Combining a Fully Connected Neural Network With an Ensemble Kalman Filter to Emulate a Dynamic Model in Data Assimilation

Using neural network technology, dynamic characteristics can be learned from model output or assimilation results to train the model, which has greatly progressed recently. A data-driven data assimilation method is proposed by combining fully connected neural network with ensemble Kalman filter to emulate dynamic models from sparse and noisy observations. First, the hybrid model couples the original dynamic model with the surrogate model. The surrogate model is learned from model forecast values and assimilation results, and its performance is verified using the training accuracy/loss and the validation accuracy/loss at different training times. Second, the assimilation process includes a "two-stage" procedure. Stage 0 generates the training sets and trains the surrogate model. Then, the hybrid model is used for the next assimilation period in Stage 1. Finally, several numerical experiments are conducted using the Lorenz-63 and Lorenz-96 models to demonstrate that the proposed approach is better than the ensemble Kalman filter in different model error covariances, observation error covariances, and observation time steps. The proposed approach has also been applied to sparse observations to improve assimilation performance. This hybrid model is restricted to the form of the ensemble Kalman filter. However, the basic strategy is not restricted to any particular version of the Kalman filter.