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Volume 146, Issue 730 p. 2332-2346
RESEARCH ARTICLE

Regularized variational data assimilation for bias treatment using the Wasserstein metric

Sagar K. Tamang

Corresponding Author

Sagar K. Tamang

Department of Civil, Environmental and Geo-Engineering and Saint Anthony Falls Laboratory, University of Minnesota–Twin Cities, Twin Cities, Minnesota

Correspondence

Sagar K. Tamang, Department of Civil, Environmental and Geo-Engineering and Saint Anthony Falls Laboratory, University of Minnesota–Twin Cities, Twin Cities, Minnesota.

Email: [email protected]

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Ardeshir Ebtehaj

Ardeshir Ebtehaj

Department of Civil, Environmental and Geo-Engineering and Saint Anthony Falls Laboratory, University of Minnesota–Twin Cities, Twin Cities, Minnesota

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Dongmian Zou

Dongmian Zou

School of Mathematics, University of Minnesota–Twin Cities, Twin Cities, Minnesota

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Gilad Lerman

Gilad Lerman

School of Mathematics, University of Minnesota–Twin Cities, Twin Cities, Minnesota

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First published: 30 March 2020
Citations: 8

Funding information: National Aeronautics and Space Administration (NASA) Terrestrial Hydrology Program (THP, 80NSSC18K1528), the New (Early Career) Investigator Program (NIP, 80NSSC18K0742) and National Science Foundation (NSF,1830418).

Abstract

This article presents a new variational data assimilation (VDA) approach for the formal treatment of bias in both model outputs and observations. This approach relies on the Wasserstein metric, stemming from the theory of optimal mass transport, to penalize the distance between the probability histograms of the analysis state and an a priori reference dataset, which is likely to be more uncertain but less biased than both model and observations. Unlike previous bias-aware VDA approaches, the new Wasserstein metric VDA (WM-VDA) treats systematic biases of unknown magnitude and sign dynamically in both model and observations, through assimilation of the reference data in the probability domain, and can recover the probability histogram of the analysis state fully. The performance of WM-VDA is compared with the classic three-dimensional VDA (3D-Var) scheme for first-order linear dynamics and the chaotic Lorenz attractor. Under positive systematic biases in both model and observations, we consistently demonstrate a significant reduction in the forecast bias and unbiased root-mean-squared error.