## 3 Results
### Comparing the Results of the Amplitude Method with D-RAP
\begin{tabular}{c} **Change in** \\ **in fmin at VT [min]** \\ \end{tabular}  & \begin{tabular}{c} **Duration of** \\ **in fmin at** \\ **UT [\%]** \\ \end{tabular}  \\ \hline
09.04.17 12:22 C7.7 & - & +73\% & - & +68\% & - & +213\% \\
09.04.17 15:30 M1.5 & - & +31\% & - & +18\% & - & +62\% \\
09.05.17 4:53 M3.2 & - & +0.4\%  
Therefore, there are 2-4 times differences between the modeled and observed values during that event. Figure 5 shows the X-Ray (a), proton flux (b) and absorption changes at 2.5 (c,d,e) and 4 MHz (f,g,h) based on the amplitude method during an X8.2 flare on 10 September (examples of ionograms recorded during the flare event are seen in Supplementary Figure S2). Increased amplitude values compared to the before the flare period were detected at both frequencies at every station. The detected absorption values increased from ~10 dB to ~20 dB at both frequencies at Juliusruh. It means that the flare caused ~10 dB changes at both frequencies. Thus, the more intense flare compared to the previous cases has a clear impact on the measured data. The impact of the energetic particles can be recognized also at Juliusruh sub-auroral station at 2.5 MHz, since the amplitude values do not decrease, but remain enhanced for a longer time period than at the other two stations. The model underestimated the measured absorption values most of the time according to the careful comparison of the measured (green dots) and the modeled values (red curve). It predicts the absorption close to zero before the flare, while the detected values are ~10 dB at most of the stations even before the flare. It is worth noting that the recorded values have the largest variation (within the period before the flare) at the VT station, where the cadence of the measurements is the longest (15 min) among the three stations (Figure 5e). Furthermore, \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & \multicolumn{4}{c}{**Measured Values [dB] at 2.5 MHz**} \\ \hline \multirow{2}{*}{**Date**} & \multirow{2}{*}{**Class**} & \multicolumn{2}{c}{**Time (UT) of Peak or of First**} & \multirow{2}{*}{**X-Ray Flux at That Time**} & \multirow{2}{*}{**JR**} & \multirow{2}{*}{**PQ**} & \multirow{2}{*}{**VT**} \\  & & & **Record After Eade-Out** & & **[Wm\({}^{-2}\)]** & & **[dB]** & **[dB]** \\ \hline
2017-9-4 & C7.7 & 12:22 & 7.79 \(\times\) 10\({}^{-6}\) & 17.120 & 23.828 & 21.122 \\
2017-9-4 & M1.5 & 15:30 & 1.53 \(\times\) 10\({}^{-5}\) & 8.127 & 20.256 & 12.7977 \\
2017-9-5 & M3.2 & 4:53 & 3.24 \(\times\) 10\({}^{-5}\) & 3.99734 & 6.773 & 8.239 \\
2017-9-5 & M3.8 & 6:40 & 3.82 \(\times\) 10\({}^{-5}\) & 13.6911 & 18.288 & 16.611 \\
2017-9-6 & X2.2 & 15:15 & 2.26 \(\times\) 10\({}^{-5}\) & 15.41 & 20.3 & 19.4613 \\
2017-9-6 & X9.3 & 15:15 & 2.26 \(\times\) 10\({}^{-5}\) & 15.41 & 20.3 & 19.4613 \\
2017-9-7 & M1.5 & 10:30 & 1.70 \(\times\) 10\({}^{-6}\) & 20.44 & 22.124 & 22.4674 \\
2017-9-7 & X1.3 & 15:15 & 2.75 \(\times\) 10\({}^{-5}\) & 15.96 & 23.6961 & 15.4766 \\
2017-9-8 & M8.1 & 8:45 & 4.65 \(\times\) 10\({}^{-5}\) & 15.67 & 19.46 & 22.0385 \\
2017-9-8 & M3.0 & 15:47 & 3.00 \(\times\) 10\({}^{-5}\) & 17.4162 & 23.627 & 18.15 \\
2017-9-9 & M3.7 & 12:15 & 6.86 \(\times\) 10\({}^{-6}\) & 15.06 & 24.01 & 21.6762 \\
2017-9-10 & X8.2 & 16:45 & 2.49 \(\times\) 10\({}^{-4}\) & 19.04 & 22.3796 & 12.7332 \\ \hline \end{tabular}
\end{table} 
Table 4: The absorption values measured by the Digisondes and determined by D-RAP at 2.5 MHz at the peak time of the flares, or—in the case of fade-out—at the first measurement time after them. The X-Ray flux values are from 0.1 to 0.8 nm wavelength band measured by the GOES spacecrafts. the predicted values at the peak time of the flare were \(\sim\)16 and \(\sim\)8 dB at 2.5 and 4 MHz, respectively, while the observed ones were a bit larger (\(\sim\)19 dB) at 2.5 MHz and much larger (\(\sim\)23 dB) at 4 MHz. Moreover, D-RAP does not take into account the impact of the particles at Juliusruh; however, it can be seen in the observation at 2.5 MHz (Figure 5c).