## 3 Results
### Modelling and Simulation during LEP Event
Simulated amplitude and phase delay values for NAA/24.0 kHz and GQD/22.1 kHz along GCP path, for the unperturbed (red) and perturbed (blue) state in waveguides on 16 November 2004, are presented in Figures 6 and 7, respectively. Areas of amplitude and phase delay changing near the Belgrade receiver site are framed and as zoomed in panels presented on the right. Parameters \(\beta\) and \(H^{\prime}\) changing along GCP path, for NAA/24.0 kHz (dashed lines) and GQD/22.1 kHz (dotted lines) VLF signal waveguides, for unperturbed (red) and perturbed (blue) ionospheric states, on 16 November 2004, are presented in Figure 8a,b, respectively (for waveguide sections of 1980 km along GCPs looking towards the Belgrade receiver; direction of view on x axis is presented by black arrows, pointing from left to right at the bottom scale when looking from transmitter T towards receiver R and pointing from left to right at the upper scale if looking from receiver R towards transmitter T). Using the expression (1), for given parameter pairs (\(\beta\), \(H^{\prime}\)), electron density height profile \(N_{e}(z)\) within ionospheric irregularity, in perturbed section of waveguide, for both analysed VLF signals, was calculated. Irregularity modelling indicates that both VLF signal traces, in some part of the waveguide, encounter an area of enhanced electron density. Electron density changing along GCP path, for NAA/24.0 kHz (dashed line) and GQD/22.1 kHz (dotted line) VLF signal waveguides, for unperturbed (red) and perturbed (blue) ionospheric states on 16 November 2004, are presented on Figure 9 (in length of 1980 km, as looking from Belgrade towards both transmitters). Electron densities along GCPs for unperturbed state (Figure 9--red) were calculated based on modelled parameter pairs  
Figure 6: Simulated amplitude and phase delay along GCP path towards the Belgrade receiver, for unperturbed (red) and perturbed (blue) ionospheric states for NAA/24.0 kHz VLF signal waveguides, on 16 November 2004. (\(\beta\), \(H^{\prime}\)) posted as unperturbed for all characteristic altitudes (Figure 8--red), where parameters \(\beta\) and \(H^{\prime}\) undergo changes due to signal propagation within the unperturbed waveguide. Electron densities along GCPs for perturbed state (Figure 9--blue) were calculated based on modelled parameter pairs (\(\beta\), \(H^{\prime}\)) for all characteristic altitudes (Figure 8--blue), where parameters undergo changes due to present irregularity and deviated from their posted unperturbed values. Transmission in entirely nocturnal unperturbed ionospheric conditions, in the case of short GCPs is described by LWPC program usually with only one parameter pair (\(\beta\), \(H^{\prime}\)), while in the case of moderate GCPs usually with several parameter pairs (\(\beta\), \(H^{\prime}\)), along the entire path. It should be noted, that in this case, the unperturbed conditions were also modelled in order to provide the best possible match with real measured data. As  
Figure 8: Parameter \(\beta\) and \(H^{\prime}\) changing along GCP path towards the Belgrade receiver, for considered VLF signal waveguides (NAA in dashed lines and GQD in dotted lines), for unperturbed (red) and perturbed (blue) ionospheric states, on 16 November 2004 (R is for receiver, T is for transmitter, black arrows on x axis point the direction of view): (a) parameter \(\beta\) and (b) parameter \(H^{\prime}\). Figure 7: Simulated amplitude and phase delay along GCP path towards the Belgrade receiver, for unperturbed (red) and perturbed (blue) ionospheric states for GQD/22.1 kHz VLF signal waveguides, on 16 November 2004.  
already mentioned, since the perturbation was recorded on both monitored signals, in order to provide the best possible match with real measured data, in cases of perturbed conditions, sections of paths of several hundred km away from Belgrade towards transmitters, were modelled.