Assessment of Vertical Redistribution of Electron Density in Ionosphere During an X-Class Solar Flare Using GNSS Data

Abstract

The impact of solar flares on the Earth’s ionosphere has been studied for many decades using both experimental and theoretical approaches. However, the accuracy of predicting ionospheric layer dynamics in response to variations in solar radiation remains limited. In particular, understanding the vertical redistribution of charged particles in the ionosphere during flares with different spectral characteristics presents a significant challenge. In this study, a method is presented for reconstructing the temporal evolution of the vertical electron concentration ($Ne$) profile based on GNSS (Global Navigation Satellite Systems) measurements of total electron content along partially illuminated satellite-receiver paths. Using this method, vertical profiles of $Ne$ were reconstructed during various phases of the X13.3-class solar flare that occurred on 6 September 2017. The resulting profiles correctly respond to the observed variations in solar extreme ultraviolet and X-ray radiation. This indicates that the method can be effectively applied to analyse other powerful solar events.

1. Introduction

During solar flares, there is a sharp increase in radiation across a wide range of wavelengths. This leads to enhanced ionisation in different regions of the Earth’s ionosphere, each characterised by distinct compositions of neutral and charged particles, as well as varying temperatures, densities, and photochemical reaction rates [1,2,3,4,5]. Consequently, different parts of the ionosphere are subject to varying degrees of ionisation depending on the spectral composition of a given flare.

It is well established that X-ray radiation during flares penetrates to the lower altitudes of the ionosphere, causing an increase in electron concentration ($Ne$) in the D region ($h<$ 90 km) by several orders of magnitude [6]. This affects the shape of the waveguide through which VLF–LF signals propagate, leading to distortions in their amplitude and phase [7,8,9,10,11,12,13,14]. The relationship between D region dynamics and VLF signal characteristics is used in developing empirical and semi-empirical models of the lower ionosphere, as well as in validating the results of theoretical models [4,13,15,16,17,18,19]. In contrast, solar extreme ultraviolet (EUV) radiation is absorbed at higher altitudes, ionising the overlying E (90 $<h<$ 120 km) and F regions ($h>$ 120 km), where the majority of the ionosphere’s charged particles are located and contribute to the total electron content ($TEC$) [20,21,22].

At present, there are many theoretical models that describe the behaviour of hundreds of ionospheric components under both quiet and disturbed conditions [23,24,25,26,27,28]. Many of them are physically detailed and comprehensive, but their complexity often results in a large number of input parameters with unknown values, such as the densities of minor neutral constituents and reaction rate constants. This limits the accuracy of predictions of charged particle dynamics, particularly under flare conditions. As a result, experimental observations and empirically derived models remain highly valuable for studying solar-terrestrial interactions [29,30,31,32,33].

Despite decades of ionospheric monitoring using various experimental methods, only a few techniques can capture the rapid dynamics of the vertical electron density profile during short-lived events such as solar flares. For instance, measurements from geophysical rockets are spatially and temporally limited, making them difficult to use in developing empirical patterns. Satellite measurements are better suited for studying gradual diurnal and seasonal variations than for observing the rapid effects of flares at specific locations. Ionosondes and incoherent scatter radars are widely used to investigate flare-induced ionospheric effects across various flare classes [27,34,35,36]. However, these instruments do not offer high temporal or spatial resolution. Moreover, the high operational cost of incoherent scatter radars prevents continuous monitoring, resulting in a lack of observational data for many events. Therefore, additional methods for evaluating ionospheric layer responses to sudden changes in solar radiation remain necessary.

