Bivariate Analysis of Discomfort Index and Remote Sensing Ecological Vulnerability Index Using Statistical Patterns and Color Matrix Relationships

The relationship between ecological vulnerability (EV) and the Discomfort Index (DI), which manifests the coupled dynamics of ecological fragility and climatic stress, remains inadequately quantified in a spatially explicit manner. In this study, multi-temporal Landsat 5 and 8 imagery and ERA5-Land reanalysis data were integrated to construct a remote-sensing ecological vulnerability index (RSEVI) through Principal Component Analysis of wetness, heat, greenness, dryness, and land degradation indicators. In parallel, DI was derived from land surface temperature and relative humidity. Spatial dependencies between the two indices were assessed using the bivariate L statistic, complemented by bivariate color mapping, to visualize synchronous clusters. The results reveal pronounced shifts between 2000 and 2025: the mean DI increased from 23.31 °C to 26.79 °C, while areas under "medical emergency" conditions expanded from 0.1% to 8.6%. Simultaneously, the share of strongly and extremely vulnerable areas will increase from 5.5% in 2000 to 18.9% in 2025. Spatial association analysis reveals a significant increase in high-high clusters (high vulnerability–high discomfort) from 48% to 74%, primarily concentrated in the southern and eastern sectors. Conversely, low-low clusters increased from 23% to 34%, consolidating resilient cores in the north. Discordant clusters exhibited divergent trajectories: low-high associations expanded from 28% to 48%, while high-low clusters remained relatively stable (~39%). These patterns underscore the dual emergence of critical hotspots and resilient strongholds while intensifying spatial heterogeneity. By developing a spatially robust framework, this study avoids spatial fallacies and provides tools to identify hotspots and resilient areas, offering a replicable method for environmental risk assessment and adaptive planning under climate change.