The distribution of the heat fluxes in the North Atlantic calculated with respect to a stochastic difference equation scheme, namely the first-order autoregressive scheme with random coefficients is sought. We used the database ERA 5 contained the geophysical data for 40 years from 1979 until 2018 yr. The coefficients for the auto-egression sequence were defined from this database earlier and also, it was shown that the conditions on the coefficients are provided the uniqueness and existence of the solution of this difference equation. The method of the calculation of the distributions is based on the consecutive integration exploiting the variance mean-mixture scheme. The numerical experiments have been performed and their analysis is studied. Additionally, it was shown that the theoretically calculated distributions well matched to their empirical counterpart. Also, earlier it was shown that under some conditions the stationary regime of this scheme is existed and non-trivial solution of the corresponding integral equation is analyzed.

data analysis, diffusion stochastic process, heat flux variability, Fokker-Planck-Kolmogorov equation, stochastic difference equation, Fredholm equation