  Machine learning techniques have seen a tremendous rise in popularity in
weather and climate sciences. Data assimilation (DA), which combines
observations and numerical models, has great potential to incorporate machine
learning and artificial intelligence (ML/AI) techniques. In this paper, we use
U-Net, a type of convolutional neutral network (CNN), to predict the localized
ensemble covariances for the Ensemble Kalman Filter (EnKF) algorithm. Using a
2-layer quasi-geostrophic model, U-Nets are trained using data from EnKF DA
experiments. The trained U-Nets are then used to predict the flow-dependent
localized error covariance matrices in U-Net Kalman Filter (UNetKF)
experiments, which are compared to traditional 3-dimensional variational
(3DVar), ensemble 3DVar (En3DVar) and EnKF methods. The performance of UNetKF
can match or exceed that of 3DVar, En3DVar or EnKF. We also demonstrate that
trained U-Nets can be transferred to a higher-resolution model for UNetKF
implementation, which again performs competitively to 3DVar and EnKF,
particularly for small ensemble sizes.
