1.6.1.1 Theory of critical slowing down

The majority of studies on early warnings of Earth system tipping points are based on searching for evidence of CSD. Essentially, if a system is forced towards a tipping point, the state it currently occupies starts to lose its stability as the restoring feedbacks that ‘pull’ the system back to that state after it is perturbed start to weaken. If the system is forced sufficiently slowly that it can remain close to steady state, this causes the system to respond more sluggishly to short-term perturbations, and thus ‘slow down’ (Wissel, 1984). 

Figure 1.6.1 shows this concept visually using the ‘ball in potential well’ analogy. When the system is more stable (represented by the well with steeper sides) recovery from any given perturbation is faster (the ball returns faster). A system closer to tipping (represented by a shallower well) has a slower recovery from the same perturbation (the ball takes longer to return). Eventually, the restoring feedbacks of the system become so weak at a tipping point that the stability of the initial state is lost, and the system moves to a new stable state. Before that point a random disturbance may cause the system to exit its initial state early.

Figure: 1.6.1
Figure: 1.6.1 Using the ‘ball in the well’ analogy to compare a system that is (left) far from tipping, and (right) close to tipping. The system that is further away from tipping recovers faster from perturbations, the steeper sides of the well describing the stronger restoring feedbacks of the system. Close to tipping, the sides of the well are shallower, such that the system will take long to return from the same perturbation as the restoring feedbacks are weaker. Adapted from: Dakos et al. (2023)

The occurrence of CSD prior to a critical transition has been identified across numerous domains (Kubo, 1966; Kawasaki, 1966; Ferrell, 1970; Wissel, 1984; Dakos et al., 2023). In most cases, it mathematically involves the leading ‘eigenvalue’ of the system (which describes the strength of damping negative feedback) approaching 0 from below. However, in reality we typically do not have the equations that govern the system’s dynamics, and as such have to estimate the occurrence of CSD with methods detailed in this chapter.

Bezos Earth Fund University of Exeter logo
Earth Commission Systems Change Lab logo Systemiq logo
Global Tipping Points logo
Share this content
Top