## 4 Discussion  
The ionospheric response to 13 solar flares that occurred in the period of 4-10 September 2017 was investigated in the current study with a special focus on the ionospheric absorption changes. A new observation method to determine the absorption variation was developed by [PERSON] et al. (2023) [18] based on the amplitude data detected by the Digison-des. The absorption changes that occurred during the 13 above-mentioned flares were carefully analyzed in the previous study. However, the method has not been compared with a model for the ionospheric absorption. The present study aims to fill this gap. Figure 10: Comparison of the modeled and measured values at the different riometer stations (y-axis, ABI (a), IVA (b), SOD (c), ROV (d), OUL (e), JYV (f)) with the X-Ray flux (x-axis). ROV (d) and JYV (f) riometers operated at 32.4 MHz, while other riometers operated at 30.0 MHz. The most commonly used model for ionospheric absorption determination globally is the D-RAP (D Region Absorption Predictions) developed by the Space Weather Prediction Center of NOAA. Previous studies found that the D-RAP model underestimates the ionospheric absorption changes during solar flares [22; 29]. Our results generally agree with this, the D-RAP model underestimates the caused ionospheric absorption changes as a result of the enhanced X-Ray flux in the 2.5-4 MHz range (ionosonde data, Figures 4 and 5). Moreover, the observed values are larger most of the time than the predicted ones at 2.5 and at 4 MHz not only during the periods under the impact of the solar flares (Figures 4 and 5), which confirms the conclusion of the validation report [27] for the European region. The main reason for the underestimation can be that the D-RAP model was originally based on the results of [PERSON] [30] who used a limited data set from one station from New Mexico (low-latitude) detected at 5 MHz (instead of the 30 MHz generally used by riometers) during noon in summertime [19]. As the validation report of D-RAP described [27], the model has been evaluated using data from several riometer stations during several historic representative events. However, riometers operate only at high latitudes and at high frequencies (the data investigated in the report were measured at stations with a latitude higher than 50\({}^{\circ}\) and at f \(\geq\) 30 MHz), thus, their data are not necessarily representative for the whole globe (especially for lower latitudes). A further explanation is that the absorption changes related to auroral particle (electron) precipitation have not been considered in the model [27]. The period between 4 and 10 September 2017 was the most active period of the Sun to produce solar flares in Solar Cycle 24. The X9.3 class flare occurred at noon (peak time is 12:02 UT) on 06 September, and it was the most intense detected solar flare of the decade. According to our results, it caused \(\sim\)1.5-2 h of total radio fade-out at every investigated ionosonde station. While the duration of the blackout during the X2.2 flare (peak time 09:10 UT on 06 September) varied between 30 and 45 min (shortest at Juliusruh) depending on the latitude (solar zenith angle, Table 3), our results agree well with previous findings. The ionospheric impact of these two events was carefully discussed in the literature because of their severity. [PERSON] et al. [31] showed that the electron density in the lower ionosphere (70-80 km height) increased by \(\sim\)2-3 orders of magnitude during the X-class solar flares on 06 September. [PERSON] et al. [32] reported that the total radio blackouts lasted for about 45 min during the X2.2 flare, while the duration of the blackout caused by the X9.3 flare was \(\sim\)1.5 h. The detected duration of the fade-outs in our study agrees very well with this. According to their results, the fade-out was seen to a global extent, which demonstrates the severity of the caused ionospheric absorption changes. [PERSON] et al.