Abstract: The stability problem is considered in terms of the classical Lyapunov definition. For this, a set of initial conditions is set, consisting of their preliminary calculations, and the spread of the trajectories obtained as a result of numerical simulation is analyzed. This procedure is implemented as a series of ensemble experiments with a joint MPI-ESM model of the Institute of Meteorology M. Planck (Germany). For numerical modeling, a series of different initial values of the characteristic fields was specified and the model was integrated, starting from each of these fields for different time periods. Extreme ocean level characteristics over a period of 30 years were studied. The statistical distribution was built, the parameters of this distribution were estimated, and the statistical forecast for 5 years in advance was studied. It is shown that the statistical forecast of the level corresponds to the calculated forecast obtained by the model. The localization of extreme level values was studied and an analysis of these results was carried out. Numerical calculations were performed on the Lomonosov-2 supercomputer of Lomonosov Moscow State University.

Abstract:

To analyze heat fluxes, observational data for 1979-2018 were used for the North Atlantic. The spatiotemporal variability of the total heat flux was modeled by a stochastic diffusion process. The coefficients of the stochastic differential equation were estimated by using nonparametric statistics. Previously, the existence and uniqueness of a solution in the strong sense of the stochastic differential equation generated by the constructed diffusion process was proven when Kolmogorov's conditions were met. In this work, the coefficients of the equation were approximated in time by trigonometric polynomials, the amplitudes and phases of which depended on the flow values. Using a given series of 40 years in length from 1979 to 2018, spatial maps and time curves were constructed. The results are shown for 1999 and 2018, and their comparative analysis is also carried out. Numerical calculations were realized on the Lomonosov-2 supercomputer of the Lomonosov Moscow State University.