Surrogate-based Bayesian calibration methods for climate models: a comparison of traditional and non-traditional approaches

Parameter calibration is crucial for reducing uncertainty and improving simulation accuracy in physics-based models, yet computational constraints pose significant challenges. Bayesian calibration methods offer a principled framework for combining prior knowledge with data while rigorously quantifying uncertainty. In this work, we compare four emulator-based Bayesian calibration methods: Calibrate-Emulate-Sample (CES), History Matching (HM), Bayesian Optimal Experimental Design (BOED), and a novel Goal-Oriented BOED (GBOED) approach, using the Lorenz '96 multiscale system as a testbed. Our GBOED formulation explicitly targets calibration-relevant quantities and leverages information-theoretic criteria for data selection. We assess each method in terms of calibration accuracy, uncertainty quantification, computational cost, and convergence behavior. We evaluate each method's performance in balancing computational cost, implementation complexity, and uncertainty quantification (UQ), with additional insights into convergence behavior as model evaluations increase. We find CES offers excellent performance but at high computational expense, while GBOED achieves comparable accuracy using fewer model evaluations. Standard BOED underperforms with respect to calibration accuracy, and HM shows moderate effectiveness but can be useful as a precursor. Our results highlight trade-offs among Bayesian strategies and demonstrate the promise of goal-oriented design in calibration workflows.