A Moment Matching Particle Filter for Nonlinear Non-Gaussian Data Assimilation

The ensemble Kalman filter is now an important component of ensemble forecasting. While using the linear relationship between the observation and state variable makes it applicable for large systems, relying on linearity introduces non-negligible bias since the true distribution will never be Gaussian. We review the ensemble Kalman filter from a statistical perspective and analyze the sources of its bias. We then propose a de-biasing method called the nonlinear ensemble adjustment filter. This new filter transforms the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance which is calculated by importance sampling. We also show that the new filter is easily localizable and hence potentially useful for large systems. The new filter is tested through various experiments on Lorenz 63 system and Lorenz 96 system, showing promising performance when compared with other Kalman filter and particle filter variants. The results show that the new filter is stable and accurate for very challenging situations such as nonlinear, high dimensional system with sparse observations.