Ensemble filtering for nonlinear dynamics

A method for data assimilation currently being developed is the ensemble Kalman filter. This method evolves the statistics of the system by computing an empirical ensemble of sample realizations and incorporates measurements by a linear interpolation between observations and predictions. However, such an interpolation is only justified for linear dynamics and Gaussian statistics, and it is known to produce erroneous results for nonlinear dynamics with far-from-Gaussian statistics. For example, the ensemble Kalman filter method, when used in models with multimodal statistics, fails to track state transitions correctly. Here alternative ensemble methods for data assimilation into nonlinear dynamical systems, in particular, those with a large state space are studied. In these methods conditional probabilities at measurement times are calculated by applying Bayes's rule. These results show that the new methods accurately track the transitions between likely states in a system with bimodal statistics, in which the ensemble Kalman filter method does not perform well. The proposed new ensemble methods are conceptually simple and potentially applicable to large-scale problems.