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# A New Method Linking the Solar Wind Speed to the Coronal Magnetic Field

Marta Casti¹,² ID, Charles N. Arge¹ ID, Alessandro Bemporad³ ID, Rui F. Pinto⁴,⁵ ID, and Carl J. Henney⁶ ID

¹NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA; marta.casti@nasa.gov

²The Catholic University of America, Washington, DC 20064, USA

³National Institute for Astrophysics, Astrophysical Observatory of Torino, Via Osservatorio 20, I-10025 Pino Torinese (TO), Italy

⁴Dept. d'Astrophysique/AIM, CEA/IRFU, CNRS/INSU, Université Paris-Saclay, F-91191 Gif-sur-Yvette Cedex, France

⁵IRAP, Université Toulouse III—Paul Sabatier, CNRS, CNES, Toulouse, France

⁶Air Force Research Laboratory, Space Vehicles Directorate, KAFB, NM, USA

Received 2022 December 12; revised 2023 March 17; accepted 2023 March 27; published 2023 May 25

## Abstract

The release and acceleration of the solar wind is still an outstanding question. There are several aspects related to this phenomenon that still need to be investigated, and one of these is the identification of the region within the inner corona where the larger fraction of acceleration occurs. To address this matter, it is necessary to have reliable measurements of the solar wind speed between 1 and 10 solar radii ($R_⊙$). Moreover, in order to describe the coronal plasma behavior, it is important to consider its interaction with the magnetic field. Within this context, our intent is to investigate a method to combine measurements of the solar wind with the extrapolated magnetic field in the corona to derive how the solar wind velocity evolves along the magnetic field lines, aiming at better understanding the sources, origins, and acceleration of the solar wind. To this purpose, we used outflow speed measurements of the coronal plasma derived by applying the Doppler dimming technique, as well as the global magnetic field configuration derived from the measured photospheric magnetic field by using the Wang–Sheeley–Arge model. These two sets of data are then combined for heliocentric distances between 2.6 and 5 $R_⊙$. This paper presents the proposed method and the results obtained over two different Carrington rotations (CR 1923 and CR 1924), demonstrating the applicability of the method and the capability to link measured solar wind velocity to the extrapolated coronal magnetic field in order to derive the velocity profile.

Unified Astronomy Thesaurus concepts: Solar wind (1534); Solar magnetic fields (1503); Solar corona (1483)

## 1. Introduction

The increasing number and variety of solar observations has been essential for improving our understanding of the fundamental physics of the Sun, and consequently, our ability to enhance models of it. Nevertheless, several issues and critical questions of its physics remain still unanswered. Viall & Borovsky (2020) outline nine outstanding questions in the framework of solar wind physics; one of these concerns the mechanisms accelerating the solar wind.

The ability to accurately map the solar wind speed, especially near the Sun, can help to understand the physics behind its acceleration. The solar wind has been measured using in situ instruments since the 1960s (Ness 1996; Obridko & Vaisberg 2017), but the majority of these observations consist of single-point measurements of the interplanetary medium acquired at 1 au and mainly in the plane of the ecliptic. Since 1994, when the Wind satellite was launched, we have collected continuous observations from the L1 Lagrangian point of the plasma and the magnetic field reaching Earth. In 1990, the space mission Ulysses (Wenzel et al. 1992) was launched with the purpose of providing measurements of the heliospheric medium out of the ecliptic plane, from 1 to 5 au. Moreover, between 1974 and 1979, the two Helios spacecraft (Porsche 1981) provided sets of in situ measurements in a range of heliocentric distances between 0.3 and 1 au. Based on all these measurements acquired over the last 50 yr, the solar

wind has traditionally been divided into two distinct types: slow and fast. It is worth noting that, from its formation to the point of observation, the solar wind evolves, undergoing processing and mixing, and observing its whole evolution is challenging. Missions such as the Parker Solar Probe (Fox et al. 2016), launched in 2018, and the Solar Orbiter (Müller et al. 2013), launched in 2020, are currently providing extensive data sets to better characterize the solar wind evolution.

For obvious reasons, it is not possible to use in situ instruments to probe the solar wind within the inner corona. The Parker Solar Probe mission (Fox et al. 2016) will allow to measure for the first time the solar wind properties down to less than 10 solar radii with in situ instruments, but the inner acceleration region below this altitude will never be reached. To overcome this limitation, in the absence of in situ measurements near the Sun, three main methods have been developed to derive the wind speed from phenomena that are directly related with the plasma outflow velocity. One of these techniques makes use of interplanetary scintillation (IPS) measurements using both natural radio sources and spacecraft radio signals to track small-scale (≈100 km) density irregularities and to derive their propagation speed. Dennison & Hewish (1966) were the first to suggest this technique to obtain out of the ecliptic velocity measurements. Over the years, this method has been improved, and more details can be found in Scott et al. (1983), Woo & Martin (1997), and Imamura et al. (2014). Sheeley et al. (1997) and Wang et al. (2000) measured the outflow speed between 2 and 30 solar radii by tracking moving features in the inner corona that are clearly evident in sequences of running differences derived from observations made by the Large Angle Spectrometric Coronagraph (LASCO) C2 and C3 coronagraphs (Brueckner et al. 1995)

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on the Solar and Heliospheric Observatory (SOHO) spacecraft. The third technique developed to measure the radial speed of the solar wind is using Doppler dimming methodology. It is based on the Doppler dimming effect, and it is described in detail by Withbroe et al. (1982) and Noci et al. (1987). Thanks to the Ultraviolet Coronagraph Spectrometer (UVCS) instrument (Kohl et al. 1995) on board the SOHO mission, designed to perform ultraviolet spectroscopy of the solar corona, this method has been extensively used to directly measure the proton and heavy ion expansion speed in regions of interest (Kohl et al. 2006; Antonucci 2007). Recently, the Doppler dimming technique has also been used to obtain 2D images of the solar wind speed from the so-called synoptic UVCS observations used to build 2D coronagraphic Lyα intensity images, and then coupled with coronagraphic observations in visible light (Bemporad 2017; Dolei et al. 2018; Bemporad et al. 2021). Moreover, the solar wind speed is now measured with the same technique by the Metis coronagraph on board the Solar Orbiter (Romoli et al. 2021), also linking observations acquired by the Parker Solar Probe (Telloni et al. 2022), but the observations analyzed so far do not extend below 3.5 solar radii, thus still missing the inner acceleration region, and currently available data only cover short time intervals (much shorter than one full solar rotation).

