Li et al. (2026) Self-similarity criticality of the world’s large river systems

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-09-07
• Authors: Zhenqi Li, Yichu Wang, Jinren Ni
• DOI: 10.1016/j.jhydrol.2026.136377

Research Groups

• The Key Laboratory of Water and Sediment Sciences, College of Environmental Sciences and Engineering, Peking University, Beijing 100871, PR China
• College of Water Sciences, Beijing Normal University, Beijing 100875, PR China
• Eco-environment and Resource Efficiency Research Laboratory, School of Environment and Energy, Peking University Shenzhen Graduate School, Shenzhen 518055, PR China

Short Summary

This study investigates the self-similar criticality of global large river systems using a unified approach combining high-resolution geospatial analytics, energy-slope coupling models, and nonlinear dynamics theory. The research reveals that river networks converge at low-to-medium stream orders but diverge at higher orders, with a dominant range of 0.57–0.67 for the self-similar validity ratio (SVR) distribution aligning with the golden-ratio conjugate.

Objective

• Investigate the mechanisms constraining the self-similarity boundaries of river networks.
• Quantify the persistence of scale-invariant organization in river networks using a universal metric.
• Decode the geoclimatic and energetic thresholds at which self-similarity collapses.

Study Configuration

• Spatial Scale: Global large river basins (≥100,000 km2)
• Temporal Scale: Not specified

Methodology and Data

• Models used: HydroATLAS dataset, Horton's laws, Strahler's stream ordering system
• Data sources: HydroATLAS v1.0 database, SRTM DEM, ESRI’s D8 single flow direction algorithm

Main Results

• The self-similar validity ratio (SVR) distribution aligns with the golden-ratio conjugate.
• Three self-similarity criticality regimes are identified: sub-golden, golden-aligned, and supra-golden rivers.
• Critical channel slope (CS) and critical streamflow (CQ) describe two complementary attributes of the same critical boundary.

Contributions

• This study transforms self-similarity from a structural observation into a physically based diagnostic framework.
• The research provides a unified approach combining high-resolution geospatial analytics, energy-slope coupling models, and nonlinear dynamics theory to investigate river network organization.
• The findings advance predictive tools for basin resilience under climate change.

Funding

• Not specified

Citation

@article{Li2026Selfsimilarity,
  author = {Li, Zhenqi and Wang, Yichu and Ni, Jinren},
  title = {Self-similarity criticality of the world’s large river systems},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.136377},
  url = {https://doi.org/10.1016/j.jhydrol.2026.136377}
}