A reversible-jump Markov chain Monte Carlo algorithm to estimate paleo surface CO2 fluxes linking temperature to atmospheric CO2 concentration time series

Future goals and strategies for mitigating ongoing climate changes rely on the understanding of the global carbon cycle and its connections to climate. Evidence from ice cores regarding past atmospheric CO₂ and temperature changes through glacial-interglacial oscillations provide crucial insight into the natural variability of carbon cycling. However, poor constraints on atmospheric CO₂ input and output fluxes limit our quantitative understanding of late Pleistocene carbon cycling and climate changes. In this study, we describe an inversion method based on a reversible-jump Markov chain Monte Carlo (rj-McMC) algorithm and a general formulation of the geological carbon cycle to estimate paleo-fluxes of CO₂. We present results from two synthetic tests and a real case study based on data from the ice core of Dome Fuji. Results from synthetic tests demonstrate the capability of the algorithm to retrieve reliable estimates of atmospheric CO₂ input and output fluxes inverting the time derivative of the atmospheric CO₂ record and using its temperature time series as a further constraint. Results from the Dome Fuji case study underscore systematic pulses of input CO₂ fluxes into the atmosphere during deglaciations predating peaks of T and output CO₂ fluxes by ∼2.5 kyrs. The retrieved surface source and sink CO₂ fluxes as well as future applications of the algorithm presented here will provide new insights to assess past climate driving mechanisms and inform projections of future climatic trajectories.