# Cross-Correlation Wavelet-Domain-Based Particle Swarm Optimization for Lightning Mapping
## 3 Results and Discussions
### Lightning Mapping Optimization  
In this section, we provide a novel CCWD-PSO-based lightning mapping algorithm processing. The implementation of the wavelet technique was used because of the capability of wavelet transform to further enhance the signals and reduce the noise effects, providing better time-domain resolution and reliable estimation of initial lightning maps (i.e., before optimization). To optimize the initial lightning map, an objective function was defined using window size as the regularization parameter. Tuning window size at best fitness value of the 300 iterations PSO, resulting from the objective function, was found to be \(W_{s}=282\). Thus, the localization scheme of the lightning mapping was carried out directly in the wavelet domain using a tuning window size \(W_{s}=282\). Here, we analyze three ITF NBEs data. Figure 9: Interferometer data: (**a**) NBE2 and (**b**) NBE3 using lightning event extraction. The first NBE1 discharge occurred as the storm intensified on 4 December 2017, UTC+8 03:01:42. Figure 10 shows the constructed map of the lightning source location for the first positive NBE1, where the constructed map of lightning source location was observed using the CCWD-PSO algorithm. The color changes in Figure 10a, with time from blue to green, correspond to the lightning progression time. In NBE1, the channel from the bottom (27\({}^{\circ}\) elevation) to 33\({}^{\circ}\) elevation was approximately straight with small changes in azimuth angles range, corresponding to the trajectory of the lightning flash. Figure 10b shows the expanded view of the lightning mapping plotted in azimuth vs. elevations. Figure 10c indicates that the radiation elevation angles and the fast-electric field observations (black waveform) are superimposed on the VHF waveform (blue), showing the downward propagation of the emitted VHF source. This is due to the downward pointing of the electric field (E change). The second NBE2-initiated flash occurred sequentially with the NBE1 as the storm intensified on 4 December 2017, UTC+8 03:21:13. Figure 11 shows the estimated map of the lightning source location of the FA and ITF observations for the positive NBE2. The color changes in Figure 11a, with time from blue to green, correspond to the lightning progression time. Figure 11b shows the expanded view of the lightning map of a. The VHF radiation source for the NBE2 decreased in the elevation angle with an approximate range of 22\({}^{\circ}\) to 29\({}^{\circ}\) with small breakdown changes in the azimuth angles, corresponding to the trajectory of the lightning flash. The elevation angle and the change of fast-electric field (E changes) observations (gray waveform) show a downward propagation of the VHF source. It can be observed that the NBE2 has a narrow input current pulse (fast-electric field) due to the small charge involved in the return stroke sequence. In addition, NBE2 occurred over a time expanded window (time interval) of 20 \(\upmu\)s (5000 samples), compared to NBE1 and NBE3, as they occurred over a time interval of 19 \(\upmu\)s. Figure 11c indicates the breakdown with each colored circle-marker, denoting the elevation angle (altitude) vs. time. A simultaneous observation of the second NBE3 discharge occurred on 13 December 2017, UTC+8 05:08:16. The lightning map was produced for NBE3 discharge using the CCWD-PSO algorithm, as shown in Figure 12. It can be seen that the VHF radiation source for the NBE3 is slightly decreased in elevation angle through time, with the lightning channel propagating from 24\({}^{\circ}\) to 30\({}^{\circ}\) elevation. This measurement represents a time-expanded window of approximately 19 \(\upmu\)s. For NBE2, compared with NBE1, the lightning discharge breakdown orientation appears to be vertical. This indicates that the retrieved azimuth angles at which the breakdown occurred were constant.