All of the abovementioned techniques provide measurements of the solar wind speed without relating them to measurements of the critical player in the wind acceleration process, i.e., the magnetic field. In fact, the solar magnetic field has been recognized as the key element of the solar wind heating and acceleration phenomena. It connects the solar surface to the chromosphere and the corona, and it is the vector through which the energy needed to heat the solar corona and to accelerate the solar wind is transferred.

Observations of the coronal magnetic field are sparse and measurements are difficult to obtain, especially in the inner corona. This leads to the use of models based on the measurements of the photospheric magnetic field to extrapolate the configuration of the coronal field. A list of these methods is provided in Wiegelmann et al. (2017), together with a complete overview of magnetohydrodynamic, magnetohydrostatic, force-free, and potential field models. During the years, empirical models such as the Wang-Sheeley-Arge (WSA) model, based on physics and observations, have been developed to link the solar wind properties measured by in situ instruments at 1 au with certain characteristics of the solar magnetic field in the corona, such as the expansion factor ($f_s$) and the minimum angular separation between the solar wind source location (i.e., a flux tube foot point) and the nearest coronal hole boundary (Wang & Sheeley 1990, 1992; Arge & Pizzo 2000; Arge et al. 2003, 2004).

In this work, we investigate a strategy to combine the measurements of the solar wind outflow velocity obtained by exploiting the Doppler dimming technique with the coronal magnetic field configuration derived from photospheric field maps using the WSA model. A similar analysis (Fujiki et al. 2015) was made to find a relationship between the solar wind speed and the properties of the coronal magnetic field. In that case study, velocity values were obtained from IPS measurements within a range from 0.1 to 1.0 au and then back-projected by means of a radial distribution to the Source Surface of the Potential Field Source Surface (PFSS) model (Hakamada & Kojima 1999) located at 2.5 solar radii. The

magnetic field was then extrapolated from the photosphere measurements using the PFSS coronal field extrapolation. In Tokumaru et al. (2017), the speed values derived from IPS data are linked to areas occupied by coronal holes.

The final goal of our analysis is to investigate the possibility to find a link between the measured wind velocity profile along the field lines and certain characteristics of the magnetic field on corona, aiming at finding useful insights to improve solar wind models—and because transient phenomena propagate in the solar wind, the current ability to forecast space weather events. Section 2 explains how measurements of the solar wind outflow velocity and the coronal magnetic configuration are derived from instrumental observations, providing a description of the exploited algorithms and techniques and their limitations. The method developed to link these two data sets is then described with a detailed explanation of the steps followed and of the approximations that we took into account. Section 3 shows an application of the proposed method on instrumental observations, describing the used input data. In Section 4, the results obtained are shown and discussed, while Section 5 provides our conclusions.

## 2. Data and Method

The following describes the methodology used for combining the global magnetic field of the Sun and the outflow velocity of the solar wind to infer how solar wind speed evolves along the magnetic field lines in corona. We make use of the Wang-Sheeley-Arge (WSA) model to extrapolate the most likely coronal magnetic field configuration, and we exploit the Doppler dimming technique to measure the outflow velocity on the plane of the sky. To combine these two sets of data, the images containing the outflow velocity information are used to generate synoptic maps gathering the distribution of the solar wind speed in the corona over the analyzed period. Finally, we identify and describe a method to verify the proposed approach.

### 2.1. The Outflow Speed: The Doppler Dimming Technique

The exploitation of the Doppler dimming technique to probe the solar wind acceleration region was first investigated by Withbroe et al. (1982). This method relies on the Doppler dimming effect (Hyder & Lites 1970; Beckers & Chipman 1974), which is observable on intensities and profiles in UV and EUV spectral lines whose emission is due to resonant scattering of chromospheric light, to measure the radial component of the solar wind speed. In this paper, we consider the coronal emission in the Lyα line (1.6 nm). In the corona, the Lyα emission is mainly due to resonant scattering (Gabriel 1971) of the chromospheric emission: photons from the chromosphere emitted in the Lyα line are resonantly scattered by neutral hydrogen atoms in the corona. The intensity of the coronal emission is related to the relative velocity between the atoms emitting the exciting radiation and the atoms absorbing the radiation, which consequently undergo transition into an excited state followed by spontaneous emission: if the speed of the atoms is nonzero within their reference frame, then the chromospheric emission is Doppler shifted in the spectrum, reducing the value of the convolution integral between the emission and absorption line profile (see Equation (9) in Bemporad et al. 2021). This results in a less efficient scattering process, meaning that the absorption is
reduced, and consequently so is the emission observable on the line of sight and incoming from the H I atoms. Of course, the total observed intensity in the Lyα line also depends on the chromospheric Lyα intensity, on the plasma density, on the proton temperature (affecting the width of the atomic absorption profile), and on the electron temperature (affecting the fraction of neutral H atoms). Moreover, the range of sensitivity of the Doppler dimming technique is limited by the wavelength and the width of the spectral line of interest. In the case of the Lyα emission, this range goes from 50 km s⁻¹ to about 500 km s⁻¹.

The Doppler dimming technique can be implemented following different strategies; Kohl & Withbroe (1982) give an overview of all of the possibilities. In this analysis, we consider the outflow velocity derived directly from the ratio between the intensity measured in the Lyα line, which is affected by Doppler dimming, and the observed visible light polarized brightness, which is not affected by this phenomenon. This technique, recently applied by Bemporad (2017), was first suggested by G. Noci (personal communication with Withbroe, G.L.) and allows the electron density, which is the quantity undergoing major variations along the line of sight, to be eliminated because it cancels in the ratio (see Equation (23) in Bemporad et al. 2021). A higher level of detail can be found in Bemporad et al. (2021). To apply this technique, acquired observations in Lyα and in visible light must be simultaneous and from the same point of view, in order to have exactly the same contribution both in visible light and UV of the line-of-sight integral of the plasma electron density.

## 2.2. Magnetic Field Configuration: The Wang-Sheeley-Arge Model

The Wang-Sheeley-Arge (WSA) model (Wang & Sheeley 1992; Arge & Pizzo 2000; Arge et al. 2003) is an empirical and physical model capable of predicting the solar wind speed and the interplanetary magnetic field (IMF) at any location in the inner heliosphere starting from the measured photospheric magnetic field.

