Lead-time limits for forecasting extreme events in chaotic systems
In plain words
Even with a perfect model, an extreme event can be forecast only some time ahead, set by how errors grow. The open question is how this lead time compares with the ordinary forecast limit, and whether rare events are more or less predictable than typical ones.
Precise statement
For a chaotic system with known equations (Kolmogorov flow, high-dimensional Lorenz-96) and initial uncertainty $\delta_0$, determine the maximal lead time at which events of an observable above its 99.9th percentile can be forecast with given precision and recall, in units of the inverse maximal Lyapunov exponent, and its relation to finite-time Lyapunov exponents along precursor trajectories. An answer is a scaling law for lead time versus $\delta_0$ and event size.
What would settle it
Ensemble forecasts in model flows at several $\delta_0$ and thresholds, matched by a theory based on finite-time instabilities.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
A 2024 study examines limits to extreme-event forecasting in model chaotic flows (arXiv:2401.16512).
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