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Data assimilation as an inverse problem: mathematical theory and computational challenges

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If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

We provide a theoretical framework for data assimilation, a specific type of inverse problem arising in numerical weather prediction, hydrology and geology. We show that data assimilation techniques such as three-dimensional and four-dimensional variational data assimilation (3DVar and 4DVar) as well as the Kalman filter and Bayes data assimilation are, in the linear case, merely a form of cycled Tikhonov regularisation. Furthermore, we provide an error analysis for the data assimilation process in general. We then show that results from regularisation theory can be applied to data assimilation and give numerical examples.

This talk is part of the Applied and Computational Analysis series.

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