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Regularization techniques for ill-posed inverse problems in data assimilation

Budd, C.J., Freitag, M.A. and Nichols, N. (2011) Regularization techniques for ill-posed inverse problems in data assimilation. Computers & Fluids, 46 (1). pp. 168-173. ISSN 0045-7930

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To link to this article DOI: 10.1016/j.compfluid.2010.10.002

Abstract/Summary

Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L2, regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the presence of model error, this approach does not capture the initial state of the system accurately, as the initial state estimate is derived by minimizing the average error between the model predictions and the observations over a time window. Here we examine an alternative L1 regularization technique that has proved valuable in image processing. We show that for examples of flow with sharp fronts and shocks, the L1 regularization technique performs more accurately than standard L2 regularization.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:27467
Uncontrolled Keywords:ill-posed inverse problems, Tikhonov and L1 regularization, variational data assimilation, nonlinear least-squares optimization, model error, Burgers’ equation
Publisher:Elsevier

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