To extrapolate the coronal magnetic field from photospheric field maps, WSA combines the magnetostatic Potential Field Source Surface (PFSS; Schatten et al. 1969; Altschuler & Newkirk 1969; Wang & Sheeley 1992) and the Schatten Current Sheet (SCS; Schatten 1972) models. The PFSS model is based on the assumption that the coronal magnetic field is current-free in the region between the solar surface and the so-called source surface and that the magnetic field is radial at this higher assigned boundary. The PFSS model does not impose a value for the surface's radius, but several studies and observations found 2.5 R⊙ to be optimal, because it gives the best overall agreement between calculated and observed IMF polarity (Altschuler & Newkirk 1969; Hoeksema et al. 1983). Above the source surface, WSA extrapolates the field configuration by applying the Schatten model: the magnetic field is reoriented at the source surface such that it is outward-directed everywhere, and the field is calculated using a Legendre polynomial expansion. The original field polarities are then reassigned after the field is calculated.

Because the PFSS model constrains the field to be radial at the source surface and the SCS model does not require such configuration at its lowest boundary, these inconsistent boundary conditions often produce nonphysical kinks in the field. To mitigate this problem, the WSA model makes use of a

second surface placed at the heliocentric distance defined by the interface radius (i.e., 2.49 R⊙ as default), which can smooth the connection point between the segments of the same field line derived using the two models, reducing the observed kinks (McGregor et al. 2008). As the optimization of these two boundary radii is still under investigation, in this study we used the default WSA values for the source surface and interface radii (2.51 R⊙ and 2.49 R⊙, respectively). A small overlap region between the two models permits magnetic field lines to be traced more easily. We will explore using different source surface and interface radii, as well as which combination of the two will minimize kinks in the resulting field lines, in a future paper.

Once the configuration of the coronal magnetic field is derived from the photospheric field maps, the WSA model predicts the solar wind speed by exploiting the empirical relationship that links the solar wind velocity to the flux tube expansion factor ($f_s$) and to the distance of the field line foot point to the nearest coronal boundary ($\theta_b$) (Wang & Sheeley 1990; Arge & Pizzo 2000; Arge et al. 2004). The first parameter is a measure of how much the magnetic flux tube expands in solid angle between the photosphere and the source surface, and it is given by

$$f_s = \left(\frac{R_{\odot}}{R_{ss}}\right)^2 \cdot \frac{B_0}{B_{ss}} \quad (1)$$

where $B_0$ and $B_{ss}$ are the field strengths at $r \approx R_{\odot}$ and $r = 2.5 R_{\odot}$, respectively.

The other parameter, $\theta_b$, refers to the minimum angular separation between the solar wind source location (i.e., a flux tube foot point) and the nearest coronal hole boundary. These two parameters are linked in the sense that, the more slowly the flux tube diverges in the corona and the deeper inside a corona hole an open magnetic field foot point resides, the greater the final solar wind speed is along that magnetic field line—and vice versa. This empirical relation between the solar wind speed and $f_s$ was first introduced by Wang & Sheeley (1990, 1992) and Arge & Pizzo (2000), and it was then extended to $\theta_b$ by Arge et al. (2003, 2004).

Because WSA uses photospheric field synoptic maps as boundary conditions for the coronal field extrapolation, the resulting forecast is strictly dependent on the map provided as input to the model. For this reason, a highly reliable mapping of the magnetic field is essential, and the method used to construct these maps assumes a key role. Nevertheless, the Carrington maps of photospheric magnetic fields are typically built from a single viewpoint over one full solar rotation, mixing both the spatial and temporal evolution of the fields. Hence, instead of using traditional maps that are essentially a time history of central meridian, more sophisticated methods have been developed to generate these maps. The Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model (Arge et al. 2010, 2011; Henney et al. 2012; Arge et al. 2013; Hickmann et al. 2015; Schonfeld et al. 2022), developed by the Air Force Research Laboratory in collaboration with the Los Alamos National Laboratory (LANL) and the National Solar Observatory (NSO), utilizes a modified version of the Worden and Harvey (WH) flux transport model (Worden & Harvey 2000) combined with rigorous data assimilation techniques. The WH model evolves the magnetic flux on the Sun to approximate the instantaneous magnetic flux distribution while accounting for various factors, such as the differential rotation,
the meridional circulation, the supergranulation diffusion, and random flux eruptions. Data assimilation techniques are then applied to update the modeled flux when new observations are available, taking into account both data and model uncertainties. The use of different model parameters generates a set of 12 possible configurations of the photospheric magnetic field for a moment in time, i.e., 12 photospheric synchronic maps, that we refer to as “realizations.”

The WSA model extrapolates a configuration of the coronal field from each one of these realizations, and consequently returns a different prediction of the solar wind speed and of the IMF at a given location in the inner heliosphere for each one of the maps provided as input.

## 2.3. Data Collection Method

The proposed method is based on the main assumption that, during the solar minimum phase, when the Sun experiences quiet conditions, the solar magnetic field is expected to be slowly evolving. Starting from this assumption, we collected the ADAPT maps describing the photospheric field over a whole Carrington rotation (i.e., one set of ADAPT maps for each day during the rotation) and then ran WSA to find the realization generating solar wind speed and IMF polarity predictions that best match satellite measurements near Earth. The coronal magnetic field extrapolated from this particular map realization is then geometrically combined with a data cube of synoptic maps derived from the measurements of the outflow speed obtained by applying the Doppler dimming technique to coronagraphic images. Because each line of the extrapolated magnetic field is given as a sequence of points characterized by a set of three coordinates (i.e., polar angle, longitude, and heliocentric distance), this makes it possible to relate each one of these field line points to the outflow speed measured in that particular location, and finally, to derive how the radial component of the solar wind speed evolves along the open magnetic field lines.

The first step required to implement the method described above is to identify the optimal photospheric magnetic field map that the WSA model will use to extrapolate the coronal magnetic field, which is then used to predict the solar wind speed and the IMF polarity at a given in situ location (e.g., Earth). Until the recent launch of the Solar Orbiter, photospheric magnetic field maps have generally been constructed by assembling full-disk magnetograms over a span of about 27 days. There are several methods for generating such maps, such as the traditional approach of stitching together narrow longitudinal strips centered on the central meridian of each magnetogram over the span of a solar rotation (i.e., a dichronic Carrington map) or using magnetic flux transport models, such as the Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model, which evolves an existing ensemble of global magnetic maps forward to the time of the next magnetogram for data assimilation. Flux transport models generate global photospheric magnetic field maps that are more closely synchronic (i.e., instantaneous) in nature. As mentioned in Section 2.2, ADAPT is an ensemble model that generates a set of 12 maps (or realizations) at any given moment in time. The realizations differ from one another based on the specification of the supergranulation, which is done statistically. Ideally, the ensemble realistically represents the range of possible configurations of the global photospheric magnetic field at any given moment in time. ADAPT provides the maps in two formats.

