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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/npg-2020-9
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2020-9
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 17 Apr 2020

Submitted as: research article | 17 Apr 2020

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This preprint is currently under review for the journal NPG.

Behavior of the iterative ensemble-based variational method in nonlinear problems

Shin'ya Nakano1,2 Shin'ya Nakano
  • 1The Institute of Statistical Mathematics, Tachikawa, 190–8562, Japan
  • 2Center for Data Assimilation Research and Applications, Joint Support Center for Data Science Research, Tachikawa, Japan

Abstract. The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4-dimensional ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, where system nonlinearity is significant, are solved by applying this method iteratively. However, it is not necessarily trivial how the algorithm works in highly uncertain problems where nonlinearity is not negligible. In the present study, an ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in nonlinear context. The findings as the results of the present study were also experimentally supported.

Shin'ya Nakano

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Short summary
The ensemble-based variational method is a method to solve nonlinear data assimilation problem by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, where system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to closely analyze its behavior, and clarified the conditions for monotonic convergence in nonlinear context.
The ensemble-based variational method is a method to solve nonlinear data assimilation problem...
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