Debiasing the Ensemble Kalman Filters: The NLEAF Algorithm

The ensemble Kalman filter (EnKF) is now an important component of ensemble forecasting. While the use of linear relationship between the observation and state variable makes it applicable for large systems, relying on linearity introduces non-negligible bias in the update since the true distribution will never be Gaussian. We review the EnKF from a statistical perspective and analyze the sources of its bias. We then propose a partial debiasing method called the non-linear ensemble adjustment filter (NLEAF). The performance of NLEAF is illustrated through various experiments on Lorenz systems.
This is joint work with Peter Bickel.