A novel method for correcting water budget components and reducing their uncertainties by optimally distributing the imbalance residual without full closure

Achieving water budget closure improves the consistency of water budget component datasets, including precipitation (P), evapotranspiration (ET), streamflow (Q) and terrestrial water storage change (TWSC), thereby advancing our understanding of basin-scale water cycle dynamics. Existing water budget closure correction (BCC) methods typically aim to eliminate the entire water imbalance error (ΔRes) by fully redistributing it across budget components. However, this often overlooks the trade-off between achieving perfect closure and the errors introduced into the corrected components through this redistribution. Moreover, inaccurate estimation of redistribution weights can lead to contradictory outcomes, such as negative values in P, ET, or Q. In this study, we quantify the uncertainties introduced by four existing BCC methods (CKF, MCL, MSD, and PR) at the monthly scale across 84 basins spanning diverse climate zones. We then propose a novel method, IWE-Res, which identifies an optimal redistributing strategy by minimizing the combined error from both the errors introduced to individual budget components and the remaining ΔRes error. This method also reduces the occurrence of negative values in the corrected datasets. Our results show: (1) Existing BCC methods can result in negative values in 0 %–10 % of the time series for each corrected budget component (typically %); (2) The proposed IWE-Res method improves the accuracy of corrected components compared to existing methods, reducing RMSE by 29.5 % for P, 24.7 % for ET, 69.0 % for Q, and 6.8 % for TWSC; and (3) For most basins, excluding those in cold regions, the optimal redistribution is achieved when 40 %–90 % of ΔRes is redistributed. By offering a more balanced approach to water budget closure, this study improves the accuracy and reliability of corrected budget component datasets.