Cheng et al. (2025) A more appropriate framework for graphical attribution of hydrological change in the water-energy partitioning space

Identification

• Journal: Journal of Hydrology Regional Studies
• Year: 2025
• Date: 2025-12-17
• Authors: Changwu Cheng, Wenzhao Liu, Xunchang John Zhang, Rui Chen, Zhaotao Mu, Xiaoyang Han, Yuanjun Zhu
• DOI: 10.1016/j.ejrh.2025.103048

Research Groups

• State Key Laboratory of Soil and Water Conservation and Desertification Control, the Research Center of Soil and Water Conservation and Ecological Environment, Chinese Academy of Sciences and Ministry of Education, Yangling, Shaanxi, China
• College of Geography and Remote Sensing Sciences, Xinjiang University, Urumqi, China
• University of Chinese Academy of Sciences, Beijing, China
• College of Soil and Water Conservation Science and Engineering, Northwest A&F University, Yangling, Shaanxi, China
• USDA-ARS Grazinglands Research Lab., El Reno, OK, USA
• College of Resources and Environment, Xinjiang Agricultural University, Urumqi, China

Short Summary

This study critically evaluates existing graphical attribution methods (OGA and BGA) for hydrological change in the water-energy partitioning space, identifies limitations of OGA, and proposes the two-path Budyko-based graphical attribution (BGA) as a more appropriate framework, applying it to 15 catchments in the Chinese Loess Plateau. The improved method found that the direct effect of the dryness index (∅) and the regulating effect of the land-atmosphere system contributed, on average, 18 % and 82 %, respectively, to runoff change.

Objective

• To investigate the fundamental differences between the orthogonality-based graphical attribution (OGA) and Budyko-based graphical attribution (BGA) methods.
• To clarify the implementation of the two-path approach in the water-energy partitioning (WEP) space.
• To apply the proposed two-path BGA method to separate the relative contributions of the direct effect of the dryness index (∅) and the regulating effect of the land-atmosphere system to runoff (Q) change for 15 catchments in the Chinese Loess Plateau (CLP).

Study Configuration

• Spatial Scale: 15 catchments in the Chinese Loess Plateau (CLP), covering areas from 1263 km² to 43,216 km².
• Temporal Scale: Long-term (1960–2020) data for runoff, precipitation, and potential evapotranspiration. Attribution periods for individual catchments ranged from 22 to 38 years, determined by Pettitt analysis.

Methodology and Data

• Models used:
  • Budyko-based graphical attribution (BGA)
  • Orthogonality-based graphical attribution (OGA)
  • Budyko-MCY equation (E/P = [(EP/P)⁻ⁿ + 1]⁻¹/ⁿ)
  • Two-path graphical attribution method (an improved BGA in WEP space)
• Data sources:
  • Runoff (Q) data: Observed at hydrological stations, obtained from the Loess Plateau Subcenter of the National Earth System Science Data Center (https://loess.geodata.cn).
  • Precipitation (P) data: Interpolated from meteorological station observations (sourced from Cheng et al., 2023).
  • Potential Evapotranspiration (EP) data: Calculated using the Penman equation (Penman, 1948), accounting for air temperature, radiation, wind speed, and vapor pressure (sourced from Cheng et al., 2023).

Main Results

• The orthogonality-induced linearization in OGA can fail to capture nonlinear Budyko relationships, potentially violating water and energy balance constraints (0 ≤ E/P ≤ 1 and 0 ≤ E/EP ≤ 1), making the two-path approach infeasible in some cases.
• The study elucidated inconsistencies between OGA and BGA in both decomposition orders and paths, demonstrating that the two-path BGA is a more appropriate and physically consistent attribution framework in the WEP space.
• The Budyko model parameter (n) is essentially a lumped variable representing the integrative effects of the climate and underlying surface system, rather than solely land surface characteristics.
• Application of the two-path BGA to 15 CLP catchments showed that, on average, the direct effect of the dryness index (∅) contributed 18 % and the regulating effect of the land-atmosphere system contributed 82 % to runoff changes.
• Runoff decreased in 13 catchments (ranging from 13.0 mm yr⁻¹ to 46.6 mm yr⁻¹), primarily due to the regulating effect. Two catchments (Qingshui and Kushui) showed increased runoff (1.7 mm yr⁻¹ and 17.5 mm yr⁻¹, respectively), where the regulating effect outweighed the direct effect of ∅.
• The one-path approach showed substantial bias in quantifying the direct effect of ∅ compared to the two-path approach, while remaining relatively consistent for the regulating effect.

Contributions

• Identified theoretical limitations of the Orthogonality-based Graphical Attribution (OGA) method, including potential violations of water and energy boundaries and path selection issues.
• Elucidated the essential differences between OGA and Budyko-based Graphical Attribution (BGA) in decomposition orders and paths within the Water-Energy Partitioning (WEP) space.
• Proposed and implemented the two-path BGA as a more appropriate, objective, and rational graphical attribution framework in the WEP space.
• Refined the conceptual understanding of hydrological change drivers, interpreting them as the direct effect of the dryness index (∅) and the regulating effect of the land-atmosphere system.
• Advanced hydrological change attribution methods by providing a physically consistent and robust framework.

Funding

• National Natural Science Foundation of China (No. 41971049 and 41571036)

Citation

@article{Cheng2025more,
  author = {Cheng, Changwu and Liu, Wenzhao and Zhang, Xunchang John and Chen, Rui and Mu, Zhaotao and Han, Xiaoyang and Zhu, Yuanjun},
  title = {A more appropriate framework for graphical attribution of hydrological change in the water-energy partitioning space},
  journal = {Journal of Hydrology Regional Studies},
  year = {2025},
  doi = {10.1016/j.ejrh.2025.103048},
  url = {https://doi.org/10.1016/j.ejrh.2025.103048}
}