Dynamically Weighted Fusion of Daily Multi-Source Precipitation Products over the Haihe River Basin Using a Physically Constrained Two-Stage Framework

Daily precipitation estimates over the Haihe River Basin show strong terrain-related error contrasts. We developed a regional two-stage post-processing fusion workflow for five gridded precipitation products. Physically constrained XGBoost-Tweedie regression uses non-negativity and an archive-derived MaxPrec reference to generate a bias-corrected candidate, ENS_Reg. Dynamic Classification Probability Weighting (DCPW) then uses classifier softmax outputs to weight ENS_Reg and the five original products, producing ENS_RegCla. Models were developed using 2000–2018 data and evaluated on 357,134 station-day records from 2019 to 2023. With the original 1961–2022 MaxPrec reference, ENS_RegCla achieved MAE = 1.064 mm/day, RMSE = 4.807 mm/day, R2 = 0.666, and KGE = 0.746. MAE was 12.6–15.3% lower than for the evaluated equal-weight, inverse-error, and neighborhood error-variance weighting baselines. At a 0.1 mm/day threshold, CSI = 0.653 and HSS = 0.720 exceeded the two specified ablations. Grouped RMSE favored the ablations, whereas grouped MAE differences were not robust. Restricting MaxPrec to 1961–2018 retained better MAE, RMSE, and KGE than all five original products. However, CSI/HSS fell to 0.633/0.698, approximately matching GSMaP-Gauge in CSI but falling below its HSS. The event-skill advantage over the ablation without MaxPrec nearly disappeared, indicating strong dependence on the reference period. Full-sample evaluation included both training and temporal-evaluation periods and yielded pooled MAE = 0.677 mm/day and KGE = 0.783. Of the 2,004,598 full-sample records, 1,647,464 (82.2%) were from model development. GTCH provided an assumption-limited relative-uncertainty diagnostic; the lower minimum statistic after candidate-set expansion was interpreted descriptively, without establishing true uncertainty reduction. Candidate errors may be correlated because ENS_Reg is derived from the original products. The framework supports condition-aware regional precipitation reconstruction, while moderate and heavy rainfall remain priorities for refinement.