Continuous-time state space analysis of d18O, d13C, and CO2 in the Cenozoic Era

2026-06-23

AI Summary

This study addresses the challenge of integrating irregular, multi-source, and heterogeneous paleoclimate proxy data spanning the Cenozoic (last 67 million years) by proposing the first continuous-time state-space model that treats δ¹⁸O, δ¹³C, and atmospheric CO₂ as coupled continuous stochastic processes. The model incorporates site-specific uncertainties, bias corrections, and climate-state-dependent orbital forcing from the La2004 solution, with parameters estimated via maximum likelihood using a diffusion-initialized Kalman filter. This approach enables, for the first time, a joint reconstruction of these three proxy types within a unified continuous-time framework, revealing a sign reversal in isotopic correlations between greenhouse and icehouse climates and quantifying the amplification of orbital sensitivity due to ice-sheet growth. It also yields a probabilistic CO₂ trajectory with confidence intervals, identifying critical CO₂ thresholds associated with major glaciation events and contextualizing them relative to present-day concentrations.

Abstract

We develop a continuous-time state-space framework for the joint reconstruction of three Cenozoic climate proxies, benthic foraminiferal d18O and d13C and atmospheric CO2, from irregularly and unevenly sampled multi-site, multi-method data spanning the last 67 million years. The latent signals follow a trivariate random walk in continuous time; the measurement equation differentiates the error variance by drill site for the isotopes and by proxy group for CO2, with bias intercepts placing all sources on a common scale, and the transition equation lets the innovation covariance and a deterministic La2004 Milankovitch forcing depend on the prevailing climate state. All parameters are estimated by maximum likelihood through the Kalman filter with diffuse initialization. The estimated cross-proxy correlations reverse sign between the early Cenozoic greenhouse and the icehouse, the orbital sensitivity of the isotopes strengthens as continental ice sheets grow, and the reconstructed CO2 path, reported with calibrated confidence bands, places the atmospheric CO$_2$ thresholds of the major Cenozoic glaciations in relation to present-day concentrations.

Problem

• Cenozoic climate proxies
• continuous-time reconstruction
• irregularly sampled data
• joint state estimation
• paleoclimate

Innovation

• continuous-time state-space model
• multivariate proxy reconstruction
• climate-state-dependent dynamics
• Kalman filter with diffuse initialization
• Milankovitch forcing