Convergence properties of a Gauss-Newton data-assimilation method

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-N...

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Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Abedini, Nazanin, Dubinkina, Svetlana
Format: Article
Language:English
Subjects:
Convergence
Cost function
Dynamic models
Iterative methods
Least squares method
Parameter estimation
Online Access:Get full text
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Summary: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.
ISSN:2331-8422