Revisiting scaling laws in river basins: New considerations across hillslope and fluvial regimes

Increasing availability of high-resolution (1 m) topography data and enhanced computational processing power present new opportunities to study landscape organization at a detail not possible before. Here we propose the use of directed distance from the divide as the scale parameter (instead of Horton's stream order or upstream contributing area) for performing detailed probabilistic analysis of landscapes over a broad range of scales. This scale parameter offers several advantages for applications in hydrology, geomorphology, and ecology in that it can be directly related to length-scale dependent processes, it can be applied seamlessly across the hillslope and fluvial regimes, and it is a continuous parameter allowing accurate statistical characterization (higher-order statistical moments) across scales. Application of this scaling formalism to three basins in California demonstrates the emergence of three distinct geomorphic regimes of divergent, highly convergent, and moderately convergent fluvial pathways, with notable differences in their scaling relationships and in the variability, or spatial heterogeneity, of topographic attributes in each regime. We show that topographic attributes, such as slopes and curvatures, conditional on directed distance from the divide exhibit less variability than those same attributes conditional on upstream contributing area, thus affording a sharper identification of regime transitions and increased accuracy in the scaling analysis.