3.1.1. K-Means

A detailed investigation was carried out to assess the performance of the clustering algorithms. Figure 4 shows how three performance metrics SCI, CHI and DBI change with different cluster numbers when using K-means to cluster the time-series water depth data. Values for the CHI value increase with higher cluster numbers, whereas the SCI and DBI values fluctuate. The SCI and DBI values show opposite trends, reflecting the different methods by which they are calculated (see Section 2.3 above). In particular, Figure 5b,c show that the best solution is with eight clusters, reflected in the largest SCI value and smallest DBI value. These results suggest that the SCI and DBI are more suitable to assess the performance of K-means, while any peak in the CHI related to cluster quality is eclipsed by the influence of increasing the number of clusters. Based on the SCI and DBI value in Figure 5a, the optimal number of clusters is six for the two year-3 h and five year-3 h rainfall scenarios. The differences in the optimal number of clusters in Figure 5a–c indicate that rainfall duration has impacts on the number of clusters when utilizing K-means to group time-series water depth datasets.

**Figure 5.** Performance evaluation for K-means Clustering with different cluster numbers under synthetic rainfall scenarios including (**a**) 3-h (left 2-year and right 5-year), (**b**) 12-h (left 2 year and right 5 year), and (**c**) 48-h duration (left 2 year and right 5 year).
