  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.
