A Moment Matching Ensemble 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 variables makes it applicable for large systems, relying on linearity introduces nonnegligible bias since the true distribution will never be Gaussian. This paper analyzes the bias of the ensemble Kalman filter from a statistical perspective and proposes a debiasing 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. It is also easily localizable and, hence, potentially useful for large systems. Its performance is demonstrated and compared with other Kalman filter and particle filter variants through various experiments on the Lorenz-63 and Lorenz-96 systems. The results show that the new filter is stable and accurate for challenging situations such as nonlinear, high-dimensional systems with sparse observations.