On the Predictability of Possible Storylines for Forced Complex Systems

It is well-known that even for fairly simple deterministic nonlinear systems, exact prediction of future state is, on average, impossible beyond some small multiple of the Lyapunov time that quantifies the rate of separation of trajectories within an attractor. Nonetheless, it may be possible to find a physical measure that is the distribution of a trajectory within the attractor. In that sense, there can be a still weaker form of predictability. In this paper, we show that this can also fail but an even weaker form of predictability can appear for non-autonomous (i.e. forced) systems in the presence of tipping points. The predictability of possible storylines appears when one can interpret the frequencies of runs within an ensemble arriving at one of several possible future attractors (storylines) in a probabilistic manner. As predictability is a major concern and a challenge in climate science, we illustrate this notion of predictability with two climate-related examples: a chaotic energy balance model and a global ocean model featuring a tipping point of the Atlantic meridional overturning circulation.