A Hybrid Ensemble Kalman Filter to Mitigate Non-Gaussianity in Nonlinear Data Assimilation

Research on particle filters has been progressing with the aim of applying them to high-dimensional systems, but alleviation of problems with ensemble Kalman filters (EnKFs) in nonlinear or non-Gaussian data assimilation is also an important issue. It is known that the deterministic EnKF is less robust than the stochastic EnKF in strongly nonlinear regimes. We prove that if the observation operator is linear the analysis ensemble perturbations of the local ensemble transform Kalman filter (LETKF) are uniform contractions of the forecast ensemble perturbations in observation space in each direction of the eigenvectors of a forecast error covariance matrix. This property approximately holds for a weakly nonlinear observation operator. These results imply that if the forecast ensemble is strongly non-Gaussian the analysis ensemble of the LETKF is also strongly non-Gaussian, and that strong non-Gaussianity therefore tends to persist in high-frequency assimilation cycles, leading to the degradation of analysis accuracy in nonlinear data assimilation. A hybrid EnKF that combines the LETKF and the stochastic EnKF is proposed to mitigate non-Gaussianity in nonlinear data assimilation with small additional computational cost. The performance of the hybrid EnKF is investigated through data assimilation experiments using a 40variable Lorenz-96 model. Results indicate that the hybrid EnKF significantly improves analysis accuracy in high-frequency data assimilation with a nonlinear observation operator. The positive impact of the hybrid EnKF increases with the increase of the ensemble size.