Urban–rural divide in pluvial inundation: the nonlinear role of building development intensity under extreme rainfall in Beijing

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Abstract Context Developed cities, with dense populations and intensive construction, are increasingly vulnerable to extreme pluvial events. Understanding the relationship between Building Development Intensity (BDI) and Pluvial Inundation (PI) is thus essential for strengthening urban–rural flood resilience. This study conceptualizes urban flood risk as an emergent property of socio-hydrological systems, emphasizing the nonlinear interactions that shape inundation patterns. Objectives We investigate how BDI influences PI during extreme rainfall in Beijing, aiming to provide a scientific basis for optimizing spatial development and disaster mitigation. Methods Using 10,331 inundation points, we apply a Gradient Boosting Decision Tree model with Partial Dependence Plots to examine the nonlinear effects and urban–rural heterogeneity of BDI on PI. Results (1) BDI strongly affects PI, with Floor Area Ratio (FAR) and Building Density (BD) as primary drivers of Inundation Severity (IS) and Inundation Extent (IE). In urban areas, PI is more sensitive to BD, while in rural areas, it is more sensitive to FAR. (2) The relationship is complex, combining near-linear patterns with threshold effects. BDI exerts opposite influences on IS and IE in urban versus rural settings, while its effect on Inundation Depth (ID) remains consistent across the city. (3) Interaction analysis shows significant synergistic and complementary effects. For example, BD–FAR complementarity mitigates IS and IE, whereas BD–Low-grade Road Density synergy amplifies ID. Conclusions BDI shapes PI in nonlinear and heterogeneous ways across the urban–rural divide. Effective flood risk mitigation requires differentiated management of BD and FAR, alongside integrated resilience planning that aligns infrastructure hierarchy with building development morphology.

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