## 3 Results
### Comparing the Results of the Amplitude Method with D-RAP
Figure 4: X-Ray (panel (**a**)) and proton flux (panel (**b**)) on 08 September, and the changes measured by the European Digisondes (green stars) and determined by the D-RAP model (red diamonds) at 2.5 MHz (panels (**c–e**) and at 4 MHz (panels (**f–h**)). The radio fade-outs that occurred at certain frequencies are indicated by gray rectangles (left). The X-Ray data plotted on panel (**a**) are the 0.1–0.8 nm X-Ray flux measured by the GOES spacecrafts. The blue dashed lines indicate the peak time of the M-class flares. The increased ionospheric absorption caused total radio fade-outs and increased values of the fmin in the ionograms measured by the ionosondes. Table 3 presents the duration of the total radio fade-outs and the percentage changes of the fmin parameter, recorded at the three stations at the peak time of the 13 flares or after the blackout, compared to its values during the quiet reference period (X-Ray < 1 \(\times\) 10\({}^{-6}\)). Please see the details in [PERSON] et al. (2023) [18]. Figure 5: X-Ray (panel (**a**)) and proton flux (panel (**b**)) on 10 September, and the changes measured by the European Digisondes (green stars) and determined by the D-RAP model (red diamonds) at 2.5 MHz (panels (**c–e**)) and at 4 MHz (panels (**f–h**). The radio fade-outs that occurred at certain frequencies are indicated by gray rectangles. The X-Ray data plotted on panel (**a**) are the 0.1–0.8 nm X-Ray flux measured by the GOES spacecrafts. The magenta dashed line indicates the peak time of the X-class flare. Table 4 presents the measured (upper part) and the modeled (lower part) values at 2.5 MHz at the three ionosonde stations. The date and the class of the selected flares are seen, respectively, at the first two columns. In some cases, long total radio fade-out occurred during and after the flares (see Table 3), thus, we decided to do the comparison between the measured and modeled values at the time of the first record (ionogram) after the blackout (measured and modeled values at the peak time of the investigated flares are shown in Supplementary Table S2). The time of the peak, or the first record after the fade-outs are shown in the 3 rd column, while the X-Ray flux at that time is in the 4 th column. The absorption values calculated by the amplitude method at JR, PQ and VT are shown, respectively, in the next columns. Table 5 shows the same but for 4 MHz. Looking through the values, the picture seems to be quite complicated. According to the D-RAP values (lower part of Tables 4 and 5), the more intense flares caused larger changes in the ionospheric absorption. However, the time of the investigated impact also plays an important role, e.g., the effect of the C7.7 flare which occurred around noon (peak time is 12:22 UT) is larger than the response to the X-class flares in the afternoon hours. This is true also for the measured values, which are larger at the time of a C7.7 flare than, e.g., at 15:15 after an X1.3 flare on 07. September. This is not that evident for the values recorded at 4 MHz (upper part of Table 5). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Measured Values [dB] at 4 MHz**} \\ \hline  & & \multicolumn{2}{c}{**Time (UT) of Peak or of First**} & \multirow{2}{*}{**X-Ray Flux at That Time**} & \multirow{2}{*}{**JR**} & **PQ** & **VT** \\
**Date** & & & **Record After** & & **[Wm\({}^{-2}\)]** & **[dB]** & **[dB]** \\  & & & **Fade-Out** & & & & \\ \hline
2017-9-4 & C7.7 & 12:45 & 4.73 \(\times\) 10\({}^{-6}\) & 13.46 & 11.86 & 16.06 \\
2017-9-4 & M1.5 & 15:30 & 1.53 \(\times\) 10\({}^{-5}\) & 6.24 & 9.29 & 9.08 \\
2017-9-5 & M3.2 & 4:53 & 3.24 \(\times\) 10\({}^{-5}\In order to show the results of the comparison in a clearer way, we show diagrams about the flare intensity dependence of the modeled and measured values (Figure 6 for the results at 2.5 MHz, while Figure 7 for the results at 4 MHz).