Turbulence is chaotic. Extreme events — episodes where enstrophy or other quantities spike far above the mean — should be the hardest to predict, since they emerge from nonlinear amplification of small perturbations. But predictability is not uniform across extremes.
Yang, Dong, and Mengaldo train an autoregressive conditional diffusion model on direct numerical simulations of 2D Kolmogorov flow. The model reveals a hierarchy: different extreme events have prediction horizons ranging from approximately 1 to more than 4 Lyapunov times. Some extremes are barely more predictable than generic turbulent states. Others can be forecast four times longer than the nominal predictability limit.
The hierarchy is controlled by coherent structures. Intense strain cores surrounded by quadrupolar vortex packets precede extreme enstrophy events. When these structures are persistent — maintaining their configuration over multiple Lyapunov times — the resulting extreme event is predictable far in advance. When the structures are transient, the extreme is barely forecastable.
The structural insight: predictability in chaotic systems is not a scalar property of the system. It's a property of individual events, determined by the coherence of the precursor structures that generate them. The same turbulent flow produces events spanning a factor-of-four range in predictability, and the range is explained by a single physical variable — the persistence time of the coherent structures that precede the extreme.
Chaos sets the floor. Structure raises the ceiling. The hierarchy between them is the forecast.