*3.2. Clustering Performance Testing*

The analysis of cluster performance in the previous section is based on synthetic rainfall datasets, due to lack of water depth data in the drainage network. However, the use of noise-free synthetic data may have a significant impact on the results obtained [69], and our results may not represent real storm situations or current climate conditions. In contrast, the trends identified here might be masked by time series noise, making it more difficult to identify optimal solutions. In order to validate that the results obtained from designed rainfalls can also be applied to non-stationary real-storms, we evaluate the performance of the clusters in grouping flooding water depth datasets generated by two real flood events described below.

The left plot in Figure 8 indicates that the best number of clusters for the 5 May 2015 event (Figure 8a) and 8 July 2015 event (Figure 8b) are five and four, respectively. Increasing the number of clusters beyond this causes both the SCI and the DBI to decline. The distribution of different clusters obtained is shown in the PCA plots in the right panel of Figure 7. These show that the cluster analysis resulted in a good separation of the storm events (indicated by the lack of overlap between the gray circles).It should be noted that both subplots 8a and 8b have an isolated cluster on the top. This is the only cluster composed of one sample, which means the water depth from the corresponding junction is significantly distinguishable to others. One possible reason for this phenomena is that the flooding or overflow events have occurred, triggering a very different signal in water depth at this location. Besides, as the rainfall duration increases from 3 h (the 5 May 2015 storm) to 24 h (the 8 July 2015 storm), the reduction in the number of clusters selected is in line with the results of Section 4, supporting the negative correlation between the number of clusters and event duration.

**Figure 8.** Cluster analysis test for time-series water depth generated by (**a**) 5 May 2015 flooding event; (**b**) 8 July 2015 flooding event (gray circles same to clusters), (x\_pca means the first component score; y\_pca means the second component score; The principal component scores are used to examine if these two clusters are reasonably distinguished from each other clustering).
