Making a prediction for a chaotic physical process involves specifying the probability associated with each possible outcome. Ensembles of solutions are frequently used to estimate this probability distribution. However, for a typical chaotic physical system $H$ and model $L$ of that system, no solution of $L$ remains close to $H$ for all time. We propose an alternative. This Letter shows how to inflate or systematically perturb the ensemble of solutions of $L$ so that some ensemble member remains close to $H$ for orders of magnitude longer than unperturbed solutions of $L$. This is true even when the perturbations are significantly smaller than the model error.

• Received 11 May 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.144102