INFERRING THE NONLINEAR SEA-LEVEL RESPONSE TO ATMOSPHERIC PCO2 VARIATIONS OVER THE PAST 2 MA

Recent reconstructions of atmospheric CO2 levels provide continuous estimates across entire glacial-interglacial cycles during the early Pleistocene (Chalk et al., 2017; Dyez et al., 2018). Regressions between sea level reconstructions and CO2 climate forcing across these cycles have evoked suggestions that ice sheets responded less sensitively to radiative forcing in the early Pleistocene than in the late Pleistocene. The apparent shift in sensitivity was proposed to reflect a mid-Pleistocene shift in ice-sheet dynamics (Clark et al., 2006) as part of a broader transition that produced greater glacial-cycle amplitude and the emergence of strong ~100 ky glacial variability. But inferring the sensitivity of early-Pleistocene ice sheets to radiative forcing is challenging because (1) sea-level reconstructions are highly uncertain and atmospheric CO2 data are sparse during this interval, (2) ice accumulation is known to be nonlinear, and (3) ice sheets are not expected to be at equilibrium throughout the Pleistocene. We infer a statistical-dynamical relationship between sea-level and atmospheric pCO2 using a hierarchical Bayesian method that fully quantifies uncertainties and incorporates nonlinearity in ice-sheet behavior. The model represents a Budyko-type zonally averaged energy balance model coupled to a highly idealized ice-sheet that responds to orbital forcing and changes in atmospheric CO2. Probability distributions for model parameters and autoregressive error properties are jointly inferred from available Pleistocene sea-level and atmospheric pCO2 estimates. A joint posterior distribution for model parameter values is inferred from data spanning the past 400 kyr, and we show that these parameters correctly predict ice-core pCO2 between 400 and 800 ka when the model is forced with sea-level estimates. We employ these parameter values to predict the pCO2 required to explain estimated sea-level over the past 2 Ma. The predicted pCO2 agrees with previously-reported Boron-derived pCO2 estimates for the early Pleistocene. By explaining early-Pleistocene pCO2 patterns with a model inferred only over late Pleistocene data, our results suggest that a change in the sensitivity of ice sheets to climate forcing need not necessarily have occurred. We propose instead that differences in the pCO2-sea level relationship between the early and late Pleistocene arises from nonlinearities that were amplified by the emergence of larger late-Pleistocene ice sheets, with an important role for the ice-albedo feedback.