It is well known that $TEC$ fluctuations caused by solar flares have been successfully measured for many years using data from Global Navigation Satellite Systems (GNSS) [37,38,39,40,41]. Radio waves of different frequencies experience different code and phase delays as they propagate through the ionosphere, making it possible to determine the number of electrons along the satellite–receiver path. Therefore, the total electron content can be calculated using signal delay measurements at two GPS (Global Positioning System) frequencies: L1 (1575.42 MHz) and L2 (1227.60 MHz). This ionospheric monitoring method offers a good time cadence and enables the assessment of $TEC$ variations across the illuminated side of the Earth during various phases of a flare. Recent studies highlight the growing popularity of this method for identifying, analysing, and quantitatively assessing ionospheric disturbances caused by solar flares, as well as their consequences. For example, Yasyukevich et al. [37] conducted a comprehensive analysis of the effects of two powerful X-class flares that occurred on 6 September 2017 on global $TEC$ variations, using data from various GNSS. According to their estimates, during the stronger of these two flares, $TEC$ increases exceeded 10 tecu (1 tecu $={10}^{16} {\mathrm{m}}^{-2}$) at some latitudes, and a significant degradation in the GNSS positioning accuracy was observed, lasting for approximately 30 min after the event. The ionospheric and geomagnetic response to another intense X-class flare, which occurred on 13 December 2001, was investigated by Meza et al. [38]. The authors compared the response times and rates of change in both electron density and magnetic field variations and demonstrated the influence of different parameters on vertical $TEC$. Additionally, the high temporal resolution of GNSS data has enabled wavelet analysis to detect flare-induced ionospheric effects, as demonstrated in the study by López-Urias et al. [39]. This approach reliably identified disturbances caused by flares weaker than X2, including those that occurred near the solar limb, which are associated with reduced fluxes of geoeffective EUV emissions responsible for the main $TEC$ enhancement. A large statistical study by Sreeraj et al. [41] examined how electron density enhancements during 49 X-class flares of Solar Cycle 24 varied with solar zenith angle (SZA). Their findings also emphasise the crucial role of flare location on the solar disk, which determines the degree of absorption of different geoeffective EUV emissions in the solar atmosphere. In other words, the position of a flare affects its spectral output, particularly the ratio of X-ray to EUV radiation, which in turn ionises different layers of Earth’s ionosphere. As a result, each solar flare produces a distinct vertical profile of electron density enhancement.

Since theoretical models remain limited in their accuracy, and $TEC$ is an integrated value that does not provide information on the vertical distribution of electron density, our understanding of how flares with distinct spectra redistribute charged particles across ionospheric altitudes remains incomplete. Yet it is precisely the increase in $Ne$ at specific heights that determines the propagation, reflection, and absorption of radio waves across different frequencies [10,11,35,37]. However, previously, Leonovich et al. [42,43] proposed an experimental method to estimate the vertical $Ne$ profile by analysing $TEC$ enhancements along a set of partially illuminated satellite–receiver paths during several X-class flares between 1998 and 2002. This method assumes that only the illuminated part of the ionosphere undergoes ionisation, while the contribution of scattered radiation is negligible. A combined analysis of the ionospheric illumination boundary height ($H_0$) and the corresponding $\Delta TEC$ along each path allowed the authors to conclude that the bulk of ionisation during flares occurs at altitudes below 300 km. In their studies, they successfully constructed empirical relationships between $\Delta TEC$ and $H_0$ at the time of maximum ionospheric ionisation, based on data from several dozen GPS stations.

This study presents a refinement of this method to reconstruct the temporal evolution of the vertical electron density profile using GNSS data collected during the most intense solar flare of Solar Cycle 24, which occurred at 12:02 UT on 6 September 2017 (X13.3, S08W32). Additionally, the obtained $Ne$ dynamics are analysed alongside variations in EUV and X-ray radiation to empirically illustrate their absorption at different ionospheric altitudes.

Section 2 describes the method used in this study. Section 3 presents the solar and ionospheric data sets employed. Section 4 provides the results and discussion. Section 5 summarises the main conclusions.

2. Method

As outlined in the Introduction, the method proposed in this study is based on the approach introduced by Leonovich et al. [42,43]. It utilises $TEC$ measurements from GPS ground stations near the solar terminator, resulting in partially illuminated satellite–receiver paths. Figure 1 schematically illustrates such paths. On the illuminated segments (shown in red), changes in the electron density occur and therefore contribute to variations in $TEC$. In contrast, on the shaded segments (shown in purple), no ionisation occurs due to the absence of ionising solar photons. The presence of stations with varying altitudes of the illumination boundary above them, denoted as $H_0$, makes it possible to determine the portion of the total electron content located above different altitudes. This enables the vertical electron density profile to be reconstructed through successive iterations. Unlike previous applications of this method, the present study investigates the temporal evolution of the function $\Delta TEC$($H_0$, t), allowing the reconstruction of the vertical $Ne$ profile not only at the ionisation peak but throughout the entire duration of the solar flare.

3. Experimental Data

3.1. Solar Data

To understand the causes of ionospheric changes during different phases of the X13.3 solar flare that occurred on 6 September 2017, variations in X-ray and extreme ultraviolet (EUV) radiation fluxes were analysed. These data were obtained from the EUVS (Extreme Ultraviolet Sensor, Boulder, CO, USA) and XRS (X-ray Irradiance Sensor, Suitland, MD, USA) instruments onboard the GOES-R (Geostationary Operational Environmental Satellite—R Series, Suitland, MD, USA) and the MEGS-B (Multiple EUV Grating Spectrograph, Palo Alto, CA, USA) instrument onboard the Solar Dynamics Observatory (SDO, Greenbelt, MD, USA).

