## 4 Results and Analysis
### Assessing the Impact of Various Clustering Algorithms on the Cluster Analysis Locating Method
It is evident that the K-means-CAL method exhibits higher arithmetic mean, geometric mean, and standard deviation values for the TDRD when compared to the other methods. This discrepancy is likely due to the necessity of predefining the number of clusters in the K-means algorithm, which, as depicted in Figure 2, can lead to significant errors when clusters 3, 4, and 5 are merged. The percentage of events where the TDRD does not exceed 50 km, as determined by comparing the MS-CAL method's results with those of the WWLLN-SCL method, stands at 76.67%. This is a higher rate than the 68.89% achieved by the DBSCAN-CAL method and the 66.67% of the K-means-CAL method. This superior performance may be attributed to the MS algorithm's focus on identifying the densest cluster centers, which often align with areas of high lightning frequency, thus better reflecting the patterns of lightning occurrence. Figure 5: Evaluation of comprehensive scores for the three CAL methods under varying parameter selections. Panel (**a**) represents the K-means-CAL; panel (**b**) illustrates the MS-CAL; panels (**c**) and (**d**) correspond to the DBSCAN-CAL. Note: the comprehensive score refers to the mean of the arithmetic mean, geometric mean, and standard deviation of the TDRD of the locating results between the CAL method and the WWLLN-SCL method. However, the MS-CAL method's TDRD metrics are slightly higher than those of the DBSCAN-CAL method, suggesting a less-precise overall match. This could be due to the presence of isolated noise points in the WWLLN data, which the DBSCAN algorithm can effectively mitigate by using its sweep radius to define cluster boundaries. Nevertheless, the DBSCAN-CAL method, which calculates the geometric center of clusters, may yield results that deviate from the actual lightning event center in cases of cluster fragmentation or noise, as illustrated in Figure 2 for clusters 1 and 2. This could explain why the proportion of events with a TDRD less than 50 km for the DBSCAN-CAL method is lower than that for the MS-CAL method when compared to the WWLLN-SCL method. In summary, to bolster the precision and dependability of the CAL method, the clustering process has been enhanced with the following steps: Initially, the DBSCAN algorithm clusters the dataset \(S\), and any clusters with fewer than five events (among values from 1 to 10, this one yields the most favorable comprehensive score) are filtered out, yielding a cleansed dataset named _S_new_. Subsequently, the MS algorithm is applied to _S_new_, and the other procedures are unchanged. This refined approach is termed the mean shift denoised (MSDN)-CAL method. With the optimal parameter configurations (as previously discussed), the proportion of the TDRD of the locating results between the MSDN-CAL method and the WWLLN-SCL method less than 50 km is 81.11%. Furthermore, the method in question achieves the most favorable comprehensive score for locating error, which stands at 56.06 km. In comparison, the other three CAL methods yield comprehensive scores of 58.51, 100.24, and 80.16 km, respectively. The MSDC-CAL method demonstrates superior precision and dependability compared to the other three CAL methods, as illustrated in Figure 6.  
Using the MSDN-CAL method, we successfully obtained two-dimensional geographical locations for 82.39% (861 out of 1045) of the WEMPD-recorded events that match the WWLLN observations within \(\pm\)150 s. Among these, TIPP and TISP events constitute 79.44%  
Figure 6: Statistical histograms of the TDRD of the locating results between the four CAL methods and the WWLLN-SCL method. Panel (**a**) presents the DBSCAN-CAL; panel (**b**) shows the K-means-CAL; panel (**c**) corresponds to MS-CAL; and panel (**d**) represents the MSDN-CAL. The figure presents 86 samples, which correspond to the successful determination of geographical locations using the CAL method out of a total of 90 events. These events are characterized by a time difference (\(\Delta t\)) of less than 100 μs between the WEMPD and the GHMLL.