A two-stage hierarchical runoff bias correction framework for observation-constrained river flow reconstruction

Accurate reconstruction of long-term river flow across all stream orders is essential for managing water resources. However, modeling simulations often exhibit significant biases, and traditional corrections at individual gauging stations typically ignore upstream-downstream connectivity and mass balance. Here, we introduce the Two-Stage Hierarchical Bias Correction (TSH-BC) framework to correct ERA5 runoff at the source through a cascading water-balance logic. The framework first establishes headwater baselines and then isolates and corrects incremental biases of lateral inflows between successive gauging stations. Applied to 40,000 reaches in the Yangtze River Basin, we reconstructed daily discharge from 1980 to 2024 and compared long-term and multi-year monthly correction strategies against raw ERA5. Results show the TSH-BC framework elevated the median Kling-Gupta Efficiency from 0.45 to 0.74, while the monthly correction specifically improved low-flow representation with a median logarithmic Nash-Sutcliffe Efficiency of 0.72. These metrics represent full-period in-sample reconstruction performance. The adjusted runoff acts as an effective source term that absorbs structural, forcing, and regulatory uncertainties, ultimately providing a topology-aware, observation-constrained baseline for historical water resources assessment.