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Correction of Systematic Error and Estimation of Confidence Limits for one Data Assimilation Method

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Abstract

The paper studies the properties of the previously proposed method for assimilating observational data into a hydrodynamic model, which is an author’s version of the generalized Kalman filter. This method generalizes the well-known ensemble Kalman filter method. The equations of the generalized Kalman filter are extended to the case when the initial hydrodynamic model is biased relative to the observations, that is, it has a systematic error. In addition, the problem of estimating the confidence limits of the model variables (analysis) constructed after assimilation is considered. The corresponding Fokker–Planck–Kolmogorov equation for these estimates is given. For a special case, which is usually encountered in practice, an analytical solution of this equation is given by the perturbation theory method. Numerical examples are also carried out for a specific dynamic model, and an analysis is discussed of these calculations.

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Funding

This work is executed according to the state task of Ministry of Science and High Education of the Russian Federation (for first author no. 0149-2019-0004) and partially supported by grant no. 18-29-10085 mk of the Russian Foundation of Basic Research.

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Authors and Affiliations

  1. Shirshov Institute of Oceanology of Russian Academy of Sciences, 117218, Moscow, Russia

    K. P. Belyaev

  2. Federal Research Center ‘‘Computer Sciences and Control,’’ Russian Academy of Sciences, 119333, Moscow, Russia

    K. P. Belyaev & N. P. Tuchkova

  3. Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047, Moscow, Russia

    A. A. Kuleshov

Authors
  1. K. P. Belyaev
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  2. A. A. Kuleshov
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  3. N. P. Tuchkova
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Corresponding authors

Correspondence to K. P. Belyaev, A. A. Kuleshov or N. P. Tuchkova.

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(Submitted by A. V. Lapin)

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Belyaev, K.P., Kuleshov, A.A. & Tuchkova, N.P. Correction of Systematic Error and Estimation of Confidence Limits for one Data Assimilation Method. Lobachevskii J Math 41, 1964–1970 (2020). https://doi.org/10.1134/S1995080220100054

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  • DOI: https://doi.org/10.1134/S1995080220100054

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