Lorenz-96 — Atmospheric Chaos & Ensemble Spread

Lorenz's toy atmosphere: advection + forcing. Ensemble divergence quantifies predictability loss.

N (variables) 20

Forcing F 8.0

Ensemble Size 12

Speed 6

Time: 0.00

Ensemble Spread: 0.000

Max Lyapunov ≈ —

Lorenz (1996): dX_k/dt = (X_{k+1}-X_{k-2})X_{k-1} − X_k + F. Critical forcing F≈5.9 for chaos. Ensemble forecast: small perturbations amplify exponentially — quantifying weather predictability limits (~2 weeks in real atmosphere).