Analog ensemble data assimilation and a method for constructing analogs with variational autoencoders

It is proposed to use analogs of the forecast mean to generate an ensemble of perturbations for use in ensemble optimal interpolation (EnOI) or ensemble variational (EnVar) methods. A new method of constructing analogs using variational autoencoders (VAEs; a machine learning method) is proposed. The resulting analog methods using analogs from a catalog (AnEnOI), and using constructed analogs (cAnEnOI), are tested in the context of a multiscale Lorenz-`96 model, with standard EnOI and an ensemble square root filter for comparison. The use of analogs from a modestly-sized catalog is shown to improve the performance of EnOI, with limited marginal improvements resulting from increases in the catalog size. The method using constructed analogs (cAnEnOI) is found to perform as well as a full ensemble square root filter, and to be robust over a wide range of tuning parameters.