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

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.