Ensemble filtering and forecasting for nonlinear large-dimensional systems

Abstract:

Two non-Gaussian ensemble filtering methods are tested for the Lorenz-96 model and compared with the Ensemble Kalman filter (EnKF). The first method uses importance sampling to generate new members (particles) with the appropriate unbiased mean and covariance. The second method is an adaptation of the Bootstrap particle filter; it processes observations serially, and combines resampled members with prior members using a tapering function, so that posterior members are close to the Bootstrap filter solution near observations, but approach the prior members away from observations. Because both non-Gaussian methods use tapering functions to limit the impact of an observation on distant state variables in the posterior error distribution, they may be computationally feasible for dynamical systems with large spatial dimensions, such as the atmosphere and oceans. The advantages and disadvantages of these two methods---relative to the EnKF---are explored using the Lorenze-96 model for a number of configurations and observation networks.