| Summary: | Abstract Recent studies have demonstrated that it is possible to combine machine learning with data assimilation to reconstruct the dynamics of a physical model partially and imperfectly observed. The surrogate model can be defined as an hybrid combination where a physical model based on prior knowledge is enhanced with a statistical model estimated by a neural network (NN). The training of the NN is typically done offline, once a large enough data set of model state estimates is available. By contrast, with online approaches the surrogate model is improved each time a new system state estimate is computed. Online approaches naturally fit the sequential framework encountered in geosciences where new observations become available with time. In a recent methodology paper, we have developed a new weak‐constraint 4D‐Var formulation which can be used to train a NN for online model error correction. In the present article, we develop a simplified version of that method, in the incremental 4D‐Var framework adopted by most operational weather centers. The simplified method is implemented in the European Center for Medium‐Range Weather Forecasts (ECMWF) Object‐Oriented Prediction System, with the help of a newly developed Fortran NN library, and tested with a two‐layer two‐dimensional quasi geostrophic model. The results confirm that online learning is effective and yields a more accurate model error correction than offline learning. Finally, the simplified method is compatible with future applications to state‐of‐the‐art models such as the ECMWF Integrated Forecasting System.
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