Optimal transport for variational data assimilation

Nelson Feyeux 1 Arthur Vidard 1 Maëlle Nodet 1
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
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 to adapt variational data assimilation to the use of such a measure. It provides a short introduction to 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 minimisation process. These algorithmic changes are tested on a non-linear shallow-water model, leading to the conclusion that optimal transportbased data assimilation seems to be promising to capture position errors in the model trajectory.
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Nelson Feyeux, Arthur Vidard, Maëlle Nodet. Optimal transport for variational data assimilation. Nonlinear Processes in Geophysics, European Geosciences Union (EGU), 2018, 25 (1), pp.55-66. ⟨10.5194/npg-25-55-2018⟩. ⟨hal-01342193v2⟩

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