Linear regime duration: Is 24 hours a long time in synoptic weather forecasting?

Day-to-day variations in the growth of uncertainty in the current state of the atmosphere have led to operational ensemble weather predictions in whic h an ensemble of different initial conditions, each perturbed from the best estimate of the current state and yet still consistent with the observatio ns, is forecast. Contrasting competing methods for the selection of ensembl e members is a subject of active research; the assumption that the ensemble members represent sufficiently small perturbations so as to evolve within the "linear regime'' is implicit to several of these methods. This regime, in which the model dynamics are well represented by a linear approximation, is commonly held to extend to 2 or 3 days for operational forecasts. It is shown that this is rarely the case. A new measure, the relative nonlineari ty, which quantifies the duration of the linear regime by monitoring the ev olution of "twin'' pairs of ensemble members, is introduced. Both European and American ensemble prediction systems are examined; in the cases conside red for each system (87 and 25, respectively), the duration of the linear r egime is often less than a day and never extends to 2 days. The internal co nsistency of operational ensemble formation schemes is discussed in light o f these results. By decreasing the optimization time, a modified singular v ector-based formation scheme is shown to improve consistency while maintain ing traditional skill and spread scores in the seven cases considered. The relevance of the linear regime to issues regarding data assimilation, adapt ive observations, and model sensitivity is also noted.