We consider a data assimilation problem for imperfect models. We propose a novel shadowing-based data assimilation method that takes model error into account following the Levenberg-Marquardt regularization approach. We illuminate how the proposed shadowing-based method is related to the weak constraint 4DVar method both analytically and numerically. We demonstrate that the shadowing-based method respects the distribution of the data mismatch, while the weak constraint 4DVar does not, which becomes even more pronounced with fewer observations. Moreover, sparse observations give weaker influence on unobserved variables for the shadowing-based method than for the weak constraint 4DVar.

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Keywords Optimization and Control, Dynamical Systems
de Leeuw, B.M, & Dubinkina, S. (2018). Regularized shadowing-based data assimilation method for imperfect models and its comparison to the weak constraint 4DVar method.