The first is in the 0° (left edge of map) to 360° (right edge) fixed Carrington format, while the second one consists of an identical set of data but with the central meridian of the latest magnetogram assimilated into the map, positioned at the center of the synoptic map. The latter type of map is often preferred by solar wind modelers, as it puts the seam of the map on the opposite side of the Sun, at least for Earth-based forecasts. For the first type of map, the ADAPT maps superficially appear as standard Carrington maps but actually differ from one another based on when they were last updated with new magnetograms, as well as the supergranulation pattern. For the ADAPT maps used in this study, which were updated daily, 27 × 12 = 324 maps were generated for each rotation and then run in WSA. The WSA-PM metric (Meadors et al. 2020) was used to identify the best-performing ADAPT map. This metric evaluates the discrepancies between WSA predictions and in situ measurements of the solar wind speed and of the IMF over a selected temporal running window (i.e., one Carrington rotation in this study) and assigns a score to each realization.

The outflow speed images obtained from coronagraphic observations can be used to construct synoptic maps showing the global distribution of the measured wind velocity in the corona over a solar rotation at a specific solar radius. Usually, in the case of coronagraphic observations, where the solar disk is occulted, synoptic maps are constructed by extracting circular profiles at a given radial distance from the center of the Sun from images acquired over a complete solar rotation and stacking them vertically, as depicted in Figure 1. By considering a range of different heliocentric distances, it is then possible to build several synoptic maps, each one showing the distribution of the solar wind speed in the corona at a given solar radius. It is worth noting that each extracted circular profile contains data related to both the eastern and the western limb. If we assume the Sun and the corona to be rigidly rotating together and evolving very slowly, the portion of the extracted circular profile residing on the eastern limb will contain information about the corona that will appear at the central meridian after one quarter of a solar rotation. On the other hand, the information that we extrapolate at the western limb will correspond to the portion of corona that was positioned earlier at the central meridian of the solar rotation. It is necessary to point out that the corona is optically thin, so our observations are the result of the integration on the line of sight. Moreover, we are not taking into account the differential solar rotation, nor the possible decouplings between the photospheric and coronal rotations occurring in the inner corona (see Giordano & Mancuso 2008). However, because this method has been developed for periods of solar minima, we believe that the error introduced by these approximations is still acceptable.

The next step for building the final stack of synoptic maps (i.e., one map for each heliocentric distance in the reference interval) is to divide the maps into two parts by separating the observations of the eastern and western limbs (the upper and lower parts, respectively, of the synoptic map shown in Figure 1). This process results in two different synoptic maps, each one containing information of the solar corona observed in a specific limb, over a whole rotation. It should be noted that the western limb map needs to be rotated by 180° to bring the north pole into the upper part of the map.

Different strategies can be used to correlate the Doppler dimming derived outflow velocity with the extrapolated magnetic field configuration obtained from WSA. For instance,
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Schema of the method used to construct the solar wind outflow speed synoptic map from images of the measured wind velocity in the corona. Circular profiles are extracted from images of measured outflow speed collected daily over the span of a solar rotation. These profiles refer to a given heliocentric distance and are then vertically stacked to build a global map showing the distribution of the solar wind speed in the corona during the considered solar rotation at that specific heliocentric distance. Such maps contain data of the eastern (synoptic map upper part) and western (synoptic map lower part) limbs, resulting in a composite of two synoptic maps, each one related to one of the limbs.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Schema of the method used to combine the open magnetic field lines to the synoptic maps obtained by collecting the outflow speed measurements at different heliocentric distances. Based on its distance to the center of the Sun, each point of a single field line is at first linked with the synoptic map generated for that specific heliocentric distance. Then, using its longitude and the polar angle, it is linked to the specific value of speed reported on the synoptic map for that specific location.</figcaption></figure>

a Doppler dimming synoptic map can be created that is comprised of observations exclusively from one limb or from a combination of both. In this study, we chose to combine data from the two single-limb maps to build a new map made from outflow speed values that are as close in time as possible to that of the optimal ADAPT photospheric map realization. In fact, once the best ADAPT realization has been selected, its time stamp (i.e., the day and time it was evolved to) can be used as a reference point to build the new outflow velocity map. Assuming rigid rotation of the corona, and using the time stamp of the ADAPT photospheric field map, the Doppler dimming outflow values closest in time to that of the ADAPT map can be selected from the eastern and eastern limb maps (accounting for the 7 day rotation offset from the limb to the central meridian) to generate a full 360° velocity flow map that is centered in time on the ADAPT map (see Section 3.3). These maps are made for several different radial heights spanning from 2.6*R<sub>☉</sub> to 4.9*R<sub>☉</sub> with 0.1*R<sub>☉</sub> steps in height. Measurements below or above these inner and outer radii are unreliable.

The extrapolated coronal field configuration and the obtained outflow speed maps can then be combined, and a measured value of radial velocity can be associated with a point on each field line by means of its geometrical position in the three-dimensional space. The left side of Figure 2 provides a graphical representation of the context of the WSA solution, showing three samples of open magnetic field lines. The image,

with the Sun at the center, shows (i) the outer radius, which is the outer boundary of the extrapolated magnetic field, (ii) the photospheric level, (iii) two circumferences at specific heliocentric distances (i.e., 4.9*R<sub>☉</sub> and 2.6*R<sub>☉</sub>) as examples, and (iv) three magnetic field lines, which are drawn as an ensemble of points. The right side of the same figure shows the process used to correlate each point of a magnetic field line with a specific area on the outflow speed synoptic maps. The applied method considers each line, and starting from the highest heliocentric altitude, associates to each line point the velocity value measured in correspondence with the same coordinates (i.e., longitude, polar angle, and solar radius). This process leads to a list of field lines, which are geometrically defined and associated with an outflow speed profile.

