Introduction

Solar flares have a significant impact on the solar-terrestrial environment. An accurate understanding of the relationship between solar flare emissions and Earth’s ionosphere is important for the safe construction and use of space infrastructure. When a solar flare occurs, electromagnetic emission in X-ray and EUV wavebands. In particular, it is well-known that X-rays (0.1–10 nm) and extreme ultraviolet (EUV) (10–121.6 nm) emitted during solar flares, enhanced to several 10 to a 1000 and sometimes to 10,000 during flare events, affect the Earth's ionosphere. The phenomena caused by the sudden ionization of the Earth's upper atmosphere by X-rays and EUV emitted from solar flares are widely known as sudden ionospheric disturbances (SIDs) (Davies 1990; Donnely 1969; Mitra 1974). SIDs are sudden disturbances of the ionosphere and are a superset of events, which consists of Dellinger effect (Dellinger 1937), short-wave fadeout (SWF) (e.g., Chakraborty et al. 2018, 2019, 2022; Fiori et al. 2018, 2022), sudden frequency and phase deviation (SFD/SPD) (Chakraborty et al. 2018; Watanabe and Nishitani 2013), solar flare effects (SFEs) (e.g., Curto et al. 2018), and sudden increase in total electron content (SITEC) (e.g., Tsugawa et al. 2006; Zhang et al. 2002; Shinbori et al. 2020; Tsugawa et al. 2018). The relative observation accuracy of this TEC is 0.02 TEC unit (TECU) (Hofmann-Wellenhof et al. 1992). One TECU equals 1012 electrons cm−2. We used the TEC observation data provided by the National Institute of Information and Communications Technology (NICT) and Nagoya University.

We used the Earth’s atmospheric model, GAIA, to study the TEC variations caused by different flare emission spectra. The GAIA is constructed by combining the whole atmospheric general circulation model (GCM) (Fujiwara and Miyoshi 2006, 2009, 2010; Miyoshi and Fujikawa 2003, 2006, 2008), the ionospheric model (Shinagawa et al. 2007; Shinagawa and Oyama 2006), and an electrodynamics model (** et al. 2008). The GCM treats physical processes suitable for the troposphere, stratosphere, mesosphere, and thermosphere as neutral atmospheric regions. The horizontal grid spacing was 2.8°, the vertical resolution was 0.2 scale heights above the tropopause, and the temporal resolution was 20 s. The ionospheric model solves the mass, momentum, and energy equations for the major ions and electrons. The horizontal grid spacing is 2.5° in the longitude direction, 1° in the latitude direction, 10 km in the vertical direction up to 600 km, and the time resolution is 1–4 s. The electromagnetic model treats the global ionospheric current induced by the neutral wind dynamo and polarization electric field. The model assumes that the geomagnetic field lines are equipotential and that the current dissipates at the low-altitude boundary (70 km) and is conserved along the magnetic field lines between the north and south high-altitude boundaries (720 km) along the same magnetic field lines. The horizontal grid spacing at an altitude of 70 km is 2.8° in the longitude direction and 0.2–0.6° in the latitude direction. The coupling between the three model components was achieved by introducing a main module called the "coupler" and arranging each model component in the form of an FORTRAN subroutine or module and calling it in the coupler program. The coupler handles the general procedures for running the integrated model, such as setting common parameters and conditions, controlling time increment, and exchanging physical variables between model components. Since the time and grid resolution of each model is different, the coupler module is used to perform coordinate transformations in variable exchanging. The latest version of GAIA allows solar emission spectra, rather than single wavelength solar emission, to be input to simulate the response of the Earth’s atmosphere, including the ionosphere. The ionization cross sections of the atoms and molecules that make up the ionosphere, corresponding to each wavelength of solar emission, are given by Solomon and Qian (2005).

Data analysis and results

We input the EUV flare emission spectra from FISM2 and the model proposed by Kawai et al. (2020) into GAIA to reproduce the TEC enhancements due to flare events, and compared the calculated results with the observations. First, among the nine flare events analyzed in this study, we present the results of the case study analysis that illustrate the response of the ionosphere to different solar flare emission spectra, followed by the results of the statistical analysis.

Figure 1 displays an example of the observed and reproduced light curves of GOES/XRS-B during the X1.1-class flare on November 8, 2013. The solid red, blue, and black lines indicate the light curves obtained from the SFEM, the flare component of FISM2 (FISM2 flare), and the GOES/XRS observation, respectively. The dotted blue line indicates the daily component of FISM2 (FISM2 daily). Figure 1 shows that the magnitude of the soft X-ray flux is accurately represented in the SFEM, and the time evolution of FISM2 is also accurately reproduced, because GOES/XRS is used as a proxy. The following correction was made when inputting the emission spectrum obtained by the SFEM into the GAIA. When the emission intensity was smaller than that of FISM2 daily, it was replaced by FISM2 daily. This is because the flare emission spectrum of the SFEM tends to decay rapidly around the flare end time, as it roughly and virtually reproduces the multi-flare loop emission from the calculated single-flare loop (see Sect. 4.4 of Nishimoto et al. 2021).