Since 2017, the EUVS instrument on GOES-R has been measuring EUV emissions from the solar spectrum at a 1-minute cadence, including the He II 30.4 nm and Fe XV 28.4 nm emission lines. The He II 30.4 nm line is the most geoeffective during the impulsive phase of a solar flare, contributing most significantly to increases in total electron content [5,22,44]. The Fe XV 28.4 nm line is another important emission that also causes significant ionisation in the ionosphere, particularly during the flare’s late phase [40,44,45]. These two lines, together with X-ray radiation in the 0.1–0.8 nm range measured by GOES, are considered the primary sources of ionospheric ionisation.

Due to the 1-minute temporal resolution of GOES-R measurements, 10-second cadence data from MEGS-B, covering wavelengths from 33 to 106 nm, were used to refine the identification of emission peaks. Although MEGS-B does not observe the 30.4 nm and 28.4 nm lines, it measures C III 97.7 nm and Fe XVI 33.5 nm emissions, which originate from the same regions of the solar atmosphere and have similar temperatures as He II and Fe XV, respectively. Consequently, they exhibit nearly synchronous variations with the target geoeffective lines [44].

The temporal evolution of the irradiance of the considered emissions is shown in Figure 2. The vertical dotted line indicates the time moment of the X-ray flux peak, which occurred at 12:02 UT. The 1-minute He II and Fe XV measurements are shown as circular markers. The main peak of Fe XV radiation typically occurs later than the impulsive phase and corresponds to the flare’s late phase [44,45,46]. However, in this case, the peak of the warm coronal emissions was observed shortly after the impulsive phase—approximately 9 min after the He II peak and 4 min after the X-ray peak.

The shaded areas on the plot represent ±1 min intervals around the local maxima of the He II and Fe XV emissions. As expected, the local maxima of the 10 s C III and Fe XVI emissions fall within these shaded intervals. Analysing the red curves in Figure 2, it can be concluded that the first He II peak likely occurred slightly later, and the second slightly earlier, than the observed maxima, though both actual peaks still fall within the shaded intervals. The Fe XV and Fe XVI emissions usually show less synchrony than He II and C III, so it is not possible to definitively determine the exact timing of the real Fe XV peaks. Nevertheless, given the cadence of the available solar observational data, the analysis of the $Ne$ response to geoeffective solar radiation will primarily rely on the shaded time intervals rather than the precise EUV lightcurve peaks.

3.2. Ionospheric Data

To investigate the temporal dynamics of the ionospheric response to the X13.3 solar flare, GNSS data from the SOPAC (Scripps Orbit and Permanent Array Center) network were used, with a temporal resolution of 15 s. Stations were selected so that the height of the illumination boundary ($H_0$) just before the flare (11:48 UT, 6 September 2017) ranged from 50 to 500 km. This corresponds to solar zenith angles at the stations between 97.1° and 111.8°. To minimise latitudinal effects and reduce data dispersion, only stations located within the 30°–35° latitude band were included. Additionally, only signals from GPS satellites with elevation angles greater than 60° were used, reducing errors when converting slant $TEC$ to vertical $TEC$ along partially illuminated paths.

After filtering out noisy data and applying the selection criteria above, 56 stations remained for analysis. Their locations are shown on the left panel of Figure 3, where the colour of each marker indicates the height range of the illumination boundary above the station at the pre-flare moment (11:48 UT). The right panel of Figure 3 shows the decrease in average $H_0$ for each station group during the flare. The following analysis focuses on these selected groups.

The flare-induced $TEC$ enhancement ($\Delta TEC$) was calculated by detrending the measured total electron content variations, following the method described in [33,44]. According to this method, a parabolic trend associated with the trajectory of the GPS satellite is subtracted from the measured variations in relative total electron content. The resulting difference reflects the dynamics of $TEC$ enhancement during the flare for a specific station–satellite pair. As an example, the left panel of Figure 4 shows the variations in relative vertical $TEC$ (solid black line) measured at “sg33” GPS station (31.8° N 106.5° W). The parabolic trend is shown as a black dotted line, and the time intervals used to construct the parabola are marked in blue. These intervals are selected from periods before the initial rise in ionisation and after the flare has ended. In the right panel of Figure 4, the black line represents the resulting $\Delta TEC$ dynamics, while the red curve indicates the altitude of ionospheric illumination ($H_0$) above this station during the flare. The $\Delta TEC$ dynamics for all stations shown in Figure 3 were calculated using this method.

