A Copula-Based Framework for Emergent Constraints Using MCMC Simulations
Xu Zhang, Jinbao Li, Qianjin Dong, Cong Gao, Hao Chen · Journal of Climate · 2025
Abstract Emergent constraints reduce uncertainties in future climate projections by the comparison with current climate and observations. However, previous methods for emergent constraints are limited to variables following normal or multivariate normal distributions. Here, we devise a copula-based emergent constraint (CEC) framework that enables the flexible selection of marginal distribution functions and the combination of multiple constraints. The Markov chain Monte Carlo (MCMC) algorithm is applied to numerically estimate the posterior distribution derived from Bayes’ theorem. This new framework achieves narrower uncertainties in the projections of future global warming than previous approaches that assume normal distributions. Combining two constraints in the Northern and Southern Hemispheres further reduces uncertainties after the integration of different information. Due to the flexibility in distribution functions and constraint size, the CEC framework is applicable to more variables and interactions across various spheres of Earth’s system.