Spatial entanglement of urban zonal indicators: A novel GIS-based metric for measuring geographically multivariate dependencies

This study introduced a spatial entanglement index (SEI) as a quantitative metric for systemic multilayer coevolution in urban environments. SEI integrates geographical variables through multivariate spatial entanglement calculus, incorporating temporal persistence, spatial proximity, and capacity thresholds. This integration is accomplished through non-parametric computation, validated by kernel density estimation and Q-Q plots. Applying the index for Kuwait's urban transition (2017–2025), Sentinel-2 Level-2A imagery was subjected to object-based classification to compute neighborhood-aggregated transitions and changes. The framework yielded significant insights: southeastern hotspots (SEI >34) exhibited strong entanglement between built-up expansion and green-space fragmentation; optimization surfaces indicated maximum entanglement when moderate increases in green space coincided with reductions in built areas; road and barren land expansion functioned as linear disentanglers; and temporal dynamics accounted for 40–60 % of the variance. Parallel coordinate plots illustrate that significant entanglement necessitates synchronized temporal capacity peaks. Overall, the SEI findings revealed a move to systemic coevolution assessment, dynamic temporal precedence, and unified diagnostic methods. This technique may offer a foundation for simulating cities and urban zones as interdependent systems, and provide planners with a transformative metric to address the inherently connected layer dynamics in sustainable interventions.