## 3 Results  
### Spatial-Temporal Co-Clustering Result Analysis  
Firstly, we selected the SST data of the SCS from 2003.12 to 2004.11. The results are shown in Figure 4. The temporal patterns show obvious seasonality. Time_cluster0 includes December of 2003, January, and February of 2004 (DJF). Time_cluster1 includes March, April, and May of 2004 (MAM). Time_cluster2 includes June, July, and August of 2004(JJA). Time_cluster3 includes September, October, and November of 2004 (SON). This conclusion is consistent with previous research [34]. We can observe that the spatial patterns of the SST in the SCS differ across various temporal clusters. This uniqueness of the algorithm allows it to identify different spatial patterns on different time clusters in a single iteration. We can see that the spatial patterns of the SST in the SCS is clustered into two categories in winter (time_cluster0); the spatial patterns of the SST in the SCS in spring and autumn (time_cluster1, time_cluster3) is similar, and both are divided into three categories. Because spring and autumn are defined as transition seasons, they have similar spatial patterns. This point was also mentioned in paper [34]. Due to the changeable climate in summer, the SST spatial clustering results of the SCS in summer are clustered into five categories (time_cluster2). Additionally, the spatial patterns reveal that category boundaries near the land are more inclined, indicating that SST close to land is more affected by terrestrial factors, including differences in heat capacity between the land and sea, as well as human activities [35]. In winter, the spatial patterns of the SST in the SCS are usually divided into two categories. We call these two types of areas cold water areas and warm water areas. The central and northern parts of the SCS and the sea areas close to mainland China are usually cold water areas. In the cold water areas, the SCS is usually affected by the northeast monsoon circulation in winter. The northeast monsoon is a seasonal wind system that usually blows from the northeastern part of mainland China to the SCS in winter [36]. As a result, the northern and western areas of the SCS were affected by this cold wind. And the northeast monsoon is cold and dry as it blows across mainland China, bringing cold air and low humidity. This cold and dry air causes the SST to drop as it blows across the SCS. Warm water areas are typically affected by tropical ocean currents and tropical climate systems during the winter. These areas are typically affected by tropical air currents, which bring relatively warm air. This helps maintain a higher SST [37]. Due to the warmer SST and relatively abundant nutrients, these areas often support rich marine biodiversity, including coral reefs, tropical fish, and other marine life. These factors also contribute to a higher SST. In addition, these areas are usually affected by tropical currents, which bring relatively warm water bodies and help maintain a higher SST. The reasons why the SST in the SCS is divided into three categories in spring and autumn involve different climate and ocean dynamic processes. We divide it into a cold water area, transition area, and warm water area. The reasons for it being divided into these three regions are probably as follows: in spring and autumn, the northern part of the SCS and the sea areas close to the land are still affected by the northeast monsoon, which leads to a lower SST in these areas [38; 39]. These areas are still cold water areas. The cold water area may also be impacted by some ocean circulation, such as tropical currents. These currents may flow in the northern part of the SCS, bringing relatively cold water and strengthening the SST characteristics of the cold SST area. Equatorial waters in the SCS tend to be warmer in spring and autumn than in winter. The higher temperatures in these areas are primarily attributed to the influence of the southeast monsoon and tropical currents [40].