  Various subsystems of the Earth system may undergo critical transitions by
passing a so-called tipping point, under sustained changes to forcing. For
example, the Atlantic Meridional Overturning Circulation (AMOC) is of
particular importance for North Atlantic heat transport and is thought to be
potentially at risk of tipping. Given a model of such a subsystem that
accurately includes the relevant physical processes, whether tipping occurs or
not, will depend on model parameters that typically are uncertain. Reducing
this parametric uncertainty is important to understand the likelihood of
tipping behavior being present in the system and possible tipping locations. In
this letter, we develop improved estimates for the parametric uncertainty by
inferring probability distributions for the model parameters based on physical
constraints and by using a Bayesian inversion technique. To visualize the
impact of parametric uncertainty, we extend classical tipping diagrams by
visualizing probabilistic bifurcation curves according to the inferred
distribution of the model parameter. Furthermore, we highlight the uncertain
locations of tipping points along the probabilistic bifurcation curves. We
showcase our probabilistic visualizations of the tipping behavior using a
simple box-model of the AMOC, the Stommel-Cessi model [5].
