Supplementary material 1. Experiments on the contrast between the cluster flows and noise flowsAs shown in Figure S1, four simulated data sets are generated with the number of cluster flows = 1000 and number of noise flows = 500, 2000, 5000, and 10000, respectively, in which the shape of the cluster is like 'cylinder-cylinder' with the spatial scale 𝑠 = 0.1 and temporal scale 𝑡 = 0.1. We then run our method for each data set. The results of global STflowL are shown in Figures S1(a), (c), (e), and (g), and the identified clusters are displayed in Figures S1(b), (d), (f), and (h). Fifty simulations are generated for each scheme and the average number of false flows for each scheme is listed in Table S1. From these results, we can draw the following conclusions: first, the spatial and temporal scales of the cluster estimated by the global STflowL are not significantly influenced by the ratio between the number of cluster flows and that of noise flows, i.e., the estimated scales are all 𝑠 = 0.1 and 𝑡 = 0.1, which are the same as the true values; second, the accuracy of identifying clusters is not sensitive to the ratio as the numbers of false flows are all below 3 for each data scheme. In all, our method is not influenced by the ratio between the number of cluster flows and that of noise flows.