Fig. 1
figure 1

Example of the observed and modeled soft X-ray fluxes of GOES/XRS-B. The soft X-ray fluxes of GOES/XRS-B during the X1.1-class flare on November 8, 2013. The solid red, blue, and black lines indicate the light curves obtained from the SFEM, the flare component of FISM2 (FISM2 flare), and the GOES/XRS observation, respectively. The dotted blue line indicates the daily component of FISM2 (FISM2 daily)

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Figure 2 displays an example of the observed and reproduced flare time-integrated spectra and the ratio of the observed data to the calculated data for the X1.1-class flare on November 8, 2013. The solid blue, red and black lines indicate the flare time-integrated spectrum obtained from the FISM2 flare, SFEM, and SDO/EVE MEGS-A observations, respectively. As shown in Fig. 2a, the SFEM and FISM2 both reproduce the observed trend. However, the value of the SFEM becomes significantly smaller when the wavelength is longer than ~ 70 nm, because the SFEM does not consider the reproduction of the optically thick emission or the continuum component emitted from the solar atmosphere at altitudes lower than the transition region. The emission intensity of the optically thick SFEM is larger than that of FISM2 in the soft X-ray region, where the wavelength is shorter than 10 nm. Figure 2b shows that FISM2 reproduces the observed flare time-integrated irradiance for the wavelength range of 5–37 nm accurately. However, at wavelengths of 10–11 nm, 28–29 nm, and 32–34 nm, the SFEM is more than twice as large as the observed values.

Fig. 2
figure 2

Example of the flare time-integrated spectra and ration of the observed and calculated data. a Flare time-integrated spectra and b ratio of the observed data to the calculated data for the X1.1-class flare on November 8, 2013. The solid red, blue, and black lines indicate the flare time-integrated spectrum obtained from the SFEM, the FISM2 flare, and the SDO/EVE MEGS-A observation, respectively. The solid black line in b shows the line with a ratio of 1

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Previous studies have suggested that X-ray and EUV emissions at wavelengths shorter than 45 nm are important indicators of the response of the Earth’s ionosphere (Woods et al. 2011; Zhang et al. 2002). For the DTEC of calculation data, the TEC value of RUN-Fd, which does not contain a flare component, was subtracted from the TEC calculation value of each RUN. In this study, SITEC value is defined to quantitatively evaluate the TEC enhancement due to flare as the difference between the minimum value of DTEC around the flare start time and the maximum value of DTEC during the flare.

Table 1 Flare parameters and TEC parameters for the nine flare events analyzed in this study
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Figure 7 displays the time variation of the DTEC for the nine flare events. The solid black, dashed red, orange, blue, and green lines indicate the DTEC obtained from the observations, RUN-Ff, RUN-FS35, RUN-FS15, and RUN-FS10, respectively. The DTEC observed and calculated values were obtained at the point, where the local time was around noon when each flare event occurred. To derive the DTEC, we subtracted the 30-min running average from the absolute TEC observational data. For the calculation data, the TEC value of RUN-Fd, which does not contain flare component, was subtracted from the TEC calculation value of each RUN. In this study, SITEC is defined as the difference between the minimum value of DTEC around the flare start time and the maximum value of DTEC during the flare. As shown in Fig. 7, the DTEC increases with the start of the flare, and the observed SITEC variation is 0.34–2.36 TECU. This variable value of SITEC is reasonable in comparison with previous studies (e.g., Qian et al. 2011; Yasyukenvich et al. 2018; Zhang et al. 2011).

