Improving Background Error Covariance and Square Root Estimation with the Convolution Neural Network (CNN) in the Local Gain form Ensemble Transform Kalman Filter (LGETKF)

One of the challenges in quantifying background error statistics in ensemble-based data assimilation systems is addressing sampling errors caused by a limited number of ensemble members. Expanding the ensemble size through modulating the raw ensemble perturbations with the square root of the localization matrix is adopted by the Local Gain form Ensemble Transform Kalman Filter (LGETKF) to mitigate these errors. In this study, we propose a novel approach that utilizes Convolutional Neural Networks (CNN) to generate expanded ensembles. Experiments using a noncycled statistical model demonstrate that the background error covariance estimated from CNN-modulated ensembles more accurately resembles the shape of the true small and large-scale covariances. The CNN-based covariances are observed to be spatially and temporally adaptive. The ability of CNN to capture complex spatial patterns enables better representation of the different possible states of the priors. Furthermore, the performance of expanded ensembles generated by CNN in generating analysis was evaluated with the LGETKF. The results indicate that mean analysis from CNN ensembles is more accurate than the best-performing standard ensemble analysis especially for large scale background covariances.