4. Results and Discussion

4.1. Calculation of $\Delta TEC$ in Different Ionospheric Regions

It is well known that the increase in concentration of charged particles strongly depends on the solar zenith angle. To isolate the effect of partial illumination of the satellite–receiver path, the $\Delta TEC$($H_0$, t) functions were normalised using a dynamic coefficient to compensate for variations in SZA between 11:48 and 12:24 UT. While cosine-based functions of SZA are commonly used for $TEC$ normalisation under SZA < 60° [31,41,42,47,48], in this case, normalisation coefficients had to be determined for much larger angles, because the minimum solar zenith angle recorded at the stations used during the considered time period was 87°.

For 80° < SZA < 96°, an empirical relation describing the decrease in $\Delta TEC$ was derived using data from GNSS stations located where the ionosphere was fully sunlit during the flare under consideration. The red circles in the left panel of Figure 5 show the peak $TEC$ increases measured at approximately 250 such stations with varying solar zenith angles. A clear linear relationship between $\Delta TEC$ and SZA value was observed, with a coefficient of determination of ${\mathrm{R}}^2$ = 0.97. This relation showed that $\Delta TEC$ decreases according to the formula: $\Delta TEC=-0.08·$ SZA $+7.6$. Therefore, during the period when $H_0$ remained below the ionospheric lower boundary (i.e., for SZA < 96°), this empirical function was applied. Correction coefficients for the considered SZA range were needed during the later stages of the flare, when the ionosphere above some stations became illuminated.

For SZA ≥ 96°, an exponential decay factor was applied, since the electron concentration was sufficiently low to cause a subsequent decrease. The exponential decay coefficient (k) was defined based on theoretical estimates, specifically from the results of the International Reference Ionosphere (IRI) model, for the heights of the ionospheric electron density maximum (250–300 km) and the heliogeophysical conditions considered in this study. The value of the exponential decay coefficient k within the considered altitude range varied from 0.02 to 0.06. In this study, a value of $k=-0.05$ was used for the calculations. Ultimately, using the boundary values of k leads to variations in $Ne$ of up to 20%, with the maximum deviation observed at the peak of the flare.

As a result, the reduction coefficient function was piecewise-defined: for SZA values up to 96°, an empirically derived formula was applied; beyond 96°, an exponential reduction based on theoretical modelling was used. The corresponding curves are shown in the right panel of Figure 5, where the black line represents the resulting values of the $TEC$ reduction coefficient for solar zenith angles between 90° and 110°. These coefficients were used to normalise each individual $\Delta TEC$ curve shown in the right panel of Figure 4 according to the SZA dynamics at the corresponding station during the flare.

The resulting $\Delta TEC$ variations were grouped based on the $H_0$ for each GNSS station at the pre-flare moment. As described in Section 3.2, eight $H_0$ intervals were selected, ranging from 50 to 450 km in 50 km increments. Figure 6 shows the average $\Delta TEC$ dynamics for these groups before (left panel) and after applying dynamic normalisation (right panel), which accounts for changes in SZA during the flare. The curves in the right panel represent the electron content increase above $H_0$, which is normalised as if the Sun were at the zenith.

4.2. Analysis of the Obtained $\Delta TEC$ Curves

On the right panel of Figure 6, the red and blue shaded areas correspond to the same time intervals as in Figure 2. In this section, a joint analysis of the solar irradiance and the behaviour of the five upper curves from the right panel of Figure 6 is presented. The shape of the three lower curves ($H_0$ > 300 km) is not analysed here, as they correspond to regions with very limited ionospheric illumination, and their variations may primarily reflect noise.

As seen from the right panel of Figure 6, within the red-shaded regions, there are no clear peaks or inflections in the two upper curves (yellow and purple), which account for ionisation across almost the entire ionosphere, including ionisation in the D and E regions by X-ray radiation. Since X-ray ionisation significantly contributes to changes in $TEC$ during the initial phase of the flare, a pronounced $Ne$ response to EUV peaks is not observed in these curves. However, within the right red-shaded region (12:00–12:02 UT), a change in the shape of the red and grey curves can be seen, reflecting variations in electron concentration above 150 km and 250 km, respectively. Since the X-ray ionised ionosphere below 150 km is cut off here, the response to the primary He II peak is more differentiated. It should be noted that the inflections in the red and grey curves occur on the left side of the red rectangle, meaning that the decrease in ionisation begins slightly before the He II peak shown in Figure 2. This timing corresponds to a more precise position of the peak in the cold chromospheric lines (He II and C III), as determined from 10 s measurements of C III 97.7 nm. This observation further highlights the sensitivity of $Ne$ to specific emissions.