## 2.4. Verification Method

The method to verify this study is based on our current knowledge of coronal holes. They are regions of the solar corona characterized by very low emission, with respect to the surrounding areas, and by open magnetic field lines, from where the hot coronal plasma escapes outward into the heliosphere. The central portions of coronal holes are known to originate the fast solar wind (Cranmer 2002). Remote observations of the Sun in EUV and white light suggest that magnetic field lines rooted in coronal holes spread radially
when their foot points reside near the center of the hole, while they arch away when near the boundary (Krieger et al. 1973). The same pattern is followed by the flow lines of the expanding solar wind, which in the low-beta inner corona (typically below $5R_⊙$), moves along magnetic field lines and thus expands radially near the central region of coronal holes and superradially near their edges. Consequently, field lines rooted in the central portion of coronal holes are characterized by small values of the expansion factor ($f_s$) and larger angular distances from coronal boundaries ($\theta_b$). Conversely, lines near the boundary are associated with large expansion factors and small coronal hole boundary distances. As mentioned before, previous studies (Wang & Sheeley 1990; Arge & Pizzo 2000; Arge et al. 2003) found $f_s$ and $\theta_b$ to be correlated with the speed of the solar wind associated with the open magnetic field lines. In particular, the fast solar wind is associated with field lines rooted deep inside coronal holes (large $\theta_b$ and small $f_s$), while slow solar wind is associated with field lines near the hole boundary (small $\theta_b$ and large $f_s$).

To gain confidence in the analysis methodology described in this paper, we verify that our approach of combining the extrapolated magnetic field lines with measured outflow speeds in the corona produces velocity profiles that are consistent with the previous findings in terms of the relationship between $\theta_b$, $f_s$, and $v_w$, i.e., solar wind speed. In other words, we expect the higher values of solar wind speed to be associated with field lines rooted deep inside coronal holes and having a small value of expansion factors and large coronal hole boundary distances, while field lines residing near the boundaries of coronal holes have the opposite relationship with expansion factor and coronal hole boundary distance. The procedure identified to validate the proposed method is comprised of three steps:

1. Field lines are grouped based on the distance of their foot point to the nearest coronal boundary ($\theta_b$),

2. For each considered group of lines, we collect the velocity values associated with all line points located at the same heliocentric distance, and we average them. The error associated with the result accounts for the number of points that have been averaged.

3. For each field line group, we compute the mean expansion factor ($f_s$) by averaging the expansion factors of the field lines within that group.

We consider the method used to associate the outflow speed and the magnetic field to be valid if the group of lines with the smallest value of $\theta_b$ and the largest value of $f_s$ shows a velocity profile characterized by slower corona plasma outflow speeds compared to the group of field lines with the largest $\theta_b$ and smallest $f_s$. It is worth noting that the verification method just described groups the magnetic field lines based on the proximity of the foot points to the nearest coronal hole boundary (without imposing any additional constraints on them) and then determines the average $f_s$ and the resulting radial speed profile of each of the groups.

### 3. Input Data

To apply the Doppler dimming technique described in Section 2, continuous and simultaneous observations of the solar corona in polarized brightness of visible light and the Ly$\alpha$ line are needed. A set of data with such characteristics were acquired from 1997 June 1 to 1997 June 28 by the ground-based Mauna Loa Solar Observatory (MLSO) MK3 coronagraph and by the space-based SOHO/LASCO-C2 (Brueckner et al. 1995) and SOHO/UVCS (Kohl et al. 1995) instruments. This period is the only one during which the solar corona has been observed extensively and daily both in visible light and UV Ly$\alpha$, as well as from near the solar limb out to $6R_⊙$. This 28 day time interval spans slightly more than a complete solar rotation, encompassing the second half of the 1923 and the first half of the 1924 Carrington rotation. These observations were made near the time of the 23rd solar cycle minimum, when the solar atmosphere was characterized by a simple distribution of the coronal structures, i.e., extended polar coronal holes and broad equatorial streamers, due to an almost dipolar configuration of the global magnetic field.

The photospheric magnetic field maps considered for this analysis are based on the NSO Kitt Peak Vacuum Telescope (KPVT; Pierce et al. 1976) observations, using the NASA/NSO Spectromagnetograph (Jones et al. 1992), and they cover the same period of time of the available coronagraphic images. Because we are interested in the global configuration of the magnetic field lines in corona, we decided to consider photospheric maps that collect magnetograms acquired during a full Carrington rotation (CR), starting and ending at Carrington longitudes of 0° and 360°. As it has been described in Section 2.2, this type of maps differs from that usually considered by modelers, with the central meridian of the latest magnetogram assimilated into the map positioned at the center of the synoptic map. The maps used refer to CRs 1923 and 1924.

#### 3.1. Outflow Speed Images

The radial outflow speed was obtained by combining observations from the MLSO MK3 coronagraph and the SOHO/LASCO-C2 and UVCS instruments. By design, these instruments have different characteristics, and therefore the images require careful pre-processing before they can be combined. SOHO/LASCO-C2 acquires full-disk images of the solar corona in visible polarized light with a field of view ranging from approximately 2.1 to $6.0R_⊙$. To extend the visible light observations to lower heliocentric distances, the SOHO/LASCO-C2 images were combined with those acquired from the ground-based MLSO MK3 coronagraph using the methodology described in Bemporad (2017), which extended the observational coverage of the solar corona down to $1.1 R_⊙$. On the other hand, SOHO/UVCS synoptic spectrometric observations consist of raster scans of the full corona at eight different angular positions separated by 45° and covering a range between $1.4R_⊙$ and $3R_⊙$. During the period of interest for this analysis, UVCS observations were acquired each day over a time interval of about 10 to 12 hr that, due to the solar minimum conditions, can be considered representative of the average Ly$\alpha$ emission over the whole day.

To combine these two sets of data, it is necessary to interpolate and extrapolate SOHO/UVCS observations to obtain a full image of the solar corona comparable with SOHO/LASCO-C2 data in terms of the field of view. The method used to measure the outflow velocity starting from these data sets and the assumptions made are described in detail in Bemporad (2017).

The analysis presented in this paper makes use of the outflow speeds obtained from the above approach for heliocentric distances ranging from 2.5 to $5.0R_⊙$. This range was selected because the uncertainties in the outflow speeds above and
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Plot of the IMF and of the solar wind speed predictions (blue dots) at 1 au obtained by running KPVT ADAPT maps of 1997 June 7, for realization number 008, compared to the values measured by the ACE satellite (black line) at 1 au.</figcaption></figure>

below this interval were generally too large for them to be
useful for our analysis.

