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This study proposes a theory of unsupervised super-resolution dataassimilation (SRDA) using conditional variational autoencoders (CVAEs). Wederive an evidence lower bound for unsupervised learning, showing that ourtheory is an extension of a traditional data assimilation (DA) method, namelythe three-dimensional variational (3D-Var) formalism. In contrast to 3D-Var,our theory exploits the non-locality of super-resolution (SR) to learnbackground covariances without explicitly imposing them for assimilatingdistant observations. For linear SR, SR operators serve as background errorcovariance matrices,whereas for nonlinear SR, error backpropagation through SRneural networks induces covariance structures in inference. SRDA can naturallybe realized with CVAEs because the loss function for CVAEs is generally anevidence lower bound. By incorporating the SR neural network into the CVAE, theencoder estimates the high-resolution (HR) analysis from HR observations andlow-resolution forecasts. The decoder acts as the observation operator byreconstructing the HR observations from the estimated HR analysis. Theeffectiveness of SRDA was evaluated through numerical experiments using anidealized barotropic ocean jet system. Compared to inference with an ensembleKalman filter, SRDA demonstrated superior accuracy in HR inference. SRDA wasalso computationally efficient because it does not require HR numericalintegration or ensemble calculations. The findings of this study provide atheoretical basis for integrating SR and DA, which will stimulate furtherresearch in this direction.

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