After the vertical dotted line corresponding to the X-ray radiation peak, we observe distinct peaks in the yellow, purple, and red curves, all of which incorporate this ionisation source. As expected, the green and grey curves show no response to the X-rays, as the ionosphere below 200 km was not illuminated.

In the left blue region, when the first peak of the warm coronal radiation occurred, we observe peaks in all the considered curves because the X-ray radiation had already begun to decay and no longer contributed as strongly as during the initial minutes of the flare. A similar behaviour is observed in the right blue region when the second Fe XV peak occurred, except for the grey curve. It is most likely that the peak on this curve is not differentiated, as ionisation by the 28.4 nm line occurred below 250 km, similar to what is shown in theoretical models [2,22].

4.3. Reconstruction of the Electron Concentration Profile During the Flare

In Figure 7, the blue dots represent the $\Delta TEC$ increment above the corresponding ionospheric height at various moments in time. These are the same results as those on the right panel of Figure 6, but presented as altitude profiles. The height step is non-uniform, as the actual average $H_0$ values of each station group were used. The electron concentration profile was calculated by subtracting the accumulated $\Delta TE{C}_1$ above height $H_1$ from the accumulated $\Delta TE{C}_2$ above height $H_2$, in order to determine the number of electrons formed in the altitude range from $H_1$ to $H_2$. This calculation was performed for different time moments during the flare. The resulting dynamics of the electron concentration profile in the ionosphere are shown as red horizontal bars in Figure 6.

The red bars in Figure 7 clearly demonstrate the key stages of the flare’s development in the ionosphere. From moment A (11:57 UT) to moment B (11:58 UT), a gradual increase in EUV and X-ray radiation leads to an increase in $Ne$ between 50 and 250 km. The maximum $\Delta TEC$ is observed around 100 km, where soft X-rays are the dominant ionisation source. The subsequent increase in radiation from cold chromospheric lines (He II and C III) shifts the $\Delta Ne$ peak to the 120–160 km height range (panel C; 11:59 UT). As expected, at the peak of the X-ray radiation (panel D; 12:02 UT), we observe the highest ionisation in the ionospheric D and E regions, which gradually decreases about a minute later (panel E; 12:03 UT). By the time of the first peak in the warm coronal EUV lines (panel F; 12:06 UT), the main ionisation shifts higher, as these wavelengths ionise the ionospheric F regions. A sharp drop in the Fe XV and Fe XVI radiation fluxes follows, which stops the growth of charged particle concentration in the F region (panel G; 12:11 UT). The observed high value of $\Delta Ne$ in the 100–140 km range on panel G can be disregarded, as it results from an inadequately low value of the blue curve at 140 km, which creates a sharp gradient in $\Delta Ne$ on either side of this boundary. In reality, electron concentration exhibits a smoother vertical profile. On the final panel H (12:17 UT), we observe the overall relaxation of the medium after the flare and the residual ionisation from decaying ultraviolet radiation above 100 km. Thus, the reconstructed variations of the vertical electron density profile using GNSS data are fully consistent with and appropriately reflect the variations in geoeffective radiation (Figure 2).

5. Conclusions

The question of the ionospheric response to solar flares remains open and presents a significant challenge. Existing models still do not provide sufficient accuracy in predicting the response of charged components to flares with various dynamics and spectral compositions. Experimental measurement methods either lack sufficiently high temporal and latitudinal-longitudinal resolution or do not provide vertical profiles of the parameters. Therefore, to improve the prediction of ionospheric layer dynamics under the influence of solar radiation variations, it is necessary to combine theoretical and experimental approaches or develop new mathematical methods for processing experimental data.

In this study, a new method is presented for reconstructing the dynamics of the vertical electron concentration profile using GPS measurements of total electron content along partially illuminated paths. This method is based on the idea of Leonovich et al. [42,43] and operates under the assumption that ionisation occurs only in the illuminated region of the ionosphere, neglecting the ionisation from scattered radiation. By considering stations with varying altitude of ionospheric illumination above them, the dynamics of the vertical $Ne$ profile during the X13.3 flare on 6 September 2017 were successfully reconstructed. The temporal dynamics of the reconstructed electron concentration profile show excellent agreement with the evolution of geoeffective solar radiation fluxes. In other words, the demonstrated method allowed for the experimental observation of the absorption of specific wavelengths in different ionospheric regions and proved reliable for addressing this type of problem.

The necessary conditions for applying this method include a sufficiently powerful flare, so that $TEC$ curves can be detrended under partial illumination, and the availability of enough GPS stations with solar zenith angles between 97° and 112°. At such zenith angles, the boundary of ionospheric illumination is located between 50 and 500 km in altitude, where we observe variations in electron and ion concentrations caused by solar flares of different classes.