Making forecasts for chaotic physical processes.

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 and model of that system, no solution of remains close to for all time. We propose an alternative. This Letter shows how to inflate or systematically perturb the ensemble of solutions of so that some ensemble member remains close to for orders of magnitude longer than unperturbed solutions of . This is true even when the perturbations are significantly smaller than the model error.