Fig. 7
figure 7

Time variation of DTEC for the events analyzed in this study. The time variation of DTEC for the nine flare events analyzed in this study during the flare occurrence. The solid black, dashed red, dashed orange, dashed blue, and dashed green lines indicate the DTEC obtained from observations, RUN-Ff, RUN-FS35, RUN-FS15, and RUN-FS10, respectively. The observed and calculated DTEC were obtained at points, where the local time was around noon when each flare event occurred. The vertical dotted lines indicate, from left to right, the flare start and end times, respectively

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Figure 8 shows the relationship between the observed and calculated SITECs for the nine flare events. The results of RUN-Ff, RUN-FS35, RUN-FS15, and RUN-FS10 are plotted in red, orange, blue, and green, respectively. The dashed line indicates the regression of each plot, and the black solid line indicates a straight line with a slope of 1. The correlation coefficients (CC) for RUN-Ff, RUN-FS35, RUN-FS15, and RUN-FS10 were 0.78, 0.37, 0.94, and 0.91, respectively. The mean absolute errors (MAE) between the line with slope 1 and the regression line were 0.49, 1.19, 0.28, and 0.33 for RUN-Ff, RUN-FS35, RUN-FS15, and RUN-FS10, respectively. Note that we show a more robust maximal information coefficient (MIC) due to the small number of analysis events; MIC is a measure of the dependence between two variables and calculates the grid delimitation that maximizes the value of the mutual information content and its maximum value (Reshef et al. 2011). The MIC for RUN-Ff, RUN-FS35, RUN-FS15, and RUN-FS10 were 0.32, 0.59, 0.59, and 0.59, respectively. The results showed that RUN-FS15 and RUN-FS10 effectively reproduced the observed values of the SITEC.

Fig. 8
figure 8

Relationship between the observed and calculated SITEC for the events analyzed in this study. The relationship between the observed and calculated SITEC for the 9 flare events analyzed in this study. The results for RUN-Ff, RUN-FS35, RUN-FS15, and RUN-FS10 are plotted in red, orange, blue, and green, respectively. The dashed line shows the regression for each plot, and the black solid line shows a straight line with slope 1. For each regression line, 95% confidence intervals are shown in shading. The correlation coefficients (CC) and maximal information coefficient (MIC) are shown at the upper left, where the text color corresponds to the symbol color

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Figure 9 shows the relationship between the solar emission wavelength and the difference in ion production rate investigated using RUN-FS15, which best reproduces the SITEC observations in Fig. 8. Figure 9 indicates that the solar emission that contributes the most significantly to the TEC enhancement during flares is soft X-ray emission with wavelengths shorter than 10 nm. For EUV emission, the wavelengths of 10–15 nm and 30–35 nm contribute to the improvement of TEC. For most flare events, the ion production rate peaks at 1–2 nm in soft X-ray emission, and at 10–11 nm and 30–31 nm in EUV emission. The ratios of integrated ion production rate by EUV emission with wavelengths of 10–15 nm and 30–35 nm to integrated ion production rate by soft X-ray emission with wavelengths shorter than 10 nm, obtained from Fig. 9, were 12.4–23.8% (average 18.8%) and 0.5–23.1% (average 6.5%), respectively.

Fig. 9
figure 9

Relationship between the solar emission and the difference in ion production rate. The relationship between the solar emission and the difference in ion production rate between pre-flare and DTEC peak time calculated by GAIA with RUN-FS15. The difference in ion production rate is the difference between the pre-flare and the DTEC peak time, integrated over height. Data from points where the local time was around noon at the time of each flare event are used. The red triangles in each panel indicate the top five wavelengths at which the ion production rate was the greatest

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Discussion and summary

We used a solar flare emission spectral model with a wavelength resolution of 0.1 nm and the Earth's atmospheric model to reproduce the response of Earth's ionosphere to solar flare emission and to identify the wavelengths of solar flare emission that control the TEC enhancement. We verified the relationship between the observed and calculated DTEC, and between the observed and calculated solar flare emission spectra by statistically comparing nine flare events.

From Fig. 8, which shows the comparison between the observed and calculated values of SITEC, RUN-Ff tends to be smaller than the observed value; RUN-FS35 tends to be larger than the observed value, and both RUN-FS15 and RUN-FS10 reproduce the observed value of DTEC accurately. To consider the reason for this result, we focused on the solar flare emission spectra derived by FISM2 and the SFEM. The SFEM shows larger soft X-ray emission shorter than 10 nm than FISM2, and larger EUV emission at wavelengths of 10–11 nm, 28–29 nm, and 32–34 nm than FISM2 and SDO/EVE MEGS-A (Fig. 2). The dominant lines at wavelengths of 10–11 nm are high-temperature coronal lines, such as Fe XVII line and Fe XIX lines, while the dominant lines at 28–29 nm and 32–34 nm are relatively low-temperature coronal lines, such as the Fe XV line and Fe XVI line, respectively. Thus, the difference in SITEC between RUN-Ff and RUN-FS10 is due to soft X-ray emission, the difference between RUN-FS15 and RUN-FS10 is due to high-temperature coronal line emissions, and the difference between RUN-FS35 and RUN-FS15 is due to relatively low-temperature coronal line emissions. Therefore, the SFEM could more accurately reproduce the total energy of soft X-ray emission and high-temperature coronal line emission. The high-temperature line emissions show the cooling process through the contribution function of various blend lines, which are known to be difficult to reproduce in empirical models (Chamberlin et al. 2020; Ryan et al. 2013). A physics-based model is a useful solution to this discrepancy. As shown in Figs. 5 and 6, the TEC enhancement by flare emission results in integrating the number of electrons in the D, E, and F regions, and the low-temperature coronal line emission that contributes to ionization in the F region is the most efficient contributor to the TEC enhancement. In fact, the photoionization and photo-dissociative ionization cross sections corresponding to the EUV emissions employed in GAIA are relatively large (see Fig. 5 of Watanabe et al. 2021). Furthermore, the timescale of electron recombination in the D and E regions of the ionosphere ionized by soft X-ray emission and high-temperature coronal line emission is a few minutes, whereas the timescale of recombination in the F region ionized by low-temperature coronal line emissions is, on average, hours, suggesting that low-temperature coronal line emissions are important for TEC enhancement (Zhang et al. 2011).

