Research On Early Warning Method Of Abrupt Change Based On Long-range Correlation

Abrupt climate change often has severe and even catastrophic effects on human society and the ecological environment.Therefore,it is particularly important to predict / warn sudden changes in climate.In recent years,under the background of global warming,the climate and ecology,which are closely related to human activities,have undergone significant changes.With the expansion of the field of human activities,abrupt changes in space climate have also begun to enter people's vision.However,due to the nonlinear characteristics of the climate system,under existing theoretical and technical conditions,it is very difficult to predict such sudden changes as early warning / warning.Some studies in recent years have shown that when a dynamic system slowly approaches its critical point,some statistical physical quantities of the system will undergo some obvious changes,which can be used as early warning signals before the onset of mutation.The climate system and the space weather system have long-range correlation,which means that the evolution of the system is not totally random but self-organizing.Therefore,in the process of a dynamic system approaching its critical transition point,it is a question worthy of further study whether its long-range correlation will have some general change characteristics.In view of this,this article uses three stochastic differential models with folding bifurcation points to design a numerical experiment that makes the system approach its own critical transition point by two different approaches,and studies in detail the system approaching its critical transition point.In the process,the long-range correlation of the system changes,and then the monitoring and detection system based on the change of the long-range correlation can provide a new way of early warning for the sudden transition caused by the critical transition,and developed based on the Rescaled Range Analysis(R / S),a new method for early warning of mutations,and at the same time,systematically tested the applicability of Detrended Fluctuation Analysis(DFA)in early warning of mutations.In this paper,the research results show that for the sudden changes caused by the critical control parameters of the system slowly approaching the critical point,the Hurst exponent,which quantitatively characterizes the strength of the long-range correlation,will show a continuous increase in the process of approaching the critical point.With the help of Kendall's rank correlation test,we find that this increasing trend of the Hurst index is statistically significant(significance level ? = 0.05),which means that the increase of the Hurst exponent may be that the control parameters of a system are approaching its criticality early warning signal of the transition point.However,for the mutation caused by only gradually increasing the random external forcing,the Hurst exponent of the system has no obvious change trend when the system approaches the mutation,and there is only a weak warning signal when the control parameter is close to the critical point,which means The Hurst exponent may not have early warning capabilities for mutations caused by external coercion.Considering that there are different degrees of observation errors(i.e.,noise)in real systems,this paper analyzes the effects of continuous random white noise and quantitative spike noise on the early warning effect of long-range correlation exponent as mutation.The results show that the small continuous noise or little spike noise will make the Hurst exponent of system state,which is far away from the critical point,smaller,while the Hurst exponent,which is near the critical point,remains basically unchanged,and the early warning effect of Hurst exponent is basically unaffected.If the intensity of continuous noise is too large and the original sequence is completely covered,the warning duration of Hurst exponent will be greatly shortened or even become invalid.If the amount of spike noise is too much,as the system with a small initial fluctuation approaches its critical point,the early warning effect of the Hurst exponent may fail.In a real complex system,various nonlinear feedbacks are not always instantaneous,that is,there is a certain time lag.To this end,this paper studies the abrupt early warning performance of the early warning method based on the long-range correlation in the time-delay dynamic model,and finds that the effect of the time lag term on the early warning performance of the long-range correlation exponent cannot be ignored,that is,as the As the time lag coefficient continues to increase,the early warning time limit of the Hurst index will shorten,and even the early warning will be completely invalid.