Ensemble Riemannian data assimilation over the Wasserstein space

Tamang, Sagar; Ebtehaj, Ardeshir M.; Leeuwen, Peter Jan van; Zou, Dongmian

doi:10.5194/npg-28-295-2021

Cited by 6 publications

(1 citation statement)

References 78 publications

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“…It can for instance be used to adjust the posterior discrete probability density functions (pdf) in the particle filter. It has similarly been used to assist ensemble DA (Tamang et al, 2021(Tamang et al, , 2022. Finally, it has also very recently been used to compare forecast ensembles for sub-seasonal prediction (Le Coz et al, 2023;Lledó et al, 2023), or precipitation (Duc and Sawada, 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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