3.2. Magnetic Field Configuration

To obtain the global solar magnetic field configuration over
the period of interest, we ran the WSA model using ADAPT
photospheric magnetic field maps derived from KPVT
magnetograms. As briefly described in Section 2.3, the ADAPT
magnetic flux transport model evolves the global field forward
in time until a new a magnetogram is obtained (for KPVT, this
generally occurred once a day) and generates an ensemble of
12 different realizations, resulting in 324 different maps if a
complete solar rotation is considered (i.e., 27 days multiplied
by 12 realizations).

Available coronagraphic data were acquired over two
different CRs, hence we ran WSA over two different ADAPT
map sets, each one corresponding to one of the CRs. We
considered the following collections of photospheric maps: (i)
from 1997 May 22 and 1997 June 17, i.e., CR 1923; and (ii)
from 1997 June 18 to 1997 July 15, i.e., CR 1924.

For both CRs, the WSA model was run and solar wind
predictions at Earth were compared to in situ spacecraft
observations of the solar wind speed and of the IMF polarity
from the WIND satellite (Acuña et al. 1995). The model run
having the best agreement with observations was then deemed
the one mostly likely to have the best coronal magnetic field
solution. For this study, we used WSA to extrapolate the
coronal magnetic field up to 5.0R⊙. As explained in

Section 2.3, the best realization is identified quantitatively by
using the WSA Prediction Metric (Meadors et al. 2020), which
is basically the ratio of the fractional agreement between model
prediction and observations in IMF polarity over the rms
residual of these values. In this case study, the score was
computed over a complete Carrington rotation, i.e., a temporal
window of about 27 days, and considering WSA predictions 4
days in advance. Once the best realization for each day of the
CR under analysis was retrieved, we selected the best one by
visually comparing WSA predictions and measured values.

The best ADAPT realization found for CR 1923 was
obtained from photospheric maps from 1997 June 7. Figure 3
shows WSA predictions (blue dots) with respect to the values
measured at 1 au (black line) by the ACE satellite. As seen in
the figure, the predictions and measurements are generally in
good agreement, except for the period between 1997 June 13
and 1997 June 15, where solar wind predictions overestimate
the solar wind speed at 1 au.

Figure 4 shows the coronal holes derived by the WSA model for the selected realization. The color code of the plot refers to the speed reached at 1 au (or the terminal solar wind speed) by the solar wind associated with magnetic field lines rooted at the photosphere.

3.3. Outflow Speed Synoptic Map

As explained in Section 2, our strategy consists of creating
Doppler dimming outflow speed synoptic maps derived by
using observations from the visible portions of both the eastern
WSA_V5.3 AKPVT R008 06/07/1997 20h:00m:00s s/c = EARTH

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Coronal hole configuration derived by the WSA model for realization number 008 obtained from the photospheric ADAPT KPVT map generated on 1997 June 7.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Schematic showing the composition of the outflow speed synoptic map obtained for the CR 1923 by combining observations acquired in correspondence of both the eastern and the western limb. Starting from the portion of the Sun that was at the central meridian on 1997 June 7 (i.e., day of the best found ADAPT realization), we located the observations of the eastern and western limbs in the same map by considering when those portions of corona would be and/or were at the central meridian. The map is then consequently filled out with the available observations of the solar corona at the limb.</figcaption></figure>

and western limbs of the solar corona. The observations used are those nearest in time to that of the time stamp of the ADAPT realization that provided the best overall coronal and solar wind solution. Of course, in constructing such maps, we also needed to account for the limited availability (due to, e.g., data gaps or regions where the speeds could not be derived) of the coronal observations in Ly$\alpha$, and consequently of the outflow speed images.

Figure 5 shows the technical steps applied to construct such Doppler dimming outflow speed synoptic maps. As reported in Section 3.2, we found that, among the set of ADAPT maps related to the CR 1923, realization number 008, calculated starting from the magnetogram generated on 1997 June 7, was the one providing the best overall agreement between the predicted and the observed solar wind speed and the IMF

polarity values at 1 au. For this reason, we constructed a new synoptic map centered in time on this day.

On June 7th, coronal plasma at central meridian was not visible in the coronagraphic images, because it was occulted by the instrument occulter. Assuming rigid rotation of the Sun, it follows that the portion of corona visible on the western limb in the coronagraphic images acquired on 1997 June 7 was at the central meridian on 1997 May 31, i.e., 7 days prior. We rounded this time difference to 7 days, instead of ≈6.7, to simplify the process. Given that the longitudinal resolution of the Doppler data is ≈13°/2, this difference in time corresponds to a longitudinal shift less than that of a grid cell. On the other hand, the eastern limb was showing the “future,” i.e., the portion of corona that would be positioned at the central meridian on 1997 June 14 (see Figure 5). As shown in Figure 1,
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Example of outflow speed synoptic maps obtained by combining eastern and western limb observations for the CR 1923. It refers to the heliocentric distance of $5.0R_⊙$.</figcaption></figure>

each day of coronagraphic observations produces a 13°2 wide longitudinal strip (i.e., 360°/27.2753 days) of the final 360° wide synoptic map comprised of observations from both eastern and western limbs. The approach taken was to begin with eastern and western limb observations from 1997 June 7 and place them in the appropriate longitudinal locations on the map. The next step consisted in adding the eastern and western longitudinal strips of data from the day before and after the 7th, and so on, until the entire map was filled with Doppler dimming outflow speeds. Such maps were created for differing heliocentric distances ranging from $2.5R_⊙$ to $5.0R_⊙$ with steps of $0.1R_⊙$.

Figure 5 shows the composition of the map created by applying the method we just described. It is worth to point out that, due to the limited time cadence of wind speed maps, resulting in a low longitudinal resolution in the synoptic maps, we were forced to use “future” eastern limb data to fill the first 3 days of the map (right columns of the synoptic map). The resulting map is composed of observations of the eastern and western limb in the temporal range from June 1st to June 13th and from June 1st to June 14th, respectively. Moreover, each element on the x-axis of the map corresponds to one day of observation, resulting in a grid of 13°2.

Figure 6 shows the solar wind map obtained for the heliocentric distance of $5.0R_⊙$. As can be seen in the figure, there are no solar wind speed measurements near the solar equator. This is due to the fact that the Doppler dimming technique is only sensitive to outflow speeds higher than 50 km s⁻¹; for solar wind streams under this speed limit, it is not possible to assign a value. On the other hand, the two vertical white strips centered at 59°9 and 246°1 of longitude are due to lack of instrumental observations.

