Nonlinear sensitivity of ice sheets to glacial-interglacial variations in pCO2 over the past 2 Ma

Abstract:

Recent Boron-derived reconstructions of early-Pleistocene pCO2 have evoked proposals that ice sheets were less sensitive to radiative forcing in the early Pleistocene than in the late Pleistocene (Chalk et al., 2017; Dyez et al., 2018), possibly due to a change in ice-sheet dynamics (Clark & Pollard, 1998; Willeit et al., 2019) or phase-locking of an internal mode of climate variability to external forcing (Tziperman et al., 2006). Inferring the sensitivity of early-Pleistocene ice sheets to radiative forcing is challenging, however, because during this interval sea-level reconstructions are highly uncertain and pCO2 data are sparse. Past approaches have assumed equilibrium to estimate a linear (e.g., Chalk et al, 2017, Dyez et al., 2018) or nonparametric (e.g., Martínez-Botí et al., 2015) regression between sea-level and CO2 climate forcing. We introduce a different approach that infers a statistical-dynamical relationship between sea-level and pCO2 using a hierarchical Bayesian method that incorporates observational uncertainties and known nonlinearities in ice-sheet behavior. The method represents a Budyko-type zonally averaged energy balance model coupled to a highly idealized ice sheet that responds to changes in atmospheric CO2 and orbital forcing. Probability distributions for model parameters are first inferred from both pCO2 and sea-level reconstructions over the past 400 ky. These parameters are shown to correctly predict ice-core pCO2 between 400 and 800 ka when forced with sea-level estimates. We then use the model to infer the pCO2 required to explain estimated sea-level over the past 2 Ma, and show that the model prediction agrees with Boron-derived early-Pleistocene pCO2 reconstructions. That a set of model parameters inferred over the late Pleistocene alone can explain early-Pleistocene pCO2 suggests that a middle-Pleistocene change in the sensitivity of ice sheets to radiative forcing need not have occurred. The previously proposed sensitivity shift is instead explained on the basis of nonlinearity in the response of ice sheets to pCO2 variations and orbital forcing.