A novel hybrid approach for enhancing precipitation data fusion: Bayesian and geographical regression integration for hydrological applications

This study focuses on the Shahe River Basin, a data-sparse, mountainous watershed located in Hebei Province, China, where accurate precipitation estimation is challenging. Generating high-quality precipitation data in complex terrain is a critical challenge. This study proposes and systematically validates a novel, three-stage hybrid fusion framework. The framework is designed to determine the optimal merging strategy by comparing two distinct paradigms: "Correct-then-Combine" versus "Combine-then-Correct". The core of the framework synergistically integrates Mixed Geographically Weighted Regression (MGWR) for correcting spatially structured biases and the Bayesian Three-Cornered Hat (BTCH) method for minimizing random errors. We systematically evaluated four different fusion pathways (MGWR-BTCH, BTCH-MGWR, MGWR-EA, EA-MGWR) to identify the superior architecture. Furthermore, to isolate the specific contribution of the multi-scale regression strategy and ensure robustness under sparse gauge coverage, we conducted rigorous benchmarking against standard Geographically Weighted Regression (GWR) and a Leave-One-Out Cross-Validation (LOOCV). The comprehensive performance of the resulting products was then assessed using a dual-level validation framework, encompassing both direct statistical metrics and hydrological simulations with the GXAJ-DAR model. The "Correct-then-Combine" pathway, embodied by the MGWR-BTCH product, was demonstrated to be the optimal framework. This product significantly outperformed simpler fusion products (e.g., reducing RMSE by 54% compared to a single-stage BTCH product) and consistently, albeit incrementally, surpassed other advanced pathways in precipitation metrics (BIAS = 0.04 mm/day, R = 0.83). Crucially, this seemingly modest statistical edge was amplified into a highly significant improvement in hydrological utility. When driving the GXAJ-DAR model, the MGWR-BTCH product yielded an excellent streamflow simulation (hourly NSE = 0.91), drastically reducing the peak discharge error from −29.7% to a mere −3.87%. This study validates that an optimized fusion architecture is key to producing hydrologically superior precipitation data, providing a robust solution for water resource management in the Shahe Basin and similar data-scarce mountainous regions. • A novel three-stage framework evaluates precipitation fusion architectures systematically. • The "Correct-then-Combine" paradigm is proven as the optimal fusion architecture. • Synergy is key: MGWR corrects spatial biases, while BTCH minimizes random errors. • Minor metric gains amplify to major hydrological improvements (NSE 0.52–0.91). • A 1-km, hourly dataset is proven highly effective for a data-scarce mountain basin.