## 4. Results

We present here the preliminary results obtained by applying the methodology described in Section 2. We divided the magnetic field lines into three groups by considering the distance of their respective foot points to the nearest coronal hole boundary as the grouping criterion. The selected groups are: (1) 0° < $\theta_b$ < 4°; (2) 4° < $\theta_b$ < 8°; and (3) 8° < $\theta_b$ < 20° (i.e., the maximum found value). These value ranges were chosen in an attempt to distinguish between the sources of slow ($\theta_b$ < 4°) and fast wind ($\theta_b$ > 8°), with values in between exploring intermediate solar wind speeds. As a consequence of this classification, the first group collects all magnetic field lines near the hole boundaries, group 3 contains the field lines rooted deep inside the coronal holes, and the second one is composed of field lines in between these two conditions.

Figure 7 displays the resulting velocity profiles for the three groups of field lines obtained for the analysis performed on CR 1923 over a heliocentric distance range from 2.5 to $5R_⊙$. The solid line refers to group 1, the dashed line to group 2, and the dotted line to group 3. Each point is the average of all velocity values of the grouped field lines for that specific heliocentric distance, the error bars represent the standard error of the mean for that point, and the surrounding colored area represents the estimated uncertainty on speed measurements performed with the Doppler dimming technique. Such uncertainties have been estimated by comparing the 2D outflow speed measurements on the plane of sky (POS) derived with the quick inversion method, with the plasma velocities on the POS based on 3D MHD simulations (Bemporad et al. 2021). This analysis led to a two-dimensional map in which each value represents the estimated relative error of the measured outflow speed in that specific position in the corona, i.e., solar radius and latitude. By using this information, it was then possible to associate an
Solar wind outflow speed wrt
the distance to the nearest coronal hole boundary
CR 1923

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Solar wind speed profiles obtained for each group of field lines resulting from the analysis of CR 1923 data. Group 1 in blue (solid line) is associated with values of $\theta_b$ in the range $0^{\circ} < \theta_b < 4^{\circ}$; group 2 in red (dashed line) with $4^{\circ} < \theta_b < 8^{\circ}$, and group 3 in green (dotted line) with $8^{\circ} < \theta_b < 20^{\circ}$. Each point is given by the mean of the velocity values obtained for that specific heliocentric distance. Error bars represent the standard error of the mean and are linked to the number of points available to compute the corresponding averaged speed value in this analysis. The colored area surrounding the lines shows the uncertainty related to the inversion method used to retrieve the outflow speed with the Doppler dimming technique for the corresponding heliocentric distance.</figcaption></figure>

absolute error with each speed value assigned to a field line's point; the area shown in Figure 7 is the average of the uncertainties on the speed values associated with the field line's points that belong to that group and are located at the corresponding heliocentric distance. Because we were not able to associate a speed value with each point of the extrapolated field lines, each point of the plot shown in Figure 7 was obtained by averaging a different number of speed values. It is then useful to use the standard error of the mean to give an idea of the difference among the plotted points in terms of amount of used data. As it is possible to observe, both low heliocentric altitudes and points belonging the first group of lines are associated with larger error bars. This is due to the fact that, for field lines in the equatorial region and for low heliocentric distances, the outflow speed is too low ($<$50 km s⁻¹) to be measured with the Doppler dimming technique. It is important to point out that the error bars are strictly related to the statistic analysis performed on the results of the method proposed here, with the surrounding colored area giving an idea of the uncertainties due to the inversion technique being used. It is also worth mentioning that the presented method and its verification rely on the extrapolation of the magnetic field obtained with WSA model, and hence not on the real configuration of the coronal field. For instance, small coronal holes and streamers may not be represented. This might result in erroneous values of the expansion factor and distance to the nearest coronal hole boundaries; therefore, in an effort to mitigate these types of errors, we used a statistical approach

<table><caption>**Table 1**
Summary of Field Line Groups</caption><thead><tr><th>Group Number (1)</th><th>θ<sub>b</sub> (deg) (2)</th><th>Lines Number (3)</th><th>f<sub>s</sub> (4)</th><th>max v<sub>w</sub> - min v<sub>w</sub> (km s<sup>-1</sup>) (5)</th></tr></thead><tbody><tr><td>1</td><td>0-4</td><td>461</td><td>20.7</td><td>89.0 ± 16.7</td></tr><tr><td>2</td><td>4-8</td><td>2747</td><td>10.9</td><td>105.9 ± 45.2</td></tr><tr><td>3</td><td>8-20</td><td>8407</td><td>6.8</td><td>149.7 ± 7.3</td></tr></tbody></table>

that considers the average of several lines. We believe that the analysis of the error associated with the averaged speed value is a complex matter that should be addressed in a dedicated paper, because it involves not only the contribution of the error associated with the measurements of the solar wind speed through the Doppler dimming technique and the uncertainty related to the extrapolated magnetic field configuration, but also a quantification of the error introduced by the considered assumptions.

Table 1 provides a summary of all the key values associated with each selected group of field lines. The first column indicates the magnetic field line group number, and the second column reports the boundary values of $\theta_b$ considered for the group. The third column provides the number of magnetic field lines residing in a given group. Group 1 has significantly fewer lines compared to group 3, because the typical speeds within this group are near the Doppler dimming measurement threshold (i.e., fewer of the field lines have measurable solar wind speeds associated with them). The fourth column of the table reports the mean value of the expansion factor obtained for each group of lines, while the last column shows the difference between the speed values measured at the highest and at the lowest height.

The curves shown in Figure 7 and the numbers reported in Table 1 are in accordance with the expectations described in Section 2.4. The first group of lines rooted between 0° and 4° is associated with the largest averaged value of expansion factor, and the velocity profile is the one associated with the lowest value of speed at $5 R_⊙$. On the other hand, the third group that collects the lines residing between 8° and 20° is associated with a small value of the mean expansion factor and with the highest speed value at $5 R_⊙$. This group of lines is also the one that experiences the highest increase in speed within the selected range of heliocentric distances. The second group returned results in between those found for the other two.

It is also interesting to note the evolution of the three velocity profiles shown in Figure 7: the curve related to group 1 is slow and tends to fluctuate between higher and lower values of speed, with an initial semi-steady increase in speed, followed by a slight decline at $3.5 R_⊙$, and then a resumption in the steady increase in speed. Group 3 (dotted line) shows a decisive and steady increase in speed.

