A Probabilistic Framework for Bias Correction and Fusion of Multi-Model Datasets

Reliable outputs from physics-based models are essential for a wide range of scientific and operational applications, such as energy systems. However, physics-based numerical models often produce systematically inconsistent outputs due to variations in spatial resolution, parameterizations, boundary conditions, and numerical schemes. While these discrepancies pose challenges, the diversity among models also offers complementary insights into the same physical processes. Integrating outputs across multiple models rather than relying on a single source can therefore yield more robust and informative results. This study presents a general two-step framework for correcting and integrating multi-model outputs with observations. First, a copula-based bias correction method is applied to align both the marginal distributions and dependence structure of each model with observational data, using the Bulk-and-Tails (BATs) distribution to capture complex behaviors such as asymmetry and tail dependence. Second, Bayesian Model Averaging (BMA) is used to probabilistically combine the bias-corrected outputs, assigning weights based on each model’s historical predictive performance. The resulting ensemble preserves key statistical features, quantifies uncertainty, and enhances physical realism. This approach improves the fidelity and interpretability of integrated model outputs and is broadly applicable to domains requiring model-data fusion, including Earth system science, infrastructure risk assessment, and environmental monitoring.