  Data assimilation (DA) is integrated with machine learning in order to
perform entirely data-driven online state estimation. To achieve this,
recurrent neural networks (RNNs) are implemented as surrogate models to replace
key components of the DA cycle in numerical weather prediction (NWP), including
the conventional numerical forecast model, the forecast error covariance
matrix, and the tangent linear and adjoint models. It is shown how these RNNs
can be initialized using DA methods to directly update the hidden/reservoir
state with observations of the target system. The results indicate that these
techniques can be applied to estimate the state of a system for the repeated
initialization of short-term forecasts, even in the absence of a traditional
numerical forecast model. Further, it is demonstrated how these integrated
RNN-DA methods can scale to higher dimensions by applying domain localization
and parallelization, providing a path for practical applications in NWP.
