# Low Ionosphere under Influence of Strong Solar Radiation: Diagnostics and Modeling
## 3 Results
### Comparison of Obtained Ionospheric Parameters  
As it was said in Section 2, with the sharpness parameter \(\beta\), which usually takes values 0.3-0.6 km\({}^{-1}\), and with a reference height \(H^{\prime}\) with values in range 74-50 km, one can describe the electron density height profile, rate coefficients, etc. in the lower ionosphere. We noted that there is a lack of agreement for sharpness values obtained by different models and techniques. Although the values of the \(\beta\) parameter are in the range between 0.3-0.6 km\({}^{-1}\), in some papers \(\beta\) values are higher, i.e., 1.0 km\({}^{-1}\) at daytime and \(\sim\)3.0 km\({}^{-1}\) at nighttime (see e.g., [35]). Such a deviation illustrates the general deficiency of precision in the ionosphere D-region research and the need for new and more precise methods and techniques for its investigation. Therefore, we presented a comparison of obtained ionospheric parameters with the other authors. The sharpness parameter \(\beta\) and reflection height \(H^{\prime}\) (red squares) calculated in present work are plotted in Figures 12 and 13 together with results of other authors [41; 42; 43; 44]. In Table S3, one can find the data of amplitude and phase perturbations of the VLF signal and the ionospheric parameters induced by different SF events which were also analyzed in this study. In Figure S4, we also give the electron density at reference height evaluated from the data presented in Figures 12 and 13. We can point out that the results of the sharpness parameter \(\beta\) and reflection height \(H^{\prime}\) presented in this paper are in good agreement with the results of most authors found in the available literature. Figure 11: **(left)** Observed amplitude perturbations on GQD/22.10 radio signals, due to solar X-ray flares, measured at Belgrade during (2003–2017), as a function of X-ray flux. (**right**) Same as left but for observed phase perturbations. Two hundred events of solar X-ray flares were examined. Values of electron density at reference height, against maximum intensity of X-ray flux obtained by Equation (3) are presented. The color of the point is proportional to the electron density values change—darker color indicates larger values of electron density. It can be noticed that, when the intense solar flux increases during SF, values of the reflection height \(H^{\prime}\) decrease. Looking at Figure 12, generally speaking, there is a good agreement in the values of the reflection height from the literature [41; 42; 43; 44]. When the intensity of radiation increases from \(10^{-6}\) to \(10^{-3}\) Wm\({}^{-2}\) (i.e., when we go from normal conditions of the ionosphere to the perturbed ionosphere due to strong X-class SF), the reflections go down from 74 km to 50 km. Figure 13 gives the simple dependence for \(H^{\prime}\) with the well-defined slope  
\[y=k_{1}+k_{2}\cdot\log(1x), \tag{4}\]  
Figure 12: The effective reflection height (red squares) calculated for this study is plotted together with the results of other authors [41; 42; 43; 44]. Figure 13: Same as in Figure 12 but for the sharpness parameter. where \(k_{1}\) = 36.85032 and \(k_{2}\) = \(-\)6.12059. A larger deviation can be noticed only in the results from [PERSON] et al., where a very strong flare of X-class with the \(I\)\(\sim\)\(10^{-3}\) Wm\({}^{-2}\) induce a very small decrease in the reflection height (\(H^{\prime}\)- 65 km), like the M3-class gives. Looking at the Figure 13, one can see a totally different situation for the results of sharpness parameter. Generally speaking, sharpness parameter \(\beta\) increases with the increase in X radiation intensity. However, the results are more scattered with the huge disagreement for the cases of strong X-class solar flares (right corner of the Figure) due to results of [PERSON] et al. [44]. These results of [PERSON] et al. deviate a lot from the slope obtained from the results of other authors.