## 4 Results and Analysis
### Assessing the Impact of Various Clustering Algorithms on the Cluster Analysis Locating Method  
The strong EMPs detected by the WEMPD closely match the observations of the WWLLN and GHMLNS on a nearly one-to-one basis within a +3 ms window. Notably, there are two TIPP instances respectively corresponding to two separate events in the WWLLN within this timeframe (refer to Table 1). However, the multiple events in both sets of matches link to nearly identical locations. Consequently, under these specific space-time conditions, the origins of these events can be distinctly identified, allowing for the calculation of the time difference (\(\Delta t\)) between the 'occurrence' time of the WEMPD-detected events and the timestamps provided by the ground-based location networks (as illustrated in Figure 4). The events with an absolute time difference (\(|\Delta t|\)) less than 100 \(\upmu\)s, as identified by the WWLLN and the GHMLNS, account for 8.48% (90 out of 1061) and 1.79% (19 out of 1061), respectively. This indicates that the SCL based on data from the WWLLN and the GHMLNS can reliably pinpoint the geographic locations for approximately 10% of the WEMPD-detected events. The capacity to pinpoint the geographical locations of events through the CAL method is contingent upon the MR and MMC between the WEMPD-detected events and those of the WWLLN across various timeframes. As illustrated in Table 1, both detection systems demonstrate an MR exceeding 90% within the broader time windows of \(\pm\)30 s, \(\pm\)150 s, and \(\pm\)300 s. These high MRs are instrumental in establishing the geographic locations for the majority of events, effectively compensating for the limitations of the SCL method. The WEMPD's detection capability for strong EMPs is circumscribed within a spherical radius of 800 km from the subsatellite point, resulting in a typical detection duration of 3 to 5 min within any given locale. To mitigate the inclusion of extraneous events, dataset \(S\) is chosen for cluster analysis. This dataset is composed exclusively of the WWLLN events that coincide with a WEMPD-recorded event within \(\pm\)150 s.  
Figure 5 illustrates the comprehensive scores of the three CAL methods based on the density-based spatial clustering of applications with noise (DBSCAN), the K-means, and the mean shift (MS) when employing various parameter settings. The comprehensive score, which evaluates the performance, is calculated as the mean of the arithmetic  
Figure 4: Statistical histograms of the time discrepancy (\(\Delta t\)) between the corrected ‘occurrence’ times of the WEMPD-detected events, accounting for distance and ionospheric effects, and the event timestamps recorded by the ground-based lightning location networks. Panel (a) represents the comparison with the WWLLN, while panel (b) corresponds to the GHMLNS. mean, geometric mean, and standard deviation of the two-dimensional range deviation (TDRD) of the locating results between the three CAL methods versus the WWLLN-SCL method. A lower score indicates superior performance. For the K-means algorithm, the optimal performance is observed when the number of clusters is set to 2. In the case of the MS algorithm, a smaller bandwidth for the Gaussian kernel function generally yields better results, with little variation in performance when the bandwidth is set to 0.1, 0.3, or 0.5. However, considering the trade-off between performance and computational cost, a bandwidth of 0.5 is deemed the most effective choice due to its balance between effectiveness and reduced computational demand. The DBSCAN algorithm is governed by two parameters: the sweep radius and the minimum inclusion points. When both parameters are assigned a value of 1, the comprehensive score attains its minimum value, which is 58.51 km, indicating optimal performance (as shown in Figure 5c,d). Figure 6 provides a detailed comparison of the TDRD distribution of the locating results between the three CAL methods and the WWLLN-SCL method.