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). 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.