Unsupervised Super-Resolution Data Assimilation Using Conditional Variational Autoencoders with Estimating Background Covariances via Super-Resolution

Abstract

This study proposes a theory of unsupervised super-resolution data assimilation (SRDA) using conditional variational autoencoders (CVAEs). We derive an evidence lower bound for unsupervised learning, showing that our theory is an extension of a traditional data assimilation (DA) method, namely the three-dimensional variational (3D-Var) formalism. In contrast to 3D-Var, our theory exploits the non-locality of super-resolution (SR) to learn background covariances without explicitly imposing them for assimilating distant observations. For linear SR, SR operators serve as background error covariance matrices,whereas for nonlinear SR, error backpropagation through SR neural networks induces covariance structures in inference. SRDA can naturally be realized with CVAEs because the loss function for CVAEs is generally an evidence lower bound. By incorporating the SR neural network into the CVAE, the encoder estimates the high-resolution (HR) analysis from HR observations and low-resolution forecasts. The decoder acts as the observation operator by reconstructing the HR observations from the estimated HR analysis. The effectiveness of SRDA was evaluated through numerical experiments using an idealized barotropic ocean jet system. Compared to inference with an ensemble Kalman filter, SRDA demonstrated superior accuracy in HR inference. SRDA was also computationally efficient because it does not require HR numerical integration or ensemble calculations. The findings of this study provide a theoretical basis for integrating SR and DA, which will stimulate further research in this direction.