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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2018-5
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
24 Jan 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).
Ensemble Variational Assimilation as a Probabilistic Estimator. Part I: The linear and weak non-linear case
Mohamed Jardak1,2 and Olivier Talagrand1 1LMD/IPSL, CNRS, ENS, PSL Research University, 75231, Paris, France
2Data Assimilation and Ensembles Research & Development Group, Met Office, Exeter, Devon, UK
Abstract. Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte-Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure: perturb the data according to the probability distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called Ensemble Variational Assimilation (EnsVAR), is studied in the two parts of the paper on the non-linear low-dimensional Lorenz-96 chaotic system, the assimilation being performed by the standard variational proce- dure. In Part I, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5 days of the system). The performances of the algorithm, considered as a statistical estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for Ensemble Kalman Filter and Particle Filter (although at a higher cost). Globally similar results are obtained with the Kuramoto-Sivashinsky equation.

Citation: Jardak, M. and Talagrand, O.: Ensemble Variational Assimilation as a Probabilistic Estimator. Part I: The linear and weak non-linear case, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2018-5, in review, 2018.
Mohamed Jardak and Olivier Talagrand
Mohamed Jardak and Olivier Talagrand
Mohamed Jardak and Olivier Talagrand

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Short summary
Ensemble Variational Assimilation (EnsVAR) has been implemented on two small dimension non-linear chaotic toy models, as well as on linearized version of those models. In the linear case, EnsVAR is exacly Bayesian and produced highly reliable ensembles. In the nonlinear case, EnsVAR, implemented on temporal windows on the order of magnitude of the predictability time of the systems, shows as good performance as in the exactly linear case. EnsVar is a good as an estimator as EnKF and PF.
Ensemble Variational Assimilation (EnsVAR) has been implemented on two small dimension...
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