The Atlantic Meridional Overturning Circulation might collapse. If it does, the consequences for European climate, tropical rainfall patterns, and global heat distribution would be severe. The probability of this collapse matters enormously for climate policy, but estimating it is computationally brutal — the event is rare, the system is high-dimensional, and brute-force simulation would require running thousands of ocean-climate models for centuries of simulated time.
Esclapez and colleagues develop a method to estimate the transition probability efficiently by constructing score functions — mathematical objects that measure how close a given ocean state is to the tipping threshold. Instead of waiting for the rare event to happen in simulation, the score function identifies the most likely pathways to collapse and concentrates computational effort along them.
The key insight is dimensional reduction. The full ocean state lives in a space with millions of variables — temperature, salinity, velocity at every grid point. But the transition to collapse depends on a much lower-dimensional projection: a few integrated quantities like the total freshwater transport or the density contrast between North and South Atlantic. The score function operates on this reduced space, making the probability estimate tractable.
The method produces low-variance probability estimates using minimal ensemble trajectories. Where a direct simulation might need thousands of model runs to see a single collapse event, the score-function approach identifies the most productive initial conditions — those poised near the tipping pathway — and weights them appropriately.
The probability of a catastrophe that hasn't happened is not zero or unknowable. It's the output of a calculation, if you can find the right coordinate system to perform it in.