# Low Ionosphere under Influence of Strong Solar Radiation: Diagnostics and Modeling
## 3 Results
### Recorded Variations of VLF Amplitude and Phase Data  
In this paper we analyzed around 200 solar X-ray flares events starting from the year 2003. Intensity of those X-ray flares were in range from C1- to X17-class, 1 \(\times\) 10\({}^{-6}\) Wm\({}^{-2}\) to 1.7 \(\times\) 10\({}^{-3}\) Wm\({}^{-2}\), respectively. For each flare, we measured amplitude and phase perturbations on VLF signal, except when the transmitter was off-air. The amplitude perturbations were estimated as a difference between values of the perturbed amplitude  
Figure 2: Example of VLF signal variations of GQD signal recorded at Belgrade station due to SF event X3.6-class at 09 Oct 2005 (start 09:42, peak 09:59, end 10:08 UT). At peak time the measured variations of amplitude and phase \(\Delta A=\) 7.25 dB and \(\Delta P=\) 50 deg, respectively.  
induced by X-ray flux and amplitude in the normal ionospheric condition \(\Delta A=A_{\rm per}-A_{\rm nor}\). Phase perturbations were estimated as \(\Delta P=P_{\rm per}-P_{\rm nor}\).  
Data points of the observed GQD/22.10 kHz are shown in Figure 3--amplitude and phase perturbations as a function of solar X-ray intensity. The range of size in amplitude and phase perturbations varies for different X-ray solar flares. The amplitude perturbations of GQD/22.10 kHz radio signal are distributed between enhancement and attenuation, which depends on signal frequency and the angle of reflection in a function of intensity of solar X-ray flux (see also [40]). On the GQD-BEL path, amplitude decreases during occurrences for C-class solar flares (see Figure 3). The size of amplitude perturbations is proportional to the intensity of solar X-ray flux. A phase change on this path is complicated, displaying an increase or decrease during independent to SF-class. During M-class solar flares, amplitude perturbation is between rising and falling but there are more cases of rising, while during X class SF amplitudes always have positive enhancement.  
In order to visualize the distribution of the amplitude and phase data, we give Figure 4. In Figure 4, a rug plots of VLF data are displayed as marks along an axis. A small tick on the edge of the rug plot represents each individual observation. The influence of different classes of SF explains the shape of the rug plots. Some grouping of ticks around \(\Delta A=-2\), \(-1\), \(-0.3\), \(0.8\) dB can be noticed, which correspond to the influence of C-class of SF and around \(3.4\), \(6\), \(7\) dB, which is due to M-class and X-class SF, respectively. Similarly, for \(\Delta P\), a grouping of ticks around \(3\) and \(5\) deg can be noticed, due to C-class SF and also around \(-20\) and \(20\) deg which correspond to M-class. Around \(40\), \(60\) deg, some grouping exists due to X-class SF.  
Figure 3: **(left)** Observed amplitude perturbations on GQD/22.10 kHz radio signals due to solar X-ray flares, measured at Belgrade station during period (2003–2017) as a function of X-ray flux. **(right)** Observed phase perturbations under same conditions. Two hundred events of solar X-ray flares were examined.