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arXiv · 2304.05858

Convergence properties of a Gauss-Newton data-assimilation method

Nazanin Abedini·Svetlana Dubinkina
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Abstract

Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations and model error over time. It can be formulated as a Gauss-Newton iteration of an associated least-squares problem. In this paper, we introduce a parameter in front of the observation mismatch and show analytically that this parameter is crucial either for convergence to the true solution when observations are noise-free or for boundness of the error when observations are noisy with bounded observation noise. We also consider joint state-parameter estimation. We illustrated theoretical results with numerical experiments using the Lorenz 63 and Lorenz 96 models.

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Nazanin Abedini, Svetlana Dubinkina. 2023-04-12. Convergence properties of a Gauss-Newton data-assimilation method. https://arxiv.org/abs/2304.05858

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