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.

Reservoir Computing (RC), a simplified form of recurrent neural network , is composed with the Fourier Transform to produce data-driven prediction of multi-scale coupled quasi-geostrophic flows. Experiments are conducted using the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM) [10], a coupled quasi-geostrophic model that includes a 2-layer atmosphere (fast dynamics) and 1-layer ocean (slow dynamics). The Fourier Reservoir Computing (FRC) approach produces forecasts that extend the skillful forecast horizon beyond a comparable RC model trained on data in physical grid space. The FRC approach can be enhanced by applying localization in physical space, which extends the skillful forecast horizon further and facilitates practical application to high-dimensional geophysical problems. Plain Language Summary The science of predicting changes in weather and climate is typically enabled using a combination of idealized physical models and instrument measurements. Here, we offer a contribution as part of a growing community that is attempting to advance the use of machine learning for weather and climate prediction. We use a simplified coupled atmosphere-ocean model to generate synthetic ‘observa-tions’, and show that reliable forecast models can be generating using machine learning applied to these observation data alone. We also provide an approach for scaling this method for use in more realistic operational weather prediction scenarios.