Nonlinear Data Assimilation by Deep Learning Embedded in an Ensemble Kalman Filter

Recent progress in the particle filter has made it possible to use it for nonlinear or non-Gaussian data assimilation in high-dimensional systems, but a relatively large ensemble is still needed to outperform the ensemble Kalman filter (EnKF) in terms of accuracy. An alternative ensemble data assimilation method based on deep learning is presented, in which deep neural networks are locally embedded in the EnKF. This method is named the deep learning-ensemble Kalman filter (DL-EnKF). The DL-EnKF analysis ensemble is generated from the DL-EnKF analysis and the EnKF analysis deviation ensemble. The performance of the DL-EnKF is investigated through data assimilation experiments in both perfect and imperfect model scenarios using three versions of the Lorenz 96 model and a deterministic EnKF with an ensemble size of 10. Nonlinearity in data assimilation is controlled by changing the time interval between observations. Results demonstrate that despite being such a small ensemble, the DL-EnKF is superior to the EnKF in terms of accuracy in strongly nonlinear regimes and that the DL-EnKF analysis is more accurate than the output of deep learning because of positive feedback in assimilation cycles. Even if the target of training is an EnKF analysis with a large ensemble or a simulation by an imperfect model, the improvement introduced by the DL-EnKF is not very different from the case where the target of training is the true state.