# Low Ionosphere under Influence of Strong Solar Radiation: Diagnostics and Modeling
## 3 Results
### Long Lasting Intense Solar Radiation: An Analysis of Strong SF  
M3.7-class SF that occurred on 9 September 2017 is an illustrative example of long-lasting intense solar radiation (\(\sim\)60 min) which induced SID and caused variation in VLF signal. Furthermore, this example is good for showing the methodology of our analysis.  
In Figure 5, we present simultaneous variations of X-ray flux, amplitude, and phase of GQD/22.10 kHz signals against universal time during the occurrence of M3.7-class SF on 9 September 2017. The lower panel shows observed amplitude perturbations on GQD radio signals measured at the Belgrade station with calculated values (red line). Middle panel shows observed and calculated phase perturbations (red line). Time variation of X-ray flux measured by the GOES-15 satellite on 9 September 2017 is on the upper panel. Shapes of the VLF signal parameters are observably modified similar to the shape of the X-ray flux.  
Figure 4: A rug plot of two hundred data points. (**upper panel**) Delta amplitude distribution. (**lower panel**) Delta phase distribution, that appears in blue along the X-axis. The points are sampled from the kernel smooth distribution shown in black.  
Figure 5: Simultaneous variations of X-ray flux, delta amplitude, and phase of GQD/22.10 signal against universal time during occurrence of M3.7-class solar flare on 9 September 2017. (**lower panel**) Observed amplitude perturbations on GQD, radio signals measured at the Belgrade station and calculated values. (**middle panel**) Observed and calculated phase perturbations. (**upper panel**) Time variation of X-ray irradiance measured by GOES-15 satellite.  
We simulated propagation of VLF radio signal through the waveguide in the perturbed D-region induced by additional X-ray radiation for resolution of 1 min during the flare duration using a procedure which relies on LWPC code.  
The procedure is explained in detail in Section 2. Parameters were obtained when the calculated amplitude and phase perturbations matched as well as possible with observed data (see lower panels of Figure 5). The obtained Wait's parameters \(\beta_{\rm per}\) and \(H^{\prime}_{\rm per}\) were used for our further calculations of ionosphere parameters.  
In Figure 6, calculated parameters are shown (obtained by the method explained in Section 2): time dependent effective reflection height \(H^{\prime}\), sharpness \(\beta\), and electron density at reference height during occurrences of M3.7-class solar flare on 9 September 2017 from lower to upper panel, respectively.  
The variation of \(H^{\prime}\)(t) with time has expected behavior, i.e., after starting SF, it drops dropped rapidly to minimum, as expected, and after peak time of X-ray, it slowly keeps rising to referent value (see Figure 6 middle panel). The behavior of \(\beta\)(t) plot is in correlation with changes of X-ray flux. At 11:04 UT, peak of the solar X-ray flux reached \(I\)x = 3.78 \(\times\) 10\({}^{-5}\) Wm\({}^{-2}\), and induced perturbations of amplitude and phase \(\Delta A\) = 5.6 dB and \(\Delta P\) = \(-\)5.6 deg, respectively. For the sharpness, we obtained values \(\beta\) = 0.49 km\({}^{-1}\) and, for reflection, height \(H^{\prime}\)= 62.5 km. This means that during this SF the reflection height drops by 11.5 km. We obtained that the electron density increased at reference height \(h\) = 74 km from 2.2 \(\times\) 10\({}^{8}\) m\({}^{-3}\) to 6.7 \(\times\) 10\({}^{10}\) m\({}^{-3}\).