td><td>1.84</td></tr><tr><td>6</td><td>0.30</td><td>0.75</td><td>0.91</td><td>1.02</td></tr><tr><td>7</td><td>0.58</td><td>1.33</td><td>1.52</td><td>1.65</td></tr><tr><td>8</td><td>0.87</td><td>1.44</td><td>1.69</td><td>1.86</td></tr></tbody></table>

Note. Column (1) indicates the number of the PSP encounter, while columns (2)–(5) show the SSF skill score for predictions performed with the default WSA configuration and the three optimal WSA configurations of Figure 4. The closer the SSF is to zero, the better the forecast is.

the WSA equation should be globally modified when coupled with MHD models beyond just choosing a unique pair of [w, β] to describe both the slow and fast solar wind.

## 5.2. Adding Heating to the System

Since the supposably optimal WSA configurations (magenta circled boxes in Figure 4) led to systematically underestimated solar wind forecasts at Earth (see Figure 7 and Table 1), we checked what is the effect of additional heating on the heliospheric part of EUHFORIA, which extends from 21.5 $R_⊙$ onward. Could this provide more acceleration to the system and improve the results? The heliospheric part of EUHFORIA is based on a polytropic MHD approach with a polytropic index ($\gamma$) equal to 1.5 (Pomoell & Poedts 2018). To simulate additional heating and thus additional acceleration, we decreased $\gamma$ from 1.5 to 1.1. We also tested the output for $\gamma = 5/3$ (adiabatic case).

Our results show that the change in the modeling output at Earth based on the different $\gamma$ is noticeable for temperature and mildly noticeable for velocity (Figures 9(a), (b)). This behavior is expected and can be predicted from the analysis of the heliospheric part of Parker's polytropic solar wind solutions. Figure 10(a) shows how the velocity varies as a function of heliocentric distance for three synthetic solar wind stream cases with an initial velocity of 300, 500, and 700 km s$^{-1}$ at 0.1 au. Different colors correspond to different $\gamma$ values. Figure 10(b) presents how the temperature varies as a power law with heliocentric distance for the same solar wind streams and $\gamma$ values. When we change the $\gamma$ at 0.1 au we practically change the temperature slope. Therefore, at any heliocentric distance the temperature will differ depending on the $\gamma$ employed and the different slope that this change caused. However, this effect is only slightly apparent for velocities. All curves after $\approx 0.25$ au have very similar slopes. As we are varying $\gamma$ only from 0.1 au upward, the effect on the velocity is minimal because the flows are already well supersonic and approaching their asymptotic values. The radial decay of temperature, on the other hand, depends directly on $\gamma$, and differences can be significant at 1 au

even for a modification of $\gamma$ from 0.1 au upward only. Therefore, adding more heating to the system by lowering $\gamma$ is not expected to lead to better velocity predictions at Earth.

## 6. Summary and Conclusions

In this study we investigated how the calibration of the WSA model, as implemented in EUHFORIA, can be performed based on single-point PSP observations. We employed PSP data between 0.1 and 0.4 au from the first eight encounters during the solar minimum period of solar cycle 24–25 so that the influence from solar transients is minimal. We focused on the calibration of four constants in the WSA relationship shown in Equation (1), namely, those that could be fine-tuned based on observations and past studies according to the methodology of McGregor et al. (2011). These are the parameters $V_0$ and $V_1$, which correspond to the lowest velocity observed at the heliocentric distance of interest and the maximum velocity range that solar wind can vary above $V_0$, respectively. Also, the parameter w indicates the angular distance from the CH boundary at which the transition from slow to fast solar wind takes place, and the parameter β shows how abrupt this transition is.

