Monitoring in dynamic systems with tipping based on the principle of large deviations

Abstract

The problem of predictability of the El Niño phenomenon on the basis of the well-known Gin-Timmerman model is considered. The presence of uncompensated instability in the model against the background of statistical data accumulated over the entire time of observations on the problem leads to the idea of the presence of some hidden damping mechanism, however small: critical events of sharp temperature increase do not occur too often and between them, on average, there are 7-12 years of rather stable behavior. Without fully revealing what this mechanism is, some small noise can be introduced into the system and an attempt is made to use this for research. An attempt is made to create a prediction algorithm by using the principle of large deviations in the vicinity of the equilibrium state in combination with global deterministic analysis. The paper applies such methods as the Runge-Kutta method of the 4th order, the search of the instanton by methods of the large deviation theory. The explicit analytical formulas for calculating the most probable trajectories of realization of the event of exceeding the high temperature difference between the eastern and western surface zones of the equatorial part of the Pacific Ocean are shown. The corresponding results for several levels are given. An example with identification of a linear model, which is used for local forecasting of a hazardous event, is shown. We have shown that even small changes in the initial conditions can lead to a sufficiently large difference in the time required for the temperature ejection phenomenon to occur. This complicates the process of El Niño research and reduces the window of time for forecasting.