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How can a glacial inception be predicted?

The Early Anthropogenic Hypothesis considers that greenhouse gas concentrations should have declined during the Holocene in absence of humankind activity, leading to glacial inception around the present. It partly relies on the fact that present levels of northern summer incoming solar radiation are close to those that, in the past, preceded a glacial inception phenomenon, associated to declines in greenhouse gas concentrations. However, experiments with various numerical models of glacial cycles show that next glacial inception may still be delayed by several ten thousands of years, even with the assumption of greenhouse gas concentration declines during the Holocene. Furthermore, as we show here, conceptual models designed to capture the gross dynamics of the climate system as a whole suggest also that small disturbances may sometimes cause substantial delays in glacial events, causing a fair level of unpredictability on ice age dynamics. This suggests the need of a validated mathematical description of the climate system dynamics that allows us to quantify uncertainties on predictions. Here, it is proposed to organise our knowledge about the physics and dynamics of glacial cycles through a Bayesian inference network. Constraints on the physics and dynamics of climate can be encapsulated into a stochastic dynamical system. These constraints include, in particular, estimates of the sensitivity of the components of climate to external forcings, inferred from plans of experiments with large simulators of the atmosphere, oceans and ice sheets. On the other hand, palaeoclimate observations are accounted for through a process of parameter calibration. We discuss promises and challenges raised by this programme.