Paper ID: 2210.13817

Online model error correction with neural networks in the incremental 4D-Var framework

Alban Farchi, Marcin Chrust, Marc Bocquet, Patrick Laloyaux, Massimo Bonavita

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. Data assimilation is used to estimate the system state from the observations, while machine learning computes a surrogate model of the dynamical system based on those estimated states. 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. The training of the neural network is typically done offline, once a large enough dataset 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 neural network 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 centres. The simplified method is implemented in the ECMWF Object-Oriented Prediction System, with the help of a newly developed Fortran neural network 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.

Submitted: Oct 25, 2022