Efficient Bayesian Calibration of Climate Models via Machine Learning Emulation: Application to Dansgaard-Oeschger Events

Accurately representing abrupt climate transitions such as Dansgaard–Oeschger (DO) events in climate models is essential for understanding past climate dynamics and improving projections of future tipping points. However, these models contain numerous uncertain parameters that are traditionally tuned manually, a process that is not only time-consuming but also subjective and limited in its ability to quantify parameter uncertainty. While systematic calibration approaches can provide rigorous parameter estimation, Bayesian inference methods such as MCMC require many sequential model evaluations, making them computationally prohibitive for complex climate models.

We present a systematic framework for climate model calibration that combines machine learning emulation with Bayesian inference to rigorously estimate model parameters and their uncertainties. Using CLIMBER-X, an Earth system model of intermediate complexity that successfully simulates DO-like oscillations in the Atlantic Meridional Overturning Circulation (AMOC) (Willeit et al., 2024), we develop a proof-of-concept for this calibration approach. We train an emulator that accurately approximates the model's AMOC response for a set of key ocean parameters, enabling efficient model evaluations.

We employ both Markov Chain Monte Carlo (MCMC) sampling and Simulation-Based Inference (SBI, Cranmer et al., 2020) techniques to estimate posterior distributions of these key model parameters. The ML emulator reduces computational cost by several orders of magnitude, making systematic parameter estimation and efficient exploration of the parameter space feasible. Since CLIMBER-X already produces realistic DO-like events, this serves as an ideal test case for validating the calibration framework. This work emphasizes the potential of ML-based emulation to accelerate systematic calibration in paleoclimate modelling.

References:

Willeit, M., Ganopolski, A., Edwards, N. R., and Rahmstorf, S.: Surface buoyancy control of millennial-scale variations in the Atlantic meridional ocean circulation, Clim. Past, 20, 2719–2739, https://doi.org/10.5194/cp-20-2719-2024, 2024.

Cranmer, K., Brehmer, J., and Louppe, G.: The frontier of simulation-based inference, Proc. Natl. Acad. Sci. USA, 117, 30055–30062, https://doi.org/10.1073/pnas.1912789117, 2020.