Bayesian analysis of sea-level sensitivity to CO2 forcing across the mid-Pleistocene transition: possible implications for early-Pleistocene ice-sheet extent

Foregoing studies have found that sea-level transitioned to becoming approximately twice as sensitive to CO₂ radiative forcing between the early and late Pleistocene (Chalk et al., 2017; Dyez et al., 2018). In this study we analyze the relationships among sea-level, orbital variations, and CO₂ observations in a time-dependent, zonally-averaged energy balance model having a simple ice sheet. Probability distributions for model parameters are inferred using a hierarchical Bayesian method representing model and data uncertainties, including those arising from uncertain geological age models. We find that well-established nonlinearities in the climate system can explain sea-level becoming 2.5x (2.1x - 4.5x) more sensitive to radiative forcing between 2 and 0 Ma. Denial-of-mechanism experiments show that the increase in sensitivity is diminished by 36% (31% - 39%) if omitting geometric effects associated with thickening of a larger ice sheet, by 81% (73% - 92%) if omitting the ice-albedo feedback, and by more than 96% (93% - 98%) if omitting both. We also show that prescribing a fixed sea-level age model leads to different inferences of ice-sheet dimension, planetary albedo, and lags in the response to radiative forcing than if using a more complete approach in which sea-level ages are jointly inferred with model physics. Consistency of the model ice-sheet with geologic constraints on the southern terminus of the Laurentide ice sheet can be obtained by prescribing lower basal shear stress during the early Pleistocene, but such more-expansive ice sheets imply lower CO₂ levels than would an ice-sheet having the same aspect ratio as in the late Pleistocene, exacerbating disagreements with 𝛿¹¹B-derived CO₂ estimates. These results raise a number of possibilities, including that (1) geologic evidence for expansive early-Pleistocene ice sheets represents only intermittent and spatially-limited ice-margin advances, (2) 𝛿¹¹B-derived CO₂ reconstructions are biased high, or (3) that another component of the global energy balance system, such as the average ice albedo or a process not included in our model, also changed through the middle Pleistocene. Future work will seek to better constrain early-Pleistocene CO₂ levels by way of a more complete incorporation of proxy uncertainties and biases into the Bayesian analysis.