Extreme events and predictability in chaotic systems

4 problems

• Lead-time limits for forecasting extreme events in chaotic systems

  Open

  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.

• Finite predictability horizon in multiscale chaotic flows

  Partially resolved

  In 1969 Lorenz argued that in flows with motion on many scales, shrinking the initial error buys almost no extra forecast time, because errors pass quickly from small to large scales. Whether this hard limit exists in real turbulence, and what sets its value, is still studied.

• When single optimal paths dominate extreme events

  Partially resolved

  For very rare large events in noisy or chaotic systems, theory often assumes they occur along one most likely route, called an instanton. Whether and when that holds in high-dimensional systems like turbulence decides whether extremes can be computed rather than waited for.

• Effect of modulational instability on rogue wave statistics

  Contested

  Rogue waves are ocean or optical waves far taller than their neighbors. It is disputed whether they come mostly from random addition of ordinary waves or from a nonlinear focusing instability, and how much the instability raises their probability.