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Accepted · first revision · record

Title: Lead-time limits for forecasting extreme events in chaotic systems
Plain: 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: 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.
Settled by: Ensemble forecasts in model flows at several $\delta_0$ and thresholds, matched by a theory based on finite-time instabilities.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: A 2024 study examines limits to extreme-event forecasting in model chaotic flows (arXiv:2401.16512).
Posed since: (empty)