Climate and human organization decouple geometric and functional scaling in river networks

Abstract. Scaling laws are widely regarded as fundamental organizing principles of river networks, however, whether different scaling relationships emerge from common or distinct mechanisms remains unresolved. Using 41,677 rivers across China, we show that geometric and functional scaling exhibit fundamentally different sensitivities to climatic and anthropogenic forcing. The classical Hack’s law relationship between river length and drainage area remains remarkably stable across river hierarchies, climatic gradients, and major basins, indicating a highly conserved geometric organization of river networks. In contrast, runoff-efficiency scaling varies systematically with precipitation, transitioning from strongly negative exponents in arid regions to near-zero values in humid environments. This climatic dependence is associated with hydrological connectivity: river-network structure suppresses runoff efficiency, whereas lake systems enhance the scaling efficiency of runoff generation and transport across basin sizes. Furthermore, administrative fragmentation weakens natural geometric scaling while generating apparent functional scaling relationships absent in intact drainage systems. These findings reveal a fundamental asymmetry in river-network organization: geometric scaling remains highly conserved, whereas functional scaling is strongly shaped by climate, connectivity, and human spatial partitioning. Our results suggest that the organizing principles governing river systems are not fixed properties of natural landscapes, but emergent behaviors continually reshaped by climate variability, hydrological connectivity, and human modification.