Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation

Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation Optim Eng https://doi.org/10.1007/s11081-018-9389-2 RESEARCH ARTICLE Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation 1 2,3 4 • • • Mark Ka¨rcher Se´bastien Boyaval Martin A. Grepl Karen Veroy Received: 6 March 2017 / Revised: 31 January 2018 / Accepted: 12 May 2018 Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We propose a certified reduced basis approach for the strong- and weak- constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. While the standard strong-constraint 4D-Var approach uses the given observational data to estimate only the unknown initial condition of the model, the weak-constraint 4D-Var formulation additionally provides an esti- mate for the model error and thus can deal with imperfect models. Since the model error is a distributed function in both space and time, the 4D-Var formulation leads to a large-scale optimization problem for every given parameter instance of the PDE model. To solve the problem efficiently, various reduced order approaches have This work was supported by the Excellence Initiative of the German federal and state governments and the German Research Foundation through Grant GSC 111. & Karen Veroy veroy@aices.rwth-aachen.de Mark Ka¨rcher kaercher@aices.rwth-aachen.de Sebastien Boyaval sebastien.boyaval@enpc.fr Martin A. Grepl http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimization and Engineering Springer Journals

Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Optimization; Engineering, general; Systems Theory, Control; Environmental Management; Operations Research/Decision Theory; Financial Engineering
ISSN
1389-4420
eISSN
1573-2924
D.O.I.
10.1007/s11081-018-9389-2
Publisher site
See Article on Publisher Site

Abstract

Optim Eng https://doi.org/10.1007/s11081-018-9389-2 RESEARCH ARTICLE Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation 1 2,3 4 • • • Mark Ka¨rcher Se´bastien Boyaval Martin A. Grepl Karen Veroy Received: 6 March 2017 / Revised: 31 January 2018 / Accepted: 12 May 2018 Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We propose a certified reduced basis approach for the strong- and weak- constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. While the standard strong-constraint 4D-Var approach uses the given observational data to estimate only the unknown initial condition of the model, the weak-constraint 4D-Var formulation additionally provides an esti- mate for the model error and thus can deal with imperfect models. Since the model error is a distributed function in both space and time, the 4D-Var formulation leads to a large-scale optimization problem for every given parameter instance of the PDE model. To solve the problem efficiently, various reduced order approaches have This work was supported by the Excellence Initiative of the German federal and state governments and the German Research Foundation through Grant GSC 111. & Karen Veroy veroy@aices.rwth-aachen.de Mark Ka¨rcher kaercher@aices.rwth-aachen.de Sebastien Boyaval sebastien.boyaval@enpc.fr Martin A. Grepl

Journal

Optimization and EngineeringSpringer Journals

Published: Jun 4, 2018

References

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