# Low Ionosphere under Influence of Strong Solar Radiation: Diagnostics and Modeling
## 1 Introduction  
In today's science, special attention is given to the extreme weather events, climate change, preservation, and protection, because they have been identified as crucial for sustainable development in our century. Consequently, a very important question nowadays in modern society is: can we predict the magnitude of impact of explosive solar events (such as solar flares) on Earth, humans, electronic equipment, and nature in general? By analyzing past instances of these phenomena, we cannot predict the occurrence of each new event itself with certainty, but we can statistically estimate the consequences of phenomena on ionospheric parameters, perhaps predict damage to electronic equipment, predict disruption of GPS, etc. The ionosphere is a part of the atmosphere that contains ionized gases with various kinds of particles, ions, and tens of different species [1, 2, 3, 4] with the degree of ionization which depends mainly on the incident radiation that is solar extreme ultraviolet and X-ray radiation [5, 6]. This ionizing solar radiation depends on the Sun activity during the solar cycle and varies around order of magnitude during the solar minimum and the solar maximum. Furthermore, ionosphere as a huge segment of atmosphere has a tendency to be constantly separated in different regions D, E, and F, with different physical characteristics and chemistry [7, 8, 9, 10, 11] which depend on the incident radiation. During stronger solar activity,the violent solar radiation and activity can induce sudden ionospheric disturbances (SIDs) as well as affect electronic equipment on the ground and signals from space, disrupt GPS, and bring damage to power grid components as a consequence [12; 13; 14; 15]. Furthermore, many investigations indicate potential connections between this extreme activity and natural disasters such as tropical cyclones or forest fires (see e.g., [16; 17; 18]). Signals of very low frequency (VLF) in the narrow band (3-30 kHz) of electromagnetic (EM) spectrum are generated in Earth's atmosphere by natural sources such as lightning discharges and meteor showers, and likewise VLF EM can be created by man-made sources, e.g., radio emitters [19; 20]. The sensitivity of propagation of man-made VLF signals in the lower ionosphere makes them an ideal tool for remote monitoring of this medium under unperturbed/perturbed conditions [9; 21]. During solar flares (SFs) and consequently SID events, an increase in ionospheric electron concentration and other ionospheric parameters at all altitudes is noticeable. As a result of radiation effects, the solar-induced SID and plasma irregularities cause perturbations in the received amplitude and phase of VLF EM signals mainly in the D-region which is part of the ionosphere. In this contribution, we focus on amplitude and phase data of radio signals recorded by BEL system (Belgrade, Serbia) [22; 23; 24]. Emitted VLF signals [25] are constantly recorded by the equipment at BEL site since 2003. Intensity of X-ray flux during SFs, which are monitored by Geostationary Operational Environmental Satellite (GOES), are simultaneously analyzed with recorded data by BEL system of receivers. For these events, amplitude and phase perturbations are measured and analyzed during the daytime. The aim of this study is to accurately model the perturbed D-region. We determine ionospheric parameters during huge SFs which may continuously perturb this region for several hours. Furthermore, for the perturbed ionospheric D-region, we give a simple approximative formula for altitude-dependent electron density which makes results easy for use. The results presented here are ready for further use with a particular emphasis on the astrophysical applications, more precisely in the rapid investigation of the low ionosphere under the influence of strong solar radiation.