A variational formulation for translation and assimilation of coherent structures

Plu, Matthieu

doi:10.5194/npg-20-793-2013

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…Let us now go back to DA and narrow our focus to the use of advanced metrics in DA. Accounting for displacement error in DA and hence relying on nonlocal verification metrics has been advocated by Ravela et al (2007); Plu (2013). Metrics built on a multiscale analysis of the fields to achieve a similar goal have been proposed by Ying (2019); Ying et al (2023).…”

Section: Nonlocal Multiscale Metrics and Data Assimilationmentioning

confidence: 99%

Bridging classical data assimilation and optimal transport

Bocquet,

Vanderbecken,

Farchi

et al. 2023

Preprint

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Abstract. Because optimal transport acts as displacement interpolation in physical space rather than as interpolation in value space, it can potentially avoid double penalty errors. As such it provides a very attractive metric for non-negative physical fields comparison – the Wasserstein distance – which could further be used in data assimilation for the geosciences. The algorithmic and numerical implementations of such distance are however not straightforward. Moreover, its theoretical formulation within typical data assimilation problems face conceptual challenges, resulting in scarce contributions on the topic in the literature. We formulate the problem in a way that offers a unified view on both classical data assimilation and optimal transport. The resulting OTDA framework accounts for both the classical source of prior errors, background and observation, together with a Wasserstein barycentre in between states that stand for these background and observation. We show that the hybrid OTDA analysis can be decomposed as a simpler OTDA problem involving a single Wasserstein distance, followed by a Wasserstein barycentre problem which ignores the prior errors and can be seen as a McCann interpolant. We also propose a less enlightening but straightforward solution to the full OTDA problem, which includes the derivation of its analysis error covariance matrix. Thanks to these theoretical developments, we are able to extend the classical 3D-Var/BLUE paradigm at the core of most classical data assimilation schemes. The resulting formalism is very flexible and can account for sparse, noisy observations and non-Gaussian error statistics. It is illustrated by simple one– and two–dimensional examples that show the richness of the new types of analysis offered by this unification.

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Section: Nonlocal Multiscale Metrics and Data Assimilationmentioning

confidence: 99%

Bridging classical data assimilation and optimal transport

Bocquet,

Vanderbecken,

Farchi

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Bridging classical data assimilation and optimal transport: the 3D-Var case

Bocquet,

Vanderbecken,

Farchi

et al. 2024

Nonlin. Processes Geophys.

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Abstract. Because optimal transport (OT) acts as displacement interpolation in physical space rather than as interpolation in value space, it can avoid double-penalty errors generated by mislocations of geophysical fields. As such, it provides a very attractive metric for non-negative, sharp field comparison – the Wasserstein distance – which could further be used in data assimilation (DA) for the geosciences. However, the algorithmic and numerical implementations of such a distance are not straightforward. Moreover, its theoretical formulation within typical DA problems faces conceptual challenges, resulting in scarce contributions on the topic in the literature. We formulate the problem in a way that offers a unified view with respect to both classical DA and OT. The resulting OTDA framework accounts for both the classical source of prior errors, background and observation, and a Wasserstein barycentre in between states which are pre-images of the background state and observation vector. We show that the hybrid OTDA analysis can be decomposed as a simpler OTDA problem involving a single Wasserstein distance, followed by a Wasserstein barycentre problem that ignores the prior errors and can be seen as a McCann interpolant. We also propose a less enlightening but straightforward solution to the full OTDA problem, which includes the derivation of its analysis error covariance matrix. Thanks to these theoretical developments, we are able to extend the classical 3D-Var/BLUE (best linear unbiased estimator) paradigm at the core of most classical DA schemes. The resulting formalism is very flexible and can account for sparse, noisy observations and non-Gaussian error statistics. It is illustrated by simple one- and two-dimensional examples that show the richness of the new types of analysis offered by this unification.

show abstract

A variational formulation for translation and assimilation of coherent structures

Cited by 2 publications

References 23 publications

Bridging classical data assimilation and optimal transport

Bridging classical data assimilation and optimal transport

Bridging classical data assimilation and optimal transport: the 3D-Var case

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