model forecasts with direct / indirect, inhomogeneously distributed observations to achieve an optimal state estimate of a dynamical system. The advances of deep learning (DL) provide innovative pathways for the development of DA, which leads to incorpating DL into DA. This integration leverages the strengths of DL in perceiving the uncertainties and capturing nonlinear features from the data. Three perspectives from which DL enhnances the ensemble-based DA are presented here. 1) An adaptive localization based on the convolutional neural network (CNN) for an ensemble Kalman filter. Compared to traditionally used localization methods, the CNN-based localization can provide localization functions that are nonlinear, spatially and temporally adaptive, and non-symmetric with respect to displacement, without requiring any prior assumptions for the localization functions. It produces smaller errors of the Kalman gain, prior and posterior than the best reference localization. 2) Assimilation of the convolutional autoencoder (CAE)-based reconstruction from all-sky infrared (IR) radiances. The challenges for assimilating all-sky IR radiances include the nonlinearity of the forward operator and non-Gaussian error distributions. One alternative approach is to use CAE to reconstruct the atmospheric state below the cloud, and then assimilate the reconstructions. Compared to the direct assimilation of all-sky IR radiances, assimilating the CAE-based reconstructions leads to improved assimilation and forecasts of tropical cyclone intensity. 3) Online paleoclimate DA based on a DL-based network. The online paleoclimate DA utilizes climate forecasts from a DL-based network and the integrated hybrid ensemble Kalman filter to assimilate proxies over the Common Era. It produced improved temperature reconstruction than an online DA with linear inverse method and offline DA. 

data assimilation,deep learning