Challenges of long-term AMOC prediction due to riddled basins in coupled atmosphere-ocean models

Low-order coupled models of the atmosphere and ocean can illuminate the role of weather-climate interactions in long-term climate prediction. An important example is models that bring together the interplay between the Atlantic meridional overturning circulation (AMOC) with mid-latitude quasi-geostrophic dynamics of the atmosphere, as in the coupled model introduced by Van Veen et al (2001). In such models, the AMOC can transition from its present thermally driven to a much weaker salinity-driven state, through a tipping point. We show using these coupled models that, for scenarios with intermediate forcing between a strong and weak circulation, the long-term evolution shows extreme sensitivity to initial conditions, due to the appearance of riddled basins of attraction. The literature on dynamical systems has extensively examined such dynamics when two distinct basins of attraction are riddled, that is any small part of one attractor’s basin also includes a piece of the other. Moreover, in the presence of feedback from the atmosphere to the ocean, initial atmospheric conditions are amplified to the extent that long-term prediction in these models is inhibited by the finite precision at which the atmospheric state is known. We propose to describe the various facets of this phenomenon and consider the lessons for understanding and predicting long-term climate (in our case, thermohaline circulation), given initial state uncertainty. Furthermore, the resulting challenges of long-term prediction are not necessarily ameliorated by the real-world asymmetries in the model. When the relevant symmetries that yield riddled basins are broken through perturbations to the vector fields, the asymptotic dynamics become perfectly predictable given the initial conditions; however, long-term uncertainties in the transient state (strong vs weak circulation) persist for centuries, owing to ocean timescales.