4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models

• URL: http://arxiv.org/abs/2408.02767v1
• Date: Mon, 5 Aug 2024 18:36:13 GMT
• Title: 4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models
• Authors: Kylen Solvik, Stephen G. Penny, Stephan Hoyer,
• Abstract summary: We show that an efficient alternative approximation of the Gauss-Newton method can be applied by combining backpropagation of errors with Hessian approximation. The results indicate potential for a deeper integration of modeling, data assimilation, and new technologies in a next-generation of operational forecast systems.
• Score: 1.3142789604525646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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