Calibrating the WSA model at 0.1 au based on PSP observations did not lead to better predictions at Earth. Even though we achieved good resemblance between WSA velocities and PSP observations close to the Sun by finding appropriate values of $V_0$, $V_1$, w, and β, the predictions at Earth usually ended up worse than the ones produced by the default WSA model. Therefore, we approached the problem backward, namely, by looking for the best set of parameters (specifically [w, β]) that give the best predictions at Earth and verifying whether they could be applied to resemble PSP observations close to the Sun. It appears that the Earth-bound set of parameters do not agree with the optimal ones for low heliocentric distances. By evaluating all performed runs and encounters based on the DTW technique, we saw that the optimal predictions at Earth were achieved by a pair of [w, β] values other than those displayed in Figure 4 and shown in Figures 5(b)–(d). Even though the latter pairs of [w, β] resulted in a good resemblance between the WSA model and PSP observations close to the Sun, they led to poor predictions at Earth. Our results with DTW showed that the only way to optimize the predictions at Earth was to calibrate the WSA model with higher velocities closer to the Sun, something that was in contradiction with the very slow velocities recorded by PSP. Depending on the case, higher modeled velocities close to the Sun can be achieved either by reducing the value of w, which increases the region covered by the fast solar wind regime, or by raising the value of β, which eventually creates an increasingly bimodal distribution with one peak in the slow and another peak in the fast velocity regime (see examples of how the WSA distribution changes for different values of [w, β] in Figures 15 and 16). The smaller the w value is close to the Sun, the higher the levels of background solar wind at Earth that will be provided and vice versa (see Figure 13). Additionally, the smaller the β value is, the smoother and slower the transition between the slow and fast solar wind becomes, diminishing the ability of the model to capture fast solar wind flows (see Figure 14). This is indeed what we saw at Earth. Ignoring the default WSA configuration for a moment, the w value that provided good predictions for all encounters was the lowest considered value (0.017 rad), except for E5,
<figure><img src="image_22.png" /><figcaption>**Figure 9.** Comparison between OMNI data and EUHFORIA simulations. Colorful solid lines correspond to heliospheric simulations made with different $\gamma$. Panel (a): velocity signatures. Panel (b): temperature signatures.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 10.** Velocity and temperature variations as a function of heliocentric distance for three synthetic solar wind streams that have initial velocities of 300, 500, and 700 km s⁻¹ at the inner boundary of EUHFORIA’s heliospheric domain (0.1 au).</figcaption></figure>

which was characterized by overall slower velocities and fewer HSSs (for this case, the best *w* value was 0.020 rad). On the contrary, the *w* values closer to the Sun that made the WSA modeling distribution to be in good agreement with the PSP one were 0.026, 0.031, and 0.035 rad (see Figures 4 and 5(b)–(d)). However, those values underpredicted the solar wind velocity at Earth, as discussed in Section 4 and shown in Figure 7. Our results show the following:

1. There should be some processes that still accelerate the solar wind from distances close to the Sun (i.e., 0.1–0.4 au) to Earth that cannot be captured efficiently (or at all), by EUHFORIA. Such processes could include residual acceleration of the solar wind (see, e.g., Schwenn 1990; Riley & Lionello 2011; Marino & Sorriso-Valvo 2023), as well as interactions between neighboring wind streams, corotating interaction regions, and CMEs (see, e.g., Sanchez-Diaz et al. 2016, who state

that the slowest of all streams detected by Helios disappear with height, presumably due to this kind of interaction).

2. Even when the calibration of the WSA equation is performed solely during a period of low solar activity, unique values of $V_0$, $V_1$, $w$, and $\beta$ may still not be enough to properly describe the solar wind at a specific heliocentric distance for different Carrington rotations (see, e.g., the difference between solar wind velocities during E5 and the rest of the encounters). In their work, Kumar & Srivastava (2022) and Riley et al. (2015) showed, for example, that the optimal WSA parameters can vary greatly from one Carrington rotation to another. Can this problem be overcome? To answer this question, efforts toward reforming the WSA equation in a way that would better reflect the physics and dynamics of slow and fast solar wind in association to their source regions on the Sun should be undertaken.
<figure><img src="image_24.png" /><figcaption>**Figure 11.** Speed distributions at Earth based on OMNI data for years during different solar minimum periods. Panel (a): yearly speed distributions during past consecutive solar minima. Panel (b): yearly speed distributions during the latest solar minimum.</figcaption></figure>