Finally, the highest value of speed reported in the velocity profile plot (≈200 km s⁻¹) is in accordance with results obtained from other studies showing that, in the range of the heliocentric distances considered in this analysis, i.e., 2.5 to 5.0 $R_⊙$, the solar wind is not expected to reach the final speed value measured at 1 au (Wang et al. 2000; Imamura et al. 2014). However, the plot also indicates that, even at low heliocentric distances, it is possible to separate the two types of wind.

We used the same method here described to also analyze data related to the CR 1924. In this case, the best ADAPT
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Solar wind speed profiles obtained for each group of field lines resulting from the analysis of CR 1924 data. Group 1 in blue (solid line) with $0^{\circ} < \theta_b < 4^{\circ}$; group 2 in red (dashed line) with $4^{\circ} < \theta_b < 8^{\circ}$, and group 3 in green (dotted line) with $8^{\circ} < \theta_b < 20^{\circ}$. Each point is given by the mean value of velocity values obtained for that specific heliocentric distance. Error bars are the standard error of the mean and are linked to the number of points available to compute the corresponding averaged speed value. The colored area surrounding the lines shows the uncertainty related to the inversion method used to retrieve the outflow speed with the Doppler dimming technique for the corresponding heliocentric distance.</figcaption></figure>

realization was 009, obtained from 1997 July 3. Starting from this date, we constructed a new data cube composed of synoptic maps, as for CR 1923, that combines speed measurements performed over both solar limbs. Figure 8 shows the obtained results. As it is possible to see in the figure, field lines near the coronal hole boundary ($0^{\circ}-4^{\circ}$ group, solid line) are associated with slower solar winds, while those having their foot points deep inside the coronal hole ($8^{\circ}-20^{\circ}$ group, dotted line) show higher values of speed, especially at the highest solar radius considered in this analysis. It is also important to note that the shape of the obtained curves is comparable to that found for the CR 1923. The increase in speed for lines rooted deep inside the coronal hole follows a well-defined curve with a continuous increase in speed. On the other hand, it seems that flows following lines having their foot points near the hole boundaries experience periods where the speed increase slowly overall but with a clear, temporary decline starting around $3.7R_{\odot}$, followed by a resumption in the acceleration starting at $4.2R_{\odot}$. The slow wind profile may suggest that there is more than one acceleration acting on it.

## 5. Conclusions

The goal of this study was to derive velocity profiles of the solar wind along magnetic field lines in the acceleration region of the corona. To accomplish this, we combined measurements of the solar wind radial speed obtained using the Doppler dimming technique with the coronal magnetic field

configuration derived from the WSA model driven by photospheric field maps.

We applied the method described here to observations of the solar corona acquired between 1997 June 1 and 1997 June 28 by the SOHO/LASCO-C2 and the SOHO/UVCS instruments and to KPVT magnetograms acquired during the same period. Then, we validated it by comparing the obtained results with our previous knowledge of the relationship between the flux tube expansion factor ($f_s$), the distance from the field line foot point to the nearest coronal boundary ($\theta_b$), and the speed of the solar wind. In particular, we verified that the fast solar wind is associated with field lines rooted deep inside coronal holes (large $\theta_b$ and small $f_s$), and the slow solar wind is associated with field lines near hole boundaries (small $\theta_b$ and large $f_s$). Given the coarse resolution of the solar wind measurements, the subtleties of the slow solar wind (e.g., different possible sources and acceleration mechanisms) beyond proximity to coronal hole boundaries were not explored in this work.

We obtained results for two different Carrington rotations (CR 1923 and CR 1924), demonstrating the applicability of the method and its capability to link measured solar wind velocity to the extrapolated coronal magnetic field. The results show a steady increase in the fast solar wind from 2 to $5R_{\odot}$ that suggests a single acceleration mechanism acting on it. The slow solar wind displays more complex behavior. It emerges low in the corona with speeds slower than the fast wind and then accelerates until it reaches a height of about $3.7R_{\odot}$, where it briefly slows and decelerates before resuming its acceleration. This behavior appears more evident in CR 1924, with a more pronounced brief slowing and deceleration. This apparent two-stage acceleration behavior may suggest that more than one acceleration mechanism is acting on the slow wind, one lower in the corona and another (possibly the same one acting on the fast solar wind) further out.

The velocity profiles obtained represent the starting point for future analyses aimed at improving our understanding of the acceleration of the solar wind, as well as improving our ability to predict the speed of the background solar wind. For instance, the approach presented here can be used to analyze the relationship between the velocity and the characteristics of the magnetic lines (e.g., expansion factor; proximity to coronal hole boundaries, active regions, and other structures; and magnetic topology), leading to new and improved, radially dependent, empirical relationships between the extrapolated global magnetic field and the solar wind velocity. It could also result in new constraints for coronal and solar wind models that are currently used for space weather purposes, such as predicting the arrival times of high-speed streams and coronal mass ejections (CMEs) or the magnetic connectivity between a spacecraft and the Sun.

While the method described in this paper is limited by several approximations and simplifying assumptions (e.g., rigid rotation of the corona), the coarse resolution of the observations, and having a small amount of data available to test it, the approach has demonstrated the usefulness of the technique. It has also resulted in a potentially useful tool capable of being applied to data from the Metis/Solar Orbiter, as well as those from the upcoming CODEX mission.

This work was supported by NASA Goddard Space Flight Center through Cooperative Agreement 80NSSC21M0180 to
the Catholic University, Partnership for Heliophysics and
Space Environment Research (PHaSER).

The ADAPT model development is supported by the AFRL and Air Force Office of Scientific Research (AFOSR) tasks 18RVCOR126 and 22RVCOR012. The views expressed are those of the authors and do not reflect the official guidance or position of the United States Government, the Department of Defense, or the United States Air Force. The appearance of external hyperlinks does not constitute endorsement by the DoD of the linked websites or the information, products, or services contained therein. The DoD does not exercise any editorial, security, or other control over the information you may find at these locations. The input data utilized here by ADAPT was obtained by the National Solar Observatory.

C. N. Arge and the Wang-Sheeley-Arge (WSA) model are supported by the NASA Internal Scientist Funding Model (ISFM).

ORCID iDs

Marta Casti https://orcid.org/0000-0002-9716-3820

Charles N. Arge https://orcid.org/0000-0001-9326-3448

Alessandro Bemporad https://orcid.org/0000-0001-5796-5653

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

Carl J. Henney https://orcid.org/0000-0002-6038-6369

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