Rachel Lupien | Searcharxiv

arXiv2026

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

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.

stat.AP↗

arXiv2024

Continuous-time state-space methods for d18O and d13C in the Cenozoic Era

Time series analysis of d18O and d13C from benthic foraminifera for paleoclimatology poses significant challenges. The data span tens of millions of years, with sparse early records, dense later ones, uneven time stamps, and occasional multiples. These time series are largely non-stationary, exhibiting temporary, varying trends. We propose a continuous-time state space framework that handles these irregularities effectively. Univariate signal-plus-noise models are specified for d18O and d13C, with parameters estimated via maximum likelihood using Kalman filter recursions for signal extraction and likelihood evaluation. The framework interprets state space models as time-domain Butterworth filters. Measurement-error variances are differentiated by deep-sea drill site, including site-specific level offsets, and the record is partitioned into sub-periods reflecting the distinct climate states that drive the transition variance. Two extensions of the univariate model are explored: (i) modifying the signal specification for the Kalman filter to approximate a Butterworth filter of any order, and (ii) specifying a bivariate signal-plus-noise model for joint analysis. Results reveal substantial signal changes during the ``icehouse'' period (3.3 to 0.0006 Ma); the correlation between d18O and d13C signals is generally positive but turns negative during this period.

stat.AP↗