3. The optimal set of WSA parameters (especially [$w, \beta$]) necessary to correctly approximate PSP observations close to the Sun is different from those identified to give the best predictions at Earth after running the MHD part of EUHFORIA. Because of this discrepancy, and to better understand how the WSA should be modified when coupled with the current MHD model, an efficient uncertainty quantification study of the free parameters of the whole chain of models (WSA+EUHFORIA) would be useful. In their recent study, Issan et al. (2023) performed a sensitivity analysis of all the free parameters in the PFSS+WSA+HuX chain. They found the five most influential parameters that are all related to the WSA model and vary from one Carrington rotation to another. In a future study, it would be interesting to apply their uncertainty quantification framework for the more complex WSA+EUHFORIA pipeline to understand the sensitivity of the different parameters for both modeling parts and get a better understanding of its efficiency.

Our findings are different from those of McGregor et al. (2011) who, by following a similar approach, improved solar wind forecasts at 1 au during the years 1996–2003 and at Ulysses during 1994–1995 by calibrating the WSA model with Helios data. The outcome of our work raises questions as to why this difference between the two studies occurs. First, we were expecting a direct improvement of the solar wind predictions with EUHFORIA because we employed observations much closer to the Sun than McGregor et al. (2011) did for the calibration of WSA. This means that the fine-tuning of WSA boundary output based on PSP data was more consistent in our case. Second, the magnetograms we used to produce the WSA output at 0.1 au referred exactly to the same period as the PSP observations employed for the calibration (i.e., 2018–2021, during the first eight PSP encounters). In their work, McGregor et al. (2011) exploited Helios measurements from the solar minimum period 1974–1976 to calibrate the WSA output more than 20 yr later (1996–2003). To justify their choice, they showed that a number of consecutive solar minimum periods behaved the same by displaying the

similarity of speed distributions at 1 au. We show these distributions in Figure 11(a) for the years that McGregor et al. (2011) present in their study. We notice that all speed distributions at Earth during 1976, 1985, 1995, and 2006 show a bimodal shape with a high peak at slow speeds and a low peak at high speeds. This, however, does not seem to be the case for the latest solar minimum during which PSP operated (Figure 11(b)). In the latter plot, only a single peak in slow speeds is visible for all 4 yr that were taken into account (2018–2021). By comparing similar distributions closer to the Sun, the same pattern is revealed when we set side by side observations from past solar minimum periods and the latest one. Namely, a bimodal pattern is apparent in the speed distribution from Helios measurements between 0.3 and 0.4 au during the years 1975–1976, which were part of the solar cycle 21–22 minimum. This is similar to the distribution that McGregor et al. (2011) used to calibrate the WSA model, and it is presented in Figure 12(a). However, as seen in Figure 12(b), a bimodal distribution is missing from PSP observations. The red distribution in the latter figure represents speeds within the range 0.1–0.4 au. The black distribution depicts speeds within 0.3–0.4 au, which can be directly compared to Figure 12(a). We note that the integrated area under each of the histograms in Figures 11 and 12 is equal to one.

From the observational point of view, we believe that the scarcity of fast solar wind velocities recorded by PSP close to the Sun during the latest solar minimum period is another reason why this study did not yield improved solar wind predictions after the WSA calibration. Even though the observations and input data used to perform this analysis were more accurate compared to the case of McGregor et al. (2011), the PSP velocities themselves—based on which the whole study was relied on—were by far too low to lead to a reasonable calibration of the model. We calibrated WSA according to unexpectedly slow velocities, and consequently, we not only got a general underestimation of the predictions but also could not improve the dynamics between the slow and the fast solar wind throughout the heliosphere since there was no fast solar wind recorded by PSP to account for. In a future
<figure><img src="image_25.png" /><figcaption>**Figure 12.** Speed distributions closer to the Sun. Panel (a): speed distributions as measured by Helios between 0.3 and 0.4 au during the solar minimum of 1975–1976. Panel (b): speed distributions as measured by PSP (first eight encounters) between 0.1 and 0.4 au during the latest solar minimum.</figcaption></figure>

