Online Model Error Correction With Neural Networks in the Incremental 4D‐Var Framework.

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. Plain Language Summary: We have recently proposed a general framework for combining data assimilation (DA) and machine learning (ML) techniques to train a neural network for online model error correction. In the present article, we develop a simplified version of this online training method, compatible with future applications to more realistic models. Using numerical illustrations, we show that the new method is effective and yields a more accurate model error correction than the usual offline learning approach. The results show the potential of incorporating DA and ML tightly, and pave the way toward an application to the Integrated Forecasting System used for operational numerical weather prediction at the European Centre for Medium‐Range Weather Forecasts. Key Points: Variants of weak‐constraint 4D‐Var can be used to train neural networks for online model error correctionOnline learning yields a more accurate model error correction than offline learningThe new, simplified method, developed in the incremental 4D‐Var framework, can be easily applied in operational weather models [ABSTRACT FROM AUTHOR]