Efficient Reconstructions of Common Era Climate via Integrated Nested Laplace Approximations

Paleoclimate reconstruction on the Common Era (1–2000 AD) provides critical context for recent warming trends. This work leverages integrated nested Laplace approximations (INLA) to conduct inference under a Bayesian hierarchical model using data from three sources: a state-of-the-art proxy database (PAGES 2k), surface temperature observations (HadCRUT4), and latest estimates of external forcings. INLA’s computational efficiency allows to explore several model formulations (with or without forcings, explicitly modeling internal variability or not), as well as five data reduction techniques. Two different validation exercises find a small impact of data reduction choices, but a large impact for model choice, with best results for the two models that incorporate external forcings. These models confirm that man-made greenhouse gas emissions are the largest contributor to temperature variability over the Common Era, followed by volcanic forcing. Solar effects are indistinguishable from zero. INLA provide an efficient way to estimate the posterior mean, comparable with the much costlier Monte Carlo Markov Chain procedure, but with wider uncertainty bounds. We recommend using it for exploration of model designs, but full MCMC solutions should be used for proper uncertainty quantification. Supplementary materials accompanying this paper appear online.