Probabilistic Analysis of the Coefficients of Stochastic Differential Equations in Their Modeling of the Air–Sea Interaction in the North Atlantic

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI:10.1134/s1995080224602406

K. P. Belyaev, N. P. Tuchkova, K. A. Romashina

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Abstract

The observational data for 1979–2018 in the North Atlantic region have been used for the analysis of the heat fluxes. The dynamics of air-sea interaction between ocean and atmosphere has been modeled by the stochastic differential equation (SDE) which use the heat fluxes observations taken from those databased. The coefficients of the SDE represented the diffusion stochastic process have been statistically defined from the original dataset. Earlier the existence and uniqueness of the solution in strong sense of SDE generated by the modeled diffusion process has been proved. In the current work the drift and diffusion coefficients have been smoothed and approximated by the trigonometric functions with sought amplitude and phase characteristics within chosen year. Their spatial and temporal intra-annual variability of those characteristics has been studied and analyzed. Also, the corresponding Fokker–Planck–Kolmogorov (FPK) equation for the SDE with smoothed coefficients has been constructed and numerically solved. Numerical calculations realized on the Lomonosov-2 supercomputer of the Lomonosov Moscow State University.

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北大西洋海气相互作用模型中随机微分方程系数的概率分析

摘要利用北大西洋地区 1979-2018 年的观测数据分析了热通量。通过随机微分方程（SDE）模拟了海洋与大气之间的海气相互作用动态，并利用了这些数据中的热通量观测资料。由建模扩散过程生成的 SDE 的广义解的存在性和唯一性已经得到证明。在目前的工作中，漂移和扩散系数已被平滑化，并用三角函数近似，其振幅和相位特征在所选年份内得到了寻求。研究和分析了这些特征的空间和时间年内变率。此外，还构建并数值求解了平滑系数SDE 的相应 Fokker-Planck-Kolmogorov (FPK) 方程。数值计算在莫斯科国立罗蒙诺索夫大学的罗蒙诺索夫-2 超级计算机上实现。

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.