Tipping mechanisms in a carbon cycle model

TL;DR

This paper analyzes how a carbonate system in the upper ocean can undergo tipping due to rapid parameter changes or random noise, using computational methods to understand the most probable escape paths in a complex, asymmetric system.

Contribution

It investigates both rate-induced and noise-induced tipping in a realistic ocean carbon cycle model, especially addressing challenges posed by a periodic basin boundary and non-small noise.

Findings

Both R-tipping and N-tipping are possible in the model.

The most probable escape path (MPEP) can be computed for the system.

The model's susceptibility to tipping mechanisms is confirmed.

Abstract

Rate-induced tipping (R-tipping) occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states, while noise-induced tipping (N-tipping) occurs when there are random transitions between two attractors of the underlying deterministic system. This work investigates R-tipping and N-tipping events in a carbonate system in the upper ocean, in which the key objective is understanding how the system undergoes tipping away from a stable fixed point in a bistable regime. While R-tipping away from the fixed point is straightforward, N-tipping poses challenges due to a periodic orbit forming the basin boundary for the attracting fixed point of the underlying deterministic system. Furthermore, in the case of N-tipping, we are interested in the case where noise is away from the small noise limit, as it is more appropriate for the application. We compute the most probable escape path (MPEP) for our system, resulting in a firm grasp on the least action path in an asymmetric system of higher scale. Our analysis shows that the carbon cycle model is susceptible to both tipping mechanisms when using the standard formulations.