Unraveling Scale Effects in Naturalized Runoff Processes: Insights from Interpretable Machine Learning Across the Yellow River Basin

Effective water resource management requires a comprehensive understanding of runoff processes across spatial scales and their interconnections. However, scale effects pose major challenges to deriving a universal spatial scaling law when extrapolating runoff research from fine to broad scales. Previous studies have mainly focused on relatively small catchments (<100 km²), potentially overlooking the heterogeneity of environmental drivers affecting runoff processes. Furthermore, traditional point-based, short-term, or infrequent measurements are insufficient to accurately capture nonlinear behavior of runoff processes. To address these issues, we integrated global runoff data products with interpretable machine learning approaches to analyze runoff processes across spatially nested basins within the Yellow River Basin. Spatial scale effects and their driving factors are systematically evaluated, extending the analysis to the river-basin scale (>100 km²). Our results indicate that the runoff coefficient of most sub-basins in the Yellow River Basin exhibits multi-scaling behavior, with spatial patterns varying across scales. Rather than following a single trend, the scale effects of the runoff coefficient are complex and non-monotonic. In smaller sub-basins, the spatial distribution of precipitation primarily controls runoff scale effects, whereas in larger sub-basins, land-use patterns become the dominant governing factor.