An Ensemble Multiscale Filter for Large Nonlinear Data Assimilation Problems

Abstract Operational data assimilation problems tend to be very large, both in terms of the number of unknowns to be estimated and the number of measurements to be processed. This poses significant computational challenges, especially for ensemble methods, which are critically dependent on the number of replicates used to derive sample covariances and other statistics. Most efforts to deal with the related problems of computational effort and sampling error in ensemble estimation have focused on spatial localization. The ensemble multiscale Kalman filter described here offers an alternative approach that effectively replaces, at each update time, the prior (or background) sample covariance with a multiscale tree. The tree is composed of nodes distributed over a relatively small number of discrete scales. Global correlations between variables at different locations are described in terms of local relationships between nodes at adjacent scales (parents and children). The Kalman updating process can be carri...