A more appropriate framework for graphical attribution of hydrological change in the water-energy partitioning space

Authors: CHENG, CHANGWU - Northwest A&f University; LIU, WENZHAO - Northwest A&f University; Zhang, Xunchang; CHEN, RUI - Xinjiang Agricultural University; MU, ZHAOTAO - Northwest A&f University; HAN, XIAOYANG - Northwest Agriculture And Forestry University; ZHU, YANJUN - Northwest A&f University

Submitted to: Journal of Hydrology: Regional Studies
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/12/2025
Publication Date: 12/17/2025
Citation: Cheng, C., Liu, W., Zhang, X.J., Chen, R., Mu, Z., Han, X., Zhu, Y. 2025. A more appropriate framework for graphical attribution of hydrological change in the water-energy partitioning space. Journal of Hydrology: Regional Studies. 63. Article 103048. https://doi.org/10.1016/j.ejrh.2025.103048.
DOI: https://doi.org/10.1016/j.ejrh.2025.103048

Interpretive Summary: Precipitation and potential evapotranspiration (potential water evaporation by soil and transpiration by plants) play a dominant role in water cycles at a catchment scale. Two graphical methods are often used to visually separate the direct effect of dry weather and the indirect feedback effect of the land-atmosphere systems on water runoff generation. Both methods initially adopted a single path for separating the two effects. Later studies have indicated that averaging the two possible paths could be more accurate. Here, we identified the limitation of the two-paths approach and standardized the two-paths approach for both methods. The improved method was then applied to partition runoff changes for 15 catchments in the China’s Loess Plateau. The results showed that the average relative contributions to water runoff generation by the direct effect of dry weather and the indirect effect of the land-atmosphere systems across the 15 catchments were 18% and 82%, respectively. By proposing a better two-paths approach to graphically separating water runoff generation, this work substantially advanced the methods for partitioning runoff water at a catchment scale. The work provides hydrologists and water resources managers an improved method for understanding and characterizing the drivers that influence runoff generation.

Technical Abstract: In catchment-scale hydrological processes, precipitation and potential evapotranspiration play a dominant role, while the interplay of all relevant factors from the catchment characteristics to the atmosphere plays a regulating role. The Budyko-based and the orthogonality-based graphical attribution methods (BGA and OGA, respectively) can visually separate the direct effect of dryness index Ø (the ratio of potential evapotranspiration to precipitation) and the regulating effect of the land-atmosphere systems. Both methods initially adopted a single, predefined attribution sequence (i.e., the one-path approach) to separate the two effects. Later studies on BGA have shown that averaging the hydrological changes along two possible attribution paths (i.e., the two-paths approach) is more objective and reasonable. However, the path selection for the OGA method and its essential difference from the well-established BGA remain unexplored. Here, we identified the limitation of applying the two-paths approach to OGA, given that OGA arises from the linearization implied by the orthogonality assumption and may fail to capture the nonlinear Budyko relationship. By mapping the Budyko equations in the water-energy partitioning (WEP) space, we elucidated the differences both in decomposition sequences and paths between the OGA and BGA methods, demonstrating that the two-path BGA provides a more appropriate framework for graphical attribution in the WEP space. The improved method was then applied to attribute the runoff changes for 15 catchments in the China’s Loess Plateau. The results showed that the average relative contributions of the direct effect of Ø and the regulating effect of the land-atmosphere systems across the 15 catchments were 18% and 82%, respectively. By uncovering the fundamental differences between BGA and OGA and further proposing a better approach to graphical attribution in the WEP space, this work substantially advanced the development of the hydrological change attribution methods.