Figure 9 shows the solar emission and the difference in ion production rate between pre-flare and DTEC peak time. From Fig. 9, the neutral atmosphere is most ionized by soft X-ray emission, followed by EUV emission with a high formation temperature of 10–15 nm, and then EUV emission with a low formation temperature of 30–31 nm. Among these solar flare emissions, the wavelengths of soft X-ray and EUV emissions that contribute to the TEC enhancement are 1–2 nm and 10–11 nm and 30–31 nm, respectively. The dominant lines at these EUV emissions are Fe XVII 10.08 nm, Fe XIX 10.85 nm, and He II 30.38 nm. The He II line is strong solar emission in flare emission, which mainly ionizes the F layer and thus contributes efficiently to the TEC enhancement. The soft X-ray emissions mainly ionize the D layer, which has a short time scale for recombination, and the photoionization and photo-dissociative ionization cross sections are also small. However, it is the most intense emission during flare, and its intensity is several orders of magnitude higher than that of EUV emission. In addition, photoelectron impact ionization becomes more than an order of magnitude greater than direct photoionization in this wavelength range (Solomon and Qian 2005). Therefore, its efficiency is poor, but it is expected to have an impact on the TEC variation. Furthermore, the soft X-ray and hot coronal line emissions were emitted from the optically thin solar corona and were not affected by the CLV. Therefore, the soft X-ray emission with a wavelength of 1–2 nm and Fe XVII and Fe XIX line emission are considered to be the best indicators of TEC enhancement.

In this study, the response of the ionosphere to solar flare emissions was investigated using the models for nine events with flare magnitude varying from X1.0–X9.3 and durations of 10–33 min. The observed SITEC variation for these flare events was 0.34–2.36 TECU. As shown in Fig. 8, solar cycle 24, mainly analyzed in this study, had low solar activity (Iijima et al. 2017; Imada et al. 2020) and did not produce any large-scale events that exceeded the X10 class. Furthermore, no flare events with EUV late phase, which is the second peak of the Fe XV and Fe XVI line emission, were found in this statistical study. It is possible that FISM2 and SFEM have not been able to reproduce the EUV late phase, but this cannot be confirmed due to the absence of SDO/EVE MEGS-A observations. Although the EUV late phase occurs in only about 13% of all flare events, it contributes to the ionization of the Earth's ionosphere, because its duration is longer than the flare main phase and its emission energy is larger (Woods et al. 2011). It is important to analyze large-scale flares and flares with EUV late phase from the perspective of space weather, because they have large emission energies and a large impact on the Earth's ionosphere. For future work, we need to continue to analyze flares with these characteristics that have occurred in the past and that will occur in solar cycle 25.

In this paper, we used only TEC as the ionospheric observation data. To evaluate the unusual electron density increase in the D and E regions related to the Dellinger effect in more detail, future work will require the use of ionosonde data (e.g., Tao et al 2020) and HF radar data (e.g., Watanabe and Nishitani 2013; Nishitani et al 2019; Chakraborty et al. 2021) and other ionospheric observation data.

The results of this study indicate that the TEC enhancement due to flare emission is determined by soft X-ray emission and EUV emission with wavelengths shorter than 35 nm. The TEC enhancement is found to be largely due to the change in the soft X-ray emission and EUV line emissions with wavelengths, such as Fe XVII 10.08 nm, Fe XIX 10.85 nm and He II 30.38 nm. Finally, we believe that the integration of the method introduced in this study, which uses the SFEM based on the physical processes of flare loops and the Earth’s atmospheric model GAIA, into space weather forecasting will contribute to improving the forecast accuracy of space weather phenomena.