Di et al. (2026) Quantifying Predictability and Information Transfer in Rainfall-Runoff Process

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: Chongli Di, Shailesh Kumar Singh, Jianzhi Dong, Jianzhu Li, Jun He
• DOI: 10.1007/s11269-025-04431-z

Research Groups

• Institute of Surface-Earth System Science, School of Earth System Science, Tianjin University, P. R. China
• National Institute of Water and Atmospheric Research, Christchurch, New Zealand
• State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University, China
• The General Institute of Water Resources and Hydropower Planning and Design of the Ministry of Water Resources, Beijing, China

Short Summary

This study integrates chaos theory and information entropy to characterize rainfall-runoff predictability under human interventions. It reveals that streamflow predictability systematically deteriorates downstream due to reservoir operations, which also significantly disrupt the directional information transfer from rainfall to runoff.

Objective

• To characterize rainfall-runoff predictability under the influence of human interventions by a novel integration of chaos theory and information entropy.
• To evaluate how predictable rainfall and runoff systems are, and how effectively predictability is transmitted between them.

Study Configuration

• Spatial Scale: Luanhe River Basin (LRB) in northern China, covering 44,900 square kilometers, with data from 20 hydrological and rainfall stations across upstream, midstream, and downstream regions.
• Temporal Scale: Daily and monthly time series data for rainfall and streamflow.

Methodology and Data

• Models used:
  • Chaos theory: Phase Space Reconstruction (PSR), Largest Lyapunov Exponent (LLE) to quantify chaotic dynamics and predictability.
  • Information entropy: Transfer Entropy (TE) to evaluate directional information transfer.
  • Reservoir Index (RI) to quantify dam-induced alterations.
  • Spearman's rank correlation for analyzing relationships between complexity indices and environmental factors.
• Data sources:
  • Daily rainfall and streamflow data: Hydrological Yearbook of the Haihe River Basin.
  • Digital Elevation Model (DEM): 30 meter resolution from the Resources and Environment Science Data Center of the Chinese Academy of Sciences.
  • Aridity Index (AI): Calculated from mean annual potential evapotranspiration and mean annual precipitation.
  • Normalized Difference Vegetation Index (NDVI): 16-day temporal resolution, 500 meter spatial resolution (MODIS).

Main Results

• Phase-space analysis confirmed chaotic behavior in both rainfall and runoff, with streamflow predictability systematically declining from upstream to downstream.
• Rainfall predictability exhibited uniformly chaotic behavior across the basin, with LLE values ranging from 0.33 to 0.67.
• Transfer entropy analysis showed stronger rainfall–runoff coupling in upstream regions (TE: 0.45 to 0.74), indicating efficient information transfer.
• Downstream areas experienced significantly disrupted information transfer (TE: 0.10 to 0.30), representing a 60% to 78% decline compared to upstream systems, primarily due to reservoir operations.
• Reservoir operations substantially reduced downstream predictability, with Reservoir Index (RI) values exceeding the critical threshold (e.g., Daheiting RI = 0.653, Luanxian RI = 0.538).
• Streamflow complexity (LLE) correlated positively with precipitation variability (rs = 0.799) and mean annual potential evapotranspiration (rs = 0.606), but negatively with the aridity index (rs = -0.688) and elevation (rs = -0.769).
• Daily streamflow exhibited longer predictability horizons (Lyapunov Time: 8.35 to 105.26 days, average 31.38 days) compared to monthly streamflow (1.49 to 8.89 months, average 3.75 months).

Contributions

• Introduces a novel framework integrating chaos theory (Largest Lyapunov Exponent) and information entropy (Transfer Entropy) to holistically diagnose rainfall-runoff processes under human influence.
• Provides a robust diagnostic tool for assessing predictability loss and altered information pathways in human-impacted river basins.
• Offers valuable insights for adaptive water management by linking quantitative predictability diagnostics with actionable decisions.
• Clarifies the dominant influence of climatic (precipitation variability, evapotranspiration, aridity) and topographic (elevation) drivers on hydrological predictability and information transfer.

Funding

• National Natural Scientific Foundation of China (42571091, 42201019)

Citation

@article{Di2026Quantifying,
  author = {Di, Chongli and Singh, Shailesh Kumar and Dong, Jianzhi and Li, Jianzhu and He, Jun},
  title = {Quantifying Predictability and Information Transfer in Rainfall-Runoff Process},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04431-z},
  url = {https://doi.org/10.1007/s11269-025-04431-z}
}