Ensemble prediction in a model with flow regimes

The primary goals of ensemble prediction are the identification of particularly unpredictable situations, and the prediction of forecast error. In the medium range, major forecast failures are associated with regime transitions. The predictions of linear theories on error dynamics are inadequate to describe these situations, characterized by the rapid growth of errors which are far from being infintesimal. Little is known about the efficiency of ensemble forecasting methods when applied to highly nonlinear situations like those associated with a change of regime. This problem is examined in an atmospheric model with two regimes and a small number of degrees of freedom by comparing current ensemble forecasting methods with ensemble forecasts that span all the degrees of freedom of the system. The study, performed in a perfect model environment, shows how the statistical properties of errors are affected by regime transitions. Results obtained selecting initial perturbations in the direction of the leading Lyapunov vectors (LVs) and singular vectors (SVs) are compared with those obtained with initially random vectors (RVs) spanning the whole phase space. It is found that the LV ensembles do not necessarily capture those particular perturbations that eventually lead to a regime transition, but closely reproduce the average RV distribution. On the other hand, the SV ensembles reproduce very closely the distribution obtained by selecting the maximum amplitude of random perturbations, although their consistency with the distribution of the full RV ensemble is poorer than in the LV ensembles. When the spread of individual RV ensembles is analysed by an empirical orthogonal function (EOF) decomposition, one finds that the variations in the amplitude of the first EOF (which carries the bimodal signature of regime transitions) is better estimated by the SV than by the LV ensembles. In verification-based contingency tables, incorrect categorical forecasts of transition probability are more frequent in the LV than in the SV ensembles.