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Many real-world dynamic features such as ocean eddies, rain clouds, and air masses may split or merge while they are migrating within a space. Topologically, the migration trajectories of such features are structurally more complex as they may have multiple branches due to the splitting and merging processes. Identifying the spatial aggregation patterns of the trajectories could help us better understand how such features evolve. We propose a method, a Global Similarity Measuring Algorithm for the Complex Trajectories (GSMCT), to examine the spatial proximity and topologic similarity among complex trajectories. The method first transforms the complex trajectories into graph structures with nodes and edges. The global similarity between two graph structures (i.e., two complex trajectories) is calculated by averaging their topologic similarity and the spatial proximity, which are calculated using the Comprehensive Structure Matching (CSM) and the Hausdorff distance (HD) methods, respectively. We applied the GSMCT, the HD, and the Dynamic Time Warping (DTW) methods to examine the complex trajectories of the 1993–2016 mesoscale eddies in the South China Sea (SCS). Based on the similarity evaluation results, we categorized the complex trajectories across the SCS into four groups, which are similar to the zoning results reported in previous studies, though difference exists. Moreover, the yearly numbers of complex trajectories in the clusters in the northernmost (Cluster 1) and the southernmost SCS (Cluster 4) are almost the same. However, their seasonal variation and migration characteristics are totally opposite. Such new knowledge is very useful for oceanographers of interest to study and numerically simulate the mesoscale ocean eddies in the SCS.

Clustering Complex Trajectories Based on Topologic Similarity and Spatial Proximity: A Case Study of the Mesoscale Ocean Eddies in the South China Sea