Ensemble Riemannian data assimilation over the Wasserstein space

In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of squ...

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Bibliographic Details
Published inNonlinear processes in geophysics Vol. 28; no. 3; pp. 295 - 309
Main Authors Tamang, Sagar K., Ebtehaj, Ardeshir, van Leeuwen, Peter J., Zou, Dongmian, Lerman, Gilad
Format Journal Article
LanguageEnglish
Published Gottingen Copernicus GmbH 06.07.2021
Copernicus Publications
Subjects
Data
Data assimilation
Data collection
Euclidean geometry
Geometry
Normal distribution
Parameter estimation
Probability distribution
Probability theory
Riemann manifold
Systematic errors
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Summary:In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of square-integrable probability distributions of the background state and observations. This enables us to formally penalize geophysical biases in state space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics, and its potential advantages and limitations are highlighted compared to the classic ensemble data assimilation approaches under systematic errors.
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ISSN:1607-7946
1023-5809
1607-7946
DOI:10.5194/npg-28-295-2021