This study presents the results obtained from modeling the lower ionosphere response to C‐, M‐ and X‐class solar X‐ray flares. This model is based on a 5‐component scheme for the ionization‐recombination cycle of the ionospheric D‐region. Input parameters for the plasma‐chemical model under different heliogeophysical conditions corresponding to selected X‐ray flares were determined by using data received from the AURA, SDO, and GOES satellites. Verification of the obtained results was carried out with use of ground‐based radiophysical measurements taken at the geophysical observatory Mikhnevo. The results obtained from a comparison of the calculated and experimental radio wave amplitude variations along six European very low frequency (VLF) paths show that the average normalized root mean square error is ∼7%, 14%, and 18% for C‐, M‐, and X‐class flares, respectively. Qualitative and quantitative analysis of the verification results for the VLF signal amplitude show good predictive capability of the model built for describing weak and moderate ionospheric disturbances.

It is demonstrated that it is required to create probabilistic statistical models of the ionosphere for calculating radio propagation in a wide frequency range. This, in fact, presents a new type of ionospheric modeling. These models are classified into pure statistical and deterministic-stochastic. We describe the key principles of building such models, present some examples of their construction, and discuss some difficulties arising from them.

Variations in X-ray and extreme ultraviolet (EUV) irradiance during solar flares lead to a noticeable increase in the electron concentration in the illuminated part of the Earth’s ionosphere. Due to the large amount of experimental data accumulated by global navigation satellite systems, the total electron content (TEC) response to the impulsive phase of a solar flare has been studied quite well. However, recent studies have shown that a large fraction of X-class flares have a second strong peak of warm coronal emission (which is called “EUV late phase”), whose influence on the ionization of ionospheric layers is not yet clear. A combined analysis of successive solar emissions and the caused TEC changes made it possible to numerically estimate the ionospheric response to the impulsive, gradual, and late phases of the X2.9 solar flare that occurred on 2011 November 3 and demonstrate the high geoeffectiveness of the rather weak Fe xv 28.4 nm solar emission during the EUV late phase. It was found that the ionospheric response to the relatively weak emissions of the EUV late phase of the X2.9 solar flare amounted to almost a third of the TEC increase during the impulsive phase.