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

The observational data for 1979–2018 in the North Atlantic regionhave been used for the analysis of the heat fluxes. The dynamicsof air-sea interaction between ocean and atmosphere has beenmodeled by the stochastic differential equation (SDE) which usethe heat fluxes observations taken from those databased. Thecoefficients of the SDE represented the diffusion stochasticprocess have been statistically defined from the original dataset.Earlier the existence and uniqueness of the solution in strongsense of SDE generated by the modeled diffusion process has beenproved. In the current work the drift and diffusion coefficientshave been smoothed and approximated by the trigonometric functionswith sought amplitude and phase characteristics within chosenyear. Their spatial and temporal intra-annual variability of thosecharacteristics has been studied and analyzed. Also, thecorresponding Fokker–Planck–Kolmogorov (FPK) equation for theSDE with smoothed coefficients has been constructed andnumerically solved. Numerical calculations realized on theLomonosov-2 supercomputer of the Lomonosov Moscow StateUniversity.