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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 25, 55-66, 2018
https://doi.org/10.5194/npg-25-55-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
30 Jan 2018
Optimal transport for variational data assimilation
Nelson Feyeux, Arthur Vidard, and Maëlle Nodet Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
Abstract. Usually data assimilation methods evaluate observation-model misfits using weighted L2 distances. However, it is not well suited when observed features are present in the model with position error. In this context, the Wasserstein distance stemming from optimal transport theory is more relevant.

This paper proposes the adaptation of variational data assimilation for the use of such a measure. It provides a short introduction of optimal transport theory and discusses the importance of a proper choice of scalar product to compute the cost function gradient. It also extends the discussion to the way the descent is performed within the minimization process.

These algorithmic changes are tested on a nonlinear shallow-water model, leading to the conclusion that optimal transport-based data assimilation seems to be promising to capture position errors in the model trajectory.


Citation: Feyeux, N., Vidard, A., and Nodet, M.: Optimal transport for variational data assimilation, Nonlin. Processes Geophys., 25, 55-66, https://doi.org/10.5194/npg-25-55-2018, 2018.
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Short summary
In geophysics, numerical models are generally initialized through so-called data assimilation methods. They require computation of a distance between model fields and physical observations. The most common choice is the Euclidian distance. However, due to its local nature it is not well suited for capturing position errors. This papers investigates theoretical aspects of the use of the optimal transport-based Wasserstein distance in this context and shows that it is able to capture such errors.
In geophysics, numerical models are generally initialized through so-called data assimilation...
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