4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models
<|reference_start|>4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models: Constraining a numerical weather prediction (NWP) model with observations via 4D variational (4D-Var) data assimilation is often difficult to implement in practice due to the need to develop and maintain a software-based tangent linear model and adjoint model. One of the most common 4D-Var algorithms uses an incremental update procedure, which has been shown to be an approximation of the Gauss-Newton method. Here we demonstrate that when using a forecast model that supports automatic differentiation, an efficient and in some cases more accurate alternative approximation of the Gauss-Newton method can be applied by combining backpropagation of errors with Hessian approximation. This approach can be used with either a conventional numerical model implemented within a software framework that supports automatic differentiation, or a machine learning (ML) based surrogate model. We test the new approach on a variety of Lorenz-96 and quasi-geostrophic models. The results indicate potential for a deeper integration of modeling, data assimilation, and new technologies in a next-generation of operational forecast systems that leverage weather models designed to support automatic differentiation.<|reference_end|>
@article{solvik20244d-var,
    title={4D-Var using Hessian approximation and backpropagation applied to
  automatically-differentiable numerical and machine learning models},
    author={Kylen Solvik, Stephen G. Penny, Stephan Hoyer},
    journal={arXiv preprint arXiv:2408.02767},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.02767},
    primaryClass={cs.LG math.DS physics.geo-ph}
}