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

Konstantin P. Belyaev, Andrey K. Gorshenin (), Victor Yu. Korolev and Anastasiia A. Osipova
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Konstantin P. Belyaev: P.P. Shirshov Institute of Oceanology of Russian Academy of Sciences, 36 Nahimovskiy Pr., Moscow 117997, 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
Anastasiia A. Osipova: Federal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, Russia

Mathematics, 2024, vol. 12, issue 2, 1-21

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.

Keywords: stochastic model; stochastic differential equation; parametric estimation; nonparametric estimation; semiparametric approach; finite normal mixtures; EM algorithm; heat fluxes; air–sea interaction; North Atlantic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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