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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.02767 |
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| _version_ | 1866911979288920064 |
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| author | Solvik, Kylen Penny, Stephen G. Hoyer, Stephan |
| author_facet | Solvik, Kylen Penny, Stephen G. Hoyer, Stephan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models Solvik, Kylen Penny, Stephen G. Hoyer, Stephan Machine Learning Dynamical Systems Geophysics J.2; I.6.5; G.1.6 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. |
| title | 4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models |
| topic | Machine Learning Dynamical Systems Geophysics J.2; I.6.5; G.1.6 |
| url | https://arxiv.org/abs/2408.02767 |