## 4 Conclusions and Perspectives  
In this paper we analysed SF events with extreme radiation in the X-spectral range. The perturbed VLF data were collected by monitoring the NAA/24.00 kHz VLF signal (transmitted in Maine, USA and then received in Belgrade, with GCP = 6540 km) and used together with GOES satellite data. The magnitude of impact of SFs on D-region and the consequences of these explosive events were analysed using measurements over a long path. The amplitude and phase data and ionosphere parameters during the enhancements of radiation due to the SF obtained in our study, are presented. The GCP from the NAA transmitter to the Belgrade receiver is about 6540 km long and characterized as a long, dominantly sea path, and we studied cases when it is entirely sunit. The data obtained here demonstrate the advantages of using these long-path measurements due to stable form of phase and amplitude variation caused by SID in contrast to the VLF perturbations on the short path which display more complexity and oscillations, including decreases and increases depending on the flare intensity. This is very important during the modelling process. Furthermore, we conclude that the intensity of amplitude and phase perturbations on VLF kHz signal over a long path is in correlation with the size and shape of X-ray flux. This is in line with previous studies. The most effective influence on the enhancement of the ionization rate in the D-region during the observed SFs is due to the increased intensity of spectral lines in the X-ray spectra. Moreover, X-ray SFs with larger line intensities produce a larger increase in electron density. The computation was applied, and we obtained coefficients, i.e., sharpness, reflection height, and time delay needed for modelling this medium under increased radiation in the X-spectral range. One can notice that the intensified solar radiation in the X-spectral range changes D-region parameters and conducts an enhanced production rate, consequently deforming the VLF signal. The dependence of electron density on X-ray flux has slightly lower slope but is in fair agreement with previous studies. Figure 14: Electron-density data (calculated, simulated and approximated) at reference height \(h\) = 74 km and maximum of \(I_{x}\) flux during occurrence of different class SFs. The data are compared with results from [16; 37; 40; 41; 42]. Area of importance is between the two red lines. The present manuscript offers an extension of the electron-density modeling in the daytime, SF-perturbed D-region of the ionosphere already introduced in [37]. In particular, the extension includes time delays from ionospheric sluggishness in \(N_{e}\) modeling, making use of data over a long GC path that ensures enhanced stability of SID-induced variations in phase and amplitude shape. The construction of the associated flarED GitHub project is designed to be easily applicable. Moreover, we introduce novel methods and provide a simple, modified expression for \(N_{e}\) as a function of \(I_{x}\), valid for unperturbed and perturbed conditions. We develop the expression by taking into account the delay time of the ionosphere response, making it more physical. The analysis and software are provided on GitHub under the MIT license. In addition, the observed increase in the atmospheric aerosol number density after the event of SFs in February and March 2011, as well as high-level cloud formation in the upper atmosphere, reveal the importance of further investigation of SF and possible influence on particle-electrification mechanisms [43; 44; 45]. Recent studies [46] have introduced reconsideration of atmospheric aerosol-electricity interactions, which could improve theoretical understanding and simulations of the aerosol lifecycle, opening new horizons for weather and climate science. Future research will focus on a multidiscipline approach, investigating solar-geomagnetic activity effects on aerosol particles and on radiative transfer. Conceptualization, V.A.S. and D.M.S.