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 CO 2 and temperature changes through glacial-interglacial oscillations provide crucial insight into the natural variability of carbon cycling. However, poor constraints on atmospheric CO 2 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 CO 2 . 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 CO 2 input and output fluxes inverting the time derivative of the atmospheric CO 2 record and using its temperature time series as a further constraint. Results from the Dome Fuji case study underscore systematic pulses of input CO 2 fluxes into the atmosphere during deglaciations predating peaks of T and output CO 2 fluxes by ∼2.5 kyrs. The retrieved surface source and sink CO 2 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. • Retrieved time histories of atmospheric input and output CO2 fluxes over the last 340 kyrs. • Systematic input pulses of CO2 into the atmosphere during the deglaciations. • Systematic peaks of atmospheric CO2 output fluxes 2.5 kyrs after the peak of input pulses. • Rj-McMC algorithm successfully applied to ice core data for paleoclimate investigations.