## 3 Results
### Spatial-Temporal Co-Clustering Results Analysis during the ENSO Period  
We also selected for experiments the SST data in the SCS when the ENSO phenomenon occurred. First, the time range of the SST data we selected spans from 2020.06 to 2022.11. During this period, the La Nina phenomenon occurred. Based on the clustering results during this period, we analyzed the similarities and differences with SST spatial-temporal co-clustering in the non-ENSO period. The clustering results are shown in Figure 5. The temporal clustering results and the spatial pattern of each temporal cluster are shown in Figure 5. We find that even when the ENSO phenomenon occurs, the spatial distribution of the SCS will not change greatly. The spatial distribution of time_cluster0 corresponds to the winter of the non-ENSO period, the spatial distributions of time_cluster1 and time_cluster2 correspond to the spring and autumn of the non-ENSO period, respectively, and the spatial distribution of time_cluster3 corresponds to the summer of the non-ENSO period. However, the seasonal characteristics of the temporal clustering results have been disrupted. Figure 5: Spatial–temporal co-clustering results of SST in the SCS when La Níña occurs between 2020.06–2022.11, seasonal characteristics are destroyed, co-clustering result exhibits abnormal temporal patterns. Abnormal time clustering is seen in time_cluster1 and time_cluster2. Time_cluster1 includes the months of November 2020 and 2021, as well as the months of June 2021 and 2022. Time_cluster2 includes the months of December 2020 and 2021, as well as the months of May 2021 and 2022. We postulate that these irregularities reflect the La Nina phenomenon's influence on the SST in the SCS, an impact that resurfaces periodically. Similarly, when El Nino occurs, the similar clustering results appear. This abnormal clustering result has also been found in the Yellow Sea and the Bohai Sea [42]. This paper will select ENSO events of different intensities to verify this abnormal pattern, specifically includes June 1998 to June 2000 (strong La Nina event), June 2010 to June 2012 (mild La Nina event), February 1997 to April 1998 (strong El Nino event), February 2014 to April 2015 (mild El Nino event). Temporal Clustering Results under ENSO Events of Different Intensities  
Here, we set the number of time clusters to three and select two La Nina events for experimental purpose. From 1998.06 to 2000.06, when an intense La Nina event was observed, and from 2010.06 to 2012.06, when a mild La Nina event was observed. Similarly, the clustering results of these two periods mirrored those of the appeal experiment, as illustrated in Figures 6 and 7. Figure 6 shows the temporal clustering result under an intense La Nina event. We can see that the abnormal category is time_cluster1, including 1998-06, 1998-11, 1998-12, 1999-04, 1999-05, 1999-06, 1999-11, 1999-12, 2000-04, 2000-05, and 2000-06. Figure 7 shows the temporal clustering result under a mild La Nina event. The abnormal category is time_cluster1, including 2010-06, 2010-11, 2010-12, 2011-05, 2011-06, 2011-11, 2011-12, 2012-05, and 2012-06. We found that in the case of mild La Nina, there are no 2011-04 and 2012-04 in the abnormal category. This indicates that the SSTs in 2010-11 and 2010-12 produced corresponding responses in the SCS again 5 months later. Under the intense La Nina incident, this time was shortened to 4 months. Figure 6: Temporal results of SST in the SCS when intense La Nina occurs between 1998.06–2000.06, months-cluster1 is the anomaly category. Figure 7: Temporal results of SST in the SCS when mild La Nina occurs between 2010.06–2012.06, months-cluster1 is the anomaly category. Similarly, we also selected data during the El Nino event period for experiments, specifically including data from 1997.02 to 1998.04 when an intense El Nino event was observed, and 2014.02 to 2015.04 when a mild El Nino event was observed. The experimental results are shown in Figures 8 and 9.