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Abstract

Coastal systems are shaped by complex interactions among physical, chemical, and anthropogenic factors, yet diagnosing system-level transitions remains a major challenge due to their multivariate and dynamic nature. Here, we introduce a novel framework based on Eigen Microstates Theory (EMT) to capture the evolving dynamics of multivariable coastal systems through emergent patterns in variable interactions. Applying this theory to the Bohai Sea, a representative coastal complex system, we quantify system disorder using the entropy of eigen microstates and identify state transitions in Bohai Sea corresponding to ecological events such as red tides. These emergent eigen microstates reflect coupling among variables, allowing the identification of dominant drivers and attribution of variable behavior to anthropogenic versus climate-induced influences. Human activity is identified as the primary long-term driver of eutrophication, while natural variability modulates its intensity and timing. Furthermore, the EMT framework allows for the disentanglement of overlapping effect from different drivers, providing a robust basis for evaluating the effectiveness of environmental policies. Our analysis reveals that recent regulatory interventions, though successful in curbing nutrient inputs, were not fully reflected in nutrient dynamics because of the concurrent increases in climate-driven nutrient transport. These results underscore the importance of coordinated monitoring and management strategies that account for both human and natural contributions to coastal change, aligning with the United Nations Sustainable Development Goal (SDG) 14.1 and providing support for its implementation. This framework offers a transferable tool for uncovering state transitions and disentangling interacting drivers in complex coastal systems under global change.