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Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments

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  • Konstantin P. Belyaev

    (P.P. Shirshov Institute of Oceanology of Russian Academy of Sciences, 36 Nahimovskiy Pr., Moscow 117997, Russia
    Federal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia)

  • Andrey K. Gorshenin

    (Federal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, Russia)

  • Victor Yu. Korolev

    (Federal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia
    Moscow Center for Fundamental and Applied Mathematics, GSP-1, Leninskie Gory, Moscow 119991, Russia)

  • Anastasiia A. Osipova

    (Federal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, Russia)

Abstract

This paper compares two statistical methods for parameter reconstruction (random drift and diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of stochastic modeling of air–sea heat flux increment evolution. The first method relates to a nonparametric estimation of the transition probabilities (wherein consistency is proven). The second approach is a semiparametric reconstruction based on the approximation of the SDE solution (in terms of distributions) by finite normal mixtures using the maximum likelihood estimates of the unknown parameters. This approach does not require any additional assumptions for the coefficients, with the exception of those guaranteeing the existence of the solution to the SDE itself. It is demonstrated that the corresponding conditions hold for the analyzed data. The comparison is carried out on the simulated samples, modeling the case where the SDE random coefficients are represented in trigonometric form, which is related to common climatic models, as well as on the ERA5 reanalysis data of the sensible and latent heat fluxes in the North Atlantic for 1979–2022. It is shown that the results of these two methods are close to each other in a quantitative sense, but differ somewhat in temporal variability and spatial localization. The differences during the observed period are analyzed, and their geophysical interpretations are presented. The semiparametric approach seems promising for physics-informed machine learning models.

Suggested Citation

  • Konstantin P. Belyaev & Andrey K. Gorshenin & Victor Yu. Korolev & Anastasiia A. Osipova, 2024. "Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments," Mathematics, MDPI, vol. 12(2), pages 1-21, January.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:288-:d:1320090
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    References listed on IDEAS

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    1. Marko Voutilainen & Lauri Viitasaari & Pauliina Ilmonen & Soledad Torres & Ciprian Tudor, 2022. "Vector‐valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 992-1022, September.
    2. Konstantin Belyaev & Andrey Kuleshov & Natalia Tuchkova & Clemente A.S. Tanajura, 2018. "An optimal data assimilation method and its application to the numerical simulation of the ocean dynamics," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 24(1), pages 12-25, January.
    3. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
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