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

Study region: 15 catchments in the Chinese Loess Plateau (CLP) Study focus: In catchment-scale hydrological processes, both precipitation and potential evapotranspiration play dominant roles, while all relevant factors from the land surface to the atmosphere are coupled together to play a regulating role. The Budyko-based and orthogonality-based graphical attribution methods (BGA and OGA, respectively) visually separate the direct effect of dryness index (∅) and the regulating effect of land-atmosphere system. This study identified the limitations of OGA in its path section and accuracy, explored its essential difference from the well-established BGA, and proposed a more appropriate graphical attribution method in the water-energy partitioning (WEP) space. Finally, the proposed method was applied to attribute runoff change for 15 CLP catchments. New hydrological insights for the region: The orthogonality-induced linearization in OGA may fail to capture nonlinear Budyko relationships, potentially leading to violations of the water and energy boundaries. By mapping Budyko curves in the WEP space, we elucidated the inconsistencies between OGA and BGA in both decomposition orders and paths, and proposed the two-path BGA as a more appropriate attribution framework in the WEP space. The improved method uncovered that, on average, the direct effect of ∅ and the regulating effect of land-atmosphere system contributed 18 % and 82 %, respectively, to runoff change for 15 CLP catchments. This study contributes to the advancement of hydrological change attribution methods.