A framework for data assimilation and forecasting in high-dimensional non-linear dynamical systems

We present efficient sample based approximations to the problem of sequentially estimating and tracking atmospheric states for numerical weather prediction. The problem is characterized by high-dimensional, nonlinear systems and poses difficult challenges for real-time data assimilation (updating) and forecasting. The presented method extends the ensemble Kalman filter using mixtures, and represents local covariance structures using nearest neighbors. The resulting algorithm, referred to as a mixture ensemble Kalman filter (XEnsF), is shown to be superior to existing methods in simulations on a low-dimensional model. The mixture filter also scales to high-dimensional systems by limiting (localizing) the impact of observations on estimates of the state vector. A second algorithm, referred to as a Local-local ensemble filter (LLEnsF), sequentially updates the state of the system using localizations in both phase space as well as physical space. This filter is