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 solar flare emission model, 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 solar flare emission model, 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 solar flare emission model 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 solar flare emission model 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 Section 4.4 of Nishimoto et al. 2021).
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 red, green, and orange lines indicate the flare time-integrated spectrum obtained from the FISM2 flare, solar flare emission model, and SDO/EVE MEGS-A observations, respectively. As shown in Fig. 2(a), the solar flare emission model and FISM2 both reproduce the observed trend. However, the value of the solar flare emission model becomes significantly smaller when the wavelength is longer than ~ 70 nm because the solar flare emission model 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 solar flare emission model is larger than that of FISM2 in the soft X-ray region, where the wavelength is below 10 nm. Figure 2(b) 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 solar flare emission models are more than twice as large as the observed values.
Previous studies have suggested that X-ray and EUV emissions at wavelengths below 45 nm are important indicators of the response of the Earth's ionosphere (Woods et al. 2011; Zhang et al. 2011). Therefore, in this study, we focused on the 5–35 nm region observed by SDO/EVE MEGS-A, which has a strong intensity emission during flare and input five types of solar flare emission spectra into the GAIA using FISM2 and the solar flare emission model to investigate in detail the wavelengths of solar emission that determine TEC enhancements. The five types of flare emission spectra input to the GAIA are as follows: the FISM2 daily (RUN-Fd), the FISM2 flare (RUN-Ff), the FISM2 flare replaced by the solar flare emission model at wavelengths below 35 nm (RUN-FS35), the FISM2 flare replaced by the solar flare emission model at wavelengths below 15 nm (RUN-FS15), and the FISM2 flare replaced by the solar flare emission model at wavelengths below 10 nm (RUN-FS10).
Figure 3 shows the observed TEC distribution at the GOES/XRS-B soft X-ray peak time for the X1.1-class flare on November 8, 2013. As shown in Fig. 3, TEC in the Asia-Oceania region (day time) is larger than that in other regions because TEC depends on local time. In this study, we used TEC observation data from Asia and Oceania, the Americas, and Europe; all of which are regions with dense GNSS observation networks.
Figures 4 and 5 show the TEC distribution of each RUN and its ratio to RUN-Fd at 130°E, where the local time is around noon when the flare occurs. From these figures, we can see that the TEC enhancement due to flare emission is not confirmed in RUN-Fd, is similar for RUN-Ff, RUN-FS15, and RUN-FS10, and is the largest in RUN-FS35. The TEC variation in RUN-Fd, which does not contain a flare emission, is due to the fact that TEC varies with the solar zenith angle.
Figures 6 and 7 show the difference in ion production rates between the pre-flare and the flare peak calculated with RUN-Ff and RUN-FS35 for the X1.1 class flare on November 8, 2013, respectively. These figures show that the neutral atmospheric compositions are ionized mainly by flare emission with wavelengths below 35 nm. It is clear that the ion production rate of RUN-FS35 was greater than that of RUN-Ff. The major difference between RUN-Ff and RUN-FS35 is the difference in ion production rates of O+, N+, and N2+ at wavelengths below 10 nm and around 10–15 nm that ionize the D and E regions, and O+ and N+ corresponding to solar emission at 25–35 nm that ionize the F region. The difference in ion production rates between RUN-Ff and RUN-FS35 corresponds to the wavelength region where the intensity of solar flare emission by the solar flare emission model is larger than the observed value (see Fig. 2).
3.2 Statistical result for TEC enhancement due to flare emission
We compared the difference of TEC (DTEC), which indicates TEC enhancement due to flare emission obtained from the GAIA calculations and the observations for nine flare events. The flare parameters and TEC parameters of these flare events are listed in Table 1. The DTEC observed and calculated values were obtained when the local time was around noon when each flare event occurred. The DTEC of observational data was derived by subtracting the running average for 30 minutes from the absolute TEC value. As the TEC value obtained from the GNSS carrier phase is relative, a correction is required to obtain the absolute value. The absolute TEC value is obtained by the method proposed by Shinbori et al. (2020). First, the TEC value calculated using the carrier phase was adjusted to the level of the TEC value calculated using the two pseudo-ranges. However, as this value contains the instrumental bias, it is necessary to estimate the instrumental bias to obtain the absolute value of the TEC. This bias was estimated by the hourly TEC average and the interfrequency bias using the weighted least-squares fitting of the relative TEC values obtained from each GNSS station and excluded from the relative TEC values (Otsuka 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, a sudden increase in TEC (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.
Figure 8 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, DTEC is defined as the difference between the minimum value of TEC around the flare start time and the maximum value of TEC during the flare. As shown in Fig. 8, the DTEC increases with the start of the flare, and the observed DTEC variation is 0.34–2.36 TECU. This variable value of DTEC is reasonable in comparison with previous studies (e.g., Qian et al. 2011; Yasyukenvich et al. 2018; Zhang et al. 2011).
Figure 9 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. The results showed that RUN-FS15 and RUN-FS10 effectively reproduced the observed values of the SITEC.
Figure 10 shows the relationship between the solar emission wavelength and the difference in ion production rate was investigated using RUN-FS15, which best reproduces the SITEC observations in Fig. 9. Figure 10 indicates that the solar emission that contributes the most to the TEC enhancement during flares is soft X-ray emission with wavelengths below 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 below 10 nm, obtained from Fig. 9, were 12.4–23.8% (average 18.8%) and 0.5–23.1% (average 6.5%), respectively.