## 3 Results
### Modelling and Simulation during LEP Event  
NAA/24 kHz signal propagates along W-E direction and has a long (GCP distance D = 6540 km) and mostly oversea path, while GQD/22.1 kHz signal propagates along a short (GCP distance D = 1980 km) and mostly overland path (Figure 5). Disturbance occurred on both analysed signal traces, so it is reasonable to assume that ionospheric irregularity caused by an LEP event was located in the vicinity of the Belgrade receiver site. That is why, both for unperturbed and perturbed ionospheric conditions, the VLF propagation conditions were modelled only in that section of waveguide which is just a few hundred km away from the Belgrade receiver site (44.85\({}^{\circ}\) N, 20.38\({}^{\circ}\) E). By means of Long Wavelength Propagation Capability computer program (LWPCv21) [51], the propagation paths of NAA/24.0 kHz and GQD/22.1 kHz signals were simulated and modelled. Best fitting pairs of parameters sharpness \(\beta\) (km\({}^{-1}\)) and reflection height \(H^{\prime}\) (km) were estimated in order to obtain values as close as possible to real measured values of the signals' phase delay (deg) and amplitude (dB) at the place of the receiver in Belgrade, for both cases of regular and disturbed ionospheric conditions in observed sections of waveguides. The estimated amplitude and phase delay values obtained by the LWPCv21 program are in good agreement with  
Figure 4: Amplitude (solid lines) and phase delay (dotted lines) time evolution before and during the LEP event occurred on 16 November 2004 on considered VLF signal traces: (a) NAA/24.0 kHz and (b) GQD/22.1 kHz. Figure 5: Possible paths for considered NAA/24.0 kHz (red) and GQD/22.1 kHz (yellow) VLF signals emitted towards Belgrade (Serbia) from Maine (USA) and Skelton (UK). the Belgrade receiver site (Table 1: first and third rows indicate unperturbed VLF signal values, while the second and fourth rows indicate the perturbed ones). The amplitude change \(\Delta A\) (dB), was obtained as the difference between the maximum value of the amplitude during the perturbation and the value of the amplitude in undisturbed signal. The phase delay change \(\Delta P\) (\({}^{\circ}\)) was obtained as the difference between the phase delay value that corresponds in time to the maximum value of the amplitude during the perturbation and phase delay value in the undisturbed signal interval that corresponds in time to the amplitude value chosen as unperturbed. The model for the propagation of VLF signals within the Earth-ionosphere waveguide is defined by pairs of parameters (\(\beta\), \(H^{\prime}\)) and analytically described by equations for the calculation of the electron density height profile \(N_{e}(z)\) (m\({}^{-3}\)) during daytime ionospheric conditions is given in [56]. The procedure for the computation of the electron density height profile is based on the equation for determining the electron density \(N_{e}(z)\) (m\({}^{-3}\)) within the Earth-ionosphere waveguide during night-time conditions [14], where the electron density was calculated as a function of a certain pair of parameters \(\beta\) and \(H^{\prime}\), at the height z (km), based on the equation adapted for the nocturnal ionosphere [14]. Electron density height profile \(N_{e}(z)\) (m\({}^{-3}\)), for given parameters \(\beta\) and \(H^{\prime}\), was calculated using the expression for the night-time ionosphere given by [14]:  
\[N_{e}(z,H^{\prime},\,\beta)=1.86\times 10^{11}\cdot\mathrm{e}^{-0.15\cdot z} \cdot 78.57\cdot\mathrm{e}^{\beta(z-H^{\prime})},\ \ \ \ \ \ (\mathrm{m}^{-3}) \tag{1}\]  
Parameter \(\beta\), for night-time ionospheric conditions, is in the range 0.47-0.50 km\({}^{-1}\), while parameter \(H^{\prime}\) is in the range 50-87 km. Electron density was calculated at the reflection height, when \(z=H^{\prime}\), and in that case (1) takes the form:  
\[N_{e}(z)=146.1402\times 10^{11}\cdot\mathrm{e}^{-0.15\cdot z},\ \ \ (\mathrm{m}^{-3}) \tag{2}\]  
For modelling of parameters \(\beta\) and \(H^{\prime}\), the LWPC software was used.