study, it would be interesting to explore why this scarcity of fast solar wind velocities happens during the latest solar minimum compared to previous ones. However, PSP observations should not be the only factor to blame for not achieving better predictions at Earth after the calibration. They currently consist of the only in situ ground truth for distances close to the Sun, and this is why we relied on them. Our results showed that the WSA configurations, which optimally resembled the PSP observations close to the Sun, were different from the ones needed to provide better predictions at Earth. Therefore, missing physical processes from the heliospheric part of EUHFORIA can be one factor contributing to this discrepancy. Another factor can be the fact that the currently employed WSA relationship coupled to a heliospheric MHD domain may need to be globally reformed beyond just updating the four $V_0$, $V_1$, *w*, and $\beta$ constant factors in order to better capture the physics taking place. Other factors that should be mentioned, although we believe they do not drastically influence the results, are the date, the type of magnetograms used, the observatory that the magnetograms came from, and the disadvantages of single-point observations compared to multipoint ones. In a future study, we aim not only to use multipoint observations during different periods of solar activity to calibrate the boundary conditions from WSA in an effort to decrease the uncertainties coming from single-point observations but also to extend this analysis for both solar minimum and maximum intervals.

The last part of this study was devoted to better understanding the influence of the acceleration from the heliospheric MHD part of EUHFORIA on the solar wind boundary velocities provided by the WSA model at 0.1 au. The goal was to verify if we can correct for the systematic underestimation of the solar wind seen in the predictions at 1 au by decreasing the polytropic index ($\gamma$) of the MHD part of EUHFORIA. With that, we aimed to provide more heating and thus more acceleration to the system. However, this was not eventually the case as a change in $\gamma$ at 0.1 au mainly affects the temperatures of the system but not so much the velocities.

## Acknowledgments

We thank the anonymous referee for the fruitful comments and insights on this work. E.S.'s 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. C.N.A. is supported by the NASA competed Heliophysics Internal Scientist Funding Model (ISFM). J.M. acknowledges funding by the BRAIN-be project SWiM (Solar WInd Modelling with EUHFORIA for the new heliospheric missions) and funding from the FED-tWIN project PERIHELION. EUHFORIA was created as a joint effort between KU Leuven and the University of Helsinki and is being developed further by the the project EUHFORIA 2.0, a European Union Horizon 2020 research and innovation program under grant agreement No. 870405. The ROB 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 No. 4000134474. N.W. acknowledges support from the Research Foundation—Flanners (FWO-Vlaanderen, fellowship No. 1184319N).

## Appendix

### Influence of Different *w* and $\beta$ at Earth and 0.1 au

Figures 13 and 14 show how the predictions at Earth during the period of PSP encounter 1 vary for the same *w* and different values of $\beta$ and for the same $\beta$ and different values of *w*, respectively. In Figure 13 we notice a systematic shift toward lower velocities as *w* grows. This is because, according to Figures 3(a)–(c), as *w* grows bigger, the transition from slow to fast solar wind mitigates deeper into the CH, causing the intermediate solar wind velocities to become increasingly slower. In Figure 14 we notice that, for a fixed *w*, higher $\beta$ values invoke sharper and bigger changes between slow and fast solar wind. Figures 15 and 16 show how the velocity distributions close to the Sun vary for different values of *w* and $\beta$ compared to the same PSP velocity distribution between 0.1 and 0.4 au.
<figure><img src="image_26.png" /><figcaption>**Figure 13.** Comparison of predicted solar wind velocity time series at Earth for the same $\beta$ and different values of $w$ during PSP encounter 1.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 14.** Same as Figure 13 but for the same $w$ and different values of $\beta$.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>**Figure 15.** Examples of how the WSA-modeled velocity distributions at 0.1 au vary compared to PSP observations for *w* = 0.017, 0.020, and 0.026 rad and *β* = 0.25, 0.50, 0.75, and 3.0.</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>**Figure 16.** Continuation from Figure 15 for *w* = 0.031 and 0.035 rad and the same *β* values.</figcaption></figure>

## ORCID iDs

E. Samara https://orcid.org/0000-0002-7676-9364

R. F. Pinto https://orcid.org/0000-0001-8247-7168

N. Wijsen https://orcid.org/0000-0001-6344-6956

M. L. Stevens https://orcid.org/0000-0002-7728-0085

S. Poedts https://orcid.org/0000-0002-1743-0651

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