The predictability problem in systems with an uncertainty in the evolutionlaw

The problem of unpredictability in a physical system due to the incomplete knowledge of the evolution laws is addressed. Major interest is devoted to the analysis of error amplification in chaotic systems with many characteri stic times and scales when the fastest scales are not resolved. The paramet rization of the unresolved scales introduces a non-infinitesimal uncertaint y (with respect to the true evolution laws) which affects the forecasting a bility on the large resolved scales. The evolution of non-infinitesimal err ors from the unresolved scales up to the large scales is analysed by means of the finite-size Lyapunov exponent. It is shown that proper parametrizati on of the unresolved scales allows one to recover the maximal predictabilit y of the system.