Unraveling multi-scale associations and nonlinear threshold relationships between urban spatial structure and water quality in cold cities based on interpretable machine learning

The tension between urban development and water quality improvement is a major challenge for river-basin management, particularly in cold regions characterized by pronounced freeze–thaw processes. Focusing on the Songhua River Basin, this study integrated water quality monitoring and road-network data (2020–2024) with space syntax and the interpretable machine learning framework XGBoost–SHAP to investigate the nonlinear and cross-scale associations between urban spatial structure and river water quality. The overall City Water Quality Index (CWQI) increased by 6.25% during the study period, indicating an overall deterioration in water quality. Water quality was generally better during the ice-covered period than during the snowmelt period. Dissolved oxygen (DO) was the dominant water-quality indicator during the ice-covered and dry periods, whereas permanganate index (COD Mn ) was more influential during the snowmelt and flood periods. Spatially, water quality was highest in the upstream region, followed by the downstream and midstream regions. Space syntax analysis showed that spatial centrality decreased by 2.3%, with the most pronounced decline occurring at the urban scale, forming a “dual-core, dual-node, and multi-point” pattern. By contrast, spatial hierarchy increased by 1.71%, with the largest increase occurring at the block scale, forming a “one-axis, two-belt, and three-corridor” pattern. XGBoost–SHAP analysis revealed nonlinear and scale-dependent associations between spatial structure and predicted CWQI. During the non-freeze–thaw phase, urban-scale NAIN exhibited relatively larger SHAP contributions and stronger associations with predicted CWQI than district-scale and block-scale indicators. During the freeze–thaw phase, these associations became more strongly cross-scale, with the direction and strength of SHAP contributions changing across different indicator-value ranges, indicating threshold-dependent and nonlinear responses.